Hydrophile - Lipophile Balance of Surfactants and Solid Particles (Studies in Interface Science)

STUDIES IN INTERFACE SCIENCE

Hydrophile-Lipophile Balance of Surfactants and Solid Particles Physicochemical Aspects and Applications

STUDIES

IN INTERFACE

SERIES D. M 6 b i u s

Vol. I Dynamics of Adsorption at Liquid Interfaces

Theory, Experiment, Application by S.S. Dukhin, G. Kretzschmar and R. Miller Vol. z An Introduction to Dynamics of Colloids by J.K.G. Dhont Vol. 3 Interracial Tensiometry by A.I. Rusanov and V.A. Prokhorov Vol. 4 New Developments in Construction and Functions of Organic Thin Films edited by T. Kajiyama and M. Aizawa

Vol. 5 Foam and Foam Films by D. Exerowa and P.M. Kruglyakov Vol. 6 Drops and Bubbles in Interfacial Research edited by D. M6bius and R. Miller

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SCIENCE

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Vol. 8 Dynamic Surface Tensiometry in Medicine by V.N. Kazakov, O.V. Sinyachenko, V.B. Fainerman, U. Pison and R. Miller

Vol. 9 Hydrophile-Lipophile Balance of Surfactants and Solid Particles

VhysicochemicalAspects and Applications by P.M. Kruglyakov

Hydrophile-Lipophile Balance of Surfactants and Solid Particles Physicochemical Aspects and Applications

PYOTR M. KRUGLYAKOV

State Academy of Architecture and Building Penza, Russia

2,000

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Preface The amphiphilicity is a fundamental characteristic of any surfactant, which becomes evident in various surface and bulk properties, for example, adsorption, micelle formation, formation of stable liquid films in foams and emulsions, wetting films, lipid membranes, formation of vesicles (liposomes), in the distribution of matter between heteropolar phases, in the operation of various biologic systems, etc. To access the quantitative measure of the amphiphilicity, the so-called hydrophile-lipophile balance is widely used, which in a certain way reflects the relative efficiency of the heteropolar parts of the surfactants. The most commonly used characteristics of the hydrophile-lipophile balance with respect to the application of surfactants are Griffin's HLB numbers and Davies' HLB numbers. These numbers were introduced in response to technological needs, where a quantitative characterisation of a surfactant was required to facilitate the choice and selection of the particular compound in a specific application (the development of a detergent compositions and solubilisers, stabilisation of foams and emulsions, etc.) The studies dealing with the concept of the hydrophile-lipophile balance were mainly concerned with establishing correlations between Griffin's or Davies' HLB numbers and various properties of surfactants, the substantiation or criticism of the Griffin's HLB system, the refinement of various methodological details of experimental measurements or theoretical calculations of HLB numbers, and with the proper account for various factors (molecular structure, medium, temperature etc.) which have been ignored in the HLB numbers system. It should be noted that the applicability of the system of HLB numbers is often overestimated. Clearly, any complex phenomena, and, in particular, the stabilisation of emulsions or detergency, cannot be characterised by a single parameter of a surfactant irrespective of the temperature and ambient medium. It should also be noted that, following Davies, many authors considered the calculated Davies' and Griffin's HLB numbers as the same quantities. This point of view cannot, however, cannot be shared. Generally speaking, these two systems of numbers represent different hydrophility scales.

From the viewpoint of the physical chemistry of surfactants, it appears that the problem of the search, establishing and study of the practically important characteristics of the hydrophilelipophile balance which, as applied to surfactants, possess a simple and unambiguous physical meaning, and are applicable to all types of surfactants (micellar and non-micellar, ionic and non-ionic) is much more important. It was stressed by P.A. Rebinder that "... the development of a quantitative theory of hydrophile-lipophile balance ... should be considered as the most important goal of the physical chemistry of surfactants. The solution of this problem should lead to the scientific foundations for the estimation of the efficiency of the developed application of surfactants". Here two aspects of the problem should be kept in mind: the choice of a general and physically meaningful characteristic which employs both the balance of the heteropolar parts of a surfactant and the amount (force) of the "lever arm" of the balance, and the application of the constituents of this balance and the hydrophile-lipophile balance value to give an explanation for various surface and bulk properties (with respect to micelle formation or adsorption) and more complicated phenomena, for example the formation of vesicles, microemulsions, emulsions, foams etc. The energetic treatment of the hydrophile-lipophile balance can possibly be the most general and useful concept, because all colloid and surface phenomena are closely related with the energetic characteristics of surfactants. This approach, however not consequently, was adopted already in the concept of Davies' numbers for functional groups of surfactants. In his studies, Davies introduced the energetic treatment of the hydrophile-lipophile balance when comparing the empirical group numbers corresponding to the functional groups of surfactants, and the activation barrier for the breaking of emulsion films. In recent years, a quite extensive scope of knowledge was accumulated in the area of the energetic characteristics of surfactant molecules and their particular parts with respect to adsorption, micelle formation, distribution between bulk phases etc. However, the hydrophilelipophile balance concept based on these characteristics by no means became widespread. The main idea of the proposed book is the energetic concept of hydrophile-lipophile balance as applied to surfactants and solid particles (acting mainly as stabilisers of emulsions). At the

vii same time, the monograph systematises a number of other branches of studies regarding the hydrophile-lipophile balance. The first chapter summarises the known surface and bulk properties of surfactants which are directly related to the hydrophile-lipophile balance concept and are used either to determine the HLB numbers or to provide an independent measure of the hydrophile-lipophile balance. Along with the systematic exposition of known properties of surfactants, this chapter contains new theoretic data concerning the calculation of interfacial tension, determination of the adsorption of surface-active electrolytes, estimation of the energy of adsorption, and also summarises the studies performed by the author in relation with the Antonov's rule, Traube's rule and the comparison of the contribution to Gibbs' energy for various structural groups of surfactant molecules as applied to their transfer from bulk phases through the dividing surface to micelles and other bulk phases. The second chapter systematises the most important properties of emulsions (properties of films, phase inversion, and the kinetics of flocculation and coalescence) which are directly related to the stability of emulsions, to the formulation of HLB numbers by Davies, and to the concept of the HLB temperature (phase inversion temperature, PIT) introduced by Shinoda. The third chapter presents a comprehensive analysis of the systems of Griffin's and Davies' HLB numbers (experimental evaluation and calculation of HLB numbers and a comparative analysis of the original systems and modifications proposed by various authors), the determination of the characteristics of the hydrophile-lipophile balance based on the energetic properties of surfactants (distribution coefficients, work of adsorption and energy of micelle formation). In the fourth chapter, the methods are described which are used to express hydrophile-lipophile balance for solid particles of various nature and dispersity (macroscopic, gel-like or colloiddisperse) employed as emulsifying agents or foam stabilisers, and the properties of emulsions stabilised by solid particles. The fifth chapter briefly summarises some practical applications of the concept of the hydrophile-lipophile balance in various branches of science and technology.

VIII

The author acknowledges the contributions made by his co-workers, namely T.V. Mikina A.I. Bulavchenko, L.L. Kuznetsova, S.M. Selitskaya, V.D. Mal'kov and T.N. Khaskova, to the studies related to the hydrophile-lipophile balance concept, summarised in this book. I should like to acknowledge the support by R. Miller, Max-Planck-Institut Rir Kolloid- und Grenzflachenforschung, which was of enormous help during the preparation of this book and in fact, enabled the study to be published. The author expresses his thanks to E.V. Aksenenko, Institute of Colloid Chemistry and Chemistry of Water, Ukrainian National Academy of Sciences, who helped in the translation of the book into English, and to O.N. Kuznetsova for her significant technical assistance during the preparation of the book.

Penza, May 2000

Pyotr M. Kruglyakov

ix

LIST OF CONTENTS Preface

V

List of contents

ix

Introduction

Chapter 1 Physicochemical properties of surfactants used in the definition of hydrophilelipophile balance

1.1.

Classification of surfactants with respect to structure and chemical nature

4

1.2.

Surface-related properties of surfactants

7

1.2.1. Interfacial tension 1.2.2. Adsorption at liquid/liquid or liquid/gas interface and the structure of the

7 16

interface region 1.2.3. Structure and properties of adsorption layers

21

1.2.4. Work of adsorption

27

1.2.5. Surface activity

35

1.3.

Bulk Properties of Surfactants

40

1.3.1. Solubility of Surfactants

40

1.3.2. Distribution of matter between two non-mixing liquids

51

1.3.3. Micellisation and solubilisation

55

1.3.4. Formation of micellar (microemulsion) systems

66

1.4.

The contributions to Gibbs' energy corresponding to the transfer of

71

surfactant molecules from bulk phases to interfaces as compared to the transfer to other bulk phases. The interpretation of Traube's rule 1.5.

Brief Review of Surfactant Chromatography

83

1.6.

References

89

Chapter 2

100

Stabilising ability of surfactants in emulsification and foam formation

2.1.

Physicochemical properties of emulsion films

103

2.1.1. Kinetics of emulsion films thinning

103

2.1.2. Molecular, electrostatic and steric interactions in the emulsion films

106

2.1.3. Concentration of black spots formation

111

2.2.

Kinetics of flocculation and coalescence

116

2.3.

Phase inversion in emulsions

124

2.4.

Effect of temperature on emulsion stability - phase inversion temperature PIT

130

2.5.

Relation between foam stability and hydrophile-lipophile balance

138

2.6.

References

140

Chapter 3

146

Hydrophile-lipophile balance of surfactants

3.1.

Griffin's system of HLB numbers

3.1.1. Definition of HLB numbers based on the comprehensive estimation of the

146 146

surfactant properties. Required HLB numbers of oils 3.1.2. Determination of HLB numbers from the molecular composition of the

153

surfactant 3.1.3. Interrelation between HLB numbers and various properties of surfactants 3.2.

Kinetic and thermodynamic rationalisation of HLB numbers - Davies'

158 173

HLBD number 3.3.

Critical micellisation concentration and HLB numbers

181

3.4.

Phase inversion temperature in emulsion-measure of hydrophile-lipophile

190

balance 3.5.

Hydrophile-lipophile balance and chromatographic characteristics of surfactants

195

xi 3.6.

Comparative analysis of Griffin's and Davies' HLB numbers,

205

consideration of the influence of the medium and the surfactant structure on the HLB number systems 3.7.

Thermodynamic approaches to the determination of hydrophile-lipophile

215

balance 3.7.1. Determination of hydrophile-lipophile balance from the distribution

216

coefficients of the surfactant 3.7.2. Determination of hydrophile-lipophile balance from the work of transfer of

218

polar and apolar parts of a surfactant molecule 3.7.3. Hydrophile-oleophile ratio determined from the adsorption works

224

3.7.4. Hydrophilic-oleophilic ratio for the mixture of surfactants

230

3.7.5. Hydrophile-oleophile ratio determined from the micellisation energy

237

3.8.

Hydrophile-lipophile balance and phase inversion of emulsions

244

3.8.1. Studies of phase inversion in emulsions using the black spot formation

245

concentration 3.9.

Hydrophilic-oleophilic ratio and the formation of micellar systems

252

(surfactant phases) 3.10.

References

Chapter 4

259

267

Hydrophile-lipophile balance of solid particles 4.1.

Behaviour of drops at solid surfaces, and solid spherical particles at

268

liquid/liquid interface 4.2.

Stabilisation of emulsions by solid particles

274

4.3.

Work of wetting and determination of the hydrophile-lipophile balance for

283

solid particles 4.4.

Calculation of the hydrophile-lipophile balance for highly disperse solid emulsifiers

288

xii 4.5.

The dependence of emulsion stability on the work of wetting of emulsifier

293

particles. HLB used as criterion of phase inversion in emulsions stabilised by solid particles 4.6.

References

Chapter 5

310

314

Examples of the implementation of hydrophilicity-lipophility concepts in the development of the formulations of surfactants and selection of solid particles for certain purposes

5.1.

Physicochemical properties of microemulsion systems

315

5.2.

Emulsion systems and emulsion technologies

321

5.2.1. Specificities of the preparation of highly concentrated emulsions

323

5.2.2. Preparation of multiple emulsions

327

5.3.

Use of microemulsion systems for enhanced oil recovery from reservoirs

331

5.4.

Breakdown of dilute emulsions

333

5.5.

Hydrophile-lipophile balance and foaming properties of microemulsions

338

5.6.

Hydrophile-lipophile balance and selection of reagents in the processes of

348

surface (foam) separation of dissolved substances, colloid particles and oil drops 5.7.

Hydrophile-lipophile balance and sanitary-technical characteristics of

350

surfactants 5.8.

Hydrophile-lipophile balance and protein structure

353

5.9.

Use of the hydrophile-lipophile balance concept for the characterisation of

356

solid surfaces with respect to its application 5.10.

References

365

List of Symbols

374

Abbreviations of surfactants and surfactant mixtures

378

Acronyms

380

Subject Index

382

Introduction

The concepts of lyophilicity and lyophobicity (or, as applied to aqueous media, hydrophilicity and hydrophobicity) are commonly used in colloid chemistry. At the early stages of the studies of disperse systems, the terms 'lyophilicity' and 'lyophobicity' were used to discriminate between systems which possess weak affinity of the disperse phase to the medium (suspensoids) and those displaying a pronounced interaction between the particles and the medium (emulsoids). From the modem point of view, lyophobic colloidal solutions and other dispersions are thermodynamically non-equilibrium systems, while lyophilic colloids are equilibrium systems. Another meaning is ascribed to the terms 'lyophilicity' and 'lyophobicity' with respect to the phenomena of wetting and stabilisation of emulsions by solid particles. In this case the hydrophility (or hydrophobicity) of the particle is characterised by the contact angle 0 for the selective wetting, that is, for the contact of the solid surface with a pair of immiscible heteropolar liquids (e.g., water/oil), or by other parameters, for example the work of wetting, quantitatively related to the wetting angle. The surface is called hydrophobic (oleophilic) if it is better wetted by non-polar liquids, 0 > 90 ~ Alternatively, if it is better wetted by water, 0 < 90 ~ the surface is called hydrophilic (oleophobic). Hereinafter the wetting angle is counted through the polar liquid. According to these two concepts of lyophilicity, the behaviour of quartz, for example, corresponds to hydrophilic (oleophobic) particles with respect to wetting by water; at the same time the sol of SiO2 (or SiO2 suspensions) in water demonstrates the properties of a hydrophobic colloidal system. The concept of hydrophile-lipophile balance as the quantitative measure of the amphiphilicity of surfactants (primarily emulsifying agents) arose much later (in the late 40s and early 50s), especially in connection to the synthesis and application of non-ionic surfactants, for example, oxyethylated derivatives of alcohols, acids and alkyl phenols.

2 In particular, W. Clayton in his well-known monograph The Theory of Emulsions and their

Technical Treatment ([1] p. 243) refers to patents in which substances are proposed that prevent splashing of liquid margarine, and emulsifying agents with balanced contents of hydrophilic and hydrophobic groups. In these years, in the studies of non-ionic surfactants [2-5] it was shown that the existence of a definite hydrophile-hydrophobe balance (the ratio of the mean number of moles of ethylene oxide to the number of hydrophobic fragments, e.g. methylene groups) is required to achieve the optimum condition of wetting, detergency, emulsifying and de-emulsifying action, solubilisation, foam formation etc. This concept was subsequently extended over other classes of surfactants; at the same time, the quantitative measure of the hydrophile-lipophile balance for these substances is still controversial. Clearly, the relative efficiency of the polar and apolar parts of surfactant molecule can be expressed via the particular properties of these parts (or the substance as a whole); it should be also kept in mind that different ways of the estimation of hydrophile-lipophile balance can turn to be practically convenient for different processes in which the surfactants play an important role. Among the parameters which can be employed to estimate the hydrophile-lipophile balance are the structural characteristics (the volume and configuration of the parts of a surfactant), massdependent (various functions of mass of hydrophilic or hydrophobic parts) or energydependent characteristics (the work of transfer from one phase to another, the work of adsorption from various phases, including those determined in chromatographic processes, the heat of dissolution, the work of micelle formation), and other complex characteristics (the stability and the type of emulsions formed, phase inversion temperature, detergency, solubilisation, etc.) In turn, the energetic characteristics can be subdivided into direct (primary) and indirect (secondary) parameters. The primary characteristics are related to the surfactant itself (or to its specific parts). These characteristics, however, depend also on the type of the phases, between which the surfactant is distributed and with which it interacts. Among these characteristics are the energy of the transfer of surfactant from one phase to another, the work of surfactant adsorption, the heat of dissolution and the heat of adsorption, the work of micelle formation.

3 The indirect characteristics refer to the system as a whole, for example, to the water/oil system in the presence of a surfactant, or to different parts of the system. This group includes interfacial tension, spreading coefficient, activity coefficients for water and oil in the presence of the surfactant and some other parameters. Possibly the most general characteristic of the hydrophile-lipophile balance should be expressible through some fundamental properties, which are immanent to any surfactant, reflects the influence of both parts of the surfactant molecule, and possesses a clear physical meaning. For example, the characteristics related to the micelle formation do not satisfy these requirements, because micelle formation is not immanent to all kinds of surfactants. On the other hand, the stabilising ability (in foams, emulsions, suspensions) or detergency of surfactants, while belonging to the important properties of these substances, also cannot satisfy these requirements because these properties follow from the complex action of several simple properties, evident in complex kinetic processes and equilibrium states. References

1.

W. Clayton, The Theory of Emulsions and their Technical Treatment, 4 a~Ed., London, 1943.

2.

J.P. Sisley, Am. DyestuffRept., 38, 513-21.

3.

J.M. Cross, Soap Sanit. Chemicals. Special issue. Off. Proc. CSMA, 26, No CSMA 1.

4.

W.C. Griffin, Proc. Sci. Sect. Toilet Goods Assg. N.6, (1946)43.

5.

R.L. Mayhew, R.C. Hyatt, J. Am. Oil Chemists' Sot., 29(1952)357.

Chapter 1

Physicochemical properties of surfactants used in the definition of hydrophile-lipophile balance

1.1. Classification of surfactants with respect to structure and chemical nature Surfactants are substances which decrease the surface (interracial) tension. It should be noted, of surfactants with respect to the structure and chemical nature however, that the interface can be chosen in such a way that any particular substance, being in a liquid or vapour phase, or a solution component, can act to decrease the surface or interracial tension. In a more specific sense, the term "surfactant" denotes amphiphilic organic substances of an asymmetric molecular structure. Typically, surfactant molecule consists of two parts, which possess properties that are opposite to each other by their nature. One part of the molecule (or ion) is the hydrophilic polar group, for example,-NH2,-OH,-COOH,-SO3H,-OSO3H,-COOMe,-OSO3Me,-N(CH3)3CI, -CH2CH20. Another part is formed by a rather long hydrocarbon or hydrofluorine hydrophobic (oleophilic) chain. High molecular-weight surfactants (proteins, polyvinyl alcohols, polyacryl amide etc.) contain alternating hydrophilic and hydrophobic molecular groups distributed along the whole molecule. These typical surfactants demonstrate always some surface activity at the water/gas and water/oil interface, and are often surface active at the interface between a solution and some solid phases. With respect to their structure and chemical nature, surfactants can be divided into two major groups - non-ionic surfactants and surface-active electrolytes (colloidal electrolytes) which consist of a long-chain ion (surface active ion) and an ordinary inorganic ion (counterion).

5 The molecules of non-ionic surfactants contain polar groups unable to dissociate and possessing a significant affinity to water and other polar substances. Usually these groups incorporate atoms of oxygen, nitrogen, phosphorus or sulphur (alcohols, amines, ethers etc.). Among the substances of this group of surfactants, the most significant are oxyethylated alkyl phenols, fatty alcohols, fatty acids, amines and block-copolymer surfactants (oxyethylene nonionic surfactants), in which the polar part of the molecule consists of repeated oxyethylene group-CH2-O-CH 2- and closing-OH, -COOH or-NH 2 group. The most common oil-soluble surfactants which belong to this group are ethers of fatty acids and polyatomic alcohols - pentaerythritol, triethanol amine, unhydro sorbite and unhydro xylite (like Span, Tween etc.) The ionic surfactants, in tttm, can be subdivided into two groups: anionic (anion-active) substances, for which the hydrophobic long-chain part responsible for the surface activity is incorporated into the anion, and cationic (cation-active) surfactants, where the cations are incorporated into the hydrocarbon or other hydrophobic radical which is responsible for the surface activity. Among the anionic surfactants, the most significant are the soaps of carbon acids (RCOOMe), alkyl sulphates (sulphoether salts) ROSOaMe, alkane sulphonates RSOaMe, alkyl aryl sulphonates RC6H5SO3Me, alkyl phosphates ROPO(OMe)2, salts of sulphosuccinic acids. The typical surfactants which belong to this class are sodium dodecyl sulphate, sodium oleate and sodium dodecyl benzene sulphonate. Among the cationic surfactants, the most common are the salts of (primary, secondary and tertiary) amines, and quaternary salts of ammonium, for example, cetyl ammonium bromide and octadecyl pyridinium chloride. The ampholytic surfactants, which demonstrate either anionic or cationic properties depending on the properties of the medium (pH), can be regarded to as a particular class. These substances usually comprise some polar groups, for example, dodecyl-13-alanine C I2H25NHC2H4COOH contains both carboxy group and amino group. Depending on the ambient conditions (primarily on the pH value in aqueous media), in the solution these surfactants can form either surfaceactive anions or surface-active cations.

6 Finally, zwitter-ionic surfactants can be regarded as an intermediate between non-ionic and ampholytic surfactants. The polar parts of these molecules, while neutral as the whole, contain opposite charges, separated from each other by another structural elements: here the betaine can be referred to as an example: RN+(CH2C6Hs)(CH3)CH2COO -, where R is the hydrocarbon radical possessing 8 to 12 carbon atoms. As the hydrophobic chain of a surfactant comprises a number of identical elements (CH 2, CF 2, etc.), many of the properties of a surfactant depend additively on the number of such elements, such as vapour pressure, solubility, distribution coefficient, surface activity, adsorption, micelle formation and many others. This additivity is also evident with respect to the variation in the number of oxyethylene groups (EO) in non-ionic oxyethylated surfactants. The additivity usually holds well for straight chains and small variations in the number of structural elements, AnCH2= 4- 5, sometimes to A

nCH2 =

10; for higher values of this number, deviations from

additivity become evident. The additivity with respect to some properties is violated also when the position of a polar group in the hydrocarbon chain is changed, or when any isomerism is introduced into this chain. To be efficient, surfactants should not only be amphiphilic, but, in addition, should possess 'strong' and well-balanced hydrophobic and hydrophilic parts, which enable them to remain at the interface, to form micelles, and to participate in other processes. Depending on the strength of both polar and non-polar parts, and on the value of the hydrophile-lipophile balance, the surfactants can be classified with respect to their technological applications (foaming agents, emulsifiers, wetting agents, solubilisers, detergents etc.) The synthesis, structure and various properties of surfactants are considered in detail in a number of monographs and handbooks [1-8]; the reader can also turn to volumes of the Surfactant Science Series [9-14]. The most recent publication to refer to in respect to a systematisation of surfactants, their synthesis, chemical and physico-chemical characterisation, and practical applications in many technological field is the monograph to be published in this Series

[15].

This volume entitled " S u r f a c t a n t s -

Chemistry, Interfacial Properties,

Applications" will appear in the beginning of 2001 with Elsevier Science B.V., co-authored by B.E. Chistyakov, V.B. Fainerman, D.O. Grigoriev, M.Yu. Pletnev, A.V. Makievski, R. Miller and B.A. Noskov.

1.2. Surface-related properties of surfactants 1.2.1. Interfacial tension The energy excess of molecules (or other particles) in the interface region, as compared to the with each other strongly energy which these entities possess when they exist in the respective bulk phase and interact results in a free interfacial energy. From the viewpoint of surface science, the intensity of the field of molecular forces, characterised by the surface tension, is the polarity. This characteristic is closely related to some parameters of a liquid, in particular, the dipole moment, polarisability and dielectric permittivity. The interfacial tension is determined by the difference in the intensity of force fields. The stronger the interracial interaction at the interface (i.e., the larger the affinity of the organic phase to the water) is, the lower is the interfacial tension. The calculations of surface tension based on statistical mechanics, involving a radial distribution function I g(r) and the interaction function e(r) between the molecules, say, Lennard-Jones equation, lead to satisfactory results only for fluids consisting of spherical monoatomic molecules, for example, He or Ar [ 16-19]. To calculate the interfacial tension, statistical methods are employed, where the average molecular density is used instead of the radial distribution function [16]. In this way, approximate expressions for the interfacial tension (OAB) were derived, valid for a pair of liquids, with one of the pair being a saturated hydrocarbon. In the calculations performed by Girifalko and Good [ 10] (3"AB - - 13'A + O ' B -

2(~'(13"At3B)1/2,

(1 .1 )

I The radial distribution function g(r) is the probability for a molecule to be found at the distance r from the given one, within a spherical layer of thickness dr, while the function G(r) = 4zrr2dr is the number of molecules within this layer.

8

where ~ is a function which depends on the molar volumes of the adjacent liquids. The value of is usually between 0.5 and 1.15. In similar calculations performed by Fowkes [21] it was assumed that the energies of mutual interaction of hydrocarbons and their interaction with water are determined solely by dispersion forces. Therefore Eq. (1.1) can be written as t~AB = O'A + (~B -- 2 (o d Bt~A

(1.2)

,

d

where o a is the contribution from dispersion forces into the surface tension of water, and = 1. Some attempts were made to apply the equations (1.1) or (1.2) for the calculation of the interfacial tension in systems where non-ionic surfactants are present [22]. While the values of OAa for the systems studied in [22] agree with the theory presented in [21], the interfacial tension depends strongly on the type of the hydrocarbon phase, and on the number of EO groups in the non-ionic surfactant molecule. These results are briefly summarised in the monograph [23]. For most types of other systems, these calculations were found to be unreliable, and the main assumptions made in [20, 21 ] were strongly criticised, see [ 17, 24]. To describe the thermodynamic equilibrium for liquid/vapour and liquid/liquid systems, in recent years equations (models) for the local composition of the interface region are widely used [25]. One of these well-known approaches is the Universal Quasi-Chemical model (UNIQUAC) [26] which, from the calculation point of view, combines the local composition concept with the Guggenheim-Staverman quasi-chemical thermodynamic lattice model. The most complete and rigorous description of these concepts and procedures used to calculate CrAB can be found in the studies presented by Kahlweit [27] and Li & Fu [28]. In particular, the expression for OABproposed by Kahlweit is

2f

"-

(YAB=~ Gmix(X~)-Gmix(Xl)-[Gmix(Xl)-Omix(X;)] XI-Xi

t

x; x;

dx,

(~.3)

where V is the average molar volume of the mixture in the interfacial region, Gmix is the Gibbs energy of the mixture per mole, x~ and x~ are the volume solubilities (expressed as

9 molar fractions), x denotes the molar fraction of a component, x s is the molar fraction in the interfacial region, z is the co-ordinate within the layer (normal to the dividing surface). In [28], also based on Kahlweit's concept which assumes the mutual solubility of phases in the water/benzene system and takes into account the interfacial region profile, the surface and volume contributions to the total free energy of mixing were calculated, and then the sum of these contributions was taken over all the transition region. To calculate the activity coefficients and the interaction energy, the UNIQUAC method was employed. The values CrAB were calculated for 45 binary systems. Table 1.1 summarises results for some pairs of liquids. Table 1.1. Calculated v s experimental values of interfacial tension CrAa(the second liquid is water) First liquid

CRAB,mN/m Experimental values

Calculated values

Benzene, 20~

33.9

33.4

Toluene, 20~

36.1

36.7

Hexanol

6.8

7.6

Pentane

50.1

47.5

Octane

50.2

54.4

The average difference between the calculated and experimental CrABvalues is 1.4 mN/m, while the maximum difference does not exceed 5.1 mN/m. The number of molecular layers in the transition region, which were accounted for in the calculations, was 2 to 4. Long before the calculations in [21-28] were performed, the following empirical equation, known as Antonov's rule [29] O'AB -" C A ( B ) " O'B(A),

(1.4)

was proposed to estimate the surface tension between two liquids. Here CrABis the equilibrium interfacial tension of mutually saturated liquids A and B, CA(B)is the surface tension of liquid A being in contact with the saturated vapour of liquid B. The analysis and verification of the Antonov rule was the subject of a number of publications [30]. It was shown that this rule holds satisfactorily for water in contact with many organic liquids, e.g., saturated

10 hydrocarbons, lower ethers, ketones, nitrobenzene, chloroform. At the same time, for a number of other liquids (higher fatty alcohols and acids, phenol, cresol, benzene, methylene iodide) significant deviations from this rule were observed, amounting to some and even tens of mN/m, as demonstrated for example in [31-33]. Even in the first studies dealing with Antonov's rule, its interrelation with the equilibrium coefficient of spreading S was pointed out. It was shown that the Antonov rule holds for S = 0, and does not hold if S < 0. The physical nature of this dependence was explained in [30], where the shape of the disjoining pressure isotherm for a films of liquid A spread on the surface of the other liquid B was analysed. It is known [ 17, 31, 34, 35] that the equilibrium coefficient of spreading for the liquid B over the surface of liquid A is (1.5)

S B "- f A ( B ) - f B ( A ) - l A B .

Therefore, l A B --

OA(B)

(1.6)

- fB(A) " SB.

It is seen from Eq. (1.6) that the condition

SB -

0 corresponds to the case when Antonov's rule

is valid: f A B -- f A ( B ) - fiB(A).

Therefore, the spreading coefficient SB can characterise the sign and the magnitude of the deviations from the Antonov rule. Equation (1.5) refers to the thermodynamic equilibrium between the two liquid bulk phases A and B. Therefore the values of SB can be determined from the Young-Neumann equation, see Fig. 1.1. Here it should be kept in mind that fACa) corresponds to the state when an equilibrium between the liquid A and the saturated vapour B exists. The formation of an equilibrium adsorption film (with the thickness h0) of the substance B at the surface of the liquid A (for the relative pressure PB/PB(0)= 1) can take place if the inequality 0 /1;B(A) -- f A

-- f A ( B )

> 0

11 0 holds (see [30, 34]), where riB(A) is the spreading pressure, and G'A is the surface tension of the

pure liquid A. This condition is usually held when OB(A)< OA(B).

I vopour

! O'a(B)

~oB(A~

_ . ~ _ ~_

h0

~A(B)

O'B..~ (A) ~_ ~ ~ O ~ A 8

A

%o Fig. 1.1. Equilibrium wetting film of liquid B formed at the surface of liquid A in contact with the bulk phase of liquid B; see text for details.

From Fig. 1.1 it is clear that the horizontal forces resultant exists if CA(a) = OB(A)-COS0B + OA(B)'COS0BA,

(1.7)

where OA(B) is the surface tension of the liquid A covered with the adsorption film of liquid B (the meaning of the other symbols is evident from Fig. 1.1). The contact angles 0a and 0BA are related to each other via the condition OB(A)-sin OB = OAB.Sin OB(A),

(1.8)

which reflects the fact that the projection of the force resultant onto the vertical axis in Fig. 1.1 should be equal to zero. The value of t~A(B) can be regarded to as the tension of a thin film of B existing at the surface of liquid A. This tension consists of the sum of surface tensions of bulk liquids at the interfaces, viz., era(A) and CAB, and the specific (per unit film area) isothermal work required for the decrease of the film thickness of liquid B from a value h = oo to the value h = h0 which corresponds to P/Ps = 1, see Fig. 1.1. According to the well-known Derjaguin-Frumkin theory of wetting [36], we have oo

OA(,) = OB(,)+OAB + IfIB(h):lh. ho

(1.9)

12 Ha(h) is the disjoining pressure isotherm for the film of liquid B existing at the surface of the bulk liquid A, corresponding to the state of mutual saturation. Comparing Eqs. (1.9) and (1.5), one obtains at)

s.- In.(h)dh. ho

Thus, the spreading coefficient can be determined from the disjoining pressure isotherm. 0 For negative spreading pressure ha(A) OA(B)), the

formation of the equilibrium film of the liquid B at the surface of liquid A is thermodynamically

unfavourable.

However,

for

this

case

usually

the

inequality

0 rrA(B) =CrB--aB(A)>0 holds, and therefore for the spreading coefficient SA an expression analogous to Eq. (1.10) is valid. To analyse possible values of the equilibrium spreading coefficient S, one can consider various types of disjoining pressure isotherms for wetting films, see Fig. 1.2.

,/7

-/7 Fig. 1.2. Disjoining pressure isotherms for wetting films: (1) - complete wetting of the substrate by liquid B; (2) -

complete wetting of the substrate for a small portion of the isotherm with H < 0; (3) - partial wetting

(area of the plot H(h) in the region H < 0 is lower than that in the region II > 0); (4) - partial wetting with large contact angle.

13 It is known that for complete wetting, the entire isotherm H(h) is located in the region FI > 0. This means that the forces between the surfaces of the film (curve 1) are repulsive. For this case, when p/ps = 1, i.e., FI =-(RT/Vm).ln(p/ps)- 0, the equilibrium thickness of the film is h 0 - oo. Here Vm is the molar volume of the liquid B. Therefore, as the upper integration limit in Eq. (1.10) is equal to the lower one, both the integral and the spreading coefficient SB are zero. In this case, in the equilibrium state, the surface of the liquid A can be covered only with a macroscopic layer of the bulk liquid B. Thus, the Antonov rule (1.4) is rigorously valid only for a complete wetting of liquid A by liquid B. It should be noted that for the same pair of liquids, when the liquid A spreads over the liquid B, Antonov's rule does not hold. This becomes evident from the corresponding expression for the spreading coefficient of liquid A over B (1.11)

S A = t~B(A) " (~A(B) = ~ A B .

The sum of Eqs. (1.5) and (1.11) yields

SA -

-SB -

2r

It follows from this expression that for

a complete wetting of liquid A by liquid B, when SB- 0, SA- -2gAB, the deviation from Antonov's rule is large and positive. It is known, for example, that for octane (liquid B) spread over mercury (liquid A) the value of SB - 0, while at the same time for mercury on an octane surface SA = -756 mJ/m 2. This can be ascribed to the large stability (FI > 0) of octane films on the mercury surface, while the formation of mercury films on octane is impossible. It is known, that the molecular component (which is responsible for the interaction in octane films) determines the stability of the films the refractive index of which na is lower than that of the substrate ng (see [37]). For octane nB---- 1.38, while for mercury n g = oo. This explains why the surface of mercury is completely wetted by octane. With respect to organic liquids on a water surface a similar situation is observed only for light saturated hydrocarbons (up to heptane), see [34, 35, 38]. This fact is also in agreement with calculations of the molecular interaction forces in these systems [39, 40].

14 If the wetting is complete, but the isotherm H(h) is not significantly extended I into the region FI < 0 (curve 2), then the values of h0 become finite, which results in a positive values of the integral in Eq. (1.10), and positive values of spreading coefficient SB > 0 are obtained. However, for such wetting (when the meniscus of the bulk liquid yet does not form a finite contact angle with the substrate, while the isotherm extends in part into the region FI > 0), the value of h0 is finite but quite large. Therefore the value of the integral is small and positive. It means, that the deviations from Antonov's rule A = -SB will be small and negative, which is the consequence of the rapid decrease of surface forces with increasing film thickness. When the isotherm extends more into the region of negative disjoining pressure (the attractive forces of some origin between the surfaces become significant), and the area enclosed by the curve of H(h) in the region H < 0 becomes larger than the area enclosed by the graph in the region H > 0, then the conditions for incomplete wetting 0 > 0

becomes valid. This

corresponds to curve 3 in Fig. 1.2. For incomplete wetting, both the integral in Eq. (1.10) and the spreading coefficient become negative. The situation when the contact angle for the wetting of the liquid by another one differs from zero is quite common. Therefore, positive deviations from Antonov's rule, obviously caused by incomplete wetting, are most frequently observed. With further contact angle increase and decrease of h0 (curve 4 in Fig. 1.2), positive deviations from Antonov's rule should become more significant. For example, when the wetting of mercury (liquid A) by water (liquid B) is considered, where the wetting is lower than for octane, then instead of Sa = 0 the equilibrium spreading coefficient becomes negative: Sa = 0.04 J/m E [ 17]. It was shown in [39-41 ] that the theoretical disjoining pressure isotherm H(h) calculated for an octane film (B) on a water surface (A) has the form of curve 4 in Fig. 1.2. At the same time, it corresponds to a very low contact angle, 0 = 0.5 ~ and a film thickness of 4 nm. It follows from the experimental data that octane forms small lenses at the water surface [38], which means that S is negative. However, as incomplete wetting in this case can be ascribed to the action of

I When the area under the curve H(h) in the region H < 0 is smaller than the area under the curve at FI > 0.

15 relatively small dispersion forces, the deviation from Antonov's rule is extremely small. From the theoretical values of Hamaker's constant and the isotherm FI(h) constructed with electromagnetic retardation, we get negative values of the integral in Eq. (1.10) of the order of -10 "6 J/m 2. It is usually expected (see [42]) that the equilibrium value for Sa (or SA) is in the range -2Crag < SB < 0. Thus, the spreading coefficient can also be positive, Sa > 0 (or SA > 0). For wetting films, if the disjoining pressure is positive (in contact with the meniscus), rI - Pc, > 0 (Pc, is the capillary pressure), then the more general expression

SB =

rl(h~oo) ~hdFl rI(h,,)

(1.12)

can be used instead of Eq. (1.10), see [35, 43]. In this case, the increase of Sa is Hh. The cases when the value Sa can be positive were considered by Hirasaki [43] for thin films, when Pa> 0. Experimental isotherms H(h) were discussed in relation with the conditions of spreading and stability of films for some other systems in [35]. It is seen from the above analysis that deviations from the Antonov rule can be explained by the fact that at the surface of one liquid, thin adsorption films of another liquid possessing lower surface tension can exist, so that the disjoining pressure, which acts in this film, affects the equilibrium conditions. The Antonov rule can hold only if the tension of this film is equal to the sum of surface tensions of the bulk phases, i.e., at complete wetting. The larger the changes in film tension caused by surface forces acting therein, the more significant are the deviations from Antonov's rule. The sign of the deviation depends on the shape of the disjoining pressure isotherm, which, in turn, is determined by the physical properties of the interacting liquids. Semi-quantitative empirical dependencies of the interfacial tension on the polarity difference Ae expressed via the dielectric permittivity e, A~;= ~;A--I EA+2

ca-1 e B+2

(1 13)

16 were given by Abramson [6]. It was shown that a linear dependence of CrABon Ae is observed only for symmetric molecules of low volatile substances. For other substances, this dependence is greatly affected by the vapour pressure, mutual solubility, the presence of hydrogen bonds, orientation of the molecules at the interface and other factors. In spite of the fact that a large number of studies were concerned with the determination of the minimum interfacial pressure (or interfacial pressure at the same concentration), no general quantitative rules were found for the dependence of this characteristic pressure on the nature of the surfactant. It was shown for non-ionic surfactants that, depending on the type of surfactant (oxyethylated acid or nonyl phenol) and the hydrocarbon (saturated or aromatic), the interfacial tension either decreases monotonously with increasing number of EO groups, or acquires a minimum at some nOE value [22, 23, 44, 45]. In particular, it was found that, within a homologous series of non-ionic surfactants, the minimum tension is increased with the increase of the degree of oxyethylation, and decreased with the increase in the number of methylene links [46, 47]. Therefore, it can hardly be expected that any general relationship can be established between the HLB number and the interfacial tension of a surfactant solution, in spite of the attempts undertaken in [23, 44, 45, 48, 49]. Similar conclusions can be drawn with respect to the interrelation between the spreading coefficients of one liquid over another, and the HLB values [23, 50, 51 ]. When three-phase systems water/microemulsion (middle) phase/oil are formed, the interfacial tension at the interfaces middle phase/water and middle phase/oil are very low (< 10.4 or even < 10.5 mN/m). The ability of a surfactant to decrease the interfacial tension to such small values (caused by some relationship between the number of EO groups and methylene links and the type of the oil studied), was also proposed to be used in the calculations of HLB numbers [52].

1.2.2. Adsorption at liquid~liquid or liquid~gas interface and the structure of the interface region The Gibbs adsorption equation can be presented as do = -)-~ FiSdpi = - R T ~ , FiSdIn CiTi, i

i

(1.14)

17 where o is the surface (interfacial) tension, Fis and ~1,i are the adsorption and chemical potential of the i th component, respectively, C i and Yi are the concentration and activity coefficient of component i in the solution. The value of F s depends on the choice of the location of the dividing surface. For flat surfaces, Eq. (1.14) can be transformed into the expression [16, 53, 54]

do" = -

Fis - F s p~

--

Pi

bti = -

S

Fi(j)d~ i ,

(1.15)

where p~ is the density of component i in phase a. Fi~j) is then the relative adsorption, which is invariant with respect to the location of the dividing surface. In particular, for F s = 0 the dividing surface is called equimolecular with respect to the jm component. For water/organic phase interfaces, as water and oil are mutually insoluble (cf. [55]), Eq.(1.15) can be transformed into

(1.16)

Here

s

and the superscripts tx and 13 refer to the organic and water phases, respectively, and the subscripts 1 and 2 denote water solvent and organic solvent, respectively. For the case of ionic surfactants , average ionic activity coefficients are used, and Eqs. (1.14)-(1.16) become more complicated. The particular cases when either any indifferent electrolyte is absent, or for an excess of the electrolyte containing the same ion as the surfactant counterion (subscript 2), e.g., NaCI + NaR, where R is a hydrophobic radical, the equations for adsorption can be expressed as (see [4, 54])

18 l_.2s=

1 do 2RT dlnC2~/2 '

(1.17)

FS= _ 1 do ~ ' ~ , RT dlnC2Y 2

(1.18)

respectively, where ~, is the activity coefficient. For any ratio between the amounts of surface-active and indifferent electrolyte, rigorous expressions for the adsorption were derived by Tajima and Ikeda [56] and Rusanov [54, 57]. In particular, for the mixture of NaR and KCI, the equation transforms to do =-2RT(FSd In C2Y+ + FS~_dlnCsYs•

(1.19)

where C2 is the concentration of the surface-active component, Cs is the electrolyte concentration. Therefore, the effect of the electrolyte on the surfactant adsorption Fs is expressed only via changes in ),• For mixtures like NaR + NaC1, containing the comparable quantities of the components, assuming that the adsorption Fcff= 0 (for Ccff< 0.01 mol/1), the adsorption equation can be transformed into a form similar to Eqs. (1.17) and (1.18) (do)c~ = -nRTFSd In C 2Y~,

(1.20)

where n = 1 + C2/(C2 + CS) can vary in the range 1 to 2. For mixtures like NaR + NaCI, Eq. (1.15) or (1.16) can be written in the form (cf. [56]) do = -RT(FSd lnC2~• + FSdlnCs?s•

(1.21)

where C2 s C2 F2 = 1+ C.2 +CsF~ + C2 +Cs

cs

Fs-c+csFS-+

( cs/ I+C+Cs

s )

rc,_

,-"

,

19 Similarly to Eqs. (1.19) - (1.21) C2 is the concentration of the surface-active component. Equivalent to Eq. (1.21), we can also get (see [54])

d~nC do 2 = - R T

2C2 +Cs C2 s s 01nY2.• 01n)'s.• Cs +C-2 r2s(3)+ C s +' C 2 ['s(3) + 2['2(3) ~a l n C 2 + 2Fs(3) 01nC 2

(1.22)

where the component 3 is the solvent water. For mixtures of a non-electrolyte and an electrolyte like NaR + KCI or RCI + NaBr, where the abilities of CI- and Br- ions to adsorb are different, and an ion exchange can take place, the adsorption of the components can be determined from the expression (see [54, 57]) 1 da __)--]F,]j)01nC,~'r s k 01nCkYk• + ~ rk(j)C s s 0 ln(C k/C s) ,~ VikVis , _ _ ~-']Fk(j)v RT dlnC, , OlnC, k 01nC, ,,s Oln(2-] 9 y'c~,vi, t

(1.23) where vit are the stoichiometric coefficients, the subscript r refers to the non-electrolyte (if

present), 1 runs through all r and k values, and subscripts s and t refer to the dissociating substances and run over the same values that the subscript k does, i denotes the substance (ion). The number of resulting equations is equal to the number of different adsorptions F s and F s . In our particular case when four ions are present, Eq. (1.23) describes three electrolytes having common ions, and a set of three equations results from which the adsorptions F2(l), F3(I) and r4(l) can be determined, see [54]. The position of surfactant molecules at the interface corresponds to the state of minimum energy of interaction with medium: polar parts of the molecules are immersed into the aqueous medium, while the apolar parts extent to the organic phase. It was shown [58, 59] that in a saturated adsorption layer the hydrocarbon chains of a surfactant at the water/saturated hydrocarbon interface are completely stretched and their orientation is almost vertical. At the interface with more polar solvents (benzene, toluene etc.) the adsorption is lower, and the hydrocarbon chains are inclined at some angle with respect to the interface (for example, in case of benzene and the surfactant Xylan-o the value of the average angle is tx ~ 33~ In diluted adsorption layers the hydrocarbon chains of a surfactant

20 are chaotically oriented, and any orientation is possible, ranging from a vertical to a horizontal direction. Recent developments on molecular orientation or two-dimensional aggregation of adsorbed surfactants and changes due to variations in the surface coverage or surface pressure are described in detail in [15]. Theoretical models as well as experimental evidence are provided to understand reorientation and aggregation processes in adsorption layers of different types of surfactants. The position of the point of junction between hydrophilic and hydrophobic parts of a surfactant molecule (hydrophilic-lipophilic centre, HLC) with respect to the oil/water interface is also important. A qualitative discussion of this question can be found in [54, 60]. The molecular structure of the interface is characterised by concentration profiles of the system components, as schematically shown in Fig. 1.3.

C~

, j _ _ "~__

~t~

I

m I

0

Z L v

Zm

Fig. 1.3. Stepwise(1) and real profile of the local concentration of water Cl(z) (2) and surfactant C2(z) at the water/hydrocarboninterface, and the position of surfactant molecules at the interface.

If the phases were homogeneous to some geometric plane, the concentration (or density) profile would have a discontinuity at this plane. Actually the profiles are asymptotic curves with an inflection point, which can be taken as the origin for the co-ordinate z along which the distance from the separating plane is measured. If the phases from both sides of the interface were homogeneous up to the point z = O, and the position of the HLC of the molecules were

21 located at this point as well, then it would be energetically preferable when the polar group is entirely in the water phase and the hydrophobic group in the polar medium. It is known that the van der Waals interaction in either medium is quite the same. If we now consider for the position of the surfactant molecule (or ions) the real smooth profile of the interface region, this cannot significantly affect the state of the lipophilic part of the molecule which now becomes influenced by the aqueous medium. At the same time, the interaction of the hydrophilic group with the apolar medium will be significantly lower as compared to its interaction with the polar phase. Therefore this group, due to the interaction with the aqueous phase, will be displaced towards it in a distance sufficient to be immersed into the entirely homogeneous polar medium. As the lipophilic group will also be displaced, the hydrophobic effect arises due to the immersion of this group into the aqueous medium. When the attraction of the polar group to the water becomes counterbalanced by the hampering effect caused by the hydrophobic repulsion of the lipophilic group, the state of hydrophilichydrophobic balance (HHB) corresponding to the minimum of work necessary to introduce the surfactant from vacuum is reached. Therefore, the surface which corresponds to the HHB should be located at some distance Zm from the boundary surface. Of course, the quantitative value of Zm depends on the nature of the neighbouring phases and the functional groups of the surfactant molecule. It was argued by Tanford [61, 62] that one methylene link adjacent to the HLC, affected by the surfactant polar group and structured water, is not hydrophobic. This should influence both the position of the HLC in the molecule itself, and the HLC coordinate measured from the inflection point at the bulk phases' density profile.

1.2.3. Structure and properties of adsorption layers Let us consider now the properties of adsorption layers which determine the work of adsorption and the surface activity of a surfactant. For very low adsorptions (F < A~/RT) the surfactant concentration both in the solution bulk and in the surface layer is small, i.e. the two solutions (the bulk and the surface) are ideal. Therefore the ratio of the concentrations (C) obeys the Henry equation

22 Cs = exp(! a~ - l a s ] =const. Cv RT

(1.24)

Here the subscripts S and V refer to the surface phase and the solution, respectively. Comparing this dependence with the simplest expression of Gibbs' equation (1.14)-(1.16) one obtains the relationship

o~ . . . .

do dC

F g RT-- = 5RT exp C

s

,

(1.25)

which is valid within the concentration range where the surface solution is ideal, and Cs = F/8, where 6 is the adsorption layer thickness. The integration of Eq. (1.25) for constant o~results in a dependence o(C) n = o 0 - o(c) = tx-C.

(1.26)

According to Eq. (1.25), the linear decrease in the surface (interfacial) tension, or linear increase of surface pressure, corresponds to a linear increase in adsorption F = Cot/RT,

(1.27)

and the linear increase of the surface pressure with increasing the adsorption gives =FRT

or rcA=RT,

(1.28)

where A = 1/F is the area per mole surfactant in the adsorption layer. This last formula is the equation of state for the surface layer which corresponds to the equation of state for an ideal gas, i.e., the adsorbed substance behaves analogous to a twodimensional ideal gas. It should be noted that for high surface activity the adsorption in Eq. (1.27) is identical to the absolute surface concentration (amount of the substance per unit

area). If the interaction between the adsorbed molecules is negligible, but their real volume is taken into account, then instead of Eq. (1.27) one obtains the Langmuir equation

23 r=V

KC C =r (A ~Ol+KC ~ C + e x p ~~

where K = exp(A~t~

)

exp[~-~t~

(1.29)

'

is the adsorption equilibrium constant, F~o is the

limiting adsorption value. Another interpretation of this expression was proposed in [63]: the equation can be regarded as the relation between ideal solutions in the bulk and at the surface, formed by dissolved molecules that do not interact with each other, but occupy equal areas. With regard to the typical amphiphilic molecules (which have an asymmetric form, so that the area occupied at the interface depends on the orientation), there exists an ambiguity with respect to the main presuppositions used for the derivation of the Langmuir equation: the number of adsorption sites increases with the monolayer coverage. Comparing Eq. (1.29) and the Gibbs' equation, one obtains o = o0 - F| RT In(1 + ~r

(1.30)

where a0 is the surface tension of the solvent. Equation (1.30) is similar to the von Szyszkowski equation: o = o 0 - b ln(~cC + 1)

(1.31)

with b = FooRT, • = exp(A~t~ The elimination of KC from Eqs. (1.29) and (1.30) yields the expression

n = -RTF~ In

F~ F~o - F

(1.32)

which relates the surface pressure with the area per mole of the adsorbed surfactant. This equation describes the state of the real surface gas, taking into account the real volume (1/Foo), but disregarding the intermolecular interaction both with the solvent and among the dissolved surface active substance. Volmer and Manert [17] introduced a correction into this equation of state for ideal surface layers, to account for the correct area of the surfactant molecules A0, which is equivalent to the effective repulsion

24 rffA - Ao) = RT

( 1.33)

For high surface pressures, this expression similar to the equation of Amaga for gases [ 17] is often used to account for the cohesion forces, n(A- Ao) = gRT,

(1.34)

where g is a correction factor which describes the cohesion forces. For condensed adsorption layers, an expression similar to the van der Waals equation for gases is often used

rt +

A - A0)= RT

(1.35)

which can be represented as a dependence on the reduced adsorption F/Foo [64]

= nRTF~o l - F/Foo - as ~

"

(1.36)

The parameter n is equal to the coefficient in the Gibbs equation (1.20) and for non-ionic surfactants we have n = 1. The constants a and as characterise the intermolecular attraction (cohesion forces). In more detailed, Eq. (1.35) was obtained by Guastalla and Davies [4]

rc +

400. nCH~ )( A3/2 A - A 0) = RT,

(1.37)

where riCH~ is the number of methylene links in the surfactant molecule. The applicability of this equation was confirmed by Matijevic and Pethica [4] for monolayers of n-octyl carbonic acid with the addition of 0.1 M HCI. Introducing into Eq. (1.32) a correction with respect to the interaction, one obtains the Frumkin equation of state for real surface layer [64]

/ -7)

n = - n R T F ~ In 1 -

A2.

(1.38)

25 The surface pressure can also be expressed in the form of a virial expansion, similar to that valid for real gases 1tA = RT + an

+

bn 2 +

...

