物理缔合高分子溶液体系相行为的格子自洽场研究
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摘要
物理缔合高分--子溶液体系能够表现出丰富的相行为,其中包括热可逆凝胶化和相分离。针对这种现象的定性解释早在三十年前就已提出。但仍有很多基本问题如溶胶-凝胶转变的“级数”尚未认识清楚。自治场方法作为平均场层次中的最准确方法,在嵌段共聚物体系的自组装行为的研究中已经被广泛使用。自洽场方法能够得到相对准确的数值结果,这是其它平均场方法所不能比拟的。因此,本文将格子自洽场方法应用到物理缔合高分子溶液体系当中,来研究系统的热力学性质和结构行为,并得到了预期结果。此外,作为外场动力学方法应用的尝试,本文还利用格子自洽场方法和格子外场动力学方法研究了棒-棒二嵌段共聚物体系的自组装行为。
全文共分四个部分:
第一部分,特定高分子链结构(链长101,每十个单体含有一个粘性单体)的多点物理缔合高分子体系的相行为。
在模拟中,我们观察到溶液体系的两种不均匀的结构:一种是微涨落结构:另一种是随机密堆积胞结构。当(?)_P≥0.08,且均匀高分子溶液体系温度降低到一定程度时,微涨落结构在系统中首先出现,同时系统从均匀相完全转变为微涨落相。如果温度继续降低,随机密堆积胞结构也将会出现。但当(?)_P＜0.08,且均匀溶液体系的温度降低到一定程度时,随机密堆积胞结构直接出现在系统中.当(?)_P＜0.53,胞结构的出现伴随着系统宏观相分离的发生;当(?)_P≥0.53时,系统由微涨落相完全转变为随机密堆积胞相。随后进一步计算了系统的比热值。结果发现,在上述的每一个转变点都有和温度相关的比热峰出现。不同转变点的比热峰形状表现出不同的特征。最后还发现,微涨落相和随机密堆积胞结构自由能landscape的能量盆个数和深度都是不同的;而且很难通过热涨落从某个某个结构的能量盆中逃离而进入到其它的结构的能量盆.
第二部分,多点物理缔合高分子溶液系统中,高分子链结构的改变对相边界的影响。
描述高分子链结构的参数有链长N和相邻的两个粘性单体间隔l。结果表明,当l=10且N＞11时,高分子的链长的增加有利于微涨落结构的稳定。相对于微涨落结构受到链长增加的影响来说,胞结构受到的抑制影响要弱得多。当链长(N=61)保持不变,l从10减少到6时,微涨落相边界的变化和增加链长时的变化基本相似,但同时l的降到也促进了胞结构的出现,这与链长增加的影响是不同的。在l不同的系统中,(?)_(tp)(微涨落相和胞相两者相边界交点对应的(?)_P)随着链长增加的变化趋势基本满足相同的函数关系。对于胞结构的相边界,我们利用方程ln(φ_P)=A+B/T进行了拟合,拟合关系是否成立和N和l的值都相关。
第三部分,研究了对称结构的末端物理缔合高分子链体系胞相边界的性质。此部分可分为三个方面:
首先,在末端物理缔合高分子链体系中,研究了末端粘性嵌段单体数N_(st)的大小对胞相边界的影响。结果表明,不同N_(st)系统的胞相边界线随高分子浓度(?)_p的变化趋势表现出不同的特征。其次,探讨了N_(st)的改变对胞结构形状的影响.从计算结果中得知,当N_(st)=1或N_(st)=2时,只有近球状胞结构㈩现:当N_(st)=3时,近球状、块状和蠕虫柱状胞结构都会出现。随后计算的高分子体积分数随离胞核的距离增加的变化趋势也在一定程度上证实了胞结构的形状变化,同时它也给出了胞结构近邻分布的变化。最后,考察了N_(st)的改变对相边界线系统胞数(相当于胞核的体积)的影响。从计算结果中得知,N_(st)的改变对低的高分子浓度体系和中间高分子浓度体系的胞数随(?)_P的变化趋势影响较小,但在高浓度体系中,N_(st)的改变对胞数随(?)_P变化趋势产生了显著的影响。
第四部分,利用格子自洽场方法和格子外场动力学方法研究棒-棒二嵌段共聚物体系的自组装行为。
首先,在面心立方格子中利用自洽场格子模型,研究了棒-棒二嵌段共聚物高分子体系的自组装行为,建立了系统的相图。在模拟计算中,我们观察到了四种稳定的有序形貌,即交叠柱状、柱状、层状和zigzag层状形貌;此外,我们获得了胞状和zigzag柱状两个亚稳的有序形貌。其次,利用外场动力学方法,讨论了层状、柱状和zigzag柱状结构的形成过程。结果表明,这些形成过程都可以分为三个阶段,初期阶段是同种成分汇集成双连通区域;中期阶段系统中出现了相应结构的雏形;末期阶段系统演化出基本有序的自组装结构。三种结构的形成过程表现出了共同的特征,即由小的某种成分富集区形成系统渗流的双连通区域。不同的是,在柱状结构的形成中,出现了局域的类zigzag柱状中间结构。
The rich phase behavior in physically associating polymer solutions(PAPS),which consists of the reversible gelation and phase separation,the fundamental explanations about them have existed for more than three decades.After that,many theories and methods have been used to account this system.But so far,many fundamental problems,such as the thermodynamic nature of the transition from a sol state to a gel state,and vice versa sol/gel transition,has not yet been clarified.Further,the explanations about new phenomena appearing in experiments challenge the theoretical physicists.Self-consistent field theory (SCFT),which is the most precise methods of the mean-field framework,is applied widely in the field of the assembly of block copolymers.Using SCFT the self-assembly of flexible-chain system is studied,and the results of the rigid block copolymers accounted by SCFT are also demonstrated by the related experiments.In contrast to the other mean-field methods, the advantage of SCFT,which begins with the analytic onset,can obtain the relatively accurate numerical result.Therefore,the lattice SCFT is applied to physically associating polymers to study the thermodynamic property and structure behavior in the paper,and the expectant results are obtained.
