Dynamics of Adsorbed Star‐Branched Polymer Chains: A Computer Simulation Study

The simple cubic‐lattice model of polymer chains was used to study the dynamic properties of adsorbed, branched polymers. The model star‐branched chains consisted of f = 3 arms of equal lengths. The chain was modeled with excluded volume, that is, in good solvent conditions. The only interaction assumed was a contact potential between polymer segments and an impenetrable surface. This potential was varied to cover both weak and strong adsorption regimes. The classical Metropolis sampling algorithm was used for models of star‐branched polymers in order to calculate the dynamic properties of adsorbed chains. It was shown that long‐time dynamics (diffusion constant) and short‐time dynamics (the longest relaxation time) were different for weak and strong adsorption. The diffusion of weakly adsorbed chains was found to be qualitatively the same as for free nonadsorbed chains, whereas strongly adsorbed chains behaved like two‐dimensional polymers. The time‐dependent properties of structural elements such as tails, loops, and trains were also determined.

The mean lifetimes of tails, loops, and trains versus the bead number for the chain with N = 799 beads for the case of the weak adsorption ε_a = −0.3.     

Mesophase Formation in Solutions of Diblock Copolymers Simulated Using the Bond Fluctuation Model

The behavior of symmetric diblock copolymer chains of two different lengths at different concentrations is simulated by means of the bond fluctuation model. Two alternative sets of energies between interacting neighbors are proposed. In one of the sets, attractions between monomers of the same type are considered. In the other set, repulsions between monomers of different types are considered. The collective scattering of the simulation boxes is computed for different values of the reduced energy interaction parameter and the total polymer volume fraction. The analysis of this property is used to locate the transition associated with the formation of mesophases (lamellae) as a function of these two variables. A comparison between the results corresponding to the two different models is performed. When the significant excluded volume corrections are introduced in the model with repulsive interactions, both sets of data agree, except for the most dilute samples. The agreement with the self‐consistent field theory is only fair, and important differences are observed in the intermediate concentration regime. These differences were expected, since the theoretical treatment is only rigorously valid for very long chains.

Comparison of the simulation data for the transition points with the prediction of the self‐consistent field theory (solid line).     

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 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.     

Perturbation Theory of Polymer Chains Revisited, 2—Intermolecular Excluded Volume of Random and Self‐Avoiding Walks

The intermolecular compatibility of 10⁷–10⁸ independent pair configurations of linear chains (chain length 64 ≤ N ≤ 8192) with and without intramolecular interaction on various lattices is checked and the intermolecular excluded volume u evaluated. From the (average) number of possible i‐tuples of overlaps in the pair configurations the parameters C_k of the perturbation theory are calculated. Differences between the various lattice types at finite N vanish completely for N → ∞. While the theoretical values of C₁ and C₂ were recovered within very narrow limits for chains without intramolecular interaction, markedly higher figures apply to self‐avoiding walks. The excluded volume u itself and higher C_k parameters are called upon to test several classical and renormalized perturbation theories.

     

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.

     

The Effect of Chain Architecture on the Dynamics of Copolymers in a Homopolymer Matrix: Lattice Monte Carlo Simulations using the Bond‐Fluctuation Model

Summary: The effects of copolymer sequence distribution on the dynamics of a copolymer in a homopolymer matrix are studied using computer simulations within the framework of the bond‐fluctuation model on blends containing low concentrations (10%) of copolymers dispersed in a homopolymer matrix. The sequence distribution of the two copolymer components was changed while maintaining the overall copolymer composition at 50/50. Our results indicate that copolymers with disordered sequence distributions exhibit dynamics that are faster than that of a homopolymer melt, while those with ordered sequence distributions exhibit a tendency to form aggregates that lead to slower dynamics as well as phase separation. Analysis of the structure suggests that copolymers with an alternating sequence distribution form large aggregates that are short‐lived, while diblocks form permanent micelle‐like structures. Analysis of the local composition around a copolymer molecule indicates that aggregation between copolymer chains has a direct impact on the local composition. This in turn has a significant impact on system dynamics. Our results indicate that the dynamics of random, random‐blocky, and alternating copolymers are nearly identical and are faster than that of a homopolymer melt. However, alternating copolymers form aggregates and hence are not uniformly distributed throughout the matrix phase. Thus, alternating copolymers are at a disadvantage in their ability to be effective compatibilizers. From a dynamic perspective, copolymers with random and random‐blocky copolymers seem to be ideal compatibilizers since they are distributed uniformly throughout the system and move rapidly through the matrix phase.

Snapshots of aggregates of alternating copolymer chains. Dark and bright spheres represent A and B monomers, respectively.     

