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In this paper, we study a system of entangled chains that bear reversible cross-links in a melt state. The cross-links are tethered uniformly on the backbone of each chain. A slip-link type model for the system is presented and solved for the relaxation modulus. The effects of entanglements and reversible cross-linkers are modelled as a discrete form of constraints that influence the motion of the primitive path. In contrast to a non-associating entangled system, the model calculations demonstrate that the elastic modulus has a much higher first plateau and a delayed terminal relaxation. These effects are attributed to the evolution of the entangled chains, as influenced by tethered reversible linkers. The model is solved for the case when the linker survival time τs is greater than the entanglement time τe, but less than the Rouse time τR. [ABSTRACT FROM AUTHOR]

This paper investigates the conformational and scaling properties of long linear polymer chains. These investigations are done with the aid of Monte Carlo (MC) and molecular dynamics (MD) simulations. Chain lengths that comprise several orders of magnitude to reduce errors of finite size scaling, including the effect of solvent quality, ranging from the athermal limit over the θ-transition to the collapsed state of chains are investigated. Also the effect of polydispersity on linear chains is included which is an important issue in the real fabrication of polymers. A detailed account of the hybrid MD and MC simulation model and the exploited numerical methods is given. Many results of chain properties in the extrapolated limit of infinite chain lengths are documented and universal properties of the chains within their universality class are given. An example of the difference between scaling exponents observed in actual solvents and those observed in the extremes of “good solvents” and “θ-solvents” in simulations is provided by comparing simulation results with experimental data on low density polyethylene. This paper is concluded with an outlook on the extension of this study to branched chain systems of many different branching types. [ABSTRACT FROM AUTHOR]

In a recent paper [J. Chem. Phys., 121, 6064 (2004)] we developed a method to solve the wormlike chain model of semiflexible polymers. In this note we apply this method to evaluate the force-elongation relationship. It is found that our result agrees qualitatively with experimental data and the results obtained using three other theoretical treatments of semiflexible polymers for all values of the semiflexibility parameter. Quantitative comparisons are presented in the limit of long chains where good quantitative agreement with experimental data and two of the aforementioned theoretical studies are observed for elongations up to 60%, approximately. The limit of stiff chains was also studied and good quantitative agreement with other theoretical results is observed. These results complement the ones reported in our previous paper and show the robustness of our method.© 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The structural and dynamical properties of macromolecules in confining or crowded environments are different from those in simple bulk liquids. In this paper, both the conformational and diffusional dynamics of globular polymers are studied in solutions containing fixed spherical obstacles. These properties are studied as a function of obstacle volume fraction and size, as well as polymer chain length. The results are obtained using a hybrid scheme that combines multiparticle collision dynamics of the solvent with molecular dynamics that includes the interactions among the polymer monomers and between the polymer beads and obstacles and solvent molecules. The dynamics accounts for hydrodynamic interactions among the polymer beads and intermolecular forces with the solvent molecules. We consider polymers in poor solvents where the polymer chain adopts a compact globular structure in solution. Our results show that the collapse of the polymer chain to a compact globular state is strongly influenced by the obstacle array. A nonmonotonic variation in the radius of gyration with time is observed and the collapse time scale is much longer than that in simple solutions without obstacles. Hydrodynamic interactions are important at low obstacle volume fractions but are screened at high volume fractions. The diffusion of the globular polymer chain among the obstacles is subdiffusive in character on intermediate time scales where the dynamics explores the local structure of the heterogeneous environment. For large polymer chains in systems with high obstacle volume fractions, the chain adopts bloblike conformations that arise from trapping of portions of the chain in voids among the obstacles. [ABSTRACT FROM AUTHOR]

In this paper we present theoretical analysis of the electron transport in conducting polymers being in a metal-like state. We concentrate on the study of the effects of temperature on characteristics of the transport. We treat a conducting polymer in the metal state as a network of metalliclike grains embedded in poorly conducting environment, which consists of randomly distributed polymeric chains. We carry out the present studies assuming that the intergrain conduction is mostly provided by electron quantum tunneling via intermediate states localized on polymer chains between the grains. To analyze the effects of temperature on this kind of electron intergrain transport we represent the thermal environment as a phonon bath coupled to the intermediate state. The electron transmission is computed using the Buttiker model within the scattering matrix formalism. This approach is further developed, and the dephasing parameter is expressed in terms of relevant energies including the thermal energy. It is shown that temperature dependencies of both current and conductance associated with the above transport mechanism differ from those typical for other conduction mechanisms in conducting polymers. This could be useful to separate out the contribution from the intergrain electron tunneling to the net electric current in transport experiments on various polymer nanofibers. The proposed model could be used to analyze inelastic electron transport through molecular junctions. [ABSTRACT FROM AUTHOR]