There are two chain architectures for associating polymer.One is the physically associating polymer which has many associating points distributing along the backbone,the other is the physically associating polymer which only has end-associative points at the two ends of the chain.The systems of the two chain models are systematically studied in this paper.
Further.the trial application of lattice external field dynamic method is that the assembly of rod-rod block copolymers is studied by the lattice SCFT and lattice external field dynamic method.
This paper consists of four sections:
In the first section,we study the phase behavior of PAPS.where the polymer has many associating points distributing along the backbone.Chain length of N=101 is considered, where each sticker monomer is regularly placed ten monomer apart.
In the simulation,two inhomogenous structures in the solutions are observed.One is a micro-fluctuation homogenous(MFH) structure,the other is a randomly-closely packed micelle(RCPM) structure.The structure of the micelle in RCPM is similar to that of the "flower micelle" in the telechelic associative polymer system.When(?)_P≥0.08 and the homogenous associating polymer solution is cooled,the MFH structure firstly appears,and the system transits from the homogenous solutions(HS) to the MFH phase entirely.If the solutions are cooled further,the RCPM structure appears.When(?)_P＜0.08 the system immediately transits from the homogenous solutions(HS) to the RCPM morphology entirely when the polymer solution is cooled to be sufficiently low.At the same time,if(?)_P＜0.53, a macroscopic phase separation accompanying the occurrence of RCMP occurs,where the polymer rich phase consists of RCPM morphology,otherwise the system entirely transits from MFH morphology into RCPM morphology.
Furthermore,a peak appears in the temperature-dependent specific-heat curve C_V(χ)/(?)_P at each transition point.For the HS-MFH transition the peaks are unsymmetrical,i.e., C_V(χ)/(?)_P has an abrupt increase and a slow decrease,whereas for the MFH-RCMD phase transition C_V(χ)/(?)_P shows an approximately symmetrical character.Finally,the system in MFH phase may be trapped in one of the two energy basins in a experimental time scale. However,the appearance of RCPM structure means that the system is trapped in one of the series of "deeper" energy basins,and it is difficult to jump off this deep basin into one of the MFH or one of the other RCPM structures through thermal fluctuations.
