Диссертация (1097582), страница 39

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perpendicular2 hRe,xy i = (hRe,x i + hRe,y i)/2,22246 i = (hRe,x i + hRe,y ithez axis,hRe,zi,andin thexyforplane,hRthe22to=the2 isasknown2 betweene,xybiaxialphases.2 bein22for2hR2theirparallelwalls,wellasprofilesalongthez-axis.FrommeasurementsofPSStobeagoodorderparametertransitionsbetween uniaxialowntoagoodorderparametertransitionsuniaxialandRi,andthexyplane,hRi=(hRi+i)/2,i.e.perpendicularand3xis,hRi,andinthexyplane,hRi=(hRi+hRi)/2,i.e.perpendicularande,ze,xye,xe,ye,zin thee,xye,xe,yohniquethe walls,as nextwell astheiralongz-axis.Fromf = profiles8, willε0=0растворажесткоцепныхмакромолекулв плоском(см.section,weturntothethediscussionourmeasurementsresultsandparalleltoдляthewalls,as wellasofthetheirprofilesalongofthe z-axis.Fromслоеthe measurement5 recoparalleltothewalls,aswellastheirprofilesalongthez-axis.46In Eq.2,our simulations,wehavebiaxialphases.theaverageend-to-enddistancewe FromcalculatetheaspectofratioofA,as our globalstiffnesshetowalls,as wellastheirprofilesalongthe z-axis.Fromthemeasurementsthewalls,aswellastheirprofilesalongthez-axis.themeasurementsподраздел4.3.3).ge end-to-end distance we calculatethe aspectratio A,Eq.2, asglobal stiffnessthe averageend-to-enddistanceweourcalculatethe aspect ratio A, Eq.2, as our global stiffntheaverageend-to-enddistancewecalculate theaspect ratioA,theцепейmean-squaredend-to-enddistanInoursimulations,wehaverecordedalsosingle-chaincharacteristicssucE5measure.nd-to-enddistancewecalculatetheaspectratioA,Eq.2,asourglobalstiffnessons,wehaverecordedalsostandardsingle-chaincharacteristicssuchasДляописанияконформационныхсвойствполимерныхмы рассчитывалиrage end-to-end distance we calculate the aspect ratio A, Eq.2, as our global standardstiffnessmeasure.2measure.2 For the2theaxis,hRe,zi, вдольandinосиthexymean-squaredend-to-enddistancehRe2 ifunction,ofthe компонентыchainsand thecomponentsofsepahRe2plaiaidealchains,orientationalCkz, betweenbondvectorsnd-to-enddistancehRiofthechainsand the междуcomponentsofcorrelationhRi alongсреднийквадратрасстоянияконцамицепииегоe.eeeal chains, the orientational correlationfunction,C,betweenbondvectorssepakFor ideal chains, the orientational correlation function, Ck , between bond vectors seForxyidealchains,2 the orientational22 the walls, function,k, b2 correlation2axis,22unitsparalleltocorrelationwell asCtheithezmonomerhRe,yi, Candintheplane,hRi = (hRi)/2, i.e.

asperpendicularratedbykcorrelationthechain,chains,thexyorientationalfunction,, i.e.betweenbondvectorssepandintheplane,hRi=(hRi+hRperpendicularande,zi)/2,e,xye,x i + hRe,ykalongidealchains,theorientationalfunction,C,betweenbondvectorssepae,xye,xkzивплоскостиxy,атакжехарактеристическоеотношениеAk monomer units along the chain,rated by k monomer units along the chain,rated bymonomerunits alongthechain,averageend-to-enddistance we cparalleltotheтого,walls,asas ktheirprofilesthez-axis.From функцияthe measurementonomeralongthechain,wellunitsas theirprofilesalongz-axis.Fromthewellmeasurementsof alongtheys,kasmonomerunitsalongtheпо формуле chain,(81).theКромебыларассчитанаориентационнаякорреляционнаяCрасстоянииeweecalculate= hcos✓цепиi, ratio A, Eq.2, as our global(6)k = h~i ·~i+ki,i+kend-to-enddistancetheaspectstiffвдольCпоцепивекторовсвязинаk iвдольпоend distance we calculatetheA,✓i,i+kEq.2,ourglobalh~ethe· ~дляeaverage= hcosi, as(6)measure.k =iaspecti+k i ratioCk =stiffnessh~ei · ~ei+k i = hcos✓i,i+k i,Ck = h~ei · ~ei+k i = hcos ✓i,i+k i,Ck = Ch~eki ·=~emeasure.hcos(6) (6)Forideal chains,(82)the orientationai+kh~ei i· =~ei+ki =✓i,i+khcosi,✓i,i+k i,,shows an exponentialbehaviorrated byCkk ,зависимостиmonomerthesForidealtheorientationalcorrelationfunction,between unitsbondотalongvectorsкотораядляидеальнойцепиимеетвидэкспоненциальнойexponentialbehaviorshowsanexponentialbehavior, the orientationalcorrelationfunction,Cchains,bondvectorssepak , betweenshowsanexponentialbehavior0Ck the⇠ exp(k/lp ),(7)onentialbehaviornexponentialbehavior0расстояния вдольпо kцепиbymonomerunits alongchain,k/l(7)0k ⇠ exp(p ),Cer units along the chain, Crated0k ⇠ exp( k/lp ),Ck ⇠ exp( k/lp ),Ck ⇠ Cexp(k/lp0 ),, k/lp0 ),(7) (7)Ck =k ⇠ exp((83)0and the persistence length lp can be defined from this equation.

