Localization of a multiblock copolymer at a selective interface: scaling predictions and Monte Carlo verification

We investigate the localization of a hydrophobic-polar regular copolymer at a selective solvent-solvent interface with emphasis on the impact of block length M on the copolymer behavior. The considerations are based on simple scaling arguments and use the mapping of the problem onto a homopolymer adsorption problem. The resulting scaling relations treat the gyration radius of the copolymer chain perpendicular and parallel to the interface in terms of chain length N and block size M, as well as the selectivity parameter chi. The scaling relations differ for the case of weak and strong localization. In the strong localization limit a scaling relation for the lateral diffusion coefficient D( parallel) is also derived. We implement a dynamic off-lattice Monte Carlo model to verify these scaling predictions. For chain lengths in a wide range (32相似文献   

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   

High-frequency dielectric and conductometric properties of poly-l-lysine aqueous solutions at the crossover between semidilute and entangled regime

The dielectric and conductometric properties of poly-l-lysine aqueous solutions have been investigated in the frequency range from 1 MHz to 1.8 GHz, where micro-Brownian dynamics and internal motion of side-chain polar groups result in a well-defined relaxation process, intermediate between that caused by counterion polarization (characteristic of the polyelectrolyte nature of the polyion investigated) and that associated with the orientational polarization of the aqueous phase. The polymer concentration has been varied in a wide interval in order to investigate the influence of different chain conformations on the dielectric parameters as a consequence of the different concentration regimes occurring in these systems. With the help of polymer scaling theories, scaling relations for the dielectric strength and the relaxation time are presented, predicting, as the polymer concentration is increased, a transition from semidilute-unentangled to semidilute-entangled regimes. We compare these predictions with the experimental findings over the whole concentration range investigated, with a qualitative agreement. Deviations from the scaling behavior related to a crossover regime between unentangled and entangled regions are briefly discussed. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 3123–3130, 1999     

Polymer chains confined into tubes with attractive walls: A Monte Carlo simulation

A bead-spring off-lattice model of a polymer chain with repulsive interactions among repeating units confined into straight tubes of various cross sections, D_T², is studied by Monte Carlo simulation. We are also varying the chain length from N = 16 to 128 and the strength of a short-range attractive interaction between the repeating units and the walls of the tube. Longitudinal and perpendicular static linear dimensions of the chains are analyzed, as well as the density profile of repeating units across the tube. These data are interpreted in terms of scaling concepts describing the crossover between three-dimensional and quasi-one-dimensional chain conformations and the adsorption transition of chains at flat infinite walls, respectively. We also study the time-dependent mean-square displacements of repeating units and obtain various relaxation times. It is shown that both relaxation times scaling proportional to N² and to N³ play a role in the reptative motion of the chain in the tubes.     

From caging to Rouse dynamics in polymer melts with intramolecular barriers: a critical test of the mode coupling theory

By means of computer simulations and solution of the equations of the mode coupling theory (MCT), we investigate the role of the intramolecular barriers on several dynamic aspects of nonentangled polymers. The investigated dynamic range extends from the caging regime characteristic of glass-formers to the relaxation of the chain Rouse modes. We review our recent work on this question, provide new results, and critically discuss the limitations of the theory. Solutions of the MCT for the structural relaxation reproduce qualitative trends of simulations for weak and moderate barriers. However, a progressive discrepancy is revealed as the limit of stiff chains is approached. This disagreement does not seem related with dynamic heterogeneities, which indeed are not enhanced by increasing barrier strength. It is not connected either with the breakdown of the convolution approximation for three-point static correlations, which retains its validity for stiff chains. These findings suggest the need of an improvement of the MCT equations for polymer melts. Concerning the relaxation of the chain degrees of freedom, MCT provides a microscopic basis for time scales from chain reorientation down to the caging regime. It rationalizes, from first principles, the observed deviations from the Rouse model on increasing the barrier strength. These include anomalous scaling of relaxation times, long-time plateaux, and nonmonotonous wavelength dependence of the mode correlators.     

