Structures and Properties of Rubberlike Networks (Topics in Polymer Science)

STRUCTURES

PROPERTIE S RUBBERLIKE

AND

OF

NETWORK S

TOPICS IN POLYMER SCIENCE

II

s.,it, I IId,,.,,01:. XubfH.rlike Elasticity. A Mol~c ular Pri_f. As such, ;1 has much in common "ilb it< predecessor. panicularly ils Mrong emphasis on molecular concepls and lheories. Similarly. only equilibrium properlies are co",,"'" in any dClai!. This i! n"o~ treats mucb the ",me ,ubjtel maller, buI j, meanl to be a more oo"' l,rehen,i,,,, some".-hat more sophis· ticated. Ir~atm.nl. Ikcaus l11is /xige illld·Chain Modeb under Uniaxia l Stress 4l! 5.4.1 TI\(: Slip-Link Modd 4l! 5.4.2 The ConSiraint>d·Chain Mood 49 5.5 Comparison of Slress Sirain Relations wilh Experimental Data 49 References 52 6 Swelli ng 01 N .. wor~. 53 6.1 Free Energy or a Swollen Network

53

6.2 The Solvent Cl\(:micai Potent ial for an lsotropically S"'olkn NCI"wk 55 6.3 Thermodynamics of a Network Uniaxially StTetchcd in Sol"em 6.4 Elastic Activity of a Swollen Nelwork 60 6,5 MOTe Recent Treatments of Nelwork Sw.;lIing 62 6.6 Sorption and E "f"~C1ion of Diluents 63 6.6, I Line~r Diluent, 63 6.6,2 Branched Diluents 65 6.6,3 Cyclic Dil""nts 66 6.7 T rapping of C)'ct;';s witnin Network Struclures 66 6.7 ,1 Experimental Results 66 6.7 ,2 Theoretical Interpretations 67 6.7,3 Olympic Nelworks 69 Kef.renees 70 7 Crit ic.1 Phenomena and Ph..., Tran.itions in Gel. n 7. 1 Theory of Critical PhenOln."" and Phase Transitions 7.2 ThcrmOTC'ICr>ible Gels 79 References 83

57

74

8 Calcu lation •• nd Sim ulation. 87 8, I Spati"l Configurat ions of an Isolated Chin 87 8.2 Statistical A '''''''ges of Configurational Variables 92 8.3 Distributions for End.to·"nd Scpanltions for SptciflC T ypes of Chains 94 K4 Stress_Strain lso(henns Cakolatw from the Non·Gaussian J)i s( ributions 100 8.5 Molecular Dynamics Calculations 104 Reference. 104

Nctwor~

CONTENTS

i~

107 9.1 Tl>cory 108 9.2 T ypiclll Stress- Temperature Ddta 11 0 9. 3 IIlumati,"" Th.rn'oela"i~ R~~ul!~ 112 9.4 Relevan! Cal",imet';e SlUdic. of Elastic Deformation. 121 9.S Relevant Vi !Cosily-Tcmpo:1""~turc ResuilS On Dilute Polymer Solutions 122 9.6 Rotali l)eI"n",uon a nd O"o" ,,,,ion 174

