Theoretical Evidence for a Dense Fluid Precursor to Crystallization

Abstract

We present classical density functional theory calculations of the free energy landscape for fluids below their triple point as a function of density and crystallinity. We find that for both a model globular protein and for a simple atomic fluid modeled with a Lennard-Jones interaction, it is free-energetically easier to crystallize by passing through a metastable dense fluid in accord with the Ostwald rule of stages but in contrast to the alternative of ordering and densifying at once as assumed in the classical picture of crystallization.PACS numbers: 82.60. Nh,87.15.Nn,05.20.Jj Crystallization is an intricate process of fundamental importance in many areas of physics, chemistry and engineering. The classical picture of crystallization from supersaturated solutions goes back to Gibbs and consists of the spontaneous formation of crystalline clusters which then either grow or shrink depending on the relative importance of the free energy gain due to the lower bulk free energy of the crystal cluster and the free energy penalty due to the surface tension between the two phases. In this picture, the local density is the only order parameter: the crystalline cluster is (in general) denser than the fluid. In recent years, this picture has been called into question by simulation, theory and experiment for the particular and important case of the crystallization of globular proteins. ten Wolde and Frenkel (hereafter tWF) showed by means of simulation that the free energy landscape of protein crystal clusters as a function of the number of atoms in the cluster and the "crystallinity " favored paths leading from no clusters to clusters with low order to ordered clusters over paths moving from no clusters directly to ordered clusters [1]. This picture was confirmed by Talanquer and Oxtoby [2] and Shiryayev and Gunton[3] who showed using a parameterized van der Waals-type model of globular proteins that surface wetting did indeed lower the free energy of crystal clusters. More recently, the simple picture has also been challenged by novel experimental investigations. Vekilov and co-workers have shown that, prior to crystallization, protein solutions harbor metastable droplets of dense fluid and they have suggested that these droplets are necessary precursors of crystallization [4,5,6,7]. The picture that emerges is one of the formation of metastable droplets of dense fluid which then subsequently crystallize. In this paper, we show by means of classical density functional theory calculations that there is an intrinsic free-energy advantage in first densifying into a metastable densefluid state and then crystallizing rather than following the classical path which goes directly from gas to crystal. Furthermore, our calculations suggest that a similar advantage exists for fluids of small molecules, modeled here via the Lennard-Jones (LJ) interaction, thus indicating that this mechanism may underlie most crystallization processes.The starting point for our analysis is classical density functional theory (DFT) which is based...

Self-Assembly at a Nonequilibrium Critical Point

“…Although self-assembly is a nonequilibrium process, much of our understanding of it is based upon a physical picture that assumes dynamics to play no role except to convey a system along the "easiest" pathways on its free-energy landscape [3]. This "nearequilibrium" or "quasiequilibrium" assumption tends to hold, for instance, for simple one-component systems under mild nonequilibrium conditions [4][5][6][7][8]. It fails when there exist time scales within a given self-assembly process that exceed the time of the experiment or computer simulation.…”

Effect of mixing, concentration and temperature on the formation of mesostructured solutions and their role in the nucleation of dl-valine crystals

“…On the other hand, when solutions were prepared by 5 isothermal rapid initial mixing followed by quiescent isothermal crystallization, induction times were at least two orders of magnitude shorter than in solutions of the identical composition prepared by cooling. We have also seen that application of rapid initial mixing results in much larger size of mesoscale clusters 10 ( Figures 4 and 5). We hypothesize that once mesoscale clusters reach a critical size, a much more rapid nucleation process can be accessed and crystallization follows quickly.…”

“…Bonnett et al have studied the liquid-liquid phase separation during cooling induced crystallization of an organic substance from solvent mixtures 27 . Formation of quasi-emulsions (consisting of apparently stable 10 droplets with diameter of 100-1000 nm) during antisolvent precipitation of small organic compounds was reported by Wang et al 34 The optically clear quasi-emulsion can increase induction time, stabilizing crystallizing solution for days and can have impact on polymorph formation 35 . Recent studies of effects of 15 fluid shear on kinetics of primary nucleation pointed towards the possible role of colloidal scale clusters in crystal nucleation in butylparaben solutions in ethanol 36 and glycine solutions in water 25 .…”

“…Molecular selforganization due to solute-solute and solute-solvent interactions have been examined in undersaturated, saturated and 35 supersaturated crystallizing solutions using X-ray Small-Angle Scattering (SAXS) [1][2][3] , Wide-Angle X-ray Diffraction (WAXD) 1 , Fourier Transform Infrared Spectroscopy (FTIR) 4 , Nuclear Magnetic Resonance (NMR) 5 , Small Angle Neutron Scattering (SANS) 6 , Empirical Potential Structure Refinement (EPSR) 7 and 40 molecular modelling 8,9 . A common finding from these studies has been that solutes associate to form clusters in supersaturated solutions [10][11][12][13][14] . However, identification of a direct relationship between the solute molecular clusters and subsequent formed crystal has been found to be challenging [15][16][17][18] .…”

Crystal templating through liquid–liquid phase separation

“…17,18 However, the direct application of a theory for suspensions of mesoscopic objects to small molecules in solution is unlikely to be straightforward as the interaction strengths are very different. 19,20 Here we will study the nucleation of crystals in highly nonequilibrium conditions experimentally. There have been many previous experiments in which crystallization in deeply supersaturated solutions was studied.…”