复杂高分子体系的自洽场理论研究及微管动力学的蒙特卡罗模拟
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摘要
高分子、胶体、膜及蛋白质等软物质与人们的生活密切相关,在自然界、生命体系和日常生活中广泛存在。生物体与高分子体系之间的联系十分密切,生命物质大多由高分子构成,如生物膜可看作由两亲性分子所形成的囊泡结构等等。嵌段共聚物组分间的相互作用及分子链的拓扑构型都会对其相分离形态产生很大影响,因此考察含有特殊分子链结构的高分子共混体系、溶液体系及受限体系的相分离行为对于软物质形态结构的研究具有非常重大的意义。微管为真核细胞所特有,是细胞骨架系统的主要组成部分之一,在细胞运动、细胞分裂及细胞内物质的运输等细胞活动中起着重要的作用。微管由微管蛋白异二聚体聚合而成,聚合的同时还伴随着解聚及与微管蛋白结合的GTP水解的过程,其动力学行为非常复杂。本文首先基于自洽平均场理论研究了含有星型高分子链结构的高分子体系的相分离行为,然后应用蒙特卡罗方法对微管的动力学过程进行了探讨。主要包括以下内容:嵌段共聚物与星型均聚物共混体系的相行为、星型三嵌段共聚物本体及其在选择性溶剂中的相行为、受限星型三嵌段共聚物薄膜的相行为以及微管动力学的蒙特卡罗模拟。
第一部分:聚合物共混体系中各组分间的相容性是影响体系结构和性能的重要因素。对于嵌段共聚物/均聚物共混体系,其相分离行为不仅包含嵌段共聚物与均聚物之间的宏观相分离和嵌段共聚物本身不同链段间的微相分离,还包括这两种相分离之间的竞争,这些因素极大程度影响了共混体系的相分离形貌和结构,从而最终影响材料的性能。本文应用自洽场理论系统研究了嵌段共聚物AB与星型均聚物A的共混体系的相行为,着重讨论了当嵌段共聚物的组成一定时,体系中星型均聚物的体积分数及均聚物与嵌段共聚物链长之比对体系相形态的影响,此外,还考察了星型均聚物在共混体系中的分布情况,并从熵和相互作用能的角度加以解释,我们还观察到星型均聚物由于链拓扑结构的特殊性使其与嵌段共聚物分子间的相互作用不同于线型均聚物共混体系。
第二部分:为了考察分子参数和分子链拓扑构型对聚合物相结构的影响以及发现新的有序结构,在实验上需要合成大量的嵌段共聚物。在嵌段共聚物溶液中,溶剂的存在不但拓宽了嵌段共聚物的自组装形态,而且连续改变体系的浓度可以达到改变组分间相互作用能的目的。因此,通过嵌段共聚物和小分子溶剂共混,可考察分子参数对体系微相结构的影响。本文应用自洽场理论研究了星型ABC三嵌段共聚物本体及浓溶液体系的相行为,考察了在不同的组分间相互作用参数下,聚合物浓度对嵌段共聚物微相分离的影响,并给出了一维相图;还对星型嵌段共聚物本体及溶液中的相分离情况进行了详细的对比。通过聚合物本体及在两种浓度下相分离行为的比较,发现对嵌段C具有选择性的溶剂的加入相当于增加了嵌段C的有效体积分数,对于另外两个嵌段来说相当于升高了相分离温度,致使体系在一定的组分范围内,发生溶致性相转变。在相同聚合物浓度下通过比较两种对嵌段C具有不同选择性的溶剂对相分离的影响,发现即使都是C嵌段的良溶剂,当其选择性不同时,体系的相分离行为也有很大差别。我们的研究有助于加深对星型三嵌段共聚物本体及浓溶液体系的相分离行为的理解,从而指导嵌段共聚物有序结构的预测和设计。
第三部分:薄膜是一种非常普遍而且重要的受限体系。边界的受限效应给高分子的熵带来变化的同时,受限边界对不同嵌段的浸润性质也会引起表面能的变化,两者的共同作用往往很大程度地改变边界附近的高分子构型,从而改变表面附近区域的微相分离形态。本文应用自洽场理论系统模拟了在两个平行基板之间受限的星型ABC三嵌段共聚物薄膜的相行为。在模拟中,体系各个组分的体积分数选取近似相等以突出星型高分子链的特征结构;考察了在不同的组分间相互作用参数下,薄膜的厚度(基板的距离)及表面场的强度对共聚物薄膜相行为的影响。研究结果表明,在受限及表面场作用下出现了一系列稳定的相形态,包括柱状相、波浪柱状相、层状相和交替柱状相、穿孔层状相及交替分散的球状结构等,这些结构在实验和理论上都已被发现。在我们的计算中也发现了一些新的结构,如柱状与交替螺旋结构及复杂的网络结构等。当基板对各组分均为中性时,与聚合物本体的相形态相似,受限体系大多形成柱状形态,并且由于星型交联点的限制作用,柱的形状和直径都可自发地进行自我调节以适应不同的膜厚。当表面场较弱时,柱状结构比较普遍,薄膜的相结构主要由体系受限效应及膜厚与相结构周期的匹配性来控制;然而,随表面场强度的增加,表面场对薄膜结构的影响变得重要;当表面场强度足够大时,会导致体系由柱状结构转变成非柱状相。我们关于星型ABC三嵌段共聚物薄膜的研究有助于理解薄膜体系中受限效应、表面场、组分间相互作用及分子链拓扑结构之间复杂的共同作用,从而帮助和指导实验,并得到更多更新颖的纳米级有序材料。
