Crystal-liquid interfacial free energy via thermodynamic integration

Horbach, Jürgen

doi:10.1063/1.4891220

Cited by 38 publications

(42 citation statements)

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“…Method.-We adopt a thermodynamic integration scheme based on a similar approach developed by us earlier to compute the interfacial free energy of a LJ liquid/crystal in contact with structured walls [14] and a method to compute the crystal-liquid interfacial free energy [15]. Our scheme consists of two steps.…”

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confidence: 99%

Excess free energy of supercooled liquids at disordered walls

Horbach

2014

Phys. Rev. E

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Using a novel thermodynamic integration scheme, we compute the excess free energy, γ, of a glassforming, binary Lennard-Jones liquid in contact with a frozen amorphous wall, formed by particles frozen into a similar structure as the liquid. We find that γ is non-zero, becoming negative at low temperature. This indicates that the thermodynamics of the system is perturbed by the effect of the amorphous wall.Recently, several studies have investigated the relaxation dynamics of glass-forming systems in contact with a wall, formed by particles that are frozen into a similar disordered structure [1][2][3][4][5][6][7][8][9]. One of the objectives in these studies has been to identify a growing static length scale associated with the dramatic slowing down of glassy dynamics in the bulk [10]. This is based on the assumption that the thermodynamics of the system is unaffected by the disordered wall, provided an average is performed over the thermal fluctuations as well as a sufficient number of wall realizations [5].Since in such systems, the mobile particles are in contact with an amorphous wall, albeit whose structure is similar to that of the liquid, it involves the presence of an interface. A key question then is to ask what the free energy cost of the formation of such an interface is. The absolute free energy of a system is difficult to compute directly, as the free energy is not a simple function of the phase space variables. However, in an atomistic simulation the free-energy difference of a given state from a reference state of known free energy can be computed using thermodynamic integration (TI) [11].In this work, we compute the excess free energy, γ, of a binary glass-forming Lennard-Jones (LJ) liquid [12] in contact with quenched disordered walls on either side over the bulk free energy, using a novel TI scheme in combination with molecular dynamics (MD) simulation [13]. We consider the distance between the walls to be large enough for the two interfaces to be independent of each other. The interfacial free energy γ is computed as a function of temperature. For low temperatures, we find that γ becomes negative and thus the amorphous wall imposes an attractive pinning field on the supercooled liquid. Furthermore, the non-zero value of γ indicates that the free energy of the liquid is affected by the amorphous walls, although these walls have a similar structure as that of the liquid. Therefore, one has to be careful with respect to the interpretation of the relaxation behavior of the supercooled liquid and following conclusions about the structural relaxation in the bulk liquid.Model Potential.-We consider a two-component (particles of type A and B) 80:20 Kob-Andersen (KA) binary Lennard-Jones mixture [12] with the interaction parameters chosen to yield a supercooled liquid at low temperatures. We denote the interaction potential by u(r), r being the distance between the particles. The N binary LJ particles are enclosed within a simulation cell of size L x × L y × L z , with periodic boundary conditions in th...

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confidence: 99%

Excess free energy of supercooled liquids at disordered walls

Horbach

2014

Phys. Rev. E

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“…In order to prevent any crystalline particle from penetrating the wall, a short-ranged flat wall, modeled by a Gaussian potential is inserted at the boundaries along the z direction (at z = 0 and L z ). As shown in our earlier works [25,26], such a short-ranged flat wall leads to a negligible contribution to the interfacial free energy (≈ 0.001γ).…”

Section: System Setupmentioning

confidence: 91%

“…This reduces the computational efficiency since the other forces in the simulation such as those between the crystalline particles are more comparatively long-ranged (∼ σ). However, by the use of a multiple time-step scheme [24][25][26], the computational overhead is reduced significantly and our simulations are slightly less than two times slower than those carried out with a single large time-step.…”

Section: Thermodynamic Integrationmentioning

confidence: 99%

“…We obtained a non-zero interfacial free energy for particles interacting via a Lennard-Jones potential [25], which increases with increasing density of the crystal suggesting that the thermodynamics of the crystal in contact with such a wall is perturbed and not the same as in the bulk. Moreover, at low densities γ is negative, indicating an increase of entropy as compared to the bulk.…”

Section: Introductionmentioning

confidence: 99%

“…The thermodynamic integration scheme adopted in this work is based on a similar approach devised by us in previous studies to compute the interfacial free energy of a liquid/crystal in contact with structured walls [7][8][9] and to determine the crystal-liquid interfacial free energy [25,26]. The goal is to transform a bulk crystal with periodic boundaries in all three Cartesian-axes directions into a crystal in contact with frozen crystalline layers comprising the frozen walls on either side.…”

Section: Thermodynamic Integrationmentioning

confidence: 99%

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Free energy cost of forming an interface between a crystal and its frozen version

Horbach¹

2015

Phys. Rev. E

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Using a thermodynamic integration scheme, we compute the free energy cost per unit area, γ, of forming an interface between a crystal and a frozen structured wall, formed by particles frozen into the same equilibrium structure as the crystal. Even though the structure and potential energy of the crystalline phase in the vicinity of the wall is same as in the bulk, γ has a non-zero value and increases with increasing density of the crystal and the wall. Investigating the effect of several interaction potentials between the particles, we observe a positive γ at all crystalline densities if the potential is purely repulsive. For models with attractive interactions, such as the Lennard-Jones potential, a negative value for γ is obtained at low densities.

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