,

(1.39)

where a and b are constants. The monolayer ionisation (or ion adsorption) affects significantly the behaviour of adsorption layers. Unfortunately, the state of electrolytes and, in particular, the degree of dissociation at liquid/gas and liquid/liquid interfaces was not as yet comprehensively studied. Clearly the degree of ionisation in an aqueous solution bulk and at the surface cannot be the same: the degree is lower at the surface layer due to the effect produced by the adjacent apolar medium. The assumptions most frequently used are either a complete dissociation of the electrolyte in the adsorption layer, or a complete absence of any dissociation. In reality, the dissociation degree is a complicated function of the position of the surfactant at the interface, and also of the nature and concentration of the surfactant. The analysis of various models for charged monolayers is presented in the monographs [ 17, 65]. To calculate the ionisation degree, the simultaneous solution of the equations which express the equilibrium constant (counterions binding constant) in the surface layer, and the dependence of surface potential on the surface charge density are used [66, 67]. For example, the dissociation degree calculated for dense AOT monolayer is 0.3 [67], which agrees with the values measured in [68]. In the mixed monolayer AOT + CI2E5 the increase in the dissociation degree was observed with the increase of the portion of C~2E5, while this degree approaches 1 when the portion of AOT becomes close to 0. From the Gouy model of the electric double layer, the equation of state for dilute solutions was derived by Davies [4] nA = 3RT,

(1.40)

while Phillips and Rideal had proposed the equation nA - 4RT.

(1.41)

For very high area values (A >>A0) the coefficient in Davies' equation becomes equal to 1, while the coefficient in the equation of Phillips and Rideal becomes 2 [4].

26 From the analysis of various procedures used to take the electrostatic interaction into account, various equations of state were derived, and also from a comparison of experimental results obtained by Tajima et al., it was concluded [64] that good results correspond to Eqs. (1.36) and (1.38), where the values of n vary within the range 1 to 2 depending on the degree of surfactant ionisation. The best results throughout the whole range of relative adsorption were obtained from Eq. (1.38) for n = 1.3 (instead of n = 2 which corresponds to a complete dissociation). A recent comprehensive discussion of the effect of counterion binding on the equation of state for ionic surfactants was given by Kralchevsky et al. [69]. A detailed description of the thermodynamics of adsorption layers of ionic surfactants in presence and absence of an indifferent electrolyte is also contained in an up-coming volume of this series [ 15]. Finally, two more properties of the monolayers, closely related to each other should be considered: the spontaneous curvature of a surfactant monolayer in microemulsions and the bending and saddle splay moduli. These properties are closely involved in mechanism of the formation of various microstructures, the inversion of phases in emulsions, and therefore they are related to the hydrophile-lipophile balance problem [70-75]. It is known [16, 53] that even in single-component liquids the interfacial (surface) tension depends on the radius of curvature, with the bending of the plane surface towards one side leads to a decrease of the surface tension, while the bending towards the other side, on the contrary, results in an increase of the respective tension. It follows from the data reported by Rusanov [53] that, for extremely small radii of curvature, the surface tension decreases with the radius of curvature. These dependencies were also observed in systems with surfactant adsorption layers [53]. At the same time, it is generally accepted that if a surfactant adsorption layers exist, the bending of a plane adsorption layer or the deformation of a curved surfaces leading to the variation of the curvature require some energy to be spent due to the changes in the "packing" of surfactant molecules. This deformation energy depends on the rigidity constant of the interface. According to Helfrich [75], the bending energy of a surfactant monolayer is determined by the expression

W = KB2

2 Ro

1 R1

1 A + Kss dA. R2 RIR 2

(1.42)

27 Here KB and Kss are the bending and saddle splay moduli, respectively; Rl and R2 are the principal radii of curvature of the monolayer, R0 is the spontaneous radius of curvature, and dA is the surface area element. The constants KB and Kss have the dimension of an energy and their value is of the order of 1 kT for a "flexible" monolayer and 10 to 100 kT for "rigid" monolayers [73]. In particular, in the framework of this concept, the energy caused by the variation of the interfacial curvature of emulsion drop from 1/R to zero (plane film) was calculated by Petsev et al. [76] to be

WB =_2na2B0 ~-1

(1.43)

1

where a is the film radius, R is the radius of curvature, B 0 =-4K~3 R0 is the bending moment of a flat interface, K~ is the bending elasticity constant, I/R 0 is the spontaneous curvature. It was shown by the calculations performed in [74, 76] that for microdrops with a size of ca. 5.10 -5 cm and K~ ~ kT that the contribution of the deformation energy is of the order of 15 kT. Recently, experimental methods for measuring rigidity constants and theoretical approaches were developed [70, 73, 75, 77]. It was shown that co-surfactants (lower alcohols and acids), added to a micellar surfactant solution, decrease the monolayer rigidity [73, 78]. For example, the addition of 1-pentanol to a micellar surfactant solution in a microemulsion results in a twofold decrease of KB [78]. The effect produced by the curvature and rigidity constants on the type and stability of emulsions and microemulsions will be considered below in Chapter 2. 1.2. 4. Work of adsorption

The energetic characteristics of the adsorption process, i.e. the work and heat of adsorption, can provide insight into the structure of solutions and adsorption layers, and can provide information about the stabilising action of surfactants in foams, emulsions and more complicated disperse systems [17, 34, 58, 61]. These characteristics are most promising in respect to a quantitative estimation of the hydrophile-lipophile balance [58, 75].

28 Let us at first consider the methods applicable for the calculation of the adsorption work. The chemical potential of the ith component at infinite dilution of a binary solution of a nonelectrolyte is given by the expression Itti = bt?(T,p)+ RTlnx i

(1.44)

or

~i =lAi~

RTlnC i"

(1.45)

Here R is the gas constant, T is the absolute temperature, xi and Ci are the molar fraction and 0

molar concentration of the ith component (the surfactant), respectively, ~i is the standard chemical potential, and p is the pressure. For an infinitely diluted surface solution (adsorption layer) the corresponding expression reads P'is = l.t0,s(T, pN ,0)+ RT lnx~ ,

(1.46)

where xis is the molar fraction of the i th component in the surface layer; o is the surface (interfacial) tension, and PN is the normal component of the pressure tensor. The standard states s are those corresponding to the hypothetical state at xi = 1 and x i = 1. It was mentioned in Section 1.2.3 that in the surface solution cS= kC or x ~ - K~x i, see Eq. (1.24), and the equation of state is expressed by Eq. (1.28). Then, as the value x~ can be represented by the ratio A0/A, one can rewrite Eq. (1.46) in the form

s

0.(T ,pN,xis) + R T l n n ,

lai =kt i'

(1.47)

where n is the surface pressure. One can derive this expression directly, assuming that the adsorbed molecules constitute a twodimensional gas. In real solutions and real surface layers, the activity or fugacity coefficients have to be used.

29 In equilibrium the chemical potentials in the solution bulk are equal to those in the surface layer and therefore, the right hand sides of Eqs. (1.44) or (1.45) and (1.46) or (1.47) are pairwise equal to each other. It follows then that 0s

A~ti' =

~t0,s.

0

xi

- ~i = RT ln--K

(1.48)

Xi

or

0,n

A~ti

0 n

Xi

= I.ti' - ~t~ = RT In m .

(1.49)

7t

The differential work of adsorption -A~t~ = W a corresponds to the difference in the energetic states of the component in the bulk and at the surface for

Xi =

1 and x~ = 1, or xi = 1 and n = 1.

In the expressions (1.48) and (1.49), molar concentrations are often used instead of molar fractions of the surfactant; therefore, instead of these equations one obtains (cf. [24, 25]) Cs - A~t ~ = R T In ~

C

F = RT In---

5C

o~ = RT ln~,

(1.50)

RT5

where it is assumed that Cs = F/5, tx = -

, 6 is the thickness of adsorption layer, and C~0

Al.t = RT In c/n = - R T In et with a =

(1.51)

. C--~0

Comparing Eqs. (1.50) and (1.51), one can see that these expressions are equal for Cs = F/~5, if RT8 = 1. It follows then that the standard state of the surface layer at n = 1 corresponds to a state in which the "bulk" concentration in the surface layer c S = 1 for some adsorption (which depends on the system of units chosen). For example, if n = 1 mN/m, c S = 1 mol/dm 3, R - 8.3 J/mol, then 5 = 4.10 .8 cm. An expressions for the adsorption work was derived by Stauff [63] using statistical and thermodynamic dependencies for the entropy of dilution in ideal and non-ideal monomolecular

30 adsorption layers in the framework of the theory of regular solutions. For ideal solutions of and surface layer of a surfactant, the adsorption can be expressed as (cf. Eq. (1.29)) x

F=F~o x + exp (Ag0/RT)'

(1.52)

and the dependence of Ao on C is equivalent to the von Szyszkowski equation

/

x /

Act = o o -cr = FRT In 1 + ~ Ag~

.

(1.53)

The variation of the Gibbs partial molar energy (chemical potential) is s

v

Ag o = go - go = RT In

- 1 9x.

(1.54)

Here the standard state in the solution is the infinitely diluted solution at x = 1, while that in the surface layer is the ideal solution for the adsorption value F - F J2. For non-ideal regular solutions and surface layers, the adsorption work can be determined from the modified Szyszkowski- Frumkin equation [63] in the form At~ = F,oI R T I n x~ - Ag o -b(1 -~o )2]

(1.55)

where 0 = F/1-'oo,b = Qst/(RT| 2) is a constant, Qsf is the partial heat of surfactant dissolution. Rewriting this expression in the form

~=lg x - A ~ ~ =----~-1 lag~ + b(1 - q0)~] 0 2.3RTr. Z3RT

(1.56)

one can use the plot of the dependence of qo on (1 -0) 2 to determine the adsorption work -Ag ~ Here the standard state of the surface layer is the ideal solution at 0 = 0, with the extrapolation to (1 -0)2= 1, or the saturated adsorption layer at 0 = 1, with the extrapolation to (1 -0)2= 0. To determine the adsorption work for non-ionic surfactants, Haydon and Taylor [80] used the Langmuir adsorption equation in the form

31

A - Ao

l

= a exp -

(1.57)

RT J

where A is the area per mole of the surfactant, A0 is the limiting area per mole, a is the activity of the surfactant in the solution bulk. This equation is completely analogous to Eq. (1.54) for a = x. For the water/oil interface, a better approximation is provided by the expression

()

A~ exp AA =aexP-RT A-A o A o

)

(1.58)

which coincides with Eq. (1.57) only for large values of A (A > 1 nm2). For charged surfaces (ionic surfactants) Haydon and Taylor [80] used the isotherm

A A_Ao ~ ~ exp/AAAo ) e x p / ~ T ) = a e x p / - A---~-) G~

(1.59)

where W is the surface potential calculated from the Gouy equation, and e is the proton charge. Another method for the calculation of the adsorption work applicable to surface pressures n > 20 mN/m, where A is almost constant, was proposed in [81]. Here the dependence of the chemical potential in the surface layer is given by

las - ~t~ + ~Adn 11:=0

or ~ts = Ix~ - ~A&r

(1.60)

0 0

Here the saturated monolayer is assumed to be the standard state, Foo = l/A0, but n = 0. In this case

la = l-t~ + A0n

(1.61)

and the adsorption work for this definition of the standard state is g~ -I.t~ = -Ag O = RTInC. - nA o

(1.62)

where C is the concentration which corresponds to the surface pressure n, or A~t0 = RTInC'

(1.63)

32 where C' is the concentration which corresponds to the point of intersection of the linear part of the dependence o(ln C) with the line o = o0. The calculation can also be performed at C-Cm, where Cm is the critical micelle concentration. Comparing the values A~t~ and Ap~ o

o

o

A~I, Ads/Mic "-- g Ads -- gMie =

at this concentration, one obtains (1.64)

-hA0.

Thus, the adsorption energy exceeds the micelle formation energy. The values of the adsorption work for a large number of surfactants determined under the given standard conditions are summarised in [81, 82]. To calculate the adsorption work for ionic surfactants from the comparison of the concentration or surface tension dependencies of the chemical potential at the surface and in the solution bulk, one has to account for the ionisation of the surfactant both in the bulk and in the surface layer, i.e. Eqs. (1.42)-(1.45) have to be modified. For the dependence of the chemical potential in the solution bulk, Eqs. (1.44)-(1.45), instead of the concentration one has to introduce the activity expressed via the average activity coefficients of the electrolyte, while for the surface layer, the dependence p(n) should be used which corresponds to the equation of state for the ionised adsorption layer. In the solution bulk, the dependence of the chemical potential on the activity of ionic surfactant is given by the equation 0 ~tM. R- "-~I,M§ R- +

0

RT In aM, R_ -" }.I.M+R-

2

q-

RT InT•

C R_

(1.65)

where M § is the cation, R is the anion, and ~ is the mean ionic activity coefficient. In the presence of inactive electrolyte, which incorporates the ion similar to that of the surfactant, CM+* CR-. If the ionic surfactant completely dissociates in the surface layer, then it can be assumed that the equation of state is given by nA = 2RT (cf. Section 1.2.3). Therefore, if an inactive electrolyte is absent, then

d~tS _ d__nn_ Adn - 2RT d In n

rMR

(1.66)

33 and laS= ~t~ + RT In n 2,

(1.67)

where ~t~ corresponds to n = 1. From the Eqs. (1.65) to (1.67), one obtains

A~t~ = RT In

= 2RT In --n--n= 2RT In a_+ y_+C+_

(1.68)

For a surfactant and an excess of the electrolyte possessing the ion of the same polarity, one obtains ~ts= ~0, s + RT In n

(1.69)

and la v =It ~ + RTln(CMRCs72•

(1.70)

Therefore,

A~t ~ = RTIn ~

(1.71)

CmCsy2, "

The most complicated case with respect to the calculation of the adsorption work is the mixture of a surfactant and electrolyte (S) at any ratio CMR/Cs. In the solution bulk, lay =g0.v +RTln(CM" +Cs)CR_Y2.

(1.72)

In this case, an expression for the dependence of ~s on n was proposed in [83] la~

0,~

= larvm + R T I n

~2

with y. = (RTS) 2 2 -

(1.73)

y,~ 9

Css--In CMR +Cs

CMR

Cs

9It follows then that

34 2

A~t~ = RTIn

n .y= CMR (CMR + Cs)~ 2 9

(1.74)

The dissociation of surfactants at the surface is lower as compared to that in the aqueous bulk phase, as the surface is located close to the non-polar phase, and the concentration of the surfactant is higher at the surface. Therefore, for some classes of surfactants (e.g., for carbonic acids) a completely non-dissociated state can be considered as the standard state for the surface [79, 80]. Then, the dependence of ~ts(n)is expressed by Eq. (1.69), while the dependencies of ~ts on C s or F are determined by Eq. (1.65). Equating these expressions, one obtains [79]

A~ ~ = RT In ~

7[

W

= RT In a a ,

(1.75)

aMR "x

where ~ = .... dow /

The superscript W refers to the activity and surface activity for the

daMR ) a ~ 0

adsorption from aqueous the phase. If the equality CM+ = CR- holds (if any inactive electrolyte is absent), then do 1 ct = - d(e2y2)= - ~ . y •

(do) dCmy~ c,--,o

(1.76)

If the quantities of a surfactant and salt are comparable to each other, CMR ~" CS,

Of,a

d ad~m ) a-,0

do

y•2 CMR(CMs +Cs)]c,~_,o

(1.77)

And, finally, for the case when an excess of inactive salt exists, do .... 1 (do) 1 a , = - d [ ( C u a . C s ) q ( 2 ] = - 2YtCs" dCMR =,},•

(1.78)

In conclusion we can say that, as some portion of the adsorbed surfactant molecule is located within the inhomogeneous interfacial region (see Chapter 1.2.2), the work of adsorption for the functional groups, which are located in this region, should depend on their location. This is primarily the case for the polar portion of the surfactant molecule, and for the nearest

35 methylene group (or two or three of these groups). For the other parts of the surfactant molecule, the additivity of the adsorption work is observed, similar to that existing for the transfer form one bulk phase to another.

1.2. 5. Surface activity The expressions for the adsorption work, Eqs. (1.48), (1.49), (1.54) and (1.62), depend on the ratios of the surfactant concentration in the surface layer to that in the bulk, or on the ratios of surface pressure to the concentration in the bulk phase. The constant n/c =-(dct/dc)c~0 is referred to as the surface activity (or, sometimes, as Traube rule constant). The concept of the surface activity, as a measure for the surfactant adsorption ability, was introduced by Rebinder [86]. Initially this quantity was expressed as the derivative g =-dc#dc at any point on the isotherm ~(c). This definition is accepted in some studies even now, but in this case the surface activity is not a characteristic constant. To make the surface activity a unique characteristic of a given substance with respect to the adsorption at a definite interface, it was proposed by Rebinder [87] to calculate the derivative -(dc#dc) at the linear portion of the isotherm a(c), that is, according to the expression (1.25). This definition of surface activity is often used also for solutions of ionic surfactants. It was shown experimentally, however, that this is possible only in presence of an excess quantity of inactive electrolyte, with one ion idemical to the surfactant counterion (for example, the mixture of SDS with an excess quantity of NaC1, [88]). If there is no excess of inactive salt (and even for Cs = 0.001 or 0.1 mol/l), the isotherm t~(C) is non-linear, even at very low surfactant concentrations ( C - ~ 0) [88], or the shape of the isotherm is such that da/dC approaches zero [85]. It was suggested in [85] to express the surface activity as

eta .

do)

. v . . or dC_+ c-~o

eta

-dC_+ - - r coo ,

(1.79)

where v is the stoichiometric coefficient of the dissociation equation. Here it is assumed that the solution contains no additional electrolytes, and dissociation of the surfactant in the surface

36 layer does not occur. Similar, while more general expressions were derived earlier [84], where mixtures of electrolytes possessing the charges of the same sign (1-1 or 2-2) were considered. For ionic surfactants in excess of electrolyte, Eq. (1.78) was derived, for the case when the electrolyte is absent, Eq. (1.76) analogous to Eq. (1.79) was obtained, while for comparable quantities of surfactant and electrolyte (Cs ~ CsAs) the following expression

v : d [ C ~ ( C m +Cs)]c,_,0

Ot, a - - ' - -

(1.80)

was shown to be valid. If the state of adsorbed surfactant corresponds more closely to a complete dissociation, then it follows from Eqs. (1.68), (1.71) and (1.74) that

(X a =

(1.81)

= (X C

should be taken as the surface activity. Here, in absence of inactive electrolyte do ~C

- - - - ~ = - - ~

T•

T_+dC:~

9For an excess of inactive electrolyte, one again obtains Eq. (1.78),

while in the general case for a mixture of surfactant and salt dc ~a

-"

--

d[C~,m (C m + Cs)],/2

Cm ~0

(1.82)

with y+ = I. With respect to experimental measurements of the surface activity, some problems arise related to the adsorption kinetics and the effect of surface active impurities. Surface active impurities, if present even in very small quantities (as traces) can significantly affect the surface tension and other properties of a surface [89]. A number of methods for surface based cleaning prior to the study of surfactant adsorption was proposed. This area of studies is not considered here in details, however, the following publications concerning the purification of surfactants and the methods used to estimate the degree of purity should be mentioned [90-92].

37 The time necessary for the adsorption equilibrium to be established depends on the surfactant concentration and the size of adsorbed molecules. If the solution is dilute, and the molecular mass is large, then sometimes the system attains the equilibrium state only after hours [93, 94]. For polymeric surfactants or protein substances, this equilibrium state often cannot be attained during the time periods normally available by experimental methods. For example, the data reported by Trapeznikov et al. [94] had shown that the relaxation period for gelatin solutions (C = 0.02 - 0.06%) is ca. 600 minutes. In such cases, various kinetic dependencies of cr on ~ are employed to determine equilibrium values of surface activity. For example, in [95], and, subsequently, in [94-97], the following expression was used o = o~o + (o 0 - o~o).e"~/~

(1.83)

Here o0 is the surface tension of the solvent, o and ooo are the measured and equilibrium surface tension values for the solution, 0 is the relaxation period (constant), x is the time. Another empirical expression was proposed by Lange [98] o = o 0 - ( o 0 -o=)//(x-~b/2-1]

(1.84)

where b is a constant. In Hansen's equation [99] the dependence of cr on x is given by do RTF2( 1 ) 2 d---~--~= ~ ~-~

(1.85)

where D is the diffusion coefficient. A dependence convenient for numerical processing a

b

T

T

0"=00o +-----~

(1.86)

or do x ~ + 2o = 2c~ dx

a + x

(1.87)

38 was proposed by Nakamura & Sasaki [100] (a and b are constants). From the dependence (1.87) plotted in the co-ordinates cr vs 1/x one can estimate the value of 2ooo (at 1/x ~ 0), and the value of a, which is the slope of the curve). A number of other kinetic dependencies also can be used. For polymer systems, physically founded but more sophisticated kinetic dependencies o(x) are given in [101, 102]. A detailed analysis of the kinetic properties of adsorption layers from the solution of surface active compounds are given in the books [ 103, 104], or more recently in [ 15]. Various methods can be used to diminish experimental errors introduced in the measurements of surface activity. For example, in [105] the dependence of n on A was represented in a virial form, which yields the dependence of n on C n C=

exp -

,

(1.88)

0

where a is the virial coefficient. In the first approximation, this dependence can be written as

C

0

which, plotted in the co-ordinates ~/C vs re, gives to a straight line, from which the value cx = (~/C)0 can be estimated. The surface activity can also be determined in the concentration range where the isotherm n(C) is non-linear due to the non-ideality of the surface layer. In such cases the surface fugacity (n*) should be used instead of the surface pressure. To determine the activity coefficient of adsorbed molecules 3r = n*/n, in the studies performed by Ward & Tordai [106] and Posner et al. [107], the Amaga and Langmuir equations were employed. The equation ~t = ~t0 + ~Adn, 0

combined with Amaga's equation, yields the dependence of n* on n:

(1.90)

39 nAo Inn* = glnn + ~ . RT

(1.91)

From the Langmuir equation (1.35), represented as (n- % ) ( A - A0)= RT, the dependence of n* on n can be expressed by nA 0 In n* = ln(n - n 0)+ ~ RT'

(1.92)

while the Volmer-Mahnert equation (1.33) (which describes the liquid/liquid interface), yields the following dependence

In n* = In n + h A ~

RT

9

(1.93)

The deficiency of this approach was demonstrated by Betts & Pethica [108]. They proposed to determine n* or ~t directly from the equation of state for an ideal monolayer and the experimental data Act(C), n* A = H A = RT, where n ' = e t . C =

(1.94) D

(d-;-~1

.

C" In this case, the activity c~

"/= n*/n for a non-ideal

\ o t _ , j c-~0

surface layer can be determined from the equation

3r=exp --~-~

drt , n-~0

(1.95)

Y

where 13= RT/n- A. It is known [109] that for relatively low values of n the correction 13 is equal to the second virial coefficient in Eq. (1.39). Some other procedures for the calculation of the surfactant activity coefficient in surface layers were considered in the studies performed by Gershfeld, see [ 17].

40

1.3.

Bulk Properties of Surfactants

1.3.1. Solubility of Surfactants The solubility of surfactants in aqueous media, similarly to other properties of surfactants (wetting, stabilisation of oil/water or water/oil emulsions) is a property which was initially considered as the basis for the system of HLB numbers [110]. Also the Hildebrand solubility parameter was used to establish a relationship with the stability of emulsions [111] and the HLB numbers [112]. In this context, we will consider the main principles which characterise the dependence of the solubility on the nature of the solution. The solubility of a liquid or a solid in an ideal solution does not depend on the nature of the solvent, and is determined by the melting heat and temperature. However, for real solutions the solubility is rather different from that observed in ideal solutions, and general trends are superseded by rules which are qualitatively valid for specific types of solutions (regular, athermal etc.). For example, it is known that the mutual solubility of non-polar substances is higher than the solubility of non-polar substance in a polar one and vice versa. The most significant deviation of the observed behaviour from theoretical predictions is the fact that the real solubility often decreases with increasing temperature, while the theory can predict only an increase. Similarly to other processes which involve the distribution of matter between the phases, for the dissolution of a substance (2) in the solvent (1) the equilibrium is determined by the relation ~(l) 2,SAT = ~2,SOLID

, (l) or

1~2,SAT -- ~t2,LIQUID

(1.96)

where ~h is the chemical potential of the dissolved substance (2), ~t~l) = ~t~O) + RTlnx 2

(1.97)

Therefore, AG ~ = l.t~0) - I.t2,SOUD= -RT In x 2

(1.98)

41 where x 2 is the molar fraction of the dissolved substance, AG~ is the variation of Gibbs' energy during the dissolution (the work of the transfer of molecules from a solid state to the solution). In the general case, for example when the solubility is high, we have 0

A~tp = - R T l n x 2 - RTlny2

(1.99)

where ~2 is the activity coefficient.

The concentrations and the concentration dependencies of the chemical potentials can be expressed also in another way, avoiding molar fractions (cf. Sections 1.2.4 and 1.3.1). It should be noted in this regard that in the expression for ~t on x, the value la~ involves only the Gibbs energy of the molecules themselves, and the energy of their interaction with the medium [61]. As the "intemar' Gibbs energies of dissolved molecules in different solvents are equal, the value A~t~ would be exactly equal to the difference between the Gibbs interaction energies in different media. If other concentrations are used, the values ~t~ (and Ait~ would also involve the contribution from the entropy of mixing at unit concentration. To establish the influence of the surfactant hydrocarbon chain length on the solubility, it would be instructive first to consider the dependence of the hydrocarbon (13) solubility in water (ct) on the length and structure of the hydrocarbon chains. The solubility of various homologues of hydrocarbons at 25~

in water was studied by McAuliffe [61, 62, 113]. It was shown that the

change in the interaction energy is directly proportional to the number of water molecules which immediately contact the dissolved hydrocarbon molecule. For saturated hydrocarbons with straight chains, the following dependence was obtained l Alt0.~ =l.tl~o -~t~0 = (_ 2102ncH 3 --884riCH 2 ) "4.187"10 -3 where the sequence of indices indicates the direction of the transition: ct -~ 13.

(l.100)

42 For isomers, discrepancies with Eq. (1.100) become evident. For example, for isobutane A~0=-24.49 kJ/mol, which differs from the value -26.38kJ/mol

which follows from

Eq. (l. 100). For alkenes we have A~~

== ( - 1 5 0 3 - 884ncH 2 ).4.187.10 -3

(1.101)

while for all dienes A~~

== l- 903 - 860 rich 2 ). 4.187.10 -3 .

(1.102)

With respect to the interaction energy, one benzene ring is equivalent to about 5 methylene groups, A~~

= 19.34kJ/mol. The presence of salt (1M NaC1, LiCl and KJ) affects only

slightly the value of A~t~ For fatty acids, it follows from the data reported by Goodman I114] and Smith and Tanford (see [61]), that Al.t~

= (4260--825riCH 2 )'4.187"10 -3

(1.103)

From the data reported by Tanford we find, assuming the increment value Aj.tcn3 = 8.79 kJ/mol, 0 and one methylene group to be non-hydrophobic, that A~tcooH =16.33kJ/mol

for the

homologues in the range C 8 to C22. For fatty alcohols, it follows from the data reported by Kinoshita (see [61 ]) Akt~

= (833--82IncH 2 )'4.187-10 -3

The

contribution

(1.104)

from the polar OH group is significantly lower than the value

4260.4.187-10 3, which can be ascribed to the fact that OH groups form less hydrogen bonds as compared with carboxy group. 2

i In the original publications [61, 62, 113] and other references, the coefficients at riCH3 and riCH2 in Eqs. (1.100) (l.104) and (1.143)- (1.146) are expressed in cal/mole. Here we reproduce the same coefficients, multiplied by the factor -4.187 J/cal to express the resulting values in kJ. 2 It should be mentioned also that the data for the adsorption of fatty alcohols and acids lead to significantly differences for the transfer energy of COOH and OH [81, 82] (of. Section 1.4).

43 0 It was shown [6] that liquids for which the value of lAGs[ is in the range of 6 to 7 kJ/mol are

well soluble in water (can be mixed with water). For regular solutions, where the entropy of mixing is equal to the entropy of mixing for an ideal solution, the activity coefficients of the components (~'i) can be expressed by (see [ 102, 109]) RT In Yi = Qi

(1.105)

m

where

Qi is the partial molar heat of dissolution. The molar heat of dissolution, e.g., for

component 1 is

Q-~ = ln~,, V~ I(AU~lV2 " ~ , 2 - [ AU2 / RT = vo ) k vo )

2

)2 = A ( 8 , - 8 2 tp22

(1 106)

where V ~ are the molar volumes of the pure components, AU~ are the variations of intemal energy of evaporation of the pure components, q~2 nlV n2V~ 0 + n2VO is the volume fraction of the second component, nl and n2 are the numbers of moles of solvent and solute, respectively, [

0 "xl/2

andSi = ~| AUi V?J |

is the Hildebrand solubility parameter which characterises the difference

between the energies of molecular interaction between pure liquids (per unit volume of liquid, "integral" internal pressure or cohesion energy density). The equation for the second component is analogous to (1.106). Using )/1 and )'2 calculated from Eq. (1.106), and the temperature dependence of the solubility in an ideal solution, one can determine the solubility of a substance in a regular solution. For polymers, the following empirical rule is useful" the polymer is soluble in a solvent, if the value of 181 - 521 < (2 + 2.4) (MPa)v2 [ 102, 115]. The values of Hildebrand's parameter for some typical solvents are listed in Table 1.2 [ 115]. For the same substance dissolved in different solvents, the value 5 should be constant. For example, for solutions of iodine in eight solvents, the value of 8 was in the range between 13

44 and 14 (MPa) I/2, while for an ideal solution this value should be 13.6 [109]. The solubility parameters for many solvents are listed in handbooks, such as [102, 115, 116].

Table 1.2 Hildebrand solubility parameters for some solvents Solvent

8, (MPa) la

Hexane

Solvent

14.9

Cyclohexane

.... i 6.8 ...............

8, (MPa) m

Be~ene ....

18.8

Chloroform

19

Acetone -

20.3

Dioxane

20.5

,,

CCI 4

17.6

(~S2

9.9

Decalin

18

n-butyl alcohol

23.3

"l;01uene

18.2 . . . . . . . . . .

Water

47.9

. . . . . .

"

The colloid (micellar) solubility depends on the nature of the polar group and the number of carbon atoms in the hydrocarbon chain. For surfactants which possess straight hydrocarbon chains, the critical concentration of micellisation can be expressed as (see [117-119])

C m = A o exp

WEE -- n CH21~vw

(1 107)

RT

where A0 is a constant, WEL is the electrostatic contribution into the micellisation energy (per mole), ncm is the number of methyl and methylene groups, ~ is the energy variation corresponding to the transfer of one methylene group from the hydrocarbon medium (inside the 0

micelle) to the aqueous medium (this value is close to Alan.c,, of. Section 1.4.). Eq. (1.107) can be rewritten in the following form lg

Cm -

A - B. ncn 2

(1.108)

where

n

~

~vw

(1 + 13)RT. 2.303

,

(1.109)

45 A = I g A o+

w~ --t:L , 2.303 RT

(1.110)

and 13is the binding degree of ions to the micelle. For surfactants which belong to various classes and are characterised by different structures the values of the constants A and B are listed in Tables 1.3 and 1.4 (compiled from the data calculated by Shinoda et al. [4] and Tanchuk [120-122]). For non-ionic surfactants in aqueous solution the value of B is close to 0.5. For ionic surfactants it follows from Eq. (1.109) that this value should be lower, and varies in the range from 0.2 to 0.5. l The range of variation for the constant A is between 1.25 and 2.5. Table 1.3. Values of A and B for various surfactants

!

p

p

|

P

|

,

I

i

| ,

Surfactant CnH2n+I-CH2-COONa R-COOK R-COOK R-SOsNa R-OSO3Na R-CH(COOK) 2 RNHsCI RSOsNa RNH2C2H4CI RN(CH3)2CH2C6HsCI RC6H4SO3Na R2N(CH3)2CI /COOH R -CH -\SO3 H

....

.

.

.

.

.

.

,,

,

,

,

R -CH _/COOCnF2n+l H(CF2)nCOONH 4 H(CF2)nCOOH .

.

.

.

.

.

.

.

.

.

.

A 1.40 1.63 1.74 1.59 1.42 1.54 1.79 1.60 1.639 0.33 0.40 3.10 1.245

IB 0.260 0.290 0.292 0.294 0.295 0.220 0.296 0.300 0.314 0.252 0.200 0.278 0.300

2.700

0.462

3.00

0.666

1.531 1.273

0.361 0.349

t, ~ 25 25 45 40 45 25 45 25

.

.

.

.,

.

.

.

.

.

.

_,

.

J For the analysis of the dependence of lg C m o n ncm and, in particular, the values of B and 13one can refer to Rusanov monograph [54].

46 CnF2n+ICOOH CnF2n+tCOOK .

.

.

.

1.165 2.334 .

.

.

.

.

.

.

.

.

-0.444 ..... 0.572 . . . . . . . . .

.

To analyse the homologous series of surfactants with respect to the micellisation, Tanchuk [120-122] introduced the parameters pm and lg Co, which were derived from a comparison between two equations of the type (1.108) l g C ' - lgC~ = - B ' n

(1.111)

lg C - lg C o = -Bn

(1.112)

Here the parameters C', C~ and B' correspond to the reference series, the sodium soap of fatty acid series with normal structure, and n is the number of methylene groups. Table 1.4. Values of A and B for non-ionic surfactants Surfactant

A

CnH2n+1CH2(CH2CH20)I2OH

1.60

0.455

R(C2H40)90H

1.84

0.467

R(C2H40)6OH

2.360

0.504

2.398

0.469

R(C2H40)30H

"

Dividing Eq. (1.112) by Eq. (1.111) one obtains the dependence lg(C/Co) __ -~B n =pm lg(C'/Co) - B ' n

(1.113)

If for the 'reference' homologous series the relation Ig(C'/C~)) = O m "riCH2 holds, then for any series

(1.114)

47

=

=

.

. ncrt2

(1.115)

Comparing Eqs. (1.108), (1.112) and (1.I 15), one can see that B = - p m . r~m

(1.116)

A = lg Co - om. pm

(1.117)

For oxyethylene derivatives, the dependence of Cm on nEO in a homologous series can also be expressed by an equation similar to Eq. (1.108). For example, it follows from the data presented in [ 123] that for octyl phenols In Cm = 0.056 nEO + 3.87

(~.118)

For oxyethylene derivatives of dodecanol and nonyl phenol, similar dependencies on the number of EO groups were derived in [49] l lg Cm = -1.827 + 0.0308 nEO (for derivatives of dodecanol)

(1.119)

lg Cm =-1.671 + 0.04304 nzo (for nonyl phenol)

(1.120)

For the derivatives of iso-nonyl phenol, the dependence reported by Vamavskaya et al. [124] reads lg Cm = -4.22 + 0.024 nEO (for n = 6 + 16)

(1.121)

For the CMC in octane (for n = 1 + 6) the dependence of lg Cm on nEO was obtained in the form lg C ~ = - 1 . 2 6 - 1 . 1 8 nEo

(1.122)

However, it was shown by Crook et al. [46] that in a wide range of nEO this dependence does not hold for pure surfactants as well as for mixtures a Poisson distribution of EO groups, as one can see in Fig. 1.4. It follows from the data reported by Crook et al. [46] and Schick [ 125] that this dependence can be approximated by two straight lines: in the interval nEO _< 10 - with a

I Here Cm is expressed in g/1.

48 strong decrease in the hydrophobicity, and for nEO > 20

-

with a weak variation of the

hydrophobicity and CMC, respectively.

I0

-L _

_

lO-~ -

///.0

,

2

~..__~

5

/

. / Fig. 1.4.

Dependenceof critical

micellisation concentration (CMC) on

_

_

the number of oxyethylene links (nEO):

_

_

_

(1), individual octyl phenols; (2), octyl phenols, normal distribution of nEo; (3), 7o

2o

;0 20

ko }o nfo

nonyl phenols, narrow distribution of nEO

For oxyethylated non-ionic surfactants, many attempts were undertaken to establish a relation between the number of methylene groups in the hydrocarbon radical and the number of oxyethylene groups, which determines the solubility of the surfactant in water. For example, it was shown by Cohen [3] that in some intervals (Ca to C9 and Cl2 to Cl6) of the homologous series of alcohols H(CH2)n(OC2H4)m OH the variation of the ratio noE/ncm was roughly linear; the solubility was ensured when m = n - 3

(for n>> 1, nOE/nCH2 ~ 1). The solubility of

oxyethylated alcohols was complete when the values of nEo were 8.3 + 9 for dodecanol, 8.3 + 9 for tetradecanol and 8.3 + 9 for hexadecanol. It follows from the data reported by Sch611er [3] that extremely low solubility corresponds to the value noE/ncm= 0.33, average solubility to noE/ncm = 0.5. Good solubility is observed for noE/ncm = (1 + 1.5), while the data reported by Moore and Bell [ 126] suggest that noE/ncm = 2/3.

49 Another dependence of the solubility on the number of EO groups was proposed by Chakhovskoy [3]: soluble non-ionic surfactant should contain nEO = M/44 (where M is the molar mass of the surfactant); this is valid for alcohols with C4 to C8, and for C~2. The studies summarised in [ 127] had shown that for oxyethylated alcohols and penthaerythrites the dependence of nzo on ncm is non-linear, so that the ratio noz/ncm varies in the range from 0.2 to 0.74. Quite expectedly, this relation is significantly affected by the nature of the terminating polar group (OH, COOH, NH2 etc.). Let us now discuss another important parameter of non-ionic oxyethylated surfactants - the cloud point. When oxyethylated non-ionic surfactant are dissolved in water, hydrogen bonds are formed between water molecules and etheric oxygen. The increase in the number of OE groups leads to an increase in the number of water molecules which are attached to the etheric oxygen atoms. The energy of hydrogen bond is rather low (~ 30 kJ/mol), therefore the dehydration of EO groups occurs with increasing temperature, and the solution becomes cloudy. The cloud point is a very sensitive characteristic of the hydrophilicity of a non-ionic surfactant, and can be used to determine the HLB numbers ([3, 23], see also Chapter 3). The cloud point depends not only on the nature of the surfactant, but also on the contents of electrolyte and organic additives in the solution. Maclay published one of the earliest works, where the effect of various factors on the cloud point was studied [ 128]. The data concerning the influence of the nature of surfactants and various other factors on the cloud point are systematised in a number of monographs [3, 4, 9, 14] where non-ionic surfactants are considered. Therefore we present here only a brief summary of the relevant points. To determine experimentally the tcp, solutions of 1% non-ionic surfactants are usually studied. According to the data reported by Maclay, the value of tcp is almost independent of the concentration: for example, for the Triton X-100 concentrations in the range 0.25 to 4% the cloud point is at t c p = 64~

for a concentration of 7% we get tcp=65~

concentration of 10% we find tcp= 66~

and for a

Only at a concentration as high as 33% the cloud

point temperature rises to 76~ The dependence of tcp on the number of EO groups for oxyethylated nonyl phenols is shown in Fig. 1.5 (the values are determined in aqueous solution of alcohol). The nature of the

50 terminating polar group (for alcohol, acid, etc.) also affects significantly the tcp value. This is illustrated by the data given in Table 1.5. It is seen that for the same number of EO groups, the value of tcp notably depends on the hydrocarbon radical length and on the presence of double bonds. In the above table, some anomalies can be noted: for example, the cloud point temperature for 20-oxyethylated stearic acid is higher than that for 20-oxyethylated laurie acid. In [3] this effect was ascribed to the formation of diethers. Table 1.5. Values of cloud point temperature for 1% solutions of oxyethylatedacids Acid

, ,

Laurie .

.

.

.

.

.

,,Myristic Palmitic Stearic Oleic Phenyl stearic

Mean.numberofEOgroups 10 15 20 46 " 70 79 65 80 54 70 85 92 85 49 65 .

,

.

.

.

.

.

.

.

25 83 86 .

m

,,

94 87 78

....

~o 85

40

89 100 100 89 89

92

87 w

92

100 90_ 80_

o

o..-70d")

--~6050_ 40502O

Fig. 1.5. Dependence of cloud point temperature

f

tcp on the number of oxyethylene groups nEO in the I

+--

t

t

surfactant molecule.

8 1O121416 n

E0

For oxyethylated alcohols (nEO= 10) the cloud point decreases with increasing hydrocarbon radical length"

51 dodecanol

88~

tetradecanol

75~

hexadecanol

74~

octadecanol

68~

octadecynol

57~

For salt solutions, the tcp decreases. From the data reported by Maclay it follows that this decrease is linear with the ionic strength of the solution. The most significant salting-out effect is characteristic for iron(II)sulphate. In a 10% solutions of 10-oxyethylated nonyl phenol, a cloudiness was observed when more than 20% of CaC12, FeCI2, NiCI2, FeCI3 or AICI3 was present, for NaCI this amount was 10%, while the necessary concentration of FeSO 4 was only 3%. The addition of agents which destroy the structure of water (I-, SCN- and other ions) leads to an increase of the cloud point [129, 130]. A linear decrease of tcp is also observed with the increase of the solution pH. However, the study of solutions of Triton X-100 in the presence of a buffer mixture of disodium phosphate and citric acid has shown that the variation of pH within the range of 5.5 units produced no effect on the cloud point [4]. The additions of non-polar liquids and polyelectrolytes of anionic surfactants lead to a significant increase of the cloud point[131, 132]. On the contrary, the addition of polar substances leads to a decrease of tcp. However, it should be noted that in mixtures of non-ionic and anionic surfactants, a 'cloud interval' of 10 to 20~

width is

observed instead of a sharp cloud point. And finally, the solubilisation of long-chain aliphatic hydrocarbons leads to an increase in the cloud point, while the solubilisation of polar hydrocarbons (phenol, benzene) makes this cloud point lower [4, 9, 102]. 1.3.2. Distribution of matter between two non-mixing liquids Let us consider a system which consists of two mutually insoluble liquids (tx and 13) or liquids with limited mutual solubility. If a substance (i) soluble in both liquids is added to the system, this component will be distributed between the two phases with respective concentrations. In equilibrium the chemical potentials in the two phases must be equal, ~t~ = ~t~. Equating the right hand sides of the respective relations

52 ot

P'i =

txO

I-ti ' + RTlnxi

ot

(1.123)

~t~ = g~,0 + RT In x~

(1.124)

(x~ and x~ are the molar fractions of the third component in the phases a and 13), one obtains the expression for the work of transfer of one mole of the solute from phase 13to phase ~x ocx

P

W 13~= A~t~'~a = ~ti ' - ~t~'~ = RT In x--L CI

(1 125)

xi or

xiQI~ = K x xi

where Kx is the distribution constant which depends on the properties of the phases, the substance distributed, and the temperature. In extremely diluted solutions, the distribution coefficient can also be expressed via the molar-volumetric concentrations ot

K c = Ci C~

(1.126)

However, it was already mentioned in Section 1.3.1 that only Eq. (1.125) corresponds to the "pure" difference in the Gibbs interaction energies in different media (i.e., when the entropy of mixing does not affect this difference). For non-ideal solutions, the molar portions in Eq. (1.125) should be replaced by the activities

Ka = a--k-i af

(1.127)

The Eqs. (1.125) - (1.127) are valid for the distribution of substances which undergo neither a dimerisation nor a dissociation into ions. If association or dissociation takes place, the distribution constant can be expressed via the molar portions or molar-volumetric concentrations in one phase raised to the power 1/2 or 2, for dimers or molecules decomposed into two ions, respectively. For substances which contain repeated atomic groups (say,

53 methylene links in the hydrocarbons or oxyethylene groups in non-ionic surfactants), the work of transfer, similarly to Eqs. (1.100) - (1.104), is additive W a13 = Wh 13+ W? 13= W~0) 9nh + Wc~ 2 .riCH2

(1.128)

where Wh 13 and Wi'~13 are the energies of the transfer of hydrophilic and lipophilic parts of the surfactant, and Wh~0) and Wc~ 2 are the increments corresponding to one hydrophilic group (e.g., CH2CH20 group) and one methylene link, respectively. The dependence of In K x on the number of bonds for primary aliphatic amines [5] and the dependence of In K x on the number of methylene groups in the series of fatty alcohols [133, 134] is shown in Fig. 1.6.

-2 -1

~cH -I

Fig. 1.6. Dependencies

of

the

distribution

coefficient (Kx) for amines (1) on the number of CH-bonds, and distribution coefficients for fatty

-?

alcohols (2) and acids (3) on the number of methylene links (riCH2).

The value of AG O per CH bond for the transfer of amines into water is 1.67 kJ/mol (or 3.34 kJ/mol per mole of CH 2 groups). For the distribution of alcohols in all alkanes the energy of transfer of one CH 2 group from an organic into the aqueous phase is 3.3 kJ/mol, while the energy of transfer of the polar group, calculated from the dependence of In Kx on ncm is 0

AGoH - - 1 0 k J / m o l , which exceeds three times the values estimated from the data obtained from the solubility of alcohols (cf. data obtained by Kinoshito as reported in [61 ]). The distribution studies of acids between water and saturated hydrocarbons (decane, hexadecane) show [ 134] that acids form dimers in the aqueous medium, therefore

54 1 0~ (x~/2) 1/2 AGo a = - ~ ' ~ -11,' = - R T l n

x7

(1.129)

where x Pi is the analytical concentration of the dimerised molecule in oil (per monomeric OL

molecule), and x i is the acid concentration in water. The dependence of AG Oon the number of methylene groups for the distribution between octane and water is shown in Fig. 1.6, curve 3. The increment corresponding to the transfer of one CH2 group from water to oil is equal to 3.3 kJ/mol, a value similar to that characteristic for the distribution of alcohols, while the work of transfer of a carboxyl group cannot be determined from the distribution constant, because it involves the dimerisation constant. To calculate this work of transfer, information about the extent of dimerisation and the dimerisation constant should be known. Unfortunately, these data have not been provided by Aveyard and Mitchell in their work [ 134]. The dependence of Kc for octyl phenols on the number of oxyethylene groups in the water/iso-octane system at 25~

is shown in Fig. 1.7 [135]. It is seen that the linearity of the

dependence of In Kc on nEO and, therefore, the additivity of the transfer energy with respect to the number of EO groups is observed only for specially synthesised individual surfactants. The increment for the transfer of one EO group is 2.52 kJ/mol. For technical surfactants with a Poisson distribution in the number of EO groups this additivity does exist, because the distribution coefficient obtained from the experimental data corresponds to the average over all homologues oo

Z X i~ Kc = i--] oo

(1.130)

Ex, i=l

and can be calculated from the distribution coefficients of the individual non-ionic surfactants and the distribution function over the number of EO groups [135]. In a recent study [136], much lower values were reported for the increments corresponding to the EO groups, estimated from the work of adsorption. This was ascribed to the fact that oxyethylated nonyl phenol was used in these studies instead of octyl phenol as studied in [ 135].

55

tO

~,::,-, ]0 -7_

70-L 7g-;70-~ o J

Fig. 1.7. Dependence of the distribution coefficient (Kc) on I"

1

I

I

1

I

6

8

U

/2

14

%

the number of oxyethylene links: 1 - individual octyl phenols; 2 - octyl phenols, normal (Poisson) distribution of oxyethylene links (nEo).

This difference, however, seems to be irrelevant. The value of the distribution constant depends essentially on the nature of solvents. To account for this effect, the following relation was proposed by Uhlig [6]

lnK c =

o0S 0 + AG ~ RT

(1.131)

where o0 is the tension of the interface between the pure solvents, S O = (M/p) 2/3N11/3 is the mean cross-section of the molecules, M is the molar mass, P is the density, NA is the Avogadro number, AGa13 is the difference between the interaction energies of the substance with the solvent molecules. The applicability of Eq. (1.131) is limited: for example, this equation is invalid when the interfacial tension is low [6]. Another form of a dependence for the distribution coefficient for polar substances on the nature of the interacting phases (dielectric permittivity, refraction index, etc.) was proposed in [137]. The equation derived incorporates a number of unknown parameters. In addition, this equation was derived under the assumption that no entropy change of the distributed solute occurs when the transfer from one medium to the other takes place. This entropy variation, however, is of principal importance for a dissolution in water.

56 1.3.3. Micellisation and solubilisation

The formation of micelles is one of the most pronounced and characteristic properties of surfactants, which reflects the existence of the balance between polar and apolar parts of the surfactant, and the "strength" of hydrophilic and hydrophobic groups (the magnitudes of the surfactant levers). There exists enormous literature dealing with various properties of micelles, for example the following monographs [4, 15, 54, 138-141]. In this section we present a short summary of the properties of micelles which are related to the determination of the hydrophile-lipophile balance, and to the interrelation between the HLB numbers and some properties of micelles, in particular, the critical micellisation concentration (CMC) and the energy of micellisation and solubilisation. A number of surfactants, in particular, the so-called colloidal surfactants, exhibit a selfassociation in solutions. This effect results in a spontaneous formation of aggregates which are characterised by a rather high degree of association (m = 20-100). At small concentrations such surfactants form real solutions, which contain the dissolved substances as single molecules (or ions). When the concentration becomes higher, the formation of micelles sets in. These micellar dispersions (colloidal solutions) contain single molecules (or long-chain ions) of the surfactant, and also the micelles. In aqueous solutions, the organic parts of the molecules in the micelles are merged into the liquid hydrocarbon core, while the polar hydrated groups are directed to the water. Therefore the total surface over which the hydrophobic parts of the molecules are in contact with water, is essentially decreased. As the hydrophilic polar groups surround the micelle, the interfacial tension at the core/water interface becomes lower, and the value of this tension ensures that such aggregates are thermodynamically stable as compared with the molecular solution and the surfactant macrophase. Not all surfactants are capable of forming micelles. This property is characteristic only to those surfactants which possess a specific structure and hydrophile-lipophile balance and, in particular, those which comprise polar groups strong enough to be able to screen the apolar core over a sufficiently large area, and long but flexible hydrophobic chains. It follows from the data reported by Fox [ 142] that micelles in aqueous media are formed by surfactants with a HLB number larger than 13. Molecules which have weak polar groups (OH, NH2, COOH),

57 short hydrocarbon chains (shorter than C7) , rigid aromatic or acyclic apolar parts (e.g., various dyes), are able to form dimers and trimers but cannot form micelles. Some surfactants which possess two long hydrocarbon radicals (lecithin, kephalin) can form another type of associates in solution, so called vesicles. These are closed bilayer or multilayer films with a water phase confined between them [59, 102]. Vesicles in aqueous solution of a lecithin were first obtained and studied by Bangham (1965) [102]. Ultrasound can destruct vesicles, and transforms them into small (ca. 10 nm) monolamellar vesicles, which are called liposomes [ 102]. The main prerequisites to form spherical vesicles are the temperature which should be lower than the "melting" temperature of the hydrocarbon chains (Tr and the "conical" (wedge-like) shape of the lipid molecules which corresponds to the size and shape of a vesicle (a sort of steric balance between the parts of the molecule) [59, 102]. The main characteristics of micelles are the micellar mass (the sum of the masses of the involved molecules), the aggregation number (number of molecules), critical micelle concentration (Cm) and the charge and degree of binding of ions 13 (for micelles of ionic surfactants). The critical micelle concentration Cm is defined as the concentration (or very narrow concentration range) at which a multiple formation of micelles takes place accompanied by drastic changes in the properties of the solution. The critical micelle concentration corresponds to a qualitative transformation of the system - the transition of a homogeneous solution to a micro-heterogeneous colloidal system. This transition becomes evident from sharp changes in the experimental dependencies of various properties of the solution (surface tension, light scattering, electric conductivity, etc) on the total concentration of the surfactant. For low 'postmicellar' concentrations, spherical micelles (Hartley micelles) with liquid apolar cores are formed. This is seen from the formation of micelles which are characterised by a wide range of composition and nature of surfactant mixtures, the solubilisation of liquid hydrocarbons and other substances. The liquid state of the micellar core is different from the state of a liquid bulk phase of a pure hydrocarbon (for example, in emulsion drops). As a preferential orientation of the polar parts of the molecules exists, and the capillary pressure is high (due to the small radius of the

58 micelles), micelles are characterised by a liquid crystalline state, and its diameter is somewhat lower than the length of the completely stretched hydrocarbon chains. Therefore the layer of the polar groups is protruded over the core surface into the water medium by 0.2-0.5 nm. The micelles formed by ionic surfactants are charged: the internal DEL plane is formed by the ionic groups of the surfactant, while the external plane consists of free or partially bounded counterions. The fraction of bound ions 13= 1 - e t (where ct is the degree of ionisation) is usually equal to 0.2-0.6. The data reported by Lin [143] for fluorine carbonic acids CnF2n+ICOOH are 13= 0.96, and for potassium salts of these acids 13= 0.52. For a number of other surfactants estimated values for 13are summarised in [54]. For higher concentrations, the increase in the number of spherical micelles is accompanied by the change of their shape, namely the transformation into the aniso-diametric, more ordered aggregates (McBain micelles - ellipsoidal, cylindrical, plate-like or other pseudo-phases, also called mesophases). The structure of worm-like and plate-like micelles is similar to that of a multilayer (stratificating) foam and emulsion films, which are formed during the thinning of thick films formed by concentrated solutions of many surfactants [58, 144-147]. The aggregation number for micelles is usually between 20 and 100, thus not high enough to be regarded as a macroscopic phase. Aggregate of micelles, however, can be considered as a 'pseudo-phase'. For the description of the micelle formation, one can use either the heterogeneous approach, based on the phase equilibrium (~t~ =l.t~), or the homogeneous treatment, where the equilibrium surfactant molecules ~ micelles is considered to determine the equilibrium constant. The energetics of the micelle formation determines the conditions under which the micelles have some optimum association degree and optimum radius (which is equal to, or somewhat less than the length of the stretched hydrocarbon chain). For example, the minimum diameter for SDS micelles is 5.5 nm and for sodium oleate 5 nm, the association degree is 60-70 at 25oc. For lower association degrees, the portion of the 'open' surface of the core is much higher, while for higher association degrees, the penetration of polar groups into the hydrocarbon core should be more significant. Both these processes would result in a significant increase of the surface energy of the micelles.