第四部分:在合适的温度及微管蛋白浓度下,微管蛋白异二聚体可以聚合成微管,聚合的同时还伴随着解聚及与微管蛋白结合的GTP水解的过程,其动力学行为非常复杂,对微管动力学的研究一直都是生命科学中的热门课题。本文应用蒙特卡罗方法模拟了微管的生长过程以及成核速率、微管蛋白单体浓度、聚合及解聚速率对微管生长动力学的影响,重点考察了耦合水解反应后微管的动力学行为。研究结果表明,单体浓度的升高会促进微管的聚合,因而微管平均长度增加;当单体浓度低于临界值时,微管不会生长;在绝大多数反应参数下,微管生长都会达到稳态;耦合了水解反应后,单根微管长度随时间变化的动力学过程与实验结果基本相符;在计算中我们发现微管动力学模型及GTP水解反应模型的选取对于研究微管的动力学过程十分重要。尽管本部分研究工作仅得到一些初步的结果,但对进一步研究微管动力学提供了有力的指导及数据积累。本研究有助于在现有知识的基础上更加深入地理解、解释一些生命过程和现象。
Soft matter is closely related to human's lives, which widely exists in nature, life body and daily life, such as polymer, colloid, membrane and protein. There is a close relation between organisms and polymers, for example, biological membrane can be regarded as vesicle consisting of amphiphilic molecules. The microdomain structure of block copolymer is determined mainly by the molecular architecture and the interaction between the different components, thus the study of phase behavior of polymer system which contains special molecular chain architecture is significant to research the morphologies of soft matters. Microtubules are essential component of the cytoskeleton and are widely spread throughout the cytoplasm of eukaryotic cells. They play critical roles in a variety of cell processes, including cell shaping, intracellular tracking, cell division, and cell migration. The polymerization of microtubule is accompanied with the depolymerization of tubulin dimers and the hydrolysis of GTP (Guansine Triphosphate) within the microtubules, thus the microtubule dynamic behavior is very complicated. In this thesis, we first study the phase behavior of the polymer system which contains star molecular chains based on self-consistent field theory, and then research the microtubule dynamics by using Monte Carlo methods. The study mainly includes the following four aspects: (i) the phase behavior of diblock copolymer and star homopolymer blends; (ii) the phase behavior of star triblock copolymers both in bulk and in selective solvents; (iii) the phase behavior of star triblock copolymer thin films; (iv) the Monte Carlo simulation for microtubule dynamics.