Phenomenological analysis of elongational flow birefringence in semidilute solutions of hydroxypropylcellulose

The relaxation time of a polymer chain in an elongational flow field was investigated for hydroxypropylcellulose (HPC) semidilute solution systems by two methods: phenomenological analysis of elongational flow-induced birefringence, and dynamic light scattering (DLS) and rheological measurements. To understand the relaxation time of an entangled semiflexible polymer solution in an elongational flow field, scaling analysis of the elongational flow-induced birefringence curve was performed. The results of both temperature and concentration scaling analyses showed that birefringence curves at different temperatures and at several HPC concentrations were described well by a universal birefringence–strain rate curve. This scaling behavior was compared with the "fuzzy cylinder" model. The critical strain rate corresponded to the correlation time of the slow relaxation mode determined by DLS measurement and the relaxation spectrum obtained by dynamic viscoelasticity measurement. The elongational flow-induced birefringence observed in an HPC semidilute solution was concluded to be attributed to the orientation of the HPC segment in the entangled molecular system, because the dominant relaxation mode is found to be the concentration fluctuation of an entangled molecular cluster in a quiescent state.     

Influence of molecular topology on the static and dynamic properties of single polymer chain in solution

The influence of molecular topology on the structural and dynamic properties of polymer chain in solution with ring structure, three-arm branched structure, and linear structure are studied by molecular dynamics simulation. At the same degree of polymerization (N), the ring-shaped chain possesses the smallest size and largest diffusion coefficient. With increasing N, the difference of the radii of gyration between the three types of polymer chains increases, whereas the difference of the diffusion coefficients among them decreases. However, the influence of the molecular topology on the static and the dynamic scaling exponents is small. The static scaling exponents decrease slightly, and the dynamic scaling exponents increase slightly, when the topology of the polymer chain is changed from linear to ring-shaped or three-arm branched architecture. The dynamics of these three types of polymer chain in solution is Zimm-like according to the dynamic scaling exponents and the dynamic structure factors.     

Equilibrium conformational dynamics of a polymer in a solvent

Molecular dynamics simulations were used to study the conformational dynamics of a bead-spring model polymer in an explicit solvent under good solvent conditions. The dynamics of the polymer chain were investigated using an analysis of the time autocorrelation functions of the Rouse coordinates of the polymer chain. We have investigated the variation of the correlation functions with polymer chain length N, solvent density rho, and system size. The measured initial decay rates gamma(p) of the correlation functions were compared with the predictions from a theory of polymer dynamics which uses the Oseen tensor to describe hydrodynamic interactions between monomers. Over the range of chain lengths considered (N = 30-60 monomers), the predicted scaling of gamma(p) proportional to N(-3nu) was observed at high rho, where nu is the polymer scaling exponent. The predicted gamma(p) are generally higher than the measured values. This discrepancy increases with decreasing rho, as a result in the breakdown in the conditions required for the Oseen approximation. The agreement between theory and simulation at high rho improves considerably if the theoretical expression for gamma(p) is modified to avoid sum-to-integral approximations, and if the values of (R(p)2), which are used in the theory, are taken directly from the simulation rather than being calculated using approximate scaling relations. The observed finite-size scaling of gamma(p) is not quantitatively consistent with the theoretical predictions.     

Study on the coil–globule transition and dynamics of polymer chain confined in slit

The coil–globule transition and dynamics of a lattice self‐avoiding bond fluctuation polymer chain confined in slit are studied by Monte Carlo simulations. The coil–globule transition temperature of polymer chain is increased at intermediate slit height H (H ∼ R_G0 with R_G0 the radius of gyration of polymer in dilute solution) due to the squeeze of the polymer in the repulsive slit, but it is decreased by surface attraction as the polymer is extended along the surface. We have compared the difference between the rotational relaxation time τ_R for the reorientation of end‐to‐end vector and the relaxation time τ for the polymer diffusing over a distance of the size of polymer. We find that τ_R is clearly distinct from τ as they have different scaling exponents in their slit height‐dependent behaviors and for the polymer in the extended coil state, that is, α_R > α. And both exponents increase with an increase in the intrapolymer attraction and surface attraction. However, these scaling relations are destroyed by strong surface attraction when the polymer is adsorbed on surfaces. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 1053–1062     

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.     