x CON TE NTS 12.L6

[""lropic--N~matic

Phase T ransitions in Deformed Polymer Nctworks 17S ]2,2 Strain·l nduced Crystall ization 178 12.2. 1 General Feat ures 178 12.2.2 Models for Strain- Induced Crystallization in Stretched Networks 179 12.2.3 Predictions of the Molecular Theories 180 12.2.4 The Effects of Str~in_I nduced Cryitalli,ahon on Mochan;.;al Properties 182 References 185 13 Network> Hoving Mu lli mod~1 Chain_ Length Dist ribution. 188 [J . I Ultimate Properties and Non_(iauuian EfTects 188 13.2 lIi mo,:!. 1 Network. 189 13.2.1 Materials a"d Synthetic Tochniqucs IIW 13.2.2 T esting or the Weakest- l ink T heory 191 13.2.3 Elongation Result. 193 13.2.4 Result. in Other Mechan ical Deformations 203 13.2.5 Results On Nu nmcations 235 15.2 CIlcmical Aspects of Protein Biocl"stomer1 237 15,2.1 O"cfall Amino Aeid Cuml"',ition 237 15, 2.2 Amino Acid Scque,,,,ing 2.19 152..1 Crss_l.inking Chemipy 270 16.2.4 Scanorina Toch niques 27 1 16.2.5 NlIClcar Magnetic Rewna ~ 272 16.2.6 A8ina 275 16.2.1 0 0n.i1i.. 2H 16.1.8 Calorimetry 275 16.2.9 Thorm"iravirr"'lIic Analysi, 2 76 16.2.10 Mechanica l Propcllies and !;quilihriu m S ....ellin' 276 16.2.11 Compori",n. amons Vari"". Silica· Hased fillers 287 16.2.12 Oth" Polymers 288 16.2.1l OIMr u",mic- Typr "i lien 2~8 16.l Prcpo "'lion of 6 icOllI,n"",,1 Syslcml 2119 16.4 10 Situ Genc: .... 1ion of EJastomcn In Ccnn,ia 290 16.5 In Situ GenerlOt;on of CatalystS in Polymers 291 16.6 In Silu PoI)...,..ri>.aI'oru ofGbSf,Y PoIy"",rs 292 16.6.1 Isotropic SY$IC1nS 292 16.6.2 Anisotmpoc S)'lIcmJ 29S 16.7 Filler. R"''''''''!'n, 10 MalJlCl ic l'"icJoca use of th.ir res beyond the Gaussian chain model to diseuss the properties of the isolated chain from the Yicwpoint of the 'Olational iso"'eric state (R1 S) fo"nali ,m. This apprn.ach ta kcs into account the usual structural features of interest in any molecule (i .... bond lengths, bond "n<s. and the locations and energies of bond rotational states). Specific application" of the R1 S seheme to problems of rubber elasticity are gi"en lale. in tbe chapter. along with \he expressions of the end-toend ."",tor distribution fune tlaSIOmeric quantitie, into cntropic ~nd energetic components, a nd to lest some of Ihe major postulate, or ,"" 'nolccular theory deseribed ill chapter 2. Thi . ,uhject or nctwork "thcm,oeb$ticity" il th~refof< co,-crcd scpam tcly. in chapter~,

