The shape of a flexible polymer in a cylindrical pore

We calculate the mean end-to-end distance R of a self-avoiding polymer encapsulated in an infinitely long cylinder with radius D. A self-consistent perturbation theory is used to calculate R as a function of D for impenetrable hard walls and soft walls. In both cases, R obeys the predicted scaling behavior in the limit of large and small D. The crossover from the three-dimensional behavior (D --> infinity) to the fully stretched one-dimensional case (D --> 0) is nonmonotonic. The minimum value of R is found at D approximately 0.46R(F), where R(F) is the Flory radius of R at D --> infinity. The results for soft walls map onto the hard wall case with a larger cylinder radius.     

Unmixing of polymer blends confined in ultrathin films: crossover between two-dimensional and three-dimensional behavior

The interplay between chain conformations and phase separation in binary symmetric polymer mixtures confined into thin films by "neutral" hard walls (i.e., walls that do not preferentially attract or repel one of the two components of the mixture) is studied by Monte Carlo simulations. Using the bond fluctuation model on a simple cubic lattice in the semi grand canonical ensemble, we locate the critical temperature of demixing via finite size scaling methods for a wide range of chain lengths (16 infinity, and hence T(c) proportional, variant N. However, strong deviations from the Flory-Huggins theory occur as long as the unperturbed chain dimension exceeds D, and the critical behavior falls in the universality class of the two-dimensional Ising model for any finite value of D.     

Polymer chains in good solvent within attracting walls

It is known that a polymer chain in an ideal solvent confined within parallel attracting walls undergoes a second-order transition at the temperature T* satisfying the equation exp[-ε/(k_BT*)]=6/5; here the model consists of a chain placed on a cubic lattice, and ε (<0) is the attractive energy experienced by a chain segment contacting a wall. We then investigate the effect induced by a good solvent upon the chain behavior. A single chain is considered; within the Gaussian approximation, we assume that its partition function may be factorized in two terms, one across the wall planes and another parallel to them. For an interplanar distance L significantly smaller than the average radius of gyration the compressed chain is assumed to reach a uniform density, so that the free energy contribution due to the intrachain atomic contacts is a function of the density alone. It may be shown that the effective value of ε/(k_BT*)(=σ) is the difference between the value to be expected “in vacuo” and β/(z-2), where z is the degree of coordination of the lattice and β is the excluded-volume parameter. As a result, for large values of L we may have an attractive effect exerted by the chain on the walls whereas at small L's we invariably have a repulsion. For the cubic lattice we have a repulsion and an attraction for large L approximatively for σ < ln(6/5)+β/(z-2) and for σ > (ln(6/5)+β/(z-2), respectively, whereas we have inversion between the two regimes at some distance L for intermediate values of σ. In the limit of an infinite molecular weight the inversion translates into a thermodynamic transition. We believe the present model may explain some important features seen in polymer adhesion.     

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     

Universal properties of a single polymer chain in slit: Scaling versus molecular dynamics simulations

We revisit the classical problem of a polymer confined in a slit in both of its static and dynamic aspects. We confirm a number of well known scaling predictions and analyze their range of validity by means of comprehensive molecular dynamics simulations using a coarse-grained bead-spring model of a flexible polymer chain. The normal and parallel components of the average end-to-end distance, mean radius of gyration and their distributions, the density profile, the force exerted on the slit walls, and the local bond orientation characteristics are obtained in slits of width D=4/10 (in units of the bead diameter) and for chain lengths N=50/300. We demonstrate that a wide range of static chain properties in normal direction can be described quantitatively by analytic model-independent expressions in perfect agreement with computer experiment. In particular, the observed profile of confinement-induced bond orientation is shown to closely match theory predictions. The anisotropy of confinement is found to be manifested most dramatically in the dynamic behavior of the polymer chain. We examine the relation between characteristic times for translational diffusion and lateral relaxation. It is demonstrated that the scaling predictions for lateral and normal relaxation times are in good agreement with our observations. A novel feature is the observed coupling of normal and lateral modes with two vastly different relaxation times. We show that the impact of grafting on lateral relaxation is equivalent to doubling the chain length.     

嫁接于平行板的受限紧密高分子链末端距分布函数的研究

采用剪除增加Rosenbluth方法(Pruned-enriched-Rosenbluth method,PERM)算法计算了嫁接于平行板的受限紧密高分子链的末端距分布函数.由于受限紧密高分子链具有各向异性,重点研究了平行板方向x轴上的分布函数P(x),发现P(x)可以表示为ln[P(x)/Pm(x)]/ND-5/3=a0+a1u+a2u2+a3u3(其中u=x/ND-2/3).这里N为链长,Pm(x)为分布函数P(x)的最大值,两平行板的间距为D+1.通过计算P(x)的Shannon熵发现末端距分布函数P(x)的Shannon熵可以用来描述高分子链受限的程度,Shannon熵对平行板间距的变化非常敏感,对于同一链长N,P(x)的Shannon熵会随着D的增大而迅速减小,超过临界值Dc会趋向一个定值,即当D≥Dc时Shannon熵将趋于稳定,也说明了此时受限条件对紧密高分子链影响非常小.同时临界值Dc与链长N有关,Dc~Nλ,其中λ=0.543,并进行了一定的理论分析.     

