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)].     

Calculations of crystal-melt interfacial free energies by nonequilibrium work measurements

We developed a multistep thermodynamic perturbation method to compute the interfacial free energies by nonequilibrium work measurements with cleaving potential procedure. Using this method, we calculated the interfacial free energies of different crystal orientations for the Lennard-Jones system. Our results are in good agreement with the results by thermodynamic integration method. Compared with thermodynamic integration method, the multistep thermodynamic perturbation method is more efficient. For each stage of the cleaving process, only a few thermodynamic perturbation steps are needed, and there is no requirement on the reversibility of the path.     

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.     

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.     

An empirical equation-of-state for solid-fluid interfacial free energies

The contact angle,, formed by a liquid on a solid surface in air depends on the solid-air ( _S ), liquid-air ( _L ) and solid-liquid ( _SL ) interfacial free energies, as described by Young's equation. Critical examination of reported contact angles for numerous liquids and solids leads to an empirical correlation between _sL and both _Y and _S . Combination of this correlation with Young's equation gives an empirical relation allowing calculation of _S from _L and Calculations made with these empirical relations agree well with estimations of _S obtained by the method of critical spreading, and are consistent with Young's equation.Founded and supported by F. Hoffmann-La Roche and Co., Limited Company, Basel, Switzerland.     

Equilibrium adsorption at crystal-melt interfaces in Lennard-Jones alloys

Although the properties of crystal-melt interfaces have been extensively studied in pure materials, effects of alloying on the interfacial free energy remain relatively poorly understood. In this work we make use of Monte Carlo computer simulations for model binary Lennard-Jones alloys to explore the effects which variations in atomic-size mismatch and the chemical contributions to mixing energies have upon density and composition profiles, as well as the resulting magnitudes of equilibrium adsorption coefficients in concentrated alloys. We study four different model systems covering a range of chemical and size mismatch, finding relatively small adsorption values which are nevertheless statistically different from zero.     

Sizes and interfacial free energies of crystallites formed from fractionated linear polyethylene

Replicas of fracture surfaces of fractions of linear polyethylene, which were crystallized at elevated temperatures for extended time periods, were examined by electron microscopy. Striated. lamella-type crystallites were observed for all molecular weights over the range 3.2 × 10³?5.7 × 10⁵. In agreement with Anderson's previous report, for molecular weights of 12,000 or less, the crystallite thicknesses were comparable to the extended chain length. As the molecular weight increased above this level, however, the crystallite sizes increased only slightly and hence at high molecular weights were very much smaller than the extended chain length. From the measured melting temperatures, crystallite interfacial free energies were calculated from the theory for the melting of finite size crystals comprised of chains of finite length. The crystallite interfacial free energy was found to increase with molecular weight. Based on these results, a crystallization process is outlined which allows for the formation of either extended chain crystallites, or crystallites whose size is much smaller than the extended chain length without any change in nucleation mechanism or arbitrary adjustment in growth mechanism with molecular weight.     

Wall-liquid and wall-crystal interfacial free energies via thermodynamic integration: A molecular dynamics simulation study

A method is proposed to compute the interfacial free energy of a Lennard-Jones system in contact with a structured wall by molecular dynamics simulation. Both the bulk liquid and bulk face-centered-cubic crystal phase along the (111) orientation are considered. Our approach is based on a thermodynamic integration scheme where first the bulk Lennard-Jones system is reversibly transformed to a state where it interacts with a structureless flat wall. In a second step, the flat structureless wall is reversibly transformed into an atomistic wall with crystalline structure. The dependence of the interfacial free energy on various parameters such as the wall potential, the density and orientation of the wall is investigated. The conditions are indicated under which a Lennard-Jones crystal partially wets a flat wall.     

Estimating relative free energies from a single ensemble: Hydration free energies

The ability to determine the free energy of solvation for a number of small organic molecules with varying sizes and properties from the coordinate trajectory of a single simulation of a given reference state was investigated. The relative free energies were estimated from a single step perturbation using the perturbation formula. The reference state consisted of a cavity surrounded by solvent. To enhance sampling a soft-core interaction was used for the cavity. The effect of the size of the cavity, the effective core height, and the length of simulation on the ability to reproduce results obtained from thermodynamic integration calculations was considered. The results using a single step perturbation from an appropriately chosen initial state were comparable to results from thermodynamic integration calculations for a wide range of compounds. Using a large number of compounds the computational efficiency was potentially increased by 2–3 orders of magnitude over traditional free energy approaches. Factors determining the efficiency of the approach are discussed. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1604–1617, 1999     

A comparison of the fcc(111) and (100) crystal-melt interfaces by molecular dynamics simulation

The molecular dynamics simulation technique is employed to study the fcc (100) and (111) crystal—melt interfaces of a system of Lennard-Jones atoms near the triple-point. A comparison of the structure and thermodynamics of the two interfaces results in a simple picture concerning the role of crystal orientation on the structure of the liquid neighboring the crystal face.     

Anisotropic fluctuation model for surfactant-laden liquid-liquid crystal interfaces

A model for thermal fluctuations on surfactant-laden liquid-liquid crystal interfaces is formulated and used to derive the expression of the mean square displacement as a function of four elastic moduli of the interface. The measurable liquid crystal contributions to thermal roughness include the average molecular orientation, the interfacial anchoring modulus, and the bulk elasticity modulus. Surfactant-driven interfacial orientation transitions provide an additional means to extract interfacial elastic moduli parameters in surfactant-laden liquid-liquid crystal interfaces in conjunction with thermal roughness measurements.     

Comment on theories of interfacial tension of polymeric interfaces

A simple scaling argument is shown to give the correction to the interfacial tension of two infinite-molecular-weight immiscible homopolymers arising from the translational entropy of finite-sized chains. It is suggested that the qualitative nature of the Flory-Huggins model, as shown by Binder and coworkers, precludes meaningful detailed comparison of experimental data with current theoretical expressions for the interfacial tension.     

Neutral carbon chain free energies

The structures and energies of singlet and triplet neutral carbon linear chains up to 22 atoms – and frequencies of vibrations for chains up to 17 atoms – are obtained using density functional theory (B3LYP) with a polarized split-valence basis set (6-31G*). Analytical expressions for the dependence of the energy with the number of atoms in the chains are presented with an explicit identification of the electrostatic contribution. The addition reaction free energies of two linear chains allow to visualize the reaction pathways of formation of chains up to 17 carbon atoms and to establish their dissociation temperatures. Free energy calculations show that odd chains of more than 15 atoms have triplet ground states at experimental accessible temperatures. Cycling characteristics of linear chains are discussed.     

Accurate free energies of micelle formation

We determine the free energy of micelle formation for model surfactants in a Lennard-Jones solvent by employing a hybrid semi-grand Monte Carlo simulation scheme in combination with umbrella sampling and configurational bias techniques. Comparing the results to theoretical prediction, we obtain good agreement for large micellar sizes. We also study the effect of changing the surfactant headgroup size and tail length on the critical micelle concentration. The values of and the trends in the calculated critical micelle concentrations do agree with experimental observation for nonionic surfactants. The results open up the way for the calculation of critical micelle concentrations using realistic atomic force fields.     

Interfacial free energies of ionic crystals

Minimum values of the liquid-crystal interfacial free energy have been obtained from data on the maximum supercooling of small droplets of solutions of ionic crystals.