平行壁面间平衡聚合物吸附行为的自洽场分析

采用自洽场理论研究了平衡聚合物在平行壁面间的吸附规律.结果表明,平衡聚合物的吸附行为可根据壁面吸附强度划分为弱吸附和强吸附两个区间.在强吸附区间,平衡聚合物可以形成明确的吸附层,增大吸附强度能够引起平均分子链长的陡增,但不会改变链长分布的指数形式.平衡聚合物的长链分子在强吸附条件下较短链分子更靠近吸附壁面,在弱吸附条件下,则更接近体系中心.通过计算壁面压强发现:在弱吸附作用下,吸附壁面始终受到分子链的推斥作用;在强吸附作用下,分子链对壁面的作用随壁面间距的加大由推斥转变为吸引.平衡聚合物的溶解性和排空效应以及壁面吸附作用之间存在竞争关系,加大排除体积作用参数会引起分子链密度分布的均一化和壁面承受压强的降低.     

高分子链在球内表面上的吸附/排空转变

应用自洽场理论(SCFT)研究了受限于球内的高分子溶液的结构,重点关注高分子链在受限壁附近的行为.根据自洽场理论数值计算结果,讨论了球半径、高分子与球限制壁的相互作用、高分子平均浓度等因素对球内高分子浓度分布的影响.从高分子浓度分布和吸附/排空层厚度可以发现,在一定的条件下,受限的高分子在受限壁上会发生吸附/排空转变.吸附/排空转变与受限球大小、高分子链长和平均浓度,以及高分子链与受限壁之间相互作用都有关系.理论预测发生吸附/排空转变时的高分子与球限制壁的临界相互作用参数与链长的倒数成线性关系,且斜率与球半径有关.限制球越小,要发生吸附/排空转变,需要高分子与球之间有更大的临界吸引能.     

Conformational structures and thermodynamic properties of compact polymer chains confined between two parallel plane boundaries

In this paper, the authors investigated the adsorption phenomenon of compact chains confined between two parallel plane boundaries using a pruned‐enriched Rosenbluth method. The authors considered three cases with different adsorption energies of ε = 0, ?1, and ?3 (in units of k_BT) for the confined compact chains of different chain lengths N, respectively. Several parameters were employed to describe the size and shape of compact chain, and some special behaviors in the conformational structures were investigated for the first time. For example, the size and shape of confined compact chains undergo distinct changes in the adsorption cases of ε = ?1 and ?3, and pass through the maximum values at the characteristic distances D_c. The authors found that this characteristic distance D_c could be scaled as D_c～ (N + 1)^ν (ν = 0.56 ± 0.01) in the case of ε = ?3. In addition, the microstructures of chains were investigated, and several significant results were obtained by analyzing the segment density distribution and the mean fractions of segment in tails, trains, bridges, and loops structures. On the other hand, the thermodynamic properties were also investigated for the confined compact chains, such as average energy per bond, Helmholtz free energy per bond, and elastic force per bond. Results show that elastic forces f have different behaviors in three cases, indicating that it is not necessary to exert an external force on the boundaries in the nonadsorption case. At the same time, the average contact energy of compact chain obviously changes when the distance between the two parallel boundaries D increases, which is similar to those of the size and shape parameters. The authors also conclude that these thermodynamic properties of compact chains depend strongly on not only the adsorption energies but also the chain lengths and the confined condition. In addition, several results of the conformational and thermodynamic parameters, such as the segment density distribution and free energy, were compared with the results from the self‐consistent field theory. These investigations may help us to deepen the knowledge about the adsorption phenomenon of confined compact chains. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2888–2901, 2006     

平行板间高分子链构象熵的动力学Monte Carlo模拟

用动力学Monte Carlo方法模拟了受限于两平行板之间的高分子链,并用扫描法计算了链的构象熵S,研究了构象熵相对于自由链的减小量(S0-S)与平行板间距D和高分子链长n的关系.结果证实了de Gennes的自由能标度关系,并给出了标度关系适用的范围.当D非常小时,高分子链受到强烈限制,S0-S与n成正比,表明单链节受到平行板的平均排斥作用力与链长无关.随着D增大,平行板对构象熵的影响越来越弱,单链节受到平行板的平均排斥作用力随链长的增长而增大.当D比较大时,平行板对构象熵的影响近似可以忽略,高分子链构象熵与自由空间中的结果一致.     

