Analysis of nucleation using mean first-passage time data from molecular dynamics simulation

Abstract

We introduce a method for the analysis of nucleation using mean first-passage time (MFPT) statistics obtained by molecular dynamics simulation. The method is based on the Becker-Döring model for the dynamics of a nucleation-mediated phase change and rigorously accounts for the system size dependence of first-passage statistics. It is thus suitable for the analysis of systems in which the separation between time scales for nucleation and growth is small, due to either a small free energy barrier or a large system size. The method is made computationally practical by an approximation of the first-passage time distribution based on its cumulant expansion. Using this approximation, the MFPT of the model can be fit to data from molecular dynamics simulation in order to estimate valuable kinetic parameters, including the free energy barrier, critical nucleus size, and monomer attachment pre-factor, as well as the steady-state rates of nucleation and growth. The method is demonstrated using a case study on nucleation of n-eicosane crystals from the melt. For this system, we found that the observed distribution of first-passage times do not follow an exponential distribution at short times, rendering it incompatible with the assumptions made by some other methods. Using our method, the observed distribution of first-passage times was accurately described, and reasonable estimates for the kinetic parameters and steady-state rates of nucleation and growth were obtained. C 2016 AIP Publishing LLC. [http://dx

Molecular simulation of flow-enhanced nucleation in n-eicosane melts under steady shear and uniaxial extension

“…3(a), and agrees well with the values from Eq. (13), suggesting that Shneidman's approximation 51 is in reasonable agreement with our analysis method 28 for the purposes of calculating this quantity, even when the energy barrier is diminished by flow. The nucleation rate exhibits a monotonic increase with strain rate aboveε c .…”

“…For this study the values P 2,th = 0.52, r P2 = 1.5σ lj , and r th = 1.3σ lj were used, where σ lj = 0.401 nm is the van der Waals diameter of a CH 3 united atom. This results in a more local measure of orientational order as compared to our previous study, 28 which used P 2,th = 0.40, r P2 = 2.5 σ lj , and r th = 1.3 σ lj from Yi and Rutledge. 43 The smaller value of r P2 was chosen because it is more sensitive to fluctuations in orientational order associated with nucleation events for FEN simulations, which exhibit significant background orientation associated with the applied flow field.…”

“…For simulations of quiescent nucleation, the value used in this study yields similar MFPT curves, and therefore similar kinetic parameters including the free energy barrier and critical nucleus size, as our previous study. 28 In general, a small change in P 2,th results in a small change in the critical nucleus size, leaving the remaining kinetic parameters and steady-state rates largely unaffected. For each run, the size of the largest cluster in the system was monitored and the first-passage time curves T largest,sim (1 → n) were recorded as the earliest time that a cluster of size ≥n was observed.…”

“…The MFPT curve τ largest,sim (1 → n) was found by averaging the first-passage times at each value of n for all 40 runs. The standard deviation curve σ largest,sim (1 → n) was computed from the sample variance of T largest,sim (1 → n) at each value of n. The analysis of mean first-passage time data was performed using our recently reported method 28 for analyzing nucleation processes that exhibit small separation between time scales for nucleation and growth. In this method, firstpassage time data from molecular simulation are fit to a stochastic nucleation model 48 in order to extract kinetic parameters and rates associated with the underlying nucleation process.…”

“…The method makes use of NEMD simulation in order to observe nucleation under shear and uniaxial extension with varying strain rates. These observations are then used to parameterize a stochastic model of nucleation that is based on kinetic nucleation theory and valid for small nucleation barriers, 28 in order to determine the strain rate-dependencies of nucleation and growth rates and of critical kinetic parameters. By studying both planar shear and uniaxial extension, the effect of the type of applied flow field, in addition to its intensity, is discerned.…”