In the second section,the effect of the changes of chain architecture on the boundary of the phase is studied.
The parameters of the architecture of chain is N and l.When the chain length increases when l=10 and N＞11,the boundary of the MFH occurrence occurs at lowerχand (?)_P.However,the boundary of the micellar occurrence occurs in largerχ,and changes weakly.The triple point,which corresponds to the intersection between the boundaries of the MFH and micellar structures,moves to lower polymer concentration(?)_(tp).The above results demonstrate that MFH structure is dependent on the chain length,the increase of the chain length is favorable to the stability of MFH structure.Note that it is not observed in the system for N=11 in this simulation.This confirms the dependence of the MFH structure on the chain length.
When l decreases from 10 to 6 for fixed N=61,the behavior of MFH morphology is similar to the case of the increase of chain length.However,the boundary of the micellar occurrence also goes down to the lowerχwhen decreasing l.When the chain length increases, the values of(?)_(tp) for the different l systems basically satisfy the same functional relationship. For the boundary of the micellar occurrence,we examine wether the equation ln(φ_(cmc))= A+B/T,where A,B are parameters,fulfils.When the chain length is short the functional relationship fulfils.The increase of chain length make it not fulfil,which is dependent on the l.
In the three section,the phase behavior of end-associating polymer of symmetrical end block in a solvent is studied.
Firstly,the effect of the number of sticker monomers of end block N_(st) on the boundary of micellar phase on the phase diagram is systematically studied.The variations of the micellar boundary with(?)_P are different for different N_(st) systems.In the case of N_(st)=1,the saturate phenomenon occurs in the high(?)_P range,i.e..the increase of(?)_P does not continue to decrease the values ofχon the boundary of micellar phase.In the systems of N_(st)=2 and N_(st)=3,however,this saturate phenomenon disappears.Furthermore,the increase of N_(st) from 1 to 2 makes micelle occur in the regime of lower(?)_P,whereas when N_(st) increases from 2 to 3,similar effect becomes much weaker and the critical micellar concentration almost does not change.
Secondly,the variations of the micellar shapes with N_(st) and(?)_P are studied.In the systems for N_(st)=1 and N_(st)=2.only sphere-like micelle is observed.In addition to sphere-like micelle,bulk micelle and worm-cylindrical micelle are observed in the system of N_(st)=3.
Finally.the changes of the micellar numbers in the systems on the boundaries of the micellar phase are accounted in the cases of different N_(st).The variation of the micellar number with(?)_P is dependent on the magnitude of(?)_P In the low range of polymer concentration, the increase of the micellar number with(?)_P is very slow.In the intermediate range of polymer concentration,the micellar number increases slowly with(?)_P.In the above two ranges of polymer concentration,the change of N_(st) has weak effect on the variation of micellar numbers with(?)_P.In the high range of polymer concentration,the different behaviors are observed in the systems of different N_(st).For N_(st)=1,the micellar numbers increase less 10%for a increase of(?)_P= 0.1,which behaves hke the constant.For N_(st)= 2,there is a valley in the curve of the variation of the micellar number with(?)_P,on the onset of the high range of polymer concentration.It may be relative to the changes of the positions of the near-neighboring micelles.There is a linear variation of the micellar number with(?)_P in the system of N_(st)=3.
In the fourth section,the self-assemble behavior of rod-rod diblock copolymers is studied by means of self-consistent field lattice model(SFLM) and external field dynamic lattice method(EFDLM).
Firstly,using SFLM in the face center lattice,the self-assemble behavior of the rod-rod diblock copolymers is studied,and the phase diagram is constructed.It is shown that the order-disorder transition point of rod-rod diblock copolymers is lower than that of coil-rod diblock copolymers,which is consistent with the other theoretical prediction.Four stable structures are obtained,i.e.,overlapping cylinders,cylinders,lamellae and zigzag lamellae. Furthermore,tow metastable states are observed,i.e.,micelles and zigzag cylinders.
