Nonuniform extension of chain segments of a polymer coil in dilute solution

An isolated, flexible polymer chain in dilute solution assumes a random configuration. In reality such a polymer coil is not completely random, because an excluded volume effect requires a modification from randomness. In addition, the coil placed in a better solvent is more expanded than that in a poor solvent. In other words, the polymer chain segments in a better solvent are more extended, compared to those in a neutral solvent. In the present study we have discovered an indication that the chain segments lying on the periphery of the coil are more extended than those in the interior. This discovery has been made in the course of relating intrinsic viscosity to thermodynamic interaction between polymer and solvent. The resulting relationship provides a means of evaluating the thermodynamic interaction parameter from the measured value of intrinsic viscosity, if the molecular weight of the polymer, its intrinsic viscosity in a neutral solvent, and the degree of excess extension of chain segments are known. The last is the parameter discovered in this work. This observation is independent of particular thermodynamic theory, so long as the experimental data are used in a consistent manner. In this work Maron's theory was used, because it is applicable to infinite dilution as well as concentrated solutions.     

Polymer-like Behavior of Inorganic Nanoparticle Chain Aggregates

Studies of the behavior of nanoparticle chain aggregates (NCA) have shown properties similar to those of molecular polymers. Like polymer chains, NCA tend to gather up and become more compact when heated. Under tensile stress, folded chain segments pull out and the NCA elongates. When the tension is relaxed, the chains contract. The stretching of NCA may contribute to the ductility of compacts made from nanoparticles, a subject of current research interest. In a well established technological application, carbon black and pyrogenic silica NCA produce remarkable increases in elastic modulus and tensile strength when added to commercial rubber. This may be due to the mechanical interaction between the polymer chains and NCA. However, basic mechanisms of NCA elasticity differ from those of molecular polymers. The alignment of chain segments when the NCA are subjected to tension probably results from rotation and translation at grain boundaries between neighboring nanocrystals. The elastic properties depend on the van der Waals forces between segments of the chain that fold to minimize surface free energy. Under tension, these segments pull out, but tend to reform when the tension is relaxed. The processes that lead to NCA formation and control the strength of interparticle bonds are briefly reviewed.     

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.     

Helix coil mixing in twist-storing polymers

Twist-storing polymers respond with elastic energy penalty to coherent or random twisting along the local chain axis away from its equilibrium, which can be straight (as in “ribbons”) or helical (as in DNA and other biopolymers). Here we study the equilibrium conformation of such polymers, focusing on the thermodynamic balance between twist and writhe, resulting from the competition between the random coil entropy and the potential energy stored in superhelical portions of the polymer chain. Two macroscopic variables characterise such a chain, the end-to-end distance R and the link number Lk, which is a topological invariant of a given polymer with clamped ends. We find that with increasing link number Lk, the chain accommodates its excess twist in growing plectonemes, unless forced out of this state by stretching its end-to-end distance R. We calculate the force-extension relation, which exhibits crossovers between different deformation regimes. Received 16 November 2000 and Received in final form 6 February 2001     

Studies on mechanical and swelling behavior of polymer networks on the basis of the scaling concept. 6. Gels immersed in polymer solutions

In order to describe the mechanical and swelling behavior of gels immersed in polymer solutions, theoretical considerations based on both classical and scaling theories are discussed and compared with experimental findings. Three situations are studied: (1) the gel is separated from the surrounding solution by a semipermeable membrane; (2) the gel is immersed in the semidilute solution of a chemically identical polymer; (3) the gel is directly immersed in the semidilute solution of a chemically different polymer. An attempt is made to take into account the effect of the penetrating polymer on the elastic modulus and the swelling pressure of the gel. Experimental data referring to chemically cross-linked poly(vinyl alcohol) and poly(vinyl acetate) networks are presented. It was found that the concentration of the free chains inside moderately cross-linked networks may be considerable even for polymers having relatively long chains (27,000 < < M _n < 130,000). Experimental results indicate that the presence of free chains only slightly alters the elastic modulus; however, the swelling pressure is considerably affected by the penetrating polymer. The analysis of mechanical and equilibrium deswelling measurements carried out on several series of gel homologues shows that scaling theory satisfactorily describes the experimental data.     

