Entropic Sampling of Free and Ring Polymer Chains

Summary: We extend Monte Carlo (MC) methods developed in our previous paper (J. Phys. A, Math. Gen. 2004 , 37, 1573) and based on entropic sampling within Wang‐Landau (WL) algorithm to the simulation of lattice and continuous models of ring polymers. For a continuous freely joined ring chain (an equilateral polygon) with hard sphere monomer units, the excess entropy of rings relative to the corresponding reference system, a phantom ring chain, is obtained. The excess specific entropy is calculated for a set of various diameters of monomer units d and chain lengths N. Its limiting values for ( ) are estimated for each d and coincidence with those for corresponding free chains is demonstrated. We also develop a WL approach to calculate thermal properties of free and ring continuous chains with an Lennard‐Jones attraction between nonbonded beads being added to hard core repulsion at fixed d. The obtained energy distributions provide calculation of canonical properties such as conformational energy, heat capacity, entropy, and mean square radius of inertia. Thermal results for free and ring chains are being finally compared. Analogous calculations are performed for lattice‐free chains and rings.

     

Molecular Simulation of the Adsorption of Rod/Coil Blends on Nano‐Patterned Surfaces

The adsorption of rod/coil blends onto patterned surfaces with periodic stripes of width w was simulated using Monte‐Carlo methods. The rods and the coils were taken to be fused monomers of diameter σ, interacting with the stripes by a square‐well potential of depth ε and width σ. When the interaction was through excluded‐volume interactions only, we observed segregation of the components in the adsorbed layer. The adsorbed rods are strongly aligned along the stripe for w = σ, but lose their orientational order for larger w. When a repulsive interaction between the rods and the coils was introduced, an increase in the surface coverage of the rods with better recognition of the stripes was observed.

     

层柱状微孔材料吸附存储天然气的Monte Carlo模拟

采用巨正则系综MonteCarlo方法模拟了天然气中主要成分甲烷在层柱状微孔材料中T=300K下的吸附存储,在模拟中层柱状微孔采用Yi等人建立的柱子均匀分布在两炭孔墙之间的模型来表征。甲烷分子采用Lennard-Jones球型分子模型,炭孔墙采用Steele的10-4-3模型,对孔宽为1.36nm的层柱微孔,模拟了四个不同孔率的层柱材料吸附甲烷的情形。得到了孔中流体的局部密度分布以及吸附等温线,对比不同孔率下甲烷的吸附量,得到了此情形吸附甲烷的较佳孔率为0.94。     

Absorption and engulfing transitions in nanoparticle infiltration into a polymer brush: A monte carlo simulation

We study the structure of an infiltrating hard spherical nanoparticle into a polymer brush using extensive off‐lattice Monte Carlo simulations of a basic theoretical model. We show that as long as the spherical particle is coated with a surface layer that interacts attractively with brush monomers, it can penetrate deeply into a dense polymer brush near the grafting surface. The infiltration process contains two stages: diffusing nanoparticle absorbing onto the surface of the polymer brush and engulfing of the nanoparticle by polymer chains. After the nanoparticle fully immerses in the dense polymer brush region, the buoyant forces levels off because of symmetric repulsions that endows increasing nanoparticle mobility and encourages the second transition. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Adsorption of Semiflexible Chains on Nanostriped Surfaces: Monte Carlo Simulations

Monte Carlo simulations were carried out to investigate the adsorption of semiflexible chains from a semidilute solution to substrates with periodic stripes of width w. The chains are made of fused N = 10 monomers of diameter σ interacting with each other through excluded volume interactions and with the stripes via a square‐well potential of depth ε and width σ. The surface coverage was found to increase upon increasing the chain stiffness and decreases on increasing the width of the stripes. At small w, more flexible chains are adsorbed than stiff chains. Analysis of the radius of gyration for the chains showed that when w < 8σ, the component along the stripe direction is significantly larger than the others. Orientational order parameter reveals that, for small w, chains have preference to align along the stripe direction.

