ReceiVed January 10, 2007 ReVised Manuscript ReceiVed April 30, 2007 Introduction. When charged polymers are present in dilute solution in a polar solvent, the counterions are typically released into solution due to the dominance of entropic effects (“polyelectrolyte” behavior). In the opposite case of a medium with very low dielectric constant (“ionomer” melt state), the energetic cost associated with counterion release dominates, and hence the neutralizing counterions are closely coupled to the chains in the form of transient local dipoles.1-7 It has been speculated that these dipoles stick together into small multiplets, which serve to bridge chains and create a long-lived transient polymer network.8-11 This network formation is consistent with the unusual transport behavior of ionomers.12,13 The spatial coupling of the counterions with the chains and the resulting interesting transport properties have made ionomers relevant to a range of applications, e.g., in coatings,14,15 proton exchange membranes,16-18 biomedical implants,19,20 and binders in composites.21,22 To understand the morphological and dynamical properties of ionomer melts requires an explicit treatment of Coulomb interactions. While previous workers, primarily the group of Khokhlov,23-28 have theoretically sought to understand the relationship between transient dipoles and network formation, most simulation studies have ignored Coloumb effects29-31 because of the difficulty in accounting for these long-range interactions. To elaborate: the long-ranged Coloumb interaction varies with distance, r, as 1/r. Thus, the calculations of thermodynamic quantities, such as the system energy, which require a spatial integration of this potential do not readily yield a converged value. (Standard tricks that work for short-ranged potentials, such as cutting off the potential at some (short) distance rc and including the contribution from all larger distances by assuming the pair distribution, g(r) ) 1, will thus not be appropriate.) While there is a suite of simulation tools (e.g., Ewald sums) that have been developed to circumvent these difficulties and give finite converged values for thermodynamic quantities, the point being made is that these are computationally expensive (and often intractable). In contrast to these practical matters, it seems evident that including Coloumb interactions will be crucial for determining the temperature at which the ions pair into dipoles and presumably the self-assembly of ionomers into transient networks. Further, the inclusion of explicit counterions is necessary to properly understand the mechanisms of charge transport in such materials. Recent molecular dynamics (MD) simulations which explore charge transport in ionomer solutions do account explicitly for ionic interactions.23,26,32-36 While these last class of simulations have focused on the relevant problem of charge transport and on the relationship between morphology and transport, little attention has been paid to the self-assembly phenomenon which apparently is critical to the behavior of ionomers. To our knowledge, most work focused on the self-assembly of ionomers have modeled the behavior of solutions of chains where ionic interactions have been simplified, and each transient dipole (i.e., a transient ion-counterion pair) is replaced by a “sticker”.37-41 To make progress in this area, we start with the polymer analogue of the “primitive model” of electrolyte solutions42-44 where each chain is modeled as a string of catenated hard spheres. We have performed molecular dynamics simulations on melts of telechelic chains where each chain end has a charge of -q. An equal number of hard-sphere counterions (with the same size as the chain monomers) are introduced to maintain charge neutrality. This is a basic reference model from a computational standpoint, and we explore the extent to which this minimal model of ionomers can reproduce experimental trends, e.g., the tendency to form multiplet structures having the form of sheetlike or compact globular forms, the presence of multiple glass transitions governing properties, and evidence for transitions in the counterion mobility. Simulation Methods. We use the bead-spring polymer model45 and augment this with Coulomb interactions. The interaction between any pair of beads is modeled by a soft repulsive potential:
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Oct 24, 2024
D Serebryakov 
Open Access
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