Molecular-dynamics simulations of the transport properties of a single polymer chain in two dimensions

Molecular-dynamics simulations are conducted to elucidate the critical factors affecting the transport properties of isolated polymer chains in strictly two dimensions. The relevance of surface inhomogeneity is critically examined. We unequivocally find that surface inhomogeneity is critical in obtaining transport behavior consistent with the recent measurements of surface diffusion for polymers adsorbed at the solid-liquid interface. For a systematic investigation of this point, heterogeneity was introduced by decorating the surface with impenetrable elements and we find that chain diffusivity crossed over from Rouse-type behavior to reptationlike with increasing surface coverage of obstacles. This transition in behavior occurred when the mean distance between obstacles is approximately equal to the end-to-end distance, Re, of the two-dimensional chain. Our results underscore the importance of surface disorder (not only literal obstacles but by reasonable extension also to other types of disorder) in determining the transport behavior of chains adsorbed to solids.     

SEGMENT DENSITY PROFILES OF COMPACT POLYMER CHAINS CONFINED BETWEEN TWO PARALLEL PLANE WALLS

We use the pruned-enriched Rosenbluth method to investigate systematically the segment density profiles of compact polymer chains confined between two parallel plane walls.The non-adsorption case of adsorption interaction energyε=0 and the weak adsorption case ofε=-1 are considered for the compact polymer chains with different chain lengths N and different separation distances between two walls D.Several special entropy effects on the confined compact polymer chains,such as a damped oscillation in the segment density profile for the large separation distance D,are observed and discussed for different separation distances D in the non-adsorption case.In the weak adsorption case,investigations on the segment density profiles indicate that the competition between the entropy and adsorption effects results in an obvious depletion layer.Moreover,the scaling laws of the damped oscillation period T_d and the depletion layer width L_d are obtained for the confined compact chains.Most of these results are obtained for the first time so far as we know,which are expected to understand the properties of the confined compact polymer chains more completely.     

Polymer chains in a soft nanotube: a Monte Carlo study

We study the equilibrium properties of flexible polymer chains confined in a soft tube by means of extensive Monte Carlo simulations. The tube wall is that of a single sheet six-coordinated self-avoiding tethered membrane. Our study assumes that there is no adsorption of the chain on the wall. By varying the length N of the polymer and the tube diameter D we examine the variation of the polymer gyration radius Rg and diffusion coefficient Ddiff in soft and rigid tubes of identical diameter and compare them to scaling theory predictions. We find that the swollen region of the soft tube surrounding the chain exhibits a cigarlike cylindrical shape for sufficiently narrow tubes with D相似文献   

Molecular flexibility effects upon liquid dynamics

Simulation results for the diffusive behavior of polymer chain/penetrant systems are analyzed. The attractive range and flexibility of simple chain molecules were varied in order to gauge the effect on dynamics. In all cases, the dimensionless diffusion coefficient, D*, is found to be a smooth, single-valued function of the packing fraction, eta. The functions D*(eta) are found to be power laws with exponents that are sensitive to both chain stiffness and particle type. For a specific system type, the D*'s for both penetrant and chain-center-of-mass extrapolate to zero at the same packing fraction, eta0. This limiting packing fraction is interpreted to be the location of the glass transition, and (eta0-eta), the distance to the glass transition.     

Modeling the conformations and motions of isolated polymer chains in the narrow channels of their crystalline inclusion compounds with small-molecule,host clathrates

The narrow channels occupied by polymer chains in their crystalline inclusion compounds(IC) with small-molecule, host clathrates, such as urea and perhydrotriphenylene(PHTP), provide a unique, solid state environment. Single polymer chains are confined to occupy narrow cylindrical channels whose walls consist of a crystalline matrix of the small-molecule, host clathrate. Because the IC channels are well-separated, each included polymer chain is isolated from its neighbors, and is therefore free from cooperative, interpolymer interactions which often dominate and complicate the behavior of bulk polymers. We have modeled polymer chains included in their IC channels by restricting the conformations accessible to small chain fragments(9–20 backbone bonds) to those which fit into a cylinder whose diameter(5.5Å) mimics the observed channel cross-section. After establishing the population of channel conformers, a test is performed to determine the possibility of interconverting between them without any portion of the polymer chain fragment leaving the channel during any step in the interconversion process. The results of our modeling are compared to observations made on a variety of polymer-IC's formed with either or both of the host clathrates, urea and PHTP. General agreement is found between the modeled conformations and mobilities of cylindrical polymer chain fragments and those observed directly from the crystalline polymer-IC's, principally by solid state NMR, DSC, and X-ray diffraction.     

