Stereocomplex Crystallization in Asymmetric Diblock Copolymers Studied by Dynamic Monte Carlo Simulations

Stereocomplex crystallization in asymmetric diblock copolymers was studied using dynamic Monte Carlo simulations, and the key factor dominating the formation of stereocomplex crystallites(SCs) was uncovered. The asymmetric diblock copolymers with higher degree of asymmetry exhibit larger difference between volume fractions of beads of different blocks, and local miscibility between different kinds of beads is lower, leading to lower SC content. To minimize the interference from volume fraction of beads, the SC formation in blends of asymmetric diblock copolymers was also studied. For the cases where the volume fractions of beads of different blocks are the same, similar local miscibility between beads of different blocks and similar SC content was observed. These findings indicate that the volume fraction of beads of different blocks is a key factor controlling the SC formation in the asymmetric diblock copolymers. The SC content can be regulated by adjusting the difference between the contents of beads of different blocks in asymmetric diblock copolymers.     

Monte Carlo Simulations of Self-Assembling Copolymer Brushes

We studied a simplified model of a polymer brush formed by linear chains, which were restricted to vertices of a simple cubic lattice. The macromolecules consisted of a sequence of two different kinds of united atoms arranged in a specific sequence. The chains were grafted to an impenetrable surface, i.e. they were terminally attached to the surface with one end. The model system was studied at different solvent quality from good to poor solvent. The properties of this model system were determined by means of Monte Carlo simulation using a Metropolis-like sampling algorithm based on local changes of chain's conformations. The size and the structure of the brush were determined.     

不对称两嵌段共聚物熔体在平板狭缝中微相分离的Monte Carlo模拟

采用改进的键长涨落空穴扩散算法对平板狭缝中不对称两嵌共聚高分子熔体的微相分离进行了Monte Carlo模拟。模拟结果表明：在吸引壁条件下，靠近壁面处将形成平等于壁面的层状相；在弱吸引壁条件下，靠近壁面处将形成垂直于壁面的层状相；不对称共聚物在远离壁面处有丰富的微区形态。从结构因子上分析可知，弱吸引壁条件下不对称共聚物的结构比强吸引壁条件下更接近对称共聚物。     

Monte Carlo Study of Heteroarm Star Copolymers in Good and Selective Solvents

Lattice Monte Carlo simulations of conformations of hereroarm star copolymers A_nB_n in selective solvents were performed using a special variant of the Siepman and Frenkel algorithm. The effects of solvent quality, the number and lengths of blocks on the collapse of the insoluble block A, segregation of the two types of blocks and the behavior of the soluble blocks B were studied mainly for “hairy” stars containing high numbers of long arms. The simulation shows that insoluble blocks collapse in strongly selective solvents and the gravity centers of soluble and insoluble blocks separate which suggests the possibility of the formation of non‐spherical structures.

Snapshots of star a in a very bad solvent (T = 3.00) for blocks A. There are two different views of the star with a total number of arms f = 16 and number of segments N = 300.     

On the Ergodicity of Dynamic Monte Carlo Simulations of Multichain or Star Systems

Summary: The behavior of complex polymer structures, e.g., star and comb polymers or shells of polymer micelles, is often studied by dynamic Monte Carlo simulations. The algorithm, which is based on a sequence of independent steps, each of them consisting in dissolving and regrowing a randomly chosen tethered chain by the configuration‐bias Monte Carlo (CBMC) method, is considered. During each step, the remaining self‐avoiding walks (SAWs), which occupy the space, create geometrical restriction for the new SAW and hinder certain conformations. Hence, the reconstruction of the SAW under consideration depends on conformations of the other SAWs forming the system, and therefore, it is not directly evident whether the a priori ergodicity of SAW for a single untethered chain has been retained in the final algorithm for the whole multichain system. The proof of ergodicity of this type of simulations for an arbitrary number of SAWs tethered to the convex core is presented.

2D scheme of the alignment of the SAWs.     

