Quantitative Equivalence and Performance Comparison of Particle and Field-Theoretic Simulations

Particle and field-theoretic simulations are both commonly used methods to study the equilibrium properties of polymeric materials. Yet despite the formal equivalence of the two methods, no comprehensive comparisons of particle and field-theoretic simulations exist in the literature. In this work, we seek to fill this gap by performing a systematic and quantitative comparison of particle and field-theoretic simulations. In our comparison, we consider four representative polymeric systems: a homopolymer melt/solution, a diblock copolymer melt, a polyampholyte solution, and a polyelectrolyte gel. For each of these systems, we first demonstrate that particle and field-theoretic simulations are equivalent and yield exactly the same results for the pressure and the chemical potential. We next quantify the performance of each method across a range of different conditions including variations in chain length, system density, interaction strength, system size, and polymer volume fraction. The outcome of these calculations is a comprehensive look into the performance of each method and the systems and conditions when either particle or field-theoretic simulations are preferred. We find that field-theoretic simulations are equal to or faster than particle simulations for nearly all of the systems and conditions examined. In many situations, field-theoretic simulations are several orders of magnitude faster than particle simulations, especially if the polymer chains are long, the system density is high, and long-range Coulombic interactions are present. We also demonstrate that field-theoretic simulations are considerably faster at calculating the chemical potential and bypass the challenges associated with particle-based Widom insertion techniques. Taken together, our results provide quantitative evidence that field-theoretic simulations can reach and sample equilibrium considerably faster than particle simulations while simultaneously producing equivalent results.