Optical and magnetic studies on the phosphorescent state of phthalazine in polar and non-polar hosts

The ground state potential energy curve for the beryllium dimer is calculated using non-degenerate many-body perturbation theory and the multi-configuration self-consistent-field/configuration interaction method. Quasi-degeneracy in this system makes it useful in exploring the limitation of the applicability of the non-degenerate formulation of diagrammatic many-body perturbation theory. Both methods are applied within the algebraic approximation defined by a contracted gaussian basis set of triple zeta quality. It is shown that non-degenerate perturbation theory can lead to a potential energy curve which is in close agreement with the configuration interaction curve when taken to third order in the energy and [2/1] Padé approximants constructed.     

Post-Newtonian perturbed theory of elastic astronomical bodies in rotating spherical coordinates

In this paper the dynamical equations for an elastic deformable body in the first post-Newtonian approximation of Einstein theory of gravity are derived in rotating spherical coordinates. The unperturbed rotating body (the relaxed ground state) is described as uniformly rotating, stationary and axisymmetric configuration in an asymptotically flat space-time manifold. Deviations from the equilibrium configuration are described by means of a displacement field. By making use of the schemes developed by Damour, Soffel and Xu, and by Carter and Quintana we calculate the post-Newtonian Lagrangian strain tensor and symmetric trace-free shear tensor. Considering the Euler variations of Einstein's energy-momentum conservation law, we derive the post- Newtonian energy equation and Euler equations of elastic deformable bodies in rotating spherical coordinates.     

Elastic Behavior of Polymer Chains

在三维非格子模型中研究了高分子链的弹性行为. 使用蒙特卡罗方法在构相空间中对高分子链抽样,每种链都得到了超过109个样本,然后使用类橡胶弹力的非高斯理论对这些样本进行数值分析并进行统计分析. 通过观测链柔性以及伸长量对高分子链的均方末端距、平均能量、平均赫尔姆霍兹自由能、弹力、能量对弹力的贡献和熵对弹力的贡献等性质的影响,发现刚性链比柔性链更加容易被拉伸. 而由于熵的作用,当拉伸长度大到一定程度时,刚性链的拉伸难度会大大增加.     

Single long-polymer translocation through a long pore

This paper theoretically studies the free energy and conformational entropy of a long polymer threading a long nanopore (n₀/N \ge 0.1) on external electric field. The polymer expanded model is built in this paper, that is, a single long polymer chain with N monomers (each of size a) threading a pore with n₀ monomers can be regarded as polymer with N+n_{0} monomers translocating a 2-dimension hole embedded in membrane. A theoretical approach is presented which explicitly takes into account the nucleation theory. Our calculations imply that, the structure of polymer changes more acutely than other situation, while its leading monomer reaches the second vacuum and its end monomer escapes the first vacuum. And it is also shown that the length scale of polymer and pore play a very important role for polymer translocation dynamics. The present model predicts that the translocation time depends on the chemical potential gradient and the property of the solvent on sides of pore to some extent.     

