Behavior Of Long Chains Research Articles

Single polymer gating of channels under a solvent gradient

We study the effect of a gradient of solvent quality on the coil-globule transition for a polymer in a narrow pore. A simple self-attracting, self-avoiding walk model of a polymer in solution shows that the variation in the strength of the interaction across the pore leads the system to go from one regime (good solvent) to the other (poor solvent) across the channel. This may be thought to be analogous to thermophoresis, where the polymer goes from the hot region to the cold region under the temperature gradient. The behavior of short chains is studied using exact enumeration while the behavior of long chains is studied using transfer matrix techniques. The distribution of the monomer density across the layer suggests that a gatelike effect can be created, with potential applications as a sensor.

Termination and Transfer Kinetics of Butyl Acrylate Radical Polymerization Studied via SP-PLP-EPR

Butyl acrylate (BA) solution polymerization (1.5 M in toluene) was investigated via single-pulse pulsed laser polymerization in conjunction with electron paramagnetic resonance spectroscopy (SP-PLP-EPR) with emphasis on the termination and transfer kinetics of the system in which two distinctly different types of radicals, secondary chain-end radicals (SPRs) and midchain radicals (MCRs), are present. MCRs are produced by intramolecular hydrogen transfer (backbiting). They may react back to SPRs by monomer addition. The evolution of SPR and MCR concentrations after photoinitiation with an intense laser pulse was measured via highly time-resolved EPR at temperatures between −40 and +60 °C. At very low temperatures the MCR concentration is negligible, enabling the chain-length-dependent rate coefficient of SPR termination, ktss(i,i), to be directly determined. At higher temperatures it was necessary to use PREDICI simulation of the radical concentration vs time traces, a process which yields the chain-length-dependent rate coefficient of SPR termination for monomeric radicals, ktss(1,1), as well as the rate coefficients for backbiting, kbb, for monomer addition to an MCR, kpt, and for SPR-MCR cross-termination, ktst. The composite model adequately represents ktss(i,i), with the power-law exponents αs = 0.85 ± 0.09 and αl = 0.16 ± 0.07 for short-chain and long-chain radicals, respectively, and a crossover chain length between short-chain and long-chain behavior at around ic = 30. The activation energy for both ktss(1,1) and ktst(1,1) is found to be as one would expect for translational diffusion of small molecules.

Equation of state for polymer chains in good solvents

A free-energy model is developed for polymer chains in good solvents. This model, which combines the ideas of polymer field theory with liquid-state theory, is valid in the dilute, semidilute, and concentrated regimes. The model is compared against computer simulation data for the equation of state of tangent hard-sphere chain fluids. At low concentrations, it accurately describes the thermodynamics of tangent hard-sphere chains, reproducing the universal scaling behavior of long chains. At high concentrations, the model has an accuracy comparable to those of previous equations of state for tangent hard-sphere chains.

Thermodynamic behaviour of homonuclear and heteronuclear Lennard-Jones chains with association sites from simulation and theory

Monte Carlo simulation and theoretical results are presented for mixtures of associating and non-associating Lennard-Jones chains. The molecular model accounts explicitly for repulsive, dispersive, chain, and association interactions. A modified statistical associating fluid theory for Lennard-Jones chains is used to compare with the NPT and Gibbs ensemble Monte Carlo simulation results. The equation is extended to describe heteronuclear Lennard-Jones chains, and results are compared with those obtained by Monte Carlo simulations. The influence of several variables, such as chain length, segment size and dispersive energy, polydispersity, etc., on the supercritical properties and the phase equilibria behaviour of these systems is discussed here. The theory seems to predict more accurately the behaviour of long chains rather than of those of intermediate length, due to the approximations made in the radial distribution function of the fluid.

Universal viscometric functions for dilute polymer solutions

The Gaussian approximation has been shown previously to be excellent for the treatment of hydrodynamic effects in dilute polymer solutions. However, the computational time required to find the viscometric functions in simple shear flow is prohibitively long for chains with a large number of beads. Here we introduce a new approximation which retains the accuracy of the Gaussian approximation but is significantly less computationally intensive. Thus the rheological behavior of long chains may be explored. Extrapolation of results obtained numerically for long chains to the infinite chain length limit is shown to lead to predictions independent of model parameters. As a result, within the context of the approximation introduced here, universal viscometric functions for dilute polymer solutions in simple shear flow under theta conditions are obtained.

Complexity of entanglements and degree of folding in branched polymers with excluded-volume interaction

A methodology to characterize large-scale shape of macromolecular conformations is generalized and applied to a simple model of branched polymers. The standard global analysis of polymer configurations uses geometric shape descriptors, such as the mean radius of gyration. However, geometric descriptors alone do not depict well the intrincate folding features found in many macromolecules. For a more complete characterization, we employ here a new class of shape descriptors which convey the degree and complexity of the “entanglements” in a branched chain. Recently, the methodology has been applied to study statistical properties of linear polymer chains. In the present work, we extend the technique to branched polymers and analyze the configurational and long-chain behavior of their entanglement descriptors. A family of “stars” (polymers with a single branchpoint) with excluded volume interaction is studied, and the results are contrasted with those for linear chains. The relation between changes in geometric and shape descriptors within the polymer conformational space is presented. The complexity of entanglements for large chains and large stars are compared. The results suggest a similar scaling behavior of the entanglement descriptors for the two polymer architectures. © 1994 John Wiley & Sons, Inc.

Periodic solutions of non linear differential difference equations

In this paper we will be interested in the behaviour of long chains of coupled gravitational pendula. We will prove existence and uniqueness of periodic solutions for such chains under periodic forcing and will prove that under some smoothness assumptions the chain behaves as an uncoupled one. We will also analyse a more general class of differential difference equations and prove existence and unicity results for periodic solutions.

Macromolecular configurations simulated by random walks with limited orders of non-self-intersections

Computer computations have been carried out for various orders of self-avoiding random walks used to simulate flexible macromolecules. (The order of a walk is defined as the number of steps in the longest loop excluded by reason of the self-avoiding feature.) Calculations have been carried out for walks of orders up through 10 on a simple square lattice in two dimensions and for walks of orders up through 12 on a tetrahedral lattice in three dimensions. The calculations established precisely the parameters associated with the asymptotic behavior of long chains subject to the model assumed. The results are in agreement with earlier theoretical predictions as to form, and they serve to identify the factors contributing to increasing chain dimensions with length of walk. Asymptotically, the mean square end-to-end separation is linear in the number of steps for any self-avoiding walk of finite order. The behavior of completely self-avoiding walks (i.e., those of unlimited order) is represented very closely by the envelope of asymptotes corresponding to walks of different orders. In addition, the largest symmetric and antisymmetric eigenvalues associated with the transition matrix governing unit increments in contour chain length have been evaluated. Those eigenvalues determine an upper limit to the asymptotic behavior of long model chains.

On the adsorption of a polymer chain at a boundary

AbstractOn the basis of a simple lattice model, the adsorption of a polymer chain on a surface is discussed, taking excluded volume effects (intrachain interactions) into account. Configurations of finite chains of n elements (self‐avoiding walks) are enumerated exactly for n ≤ 13 on the simple cubic lattice. Some predictions concerning the asymptotic behavior of long chains are derived from these data by using extrapolation methods previously devised by Domb and Sykes for bulk properties.