Segmental distribution properties of a polymer chain near an interacting barrier

The exact distribution of segments for self-avoiding walks of lengths N=4–14 bonds in the presence of an interacting barrier on the diamond lattice has been obtained by the method of direct enumeration. Behavior for the infinite chain was estimated and compared with Rubin's results for the normal random walk. It is shown that the onset of a well defined transition for the self-avoiding walk coincides with the location predicted for the normal random walk. It was found that for a self-avoiding walk a plot of θ₂ (the fraction of segments in level z) versus the interaction parameter φ is shifted to the right (higher φ), for all z, as compared with a similar plot for the normal random walk. Conditional probabilities for a self-avoiding walk having its t th segment in level z (when φ=0) are reported.     

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.     

The critical adsorption point of self-avoiding walks: a finite-size scaling approach

The critical adsorption of self-avoiding polymer chain in a simple cubic lattice onto a flat surface is studied with Monte Carlo simulations. The dependence of number of surface contacts M on chain length N and polymer-surface interaction epsilon is investigated by a finite-size scaling approach. We estimate the critical adsorption point epsilon(c)=0.291+/-0.002 and the exponent phi=0.54+/-0.01. The asymptotic behaviors M proportional variant N for epsilon>epsilon(c) and M proportional variant N(0) for epsilon相似文献   

Surface enrichment of branched polymers in linear hosts: effect of asymmetry in intersegmental interactions and density gradients

Variable density lattice treatment of surface enrichment of f-arm star-branched chains in star/linear polymer blends is compared with results of an analytical response theory proposed by Wu and Fredrickson [Macromolecules 29, 7919 (1996)]. We find that differences in treating the intersegmental interactions in the small interfacial region near a free surface lead to significant differences in the potentials by which polymer chain ends are attracted towards the surface. Consideration of an asymmetric relationship between segment potentials and density changes in polystyrene at 450 K and 0.1 MPa, for example, gives typically a threefold to fourfold enhancement in composition of star molecules at a vacuum interface. When contributions from gradients in density are included in the analysis even greater levels of surface enhancement (fivefold to sixfold increases) are observed. By appropriately estimating the attraction of chain ends and repulsion of branch points at a free surface, we show that concentration profiles of branched polymers predicted in the lattice model are consistent with results obtained in the analytical response theory.     

Continuum mesoscopic framework for multiple interacting species and processes on multiple site types and/or crystallographic planes

While recently derived continuum mesoscopic equations successfully bridge the gap between microscopic and macroscopic physics, so far they have been derived only for simple lattice models. In this paper, general deterministic continuum mesoscopic equations are derived rigorously via nonequilibrium statistical mechanics to account for multiple interacting surface species and multiple processes on multiple site types and/or different crystallographic planes. Adsorption, desorption, reaction, and surface diffusion are modeled. It is demonstrated that contrary to conventional phenomenological continuum models, microscopic physics, such as the interaction potential, determines the final form of the mesoscopic equation. Models of single component diffusion and binary diffusion of interacting particles on single-type site lattice and of single component diffusion on complex microporous materials' lattices consisting of two types of sites are derived, as illustrations of the mesoscopic framework. Simplification of the diffusion mesoscopic model illustrates the relation to phenomenological models, such as the Fickian and Maxwell-Stefan transport models. It is demonstrated that the mesoscopic equations are in good agreement with lattice kinetic Monte Carlo simulations for several prototype examples studied.     

近壁模型高分子链的计算机模拟

采用简立方格点上的普通无规行走 (NRW)和自避行走 (SAW )为模型链 ,研究了不可穿透的刚性壁附近高分子的构象性质 ,得出近壁链的构象熵和尺寸随一端点与壁之间距离z0 的变化 .所用的计算机模拟技术包括精确计数和MonteCarlo模拟 .数值结果表明 ,近壁链的构象熵降低遵循一种简单规律 ,即当链长愈长或一端愈接近于壁时 ,与长度相同的自由链相比 ,链因壁限制所致构象熵的降低愈大 .当链十分接近于壁时 ,其均方末端距〈R2 〉(尤其是与壁垂直的分量〈R2z〉)大于自由链的相应值 ;随z0 增大 ,〈R2 〉及〈R2z〉开始减小 ,通过某一极小值 ,然后上升 ;当z0 →∞时 ,趋于自由链的极限值 .换言之 ,近壁模型链的线团经历一个收缩再逐渐扩张的过程     

聚乙烯型尾形链构象统计的Monte Carlo研究

以聚乙烯型尾形链为例 ,根据链的实际键长、键角和Θ条件下每一链段处于不同旋转异构态的条件概率 ,用MonteCarlo模拟方法生成样本链分子 ,计算了尾形链的均方末端矩及其分量、构象数 ,并与完全计算法及理论推导值作了比较 ,讨论了尾形链构象数和沿边界方向及法线方向均方末端矩分量随链段数n及键角Φ的变化 .     