Interface Orientation and Chain Conformation in Simulated Symmetric Diblock Copolymer Lamellar Systems

Summary: We describe the results of Monte Carlo simulations, based on the cooperative motion algorithm, of the lamellar structure generated at finite temperature by a symmetric diblock copolymer. The (70 × 70 × 70) simulation box in which the polymer chains were embedded for each simulation was rotated, based on the interface orientation, to bring the interfacial planes of the simulated structure into parallel. We found that the interface thickness, as defined by the distribution of the junction points, became narrower at lower temperature, and that the interface plane was characterized by a waviness with a maximum peak‐to‐valley distance of 20–30 lattice bonds. Compared with the isotropic state (T/N = ∞), chains at lower temperatures were stretched in the direction perpendicular to the interface; but only modestly compressed in the direction parallel to the interface. Individual block chains within the lamellar domains still behave like random coils. The block copolymer molecules exhibit only a modest tendency to orient themselves with their end‐to‐end vector perpendicular to the plane of the lamellar interface. Considered as an ensemble average, the results we obtained are similar to those reported from small angle neutron scattering measurements for the mean conformation of the PSd blocks of symmetrical PSd‐PVP diblock copolymers.

2‐D projections onto the X‐Z plane of the end beads for the A‐ and B‐chains (gray) and the junction points J (black) at T/N = 0.2. The interface plane is oriented parallel to the Y‐Z plane by rotating the simulation box. The distribution profiles of junction points and the end beads across the system in the direction of interface normal are shown in the lower part of the figure.     

Microdomain Morphology of Symmetrical Diblock Copolymer Thin Films Confined in a Slit

The microphase separation and morphology of symmetric diblock copolymer thin films confined in a slit with neutral or attractive surfaces were studied by the cell dynamic system method (CDS) and Monte Carlo simulation. The size effect, especially in CDS, was carefully investigated indicating that excessively small sizes in the X‐ and Y‐directions will give incorrect results although periodic boundary conditions are imposed. When the walls are neutral, parallel ordered lamella structure only exists over a short range, while irregular microdomain morphology occurs over the whole region. When directional quenching is applied, or the walls are attractive to one of the blocks, a periodical lamellar structure of alternating A‐rich and B‐rich layers occurs over the whole region of the film. Changing the slit width and the strength of interaction will influence the period and arrangement of lamellae. Agreement between the results from CDS and those from simulation is satisfactory indicating the reliability of the CDS method. Comparisons with corresponding experimental results are also discussed.     

基于格子链的缩聚反应的动态Monte Carlo模拟

采用描述自回避格子链的键长涨落模型, 以动态Monte Carlo方法对AB型单体的线型缩聚反应动力学过程进行了模拟. 通过该方法可以得到反应过程中链的瞬时构象, 还可以得到反应程度、聚合度、分子量分布及其随时间的演化. 模拟得到了合理的结果, 同时验证了无规线团尺寸与平均链长的标度关系, 表明该方法用于研究逐步聚合反应过程是可行的, 并且与一般的研究聚合反应的Monte Carlo方法相比, 还能够同时得到构象等空间信息. 还比较了不同大小的模拟体系所得到的分子量和多分散系数的异同, 讨论了有限元胞效应.     

Wavelet-accelerated Monte Carlo sampling of polymer chains

We introduce a new method for coarse-graining polymer chains, based on the wavelet transform, a multiresolution data analysis technique. This method, which assigns a cluster of particles to a coarse-grained bead located at the center of mass of the cluster, reduces the complexity of the problem significantly by dividing the simulation into several stages, each with a small fraction of the number of beads in the overall chain. At each stage, we compute the distributions of coarse-grained internal coordinates as well as potential functions required for subsequent simulation stages. We show that, with this wavelet-accelerated Monte Carlo method, coarse-grained Gaussian and self-avoiding random walks can reproduce results obtained from atomistic simulations to a high degree of accuracy in orders of magnitude less time. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 897–910, 2005     

Percolation in Two‐Dimensional Copolymer Systems

The aim of the study is the investigation of the percolation phenomena in some model copolymer systems. Diblock, triblock, random copolymers, and a blend of homopolymers are studied. For this purpose, we developed an idealized model of polymeric systems. The positions of polymer segments are restricted to vertices of a simple cubic lattice. The chains are at good solvent conditions – the excluded volume is the only interaction between the segments of the chain. The properties of the model chains are determined by means of Monte Carlo simulations with a sampling algorithm based on chain's local changes of conformation. The differences and similarities in the percolation behavior are shown and discussed. The percolation threshold is found to be very weakly dependent on the chain length, however, it appears that the main factor that influenced the percolation threshold is the screening effect of other parts of chains.