Polymers with both soluble and insoluble blocks typically self-assemble into micelles, which are aggregates of a finite number of polymers where the soluble blocks shield the insoluble ones from contact with the solvent. Upon increasing concentration, these micelles often form gels that exhibit crystalline order in many systems. In this paper, we present a study of both the dynamics and the equilibrium properties of micellar crystals of triblock polymers using molecular dynamics simulations. Our results show that equilibration of single micelle degrees of freedom and crystal formation occur by polymer transfer between micelles, a process that is described by transition state theory. Near the disordered (or melting) transition, bcc lattices are favored for all triblocks studied. Lattices with fcc ordering are also found but only at lower kinetic temperatures and for triblocks with short hydrophilic blocks. Our results lead to a number of theoretical considerations and suggest a range of implications to experimental systems with a particular emphasis on Pluronic polymers. [ABSTRACT FROM AUTHOR]

We present in this work a new model to describe the component segmental dynamics in miscible polymers blends as a function of pressure, temperature, and composition. The model is based on a combination of the Adam-Gibbs (AG) theory and the concept of the chain connectivity. In this paper we have extended our previous approach [D. Cangialosi et al. J. Chem. Phys. 123, 144908 (2005)] to include the effects of pressure in the component dynamics of miscible polymer blends. The resulting model has been tested on poly(vinyl methyl ether) (PVME)/polystyrene (PS) blends at different concentrations and in the temperature range where the system is in equilibrium. The results show an excellent agreement between the experimental and calculated relaxation times using only one fitting parameter. Once this parameter is known the model allows calculating the size of the relevant length scale where the segmental relaxation of the dielectrically active component takes place, i.e., the so called cooperative rearrangement region (CRR) in the AG framework. Thus the size of the CRR for PVME in the blends with PS has been determined as well as its dependence with pressure, temperature, and concentration. [ABSTRACT FROM AUTHOR]

It is the purpose of this paper to establish a bottom-up multiscale approach for dendronized polymers. Based on our understanding of the phenomenology of an atomistic model for this class of polymers, we introduce a “Janus chain” (JC) model which adds a vectorial degree of freedom (Janus vector)—related to the sectorial amphiphilicity—to each segment of the linear backbone of a (classical) uncharged, semiflexible, and multibead chain representation of a polymer. The JC features induced polymeric curvature and ultimately triggers complexation. JC parameters related to the topology and chemical details are obtained from the atomistic level. Available experimental observations including the formation of superstructures and double helical conformations are well reproduced by the JC model. JC is efficiently solved via Brownian dynamics simulation and can be seen as a member of a universality class which is one (two) level(s) above the magnetic (semiflexible) chain model. It therefore should allow to model not only dendronized polymers but also structures belonging to the same class—exhibiting induced (or spontaneous) curvature—such as single stranded DNA and actin filaments. [ABSTRACT FROM AUTHOR]

Bounded potentials are good models to represent the effective two-body interaction in some colloidal systems, such as the dilute solutions of polymer chains in good solvents. The simplest bounded potential is that of penetrable spheres, which takes a positive finite value if the two spheres are overlapped, being 0 otherwise. Even in the one-dimensional case, the penetrable-rod model is far from trivial, since interactions are not restricted to nearest neighbors and so its exact solution is not known. In this paper the structural properties of one-dimensional penetrable rods are studied. We first derive the exact correlation functions of the penetrable-rod fluids to second order in density at any temperature, as well as in the high-temperature and zero-temperature limits at any density. It is seen that, in contrast to what is generally believed, the Percus-Yevick equation does not yield the exact cavity function in the hard-rod limit. Next, two simple analytic theories are constructed: a high-temperature approximation based on the exact asymptotic behavior in the limit T→∞ and a low-temperature approximation inspired by the exact result in the opposite limit T→0. Finally, we perform Monte Carlo simulations for a wide range of temperatures and densities to assess the validity of both theories. It is found that they complement each other quite well, exhibiting a good agreement with the simulation data within their respective domains of applicability and becoming practically equivalent on the borderline of those domains. A comparison with numerical solutions of the Percus-Yevick and the hypernetted-chain approximations is also carried out. Finally, a perspective on the extension of our two heuristic theories to the more realistic three-dimensional case is provided. [ABSTRACT FROM AUTHOR]