For nonideal systems,where0ersistence length lp can be definedfromthis equation.Fornonidealsystems,whereand thepersistencelengthlp0thecanbedefinedfromequation.For fromnonidealwhCei · ~ei+ki = thishcos✓i,i+ki,k = h~andpersistencelengthlp0 .canbeнеидеальныхdefinedthis systems,equation.F0изкоторойможноопределитьперсистентнуюдлинуДляцепейсC=h~e·~ei=hcos✓i,(6)0bekii+ki,i+kstencelengthlcandefinedfromthisequation.Fornonidealsystems,whereexcludedvolumeinteractionsplayarole,andindependentofthesolventqualityorsolutionpersistencelengthlcanbedefinedfromthisequation.Fornonidealsystems,whereppvolume interactions play a role,and independentof the solventqualityor solutionshows anexponentialbehaviorexcludedvolume interactionsplayvolumea role,interactionsandindependentthe andsolventqualityorofsolutexcludedplay aofrole,independenttheисключенным объемом это соотношение(83)41,42неприменимо независимоот плотностиumeinteractionsplayarole,andindependentofthesolventqualityorsolutiondensity,suchananalysisisnotapplicable.Nevertheless,theaveragecosinebetweentwod volume interactions play a role,41,42and independent of the solvent qualityorsolution41,42uch an analysis is not applicable.thecosine betweentwoanNevertheless,exponentialbehaviordensity,suchananalysisisaveragenotthe averagecosine41,42системы и showsоткачестварастворителя.Ноapplicable.тем anнеanalysisменее,Nevertheless,среднийкосинусугламеждуbetweendensity,suchisnot applicable.Nevertheless,the aal behavior41,42 41,42ananalysisisnotapplicable.Nevertheless,theaveragecosinebetweentwosubsequentbondvectorsalongthechain,hcos✓i,stillgivesareasonableestimationofsuch an analysis is not applicable.Nevertheless, the average cosinei,i+1between two0nt bond vectors alongthe chain,hcos ✓вдольi, поstillgivesвекторамиa reasonableofi,Ckestimation⇠ hcosexp( k/li,i+1subsequentbondvectorsalongthe bondchain,stillgivesa hcosreasonableestimationp ),0последовательнымицеписвязейвсеравнодаетразумнуюsubsequentvectors✓i,i+1alongthechain,✓lengthgivesi,i+1 i, stillC⇠exp(k/l),(7)andthepersistencelp0 canbe41,42kpond bondvectorsalongthechain,hcos✓i,stillgivesareasonableestimationofthechainstiffnessuentvectorsalongthechain,hcos✓i,stillgivesareasonableestimationofi,i+1i,i+1 41,4241,42stiffnessthe chain stiffnessоценку внутрицепнойжесткости дляполимерных41,42 систем [368, 369]:theлюбыхstiffness041,42 41,42volumeinteractionsplayaand the persistence lengthllchainbedefinedfromequation.For nonidealsystems,p0 canffness=hli/lnhcos✓i,i+1thisi, excluded(8) w0instiffnessp systems,00 b wherelength lp can be defined lfromthisequation.Fornonideal=hli/lnhcos✓i,(8)bi,i+1lp = hlb i/ lnhcos ✓i,i+1 i,l0 = hl i/ lnhcosp,(84)✓i,i+1i, orapplip ofsuchanalysisis notexcludedvolumeinteractionsplay a role, and independentthebansolventqualitysolulp0 = lp0hl=✓i,(8) density,hli/lnhcos✓i,(8)b i/ lnhcosi,i+1bi,i+1teractions play a role,whereand independentofthesolventqualityorsolutionhlb i isестьthe averagebondlengthwhichwe monitorAsan alternativetoгдеwhichсредняядлинасвязеймеждумономернымизвеньями,которуюмы41,42 in the simulation.vectorsalongthedensity,aninanalysisis notapplicable.Nevertheless,thebondaveragecosinebetweenis the average bond lengthwehlmonitorthesimulation.As whichan alternativetosubsequentwherei is theaveragebondlengthwe monitorin thewhichsimulation.Asaninalternativbsuchwherehliistheaveragebondlengthwemonitorthesimu41,42balysisisnotapplicable.Nevertheless,theaveragecosinebetweentwoheaveragebondlengthwhichwemonitorinthesimulation.Asanalternativetoможемрассчитыватьв ходеtheaverageof theмоделирования.anglesubsequentbond vectors,for our modell i is the average bondlengthwhichcosinewe monitorinthe betweensimulation.As an alternativeto41,42Hamiltonianalongthechain,hcos ✓i,i+1i, stillgivesa reasonableestimatiothechainstiffnessgeb cosine of the angle betweensubsequentsubsequentbond vectorsvectors,for ourmodelHamiltoniantheaverage bondcosineof thetheanglebetweensubsequentbondvectors,forour modelaveragecosineoftheanglebetweensubsequentbondHamiltonvectors,ectorsalongthechain,hcos✓i,stillgivesareasonableestimationofi,i+1osineoftheanglebetweensubsequentbondvectors,forourmodelHamiltoniantheenergysubsequentof the systemcanbe usedto Hamiltonianquantify this local stiffness.