59 In non-aqueous media, inverse micelles can be formed, for which the orientation of the surfactant molecules is opposite to that characteristic for aqueous micelles. In such inverse micelles, the polar groups are comprised into a hydrophilic core, while the hydrophobic chains are protruded into the apolar medium. The self-association properties for inverse micelles are much less pronounced. The degree of association of inverse micelles (usually m < 15-20) is much lower than in direct micelles. This fact is ascribed to the molecular geometry (small polar groups and long tails) which makes small micelles energetically favourable. The micellisation in non-aqueous media requires maximum apolarity, similar to the apolarity of surfactant hydrocarbon tails. In media of high polarity (e.g., lower alcohols) a micellisation becomes unfavourable. In addition, it follows from available experimental data that in apolar media the aggregates exist even at very small concentrations (10 -6 mol/l and lower). With increasing concentration, the number and size of such aggregates become also higher, so that it seems impossible to define the concentration which could be referred to as critical micelle concentration. Therefore, some authors express doubts concerning the existence of a CMC in non-aqueous media, even in very apolar ones, see [ 148]. For the heterogeneous treatment of micellisation in a solution at C = Cm we have ~t~ = la~'s + RTlnC m

(1.132)

where las is the chemical potential of a surfactant in the solution, while in the micellar phase lx~ = la~'M , assuming aM = 1 for the standard state of matter in the micelle. Therefore, Al.t~ = ~t~'M -l.t~ 's = RTlnC m

(1.133)

where the superscripts S and M refer to the solution and micelles, respectively. This simple approach to the micellar equilibrium is however deficient, because a micelle cannot be treated as the macroscopic phase. Here the dependency of the chemical potential on the surface curvature, the motion of surfaces and mixing effects should have to be taken into account [54].

60 In the framework of the homogeneous approach, the most simple equation which describes the equilibrium between the surfactant micelles and the surfactant in the molecular state, can be expressed (in the quasi-chemical approximation) by v(surfactant) = (surfactant)v = M

(1.134)

where v is the degree of aggregation. The equilibrium constant for this reaction is nM/NA CM "~M K M............. c

(1.135)

where nM is the concentration of micelles (number of micelles per unit volume), Cm is the concentration of the molecularly dissolved substance corresponding to CMC, CM is the molar concentration of micelles, and NA is the Avogadro number. The variation of Gibbs' free energy during the micellisation per mole surfactant in the molecular form is

AG ~ = _~RT InKM = . V

RT V

lnC . m + .RTInC. m

RT

'YM

V

yv

-~ In

.

(1.136)

If we take the infinitely diluted solution at C = 1 (e.g., mol/l) as the standard state, then both the first and the last term in Eq. (1.136) can be neglected AG O M ~ RTInCm 9

(1.137)

For ionic surfactants, which dissociate in water to ions, the micellisation obeys the relationship (see [54, 149])

vg+ K + + VA_A- ~ M v'--vK+ ,

(1.138)

where K + and A- refer to cations and anions, respectively. Then the equilibrium constant for the reaction (1.138) is CM

KM = CK~§ "CVs-A-

~M VK+

VA-

K+ "YA-

(1.139)

61 and the energy of micellisation (per mole of the monomer) AG O

RT

RT

RT

,,,,.

,,

RT

YM

M= - - ~ l n K M = - - ~ I n C M + InCK+ .CA"_- In VK+ VA- . VAVAVAVA- ~ r + "~A-

(1.140)

The first and last terms in this expression are small and can be neglected. Also, if there is no excess electrolyte, then CK+ = CA- = Cm, and finally

AG~ =

vv

RT InCK~ "-

(vK./

RT 1 +

lnCm

RT(1 +

VA-,]

V A -

,)'nCm

141

Thus, for complete dissociation of a surfactant in the micelle (13 = 1) a factor of 2 results before In Cm, while for different values of dissociation degree 0 < ct < 1 this coefficient is in the range

1 0 more hydrophilic and hydrophobic region, respectively, are observed. In the system 1% SDS + 1.75% NaCI + kerosene (for a l:lwater to oil ratio), with increasing amounts of amyl alcohol, a maximum in the O/W emulsion stability is observed for SAD values slightly below zero, followed by a sharp stability decrease at SAD = 0, and a subsequent increase of the stability for W/O emulsions. Similar variations of the volume and stability of foams are observed, as shown in Fig. 2.8. Here in the presence of kerosene the volume and stability of foam are decreased almost to zero for SAD > 0, while in absence of oil, a deep minimum of volume and stability exists at SAD = 0, followed by minor increase at SAD > 0. Similar decrease of the foam stability with increasing SAD due to the increase of the salt concentration in the systems: SDS + alcohol plus foaming agent Coatex M350 + isooctane (W:O ratio 1"1), and due to the decrease in the number of EO groups in the system containing solutions of oxyethylated octyl phenol. Here also the formation of stable foams is possible only for SAD < 0. Notwithstanding the destruction mechanism, the instantaneous coalescence for foams and emulsions is observed in the region where a micellar phase is formed. Similar results were reported by Friberg and co-workers in earlier publications [99, 103], where the dependence of the stability of foams prepared from a 15% SDS solution on the pentanol concentration was studied.

140

1 f oo rn 10

foomed emuls/on tee pho se reylon

Fig. 2.8. Dependence of the stability of foam and foamed emulsion obtained from

c:b

_

1% solution of SDS with the addition of 1.75% NaCi, on the pentanoi concentration (wt%); ordinate: volume of

2

~ 6

8

lg C, %mass

the foam obtained by outpouring of the test solution, O/W ratio I:1; 1 - foam from aqueous solution; 2 - foamed emulsion.

The results presented in [100, 102], where the stability of aqueous foams with a large contents of solubilised oil (up to 20-25%) in the surfactant hydrophile-lipophile balance region close to the formation of the microemulsion phase (Winsor III) was studied in connection with the formation of multilayer films, will be discussed later in Chapter 5. 2.6.

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146

Chapter 3

Hydrophile-lipophile balance of surfactants

3.1. Griffin's system of HLB numbers The quantitative characteristics of the hydrophile-lipophile balance were first introduced in connection with the application of solutions of non-ionic surfactants with variable numbers of ethylene oxide groups. The first ever successful attempt of a quantitative characterisation of the hydrophile-lipophile balance for various classes of surfactants was the HLB number scale, introduced by Griffin, and presented by the Atlas Powder Company in the trade catalogue 'Atlas of Surface Active Agents', Wilmington, Del., 1948, p. 26-27. The detailed description of the system of HLB numbers, including the interpretation of the main concepts and the experimental methods used to determine these numbers and calculation formulas, used at the early stages of the employment of this system, were presented in [1-8]. More recent reviews on this subject and an updated list of HLB numbers can be found elsewhere [9-13]. It was argued by Griffin that the HLB concept reflects the balance (equilibrium) between the hydrophilic and hydrophobic parts of the surfactant molecules with respect to their strength and efficiency. It was noticed in [1 ] that the classification of surfactants by HLB numbers enables one to make certain predictions of the behaviour of these substances, facilitating the choice of emulsifiers, wetting agents and other types of agents, and building a bridge between theory and practical applications. The HLB numbers were introduced mainly as a means to make an optimum choice of emulsifying agent.

3.1.1. Definition of HLB numbers based on the comprehensive estimation of the surfactant properties. Required HLB numbers of oils The HLB numbers were introduced on the basis of a comprehensive analysis of the properties of a surfactant (dispersibility in water, solubility, wetting, emulsion type, etc.). Low HLB

147 numbers were ascribed to lipophilic surfactants, while hydrophilic surfactants are considered to possess high HLB numbers. The average HLB value was assumed to be 10, and the entire HLB range extends over the values from 1 (for oleic acid) l to 40 (for sodium dodecyl sulphate). For oxyethylated surfactants the HLB values do not exceed 20, while for surfactants perfectly soluble in water, say, potassium oleate, the HLB is 20. It is assumed that the HLB number for a mixture of two or more surfactants is an additive function of the HLB numbers characteristic to the individual surfactants. For example, the mixture formed by three parts of the emulsifier A with the HLB = 8, and one part of the emulsifier B with the HLB= 16, is characterised by the HLB number calculated as (3-8 + 1.16)/4 = 10. The most important property used in the determination of HLB numbers is the emulsification behaviour of the surfactants. It was noted by Griffin that "our original estimation of empirical HLB values for many Atlas surface-active agents was based on results observed in a large number of emulsification studies conducted over several years. These studies were predominantly of O/W emulsions" [1 ]. For these surfactants, the HLB numbers are in the range between 9 and 12. To prepare W/O emulsions, one should use more lipophilic surfactants, with HLB numbers in the range 4 to 6. Table 3.1 represents the concept of the 'linear' HLB number scale, which characterises various properties of surfactants relative to their behaviour in water. It was stressed by Griffin that the hydrophile-lipophile balance cannot be completely determined by the solubility, while there exists a certain interrelation between these two properties. "Two emulsifiers may have the same HLB number and exhibit different solubility characteristics" [1, p. 313]. To determine the HLB for a new surfactant, a series of experiments has to be performed in which the emulsifying ability of the surfactant in question is compared with the behaviour of a mixture of this surfactant with other surfactants with known HLB values, or the ratio of two surfactants with known HLB numbers is selected to match the emulsifying properties of the studied surfactant.

If the substance demonstrates no hydrophility,then HLB = O.

148 Table 3.1. Effect of hydrophile-lipophilebalance on the state of a surfactant in aqueousmedia (Griffin [ 1-3]) State of the surfactant in water

HLB number range

Corresponding application

Non-dispersible

1.5-3

Anti-foaming agent

1-4

Emulsifier for W/O

'

-

emulsions Poorly dispersible

2-6

Turbid unstable dispersion

6-8

l Turbid stable' dispersion

8-10

Semi-transparent dispersion

10-13

Wetting agent

Emulsifier for O/W emulsions

89

solution ....

i3 and more 13-15

Detergent

15-18

Solubiliser

As the optimum conditions for emulsification (mainly the stability of an emulsion), depend not only on the surfactant type, but also on the nature of the organic phase (the type of the oil), the concept of the required HLB number of the oil is introduced: this value is equal to the HLB number of the surfactant which ensures the best emulsification of the oil. As two types of emulsions can be formed, each oil should be charactedsed by two values of the required HLB numbers. The required HLB numbers for some oils are listed in Table 3.2, see [1, 3, 14]. The HLB numbers required for some other oils are listed in the paper by Fox [15]. To determine the required HLB for any oil, a set of reference mixtures with known HLB numbers is used by Atlas Powder. This set covers the HLB range from 2 to 18. The accuracy to which the HLB number of a studied substance can be determined using this set is believed to be +_ 1 [8]. In order to determine the optimum proportion of a mixture of two surfactants (A and B) to be used for emulsifying an oil, the HLB number for the mixture (the required HLB number) should be calculated assuming additivity of the individual HLB numbers, HLB = HLBA.X^ + HLBB.XB,

(3.1)

149 where the subscripts A and B refer to the emulsifiers A and B, respectively, and XA and Xa are the mass fractions of the corresponding emulsifier I. Equation (3.1) can be used to determine HLB value for a mixture, or the unknown HLBA value of new surfactant, provided that HLB B and required HLB number for oil are known. Table 3.2. Required HLB numbers for some oils Oil Benzene

Emulsion type W/O O/W 13-15

Toluene

15-16

Xylene

14

Oleic acid

17

Maximum solubilisation of oil in water ,,,

. . . . .

Stearic acid

15-17

Cetyl alcohol

13-15

Lanolin (anhydrous)

8 ......

15

Cottonseed oil

7.5

Ethereal oil

16.5

Sunflower oil

8

Heavy mineral oil

....

4

10.5

Light mineral oil

. . . . .

4

i0-12

Petrolatum

4

10.5

Beewax

5

10-16

Paraffin

4

9-11

5-7

12

Vaseline '

15.5

....

In the experiments performed by Griffin, 10 g of emulsifier, 95 g of oil and 95 cm 3 of water were mixed, and base or amines were added if necessary. The emulsions prepared by shaking were allowed to stand for 5 minutes, then were shaken once more and allowed to stand at room temperature (for resins and beewax - at 60-70~

for 24 hours before the stability of the

emulsion was determined. According to Griffin, the emulsion in which the separation into cream and dispersion medium is least pronounced, is considered to be the most stable

It was noted in [ 16] that more reliable values can be obtained if the additivity of molar fractions is used.

150 emulsion. Therefore, the rate of the dispersion medium outflow from the emulsion was actually studied, however, the relation between this rate and the coalescence rate is quite implicit and complex I. It was shown in [4] that the highest efficiency of an emulsifier corresponds to the same weight quantity of the hydrophilic groups of a non-ionic surfactant. It should be noted that, one should, in addition, consider the effect of the structure of the substance on the efficiency of the emulsifier for surfactants with the same HLB number. For systems which consist of non-polar oil (40%), surfactant (4%) and water (56%), the HLB value obtained from the emulsification method for a mixture of surfactants (one of which is the reference surfactant) assuming additivity, was compared by Ohba [18] with those calculated from Griffm's formulae [3]. When two different standards (HLB =4.7 for Arlacel-60, and HLB = 14.9 for Tween-60) were used, the corresponding required HLB values for the most stable emulsions were also found to be different. This illustrates the non-additivity and the influence of the surfactant nature. In different experiments the HLB values obtained were: 10.5+1.1, 10.2+0.3, 9.7+1.6, 9.0+0.6, 8.9+0.8. The higher the number of oxyethylene groups in the surfactant molecule, the more significant were the deviations from the linear dependence of HLBE on HLBG (here the subscript E refers to the numbers estimated from experiments on the emulsion stability, while the subscript G denotes the numbers calculated from Griffin's formula). For oil mixtures [19] (a set of 15 different oils) the additivity was observed only when the fraction of fatty alcohol or acid added to the main mineral oil was lower than a certain value; for other oils no additivity at all was observed. For example, the dependence of the HLB for a mixture on the weight fraction of the oleic acid added (as oil) exhibits a maximum and minimum. Besides the direct experimental method based on the emulsifying ability to determine the required HLB number from Eq. (3.1), further attempts were made to establish relations between the required HLB numbers and some simple physical properties. For example, it was proposed by Bonadeo [20] to determine the required HLB numbers from the dioxane distribution between water and oil. In this method, 10 ml of the studied oil at 20~

was

dissolved in a certain volume of dioxane (20 ml), then 10 ml distilled water was added (the

In subsequent publications concerned with the relation between HLB numbers and emulsion stability [6, 17], an explicit stabilitycharacteristics were also used.

151 same amount equal as that of oil) and the mixture was emulsified then. After separation, the increase of the oil volume and the decrease of the water volume were determined, and the 'volumetric' distribution coefficient of dioxane Kv was calculated. However, the variation in the partial molar volumes was disregarded. These experiments found for apolar oils Kv = 2, for ethers Kv = 3.5, and for fatty alcohols Kv = 5. Comparing these coefficients with the HLB numbers, one obtains two straight lines with the intersection point at Kv = 0.37 and HLB = 8.2. For Kv -< 0.37 we obtain HLB = 1 2 - 10.27.Kv,

(3.2)

while for 0.37 < Kv < 1.7 we get HLB = 5.75 + 6.6.Kv.

(3.3)

Gorman and Hall [21 ] and Lo et al. [22] detemained the required HLB numbers for 12 different oils and compared these values with the dielectric permittivity e of the oils. For the series of saturated hydrocarbon a linear dependence between the required HLB number and lg(e) was found [22]: the higher the HLB, the lower is the e value. For example, for tetradecane e = 2.036 and HLB = 8, while for hexane e = 1.89 and HLB = 10.5 - 11. For various oils, the usual trend is increasing HLB number with increasing dielectric permittivity of an oil, cf. Table 3.3. An empirical dependence of the required HLB number on surface tension and molar volume of the oil was also proposed in [10, 23]. A faster method to determine the HLB numbers (for surfactants and oils) was proposed by Roberts and Bhatia [24], based on the study of the separation kinetics of dispersion media from an emulsion in a centrifugal field. When the Griffin methodics is used, the separation of the dispersion medium from the emulsion should be observed during 24 hours, while in the centrifution process (1500 rpm) the observation time is essentially shorter (ca. 2 min), and the accuracy becomes better. Direct emulsions are prepared in a mixer, the hydrophobic surfactant (Span) is introduced into the oil, while the hydrophilic surfactant (Tween) is added to water; the phases ratio O:W= 1:1. It is recommended to repeat the experiments 5 times. The main deficiency, however, is that the emulsion for which the separation of the dispersion medium is slowest, is considered to be the most stable (optimal) one.

152 Table 3.3 Required HLB numbers comparedwith the dielectric permittivityc of various oils [22] Oil

c

Required HLB number*

Kerosene

2.1

Cyclohexane

2.023

12

Decaline

2.26

10 - 11

Benzene

2.26

12

Toluene

2.28 (2.38)*

12 (11)

Xylene

2.57 (2.3)

12 (10)

Carbon tetrachloride

(2.1)

(9)

Ethyl oleate

3.17

10 - 12

Oleic acid

(2.46)

(11)

Laurie alcohol

(6.5)

(13)

* The data in parentheses have been reported in [21]. In contrast to the method developed by Griffin and Behrens, Wachs and Reusche [17] had proposed to use a direct (more correct) characteristic in studies of the dependence of emulsion stability on HLB numbers. The volume of the disperse phase separated in the centrifugal field (3000 rpm) was measured. The slope of the dependence of the separated phase volume (measured in ml) on the observation time was determined. The value inverse to this slope was employed as stability measure (Merill's method [25]). Studies of direct (undecane in water) and inverse (water in decalin) emulsions have shown that the stability of inverse emulsions increases with increasing HLB numbers from 2 to 10. The inverse emulsions are unstable (become separated into layers) for emulsifiers with HLB = 10 (for mixtures, with HLB = 6-8). For surfactant mixtures with HLB = 2 - 7, the stability increases up to HLB = 9.5+0.5, while for mixtures with HLB = 6.7- 11 the stability is quite high even at HLB = 10 (but not higher than 11). The stability maximurn for O/W emulsions was exhibited at HLB = 9.5. To prepare the emulsions, the surfactants of the Span and Tween type were used. To calculate HLB numbers, the phase inversion point determined from the variation of any property can be used [26-29]. In particular, it was shown by Davies [27] that the volume fraction of oil corresponding to the phase inversion observed in emulsification machines,

153 depends linearly on the HLB numbers. However, the critical value of the volume fraction depends also on the material of the plates. A simple method proposed by Marszall is to determine the phase inversion point from the amount of water (per 1 ml of oil) to be added to 50 cm 3 of the surfactant solution in paraffin oil to induce a phase inversion [28, 29]. A graphic method to estimate the HLB number was proposed in [30], which is based on studies with mixtures of the respective surfactant with two other surfactants of known HLB numbers.

3.1.2. Determination of HLB numbersfrom the molecular composition of the surfactant It was shown experimentally by Griffin that the stability of emulsions depends on the weight fraction of the hydrophilic part of a surfactant or surfactant mixture. Therefore he proposed to calculate HLB numbers using the formulas which involve the weight fraction of the hydrophilic part or any values which are proportional to this fraction, e.g., the saponification number [3]. For example, for fatty acid ethers, polyatomic alcohols or oxyethylated fatty acids one can use the expression

HLB= 20(1 _ V ) ,

(3.4)

where V is the saponification number or coefficient of the compound (the quantity of potassium hydroxide, in mg, required for the neutralisation of free acids and the saponification of ethers, per 1 g of fat), S is the acid number (the quantity of potassium hydroxide, in mg, required for the neutralisation of free acids, per 1 g of fat). For example, for Tween-20, with V = 45.5 and S = 276 [3], the following value results, HLB = 20.(1 -45.5/276)= 16.7. For the same class of substance, HLB numbers can be calculated from the relationship HLB = (E + P)/5,

(3.5)

where E is the weight fraction of ethylene oxide (in percent), and P is the weight fraction of alcohol groups (glycerine, sorbite, etc.). If a non-ionic surfactant does not contain polyatomic alcohols, Eq. (3.5) transforms into:

154 HLB = E/5

(3.6)

It is seen from Eqs. (3.4)-(3.6) that for non-ionic surfactants the HLB number cannot exceed 20. An improvement of the method used to determine HLB numbers from Eq. (3.6) was suggested by Heusch [32], who proposed to consider the HLC position at the interface. He postulated (without an analysis of the interface region structure) that for non-ionic surfactants with a HLC exactly corresponding to the position of the physical interface, a value HLB = 10. For this case, HLB = 20.(Mh/M)= E/5 is the ideal value HLBI. Here Mh is the molecular mass of the hydrophilic part of the molecule, and M is the molecular mass of the whole molecule. If for a surfactant the HLC does not coincide with the boundary surface, the actual value HLBR should be calculated from the expression:

HLB R = 20

Mh + C = HLB~ + C M

(3.7)

Here C is a correction: for positive C, the polar part of a surfactant is deeper immersed into water than in the ideal case. Heusch assumed that the 'ideal balance' (when the HLC position as defined in Section 1.2.2 coincides with the real surface) should correspond to the situation when the areas of the hydrophobic and hydrophilic parts of the molecule are equal to each other. This can be estimated from the kink point of the dependence of the area per molecule in the adsorption layer on the number of EO groups. For example, for oxyethylated stearyl alcohols this kink was observed at nEO = 6.9, as for this nEO the HLB - I 1.2. Then it follows from Eq. (3.5) that the correction is C =-1.2. For ethanol amine salts of alkyl benzene sulpho acids one can find in a similar way that C = 2.05. It should be noted, however, that for this class of substances the applicability of Eqs. (3.6) and (3.7) is doubtful. For oxyethylated p-isooctyl phenols the kink was observed at nEO = 7.8, HLBI = 10, and HLBR = 11.9. Therefore, for this class of surfactants Heusch's method should involve the calculation of HLBc from Eq. (3.5) with the correction value of C --1.6, see Table 3.4. Another method to improve the HLB numbers calculated from Eq. (3.6) was proposed in [33, 34]. It was based on the fact that the properties of emulsions, and, in particular, the emulsion stability, are determined by the composition of the adsorption layer. Therefore, it was

155 suggested that for mixtures of surfactants, in particular, for usual non-ionic surfactants characterised by a Poisson distribution of polymeric homologues, the HLB numbers should be calculated from the expression HLBmix = ~" HLBiX i ,

(3.8)

i

where HLB i is the HLB number for the non-ionic surfactant with i EO groups, calculated from Eq. (3.6), and X i is the molar fraction of this surfactant in the surface layer. For this calculation method, the HLB number appears to depend not only on the composition of the mixture, but also on the total concentration and water:oil ratio. Table 3.4. HLBInumbers as compared with HLBRnumbers for oxyethylatedoctylphenols [32] EO groups number

HLB~ = HLBI

HLBR

1

4.9

3

3

8.8

6.9

5

11.1

9.2

7

12.6

10.7

Equations (3.5) and (3.6) cannot be recommended for the calculation of HLB numbers of surfactants containing the following groups: propylene or butylene oxide, sulpho-group, and other polar parts of ionic surfactants. The idea to employ the ratio of hydrophilic to lipophilic weight fractions of a surfactant as an independent scale of the hydrophile-lipophile balance was also proposed in a number of publications. Schick and Bayer [35] and also Chun and Martin [36] proposed to express the hydrophile-lipophile balance in terms of a H/L number, the ratio of the number of oxyethylene groups to the number of carbon atoms (the number of methylene and methyl groups) in the hydrophobic part of the molecule H/L

=

(nEo/ncH2). 100%.

(3.9)

The contribution of the benzene ring is assumed to be equal to 3.5 carbon atoms [32, 37]. This concept was used by Moore and Bell [38] to develop the particular scale, where the ratio

156 2/3 (nEo/ncm) was taken as unity. According to Chun and Martin [36], the relation between H/L and HLB numbers (for non-ionic surfactants with nEO < 20) Can be expressed by lg H/L = 0.0971.HLB + 0.544.

(3.10)

The HLBB numbers introduced by Budewitz [32] are expressed as the weight fraction (in %) of the hydrophilic portion of a surfactant, i.e. HLBB - E(%)

(3.11)

therefore, HLB a = 5.HLB G. To calculate HLB numbers, the equation HLB = 7 + 11.7.1g(Mh/Mi)

(3.12)

was proposed by Kawakami [39], where M h and M ! are the molar masses of hydrophilic and lipophilic parts of a non-ionic surfactant, respectively. The dependencies of HLB numbers for non-ionic surfactants on mass fractions was considered in detail by Marszall [40, 41 ], where the homologues with either fixed ncm and variable nEO, or with fixed nEO and variable riCH, were studied. The dependence of HLB number on the molecular mass M of a non-ionic surfactant for fixed ncH2 is expressed by HLB = 8 . 6 6 - 0.57. non2 + 7.49.10 .3 M,

(3.13)

while for constant EO groups number the equation reads HLB = 9.54 + 1.82. nEO -- 3.39.10 .2 M.

(3.14)

Another formula to calculate HLB numbers from the molecular weights of different functional groups constituting a non-ionic surfactant molecule (McH3, MCH2, Moll , MEO, etc.) was also proposed by Marszall [41], HLB= hoE" M~ + ncn~ "Mcrt~ +8.425, 133.47 29.51

(3.15)

157 where the coefficients 29.51 and 133.47, according to the data reported in [41], correspond to the unit increment of HLB value for the increase of the mass of the hydrophobic and hydrophilic part of the chain, respectively. For the same non-ionic surfactants, the HLB values calculated from Eqs. (3.13) and (3.14) are different. It is unclear which value should be preferred. In addition, these equations disregard the effects caused by isomerisation, double bonds and aromatic rings. For the blockcopolymers of ethylene oxide and propylene oxide, the studies of 32 various non-ionic surfactants [42] yield in the following dependence of HLB on the mass fraction of EO groups HLB = 3.01 - 0.00231.M1 + 1.94.10-7 MI2 + 0.371 E,

(3.16)

where MI is the molecular mass of the hydrophobic part (propylene oxides), and E is the mass percent of the oxyethylene chains. In addition to the methods where the HLB number are expressed via the weight (mass) portions (or percents), the hydrophile-lipophile balance can be determined as the volume ratio of the hydrophilic heads to lipophilic tails Vh/VI [43]. For example, for a 9% mixture of Triton X-15 (1 EO group) at 25~ and Triton X-114 (7.5 EO groups) in the water-hexadecane system (1:1), the three-phase region arises at Vh/Vi =0.77- 0.83. The intersection of Vw/rVsurfactant and

Vo/Vsurfactant (where Vw/Vsurfactant and Vo/Vsurfactant are the ratios of water (W) or oil (O) volume to the surfactant volume in the micellar phases, i.e., the solubilisation numbers), which corresponds to the PIT, was observed at Vw/Vo=0.78, which for 25~

corresponds to

HLB = 9.5. The molar volume of an EO group is determined from the slope of the dependence of the specific volume on the molecular mass for homologous series of oxyethylated octyl phenols with different numbers of EO groups (the set of Tritons X), VEO = 39 cm 3. The volume molar contribution of an OH group (VoH = 8.5 cm 3) can be determined from the extrapolation of the dependence of the molecular mass (M/p) on ncm for homologous series of alcohols and glycols to nCH2 = 0, while the volume contribution of the hydrocarbon part (Vcm) is obtained from the ratio M/p for octyl phenols. This definition of the HLB, similarly to that involving the molar masses, can possibly be applied to surfactants which belong to a certain homologous series, but is quite useless for mixtures of surfactants from different classes, because this

158 definition disregards the differences in the nature of polar groups (not only the non-additivity of the molar volumes of the mixture, but also the differences in their energetic characteristics). Another attempt to establish a relation between HLB numbers and structure parameters, the length of the hydrophobic (10 and hydrophilic (In) part of non-ionic surfactant molecules was made by Zaev [44]. This relation was shown to obey the formula HLB = 12.5- 12"(1/lh- 1/lj)

(3.17)

where 1 is expressed in nm. The length of the hydrophobic part of the non-ionic surfactant molecule was taken to be the average between the length of the completely stretched form and the diameter of a statistical coil, while the length of the hydrophilic part of the molecule was assumed to be equal to the statistical diameter of the EO chain coil. It was argued in [44] that this dependence reflects the relation between the hydrophile-lipophile balance and a force f which bends the drop surface during emulsification under nonequilibrium conditions f= Al.tsv.(1/lh- I/1,).

(3.18)

Here AP,sv is the change of the chemical potential of the surfactant molecule in a nonequilibrium adsorption layer, caused by an external perturbation. The linearity of the dependence of HLB on (1/lh- 1/10 implies that A~tsv = const. This is rather doubtful as the reason of this constancy is unclear. The correlation discussed above is valid only for oxyethylated non-ionic surfactants, and could hardly be extended to surfactants classes with other polar groups.

3.1.3. Interrelation between HLB numbers and various properties of surfactants The dependence of HLB numbers on various properties of surfactants was studied in a number of publications. In this section, the most significant attempts are analysed. The relation between HLB numbers and the critical micellisation concentration, phase inversion temperature and chromatographic parameters of a surfactant is considered below in Sections 3.3.3 and 3.4.3, in combination with other characteristics of the hydrophile-lipophile

159 balance (hydrophobicity index, Tanchuk's hydrophobicity constant, Huebner's polarity index, Kovats' index, etc.). a)

HLB numbers and interfacial tension

It was mentioned in Section 1.2.1 that any general relationship between the minimum (or any other) characteristic interfacial tension and the type of a surfactant (and, therefore, with HLB numbers) is still unknown. Nevertheless, attempts to establish such a dependence of HLB numbers on the interfacial tension ~ were made for some particular systems.

18 01920 16

.0P9,7

14

Fig. 3.1. Dependence of the HLB numbers on the interfacial tension of oxyethylated alkyl phenol solutions at the water/iso-

12

10

'

I0

2o 3'o 4'o 5o

mi.w

-1

octane interface

For example, it follows from the data presented by Greenwald et al. [45] that the dependence illustrated by Fig. 3.1 exists between the HLB numbers calculated from Eq. (3.6) and the interfacial tension of 10-4M aqueous solution for five oxyethylated octyl phenols at the interface with iso-octane. It is seen that the dependence is non-linear, and the value for the most hydrophilic surfactant (that containing 20 EO groups) absolutely disagrees with this dependence. The dependencies of tr on HLB for the systems studied by Wachs and Reusche [17] (waterundecane-direct emulsions, water-decaline-W/O emulsions, Brij-30 and Tween-61 surfactants) either exhibited a minimum at certain a HLB value, or were monotonic, with a decrease of the interfacial tension when the HLB increases.

160 Possibly, the most extensive set of non-ionic surfactants of different nature was studied by Chun and Martin [36]. In this publication, the HLB numbers and hydrophility parameter H/L were compared with the interfacial tension of 0.1% aqueous solutions of the surfactants at the water/toluene interface and the following linear dependencies were obtained o = 4 5 . 7 - 2.36 HLB,

(3.19)

HLB = 19.36 - 0.424 o.

(3.20)

The authors emphasised however, that this method is unsuitable for solutions of surfactant mixtures. The measured interfacial tension of solutions of a mixture of surfactants was lower than that calculated from Eq. (3.19). For the mixture of Igepal C-430 and Igepal C-480, a value = 7.1 mN/m was measured instead of the calculated value of c = 15.0 mN/m. No correlation between the HLB numbers for mixtures, estimated from the stability of emulsion, and those calculated from cr values was observed. Two other dependencies of the HLB on the interfacial tension o, valid in the surfactant concentration range above the CMC (where o is independent of c), were reported by Schott [46]. For the oxyethylated dodecanol the dependence reads HLB = 1.93 + 0.345 or,

(3.21)

while for nonylphenols it was obtained HLB = 1.55 + 0.38 o.

(3.22)

However, even the author himself acknowledged that the physical sense of these simple dependencies is obscure. The spreading coefficients of oil over 1% aqueous solution of non-ionic surfactants (for O/W emulsions) and of water over the non-aqueous solution of a surfactant (for W/O emulsions) were compared with HLB numbers by Ross et al. [47]. Paraffin and castor oil were used as the organic phase, while the surfactant compositions were formed by mixtures of Span-80 and Tween-80. It followed that the spreading coefficients were not equilibrium values (Se). Possibly, these coefficients were closer to the initial spreading coefficients (for spreading coefficients S, ef. Section 1.2.1.). Also, the emulsion stability was studied using the method

161 proposed by Griffin and Behrens [2]. It was assumed by the authors that the spreading coefficient should be negative to ensure emulsion stability. It followed from visual observations of the separation of the disperse phase that the most stable O/W emulsions corresponded to S-values in the range of 0 to -5. The dependence of HLB on S (see Fig. 3.2) was linear in the range HLB > 8, and the deviations from linearity were explained by the fact that the emulsifier was not completely soluble in the aqueous phase.

16

12

8 Fig. 3.2. Dependence of the HLB number on the spreading coefficient S of castor oil

-20

t -IG

I -12

I -8

I -4

J 0

t

s, ~ - ,

over the surface of 1% aqueous solutions of mixtures of Tween-80 and Span-80.

Similar comparison between HLB and S was performed for W/O emulsions, as shown in Fig. 3.3. In these systems, the linear increase of the spreading coefficient with the increasing HLB number of surfactant mixture was always observed in the HLB range from 4 to 10, while the coefficient S was in all cases negative. Deviations from the linear behaviour were found for HLB= 10. Stable W/O emulsions could not be prepared. Most probably, this linear dependence can be explained by low variations in the nature and composition of the polar groups (number of EO groups) in a narrow range of HLB numbers (8 - 16 for direct emulsions and 2 - 10 for inverse emulsions) when the composition of the hydrophobic part, the monooleic radical, was the same for both surfactants. If micellar phases (microemulsion) in the three-phase system are formed (see Section 1.3.4), the decrease in interfacial tension between this phase and water or oil, respectively, to values of the order of 10-3 to 10-4 mN/m was sometimes observed, see [48-50].

162

10

6

2 -3O

I -38

t -46

I -54

I -62

Fig. 3.3. Dependence of HLB numbers on the

g mNm-1

spreading coefficient S of water over the surface of 1% surfactant solutions in castor oil.

It was proposed in [51] to characterise the ability of surfactants to decrease the interfacial tension to extremely low values at the interface with hydrocarbons, by a minimum (extrapolated) number of carbon atoms for oil, nc,min. It was shown that for oxyethylated nonionic surfactants (3.23)

nc,min = nc(0) + m (nEO(O)-- n~.o)

where nc(0) is the minimum nc value for the homologous series of surfactants which possess a number of nEO EO groups, m =Anc,

min/AnEo.

From the comparison between Eq. (3.23) and Griffin's formula (3.6), the equation follows 0.0_SM- HLB) n~.~a. = n~(0) + m n~o(0) - 44 - 2.2HLB)"

(3.24)

M is the molar mass of the alcohol. It was shown in studies summarised in [51] that branching of the hydrocarbon chains only slightly affects the interfacial tension for micellar phases formed by non-ionic surfactants like oxyethylene derivatives, but significantly affects the c-value in the case of sulphonates. Therefore, the application of the HLB number concept for anionic surfactants is by no means straightforward.

163 b)

HLB numbers and solubility of surfactants

It was already mentioned above that the solubility as one of the characteristics of a surfactant, can be used to determine HLB numbers (cf. Table 3.1). The dependence of the solubility on the ratio of the number of EO groups to that of the methylene links was analysed in Section 1.3.1. Using this dependence and the relationships proposed by Griffin for the HLB numbers of nonionic surfactants, one can derive equations for the calculation of HLB numbers. However, as the dependence for the EO group numbers nzo, where complete solubility is ensured, on ncH, is non-linear, and affected by the nature of polar groups, such equations are expected to be applicable in narrow ranges of ncm and nEO only. The relation between the variations in the solubility of non-ionic surfactants in water caused by temperature increase up to the cloud point was proposed as a method for the determination of HLB numbers in several publications [6, 52-55]. As an example, the dependence of the cloud point temperature tcp on HLB numbers obtained from Griffin's data, is presented in Fig. 3.4.

100o o

o

0

60-

~X) ~

0, I

12

14

HLB

16

18

Fig. 3.4. Cloud

point

dependence

on

HLB

numbers.

The data reported by Marszall [56, 57] who extensively used the top value in his studies of the effects caused by the addition of various compounds on the HLB numbers, suggest that the best (almost linear) correlation is observed when the solutions with equal (equimolar) concentrations are employed (0.025 M). Various empirical dependencies (linear and parabolic) were proposed for the calculation of cloud point temperature tep for different HLB numbers. In view of the information presented in Section 1.3 concerning the effect of various factors on top,

164 one could hardly expect that any general dependence of top on HLB for various non-polar surfactants could exist. In [58], Little compared the HLB numbers with Hildebrand's solubility parameters 5 (see also Section 1.3.1). For non-ionic surfactants, the HLB numbers were taken from the catalogue, i.e., assumed to be the HLBc numbers, while for ionic surfactants these were calculated from the Davies group numbers, that is, assumed to be the HLB D numbers. Table 3.5. summarises the obtained results. Table 3.5. Dependence of HLB on the Hildebrand solubilityparameter 8 Surfactant

8

Oleic acid

8.2

Glycerine monostearate

8.3

3.8

Sorbitane monolaurate

8.6

8.6

Oleilic ether EO-10

8.9

12.4

Oleilic ether EO-20

9.1

15.7

Sodium octadecanoate

9.3

18.0

Sodium dodecanate

9.6

20.9

Sodium dodecyl- l-sulphate

14.1

40.0

Sodium decyl- 1-sulphate

14.8

40.9

Sodium octyl- 1-sulphate

15.8

41.9

HLB

From the comparison of HLB numbers and the values of ~5, the following dependencies were derived 5-8.2 HLB = 5 4 ~ 8-6'

8=

118.8 5 4 - HLB

+6.

(3.25)

(3.26)

It follows from Eqs. (3.25) and (3.26) that the HLB = 0 for 8 = 8.2 (however, for oleic acid 5 = 8.2, but the HLB = 1), while for 5 = 10, the HLB attains a value of 24.0. In particular, for

165 iodine mentioned above (~5~ 13.6 - 14.3), this formula predicts a value of HLB = 40. (Note that from Davies' formula (3.52), for the distribution between water and CCI 4 (Kc = 1.67.10 -3) the HLB number for iodine should be 4.61. See below.) This reflects the limited applicability of these formulae. The parameter 6 seems unsuitable to express the hydrophile-lipophile balance. Greenwald et al. [45] proposed to use the distribution coefficient Kc of non-ionic surfactants between water and iso-octane as a direct measure of the hydrophile-lipophile balance. The distribution for five oxyethylated octyl phenols with averaged numbers of the EO groups of 5, 7.5, 9.7, 12.3 and 20 were determined. To ensure that the systems are in the equilibrium state, they were left for 15 - 19 weeks. For one of the surfactants (nEo = 9.7) it was shown prior to these experiments that in the concentration region below CMC the Kc value remains constant when the concentration is varied by 3000 times. The results obtained for Kc are summarised in Table 3.6. Table 3.6. Determined values of Kl2

EO

Cm"104,

groups

mol/1

number

Phase into which the surfactant is introduced

~,

C'104,

mN/m

mol/1

Cw

KI2

Co

Experiment

Calculated from

Zq. (3.25) 5

W

55.1

turbid

1.21

59.1

0.14

1.20

0.12

W

16.0

0.53

1.17

0.45

O

13.8

0.43

1.06

0.41

W

11.1

0.87

0.80

1.08

O

10.2

0.76

0.76

0.94

W

6.3

1.34

0.61

2.]9

O

6.8

1.12

0.54

2.08

W

35.6

0.62

0.027

23.0

0.36

turbid

-

O 7.5

9.7

12.3

20.0

:

0.19

0.43

0.90

2.16

,,

O

33.7 ,,

28

166 It was shown that the dependence between the distribution coefficient and the number of EO groups can be expressed by the equation (3.27)

lg K c = 0.145 (nEO- 10).

More comprehensive data conceming the distribution coefficients for oxyethylated non-ionic surfactants, either with Poisson distribution of the EO groups, or specially synthesised individual oxyethylated non-ionic surfactants, are presented in [50, 59-61]. In these publications, however, no comparison between Kc and HLB numbers were made.

14 I

1,9 10

2 Fig. 3.5. HLB numbers dependence on the distribution coefficient Kc of non-ionic surfactants: alkyl

-4

-~

0

2

Kv0

I, HLBo for oxyethylated

phenols;

2, HLB

for

Spans;

3, HLBo.

The values of Kc for two non-ionic surfactant classes, Span and NP, were determined by Schott [63] with reference to the formula derived by Davies [27, 62]. These values were compared with HLB numbers calculated from Eqs. (3.6) and (3.52). The results are presented in Table 3.7 and Fig. 3.5. For sorbitans the HLB numbers calculated from Eqs. (3.6) and (3.52) are mutually consistent. However, for the given oxyethylated octyl phenols the values calculated from the two equations are quite different. Therefore, the conclusion was drawn in [63] that neither Eq. (3.6) nor Eq. (3.52) is applicable for the calculation of HLB numbers for non-ionic surfactants. As the HLB numbers scale in the Atlas Powder trade catalogue was based on Eq. (3.6), it should

167 be considered that the Davies formula is unsuitable for the calculation of Griffin's HLB numbers. The dependence between Kc in the chromatographic process and HLB numbers is described in Section 3.4. Table 3.7. Dependence of HLB numbers on the distribution coefficient Kc Substance

Kc

HLB number calculated from Eq. (3.52)

Eq. (3.6)

Octylphenols: EO groups n~maber = 1

1.84-10 -4

3.9

3.5

3

3.13.10 -3

4.9

7.8

6

5.92.10 -2

6.0

11.2

10

3.85

7.5

13'6

80

3.7.10 -4

4.2

4.3

60

6.16.10 -4

4.3

4.7

40

0.314

6.6

6.7

10

3.67

9.1

9.2

Sorbitans:

c)

. . . .

HLB numbers and heat of dissolution

The correlation between the HLB numbers and the heat of dissolution of oxyethylated nonionic surfactant in water (for hydrophilic surfactants) and oil (for hydrophobic surfactants) was studied by Racz and Orban [64]. In Table 3.8 the HLB numbers of the hydrophilic Tweens are compared with the heat of dissolution in water. From these data, the empirical dependence was obtained HLB = 0.42 Q + 7.5, where Q is the dissolution (hydration) heat, expressed in cal/g.

(3.28)

168 It was noticed in [64] that this dependence holds only for liquid non-ionic surfactants, while for solid ones the change in the enthalpy caused by the phase transition from the solid to the liquid state should be additionally considered. Table 3.8. Dependenceof HLB numberson the dissolution heat Surfactant

HLB

Dissolution heat cal/g

J/g

Tween 20

16.7

21.55

90.23

Tween -40

15.6

19.88

83.23

Tween- 60

14.9

19.88

....83.23

Tween - 80

15.0

19.64

82.22

I Tween - 21

13.3

14.85

62.17

Tween 85

11.0

8.35

34.35

I Tween - 81

10.0

6.64

27.80

For hydrophobic surfactants, like Span or Tween (with HLB numbers between 1.85 and 11), the heat of mixing in organic solvents AHmix was compared with HLB numbers. For this correlation, the following formula was derived in [65] HLB =-1.06 AHmix+ 21.96.

(3.29)

The applicability of both of these formulae is, of course, limited. As the hydration heat in water is determined mainly by the energy of interaction of the polar groups with water, the dependence (3.28) is rather insensitive to the hydrocarbon chain length, and almost inapplicable for surfactants with different nature of the polar groups (e.g., with regard to ionic surfactants). d) .

H.LBnumbers and dielectric permittivity

The classification of non-ionic surfactants with respect to the hydrophility proposed by Gorman and Hall [21 ] was based on the dielectric permittivity values (e). This classification is

169 illustrated in Table 3.9. It can be seen from this Table and Fig. 3.6 that the dependence of the HLB on lg(e) is approximately linear.

/0

t3 Oo

17.5

I 0.6

t

1

0.7

0.8

t ....

0.9

1

1./7

Fig. 3.6. Dependenceof the HLB number on the dielectric permittivityc for various non-ionic surfactants. However, it is also seen from Fig. 3.6 that for some surfactants with the same dielectric permittivity, difference in the HLB numbers up to 2.5 are obtained. Some surfactants, e.g., laurie alcohol and oleic acid, listed under oils, are far apart of this dependence. It can be therefore concluded that the dependence of HLB on lg(e), similarly to the HLB dependence on Q (see [64]) can be applied only for surfactants with polar groups of a like nature (oxyethylene chains and polysaccharides). For surfactant mixtures, positive deviations from additivity with respect to the dependence H L B = a + b . l g ( e )

were observed in [21]. For some other

oxyethylated non-ionic surfactants a linear dependence of HLB on e was reported in [66]. e)

Water and pheno!numbers

The ability of a surfactant to form homogeneous systems with water and mixtures of organic solvents, can be used as a measure for the hydrophility of the surfactant. The critical composition before the clouding sets in is determined by titration. One of the first methods for the titration of aqueous solutions of surfactants by water was proposed by Greenwald et al. [67]. In this study, 11 different solvents for the surfactants were

170 tested. The best (reproducible) results were obtained for mixtures of phenyl cellulose with dioxan (1:4) and benzene with dioxane (4:96). Table 3.9. Dependence of HLB numbers on the dielectric permittivity Surfactant

c

lg e

HLB

Arlacel- 83

3.86

0.587

3.7

Span- 85

3.37

0.526

1.8

Span - 80

4.16

0.619

4.3

Span - 60

4.28

0.631

4.7

Span - 40

4.88

0.688

6.7

Span- 20

5.57

0.746

8.6

Brij - 30

6.02

0.780

9.5-9.7

PEG - 200

6.66

0.824

9.1

P E G - 300

7.27

0.862

11.3

PEG - 400

7.32

0.864

12.9-13.1

PEG - 600

8.14

0.911

14.5

Renex - 648

6.57

0.818

10.0

Renex - 688

7.25

0.860

12.5

Renex - 690

7.18

0.856

13.0

Tween - 81

7.50

0.872

10.0

Tween - 85

7.53

0.877

11.0

Tween - 80

8.75

0.942

15.0

Tween - 60

8.27

0.918

14.9

Tween - 40

9.49

0.977

15.6

T w e e n - 20

9.89

0.995

16.7

The water number of the surfactant is defined as the volume of water (in ml) which should be added to the solution of 1 g of the substance in 30 ml of the mixture of dioxane and benzene (96:4) to obtain a measurable turbidity. The larger the water number, the more pronounced are the hydrophilic properties. The dependence of the water numbers on the number of EO groups for several oxyethylated products was non-linear.

171 To determine the number of EO groups in the non-ionic surfactant molecule, another mixture of solvents, dimethyl formamide (DMF) - benzene was proposed in [68]. In this particular method of the titration, 1 g of the surfactant is placed in an Erlenmeyer flask of 125 ml volume, then 25 ml of DMF and 1.25 g of benzene are added. The solution is cooled to 20+1~

The

distilled water is added in 2 ml portions from a dosing system. After each addition the mixture is cooled in an ice bath. When the clouding is first noticed, the water dose is reduced to 0.5 ml, and then the titration is continued with the addition of water by drops. The titration is terminated when the clouding becomes visible, which is indicated by the moment when the letters become unreadable through the solution. In the experiments with oxyethylated alcohols, the volume of the water is increased from 13.4 ml for nEO = 5 to 25.85 ml for nEO = 9.9. Another method to determine the hydrophility of a non-ionic surfactant was proposed by Karabinos [69]. Here the titration of an aqueous solution of the surfactant (1 g of the substance in 50 ml of water at 20~

by a 5% solution of phenol is performed until the clouding becomes

visible. The amount of the solution (expressed in ml) required to obtain the clouding is called the clouding number or phenol index (Ph.I.). The experiments performed with decyl, dodecyl, tetradecyl and octadecyl ethers of polyethylene oxide show that the phenol index depends not only on the number of EO groups, but also on the radical length. The dependence of the phenol index on nEO is non-linear. The method proposed by Karabinos was used by Marszall [57, 70] to study the effect of various water-soluble organic substances (acetone, dioxane, formamide derivatives etc.) on the cloud point temperature, phenol index and HLB value of a surfactant. The titration was performed with equimolar concentrations (0.025 mol/l) of a surfactant in water at 25~

In this case the dependencies of the HLB on the amount (in ml) of 5.0%

aqueous solution of phenol (Ph.I.) are linear. The experiments performed with NP solutions with nzo = 8- 16 and nEO = 20, 25 and 50 (cf. Fig. 3.7) yield the dependence HLB = 0.28 (Ph.I.) + 11.4,

(3.30)

172 which is quite different from that proposed earlier by Tanaka [71 ]1 HLB = 0.89 (Ph.I) + 1.11.

(3.31)

28

"~20

.t

/ )

10

J I

I

t

I

12 14 16 18 gO

HLD

Fig. 3.7. Dependence of the phenol index of nonionic surfactants as a function of the HLB.

Marszall argued that the increase of the phenol indices and the cloud point temperatures of non-ionic surfactants caused by the addition of polar compounds (formamides, urea, acetone, dioxane etc.) should be regarded as an increase of the 'effective' HLB number. The influence caused by the medium on the hydrophile-lipophile balance of a surfactant, and, in particular, on the HLB number, is considered in more detail in Section 3.6. The ethanol number, defined as the amount of ethanol (in ml) necessary to transform the dispersion of a surfactant of a certain concentration into a homogeneous system was proposed by Rimlinger [72]. The nature of the phenomena observed in the clouding process in the experimental determination of the water number and phenol index is still unclear. Another version of the titration method for the determination of the HLB, based on the change in the hydrophility of carbon black caused by surfactant adsorption was proposed in [73]. 10 ml of 5% solution of the surfactant with known large HLB number is put into a cylinder (100 ml), 0.12 g of carbon black is added, and the mixture is shaken until complete wetting of

! Note that Eqs. (3.30) and (3.31) yield the same HLB values only for Ph.l. ~ 17.

173 the carbon black. Then, water is added to obtain a total volume of 80 ml. Then 10 g of oil is added, and the vessel is shaken carefully, to avoid the formation of excessive foam. The surfactant with low HLB number is dissolved in the hydrocarbon-alcohol mixture, and added to the aqueous solution from a dosing system in 1 ml portions. Then the liquid system is shaken and examined in respect to possible phase separation. The titration is performed until the transfer of carbon black from the aqueous solution into the oil takes place. In the experiments with NP mixtures having HLB numbers between 15 and 10.7, and mineral oil and laurie alcohol (used as oil), a linear dependence was obtained HLBreq = HLBT + 8.3

(3.32)

where HLBT is the HLB number determined from titration. This method is suitable only for surfactants with HLB > 8. 3.2.

Kinetic and thermodynamic rationalisation of HLB numbers - Davies' HLBD number

The concept of the HLB number system, introduced by Davies [27, 62], is essentially based on three dependencies. The first equation assumes that the HLB numbers depend additively on the group numbers (HLB numbers) corresponding to hydrophilic and hydrophobic parts of a surfactant, N~ and NI~, respectively, with the positive contributions ascribed to the hydrophilic parts, and the negative contributions to the hydrophobic (lipophilic) parts: HLBt) = 7 + )-"N~ -)--' N,.I i

(3.33)

i

The second equation of Davies' concept is that the coalescence rate for direct and inverse emulsion obeys the Smoluchowsky theory. In this model the energetic barrier for direct emulsions is expressed via the electrostatic repulsion and hydration energy of the polar groups (disregarding the influence of hydrocarbon chains), while for inverse emulsions this barrier is expressed via the desorption energy of two opposite hydrocarbon radicals from the film into the disperse phase (disregarding the influence of the polar parts of the molecule). In later modifications, only the ratio of the coalescence rates for direct and inverse emulsions was used.