X-ray diffraction study of the structure of carboxymethylcellulose-cationic surfactant complexes.

We have investigated dilute aqueous solutions of an anionic polymer (carboxymethylcellulose) mixed with cationic surfactants of different chain lengths (dodecyl to octadecyl trimethylammonium bromides: DTAB, TTAB, CTAB and OTAB). The structures of the concentrated phases formed above the precipitation threshold were studied by X-ray diffraction. Different body-centred cubic structures with space groups Pm3n were observed in the presence of surfactant with a short aliphatic chain (DTAB), despite the fact that the polymer persistence length is comparable to the repeat distance of the structure (5 nm). For larger surfactant chain lengths (TTAB and CTAB), the structure of the precipitates can be either cubic (Pm3n) or 2D hexagonal depending on the initial surfactant and polymer concentrations. For still larger chain length (OTAB), the structure becomes lamellar. This structural evolution from micellar cubic towards 2D hexagonal and lamellar is attributed to the decrease of the local curvature of the surfactant aggregates, as observed for flexible synthetic polymers and short DNA fragments under similar conditions. Furthermore, the structure of the bulk complexes formed just below the precipitation threshold anticipates the structure seen in the precipitated phases.     

Elastic Behavior of Polymer Chains

The elastic behavior of the polymer chain was investigated in a three-dimensional off-lattice model. We sample more than 109 conformations of each kind of polymer chain by using a Monte Carlo algorithm, then analyze them with the non-Gaussian theory of rubberlike elasticity, and end with a statistical study. Through observing the effect of the chain flexibility and the stretching ratio on the mean-square end-to-end distance, the average energy, the average Helmholtz free energy, the elastic force, the contribution of energy to the elastic force, and the entropy contribution to elastic force of the polymer chain, we find that a rigid polymer chain is much easier to stretch than a flexible polymer chain. Also, a rigid polymer chain will become difficult to stretch only at a quite high stretching ratio because of the effect of the entropy contribution. These results of our simulation calculation may explain some of the macroscopic phenomena of polymer and biomacromolecular elasticity.     

Phase behavior of a fluid confined in slitlike pores with walls modified by preadsorbed chain molecules

We have studied the microscopic structure, thermodynamics of adsorption, and phase behavior of Lennard-Jones fluid in slitlike pores with walls modified due to preadsorption of chain molecules. The chain species are grafted at the walls by terminating segments. Our theoretical considerations are based on a density functional approach in the semigrand canonical ensemble. The applied constraint refers to the constant number of grafted chain molecules in the pore without restriction of the number of chains at each of the walls. We have observed capillary condensation of Lennard-Jones fluid combined with the change of the distribution of chains from nonsymmetric to symmetric with respect to the pore walls. The phase diagrams of the model are analyzed in detail, dependent on the pore width, length of chains, and grafted density.     

Confinement free energy and chain conformations of homopolymers confined between two repulsive walls

Lattice Monte Carlo simulations of polymer solutions confined between two parallel plates were performed. The confinement free energy Deltamicro(conf) per chain and the radius of gyrations of the chains parallel and perpendicular to the plates were obtained. When the concentration of the confined solution is above the overlap concentration, Deltamicro(conf) is found to scale with Na/D in a power law, betaDeltamicro(conf) approximately (Na/D)(m), with an exponent m=1.10+/-0.02 for athermal walls where N is the number of monomers in a chain, D is the slit width, and a is the lattice spacing. The presence of a weak attractive polymer/wall interaction epsilon(w) does not change the scaling variable, but the exponent m increases slightly. Extrapolating the results to melt would suggest that the predictions made by de Gennes [C. R. Acad. Sci. Paris II 305, 1181 (1987)] about the confinement free energy cost per chain in polymer melt is correct as far as the scaling variable is concerned, but is incorrect about the exponent m observed. The implication of this result on the predicted force between plates immersed in polymer melt is discussed. The parallel dimensions of the confined chain is expanded when the slit width D is narrow, however, the expansion is reduced at high concentration. It is conceivable that in melt the chain is not expanded when confined in a repulsive slit.     