     

Influence of Rigid Side Chain Attraction on Stiffness and Conformations of Comb Copolymer Brushes Strongly Adsorbed on a Flat Surface

The influence of side‐chain attraction on the conformational properties of two‐dimensional polymer brushes with rigid side chains is investigated using Monte Carlo simulations. Using a rigid backbone, a characteristic interaction strength is determined by investigating the critical interaction energy for the collapse of the side chains onto the backbone. For a flexible backbone, the persistence length of the backbone is found to decrease with increasing attraction, irrespective of whether side‐chain flipping is allowed or not. This result is in good agreement with the theoretical modeling presented before. If side‐chain flipping is allowed, the attraction between the side chains leads to aggregation of successive side chains at one side of the backbone resulting in a characteristic local spiraling of the backbone.     

二维三角格子上高分子动态 Monte Carlo模拟的协同运动算法

在动态Monte Carlo模拟的协同运动算法中,几个相邻的链节可以同时运动,这可以理解为高分子链中张力的作用引起的协同运动。将这一算法用于二维三角格子模型上RW链和SAW链的模拟。结果表明RW链的动力学行为符合Rouse理论,说明说明该算法可以用于高分子动力学研究,其优点是不需要使用键长涨落模型。     

Simulation of Copolymer Bottle-Brushes

Summary: The structure of bottle-brush polymers with a rigid backbone and flexible side chains is studied in three dimensions, varying the grafting density, the side chain length, and the solvent quality. Some preliminary results of theoretical scaling considerations for one-component bottle-brush polymers in a good solvent are compared with Monte Carlo simulations of a simple lattice model. For the simulations a variant of the pruned-enriched Rosenbluth method (PERM) allowing for simultaneous growth of all side chains in the Monte Carlo sampling is employed. For a symmetrical binary (A,B) bottle-brush polymer, where two types (A,B) of flexible side chains are grafted with one chain end to the backbone in an alternating way, varying repulsive binary interactions between unlike monomers and the solvent quality, it is found that phase separation into an A-rich part of the cylindrical molecule and a B-rich part can occur only locally. Long range order (in the direction of the backbone) does not occur, and hence the transition from the randomly mixed state of the bottle-brush to the phase-separated structure is strongly rounded, in contrast to the corresponding mean field predictions of a sharp transition to a “Janus cylinder” phase-separated structure. This lack of a phase transition can be understood from an analogy with spin models in one dimension. By estimating the correlation length for this phase separation along the backbone as a function of side chain length and solvent quality, we present strong evidence that no sharp phase transition occurs.     

Understanding the Formation of Linear Olefin Block Copolymers with Dynamic Monte Carlo Simulation

Chain‐shuttling polymerization with dual catalysts has introduced a new class of polyolefins called olefin block copolymers (OBCs). A dynamic Monte Carlo model to describe the kinetics of chain‐shuttling copolymerization in a semi‐batch reactor is developed, and used it to study how the microstructure of OBCs with different numbers of blocks per chain evolves during polymerization. The model also describes how chain‐shuttling rate constants and concentration of chain‐shuttling agent affect populations of OBCs with different numbers of blocks per chain. These model predictions are useful to make OBCs with precisely designed microstructures.

     

Dynamic Monte Carlo simulations of competition in crystallization of mixed polymers grafted on a substrate

Nowadays, preparation of poly(lactide) (PLA) with high content of stereocomplex crystallites (SCs) is receiving more and more attentions. The stereocomplex formation between enantiomeric poly(l ‐lactide) and poly(d ‐lactide) can efficiently improve the corresponding mechanical properties and thermal stability. In the current work, using dynamic Monte Carlo simulations, the microscopic mechanism of SC formation in grafted polymers was investigated. The increase in grafting density can lead to the enhancement of SC formation. On one hand, the miscibility between the chains of different types can be improved due to the grafting. On the other hand, the increase in grafting density can result in the higher degree of chain extension and the change in crystal nucleation and growth modes. The changes facilitate the stereocomplex formation. These findings not only provide an effective way to prepare PLAs with high content of SCs, but also reveal the underlying mechanisms controlling the SC formation. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 89–97     