174 The third equation expresses the relation of the surfactant transition energy from the organic phase into the aqueous phase with the equilibrium concentration of the surfactants in these phases, Eq. (1.125). It is assumed that this energy is an additive function of the transfer energies corresponding to the different parts of the surfactant, similarly to the additivity of HLB numbers with respect to the group numbers. The coagulation theory leads to the dependence of Eq. (2.12). Introducing into this equation the expression for the average drop volume, V = to/n, where to is the volume fraction of the oil in the emulsion, n is the number of drops per unit volume, this equation transforms into the form

V = to___q.+ 0 4nDRtox = V0 + 4nDRgx,

(3.34)

no

where V0 is the average initial volume of the drop. The validity of the dependence given by Eq. (3.34) was illustrated by Davies and Rideal [27] with coagulation studies performed for O/W emulsion prepared from 1% solution of sodium oleate. The dependence of V

vs

x was linear during several tens of days.

From formal considerations, assuming the existence of an activation barrier (activation energy), the time dependence of the average volume can be presented in a form similar to Eq. (2.26) l" V = V0 + 4nDRto e-(•E/Rr) 9x.

(3.35)

Assuming that D = kT/6nrlR (cf. Section 2.3), one can express the rate of variation of the average drop volume dV = ~4tokT e -aE/Rr = k he -~/RT , dx 611

(3.35a)

where Kn = 4q~kT/6rl is the hydrodynamic collision factor.

t The deficiencies of this approach, mentioned in Section 2.3, were discussed in the literature, see e.g. [6, 74, 75]. Modem studies of the flocculation and coagulation kinetics were summarised by Binks [76].

175 It was supposed by Davies that, for direct emulsions with ionic surfactant, the energetic repulsion barrier is proportional to W~ (~0 is the surface potential), with the proportionality constant B = 0.24 determined empirically from the experiments reported by Lawrence and Mills [77]. For sodium oleate, with an area per molecule of A0 = 45 nm 2, and a surface potential of ~0 = 165 mV, one obtains for the electrostatic barrier

AE,, = _ 2Bv.___~_.z= _ 11.2. RT

(3.36)

Davies argued that the total coalescence barrier AE, which should be overcome during the rupture of the aqueous film, depends on the nature of polar groups and the degree of saturation of the adsorption layer |

As initial approximation, Davies assumed that the barrier associated

with the overcome of the hydration energy AE is equal to AEh(o/w)= |

where Uh is the

dehydration energy of any particular polar group. Then for direct emulsions one obtains the general expression for the coalescence rate as

Vo/w = Khl exp '

- 0.24W~ -| RT

.

(3.37)

For example, if W0 =-175 mV, then votw = 10.5 Kh(orw). The addition of cetyl alcohol (with 0=0.5

and

AEh= 10kJ/mol)

results

in

a

decrease

of the

coalescence

rate

to

vo/w = 10.6 Kh(o/w). For inverse emulsions it is assumed that the energetic barrier is determined by the energy necessary for expelling (desorption of) the two hydrocarbon radicals in the aqueous medium located at the opposite sides of the film AEh(2) = 2.AE cm'ncm.

(3.38)

Davies assumed AEcm = 1.25 kJ/mol (300 cal/mol). Then the coalescence rate of inverse emulsion is (2AEcH~| v o/w = Kh, 2 exp RT

( 2"5ncn~| / = Kh '2 exp R-T ) .

Comparing the coalescence rates determined by Eqs. (3.37) and (3.39), one obtains

(3.39)

176

Vw/o

Kh,2 expl 0"24~ + |

h - 2.5riCH2

.| ~

Vo/w

Ku,I

~

RT

(3.40)

When the emulsions are prepared by shaking, it is assumed that the formation of multiple emulsion (containing both O/W and W/O emulsions) takes place, but only that emulsion which has a significantly lower coalescence rate survives. If vo/w/vw/o ~ 1, then the W/O emulsion is stable, while for vw/o/vo/w ~ 1 the direct emulsion is stable. A principal element of the concept developed by Davies is the postulation of the empirical dependence (3.33), which enables one to calculate HLB numbers from the chemical formulae and group numbers, see Table 3.10. Table 3.10. Group numbers HLBD[27]

Group

Group number

-SO4Na

38.7

-COOK

21.1

-COONa

19.1

Sorbitane ring (ether)

6.8

-

COOH

2.4

- OH

1.9

- O

1.3

- CH2CH20

0.33

CH2, CH, CH3

-0.475

The HLB numbers calculated from group numbers were compared by Davies and Rideal to those listed in the trade catalogue of Atlas Powder Company [27]. Such a comparison was also made in a number of other works, see e.g., [6]. Davies compared the dependence (3.40) expressed in the logarithmic form

RTIn Kh'~ 'Vw/~ = 0.24W20+ | Kh,2 9Vo/w

- 2.5ncH2|

with the equation (3.33) expressed in the form

(3.41)

177 N h

HLB-7 E m

z.., i

0.475

i

~

ncM~,

w

0.475

where 0.475 is the group number of a CH2-group. Dividing Eq. (3.4 l) by 2.5.|

RT In K h ' l " Vw/o = 0.24 w~ + ff'~Uh 2.5----~ Kh.~ 9Vo/w 2.50 2.5 - riCH2.

(3.42) one obtains:

(3.43)

Comparing Eq. (3.42) with Eq. (3.43), one can derive three important relationships which show that HLB numbers are essentially based on the emulsions breakdown kinetics. Assuming that

N~ = 1.9. lo ~,!3...-4.ro for charged polar groups, |

(3.44)

and ~Uh N~ = ~ 5.27

for non-charged polar groups,

(3.45)

and equating the right hand sides of Eqs. (3.42) and (3.43) to each other (at 293 K), the following equation is obtained

HLB o = 7 +

1

2.2 |

In

Kh i "V w/o

' . Kh,2 9Vo/w

(3.46)

If Kh,I = Kh,2 (which is correct for equal degree of surface immobility of aqueous and nonaqueous films and equal viscosity values rlw = 11o) and HLBD =7, or if O is very small, then neither emulsion cannot be preferred with respect to the stability. For direct stable emulsions (HLB = 10- 13), and therefore, for | ~ 1, and, for example for HLB = 11, one obtains vo/w = 10-4 vw/o. The ratios of coalescence rates for emulsions stabilised by lower alcohols, cf. Eq. (3.46), are compared in Table 3.11. The emulsions were prepared by shaking of water with petroleum ether. Equation (3.45) shows that the HLB group numbers for hydrated polar groups should be directly proportional to the energetic coalescence barrier arising due to the interaction of water with hydroxyl and ether

178 groups. Davies argued that this dependence is also reflected by the correlations between HLB numbers with the solubility and cloud point temperature. Table 3. I 1. Comparison of coalescence rates Emulsifier

HLBD

(Vw/o/vo/w)r162

(vw/o/vo/w)oxp

(Cw/Co) ~

19 = 1, Kh,2 = Kh, l |

HLB= 7 + 0.36.1n(Cw/Co)

,

Methanol

8.4

23

30

22

8.5

Ethanol

7.9

8

1i8

8

8.0

n-propanol

7.4

2.7

4

2.8 . . . .

7.4

n-butanol

7.0

1

1

1

7.0

r

....

"

,

According to Eq. (3.44), the HLB group numbers for charged groups depend on the surface potential ~F0 and the degree of adsorption layer saturation |

Thus, the contribution from

charged groups of a surfactant is variable. For example, for SDS the contribution of the hydrophilic group calculated from Eq. (3.44) for q~0 = 230 mV and | = 0.29 is 35. Therefore, according to Eq. (3.42), the HLB number is determined by the sum)-'~Ni, i.e., HLBo = 36. The experimental values of HLB numbers for SDS (from Griffin's data) are HLBc = 36 - 40. Comparing the energies of transfer of a surfactant from one phase into another with the dependence (3.42), one can establish a relation between the HLB numbers and the distribution coefficient. The energy of the transfer of a surfactant from the aqueous phase to an organic one is comprised of the energies corresponding to the hydrophilic (h) and hydrophobic (1) parts of a surfactant

0 o . ~ A G. h ~. A G j . AGw.

RTIn Cw . Co

(3.47)

In particular, for alcohols it was assumed by Davies that AGoH= 1.339kJ/mol, and AGcm=-0.335 kJ/mol (more accurate data are presented above in Section 1.4). Considering the contribution of CH 2 groups in Eq. (3.47) separately, one obtains

179 RT In Cw ~ AGh 0.33-----'5 cO = 0.335 -ncH2"

(3.48)

Comparison with Eq. (3.43) results in ,-

\0.75|

(3.49) Kh,2 Vo/w provided that for uncharged polar groups we have )-'~Eh = 0.75 AG~v,o,

(3.50)

and for charged polar groups o 0.32tFo 2 AGw'~ = O "

(3.51)

Note that for the derivation of Eq. (3.49) it was assumed that the coalescence barrier for direct 0 emulsions is proportional to the surfactant molecule transfer energy AGw, o . The values

Vw/o/Vo/w are compared with Eq. (3.49) in Table 3.11. For

Kh,2 -

Kh,l the expression (3.49)

confirms the Bancroft rule for non-ionic surfactants. For ionic surfactants this rule is applicable only when Eq. (3.51) holds. And, finally, comparing Eqs. (3.42) and (3.48) one obtains

HLB o = 7 + 0.361n Cw

(3.52)

Co provided that N~ = AG~176 0.703 N~ - AG~176 0.703

,

(3.53)

ed) '

(3.54)

180 0

0

where AGw.o(uncharged) and AGw.o(charged) are the Gibbs energies corresponding to the transfer of polar uncharged and polar charged groups from water to oil. If Eqs. (3.53) and (3.54) are valid, it follows from Eq. (3.52) that there is a quantitative relation between Bankroft's rule and the HLBo numbers. As shaking was assumed in the preparation of the emulsions, a dependence of the volume fraction q~ (for which the phase inversion of the emulsion in the emulsification machine takes place) on the HLB number was considered by Davies. The emulsification machine consisted of two plates (rotor and stator), the liquids to be emulsified are inserted through holes in the stator plate. The rotation of the upper plate leads to the emulsification, and the emulsion flows out through the outlet nozzle. For a rotation speed of 1850 rpm, the increase in ~0was linear with respect to the HLBo numbers in the range 6.7 to 16. For the same surfactant (Tween-80, HLB = 15), a strong dependence of the volume fraction on the plate material was observed, as demonstrated by the data of Table 3.12. Table 3.12. Dependenceof phase inversionon the material of the plates Plate material

Volume fraction ~pcorresponding to the transformation of a W/O emulsion into a O/W emulsion

Nylon

0.56

Glass

0.47

Sulphonated polystyrene

0.35

-stainless steel

.....

0.33

Rubber

0.32

Polystyrene

0.29

Teflon

0.25

It was already mentioned in Section 3.1, that based on these experiments Davies has proposed another method of the calculation of HLB numbers from the 9 value which correspond to the phase inversion for this emulsification technique and plate material.

181 3.3.

Critical micellisation concentration and HLB numbers

The formation of micelles is one of the most characteristic and practically important properties of a surfactant, closely related to the hydrophile-lipophile balance. Critical micellisation concentrations were determined for a wide variety of surfactants [4, 7, 78-86]. Also, the effect produced by the electrolyte concentration and various changes in the surfactant structure on the CMC was studied. Therefore, the CMC of a surfactant in the aqueous medium, and the relative CMC values for two heteropolar phases were proposed to be used as independent measures of the hydrophile-lipophile balance [87, 88]. Also, in a number of publications, relations between the HLB numbers and CMC values for surfactants (either in aqueous or non-aqueous media) were found and rationalised, see [89, 90]. In the studies performed by Demchenko [87], the hydrophile-lipophile balance (called by Demchenko the oleophile-hydrophile balance, OHB) was expressed as the ratio

O H B = ~Kl ,

(3.55)

C m

where CM is the critical micellisation concentration, the coefficient Kl = 7 is a constant. Another form is OHB = ( M - M~r)3/K2,

(3.56)

where K 2 is the constant, M is the molecular mass of the surfactant, and Mcr is a critical (limiting) value of the molecular mass below which micelles are not further formed. For solutions of sodium soaps of saturated fatty acids, alkyl sulphates, alkyl benzene sulphonates, and naphtenates, the respective critical molecular masses (Mcr) are defined as 152, 218, 231 and 164, and the difference M - Mcr was called the effective hydrocarbon radical [87]. For these homologous series, the value of K2=25.104, 7.104, 11.104 and 35.104, respectively. It follows from Eqs. (3.55) and (3.56) that when the hydrocarbon chain length decreases to M - Mcr = 0, the OHB value approaches zero. According to the scale introduced by Demchenko, for the most hydrophobic water-soluble micelle-forming surfactants the OHB values are 40 to 50. No attempt to establish the interrelation between OHB and HLB was made in [87], and it remains unclear why these

182 characteristics were assumed to be a HLB measure. Clearly, the OHB numbers are applicable to micelle-forming surfactants only. For specially purified monoethers of saccharose and fatty acids, the surface properties (kinetics of the establishment of equilibrium surface and interfacial tensions at various concentrations and interfacial tension isotherms at the water-decalin interface) were studied by Wachs and Hayano [89]. The purification degree was additionally checked using paper chromatography. The obtained CMC values (see Table 3.13) were compared with the HLBG and HLBD numbers. Table 3.13. CMC values for saccharose ethers and saturated acids [89] CMC value, mol/dm "3 ....

Acid 20~

500C

27.5~

Experiment

Calculations

data from [91]

Laurie

1.85.10-4

1.85"10-4

3.4.10 -4

Myristic

2.58.10 5

4.63.10 .5

Palmitic

1.1.10 -5

1.16.10 -5

5.5.10 -7

Stearic

4.59.10 .6

2.90.10 "6

1.i.10 7

.,,

..

The CMC values were calculated from the CMC value for lauric acid, assuming that the dependence of lgCm on ncH2 obeys Eq. (1.108), with B = lg 2. The discrepancy between the calculated and experimental values of the CMC was ascribed in [89] to the insufficient purity of the products, while that reason for the higher CMC values in [91 ] was explained by non-equilibrium g-values of the c

vs

lnC isotherms.

Comparing the dependence (3.6) represented as HLB=

2 0 ( M - M~ M + Anca2Mc. 2

where M0 and Mcm are the molecular masses of the hydrophobic part of the molecule and one methylene group, respectively, with the dependence of Eq. (1.98) represented as C m = A 2 ~c"2 ,

183 one obtains the expression

lgc~ K(HLBo A =

M

/

,

(3.57)

where K' and A' are constants. On the other hand, comparing Eqs. (1.98) and (3.33), one obtains K" lgC m = HLBD- KD,

(3.58)

where K" and KD are constants. It was shown by calculations that in both cases there exist almost linear (however different) dependencies of the HLBD and HLBG numbers on lg Cm. The dependence similar to Eq. (3.58) can be deduced comparing Kovats' indices, CMC and Davies' HLB numbers [92] (see Section 3.5). Another dependence oflg Cm on HLBD, similar to Eq. (3.58) was proposed by Lin [90, 93] lg Cm = a + b-HLBD = a + (1 + 13)-IHLBD,

(3.59)

where a and b are constants for a given homologous series, [3 is the degree of binding of counterions. In particular, for the homologous series of surfactants with hydrocarbon and fluorocarbon radicals the following dependencies were obtained [90, 94, 95] ! for CnH2n+IOSO3Na lg Cm =-26.96 + 0.621 HLBD,

(3.59a)

for CnF2n+ICOOH lgCm = -3.476 + 0.510 HLBD,

(3.59b)

and for CnF2n+~COOK lgCm =-16.155 + 0.658 HLBD.

i In a formula similarto Eq. (3.59), different coefficients are reported in [90] and [95].

(3.59c)

184 The interrelation between HLB numbers and CMC for two homologous series of oxyethylene derivatives of n-dodecanol (number of EO groups 4, 7, 14, 23 and 30) and nonyl phenol (number of EO groups 10, 15, 20 and 30) was discussed in [17]. The HLBG and HLBD numbers were calculated from Eq. (3.6) and (3.33), respectively. Using the HLB dependence on nEO, we get HLB o = 3.2 + 0.33 nEO

(3.60)

for the derivatives of the dodecanol, while the equation HLBD = 1.78 + 0.33 nEo

(3.61)

results for the derivatives of the nonyl phenol. Using the dependencies of lgCm on nEO (1.109) and (1.110), the formula for the HLBc numbers for oxyethylated dodecanol 1 0.0065 = +0.05 HLB~ lg C., + 1.827

(3.62)

results, while for nonyl phenols 1

HLB C

=

0.0108 lgC m+1.671

+0.05

(3.62)

was derived by Schott [46]. Also relationships for the HLBD numbers were derived for the derivatives of the dodecanol HLBD = 22.775 + 10.714 lg Cm,

(3.64)

and for the derivatives of the nonyl phenols HLBD = 14. 592 + 7.667 lg Cm.

(3.65)

It was shown experimentally in [46] that the dependencies (3.62)- (3.65) are quite well obeyed, and that the scales of HLB~ and HLBD numbers differ. It was noted by Schott that this fact is quite natural, because the HLBD numbers are additive and constitutive properties of a surfactant, while neither HLBG numbers, nor CMC cannot be regarded in this way. Besides, the

185 effect of the addition of EO groups on HLBo numbers (and CMC) depends on the nature of the hydrocarbon radical of the surfactant. To account for the structural changes in the hydrocarbon chain of the surfactant, the concept of the hydrophobicity index (HI) was introduced by Lin et al. [96]. The HI value was defined as the ratio of the number of effective methylene groups to the number of such groups in the reference homologous series (straight-chain sodium alkyl sulphates). To determine the number of effective methylene groups, various surface and bulk properties of a surfactant (adsorption at the liquid/gas interface, micellisation, surface tension decrease, and the ability of the surfactant to aggregate during the adsorption from solution at a solid interface) should be taken into account [96]. Let us consider the idea of this method using the studies of CMC of various homologous series of surfactants as an example. The dependence of the CMC on the concentration obeys Eq. (1.108). For sodium dodecyl sulphate with different positions of the sulphate group, the dependencies in Fig. 3.8 were obtained in [96].

!

posiLion of-SO~Na 10-1:

1 9 lg g~=l.49-O.294n e [] Igf.-/,53-o.e88n 260n

lO-Z-

10-~-

Fig. 3.8. Plot of the CMC as a function of the number of methylene groups in various sodium 10-t .... -~---~+-----I B 10 12 14

16

IH

20

/7C//z

alkyl sulphates: 1, first position of SO4Na group; 2, second position of SO4Na group; 3, fiRh position of SO4Nagroup

For example, for alkyl sulphates possessing 8 to 18 methylene groups and terminal sulphate group (1-position), the dependence (1.108) becomes

186 lgCm = 4.49 -- 0.294 ncm. Then the effective length of the hydrocarbon chain for any other surfactant can be obtained by substitution of the corresponding CMC value into this equation. In the plot of Fig. 3.8 this value is determined by the point of intersection of the straight line at the given CMC value parallel to the abscissa with the line defined as lgCm = A - Bncm for this homologous series. For example, for ncm = 17, one obtains ncm,eff= 16.4 for the 2-position of the SO4Na-group. The hydrophobicity index is defined as: n CH2.err HI = ~ .

(3.66)

nCH2

HI-values larger than 1 (i.e., ncm,efr larger than the actual nCH2value) correspond to the increase in the hydrophobicity, while values lower than 1 correspond to a decrease in the hydrophobicity. This can be attributed to differences in the surfactant structure (chain branching, presence of double bonds, etc), or to the effect of additives in the surfactant solution. This method was used in studies of the effect caused by polar groups of the surfactant and the temperature on the hydrophile-lipophile balance by Sowada [97, 98]. In these publications another parameter was introduced to characterise the hydrophobicity change, the methylene equivalent ME = ncm,eff- riCH2.

(3.67)

The values of HI and ME for some counterions of carbonic acids (as compared to the Na § ion) are listed in Table 3.14. These data were used by Sowada to calculate the corrections for Davies' formula to account for the effect of isomery on HLBD numbers. Another characteristic of hydrophile-hydrophobe balance was proposed by Tanchuk [84-86]. This characteristic can be obtained from the comparison of the dependence of CMC on the number of methylene groups in the hydrocarbon chain of the homologous series studied with the corresponding dependence on the number of groups for the fatty acid soaps, see Section 1.3.1. Each homologous series is characterised by the hydrophobicity constant pM, Eq. (1.113).

187 Table 3.14. Hydrophobicity indices and methylene equivalents of counterions

H.I0

ME

K+

1.0

0.12

Cs +

1.01

0.16

N(CH3)4+

1.005

0.05

C10H21N(CH3)3+

1.52

4.68

K§

1.03

0.31

N(CH3)4+

1.009

0.1

Temperature, ~

Ion

25

Na +

40

Na +

Introducing

oM into the expression for lgCm as a function of riCH2enables one to compare

homologous series of surfactants with different chemical structure, and to study the effect of various functional groups on the CMC and the micellisation energy via the variation of the parameter

pM.

It is assumed that the constant p M for any series can be represented in form of a sum of contributions from various counterions A ~ c , the nature of the functional group A a ~ , on the type and number of the substituents in the radical M pM _. (~M

=ac.~

c.~+~

M+

M

oc+Z(~ i=l

~

~

mi

),

Ri, and their position k:m~ (3.68)

M

where the values O c. 2 characterise the contribution of one methylene group (of the homologous series taken as the standard) into the free energy of micelle formation for a surfactant with straight radical. 9 is the value which characterises the contribution to the free energy of micelle formation per methylene group and accounts for the total contribution of all structural components of the surfactant. The values of pM and A cr~a for some surfactants are summarised in Table 3.15.

188 Table 3.15.

Hydrophobicity constants and constants which determine the contributions of various molecular structure elements

Homologous'series formula

pM

....

Functional group A ~M

-(:D

difference CnH2n+ICH2-COONa

1

Reference value

-

0.260

CnH2n+ICH2"COOK

1.115

Ac M

-0.030

0.290

CnH2n+ICH2-OSO3Na

1.135

ACroso 3M

-0.035

0.295

CnH2n+ICH2"SO3Na

1.154

AaM3

-0.040

0.30

CnH2n+ICH2NH2HOCOCH3

1.030

M AC~I~I2HOCOCH

-0.008

0.268

CnH2n+1CH2N+H(C2 H4OH)2C I-

1 9130

AaNH(C2H4OH)2C l

M

-0.034

0.294

CnF2n+I-CF2"COOK

2.538

AacMh

-0.370

0.660

CnH2,+I -C6H4-S03Na

0.769

ACM6H,

0.100

0.200

CnH2n+I-CH(COOK)COOK

0.838

AaCooKM

0.129

0.218

CnH2n+I

1.069

-

=

0.278

CH3

CI-

N+ ~ CnH2n+I

CH3

The value q) is determined by the addition of the contributions from all functional groups of the surfactant which are different from those present in the reference substance. As the micellisation (and CMC) depends on the hydrophile-hydrophobe balance, it was argued by Tanchuk that the product pM.ncm can be used as a measure for the hydrophile-hydrophobe balance HLBT = pM.ncm.

(3.69)

It can be seen that a quantitative interrelation exists between the hydrophobicity index HI, introduced by Lin and the hydrophobicity constant pM proposed by Tanchuk, see Fig. 3.9. It follows from the definition, Eq. (3.66) (cf. Fig. 3.9) that HI = nolle'eft ncn 2

189 for the same CMC value. The value of ncm,efr in the studied homologous series are related to the ncm,cfr value in the reference series via the expression (1.107), (1.108) A'

- B ' n9 cm = A - B. ncm off

hence A-A'

ncH2'ef =

+ B ' n c H 2 _ AA _ ~ B + (19M) -' riCH 2 , B

where pM = B/B'. Introducing the value of nCH2,effinto Eq. (3.66), one obtains

1

HI = ~--ff +

1 l

pM= B'ncr ~2

A)I

1 + ~ , B'ncH 2 P-g

(3.70)

where AA can be either positive or negative.

NI

IV

Ntl ~ALA=

n~

Fig. 3.9. Relation between the

effective number of

methylene groups in the radical and pM(schematically). If A = A' then HI = (pM)-~.

(3.71)

If for two series the coefficients B are equal, then PM = 1, i.e., these series are indistinguishable by Tanchuk's method, and AA A HI = 1 + ~ = --7 A BncH2

(3.72)

190 Both the characteristics HI and pM reflect the effect, caused by the difference in the structure of the hydrophobic chains or the state and type of the polar group, mainly on the difference in the energy of interaction between the hydrophobic chain and the aqueous phase for different homologous surfactant series. It should be noted that even strong differences in the hydrophility of polar groups related to their interaction with the aqueous medium and affecting the hydrophile-hydrophobe balance, plays only a minor role, acting indirectly via the change in the hydrophobicity of the radicals. Similar characteristics of the hydrophobicity can be defined based on the work of surfactant adsorption from the aqueous phase at the water/oil interface. These characteristics could be even more general characteristics, which can be applied also to non-micellar surfactants.

3.4. Phase inversion temperature in emulsion-measure of hydrophile-lipophile balance The methods used to determine the phase inversion temperature (PIT) and the dependence of the PIT on the concentration and type of the surfactant were considered in Section 2.4. It was argued by Shinoda that the PIT can serve as a new and independent characteristics of the hydrophile-hydrophobe balance, presenting arguments in favour of the fact that the PIT is a more informative property of the hydrophile-hydrophobe balance than the HLB numbers are. In Table 3.16 [99] the PIT and HLB values are compared with respect to the effect caused by various factors. Table 3.16. PIT

*** *** ***

Comparisonbetween HLB and PIT Influence factors Hydrophile-lipophile balance Nature of hydrophilic groups Nature of hydrophobic parts

HLB numbers ,

Oil type Additions to aqueous and non-aqueous phases Emulsifier concentration Volume of phases Temperature *** Emulsion type *** Correlation with other properties Ionic surfactants *** complete and exact information; ** less exact information; * crude information is available;- irrelevant to the influence of the factor. .

.

.

.

,It,

....

191 In Griffin's HLB numbers system, the type of the oil is accounted for by the introduction of the necessary HLB number. The PIT value incorporates the effect of the oil and requires no additional correction. On the other hand, the dependence of HLB on PIT can be used to determine the required HLB number. In Table 3.17, the values of the required HLB number for some oils listed in the catalogue are compared with those calculated from the PIT value. The HLB numbers and PIT values in water-cyclohexane systems for a surfactant concentration of 3wt% are compared in Fig. 3.10. The PIT value depends on the type of the oil, therefore each oil is characterised by its unique dependence of PIT on HLB, see Fig. 3.11. Table 3.17.

Comparisonof necessary HLB numbers [99] Catalogue value 10 14 14

Oil type Mineral oil Kerosene Trichlor trifluor ethane Cyclohexane Carbon tetrachloride Xylene Toluene Benzene

.

.

.

.

Value determined from PIT 10 12 12.5 13 13

.

16 14 15 15

14.5

15.5 16.5

Fig. 3.10. Dependence of HLB numbers on PIT in the system water/cyclohexane: l, Tween-40; 2, NP-17,7; 3, Tween-60; 13 i~tO

4, NP-14; 5, oxyethylated

J

dodecanol with nOE = 15; 6, oxyethylated dodecanol with

3~ I

20

t,

40

i

80

i ....

l,~

80

~

IN

I

120

nOE = 10.8; 7, OP-10; 8, NP-9,7; 9, OP-85; 0, R12-9,7;1 l, R]2-63; 12, R12-9,4.

192

6

....

Fig. 3 . 1 1 .

of HLB

number on PIT for various oils (at 1.5%

12

non-ionic

10

Dependence

J I

I

eo

t

eo

I

t, ~

-|

/oo

!

.o

surfactant

concentration):

a, benzene;

b, xylene;

c, cyclohexane;

d, heptane,

e, hexadecane;

1, NP-17,7;

2, NP-14; 3, NP-9,6, 4, NP-7,4; 5, NP-6,2; 6, NP-5,3

A quantitative empirical dependence of the HLB temperature I on the HLB value was proposed in [100, 101] THLB = Koi I (HLB- Noil),

(3.73)

where Koit and Noii are constants characteristic of particular hydrocarbons. The value of Koii = (17~

and Noit is 11.5 for xylene, 8.9 for heptane, 7.7 for hexadecane and 6.95 for

squalane. Equation (3.73) holds for individual surfactants and oils. For mixtures of oils the following equation was proposed in [ 102] THLB = THLB, I Xl + THLB, 2 X2,

(3.74)

where Xl and X2 are the molar fractions of the oils in the mixture. With this, the dependence of THLBon the HLB value can be expressed as T~s = Ko,t(HLB-~HLB~X,).,

(3.75)

193 The phase inversion temperature exhibits a strong increase with the decrease of the surfactant concentration. In [ 103], the dependence of PIT on the concentration of surfactant and oil was proposed to be expressed by the empirical formula [ 104]

t

Xo( - 1 ) ,

=--s

(3.76)

where t is the actual temperature, xo is the weight fraction of oil in the system, X is the weight fraction of surfactant in the system, and A is a constant. Another empirical dependence of the temperature of the formation of liquid crystals TLC on the HLB numbers for non-ionic surfactants was proposed by Kunieda [ 105] Tuc = Kw( HLBiX i - Nw )

(3.77)

where Kw and Nw ~ 7.4 are empirical constants which characterise the aqueous phase. A number of empirical dependencies of PIT on HLB numbers valid in the HLBG range 9 to 13 was derived by Ljubic and Gasic [106] from the comparison between Eq. (3.73), the expression proposed by Kunieda, and the dependence of PIT and HLB numbers on the number of EO groups. The most general formula was argued to be d(PIT) (HLB _ HLBo ) PIT = d(HLBc )

(3.78)

where HLBo is a constant characterising the oil. The dependence of the phase boundary at which the micellar phase arises as a function of the hydrocarbon molecular mass, the surfactant type and various additives was studied in [16]. Using a formula similar to Eq. (2.35), the constants listed in Table 2.4 were calculated. The dependencies HLBo vs riCH2 were found to be linear at different temperatures (20, 30, 40 and 50~

different electrolyte concentrations (NaC1 concentrations 1, 3, 6 and 9%) and different

The HLB temperature THLBintroduced in Section 2.4 is the temperature which corresponds to the inset of the three-phase region. At this temperature the surfactant is considered to be balanced (the analogue of the PIT).

194 concentrations of iso-amyl alcohol (1, 2 and 3%). It should be noted, however, that the range within which the HLB numbers were varied was very narrow: A HLB ~ 2. For the ionic surfactants (alkyl benzene sulphonates), the phase state of systems containing surfactant, electrolyte and additions of alcohol (butanol), was studied in [107] and described by the resulting relationship HLBo = 7.36 - 0.29 nmin

(3.79)

where nmin characterises the hydrophilicity of a surfactant with-10 < nmin < I 0, see Eq. (1.154). For systems which contain ionic surfactants, the three-phase state of the system is mostly controlled by the composition rather than by the temperature. Therefore the initial interpretation of the PIT concept given in [99] becomes irrelevant. On the other hand, a simple mathematical description of the range of composition variables within which the three-phase system can exist [ 16, 107-110] is capable of revealing the physical meaning of the hydrophilelipophile characteristics thus obtained only via their relations with the HLB numbers. In this respect, we believe that the region of the temperature-independent optimum three-phase state for various oils characterised by the ASN =_ncH2numbers, exists within quite a narrow range of HLB numbers, form 10 to I 1, and is much more important. Another type of interrelations between the PIT and HLB numbers follows from the concept which assumes the contributions of EO groups and methylene groups to the hydrophilelipophile balance. These contributions create the balance between the hydrophilic and hydrophobic parts of the surfactant and depend on temperature, see [ 112, 113]. It follows from the data reported by Shinoda [113] that, for ionic surfactants at 25~

the hydrophilic and

hydrophobic parts of a surfactant remain balanced if one EO group is added to 2-2.7 methylene groups. Similarly, for the surfactant with a PIT equal to 25~

and HLB = 10 the PIT value

would remain unchanged for the addition of 3.15 CH2 groups per EO group, while for HLB = 11.6 the PIT value remains unchanged for the proportion of 2.3 CH2 groups per EO group. One can calculate the HLB value of a surfactant mixture from the values of the PITdetermining composition for the series of mixtures, comparing these data with the PIT values of the individual surfactants.

195 It appears to be quite difficult to apply the PIT concept to ionic surfactants, cf. Section 2.4. One can vary the PIT value in systems which contain ionic surfactants by mixing them with a hydrophobic surfactants (fatty alcohols, acids or amines) and observing the existence of the three-phase region. In such systems the composition rather than the temperature is the controlling factor. For example, it follows from the data presented by Shinoda [112] that in the water-xylene-octyl amine (1) and octyl ammonium chloride (2) mixed systems, the balance exists for the components ratio of 1.22 "0.66, which enables one to make a semi-quantitative estimation of the HLB value. It was mentioned in Sections 1.3.4 and 2.4 above that the phase inversion temperature is the temperature at which the destruction of emulsion takes place due to the formation of the micellar phase. Here two temperatures can be distinguished between: those corresponding to the formation and destruction of the LPB and UPB; and those temperatures characterised by different dependencies on the composition of the system, see [ 16].

3.5. Hydrophile-lipophile balance and chromatographic characteristics of surfactants The liquid chromatography on paper was employed by Nakagawa and Nakata [114] to determine the parameter RF (ratio of the velocity of the motion of a component along the column to the frontal velocity of the carrier, see Section 1.5) for some surfactants. It was shown that for the substances studied, the dependence of RE on HLB was non-linear; this dependence was very weak in the HLB range 10 to 13, and more pronounced for HLB values of 13 to 14 and higher. The HLB numbers were calculated using a formula proposed by Kawakami [39]. This method, obviously, cannot be applied to surfactant mixtures, because during the chromatographic process they are resolved into separate bands. In similar experiments, the HLB values for solutions of hydrophobic (oil-soluble) surfactants in a mixture of heptane-ethyl

ether-acetic

acid

(70:30:1)

were

measured

using

the

thin

layer

chromatography with a silica gel. It was shown that the dependence of RE on HLB numbers calculated from Davies' group numbers is linear, while the dependence of RE on HLB numbers calculated from Eq. (3.4) shows a jump [ 115].

196 The values of R r measured using the thin-layer chromatography [ 116] in a wider range of HLB numbers for the three classes of surfactants mentioned above (see Section 1.5) and assuming that the HLB numbers should depend on the distribution coefficient in any system, are presented in Fig. 3.12. Here a silica gel was used as the stationary phase, while a water-alkyl ketone mixture was employed as the movable phase. The dependence of HLB on RF was nonlinear, similarly to the experiments performed by Nakagawa and Nakata [114], therefore in [ 116] the parameter Rm = lg (1-RF)/RF was used, cf. Eq. (1.169), to establish a relation between Kl2 and the HLB values. The dependence expressed in coordinates RF/(1-RF)

vs

HLB, see

Fig. 3.13, was linear in the HLB range 5 to 13, however, for higher HLB values this dependence becomes also non-linear.

/?/

9 - - ' - IA-9 SA-IO OA-IO

0.5--

0

.5

I ~ I ~, I-~--~ 10

t/L9

--4-I

15

a

Fig. 3.12. Dependenceof RF on HLBo: 1 - lauryl ethers; 2 - nonylphenol ethers; 3 - stearyl ethers; 4 - oleyl ethers.

As shown in Fig. 3.13 a congruence exists of all straight lines at approximately the same point (located outside the region shown in the figure). For any given number of EO groups, the more hydrophobic (the longer) the hydrocarbon chain is, the lower is the Rm value shown in Fig. 3.13, that is, the lower is the distribution coefficient between the movable and stationary phases. Quite naturally, the increase of the EO groups number for a fixed hydrocarbon chain length results in the displacement of the distribution towards the immovable (polar) phase. Therefore, the proportionality constant between HLB and K2~ for a given surfactant does not

197 depend on the hydrocarbon chain length of the surfactant, while the HLB value itself depends on the nature of the surfactant, that is, for the same K:~ value the HLB numbers are different. -

j

Fig. 3 . 1 3 .

Dependenceof RF/(I-

RF) on HLB: 1 -lauryl ethers; 2 10 ///8

15

nonylphenol ethers; 3 - stearyl ethers; 4 - oleyl ethers.

Another chromatographic method, which, in various versions, is more often used to estimate the hydrophilicity (or hydrophile-lipophile balance), is the so-called reversed chromatography l, where the surfactant is employed as the support for the chromatographic process [118-122]. The reversed gas chromatography was used by Harva et al. [119] to measure the distribution coefficient (Kl2) for various hydrocarbons and di-isobutilene between the carrier gas and the surfactant stationary (supported) phase (formed by non-ionic surfactants of Span and Tween type at 80~ It was shown in [119] that a linear dependence exists between the Kl2-Values o f water and

di-isobutilene, and the HLB values of Span, Tween and their mixtures. The HLB numbers were calculated using Griffin's formulas. However, the HLB values for different classes of surfactants are determined by different dependencies on the distribution coefficient of water

i This 'reversed' chromatography should not be mixed up with the method employing the time scanning with respect to the exit of the zones from the layer; this procedure is also called the 'reversed' chromatography [154], in

distinction from the direct chromatography, where the distribution of the concentration along the layer is

measured after some time T.

198 (that is, the values of

KI2 depend not only on the hydrophile-lipophile balance, but also on the

type and structure of the surfactants). This fact agrees well with the results obtained for the water numbers [67]. At the same time, the dependence of HLB numbers on the distribution coefficient of di-isobutylene for the two classes of surfactants can be represented by a single straight line

HLB = 2 6 - K~--z2. 2.6 It follows from this dependence that H L B = 0

(3.80) for K12=67.6, while for K12= 1 the

HLB = 25.62. The distribution coefficients were also determined for n-heptane and iso-octane and the resulting HLB dependencies for these substances on their K12-values were also linear, however the slopes of these dependencies were much lower. Therefore, these obtained dependencies were much weaker. For mixtures of Tween and Span, the differences between the HLB values calculated from Eq. (3.80) and those calculated from Griffin's formulae did not exceed _+1. If the surfactant is used as the stationary phase, then the Kovats' index (I) and the difference of Kovats' indices (AI) can be used to characterise the polarity and hydrophile-lipophile balance. The dependence of the Kovats' indices difference (AI) on the value of lg C m in heptane and on HLB numbers for ot-monoglycerides of saturated fatty acids was studied by Reinhardt and Wachs [92]. The Kovats' indices were determined with water as the polar liquid, and decalin as the apolar phase. The HLB values were calculated from Davies' formulae by summation of the group numbers. (In this work, the coalescence rate of inverse emulsions and the dependence of surface pressure on the area per surfactant molecule were also studied.) For three acids, the dependence of AI on HLB and on lg C m was linear. From the data obtained in [92], a dependence of AI on HLB was proposed for the homologous series of monoglycerides of saturated fatty acids AI = -22.22 HLB D + 431. For other homologous series, similar dependencies of AI on HLB were found,

(3.81)

199 AI = a.HLB D + b

(3.82)

with other values of the coefficients a and b. The dependence of AI on the CMC of monoglycerides was shown to be I AI = 31 lg(fm) + 175.

(3.83)

The reverse chromatographic method was mostly used to determine Huebner's polarity indices (PI) [120-125]. The experimental method for the polarity indexes is basically the same as that used to determine the Kovats indices. The polarity index (PI) is determined as follows [ 120]. The chromatographic column is filled by a solid support which contains 20wt% of the surfactant studied. Then normal hydrocarbons and methanol are injected in the evaporator of the chromatograph using a syringe. During the analysis run, the peaks are observed, which correspond to each hydrocarbon and methanol. Using the dependence of the logarithm of the retention volume on the carbon atom numbers in the hydrocarbon (the hydrocarbon number, no), cf. Eq. (1.170), the carbon number of the methanol is determined as the number of carbon atoms which would methanol possess, when being the hydrocarbon. From this carbon number of the methanol (which is equal to the Kovats index multiplied by 100), the polarity index is determined using the formula PI = 100 lg(n c - 4.7) + 60

(3.84)

where the factor 100 is introduced to obtain integer values, and the term 60 ensures that the PI is positive. The nc value is usually in the range between 5 and 9. For example, for Tween-60 n c = 7.65-7.68. The procedure is performed at a temperature above the melting point of the surfactant (usually at 70~

It was argued by Huebner that the polarity indexes determined by

this method can be regarded as a measure of the hydrophile-lipophile balance. It was shown in [ 120] that for surfactant mixtures the PI increases linearly with the fraction of the more polar surfactant, and also the dependence between PI and HLB numbers was approximately linear. In more recent publications [ 122-126] the dependence of PI on HLB was

! ComparingEqs. (3.80) and (3.82) one obtains a dependence of HLB on lg(Cm), of. Eq. (3.58).

200 studied for various oxyethylated products. In the study [126] the PI values for various classes of non-ionic surfactants were determined experimentally, and the following dependence was proposed HLB = 0.316 P I - 21.5.

(3.85)

However, in [ 124], where 9 non-ionic surfactants (of the Span and Tween type) were studied, it was shown that the dependence expressed in the coordinates lg PI vs HLB is better linear (cf. Fig. 3.14): HLB = 45.45 lg(PI)- 78.14.

(3.86)

This dependence was subsequently used by Krivich et al. to determine the HLB numbers for other classes of substances, such as oxyethylated alcohols [125], acids [127], amines [128] and isomers with double bonds in the hydrocarbon chain and various positions of the functional OH group in the radical [129].

I 1 110 2.0

100

1.9

90 80

1.8

i

..... i

z's

z'5

70

HLR

Fig. 3.14. Relationbetween polarity index and HLB values for non-ionicsurfactants. Systematic studies of the dependence of PI on the length of the hydrocarbon chain and on the number of EO groups for various classes of non-ionic surfactants shows that for alcohols and amines the dependence of PI on nEo is linear, as one can see in Figs. 3.15 and 3.16. From the extrapolation of these dependencies to nEo --~ 0 one can estimate the PI0 values for an alcohol or amine; these values were found to be independent of the chain length of the

201 compound ~ (similar to the dipole moment dependence). If the number of methylene groups exceeds 20, the PI value becomes independent of the number of EO groups. The average PI 0 values for various groups of surfactants molecules were found in [ 129] to be2: -OH

:

-COOH -NH

85.6, :

67.6,

:

100,

-NH2:

90.9.

For secondary alcohols, the PI0 values were equal to 85.6 irrespective of the location of the OH group, while the hydrophilicity of the molecule as a whole, estimated from the polarity index, strongly depends on the location of the OH group [ 129], as one can easily see in Fig. 3.16. The largest increment of the hydrophilicity with the increase of the oxyethylene chain length was observed for normal aliphatic alcohol.

/ 2

110

5 ~~_._.._..c~_-----

4

/o

-----~---'-

~

/4

/6

8

Fig. 3.15. Polarity index dependence on the number of oxyethylene links in aliphatic amines homologous series: 1 - Cl0 - decyl amine; 2 - Cll - undecyl amine; 3 - Cl2 - dodecyl amine; 4 - C14 - tetradecyl amine; 5 - Cl6 - hexadecyl amine; 6 - CIS - octadecyl amine.

For oxyethylated acids the dependence of PI on n~o was non-linear. 2 In their previous publications the authors reported different Plo values for these groups.

202

! 1

//o

2 3 1oo

r

9o

Fig. 3.16. Dependence of polarity index for oxyethylated secondary alcohols with OH group located at the second and third carbon atom on the number of oxyethylene links: 1 - 2-nonanol; 2 - 2-decanol; 3 - 3-decanol; 4 - 3-dodecanol. The presence of a double bond in oxyethylated acids leads to an increase in the hydrophilicity of the non-ionic surfactants: for one double bond this increase in the PI value amounts to 8.4 units, for two bonds the increase is 24.6, and for three bonds the PI value increase is by 29.7 units. Some additional information concerning the influence of the hydrophobicity and hydrophilicity of the parts of a surfactant on the retention indexes can be obtained from the comparison of the PI values for the surfactants (used as the carrier) and the polyethylene glycols [128]. For a number of surfactants, including solid anionic and cationic surfactants, the polarity indexes were determined in [ 130]. Using the standard Huebner method, the linearity of the PI dependence on HLB was shown to exist for oxyethylated tridecyl and hexadecyl alcohols (and the alcohols themselves), and for mixtures of NP-2 with NP-20 and TD-8 with NP-15. For mixtures of surfactants (including solid substances), the standard method becomes unsuitable (elution of methanol does not occur). Therefore for these surfactants mixtures of a non-volatile liquid (polyethylene glycol, PEG-300) with the surfactant was used. For this mixed stationary phase the PI value was calculated from the expression

PImi,, =

PIs,~.a,:mt 9A + PIpEo 9B 9 A+B

(3.87)

203 The mixture with A = 1 and B = 3 was used. The PI values are summarised in Table 3.18. Table 3.18. Polarity indices for surfactants of various classes .

.

.

.

.

.

.

.

.

.

.

.

Surfactant

.

.

Apparent number n c

Polarity

of carbon atoms in Eq. (3.84)

index

HLB numbers Eq. (3.86)

f HLB

HLB o

Anionic surfactants .

.

.

.

.

.

.

.

Potassium oleate

' 9.73

111.9

15

20

10.35

131.9

18.22

41.9

Calcium octyl sulphate

! 10.40

, 133.5

Potassium Octyl sulphat e

: 10.40

, 133.5

Sodium octyl sulphate I

Triethanol amine octyl sulphate .

.

10.54 .

.

Monoethanol amine octyl

135.5 .

10.54

135.5

9.50

103.6

9.67

109.5

9sulphate Calcium dodecyl benzene , sulphonate Sodium dodecyl benzene

14.55

, sulphonate Cationic surfactants

HLB6

Hexadecyl trimethyl ammonium brimide

9.75

i Lauryl amine , Lauryl amine acetate

112.3

8.25 .

.

, Lauryl pyridinium chloride Lauryl trimethyl ammonium

.

,9.05 .

.

15.03

51.1 .

.

, 10.2

.......

.

. . . .

,i 86.3 126.3

9.92

118.3

16.07

9.98

120.3

16.4

chloride Lauryl dimethyl benzyl ammonium chloride Non-ionic surfactants .

Poly0xyethylehe monolaurate

9.24

, , 93.9 ..... 1 !,.45

, 8.6

, Po!y0xyethylehe monolaurate

, 9.72 . . . . . .

111.5

14.9

, 16. 7

:_p0!yoxyethylene monooleate

~ 9.58 .

106.3

14.0

, 15.0

....Polyoxyethylehe dioleate

,9.15

...... 90.3

9Polyoxyethylehe trioleate

.8.93

.81.5

.

.

.

.

10.74 . . . . . . . . 8.72

12.0

. 11.0

204 The values of HLB numbers calculated from Eq. (3.86) l were found to be rather different from the HLBD and HLBo values, especially for ionic surfactants (as much as twice for octyl sulphates). It can be therefore concluded that Eqs. (3.85) and (3.86), derived from the polarity indexes of such surfactants as Span and Tween, cannot be regarded to as general relationships: possibly, they are invalid for another surfactant classes, in particular, for ionic surfactants. It is seen also that the length of the radical in ionic surfactants only slightly affects the PI value, while the PI 0 value for functional groups exhibits no dependence whatever on the length of the hydrophobic chain. This can be possibly ascribed to the fact that the main contribution into PI values comes from polar parts of the surfactant, and therefore the PI value depends on the polar group strength rather than on HLB value. Another version of the reversed chromatography is the method proposed by Becher and Birkmeier [131], where the retention volume (or retention time) is determined. The value RF =

17ethanol/q;hexane

is determined from the passage of an ethanol-hexane mixture (1:1) through

the column with liquid surfactant acting as the adsorbent. The relative retention time RF determined by this method depends linearly on the HLB number in the range from 2 to 18

(3.88)

HLB = 8.55 RF - 6.36.

One more version of the reversed chromatography was used by Micke et al. [ 132], where the retention tine of iso-amyl alcohol instead of the methanol was determined as the carrier for the surfactant studied. Similarly to [ 131 ], the dependencies of HLB on RF were linear. In the study [133] it was suggested that the activity coefficient 3, of water at infinite dilution with respect to the water content in the medium studied can be compared with the HLB instead of the PI. This coefficient is a thermodynamic parameter, which can also be determined using the reversed gas chromatography. To verify this concept, the values of In ), were determined for three

surfactant

substances:

glycerol,

di(metoxy

glycol)

phthalate

(DMGP)

and

di(2-ethyl-hexyl) phthalate (DOP). The water activity coefficient was determined from the equation

Calculations accordingto Eq. (3.75) yield quite similarHLB values.

2O5 ln~,=ln

RT P?VLK L

B~P~ RT

(3.89)

where KL is the distribution coefficient of water between the liquid (stationary) phase and the gas, defined as the ratio of its molarity in the gas to that in the liquid phase, v L is the molar volume of the stationary phase, pO is the saturated vapour pressure of the solute at the column temperature, B~ is the second virial coefficient for the vapour of the dissolved substance. The water activity coefficients at infinite dilution, determined in this way, are presented in Table 3.19. The water activity coefficient is normalised with respect to the standard state of the dissolved substance taken as the pure liquid, that is, ~, - 1 for x -- 1. It is seen that the In ), value depends significantly on the HLB number, namely, the more polar the medium, the closer is the value of 3, to unity. However, it should be mentioned that the set of 'surfactants' used was rather few and exotic. It can be also supposed that the In ), - value is affected mostly by the polar parts of the surfactant. Therefore it remains unclear, how significant the changes of this value will be caused by changes of the hydrocarbon chain length if the polar part remains the same. Moreover, it was shown in [134] that an inverse correlation exists between the adsorption of iso-octane on Tween and Span, determined by gas chromatography, and the HLB numbers. Table 3.19.

Water activity coefficients at 298 K and HLB numbers

Substance

HLB

In )'H20

Glycerol

20

0.02

DMGP

14.6

1.58

DOP

4.5

3.56

3.6.

Comparative analysis of Griffin's and Davies' HLB numbers, consideration of the influence of the medium and the surfactant structure on the HLB number systems

Many scientists and engineers, believing in the 'magic' simplicity of the HLB number concept, have tried to establish relations between these numbers and various properties of surfactants, and to reveal a physical meaning of the hydrophile-lipophile balance. It should be stressed, however, that none of the numerous correlations, which were found between the HLB numbers

206 and various properties of surfactants (see Section 3.1), could be regarded as a general property immanent to all the surfactant classes, but rather as features which characterise certain classes of oxyethylated substances (alcohols, acids or amines). In fact, it was correlations of a property with the number of EO groups or methylene groups, rather than with the hydrophile-lipophile balance, or an interrelation between two of such properties, that was established in the majority of studies. The deficiencies of the HLB numbers system were pointed out in a number of papers, therefore, we discuss here only the most important ones. The scale of HLB numbers was initially developed for practical purposes - to estimate the applicability of surfactants as emulsifiers, wetting agents, detergents etc. The main deficiency of Griffin's scale is the lack of a well-defined physical meaning. There are doubts also in respect to many specific aspects of this HLB number system. For example, the detailed studies performed by Ohba [18-19] and other authors [135-136] have shown that the additivity principle of HLB numbers for mixture of surfactants is obeyed only within a narrow range of HLB numbers of surfactants and necessary HLB numbers of oils. With respect to the use of surfactants, especially the selection of suitable emulsifiers, in addition to the surfactant nature, it is essential to consider other factors, e.g., the concentration of the surfactant, the type of the oil, the temperature, additions of electrolytes and other substances. These factors cannot be directly accounted for by the HLB numbers. Therefore, quite naturally, numerous attempts were made to introduce effective values of HLB numbers, which would reflect these influences. If the HLB numbers for surfactants are determined from their emulsification ability, then any influence of the medium (additions of electrolyte, polar organic substances, variations of temperature etc.) will be implicitly introduced into the experimental data, resulting in differences of the necessary HLB value for systems where these influences are absent. The influence of a surfactant structure (presence of double bonds, displacement of the polar group or benzene ring along the hydrophobic chain) on the HLB numbers can be accounted for in a similar way. However, some doubts remain regarding the feasibility for the hydrophilelipophile balance to be expressed in terms of the emulsion stability, because the stabilising

2O7 ability of surfactants is a rather complex property, and its mechanism is still quite obscure and cannot be expressed in a quantitative form. When Griffin's formulae are used to determine the HLB numbers of non-ionic surfactants, the hydrophilicity is estimated from the mass fraction of EO groups, irrespective of their nature, position, and the structure of the hydrocarbon chain. For a mass fraction of EO groups equal to l, the HLB number is assumed to be 20. Expressing the balance of weight fractions in form of the hydrophilic-oleophilic ratio [137] we have H HOR m = - O'

(3.90)

where H and O are the mass fractions of the hydrophilic and lipophilic parts, respectively, one obtains H/O HLB~ = 2 0 ~ . 1+ H/O

(3.91)

It is seen that the relation HORm - 1 corresponds to HLB -- 10, while the limiting value of 20 is achieved asymptotically for nv.o ~ oo. To account for the influence of the medium, in addition to the nominal HLB value (the one calculated from the formula), the effective HLB value (in the presence of additions) is introduced as the HLB number of certain individual surfactant, which, with respect to some precisely measured parameters (cloud point, CMC, phenol index, phase inversion temperature, etc.) behaves itself similar to the surfactant studied in the presence of the addition. It was mentioned in Section 3.1.3 that four methods were proposed by Marszall to determine effective HLB values [56, 57, 138]. It was shown, for example, that the unimolar additions of acetone, urea, dimethyl formamide, dioxane and other substances to 0.025 M aqueous solutions of a non-ionic surfactant result in the increase of the effective HLB values by 0.1 to 2.8 units depending on the number of EO groups and the nature of the added substance. The most pronounced increase of HLB numbers is caused by dimethyl- and diethyl formamide [57]. On the contrary, the addition of glycerine leads to a decrease of the effective HLB value [ 138]. The effect of added polyethylene glycol (PEG) is more complicated: for non-ionic surfactants with less than 14 EO groups the HLB numbers decrease, while if nEO > 14, an increase in the HLB

208 numbers was observed [138]. The effect of added alcohols depends on their molecular mass [138]. Two main approaches were proposed by Davies for the rationalisation of the HLB number system: (i)

the kinetic approach, which was based on the comparison between the breakdown rates of direct and inverse emulsion,

(ii)

the thermodynamic approach, which implies the comparison between the transfer energies from water to oil corresponding to various functional groups, and yields a linear dependence of HLB numbers on the logarithm of the distribution coefficient of a surfactant between water and oil.