In the first part, the compatibility between the components in polymeric blend system is an important factor which affects system structure and properties. For copolymer-homopolymer blends, the phase separation behavior is affected not only by the macrophase separation between block copolymers and homopolymers, the microphase separation of block copolymer chains, but also the competition between these two kinds of phase separations. In this part, we have interpreted the self-assembled morphologies of the blends of AB diblock copolymers and 3-arm star A homopolymers by using self-consistent mean field theory. We have focused on the condition that the copolymer composition is fixed while the chain length and volume fraction of the star homopolymer are varied. It is found that the phase behavior of the blend depends on both the chain length and volume fraction of the star homopolymer. The distribution of star homopolymer within the microphases is investigated based on enthalpic and entropic effects. By comparing the result of linear copolymer-homopolymer blend, we have discussed the difference between the effects of topological distinct polymers. The results of our study are supposed to be helpful for the design of novel nanomaterials involving architectural different polymers.
In the second part, we have studied the phase separation behavior of star ABC triblock copolymers both in bulk and in selective solvents by self-consistent mean field theory. In traditional experiments, abundant efforts are made to synthesize new block copolymers with the aim of investigating the molecular parameters and topological effects on discovering new morphologies. Furthermore, the introduction of selective solvent into a block copolymer melt renormalizes the segment-segment interaction and gives rise to a wide range of self-assembled structures. The segment-segment interaction can be changed with changing the concentration of copolymer or different solvents. Hence, in this way the ordered structure can be controlled and designed. By systematically varying the volume fraction of the C block, one-dimensional phase diagrams are constructed for three classes of typical star ABC triblock copolymers in terms of the relative strengths of the interaction energies between different species. The differences in the phase behaviors between the bulk and the solution are compared and explained. With the introduction of the selective solvent, the effective volume fraction of the C block is increased and the effective interaction energy is reduced for the other blocks. Then, the order-order transition is induced with specific volume fraction. The results presented here can provide valuable insight into phase behavior of both bulk star triblock copolymer and star copolymer concentrated solutions.
In the third part, thin film is a very common and important constrained system. In this part, we have described the complex phase behavior of a specific star ABC triblock copolymers confined between two identical parallel walls. To focus on the star architecture of the polymer chain, we have chosen the symmetric copolymer composition. By systematically changing the film thickness and surface field, the self-assemble structures of confined star ABC triblock copolymer melts with the symmetric and asymmetric interactions between polymer species are carried out by SCFT simulations. A variety of structures are found to be stable, such as cylinders, undulated cylinders, lamellae with cylinders, perforated lamellae and alternating versions of the sphere in matrix structures, etc. In particular, some new morphologies, such as cylinders with alternating helixes structure and complicated hybrid network structures are found in our studies. In the case of neutral walls, cylinder structures are commonly observed in thin films. Moreover, the cylinder radius and shapes are quite flexible in order to adjust themselves to different film thicknesses due to the junction point constraint of the star architecture. When surface field is weak, the cylinder phases are frequently observed because in this case the confinement effect is dominant. When surface field is strong, the effect of surface field on film morphologies is more significant. The surface field can break up the cylinder structure, and a variety of noncylindrical structures will be favored. Our results may provide a guide to understand the complex interplay between confinement effects, surface field and interaction parameters in thin films of star triblock copolymers.