Polymer modified colloidal dispersions

The effect of added polyvinyl alcohol (PVA) and polyvinyl pyrrolidone (PVP) on a dispersion of polystyrene particles stabilised with grafted methoxy PEG chains is discussed. PVA adsorbed more strongly on the particles compared to PVP. Polymer addition led to stable mixtures in the case of PVA compared to depletion phase separation observed in the case of PVP. Rheological measurements showed thickening of the dispersion and absence of any structure in the case of PVA, in contrast to structure formation in the case of PVP due to depletion phase separation. A weak gel state was reached for ca. 7% w/w PVP. The observed behaviour is in accord with the relative propensity of PVA and PVP to interact with the particle surface, the grafted chains and their solubility in water. The solvency of the free polymer chains dominated the overall behaviour while the contribution from the incompatibility between free and grafted chains was conterbalanced by differences in the free polymer adsorption on the particles.     

Hybrid density functional theory for homopolymer mixtures confined in a selective nanoslit

By integrating polymer density function theory (DFT) and single-chain molecular simulation, a hybrid DFT is developed for homopolymer mixtures confined in a selective nanoslit. Two weighting functions are adopted separately in the polymer DFT for repulsive and attractive contributions to the excess free energy functional. The theoretical results agree well with simulation data for the density profiles, configurations (tail, loop and train), adsorption amounts, layer thicknesses, and partition coefficients. The polymer-slit interaction is found to have a large effect on the density profiles and partition coefficients but is found to have a small effect on the average sizes and percentages of the configurations. Nearly half of the polymer segments form tails, and the other half form trains. In addition, bridges are observed to form for sufficiently long polymer chains. As the length difference between two polymers increases, the effect of chain connectivity becomes increasingly important.     

Depletion-induced surface alignment of asymmetric diblock copolymer in selective solvents

Phase separation of asymmetric diblock copolymer near surfaces in selective solvents is theoretically investigated by using the real-space version of self-consistent field theory (SCFT). Several morphologies are predicted and the phase diagram is constructed by varying the distance between two parallel hard surfaces (or the film thickness) W and the block copolymer concentration f(P). Morphologies of the diblock copolymer in dilute solution are found to change significantly with different film thicknesses. In confined systems, stable morphologies found in the bulk solution become unstable due to the loss of polymer conformation entropy. The vesicle phase region contracts when the repulsive interaction between the blocks is strong (strong segregation regime). The mixture of vesicles, rodlike and spherelike micelles and the mixture of vesicles and sphere-like micelles disappear in contrast to the weakly segregating regime. The walls strongly affect the phase separation of block copolymer in selective solvent, and the depletion layer near the surface contributes much to the micelle formation of the block copolymer. Interestingly, the self-assembled morphologies stay near the walls with the distance on the order of the radius of gyration of the block copolymer. The oscillation of the polymer distribution near the walls allows the surface phase separation to be observed due to the strong repulsion between the blocks A and B.     

Properties of branched confined polymers

A model of star-branched polymer chains confined in a slit formed by two parallel surfaces was studied. The chains were embedded to a simple cubic lattice and consisted of f=3 branches of equal length. The macromolecules had the excluded volume and the confining surfaces were impenetrable for polymer segments. No attractive interactions between polymer segments and then between polymer segments and the surfaces were assumed and therefore the system was a thermal. Monte Carlo simulations were carried out employing the sampling algorithm based on chain's local changes of conformation. Lateral diffusion of star-branched chains was studied. Dynamic properties of star-branched chains between the walls with impenetrable rod-like obstacles were also studied and compared to the previous case. The density profiles of polymer segments on the slit were determined. The analysis of contacts between the polymer chain and the surfaces was also carried out.     

Monomer density profiles for polymer chains in confined geometries: massive field theory approach

Taking into account the well known correspondence between the field theoretical ?(4) O(n)-vector model in the limit n → 0 and the behavior of long flexible polymer chains in a good solvent, the universal density-force relation is analyzed and the corresponding universal amplitude ratio B(real) is obtained using the massive field theory approach in fixed space dimensions d < 4. The monomer density profiles of ideal chains and real polymer chains with excluded volume interaction in a good solvent between two parallel repulsive walls, one repulsive and one inert wall, are obtained in the framework of the massive field theory approach up to one-loop order. Besides, the monomer density profiles for the dilute polymer solution confined in semi-infinite space containing mesoscopic spherical particle of big radius are calculated. The obtained results are in qualitative agreement with previous theoretical investigations and with the results of Monte Carlo simulations.     