Superselective Adsorption of Multivalent Polymer Chains to a Surface with Receptors

Multivalent polymer chains exhibit excellent prospect in biomedical applications by serving as therapeutic agents. Using three-dimensional (3D) Langevin dynamics simulations, we investigate adsorption behaviors of multivalent polymer chains to a surface with receptors. Multivalent polymer chains display superselective adsorption. Furthermore, the range of density of surface receptors at which a multivalent polymer chain displays a superselective behavior, narrows down for chains with higher density of ligands. Meanwhile, the optimal density of surface receptors where the highest superselectivity is achieved, decreases with increasing the density of ligands. Then, the conformational properties of bound multivalent chains are studied systematically. Interestingly, we find that the equilibrium radius of gyration R_g and its horizontal component have a maximum as a function of the density of surface receptors. The scaling exponents of R_g with the length of chain suggest that with increasing the density of surface receptors., the conformations of a bound multivalent polymer chain first fall in between those of a two-dimensional (2D) and a 3D chain, while it is slightly collapsed subsequently.     

Concentration dependence of the interfacial tension for aqueous two-phase polymer solutions of dextran and polyethylene glycol

We studied the interfacial tension between coexisting phases of aqueous solutions of dextran and polyethylene glycol. First, we characterized the phase diagram of the system and located the binodal. Second, the tie lines between the coexisting phases were determined using a method that only requires measuring the density of the coexisting phases. The interfacial tension was then measured by a spinning drop tensiometer over a broad range of polymer concentrations close to and above the critical point. In this range, the interfacial tension increases by 4 orders of magnitude with increasing polymer concentration. The scaling exponents of the interfacial tension, the correlation length, and order parameters were evaluated and showed a crossover behavior depending on the distance to the critical concentration. The scaling exponent of the interfacial tension attains the value 1.50 ± 0.01 further away from the critical point, in good agreement with mean field theory, but the increased value 1.67 ± 0.10 closer to this point, which disagrees with the Ising value 1.26. We discuss possible reasons for this discrepancy. The composition and density differences between the two coexisting phases, which may be taken as two possible order parameters, showed the expected crossover from mean field behavior to Ising model behavior as the critical point is approached. The crossover behavior of aqueous two-phase polymer solutions with increasing concentration is similar to that of polymer solutions undergoing phase separation induced by lowering the temperature.     

Solvent response of mixed polymer brushes

We have performed classical density functional theory calculations to study the behavior of mixed polymer brushes tethered to a planar surface. We assume no lateral segregation of the polymer at the grafting density studied and consider an implicit solvent. For a binary mixture of short and long athermal polymer chains, the short chain is compressed while the long chain is stretched compared with corresponding pure polymer chains at the same grafting density, which is consistent with simulation. This results from configurational entropy effects. Furthermore, we add a mean-field interaction for each polymer brush to simulate their different response towards a solvent. The long chain is forced to dislike the solvent more than the short chain. Through the interplay between the solvent effects and configurational entropy effects, a switch of the polymer brush surface (or outer) layer is found with increasing chain length of the long chain. The transition chain length (long chain) increases with increasing the solvent selectivity, and decreases with increasing the grafting density of the long chain. These results can provide guidance for the design of smart materials based on mixed polymer brushes.     

VISCOMETRIC INVESTIGATIONS OF POLYVINYLPYRROLIDONE IN MIXED SOLVENTS AND WITH VARYING TEMPERATURE

The viscosity behavior of polyvinylpyrrolidone (PVP) has been determined at 25℃ in mixed solvents comprising water/dimethylformamide (DMF) and water /methanol (MeOH). Analysis of the data has considered the PVP as being both host and guest polymer in solution. The intrinsic viscosity of PVP in DMF is higher than in water and in MeOH, but also increases in a mixed solvent with high water content because of the effect of polymer-solvent interactions. It was also found that the intrinsic viscosity of PVP at finite concentration, [ηpvp]c decreases with an increase in the concentration of PVP in solution. The viscosity behavior of PVP in a mixed solvent is affected by the concentration-dependent intermolecular excluded volume effect, which can be quantitatively expressed by the parameter, bY, which reflects the shrinkage of PVP chain coils, resulting in a decrease of [ηpvp]c. The effect of temperature on the viscosity behavior of PVP in MeOH shows that the interaction parameter increases up to a maximum value, and then decreases after a certain temperature.     

一种侧链液晶高分子的合成与表征

合成了一种主链为甲基丙烯酸酯 ,侧链是三个苯环以酯键相连的介晶基元 ,柔性间隔段为两个亚甲基的新的侧链液晶高分子 .聚合物和单体的化学结构、液晶相转变和液晶态织构采用红外光谱、核磁共振、偏光显微镜、差热分析和广角X光衍射进行了表征 .研究表明 ,单体呈现近晶相和向列相两个液晶相 ,聚合物在很宽的温度范围内呈向列相 .该单体和聚合物在一定条件下可形成固化诱导条带织构