A new equation of state for homo-polymers in dissipative particle dynamics

Abstract

A chain-revised Groot-Warren equation of state (crGW-EOS) was developed and tested to describe systems of homo-oligomeric chains in the framework of dissipative particle dynamics (DPD). First, thermodynamic perturbation theory is applied to introduce correction terms that account for the reduction in pressure with an increasing number of bonds at constant bead number density. Then, this EOS is modified by introducing a set of switching functions that yields an accurate second virial coefficient in the low-density limit. The crGW-EOS offers several improvements over the revised Groot-Warren equation of state and Groot-Warren equation of state for chain molecules. We tested the crGW-EOS by using it to predict the pressure of oligomeric systems and the B2 virial coefficient of chain DPD particles for a range of bond lengths. Additionally, a method is developed for determining the strength of cross-interaction parameters between chains of different compositions and sizes and for thermal and athermal mixtures. We explored how different levels of coarse-graining affect the upper-critical solution temperature.

Closed-Form Coexistence Equation for Phase Separation of Polymeric Mixtures in Dissipative Particle Dynamics

“…Minkara et al hereupon provided valuable insights by providing a DPD parameterization scheme for homo-oligomers with variable pure-phase densities. 48 However, unlike Wijmans et al, additional simulations are needed to predict phase behavior. Discrepancies between single-bead and two-bead parameterizations for the same chemistry were also observed.…”

“…interactions are considered. 8,10,47,48 We reiterate that this study is aimed at the general behavior of the DPD model and not how to parameterize the model. Therefore, we do not want to limit ourselves by choosing a specific procedure to calculate a ij for a given chemistry.…”

“…For instance, when representing the same molecule as a single bead or as a dimer, Minkara et al observed a higher solubility for the dimers. 48 The difference in repulsive behavior between monomer beads and neighboring polymer beads may be the cause of the shift in solubility. The same discrepancy in repulsive behavior may lead to the observation by Groot and Warren that the scaling behavior of the surface tension abruptly changed between monomers and polymers.…”

“…We note that Minkara et al reported an extension of the revised Groot−Warren model to include oligomers. 48 However, the proposed equation of state uses the Ornstein−Zernike relation for closure. This usage requires a priori knowledge of radial distribution functions, which needs additional simulation.…”

Molecularly Informed Field Theories from Bottom-up Coarse-Graining

“…For this reason, field-theoretic simulations become much more efficient than particle MD at high polymer molecular weight and high densities. Additionally, with a field representation, molecular insertions (or deletions) involve simply changing a parameter in the field-theoretic model, enabling efficient and accurate Gibbs Ensemble Monte Carlo (GEMC) phase coexistence calculations even for macromolecules. , Contrarily, GEMC utilizing a particle representation requires the development of complex schemes (e.g., configurational-bias − or continuous fractional component Monte Carlo techniques, among many others ,, ) to obtain reasonable acceptance for macromolecules of any appreciable size, particularly for liquid–liquid coexistence; this is also the case even when “soft”-core interactions, like those found in dissipative particle dynamics, are utilized. − …”