In the last part, microtubule can be formed by tubulin heterodimers under the suitable temperature and tubulin concentration. The polymerization of microtubule is accompanied with the depolymerization of tubulin dimers and the hydrolysis of GTP (Guansine Triphosphate) within the microtubules, thus the microtubule dynamic behavior is very complex. The dynamics of microtubule is always the hot topic in life science. In this part, we have used an iterative Monte Carlo method to simulate the growth of microtubules and the impact of nucleation rate, tubulin concentration, the polymerization rate and depolymerization rate on the dynamics of microtubule. Especially, we have studied the dynamic behavior of microtubule after coupling the hydrolysis process of GTP. The simulation results show that the increase of tubulin concentration could promote microtubule polymerization, when tubulin concentration below the critical value, the microtubule would not be formed. Under the most calculating parameters, the microtubule population could reach steady state. After coupling the hydrolysis process of GTP, the time varying dynamic process of individual microtubule is consistent with the experimental results. In the simulation, we find that the choice of the models for both microtubule dynamics and GTP hydrolysis play essential roles in the study of microtubule dynamics. Although our work only get some preliminary results, but it provided effective guidance and data accumulation for further research of microtubule dynamics. The results presented here can provide valuable insight into some biological processes.
第一部分:聚合物共混体系中各组分间的相容性是影响体系结构和性能的重要因素。对于嵌段共聚物/均聚物共混体系,其相分离行为不仅包含嵌段共聚物与均聚物之间的宏观相分离和嵌段共聚物本身不同链段间的微相分离,还包括这两种相分离之间的竞争,这些因素极大程度影响了共混体系的相分离形貌和结构,从而最终影响材料的性能。本文应用自洽场理论系统研究了嵌段共聚物AB与星型均聚物A的共混体系的相行为,着重讨论了当嵌段共聚物的组成一定时,体系中星型均聚物的体积分数及均聚物与嵌段共聚物链长之比对体系相形态的影响,此外,还考察了星型均聚物在共混体系中的分布情况,并从熵和相互作用能的角度加以解释,我们还观察到星型均聚物由于链拓扑结构的特殊性使其与嵌段共聚物分子间的相互作用不同于线型均聚物共混体系。
第二部分:为了考察分子参数和分子链拓扑构型对聚合物相结构的影响以及发现新的有序结构,在实验上需要合成大量的嵌段共聚物。在嵌段共聚物溶液中,溶剂的存在不但拓宽了嵌段共聚物的自组装形态,而且连续改变体系的浓度可以达到改变组分间相互作用能的目的。因此,通过嵌段共聚物和小分子溶剂共混,可考察分子参数对体系微相结构的影响。本文应用自洽场理论研究了星型ABC三嵌段共聚物本体及浓溶液体系的相行为,考察了在不同的组分间相互作用参数下,聚合物浓度对嵌段共聚物微相分离的影响,并给出了一维相图;还对星型嵌段共聚物本体及溶液中的相分离情况进行了详细的对比。通过聚合物本体及在两种浓度下相分离行为的比较,发现对嵌段C具有选择性的溶剂的加入相当于增加了嵌段C的有效体积分数,对于另外两个嵌段来说相当于升高了相分离温度,致使体系在一定的组分范围内,发生溶致性相转变。在相同聚合物浓度下通过比较两种对嵌段C具有不同选择性的溶剂对相分离的影响,发现即使都是C嵌段的良溶剂,当其选择性不同时,体系的相分离行为也有很大差别。我们的研究有助于加深对星型三嵌段共聚物本体及浓溶液体系的相分离行为的理解,从而指导嵌段共聚物有序结构的预测和设计。
第三部分:薄膜是一种非常普遍而且重要的受限体系。边界的受限效应给高分子的熵带来变化的同时,受限边界对不同嵌段的浸润性质也会引起表面能的变化,两者的共同作用往往很大程度地改变边界附近的高分子构型,从而改变表面附近区域的微相分离形态。本文应用自洽场理论系统模拟了在两个平行基板之间受限的星型ABC三嵌段共聚物薄膜的相行为。在模拟中,体系各个组分的体积分数选取近似相等以突出星型高分子链的特征结构;考察了在不同的组分间相互作用参数下,薄膜的厚度(基板的距离)及表面场的强度对共聚物薄膜相行为的影响。研究结果表明,在受限及表面场作用下出现了一系列稳定的相形态,包括柱状相、波浪柱状相、层状相和交替柱状相、穿孔层状相及交替分散的球状结构等,这些结构在实验和理论上都已被发现。在我们的计算中也发现了一些新的结构,如柱状与交替螺旋结构及复杂的网络结构等。当基板对各组分均为中性时,与聚合物本体的相形态相似,受限体系大多形成柱状形态,并且由于星型交联点的限制作用,柱的形状和直径都可自发地进行自我调节以适应不同的膜厚。当表面场较弱时,柱状结构比较普遍,薄膜的相结构主要由体系受限效应及膜厚与相结构周期的匹配性来控制;然而,随表面场强度的增加,表面场对薄膜结构的影响变得重要;当表面场强度足够大时,会导致体系由柱状结构转变成非柱状相。我们关于星型ABC三嵌段共聚物薄膜的研究有助于理解薄膜体系中受限效应、表面场、组分间相互作用及分子链拓扑结构之间复杂的共同作用,从而帮助和指导实验,并得到更多更新颖的纳米级有序材料。
