Monte Carlo模拟研究高分子单链在基体中扩散的拓扑效应

高分子流体的性质同高分子的链结构及其动力学行为密切相关. 在高分子共混物中,共混组分的性质不仅依赖于自身的拓扑结构,还受到其它组分分子拓扑的影响. 本文中采用基于格子模型的Monte Carlo模拟方法研究了在高分子基体中扩散的4种不同拓扑组合（环形或线形高分子链）体系中目标单链的静态和动态性质. 结果发现,环形目标单链的性质受基体分子拓扑结构的影响要大于线形目标单链;其中环/线这一拓扑组合中目标单链的扩散机理相比其本体已经发生了较大改变,链末端在其中起了重要作用. 此外,我们对引起这一现象出现的可能原因做了分析.     

Cooperativity in the Conformational Rearrangements of Polymer Chain Segments as Seen by Bond Fluctuation Model

The kinetics of structural relaxation was simulated using the bond fluctuation model. Annealing of the system in the glassy state produces a clearly nonexponential decrease in the energy in a certain temperature interval. At lower temperatures, the decrease in energy takes place by successive small steps, due to the change of the energy of individual polymer chains that modify their conformation into small neighbourhoods. This cooperativity is behind the nonexponential behaviour shown by structural relaxation at higher temperatures. A second order Markov chain is able to reproduce the nonexponentiality with quite good agreement with the bond fluctuation simulated curves. Cooperativity comes from the fact that the transition probability of a polymer chain between two energy levels depends on the history of previous transitions that took place in its neighbourhood.

     

Monte Carlo Computer Simulation of a Single Semi-Flexible Macromolecule at a Plane Surface

Summary: The properties of a single semiflexible mushroom chain at a plane surface with a long-ranged attracting potential are studied by means of lattice Monte Carlo computer simulation using the bond fluctuation model, configurational bias algorithm for chain re-growing and the Wang-Landau sampling technique. We present the diagram of states in variables temperature T vs. strength of the adsorption potential, ε_w, for a quite short semiflexible chain consisting of N = 64 monomer units. The diagram of states consists of the regions of a coil, liquid globule, solid isotropic globule, adsorbed coil and cylinder-like liquid-crystalline globule. At low values of the adsorption strength ε_w the coil–globule and the subsequent liquid–solid globule transitions are observed upon decreasing temperature below the adsorption transition point. At high values of ε_w these two transitions change into a single transition from an adsorbed coil to a cylinder-like liquid-crystalline solid globule. We conclude that for a semiflexible chain the presence of a plane attracting surface favors the formation of a globule with internal liquid-crystalline ordering of bonds.     

Carboxyl Terminated Polymer Chain Extension Using a Bisoxazoline Coupling Agent: Monte Carlo Simulation

Summary: The kinetics of the chain extension reaction of a carboxyl‐terminated polymer using a bisoxazoline coupling agent was simulated by the Monte Carlo method based on the master equation. The effects of temperature and stepwise addition of the chain extender was examined. A comparison between simulated results and those calculated by an amended kinetic model was made. The results show that the highest coupling efficiency and the highest can be obtained when the initial concentrations of carboxyl and oxazoline groups are equal, which is in good agreement with the experiments. It is found that a higher reaction temperature could lead to a bigger coupling efficiency, a higher and narrower MWDs. The stepwise addition of the chain extender can only postpone the chain extension reaction, but cannot affect the final coupling efficiency and the MWDs when the concentration of the oxazoline group is lower than that of the carboxyl group. However, stepwise addition of the chain extender favors bigger coupling efficiency and narrower MWDs when the concentration of the oxazoline group exceeds that of the carboxyl group.

The relationship among three group of polymers, r and ratios of k₂ to k₁. The dots are the data simulated by MC and solid lines are relative data calculated by the kinetic model.     

Prediction of Chain Length Distribution of Polystyrene Made in Batch Reactors with Bifunctional Free‐Radical Initiators Using Dynamic Monte Carlo Simulation

The objective of this paper is to present a dynamic Monte Carlo model that is able to simulate the polymerization of styrene with bifunctional free‐radical initiators in a batch reactor. The model can predict the dynamic evolution of the chain length distribution of polystyrene in the reactor. The model includes all relevant polymerization mechanistic steps, including chemical and thermal radical generation, and diffusion‐controlled termination. The model was applied to styrene polymerization and the Monte Carlo estimates for chain length averages were compared to those obtained with the method of moments. Excellent agreement was obtained between the two methods. Although styrene polymerization was used as a case study, the proposed methodology can be easily extended to any other polymer type made by free‐radical polymerization.