Analysing Davies' concept, one should clearly understand the origin and physical sense of the main dependencies, expressed by Eqs. (3.33), (3.46), (3.49) and (3.52). The first of these relations, Eq. (3.33), is the dependence of the HLB value on the group numbers of functional groups constituting the surfactant. This dependence, although empirical, implies that one can distinguish between the contributions of different groups of a surfactant, and calculate these contributions from the coalescence kinetics or the energies corresponding to the transfer of the surfactant from one phase to another. This relation, if taken as the basic hypothesis, should be subsequently verified with respect to various functional groups using either of the two approaches above (kinetic or energetic), and the HLB numbers thus calculated should be compared with Griffin's HLB numbers. Actually, however, only few group numbers were calculated from the formulae; also, the numbers for CH 2 and OH groups were estimated from the energetic dependencies, while for OSO3Na these values were obtained from the calculations of electrostatic repulsions (i.e., from the emulsion breaking kinetics). The origin of other group numbers is quite uncertain. In what regards the first main dependence, Eq. (3.33), another objection can be expressed concerning the additivity principle of HLB numbers irrespective of the sense which is ascribed to the group numbers. There exists an extended evidence of the fact that the hydrophilicity and hydrophobicity of functional groups depend on their position in the molecule. Thus, the additivity principle is often violated. For example, it was shown in Section 1.3.1 that even for

209 the isomers of saturated hydrocarbons the energy of interaction of single methylene links with water

is

different

from

that

characteristic

to

linear

chains.

Say,

for

iso-butane

Air0= 24.49 kJ/mol, instead of the value -26.38 kJ/mol which would be obtained if the contribution of CH 2 groups were additive. Similar non-additivity was found also for diens. The same effect with respect to the hydrophobicity was observed also for the iso-nonyl phenol radical as compared with the nonyl phenol one [139], while a difference in the interaction energies of methylene groups with respect to their transfer from water to non-aqueous media was measured in [140] using a potentiometric method employing ion-selective electrodes for alkylonium cations. For chains with normal structure the increment corresponding to a CH 2 group (

A~~

) was -3.1 kJ/mol, while for the iso-configuration this value was- 1.84 kJ/mol.

It was noted by Graciaa et al. [107] that the position of the benzene ring in the alkyl benzene sulphonates affects significantly the phase behaviour of water-oil-surfactant systems, and hence, the hydrophile-lipophile balance. A dependence between the HLBD number and the position of the benzene ring was derived HLB D = 17.5 - 0.731 (IN) - 0.49,

(3.92)

where IN is the isomeric number, indicating the number of carbon atom (counted from the beginning of the hydrocarbon chain) to which the benzene ring is attached. It is seen from this expression that the closer the ring to the centre of the chain, the higher is the hydrophobicity (the lower is the HLBD number). Another way to account for the structure of the hydrocarbon chain and the position of the polar group is to determine the effective number of CH 2 groups or the Lin hydrophobicity index (HI) from measurements of the CMC or other characteristics [63, 96]. According to this method, for example, the substitution of a single C-C bond by a double (C=C) or triple (C-C) bond leads to a decrease of nCH2,effand HI. On the contrary, the addition of a benzene ring to the hydrocarbon radical results in an increase of the HI value. It was shown empirically in [ 141 ] that, with respect to the surface activity and the effect on the CMC value, one benzene ring is equivalent to 3.5 methylene groups. This equivalence relation was used in some studies [37, 95]. However, it follows from the data reported by McAuliffe for the transfer energy of benzene from saturated hydrocarbon into water, A~t~ = 19.34 kJ/mol, that this value is equivalent to approximately 5.2 methylene groups [ 141 ].

210 It was concluded also in [107], where the equilibrium in the three-phase systems (watersurfactant phase-oil) was studied, that the benzene ring is by no means equivalent to 3.5 methylene groups. It was shown by Lin et al. [95, 96] that, in the alkyl sulphates series, the effective number of carbon atoms and the corresponding hydrophobicity index depend on the position of the OSOaNa group, see Table 3.20. The displacement of the polar group from the end of the chain to its centre leads to a decrease of ncm.cer, that is, to a hydrophilisation of the hydrocarbon chain, and, therefore, to a decrease of the group number of the methylene group, i.e., to the decrease of the hydrophobicity of the substance. These results are seen to contradict with Eq. (3.92), and it is unclear which method should be preferred. Table 3 . 2 0 Variationof the number of effective carbon atoms and the hydrophobicity index with respect to the position of the OSO3Nagroup in alkyl sulphates Position of the

Number of carbon atoms

OSO3Na group

in the chain, ncm

1

2

1

8 i

nCH2,cff

HI

3

4

8

1

i

1

12

1

14

!14

1

16

16

18

' i"8 !

1

2

"

12

1

8

7.5

0.937

2

10

9.5

0.950

2

13

12.5

0.961

2

14

13.5

0.964

2

15

14.5

0.966

2

17

16.4

0.97

2

18

17.4

0.97

6

16

14

0.875

6

18

15.8

0.877

8

15

12.4

0.826

8

16

13.2

0.825

211 The effect of positional isomery was also studied by Sowada [97] who concluded that Davies' method of calculating the HLB numbers becomes completely unsuitable for poly-functional surfactants with ionic groups. For example, the Davies formula yields HLBD = 70 as applied to alkylene sulphonates, which is far beyond the Griffin scale, while in the patent literature [97] such values of HLB are not unusual. It should be also added that it was shown in [127-129], where Huebner polarity indices were determined, that the hydrophilicity of one oxyethylene link in oxyethylated alcohols depends significantly on the position of the hydroxyl group; this means that for different isomers the group number of the EO group should be different. The influence of the medium, surfactant structure and temperature can also be accounted for in the framework of the concept assuming that the balance of the contributions from hydrophilic and hydrophobic groups is given at TUB [112, 113]. Davies' arguments regarding the coalescence kinetics was subjected to serious criticism from the very moment of its publication [62]. It was stressed by Derjaguin in a discussion on Davies' lecture at the 2 "a International Congress on Surface Activity (1954) that the calculations of the coalescence rate disregard the properties of thin films which separate the emulsion drops. Davies' theory makes no distinction between less stable emulsions stabilised, e.g., by alcohols or acids, and very stable emulsions, where thin equilibrium metastable films are formed, see Section 2.1. The expressions derived by Davies for the coalescence rate are based on the Smoluchowski theory, which describes the coagulation kinetics, whereas for stable concentrated emulsions the coalescence stage is crucial, which is govemed by the properties of thin liquid films (their thickness, disjoining pressure etc.). Moreover, until recently, the rupture theory was developed only for the case of non-equilibrium films (Scheludko-Vrij theory), while among the equilibrium films only Newton black films were studied [ 142]. In recent years, the stability of plane emulsion films was extensively studied and discussed. The reader can refer to the most instructive studies [74, 75, 142-146] concerning the stability of thin films and emulsion coalescence, where the properties of thin films and surfactant adsorption layers are considered. A comprehensive review and list of references can be found in the monographic collection edited by Binks [76].

212 As already mentioned in Section 2.3, it has be also stressed that the assumption is incorrect that the activation energy of the film breakdown can be described by a simple formal introduction of an exponential terms (of. Eq. 3.39 and 3.40). Still more formal and insufficient for the description of the influence caused by polar and apolar parts of a surfactant are the expressions in the exponent, (0.24~go2 - |

h)/RT for direct emulsions, and 2nc.20 f 9A~c.2/RT for

inverse emulsions. These expressions imply that the repulsion barrier in direct emulsions does not depend on the length and structure of the surfactant hydrocarbon chain, and in inverse emulsions this barrier is independent of the nature of the polar group. This assumption contradicts with experimental data [74]. In fact, the breakdown rate of both direct and inverse emulsions depends on the two parts of the surfactant, and the dependence of the activation energies on the energies of electrostatic repulsion, dehydration of polar groups and desorption of hydrocarbon chains is more complicated, and cannot generally be expressed explicitly. Also, it is assumed in Davies' relations, which describe the phase inversion and Bankroft's rule, that Kh,1 = Kh,2. However, even if the viscosities of water and oil are equal to each other (11o= rlw) it was shown in Section 2.1.1 that the constants Kh. ~ and Kh. 2 are essentially different, because the effect of the localisation of the surfactant in either phase on the surface tangential mobility is different. Hence, the thinning velocities will also be quite different from each another. The applicability of Eq. (3.51) to ionic surfactants is also doubtful, because this equation is correct only provided the electrostatic repulsion barrier is equal to the transfer energy of a surfactant from the aqueous phase to the oil phase. This barrier, however, depends not only on the nature of the polar group. The thermodynamic aspect of Davies' concept, Eq. (3.47), relies on the comparison of the transfer energy of the surfactant molecule from the organic phase to the aqueous phase, represented by the sum of the contributions from polar and apolar parts of the surfactant, given by the empirical dependence (3.33). No principal objections could be expressed with respect to Eq. (3.47), however, the dependencies (3.47) and (3.48) should account for any possible non-additivity of the contributions of functional groups to the interaction energy and HLB numbers. Moreover, these equations should be revised to take into account the data obtained recently for the increments in transfer energies of various groups, cf. Section 1.4.

213 Also, a number of objections could be drawn from the missing correspondence between the behaviour of emulsions and HLB numbers [6, 17, 147-150]. The Davies HLB numbers system is based on the assumption that stable direct emulsions can be obtained for HLB > 7, while stable inverse emulsions exist for HLB < 7. It is assumed that for HLB = 7 neither emulsion type can be preferred with respect to the stability. However, it was shown by Rigelman and Pichon [147] that stable direct emulsions can be prepared in the whole HLB range from 2 through 17. From the data reported by Wachs and Reusche [ 17] it follows that stable inverse emulsions (water in decalin) were obtained for HLB-values between 2 and 10 (for mixtures even up to HLB = 11), and their stability increases with increasing HLB. The maximum of the stability of direct emulsions (undecane in water) was observed at HLB = 9.5. The stability of the emulsions was determined from their destruction in a centrifuge at 3000 rpm. For the emulsions prepared from the glycerine and oleic acid with various surfactants, no dependence was found between the surfactant HLB number and the type and stability of the emulsion [ 149]. It should be noted, however, that in [ 149] the emulsions were considered to be stable, if neither the disperse phase, nor the dispersion medium were released; otherwise the systems was referred to as an unstable emulsions. In the framework of the HLB numbers system only, involving no additional assumptions, the effect of the surfactant concentration on the emulsion type and stability could hardly be explained. It is known, cf. [6, 76, 151, 152], that at low concentration many surfactants stabilise direct emulsions, while at concentrations 4-6% usually either a phase inversion takes place, or stable inverse emulsion are formed at once. To explain this phenomenon, it was suggested in [34] that the HLB values should be calculated not from the composition of the initial mixture, but from the composition of the surface layer, which depends on the nature of the surfactant, the initial composition of the mixture and the water-oil phase ratio. As the HLB number themselves contain no information about the emulsion stability, it seems more reasonable to employ any other characteristics of the hydrophile-lipophile balance which is independent of the properties of an emulsion, and to compare this characteristics with the behaviour of the emulsion, i.e. the type, stability and various concentration effects. Some results obtained by this approach are discussed in Section 3.8.

214 There were some attempts to compare Griffin's HLB numbers with Davies' HLB numbers [43, 63]. These attempts are briefly commented further below. It should be noted that, prior to such comparison, one should specify the method used to calculate these numbers, because the HLBG can be determined either from experiments on the emulsion stability, or from Eqs. (3.5) and (3.6), while the HLBD numbers can be obtained either from the group numbers or from Eqs. (3.46), (3.52). In particular, such comparison of HLB numbers for oxyethylated octyl phenols, sorbitanes and oxyethylated ether of oleic acid was performed in [63], where the calculations were performed using Griffin's formula (3.6), and Davies' formula (3.52). The results are summarised in Table 3.21. Good agreement exists between HLBD and HLB6 numbers for sorbitanes, while for octyl phenols significant discrepancies are observed. It was already mentioned by Griffin [1] that two emulsifiers characterised by the same HLB numbers can possess different solubility. Table 3.21.

ComparisonbetweenHLBGand HLBDnumbers [63]

Surfactant

Cw/Co

HLBD

HLBc

Octyl phenol, nEO = 1

1.84.10.4

3.9

3.5

Octyl phenol, nEO = 3

3.13.10 .3

4.9

7.8

Octyl phenol, nEO = 6

5.42-10 -2

6.0

11.2

Octyl phenol, nEO = 10

3.85

7.5

13.6

Sorbite monooleate

3.7.10 .4

4.2

4.3 ,,

Sorbite monostearate

6.19.10 .4

4.3

4.7

Sorbite monopalmitate

0.314

6.6

6.7

Sorbite oleate polyoxyethylated

36.7 .

.

.

.

9.1 .

.

.

9.2 .

.

.

.

In other studies reported by Schott [46] the HLB numbers were compared with CMC values for oxyethylated dodecanol possessing 4, 7, 14, 23 and 30 EO groups, and for oxyethylated nonyl phenol possessing 10, 15, 20 and 30 EO groups. The HLBD numbers were calculated from group numbers, while HLB~ numbers were determined from the weight fraction of EO groups. No consistency between the HLB numbers was found for any positive values of nEO when

215 calculated in this way, for example, for oxyethylated dodecanol with

nEO =

23.0 the values

HLBG = 16.89 and HLBD = 10.79 were obtained. It was concluded by Schott [46] that for oxyethylated non-ionic surfactants Davies' and Griffin's HLB numbers are inconsistent with each other, and these scales should be regarded to as two essentially different systems, with different dependencies of the HLB numbers on the EO group numbers.

3.7. Thermodynamic approaches to the determination of hydrophile-lipophile balance It was already noticed in Section 1.4 that the Gibbs energy difference corresponding to the transfer of a surfactant molecule from water into a hydrocarbon liquid (the work of transfer) can be used as suitable and thermodynamically rigorous measure of the hydrophobicity, and this work can be represented as the sum of the contributions caused by various functional groups of the molecule, cf. Eqs. (1.90)-(1.94). This approach was employed earlier by Davies [27, 62] who compared the HLB numbers calculated from group numbers with the energy of transfer of the surfactant from an aqueous phase to an organic phase assuming that the additivity of HLB numbers follows from the additivity of the transfer energies corresponding to different parts of the surfactant molecule. In his work [62] Davies also applied another (kinetic) approach to the substantiation of HLB numbers, which involves other thermodynamic parameters: the energetic barriers for the breakdown of aqueous and non-aqueous emulsion films. These two sets of the parameters were used in the interpretation of HLB numbers system, and from their comparison Eq. (3.49) was derived which can be regarded as the basis for the Bankroft rule. It seems to be more advantageous to construct an independent definition of the hydrophilelipophile balance concept, based on the thermodynamic parameters - the energies of interaction of the surfactant as the whole (or constituent parts of the surfactant) with water and oil. This definition should subsequently be used to establish the interrelation between various properties of surfactants and emulsions. The most simple characteristic of the hydrophile-lipophile balance could be the work of the transfer of a surfactant from the vacuum (air) into water, i.e., the affinity of a surfactant with respect to water. However, as surfactants are usually non-volatile substances, this

216 characteristics is inconvenient from a practical point of view. In this regard, the work of transfer of the surfactant from the aqueous to the organic phase is a more convenient characteristics.

3. 7.1. Determination of hydrophile-lipophile balance from the distribution coefficients of the surfactant The work of transfer W of a surfactant molecule from the aqueous (a) to the organic (13) phase is related to the distribution coefficient Kx through Eq. (1.125)

W a~ = A~~

XOt = l.t~ _ ~0.~ = RT In ~ - = RT In K x.

The distribution constant was first considered as an independent measure of the hydrophilelipophile balance in [45]. In this publication, the distribution coefficients Kc between water and

iso-octane for five oxyethylated octyl phenols with nEO= 5, 7.5, 9.7, 12.3 and 20 were determined. The corresponding values of the distribution coefficients, determined from the ratio of molar concentrations, Eq. (1.126), were found to be 0.12, 0.43, 1.01, 2.14 and 23. These values agree well with more recent data given in [59-61] (cf. Section 1.3.2). In [45], no comparison between the distribution coefficients of the surfactants with any other property of the surfactant or emulsion was made. The advantage from the use of the distribution coefficient and the work of transfer of surfactant molecules from the aqueous bulk phase into the oil phase is a rigorous standardisation of the surfactant state in the bulk phases and, therefore, the calculated value of W I~ is unambiguous, as well as the additivity with respect to the variation in the number of identical fragments of the molecule ~. These advantages of the choice of the work of surfactant transfer as a HLB measure were discussed in detail by Rusanov [154, 155] with regard to the substantiation of Davies' HLB numbers scale.

i The additivity remains valid for linear hydrocarbon chains if the range of the variation of methylene groups number is not too large; for isomersthe additivityis violated.

217 Assuming the value of the transfer work to be a measure of the hydrophile-lipophile balance, one obtains HLBE = W 13~= RT In Kx.

(3.94)

With regard to this definition, the substances possessing Kx > 1 are hydrophilic, while those characterised by Kx < 1 are hydrophobic in their nature. For some classes of surfactants (aliphatic alcohols, acids, amines and non-ionic surfactants possessing oxyethylene chains) the transfer works are known (see [ 156-161 ]), however, for typical ionic micellar surfactants the determination of the distribution coefficients is rather difficult. A suitable proportionality coefficient can be introduced into Eq. (3.94) to reduce the range of HLB values to any convenient range. For example, as the values of Kc vary within the range of 10-3 to 103, one can introduce the proportionality coefficient 1.447/RT. In this case the HLBE numbers will vary from-10 to 10. This characteristics of the hydrophile-lipophile balance has also serious disadvantages. The main characteristic feature of a surfactant is the amphiphilicity, which gives rise to the concept of the hydrophile-lipophile balance. In addition, an efficient surfactant has balanced hydrophilic and lipophilic parts, each possessing a certain 'force' (the 'levers' of the balance). The transfer work is equal to the difference between the energy of the interaction of the molecule with water and that with the organic phase. Therefore, Eq. (3.94) or (1.125) does not reflect the absolute values of the balance constituents. In fact, the balance concept in its original form, the comparing of weight values, in this case becomes inadequate. For example, the work can be zero either if the works of transfer of the two parts of the surfactant molecule are equal to each other, i.e., if an exact energetic balance between the polar and apolar parts of the surfactant exists, or if the molecule does not exhibit any amphiphilicity, the hydrophilicity-lipophility concept is inapplicable, and the interaction energies of the whole molecule with water and with oil are equal to each other. Here the values of the distribution coefficients for various low-molecular substances (acetone, iodine, hydrogen chloride, mercury chloride) between water and apolar liquids can be presented. For example, in water-chloroform systems at 20~ the distribution coefficient for iodine is K = 0.895, and Davies' formula (3.52) yields HLB = 7. On the other hand, the distribution coefficient of iodine between water and

218 carbon disulphide is K = 0.00167 corresponding to HLB = 4.7, while for the distribution between water and benzene K = 11.9, which corresponds to HLB = 9. It is quite difficult to determine the reasons for the changes in the balance corresponding to the variation of the HLB value; at the same time, from a colloid-chemical point of view it is important to understand which variations of the structure and composition of the surfactant resulted in the changes of the interaction energy and the corresponding property (micellisation, emulsion stability or phase inversion). Therefore it is important to subdivide the work of transfer into the contributions from the interaction of hydrophilic and hydrophobic parts of the compound, and to compare their values corresponding to various transfer processes (adsorption, micellisation, etc.)

3. 7.2. Determination of hydrophile-lipophile balance from the work of transfer of polar and apolar parts of a surfactant molecule The studies of the solubility of various hydrocarbons in water (see Section 1.3) have shown that the saturated hydrocarbons are most hydrophobic. If the hydrocarbon compound possesses various functional groups (double bonds, benzene rings, OH-, COOH- groups, etc.), the compound becomes less hydrophobic. If the total interaction energy can be subdivided into the contributions from the interaction of various parts of the molecule with water, then it becomes possible to estimate not only the hydrophobicity of the molecule as a whole, but also the hydrophobicity of these parts of the molecule. The ions and various polar parts can form strong bonds with water, compensating (partially or fully) the distortion or destruction of the bonds which previously existed in pure water, thus exhibiting a hydrophilic behaviour. For 'inhomogeneous' molecules, the work of transfer of the molecule from the aqueous phase into a saturated hydrocarbon, calculated from the distribution coefficient, Eq. (1.125), can be considered as a convenient and rigorous measure of the hydrophobicity. One can distinguish between the hydrophilic and hydrophobic fragments of a surfactant molecule from the changes of the contributions of chemical potential of these fragments, similarly to the estimation of the entire hydrophilicity of the molecule from the work of transfer. Those parts of the molecule for which Aix~ ,~13> 0 will be considered hydrophilic, while those with A~tC~H2< 0 should be regarded as hydrophobic fragments. Amphiphilic

219 molecules are those comprising the parts with A~t~ ~13> 0 and Ala~ ~1~< 0. For these molecules the concept of the hydrophile-lipophile balance is useful. Clearly, the most general form of the expression for the hydrophile-lipophile balance is the ratio (see [137]) HLR = Alix~ - W~~ AlxT~-------~ - W' ,

(3.95)

where A~t~ is the change of the standard part of the chemical potential, the subscripts p and 1 refer to the polar and lipophilic parts, respectively. The superscripts oc and 13refer to water and oil, respectively, and their sequence correspond to the transfer direction; Wp and Wi are the works of transfer of the polar part from oil to water, and of apolar part from water to oil, respectively. Noting that W ~ = W~~ - W~~ = RTInK x, one obtains another equivalent definition of the HLR

HLR=I+

RT In K x W~ .

(3.96)

For this definition, the range of the variation of HLR is 0 to oo: for lipophilic surfactants this range is 0 to 1, while for hydrophilic surfactants the range is 1 to oo. To determine the HLR values from Eqs. (3.95) and (3.96), one should know either the two works of transfer W~~ and W~*, which are indicative of the 'forces' of the balance constituents, or one work of transfer ( W~~a) and the distribution constant for the whole compound. As there are no direct methods for the calculation of the transfer work for separate parts of the molecule, it was proposed in [137] to estimate these values using the dependence of ln(Kx) on the number of repeating fragments (CH2, CF2, CH2CH20 etc.) and the work of adsorption of surfactants from aqueous and organic phases at the interface between them [74, 161, 162]. In homologous series of surfactants with the same polar group, the change of the hydrocarbon chain length almost does not affect the work of transfer of the polar group (the hydrophilicity characteristics). Large variation in the chain length can lead not only to the increase of the hydrophobicity, but also to the change in hydrophilicity. With respect to the hydrophobicity of

220 apolar chain, similar effects are also observed for non-ionic surfactants homologous series with variable number of polar groups of similar nature (for example, in the series of oxyethylated derivatives of alcohols, acids, amines and alkyl phenols). If the dependence of ln(Kx) on the number n of the repeating links CH 2 or CF 2 is linear, then the transfer energy for these groups can be determined from the slope of this dependence. It was

mentioned

in

Section 1.4

that

for

the

methylene

group

we

have

AI.tc~2 = 3.31- 3.46 kJ/mol, according to the data reported in various publications [157, 159161, 164-166]. In the further calculations below, the average value of A~tc~2= 3.38 kJ/mol will be used. The extrapolated value RT In (Kx) = A for nc = 0 involves the contribution of the polar group to the transfer energy, and the contribution of the hydrogen atom of the terminal methyl group (or fluorine atom, if the terminal group is CF3), with the sign opposite to the transfer work of the polar group. In addition, the interaction of few CH 2 links closest to the polar group, in particular that of the link adjacent to the polar group, with the surrounding solvent, is different from the interaction of other CH 2 links, due to the effect caused by structured water, which hydrates the polar part of the molecule. It seems quite difficult to indicate the exact values of the contributions introduced by either of these molecular parts. For the contribution of terminal methyl group in saturated hydrocarbons to the transfer energy, the value of A~tc~3=8.78 kJ/mol was reported by Tanford [157]. Assuming that Al.tc~3= 8.78 kJ/mol, and accepting for the methylene group the energy value of A~tc~2 = 3.70 kJ/mol for the transfer of hydrocarbons from water to hydrocarbon [157], one obtains W~~= 8.78 kJ/mol- 3.70 kJ/mol = 5.08 kJ/mol. It follows from the data reported by Abramson [156] that the transfer energy is additive with respect to the number of C-H bonds, and for the water and saturated hydrocarbon as bulk phases, the value is

A~t~ = 1.67kJ/mol, which corresponds to

A~tc~2=3.34kJ/mol ,

Alac~3= 5.01 kJ/mol, and hence, Al.t~~= 1.67 kJ/mol. This value is three times lower than the

221 value estimated from the data reported by Tanford. Another value for the work of transfer of the terminal hydrogen atom, calculated from Tanford's data, was presented in Rusanov's monograph [ 155] WHp= 3.45 kJ/mol. In these calculations, however, the formula W "p = RTIn(C~/C a) was used, with the standard states of the solvents normalised with respect to the molar concentrations (C'~= 1 and C p = 1), while the calculated value of W~~ is introduced into the relation (1.93) defined by Tanford [157] W~P/RT = a - b n c , with values for a and b determined in terms of molar fractions. Assuming now that one methylene link (adjacent to the polar group) does not contribute to the hydrophobicity, the contribution from the polar group is W~~ = A+ W~ta - Wc~, while the contribution of the hydrocarbon chain amounts to Wi~p = Wc~' (n c -1) + Wr~13. The hydrophile-lipophile balance calculated from Eq. (3.95) is

AI+ g + W~p - Wc~2

A

A

6

(3.97)

HLRE = Wc~'(nc - 1 ) + W ~ = Wc~n c ( W ~c ~O , 'ncWc~ -nW - -c- ~- -' -) - - ~ l-+

where the correction -

1+ 5=

A Wrap _ Wc~2 1+ ncWc~ 2

slightly increases with the increase of nc.

(3.98)

222 Another way of calculation can be proposed, where it is assumed that all methylene links are equal with respect to their hydrophobicity, while the decrease of hydrophobicity for the CH 2 links adjacent to the polar group refers to the transfer energy of the polar group itself. For fatty alcohols, according to the data presented by Aveyard and Mitchell [159] l A = 12.7 kJ/mol, for amines [156] A = 12.96 kJ/mol, while for acids [158] 2 A = 17.8 kJ/mol. Then the correction values for nc = 5 are 8ROH = 1.03, 8m~n2= 1.03, 8RCOOH = 1.00, while for nc = 10 we have 8ROH = 1.08, 8m~H2= 1.08, 8RCOOH= 1.04. If the value W~a= 1.67 is assumed, then the correction values for nc = 10 are 8 = 0.92 - 0.95 for fatty acids, alcohols and amines. Evidently, one should prefer the calculation procedure which ensures the best correspondence between the experimental values of RT ln(Kx) and the difference Wp~ - W~~ . As some uncertainty exists in the calculation of the W ~ values, and the experimental data concerning the distribution of alcohols and acids are quite ambiguous, it will be assumed in the calculations of HLRE below that 8 = 1. Then Eq. (3.95) yields for alcohols: HLRE = 12.7/(3.38 nc)= 3.76/nc

(3.99)

for amines [5 ]: HLRE = 12.96/(3.38 nc)= 3.83/nc

(3.100)

and for acids [83]: HLRE = 17.8/(3.38 nc)= 5.26/nc

(3.101)

assuming the balance (HLR = 1) for 4 carbon atoms for amines and alcohols, and 5 carbon atoms for acids. If the values of Kx are calculated from the molar fractions [ 156, 159], then the

t According to the data reported by Kinoshita [ 157], the value of A is about four times smaller (A = 2.06 kJ/mol). 2

For acids exact

data

concerning the distribution coefficients

were

presented by Aveyard and Mitchell [160]

as

K = Ca/(C[~)1/2, where the dissociation constant of dimers into monomers is involved (this constant was not determined).

223 experiments on the distribution lead also to the values Kx = 1 for nc ~ 4 for butyl alcohol and butyl amine. Similar approaches can be used to determine the HLR of non-ionic surfactants like the oxyethylene derivatives. For example, for oxyethylated octyl phenol OP(EO)n, W~t =

13a W~EnoE + W_~o_, and the value of RT In (Kc) for nEO = 0 is equal to A = 23.1 kJ/mol

[137], which corresponds to the transfer of the octyl phenol radical with one ether oxygen. Assuming that Wo~ = 19.87 kJ/mol I (if the standard states are normalised with respect to molar concentrations), and W_~o_=(1.3/1.9)Wo~ = 13.59 kJ/mol, where 1.3 and 1.9 are the Davies group numbers for the ether and hydroxyl groups [27], one obtains W~P= (23.1 + 13.59) kJ/mol = 36.69 kJ/mol. Hence

HLR~. =

W-~~ + W~ "nEO 13"59+2"51"nEO = 0.37 + 0.068nEo. W.~ = 23.1 + 13.59

(3.102)

For example, for OP(EO)10 the calculation from Eq. (3.102) yields HLRE= 1.05, while for OP(EO)9 the calculated value is HLR E = 0.982. The balance condition HLR E = 1 corresponds to the interval between nEO = 9 and nEO = 10, which agrees well with the data presented in [59]. It is seen from Eqs. (3.99)to(3.101) that the balance condition W ~ = W~~ applies when W ~ = 3.38 nc. Thus, the ratio W~/Wc~

= n 0c , which is equal to the number of carbon atoms

in the surfactant hydrocarbon chain for which the balance condition HLR = 1 is held, can be used as the hydrophilicity constant (p) of the homologous series. This characteristic of the homologous series was initially proposed by Sviridov et al. [i51, 167]. In these publications this constant was determined, however, from the energetic parameters of the transfer from aqueous micelles into the hydrocarbon ones. For oxyethylated alkyl phenols one obtains from Eq. (3.102)

z In the publication [ 137] another value for the hydroxyl group transfer energy was used, determined from the data concerning the adsorption work.

224 p = 4.02 + 0.743 nEO.

(3.103)

For example, for nEO = 10 we get p = 11.45. For ionic micellar surfactants, the hydrophilicity constant, determined from the micelle formation energies [ 157, 161 ] is in the range p = 10 - 20.

3.7. 3. Hydrophile-oleophile ratio determined from the adsorption works According to Eq. (3.95), to determine the HLR value, the transfer energy data of the hydrophilic and hydrophobic parts of a surfactant from the aqueous phase into the saturated (or other) hydrocarbon can be used. These transfer energies are very close to the adsorption works, used by Kruglyakov et al. [162, 163, 168-172] to determine the HLR values. In water-oilsurfactant system, the surfactant is distributed between the bulk phases and the interface. The adsorption of the surfactant takes place from both phases, while the surface activity for the adsorption from water is usually rather different from that for the adsorption from the oil phase. The difference between the Gibbs energy per mole of the surfactant in the bulk and that at the interface, in the standard state (for X aC~)= 1, or C aC~)= 1 and X s or C s - l) is determined by the corresponding differential work of adsorption

A~~ = gO,~_ ~o.,~ = RT In aS

(3.104)

Ag o.~ = la~ _ g0~ = RT In ~

(3.105)

where go, ~, go, t3 and g0, s are standard chemical potentials of the surfactant in the water bulk (~), oil bulk (13) and in the adsorption layer (s), as, a ~ and a s are the corresponding activities. The difference of adsorption works A~.~

A~.~

is related to the distribution coefficient via

the expression a tl . a S

Ag~

_ Ag~

= RT In a

s . a 13

= RT In K,

(3.106)

where Ka = aa/a 13 is the distribution constant expressed in terms of activities. The absolute values of the works of adsorption depend on the surfactant type, the nature of the organic phase and the method used to calculate the work of adsorption.

225 The work of adsorption of surfactant from an organic phase at the interface with water is close to the difference between the interaction energies of the polar group with the organic bulk phase and the aqueous phase adjacent to the interface. On the contrary, the work of adsorption from the aqueous phase at the interface with an organic phase corresponds to the difference between the interaction energies of the apolar chain with the aqueous bulk phase and the organic phase near the interface. If the influence of the inhomogeneity of the phases in the vicinity of the interface is neglected, and the HLC of the molecule in the adsorption layer is assumed to correspond exactly to the interface, then the work of the surfactant adsorption from water should be equal to the difference between the energies of interaction of the hydrocarbon radical with bulk phases, and determines the hydrophobicity of the surfactant. Analogously, the work of adsorption from the organic medium should be equal to the difference between the energies of interaction of the polar group (or groups) of the molecule with the bulk phases, and determines the hydrophilicity of the surfactant. The ratio of these values is indicative of the hydrophile-lipophile balance of the surfactant. This balance expressed via the adsorption energies was called in [ 162, 163] the hydrophile-oleophile ratio (HOR)"

H O R

=

A~t~,~-----T -- r.~------w F 9

(3.107)

Taking into account the relation between the work of adsorption and the distribution coefficient, Eq. (3.106), one can also express the HOR value via one of the works of adsorption and the distribution coefficient. Using suitable expression for the work of adsorption (see Section 1.2.4), one can express the HOR value via the surface activities of a surfactant and the distribution coefficient, or via the surface activities, adsorption layer thickness and distribution coefficient. For example, using Pethica's method, Eq. (1.49), one obtains

HOR -

RT In cx~ In K ~ ~ = 1+ ~ , RT In cx,, In ~x~

(3.108)

while using the method proposed in [174, 175], cf. Eq. (1.50), one can express the HOR as

226 RT ln((z~/RT6) lnK~ s HOR = RTln(c~=/RT6) = 1 + ln((z~/RTS)

(3.109)

where 5 is the adsorption layer thickness. For individual components, the hydrophile-oleofile ratio does not depend on the concentration, because the chemical potential in the standard state is defined quite unambiguously, 'automatically' accounts for the effect of the nature of the organic phase and the temperature, the presence of various additions soluble in water and oil, and depends, although slightly, on the method used for the definition of the work of adsorption (on the definition of the standard state in the surfactant adsorption layer). To determine the HOR-value for surface active electrolytes, one should apply the expressions for the adsorption work, Eqs. (1.68), (1.71), (1.74) or (1.75), with c~ expressed by Eqs. (1.76)(1.78), which depend on the concentration of the inactive electrolyte and the surfaetant degree of dissociation in the surface layer. Table 3.22 and Fig. 3.17 sumrnarise the results obtained for I~.,, Wr and W~r, the HOR values calculated for individual surfaetants and homologues of non-ionic surfaetants with a Poisson distribution of EO groups, in the water-iso-oetane system [173], and for chromatographically separated narrow fractions of the nonyl phenols ethers [60] in the waterheptane and water-benzene systems. To calculate the work of adsorption for oxyethylated p-tert-octyl phenols, the surface activity (z = da/dC was used for the lowest concentration 10-s mol/l (as indicated in [173]), while for nonyl phenol ethers the values of the surface activity listed in [60] were extrapolated to zero concentration. The calculations were performed according to the Ward-Tordai method [174, 175], where the adsorption layer thickness for all oxyethylated non-ionic surfaetants was taken to be 2 nm. In Table 3.23 we summarise the values of surface activity, distribution coefficient and adsorption work for some surfactants which belong to different classes, which have been determined experimemally by Kruglyakov et al. [74, 170, 171, 177]. Figure 3.18 illustrates the comparison between the HOR values and HLB numbers, either calculated from Eq. (3.6) or reported in [6, 9, 21 ]. It is seen from the Fig. 3.18 that the dependencies of HOR on HLB for the water-heptane (iso-oetane) and water-benzene systems are represented by two curves, which are almost straight for HOR < 1.25 (or HLB < 15).

227 Table 3.22.

Work of adsorption and distribution coefficients in water-isooctane(heptane) and water-benzene systems Calculated values of adsorption work W r, kJ/mol

number of EO groups in OP (EO)

According to [ 174] Water-isooctane Single species 2

7.17.10 -4 3.13.10 "3

26.98 30.12 30.75 31.37 33.05 ,33.54 34.30 35.6 37.67

3 4 9.83.10 -2 5 2.42.10 -2 6 5.92-10 -2 7 ,1.82.10 l 8 5.04.10 l 9 1.42 10 3.85 Normal distribution of EO in OP 2 4.14.10 .3 r 28.36 2.98 1.43.10 -2 !30.27 . . . . . . . 4.07 4.75.10 .2 32.84 5.01 1.29.10 "l 33.05 6.03 2.54.10 l 33.46 7.05 4.49.10 "l 34.3 8.03 8.22.10 "l 34.70 9.06 1.55 35.76 10 1.89 36.39 ' Water-heptane "" ', Narrow fractions of nonylphenols ,OP-5 1.6.10 .2 33.46 ,OP- 10 1.0 ~,48.10 i OP-15 40.0 56.97 Oleic acid 22.8 "Cetyl alcohol ....... Water-benzene 3.16 10.4 22.58 OP-5 3.16 10.3 32.63 OP-10 1.60 10.2 i' 38.06 OP-15 OP-20 1.60 i0 "l [43.84 |

. . . . . .

,

.....

-

I

l

....

.

,42.16

,29:58

42.12 41.87 41.20 40.24 ,37.81 36.06 34.72 34.30

,

,

32.69 33.31 33.93 35.59 36.08 36.83 38.11 40.18

47.79 47.17 44.89 43.24 42.70 i 40.30 38.57 37.24 36.83

42.67 41.12 40.58 38.27 !37.02 36.35 35.22 34.63 34.76

' 30.95 '32.90 35.38 35.59 36.00 36.83 37.24 38.28 38.90

' 45.02 43.58 43.04 40.76 39.52 38.90 37.74 37.16 37.24

i

i

!

,

i

i

)

'-

43.92 48.10 48.52 56.05 56.05

!

! According to [ 176]

.... |

,

|

,

|

-

_

,36.00 , 50.48 59.25

,46.77 , 50.48 50.90

'25.24 35.17 40.55

'45.52 49.66 i50.90

146.26

i 50.90

I

i

!

I

I

!

I

i

43.08 47.27 48.52 48.52

I

I

228

2O

I

15go /o75 ;0~ 7 8 70"~~ SO

2

/,

-

.ss g

I0 z~

8

Fig. 3.17. Relation between HLB and HOR for non-ionic surfactants. Indicated are the numbers of OE groups: A, single species; 0, polymer homologues with normal distribution of OE groups; O, narrow fractions of nonyl phenols; o, cetyl alcohol; +, oleic acid; for oleic acid and cetyl alcohol, the HOR values were calculated from the known values of the work of adsorption W~r, and the work

_

N

/ o/. 0

02 0.~ 0.6 0.8 !O 12

HOg

Table 3.23.

Substance

adsorption of the methyl link [62, 156, 157, 160, 161,174].

Distributioncoefficients and work of adsorption (at 200C) M

.... -

K~ "

Heptane ' work of adsorption, kJ/mol

] ] [ [

w:Iw:

Xylane-O Sorbitane-L* Emulfor FM Triton-X-100

398

0.3

624

Alphap0i-4 382 Aiphapol,-8,-, ,, 558 Alphapol-12 " 734 NaDBS + 0.1 M Na 348 C1 ,,

. . . .

* Measurements were performed at 50~

.10 .2 .8 .0

"

K~

I

"Benzene work of Adsorption, kJ/mol

w:

w:

51.79 41.38 49.65 34.31

135.00 12.7.10 .5 51.820 /34.551 133.311 134.31 I 1.27.10" 47.23

26.25

35.17 38.60 41'80

142.58 13.1.10-3 139.15 11.4.10-2

271-51 33.61 36.33 55.46

I38.J8.. ,

11.5.10-2 5.103

41.79 44.17 52.41 34.40

36.-43

229

20

15~~ I5//o

1oo/o12 12o/ %~l~ ~,o 5o

oO

cf)6a,A 7

Fig. 3.18. and

HOR

Relation between HLB for

various

surfactants:

r-l, narrow fractions of oxyethylated nonyl phenols; A, individual oxyethylated octyl phenols, i , octyl phenols with normal distribution of OE groups; o, Alphapols and Triton-X-100; K, Xylan-o; D, sodium

0

,,,.,,',,:,, 05

I,..,,., zO

J, =/-/0R

dodecyl benzene sulphate; +, oleic acid.

L5

For larger HLB numbers the dependence becomes non-linear. This can possibly be ascribed to the fact that Griffin's asymptotic formulae are inapplicable at nEO > 15-20. In fact, the dependence plotted in the co-ordinates H/O vs HOR (where H and O are the mass fractions of the hydrophilic and oleophilic parts of the surfactant, respectively, see Section 3.6) looks much more straight, cf. Fig. 3.19. The point representing the HLB number for NaDBS does not comply with the general trend. The HLB number for this substance estimated from the extrapolation of the linear dependence is 25 for water-benzene, and 22 for water-heptane systems. It can be thus concluded that the estimation of HLB numbers for different classes of substances, based on the emulsifying ability, is quite ambiguous: two substances possessing the same hydrophilicity can be characterised by different HLB numbers, and that Griffin's HLB numbers are suitable for the comparison of the substances which belong to the same class, i.e., oxyethylated acids or alcohols. The main problem with the determination of HOR values for hydrophilic surfactants (in particular, micellar ionic surfactants) is that many of these substances are insoluble in unsaturated hydrocarbons, it is therefore impossible to determine the distribution constants and surface activity relative to the adsorption from the organic phase.

230

lOoA/0f A

o

i//?,

Fig. 3.19. Relation between H/O and HOR; indicated are the numbers of OE groups: polymer homologues with normal distribution of OE groups; o, narrow fractions of ~

'

--- t t O R

oxyethylated nonyl phenols; A, individual oxyethylated octyl phenols.

3. 7. 4. Hydrophilic-oleophilic ratio for the mixture of surfactants Surface active substances used as emulsifiers, foaming agents, detergents etc. are typically mixtures which, in addition to the surfactants, can contain electrolytes and various lowmolecular additions (alcohols, amines, etc.). In the HLB numbers system it is assumed that for surfactant mixtures the HLB numbers are additive with respect to the HLB numbers of the individual substances, with their weight or molar fractions as proportionality coefficients [1, 16]. In some recent publications [34, 178] it was proposed to calculate the HLB numbers for mixtures from their composition in the adsorption layers at the water-oil interface, in micelles or micellar phases, which, in addition to the surfactant mixture, contain oil and water. It follows from the energetic interpretation of Davies' HLB numbers that the group numbers, which are added to calculate the HLB numbers, are the partial works of transfer of the certain molecular groups, taken with some adjusting coefficients. In the framework of this concept it is evident that the works of transfer of the polar and apolar parts of the surfactants in a mixture should be regarded as the weighted averages with respect to the number of moles and the values of the energy of transfer of the polar and apolar fragments of the surfactants.

231 The method which can be used to calculate the average of the works of transfer from water to oil, the adsorption works and, therefore, the HLR or HOR values, is by no means unique. In addition to the averaging of the HOR with respect to the molar fractions (X), as discussed above

HOR = H O R ~ X l + H O R 2 X 2 + . . . = ~ H O R i X i ,

(3.1 lO)

i=!

one can determine the chemical potential using the relationships [ 155, 179] (3.111)

lamix --- Z~tiCi/Cmi~. i

where (3.112)

C m i x -- E C i , i

or can perform the averaging of the works of transfer with respect to the molar fractions W ~ = '~7'Wi~Xi .

(3.113)

i

Also, to determine the HOR value from the work of adsorption, one can use the method based on the calculation of mean surface activity of the surfactants mixture [170] and the mean (conventional) value of the distribution coefficient for the mixture

Ex;

--g

x,

(3.114) i

This conventional distribution coefficient is widely used for mixtures of non-ionic surfactants characterised by a normal distribution of oxyethylene groups [59, 60, 180]. In solutions of surfactants mixture at low concentrations (Henry region for adsorption) the decrease of the interfacial tension is an additive function of the decreases of the interfacial tension AO i caused by each component

232 n

- A6z = -

Aeri= )-"~otiCi, i=!

(3.115)

i=l

where Aoz is the decrease in the interface tension for total mixture concentration Cmix = s C~, i=l

cx, = (-dc/dC, )c-~0 is the surface activity of the ith component. Introducing the mean surface activity of the surfactant mixture,

~=

/Acrz ~

(3.116)

and the mean distribution coefficient K ~

C~x

~ (C~/K~ I~) = ~-~"

(3.117)

i

where K~~ is the actual (thermodynamic) distribution coefficient for the ith component, one obtains the expression for the HOR of the mixture in the following form RT In ~" In Ka" HOR = RT ln------~= 1 + In ~a

(3.118)

Here, similarly to Section 3.7.3, the superscripts cx and [3 refer to aqueous and organic phase, respectively. In practical applications (studies of phase inversion in emulsions, preparation of micellar phases, etc.) high surfactant concentrations are often used. It is therefore expedient to derive relations which express the HOR of the mixture via the composition of the mixture in the region where the concentrations cannot be used instead of activities without taking into account the respective activity coefficients. Let us consider a system which consists of mutually non-mixable aqueous and organic phases, two surfactants possessing the activities al and a2, and assume that K~"< K~~, where K~" = a~/a~. The values of K and ~

in Eqs. (3.116) and (3.117) can be expressed via the

activities of the components and the surface activities in one of the phases, e.g., in the organic phase

233 K, K 2 I+~a~ +a t _ K2a ~ +K,a~ _ + (" a~'~-

~a=

a~ a~

a~,l+a-~2)

~ a i(3~i ~ ,~

(31;2 + - -

i

Eat i

a~]

(

(3.119)

l+a~

ot

(glal K2a~ K 1 a~ ' +___

(3.120)

K 2 a~

where the known relation

%ai

(3.121)

was used [181 ]. Introducing the expressions for K and ~

into Eq. (3.118), one obtains

a2)K2

HOR = 1 -

a~ a~"

(3.122)

(I, 2 + - - . ~

lg

K 2 a~ K i a~ 1+ . . . . K 2 a~

In some cases it is more convenient to calculate HOR via the total concentrations or activities of the components in the two phases. A number of important expressions for some particular cases follows from Eq. (3.122). For example, for very low concentrations of non-ionic surfactant (C ~t CMC), it can be assumed that the activity coefficients fulfils the relation 7~ = Y~ = ~'~ = ?~ = 1. In this case, concentrations can be used instead of the activities, and Eq. (3.122) transforms into

234

(

1+ Cln] 1

HOR=I-

(tx"+ ct~ Cin]"

(3.123)

If, in addition, the first component is insoluble in the aqueous phase, then we get

HOR=I-lg

lg

l+-cg2

+

)

For the case when the first component is soluble only in the organic medium, and the second one is soluble in the aqueous medium, one obtains from Eq. (3.123)

HOR - 1-

- 1lg a~+o~Ci- )

lg a~ +O~C-~-)

If in one of the phases the micellisation takes place with the formation of mixed micelles, and in the other phase the concentrations are small, then it can be assumed in many cases that in the micellar phase the activity coefficients of the two components are equal to each other (ideal micelles), and in the other phase these activity coefficients are equal to unity. For example, if the micellisation takes place in the organic phase, then mixed micelles are formed, and the following approximation are valid: ~,~ =~,~ (see [182]), and ~,~ =y~ =1. For this case Eq. (3.122) yields a relation similar to Eq. (1.123). If, in addition, K l ~ 1, then one obtains Eq. (3.124) again. Replacing C~ by C~, one obtains

235 lg

HOR = 1 -

+ y~( ,~ a aC~ C~)" lg a 2 + a~ 72 Cz

(3.126)

In a similar way one can derive the formulae for systems where mixed ideal micelles are formed in the aqueous phase, where y~ = Y2 and Y"2= 7~ = 1" ]

1 C~

K2

Yza "C--~-2 __

~ d -

1 +--~-Y2 C2

lg HOR = 1 -

.

(3.127)

.... v_~~~ 1+ K1. Y2 C2

lg

If one of the components is an ionic surfactant, and the excess of the electrolyte with the like charged ion, and the micelle are formed in the oil (y~ = y~, and a 2a =

2

y•

a

2C s

), one obtains

from Eq. (3.122)

1

y~

C~

K, Csy~ C~ lg nOR=l-

[ /

L

l+CsY~ "C~ a ~',a C~ a --

Ill

"

(3.128)

.

C sY_* 2 C2a

Fig. 3.20 illustrates the dependencies of the HOR values of the mixture of surfactants on the composition of the mixture, calculated using different averaging methods. It should be noted that in the limiting case al = 0 (or Cl = 0), or a2 = 0 (or C2 = 0), Eqs. (3.122) to (3.128) can be reduced to simple expressions [162, 163] similar to Eq. (3.108)

236

HOR = 1 +

lgK~ p

where the subscript i refers to the remained surface active component.

i.o

o.9

Fig. 3.20. Dependence of HLR for the

~ o.o

mixture of surfactants on the mixture composition: 1, averaging of adsorption work with respect to molar fractions, Eq. (3.113); 2, averaging of HLR with respect to molar fractions, Eq.(3.110);

0

ae

4

0.6

o.8

1.o molar [faction o[ xfian,

3, averaging with respect to surface activities, Eq. (3.123).

Finally we present an example of the calculation of the HOR value for the mixture of the nonionic surfactants Xylan-o (1) and Triton X-100 (2), with the molar ratio 1:1 in the waterheptane system (1:1 by volume), cf. [ 170]: Xylan-o

Triton X- 100

KI ~ 10-3

K 2 = 1.00

ct~ = 1.8.106

ct 2 = 1.06.106

HOR = 0.676

HOR = 1.00

C_______~l C~ + ~ = 0.999 + 0.001 = 1 +

0.5 + 0.5

The calculations can be performed according to Eq. (3.123), HOR--0.926. This example illustrates the fact that the HOR value for the mixture of two components is non-additive with respect to the HOR values of the pure components. The HOR value for the mixture is much closer to that of the surface active component with the larger distribution coefficient.