     

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     

Free Energy of Polymers Confined in Open and Closed Cavities

Distinct differences between the thermodynamics of open and closed cavities are observed in confinement free energy of macromolecules as a function of chain length and cavity radius and can be of special importance in the case of processes in spatially heterogeneous confinements encountered in various nano‐ and biostructures. In treatments of the confinement free energy, special attention is given to the equilibrium conditions (a full equilibrium for free exchange of macromolecules between cavity and bulk solution or a restricted equilibrium with number of chains in cavity constant) and associated polymer concentration changes. Increased chain stiffness brings about additional effects and complexity, for which the first results are presented here.

     

Interface Structure between Immiscible Reactive Polymers under Transreaction: a Monte Carlo Simulation

Summary: The interface structure between two immiscible melts, a polycondensate polymer A (e.g., polycarbonate, polyester or polyamide) and a polymer B, was studied by means of Monte Carlo simulations using the bond fluctuation model. Polymer B contained a reactive end group (e.g., OH, NH₂ or COOH). Copolymers were generated in‐situ at the interfaces by transreactions (alcoholysis, aminolysis or acidolysis), composing of various length of block A, depending on the position of transreaction in the polycondensate chain A. The content of copolymer at the interface increased with the time, particular fast at the early stage. Fragments of polymers A were released with an end group, reactive to polymers A. This resulted in the proceeding of internal transreactions. An asymmetric interface structure was formed. The simulation also showed that copolymers generated by interfacial transreactions increased the compatibility of the two polymers and enhanced the adhesion strength at the interfaces.

     

Shape of Micelles Formed From Strongly Adsorbed Grafted Polymers in Poor Solvents

Summary: We consider the shape of strongly adsorbed polymer chains in poor solvents. Using both SCF theory and Monte Carlo simulations, we find these chains undergo an instability which is driven, surprisingly, by polymer entropy. This instability occurs above some critical grafting separation and the intermediate segregation regime. An analytical calculation also suggests that this instability occurs for strongly adsorbed polymer chains. We proceed to study multi‐chain systems and observe a number of novel morphological structures including circular polymer droplets, lamellae and a polymer layer with a solvent‐filled hole.

Shape of strongly adsorbed multi‐chain polymer globules.     

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.     

Combinational simulations of free energy of polymer solution

It is conceptually proposed that the total entropy of polymer solution is contributed from two distinct parts: the positional and the oomformational. The former can be represented analytically, while the latter can be simulated with the random self-avoiding walk model on the simple cubic lattice for multichain systems. The obtained results indicated that both the conformational entropy and the mixing heat are consistent with the scaling laws wry well.     

Free Energy of Deformation of the Radius of Gyration in Semiflexible Chains

The distribution function P(S) of the radius of gyration S, the corresponding elastic free energy A(S) and the mean force were computed from simulations based on the wormlike chain (WLC) model. The relation of the S‐conjugated elastic functions to the analogous functions based on the chain vector R and their connection to the statistical‐mechanics ensembles was elucidated. Simulation data revealed that available analytical functions for P(S) fail to predict the behavior of semiflexible chains. When the power‐law function P(S) was used instead, the exponents sizeably raised with stiffness at chain expansion. The exponents deduced from elastic compression of a chain agreed fairly with the scaling exponents for chain confinement into a sphere.

     

Modulation of ionization and structural properties of weak polyelectrolytes due to 1D, 2D,and 3D confinement

What is the impact of reducing the space available to molecules onto their properties is a fundamental question for capillary systems, molecular biology and transport, protein and material sciences. Possibly influenced by space restriction, ionization degree has rarely been studied for confined polyelectrolytes; Monte Carlo titrations and coarse‐grained models are thus used to investigate structural and ionization changes induced on a single polyelectrolyte chain by confinement into slit (1D), cylindrical (2D), or spherical (3D) cavities. Four polyelectrolyte models differing in chain stiffness and the possible formation of charged hydrogen bonds (c? H? bonds) are studied. Low pH effective ionization constants (pK_a ) of confined chains are lower than for the free species if c? H? bonds can be formed. This is especially evident for 3D‐confined stiff chains, a finding rationalized by the impact of global compression onto chain conformations. If no c? H? bonds are allowed, chain ionization is largely unaffected by 1D or 2D confinement, while it is depressed by 3D. Chain confinement Helmholtz energy (ΔA _conf) was computed as a function of both pH and confining width (W) to gauge the impact of ionization‐induced stiffening onto ΔA _conf versus W behavior, the partition coefficient governing absorption, and the average number of c? H? bond formed. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55 , 1088–1102     

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.     

