Despite its ubiquitous character and relevance in many branches of science and engineering, nucleation from solution remains elusive. In this framework, molecular simulations represent a powerful tool to provide insight into nucleation at the molecular scale. In this work, we combine theory and molecular simulations to describe urea nucleation from aqueous solution. Taking advantage of well-tempered metadynamics, we compute the freeenergy change associated to the phase transition. We find that such a free-energy profile is characterized by significant finite-size effects that can, however, be accounted for. The description of the nucleation process emerging from our analysis differs from classical nucleation theory. Nucleation of crystal-like clusters is in fact preceded by large concentration fluctuations, indicating a predominant two-step process, whereby embryonic crystal nuclei emerge from dense, disordered urea clusters. Furthermore, in the early stages of nucleation, two different polymorphs are seen to compete.T he nucleation of crystals from solution plays an important role in a variety of chemical and engineering processes. However, the very small scale that characterizes the early stages of nucleation makes its experimental study rather challenging. In this regard, molecular simulations play an important role and much work has been devoted to the study of homogeneous nucleation in simple model systems like Lennard-Jones particles or hard spheres (1-3). More recently, growing attention has been paid to the computer simulation of nucleation from solution of organic and inorganic materials (4-11).However, these simulations have to face an important challenge. Nucleation is a typical example of a rare event occurring on a timescale that is much longer than what atomistic simulations can typically afford. The problem is most easily understood if we focus on molecular dynamics (MD), which is the sampling method used here but it plagues other methods as well. In MD, the shortest timescale to be used for a correct integration of the equation of motion is dictated by the fastest atomic motions such as vibrations or rotations. Due to this constraint in the integration step, present MD simulations can reach timescales up to microseconds unless specific hardware, accessible only to few, is used. Even in this case the scale of the accessible times can be stretched only to the milliseconds range, a far cry from the much longer scale of nucleation phenomena.These timescale limitations affect molecular simulations in several other research fields, such as ligand protein binding, protein folding, or slow chemical reactions, to name just a few. To overcome this limit, many enhanced sampling methods have been proposed (12-21). Several of them are based on the application of a suitable external bias potential (12-14) that speeds up configurational sampling and permits free energies to be evaluated and transition rates to be computed (22)(23)(24). Here, we shall use well-tempered (WT) metadynamics to enhance the nucleation...

Coulombic interactions can be used to assemble charged nanoparticles into higher-order structures, but the process requires oppositely charged partners that are similarly sized. The ability to mediate the assembly of such charged nanoparticles using structurally simple small molecules would greatly facilitate the fabrication of nanostructured materials and harnessing their applications in catalysis, sensing, and photonics. Here we show that small molecules having as few as three electric charges can effectively induce attractive interactions between oppositely charged nanoparticles in water. These interactions can guide the assembly of charged nanoparticles into colloidal crystals of a quality previously only thought to result from their cocrystallization with oppositely charged nanoparticles of a similar size. Transient nanoparticle assemblies can be generated using positively charged nanoparticles and multiply charged anions that are enzymatically hydrolyzed into mono- and/or dianions. Our findings demonstrate an approach for the facile fabrication, manipulation, and further investigation of static and dynamic nanostructured materials in aqueous environments.

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Molecular dynamics studies of chemical processes in solution are of great value in a wide spectrum of applications, which range from nano-technology to pharmaceutical chemistry. However, these calculations are affected by severe finite-size effects, such as the solution being depleted as the chemical process proceeds, which influence the outcome of the simulations. To overcome these limitations, one must allow the system to exchange molecules with a macroscopic reservoir, thus sampling a grand-canonical ensemble. Despite the fact that different remedies have been proposed, this still represents a key challenge in molecular simulations. In the present work, we propose the Constant Chemical Potential Molecular Dynamics (CμMD) method, which introduces an external force that controls the environment of the chemical process of interest. This external force, drawing molecules from a finite reservoir, maintains the chemical potential constant in the region where the process takes place. We have applied the CμMD method to the paradigmatic case of urea crystallization in aqueous solution. As a result, we have been able to study crystal growth dynamics under constant supersaturation conditions and to extract growth rates and free-energy barriers.

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