CO2 packing polymorphism under confinement in cylindrical nanopores

We investigate the effect of cylindrical nano-confinement on the phase behaviour of a rigid model of carbon dioxide using both molecular dynamics and well tempered metadynamics. To this aim we study a simplified pore model across a parameter space comprising pore diameter, CO2-pore wall potential and CO2 density. In order to systematically identify ordering events within the pore model we devise a generally applicable approach based on the analysis of the distribution of intermolecular orientations. Our simulations suggest that, while confinement in nano-pores inhibits the formation of known crystal structures, it induces a remarkable variety of ordered packings unrelated to their bulk counterparts, and favours the establishment of short range order in the fluid phase. We summarise our findings by proposing a qualitative phase diagram for this model

CO2 packing polymorphism under pressure: mechanism and thermodynamics of the I-III polymorphic transition

In this work we describe the thermodynamics and mechanism of CO$_2$ polymorphic transitions under pressure from form I to form III combining standard molecular dynamics, well-tempered metadynamics and committor analysis. We find that the phase transformation takes place through a concerted rearrangement of CO$_2$ molecules, which unfolds via an anisotropic expansion of the CO$_2$ supercell. Furthermore, at high pressures we find that defected form I configurations are thermodynamically more stable with respect to form I without structural defects. Our computational approach shows the capability of simultaneously providing an extensive sampling of the configurational space, estimates of the thermodynamic stability and a suitable description of a complex, collective polymorphic transition mechanism

Molecular Dynamics Simulations of Solutions at Constant Chemical Potential

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 (C$\mu$MD) 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 C$\mu$MD 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.Comment: 8 pages, 8 figures (Supplementary Information: 6 pages, 7 figures). Typos and labelling corrected Ver. 3: Minor comments added in Sec. 3. References 13,36,38 added. Minor text changes and typos correcte

Multiple pathways in NaCl homogeneous crystal nucleation

NaCl crystal nucleation from metastable solutions has long been considered to occur according to a single-step mechanism where the growth in the size and crystalline order of the emerging nuclei is simultaneous. Recent experimental observations suggest that significant ion-ion correlations occur in solution and that NaCl crystals can emerge from disordered intermediates which is seemingly at odds with this established view. Here, we performed biased and unbiased molecular dynamics simulations to analyse and characterise the pathways to crystalline phases from solutions far into the metastable region. We find that large liquid-like NaCl clusters emerge as the solution concentration is increased and a wide distribution of crystallisation pathways are observed with two-step nucleation pathways-where crystalline order emerges in dense liquid NaCl regions-being more dominant than one-step pathways to phase separation far into the metastable region. Analyses of cluster size populations and the ion pair association constant show that these clusters are transient, unlike the thermodynamically stable prenucleation cluster solute species that were suggested in other mineralising systems. A Markov state model was developed to analyse the mechanisms and timescales for nucleation from unbiased molecular dynamics trajectories in a reaction coordinate space characterising the dense regions in clusters and crystalline order. This allowed calculation of the committor probabilities for the system to relax to the solution or crystal states and to estimate the rate of nucleation, which shows excellent agreement with literature values. From a fundamental nucleation perspective, our work highlights the need to extend the attribute 'critical' to an ensemble of clusters which can display a broad range of structures and include sizeable disordered domains depending upon the reaction conditions. Moreover, our recent simulation studies demonstrated that carbon surfaces catalyse the formation of liquid-like NaCl networks which, combined with the observations here, suggests that alternative pathways beyond the single-step mechanism can be exploited to control the crystallisation of NaCl

Properties of aqueous electrolyte solutions at carbon electrodes: effects of concentration and surface charge on solution structure, ion clustering and thermodynamics in the electric double layer

Surfaces are able to control physical-chemical processes in multi-component solution systems and, as such, find application in a wide range of technological devices. Understanding the structure, dynamics and thermodynamics of non-ideal solutions at surfaces, however, is particularly challenging. Here, we use Constant Chemical Potential Molecular Dynamics (CμMD) simulations to gain insight into aqueous NaCl solutions in contact with graphite surfaces at high concentrations and under the effect of applied surface charges: conditions where mean-field theories describing interfaces cannot (typically) be reliably applied. We discover an asymmetric effect of surface charge on the electric double layer structure and resulting thermodynamic properties, which can be explained by considering the affinity of the surface for cations and anions and the cooperative adsorption of ions that occurs at higher concentrations. We characterise how the sign of the surface charge affects ion densities and water structure in the double layer and how the capacitance of the interface-a function of the electric potential drop across the double layer-is largely insensitive to the bulk solution concentration. Notably, we find that negatively charged graphite surfaces induce an increase in the size and concentration of extended liquid-like ion clusters confined to the double layer. Finally, we discuss how concentration and surface charge affect the activity coefficients of ions and water at the interface, demonstrating how electric fields in this region should be explicitly considered when characterising the thermodynamics of both solute and solvent at the solid/liquid interface

Properties of aqueous electrolyte solutions at carbon electrodes: effects of concentration and surface charge on solution structure, ion clustering and thermodynamics in the electric double layer

