Systematic Coarse-Graining in Nucleation Theory

In this work we show that the standard method to obtain nucleation rate-predictions with the aid of atomistic Monte-Carlo simulations leads to nucleation rate predictions that deviate $3-5$ orders of magnitude from the recent brute-force molecular dynamics simulations [J. Diemand, R. Ang\'{e}lil, K. K. Tanaka, and H. Tanaka, J. Chem. Phys. \textbf{139}, 074309 (2013)] conducted in the experimental accessible supersaturation regime for Lennard-Jones argon. We argue that this is due to the truncated state space literature mostly relies on, where the number of atoms in a nucleus is considered the only relevant order parameter. We here formulate the nonequilibrium statistical mechanics of nucleation in an extended state space, where the internal energy and momentum of the nuclei is additionally incorporated. We show that the extended model explains the lack in agreement between the molecular dynamics simulations by Diemand et al.\ and the truncated state space. We demonstrate additional benefits of using the extended state space; in particular, the definition of a nucleus temperature arrises very naturally and can be shown without further approximation to obey the fluctuation law of McGraw and Laviolette. In addition, we illustrate that our theory conveniently allows to extend existing theories to richer sets of order parameters

Normal stresses in surface shear experiments

When viscoelastic bulk phases are sheared, the deformation of the sample induces not only shear stresses, but also normal stresses. This is a well known and well understood effect, that leads to phenomena such as rod climbing, when such phases are stirred with an overhead stirrer, or to die swell in extrusion. Viscoelastic interfaces share many commonalities with viscoelastic bulk phases, with respect to their response to deformations. There is however little experimental evidence that shear deformations of interfaces can induce in-plane normal stresses (not to be confused with stresses normal to the interface). Theoretical models for the stress-deformation behavior of complex fluid-fluid interfaces subjected to shear, predict the existence of in-plane normal stresses. In this paper we suggest methods to confirm the existence of such stresses experimentall

Generalized surface momentum balances for the analysis of surface dilatational data

Dilatational rheological properties of interfaces are often determined using drop tensiometers, in which the interface of the droplet is subjected to oscillatory area changes. A dynamic surface tension is determined either by image analysis of the droplet profile or by measuring the capillary pressure. Both analysis modes tend to use the Young-Laplace equation for determining the dynamic surface tension. For complex fluid-fluid interfaces there is experimental evidence that this equation does not describe the response of the interface to deformations adequately. Generalizations of this equation are available, and in this comment we will discuss these generalizations, and the conditions for which they reduce to the Young-Laplace equatio

Modeling interfacial dynamics using nonequilibrium thermodynamics frameworks

In recent years several nonequilibrium thermodynamic frameworks have been developed capable of describing the dynamics of multiphase systems with complex microstructured interfaces. In this paper we present an overview of these frameworks. We will discuss interfacial dynamics in the context of the classical irreversible thermodynamics, extended irreversible thermodynamics, extended rational thermodynamics, and GENERIC framework, and compare the advantages and disadvantages of these framework

Dynamic surface tension of complex fluid-fluid interfaces: A useful concept, or not?

Dilatational moduli are typically determined by subjecting interfaces to oscillatory area deformations, and are often defined in terms of the difference between the dynamic or transient surface tension of the interface (the surface tension in its deformed state), and the surface tension of the interface in its non-deformed state. Here we will discuss the usefulness of the dynamic surface tension concept in the characterization of dilatational properties of complex fluid-fluid interfaces. Complex fluid-fluid interfaces are interfaces stabilized by components which form mesophases (two-dimensionional gels, glasses, or (liquid) crystalline phases), as a result of in-plane interactions between the components. We will show that for such interfaces dilatational properties are not exclusively determined by the exchange of surface active components between interface and adjoining bulk phases, but also by in-plane viscoelastic stresses. The separation of these contributions remains a challenging problem which remains to be solve

Effective interaction potentials for model amphiphilic surfactants adsorbed at fluid-fluid interfaces

Computer simulations are a useful tool to explore the effects of interactions and structure of surfactants on interfacial microstructure and properties. Starting with “molecular-level”, three- dimensional reference systems of short amphiphilic surfactants at fluid-fluid interfaces, we here derive effective interaction potentials for the corresponding two-dimensional systems of structure- less particles confined to the interface plane. These reference systems are comprised of two immiscible mono atomic fluids (water- and oil-like particles) and nonionic linear amphiphilic sur- factants. Our results show that coarse grained interaction potentials are only weakly dependent on surface concentration but their behavior is strongly dependent on surfactant interactions. The coarse grained system preserves the in-plane surfactant center-of-mass pair correlation function at the interface and the results of surface pressure-area isotherms are in a good agreement. This approach can be extended straightforwardly to other types of surfactants at both fluid-fluid and fluid-gas interfaces providing us with an effective pairwise interaction potential for the surfactant monolayer. These effective interactions can be used to explore large-scale self-assembly within the monolayer especially at low surface concentrations where reference simulations are extremely time-consuming

Gas–liquid phase equilibrium of a model Langmuir monolayer captured by a multiscale approach

The gas-liquid expanded phase transition of a Langmuir monolayer happens at very low surface concentrations which makes this phenomenon extremely expensive to explore in finite three-dimensional (3D) atomistic simulations. Starting with a 3D model reference system of amphiphilic surfactants at a 2D vapor-liquid interface, we apply our recently developed approach (Moghimikheirabadi et al., Phys. Chem. Chem. Phys. 2018) and map the entire system to an effective 2D system of surfactant center-of-masses projected onto the interface plane. The coarse-grained interaction potential obtained via a force-matching scheme from the 3D simulations is then used to predict the 2D gas-liquid phase equilibrium of the corresponding Langmuir monolayer. Monte Carlo simulations in the Gibbs ensemble are performed to calculate areal densities, chemical potentials and surface pressures of the gaseous and liquid coexisting phases within the monolayer. We compare these simulations to the results of a 2D density functional approach based on Weeks-Chandler-Anderson perturbation theory. We furthermore use this approach to determine the density profiles across the equilibrium gas-liquid dividing line and the corresponding line tensions

Self-assembly of ellipsoidal particles at fluid-fluid interfaces with an empirical pair potential

Colloidal particles adsorbed at fluid-fluid interfaces interact via mechanisms that can be specific to the presence of interfaces, for instance, lateral capillary interactions induced by nonspherical particles. Capillary interactions are highly relevant for self-assembly and the formation of surface microstructures, however, these are very challenging to model due to the multibody nature of capillary interactions. This work pursues a direct comparison between our computational modelling approach and experimental results on surface microstructures formed by ellipsoidal particles. We begin by investigating the accuracy of using pairwise interactions to describe the multibody capillary interaction by contrasting exact two- and three-particle interaction energies and we find that the pairwise approximation appears reasonable for the experimentally relevant configurations studied. We then develop an empirical pair potential and use it in Monte-Carlo type simulations to efficiently model the structure formation process for relevant particle properties such as aspect ratio, contact angle and surface coverage, and succeed in reproducing our experimental observations where we spread sterically-stabilised ellipsoidal particles onto an oil-air interface at high surface coverage. At lower surface coverages, we find that the self-assembly process falls into the diffusion-limited colloid aggregation universality class