Controlling Surface Interactions with Grafted Polymers

The interactions between surfaces modified with grafted polymers is studied theoretically. The aim of this work is to find polymer surface modifications that will result in localized attractive interactions between the surfaces. The practical motivation of the work is to find means to control the distance between bilayers and solid supports in supported membranes. Two theoretical approaches are used, the analytical treatment of Alexander and a molecular theory. It is found that grafting each end of the polymer to each surface results in an interaction with a well defined minimum. The location of the minima is found to be very close to the thickness of the polymer layer when the chains are grafted to only one of the surfaces. The predictions of the analytical theory are in excellent agreement with the molecular approach in this case. It is found that increasing the surface coverage increases the strength of the interaction. However, increasing the polymer chain length at fixed surface coverage results in a decrease of the free energy cost associated with separating the surfaces from their optimal distance. For the cases in which grafting to both surfaces is not possible, the molecular theory is used to study the effect of functionalizing segments of the chain to achieve an attractive well. It is found that by functionalizing the free end-groups of the polymers with segments attracted to the membrane, the range of the attractive interaction is significantly larger than the thickness of the unperturbed layer. Functionlizing the middle segments of the chains results in a shorter range attraction but of the same strength as in the end-functionalized layers. The optimal polymer modification is found to be such that the functionlized groups are attracted to the bare surface but are not attracted to the grafting surface. The relevance of the results to the design of experimental surface modifiers is discussed.     

A molecular model for the line tension of lipid membranes

The line tension of a symmetric, lipid bilayer in its liquid-crystalline state is calculated on the basis of a molecular lipid model. The lipid model extends the opposing forces model by an expression for the conformational free energy of the hydrocarbon chains. We consider a membrane edge that consists of a perturbed bilayer covered by a section of a cylinder-like micelle. The structural rearrangement of the lipids implies an excess free energy which we minimize with respect to the cross-sectional shape of the membrane edge, including both the micellar and the bilayer region. The line tension is derived as a function of molecular lipid properties, like the lipid chain length or the head group interaction strength. We also relate it to the spontaneous curvature of the lipid layer. We find the line tension to become smaller for lipid layers that tend to curve more towards the hydrophobic core. Our predictions for the line tension and their relation to experimentally derived values are discussed. Received 2 January 2000     

Suppression of electron-hole correlations in 3D polymer materials

We present an ab initio study of the optical absorption spectra of isolated as well as crystalline trans-polyacetylene. We include excitonic effects by solving the Bethe-Salpeter equation for the electron-hole two-particle correlation function. We observe that the strength of the electron-hole interactions drastically reduces when going from an isolated polymer chain to a crystalline arrangement. This is not only a result of enhanced screening in the 3D material, but also of the increased spatial extent of the exciton perpendicular to the polymer chains. We point out that these findings apply to crystalline phases of conjugated polymers and molecular crystals in general.     

Cracks and crazes: on calculating the macroscopic fracture energy of glassy polymers from molecular simulations

We combine molecular dynamics simulations of deformation at the submicron scale with a simple continuum fracture mechanics model for the onset of crack propagation to calculate the macroscopic fracture energy of amorphous glassy polymers. Key ingredients in this multiscale approach are the elastic properties of polymer crazes and the stress at which craze fibrils fail through chain pullout or scission. Our results are in quantitative agreement with dimensionless ratios that describe experimental polymers and their variation with temperature, polymer length, and polymer rigidity.     

A new paradigm for the molecular basis of rubber elasticity

The molecular basis for rubber elasticity is arguably the oldest and one of the most important questions in the field of polymer physics. The theoretical investigation of rubber elasticity began in earnest almost a century ago with the development of analytic thermodynamic models, based on simple, highly-symmetric configurations of so-called Gaussian chains, i.e. polymer chains that obey Markov statistics. Numerous theories have been proposed over the past 90 years based on the ansatz that the elastic force for individual network chains arises from the entropy change associated with the distribution of end-to-end distances of a free polymer chain. There are serious conceptual objections to this assumption and others, such as the assumption that all network nodes undergo a simple volume-preserving linear motion and that all of the network chains have the same length. Recently, a new paradigm for elasticity in rubber networks has been proposed that is based on mechanisms that originate at the molecular level. Using conventional statistical mechanics analyses, Quantum Chemistry, and Molecular Dynamics simulations, the fundamental entropic and enthalpic chain extension forces for polyisoprene (natural rubber) have been determined, along with estimates for the basic force constants. Concurrently, the complex morphology of natural rubber networks (the joint probability density distributions that relate the chain end-to-end distance to its contour length) has also been captured in a numerical model (EPnet). When molecular chain forces are merged with the network structure in this model, it is possible to study the mechanical response to tensile and compressive strains of a representative volume element of a polymer network. As strain is imposed on a network, pathways of connected taut chains, that completely span the network along strain axis, emerge. Although these chains represent only a few percent of the total, they account for nearly all of the elastic stress at high strain. Here we provide a brief review of previous elasticity theories and their deficiencies, and present a new paradigm with an emphasis on experimental comparisons.     