237 It seems that the best method of averaging the HOR should be chosen from practical considerations. However, as in the majority of surface phenomena (formation of mixed micelles, preparation of micellar phases and microemulsions, and phase inversion in emulsions) the governing properties are the composition of the surface layers and their surface activity, in our calculations of the HOR the averaging method based on mean surface activities will me mainly used below. 3. 7. 5. Hydrophile-oleophile ratio determined from the micellisation energy Similarly to the definition of the HOR via the work of adsorption, Sviridov et al. [88, 151] proposed a definition of the HOR based on the micelle formation energy of surfactants in aqueous and apolar phases HOR M . W~ . . RTlnCPm . . Wr~ RTInC~

(3 129)

It was assumed in [88] that when the micellisation takes place in aqueous media, the work of micelle formation is determined mainly by the hydrophobic interaction of the surfactant radical with water, and is equal to the energy of the transfer of the hydrocarbon chain from the aqueous phase to the micellar 'phase' (the hydrocarbon core). The more hydrophobic the compound, the higher is the work of micellisation. On the contrary, in apolar media the work of micellisation is determined mainly by the energy of transfer of the polar parts of the surfactant from the organic medium into the micellar core, whose properties are similar to those of the polar medium (water). The more hydrophilic the compound is, the higher is its work of micellisation in the hydrocarbon medium. Critical micellisation concentrations were determined in [88] by light scattering in aqueous solutions and in benzene, while the solutions have not been contacted with each other. The CMC values determined for the homologues of quaternary pyridinium bases, primary and secondary aliphatic amines, and carbonic acid salts are shown in Fig. 3.21. The work of micellisation for these homologues in both solvents was additive with respect to the number of methylene groups WM = W~ + Wc. 2 .ncH2 ,

(3.130)

238 W~ = W~ + Wc~.2 .nc, ~,

(3.131)

where W,CH2 ~ and Wc~H2 are the contributions of the methylene group to the work of micellisation in water (a) and oil (13), and W~ and W~ are the contributions of the polar groups to the work of micelle formation in the corresponding solvents (negative in water, and positive in benzene). The values of some contributions and the calculated values of HOR M for some surfactants are summarised in Table 3.24.

w_

k

//c/G f

f

j

J

~"

j

^

J

2'

W

O

~

~

f

..Q_ ...-O

""4

J f

f

J

"xa J--.

-12 . . l J

1

Fig. 3.21. Dependence of the CMC on the number of methylene groups: 1, salts of quaternary pyridinium bases; 2, salts of secondary aliphatic amines; 3, salts of primary aliphatic amines; 4, salts of saturated carbon acids (solid lines - in aqueous medium; dashed lines - in benzene phase.)

In addition to Eq. (3.129), the group characteristics of the hydrophilicity of the homologous series, defined as the number of methylene groups in the series for which HORM = 1, was introduced by Sviridov et al. [88, 151]. The expression for this value can be obtained by equating the right hand sides of Eqs. (3.130) and (3.131), see also Section 3.7.2,

nc.2(,oRM., ) = P = Wc~2 + WcP' 9

(3.132)

For some surfactants the values of the hydrophilicity constant are listed in Table 3.25. It was shown in [88] that for ionic surfactants the effect of the polar group on the p-value is related to the acid/base properties of the surfactant: a linear decrease of p is observed with the

239 increase of the pKH-value, where KH is the ionisation constant. On the other hand, p decreases with the increase in polarity of the solvent, temperature and Hildebrand's solubility parameter, while the increase of the interfacial tension leads to a decrease of p. Table 3.24a.

Contributionsinto free energy of micellisation and HOR values for some surfactants

Surfactant

number of

Temperature,

C~,

OH groups

~

mol/kg

8

25

[ C~, /

Octyl ammonium chloride

! mol/kg

1.8.10 "t

1.0.10 .2

|

i

i

Decyl ammonium chloride

10

25

4.0.10 .2

1.7.10 "2

Dodecyl ammonium chloride

12

25

1.5.10 "2

2.8.10 "2

Dihexyl ammonium chloride

12

25

1.6.10 .2

9.7.10 2

,

Dioctyl ammonium chloride

16

25

9.0.10-4

2.8.10 .2

Dinonyl ammonium chloride

18

25

I 3.1.10-4

3.4.10 -4

Undecyl pyridinium chloride

11

25

3.9.10 .2

1.1.10 -4

40

4.1.10 .2

6.9.10-4

55

4.3.10 .2

3.4.10 -3

25

7.8.10 -3

2.0.10 -3

40

9.0.10 .3

11.5.10 .3

55

1.1.10 .2

8.7.10 .3

F25

6.5.10-4

4.3-10-4

Tridecyl pyridinium chloride

13

i

!

i

Cetylpyridinium chloride

16

8.5.10 -4

40 i

1.1.10 .3

55 I

Sodium caprynate

9 I

Sodium laurate

25 I,,,

11 I

Sodium miristate

!

!

13

....

" 25

3.9.10

.2

!

1.8.10 "3 I

25 |

4.7.10 -3 i

,,,

1.4.10 .4 i,,,

4.3.10-4 J

2.3.10-4 i

8.3.10 .5

3.6.10 .4 j

240 Table 3.24b.

Contributions into free energy of micellisation and HOR values for some surfactants

Surfactant

,

,

w; ,

,

Wc

,

H2~

2 ~

HOR

kJ/mol

kJ/mol

kJ/mol

kJ/mol

Octyl ammonium chloride

10.04

16.86

1.7i ....

0.67

3.2

Decyl ammonium chloride

10.04

16.86

1.71

0.67

1.5

4.3.10 q

Dodecyl ammonium chloride

10.04

16.86

1.71

0.67

1.9

1.9

Dihexyl ammonium chloride

10.46

i9.62

1.74

0.67

1.1

6.1-10"

Dioctyl ammonium Chloride

10146

i9.62

1.74

0.67

" 0.5

3.1.101

Dinonyl ammonium chloride

10.46

! 19.62

1.74

0.67

0.4

1.1.10 .2

i 29.92

2.03

0.66

2.8

2.8.104

15.06

29.92

2.01

0.99

2.3

1.7.10 "2

15.90

29.92

2.00

1.32

1.8

7.9.10 .2 2.6.10 -2

5.7.i0 -~

"

I

Undecyi pyridinium chloride

14.23

I

r

Tridecyl pyridinium chloride

, Cetyl pyridinium chloride

Sodium caprylate -sodium laurate Sodium'miristate

14.2'3

29.92

2.03

0.66

1.8

15.06

29.92

' 2.01

0.99

1.4

15.90

29.92 '

2.00

1.32

1.1

i 7.9.10 q

14.23

29.92

2.03

0.66

1.1

6.6.10 q

15.06

29.92

2.01

0.99

0.8

5.5

15.90

29.92

2.00

1.32

0.5

315.10'

3.47

' 27.99

2.06

!0.66

1.4

7.8.10:2

3.47

27.99

2.06

0.66

1.1

5.3.10 -I

3.4"/

27.99

2.0'6

0.66

0.9

4.3

I

1.7.10 q I

I

241 For sodium alkyl carbonates, a decrease of the HOR value from 1.43 to 0.54 was observed when the methylene group number was increased from 9 to 17, while for sodium alkyl sulphates a decrease was from 3.8 to 1 with the increase of the methylene group number from 10 to 20, see [151]. For sodium oleate the HORM=0.63, while for sodium acetate HORM = 1.25 [151]. Table 3.25.

Hydrophilicitycoefficients for surfactants with various chemical composition

General formula for the

Temperature,

surfactant homologous

~

Organic solvent

p

25

benzene

16.4

40

benzene

14.8

55

benzene

13.2

25

carbon tetrachloride

19.0

25

n-hexane

20.5

CnH2n+INCsHsBr

25

benzene

14.8

CnH2n+INCsHsJ

25

benzene

13.0

(CnH2.+I)2NH.HCI

25

i benzene

12.5

CnH2n+INH2"HC1

25

benzene

:11.3 i

CnH2n+ICOONa

25

benzene

CnH2n+IOSO3Na

25

benzene

20.0

CnH2,+IOCS2Na

25

benzene

10.5

series CnH2n+INC6HsC1

i

Assuming, according to [182], that known relation [ 181 ] r

~ = a~C ~,

Cm~

Ill.0 I

1/a (where ot is the surface activity), and using the

242 the distribution constant Kc can be expressed via the CMC COt

Kc -

Ot

Cm

(3 133)

or

Wr~ - W~ = RT In C~m- RT In C~ = RT In K c .

(3.134)

It should be noted that the energy of transfer of one methylene link from aqueous micelles into a non-aqueous (benzene) micelle, calculated from Eq. (3.134), was 2.38 - 2.72 kJ/mol, that is, by ca. 25% lower than that corresponding to the transfer from water into saturated hydrocarbon [161] or benzene [183]. Using Eqs. (3.129) and (3.134), one can derive an expression for the HOR similar to Eq. (3.108) RT In K c HOR M = 1 + ~ .

(3.135)

However, it is possible to replace the concentrations Ca and CI~ in the expression for the equilibrium constant, Eq. (3.133), by C~m and C~m only, if these values correspond to the phase equilibrium. In the experiments performed in [88], the equilibrium state was not studied. Besides, if ever the equilibrium between the micelles I of the same substance in aqueous and organic phases is possible, this equilibrium is likely to exist at quite high concentrations, where significant corrections should be introduced to account for the decrease of the activity coefficients in the two phases. The HOR values determined by these methods were used in [151, 184] to analyse the efficiency of surfactant collectors (adsorption activity) with respect to the extraction of emulsion drops and metal ions (cuprum, cobalt, etc.). A HOR of a surfactant, determined from

The coexistence between micelles formed by various surfactants in aqueous and organic (cyclohexane) phases was reported in [ 171].

243 the work of micellisation, was proposed in [88] mainly to avoid problems with the determination of the HOR for ionic surfactants from the work of adsorption, caused by the insolubility of ionic surfactants in saturated hydrocarbons. It was mentioned in Section 1.4 that the comparison of the increments for the transition of a methylene group from water into the saturated hydrocarbon with increments corresponding to the transfer from water to the micellar core has shown that the contribution to the work of micellisation for methylene groups Alacn2 is by 15-20% smaller than that corresponding to the transfer from water to hydrocarbon, i.e., lower hydrophobicity is exhibited, as compared with the transfer between bulk phases. Using benzene as the organic phase makes the practical determination of CMC more convenient; however, the principal difficulty persists with the determination of the work of transfer of ionic groups and counterions from an aqueous phase to a saturated hydrocarbon, when maximum hydrophobicity is exhibited. In the calculations of the work of micellisation for ionic surfactants one should also know the degree of ion binding, which depends on the nature of the polar group and the presence of indifferent electrolytes. To calculate the degree of binding one has to determine the CMC for several members of a homologous series, and assume that this value is constant throughout the entire series [155]. In this approach, all restrictions caused by the inhomogeneity of water/micelle interface still persist, similarly to the situation in the case of adsorption. Nevertheless, this approach is useful in view of the determination of the hydrophilehydrophobe balance related specifically to the micelle formation process, and the studies of the effect of medium polarity and temperature on this value.

244

3.8.

Hydrophile-lipophile balance and phase inversion of emulsions

In Sections 2.3 and 2.4 the most important properties of emulsions, which govern the phase inversion processes were discussed. As mentioned in Section 2.3, to understand the mechanism of the phase inversion which caused by changes in the nature of the emulsifier, the most important phenomenon to be considered is the transition from a stable emulsion of one type to a stable emulsion of the opposite type characterised by the same type of stabilisation [185]. Note that there are various mechanisms of emulsion stabilisation. For example, if water-soluble micellar surfactants are added to a stable inverse emulsion, prepared from the organic solution of hydrophobic surfactants, like oleic acid ethers and glycerine, sorbitol, xylitol or triethanol amine, then the phase inversion takes at a certain ratio of hydrophilic and hydrophobic components: the stable inverse emulsion is transformed into a stable direct emulsion. During such transformation, the type of stabilisation remains the same, and the hydrophile-lipophile balance expressed via the interaction energies (transfer energy or work of adsorption) of the different parts of the surfactants can be employed as a phase inversion criterion [185]. The HOR interval, in which this type of phase inversion is observed, is bounded by a lower and upper limit (the minimum and maximum HOR values). Outside this interval only one type of emulsions can be stable (the inverse emulsions for HOR values lower than -~0.5, and the direct emulsions for HOR values exceeding 0.85), and a phase inversion between the stable emulsions of opposite type becomes impossible [ 162, 163]. The phase inversion process is affected not only by the nature of the emulsifier (the hydrophile-lipiophile balance of the surfactant), but also by the surfactant concentration, temperature, water/oil ratio and the properties of the vessel walls (wettability). For individual surfactants with concentrations below the CMC, the phase inversion taking place at constant hydrophile-lipophile balance and caused by the change of the emulsifier concentration, can be regarded to as a special case, which is due to the difference between the minimum surfactant concentrations required for the stabilisation of thin aqueous and non-aqueous emulsion films [172, 185]. For high surfactant concentrations (above CMC or values which correspond to the formation of microemulsion systems), the equilibrium distribution of the surfactant (and, therefore, the hydrophile-lipophile balance), both for individual surfactants and for mixtures, will depend not

245 only on the nature of the substance, but also on the water to oil volumes ratio, and on the presence or absence of micellar phases. To account for these effects, the HOR of the mixture of surfactants was calculated in [171] from the residual concentrations in water and oil after the third (micellar) phase was removes. In other studies [34, 178] it was suggested to calculate the HLB values from the composition of the interracial layer or microemulsion. In [ 162, 170] the HOR values corresponding to the phase inversion boundaries were estimated using a set of several individual surfactants with different HOR values, in some cases, by more than 0.1. To calculate the HOR values which correspond to the phase inversion boundaries more precisely, the values of HOR should be varied in a continuous way. To realise such continuous variation, one can employ mixtures of hydrophilic and hydrophobic surfactants. In addition, working with the mixtures of surfactants which belong to different classes, one can study the dependence of the HOR value which corresponds to the phase inversion boundary, on the surfactant nature.

3.8.1. Studies of phase inversion in emulsions using the black spot formation concentration In Section 3.7.4 relationships for the calculation of HOR for surfactants mixtures were given. The dependencies of HOR values on the composition are most simple, when the surfactant concentration is low, one of the components is soluble in the organic phase only, and the second component is soluble only in the aqueous phase, Eq. (3.125). For this case, any constant HOR value corresponds to a certain concentration ratio C~/C~ which can characterise the demulsifying ability (here the subscripts 1 and 2 refer to the hydrophobic and hydrophilic components, respectively, and the superscripts indicate the medium: ~ the aqueous medium and 13 the organic phase). In direct experiments where the emulsion stability is studied in the phase inversion region, significant problems arise in the estimation of this ratio, because in the HOR region close to the phase inversion boundary, the formation of mixed emulsions (of both types) takes place during the emulsifying. As stability (determined from the time required for the separation of the emulsion into aqueous and oil phases) is a relative quantity, it is extraordinarily difficult to determine the critical concentration ratio C~ /C~, and, therefore, the HOR value.

246 Therefore, another method was proposed in [172, 185] to study the phase inversion and to determine the critical concentration ratio and HOR values. This method is based on the fact that, in some cases, the concentration at which the formation of black spots sets in, Cbl, varies oppositely to the variation of the emulsion stability. For example, a sharp increase in Cbl for a surfactant takes place with the increase in the polarity of the oil, while the stability becomes lower. This effect is observed in both inverse and direct emulsions [ 17, 74, 169]. In a similar way, Cbl undergoes a rapid increase with the approach to the upper boundary of the inversion interval for inverse emulsion, and with the approach to the lower boundary for direct emulsions. In these experiments, the stability of inverse emulsions and hydrocarbon films in the aqueous medium was investigated. The emulsions were prepared by shaking in test tubes; the phase ratio was 1:1, and the total volume 10 ml. To avoid the formation of direct emulsions, the aqueous phase was added drop by drop to the organic medium during the emulsification process. The concentration at which first black spot are formed was determined in microscopic hydrocarbon (cyclohexane) films in the aqueous medium using the experimental method described in [74, 142].

10 ,..-77

_~8 E

Fig. 3.22. Dependence

6

of

Xylane-o

concentration corresponding to ~4

the

formation of black spots in cyclohexane emulsion films on the concentration of

2

hydrophilic surfactants in 0 o

l 1

~ 2

--4 J'

I 4

i ---- C w 10 ~ mo dm 3 h

'

aqueous

solution: o - Alphapol-12; A- Triton X100; 13- DDBSNa; 9- Alphapol-8.

The dependencies of Cbl for the cyclohexane film in aqueous medium, stabilised by Xylan-o, on the concentration of the hydrophilic surfactant, are presented in Fig. 3.22. All curves

247 Cbl(C2 ) exhibit a minimum in the range of low concentrations. For higher concentrations of the hydrophilic surfactant, the dependence becomes approximately linear. Each curve Cbl(C~ ) divides the concentration range into two regions: that above the curve corresponds to stable direct and inverse emulsions, while in the region below the curve only stable direct emulsion can exist. (For very low concentrations of both surfactants, in the region close to the origin, also the direct emulsions are unstable.) The dotted line represents the dependence of the CMC for Xylan-o on the concentration of the hydrophilic surfactants. The addition of the hydrophilic surfactant to the aqueous phase leads to a slight decrease of the CMC for Xylan-o. It is seen from Fig. 3.22 that no dependence exists between the CMC and the formation of stable inverse emulsions. For example, stable direct emulsions can be prepared either from micellar or non-micellar solutions. On the other hand, for high concentrations of the hydrophilic surfactants, the emulsions can be unstable also in the micellar concentration region. Hydrophilic surfactants act as classical demulsifiers of inverse emulsions. The limiting HOR value, at which an inverse emulsion can still be obtained, and an inverse emulsion can be transferred into a direct emulsion (i.e., the upper boundary of inversion with respect to HOR) corresponds to a certain ratio of the stabiliser and demulsifier concentrations. This limiting concentration ratio and the HOR value in the inversion point can be calculated from the slope of the linear portion at the Cbt(C~) curve. This value can be used as the measure of the demulsifying ability. Comparing the curves shown in Fig. 3.22, one can see that among all the compounds studied, the most efficient demulsifier is Alphapol-12. The demulsifying ability of other hydrophilic surfactants decreases in the sequence Triton X-100, NaDBS, Alphapol-8. Also, the critical concentration ratio estimated from the dependence of Cbt on C~ was compared with the ratio determined from the explicit study of the emulsion stability. For the former value, both the initial concentration of Xylan-o in cyclohexane and the initial concentration of the hydrophilic surfactant in water represent the equilibrium concentrations, because Xylan-o is almost insoluble in water, and the transition of hydrophilic surfactants into the film does not affect their concentration in the aqueous phase, as the volume of the film is

248 negligible as compared with the volume of the aqueous bulk phase. Therefore, the ratio of equilibrium concentrations C~ /C~ can be obtained immediately from the plot of Cbl vs C~. In the studies of the emulsion stability, it is convenient to use the critical ratio of concentrations expressed via the initial concentrations of surfactants in the two phases. However, for the hydrophilic surfactant (due to its distribution) the initial concentration is not in equilibrium. To determine the equilibrium concentration of a hydrophilic surfactant after the emulsification, the distribution of the surfactant was measured in terms of an arbitrary coefficient L 2 = C w / C 7 . This arbitrary coefficient L2 is different from the thermodynamic distribution coefficient Kc due to the micellisation in the aqueous medium, and to the transfer of additional amount of the hydrophilic surfactant into the organic medium caused by the solubilisation in the Xylan-o micelles. Table 3.26 summarises the values of the distribution coefficients Kc, L2, and the critical concentration ratios determined in the experiments where the stability of emulsions was studied, and from the dependencies of the black spot formation concentration. Table 3.26. Distribution coefficients L2 and KC and critical relations between the concentrations corresponding to the phase inversion Hydrophilic surfactants

Kc

L2

c

O 1,init

c 'Jo

C C 2.init J 9

Alphapol- 12

1.4

Alphapol-8

0.8

Triton X- 100

1.4 1.6

2.9 0.55

c j,

5.0

6.1

019

1.1

......

017

0.8

1.5

3.4

3.0

103

4.4

1.37

1.68

1.45

. . . . .

NaDBS ,,

The values C ~

w were calculated from the expression:

C ~

9 ' ~--- C W

C~

' t, 2.i,itJ L2

where C ~ and C w are the equilibrium concentrations of Xylan-o in the organic phase and of the hydrophilic surfactant in water, respectively; subscript 'init' refers to the initial

249 concentrations of the respective surfactants. The indices 'f' and 'e' refer to the concentration ratios determined in the films and emulsions, respectively. The concentration of Xylan-o was 10-3 mol.dm "3. The dependence of Cbl on HOR for cyclohexane films in Alphapol solutions is presented in Fig. 3.23. The HLR values were calculated using the critical concentration ratioC ~ / C 2w . This dependence should be compared with the dependence of the stability of W/O emulsions stabilised by Xylan-o on the HOR (i.e., for increasing Alphapol-12 concentrations).

~ys~

Cbl i0 4. mol dm-3 18

80

60

2

Fig. 3.23. Dependence of (1) the Xylan-o

~0

concentration required for the formation of black spots in cyclohexane emulsion

E 20

films in aqueous medium and (2) the

g o,7

8.~8

HOR

.... 8.~

1.g

emulsion stability on the HOR of the mixture.

It is seen from Fig. 3.23 that, starting from a certain HOR value, the emulsion stability decreases, while the formation concentration for black spots becomes sharply increasing. This value of HOR should be regarded to as the upper boundary for phase inversion. For other hydrophilic surfactants, the dependence of Cbl on HOR is illustrated in Fig. 3.24. It can be seen that, in the concentration range studied, irrespectively of the nature of the hydrophilic surfactants, the HOR which corresponds to the upper boundary of inversion zone is between 0.89 and 0.92. It is interesting to consider systems where the concentration of hydrophilic components is small, which can be studied by the proposed method. In this concentration region, the curve Cbl vs HOR divides the concentration area into two regions: the region where stable inverse and

direct emulsions exist (above the curve), and the region where only direct stable emulsions can

250 exist (below the curve). Therefore, in W/O emulsions, with a constant HOR value (in the interval HOR of 0.75 to 0.85), the decrease of the Xylan-o concentration leads to a decrease of the stability, and the emulsion will become unstable at the point on the curve Cbl v s HOR. At the same time, a direct emulsion remains stable. Thus, this curve can also be considered as the phase inversion boundary. The existence of this boundary is caused by the fact that the minimum concentrations necessary for the formation of stable inverse emulsions and stable direct emulsions, are different. When the Xylan-o concentration is below the curve Cbl v s HOR, stable direct emulsion can be prepared, while for stable inverse emulsion this concentration of the stabiliser is insufficient. Therefore, this boundary can be thought of as the special concentration boundary of the phase inversion zone in emulsions.

C

O~

~

"5

-

1) (e.g., pentanol, Kc = 1.56) or 5% addition of valeric acid (HLR = 1.37) also results in the formation of a three-phase system. Let us consider some more systems given in Table 3.28. In the system 2 (Tween-80, HLB = 15), the formation of the micellar phase is observed when 13.5 vol% of hexanol (Kc = 0.58) is added, while in system 4, where the more hydrophobic (with respect to the HLB number) surfactant Triton X-100 is used, the formation of a three-phase system does not take place for the addition of hexanol or pentanol up to 15 vol%. In this system, a micellar phase is formed at 23-24~

or if the electrolyte (NaCI) is added.

Finally, in the first system (1% SDS and 1.75%NaCI) the formation of micellar phase is induced by the addition of pentanol (Kc = 1.56), while the addition of Triton X-100 (Kc = 1) does not lead to the formation of a micellar phase. Depending on the hydrophility of a surfactant (estimated from Kc or HLR values), and its chemical nature, when added to a micellar phase, first this phase incorporates or releases the oil

258 (or water), and subsequently, when the added concentration is sufficiently high, the phase is destructed and releases water and oil. At the initial stage, the incorporation of oil and release of water can be regarded as the hydrophobisation of the surfactant composition which forms the micellar phase, while the incorporation of water and release of oil correspond to the increase of the hydrophility. For example, in the system 5 (see last column in Table 3.28) a small addition of hexyl alcohol leads to a hydrophobisation, while at a concentration of 6.5% a total destruction of the surfactant phase takes place. The addition of amyl alcohol also results in a hydrophobisation and then destruction (at 8 vol%). The addition of butyl alcohol leads initially (to 5%) to the incorporation of water, and subsequently to the release of water and destruction of the phase (at 26% addition of alcohol); and the addition of propyl alcohol leads to the incorporation of water, then to the release of oil, and finally to the destruction of the micellar phase at a concentration of about 9.5%. When a mixture of alcohols (C3:C4 = l:l) is added, the phase remains to exist even for a 40:1 ratio of the alcohols mixture to the micellar surfactant. It can be concluded therefore that the hydrophile-lipophile ratio for the optimum phase behaviour corresponds to the HLR of the l" 1 mixture of butyl and propyl alcohol, Kc = 11.6, HLR - 1.5. For other systems, the concentrations of additions leading to the destruction of the phase are presented in Table 3.28. It is seen that for systems 1, 5, and 6, with respect to the addition of alcohols, the Kc and HLR values correspond to Kc = 6.5 or H L R - 1.29 for butyl alcohol, and Kc - 11.6 or HLR = 1.5 for the mixture of propyl and butyl alcohol. On the other hand, even minor amounts of Triton X-100 (Kc--l) result in an immediate destruction of the micellar phase, although the Kc and HLR values suggest that this surfactant is less hydrophilic. It can be concluded therefore that the boundaries of the existence of the micellar phase depend not only on the hydrophile-lipophile balance of the mixture (whatever form is accepted to express this parameter), but also on the chemical nature of the surfactant and its structural characteristics (the form and size of its polar and apolar parts). In what regards the absolute values of HLR, which determine the boundaries of the existence of the micellar phase, these values are essentially different from those reported earlier in [169, 171 ], and therefore these values need to be determined more precisely using other methods.

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265 144. L. Lobo, I. Ivanov and D.T. Wasan, AIChE J., 39(1993)322. 145. K.D. Danov, N.D. Denkov, D.N. Petsev, I.B. Ivanov and R. Borwankar, Langmuir, 91(1993)1731. 146. A. Kabalnov and H.Wennestr6m, Adv. Colloid Interface Sci., 49 (1994)113. 147. S. Rigelman and G.Pichon, American Perfumer, 77(1962)31. 148. J. Boyd, C.Parkinson and P.Sherman, J. Colloid Interface Sci., 41(1972)359. 149. R.V. Petersen, R.D.Hamill and J.D.McMahon, J Am. Pharm. Assoc., 53(1964)651. 150. R.E. Ford and C.B.Furmidge, J. Colloid Interface Sci., 2(1966)331. 151. V.V. Sviridov, A.I.Gomzikov and L.D.Skrylev, Izv. Vuzov (tsvetnaya metallurgia), 6(1981)54. 152. B.P. Binks, Langmuir, 9(1993)25. 153. B.P. Binks, Colloids Surfaces, A71(1993)167. 154. A.I. Rusanov, Kolloidn. Zh., 49(1987)496. 155. A.I. Rusanov, Micellization in surfactant solutions, in Chemistry Reviews, Vol. 22, Harwood Academic Publishers, 1997. 156. A.A. Abramson. Poverkhnostno-aktivnye veshchestva. Khimia, Leningrad, 1975 (in Russian). 157. Ch. Tanford. The Hydrophobic Effect. Formation of Micelles and Biological Membranes, 2"ded., Wiley-Intersciene, New York, 1980. 158. D.S. Goodman, J. Am. Chem. Sot., 80(1958)3887. 159. R. Aveyard and R.W.Mitchell, Trans. Faraday Sot., 65(1969)2645. 160. R. Aveyard and R.W.Mitchell, Trans. Faraday Sot., 66(1970)37. 161. P.M. Kruglyakov, Kolloidn. Zh., 38(1976)582. 162. P.M. Kruglyakov and A.F.Koretski, Dokl. AN SSSR, 197(1971)1106 (in Russian). 163. P.M. Kruglyakov and A.F.Koretski, Izvestia SO AN SSSR, seria khim., 9(1971)11. 164. Me. Auliffe, J. Phys. Chem., 70(1966)1267. 165. P. Mukerjee, Adv. Colloid Interface Sci., 1(1967)241. 166. P. Mukerjee, in: Micellization, Solubilization and Microemulsions, vol. 1-2, K.L. Mittal (ed.), Plenum Press, New York-London, 1977, p.. 167. V.V. Sviridov, A.I. Gomzikov and V.V. Khokhlov, Kolloidn. Zh., 43 (1981)1121. 168. P.M. Kruglyakov and T.V. Mikina, Kolloidn. Zh., 47(1985)1084.

266 169. L.L. Kuznetsova, P.M. Kruglyakov T.V. Mikina and A.F. Koretski, Izvestia SO AN SSSR, seria khim., 3(1977)82. 170. P.M. Kruglyakov, T.V. Mikina and A.F. Koretski, Izvestia SO AN SSSR, seria khim., 1(1974)3. 171. T.V. Mikina and P.M. Kruglyakov, Kolloidn.Zh., 45(1983)257. 172. P.M. Kruglyakov, L.L. Kuznetsova, T.V. Mikina and A.F. Koretski, Tr. VII. Mezhdunar. Konrgessa po PAV, vol. 2, Vneshtorgizdat, Moscow, 1976, 500. 173. E.H. Crook, D.B. Fordyce and G.F. Trebii, J. Phys. Chem., 67(1963) 1987. 174. A.F.H. Ward and L. Tordai, Trans. Faraday Soc., 42(1946)413. 175. A.M. Posner, J.R. Anderson and A.E. Alexander, J. Colloid Sci., 7(1952) 623. 176. J.J. Betts and W.A. Pethica, Trans. Faraday Sot., 56(1960) 1515. 177. P.M. Kruglyakov, A.F. Koretski, I.P. Sokolovskaya, U.G. Rovin and T.V. Mikina, Izvestiya SO AN SSR, Serija khim., 1(1976) 19. 178. B.W. Brooks and H.M. Richmond, J. Colloid Interface Sci., 162 (1994)59, 67. 179. D.G. Mall, J. Chem. Soc. Faraday Trans. II, 68(1972)668. 180. U.M. Kulikov, U.L. Verderevski, N.A. Klimenko and V.I. Gusev, Kolloidn. Zh., 50(1988)678. 181. P.A. Rebinder, Zh. VKhO im. Mendeleeva, 4(1966)362, (in Russian). 182. H. Lange and K.H. Beck, Kolloid-Z Z. Polymere, 251(1973)424. 183. I.M. Korenman and Z.G. Chemorukova, Zh. prikl, khimii, 47(1974) 2523. 184. V.V. Sviridov, T.F. Kokovnina and L.D. Skryleva, Zh. prikl, khimii, 1 (1983)53. 185. P.M. Kruglyakov, Kolloidn. Zh., 39(1977) 161. 186. P.M. Kruglyakov ,T.P.Sedova and V.D. Mal'kov, (unpublished results).

267

Chapter 4.

Hydrophile-lipophile balance of solid particles

The behaviour of solid bodies in either compact or disperse form with respect to their interaction with liquids, for example, in processes of selective wetting, stabilisation of emulsions by solid particles, foam breaking by hydrophobic particles during the processes of washing-off of solid insoluble contaminations and oil flotation, and also in chromatographic processes, is determined by the ratio of the energetic affinities of the surfaces with respect to polar (water) and apolar media, i.e., the hydrophile-lipophile balance of the body. Similarly to the hydrophile-lipophile balance of surfactants, this property for solid particles can be expressed via various properties, and the practical validity of any characteristics of hydrophilicity (or hydrophobicity) depends not only on the clarity of the physical meaning of this characteristic, but also on the specific application of this characteristic (for example, in chromatography or in emulsion stabilisation)l. The hydrophilicity (hydrophobicity) characteristic used with respect to flotation and stabilisation of emulsions by solid particles, is the contact angle which arises at the 3-phase contact line between the solid, gas and liquid phases (or between two non-mixing liquids) and reflects the balance between three interfacial energies [1-3]. However, the estimation of hydrophilicity from the contact angle becomes invalid for microscopic particles (fine powders). The most pronounced demonstration of the role played by the hydrophile-lipophile balance of solid particles becomes evident when such particles are used as emulsion stabilisers. Therefore, we first consider briefly (1) the behaviour of drops at a solid surface, and (2) the behaviour of spherical solid particles at the interface of two non-mixing liquids.

Note that in a subsequent volume of this series a comprehensive presentation of various problems of particles at fluid interfaces will be published by P. Kralchevski and K. Nagayama [4]. This book will give the theoretical background of forces acting at a liquid interface on single spherical particles and organised particle ensembles, and discusses a wide range of application fields.

268

4.1. Behaviour of drops at solid surfaces, and solid spherical particles at liquid/liquid interface Let us consider the behaviour of a liquid drop on a smooth homogeneous solid interface with a gas or another liquid immiscible with the drop. For simplicity, we assume that the drop phase is water. When complete symmetry in the system exists, the drop takes the shape of a calotte, as shown in Fig. 4.1.

//

gos

dA so//d Fig. 4.1. Contactangle 0 in the solid/water/oil(S/W/O) system. As the densities of liquids in water-oil systems are close to each other, the effect of gravity can be neglected even for quite large particles (5 ~tm). If the surface energy (interfacial tension) at the solid/apolar liquid interface oso exceeds that at the solid/water interface csw, then the drop will spread, leading to a decrease of SO surface area, and an increase of the SW surface area. As this process leads also to an increase in the surface area and surface energy at the oil/water interface, two equilibrium states are possible. First a complete wetting of the solid surface can happen, when the solid/water interface replaces the solid/oil interface, and second a state can be established which corresponds to the minimum of surface energy and a certain value of the contact angle. The contact angle is defined as the angle between the solid surface plane and the tangent to the drop surface at the point where the three phases are in contact. The angle is counted towards the polar (aqueous) phase. To determine a quantitative relationship between the contact angle and the surface energies, we consider an infinitesimal displacement of the wetting line, which corresponds to the increase of the surface area wetted with water by dA. The variation of the surface free energy dG s reads dG s = (oso - r

+ Owo cos(0 - dO) dA.

(4.1)

269 In the equilibrium state (dGS/dA)= 0, and the derivative d0/dA also tends to zero for dA ~ 0, independent of the macroscopic size of the system, so that we obtain

cos 0 = ~

- ~176,

(4.2)

t~wo

where osw- oso is called the adhesion tension. It is assumed here that the two liquids are mutually saturated. Equation (4.2), which determines the wetting condition in equilibrium, is known as the Young-Laplace or Young equation. The simple derivation of Young's equation is valid for uni-component liquids. For multicomponent liquids the derivation is more complicated, the result is, however, the same, when the mechanical equilibrium of the drop is considered [2]. When 0 < 90 ~ the solid possess a hydrophilic surface (better wetted by water), and 0 > 90 ~ corresponds to a hydrophobic surface. Now, the position of the solid spherical particle at the interface between two liquids should be determined in the case of selective wetting. We consider a spherical particle of radius r, with the equilibrium wetting angle 0 determined by the equation

COS 0 = Crs~ - O'sw ~ow

located at the interface, and immersed in the organic phase by the depth h (cf. Fig. 4.2). Then the contact area of the particle with organic phase is 2nrh, and the area of contact with water is 4nr 2-2nrh.

The

area

of

the

water/oil

interface

occupied

by

the

particle

is

nl 2 = n[(r 2 - ( r - h) 2] = n(2rh- h 2) and can vary from zero to nr 2. In the equilibrium state, we have dG s = oso (2nrdh) + crsw (-2nrdh) - noow (2r - 2h)dh and dG/dh - 0 hence,

(4.3)

270 r-h (YSO -- CSW = ~

r

(YOW = O'OW COS 0

cos0 = ~ _ rh- _ Cso- Csw ' r

(4.2a)

t~ow

and the position of the particle at the interface is such, that the angle 0 becomes equal to the equilibrium angle of the Young equation [ 1].

oil water

~

o

w -__-

Fig. 4.2. Equilibrium

position

of

a

spherical solid particle at the water/oil interface.

The measured values of the static contact angles are often different from their equilibrium values for various reasons [1-3]. The existence of several stable (meta-stable) contact angles, which differ from the equilibrium contact angle, for the contact of a liquid with a solid, is called the wetting hysteresis. The wetting hysteresis is characterised by the advancing and receding contact angles. The difference between these angles can amount to 50-150". One should distinguish between the static, kinetic and physico-chemical wetting hysteresis [2]: The static hysteresis (order hysteresis) is observed for different sequences of contacts of a solid with the liquid phases. The static hysteresis does not depend on the contact time. 0

The kinetic hysteresis is caused by the fact that various barriers that hamper the spreading of the liquid exist at the solid surface. For this type of hysteresis, the contact angles depend on the time of contact between the phases.

271 3.

The physico-chemical hysteresis arises when the wetting is accompanied by some other physico-chemical processes (adsorption, dissolution, evaporation, chemical reactions etc.).

The main factors, which can lead to the creation of a barrier for the relocation of the wetting perimeter, are various contaminations which result in the variation of the surface energy of the solid, and the places on the surface, characterised by different surface tension and inhomogeneity dimensions. Another factor which can lead to a hysteresis is the surface immobility or low mobility of, say, surfactant molecule when adsorption on the solid surface or desorption to the solution bulk take place during the wetting process. In addition, the surface of real solid bodies is by no means perfectly smooth, but covered with 'buckles' of various shapes and sizes (surface roughness), for the contact with a non-wetting liquid 0 e > 90 ~ and the increase in the surface roughness leads to an increase of macroscopic contact angle, while for a wetting liquid, 0 < 90 ~ the contact angle decreases. For systems with a contact angle hysteresis, some authors have also reported 'equilibrium' or quasi-equilibrium angles which were obtained after some waiting time. It follows, however, from the results obtained by Penn and Miller [5], that for system exhibiting a contact angle hysteresis a stable 'equilibrium' contact angle different from the advancing or receding contact angle does not exist. A number of methods exist to measure the contact angle. One of the most exact is the inclined plate method [1], where the inclination angle of the plate is varied by using a precise positioner until the liquid/liquid (or liquid/gas) interface becomes plane. A large variety of drop methods is widely used. Here the contact angle can be either measured by a microscope with a goniometric scale, or the image of the drop is taken and the angle is calculated from the drop shape and diameter. The contact angle can be determined with high precision also using the Wilhelmy plate method, where the difference of the height between the meniscus top and the interface is measured [ 1, 6]. The method of 'growing-shrinking' sessile drops is suitable for the measurement of advancing and receding contact angles. In this method the size of the drop is controlled by a micrometric syringe and the contact angle value is determined either using a goniometric scale, or from the image of the drop profile [ 1, 8].

272 A number of other methods were proposed, based on the behaviour of a liquid in a capillary or the motion of a liquid through a layer formed by powders of porous material. These methods are reviewed for example in [1, 7, 8]. It would be very useful to design a method, which enables the direct measurement of contact angle at liquid/liquid interface employing small solid particles. In principle, to calculate the contact angle, one should measure the depth of immersion of a particle into one of the phases; then Eq. (4.2a) can be used. However, some problems arise with the practical implementation of this method. If the particles are large, then gravity effects are significant, while for small drops (less than 5 ~tm) optical difficulties exist [9]. The only version of contact angle measurements suitable for small spherical particles was developed recently by Clint et al. [ 1012]. This method is especially simple from a technical point of view for water/gas interface, but can also be adapted to liquid/liquid interface, and can be applied to systems containing a surfactant in one of the phases. The concept of the method is considered in more detail below. The geometry of the surface with the solid particle is illustrated by Fig. 4.2. The energy required to remove the single particle from the interface is [see Eq.4.34 in Section 4.3] ~G s$p = nR2crwo(1 + cosO) 2

(4.4)

For a hexagonal close packing, the number of particles per unit area is 1 N = tZR-------2 . # . ~~

(4.5)

It follows from Eqs. (4.4) and (4.5) that the Gibbs energy which would be spent to remove all particles from a unit area to an apolar medium phase is AG= ntr~

(1 + cos0) 2

(4.6)

and a similar expression is valid for the removal into water nc ow (1 - cos 0)2

AG= 2,/3 As one can see, these energies do not depend on the particle size.

(4.7)

273 Let us assume now that the energies given by Eq. (4.6) or (4.7) are equal to those necessary for the collapse of a densely-packed monolayer of spherical particles, i.e., the two-dimensional 'collapse pressure' (rtc) of the particle array

AG= x~176 2 , ~ (1 +- cos0) 2 "

(4.8)

The dependence of the two-dimensional pressure on the contact angle in the angle range of ca. 50 to 130 ~ is very sharp. To determine the surface pressure, a Langmuir trough is employed. The value of surface pressure is calculated from the data obtained for the variation of surface tension with a wetted plate suspended from a microbalance, or directly from the force which acts upon the barrier. A typical dependence of n on A is shown in Fig. 4.3 for 3 ~tm hydrophobic silica particles spread over an aqueous subphase [12]. The collapse pressure is determined as the intersection point of two linear portions of the n(A)-dependence. It is still unclear why the increase in surface pressure takes place beyond the collapse point. It was supposed in [ 12] that this increase could be caused by the formation of a multilayer structures. 40

9

?

close-packed monolayer at collapse pressure

eo

IO

Fig. 4.3. Surface pressure vs area isotherm o

100

200

300

400

A/cm

500

600

n(A)

for

3 lam diameter spherical

hydrophobic silica particles on aqueous solution of the cationic surfactant.

Assuming that during the monolayer collapse the particles are expelled into the phase where the wetting of particles is better, one can conclude that for contact angles below 90 ~ the water

274 advancing (oil receding) angle is measured; on the contrary, for angles above 90 ~ the oil advancing (water receding) angle is measured. The application of this technique for measuring the contact angles for colloid particles formed during the reaction or adsorption process at interfacial layers seems also to be promising, while the effect of the interaction between the particles on the measured contact angle value is still not completely clear [4, 12].

4.2.

Stabilisation of emulsions by solid particles

The fact that highly disperse solid particles can be used as emulsifiers for the preparation of O/W and W/O emulsions is well-known [13]. First detailed studies of the properties of nonsoluble emulsifiers were performed by Pickering [14]. There exists a number of substances which can be used as emulsifiers for the dispergation of oils in water: sulphates of iron, copper, zinc, nickel, aluminium, freshly deposited calcium carbonate and arsenate, lead arsenate, pyrite, carbon black, mercury iodide, glyceride tristearate, various hydroxides, fine dispersed clays, and many other substances. A comprehensive review of less recent studies was given by Clayton [13]. The main factors of the stabilisation by solid particles are summarised in [4, 15-20]. It was shown that efficient emulsifiers should possess fine disperse and loose gel-like structures. According to Rebinder [15], the particles of an efficient solid emulsifier should be coagulated to some optimal extent, and, at the same time, possess large initial (primary) dispersity. It was shown in a number of studies [ 1, 15, 21 ] that emulsions stabilised by solid particles are characterised by a certain interrelation between the emulsion type and stability, and the wetting angle at the interface of the two liquid phases with the solid particle surface. More specifically, in the study performed by Schulman and Leja [22] it was shown that in water-benzene-barium sulphate powder modified by a surfactant, both types of stable emulsions were formed only for contact angles close to 90 ~, while the results reported in [23] suggest that direct emulsions of carbon tetrachloride in water, stabilised by octadecyl amine hydrophobised quartz particles, are formed in the angle range of 60 to 85 ~. The important role played by the contact angle hysteresis and the sequence of wetting of the particles by water and oil before fixation at the interface, was mentioned in a number of

275 publications [18, 24, 25]. It was shown in the previous section that solid emulsifier particles acquire their stable position at the liquid/liquid interface for certain (equilibrium) values of the contact angle. To make the coalescence of the drops possible, the particles should be removed from the surface; therefore, the particles act as a steric barrier to coalescence. The thermodynamic analysis of the distribution of solid particles between bulk phases and the interface shows that the energy required to move the particles into one of the bulk phases is of the order of 5.104 kT for particles of 0.1 ~m in size and crow = 25 mN/m [12], while for 0.3 ~tm particles this energy is 2.106 kT for crow = 30 mN/m [20]. As the 'adsorption energy' is high, the equilibrium distribution conditions require that the particles should form a closely packed two-dimensional structure at the oil/water interface [20, 26]. Such structures were in fact observed experimentally in [19, 20, 23]. The geometric arrangement of closely packed spherical particles determined by equilibrium contact angle clearly implies the preferential formation of emulsions of either type: the surface should be bent in the direction of the less wetting liquid [12, 28]. In equilibrium conditions, the particles are positioned on the drop surface in such a way that the radius of the circle drawn around the drop centre through the centres of particles is equal to R, while the ratio of the particle radius to this radius R determines the equilibrium contact angle cos0 = r/R,

(4.9)

as it is schematically shown in Fig. 4.4 [28]. The actual radius of the drop is R sin 0. Therefore, the contact angle determines the curvature of the film formed by the solid spherical particles. The radii of the external and internal film surfaces are R + r and R- r, respectively. The ratio of these values R+r R r

+ cos - cos

(4.10)

determines the ratio of the areas wetted by the external and internal phases. The difference in these area values lead to the bending of the film towards the internal phase. The dependence of

276

the external film radius (drop + particle) on the ratio

Is+R ) 2 for various thicknesses of the

film (0.5 to 500 nm) and angles (75 ~ to 90 ~ was analysed in [28]. It was shown that when the size of the particles increases, then the emulsion drops also increase, and this dependence is non-linear. Small variations of the curvature result in significant variations of the size of the emulsion drops. The film curvature does not depend on the interfacial tension of the film. At the same time, the energy of the transfer of particles from the surface depends not only on the contact angle, but also on the interfacial tension. The bending of the interface film is by no means the only factor which determine the type of the film [12].

w

//

\ r

i !

o

/

%w i %w Fig. 4.4. Relation between

the

size of spherical solid particles with the curvature of a 'solid' film which

stabilises emulsion drops: R + 2r - external radius of drops; r - radius of solid particles; R - 'internal' radius of drops; R.sin | -

actual radius of drops.

When equal quantities of water and oil are mixed, the concentration of particles is small, and the packing of particles at the interface cannot be close, emulsions of both types can be formed. When the liquid films between the particles become thinner than the size of the solid particles, the particles may contact the other interface and can bridge thin films. In this case, if the contact angle is less than 90 ~ then the aqueous film will be stabilised by the particle. Further thinning of the meniscus between the particle and the film, results in a decreased pressure, acting opposite to the external pressure which causes the syneresis and the rupture of the film.

277 On the contrary, the position of a particle with a contact angle larger than 90 ~ is unstable. The capillary pressure, which arises in the meniscus, leads to an approach of the contact lines to each other, hence enhancing the film drainage. This mechanism of film destabilisation was considered in detail in [ 12, 29-31 ], where foam breaking by solid particles was studied. The theoretical analysis of various physico-chemical factors which influence the stabilising ability of solid particles was presented by Levine and co-authors in [20, 26]. The effect of electrostatic repulsion between two electric double layers of neighbouring solid particles at a liquid/liquid interface, the repulsion of particles caused by short range solvation and elastic forces, the intermolecular repulsion and capillary forces were considered. The theoretical [4, 26, 32, 33] and experimental [33, 34] studies have shown that capillary attraction forces caused by the deformation of the interface under the influence of gravity arise between two floating spherical particles at an interface. However, for particles smaller that 1 ~tm in radius, these capillary forces are very small [32], and in a closely packed monolayer repulsion forces arise, which are also very small [26]. The calculations of the interaction between the electric double layers (DEL) of neighbouring particles in the interface layer, based on Deryaguin's theory [35] have shown that for particles with r = 0.3 ~tm, used in the experiments reported in [20, 26], and a surface potential of ~Fs = 25 mV, assuming that the nearest neighbours number is 6, the maximum energy is 2.103 kT, that is, by three orders of magnitude lower than the energy of the particles 'fixation' at an interface, which is of the order of 106 kT. The estimation for the dipole-dipole interaction energy yields a value of about 0.8 kT, which is very much smaller than the ordinary electric double layer repulsion [26]. The calculations of solvation or hydration forces at the solid/water interface and solid elastic forces have also shown that these contributions are approximately 103 times lower than the barrier created by the surface energy of the particles (not less than

106 kT) [261. Similar results were obtained when the molecular interaction energy was compared with the energetic minimum depth for particles fixed at the interface. In addition, the concept of effective interfacial tension Cow was introduced, related to the existence of a closely packed monolayer of solid particles at the interface

278 Oow - Oo,,, [ , -

cos

(4.11)

At 0 = 90 ~ the effective interracial tension is c = 0.547 ~row, (Yow

(4.12)

where ~ow is the interfacial tension value if the particles are absent. The stability of emulsions depends strongly on the concentration of the solid phase particles [20, 36]. For low concentrations, a close packing state cannot be reached, and the emulsions break down in a few hours under the influence of gravity [20]. On the other hand, the minimum concentration of particles necessary for the stabilisation of emulsions, depends strongly on the surfactant-modifier concentration and, consequently, on the contact angle [36]. For example, for small contact angles (less than 20~ as much as 60% of the solid phase (glass powder) is necessary to prepare stable emulsions of benzene in water, while at an ODAC concentration of 4.10 -5 mol/l, and the corresponding value of 0 = 80 ~ the necessary content of the solid phase is ca. 1% [36]. The coalescence kinetics of emulsions stabilised by solid particles was studied by Whitesides and Ross [37]. Two aspects of the emulsion breakdown (called limited coalescence) were systematically studied: the coalescence mechanism, and the origin of very narrow particle size distribution. The stabilisation and breaking of emulsions were performed in two stages. First a highly disperse emulsion of dodecyl phthalate in water was prepared, stabilised by sodium laurate. Then, the emulsion was acidified in the presence of a necessary amount of silica and a promoter (co-oligomer of N-methyl-13-amino ethanol with adipic acid - AMEA), and the process of limited coalescence was studied under these conditions. In other experiments (where another method was used) the emulsion was stabilised by colloidal cuprum oxide. Then the oxide was dissolved in an acid which contained silica and a promoter, and subsequently the coalescence process was observed. This second method enables one to obtain the most accurate initial distribution of drops with respect to size. The coalescence rate caused by Brownian motion is expressed as

279 dn/dx = -kcn 2,

(4.13)

see Section 2.2, e.g. Eq. (2.11). In a stirred system, the constant kc depends on the volume of particles dn/dx = -k' n,

(4.14)

and the coalescence obeys the first-order equation In n/n0 = k'x.

(4.15)

The experiments reported in [37] have shown that the coalescence can be described rather well by a first-order equation. It was concluded by the authors that the hydrodynamic factor controls the particles collision. The dependence of the coalescence constant on the stirring rate was quite weak, and the value of the constant varied in the range 0.0039 to 0.0055 s"l. This weak dependence was ascribed to the formation of agglomerates (dimers) of monodisperse particles, which does not affect the rate order. Similarly to usual emulsions, in this case the main structure element, which determines the stability, is the liquid interlayer, which separates the emulsion drops covered by the 'armouring' layer of solid particles. For low concentrations of the solid phase, this interlayer can be modelled by a film stabilised by one layer of spherical particles which bridge this film (see Fig. 4.5). It was mentioned above that if the contact angle is lower than 90 ~ (measured in the film), the particles stabilise the film, while for 0 > 90 ~ coalescence occurs.

Fig. 4.5. Model of emulsion film with single layer of solid spherical particles. The model of such film was considered by Denkov et al. [38], where the integral capillary force which acts upon the unit surface area (the analogue of the disjoining pressure) was calculated

280 2

1-I = 2OOWb-C~sin (pc + b-C~Po.

(4.16)

Here b is the radius of the cell formed by the spherical particle itself and the liquid-liquid surface per cell, rc = a(sin(Pc + 0) is the radius of the segment projected over the film surface, (Pc is the slope angle of the generatrix of the meniscus profile at r = rc, Pa is the capillary pressure, a is the particle radius, and 0 is the contact angle. In equilibrium we have PI = Po = 2o. rc 9sin(Pc b 2 -r~ "

(4.17)

Given the dependence of the film thickness h on the value of the angle (Pc [38], one can calculate the disjoining pressure isotherm H(h) from Eq. (4.17). It follows from the calculations performed by Denkov et al. [38], that the disjoining pressure increases with the packing density, the contact angle, and with the decrease of the size of particles and the film thickness. For close packing of the particles, when the radius of a particle is a = 1 lam, cr = 30 mN/m and 0 = 60 ~ this pressure amounts to FI = 2.7.105 Pa. The hysteresis of the contact angle leads to the increase of the disjoining pressure. It is important to note that the dependence of the energy of fixation of the particles at the surface on the contact angle is opposite to that of the disjoining pressure: while the particle attachment is most stable at 0 = 90 ~ and most unstable at 0 = 0 ~ the disjoining pressure attains its maximum value at 0 = 0 ~ and is equal to zero for 0 = 90 ~ This model, however, does not reflect the actual behaviour of the emulsions. It is known from experiments and photographic images that stable emulsions are formed by those drops which are completely covered by a layer of solid particles. More realistic models assume the film between two drops is covered by a closely packed layer of solid spherical particles, with no solid particles inside the film volume, as depicted in Fig. 4.6. When thinning of this film takes place caused by the gravity force or the capillary pressure, the disjoining pressure arises in the moment when the particles 'adsorbed' on the opposite surfaces come into contact with each other. Further thinning of the film creates a capillary pressure in the porous space between the particles.