Use of numerical methods in the prediction of polymer adsorption

Average polymer segment densities and thermodynamic properties of polymer adsorbed at liquid–solid interfaces were computed by extension of the polymer adsorption theory of Forsman and Hughes. Expressions were derived for the total free energy of adsorbed polymer chains by using the Flory-Huggins theory to represent free energy of mixing. A square-well potential was used to represent segment–surface interaction, and configurational entropy was calculated from the probability density function for the radius of gyration of random-flight chains. For each specified amount of surface coverage the free energy of the adsorbed polymer was minimized by varying the density of segments normal to the adsorbing surface and using a modified gradient search algorithm on a digital computer. Two different segment densities were considered, and they both gave qualitatively the same results. The two densities were (1) the sum of two Gaussian distributions and (2) a two-step density distribution. Isotherms were then calculated by equating the partial molal free energy of polymer at the surface to that of polymer in bulk solution for each specified amount of surface coverage. The results showed that for the initial region of the isotherms the distribution of polymer segments normal to the surface consisted of a high-density layer adjacent to the surface and a low-density “tail” extending far out into the solution. At higher amounts of adsorbed polymer, i.e., in the general concentration range of the pseudo-plateau, the tail of the polymer density distribution was predicted to thicken, and a single Gaussian distribution best described the segment density. Predicted adsorptions were in good agreement with reported experimental values.     

受限混合物溶剂中胶粒的耗尽势及吸附稳定性

基于密度泛函理论和Yvon-Born-Green方程得到了胶粒耗尽势的表达式.采用密度泛函理论计算了单壁附近和平行狭缝中的混合物溶剂中胶粒的耗尽势及其在单壁处的吸附稳定性.研究结果表明,不同溶剂组分的体积分数和粒子尺寸比等因素对胶粒耗尽势的强度、力程和周期均可产生显著影响,胶粒在单壁附近的吸附稳定性与溶剂粒子尺寸比和体积分数密切相关.此外,对受限于平行狭缝的胶体悬浮液,胶粒的耗尽势阱还可随粒子尺寸比和缝宽呈振荡趋势变化.     

Steric and bridging interactions between two plates induced by grafted polyelectrolytes

If colloidal particles are grafted with a polymer, then the grafted chains can provide steric repulsion between them. If some of the grafted polymer chains are also adsorbed to a second particle, then a bridging force is generated as well. For uncharged plates and polymer, the following contributions to the free energy of the system have been taken into account in the calculation of the interaction force: (i) the Flory-Huggins expression for the mixing free energy of the grafted chains with the liquid; (ii) the entropy loss due to the connectivity of the polymeric segments; (iii) the van der Waals interactions between the segments and the plates; and (iv) the free energy of adsorption of the polymer segments of the grafted chains on the other plate. For charged plates, the electrostatic free energy as well as the free energy of the electrolyte are included in the total free energy of the system. By minimizing the free energy with respect to the segment concentration and, when it is the case, with respect to the electrical potential, equations for the segment number density distribution and for the electrical potential are obtained, on the basis of which the interactions between two plates grafted with polymer chains that can be also adsorbed on the other plate were calculated. The interaction thus obtained includes steric and bridging forces.     

THE EFFECTS OF PATTERNED SURFACES ON THE PHASE SEPARATION FOR DIBLOCK COPOLYMERS

The phase behaviors of symmetric diblock copolymer thin films confined between two hard,parallel and diversified patterned surfaces are investigated by three-dimensional dissipative particle dynamics(DPD)simulations.The induction of diversified patterned surfaces on phase separation of symmetric diblock copolymer films in snapshots,density profiles and concentration diagrams of the simulated systems are presented.The phase separations can be controlled by the patterned surfaces.In the meantime,the mean-s...     