Secondly,the forming processes of the lamellar,cylindrical and zigzag cylindrical morphologies are investigated by means of EFDLM.The three forming processes are divided into three stages:The collection of the same component occurs in the initial stage when the system behaves the doubled connected domains;In the intermediate stage the rudiment of the respective structure forms;In the final stage the system forms the ordered structure.The formation of biconnected domains from the relatively small domains,where some component is rich,is the common character of the forming processes of the three structures.Seen from the evolutive times of the above structures,the evolutive time of cylinder structure is much longer than those of the other two structures.This may be due to the formations of the zigzag cylinders in local sections of cylindrical rudiment in the evolving process(disappeared in the final stage).
全文共分四个部分:
第一部分,特定高分子链结构(链长101,每十个单体含有一个粘性单体)的多点物理缔合高分子体系的相行为。
在模拟中,我们观察到溶液体系的两种不均匀的结构:一种是微涨落结构:另一种是随机密堆积胞结构。当(?)_P≥0.08,且均匀高分子溶液体系温度降低到一定程度时,微涨落结构在系统中首先出现,同时系统从均匀相完全转变为微涨落相。如果温度继续降低,随机密堆积胞结构也将会出现。但当(?)_P＜0.08,且均匀溶液体系的温度降低到一定程度时,随机密堆积胞结构直接出现在系统中.当(?)_P＜0.53,胞结构的出现伴随着系统宏观相分离的发生;当(?)_P≥0.53时,系统由微涨落相完全转变为随机密堆积胞相。随后进一步计算了系统的比热值。结果发现,在上述的每一个转变点都有和温度相关的比热峰出现。不同转变点的比热峰形状表现出不同的特征。最后还发现,微涨落相和随机密堆积胞结构自由能landscape的能量盆个数和深度都是不同的;而且很难通过热涨落从某个某个结构的能量盆中逃离而进入到其它的结构的能量盆.
第二部分,多点物理缔合高分子溶液系统中,高分子链结构的改变对相边界的影响。
描述高分子链结构的参数有链长N和相邻的两个粘性单体间隔l。结果表明,当l=10且N＞11时,高分子的链长的增加有利于微涨落结构的稳定。相对于微涨落结构受到链长增加的影响来说,胞结构受到的抑制影响要弱得多。当链长(N=61)保持不变,l从10减少到6时,微涨落相边界的变化和增加链长时的变化基本相似,但同时l的降到也促进了胞结构的出现,这与链长增加的影响是不同的。在l不同的系统中,(?)_(tp)(微涨落相和胞相两者相边界交点对应的(?)_P)随着链长增加的变化趋势基本满足相同的函数关系。对于胞结构的相边界,我们利用方程ln(φ_P)=A+B/T进行了拟合,拟合关系是否成立和N和l的值都相关。
第三部分,研究了对称结构的末端物理缔合高分子链体系胞相边界的性质。此部分可分为三个方面:
首先,在末端物理缔合高分子链体系中,研究了末端粘性嵌段单体数N_(st)的大小对胞相边界的影响。结果表明,不同N_(st)系统的胞相边界线随高分子浓度(?)_p的变化趋势表现出不同的特征。其次,探讨了N_(st)的改变对胞结构形状的影响.从计算结果中得知,当N_(st)=1或N_(st)=2时,只有近球状胞结构㈩现:当N_(st)=3时,近球状、块状和蠕虫柱状胞结构都会出现。随后计算的高分子体积分数随离胞核的距离增加的变化趋势也在一定程度上证实了胞结构的形状变化,同时它也给出了胞结构近邻分布的变化。最后,考察了N_(st)的改变对相边界线系统胞数(相当于胞核的体积)的影响。从计算结果中得知,N_(st)的改变对低的高分子浓度体系和中间高分子浓度体系的胞数随(?)_P的变化趋势影响较小,但在高浓度体系中,N_(st)的改变对胞数随(?)_P变化趋势产生了显著的影响。
第四部分,利用格子自洽场方法和格子外场动力学方法研究棒-棒二嵌段共聚物体系的自组装行为。
首先,在面心立方格子中利用自洽场格子模型,研究了棒-棒二嵌段共聚物高分子体系的自组装行为,建立了系统的相图。在模拟计算中,我们观察到了四种稳定的有序形貌,即交叠柱状、柱状、层状和zigzag层状形貌;此外,我们获得了胞状和zigzag柱状两个亚稳的有序形貌。其次,利用外场动力学方法,讨论了层状、柱状和zigzag柱状结构的形成过程。结果表明,这些形成过程都可以分为三个阶段,初期阶段是同种成分汇集成双连通区域;中期阶段系统中出现了相应结构的雏形;末期阶段系统演化出基本有序的自组装结构。三种结构的形成过程表现出了共同的特征,即由小的某种成分富集区形成系统渗流的双连通区域。不同的是,在柱状结构的形成中,出现了局域的类zigzag柱状中间结构。
The rich phase behavior in physically associating polymer solutions(PAPS),which consists of the reversible gelation and phase separation,the fundamental explanations about them have existed for more than three decades.After that,many theories and methods have been used to account this system.But so far,many fundamental problems,such as the thermodynamic nature of the transition from a sol state to a gel state,and vice versa sol/gel transition,has not yet been clarified.Further,the explanations about new phenomena appearing in experiments challenge the theoretical physicists.Self-consistent field theory (SCFT),which is the most precise methods of the mean-field framework,is applied widely in the field of the assembly of block copolymers.Using SCFT the self-assembly of flexible-chain system is studied,and the results of the rigid block copolymers accounted by SCFT are also demonstrated by the related experiments.In contrast to the other mean-field methods, the advantage of SCFT,which begins with the analytic onset,can obtain the relatively accurate numerical result.Therefore,the lattice SCFT is applied to physically associating polymers to study the thermodynamic property and structure behavior in the paper,and the expectant results are obtained.