Configurational probabilities for monomers, dimers and trimers in fluids

A new analytical approach is proposed to model aggregation of molecules with isotropic, nearest-neighbor, attractive interactions. By treating the clustering process as a chain reaction, equations with the exact high temperature limit are derived by evaluating the occupation probabilities of nearest neighbors based on the Ono-Kondo approach for a hexagonal lattice to calculate the configurational probabilities of i-mers (i = 1, 2, 3). Equilibrium constants for dimers and trimers are calculated based on the configurational probability data. The proposed model agrees well with Monte Carlo simulations at medium and high temperatures. At low temperatures, the model can be improved by considering the full set of site densities in the first shell of a central trimer. Approximate analytical solutions derived from exact calculations of the grand partition function for monomer adsorption on a 4 x N hexagonal lattice with cylindrical boundary conditions also are presented.     

Can the Gibbs free energy of adsorption be predicted efficiently and accurately: an M05-2X DFT study

This study presents new insight into the prediction of partitioning of organic compounds between a carbon surface (soot) and water, and it also sheds light on the sluggish desorption of interacting molecules from activated and nonactivated carbon surfaces. This paper provides details about the structure and interactions of benzene, polycyclic aromatic hydrocarbons, and aromatic nitrocompounds with a carbon surface modeled by coronene using a density functional theory approach along with the M05-2X functional. The adsorption was studied in vacuum and from water solution. The molecules studied are physisorbed on the carbon surface. While the intermolecular interactions of benzene and hydrocarbons are governed by dispersion forces, nitrocompounds are adsorbed also due to quite strong electrostatic interactions with all types of carbon surfaces. On the basis of these results, we conclude that the method of prediction presented in this study allows one to approach the experimental level of accuracy in predicting thermodynamic parameters of adsorption on a carbon surface from the gas phase. The empirical modification of the polarized continuum model leads also to a quantitative agreement with the experimental data for the Gibbs free energy values of the adsorption from water solution.     

Conformational characteristics of polyethylene glycol macromolecules in aqueous solutions according to refractometry data

The aqueous solutions of polyethylene glycols with molecular masses of 600, 1000, 1500, 3000, 6000, and 20000 were studied by refractometry. The conformational polarizabilities, mean-square distances between the ends of the macromolecular chain, segment lengths, and the number of Kuhn segments in a macromolecule were determined using the Lorentz-Lorentz equation. The polarizability of a hydrated macro-molecule was represented as the sum of polarizabilities of the nonhydrated macromolecule with retained conformation and polarizabilities of the water molecules involved in hydration of macromolecules. The size of macromolecules stabilized starting from a certain concentration. It was concluded that the initial concentration of stabilization shifts toward low concentrations as the molecular mass of polyethylene glycol increases. The dependence of the mean-square distance between the ends of the macromolecular chain on the number of Kuhn segments was expressed as the exponential function with index 0.3.     

Mesoscopic analysis of conformational and entropic contributions to nonspecific adsorption of HP copolymer chains using dynamic Monte Carlo simulations

Dynamic Monte Carlo simulations of short linear HP-type copolymers exhibiting proteinlike characteristics are used to investigate both chain dynamics and changes in chain conformational entropy and their contributions to the energetics of adsorption onto a solid-liquid interface. The dMC results show that the conformations and energies of adsorbed chains are highly degenerate. The ensemble-averaged energy of the adsorbed state is dependent on temperature, chain sequence, native-state stability, and sorbent surface geometry and hydrophobicity. Mesoscopic thermodynamic analyses reveal that, although increased chain conformational entropy contributes to the driving force for adsorption in certain cases, many conditions exist where the change in conformational entropy is either negligible or unfavorable due to constraints imposed by the need to form a large and specific number of favorable intra- and intermolecular contacts and by the impenetrable nature of the sorbent surface. Step-number-averaged energy trajectories, based on sampling of a large number of energy trajectories and thus conformational states at each step number, suggest that the search for a global energy minimum is gradual, so that adsorption is first reversible but becomes apparently irreversible with longer exposure to the sorbent. These results appear to be connected to the conformational adaptability of the chain both on the surface and in solution, and an adsorption model taking chain conformational dynamics into account is proposed.     