X-ray scattering from polymer nematic liquid crystals

X-ray scattering from main chain polymer nematics is discussed from the point of view of its use in studying the ordering and fluctuations of the polymer chains that make up the nematic phase. An example of data from poly-γ-benzyl glutamate is given, with a discussion of the important features of the data, in terms of the current understanding of the nature of nematic ordering in main chain polymer systems. This includes analyses of the angular distribution function for the polymer segments, long wavelength fluctuations dictated by elastic phenomena, the effects of finite chain lengths, and effects due to the short range interactions and packing of the chains.     

Influence of the nematic order on the rheology and conformation of stretched comb-like liquid crystalline polymers

We have studied the rheology and the conformation of stretched comb-like liquid-crystalline polymers. Both the influence of the comb-like structure and the specific effect of the nematic interaction on the dynamics are investigated. For this purpose, two isomers of a comb-like polymetacrylate polymer, of well-defined molecular weights, were synthesized: one displays a nematic phase over a wide range of temperature, the other one has only an isotropic phase. Even with high degrees of polymerization N, between 40 and 1000, the polymer chains studied were not entangled. The stress-strain curves during the stretching and relaxation processes show differences between the isotropic and nematic comb-like polymers. They suggest that, in the nematic phase, the chain dynamics is more cooperative than for a usual linear polymer. Small-angle neutron scattering has been used in order to determine the evolution of the chain conformation after stretching, as a function of the duration of relaxation t _r. The conformation can be described with two parameters only: , the global deformation of the polymer chain, and p, the number of statistical units of locally relaxed sub-chains. For the comb-like polymer, the chain deformation is pseudo-affine: is always smaller than (the deformation ratio of the whole sample). In the isotropic phase, has a constant value, while pincreases as tr. This latter behavior is not that expected for non-entangled chains, in which p varies as t _r ^1/2 (Rouse model). In the nematic phase, decreases as a stretched exponential function of t _r, while p remains constant. The dynamics of the comb-like polymers is discussed in terms of living clusters from which junctions are produced by interactions between side chains. The nematic interaction increases the lifetime of these junctions and, strikingly, the relaxation is the same at all scales of the whole polymer chain. Received 5 May 1999 and Received in final form 18 October 1999     

Polaron dynamics in a system of coupled conjugated polymer chains

The motion of excitations such as polarons is believed to be of fundamental importance for the transport properties of conjugated polymers for the use in, e.g., polymer based LED's. We have investigated polaron dynamics in a system of coupled polymer chains in the presence of an external electric field. In particular, we focus on how a polaron migrates through the polymer lattice, i.e., the situation in which a polaron reaches a chain end and is scattered to the surrounding chains. We show that the outcome of this event strongly depends on the strength of the electric field, and we identify three different cases for the polaron migration.     

Entropic and conformational study of isolated double-tethered chains by three-dimensional lattice simulations

Double-tethered polymers are a kind of linear polymer with a peculiar topological constraint; that is, both of its end-points are attached to a plane which the polymer segments cannot penetrate. The effects of the constraint on the polymer's configurational and entropic properties were investigated by means of a three-dimensional lattice simulation that combined a previously proposed idea with a very efficient chain generation algorithm. In particular, the value of a topology-dependent critical exponent was estimated for the double-tethered configurations. This data is the first report on isolated and double-tethered chains. Also, two optional types of tethered-polymer were investigated as asymptotes of the double- and single-tethered configurations.     

Nanomechanical modeling of interfaces of polyvinyl alcohol (PVA)/clay nanocomposite