Monte Carlo simulation of polymer adsorption

We developed and employed the incremental gauge cell method to calculate the chemical potential (and thus free energies) of long, flexible homopolymer chains of Lennard-Jones beads with harmonic bonds. The free energy of these chains was calculated with respect to three external conditions: in the zero-density bulk limit, confined in a spherical pore with hard walls, and confined in a spherical pore with attractive pores, the latter case being an analog of adsorption. Using the incremental gauge cell method, we calculated the incremental chemical potential of free polymer chains before and after the globual-random coil transitions. We also found that chains confined in attractive pores exhibit behaviors typical of low temperature physisorption isotherms, such as layering followed by capillary condensation.     

Phase behavior of a single polyethylene chain confined between two adsorption walls

The phase behavior of a single polyethylene chain confined between two adsorption walls is investigated by using molecular dynamics simulations. In the free space, it is confirmed in our calculation that the isolated polymer chain exhibits a disordered coil state at high temperatures, and collapses into a condensed state at low temperatures, that is, the coil‐to‐globule transition, and the finite chain length effects are considered since the critical region depends on chain lengths. When the chain is confined between two attractive walls, however, the equilibrium properties not only depend on the chain length but also depend on the adsorption energy and the confinement. Mainly, we focus on the influence of polymer chain length, confinement, and adsorption interaction on the equilibrium thermodynamic properties of the polyethylene chains. Chain lengths of N = 40, 80, and 120 beads, distances between the two walls of D = 10, 20, 30, 50, and 90 Å, and adsorption energies of w = 1.5, 2.5, 3.5, 6.5, and 8.5 kcal/mol are considered here. By considering the confinement–adsorption interactions, some new folding structures are found, that is, the hairpin structure for short chain of N = 40 beads, and the enhanced hairpin or crystal like structures for long chains of N = 80 and 120 beads. The results obtained in our simulations may provide some insights into the phase behaviors of confined polymers, which can not be obtained by previous studies without considering confinement–adsorption interactions. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 370–387, 2008     

Polymer-induced depletion interaction between weakly attractive plates

Lattice Monte Carlo simulations have been employed to calculate depletion interaction of excluded volume chains in a weakly attractive slit, particularly in the region around the critical point of adsorption. The simulations were performed under full equilibrium conditions where a dilute solution in a slit was in contact with the reservoir. The free energy of confinement deltaA, the force f, and the relative pressurepI/pE on the slit walls were calculated as a function of slit width D and the attraction strength epsilon. The depletion region in the pressure profile pI/pE vs D is reduced by an increase in the attraction potential epsilon in a manner resembling the influence of polymer concentration. At the critical point of adsorption epsilonc the depletion interaction vanishes both in the pressure pI/pE and in the intraslit concentration profile phiI(x). The parameters used to assess the stability of colloidal dispersions such as the depletion potential W(D) (an integral of the net pressure deltap) reach a unique value at the critical condition. A monotonic repulsive profilepI vs D was found for chains trapped in the slit at restricted equilibrium. The mean dimensions (R2) of chains compressed in attractive slits feature a distinct minimum at intermediate slit widths.     

Effect of confinement on coil-globule transition

The equilibrium thermodynamic properties of a linear polymer chain confined to a space between two impenetrable walls (lines) at a distance D under various solvent conditions have been studied using series analysis and exact enumeration technique. We have calculated the end-to-end distance of polymer chain, which shows a nonmonotonic behavior with inter wall separation D. The density distribution profile shows a maxima at a particular value of (D=)D*. Around this D*, our results show that the collapse transition occurs at higher temperature as compared to its bulk value of 2d and 3d. The variation of theta-temperature with D shows a re-entrance behavior. We also calculate the force of compression exerted by the walls (lines) on the polymer.     

Polarizability and complex conductivity of dilute suspensions of spherical colloidal particles with charged (polyelectrolyte) coatings

The dielectric relaxation of polyelectrolyte-coated colloidal particles is examined via "exact" numerical solutions of the governing electrokinetic equations. The charged polymer coatings are characterized by a nominal charge density, thickness, and permeability. Brush-like segment density profiles are considered here, but more sophisticated segment and charge density profiles are accommodated by the model. The role of added counterions and nonspecific adsorption is considered briefly before examining how the experimentally measured conductivity and dielectric constant increments reflect the frequency of the applied electric field, the strength of the electrolyte, and characteristics of the polymer coatings, namely the charge, charge density, and permeability. Finally, a strategy is suggested by which dielectric spectroscopy and electrophoresis can be used to characterize polymer-coated particles. This approach complements experiments where electroviscous effects such as dynamic light scattering and sedimentation are weak.