There are two chain architectures for associating polymer.One is the physically associating polymer which has many associating points distributing along the backbone,the other is the physically associating polymer which only has end-associative points at the two ends of the chain.The systems of the two chain models are systematically studied in this paper.
Further.the trial application of lattice external field dynamic method is that the assembly of rod-rod block copolymers is studied by the lattice SCFT and lattice external field dynamic method.
This paper consists of four sections:
In the first section,we study the phase behavior of PAPS.where the polymer has many associating points distributing along the backbone.Chain length of N=101 is considered, where each sticker monomer is regularly placed ten monomer apart.
In the simulation,two inhomogenous structures in the solutions are observed.One is a micro-fluctuation homogenous(MFH) structure,the other is a randomly-closely packed micelle(RCPM) structure.The structure of the micelle in RCPM is similar to that of the "flower micelle" in the telechelic associative polymer system.When(?)_P≥0.08 and the homogenous associating polymer solution is cooled,the MFH structure firstly appears,and the system transits from the homogenous solutions(HS) to the MFH phase entirely.If the solutions are cooled further,the RCPM structure appears.When(?)_P＜0.08 the system immediately transits from the homogenous solutions(HS) to the RCPM morphology entirely when the polymer solution is cooled to be sufficiently low.At the same time,if(?)_P＜0.53, a macroscopic phase separation accompanying the occurrence of RCMP occurs,where the polymer rich phase consists of RCPM morphology,otherwise the system entirely transits from MFH morphology into RCPM morphology.
Furthermore,a peak appears in the temperature-dependent specific-heat curve C_V(χ)/(?)_P at each transition point.For the HS-MFH transition the peaks are unsymmetrical,i.e., C_V(χ)/(?)_P has an abrupt increase and a slow decrease,whereas for the MFH-RCMD phase transition C_V(χ)/(?)_P shows an approximately symmetrical character.Finally,the system in MFH phase may be trapped in one of the two energy basins in a experimental time scale. However,the appearance of RCPM structure means that the system is trapped in one of the series of "deeper" energy basins,and it is difficult to jump off this deep basin into one of the MFH or one of the other RCPM structures through thermal fluctuations.
In the second section,the effect of the changes of chain architecture on the boundary of the phase is studied.
The parameters of the architecture of chain is N and l.When the chain length increases when l=10 and N＞11,the boundary of the MFH occurrence occurs at lowerχand (?)_P.However,the boundary of the micellar occurrence occurs in largerχ,and changes weakly.The triple point,which corresponds to the intersection between the boundaries of the MFH and micellar structures,moves to lower polymer concentration(?)_(tp).The above results demonstrate that MFH structure is dependent on the chain length,the increase of the chain length is favorable to the stability of MFH structure.Note that it is not observed in the system for N=11 in this simulation.This confirms the dependence of the MFH structure on the chain length.
