Third-order interaction approximation for linear polymer chains

Third-order interactions imposed by a pair of atoms separated by five bonds are taken into account in computations of the mean-square end-to-end distance and the mean-square radius of gyration for linear polymer chains. The statistical weight matrices are established on the basis of the rotational isomeric state model. The conformational energy of n-hexane is calculated as a function of the C? C bond rotation angles. The third-order interaction energy is obtained by comparison with that of n-pentane. The characteristic ratio of polymethylene is 6.6 in the third-order interaction approximation, which is in agreement with experimental data.     

Semiclassical theory of group vibrations for linear polymer chains

The semiclassical spectral method (SSM), which employs molecular dynamics and spectral estimators to determine transition frequencies between quantum energy levels in molecular and atomic systems, is extended to include calculations for linear polymer chains. Average differences between harmonic and transition frequencies for the symmetric and asymmetric stretch modes of polyethylene are reported to be around 50 cm⁻¹ with smaller average frequency shifts for the other group vibration dispersion curves for a certain potential surface describing the macromolecule.     

The effect of polymer side chains on vapor sorption in polyacrylate and polymethacrylate solutions

The segment fraction Ψ₁ activity coefficients, a₁/Ψ₁, of solvents have been determined by the piezoelectric sorption method for 0.1 ≤ Ψ₁ ≤ 0.5 in binary solutions of chlorinated methanes [carbon tetrachloride (CCl₄), chloroform (CHCl₃), and dichloromethane (CH₂Cl₂)] with aromatic hydrocarbons (benzene and toluene) in poly(methyl methacrylate), poly(methyl acrylate), poly(ethyl methacrylate), and poly(n-butyl acrylate) at 23.5°C. The present results for toluene in PMMA agree with previously published values obtained by gas-liquid chromatography. For CCl₄ and the aromatic hydrocarbons, the polymer–solvent interaction parameter χ is positive and constant, while for the polar solvents (CHCl₃ and CH₂Cl₂), χ is negative and increases with increasing Ψ₁. The effect of the polymer side chains on vapor sorption in nonpolar and polar solvent systems is discussed in terms of the χ parameter.     

Modelling the elastic behaviour of real chains in polymer networks

Monte-Carlo simulations of the elastic behaviour of PDMS networks, using a realistic (R-I-S) network-chain model, are able to reproduce experimentally observed deviations from Gaussian network behaviour in uniaxial extension. The finite extensibility of the network chains is shown to cause non-affine deformation of the mean-square network-chain end-to-end distance, even at moderate sample deformations (λ≈1.5). An increase in the proportion of fully-extended chains with increasing macroscopic strain gives rise to a steady decrease in the rate of network free-energy change, causing a reduction in the network modulus at moderate macroscopic strains. There is no need to invoke a transition from affine to phantom chain behaviour as deformation increases.     

Threading-unthreading equilibrium in solution of molecular nanotubes and linear flexible polymer chains

Using the Flory-Huggins lattice model, we investigate the threading-unthreading equilibrium in a solution of linear flexible polymer chains and molecular nanotubes formed by covalently bonding the ringlike molecules, such as cyclodextrins (CDs). It is found that the threading-unthreading equilibrium depends on the temperature and the molar concentrations of the ringlike molecules and polymer chain segments but is independent of the polymer chain length, which agrees with the experimental observations. By fitting the experimental data of alpha-CD and poly(ethylene glycol) (PEG), the inclusion energy between alpha-CD and PEG, which includes the conformation energy loss of PEG resulted from the inclusion, is calculated to be approximately -20.45 kJ/mol per PEG unit.     

Entanglement effects in model polymer networks

Many fundamental questions for the understanding of polymer networks are more suitably addressed by current computer simulations than by experiments. Details of the microscopic topology, such as the elastically active cluster or loop entanglements, can be identified as well as controlled. In particular, it is possible to isolate and quantify their effects on macroscopic observables such as the elastic modulus. The constraints due to connectivity and conserved topology are more clearly present for networks than for melts. Already for strand lengths between crosslinks which are relatively short, the effect of the conserved topology is important. The mode relaxation in a network is significantly different from that of a melt. For weakly crosslinked systems the melt entanglement length is the relevant scaling parameter. The elastic modulus of a long chain network under ideal conditions reaches an asymptotic value which is about 2.2 times smaller than the prediction of an affine model for a network made of strands of the melt entanglement length. An analysis of the stress reveals that in the linear regime the contribution from the excluded volume is dominant compared to that from the connectivity along the strands. For larger elongations, however, the non-linear elastic response is dominated by the chemically and topologically shortest paths through the system, where chemical crosslinks and topological entanglements between meshes of the network play a similarly important role.     