     

Molecular Weight Distribution in Living Polymerization Proceeding with Reshuffling of Polymer Segments due to Chain Transfer to Polymer with Chain Scission, 2. Monte Carlo Simulation of Polymer Reshuffling Proceeding with Disproportionation of Chain Functionalities

The method for analyzing the reshuffling of polymer segments developed previously has been extended to systems involving the disproportionation of chain functionalities. The effect of interchain exchange reactions of this type, leading to the redistribution of chain lengths and of the chain functionalities (redistribution of living and dead chain ends), was analyzed by means of the Monte Carlo simulations. In the systems, in which no propagation occurs (monomer concentration equal to zero), a set of polymer chains containing one living and one dead end was taken as an initial material. A series of simulations were performed for systems with differing molecular weight distributions of the starting macromolecules. Uniform (no chain length distribution polymer – all chains are of the same length), Poisson, and the most probable (geometric) distributions were taken into consideration. Although the molecular weight distributions (MWDs) of functionally different chains of the same polymer were different apart from the eventual equilibrium conditions, the overall MWD was very close to that observed in analogous systems without disproportionation. The same was observed concerning MWDs in modeled polymerization systems, in which reshuffling and disproportionation accompanied propagation. Consequently, a method of estimating the ratio of rate constants of propagation and reshuffling (i. e. k_p /k _tr) in the relevant polymerization systems, using the observed polydispersity indexes, was proposed. The extent of disproportionation can be evaluated from the determined relationships of the polydispersity index and of the monofunctional chains fraction as functions of the average number of chain transformations.     

嵌段高分子尾形链构象性质的Monte Carlo研究

基于简立方格点模型对AB两嵌段高分子尾形链的构象性质及其链节的空间分布进行了MonteCarlo模拟.结果表明,链的尺寸、形状和链节的空间分布等统计性质和B链节与平面壁之间的相互吸引能有关.随着B链节与壁之间的吸引能的增加,链的尺寸和形状均呈现出先下降后升高的变化趋势,而且B链节的比例越大,这种变化越明显.     

Monte Carlo Study on Spontaneous Recoil of Confined DNA Chain

A part of a long DNA chain was driven into a confined environment by an electric field, while the rest remains in the higher-entropy region. Upon removal of the field, the chain recoils to the higher-entropy region spontaneously. This dynamical process was investigated by Monte Carlo simulations. The simulation reproduces the experimentally-observed phenomenon that the recoil of the DNA chain is initially slow and gradually increases in speed due to the presence of the confinement-entropic force. The results show that with increasing the dimension or decreasing the spacing of the nanopillars the recoil velocity of the DNA chain will increase. Further analysis suggests that the characteristic entropy per monomer in the confinement is proportional to the area fraction of the free part in the confinement.     

受限高分子薄膜界面动力学与缠结的关系

通过Monte Carlo模拟结合原始路径分析(PPA)的方法,阐述了缠结高分子薄膜的界面动力学与缠结程度的关系.研究发现,以吸附势能的临界值εwc≈-0.6 kBT附近为界,当墙壁-高分子作用势能从弱吸引到强排斥变化时,界面层中的链移动快于中心层,只有当墙壁的吸引作用增强到一定程度时,界面层中的链移动才会慢于中心层.界面动力学受到促进或阻碍可能与界面层和中心层的缠结程度直接相关:界面层的缠结程度保持在本体水平上基本不变;中心层的缠结程度在强吸引表面上低于界面层,而在弱吸引和排斥表面上高于界面层.此外,中心层和界面层中高分子链受限程度的变化对薄膜界面动力学行为的转变产生一定影响.对于薄膜中链密度分布情况随墙壁-高分子作用势能变化的分析为相关的物理化学机制提供了理论依据.     

Simulation of Chain Organization in Encapsulated Polymers

Summary : The dimensional and structural properties of polymers confined into a cavity are computed by the Monte Carlo method as a function of the chain stiffness. The reduction of the size ratio <R² > / < R> close to 2, distinctive of compact spheres, is observed at squeezing of chains into a capsule. The plots of the static structure factor S(q) computed for stiff chains show characteristic humps attributed to the toroidal structure. The orientation correlation function is found to be a very sensitive indicator of the globule – toroid transition in encapsulated chains. Evidence is presented that the toroidal morphology is formed in stiff polymers when the capsule radius approaches the chain persistence length (D ∼ P).     

Local Transient Jamming in Stress Relaxation of Bulk Amorphous Polymers

Bulk amorphous polymers become stretched and parallel-aligned under loading stress, and their intermolecular cooperation slows down the subsequent stress relaxation process. By means of dynamic Monte Carlo simulations, we employed the linear viscoelastic Maxwell model for stress relaxation of single polymers and investigated their intermolecular cooperation in the stress relaxation process of stretched and parallel-aligned bulk amorphous polymers. We carried out thermal fluctuation analysis on t...     