281

Fig. 4.6. Model of the film stabilised by two layersof solid particles. The value of the capillary pressure depends on the size of the particles, the contact angle, the packing density and the film thickness (the depth of the penetration of the extemal phase into the pores). Neglecting the components determined by the molecular attraction and DEL electrostatic repulsion, one can consider the disjoining pressure to depend only on the capillary pressure which arises in the porous space when thinning of the film takes place. For a hexagonal close packing (e.g., for a water film), the capillary pressure can be calculated from Fig. 4.7 [39] 2tSow. cos(0 + or) P~ = R ( 1 - c o s a ) + rm,. '

(4.18)

where 0 is the advancing contact angle, ct is the angle shown in Fig. 4.7,

rmin =

0.154 R is the

lowest radius of pore curvature in the equatorial plane of spherical particles.

0

Fig. 4.7. Schematic for the calculation of the capillary pressure for a thinning film.

282

The thickness, which corresponds to this capillary pressure, is given by h = 2 { R sin ot - r [1 - sin( 0 + ct)]}.

(4.19)

From the simultaneous solution of Eqs. (4.18) and (4.19), one can calculate the isotherm H(h). The capillary pressure increases until the porous cross-section (i.e., the cross-section of the gaps between the particles) becomes minimum, so that for lower film thickness the film becomes unstable. For 0 = 0, R = 1 ~tm and c =23.0 mN/m, a value of Flmax= 4.10 s Pa follows from the calculations. The real maximum value of the disjoining pressure (threshold) will possibly be lower, due to the existence of packing deficiencies or zones of cubic packing inside the hexagonal close packing zone, leading to an increase of the minimum radius of curvature of the meniscus at 0 = 0 from rmi, = 0.154 R to rmin= 0.412 R. No experimental verification of the dependence of H on h was performed. However, studies on the stability of emulsions stabilised by hydrophobic hydrolysed aluminium chloride particles (0 = 40-45 ~ for the oil advancing and 0 = 80-100 ~ for the oil receding) have shown that the stability of these emulsions for Po > 1.5.104 Pa is still high [40]. The analysis of the dependence of the 'desorption' of spherical solid particles from the liquid/liquid interface into the bulk phases on the contact angle and disjoining pressure shows that in emulsions stabilised by spherical solid particles quantitative relations exist 1) between the sizes of the drops, sizes of solid particles and contact angle; 2) between the particles fixing energy, contact angle and size of particles; 3) between the disjoining pressure, contact angle and size of particles. These dependencies provide information comprehensive enough to estimate the conditions of stabilisation of emulsions by solid particles. Comparing these stabilisation factors with the hydrophile-lipophile balance of solid particles, one can draw conclusions about the role played by the balance in determining the type and the stability of emulsions for a given type of stabilisation. It can be expected that this information will be very useful for a more precise determination of the conditions of emulsion stabilisation by surfactant adsorption layers.

283 At present, it is implicitly assumed for the calculations of various positive components (electrostatic, steric etc). of the disjoining pressure in emulsion films that the repulsion energy between the adsorption layers is much lower than the surfactant desorption energy. It is clear, however, that this condition is violated in aqueous films, for example, in the case of shortchain surfactants with a number of methylene groups lower than 6-9, while in non-aqueous films this condition is invalid for water-soluble surfactants possessing strong polar groups, that is, for some particular value of the hydrophile-lipophile balance of a surfactant, and absolute values of the desorption energies. To determine these threshold values of the surfactant hydrophile-lipophile balance, the emulsion films stabilised by solid particles can be employed as convenient system which models the stabilisation conditions. 4.3.

Work of wetting and determination of the hydrophile-lipophile balance for solid particles

The most convenient and rigorous way to express the hydrophile-lipophile balance of solid particles is to employ the increment of the Gibbs energy (AG~ for the wetting of a body by a polar medium (usually water), or the energy of wetting by a apolar liquid (typically a saturated hydrocarbon) [41]. In contrast to the surfactants, where the work corresponding to the transfer from the vacuum (air) to water or apolar liquids is usually difficult to determine due to the low volatility of typical surfactants, the increment of the Gibbs energy for the wetting of solid particles can be easily measured in the experiments. The energy of wetting of a solid body by water can be used to characterise its hydrophilicity AG ~ =Gsw -Gsc =Crsw - Ors6,

(4.20)

while the energy of wetting by oil can be used to characterise the hydrophobicity, AG O =Gso -Gs~ =Crso - Crs~,

(4.21)

see Eq. (4.6). Here, the subscripts SG, SO and SW refer to the solid/gas, solid/oil and solid/water interfaces, respectively. The superscript 0 refers to the standard state (25~ saturated gas pressure.

and the

284 The explicit measurement of the interfacial tensions Oso, Osw and Os6 is impossible. However, for macroscopic surfaces the values of AG ~ and AG ~ can be expressed via the contact angle 0, using Young's equation (4.22)

AO' = GSO - O'SL = GLO cosO,

where Ao is the adhesion tension, the subscripts SL and SG refer to liquid/gas and liquid/solid interface, respectively. Then the hydrophile-lipophile balance value can be expressed as the ratio of AG ~ to AG ~

HLR = AG~ AG o

(4.23)

and HLR0 = Ow~ cOS0w .

(4.23a)

0 0 0 cOS0o

For surfaces of high energy and well wetted by water and oil (0w ~ 0o ~, 0), HLR0

= crwo = 2 - 3.

O'OG

The work of wetting can be approximately expressed via the heat of wetting (AH), using the Gibbs-Helmholtz equation Crst -

O s ~ = A H - T a(O'sL -- ~

) .

(4.24)

0I"

For example, the heat of wetting by oil is

AH o - -Cos cos0 o -

T

a(~176 cos0). ffl'

(4.25)

Thus, the simple expression for the HLR via the wetting heats, corresponding to Eq. (4.23), is obtained

285 HLR~ = AHw t~Ho

(4.26)

as proposed by P,.ebinder in [2]. This equation is equivalent to Eq. (4.23) only if the dependence of surface tensions and contact angles on temperature can be neglected. The HLR values calculated from Eq. (4.26) are: 20 for the starch, 2 for the quartz, and 0.3 to 0.4 for activated carbon black [2, 41]. In the processes of emulsion stabilisation, washing-out of oil pollutions and other surface phenomena, a selective wetting is often relevant. It this case, the HLR can be expressed via the contact angle of the selective wetting 0ow (when the solid is contacted by two liquids):

cos 0ow = ~os - r r

.

Introducing into this expression the values of oso and r cos0 = Crwcc~

(4.27)

from Eq. (4.22) one obtains

- ~176c~176 .

(4.28)

r The introduction of the value of cos 0w into Eq. (4.28), allows to express the HLR0 value via 0wo and 0o [41 ]: HLR0w~ = 1 + ~176c~176 ~oG c~

(4.29)

The values HLRo and HLRowo do not depend on the shape of the particles and on the sequence in which the solid surfaces interact with the polar and apolar liquids. If the dimensions of the particles and the liquid phase are small, then the contribution of the line tension to the total surface energy of the system should be accounted for, see [42-44]. The dependencies (4.23) and (4.25) cannot be explicitly used for fine disperse powders or coagulates formed as gel-like films at liquid-liquid interfaces. In emulsions stabilised by solid particles, these particles are concentrated at the interface which separates the disperse phase drops, and the breakdown of emulsions is related to the energy for removing these particles from the interface into the internal or external phase. In this case, the HLR value is more representative than the ratio of the works of wetting for the transfer of particles from the

286 equilibrium position at the interface into the water and oil. Here the sequence of particle wetting and the contact angle hysteresis should be considered. It was shown in the previous sections that the position of small spherical particle of radius r at the interface between two liquids, for negligible gravity force as compared with surface forces l, is determined by the equilibrium contact angle 0ow (see Fig. 4.2). For the transfer of a particle into one of the bulk phases it is assumed that the particle consists of a single component, and that both the adsorption of the solid at the liquid/liquid interface and the transfer of medium components can be neglected2. Let us consider a surface element with the area of nr2 at the liquid/liquid interface. For a system comprised of the particle and the liquid/liquid interface area nr 2, the equilibrium surface free energy G s of all the interfaces involved consists of three terms GSw + GsSo+G~w (the subscripts and superscripts have the same meaning as in Eqs. (4.5) and (4.6))GSwo : 2nrhoos +(4nr 2 -2nrh)crws +n(r 2 -12)Oow. Noting that r 2 -

GSwo =nr

12 =

(r-

h) 2 =

(4.30)

(r c o s 0) 2, one obtains

2('2h L-~-Oos +40ws-(2h/r)Ows +OowCOS201

(4.31)

= nr 2(4Ows + 2CrowcosO-oow cos 2 0). When the particle is completely immersed in the oil phase, then G s = 47tr20-os + ~r2Gow = 7~r2(4~os + Gow),

(4.32)

and when in the water phase GSw =

4nr2Ows + rtr2Cow = n:r2(Oow + 4Cws ).

(4.33)

i The analysis of the equilibrium involving the gravity forces is more cumbersome [2, 45], while the results are qualitatively the same. 2 Expressions for the work of transfer including adsorption and transfer of the medium components were considered in [46].

287 To move the particle from its equilibrium position at water/oil interface into the oil bulk, the work of wetting is spent Wo = G O - G S o = nr2Owo(1 + cOS0ow) z ,

(4.34)

while for the transfer of the particle into the aqueous phase, the work of wetting is required W w = GSw - G S o = nr2Owo(1 - cOS0ow) 2 .

(4.35)

Similarly to Eq. (4.23), the ratio of the quantities given by Eqs. (4.34) and (4.35) gives the expression for the hydrophile-lipophile balance of spherical solid particle [24]:

/

HLRS 1 + cOS0wo o = l_coSOow

/2

.

(4.36)

It was shown in Section 4.2 that this expression is also equal to the ratio of the internal area of the drop covered by the 'film' composed of solid particles to the external area of the drop as given by Eq. (4.10). Equations (4.23), (4.29) and (4.36) were derived assuming equilibrium contact angles. Under practical conditions, the particles of solid emulsifiers are characterised by a contact angle hysteresis. For a meta-stable equilibrium, the advancing or receding angle results depending on the direction in which the wetting perimeter is moved. In this case, the development presented above is, strictly speaking, invalid, because the surface energy cannot depend on the direction of the motion. For this case, the validity of Young's equation is also doubtful [2]. However, it was shown in [47] that when a contact angle hysteresis exists, the work of wetting can be calculated from the integration of an elementary work performed against the holding (flotation) force which acts along the perimeter of the particle, when the particle is moved from the interface into the bulk phase. In the case of spherical particles, the expression for the wetting energy was derived in [48] W = m'20(1 - cos O)2Co,r,

(4.37)

where r is the radius of the spherical surface of the particle, Co,r is the constant which slightly depends on the values of 0 and r.

288 If for both works of wetting, Ww and Wo, Eq. (4.37) is valid with the contact angle hysteresis (0 ~ and 0 TM), where 0 ~ and 0 w are the oil advancing and water receding angles, and the corresponding constants C are equal to each other, then one can use Eq. (4.31) taking into account the wetting hysteresis, that is, the sequence in which the wetting of particles with water and oil takes place, and the values of the corresponding contact angles. For systems which exhibit a wetting hysteresis, the force-determined hydrophile-oleophile ratio can also be introduced, as discussed in [49]:

HLR~ = F ~ '

(4.38)

where Fw =nrOwo(1 +cos0,) is the force corresponding to the particle breakaway into the aqueous phase, F~ = nrOwo(1-cOS0a)is particle breakaway force into the oil phase, 0a is the water advancing angle, 0r is the water receding (oil advancing) angle.

4.4.

Calculation of the hydrophile-lipophile balance for highly disperse solid emulsifiers

In Section 4.3 formulae for the calculation of wetting work and HLR values of the emulsifiers (solid spherical particles prepared as a dispersion of compact macroscopic bodies) were derived. It was assumed that the properties of the surface of the dispersed phases were the same as those of macroscopic bodies, and that the contact angles characteristic for small particles could be measured by a standard technique, using macroscopic samples. However, in many cases, the emulsifier particles, which constitute a highly disperse phase (colloidal or nearly colloidal dispersion) are formed in the course of a chemical reaction or various colloid chemical processes (coagulation, peptisation etc). cannot exist in the same form as a compact solid body. In particular, such emulsifiers are formed in solutions of partially hydrolysed salts of polyvalent ions [50], in the processes of the salting-out of water-soluble surfactants, e.g., sodium stearates or oleates, leading to their transformation into non-soluble polyvalent soaps of complicated non-stoichiometric composition (see, e.g., [51, 52]), and also during the breaking of petroleum emulsions which takes place in many important industrial processes [53, 54]. The method of determination of the work of wetting and HLR values, described in the previous section, is invalid for such systems. To calculate these characteristics for highly disperse

289 particles of emulsifier which form continuous films at the water/oil interface, characterised by low energetic strength of coagulation contacts, a method proposed in [55] is discussed below. During the emulsification process, the particles which exist in the water or oil bulk, adhere to the interface and undergo partial coagulation, with the formation of an interface layer of variable thickness. One side of this layer is wetted by water, while the other is wetted by the organic medium. As the thickness of the layer usually exceeds hundreds of nanometres, the surface energy of either side of the film does not depend on that of the other side, because the intermolecular interaction energy is insignificant. Let us consider a portion of the interfacial 'armouring' layer at the interface of unit area. The surface free energy of this portion is then G s =cwS,h q" O'S,! o '

(4.39)

where ~w o t are the interface energies of the hydrophilic and hydrophobic sides of the S.h and 6S. layer formed by the particles, and the superscripts W and O refer to the aqueous and organic phase sides, respectively. With respect to the relocation of this layer from the interface into the phase bulk we assume that (i) the relocation energy for the layer of particles is much higher than the energy corresponding to the breaking of coagulation contacts of this surface portion with neighbouring particles, and (ii) the transfer energy is determined mainly by the surface energy (considering the energy of adsorption of a surfactant and medium from the particles during the transfer from one phase to the other to be small as compared to the surface energy). Then, for the transfer into the organic phase, the free energy of transfer is G~

o

o

(4.40)

= COW q" O'S,! q- t~S, h ,

while for the transfer into the aqueous phase we have Gw

=O'ow+

crw ~w S,h + s,!

(4.41)

The subscripts S, h and S, 1 refer to the hydrophilic surface of the solid-like film, and to the hydrophobic surface side adjacent to the organic phase. Subtracting Eq. (4.39) from Eqs. (4.40) and (4.41),

one obtains the expression

by the organic phase

for the work of wetting of the

layer

290 Wo

----"

Gs

--

G s "-" (YOW

o _owS,h

"F O S , h

( l + c o s 0 h)

(4.42)

o S,h w = Oow(1 + cos0 I)

(4.43)

"- OOW

and by aqueous phase Ww

=

GSw - - G s

o

= (YOW - - (YS,h +

where the subscripts h and 1 refer to the layer surface adjacent to the aqueous phase and organic medium, respectively. The difference between the energies determined by Eqs. (4.39) and (4.40) characterises the surface hydrophobicity, while the difference between Eqs. (4.39) and (4.41) characterises the hydrophilicity. Therefore, HLR = -W~ = ~176 +COS0h) I+COS0 h =~ . Ww o ow(1 - cos 01) 1 - cos 0 i

(4.44)

This expression is essentially different from that for the HLR of spherical particles: here the two contact angles are involved, and the dependence of the wetting work on the contact angle is linear rather than quadratic. It is seen from Eqs. (4.42) and (4.43) that the calculation of the wetting work and HLR value, require measurements of the contact angles for the wetting of solid-like films surfaces adjacent to the water (hydrophilic side) and oil (hydrophobic side). Direct measurements of the contact angles at the water/oil interface was found to be impossible [55]" pressing water and oil drops into the interfacial film results in an instantaneous coalescence of the drops with the interface, possibly due to the porosity of the gel-like film. Therefore, a method was developed by Kruglyakov et al. [55] for the transfer of the film to a glass substrate, with a subsequent usual measurement of contact angles, see Section 4.5. For small particles (fine powders) the wetting energy can be determined from the adsorption isotherms [41 ]. For the adsorption of vapours of liquid (or gas) at the solid adsorbent, if the state of the adsorbate is different from that of the bulk liquid, the total change of the Gibbs energy is (see for example [56], p.453): AGs = Ao + FAA~tA,

(4.45)

A~A = RTInP/Po,

(4.46)

291 where A~tAis the change of the adsorbate chemical potential, P is the adsorbate vapour pressure (P0 is the value in the initial state), the subscript A refers to the adsorbate. For low adsorption layer coverage -Ao = n = RTFA,

(4.47)

AGS/I"A = RT(InP/Po - 1).

(4.48)

Thus, the change of the chemical potential of the adsorbate contributes mainly to AGs. With increasing adsorption, the contribution of A~tA becomes lower, and when the condensation begins, A~tA= 0 and AGs = Act, similarly to Eqs. (4.20) - (4.22). Using the Gibbs' equation, one can represent the total change of the energy AGs as FA

FA

o

o

aos= IA~t~dr^=

IRTInPdFA, Po

(4.49)

where AGs is the integral variation of the Gibbs energy, and Alag =d(AGS)/dFA is the differential change of the Gibbs energy. Introducing into Eq. (4.23) the expression for AGs corresponding to the adsorption of water and apolar liquid at p = 1 [1 ], one obtains

- A o = ~FAdAI.tA =RT

P/P'--~ P o P/Pi=! P f F A d l n - = R T - PVo o o~ Vdln~0'

(4.50)

where V is the volume of the adsorbed gas per unit mass of the adsorbent [cm3/g], V0 is the molar volume of the gas at normal conditions [cm3/mol], o is the specific surface area of the solid [cm2/g]. It follows then that RT P/p,--IWd Vo co ~V ln(P/Po) w HLRA = o P/P,=I RT ~VOdln(P/p0)O

(4.51)

The integrands can be calculated from the adsorption isotherms. If, instead of the total integral energy of adsorption (before the vapour condensation), only the contribution due to the change

292 of the state of the adsorbate is taken imo account, then it follows from Eqs. (4.23), (4.45) and (4.46) that KWALt~ ALt~ HLR = KOALtO = Kwo ALtO'

(4.52)

where Kw, Ko, Kwo are constants. For this case it is convenient to consider the initial part of the isotherm, where FA = r,PA, so that for PA = P0 we obtain KwA~ A~ HLRA = KoALto = Kwo ALt~ ,

(4.53)

where Kwo = KW/K~ is a normalised (calibration) coefficient, ALtw is the differential work of adsorption for the adsorption layer coverage approaching zero. For Kwo = I one obtains the equation for the HLR value expressed via the works of adsorption of the two vapours at the surface of the studied solid: HLRA = A~ w = ln(P/Po) w A~ ~ ln(P/Po) ~

(4.54)

This expression for the HLR can also be introduced independent of the definition given by Eq. (4.51). The expression (4.54) was used in the experiments performed by Sviridov et al. [57] to determine the HLR values for fine dispersed materials. It is convenient to determine the values of ALtAin Eqs. (4.45) and (4.46) from chromatographic measurements I. In Table 4.1, the HLR values determined from chromatographic measurements and calculated using Eq. (4.44) are summarised as an example. For the calculations a computational algorithm was developed [41].

It is seen from Eqs. (4.45) and (4.46) that in this expression only the short-range interactions of the solid are accounted for, rather than all relevant interactions, and this expression reflects the total change of the adsorbate state, being only explicitly related to the nature of the adsorbent (that is, the solid body for which the HLR value is determined).

293 Table 4.1.

Hydrophile-lipophilebalance of the sorbent [41]

Sorbent processing conditions, temperature

Temperature of measurements,

and preparation time

~

HLR

150

1.11-1.17

170

1.13- 1.17

2. Initial sorbent after the contact with ethyl

150

1.16- 1.20

alcohol vapours during 2 hours, 250~

170

1.16- 1.20

150

'0.95 - 1.01

170

0.92 - 0.98

1. Initial sorigent, 250~

2 hours

5

min 3. Initial sorbent, 320~

2 hours

The data presented in the table were obtained for sorbent fractions between 0.125 and 0.160 mm. The conditions in which the sample was prepared, and the sequence of the measurements are shown in the table. The sorbates used were water and decane. The HLR values correspond to a 95% confidence interval. It is seen from the data that the proposed method for the determination of HLB values is characterised by a high sensitivity and accuracy, enabling one to account for the influence of traces of various surface 'contaminants' and different physico-chemical factors (i.e., the actual temperature) on the surface properties of the highly disperse materials.

4.5.

The dependence of emulsion stability on the work of wetting of emulsifier particles. HLB used as criterion of phase inversion in emulsions stabilised by solid particles

It was shown in Sections 4.1. and 4.3 that the equilibrium position of solid particles at the interface determines both the energy required for the transfer of the particles into the phase bulk and the curvature of the 'armouring' film existing at the surface of emulsion drops. If the particle is hydrophilic (0 < 0 < 90~ then its major part is located in the aqueous phase, which becomes the dispersion medium in the emulsification process. On the contrary, hydrophobic particles (90 ~ < 0 < 180 ~ are capable of a better stabilisation of inverse emulsions. As for the stabilisation of emulsions high energetic barriers should exist which prevent the transition of the particles from the dispersion medium film into the disperse phase, and also the work of transfer into the dispersion medium should be sufficiently high to keep the particles at the

294 interface. Thus, it is clear that the optimum conditions for the stabilisation of emulsions correspond to a contact angle not far from 90 ~ see Fig. 4.8 [58].

Wo Gow

4

! @0 30 1

-

2

-

3

-

Ww

90

120

t50

180

Fig. 4.8. Dependence of the works of -._.._

4-

O-ow

60

--

wetting (Wc/aow, Ww/aow) on contact angle of solid emulsifierparticles.

It is seen from the shape of the dependencies of W A and W B on 0 that one of the corresponding works of wetting in the 0 range 0- 60 ~ is very small, while the other is small in the interval 120 ~ 180 ~. It can be expected therefore that the optimum contact angle intervals are 60 ~ _ 13.5-16 mPa.s). In the experiments, the volume of the samples was 10% of the volume of the model pool; the volumes of aqueous phase, oil and emulsion in the sample was estimated visually, and then the amount of the recovered oil was determined. With the advancement of the microemulsion system along the model pool, the formation of water-oil "waves" in the porous medium was observed. The samples of the "wave" consisted of the emulsion, which being heated to 80~ was separated into water, oil and a microemulsion

1 darcy is the permeability of a material when a differential pressure 101 kPa maintains the volume rate of 1 e.m3/~ t h r n n o h a e u h e o f 1 e m e d g e f a r the vi.~cn~itv o f 1 fl "3 P a . ~

333 phase. In these model studies the oil recovery efficiency was 100%. Similar results were obtained with a number of other compositions. The deficiency of microemulsion technologies proposed for the displacement of oil is the strong dependence of the interfacial tension on the salt concentration in the pool (for compositions based on ionic surfactants) or the temperature (for non-ionic surfactants). Also the whole process is quite expensive. To decrease the sensitivity of the compositions with respect to salt mineralisation and temperature, various compositions were proposed based on a-olephin sulphonates, block-copolymers of ethylene oxide and propylene oxide, mixtures of non-ionic surfactants and ionic surfactants, etc. [ 114-116]. It follows from the analysis of field tests, reported in [117], that the technology is rather complicated, and the costs of the microemulsion displacement process are quite high. Therefore, at the present stage, this technology is considered to be efficient only for the application in the immediate neighbourhood of the production and injection well zone, to increase the pool permeability. This technology could also be efficient and cost-saving in applications related to cleaning of the ground from discharged oil and petroleum containing products at particular areas, e.g. in storage areas and oil pipelines. 5.4. Breakdown of dilute emulsions

The demulsification is one of the most complicated problems in various emulsion technologies (the dehydration of water emulsions in crude oil and black oil, the extraction of cream from milk, the extraction of rubber from latex emulsions, the breakdown of emulsions during the extraction etc). In this regard, emulsions are of special interest when formed by surfactant solutions in washing out processes of various oiled pollutions, or in connection with technologies involving recycled water, and also, in particular, very stable emulsions of lubricating-cooling liquids (LCL). Usual methods employed for the breakdown of diluted emulsions, in particular of LCL, are the addition of the electrolytes (coagulants) and surface active compounds (demulsifiers). This leads to the decrease of the drop charge or the decrease of the ionic atmosphere thickness of a drop, resulting in turn in coalescence and phase separation (chemical methods). Another method consist in creaming of emulsions by gravitation or centrifugal force followed by a

334 removal of the 'cream', and the action of constant or alternating electric fields or heating, especially when the emulsion is stabilised by oxyethylated non-ionic surfactants. The disperse phase of the diluted emulsions could also be separated from the dispersion medium using filtration or flotation at gas bubbles. The deficiency of the methods listed above, especially when the breakdown of LCL with high concentration of hydrophilic surfactants, is the low efficiency of the phase separation, high demand of reagents (for chemical methods), high demand of energy (for electric and thermal methods), and insufficient purification degree of the (aqueous) dispersion medium. It was shown in Sections 2.4, 2.5 and 3.8 that the stability of emulsions depends on the hydrophile-lipophile balance of the surfactant mixture. In particular in the microemulsion phase region (Winsor III), a sharp decrease of stability and phase separations requires a few minutes only. The formation of these phases can take place in the PIT region, or for certain values of HLR = 0.83-0.93. It should be noted also that such microemulsion phases are able to incorporate virtually unlimited amounts of emulsifiers, provided the HLR value of the surfactant mixture lies within the proper range. This property of a microemulsion phase was employed by Kruglyakov and Khaskova [118, 119] to develop a new method for the breakdown of dilute emulsions and, in particular, lubricating-cooling fluids, which results in more efficient and complete phase separations in these emulsions, and does not depend on the composition of the emulsifiers of the destroyed emulsion. This method is implemented as follows. The dilute emulsion to be destroyed is brought into contact with a three-phase system water/micellar phase/oil, which was prepared beforehand by mixing of the emulsion and the three-phase system or pouring out the emulsion from the threephase system. The surface-active compounds suitable for the preparation of the micellar phase are either non-ionic surfactants (like oxyethylated products) or mixtures of hydrophilic ionic and non-ionic surfactants with hydrophobic surfactants (fatty alcohols, acids and amines or ethers of anhydrosorbite or xylite and fatty acids). The three-phase systems were prepared from water solutions of sodium dodecyl sulphate (SDS), cetyl pyridinium chloride (CPC) with addition of pentanol and electrolyte, or from the non-ionic surfactant OP-4 (technical oxyethylated octyl phenol with 5 to 6 EO groups), either with or without additions of electrolyte. To test the efficiency of the method, the breakdown of model emulsions of diesel

335 fuel in water stabilised by OP-7 emulsifier and of lubricating cooling liquids (LCL) Aquol-1 and Ukrinol-4 (5% concentration) was performed. The preparation of a micellar phase from SDS and its breakdown using dilute emulsions can be considered as an example. The three-phase system was prepared by mixing of equal volumes of diesel fuel and aqueous surfactant solution ( S D S - 1 wt%), containing 1.75% NaCI and 11.2% amyl alcohol. The volume of the microemulsion phase for these concentrations was about 10% of the system volume. The surfactant (microemulsion) phase was transparent, and existed in a wide temperature range (20 to 60~ The absorbing ability of a microemulsion phase was estimated from its capability to destroy a certain volume of an emulsion before the destruction of the surfactant phase itself sets in. The emulsion of diesel fuel (disperse phase concentration 5%) or 5% emulsion of Aquol-1 was brought into contact with the three-phase system, mixed for 10 to 15 s, and kept until the separation of the aqueous and organic phases was complete. Mixing of the emulsion is not necessary for its destruction, however, the unmixed emulsion is disintegrates more slowly. The time necessary for phase separation was 10 to 20 min. The microemulsion phase with the composition above is capable of absorbing 20 to 35% of Aquol or Ukrinol emulsions, and up to 15% of the model diesel fuel emulsion, as compared to the initial volume of the microemulsion phase. The compositions and some properties of other microemulsion phases are summarised in Table 5.1. All micellar phases absorb 15 to 30% LCL. The micellar phase 2 absorbs nearly 30% of the model emulsion and phases 3 and 4 are capable to absorb more than 100% of the model emulsion (with respect to the surfactant phase volume). During the absorption of the components of the destroyed emulsions, changes in the composition of the microemulsion phase takes place, and the hydrophile-lipophile balance of the mixture is shifted towards larger values (the composition of the mixture becomes more hydrophilic). To keep the hydrophile-lipophile balance at the previous level, and to maintain the stable threephase state, one can vary the composition of the surfactant phase or the temperature, as necessary. For example, to increase the absorption ability of the microemulsion phases 1 and 2, pentanol can be added to the systems. The addition of 4% of pentanol resulted in a 2 to 2.5 times increase of the absorption ability.

336 Table 5.1. Composition and properties of microemulsion phase Surf-

Initial

Electrolyte

Alcohol

Micro-

Temperature

actant

surfactant

concentration,

concentration,

emulsion

interval

concentration

% mass

% vol

phase

coexistence,

volume,

~

in

aqueous

phase 1 SDS

1

2 CPC

2.4

of

% vol NaCI 1, 75

11.2

10

20

NaCI1 .....

6.6

22

20

25

20-26

34

33-38

J,

30P-4

13.3

caci -1 NaC1-2.9

40P-4

13.3

no electrolyte

It is known that the hydrophile-lipophile balance for non-ionic surfactants depends strongly on the temperature. Therefore, as the breakdown of emulsions progressed, the composition of the three-phase systems can be corrected by a temperature increase. For example, in the system with a microemulsion phase based on OP-4 and containing electrolytes (system 3 in Table 5.1), the temperature increase by 10-12~ leads to a 6 times increase in the absorption ability with respect to Aquol emulsions. To estimate the efficiency of this method with respect to the breakdown of emulsions, additional experiments were performed with LCL using traditional physicochemical techniques: pH variation, temperature increase, addition of coagulants containing salts of multibase acids. The results are presented in Table 5.2. It is seen that the advantages of this method as compared with the traditional demulsification processes are its universality with respect to different emulsions, high emulsion separation rate, and the high degree of the removal of oils from the aqueous phase. The implementation of this method requires constant monitoring of the state of the microemulsion (third) phase and the correction of the composition of the phase when it is used over a long period of time. Therefore, to facilitate the observation, monitoring and the correction of the microemulsion phase state, it is most convenient to use this phase as part of a three-phase system, where this phase is in equilibrium with water and oil. This method is

337 especially convenient and efficient when the aqueous phase of the three-phase system can be recycled, and the organic phase can be utilised as fuel, or used for subsequent regeneration. Table 5.2. Demulsificationefficiencyprovided by various methods Type of destroyed emulsion ' Aqu01

pH of the solution 18.5 8.5 4 - 4.5 8.5

Temperature, ~ 120 100 65 45 20 20

Demulsifier

Separation time

Oil residual in aqueous phase, % i none i 2 months '100 none 15 minute's 50 none 10-15 minutes 20 A12(SO4)3,180 mg/1 10 minutes 15-20 Micellar phases based on 10 minutes none SDS and CPC i Micellar phase based on 10 minutes none OP-4 with the addition of electrolytes; Emulsion: micellar phase ratio 3:7 ' Micellar phase based o n ' 10 minutes none OP-4 without any addition of electrolytes; Emulsion: micellar phase ratio 3:7 none 2 months 100 none 10 minutes 90 none 15 minutes 90 none 10-15 minutes 50 none 10 minutes 30 A12(SO4) 3, 180 mg/l 10 minutes 20 Micellar phases based on 10 minutes none SDS and CPC; Emulsion: micellar phase ratio 1.5:8.5 Micellar Iphase based on ' 10 minutes none OP-4 with the addition of electrolytes; Emulsion: micellar phase ratio 3:7 Micellar phase based on 10 minutes none OP-4 without any addition of electrolytes; Emulsion: micellar phase ratio 3:7 i

i Ukrinol !

i Ukrinol

. 8.2 8.0 3.0 3.0 2.5 5.0 8.2

.

.

. 20 100 20 75 75 80 20

i

!

i

i

i

!

] Ukrinol

' 20

i

I Ukrin01

' 36

338 5.5

Hydrophile-lipophile balance and foaming properties of microemulsions

It was already mentioned in Section 2.5 that the volume and stability of foams prepared from direct (aqueous) microemulsions depend essentially on the hydrophile-lipophile balance of the surfactant mixture and on the volume of the solubilised oil in the aqueous phase. In [120-123] the foam stability was studied with respect to variations in the hydrophilicity degree of the surfaetant mixture, the addition of lower alcohols to micellar surfactants, the degree of oxyethylation of non-ionic surfactants, the addition of electrolytes or the temperature. These factors were varied as they usually lead to a decrease of the foam stability [74]. Therefore, it can be argued that the study of microemulsions prepared from solutions of micelle-forming surfactants of various types, and the study of the dependence of foam-forming properties of these emulsions on the type and concentration of the surfactant, and on the amount of solubilised or emulsified oil, and the study of the properties of foam films prepared from these emulsions is more important. These studies would contribute not only to the understanding of the foam stabilisation or destabilisation mechanism, but give also insight into the structure and properties of microemulsions. The preparation of aqueous microemulsion systems of this type, and the studies of foam stability and properties of foam films prepared from these microemulsions were summarised in [12, 124, 125]. To prepare aqueous (direct) microemulsion systems possessing a large solubilisatien capacity, three mixtures of water-soluble and oil-soluble micelle forming surfactants were used: (1) technical sodium alkyl sulphate (Volgonate) and monoether of oleic acid with triethanol amine (Emulfor-FM); (2)mixtures of oxyethylated octyl phenols OP-10 and OP-7 with Alphapol-4; and (3)Tween-80 (polyoxy ethylene sorbitane oleate, mean number of oxyethylene groups 20, HLB - 15) and Span-I 0 (sorbitane monooleate, HLB = 4.3.) To characterise the hydrophile-lipophile balance of the surfactant mixture, the average HLB number (for Span-10 and Tween-80 mixture), the average EO group number (for OP-10, OP-7 and Alphapol-4 mixtures), and the volume ratio of the components (for mixture Volgonate with Emulfor-FM) were used as parameters. The ratio of surfactant required for the aqueous solution with a large solubilisation ability was obtained by titration (addition) of the hydrophobic component to aqueous solution of the

339 hydrophilic surfactant, and subsequent extensive mixing by shaking until a transparent system was formed at 21~

The maximum solubilisation of oil was determined in a similar way.

In the first system (unimolar solution: NaC1/kerosene fraction hydrocarbons/mixture of OP-10 and Alphapol-4 with concentrations of 20 to 30 vol%) a transparent aqueous solutions with a large solubilisation ability (up to 21%) was formed only when the ratio of the hydrophilic (OP-10) to the hydrophobic component (Alphapol-4) corresponds to the mean apparent number of EO groups I of 7.8 - 8. If the number of EO groups is lower than 7.6, then a three-phase microemulsion system of Winsor-III type is formed. In this case the maximum solubilisation for nEo = 7.5 was 25.8% with respect to the solution volume. The second system contained a mixture of Span-80 and Tween-80 in various proportions, with a total concentration of 20%, 1 mol/l NaCI and the organic phase (n-octane or kerosene fraction hydrocarbons). In this system, transparent aqueous emulsions existed in a narrow range of HLB numbers depending on the type of the hydrocarbon phase, and the formation of these emulsions required initial heating of the system up to 70 - 80~ emulsion) followed by cooling down to 21~

(to destroy the direct

Transparent microemulsions with n-octane

(solubilisation of 12 to 25% with respect to the solution volume) could be prepared in the interval of HLB values between 12.5 and 12.9. The maximum solubilisation (25%) was observed for HLB = 12.8. The surface tension of this composition was 29.4__.0.5 mN/m, while the viscosity of the solution was 33 to 33.5 mPa-s. Transparent microemulsions with kerosene fraction hydrocarbons were prepared for HLB = 11.7 - 12.8, while the maximum solubilisation was observed at HLB = 11.7. The third system was prepared from the mixture of the anionic suffactant Volgonate and the oil-soluble surfactant Emulfor-FM, which is a typical stabiliser for inverse emulsions. The total concentration of the surfactant mixture was 30 vol%. For a Volgonat to Emulfor ratio of 1 93, a three-phase system water-oil-microemulsion phase of Winsor III type was obtained, which contained up to 50% of oil (kerosene). Transparent aqueous solutions with large solubilisation ability were prepared with a Volgonat to Emulfor ratio not less than 2 93. This ratio was just

The mean apparent number was determined from the assumption that the number of EO groups for Alphapol-4 and OP-10 is 4 and 10, respectively, however, the real number of EO groups for OP-10 exceeds 10, see [12, 124].

340 that corresponding to the maximum solubilisation, equal to 27% of kerosene with respect to the solution volume. The surface tension of the solution with the above composition was 29.5+0.5 mN/m, with a viscosity of 34 to 34.5 mPa.s. The foam was produced by blowing air through a porous plate into the vessel containing the microemulsion. The experimental device was described in detail recently [74, 126, 127]. The foam prepared in such a way was transferred into the collecting vessel and the collapse of the foam in the gravitational field was studied for a foam layer height of 3 cm, or alternatively 2 cm when a pressure drop in the foam was created using the FPDT method [74] with Ap --- 5.102 Pa and 1.103 Pa. Figure 5.2 illustrates the dependence of the foam lifetime for the collapse in the gravitational field on the oil contents for a mean EO group number of 7.8. It is seen that the foam lifetime decreases significantly with the increase of the amount of the solubilised oil. When no oil was present, the lifetime was 48 hours, while for an oil concentration of 20% this lifetime was only 3 min.

100 "C- I0

I

}0

Fig. 5.2

15

!

20

Dependence of foam lifetime on the oil content.

The dependence of the foam stability on the HLB value (in terms of mean EO group number) in heterogeneous (turbid) systems without oil (nEo > 8) as compared to transparent microemulsions (nzo < 8) is presented in Fig. 5.3. In the heterogeneous systems containing no oil the dependence of the stability on the hydrophile-lipophile balance is weak and only a slight maximum was observed for the mean EO group number 8.2. When oil was solubilised, the stability exhibited more pronounced variations: the lifetime decreased from tens of hours to 1 - 1.5 hours. The results obtained for the foam stability in the microemulsion systems prepared from a mixture of Span-80 and

341 Tween-80 with different contents of n-octane for the mean HLB-number 12.8 of the mixture (corresponding to a maximum solubilisation) are shown in Fig. 5.4.

1000 "~ 100

2

"7I0 I 0.I

t

7

8

9

/'/E0 Fig. 5.3

Dependence of foam stability on the OE groups number.

10

.-?.6

5

15

25

Cd Fig. 5.4

Dependence of foam stability on the amount of octane present in the microemulsion system consisting of the Span-80 and Tween-80 mixture; 1 - foam collapse under gravity, 2 - foam collapse at Ap= 1 kPa.

The systems with an oil contents lower than 10% or higher than 30% were turbid (emulsions), for the oil contents of 15% the preparations were slightly opalescent, and for the oil contents of 2 0 - 25% the systems were transparent. In contrast to the first system, the maximum stability was observed when the octane contents was 25%. This system also exhibits a maximum viscosity. In the third system, similarly to the first two ones, the foam stability depends on the hydrophile-lipophile balance of the mixture, and also on the oil contents and the state of the

342 system (heterogeneous

vs

homogeneous) which in turn depends on the hydrophile-lipophile

balance and the concentration of the oil. For a HLB which corresponds to the Volgonat : Emulfor ratio of 2 : 3, a significant decrease of the lifetime was observed with increasing oil contents (15 days for systems containing no kerosene as compared with 5 days for 5% oil and a few hours for an oil contents of 27%). It should be kept in mind, however, that only the latter system was a transparent microemulsion, while the other compositions were heterogeneous. Similar dependencies of stability on oil concentration was also observed in experiments where a pressure difference of 103 Pa was imposed to the liquid phase of a foam column.

Detailed studies of the dependence of foam stability and the kinetics of equilibration on the liquid phase pressure in a foam were performed with transparent microemulsion at maximum solubilisation. In Table 5.3 below the times are presented necessary for the destruction of local foam layers of 2 cm thickness at various heights H measured from the solution level. Further increase of the foam height did not affect the time necessary for the destruction of a 2 cm high foam column, which was about 16 min. Table 5.3. Lifetimesof 2 cm thick local foam layers at various levels from the solution surface Level height H, cm

0-2

2-4

4-6

6-8

Foam layer lifetime Xp, min

45

18

17

16

On the other hand, the application of a small pressure difference (AP=102 Pa) on the liquid phase of the foam results in a strong decrease of the lifetime with increasing pressure difference, while for AP > 103 Pa this lifetime remains virtually constant. In particular, for AP = 103 Pa the lifetime Xp= 15• min. Pressure measurements in the Plateau-Gibbs borders have shown that, irrespective of the method used for the pressure decrease (either by increase of the height for the foam layer in the gravitational field, or by the creation of a pressure difference up to 6" 103 Pa using the porous plate), and irrespective of the initial foam dispersity and layer height, the maximum decrease of pressure in the liquid phase of the foam did not exceeded 600 - 700 Pa. For pressure

343 differences lower than 600 Pa, the corresponding excess equilibrium pressure was established during 2 - 3 minutes, and further increase of the pressure difference had no effect on both the excess pressure and the capillary pressure. The capillary pressure and corresponding disjoining pressure at equilibrium can be calculated from the relationship

Po

=-2G G=PM+~, r Rv

(5.1)

where PM is the liquid phase pressure measured with the micro-manometer, r is the PlateauGibbs border curvature radius, Rv is the mean foam bubble radius (with respect to the volume), and o is the surface tension. Therefore, in these experiments at Rv = 2.5.10 -2 cm the maximum capillary pressure was 850 - 950 Pa. The fact that a further increase of the capillary pressure was impossible can be readily explained by the intensive internal foam collapse caused by the coalescence accompanied with the release of excess liquid [74]. To understand the foam syneresis process in more detail, and to determine the maximum (threshold) disjoining pressure in these systems, the kinetics of thinning and the equilibrium state of the foam films were studied in [124, 125]. Microscopic foam films were prepared in a glass cell with a capillary of constant cross-section, where the films could be formed at low constant capillary pressure Pa = 30 Pa, and in a device equipped by a porous plate, which enabled to vary the capillary pressure up to 105 Pa, thus to study the disjoining pressure isotherms Yl(h) in a wide range of thickness (h) and pressure [ 128, 74]. The optical apparatus for these measurements was described in detail in [ 129]. Curve 1 in Fig. 5.5 shows the generalised isotherm Po(h) for foam films prepared from a 2" 3 Volgonate : Emulfor mixture. Each point of the Pa(h) isotherm represents a value averaged over 20 - 25 measurements, performed in an ordinary cell for Pa = const and in a cell with a porous plate. The first 6 points of the Pa(h) isotherm in the thickness range between 86 nm and 36 nm were measured at Pa = 30 Pa and a film radius of 2.10 -2 cm. Thick films become gradually thinner during approximately 16 min, when the first (meta-stable) thickness of 86.1 nm is attained. (Films prepared from aqueous solutions of surfactant without oil, for example, from a

344 3.5.10 "3 mol/1 SDS solution attain at the same film radius the equilibrium thickness of 50 nm during thinning after 2 - 3 minutes.) In the following 4 - 5 minutes, the transition to the subsequent equilibrium thickness 76 nm was observed: first black spots were formed, followed by their growth until a uniform black film appeared.

6 9

=

=

:

:

:

b

4

1 J

0 0

20

t

40

60 I I

80

I' '

i'00

h, nm

Fig. 5.5 Po vs. h isotherm for foam films stabilised by a mixture of Volgonate and Emulfor-FM.

While the initial conditions of different runs of the thick film formation were the same, the initial equilibrium thicknesses were different (between 86 and 57 nm), which means that in some experimental runs several meta-stable states did not exist. The lowest thickness measured at Po = 30 Pa was 36 nm. No further thinning with the formation of films of lower thickness was observed even for long waiting times (4 - 8 hours). Further points at the isotherm were measured using a cell equipped by a porous plate G-2 or G-3. It is seen from Fig. 5.5 that at a pressure of 2.103 Pa films of 36 nm thickness are formed. This thickness is equal to that of the final film formed at Po = 30 Pa. Then the thinning of the film follows down to the thickness of 30.9 nm. Subsequent low increase in pressure up to 2.2.103 Pa leads to three spontaneous transitions to thinner films of 24.3, 18.9 and 10.3 nm thickness. This last value remains unchanged up to a pressure of 4.5.103 Pa, when one more transition takes place, resulting in the formation of a 4.6 nm thick film, which is approximately equal to the thickness of two surfactant monolayers. Subsequent increase of pressure does not affect the film thickness, and finally at Pa = 10 kPa the film ruptured. The behaviour of the latter film suggests that in fact it represents a Newton (bilayer) film.

345 The results illustrated by curve 2 in Fig. 5.5 were obtained in experiments performed at Pa = 5" 103 Pa, which exceeds the pressure of the transition to a bilayer film as represented by curve 1. It is seen from curve 2 that at Pa = 5"103 Pa the film exhibits a typical stepwise spontaneous thinning, until the bilayer equilibrium film is formed. To summarise, in various experiments with films prepared from Volgonate and Emulfor mixtures, up to 12 different meta-stable states were observed. The smallest difference between adjacent thicknesses Ah in some experiments was 4.5 - 5 nm, while the largest difference was 10 - 11 nm, which is the double of the bilayer film thickness. It should be noted that the sharp decrease of the capillary pressure during thinning experiments does not result in any change of the film thickness, therefore, the forced stratification caused by imposed pressure is irreversible. Similar Pa(h) isotherms were obtained for foam films prepared from mixed Tween-80 and Span-80 mixtures. Here a stratification was also observed with the formation of 14 meta-stable states and a final thickness of 5.6 nm, i.e., a bilayer black film was formed. The thickness of this film remains unchanged until Pa = 2" 103 Pa, when the film ruptured. Thus, the final state of this system is again the formation of a Newton (bilayer) film which comains almost no organic phase (the solubiliser). This obviously means that the drops (or other structures) of the microemulsion were either removed from the Newton film or destroyed during the foam film thinning process. The stratification phenomenon in foam films prepared from sodium oleate aqueous solutions has been described by Johonnot [130] and Perrin [131] almost one hundred years ago, and subsequently observed and studied by a number of authors. It appears not only in foam films prepared from aqueous solutions of various surfactants [132-136], but also in hydrocarbon [137] and aqueous [138, 139] emulsion films. In spite of extensive studies performed with stratified films, a comprehensive quantitative description of this phenomenon is still missing. The layer-by-layer thinning is related to the layered ordering of molecules or micelles inside the film. During drainage these ordered layers of molecules, micelles or microemulsion droplets flow out towards the meniscus which surrounds the film, while the film thickness decreases stepwise until the final state is attained.

346 Two types of theories which explain the oscillation of Gibbs' energy were developed up to now. The first is based on the concept of the formation of bilayers of amphiphilic molecules in the film [135, 136, 140], while the second assumes the existence of cubic lattice of ordered micelles [140-143]. A detailed discussion of the stratification phenomena exceeds the scope of the book. The review of Langevin and Sonin [140] reveals the contemporary state of the problem and considers the stratification in films prepared from micellar solutions and in the films formed by micellar surfactant phases. It should be noted however, that the periodicity of the observed thinning, the step of which can be estimated by combining twice the length of an amphiphilic molecule (incorporating the solubilised oil) and the radius of microemulsion drops does not differentiate between both possible structures. To reveal the type of the structures formed, additional studies should be performed which would determine the packing parameters in the microemulsion systems considered. In this publication, the analysis of the results provided by studies of stratifying films and foams prepared form microemulsions is confined to the consideration of specific features of these systems and the comparison of the stability of foams and foam films. The stratification of foam films from micellar solutions of surfactant mixtures containing a large quantity of solubilised oil was first studied in [124-126]. Here stratification phenomena were observed for the same films at various regimes: a spontaneous process at low constant capillary pressure, a spontaneous process at increasing capillary pressure, and a forced thinning at increasing capillary pressure. The important question in this regard is the cause of the stabilisation: whether the foams are thermodynamically stable, or the stabilisation is kinetically supported. It follows from the analysis of the thinning kinetics data obtained using the two methods above (for constant or varied capillary pressure), that only Newton black films attain the thermodynamic equilibrium, with Pa = rI. Other films exist in a meta-stable state, although their thickness remains constant during quite a long time (an hour or a day). Similar to bilayer films, these films are probably stabilised by the disjoining pressure, however for these films it cannot be claimed that at these points in the Po(h) isotherm H equals Po. Therefore, the curves in Fig. 5.5 are plotted in the Po vs h coordinates, rather than II

v s h.

347 The physical origin of the disjoining pressure in the films studied cannot as yet be interpreted satisfactorily. The most possible situation could be that the equilibrium state and the stability of these films are determined by the Van der Waals (negative) component and the positive oscillatory structural

component of the disjoining pressure

[143].

The quantitative

interpretation of the rI(h)-isotherms for such complicated systems, as films containing significant quantities of solubilised oil are, is hardly possible in the framework of the existing theories [140-143] before detailed studies and a comparison of micellar structures in microemulsions and foam films is made. It was mentioned above that model films prepared from Volgonate and Emulfor-FM mixtures rupture at P,, = 10 kPa. At the same time, the capillary pressure in the foam Plateau-Gibbs borders does not exceed 0.85 - 0.95 kPa. Therefore, the question arises, why the destruction of a foam takes place at a pressure significantly smaller than that characteristic for model films? At least two reasons of this phenomenon could be proposed. First, films with a dimension larger than the dimension of single foam film always exist in a foam, and it is well known [74] that the larger the film, the higher is the probability of its rupture. Another important reason is the so-called 'collective effect' occurring in foams, when the breakdown of one film leads to the rupture of its neighbours [74, 126, 144]. It was shown recently by Kruglyakov and Khaskova [145] that the collective effect becomes noticeable even in foams formed by only two bubble layers (foam bilayers), and this effect depends significantly on the properties of the adsorbed layers. For example, this effect is extremely pronounced in foams prepared from nonionic surfactants (OP-4, OP-7, etc.), while in protein foams (with lysozyme as the foaming agent) this effect is almost absent. It should be finally noted that the data presented above suggest that the stratification of foam films prepared from direct microemulsions leads to the 'kinetic' increase of the film lifetime, because, due to the increased viscosity and the disjoining pressure barriers overcome for each meta-stable state, the thinning process becomes slower. On the other hand, the presence of solubilised oil and the structures arising in microemulsions, results in a significant decrease of the maximum (breaking) pressure of the film, as compared with films prepared from pure surfactants of the similar classes (containing no oil), and the decrease of the film and foam lifetime with respect to the destruction trader the imposed pressure difference. In particular, the films and foams prepared from SDS solutions could exist for a long time at pressures above

348 100 kPa. In foams, even for low column heights (a few centimetres), the capillary pressure is sufficient for achieve each meta-stable state of the film (including the bilayer films), therefore, the stability and other properties of the foam studied depend mainly on the properties of the bilayer films.

5.6

Hydrophile-lipophile balance and selection of reagents in the processes of surface (foam) separation of dissolved substances, colloid particles and oil drops

The methods based on either natural or artificially created ability of substance, existing in an ionic/molecular form and possessing a colloidal degree of dispersity to be transferred to the liquid/gas interface, are considered to be the most promising mechanisms for the separation and concentrating of components in dilute solutions, emulsions, suspensions and sols [74, 146149]. There is a great variety of methods of surface separation of substances. For instance, the efficiency of surface concentrating (accumulation ratio, extraction degree and minimum concentrations) of surface active substances in a foam is determined by their adsorption ability and stability, and also by other properties of the formed foam [74, 149]. To extract many other substances (present as ions, sols, drops), one should introduce special agents, the so-called collectors, which are usually surfactants. The choice of collectors possessing an optimum length of the hydrocarbon chain in each particular case is an empirical procedure, where the function to be performed by the surfactant in the flotation process (e.g., deposition due to chemical reaction, coagulation, precipitation of the sediment, ere). should be accounted for. The features characteristic to various types of flotation (ion-exchange, sedimental, etc.) were extensively studied by Sviridov et al. [150-152]. It was shown that in many cases the efficiency of the surface accumulation ability of collecting agents could be characterised by the hydrophilic-oleophilic ratio of the surfactant, determined from the work of micelle formation (HLRM), see Section 3.7.5. To study the relations between the HLRM and surface accumulation ability of a surfactant, experiments on Cu(II) and Co(II) ions extraction were performed. The concentration of chloride solutions of the metals was 1.6.10 .4 mol/l, and the concentration of the collecting agents was 3.2.10 -4 mol/l. The collectors used were anionic surfactants, such as sodium alkyl carbonates and alkyl sulphates, and sodium oleate. The pH value of the solutions was kept at the level which ensured the existence of multinuclear complexes Me(OH) + and Me(OH)2; for

349 Cu the corresponding pH was 7 to 9, and for Co this value was 10. Some of the results illustrating the flotation extraction efficiency for Cu and Co are shown in Fig. 5.6. It is seen that the best values of the extraction efficiency (a) and accumulation ratio (~,) using alkyl carbonates and alkyl sulphates correspond to values of HLRM = 1 . 0 - 1.2 (for alkyl carbonates the carbon atom number in the chain is 11 to 13, while for the sulphates the number of CHz groups is 18 to 20). The decrease in the efficiency with the increase in the hydrophilicity as compared to the optimum value was ascribed in [151] to the increase in the solubility of the complexes formed by metal ions with the surfactants, while the decrease in the efficiency with the increase in the hydrophobicity was explained by the reorientation of molecules and stabilisation of the disperse system.

a) "t

b) '/

a, %

tI, %

150

IO0

150

100

90

60

90

60

30

20

30

20

o.4 Fig. 5.6

1

~ .....

o.s

1.2

HLR m

1.0

' 2.0

' 3.0

HLR m

Dependenceof the degree of flotation recovery ct (solid lines) and accumulation ratio y (dotted lines) for copper (1) and cobalt (2) ions on the HLRM of sodium alkyl carbonates (a) and sodium alkyl sulphates (b).

