Excess free energy of supercooled liquids at disordered walls

Abstract

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...

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

“…Since all the contribution to the change in free-energy comes from the change in entropy ∆S, a negative γ corresponds to ∆S > 0, meaning that the entropy of the crystal in contact with a wall which is its frozen version, increases at low densities, if the interaction potential has an attractive component. As shown in a recent work [22], this counterintuitive finding is similar to the case of a supercooled binary LJ liquid in contact with an amorphous frozen wall having the same structure as the liquid, where a negative γ was obtained at low temperatures.…”

“…In these investigations, it is implicitly assumed that the thermodynamics of the system is unperturbed by the wall if an average is carried out over the thermal fluctuations and different realizations of the wall [13,15]. However, in a recent work we obtained a non-zero interfacial free energy for a glass-forming binary Lennard-Jones liquid [21] in contact with a wall with the same amorphous structure as the supercooled liquid, indicating that thermodynamics of the liquid is affected by the presence of such a frozen wall [22].…”

Measurements of growing surface tension of amorphous–amorphous interfaces on approaching the colloidal glass transition

“…At present, even in numerical studies on bulk supercooled liquids, evidence for a change in relaxation dynamics across T c is rather indirect 27 , 28 leading to suggestions that the non-monotonicity in ξ d may be unique to the pinned wall geometry 29 – 31 . These concerns notwithstanding, simulations find that a pinned wall can subtly influence particle dynamics by exerting entropic forces that depend on the nature of the inter-particle potential 32 . Similar problems persist even when the particles are randomly pinned.…”

Chain-Increment Method for Free-Energy Computation of a Polymer with All-Atom Molecular Simulations

“…We thus calculated the incremental free energy Δμ i incr at i = 1, 5, 10, ..., 45, and 50. At each i simulated with eq , 50 independent runs were performed for the whole procedures from the generation of the initial configuration to the production run ,− and the ensemble averages were obtained from the production of 50 ns in total. For the accuracy assessment of the approximate method of energy representation, furthermore, Δμ i incr was also computed by the incremental Widom insertion method proposed by Kumar et al ,, In the incremental Widom method for the i th monomer, its total interaction energy with water given by eq was recorded and averaged through eq to determine the (numerically) exact Δμ i incr .…”

“…Table employs an annealing procedure to facilitate the equilibration of the polymer-melt system, − and the pressure and temperature were raised at step 4 to accelerate the relaxation. The production run was carried out over 500 ps with sampling intervals of 0.25 and 0.1 ps for the solution and reference-solvent systems, respectively, and at each i for eq , the whole procedure from the initial preparation by J-OCTA to the production was repeated 500 and 100 times for the reference solvent and solution, respectively. ,− The ensemble averages were thus obtained from the total production times of 250 and 50 ns, respectively. The convergence of the computed Δμ i incr is discussed in Appendix E.…”