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.     

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.     

Monte Carlo Simulations of Adsorbed Solutions in Heterogeneous Porous Materials

We present results of a Monte Carlo simulation study of binary mixtures of ethane and methane in silica gel. The molecular model treats the adsorbent as a matrix of silica microspheres. The adsorption isotherms, adsorption selectivities and isosteric heats of adsorption have been determined for these systems. The results are compared with predictions from the ideal adsorbed solution (IAS) theory and with experiment. The heats of adsorption are accurately described by the IAS theory. The adsorption isotherms are accurately described by the IAS theory at low bulk pressure but the IAS theory overpredicts the density at high bulk pressure. This latter effect is opposite to that observed in bulk mixtures of this type where nonidealities generally lead to a density increase on mixing. The pressure dependence of the selectivity does not exhibit a maximum at low pressure. We discuss this effect in terms of the adsorbent microstructure.     

聚硅烷链形状的Monte Carlo研究

用ＭｏｎｔｅＣａｒｌｏ方法对θ溶液中考虑二级相互作用的聚硅烷链的形状进行了研究。结果表明聚硅烷链的形状明显偏离球形，它与链长有关，长链极限的比值＜Ｌ２１＞∶＜Ｌ２２＞∶＜Ｌ２３＞约为１∶２．７∶１２．１。还发现聚硅烷链转动惯量的最长主轴与末端距矢量之间夹角的统计平均值＜θ＞的极限值约为２７°。     

平行板间高分子链构象熵的动力学Monte Carlo模拟

用动力学Monte Carlo方法模拟了受限于两平行板之间的高分子链,并用扫描法计算了链的构象熵S,研究了构象熵相对于自由链的减小量(S0-S)与平行板间距D和高分子链长n的关系.结果证实了de Gennes的自由能标度关系,并给出了标度关系适用的范围.当D非常小时,高分子链受到强烈限制,S0-S与n成正比,表明单链节受到平行板的平均排斥作用力与链长无关.随着D增大,平行板对构象熵的影响越来越弱,单链节受到平行板的平均排斥作用力随链长的增长而增大.当D比较大时,平行板对构象熵的影响近似可以忽略,高分子链构象熵与自由空间中的结果一致.     

Monte Carlo模拟表面上吸附态物种的迁移对反应行为的影响

用MonteCarlo方法研究了非均相催化剂表面吸附态氢原子的迁移对催化反应活性的影响,模拟结果表明,吸附态氢原子扩散很慢时,表面活性位很快被氢原子饱和,转换频率TOF增大到一定程度时很快下降;而当表面吸附态氢原子的扩散速率达到足够大的程度时,TOF将不再受氢原子扩散的影响.     

Translocation of a protein-like chain through an interacting channel

The effect of channel-protein interaction on the translocation of a protein-like chain through a finite channel under certain electric field was studied by using dynamical Monte Carlo simulations.The interior behavior of chain conformation under different interactions was investigated,such as the number of monomers outside of channel n_out,monomers inside of channel n_m,mean-square radius of gyration〈S²〉and the average energy〈U〉.It shows that with strong attractive interaction,the translocation is more difficult than moderate interaction.At the same time,the dependence of translocation time with different interactions shows that moderate repulsive interaction(ε_cp= 0.5) accelerates the translocation.Although the waiting time for successful translocation ofε_cp = 1.0 is the longest,the average translocation time is not very large.It is far smaller than that ofε_cp=-1.0.The probability distributions of translocation time p（t’） and the probability distributions of three duration times p（t₁’）,p（t₂’） and p（t₃’） were all discussed.Log-normal distributions are found.All these findings will strengthen the understanding of protein translocation.     

Monte Carlo simulation of phase separation kinetics in a concentrated polymer solution

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Simulation of Complexes between a Charged Dendrimer and a Linear Polyelectrolyte with Finite Rigidity

Complexes comprising a 4th‐generation dendrimer with 32 positively charged end‐groups and an oppositely charged linear polyelectrolyte along with explicit counterions are studied in an athermal solvent using MC simulations. The excluded volume between monomers, the full Coulomb potential between charges and the bending energy of the chain bonds are taken into account. The chain flexibility parameter is varied in a wide range, including the limiting cases of rigid and flexible chains. As the chains become more rigid, they take locally extended conformations within the complex. The conformations of the condensed chains are described in terms of loops, trains, and tails. In the limit of strong electrostatic coupling and high rigidity, long chains show a release of tails from the complex.