Calculation of solid-liquid interfacial free energy: a classical nucleation theory based approach

We present a simple approach to calculate the solid-liquid interfacial free energy. This new method is based on the classical nucleation theory. Using the molecular dynamics simulation, we employ spherical crystal nuclei embedded in the supercooled liquids to create an ideal model of a homogeneous nucleation. The interfacial free energy is extracted by fitting the relation between the critical nucleus size and the reciprocal of the critical undercooling temperature. The orientationally averaged interfacial free energy is found to be 0.302+/-0.002 (in standard LJ unit). The temperature dependence of the interfacial free energy is also obtained in this work. We find that the interfacial free energy increases slightly with increasing temperature. The positive temperature coefficient of the interfacial free energy is in qualitative agreement with Spaepen's analysis [Solid State Phys. 47, FS181 (1994)] and Turnbull's empirical estimation [J. Appl. Phys. 21, 1022 (1950)].     

Hard spheres revisited: accurate calculation of the solid-liquid interfacial free energy

We revise the earlier [R. L. Davidchack and B. B. Laird, Phys. Rev. Lett. 85, 4751 (2000)] direct calculation of the hard sphere solid-liquid interfacial free energy by the cleaving walls method. The revisions of the method include modified interactions with the cleaving walls and the use of a nonequilibrium work measurements approach, which allows for a more robust control of the accuracy of the obtained results. We find that the new values are lower compared to the original ones, which is consistent with the more recent indirect estimates based on extrapolation from the soft-sphere results [R. L. Davidchack and B. B. Laird, Phys. Rev. Lett. 94, 086102 (2005)], as well as those obtained using the capillary fluctuations method [R. L. Davidchack, J. R. Morris, and B. B. Laird, J. Chem. Phys. 125, 094710 (2006)].     

Atomistic nature of NaCl nucleation at the solid-liquid interface

The early stage of heterogeneous nucleation of NaCl from supersaturated NaCl aqueous solution at the water-NaCl (001) interface has been investigated by molecular dynamics simulations. The critical size of the nuclei for spontaneous growth was found to be as small as two atoms (a Na(+)-Cl(-) ion pair) at high supersaturation. Due to the presence of a relatively stable water network and the effect of the hydration force at the interface, the stable nuclei formed on the NaCl (001) are found to contain more Na(+) ions than Cl(-) ions. The different deposition characteristics of the Na(+) and Cl(-) solutes lead to a positively charged substrate and thus may introduce another driving force for nucleation besides the level of solution supersaturation. The role of water was further confirmed by comparison with NaCl epitaxy growth in the vacuum.     

The anisotropic hard-sphere crystal-melt interfacial free energy from fluctuations

We have calculated the interfacial free energy for the hard-sphere system, as a function of crystal interface orientation, using a method that examines the fluctuations in the height of the interface during molecular dynamics simulations. The approach is particularly sensitive for the anisotropy of the interfacial free energy. We find an average interfacial free energy of gamma=0.56+/-0.02k(B)Tsigma(-2). This value is lower than earlier results based upon direct calculations of the free energy [R. L. Davidchack and B. B. Laird, Phys. Rev. Lett. 85, 4751 (2000)]. However, both the average value and the anisotropy agree with the recent values obtained by extrapolation from direct calculations for a series of the inverse-power potentials [R. L. Davidchack and B. B. Laird, Phys. Rev. Lett. 94, 086102 (2005)].     

Acid base contributions to interfacial free energy: self-consistency considerations

The evaluation of interfacial free energies is a subject of much discussion. Of recent times, the role of acid/base interactions has been much debated and a mathematical model devised by van Oss et al. is now commonly used. In this work, we study several polymers using recognised probe liquids and, exploiting an extended matrix analysis, obtain values of solid surface characteristics in agreement with literature values. However, by ‘inverting’ the method, and using accepted solid surface characteristics to ‘rederive’ surface free energy parameters for probe liquids, inconsistencies become apparent. Despite the conceptual interest of acid/base interactions, clearly the mathematical formulation of van Oss et al. is incomplete and further development is required.     

Experimental Gibbs free energy considerations in the nucleation and growth of single-walled carbon nanotubes

Gas feed composition and reaction temperature were varied to identify the thermodynamic threshold conditions for the nucleation and growth of SWNT from methane on supported Fe/Mo catalyst. These reaction conditions closely approximate the pseudoequilibrium conditions that lead to the nucleation and growth of SWNT. These measurements also serve to determine an upper limit of the Gibbs free energy of formation for SWNT. The Gibbs free energy of formation relative to graphite is in good agreement with literature values predicted from simulations for SWNT nuclei containing approximately 80 atoms, while considerably larger than that predicted for bulk (5,5) SWNT. Our estimate over the range 700 to 1000 degrees C of 16.1 to 13.9 kJ mol(-1) falls between the results of these simulations and literature values for diamond.     