Polymer depletion interaction between parallel walls--a Monte Carlo study

An off-lattice bead-spring model of self-assembling equilibrium ("living") polymers is used to study the polymer-induced interaction between parallel walls immersed in polydisperse solutions of different concentration by means of Monte Carlo simulation. The two walls form an open slit in contact with an external reservoir so that the confined system may exchange monomers with the surrounding phase and adapt its polydispersity in order to relax the confinement constraint. We find that the properties of the polymers in the constrained system as well as the net force deltaF acting on the walls depend essentially on the polymer concentration in the reservoir which leads to qualitative differences in their behavior with changing inter-planar distance H: In a dilute polymer solution at concentration phi below the semi-dilute threshold phi* the force between the walls is attractive and decreases steadily with growing wall separation H, so that deltaF approximately 0 at H/ Rg> or =3 if H is measured in gyration radii Rg of the unperturbed polymers. The total monomer concentration within the slit is smaller than the concentration in the reservoir and decreases monotonically with H/Rg-->0. The ratio Nin/Nout of mean chain length Nin in the slit to that in the reservoir, Nout, decreases from unity at H-->infinity, goes through a minimum at H/Rg approximately 1, and then rises again to Nin/Nout>1 for wall separations H/Rg<1. In contrast, in a dense solution of equilibrium polymers at phi>phi* one detects no indirect wall-wall interaction, deltaF approximately 0, for H larger than the monomer size. Thus, earlier speculations about the existence of possible depletion interaction between parallel walls even in a dense polymer system cannot be confirmed. Inside the slit the monomer density is found to be always larger than in the reservoir while Nin/Nout<1 and decreases steadily as H/Rg-->0. The depletion force between parallel plates has been determined also in a monodisperse solution of conventional polymers. Qualitatively the force behavior does not differ from that of living polymers.     

Phase behaviour of hyperbranched polymers in demixed solvents

Hyperbranched polymers have attracted increased interest because of their tunable properties, which are affected by their architecture and a wide range of different functional groups. Many applications of hyperbranched polymers have been proposed based on their liquid–liquid phase behaviour. In recent years, the Lattice Cluster Theory (LCT) has been used to consider the impact of the architecture on the phase behaviour of hyperbranched polymers. In the theoretical framework of the LCT, the chain architecture is included in the Helmholtz energy, so all derived properties are influenced by polymer architecture. Until now, the application of the LCT in the field of hyperbranched polymers has been limited to ternary systems composed of one polymer with an arbitrary chain structure, one trimer and one solvent. This paper aims to extend the LCT to a ternary system that includes two polymers with an arbitrary chain structure and one solvent occupying one lattice site. In contrast to previous studies, the ternary system consists of Boltorn H20?+?butan-1-ol?+?water, where all of the binary subsystems show demixing behaviour. Whereas experimental data are reported in the literature for the binary subsystems Boltorn H20?+?water and butan-1-ol?+?water, no experimental information is available for the binary subsystem Boltorn H20?+?butan-1-ol. Therefore, the phase behaviour of this subsystem was measured using the visual method. The paper discusses the possibility of predicting the ternary phase behaviour with the LCT in combination with the modified Wertheim theory based on knowledge of the phase behaviour of the corresponding binary subsystems. To verify the theoretical results, the ternary phase equilibria at constant temperature were also measured. In addition, the dependence of the thermodynamic properties on the special production lot of the commercially available Boltorn H20 is discussed.     

Effect of temperature on the intrinsic viscosity of poly(ethylene glycol) in water/dimethyl sulfoxide solutions

In this work, the intrinsic viscosities of poly(ethylene glycol) with molar mass of 20 kg mol^− 1 were measured in water/dimethyl sulfoxide solutions from (298.15 to 318.15) K. The expansion factors of the polymer chains were calculated from the intrinsic viscosity data. The expansion factor were decreased by increasing temperature; therefore the chain of PEG shrinks and the end-to-end distance become smaller by increasing temperature. Perhaps the interactions of segment-segment are favored toward segment-solvent by increasing temperature; therefore the hydrodynamic volumes of the polymer coils become smaller by increasing temperature. The thermodynamic parameters (entropy of dilution parameter, the heat of dilution parameter, theta temperature and polymer-solvent interaction parameter) were derived by the temperature dependence of the polymer chain expansion factor. The thermodynamic parameters indicate that the interactions of segment-segment were increased by increasing temperature.     

Microstructure and thermodynamics of inhomogeneous polymer blends and solutions

A free energy density functional theory (DFT) for nonuniform polymeric mixtures is proposed based on first order thermodynamic perturbation theory. The segment-density based free energy functional provides an accuracy comparable to the numerically intensive polymeric DFTs while preserving the computational simplicity of an atomic DFT. The presented applications for solutions and blends of branched and linear polymers demonstrate the capability of the theory to capture the entropic and enthalpic effects governing the microstructure.     

