Topological Identification Criteria, Stability, and Relevance of Pentagonal Nanochannels in Amorphous Ice.

Considering the potential importance of pentagonal nanochannels (PNCs) in determining the structure of the amorphous ice, we introduce topological criteria to identify the PNCs with an optimal fivefold symmetric environment. The basic building block in our criteria, termed as a bicyclo octamer, is an axisymmetric cluster formed by combination of three 6-membered boat-shaped rings. This bicyclo octamer unit serves as a seamless interface of the PNCs with cubic-hexagonal stacking patterns of the amorphous ice. This interface results in a fivefold symmetric mesostructure of relatively high stability: a central PNC with extended five branches of two-dimensional (2-D) hexagonal (wurtzite) crystalline monolayers stacked with cubic (diamond) layers. We also unearth a hierarchy of symmetric structures in amorphous ice: the PNCs, together with dodecahedron cages, form a network consisting of (nearly) equilateral triangular patterns. At the next hierarchical level of symmetry, such triangular patterns combine to form triangular pyramids with dodecahedron cages as the vertices, PNCs as the edges, and confined 2-D hexagonal crystalline monolayers as the triangular faces of the pyramids. The central core of the pyramids consists of cubic (diamond) regions with a strong local tetrahedral order. The overall structure of the amorphous ice states is found to be profoundly affected by PNCs. Specifically, in states with a relatively large number of PNCs, the cubic-hexagonal stacking is primarily in the form of hexagonal crystalline monolayers stacked from both sides with cubic crystalline layers.

Increase in local crystalline order across the limit of stability leads to cubic-hexagonal stacking in supercooled monatomic (mW) water.

At the limit of stability of a supercooled tetrahedral liquid modeled by monatomic (mW) water potential, it was recently shown that relaxation occurs across a unique value of per particle potential energy (ϕmid ), which corresponds to a dynamical (non-stationary) condition of Gibbs free energy function G(T, P, N, ϕ): [∂2(G/N)/∂ϕ2 = 0] and [∂(G/N)/∂ϕ ≠ 0]. In this work, we explore the inherent structures responsible for the formation of the amorphous states through such a mechanism of relaxation of mW liquid. We first identify 6-member boat and chair shaped rings using a criterion based on the internal dihedral angles. We then consider the stacking of the cubic diamond (10-atom cluster with 4 chair shaped rings) and hexagonal wurtzite (12-atom cluster with 3 boat and 2 chair shaped rings) units through a shared chair ring. We find that the local crystalline (tetrahedral) order is exhibited by the eclipsed bond particles of the laterally connected wurtzite units which are stacked from both sides with the diamond units (DWD stacking). Increasingly longer range crystalline order is obtained as the number of stacked wurtzite layers increases: the particles shared by the stacked (laterally connected) wurtzite layers in DWWD show a longer range crystalline order. An even longer range crystalline order is exhibited by the eclipsed bond particles of the middle (laterally connected) wurtzite layer of DWWWD stacking. We find that cubic-hexagonal stacking occurs primarily in the form of DWD layers across the limit of stability. The local tetrahedral order of the purely cubic (diamond) network particles (which are not shared with wurtzite units) deviates significantly from that of the hexagonal crystal. Nonetheless, the average length of the bonds in the purely cubic network approaches that in the hexagonal crystal very closely. Thus a large increase in the purely cubic ice across the instability also leads to an increase in the local crystalline order in the form of bond-lengths. Our results are consistent with previous experimental and simulation studies which find a significant fraction of cubic ice along with cubic-hexagonal stacking layers in deeply supercooled water.

Freezing point and solid-liquid interfacial free energy of Stockmayer dipolar fluids: a molecular dynamics simulation study.

Stockmayer fluids are a prototype model system for dipolar fluids. We have computed the freezing temperatures of Stockmayer fluids at zero pressure using three different molecular-dynamics simulation methods, namely, the superheating-undercooling method, the constant-pressure and constant-temperature two-phase coexistence method, and the constant-pressure and constant-enthalpy two-phase coexistence method. The best estimate of the freezing temperature (in reduced unit) for the Stockmayer (SM) fluid with the dimensionless dipole moment µ*=1, √2, √3 is 0.656 ± 0.001, 0.726 ± 0.002, and 0.835 ± 0.005, respectively. The freezing temperature increases with the dipolar strength. Moreover, for the first time, the solid-liquid interfacial free energies γ of the fcc (111), (110), and (100) interfaces are computed using two independent methods, namely, the cleaving-wall method and the interfacial fluctuation method. Both methods predict that the interfacial free energy increases with the dipole moment. Although the interfacial fluctuation method suggests a weaker interfacial anisotropy, particularly for strongly dipolar SM fluids, both methods predicted the same trend of interfacial anisotropy, i.e., γ100 > γ110 > γ111.