OVE RVI EW A N D SO ME FUN DAM ENTA L INf OR MATION

5

Nea rly all of the remaining cha plers are more s~ialized . For example, chapler 10 is ~boullh e already meolioo«l model elaslomers oblained by carr,'ing oul nelw",k.fonn>llion r~aclions ,nUC'h more ! valid when Ihe cbains ma king up Ihc nelwork h••'c ",miflexible ",gmenl$. This is Ihe area of liquid-cryilalline nelwork,. and great advances have now been made;n Ihi. field. The trcaln1C111 of such networks requires the descriplion of the packing enlropy of semirigid chains in a deformed lanlet, Thi. is covered in chapler 12. as is slrain·induced cryslal. 1i7-l1tion of networks in general. Cbapler 13 describes a particular lyre of model n.lwork, th.1 is, one in which the diSl ribulion of network chains is intenlionally made mu lti modal . 6 imodal elaslomer! a", Ihe .implesl and most imporlanl example of Ihi' type, and have been much siudied beeause Ihey have unusually good mO\Ohanical properli"", s~iFJeally simuhaneo usly large values of the .1""" ~nd exlensibilily. Th is, in lurn, gives la rge energies for Tuplure. lhe standard measure of the 10ught>eSS of a malerial. T he u", of Ihese nClwOfks in bolh fund.menul and applied slooies is oovcm:i, usi ng Ihi, as an OIXa,ion 10 MiiCribc mochani.al properly '4d 041 01 P~$:lJpP" ~',,, :x:>U"~ J>W.(lod)o II" "' ""P""I(I ""11"1!IIl "nb l'<JU;>ojl 'I'"J II I 'iuu:x:>uliuo pu~ ,.:'!".~ J,m'IOO ""I"I!IUCnb JO dUluuli>q "'''' ,~! 01 P~ 08 .. u.>wdol"~'p ='lI. ''''''ld'''''lP OI(l JO uo!w,=dd. J'll""l ~ JOpC'" '1(1 ""'~ "'[" pu~ '""'C INI U! ~Jo." Ap"' JO /I\,!.:u AI!I!'l!" U '1(1 SlIIj ~UI·)[\JlS "!"I(~ "'A!1' " 1('!4·" 01 ,U)Ir;) "41 ~U!guo:'iI h! ·pn",'" 'Sl:>:>ds:u JO J""wnu" "' InJ""" 'I pun " ppow "C)! ,!"W""! I""O"CIOJ 110 t»S'1ddu "! u,... ,S "I 'U!~I() ')"'/."IOOjo =uU1S IP PUo-\"IS'UoddV 'IL[l1!'U! JO lIu'PU"IU,'pUn Jeln""low ,u,M lSnb!U4:"" ~4.1 'wopue, A1411!4 puc P"IIOJIUOOUn "'. 1"4' 'UO,,8",'U",[n... Se 4'"W 's;>obIUI(""1 SU1~u'I-SWJJ IBnsn '~1 Aq poU!",qo u""I suI( ~JO/l\PU '1(1 u'4·" llu,'U,P AjJ~ln"lJ"" so "",""nJ1S ~"". JO UO!lB'!l)jJBJ" 4:J '1''''1,''0'411" II"" IC 1"1"'W)J>dX, 'SUO!,o:'iI!)SO" U111" AU"U""'., )0 '!S~ 'I(IIW)OJ lB~l :un,,,,,,,, lJON.IO" ""1 )0 uo"d,,:>s>p t"'l,epp" '.p",oJd V ' !pu:Kld. '''OS"lJ S!~1 '0.1 'P""I0.:!u"pmS J""P Ino~,c" 'I""'~JP IP," 'I "'''I:>OJ1I ~JOM1"" "'II 1"'11 ~wnSl~ ~'!,,!lS.l~ "''Iqn, JO .. U"""~,,, ll~ !SOW[" I"~I l~.J 01(' APOW'" 01 P"pnIJuI'1 'X.IPu)(ldo)o ~,,~ '1() JO lSJ~ ~U ',w'lds ~)ql J" 'wos n' poU!tlqO 'I)OJP 8u!:l.J0Ju1>j ~q' )1&.I1I"1I! 0, popnpu! S! IUO!I~WlOl'P JO ,(P!,U~ 'P'M 0 'uoriV 'A1""""1,' ~I"q 48!1( AI~u!puodm, r. pUB i\(1l!~M JOIO""[OW \(11'1( " •• ~ AII"JOuJll Q"l4," ,"WOI 'S"P U~ O)UI (UO!I'":U ~11lJ.d:>s • U! p"WJOJ) ""I" JO P"lq uoqJ"" t""IU"WOjllll~ AIP~ l,u'lq 01 lIundw'l1. Aq p""'B1qo &Qql 0) p;>Wsump'i'ms and the predictions of the two models have led to .. riou. di .. grc-ements during their de"elopment. as may be .... n from the original papers ci too carlier. The main roim ()f disagree. ment was tne magni1Ude of the (ront facI", th" t appeared in Ihe eXltression for Ihe elastic free energy and the stress, For tcttafunct ional nelwork •• the Jame,·Gulh phantom nttwork lhwry prediNs one-half thc value of Ihe fro nl facto r Ohtained by the Wall . Flory affine network ,heo'y . A1< of ne."'ork chai ... in ti>< "","",. f""ned nelwork are lhe same a•• h.,.. for an "nsemble of chains in ,he bulk. "n_ cross_linked ". Ie, The mean·sq""" eo.d·lo-cnd dimen""", of ,he lall.,.. in 1",n. are ~ .. I." ,hose of "'" ,; ngk
_.,.,-sq...

seq"""'"

.,'id."",""'.

Jomeo.Quth ItIrory,

4. Thc lotal cia";' •• "'BY of lhe network i, the 'um of the elastic cnerVos of ,hi: ir>di,'id ... 1cru.in •. Due to the .",umpti"" ttul the ohains are {=Iy join,ed•• 11 spotial arra ngements arc or lhe same .... rgy. lhe netwnr ~ fro