Ab initio studies on infinite linear hydrogen fluoride chains

Ab initio crystal orbital calculations on linear infinite chains of hydrogen fluoride and MO calculations on HF and the linear dimer have been performed. Equilibrium geometries, force constants, band structures, densities of states and longitudinal phonon dispersions are presented, and compared with the available data. In agreement with experiment the most common features of hydrogen bonding, elongation of HX bond length (ΔR_HX and decrease in HF stretching force constants, are much more pronounced in the solid state than in the isolated dimer.     

Equilibrium conformations of polymer chains Part II. Conformons in networks

With regard to the ideal network it is shown that the concept ofN non-interacting polymer chains can be transformed in a problem of non interacting excitations (called conformons) for rubber elasticity. Modelling the interaction on permanent crosslinks as a scattering problem and taking the finite chain length into account, an interpretation of the second Mooney coefficient can be given. There is some evidence that the junctions move by constrained self diffusion.Dedicated to Prof. Dr. W. Ruland on the occasion of his 60th birthday.     

Interfacial friction and adhesion of cross-linked polymer thin films swollen with linear chains

The preparation and interfacial properties of a new type of tethered, thin-film lubricant coating are presented. These coatings are composed of three components: a dense self-assembled monolayer (SAM) underlayer that presents reactive vinyl groups at its surface; a cross-linked polydimethylsiloxane (PDMS) overlayer that is covalently tethered to the SAM; and free, mobile linear PDMS chains dispersed in the network. We investigate the influence of the molecular weight (Ms) and concentration of the free PDMS chains on the structure and equilibrium swelling properties of the cross-linked films. Using a bead-probe lateral force microscopy measurement technique, we also quantify the interfacial friction and adhesion characteristics of surfaces functionalized with these coatings. We find that both the volume fraction and the molecular weight of free PDMS molecules in the coatings influence their interfacial friction and adhesion properties. For example, the addition of short PDMS chains in dry, cross-linked PDMS thin films yields tethered surface coatings with ultralow friction coefficients (mu = 5.2 x 10(-3)). An analysis based on classical lubrication theory suggests that the reduction in friction force produced by free polymer is a consequence of the gradual separation of asperities on opposing surfaces and the consequent substitution of solid-solid friction by viscous drag of the free polymer chains in the network.     

Elongational flow studies on flexible polymer chains in a pseudo-solvent

The dynamics of isolated high molecular weight (M_H) polymer chains dissolved in a nonentangled semidilute solution of a low molecular weight (M_L) polymer were investigated by monitoring the elongational flow birefringence. Because of its nonentangled nature, a low molecular weight matrix polymer solution is regarded as a pure solvent (a binary pseudo-solvent). A ternary solution consisting of a small amount of a high molecular weight probe polymer and the binary pseudo-solvent is effectively a dilute solution of the probe polymer. It was observed that the birefringence from the orientation and/or stretching of the probe polymer chains starts to increase rather abruptly at a certain critical strain rate, , and the spatial birefringence pattern is localized along the elongation axis, characteristics that are reminiscent of the coil-stretch transition of flexible polymer chains in a simple dilute solution. The relaxation time for the chain extension, _el, defined as the reciprocal of the critical strain rate , was determined at various temperatures, matrix polymer concentrations c_L, and test chain molecular weights M_H. It was found that _el varied with molecular weight as _el~M_H^a , with a ranging from 1.3 to 1.8, which is roughly consistent with the molecular weight dependence of the non-free-draining Zimm relaxation time. A scaled relaxation time _elkT/, which can be used to estimate the radius of gyration R_g of the probe polymer, decreased with increasing c_L, indicating contraction of the high molecular weight polymer due to a screening of the excluded volume effect caused by the matrix polymer in the pseudo-solvent.     