For both the 0rage cosine of the anglebetweenbondvectors,for asourwellmodel41,42chainlpy of the system can be used theas welltostiffnessquantifythisthelocalstiffness.boththe be usedenergyof the systemcanbe usedasForwellto canquantifythisaslocalForthisbothenergyof thesystemwellstiffness.to quantifylo1,42frgytheofsystemcan becanusedaswelltoquantifythis localstiffness.Forboththeglobalandthelocalstiffnessmeasure,theirprofilesA(z)andl(z)havebeendeterminedasthe systembeusedaswelltoquantifythislocalstiffness.Forboththep04.3.2.Эффективноеприbeenв объемеlнематическомhlb i/profileslnhcosупорядочении✓A(z)d the local stiffnessmeasure,their profileslцепейdeterminedi,i+1 i,globalandожестчениеtheA(z)localandstiffnessmeasure,theirand ltheirbeen determinedp = localp (z) havep (z) haveglobaland thestiffnessaswheremeasure,profileslp (z0hliistheaverageA(z)bondandlengthbl=hli/lnhcos✓i,(8)bi,i+1phelocalstiffnessmeasure,theirprofilesA(z)andl(z)havebeendeterminedasand the local stiffness measure,theirprofilesA(z)pand lp (z) have been determined asПри моделировании раствора жесткоцепныхполимеров в свободном объеме в99 b i is the average bond length which we9monitorwhere hlthe simulation.alternativtheinaveragecosinetheananglebetwe9 of Asмынаблюдализаметноеполимерных цепей в нематическом9 inrage bond length работеwhich we[188]monitortheAs anожестчениеalternative to9 simulation.the average cosine of the angle between subsequent bondvectors,modelcanHamiltothe energyof fortheoursystembe useof the angle between subsequent bond vectors, for our model Hamiltonianthe energy of the system can be180used as well to quantifythis thelocalstiffness.bothglobal andlocalstiffnessFormeasurystem can be used as well to quantify this local stiffness.

For both theglobal and the local stiffness measure, their profiles A(z) and lp (z) have been determinerated by k monomer units along the chain,Ck = h~ei · ~ei+k i = hcos ✓i,i+k i,состоянии, которое впервые обсуждалось в теоретической работе [332], а затемобсуждалось также в работах [333-336]. Мы рассчитали ориентационную корреляционнуюshows an exponential behaviorфункцию вдоль по цепи, Ck, при различных значениях плотности (объемной доли)Ck ⇠ exp( k/lp0 ),полимера φ и параметра ориентационного порядка S.

Аппроксимировав эту функциюandперсистентнойthe persistenceдлиныlength lp0 ,canbe definedfrom this equation.формулой (83), мы получили оценкукотораяпредставленавexcludedvolumeplay [188].a role, Мыand independentof thзависимости от плотности φ на рис.83, взятомизinteractionsнашей работывыбралилогарифмическуюшкалудля41,42density,such an дляanalysisis not applicable.Nevertheless, theосиординатсравненияс теоретическимипредсказаниями [332] об экспоненциальномразмеровцепиsubsequent ростеbond vectorsalongtheвдольchain,направленияhcos ✓i,i+1 i, still giveнематического директора с увеличениемконцентрациив нематической фазе для цепей сthe chainstiffness 41,42персистентным механизмом гибкости.

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