Percolation in Two‐Dimensional Copolymer‐Solvent Systems

In this work, the structure of a strictly 2D dense polymer film for some model copolymer systems: diblock, triblock, and random copolymers is studied. An idealized model of these macromolecular systems is developed where positions of polymer beads are restricted to vertices of a simple cubic lattice and chains are under good solvent conditions (the excluded volume is the only interaction between beads of the chain and solvent molecules). The properties of the system are determined by means of Monte Carlo simulations with a sampling algorithm based on chain's local cooperative changes of conformation. Scaling of the chain size is studied and the influence of the polymer concentration on the chain's size and shape is discussed. The differences and similarities in the behavior of the percolation thresholds of one component in chains with different bead sequences are also shown and discussed. The percolation threshold is found to be weakly dependent on the chain length and more sensitive to the total polymer concentration.

     

Partitioning of Semiflexible Macromolecules into a Slit in Theta Solvent

Investigation of semiflexible coil‐like chains in the process of partitioning with a slit in a solvent of variable thermodynamic quality has shown two key results. For semiflexible chains in a good solvent, the effect of chain stiffness played a role only at low concentrations. However, the situation is different with interacting chains where the effect of stiffness is also observed at higher concentrations. For theta chains, the partitioning into a slit in dilute solutions is lower for semiflexible than for flexible chains, while for higher concentrations this order is reversed. The packing ability of semiflexible chains at higher concentrations is enhanced in the theta system. Interestingly, stretching of chains on penetration into the slit is observed at higher concentrations. Decomposition of free energy change on partitioning into entropy and energy contributions gives more information on the details of partitioning of these systems, especially the differentiation between dilute and moderate concentration regimes. A positive change of partitioning entropy in the theta solvent in the semidilute regime for both flexible and semiflexible chains is noteworthy. This is related to breaking favorable interactions between chains on penetration into the slit.     

Properties of Star-Branched Polymer Chains Near a Surface

We considered two model systems of star-branched polymers near an impenetrable surface. The model chains were constructed on a simple cubic lattice. Each star polymer consisted of f = 3 arms of equal length and the total number of segments was up to 799. The excluded volume effect was included into these models only and therefore the system was studied at good solvent conditions. In the first model system polymer chain was terminally attached with one arm to the surface. The grafted arm could slide along the surface. In the second system the star-branched chain was adsorbed on the surface and the strength of adsorption was were varied. The simulations were performed using the dynamic Monte Carlo method with local changes of chain conformations. The internal and local structures of a polymer layer were determined. The lateral diffusion and internal mobility of star-branched chains were studied as a function of strength of adsorption and the chain length. The lateral diffusion and internal mobility of star-branched chains were studied as a function of strength of adsorption and the chain length. It was shown that the behavior of grafted and weakly adsorbed chains was similar to that of a free three-dimensional polymer, while the strongly adsorbed chains behave as a two-dimensional system.     

Self‐entanglement of a single polymer chain confined in a cubic box

We study the self‐entanglement of a single linear polymer chain with N monomers confined to a cubic box (L × L × L) using the bond‐fluctuation lattice model and primitive path analysis. We probe chains with N between 30 and 750 and vary the degree of confinement L/R_g0 between 0.4 and 12, where R_g0 is the radius of gyration of an unconfined polymer. We find that the conformational properties R_g/R_g0 and L_p/R_g0, where L_p is the average primitive path length, collapse onto a single master curve as a function of the degree of confinement. In the strongly confined regime, L/R_g0 < 1, we find that R_g/R_g0 ～ (L/R_g0)^0.8 and (L_p/R_g0) ～ (L/R_g0)^?2. We verify that the simulation methodology used is quantitatively consistent with experimental data, and the Colby‐Rubinstein entanglement model for unconfined concentrated polymer solutions. The most significant difference between unconfined and confined systems is the variation of L_p with monomer density ?; L_p ～ ?^5/9, in the former, and L_p ～ ?^2/3, in the latter. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 1283–1290     

Self‐diffusion coefficient of ring polymers in semidilute solution

In a topologically constraining environment the size of a flexible nonconcatenated ring polymer (macrocycles) and its dynamics are known to differ from that of linear polymers. Hence, the diffusion coefficient of ring polymers can be expected to be different from linear chains. We present here scaling arguments for the concentration and molecular weight dependence of self‐diffusion coefficient of ring polymers in semidilute solutions, and show that contrary to expectations these scaling relations are identical to what is known for linear polymers. At higher concentrations excluded volume interactions arising from possibilities of segmental overlap can become effective for large ring polymers. In this regime the diffusion coefficient of large ring polymers shows a relatively weaker dependence on concentration and molecular weight. ©2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2370–2379, 2008     

Chain confinement in polymer nanocomposites and its effect on polymer bulk properties

The issue of chain confinement in nanocomposites remains largely unanswered because experimental systems are plagued by additional complicating variables such as particle–polymer interactions and free volume increases brought upon by the addition of the particles. Using computer simulation of high length chain polymers, we show that simple excluded volume interactions between polymer and nanoparticles lead to a wealth of changes in the diffusion coefficient and entanglement density of the chains. This opens up the possibility of using nanoparticles for tuning polymer properties, such as toughness, melt viscosity, and transient rubberlike behavior. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 687–692, 2010     

ABA两亲性嵌段共聚物在双选择性溶剂中自组装行为的Monte Carlo模拟

采用Monte Carlo模拟方法研究了ABA两亲性三嵌段共聚物在两种选择性溶剂中的自组装行为.模拟结果表明,在保证溶剂总浓度一定的情况下,改变两种选择性溶剂的体积比对于ABA两亲性嵌段共聚物自组装所形成的胶束形貌结构有很大影响.随着双选择性溶剂体积比的改变,体系中胶束形貌结构将会发生由囊泡到层状,再到环状、棒状直至球...     