Morphologies of Diblock Copolymer/Homopolymer Blend Films

Summary: Using bond length fluctuation and cavity diffusion algorithm, the morphologies of diblock copolymer/homopolymer blend films, AB/C and AB/A, confined between two hard walls are studied via Monte Carlo (MC) simulation on a cubic lattice. For the AB/C film, the C homopolymer is supposed to be more compatible with the A block than with the B block, while A and B are mutually incompatible. Effects of the composition of the diblock copolymer/homopolymer mixture, the symmetry of the diblock copolymer chain, the film thickness and the selective wall field on morphologies are studied in detail. Furthermore, the simulated results are compared with that of corresponding ABA and ABC triblock copolymer thin films. Comparisons with experiments and SCF theory also show good agreement. The results indicate that both the AB/C and AB/A can be used to prepare porous AB diblock copolymer membranes, the size of the pore channel can be controlled by the volume fraction of homopolymer C or homopolymer A.

Morphology of A₆B₁₄/C₁₀ polymer blend film.     

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.     

苯-乙烯超临界烷基化反应体系在ZSM-5中吸附行为的分子模拟

运用巨正则蒙特卡罗的方法研究了超临界苯-乙烯混合体系在ZSM-5分子筛中的吸附行为.首先模拟了苯-乙烯混合物在ZSM-5分子筛中的吸附等温线.苯的吸附等温线呈现出先增大,而后渐趋平衡,最后又有减小的趋势.而苯在分子筛中的吸附位集中在弯曲通道和直通道的交叉处,且不随压力的变化而变化.从苯在两通道的交叉处产生了"类凝结"(commensurate freezing)现象的角度解释了这种现象.乙烯的情况有所不同,其吸附等温线始终呈增大的趋势,其吸附位随着压力的变化呈现明显的变化.探讨了不同主体相苯/乙烯比(进料比)下超临界的苯-乙烯的混合吸附行为.表明苯的平衡吸附量曲线基本上不随主体相苯/乙烯比的变化而变化,而乙烯随主体相苯/乙烯比的增大而减小,它们在主体相苯/乙烯比为3:1时相交.因此,由苯和乙烯生成乙苯的反应机理出发,从理论上得到了超临界条件下最优的进料比为3:1.此外,在超临界条件下,观察到苯的吸附位集中在两通道交叉处,乙烯的吸附位集中在除两通道交叉处之外的直通道和弯曲通道中,它们不随主体相苯/乙烯比的变化而变化.     

氮气和氧气在膜表面和狭缝孔内平衡吸附的分子模拟

采用巨正则系综的MonteCarlo方法(GCMC)模拟常温(T=303K)下,氮气和氧气在具有狭缝状膜孔的碳膜内的吸附.气体分子之间、气体分子与膜原子之间的相互作用均采用Shifted-Lennard-Jones势能模型.研究了303K和10MPa下,不同膜厚度和膜孔宽度时氧气在膜面和膜孔内的密度分布以及303K和压力从1MPa到10MPa变化时,氮气和氧气在狭缝膜孔内超额吸附等温线.实验结果表明,膜孔端口效应显著,膜厚和膜孔宽度对孔内吸附影响较大,而膜构型对膜面吸附影响显著.     

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.     

Simulation study on the coil‐globule transition of adsorbed polymers

Coil‐globule transition of adsorbed polymers on attractive surface is simulated by using dynamic Monte Carlo simulation. The effect of surface attraction strength E_PS and intrachain attraction strength E_PP on polymer phases is investigated. The coil‐globule transition point is dependent on E_PS, while the globule conformation is dependent on both E_PS and E_PP. At small E_PS, the conformation of adsorbed polymer is three‐dimensional layer structure. While at large E_PS, the conformation of adsorbed polymer is roughly two‐dimensional (2D) at E_PP = 0, and we observe a 2D coil‐globule transition at E*_PP and a layer‐forming transition from 2D conformation to three‐dimensional layer structure at E*_PP,L > E*_PP. The layer‐forming transition point E*_PP,L increases with E_PS as E*_PP,L = E_PS ? 1.4. In addition, we find that the adsorption suppresses the coil‐globule transition, i.e., the coil‐globule transition point E*_PP increases with the increase in E_PS. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2359–2367