This paper is aimed to develop a Brownian dynamics simulation method for strongly confined semiflexible polymers where numerical simulation plays an indispensable role in complementing theory and experiments. A wormlike chain under strong confinement is modeled as a string of virtual spherical beads connected by inextensible rods with length varying according to the confinement intensity of the chain measured by the Odijk deflection length. The model takes hydrodynamic interactions into account. The geometrical constraints associated with the inextensible rods are realized by the so-called linear constraint solver. The model parameters are studied by quantitatively comparing the simulated properties of a double-stranded DNA chain with available experimental data and theoretical predictions. [ABSTRACT FROM AUTHOR]

In this paper we consider the essential electronic excited states in parallel chains of semiconducting polymers that are currently being explored for photovoltaic and light-emitting diode applications. In particular, we focus upon various type II donor-acceptor heterojunctions and explore the relation between the exciton binding energy to the band offset in determining the device characteristic of a particular type II heterojunction material. As a general rule, when the exciton binding energy is greater than the band offset at the heterojunction, the exciton will remain the lowest-energy excited state and the junction will make an efficient light-emitting diode. On the other hand, if the offset is greater than the exciton binding energy, either the electron or hole can be transferred from one chain to the other. Here we use a two-band exciton to predict the vibronic absorption and emission spectra of model polymer heterojunctions. Our results underscore the role of vibrational relaxation and suggest that intersystem crossings may play some part in the formation of charge-transfer states following photoexcitation in certain cases. [ABSTRACT FROM AUTHOR]

It has been suggested that, due to topological constraints, rings in the melt may assume a more compact shape than Gaussian chains. In this paper, we exploit the availability of narrow fractions of perdeuterated linear and cyclic polydimethylsiloxane (PDMS) and, through the analysis of the small angle neutron scattering (SANS) profiles, demonstrate the difference in scattering properties of linear and cyclic PDMS molecules. As expected for Gaussian chains, for the H/D linear PDMS samples, log-log plots of the scattered intensity versus scattering vector Q display a Q(-2) dependence. However, for H/D cyclic blends, the scaling exponent is higher than 2, as predicted by computer simulations reported in the literature. We show that cyclic molecules in bulk display the characteristic maximum in plots of scattered intensity versus Q(-2) that is expected on the basis of Monte Carlo calculations and from the Casassa equation [E. F. Casassa, J. Polym. Sci. A 3, 605 (1965)]. It is also shown that, for rings, the Debye equation [P. Debye, J. Appl. Phys. 15, 338 (1944)] is no longer appropriate to describe the SANS profiles of H/D cyclic blends, at least up to Mw≈10 000. For these samples, the Casassa form factor gives a better representation of the SANS data and we show that this function which was developed for monodisperse cyclics is still adequate to describe our slightly polydisperse samples. Deviations from all above observations are noted for Mw>11 000 and are attributed to partial contamination of cyclic samples with linear chains. The failure of both the Debye and the Casassa form factors could be due to contamination of the cyclic fractions by linear polymers or to a real conformational change. [ABSTRACT FROM AUTHOR]