Phenomenological theory of textured mesophase polymers in weak flows

A macroscopic viscoelastic model for incompressible, isothermal, homogeneous lyotropic mesophases exhibiting the nematic polydomain texture is presented. Under equilibrium static conditions the model describes a three dimensional tessellation, where each region or nematic domain has a characteristic size and orientation, and where the polydomain texture has a random orientation. Close form expressions that define the characteristic texture size and the number of randomly oriented domains are given. When subjecting the model lyotropic liquid crystalline polymer displaying the polydomain texture to a steady rectilinear shear flow, the predicted characteristic texture size decreases with increasing shear rates. The power law scaling relations of texture size with shear rate are in excellent agreement with the experimental measurements. The steady shear flow orientation predictions, characterized by a positive shear dependent alignment angle and a low orientation, are in agreement with experimental data.     

The properties of a single polymer chain in solvent confined in a slit: A molecular dynamics simulation

A single polymer chain in solvent confined in a slit formed by two parallel plates is studied by using molecular dynamics simulation method. The square radii of gyration and diffusion behaviors of polymers are greatly affected by the distance between the two plates, but they do not follow the same way. The chain size decays drastically with increasing h (h is the distance between two plates), until a basin occurs, and a universal h/〈R _g〉₀ dependence for polymer chains with different degrees of polymerization can be obtained. While, for the chain’s diffusion coefficient, it decays monotonously and there is no such basin-like behavior. Furthermore, we studied the radial distribution function of confined polymer chains to explain the reason why there is a difference for the decay behaviors between dynamic properties and static properties. Besides, we also give the degree of confinement dependence of the static scaling exponent for a single polymer chain. Our work provides an efficient way to estimate the dynamics and static properties of confined polymer chains, and also helps us to understand the behavior of polymer chains under confinement.     

Thermodynamics and partitioning of homopolymers into a slit-A grand canonical Monte Carlo simulation study

Grand canonical ensemble Monte Carlo simulation (GCMC) combined with the histogram reweighting technique was used to study the thermodynamic equilibrium of a homopolymer solution between a bulk and a slit pore. GCMC gives the partition coefficients that agree with those from canonical ensemble Monte Carlo simulations in a twin box, and it also gives results that are not accessible through the regular canonical ensemble simulation such as the osmotic pressure of the solution. In a bulk polymer solution, the calculated osmotic pressure agrees very well with the scaling theory predictions both for the athermal polymer solution and the theta solution. However, one cannot obtain the osmotic pressure of the confined solution in the same way since the osmotic pressure of the confined solution is anisotropic. The chemical potentials in GCMC simulations were found to differ by a translational term from the chemical potentials obtained from canonical ensemble Monte Carlo simulations with the chain insertion method. This confirms the equilibrium condition of a polymer solution partition between the bulk and a slit pore: the chemical potentials of the polymer chain including the translational term are equal at equilibrium. The histogram reweighting method enables us to obtain the partition coefficients in the whole range of concentrations based on a limited set of simulations. Those predicted bulk-pore partition coefficient data enable us to perform further theoretical analysis. Scaling predictions of the partition coefficient at different regimes were given and were confirmed by the simulation data.     

Critical fluctuations and static inhomogeneities in polymer gel volume phase transitions

Thermoresponsive polymer gels exhibit pronounced swelling and deswelling upon changes in temperature, accompanied by dynamic concentration fluctuations that have been interpreted as critical opalescence. These fluctuations span lengthscales similar to that of static structures in the gels, such as the gel polymer‐network meshsize (1–10 nm) and static polymer‐network crosslinking inhomogeneities (10–1000 nm). To systematically investigate this overlay, we use droplet‐based microfluidics and fabricate submillimeter‐sized gel particles with varying static heterogeneity, as revealed on a molecular scale by proton NMR. When these microgels are probed by small‐angle neutron scattering, the detection of dynamic fluctuations during the volume phase transitions is strongly perturbed by the co‐existing static inhomogeneity. Depending of the type of data analysis employed, the temperature‐dependent evolution of the correlation length associated to the dynamic fluctuations does or does not agree with predictions by the critical scaling theory. Only the most homogeneous sample of this study, prepared by controlled polymer crosslinking in droplet microfluidics, shows a diverging correlation length in agreement to the critical scaling theory independent of the specific approach of data analysis. These findings suggest that care must be taken about polymer‐network heterogeneity when gel volume phase transitions are evaluated as critical phenomena. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1112–1122     

A scaling analysis of the fracture mechanisms in glassy polymers

Recent experimental work on craze growth in polymers has shown that the reptation model for polymer motion may be successfully applied, in certain cases, to the behavior of glassy polymers in the solid phase. In this paper, a simple scaling analysis is presented to show how the primitive path model for reptation may be applied to the behavior of glassy polymers before and during slow crack growth. Different dynamic regimes are identified and related to the relaxation times of the polymer chain. The dependence on polymer chain length for each mechanism is described. Estimates for the fracture energy of each process are presented.     