高分子动态Monte Carlo模拟的协同运动算法

在高分子动力学的研究中 ,动态 Monte Carlo模拟发挥了重要的作用 [1] .动态 Monte Carlo模拟的关键是选择具有物理真实性的高分子运动算法 .目前广为采用的算法是经 Hilhorst和 Deutch[2 ] 修正的 Verdier- Stockmayer算法 [3] 以及 Carmesin和 Kremer等的键长涨落算法 [4 ] ,陆建明和杨玉良曾提出一种高分子动态算法 [5] ,在他们的算法中很长一段链节可能作蛇行运动 ,但是冯捷等 [6 ] 指出这种运动模式不满足微观可逆性条件 .本文对该运动模式进行修正 ,得到一种协同运动算法 ,并对其动力学行为进行检验 .1　算　法在平面正方形格子…     

纳米粒子/共聚物混合体系结构的Monte Carlo模拟

基于简立方格点模型,对纳米粒子/共聚物混合体系进行了动力学Monte Carlo模拟研究. 每一共聚物链均由一个A珠子和三个B珠子组成,表示为A1B3. A1B3链的两亲性体现为B-B之间的相互吸引作用,同时憎水性的纳米粒子之间也存在相互吸引. 通过适当选取纳米粒子与B珠子之间的吸引作用势,观察到两种结构:纳米粒子/A1B3链的核-壳结构和纳米粒子分散在憎水壳层中的A1B3囊泡结构. 还研究了这两种结构的动力学演化过程,模拟结果表明在纳米粒子分散于囊泡壳层的过程中A1B3囊泡起模板作用.     

Microphase Separation of a Diblock Copolymer Dispersed in Nanorod Arrays Grafted on a Plate: A Monte Carlo Study

The microstructure of a diblock copolymer dispersed in nanorod arrays grafted on a plate are investigated via annealing MC simulation. The confinement in nanorod arrays provides a complex confined space which leads to complicated microphase separation structures. Different morphologies of top and bottom of the film in the nanorod arrays are observed by varying the inducing height of nanorod and its grafting density in the bottom. Due to a short inducing range by the nanorods, the top structures are therefore mainly dominated by the competition between the absolute height of off‐induced layer on the top and the nature of block copolymer itself; while the bottom structures are affected by the symmetry of block copolymer and the gap among rods.

     

Monte Carlo studies of tethered chains

Monte Carlo computer simulations of end-tethered chains grafted onto a hard wall have been performed. The chains were modeled as self-avoiding chains on a cubic lattice at athermal solvent conditions. The simulations spanned a wide range of chain lengths, N (100–1000, i.e., up to molecular weights of a few hundred thousands), and anchoring densities, σ (2 × 10⁻⁴ to 0.4), to properly chart the relevant parameter space. It is shown that the reduced surface coverage σ* = σπR is the most appropriate variable that quantitatively determines the mushroom, overlapping mushroom and brush regimes, where R_g is the radius of gyration of a free chain in solution. The simulation data are analyzed to determine the conformational characteristics and shape of the anchored chains and to compare them with the predictions of the analytical self consistent field theory. The strong stretching limit of the theoretical predictions is obtained only for σ* > 8. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47:2449–2461, 2009     

A Monte Carlo Simulation of Homogeneous Crystallization in Confined Spaces: Effect of Crystallization Kinetics on the Avrami Exponent

Homogeneous nucleation in polymers and subsequent crystallization in spaces confined relative to spherulitic dimensions in one direction has been simulated for a wide range of nucleation and growth rates. An empirical equation based on simulation results relating an Avrami exponent of crystallization to growth and nucleation rates along with the characteristic dimension of crystallizing volume has been proposed. It was found that for ideal homogeneous crystallization, the Avrami exponent can be significantly lower than the anticipated values for free unconstrained growth; therefore, all crystallization conditions and parameters must be taken into account in order to make a conclusion on the character of the observed crystallization.