Mesoscopic Impurities Expose a Nucleation-Limited Regime of Crystal Growth

Abstract

Nanoscale self-assembly is naturally subject to impediments at the nanoscale. The recently developed ability to follow processes at the molecular level forces us to resolve older, coarse-grained concepts in terms of their molecular mechanisms. In this Letter, we highlight one such example. We present evidence based on experimental and simulation data that one of the cornerstones of crystal growth theory, the Cabrera-Vermilyea model of step advancement in the presence of impurities, is based on incomplete physics. We demonstrate that the piercing of an impurity fence by elementary steps is not solely determined by the Gibbs-Thomson effect, as assumed by Cabrera-Vermilyea. Our data show that for conditions leading up to growth cessation, step retardation is dominated by the formation of critically sized fluctuations. The growth recovery of steps is counter to what is typically assumed, not instantaneous. Our observations on mesoscopic impurities for lysozyme expose a nucleation-dominated regime of growth that has not been hitherto considered, where the system alternates between zero and near-pure velocity. The time spent by the system in arrest is the nucleation induction time required for the step to amass a supercritical fluctuation that pierces the impurity fence.

Step Crowding Effects Dampen the Stochasticity of Crystal Growth Kinetics

“…Inspection of the instantaneous macrostep velocity as a function of time reveals similar stop-and-go dynamics as has been reported for elementary steps near growth cessation [15]. The induction time associated with a macrostep fragment breaking through two neighboring impurity atoms exhibits a Poisson distribution (see Supplemental Material [19]), which is in accordance with the nucleation-limited kinetics expected for this regime of growth.…”

“…The occurrence of such a discrepancy between theory and experiment need not be surprising if one realizes that our current picture of crystal growth is based on incomplete physics. We recently showed that an explicit treatment of the terrace-step-kink model can expose unanticipated physics that are overlooked in mean-field approaches or during the development of analytical expressions [14,15]. The groundwork we performed using kinetic Monte Carlo simulations for elementary steps now allows us to investigate the dynamics of macrostep movement and its response to a field of impurities.…”

Mechanism for the stabilization of protein clusters above the solubility curve: the role of non-ideal chemical reactions

“…This was one of the main reasons that protein crystallization became the subject of intense study in the physical-chemistry community. Protein crystallization is of also of interest because proteins are large molecules that move slowly in solution and so their behavior can be monitored at the molecular scale, thus making it possible to follow processes like nucleation and crystal growth in unprecedented detail [1,2]. One consequence of the intense interest in this subject was the discovery of the so-called "two-step" mechanism of protein nucleation wherein the formation of crystals from a dilute solution involves nucleation of an intermediate metastable phase of dense, but disordered, solution.…”

Soft matter perspective on protein crystal assembly

“…2A) [9,[60][61][62]. If it is prepared at conditions below the critical point, the system has a propensity to aggregate in a disordered, percolating network, i.e., a gel; the gelation probability increases with quench depth [63,64].…”