Similar studies were also performed for the flotation of emulsion drops by cationic surfactants [153]. In the experiments, aqueous emulsions of absorber oils (mixtures of aromatic hydrocarbons) were used with concentrations of 0.010-0.015%. The dimensions of drops were 2.5 to 5 pm. The electrokinetic potential of particles at pH 10.2 to 10.5 was 54 mV. The flotation was performed by the air blow through the emulsion with a rate of 540 cm3/min during 15 minutes. The concentration of surface-active additions was varied from 1 to 20 mg/1. It was shown that the best results in the flotation extraction of oil (with an extraction efficiency of above 90%) were achieved when a surfactant with HLRM = 1.1 - 3.2 was used. For the salts

350 of quaternary bases this corresponds to homologues with 11 to 16 carbon atoms in the alkyl chain, while for salts of primary and secondary aliphatic amines the optimum number of carbon atoms in the homologues was 8 - 11 and 8 - 12, respectively. The effect produced by cationic surfactants on emulsions is determined by the variations of the absolute value and charge sign of the drops, and by the variation in the stabilising ability of the surfactant with respect to the asymmetric air-water-oil films. With respect to other actions of collecting agents, surfactants with other HLRM values were found to be efficient. A number of specific features determined by the effect produced by other factors (concentration of impurities, electrolytes, alcohols, and temperature) which can be explained from the HLRM concept, was discussed in the following original publications [151-153].

5.7. Hydrophile-lipophile balance and sanitary-technical characteristics of surfactants The quality parameters of drinking water and water from surface reservoirs are determined from the influence of chemical substances on the organoleptic properties (taste, colour, odour, transparency, foam and film formation, etc.), from the toxicological estimate of the influence on the organism and from the influence on the sanitary regime of the reservoir (the contents of micro organisms, dynamics of the variation of biologic demand of oxygen, nitrification processes etc.) [ 154, 155]. One of the most common principles of sanitary standardisation is the threshold concept, which assumes the transition from one qualitative state of the biologic system to another when a certain (critical) concentration (dose) of the irritant is achieved. Surfactants, in a sense, can be thought of as convenient test objects for the threshold concept, because of their ability to vary a number of properties (e.g., surface tension, CMC, black spot formation concentration in films etc.) when present in water. Such properties vary jump-like, when the transition to a new state takes place. The dependence of toxic properties of surfactants on the clouding temperature and HLB numbers was studied by Bocharov [156], based on the following considerations. Surfactants, such as tertiary ammonium salts, are characterised by rather low toxicity for haematothermal animals. The lethal dose (LD50) of most anionic surfactants, including fatty amines and acids,

351 which corresponds to the death of 50% experimental animals, when administered intragastrically (typically white rats) is usually equal to 3-6 g/kg (sometimes up to 10 g/kg). The values of LDs0 expressed in moles per kilogram for most anionic surfactants (alkyl sulphates, alkyl phosphates, mono- and dialkyl sulphosuccinates, alkyl sulphoethoxylates, alkyl etoxy carboxylates, alkyl benzene sulphonates, olephine sulphonates) or non-ionic surfactants (primary, secondary and tertiary amines, oxyethylated alcohols and alkyl phenols) are 6 • 1.5 mmol/kg. It was considered by Bocharov as an evidence of non-specific interaction of these surfactants with the fermentation system and of similar mechanisms of the toxic action of all these surfactants when present in the gastroenteric tract. The experimental dependence of the fraction of dead animals in the 'acute' experiments on the surfactant dose for oxyethylated iso-nonyl phenols with nEO = 4, 6, 8, 10, 12, 14 and 16 was obtained in [156] as an S-like curve of type 2 [157]. Based on these experiments, the dependencies of LDs0 and minimum non-acting dose Cmie(according to the recommendation given in [ 158]) on the cloud point temperature and HLB numbers of surfactants: LDs0 = 1.88.104exp(3.54tr/tep)

(5.2)

LDs0 = 1.3.10 "lexp(-0.24.HLB)

(5.2a)

Cmie =

(5.3)

1.73.10 Sexp(-0.25.HLB)

where tr is the rectal temperature of experimental animals (38~

and tcp is the cloud point

temperature. It was argued in [156] that the dependencies (5.2)- (5.3) imply that the toxicity of a surfactant (used for the administration method) is determined by the energetic (adsorption) characteristics of the surfactant, its HLB value and characteristic points in the phase diagram (cloud temperature or Kraft point) rather than the chemical nature of the substance. Comparing the functions which characterise the stimulation level of the organism receptors on the stimulation intensity and sensitivity threshold on the one hand side, with the surface tension dependency on the solution composition in the bulk and at the surface (Prigogine- Defay equations [159]) on the other hand, the similarity of the mathematical forms of these dependencies leads to the conclusion that the threshold concentrations of surfactants in water

352 can be determines from the a(C) isotherms instead of organoleptic methods (which employs taste, colour, odour etc.). In [156] the CMC value and the bulk concentration for a saturated adsorption layer were used as critical (threshold) concentrations. The analysis of biodegradation processes in these systems with active sludge in a stationary regime of an aerotank, under the conditions for reactants in a flow

Cinpu t = const, and dC~

= 0,

(5.4)

dx leads to the conclusion that biodegradation is controlled by diffusion, and can be described by a first-order equation with respect to the amount of limiting reactant (surface active substance). It was shown that the rate constant Kic, in the unstable equilibrium state with respect to the surfactant biodegradation on the non-adapted active sludge, for single discharges of surfactants into the system is expressed by the equation Kir = 1.82 exp(-0.26.HLB).

(5.5)

Comparing this dependence with Eqs. (5.2) and (5.3) it was concluded in [156] that the processes in the animal organism for an intragastrical administration of surfactants in acute experiments are similar to the biodegradation processes in the aerotank with non-adapted active sludge. The concept based on the determination of the surfactant threshold concentrations in a water basin from the concentration at adsorption layer saturation instead of organoleptic toxicity indicators seems to be very attractive. However, the dependencies of LDs0 and Cm on HLB numbers are by no means general. Moreover, in this case it seems more reliable and convenient to look for relations with other phenomena, such as the adsorption characteristics of surfactants irrespective of the surfactant hydrophile-lipophile balance, because the correlations between the balance and the values of LDs0, x and Kie could possibly be accidental, and therefore should be studied more thoroughly. An example of the importance of physico-chemical parameters for medical research and practice has been given very recently in the book on "Surface Tensiometry in Medicine" [185]. It is shown how dynamic surface tensions of human liquids, such as serum and urine, provide information for a definite evaluation of the state of various

353 diseases and allow a monitoring of medical treatments. It is shown in addition that the surface rheology of these liquids can give extra insight into particular processes going on in the human body under certain circumstances. Another example of successful application of surface science phenomena to medicine was discussed in detail in [74], Chapter 11.

5.8

Hydrophile-lipophile balance and protein structure

Proteins are the most important biologic components. Surface and biologic properties of proteins are determined by their spatial structure. The variety of protein molecules can be divided into two main groups. The first group is comprised of molecules formed of long fibres (fibrilles); an example is collagen. The second group, called globular proteins, are molecules folded in spherical structures. These proteins are represented by ferments, hormones, antibodies, etc. In aqueous solution, globular protein molecules exist as compact particles. The topography of their surface is characterised by asymmetric localisations of hydrophilic and hydrophobic groups. It is the structure and topography of the surface of the globules which is responsible for the amphiphilicity and surface activity of proteins. Protein molecules can be thought of as possessing four levels of organisation, called primary, secondary, tertiary and quaternary structure, cf. e.g., [160, 161]. They are formed by long amino acid chains, tied together by peptide links. The polypeptide chain of a protein could be thought of as a co-polymer, in which the repeating entity (-CH - C(O) - HN-)n

I R contains various side groups R. The total number of various amino acids which can enter the protein structure is 20. To characterise the primary structure of a protein, the sequence of amino acids in the chain has to be specified. The polypeptide chains are bent or folded in a certain way, forming linear (secondary) structures. Examples of linear structures are helices (a-structure) and folded leaves (]3-structure). The formation of a- and [3-structures is due to the hydrogen bonding between the amino acids in the polypeptide chains.

354 In different protein molecules, the ratios between a-structures, 13-structures and irregular polypeptide chain structures are different. For example, in myoglobine the fraction of a-structures is 75%, in hen egg lysozyme it is 45%, while in chemotrypsine this fraction is only 8%. The 13-structures prevail in fibrous proteins (e.g., in silk fibroine), while in globular proteins 13-conformations in the polypeptide chains are rather unusual [162]. The number of amino acid residuals in linear structure usually does not exceed 10 (not more that 1.5 nm in length). The polypeptide chain of globular protein, being folded, forms several consecutive compact entities, so-called domains, which comprise 100 to 150 amino acid residuals. The spatial arrangement of the polypeptide chain and the localisation of its helical and linear parts determines the tertiary structure of the protein. The formation of this tertiary structure is essentially governed by chemical bonding, e.g., disulphide bridges, salt bridges (the interaction between acid groups and basic functional groups) and ordinary ionic interactions. In fibrillous proteins (collagen, silk, elastine) built of straight chains which are folded in helices but not convoluted around a common axis, the tertiary structure is well-defined. The structure of globular proteins is more complex, and therefore more difficult to be studied. In the stabilisation of the spatial structure of proteins, in addition to hydrogen and other types of bonding, hydrophobic interactions play an important role. These hydrophobic interactions promote the formation of the protein molecule conformations for which a number of non-polar side chains are 'hidden' inside the hydrophobic regions, and are unable to contact directly with water molecules. Some proteins possess the next level of structural organisation, the quaternary structure, determined by the number of protein molecules which form multimeric (super-protein) structure. An example here is the haemoglobin comprised of four protein macromolecules [186]. It was mentioned by Darncell and Klotz [163] that 537 proteins characterised by a quaternary structure were known in 1975. This quaternary structure is formed due to various types of interaction: covalent bonding, ionic and hydrophobic interactions. Changes in the tertiary and quaternary protein structure control the fermentative activity of the ferment proteins. With respect to the incorporation of oxygen into haemoglobin these structural changes were intensively studied in [ 164].

355 Various methods were proposed to establish quantitative relations between the degree of hydrophobicity of a protein molecule and its composition or structure [ 161, 165, 166]. It was supposed by Waugh [167] for example, that the protein structure is determined by the percentage of non-polar residues (the NPS parameter). Another parameter, the polarity factor p, was defined by Fischer [168] as the ratio of the volume of the polar part to the non-polar part of the globule. This parameter was shown to exhibit pronounced correlation with the protein structure: protein molecules with a volume ratio exceeding 1 can easily form multimeric molecules. For example, the value p-l= 1.12 for bovine haemoglobin and p.l= 1.1 for bovine liver catalase, thus these proteins exist in a multimeric form. On the contrary, p-l= 0.116 for klupein, p-l= 0.87 for bovine mioglobin, p-l= 0.62 for pancreatic ribonuclease, so that the quaternary structure of these protein is monomeric. The hydrophobicity scale proposed by Tanford [166] is based on the distribution constant of aminoacids between water and ethanol, while in the scale introduced by Hanch [165] the distribution between water and octanol was used. The values of Gibbs' energy change corresponding to the transfer of side chains of various proteins from the aqueous phase to an ethanol phase are reproduced from [ 166] in Table 5.4. Table 5.4. Hydrophobicityof side chains Side chain

A~t0, J/mol

Triptophane

812

Phenyl alanyne

597

Thyrosine

549

Leucine

430

Valine

358

Methyonine

310

Alanyne

119

These values of A~t~ are essentially lower than those characteristic to the transfer of pure hydrocarbons. For example, the transfer of the (CH2)3-CH3 group, as calculated from the distribution of glycine and neurolycine, yields a value of 621 J/mol, while in alkanes the transfer of the same group requires A~~

1.135 kJ/mol. This disagreement can be ascribed

356 both to the nature of the solvent (alcohol

vs

hydrocarbon), and to the influence produced by the

polar groups located nearby (one or two methylene groups located near the polar groups are less hydrophobic). The hydrophilicity of proteins is caused both by strong polypeptide groups and by polar groups located inside the chains. Janing [169] proposed to estimate the hydrophobicity of amino acid residues from the ratio of their distribution between the internal volume of the globule and the surface, averaged over a large number of known proteins. Various methods used for the estimation of the hydrophobicity for amino acids in proteins were intensively discussed by Richards [ 165]. For the quantitative description of protein adsorption from aqueous solution, the total area A of the hydrophobic portions at the surface as the main contribution to the adsorption energy AG is determined. Then, using the increment AG/AA, calculated from the dependence of the energy necessary for the transfer of amino acid residues from the surface into the globule on the total area available for the contact with the solvent (8.8 kJ/(nm2.mol) [165]), one can estimate the adsorption energy of the protein. The calculated values 27-44 kJ/mol agree well with experimental values of the adsorption energies of 30-40 kJ/mol. 5.9

Use of the hydrophile-lipophile balance concept for the characterisation of solid surfaces with respect to its application

The hydrophile-lipophile balance of solid surface, existing either in compact or disperse form, depends on the nature (type) of the solid, the manufacture of the surface (grinding, dispergation, etc.), the processing time and the time during which the surface was in contact with its environment, processing temperature, adsorption of surfactants at the surface, and on the difference between the polarities of water and the organic medium which interacts with the solid. In Chapter 4 a number of expressions were discussed which give an estimate of the hydrophilelipophile balance of a solid. If the interaction of a macroscopic body with the bulk phases of water and oil is considered, then the corresponding hydrophile-lipophile ratio (HLR) is given by Eq. (4.23), which can be expressed as the dependence on the wetting contact angles for

357 water and oil, Eq. (4.23a) or the dependence on the contact angle of selective wetting, Eq. (4.29). For spherical particles it is convenient to express the HLR value via Eq. (4.36). Equations (4.23), (4.23a) and (4.29) which give the dependencies on the contact angle, can be expressed also in terms of chromatographic quantities, see Section 4.4. If the wetting of a solid or the adsorption of vapours of water and organic liquids result in the formation of a monolayer or thin film, then the HLR value should be expressed via the variation of the chemical potential of the adsorbate (water and oil) dependent on the degree of adsorption given by Eqs. (4.52) (4.54) rather than by the integral energy of adsorption of Eq. (4.51). In addition to the influence of the HLR on the stability of emulsions stabilised by solid particles (of. Chapter 4), the HLR of a solid can be important for choosing the optimum materials for thermo-physical devices and medical equipment, in processes of foam destruction by mixtures of oil with solid particles, in the processes of washing of oily surfaces, and also in the chromatography, where a number of methods are used for the estimation of the selectivity of a sorbent. Below the physico-chemical aspects of these applications are briefly summarised. Let us consider the hydrophilicity of the walls of a heating device as an example. This value is of essential importance for the boiling regime. Also the wetting of the walls of a heat exchanger affects the heat transfer regime [ 170, 171 ]. If the wetting of a surface is good, then a condensation film of the vapour is formed, while for bad wetting the condensate is accumulated into separate droplets. The drop condensation regime provides much larger heat transfer than the film condensation regime; therefore the hydrophobisation of water vapour condensers is a usual method to enhance the condenser efficiency. It is interesting to note that the effect of the hydrophobicity on the drop condensation process at plane surfaces is quite opposite to the effect of the hydrophobicity on the gas bubble formation in liquids at solid surface. Let us consider the formation of a liquid drop at a plane solid surface. The drop shape is a fiat-convex lens, see Fig. 5.7. The formation of the drop entails the formation of two extra surfaces, a liquid/gas and liquid/solid interface, while the area of the solid/gas interface is decreased by the area of the liquid/solid interface. Therefore, to initiate a condensation, an supersaturation of the vapour would be necessary to compensate for this surface energy increase.

358

Fig. 5.7 Formationof a drop duringcondensationon a solid substrate. The increase of Gibbs' surface energy corresponding to the condensation of vapour at a solid surface is given by AGeond = (OSL - (YSG) ASL +

Oe6 ALG= nr2(ose - Os6) + 2nRhoLo,

(5.6)

where the subscripts SL, SG, LG refer to the solid-liquid, solid-gas and liquid-gas interface, respectively. The other quantities are explained in Fig. 5.7. Introduction of the relation (R - h)/R = cos 0 into Eq. (5.0, and some rearrangements yield AG~o,d = nR2ol.6(1 - cos0)2(2 + cos0),

(5.7)

where the contact angle 0 is measured through the liquid phase. Let us consider now the effect produced by wetting on the boiling process accompanied by the formation of heterogeneous gas bubbles. Some overheating is necessary to initiate boiling due to the formation of new interfaces liquid/vapour and solid/vapour. Simultaneously the solid/liquid interfacial area will be decreased when a bubble is formed. The increase in Gibbs' surface energy corresponding to the bubble formation is (of. Fig. 5.8)

AGbo~, = ALoOI~O+(OsL- Oso)Ast = OLo(A~.o- ~176

ASL).

(5.8)

359

~

Fig. 5.8

Schematic illustration of gas bubble formation in a liquid on a solid substrate.

Using the equilibrium condition (5.9)

COS 0 b "- (O'SL = O'SG)/O'LG,

one obtains from Eqs. (5.8) and (5.9): (5.10)

AGboil = CrLG ( A L G - ASL COS 0b).

This equation can be transformed into AGboil = nR2t~LG

(5.11)

(1 - c o s 0b) 2 (2 - COS 0b).

For the same surface, noting that 0r = 180 ~ - 0 b, and omitting the superscripts, one obtains AGboil = nR2OLO (1 +cos 0) 2 (2-cos 0).

(5.12)

If the wetting is complete, the condensation is easiest (no saturation takes place, AGcond -~ 0), however, the bubble formation is most hampered, (AGb-+ AGmax). On the contrary, for bad wetting the boiling onset requires much lower overheating than for good wetting, and the condensation is most hampered. For the ratio AGboil to AGcond one obtains

AGboil

. . AGr

_

(1 + cos 0) 2 2 - cos 0 . . . (1 - cos 0)2 2 + cos 0

HLR0

2 - cos 0 , 2 + cos 0

where the value HLRSo was used from Eq. (4.36).

(5 13)

360 One can see that the ratio AGb/AGcond is determined by the hydrophilic-lipophilic ratio (HLR) multiplied by a coefficient, the value of which can vary from 1/3 to 3. Therefore, if boiling and condensation take place in contact with the same (or similar) surface, then the necessary regime of the processes can be adjusted according to Eq. (5.13). Here one should use the actual wetting angle hysteresis which accounts for the wetting order: the advancing liquid for the drop, and the receding liquid for the bubble. The wetting of blood vessel can also be considered as an example. This affects significantly the blood circulation process. When the wetting of the vessel walls by blood is low, the hydraulic resistance of the vessels is relatively low. In addition, an increased wetting of the walls promotes blood coagulation and thrombosis. Therefore, for material used in the production of artificial blood vessel, the estimation of the HLR value from the wetting angle hysteresis or chromatographic data (cf. [172]) would be useful. Fine disperse suspensions of hydrophobic particles in non-polar organic and silicone oils are used as most efficient antifoaming agents [74]. The concentration of particles in the oil is usually in the range 1 - 30%, and the size of particles is in the range 1 nm to 1 ~tm [173]. The particles and oil act synergistically in the foam breakdown process, while the solid particles and oil, taken separately, can be quite inefficient antifoaming agents. The mechanism of the antifoaming action of such mixtures was analysed in detail in the book by Garrett [173] and also in a number of articles. For the review of more recent publications one can turn to [74,

174-176, 187]. It was shown by Garrett et al. I173, 174] that the action of these mixtures is irrespective of the spreading of the oil: both suspensions in oils with a spreading coefficient on foam forming solution larger unity (most silicone oils, e.g. polymethyl siloxane), and the suspensions in usual mineral oils which do not spread on foam forming solutions can act as efficient antifoaming agents. It was argued by Garrett that hydrophobic particles promote the entry of oil droplets into the film surfaces and then the oil is responsible for subsequent film ruptures. To destroy a foam film by oil droplets, two conditions are necessary: the drop could be able to enter the water/gas interface, and then is able to either form on unstable bridge across the film, or it forms a spreading organic film, on which the water film is unstable. The necessary condition for the mechanical instability of the bridge lens is [ 173]

361 2

2

2

B = t~w~ + aow -t~oc > 0.

(5.14)

Garrett terms the quantity B the bridging coefficient. The instability of water films on a substrate (oil or solid) can be predicted if the disjoining pressure isotherm II(h) for this film is known. Also in some cases this instability can be estimated from spreading coefficients or surface pressure values [74, 177]. The prediction of the instability of a wetting film from contact angles only (disregarding the H(h) isotherm) is also reasonable in the range 0WA> 40 ~ however, certain limitations exist here [74, 178]. One of the necessary conditions for a particle to be an efficient antifoaming agent is its incomplete wetting by oil. This depends on the degree of hydrophobicity of the particle and governs its ability to concentrate at liquid/liquid interface 90~ 0ow < 180 ~

(5.15)

where 0ow is the contact angle of selective wetting measured through the aqueous phase. It was shown in a more detailed analysis [176] that the necessary condition for foam film rupture is (see Fig. 5.9) 0w~ > 180 - 0ow

(5.16)

or

0we + 0ow > 180.

(5.16a)

If combined with Eq. (5.15), this means that the breakdown of a water film by spherical particle takes place for 0wo < 90 ~ It is known that such particles cannot break down a symmetric foam film as here the necessary condition is 0wo > 90 ~ The condition (5.15) is necessary for the formation of stable W/O emulsions stabilised by solid particles (cf. Chapter 4). This condition involves an equilibrium contact angle. In fact, the systems considered exhibit a strong contact angle hysteresis, and it was shown in Chapter 4 that in this case the hydrophilic-lipophilic ratio should be expressed via two contact angles (advancing and receding):

362 (1 + cos0]) 2 HLR~ = (1-cos0~) 2 '

(5 17)

where 0a~ and 0r~ are the oil advancing and receding angles, respectively. Inverse emulsions are stable for HLRo < 1.

-

-

.

oqueous .

.

[ilm

.

O~/f___~

0o~ Fig. 5.9. Mechanism of foam extinguishing by solid particles (schematically); top - equilibrium liquid film 0wG + 0ow < 180, bottom - rupturing film 0w6+ 0ow> 180

It is seen from Tables 4.5 and 4.6 that, for the transition from stable inverse emulsions to unstable inverse emulsions stabilised by graphite and hydrophobised glass powder the oil advancing (water receding) angles are - 9 0 -

130 ~ while the oil receding (water advancing)

angles are 150 - 170 ~ (lower boundary). The lower stability boundary for HLR corresponds to values of-~ 0.05 - 0.06, while the upper stability boundary corresponds to the phase inversion boundary (HLR = 1). Therefore, the HLR values calculated from contact angles assuming the given wetting sequence hysteresis provide more comprehensive information with respect to the choice of hydrophobic particles as antifoaming agents (when composed with oils), than the relationship (5.15) does. On the contrary, the composition of detergents used for washing of oily fouling pollutions containing solid particles should ensure either a complete wetting of these particles, or the wetting should be characterised by a wetting angles hysteresis which correspond to the stabilisation of a direct emulsions. The formation of a stable direct emulsion is necessary to prevent a deposition of the particles back at the cleaned surfaces. Therefore, choosing and

363 applying detergent formulations, the formation of stable direct emulsions stabilised by solid particles should be ensured, i.e., the HLR value of wetted particles should be less than unity. The application of chromatography to determine the hydrophile-lipophile balance of a surfactant is described above in Chapter 3. The main role of a solid support packed into a gas-liquid chromatography column is to provide a most efficient performance of the immobile liquid. Therefore, the support should possess a large specific area, low adsorption ability, no catalytic activity, sufficient mechanical strength, stability with respect to high temperatures, and finally, a sufficient wettability with respect to the immobile fluid [179]. Therefore, the main sorption process in this type of chromatography is the distribution of matter between liquid and gas, while the adsorption ability of the solid phase plays a minor role. On the contrary, in gas adsorption chromatography the adsorption ability is the main property of the adsorbent which ensures the separation of substances. The criterion which determines the separation of two substances is the relative retention given by Eq. (1.164). To extend the selectivity estimate over the maximum possible variety of separated substances, a more general criterion of the selectivity, e.g., the concept of 'polarity' after Rohrschneider [180] or McReynolds [ 181 ] could be employed, which involves the Kovats' indices (cf. Chapter 1), as given by Eq. (1.166). The difference between the logarithms of retention volumes (or relative retention times) of the studied substance (e.g., alcohol) and n-paraffin possessing the same number of carbon atoms is proportional to the increment of molar Gibbs' dissolution energy l per functional or structural group of the studied molecule (these groups are different from those in the paraffin chain) [ 182]. The increment value in the denominator of the above expression is proportional to the molar energy of dissolution of the methylene group in the studied immobile phase. Thus, the selectivity of the immobile phase involves both the specific interaction of the structural group (or polar group - for amphiphilic compounds), and the energy of dissolution of the methylene group in the immobile phase. Therefore, this selectivity can be represented as a function of the hydrophilic-oleophilic ratio, similarly to Eqs. (3.95) or (3.107):

It is assumed that the main process in the iso-chromatographic separation is the distribution of matter between liquid and gas.

364 I = 100 AG~ --+ 100Z = 100(HLRch + 1)Z

(5.18)

AGcH~

or

HLRch=

AG~ = I _ _ ~ _ l . AGcH` . Z 100Z

(5.19)

The analysis of complicated systems becomes significantly simpler, if a relation between the retention of the sorbates and any relevant characteristics of the immobile phase is known. The arbitrary chromatographic 'polarity' after Rohrschneider [180, 182] is often chosen to be such a characteristic. To determine this polarity, two immobile phases are chosen. For the first one (usually squalane at 30~

the selectivity value is taken to be zero, while for the second

phase (~), ~'-dizyan diethyl sulphide at 30~ in Rohrschneider's system) this value is assumed to be 100. Every mobile phase studied is characterised by a "polarity" which can be determined from the plot of the dependence lg(r)

vs

the arbitrary polarity, where r = VNI/ VN2, (cf.

Eq. 1.164). The diagram is built in such a way that the left ordinate corresponding to the r values for the sorbates measured at the column with squalane, the fight ordinate to the values at the column with 13, [3'-dizyan diethyl sulphide, and the arbitrary polarity is measured along the abscissa. The selectivity of the adsorbents (solid phase), similarly to the selectivity of immobile liquids, can be estimated also from the arbitrary chromatographic 'polarity'

after

Rohrschneider or McReynolds. It seems more important to apply the estimation of HLR values for solids from the chromatographic method according to Eqs. (4.51), (4.53) and (4.54) to highly disperse powders used in various technological applications, where the HLR estimation from contact angle values is impossible, and also for pure materials used in medicine as it was discussed in (cf. Section 4.4 and Table 4.1).

365 4.10. References

1.

Microemulsions, Theory and practice, L.M. Prince (ed.), Academic Press, New York, 1977.

2.

Micellization, Solubilization and Microemulsions, K.L. Mittal (ed.), Plenum Press, New York, 1977, vol. 1 and 2.

3.

Solution Chemistry of Surfactants, K.L. Mittal (ed.), vol. 1-2, Plenum Press, New York, 1979

~

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374

List of Symbols

A

area (film, surface per one mole of a surfactant, etc.)

A

Hamaker constant

Ao

area occupied by one mole of a surfactant in the saturated adsorption layer

a

area per molecule

a

thermodynamic activity

a, as

constants which characterise intermolecular attraction

B

constant in the definition of fully retarded molecular forces

C

concentration

C•

mean ionic concentration of electrolyte

Cbt

concentration of black spot formation in thin film

Cbi,f

concentration of the formation of stable black films

Cd

concentration of disperse phase (in emulsion and suspension)

Ch

concentration of hydrophilic surfactant

Cm

critical micelle concentration

CM

molar concentration of micelles

Cmin

minimal concentration of a surfactant solution necessary for the formation of a stable emulsion

Cs

electrolyte concentration

D

coefficient of molecular diffusion

Ds

coefficient of surface diffusion

E

entry coefficient

E

weight fraction of ethylene oxide in non-ionic surfactant

AE

activation energy

F

force

F

Faraday constant

G

Gibbs energy

g

gravitational acceleration

H

partial molar enthalpy (heat)

375 All

heat of wetting

AHmix

heat of mixing

h

film thickness

h

depth of immersion of spherical particle (segment height)

I

retention index (in chromatography)

K.

constant of matter distribution between phases expressed via activity

Kr

constant of matter distribution between phases expressed via molarity

Kn

collision factor

Kx

constant of matter distribution between phases expressed via molar fractions

K~2

constant of matter distribution between phases (in chromatography)

KB

bending modulus of monolayer

Kss

saddle splay modulus of monolayer

k

Boltzmann constant

k

rate constant in kinetic equations

L

arbitrary coefficient of surfactant distribution between water and oil

1

length of the hydrocarbon chain

M

molar (molecular) mass

Mh

molecular mass of the hydrophilic part of a molecule of a non-ionic surfactant

MI

molecular mass of the lipophilic part of a non-ionic surfactant

m

degree of association

m

mass

N

number of particles

NA

Avogadro number

n

number of atoms or repeated molecular groups in molecule

n

number of drops in a unit volume

nEO

number of oxyethylene links in a molecule

riCH2

number of methylene links in the hydrocarbon chain

P

pressure

AP

pressure difference

P~

capillary pressure

Q

heat of dissolution

376 Qi

partial molar heat of dissolution

R

gas law constant

Rf

radius (of curvature, film)

RF

ratio of the velocity of the motion of a component along a chromatographic column to the frontal velocity of the carrier

r

radius of drops, particles

r

relative retention value (in chromatography)

S

spreading coefficient

S

entropy

S

relative solubilisation

T

absolute temperature

t

temperature

tR

retention time

V

volume

V

volume of hydrocarbon chain

v

particle motion velocity (in chromatography)

v

film thinning rate

Vo/w

coalescence rate

VRe

film thinning rate for tangentially immovable interfaces

U

interaction energy, internal energy

W

energy

W

work (of adsorption, transfer, wetting)

X

molar fraction

Z

ion charge

z

co-ordinate within the surface layer dissociation degree surface activity binding degree of ions in the micelle

F Foo

surface concentration, surface excess limiting adsorption activity coefficient

377 mean ionic activity coefficient ),

film tension

5

thickness of polar groups layer

8

Hildebrand's solubility parameter specific surface area

Ae

difference of polarities

n

dynamic viscosity

~ls

surface viscosity

0

contact angle

0

degree of adsorption layer saturation

K

specific electro-conductivity

K

Debye parameter

~o

wavelength characteristic to the adsorption spectra of liquids chemical potential

V

stoichiometric coefficient in the dissociation equation

Pl

disjoining pressure

ffc

two-dimensional collapse pressure

ff

surface pressure spreading pressure

if*

surface fugacity

0

density

P pM

hydrophilicity constant

15"

surface tension

aO

initial (with respect to time) value of surface tension

T

time

~1/2

half-period of flocculation

hydrophobicity constant

energy variation corresponding to micelle formation q~

volume fraction potential of the diffuse electrical layer

378 Abbreviations

of

surfactants

and

surfactant

mixtures

trademark of a lubrication cooling liquid

Aquol

-

Aerosol MA

-sodium dihexyl sulphosuccinate

Aerosol OT (AOT)

- sodium bis-(diethyl hexyl) sulfosuccinate

Alphapol (4, 8, 12)

- oxyethylated nonyl phenols

Arlacel-60

-

Brij 93(HLB=4.9)

- oxyethylated alcohol

CiEj

- oxyethylated alcohol, e.g., CI2E5 - CI2(OCH2CH2)5OH

Coatex M350

-

sorbitane monostearate

a complex mixture of sulfated and nonionic surfactants with butylene glycol

CPC

-cetyl pyridinium chloride

CTAB

-cetyl trimethyl ammonium bromide

Dioleine

-oleic

Emulphor-FM

-triethanol

Igepal-CO

-20-0xyethylated dodecyl phenol

monolaurine

-

NaDBS

- sodium dodecyl benzene sulphonate

NaOL

-

acid diglyceride amine monooleate

lauric acid monoglyceride

sodium oleate

NP (n = 7.4, 10, 12, 20 etc.) -oxyethylated nonyl phenols ODAC

-octadecyl trimethyl ammonium chloride

Oleox-5

-

OP (n = 4.7, 10)

-oxyethylated octyl phenols

PEG

- olyethylene glycol

SDS

-sodium dodecyl sulphate

Sorbitane-L

-ether

of anhydrosorbite and lauric acid

Sorbitane-O

-ether

of anhydrosorbite and oleic acid

Span-65

-

sorbitane tristearate

Span-80

-

sorbitane monooleate

Sulphonol

-technical alkylaryl sulphonate

Triton X- 100

- 9.6-oxyethyl nonylphenol

5-oxyethylated oleic acid

379 Tween-20

-polyoxyethylene sorbitane monolaurate

Tween-80

-oxyethelated sorbitane monooleate

Volgonate

- technical alkyl sulphonate

Ucrinol

- trademark for a LCL

Xylan-o

-ether of anhydroxylite and oleic acid

380

Acronyms CMC

critical micelle concentration

DEL

electric double layer

DLVO

theory named after Derjaguin, Landau, Verwey and Overbeek

EIP

emulsion inversion point

EOR

enhanced oil recovery

HI

hydrophobicity index

HLB

hydrophile-lipophile balance

HLBact

numbers for the surfactant phase

HLBa

numbers introduced by Budewitz

HLBD

numbers introduced by Davies

HLBE

hudrophile-lipophile balance based on the distribution coefficient

HLBG

numbers introduced by Griffin

HLBI

ideal value HLB suggested by Heusch

HLBo

HLB number characterising the oil

HLBR

the achual value HLB (see Eq.3.7)

HLB,r

HLB number determined from titration

HLC

hydrophilic-lipophilic centre

HLR

hydrophilic-lipophilic ratio

HLRE

numbers based on the work of transfer

HLRM

hydrophile-lipophile ratio determined from the micellisation energy

HLRo

hydrophilic-lipophilic ratio, determined from contact angle 0

HLRSo

see Eq. (4.36)

HLRF

see Eq. (4.38)

HOR

hydrophile-oleophile ratio

HORM

hydrophile-oleophile ratio determined from the micellisation energy

IN

isomeric number, the number of atom to which the benzene ring is attached, counted from the beginning of the hydrocarbon chain

H/L

ratio of the number of EO groups to the number of carbon atoms

381 H/O

ratio of the mass fraction of the surfactant hydrophilic part to the hydrophobic part

LCL

lubrication cooling liquid

LLC

lamellar liquid crystals

LPB

lower phase boundary between three-phase system and microemulsion

ME

methylene equivalent

NBF

Newton black film

OPB

optimum phase boundary?

OHB

oleophile-hydrophile balance

Ph.I.

phenol index

PI

Huebner's polarity index

PIT

phase inversion temperature

SAD

surfactant affinity difference

UPB

upper phase boundary between three-phase system and microemulsion

382

Subject index Accumulation ratio, 349 and HLR.., 348-350 Activity coefficient, 3 of adsorbed molecules, 38 of water, 204

Szyszkowski equation, 23 Szyszkowski-Frumkin equation, 30 Antifoaming action of solid particles in oil, 360-362 Antifoaming agent efficiency, 361

Adhesion tension, 269

Antonov's rule, 9, 13, 14

Advancing contact angle, 271,295

Amphiphilicity of surfactants, 1, 63, 217

Adsorption

Attraction forces, 108

at liquid/liquid and liquid/gas Gibbs energy of, 30

Bankroft rule, 105, 128, 179, 215

Gibbs equation, 16, 22, 23, 291

Bending elasticity, 27

heat of, 2, 81

Bending energy of a monolayer, 26

interface, 16-19

Bending module, 26, 138, 322

of ionic surfactants, 18-19

Black films

of non-ionic surfactants, 16-17

common,-110, 112

work of, 28, 29, 33-35, 73

formation of, 105

Adsorption layers of surfactants

hydrocarbon, 108, 127

bending energy of, 26

Newton, 109-112, 345,346

degree of dissociation, 25

multilayer (stratified), 110, 345-347

equation of state, 22-25

Black spot formation

structure of, 21-26

concentration of, 111, 112

thickness, 22

effect of hydrophilic surfactants Cbl,

spontaneous curvature, 26

115

Adsorption isotherms Henry equation, 21-22 Frumkin equation of state, 24 Langmuir equation, 22, 39

in aqueous films, 114 in non-aqueous films, 113-115 Bridging of asymmetric films by solid particles, 360

383 Bridging coefficient, 361 Bulavchenko - Kruglyakov equation, 123

CMC, 56, 63 and HLB, 56 and parameter pm, 46

Capillary pressure, 104, 124, 280, 281

dependence on nEO, 47, 48

Cbi and polarity of organic phase, 114

dependence on nCH2 , 44

Cb~dependence on HOR, 250, 251

Coalescence kinetics, 116, 119, 121,278

Cbl dependence on demulsifiers

Cohesion energy, 43

concentration, 251 Characteristic of phase inversion in

Colloid solubility, 44-51 Comparison between HLB and PIT, 190

emulsions, stabilised by solid

Comparison HLBc and HLBo numbers, 214

particles, 301

Composition of three-phase systems, 256

Chemical potential of a surfactant, 17, 28, 40, 51, 59, 77 Chromatographic characteristics of

Contact angle, 1, 11,272, 295 hysteresis, 271,274, 280, 287, 304, 361 hysteresis and critical disjoining

surfactant, 83

pressure, 304

and HLB, 83, 86

in the solid/water/oil system, 268

coefficient of distribution, 84

of advancing oil, 295

relative retention time and HLB, 204

of receding water, 295-297

retention distance, 85

Curvature of a solid film, 276

retention index linear, 85

Davies' HLB Dnumber, 173-181

logarithmic, 85

Demulsification efficiency, 337

retention time, 84

Depletion flocculation, 122

retention volume, 84

Derjaguin-Frumkin theory of wetting, 11

selectivity of the immobile phase, 363

Dielectric permittivity, 15

transfer energies, 89 Cloud point temperature (top), 49, 50, 351 dependence on electrolyte, 51

and HLB, 168 Diffusion coefficient, 37, 105, 116 Disjoining pressure, 104, 107

dependence top on the number of

adsorption component, 110

EO-group, 49-50

electrostatic component, 109

384 isotherm for wetting films, 12-15

stabilised by solid particles, 282

molecular component, 13, 106

thickness, 110-111

of films, stabilised by solid particles

thinning, 123

oscillatory component, 346

Emulsion film stabilised by solid particles, 282

positive component, 109-110

Emulsion

structural component, 110

highly concentrated, 323

Fl(h) - isotherm, 12, 13,280

multiple, 100, 327

for emulsion films, 282

O/W/O-type, 327

of foam films maximum (threshold), 343

W/O/W-gel-like-type, 326

Displacement of crude oil, 331 Distribution constant of surfactant and HLB, 198, 216 Distribution coefficient, 52, 55, 84

W/O/W-type, 330, 327 Emulsions centrifugation method for separating a disperse phase, 124

and work of adsorption, 228

formed with highly disperse particles, 306

in chromatography, 198

highly concentrated (polyhedral), 323

DLVO theory, 109, 277 ability and HLRM, 348

influence of HLR on stability, 357 O/W-type, 125, 129-130, 327 p~mration of highly concentrated of, 323

Electric double layer (DEL), 25, 105 potential of, 109

stabilised by solid particles, 203 W/O-type, 129, 130

Electrostatic interactions, 106

Emulsion phase inversion, 124-127, 328

Emulsion breakdown, 102

Emulsion stability

of dilute emulsion, 333

concentration boundaries, 299, 308, 360

new method for, 334

dependence on the work wetting, 293

Emulsion films, 103, 104, 110

dependence on ODAC concentration, 299

breakdown activation energy, 105

effect of solid phase concentration, 305

critical thickness of rupture, 103

effect of temperature, 130-134

kinetics of thinning, 103, 105

energetic characteristics of transfer of

physicochemical properties

methylene and polar groups, 72

385 Enhanced recovery of oil from pools, 331 Equilibrium position of a spherical particle

dependence on EO-groups number, 341 Fowkes, equation, 8

at water/oil interface, 270 Ethanol number, 172

Gel-like solid emulsifier, 126, 282, 288 Gibbs energy, 30, 41

Film~

for various types of transfer, 72 asymmetric, 13, 361,362

for the wetting of solid particles, 283

adsorption, 110

of micellisation, 60, 62

Flocculation, 116, 119

Gibbs energy of

fast, 118

transfer of a methylene group from

kinetics, 119, 121,124

water to a hydrocarbon, 75

Smoluchovski's theory, 116, 120

transfer of hydrophilic parts, 53

Flotation extraction efficiency, 349

transfer of lipophilic parts, 53

Flotation recovery and HLBM, 349

transfer of one CH/group, 44, 53

Foam

transfer of one EO group, 54 collapse in gravitational field, 340

transfer of surfactant molecules, 71

collective effect in, 347

Gibbs interaction energies, 52

equilibrium thickness, 344

Gibbs surface energy of condensation of

pressure drop technique (FPDT), 123,309 pressure in Plateau borders, 342 Foam films rupture

vapour on solid surface, 358 Gibbs-Helmholtz equation, 284 Girifalko and Good, equation of, 7

necessary condition of, 361

Gouy model, 25

microscopic, 343

Group numbers HLBD, 176-178

stratification, 345-347 Fl(h)-isotherm, 13 Po(h)-isotherms, 344-345 Foam stability

Hamaker constant, 15, 106 effective, 120 Hansen's equation, 37

and hydrophile-lipophile balance, 138

Heat of adsorption, 2, 81

dependence on amount of octane, 3, 41

Heat of wetting, 284

dependence on liquid phase pressure, 342

HHB value, 21

386 Hildebrand solubility parameter and HLB, 40, 164

protein structure, 353 solid particles, 283,295

Hildebrand solubility parameters, 44

solubility of surfactants, 163

H/L and HLB numbers, 156

spreading coefficient, 160

HLB

temperature of the formation of liquid for a mixture of surfactants, 149, 335

crystals, 193

in emulsion technologies, 321

UPB, 71

influence of surfactant structure on, 205

water number, 169

influence of the medium on, 205

work of the transfer of a surfactant, 215

HLB and

HLB determined from

Bankroft rule, 180

dioxane distribution between water

chromatographic characteristics of

and oil, 150

surfactants, 195

emulsification behaviour, 147

cloud point, 49, 163

ratio of the hydrophilic heads to

CMC, 181, 184

lipophilic tails, 157

criterion of phase inversion in

molecular composition, 153

emulsions, 293

separation kinetics, 151

foaming properties of

work of transfer, 218

microemulsions, 338

HLB-numbers

heat of dissolution, 167

and activity coefficient of water, 204

highly disperse solid emulsifiers, 288

and interfacial tension, 16

HLC position at the interface, 154

and length of hydrophobic and

interracial tension, 159, 160

hydrophilic parts of a non-ionic

LPB, 71

surfactant molecule, 158

maximum solubilisation, 66

dependence on PIT, 191

mixtures of surfactants, 155

dependence on RF, 196

HLB of

HLB of solid particles, 267

phase inversion of emulsions, 244

HLB of solid surface, 356

phase inversion point, 152

HLB proposed by Tanchuk, 188

phenol numbers, 169

HLB temperature of mixture, 192

387 HLB temperature region, 131 HLBB introduced by Budewitz, 156

Hydrophile-lipophile balance of spherical solid particle, 287

HLC of molecule in adsorption layer, 225

Hydrophile-lipophile balance region, 130

H/L number, 138, 155

Hydrophile-lipophile balance temperature,

HLR, 219, 222, 256, 284, 292, 297, 304 force-determined, 288

131 Hydrophile-lipophile ratio HLR, 356

HLR for mixture of surfactants, 236

Hydrophilic-hydrophobic balance HHB, 21

HLRM concept, 350

Hydrophilicity coefficients, 241

HOR and formation of micellar systems,

Hydrophilicity of a surfactant, 69

252 HOR and micellar phase formation, 245,254 HOR determined from the adsorption work, 224 HOR determined from the micellisation energy, 237

Hydrophilicity of proteins, 356 Hydrophilicity, 72, 77, 124, 219, 222, 267, 290, 349, 356 Hydrophilic-lipophilic centre of molecule, 20 Hydrophilic-lipophilic ratio, 360 Hydrophilic-oleophilic ratio HOR, 207, 225

HOR for mixture of surfactants, 230

Hydrophobic effect, 21, 76, 77

HOR for surface active electrolytes, 226

Hydrophobicity, 63, 72, 124, 219, 222, 267,

HOR values for mixtures, 255

290, 349, 356

HOR, 233,240

of particles, 102

Huebner polarity indices, 211

Hydrophobicity constant, 186, 188

Huebner's polarity index, 199

Hydrophobicity index, 186, 210

Hydrophile-lipophile balance concept,2, 6,

Hydrophobicity index and methylene

146, 215,218 application of, 314 Hydrophile-lipophile balance HLB, 1, 3, 4,

equivalent, 187 Hydrophobicity scale based on distribution constant, 355

6, 26, 27, 56, 68, 72, 157 Hydrophile-lipophile balance

Interface

of a surfactant, 100

molecular structure, 20-21

expressed via mass portions, 157

rigidity constant, 26

388 Interracial tension, 3, 7, 26

Methylene equivalent, 186

and UNIQUAC model, 8

Micellar phase, 66, 67, 69, 253

and polarity difference, 15

Micellisation and solubilisation, 55

concept of effective o, 277

Micelle

dependence on the radius of

aggregation number for, 56, 58, 59

curvature, 26

binding degree of ions in, 44, 57, 58,

dynamic, 38

61

cr(c)-isotherm, 78, 79

degree of ionisation of ionic groups

kinetics of, 37

in, 58, 161

in microemulsion, 319

expanding from thin films, 122

minimum in water/oil/non-ionic

geometric shape, 62

surfactant systems, 320

packing of hydrocarbon radicales, 62

Intermolecular interaction, 76 Internal energy of evaporation, 43 Interrelation between work of wetting and HLR, 309 Interrelations between the PIT and HLB, 194

structure of, 56-60 Micellisation and solubilisation, 55 critical concentration of, 44 dependence on HLB, 183 equilibrium constant, 60 Gibbs energy of, 32, 60-62, 76

Inverse solubilisation, 63

heterogeneous treatment, 58-59

Inversion of W/O/W into O/W emulsions,

homogeneous approach, 58, 59-61

328 Isomeric number, 209

in non-aqueous media, 59 Microemulsion (micellar) systems, 66-69, 135, 138, 253, 315

Kovats index, 85

bicontinuous, 317, 325

Kovats index and HLB, 198

boundaries for the existence, 257 dynamic viscosity of, 317

Line tension, 285

displacing ability of, 332

Lubricating-cooling fluids, 334

mobility of, 311

Lyophilicity, 1

middle phase (Winsor III), 317, 322,

Lyophobicity, 1

324

389 oil in water (Winsor I), 310

optimal emulsion, 137

percolation electric conductivity, 317

type I (Winsor I), 66

s-type, 318

type II (Winsor II), 66

transparent, 339

type III (Winsor III), 66, 131, 140,

u-type, 318

322, 324

viscous behaviour, 317 water in oil (Winsor II), 316 Model emulsion film with solid particles, 279 Model of film stabilised by two layers of solid particles, 281

Phase inversion and black spot formation concentration, 245 Phase inversion in emulsions, 101, 115, 124, 125, 131 catastrophic inversion, 125 concentration inversion, 127

Molar heat of dissolution, 43

transition inversion, 125, 126

Molecular attraction forces, 109, 111

stabilized of solid particles, 299, 301

Monodisperse emulsions, 122

Phase inversion temperature (PIT), 64, 130, 190

Newton black films, 109-112, 345,346

dependence on HLB, 191-192 dependence on oil type, 132

OPB and HLB, 71

dependence on salt concentration, 134

Optimum phase behaviour, 70

dependence on volume fractions, 133

Osmotic stress, 123

Phase separation in emulsions

Ostwald ripening, 82, 101

Protein structure, 353-356 and hydrophobicity (hydrophilicity)

Phase behaviour, 68 Phase boundary of stability

of amino acids, 66, 355-356 Phenol index, 171

lower, 70, 134, 136

Polarity index and HLB, 200

upper, 70, 134-136

Polarity index of mixed stationary phase,

Phase diagram, 64

202

Phase diagram and HLB, 65

Polarity index of surfactants, 203

Phase equilibrium

Preparation of aqueous microemulsion, 338

optimal phase behaviour, 70, 137

390 Relation between H/O and HOR, 230 Relation between HLR and the work of wetting, 294

equilibrium, 10, 12 Spreading coefficients and HLB, 16 Spreading pressure, 11

Relation between HLB and HOR, 228

Stabilisation by solid particles, 274

Relationships between PIT and HLB, 136

Stabilisation of emulsions mechanism, 126

Relative solubilisation, 63, 64

Stabilising ability of surfactants, 3, 100, 128

Required HLB numbers of oils, 136, 146-

Stability for direct emulsions and HLR, 310

153,321

Stability of a multiple emulsion, 329

Required HLB and surface tension, 151

Standard chemical potential, 28

Required HLB and dielectric permittivity,

Steric interactions, 106

151

Steric interaction of adsorption layers, 128

Reynolds-Scheludko equation, 104

Stratification phenomenon in foam films, 345

Rigidity constant of the interface, 26

Stratifying black films, 111

Rupture of thin aqueous films, 138

Surface activity and adsorption kinetics, 36-38

Saddle splay module, 26

Surface activity of a surfactant, 21, 35

Solubilisation

Surface activity of electrolytes, 34-36

direct, 63

Surface activitY of non-ionics, 35

distribution of the solubilisate

Surface activity, 4, 79

between the dispersion medium and

Surface fugacity, 38

cores of micelles, 63

Surface potential, 109

Solubilisation and HLB, 63

Surface pressure, 22, 25, 28, 273

Solubilisation in protein globules, 66

Surface tension minima, 320

Solubility of hydrocarbons, 41

Surface tension, 7, 26

Spontaneous curvature of a monolayer, 26,

Surface separation of substances, 348

27, 137

Surfactant

Spontaneous positive curvature, 137

affinity difference (SAD), 71

Spreading coefficient, 3

activity coefficient, 39, 139

and disjoining pressure isotherm, 12

chemical potential of, 17, 28, 40, 59, 77

and HLB, 16

classification of, 4-6

391 lethal dose, 350

Water number of a surfactant, 170

molecule, 4

Weighted HLB, 100, 328

phase, 131

Wetting hysteresis, 270

solubility, 40,48

Work of adsorption, 21, 27, 34, 225

Surfactant mixture and average HLB, 338

Work of adsorption of acids and alcohols, 75

Three-phase system water/micellar phase/oil, 334, 69

Work of micelle formation, 2 Work of surfactant adsorption, 2

Toxic properties of surfactants and HLB, 350

Work of transfer, 52, 72

Transfer energy increment for one

Work of transfer of one mole solute, 52

methylene group, 88 Transfer heats of the methylene group, 74 Transfer of entire molecules from one bulk phase to another, 74

Work of wetting, 284, 288 dependence on contact angle, 294 Work of the transfer of molecules from a solid state to the solution, 41

Transfer of one methylene group, 44 Traube's rule, 71, 78, 79 Two-dimensional collapse pressure, 273

Young equation, 269

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