第四部分:在合适的温度及微管蛋白浓度下,微管蛋白异二聚体可以聚合成微管,聚合的同时还伴随着解聚及与微管蛋白结合的GTP水解的过程,其动力学行为非常复杂,对微管动力学的研究一直都是生命科学中的热门课题。本文应用蒙特卡罗方法模拟了微管的生长过程以及成核速率、微管蛋白单体浓度、聚合及解聚速率对微管生长动力学的影响,重点考察了耦合水解反应后微管的动力学行为。研究结果表明,单体浓度的升高会促进微管的聚合,因而微管平均长度增加;当单体浓度低于临界值时,微管不会生长;在绝大多数反应参数下,微管生长都会达到稳态;耦合了水解反应后,单根微管长度随时间变化的动力学过程与实验结果基本相符;在计算中我们发现微管动力学模型及GTP水解反应模型的选取对于研究微管的动力学过程十分重要。尽管本部分研究工作仅得到一些初步的结果,但对进一步研究微管动力学提供了有力的指导及数据积累。本研究有助于在现有知识的基础上更加深入地理解、解释一些生命过程和现象。
Soft matter is closely related to human's lives, which widely exists in nature, life body and daily life, such as polymer, colloid, membrane and protein. There is a close relation between organisms and polymers, for example, biological membrane can be regarded as vesicle consisting of amphiphilic molecules. The microdomain structure of block copolymer is determined mainly by the molecular architecture and the interaction between the different components, thus the study of phase behavior of polymer system which contains special molecular chain architecture is significant to research the morphologies of soft matters. Microtubules are essential component of the cytoskeleton and are widely spread throughout the cytoplasm of eukaryotic cells. They play critical roles in a variety of cell processes, including cell shaping, intracellular tracking, cell division, and cell migration. The polymerization of microtubule is accompanied with the depolymerization of tubulin dimers and the hydrolysis of GTP (Guansine Triphosphate) within the microtubules, thus the microtubule dynamic behavior is very complicated. In this thesis, we first study the phase behavior of the polymer system which contains star molecular chains based on self-consistent field theory, and then research the microtubule dynamics by using Monte Carlo methods. The study mainly includes the following four aspects: (i) the phase behavior of diblock copolymer and star homopolymer blends; (ii) the phase behavior of star triblock copolymers both in bulk and in selective solvents; (iii) the phase behavior of star triblock copolymer thin films; (iv) the Monte Carlo simulation for microtubule dynamics.
In the first part, the compatibility between the components in polymeric blend system is an important factor which affects system structure and properties. For copolymer-homopolymer blends, the phase separation behavior is affected not only by the macrophase separation between block copolymers and homopolymers, the microphase separation of block copolymer chains, but also the competition between these two kinds of phase separations. In this part, we have interpreted the self-assembled morphologies of the blends of AB diblock copolymers and 3-arm star A homopolymers by using self-consistent mean field theory. We have focused on the condition that the copolymer composition is fixed while the chain length and volume fraction of the star homopolymer are varied. It is found that the phase behavior of the blend depends on both the chain length and volume fraction of the star homopolymer. The distribution of star homopolymer within the microphases is investigated based on enthalpic and entropic effects. By comparing the result of linear copolymer-homopolymer blend, we have discussed the difference between the effects of topological distinct polymers. The results of our study are supposed to be helpful for the design of novel nanomaterials involving architectural different polymers.