端基附壁高分子模型链的塌缩转变

借MonteCarlo和模拟退火方法研究了端基附壁高分子尾形链在不同温度下的形态变化 ,链的模型采用有最近邻相互吸引作用的自避行走 .计算机实验结果表明 ,对于端基附壁的高分子尾形链 ,与自由链一样 ,当温度逐渐降低时高分子链会发生从松散的无规线团到紧密球体的塌缩转变 .计算机模拟得到了端基附壁链的均方末端距及其分量 ,均方回转半径及分布随温度的变化 .由于刚性壁的影响 ,使得有限链长的高分子尾形链与自由链相比 ,其表示链尺寸 温度关系的曲线要稍低 .模拟还发现 ,在高温时壁对链形状的影响比较大 ,壁垂直方向上尺寸明显大于平行方向的尺寸 ,后者接近于自由链的尺寸分量 .然而 ,低于θ温度时 ,尤其是完全塌缩之后 ,壁对链形状的影响已经很小 .     

Density functional approach to adsorption of simple fluids on surfaces modified with a brush-like chain structure

A density functional theory to describe adsorption of a simple fluid from a gas phase on a surface modified with pre-adsorbed chains is proposed. The chains are bonded to the surface by one of their ends, so they can form a brush-like structure. Two models are investigated. According to the first model all but the terminating segment of a chain can change the configuration during the adsorption of fluid species. The second model assumes that the chains remain "frozen", and the system is considered as a nonuniform quenched-annealed mixture. We apply simple form of interactions to study adsorption phenomena, microscopic structure, and layering transitions. Our principal findings show that new layering phase transitions can occur because of a chemical modification of the substrate under certain conditions, in comparison with nonmodified surfaces. However, opposite trends, that is, smoothing the adsorption isotherms, can also be observed, depending on the surface density of the grafted chains.     

Statistical thermodynamics for chain molecules with simple RNA tertiary contacts

A statistical thermodynamic model is developed for chain molecules with simple RNA tertiary contacts. The model, which accounts for the excluded volume effect and the nonadditivity in the free energy, enables reliable predictions for the conformational entropy and partition function for simple tertiary folds. Illustrative applications are made to conformational transitions involving simple tertiary contacts. The model can predict the interplay between the secondary and the tertiary interactions in the conformational changes. Though the present form of the theory is tested and validated in a two-dimensional lattice model, the methodology, which is developed based on a general graphical representation for chain conformations, is applicable to any off-lattice chain representations. Moreover, the analytical formulation of the method makes possible the systematic development of the theory for more complex tertiary structures.     

Conformational statistics of polymer chain terminally attached to wall (III) —NRW model loop chain

When the two end groups of a linear polymer chain are absorbed on a solid surface, the polymer chain forms the “loop” conformation. Investigation has been made on the conformational statistics of a model loop chain by the normal random walk (NRW) on a lattice confined in the half-infinite space. Based on the conformational distribution function of the NRW model tail chain, it is easy to deduce an analytical formula expressing the conformational number of the model loop chain. It was found that the ratio of the conformational number of the model loop chain to that of the free chain varies with the power functionN ^-2/3 when the chain lengthN→οο. The same result -was obtained by means of the recursion equation. The ratio of the mean square end-to-end distanceh ² for the model loop chain to its mean square bond lengthl ² is 2N/3. Compared with the free chain with the same lengthN, the mean square end-to-end distance of the model loop chain contracts to a certain extent. The basic relationships deduced were supported by the exact enumeration and Monte Carlo simulations. Project supported by the National Natural Science Foundation of China.     

Density functional theory for semiflexible and cyclic polyatomic fluids

The effects of bond angle and chain stiffness on the structures of semiflexible polyatomic fluids are investigated by incorporating the bending potential into a density functional theory [Y. X. Yu and J. Z. Wu, J. Chem. Phys. 117, 2368 (2002)] that combines a modified fundamental measure theory for the excluded-volume effects and the first-order thermodynamics perturbation theory for the chain connectivity. The refined density functional theory faithfully reproduces the density profiles and conformational properties of a variety of triatomic fluids near a hard wall in which extensive Monte Carlo simulation data are available. In particular, the theory is able to capture the structures of rigid cyclic trimers where all segments are identical. The variation of local density profiles with respect to the chain length of confined polyatomic fluids is also explored. For quadratomic fluids confined in slit pores, the density profile of the middle segments exhibits novel double peaks that are absent in a fully flexible chain model. In addition, the density functional theory is applied to predicting the conformational properties and adsorption behavior of heterogeneous triatomic fluids of type "ABB" mimicking surfactant molecules. The competition between surface adsorption and self-association of trimers consisting of surface active and self-binding "A" segments and neutral "B" segment is explored.