Laura J. Douglas Frink

Solvation forces between rough surfaces

We investigate the role of surface roughness on solvation forces and solvation free energies. Roughness is introduced by dividing a surface into an array of square tiles that are then randomly displaced in the direction perpendicular to the wall. The integrated wall strength of these tiled surfaces is independent of the surface roughness and hence this class of rough walls is ideally suited for isolating roughness effects. We use grand canonical Monte Carlo simulations of a Lennard-Jones fluid confined in a slit pore with rough walls to generate the solvation interactions as a function of roughness, tile size, and surface area. The simulation data are compared to a simple superposition approximation of smooth wall solvation interactions (obtained from simulation or density functional theory), based on a distribution of wall separations. We find that this approximation provides a surprisingly accurate route to the solvation interaction of rough surfaces. In general, increased roughness leads to a reduction...

Density functional theory for inhomogeneous polymer systems. II. Application to block copolymer thin films

We use polymer reference interaction site model (PRISM)-based density functional theory (DFT) to study the structures and morphologies of block copolymer thin films. The polymers are modeled as freely jointed chains, allowing numerical solution of the nonlinear DFT equations. The use of PRISM with DFT allows the inclusion of compressibility and local packing effects due to the finite size of the monomers. We also employ a pseudo-arclength continuation algorithm to locate phase transitions and new morphologies. We study symmetric diblock copolymers confined between two parallel surfaces which both attract one component of the diblock, for two different values of AB segregation strength and for various surface interactions. The predicted equilibrium morphologies are in good qualitative agreement with previous self-consistent field calculations and are consistent with experiment. We are able to resolve the detailed packing structure near the surfaces. We find that packing effects enhance the stability of the...

Density functional theory for inhomogeneous polymer systems. I. Numerical methods

We present a new real space Newton-based computational approach to computing the properties of inhomogeneous polymer systems with density functional theory (DFT). The DFT is made computationally efficient by modeling the polymers as freely jointed chains and obtaining direct correlation functions from polymer reference interaction site model calculations. The code we present can solve the DFT equations in up to three dimensions using a parallel implementation. In addition we describe our implementation of an arc-length continuation algorithm, which allows us to explore the phase space of possible solutions to the DFT equations. These numerical tools are applied in this paper to hard chains near hard walls and briefly to block copolymer systems. The method is shown to be accurate and efficient. Arc-length continuation calculations of the diblock copolymer systems illustrate the care required to obtain a complete understanding of the structures that may be found with this polymer-DFT approach.

Rapid analysis of phase behavior with density functional theory. I. Novel numerical methods

The phase behavior of confined fluids is rich even for simple models of fluids and simple confining geometries. There has been a great deal of work to understand these systems, and density functional theories (DFT) of inhomogeneous fluids are often applied to determine phase diagrams quickly for these simple systems where symmetry in the physical problem reduces the computational problem to a one-dimensional calculation. More recently, there has been interest in developing DFT algorithms for treating fluids in complex confining geometries or at chemically heterogeneous surfaces where two- or three-dimensional calculations are required. In this paper we present three algorithms for the rapid and robust study of phase behavior in DFT models of inhomogeneous fluids and demonstrate their utility by analyzing capillary condensation in slit pores and ordered two-dimensional arrays of cylindrical fibers. The three algorithms are arclength continuation algorithms for tracing connected stable, metastable, and unst...

Rapid analysis of phase behavior with density functional theory. II. Capillary condensation in disordered porous media

For some time, there has been interest in understanding adsorption and capillary condensation in disordered porous media from a molecular perspective. It has been documented that the free energy landscape in these systems is complex with many metastable states. In this paper we explore the complexity of adsorption and capillary condensation in several simple models of disordered porous media constructed with parallel cylindrical fibers. We present nonlocal density functional theory calculations on a Lennard-Jones model fluid adsorbing in these porous materials coupled with the arclength continuation and phase transition tracking algorithms we presented in Paper I of this series. The arclength continuation algorithm allows us to trace out all the possible states between vapor-filled and liquid-filled pores. We find that capillary condensation is likely to occur in stages at high temperatures and strong wall–fluid interactions while the condensation occurs as a single transition at low temperatures and weak wall–fluid interactions. This paper also compares the extent of hysteresis on adsorption and desorption, discusses the validity of the Gibbs adsorption equation, and considers application of simple pore models in predicting the complexity of phase diagrams in disordered porous media.