Dimensions of branched and linear polymer chains in solution: Modifications of flory's theory

It is pointed out that a theory proposed by Vrij for the expansion of a linear polymer chain in solution beyond its unperturbed size is also applicable formally to branched chains. The theory predicts the temperature at which the chain obeys random-flight statistics to be lower for a branched chain than for a linear one (for a polymer–solvent system exhibiting the usual upper critical consolute point). Vrij's derivation follows a well-known procedure of Flory, but refines it to take account of the variation of the time-averaged segment density with distance from the center of mass of the chain. This modification in combination with a somewhat different derivation is shown to lead to a similar result. Yet another scheme for “correcting” Flory's theory is outlined. Some reasons are advanced for questioning the physical significance of these small modifications of Flory's theory, all of which depend on the retention of previously ignored terms in power series expansions.     

Field-theoretic model of inhomogeneous supramolecular polymer networks and gels

We present a field-theoretic model of the gelation transition in inhomogeneous reversibly bonding systems and demonstrate that our model reproduces the classical Flory-Stockmayer theory of gelation in the homogeneous limit. As an illustration of our model in the context of inhomogeneous gelation, we analyze the mean-field behavior of an equilibrium system of reacting trifunctional units in a good solvent confined within a slit bounded by parallel, repulsive walls. Our results indicate higher conversions and, consequently, higher concentrations of gel following the gelation transition near the center of the slit relative to the edges.     

Moduli of model elastomeric networks prepared from polymer chains having a high plateau modulus,and their interpretation in terms of the constrained-chain model

High-molecular weight polybutadiene chains having approximately 47% cis-1,4 units and 45% trans-1,4 units were crosslinked through their carbon-carbon double bonds using p-bis(dimethylsilyl) benzene as crosslinking agent and chloroplatinic acid as catalyst. This particular polymer was chosen because the high plateau modulus it exhibits in the un-crosslinked state is taken to indicate large numbers of chain entanglements, and stress–strain measurements on such networks have frequently been interpreted with the assumption that the trapping of such entanglements during crosslinking should contribute significantly to their modull. It is shown in the present investigation that such results are equally well interpreted in terms of the new constrained-chain theory of rubbery elasticity. © 1993 John Wiley & Sons, Inc.     

A physical model for the longitudinal polarizabilities of polymer chains

The aim of this work is to provide a physical model to relate the polarizability per unit cell of oligomers to that of their corresponding infinite polymer chains. For this we propose an extrapolation method for the polarizability per unit cell of oligomers by fitting them to a physical model describing the dielectric properties of polymer chains. This physical model is based on the concept of a dielectric needle in which we assume a polymer chain to be well described by a cylindrically shaped nonconducting rod with a radius much smaller than its length. With this model we study in which way the polarizability per unit cell approaches the limit of the infinite chain. We show that within this model the macroscopic contribution of the induced electric field to the macroscopic electric field vanishes in the limit of an infinite polymer chain, i.e., there is no macroscopic screening. The macroscopic electric field becomes equal to the external electric field in this limit. We show that this identification leads to a relation between the polarizability per unit cell and the electric susceptibility of the infinite polymer chain. We test our dielectric needle model on the polarizability per unit cell of oligomers of the hydrogen chain and polyacetylene obtained earlier using time-dependent current-density-functional theory in the adiabatic local-density approximation and with the Vignale-Kohn functional. We also perform calculations using the same theory on truly infinite polymer chains by employing periodic boundary conditions. We show that by extrapolating the oligomer results according to our dielectric needle model we get good agreement with our results from calculations on the corresponding infinite polymer chains.     

Dielectric studies on the dynamics of polymer chains in various environments

Stockmayer's type-A chain such as cis-polyisoprene (PI) having dipole moments aligned parallel to the chain contour exhibits slow dielectric response, reflecting fluctuation of the end-to-end vector of the chain ( dielectric normal modes ). This article intends to review our own work on dielectric spectroscopy using PI as a probe for studying dynamics of large scale motion of the probe chain in binary blends with polybutadiene (PB) and in block copolymers with PB or with polystyrene. Through such studies we were able to see the features of polymer chain dynamics in various environments: Rouse-Zimm-like dynamics in overlapping-but-unentangled regimes, reptation with and without accompanying constraint release, behaviour of a subchain incorporated into block copolymers with miscible segments, and dynamics of polymer brushes in strongly segregating block copolymers in bulk and in solutions.     