When l decreases from 10 to 6 for fixed N=61,the behavior of MFH morphology is similar to the case of the increase of chain length.However,the boundary of the micellar occurrence also goes down to the lowerχwhen decreasing l.When the chain length increases, the values of(?)_(tp) for the different l systems basically satisfy the same functional relationship. For the boundary of the micellar occurrence,we examine wether the equation ln(φ_(cmc))= A+B/T,where A,B are parameters,fulfils.When the chain length is short the functional relationship fulfils.The increase of chain length make it not fulfil,which is dependent on the l.
In the three section,the phase behavior of end-associating polymer of symmetrical end block in a solvent is studied.
Firstly,the effect of the number of sticker monomers of end block N_(st) on the boundary of micellar phase on the phase diagram is systematically studied.The variations of the micellar boundary with(?)_P are different for different N_(st) systems.In the case of N_(st)=1,the saturate phenomenon occurs in the high(?)_P range,i.e..the increase of(?)_P does not continue to decrease the values ofχon the boundary of micellar phase.In the systems of N_(st)=2 and N_(st)=3,however,this saturate phenomenon disappears.Furthermore,the increase of N_(st) from 1 to 2 makes micelle occur in the regime of lower(?)_P,whereas when N_(st) increases from 2 to 3,similar effect becomes much weaker and the critical micellar concentration almost does not change.
Secondly,the variations of the micellar shapes with N_(st) and(?)_P are studied.In the systems for N_(st)=1 and N_(st)=2.only sphere-like micelle is observed.In addition to sphere-like micelle,bulk micelle and worm-cylindrical micelle are observed in the system of N_(st)=3.
Finally.the changes of the micellar numbers in the systems on the boundaries of the micellar phase are accounted in the cases of different N_(st).The variation of the micellar number with(?)_P is dependent on the magnitude of(?)_P In the low range of polymer concentration, the increase of the micellar number with(?)_P is very slow.In the intermediate range of polymer concentration,the micellar number increases slowly with(?)_P.In the above two ranges of polymer concentration,the change of N_(st) has weak effect on the variation of micellar numbers with(?)_P.In the high range of polymer concentration,the different behaviors are observed in the systems of different N_(st).For N_(st)=1,the micellar numbers increase less 10%for a increase of(?)_P= 0.1,which behaves hke the constant.For N_(st)= 2,there is a valley in the curve of the variation of the micellar number with(?)_P,on the onset of the high range of polymer concentration.It may be relative to the changes of the positions of the near-neighboring micelles.There is a linear variation of the micellar number with(?)_P in the system of N_(st)=3.
In the fourth section,the self-assemble behavior of rod-rod diblock copolymers is studied by means of self-consistent field lattice model(SFLM) and external field dynamic lattice method(EFDLM).
Firstly,using SFLM in the face center lattice,the self-assemble behavior of the rod-rod diblock copolymers is studied,and the phase diagram is constructed.It is shown that the order-disorder transition point of rod-rod diblock copolymers is lower than that of coil-rod diblock copolymers,which is consistent with the other theoretical prediction.Four stable structures are obtained,i.e.,overlapping cylinders,cylinders,lamellae and zigzag lamellae. Furthermore,tow metastable states are observed,i.e.,micelles and zigzag cylinders.
Secondly,the forming processes of the lamellar,cylindrical and zigzag cylindrical morphologies are investigated by means of EFDLM.The three forming processes are divided into three stages:The collection of the same component occurs in the initial stage when the system behaves the doubled connected domains;In the intermediate stage the rudiment of the respective structure forms;In the final stage the system forms the ordered structure.The formation of biconnected domains from the relatively small domains,where some component is rich,is the common character of the forming processes of the three structures.Seen from the evolutive times of the above structures,the evolutive time of cylinder structure is much longer than those of the other two structures.This may be due to the formations of the zigzag cylinders in local sections of cylindrical rudiment in the evolving process(disappeared in the final stage).
引文
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