Thermal properties,induction period,interfacial energy and nucleation parameters of solution grown benzophenone

The kinetic parameters (reaction order, n, activation energy, E, pre-exponential factor, A, constant rate, k) for the dehydration step due to elimination of osmotic water and hydrogen-bounded water with the carboxylic groups, and for the anhydrifying step owing to the dehydration of two neighboring (-COOH) groups, were determined under non-isothermal conditions for some carboxylic resins with acrylic-divinylbenzene (DVB) matrix. The kinetic parameters were evaluated by means of isoconversional methods from (TG/DTG) thermal analysis data. The results show a dependence of the apparent kinetic parameters on the cross-linking degree, granulation, gel/macroporous matrix nature, exchange capacity and heating rate.     

Calculation of the crystal-melt interfacial free energy of succinonitrile from molecular simulation

The crystal-metal interfacial free energy for a six-site model of succinonitrile [N triple bond C-(CH(2))(2)-C triple bond N] has been calculated using molecular-dynamics simulation from the power spectrum of capillary fluctuations in interface position. The orientationally averaged magnitude of the interfacial free energy is determined to be (7.0+/-0.4)x10(-3) J m(-2). This value is in agreement (within the error bars) with the experimental value [(7.9+/-0.8)x10(-3) J m(-2)] of Marasli et al. [J. Cryst. Growth 247, 613 (2003)], but is about 20% lower than the earlier experimental value [(8.9+/-0.5)x10(-3) J m(-2)] obtained by Schaefer et al. [Philos. Mag. 32, 725 (1975)]. In agreement with the experiment, the calculated anisotropy of the interfacial free energy of this body-centered-cubic material is small. In addition, the Turnbull coefficient from our simulation is also in agreement with the experiment. This work demonstrates that the capillary fluctuation method of Hoyt et al. [Phys. Rev. Lett. 86, 5530 (2001)] can be successfully applied to determine the crystal-melt interfacial free energy of molecular materials.     

Evidences for zeolite nucleation at the solid-liquid interface of gel cavities

The entire sequence of crystallization events, starting with formation of the initial organic-cation-free gel, proceeding through the zeolite nucleation stage, and finishing with complete transformation into LTA-type zeolite crystals, has been monitored by means of high-resolution transmission electron microscopy. Formation and development of voids, containing highly hydrated material transformed later into negative crystals, has been discovered in the solid part of the system. The evolution of these areas has been found to be an integral and noteworthy part of the chemical transformation of the gel that preceded the nucleation in the system. These void structures and, in particular, their solid-liquid interfaces have been identified as the specific locations where the formation of protozeolite nuclei took place. Further development of the system followed the classical for zeolite-yielding systems of crystallization that could be described by the autocatalytic model.     

Thermal and spectral properties and induction period, interfacial energy and nucleation parameters of solution grown anthracene

Anthracene crystals were grown by solution growth technique by adopting slow evaporation method from the solvents CS₂, CCl₄ and CHCl₃. The induction period was measured at various super saturations, and hence the interfacial energies were evaluated. Using the interfacial tension value, the nucleation parameters such as radius of the critical nuclei (r*), the Gibbs free energy change for the formation of a critical nucleus (?G*) and the number of molecules in the critical nucleus (i*) were also calculated for all these solvents at two different temperatures. The effect of surface tension, viscosity and density of these solvents are correlated with interfacial tension. The solution grown crystals were subjected to UV, FTIR, NMR and X-ray diffraction studies. The purity and high-thermal stability of the grown crystals were determined using thermal analysis.     

Direct calculation of the crystal-melt interfacial free energy via molecular dynamics computer simulation

We review our recent work on the direct calculation of the interfacial free energy, gamma, of the crystal-melt interface via molecular dynamics computer simulation for a number of model systems. The value of gamma as a function of crystal orientation is determined using a thermodynamic integration technique employing moving cleaving walls [Phys. Rev. Lett. 2000, 85, 4751]. The calculation is sufficiently precise to resolve the small anisotropy in gamma, which is crucial in determining the kinetics and morphology of dendritic growth. We report values of gamma for the hard-sphere and Lennard-Jones systems, as well as recent results on the series of inverse-power potentials. For the inverse sixth-, seventh-, and eighth-power systems, we determine gamma for both fcc and bcc crystal structures. For these systems, the bcc-melt gamma is lower than that for fcc crystals by about 25%, consistent with recent experiments and computer simulations on fcc-forming systems that show preferential formation of bcc nuclei in the initial stages of crystallization. In addition, we show that our results give a molecular interpretation of Turnbull's rule, which is the empirical relationship between gamma and the enthalpy of fusion.     