Structure of Adsorbed Polymer Chains: A Monte Carlo Study

The structure of adsorbed polymer chains was studied using simplified lattice models. The model chains were adsorbed on an impenetrable surface with an attractive potential. The dynamic Monte Carlo simulations based in the Metropolis scheme were carried out using these models. The influence of the internal chain architecture (linear, star‐branched and ring chains) and the degree of adsorption on the chain's structure was studied. It was shown that for weakly adsorbed chain regime the ring polymers which exhibit an almost twice as high degree of adsorption compared to linear and star chains have a higher number of adsorbed parts of chain (trains). But the length of such train remains almost the same for all types of a polymer chain. Star‐branched chains exhibit a slightly different change in number and the mean length of trains, loops and tails with the temperature and the chain total length compared to two other types of chain.     

Protein Folding with a Reduced Model and Inaccurate Short‐Range Restraints

Summary: A reduced high‐coordination lattice protein model and the Replica Exchange Monte Carlo sampling were employed in de novo folding simulations of a set of representative small proteins. Three distinct situations were analyzed. In the first series of simulations, the folding was controlled purely by the generic force field of the model. In the second, a bias was introduced towards the theoretically predicted secondary structure. Finally, we superimposed soft restraints towards the native‐like local conformation of the backbone. The short‐range restraints used in these simulations are based on approximate values of ϕ and ψ dihedral angles, which may simulate restraints derived from inaccurate experimental measurements. Incorporating such data into the reduced model required developing a procedure, which transforms the ϕ and ψ coordinates into coordinates of the protein alpha carbon trace. It has been shown that such limited data are sufficient for de novo determination of three‐dimensional structures of small and topologically not too complex proteins.

Protein folding based on secondary structure prediction and simulated torsion angles data.     

动力学方程控制表面反应的模拟模型和方法

提出了动力学方程控制表面反应的模拟模型和方法.该模型从最基本的质量作用定律出发,获得表面反应的动力学方程.而表面反应通过格子模拟反应器进行.通过表面催化样板反应"CO表面催化氧化"检验了该模拟模型和方法,与实验结果吻合.该模型可在其它复杂的表面催化反应体系中推广应用.     

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.     

Synthesis and characterization of poly(DTC‐b‐PEG‐b‐DTC) triblock and poly(TMC‐b‐DTC‐b‐PEG‐b‐DTC‐b‐TMC) pentablock copolymers and kinetics of the polymerization

Dihydroxyl capped biodegradable poly(DTC‐b‐PEG‐b‐DTC) (BCB) triblock copolymer and poly(TMC‐b‐DTC‐b‐PEG‐b‐DTC‐b‐TMC) (ABCBA) pentablock copolymer have been synthesized by PEG and BCB copolymer as macroinitiator in the presence of yttrium tris(2,6‐di‐tert‐butyl‐4‐methylphenolate). The copolymers without random segments have been thoroughly characterized by ¹H, ¹³C‐NMR, SEC, and DSC. Molecular weights of the obtained copolymers are dependent on the amount of PEGs and coincide with the theoretical values. The exchange reaction of yttrium alkoxide and hydroxyl end group is essential for controlling the products' molecular weight. Their thermal behaviors are relevant to the chain lengths of PEG and PDTC segments. The Monte Carlo method has been developed to estimate the chain propagation constant and exchange reaction constant. In average, one exchange reaction will occur after approximately six monomer molecules insert into the growing chain. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 1787–1796, 2005     

Combination of the Metropolis Monte Carlo and Lattice Statics method for geometry optimization of H‐(Al)‐ZSM‐5

In this article, the combination of the Metropolis Monte Carlo and Lattice Statics (MMC‐LS) method is applied to perform the geometry optimization of crystalline aluminosilicate zeolite system in the presence of cationic species (H⁺), i.e., H‐(Al)‐ZSM‐5. It has been proved that the MMC‐LS method is very useful to allow H⁺ ions in (Al)‐ZSM‐5 extra‐framework to approach the global minimum energy sites. The crucial advantage of the combination MMC‐LS method is that, in stead of simulating over thousands random configurations via the only LS method, the only one configuration is needed for the MMC‐LS simulation to achieve the lowest energy configuration. Therefore, the calculation time can be substantially reduced via the performance of the MMC‐LS method with respect to the only LS method. The calculated results obtained from the MMC‐LS and the only LS methods have been comparatively represented in terms of the thermodynamic and structural properties. © 2010 Wiley Periodicals, Inc. J Comput Chem 2010