线形、梳形和星形高分子静态和动态性质的模拟

以梳形高分子为纽带,基于粗粒化分子动力学模拟方法,研究了线形、梳形和星形拓扑结构高分子的静态和动态性质,以揭示稀溶液中高分子链行为与链拓扑结构依赖关系的一般性规律.研究结果表明,随着线形-梳形-星形的链拓扑结构转变,回转半径的标度关系由仅依赖分子聚合度转变为同时依赖链聚合度与臂数或侧链数.分析了星形高分子和梳形高分子的静态和动态性质的特征规律.星形高分子的臂数增加使其尺寸迅速减小,形状则由长椭球形转变为类球形,且扩散系数也随之增加;其均方回转半径(〈R_g〉)和扩散系数(D)与分子聚合度(N)及臂数(f)的标度规律为〈R_g〉~N~(0.581)f~(-0.402),D~N~(-0.763)f~(0.227).梳形高分子的静态与动态性质与分子聚合度及侧链数的依赖关系为〈R_g〉~N~(0.597)f~(-0.212)(每个支化点只有一条侧链)和〈R_g〉~N~(0.599)f~(-0.316)(每个支化点有多条侧链).     

Polymer brushes in solvents of variable quality: molecular dynamics simulations using explicit solvent

The structure and thermodynamic properties of a system of end-grafted flexible polymer chains grafted to a flat substrate and exposed to a solvent of variable quality are studied by molecular dynamics methods. The macromolecules are described by a coarse-grained bead-spring model, and the solvent molecules by pointlike particles, assuming Lennard-Jones-type interactions between pairs of monomers (epsilon(pp)), solvent molecules (epsilon(ss)), and solvent monomer (epsilon(ps)), respectively. Varying the grafting density sigma(g) and some of these energy parameters, we obtain density profiles of solvent particles and monomers, study structural properties of the chain (gyration radius components, bond orientational parameters, etc.), and examine also the profile of the lateral pressure P( parallel)(z), keeping in the simulation the normal pressure P( perpendicular) constant. From these data, the reduction of the surface tension between solvent and wall as a function of the grafting density of the brush has been obtained. Further results include the stretching force on the monomer adjacent to the grafting site and its variation with solvent quality and grafting density, and dynamic characteristics such as mobility profiles and chain relaxation times. Possible phase transitions (vertical phase separation of the solvent versus lateral segregation of the polymers into "clusters," etc.) are discussed, and a comparison to previous work using implicit solvent models is made. The variation of the brush height and the interfacial width of the transition zone between the pure solvent and the brush agrees qualitatively very well with corresponding experiments.     

Models for the dynamics of monodisperse polymer melts based on lateral chain motions

A recently developed model for the dynamics of monodisperse polymer melts of linear chains is briefly reviewed. Within the simplifications inherent in the model, it is found that the obstacles to the motion of a given chain, which are imposed by neighboring chains, do not suppress the lateral chain motion. The model associates a length scale with each obstacle, and compares it with the length scale for chain motion. If the obstacle length is greater than the length scale for chain motion, the obstacle is deemed impassable. The cooperative motion of the mutually impassable obstacles is considered, and this gives rise to predictions that are in excellent agreement with experimental observations. If the model were modified to include the additional complexities of real polymer systems, various features of the model might change. The implications of a number of possible modifications in the model are explored. Specifically, the impact of varying the behavior of the function which determines the fraction of obstacles that are impassable is examined in detail. In addition, in the original model it is assumed that chain memory is relaxed due to the slowing of lateral chain motion by the obstacles imposed by neighboring chains. The effect of the opposite assumption of essentially no memory relaxation is also studied. Finally, the influence of limiting the extent of the correlations between the motions of various chain segments because of finite chain length is also considered. It is found that these features have effects that can largely cancel each other. As a result, a range of lateral motion models, which are consistent with the known phenomenology of these systems, are possible.