Effects of constrained chain conformations on polymer-solute interactions in semicrystalline polymers

The chemical potential of a solute in a solid polymer includes contributions from solute-polymer chain conformations, Flory-Huggins type interaction, and elastic energy of swelling. Presence of impermeable and rigid crystallites in such systems is expected to affect all these contributions. Theoretical calculations have been performed to check the direct effects of constrained chain conformations in the amorphous domains in semicrystalline polymers. Experimental results are used to determine Flory-Huggins coefficient and elastic modulus. From all these, the primary effects are shown to be on the entropic part of the Flory-Huggins coefficient and an increase in the elastic modulus by one or two order of magnitude. Finally, these results are used to calculate the rates of solvent-induced crystallization to show that these rates can drop to negligible values as the amount of crystals formed rises. Thus, the actual degree of crystallization can lie well below the Flory-Yoon limit.     

Piezoelectricity in polymers and biological materials

The piezoelectric effect in polymers is usually explained in terms of the uniaxial orientation of the polymer crystallites and the classical piezoelectric property of these crystallites. Polarization caused by stress gradient seems to be necessary to the understanding of the geometrical relationship between stress and polarization. Studies of the temperature variation of the complex piezoelectric modulus have revealed a new type of relaxation phenomenon, which is closely related to elastic and dielectric relaxation. The possibility of a polymer piezoelectric transducer has been demonstrated by a microphone using an elongated film of poly-γ-methyl-L-glutamate. The physiological significance of piezoelectricity in biological polymers, such as its correlation with the growth mechanism of bone and with the sense of a mechanical stimulus, is worth further investigation.     

Monte Carlo studies of two measures of polymer chain size as a function of temperature

Monte Carlo simulations of single polymer chains with both excluded volume and nearest-neighbor interaction energies are discussed. Two measures of chain size are obtained in the simulation, the radius of gyration of the polymer chain and the inverse radius of the polymer chain. Both of these are reported as a function of temperature, or interaction energy, and chain length,N. The possibility of estimating the fractal dimensions of these measures from the Monte Carlo data is discussed in the context of two different interpolation functions for the temperature dependence of the fractal dimensions. The approach to the fractal dimension as a function of chain length,N, is studied. It is suggested that the approach to fractal dimension of the measures of chain size of polymers is slow, perhaps a fractional power itself.     

Applications of x-ray investigations of polymers under load. 1. Measurements of WAXS reflections shifts induced by elastic stretching of oriented polymer systems along their orientation axis

What information can be obtained by wide-angle x-ray scattering (WAXS) from elastic deformation of oriented polymer systems along their orientation axis? This article is a critical review and some generalization of answers for this question. Different cases are analyzed that occur in practice or that might occur in the future: (1) determination of Young's moduli E _c of crystalline lattices parallel to the polymer chains and establishment of correlations between E _c and chain conformation in crystalline lattices; (2) estimation of elastic properties of different fragments of polymer chains, especially of multiatomic complex fragments; (3) detection of conformational polymorphism in crystalline lattices; (4) determination of Poisson's coefficients of crystalline lattices; (5) estimation of potential ability of a given polymer for formation of systems with high moduli; (6) estimation of structural inhomogeneity of amorphous polymers; (7) study of interaction character of structural elements in oriented polymer blends; (8) investigations of systems with a combination of extended and folded-chain crystals; (9) study of influence of cross-linking on structure-mechanical behavior; (10) estimation of adhesive interaction of different components in polymer composites. Only Points 1 (see, e.g., Refs. 1–18) and 4 [19] have been considered in earlier literature by other authors, mainly for soft-chain polymers. Thus, similar results are considered here only briefly, and primary attention is focused on the peculiarities of investigations of rigid-chain polymers. As for the other points, they were considered earlier in our separate works [20–38] (or have not been considered at all) and up to now have not received wide acceptance. During the consideration here, both series and parallel models of interactions of different structural elements were used.     

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.