Molecular Dynamics Calculations of a Second Order Kinetic Phase Transition in an Open System (CSTR)

Abstract

AbstractWe performed Molecular Dynamics calculations (MD) for a few hundred reacting molecules in a continuous flow stirred tank reactor (CSTR), in order to assess the significance of fluctuations in particle numbers at the point of a second order kinetic phase transition. The latter occurs in the following mechanism A + B → C; C + B → D + B, D → 2B (net: A + 2B → 3 B) under given conditions of in‐flow of A and B into the reactor at the critical flow rate. All molecules are represented by hard spheres and periodic boundary conditions are assumed. The MD calculations for ∼500 particles show deviations from the deterministic steady states particularly at the critical flow rate where the distribution function of B particles is found to display about two maxima (MD) instead of one (Poisson distribution for the deterministic case). The magnitude of the concentration fluctuations is enhanced at low frequencies at or near the critical flow rate as exemplified by a Fourier transformation from the time to frequency domain for the MD results in analogy to the phenomenon of critical slowing down in the deterministic CSTR calculations. We conclude that the macroscopic rate laws for first and second order reactions may be applied with confidence to only a few hundred reacting molecules if one is willing to accept some scatter in the rate constants. This conclusion does not apply to the point of a kinetic phase transition in the CSTR which shows a qualitatively different behavior in the low number limit, because of the large and “slow” fluctuations at that point. We present a new approach to the MD treatment of second order rate constants. Kinetic processes in biological cells or on biological membranes may be realistically simulated by MD calculations.