Abstract

We study interfacial debonding of several representative structures of polyvinyl alcohol (PVA)/pyrophillite-clay systems – both gallery-interface (polymer/clay interface in the interlayer region containing polymer between clay layers stacked parallel to each other) and matrix-interphase (polymer/clay interphase-region when individual clay layers are well separated and dispersed in the polymer matrix) – using molecular dynamics simulations, while explicitly accounting for shearing/sliding (i.e. Mode-II) deformation mode. Ten nanocomposite geometries (five 2-D periodic structures for tension and five 1-D periodic structures for shearing) were constructed to quantify the structure-property relations by varying the number density of polymer chains, length of polymer chains and model dimensions related to the interface deformation. The results were subsequently mapped into a cohesive traction–separation law, including evaluation of peak traction and work of separation that are used to characterise the interface load transfer for larger length scale micromechanical models. Results suggest that under a crack nucleation opening mode (i.e. Mode-I), the matrix-interphase exhibits noticeably greater strength and a greater work of separation compared to the gallery-interface; however, they were similar under the shearing/sliding mode of deformation. When compared to shearing/sliding, the tensile peak opening mode stresses were considerably greater but the displacement at the peak stress, the displacement at the final failure and the work of separation were considerably lower. Results also suggest that PVA/clay nanocomposites with higher degree of exfoliation compared with nanocomposites with higher clay-intercalation can potentially display higher strength under tension-dominated loading for a given clay volume fraction.     

Local entropic effects of polymers grafted to soft interfaces

In this paper, we study the equilibrium properties of polymer chains end-tethered to a fluid membrane. The loss of conformational entropy of the polymer results in an inhomogeneous pressure field that we calculate for Gaussian chains. We estimate the effects of excluded volume through a relation between pressure and concentration. Under the polymer pressure, a soft surface will deform. We calculate the deformation profile for a fluid membrane and show that close to the grafting point, this profile assumes a cone-like shape, independently of the boundary conditions. Interactions between different polymers are also mediated by the membrane deformation. This pair-additive potential is attractive for chains grafted on the same side of the membrane and repulsive otherwise. Received 20 April 2000     

摩擦导致的聚合物表层微观结构改变

应用大规模分子动力学方法, 模拟了锥形探头在非晶态聚合物薄膜表面的滑动摩擦过程, 研究了摩擦导致的聚合物薄膜表层微观结构改变, 以及探头与基体间黏着作用、滑动速度和分子链长度对基体表层微观结构改变的影响. 当探头与基体之间为黏着作用时, 摩擦导致基体表面滑痕区域的键取向沿滑动方向重新取向, 导致表层分子链回转半径沿滑动方向伸长, 并且这些表层微观结构的改变程度随滑动速度的减小而增大. 在摩擦导致结构改变的过程中, 链端单体和链中单体的贡献作用不同, 形成了不同的分子链拉伸变形机制. 当样本缠结度较大或探头滑动速度较小时, 相比于链中单体, 探头对链端单体的拖曳作用使更多分子链发生拉伸变形. 研究还发现, 在探头与聚合物薄膜系统中, 使薄膜表层微观结构发生改变是摩擦能量耗散的重要途径.     

The effect of interface hopping on inelastic scattering of oppositely charged polarons in polymers

The inelastic scattering of oppositely charge polarons in polymer heterojunctions is believed to be of fundamental importance for the light-emitting and transport properties of conjugated polymers. Based on the tight-binding SSH model, and by using a nonadiabatic molecular dynamic method, we investigate the effects of interface hopping on inelastic scattering of oppositely charged polarons in a polymer heterojunction. It is found that the scattering processes of the charge and lattice defect depend sensitively on the hopping integrals at the polymer/polymer interface when the interface potential barrier and applied electric field strength are constant. In particular, at an intermediate electric field, when the interface hopping integral of the polymer/polymer heterojunction material is increased beyond a critical value, two polarons can combine to become a lattice deformation in one of the two polymer chains, with the electron and the hole bound together, i.e., a self-trapped polaron-exciton. The yield of excitons then increases to a peak value. These results show that interface hopping is of fundamental importance and facilitates the formation of polaron-excitons.     

The surface tension of polymer liquids

An experimental and theoretical review of the surface tension of polymer liquids is presented. New experimental methods for polymer surface tension measurement are reviewed. Numerous theoretical and empirical approaches are briefly described. Strong emphasis is placed on the accuracy and limitations of the thermodynamic information which are used as input to many of if not all these theories. It is shown that, by using accurate thermodynamic bulk properties for these liquids including polar polymers, one can use a simple corresponding states principle to describe the temperature and molecular weight dependences of the surface tension with no adjustable parameters to within a few per cent, even though the actual surface tensions may vary by a few hundred per cent. Any small inaccuracies in the predictions arise from conformational entropic effects or because one cannot accurately compute the 'real' cohesive energy density of a polymer liquid from thermodynamic properties alone. The results of recent measurements on high molecular weight polymers are compared with previous work on lower molecular weight liquids. We use the polyethylene and polytetrafluoroethylene oligomeric series to illustrate the uses and limitations of thermodynamicdata for the prediction of surfacetension. The temperature and molecular weightdependences of the surface tensions of these polymers are dominated by the dependence of the bulk thermodynamic properties on temperature and molecular weight. Limited discussion is also given to studies of copolymers and blends using surface tension and complementary techniques.     

