Onset of the crystalline phase in small assemblies of colloidal particles

Abstract

We report the findings of a computational study designed to determine the onset of a stable crystalline phase in assemblies of small numbers (13–32) of colloidal particles that interact via a depletion-based short-ranged attractive potential. Using Monte Carlo umbrella sampling with coarse graining in two order parameters, we generate free-energy landscapes that can indicate coexistence between fluid-like and crystalline phases. The emergence of a stable crystalline phase is observed as the number of particles in the assembly increases beyond a critical value. We find that the critical cluster size for crystallization onset decreases with increasing strength of the interparticle attraction.

Controlling assembly of colloidal particles into structured objects: Basic strategy and a case study

“…The top k non-trivial eigenvectors then provide a mapping to the lower-dimensional space, wherein the k coordinates of a given data point are given by the corresponding entries in these eigenvectors. In past applications to colloidal assembly [51][52][53] we have found k values in the range 2-5 for colloidal systems with n ~ 30-300 (10-100 particles in 3D), using a Hausdorff distance metric on data sets of ~10 3 -10 4 snapshots sampled from dynamic trajectories. While DMap analysis does provide a value of k and an accompanying set of reduced-space coordinates for each data point in the set, unfortunately it does not provide an explicit mapping between the n-dimensional and k-dimensional coordinates.…”

“…In the past [51][52][53] we have approached this problem by proposing a set of physically meaningful functions of the n-dimensional coordinates and evaluating the correlation between their values and the values of the top eigenvectors, across the data set. Here we consider three such functions.…”

“…Here we consider three such functions. The first two, R g * and <C 6 >, have been used in past publications [51][52][53] to which we refer the reader for more detail. R g * is the radius of gyration of the particle assembly normalized by the radius of a single particle; it is expected to be a useful metric for discriminating between diffuse and condensed phases.…”

“…With respect to the other parts of the AO depletion potential, including the repulsive contribution, we used exactly the same mathematical forms and parameter values employed in previous work. [51][52][53]63…”

Combining pressure and temperature control in dynamics on energy landscapes

“…The determination of such regions and flows requires finding the minima of the landscape and measuring the local volume in state space contained within the basins of the landscape, and furthermore the analysis of the connectivity of the landscape including the derivation of the energetic, entropic and kinetic barriers [10,28] that separate individual minima and the multi-minima basins [2]. In the a e-mail: c.schoen@fkf.mpg.de literature, one finds two complementary approaches to identifying such landscape features: indirectly via extraction from long molecular dynamics [29][30][31] and Monte Carlo simulations [32] or even from long time sequences of experimental signals [33,34], or directly from the landscape itself using various global optimization and exploration algorithms [23]. Of course, in practice, combinations of these methods are often employed, depending on the type of system and objective of the study.…”