Contacts between segments in the random-flight model of polymer chains

The probabilities of single and double contacts, and correlations among contacts were calculated for the random-flight model of a polymer chain. The problem was studied earlier by various authors using the Gaussian statistics of the random-flight chain, which is applicable only for long chains, and for contacts which are formed by pair of residues (i,j) which are far from each other (i.e. |i−j|≫1). We used the exact (non-Gaussian) solution of the random flight model, so that our results are applicable also for residues which are relatively close to each other. We applied the results to close contacts of the β-sheet type and α-helix type in proteins, and compared the exact solutions of the problem with Gaussian approximations.     

The dynamics of single chains within a model polymer melt

Discontinuous molecular dynamics simulations are performed on a system containing 32 hard chains of length 192 at a volume fraction of phi = 0.45 to explore the idea that localized entanglements have a significant effect on the dynamics of the individual chains within an entangled polymer melt. Anomalous behavior can still be observed when studying the dynamics of the individual chains, although increased time averaging causes the anomalous relaxation-memory-release behavior that was observed previously in the system to smooth out. First, the individual chain mean squared displacements and apparent diffusion coefficients are calculated, and a wide distribution of diffusive behavior is found. Although the apparent diffusion coefficient curve averaged over all chains displays the predicted long-time diffusive behavior, the curves for the individual chains differ both qualitatively and quantitatively. They display superdiffusive, diffusive, and subdiffusive behavior, with the largest percentage of chains exhibiting superdiffusive behavior and the smallest percentage exhibiting the predicted diffusive behavior. Next, the individual chain end-to-end vector autocorrelation functions and relaxation times are determined, and a wide distribution of stress relaxation behavior is found. The times when the end-to-end vector autocorrelation functions relax completely span almost an order of magnitude in reduced time. For some chains, the end-to-end vector autocorrelation function relaxes smoothly toward zero similar to the system average; however, for other chains the relaxation is slowed greatly, indicating the presence of additional entanglements. Almost half of the chains exhibit the anomalous behavior in the end-to-end vector autocorrelation function. Finally, the dynamic properties are displayed for a single chain exhibiting anomalous relaxation-memory-release behavior, supporting the idea that the relaxation-memory-release behavior is a single-chain property.     

Ab initio crystal orbital studies on linear chains of H atoms

Anab initio crystal orbital method is used to calculate the energies of an infinite chain of H atoms and of linear arrangements of H₂ molecules with different interatomic distances. The H₂ arrangements are not stable in respect to isolated molecules. The cohesive energy of an optimized arrangement of H atoms chain is 0.0354 a.u.     

Tubular linear actuators using conducting polymer, polypyrrole

Conducting polymers show an electrochemomechanical deformation (ECMD), which is able to be utilized as soft actuators. A tubular linear actuator of polypyrrole film is fabricated and the characteristics are examined. The film was electrochemically prepared on an acryl resin rod in an aqueous electrolyte solution of pyrrole and dodecylbenzensulfonic acid (DBS), followed by removing the rod. The actuations of tubular polypyrrole film due to ECMD in various conditions have been examined to clarify the mechanism. It has been found that the tubular actuator elongates upon reduction with the strain of 7%, which is more than twice of that observed in a rectangular film. The facts indicate that cations play the role of dopants instead of large DBS anion and the tubular structure gives the better performance for large strain.     

Topological coarse graining of polymer chains using wavelet-accelerated Monte Carlo. II. Self-avoiding chains

In the preceding paper [A. E. Ismail, G. C. Rutledge, and G. Stephanopoulos J. Chem. Phys. (in press)] we introduced wavelet-accelerated Monte Carlo (WAMC), a coarse-graining methodology based on the wavelet transform, as a method for sampling polymer chains. In the present paper, we extend our analysis to consider excluded-volume effects by studying self-avoiding chains. We provide evidence that the coarse-grained potentials developed using the WAMC method obey phenomenological scaling laws, and use simple physical arguments for freely jointed chains to motivate these laws. We show that coarse-grained self-avoiding random walks can reproduce results obtained from simulations of the original, more-detailed chains to a high degree of accuracy, in orders of magnitude less time.