Efficient computation of free energy of crystal phases due to external potentials by error-biased Bennett acceptance ratio method.

Free energy of crystal phases is commonly evaluated by thermodynamic integration along a reversible path that involves an external potential. However, this method suffers from the hysteresis caused by the differences in the center of mass position of the crystal phase in the presence and absence of the external potential. To alleviate this hysteresis, a constraint on the translational degrees of freedom of the crystal phase is imposed along the path and subsequently a correction term is added to the free energy to account for such a constraint. The estimation of the correction term is often computationally expensive. In this work, we propose a new methodology, termed as error-biased Bennett acceptance ratio method, which effectively solves this problem without the need to impose any constraint. This method is simple to implement and it does not require any modification to the path. We show the applicability of this method in the computation of crystal-melt interfacial energy by cleaving wall method [R. L. Davidchack and B. B. Laird, J. Chem. Phys. 118, 7651 (2003)] and bulk crystal-melt free energy difference by constrained fluid lambda-integration method [G. Grochola, J. Chem. Phys. 120, 2122 (2004)] for a model potential of silicon.

Direct calculation of solid-vapor coexistence points by thermodynamic integration: application to single component and binary systems.

We present a new thermodynamic integration method that directly connects the vapor and solid phases by a reversible path. The thermodynamic integration in the isothermal-isobaric ensemble yields the Gibbs free energy difference between the two phases, from which the sublimation temperature can be easily calculated. The method extends to the binary mixture without any modification to the integration path simply by employing the isothermal-isobaric semigrand ensemble. The thermodynamic integration, in this case, yields the chemical potential difference between the solid and vapor phases for one of the components, from which the binary sublimation temperature can be calculated. The coexistence temperatures predicted by our method agree well with those in the literature for single component and binary Lennard-Jones systems.

Evaluation of the translational free energy in a melting temperature calculation by simulation.

We present two methods suitable for controlling the translational degrees of freedom of a system when evaluating directly the free energy difference between the liquid and the solid phases by thermodynamic integration along a reversible path connecting these two phases. Such a constraint is crucial for an accurate prediction of the melting point by means of simulation. In one of the methods, the free energy difference was calculated by fixing one of the particles of the system at the center of the simulation box. In the second method, the free energy difference was calculated by constraining the center of mass of the system to a small region taken around the center of the simulation box. The correction to the free energy difference due to each constraint must be evaluated by a direct simulation. Both methods give consistent results when applied to a truncated and shifted Lennard-Jones system with cutoff radius of 2.5sigma. However, the fixed particle constraint method is found to be more efficient computationally.

Direct calculation of solid-liquid coexistence points of a binary mixture by thermodynamic integration.

We present a new thermodynamic integration method that directly connects the liquid and the solid phases of a binary mixture by a reversible path. The states along the path are simulated in the isothermal-isobaric semigrand canonical ensemble, in which temperature, pressure, the total number of particles, and the fugacity fractions of the components are held fixed. The thermodynamic integration yields the chemical-potential difference between the two phases for one of the components and this information is then used to locate the solid-liquid coexistence points. The melting temperatures predicted by our method agree well with those predicted by the Gibbs-Duhem integration for a truncated and shifted Lennard-Jones system with a cutoff radius of 2.5sigma.

Bubble nucleation in micellar solution: a density functional study.

We explore the free energetics of bubble nucleation in the micellar solution subjected to a negative pressure using a density functional model of a non-ionic surfactant solution. In this two-component model, the solvent is represented by a single hard-core sphere and the surfactant is represented by two tangent hard-core spheres connected by a rigid bond. The attractive interactions between the particles are modeled by the simple 1/R(6) form. Under all conditions of pressure and interparticle interactions we studied, the free energy barrier of bubble nucleation is found to be lower in the binary surfactant solution than that in a pure solvent and to continue to decrease as the mole fraction of the surfactant in the solution increases. We analyze the free energy surface of the model system under the conditions where both the critical bubble nucleus and the stable micelle exist in equilibrium with the same metastable solution. Our study shows that at moderately low pressures, bubbles can nucleate from the stable micelle and that the resulting free energy barrier of bubble nucleation is expected to be lower than that in the absence of this mechanism. However, as the spinodal is approached at lower pressures, the mechanism of micelle-assisted bubble nucleation becomes less effective. The liquid-liquid miscibility of the model system correlates well with the mechanism of bubble nucleation from the stable micelle.