Monte Carlo simulations of single crystals from polymer solutions

Abstract

A novel "anisotropic aggregation" model is proposed to simulate nucleation and growth of polymer single crystals as functions of temperature and polymer concentration in dilute solutions. Prefolded chains in a dilute solution are assumed to aggregate at a seed nucleus with an anisotropic interaction by a reversible adsorption/desorption mechanism, with temperature, concentration, and seed size being the control variables. The Monte Carlo results of this model resolve the long-standing dilemma regarding the kinetic and thermal roughenings, by producing a rough-flat-rough transition in the crystal morphology with increasing temperature. It is found that the crystal growth rate varies nonlinearly with temperature and concentration without any marked transitions among any regimes of polymer crystallization kinetics. The induction time increases with decreasing the seed nucleus size, increasing temperature, or decreasing concentration. The apparent critical nucleus size is found to increase exponentially with increasing temperature or decreasing concentration, leading to a critical nucleus diagram composed in the temperature-concentration plane with three regions of different nucleation barriers: no growth, nucleation and growth, and spontaneous growth. Melting temperatures as functions of the crystal size, heating rate, and concentration are also reported. The present model, falling in the same category of small molecular crystallization with anisotropic interactions, captures most of the phenomenology of polymer crystallization in dilute solutions.

Simulations of nucleation and elongation of amyloid fibrils

“…Our model shares some features with other models used in simulations of grain growth 45 and crystal growth. 46 Two slightly different algorithms are employed in the present paper: one is for multiple fibrils; the other is for a single fibril. The general setup is as follows.…”

“…For details, a step-by-step procedure is given for a similar system in our previous paper. 46 It is to be stressed that our model has several limitations and approximations. First, the collective movement of two or more assembly units is ignored, i.e., only one assembly unit is moved at a time.…”

“…However, Ostwald ripening itself is a good example showing how R c increases with time as C becomes exhausted. In fact, for a pure 2D system in a separate paper, 46 we have derived a phase diagram showing how R c increases with increasing kT or lowering C.…”

Molecular modelling of flow-induced crystallisation in polymers

“…Essentially, nucleation is an extremely rare event and so most simulation time is spent resolving the creation and dissolution of sub-critical nuclei, the majority of which do not grow into stable crystals. Faster alternatives with higher coarse-graining include kinetic Monte Carlo [40][41][42] and Langevin dynamics simulations [43]. Nevertheless, these simulations still have difficulty modelling primary nucleation, forcing them to focus on high degrees of undercooling.…”

Microphase‐Separated Brushes on Square Platelets in PS‐b‐PEO Thin Films

“…[11] Lamellar thickness is mainly predetermined in the nucleation step, when single crystals grow in polymer solutions. [21] The fold length is a function of crystallization temperature. In the regime T i < T m , the thickness of PEO crystals increases with increasing T i ( Table 1).…”