Relationship between dynamic mechanical property and thermodynamic interaction parameter of concentrated polymer solutions

The use of concentrated polymer solutions is one of the basic techniques in the application of polymers. They may be coating materials, plasticized polymers, and oil-extended rubber. In these applications the solubility relation is one of the key requirements. The polymer-solvent interaction is expected to influence the mechanical property of the mixture. It is the intent of this study to explore how the dynamic mechanical property is affected by the change of thermodynamic interaction parameter in concentrated polymer solutions. The theoretical development is based on several assumptions: (1) a polymer chain in the amorphous state and in its own environment assumes unperturbed configuration; (2) a polymer chain in a good solvent (poor) is expanded (contracted) relative to the unperturbed dimension; (3) the expanded (contracted) chain configuration results in the higher (lower) entanglement density; (4) both expanded and contracted chains store an elastic energy, the magnitude of which may be estimated; (5) the elastic energy of the deformed chain is balanced by the thermodynamic energy of interaction. The paper focuses on the development of a theory. Also, limited examples of the application of the theory are presented.     

On the number of intersections of self-repelling polymer chains

We give a detailed analysis of the intersection properties of polymers. Using the renormalization group we provide a full crossover function for the dependence of the number of intersections in a single polymer on chain length and excluded volume strength. We compare our results with Monte-Carlo data and with exact calculations for a random walk, finding good agreement in all respects. Restricting to the vicinity of the eight ternary fixed points we also calculate the number of intersections between two chains placed at a fixed distance, including the two halves of a block-copolymer. The analysis of these systems confirms the interpretation of the different contributions to the number of intersections in a single chain. Due to the highly nontrivial character of the correlations in a polymer chain the correction exponents in both cases however are different. None of the results can be extracted from any Flory-type estimate. Received: 1 April 1997 / Revised: 24 October 1997 / Accepted: 29 January 1998     

Investigation of the creep and glass transition of elastomers by the microindentation method: Epoxy resin and related nanocomposites

The experimental procedure and theoretical grounds of the applicability of the microindentation method as one of the effective techniques of relaxation spectrometry of solid-state polymers have been developed. It has been shown that the glass transition temperature and rheological parameters of the material (unrelaxed and relaxed elastic moduli, strain viscosity coefficients) can be determined from measurements of the temperature dependence of the microhardness of polymers in a high-elasticity state and in the glass transition region with the recording of the long-term creep under the indenter. These measurements provide sufficient information for the formulation of a rheological model of the material under investigation. The results of these measurements are supplemented by the concepts of thermally activated motion of molecular segments as the microscopic mechanism of structural relaxation in polymers, which makes it possible to obtain empirical estimates for the activation energies and vibrational frequencies of the molecular segments. The method is implemented in experiments on the microindentation of the epoxy resin and its composites with the addition of carbon nanotubes in the temperature range 230–300 K. The glass transition of these polymers has been observed at temperatures near 260 K, the unrelaxed and relaxed Young’s moduli have been measured, and two thermally activated relaxation processes determining the glass transition, as well as the shortterm and long-term creeps of these materials (α- and α′-processes), have been revealed.     

基于缠结微结构的非晶态玻璃态高分子材料屈服行为的分子动力学研究

非晶态玻璃态高分子材料作为结构材料在工程领域应用广泛,其机械力学性能特别是屈服变形行为受到热处理、加载应变率和环境温度的影响.采用分子动力学模拟方法研究非晶态玻璃态高分子材料不同工况下的单轴拉伸变形,基于分子链缠结微结构的概念,阐明了非晶态玻璃态高分子材料屈服和应变软化过程的内在变形机制.结果表明,拓扑缠结具有较为稳定的空间结构,难以发生解缠,决定了非晶态高分子材料屈服后的软化平台.由相邻分子链的局部链段相互作用形成的次级缠结在一定外界条件下可发生破坏或重新生成,次级缠结微结构及其演化是非晶态高分子材料发生屈服及软化的内在物理原因.     

Amorphous solidification in polymer-platelet nanocomposites

Computer simulations are used to understand the molecular basis of the rheology changes in polymer melts when loaded with platelet filler particles, specifically when the polymer and nanofiller interact attractively. With decreasing temperature, there is increasing aggregation between chains and filler and an increase in the polymer matrix structural relaxation time. These lifetimes are predicted to diverge at an extrapolated temperature, which we identify with the emergence of an amorphous solid state. Our findings suggest that filled polymers are phenomenologically similar to solutions of associating polymers and to supercooled liquids near their glass transition.