Phase transitions of equilibrium polymers with isotropic attractions
Larissa Spell and James Kindt, PhD
Department of Chemistry , Emory University, Atlanta, GA

Abstract

Computationally obtained phase diagrams of self-assembling equilibrium polymers with isotropic interactions were compared to theoretically predicted models. The simulated phase diagrams were formulated through calculations using biased Grand Canonical Monte Carlo simulations. The initial systems at set parameters were entered into the simulation. The output obtained after polymer equilibration was then used to determine the first order phase transition or coexistence region. The simulated diagrams were compared to theoretical diagrams formulated using an extension of the Flory-Huggins theory. Similarities or differences in the diagrams were formulated.

Introduction

Self-assembling equilibrium polymers are substances that reversibly form chains, and their bonds are quickly formed and broken. Due to the bonding nature, they do not have a fixed chain length. This research studies equilibrium polymers with specific interactions between the separate monomers and chains. The hard sphere monomers interact through isotropic and chain interactions governed by square well potentials. Each monomer can form one or two directional bonds, leading to unbranched chains. Additionally, a monomer can form an unlimited number of weaker, isotropic (non-directional) bonds to other monomers on the same or different chains. The isotropic attraction is governed by square well potentials but has no dependence on the angle formed by the interacting monomers. The Flory-Huggins Theory attempts to explain the effect of chain length on the phase transition and coexistence of phases of polymers. For regular polymers in which the chains have a fixed length, the longer the chains, the lower the volume fraction at the critical point concentration. The theory is the model to which the experimental calculations will be compared. However, since equilibrium polymers have varying chain lengths dependant on the conditions, the predictions made by the Flory-Huggins theory are more complicated and will be compared to the results formed through the calculations. Through the comparison of the output of series of calculations using Grand Canonical Monte Carlo simulations, similarities and differences of the phase diagrams of simple model systems of equilibrium polymers and those predicted by theoretical models such as the Flory-Huggins theory are to be analyzed and explained.

Results

The dilute and dense structures obtained from the output of the of the calculation are used to determine phase transitions. The activities at which this occurs can be obtained from a density versus activity plot. The phase transition occurred at a specific well depth which relates to the potential of isotropic interactions. The phase transitions for various well depths are placed in a phase diagram to compare the potential to the density. One unique trend noticed was in the average chain length versus density plot. As the well depth increases, the deviation from the theoretical predictions from the Flory-Huggins theory increases as well. Preliminary results suggest this results from incomplete equilibration.

Acknowledgements and Funding Attributions

This material is based upon work supported by the National Science Foundation under Grant CHE-0316076, Howard Hughes Medical Institute under Grant No. 52003727, and support from the Petroleum Research Fund of the American Chemical Society. Computational work was performed at the Cherry L. Emerson Center for Scientific Computation of Emory University, supported in part by NSF Grant No. CHE-0079627 and an IBM Shared University Research award.

In Plain English

In this research, computational chemistry was used to study polymers. Unlike typical polymers with set chain lengths, equilibrium polymers were studyed to with varying chain lengths due to their ability to make and break bond quickly. They have isotropic attractions between the monomers or particles that make up the polymer that easily can be overcome causing the chain to break or form. Some examples are worm-like micelles, ferrofluids, and self-assembling protein fibers. Through the calculations, the density of the polymers were analyzed to determine the boundaries of the phase transition and plot them on a phase diagram. The finished phase diagram was compared to predicted results from an extension of the Flory-Huggins theory.

Techniques

Biased Grand Canonical monte-carlo simulations.