Crystal growth and classical nucleation theory

Calculations were performed of the crystal growth rates in lithium disilicate glass in the low-temperature regime where homogeneous nucleation is observed. The computations were executed using the gain-loss (Becker–Doring) equations that form the framework of Classical Nucleation Theory (CNT). The growth rates were obtained in several different ways, using various choices for the kinetic model, the generalized diffusion coefficient, and the physical input data. The results of these calculations are compared with recently obtained experimental values of the growth rates.     

Effects of solid-liquid interface on the interfacial tension measured by micropipet technique

Measurement of interfacial tension (IFT) using the micropipet technique involves the solid-liquid interface. At equilibrium, oil-water interfacial tension is determined from the interface curvature and the critical pressure, according to the Young-Laplace equation. This paper aims to examine the possible contribution of the solid-liquid interface on IFT measurement. Three different experimental configurations are used to examine the sought effect. The three configurations are straight, concentric, and tapered pipets with diameters ranging from 2.5 to 30 microm. For all three configurations, the critical pressure is found to depend only on the pipet diameter. However, when the Young-Laplace equation is applied to determine the IFT, a significant error was noticed at small pipet diameters. The IFT error was described by an exponential function whose asymptote approached the independently determined IFT value with a sufficiently large pipet diameter. The IFT error is anticipated to arise from the layerlike effect of an "ultrastructured" liquid near the solid surface. The solid-induced error in oil-water IFT is noted to fade away at lowered IFT by the addition of surfactant.     

Effect of interfacial free energy on the formation of polymer microcapsules by emulsification/freeze-drying

Hollow polymer microparticles with a single opening on the surface were formed by freeze-drying aqueous polymer colloids swollen with solvent. The results show that the particle morphology is due to phase separation in the polymer emulsion droplets upon freezing in liquid nitrogen, and that morphological changes are driven largely by lowering interfacial free energy. The effects of added surfactant, volume fraction of solvent, type of solvent, and processing conditions on the particle morphology were examined and compared to theoretical predictions. The dried hollow particles were resuspended in a dispersing media and exposed to a second swelling solvent to close the surface opening and form microcapsules. The interfacial free energy difference between the inside and outside surfaces is the driving force for closing the hole on the surface. The emulsification/freeze-drying technique can be used to encapsulate hydrophilic additives in the core of the microcapsules, demonstrating the potential of the technique in controlled-release applications.     

Inhomogeneous polymer solutions: Theory of the interfacial free energy and the composition profile near the consolute point

The Flory–Huggins formulation of the combinatorial entropy, supplemented with residual free energy, is applied locally to obtain the interfacial free energy and the concentration profile of polymer in the interface between two demixed polymer solution phases. Two choices were investigated for the residual free energy: a “regular solution” formulation and an empirical formulation of Koningsveld for polystyrene in cyclohexane. Asymptotic, analytical solutions of the equations near the critical solution point and solutions obtained by numerical calculations are given as a function of temperature for several molecular weights. At temperatures farther below the critical temperature the equations have no solutions. The reason for this is not entirely clear. The local formulation of the free energy used here is an improved version of a previous one, which gave wrong results for asymmetric systems (polymer in a low molecular weight solvent). This newer version is consistent with our theory of critical opalescence and gives a relation between the interface “thickness” and the correlation range of the concentration fluctuations. The calculated correlation ranges were in good accord with those found experimentally by Debye, Chu, and Woerman. That the newer version of our equations for an interface gives no acceptable solutions at lower temperatures could be caused by a “collapse” of a diffuse to a sharp interface as suggested by Nose.     

Enhanced surface free energy of UHMWPE fibers and its interfacial adhesion behavior to PI resins

Mechanical properties of composites made up of ultra‐high‐molecular‐weight polyethylene (UHMWPE) fiber, polyimide (PI), and TiO₂ particles were investigated. The hybrid composite of 20 vol% of UHMWPE fiber with TiO₂ showed tensile strength greater than UHMWPE fiber/PI composite. A positive hybrid effect in tensile strength is obtained. It is observed that addition of small amount of TiO₂ to UHMWPE fiber/PI increased the tensile strength of the composite by 28%. With increase in TiO₂ loading to 1 to 3 vol%, the impact strength of the hybrid composite is increased from 55 KJ/m² to 69 KJ/m². This maximum value is more than one and a half times greater than the impact strength of neat UHMWPE fiber/PI composite.     

Crystal nucleation in an electric field

Nucleation of polar and apolar crystals in an electrostatic field has been analyzed. The analysis is based on the extended nucleation theory which takes into account orientation of amorphous kinetic elements and the resulting crystals. In an electric field free energy of transformation is orientation-dependent which leads to orientation and field effects in thermodynamic (critical crystallization temperature) and kinetic crystallization characteristics (thermal and athermal nucleation rates).