In the second part, we have studied the phase separation behavior of star ABC triblock copolymers both in bulk and in selective solvents by self-consistent mean field theory. In traditional experiments, abundant efforts are made to synthesize new block copolymers with the aim of investigating the molecular parameters and topological effects on discovering new morphologies. Furthermore, the introduction of selective solvent into a block copolymer melt renormalizes the segment-segment interaction and gives rise to a wide range of self-assembled structures. The segment-segment interaction can be changed with changing the concentration of copolymer or different solvents. Hence, in this way the ordered structure can be controlled and designed. By systematically varying the volume fraction of the C block, one-dimensional phase diagrams are constructed for three classes of typical star ABC triblock copolymers in terms of the relative strengths of the interaction energies between different species. The differences in the phase behaviors between the bulk and the solution are compared and explained. With the introduction of the selective solvent, the effective volume fraction of the C block is increased and the effective interaction energy is reduced for the other blocks. Then, the order-order transition is induced with specific volume fraction. The results presented here can provide valuable insight into phase behavior of both bulk star triblock copolymer and star copolymer concentrated solutions.
In the third part, thin film is a very common and important constrained system. In this part, we have described the complex phase behavior of a specific star ABC triblock copolymers confined between two identical parallel walls. To focus on the star architecture of the polymer chain, we have chosen the symmetric copolymer composition. By systematically changing the film thickness and surface field, the self-assemble structures of confined star ABC triblock copolymer melts with the symmetric and asymmetric interactions between polymer species are carried out by SCFT simulations. A variety of structures are found to be stable, such as cylinders, undulated cylinders, lamellae with cylinders, perforated lamellae and alternating versions of the sphere in matrix structures, etc. In particular, some new morphologies, such as cylinders with alternating helixes structure and complicated hybrid network structures are found in our studies. In the case of neutral walls, cylinder structures are commonly observed in thin films. Moreover, the cylinder radius and shapes are quite flexible in order to adjust themselves to different film thicknesses due to the junction point constraint of the star architecture. When surface field is weak, the cylinder phases are frequently observed because in this case the confinement effect is dominant. When surface field is strong, the effect of surface field on film morphologies is more significant. The surface field can break up the cylinder structure, and a variety of noncylindrical structures will be favored. Our results may provide a guide to understand the complex interplay between confinement effects, surface field and interaction parameters in thin films of star triblock copolymers.
In the last part, microtubule can be formed by tubulin heterodimers under the suitable temperature and tubulin concentration. The polymerization of microtubule is accompanied with the depolymerization of tubulin dimers and the hydrolysis of GTP (Guansine Triphosphate) within the microtubules, thus the microtubule dynamic behavior is very complex. The dynamics of microtubule is always the hot topic in life science. In this part, we have used an iterative Monte Carlo method to simulate the growth of microtubules and the impact of nucleation rate, tubulin concentration, the polymerization rate and depolymerization rate on the dynamics of microtubule. Especially, we have studied the dynamic behavior of microtubule after coupling the hydrolysis process of GTP. The simulation results show that the increase of tubulin concentration could promote microtubule polymerization, when tubulin concentration below the critical value, the microtubule would not be formed. Under the most calculating parameters, the microtubule population could reach steady state. After coupling the hydrolysis process of GTP, the time varying dynamic process of individual microtubule is consistent with the experimental results. In the simulation, we find that the choice of the models for both microtubule dynamics and GTP hydrolysis play essential roles in the study of microtubule dynamics. Although our work only get some preliminary results, but it provided effective guidance and data accumulation for further research of microtubule dynamics. The results presented here can provide valuable insight into some biological processes.
引文
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