Using methods adapted from the simulation of suspension dynamics, we have developed a Brownian dynamics algorithm with multibody hydrodynamic interactions for simulating the dynamics of polymer molecules. The polymer molecule is modeled as a chain composed of a series of inextensible, rigid rods with constraints at each joint to ensure continuity of the chain. The linear and rotational velocities of each segment of the polymer chain are described by the slender-body theory of Batchelor [J. Fluid Mech. 44, 419 (1970)]. To include hydrodynamic interactions between the segments of the chain, the line distribution of forces on each segment is approximated by making a Legendre polynomial expansion of the disturbance velocity on the segment, where the first two terms of the expansion are retained in the calculation. Thus, the resulting linear force distribution is specified by a center of mass force, couple, and stresslet on each segment. This method for calculating the hydrodynamic interactions has been successfully used to simulate the dynamics of noncolloidal suspensions of rigid fibers [O. G. Harlen, R. R. Sundararajakumar, and D. L. Koch, J. Fluid Mech. 388, 355 (1999); J. E. Butler and E. S. G. Shaqfeh, J. Fluid Mech. 468, 204 (2002)]. The longest relaxation time and center of mass diffusivity are among the quantities calculated with the simulation technique. Comparisons are made for different levels of approximation of the hydrodynamic interactions, including multibody interactions, two-body interactions, and the “freely draining” case with no interactions. For the short polymer chains studied in this paper, the results indicate a difference in the apparent scaling of diffusivity with polymer length for the multibody versus two-body level of approximation for the hydrodynamic interactions.© 2005 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We investigate asymptotic properties of long polymers grafted to convex cylindrical and spherical surfaces, and, in particular, distribution of chain free ends. The parabolic potential profile, predicted for flat and concave brushes, fails in convex brushes, and chain free ends span only a finite fraction of the brush thickness. In this paper, we extend the self-consistent model developed by Ball, Marko, Milner, and Witten [Macromolecules 24, 693 (1991)] to determine the size of the exclusion zone, i.e., size of the region of the brush free from chain ends. We show that in the limit of strong stretching, the brush can he described by an alternative system of integral equations. This system can he solved exactly in the limit of weakly curved brushes, and numerically for the intermediate to strong curvatures. We find that going from melt state to θ solvent and then to marginal solvent decreases relative size of the exclusion zone. These relative differences grow exponentially as the curvature decreases to zero. [ABSTRACT FROM AUTHOR]

We present a mathematical approach to the worm-like chain model of semiflexible polymers. Our method is built on a novel generating function from which all the properties of the model can be derived. Moreover, this approach satisfies the local inextensibility constraint exactly. In this paper, we focus on the lowest order contribution to the generating function and derive explicit analytical expressions for the characteristic function, polymer propagator, single chain structure factor, and mean square end-to-end distance. These analytical expressions are valid for polymers with any degree of stiffness and contour length. We find that our calculations are able to capture the fully flexible and infinitely stiff limits of the aforementioned quantities exactly while providing a smooth and approximate crossover behavior for intermediate values of the stiffness of the polymer backbone. In addition, our results are in very good quantitative agreement with the exact and approximate results of five other treatments of semiflexible polymers. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Recently we described a coarse-grained model of poly(ethylene oxide) and then employed that model to study the amount of spontaneous threading of cyclic molecules by linear chains in the melt [C. A. Helfer, G. Xu, W. L. Mattice, and C. Pugh, Macromolecules 36, 10071 (2003)]. Since the amount of statistical threading at equilibrium is small, there is interest in identifying physical changes in the system that will increase the threading. We now use that coarse-grained model to investigate the effect on threading of various hypothetical (but feasible) modifications to the two-component system of macrocycles and linear chains in the melt, and different confinement geometries, that can bring about correlations in the arrangement of the rings. Our work follows on the concept of an amphiphilic approach [C. Pugh, J.-Y. Bae, J. R. Scott, and C. L. Wilkins, Macromolecules 30, 8139 (1997)] for increasing the statistical threading in homopolyrotaxane melts. We investigate whether introducing such correlations in the macrocycles can increase the spontaneous threading. This paper shows that some of our modifications can yield more than double the amount of threading seen in purely statistical mixing. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this paper we develop a general mean-field lattice model, in the spirit of the Scheutjens and Fleer theory of polymer solutions [J. M. H. M. Scheutjens and G. J. Fleer, J. Phys. Chem. 83, 1619 (1979); Macromolecules 18, 1882 (1985)], of an N-component polymer blend in the vicinity of an impenetrable surface. We consider the special case of N=3, model one component as noninteracting holes and obtain the bulk density of this system by using the Sanchez–Lacombe equation of state. The free surface of a polymer blend is then modeled by considering the interphase which forms when this ternary mixture is phase separated. One sample case corresponding to the free surface of a symmetric isotopic polystyrenelike blend is probed and we find that the deuterated component is partitioned to the air surface in agreement with experiment. The application of the concept of the Gibbs dividing surface relative to the polymer density profile at the free surface is then examined, and we show that all comparisons to experiment must be conducted relative to this hypothetical plane. Finally, comparisons of the concentration profiles predicted by this theory to existing square gradient theories of binary polymer blends, as well as Monte Carlo simulations, are performed to highlight the usefulness of these calculations to realistic systems. [ABSTRACT FROM AUTHOR]