Surfaces are able to control physical-chemical processes in multi-component solution systems and, as such, find application in a wide range of technological devices. Understanding the structure, dynamics and thermodynamics of non-ideal solutions at surfaces, however, is particularly challenging. Here, we use Constant Chemical Potential Molecular Dynamics simulations to gather insight into aqueous NaCl solutions in contact with graphite surfaces at high concentrations and under the effect of applied surface charges: conditions where mean-field theories describing interfaces cannot be (typically) reliably applied. We discover an asymmetric effect of surface charge on the double layer structure and resulting thermodynamic properties, which can be explained by considering the affinity of the surface for cations and anions and the cooperative adsorption of ions that occurs at higher concentrations. We characterise how the sign of the surface charge affects ion densities and water structure in the double layer and how the capacitance of the interface - a function of the electric potential drop across the double layer - is largely insensitive to the bulk solution concentration. Notably, we find that negatively charged graphite surfaces induce an increase in the size and concentration of extended liquid-like ion clusters confined to the double layer. Finally, we discuss how concentration and surface charge affect the activity coefficients of ions and water in the double layer, demonstrating how electric fields in this region should be explicitly considered when characterising the thermodynamics of both solute and solvent at the solid/liquid interface

Molecular simulation approaches to study crystal nucleation from solutions: Theoretical considerations and computational challenges

Various factors, such as environmental conditions, composition, and external fields, can influence its outcomes and rates. Indeed, controlling this rate-determining step toward phase separation is critical, as it can significantly impact the resulting material's structure and properties. Atomistic simulations can be exploited to gain insight into nucleation mechanisms—an aspect difficult to ascertain in experiments—and estimate nucleation rates. However, the microscopic nature of simulations can influence the phase behavior of nucleating solutions when compared to macroscale counterparts. An additional challenge arises from the inadequate timescales accessible to standard molecular simulations to simulate nucleation directly; this is due to the inherent rareness of nucleation events, which may be apparent in silico at even high supersaturations. In recent decades, molecular simulation methods have emerged to circumvent length- and timescale limitations. However, it is not always clear which simulation method is most suitable to study crystal nucleation from solution. This review surveys recent advances in this field, shedding light on typical nucleation mechanisms and the appropriateness of various simulation techniques for their study. Our goal is to provide a deeper understanding of the complexities associated with modeling crystal nucleation from solution and identify areas for further research. This review targets researchers across various scientific domains, including materials science, chemistry, physics and engineering, and aims to foster collaborative efforts to develop new strategies to understand and control nucleation

Overcoming timescale and finite-size limitations to compute nucleation rates from small scale Well Tempered Metadynamics simulations

Condensation of a liquid droplet from a supersaturated vapour phase is initiated by a prototypical nucleation event. As such it is challenging to compute its rate from atomistic molecular dynamics simulations. In fact at realistic supersaturation conditions condensation occurs on time scales that far exceed what can be reached with conventional molecular dynamics methods. Another known problem in this context is the distortion of the free energy profile associated to nucleation due to the small, finite size of typical simulation boxes. In this work the problem of time scale is addressed with a recently developed enhanced sampling method while contextually correcting for finite size effects. We demonstrate our approach by studying the condensation of argon, and showing that characteristic nucleation times of the order of magnitude of hours can be reliably calculated, approaching realistic supersaturation conditions, thus bridging the gap between what standard molecular dynamics simulations can do and real physical systems.Comment: 9 pages, 7 figures, additional figures and data provided as supplementary information. Submitted to the Journal of Chemical Physisc

Time-independent free energies from metadynamics via Mean Force Integration

Inspired by thermodynamic integration, we propose a method for the calculation of time-independent free energy profiles from history-dependent biased simulations via Mean Force Integration (MFI). MFI circumvents the need for computing the ensemble average of the bias acting on the system c(t) and can be applied to different variants of metadynamics. Moreover, MFI naturally extends to aggregate information obtained from independent metadynamics simulations, allowing to converge free energy surfaces without the need to sample recrossing events in a single continuous trajectory. We validate MFI against one- and two-dimensional analytical potentials and by computing the conformational free energy landscape of ibuprofen in the bulk of its most common crystal phase.Comment: 8 pages, 4 figure

Building Maps in Collective Variable Space

Enhanced sampling techniques such as umbrella sampling and metadynamics are now routinely used to provide information on how the thermodynamic potential, or free energy, depends on a small number of collective variables. The free energy surfaces that one extracts by using these techniques provide a simplified or coarse-grained representation of the configurational ensemble. In this work we discuss how auxiliary variables can be mapped in collective variable (CV) space and how the dependence of the average value of a function of the atomic coordinates on the value of a small number of CVs can thus be visualised. We show that these maps allow one to analyse both the physics of the molecular system under investigation and the quality of the reduced representation of the system that is encoded in a set of CVs. We apply this approach to analyse the degeneracy of CVs and to compute entropy and enthalpy surfaces in CV space both for conformational transitions in alanine dipeptide and for phase transitions in carbon dioxide molecular crystals under pressure.Comment: 13 pages, 8 figure