A new efficient method for density functional theory calculations of inhomogeneous fluids

The accurate computation of the effects of solvation on chemical systems can be done using density functional theories (DFT) for inhomogeneous multicomponent fluids. The DFT models of interest are non-local theories which accurately treat hard-sphere fluid mixtures; attractive inter-particle potentials (Lennard-Jones) are added as perturbations. In this paper, we develop and demonstrate a new efficient method for an accurate non-local DFT. The method described here differs from previous work in the use ot fast fourier transform (FFT) methods to carry out the convolutions. As with our previous real space work (J. Comput. Phys. 159(2) (2000) 407, 425), we demonstrate that the Fourier space approach can be solved with a Newton-GMRES approach; however, we now employ a very efficient matrix-free algorithm. A simple but effective preconditioner is presented. The method is demonstrated with calculations performed for one-, two-, and three-dimensional systems, including problems with single and multicomponent fluids. Timing comparisons with previous implementations are given.

Wetting of a Chemically Heterogeneous Surface

Theories for inhomogeneous fluids have focused in recent years on wetting, capillary conden- sation, and solvation forces for model systems where the surface(s) is(are) smooth homogeneous parallel plates, cylinders, or spherical drops. Unfortunately natural systems are more likely to be hetaogeneous both in surt%ce shape and surface chemistry. In this paper we discuss the conse- quences of chemical heterogeneity on wetting. Specifically, a 2-dimensional implementation of a nonlocal density functional theory is solved for a striped surface model. Both the strength and range of the heterogeneity are varied. Contact angles are calculated, and phase transitions (both the wetting transition and a local layering transition) are located. The wetting properties of the surface ase shown to be strongly dependent on the nature of the surface heterogeneity. In addition highly ordered nanoscopic phases are found, and the operational limits for formation of ordered or crystalline phases of nanoscopic extent are discussed.

A molecular theory for surface forces adhesion measurements

Surface forces have been measured by others in undersaturated vapors to determine the adhesive energy of the solid (mica) as well as to probe the limits of the Laplace-Kelvin equation in micropores. The measured pull-off forces are complex requiring an intimate understanding of the underlying oscillatory solvation forces, adsorption, and surface deformation. While the elastic energy of the solid has been taken into account in previous theoretical studies of adhesion, the Laplace-Kelvin assumption of a uniform bulk-like fluid has always been applied. In this paper we present the first application of a modern molecular theory—a nonlocal density functional theory—to the prediction of pull-off forces with the surface forces apparatus. In this theory, the confined fluid is allowed to be nonuniform, and oscillatory solvation forces may be predicted. For rigid surfaces, it is demonstrated that the separation of forces most often used to analyze the surface forces apparatus measurements is highly accurate only wh...

Parallel Segregated Schur Complement Methods for Fluid Density Functional Theories

Numerical formulations of density functional theories for inhomogeneous fluids (fluid-DFTs) require the solution of large systems of equations with many degrees of freedom (DOF) per node on a computational grid. Historically, solvers for these problems have used simple Picard iterations across DOF or, more recently, fully coupled general algebraic techniques. In this paper we look at fluid-DFTs from a fresh perspective, retaining a fully coupled formulation but segregating variables for the purpose of introducing Schur complement formulations and specialized preconditioners. By viewing fluid-DFTs from this perspective, we develop a mathematical framework and a collection of solution algorithms that have a dramatic impact on the robustness, performance, and scalability of the implicit equations generated by fluid-DFTs.

Applying molecular theory to steady-state diffusing systems

Predicting the properties of nonequilibrium systems from molecular simulations is a growing area of interest. One important class of problems involves steady-state diffusion. To study these cases, a grand canonical molecular dynamics approach has been developed by Heffelfinger and van Swol [J. Chem. Phys. 101, 5274 (1994)]. With this method, the flux of particles, the chemical potential gradients, and density gradients can all be measured in the simulation. In this paper, we present a complementary approach that couples a nonlocal density functional theory (DFT) with a transport equation describing steady-state flux of the particles. We compare transport-DFT predictions to GCMD results for a variety of ideal (color diffusion), and nonideal (uphill diffusion and convective transport) systems. In all cases, excellent agreement between transport-DFT and GCMD calculations is obtained with diffusion coefficients that are invariant with respect to density and external fields.