Dynamical density functional theory: phase separation in a cavity and the influence of symmetry

Consider a fluid composed of two species of particles, where the interparticle pair potentials $u_{11} = u_{22} \neq u_{12}$. On confining an equal number of particles from each species in a cavity, one finds that the average one body density profiles of each species are constrained to be exactly the same due to the symmetry, when both external cavity potentials are the same. For a binary fluid of Brownian particles interacting via repulsive Gaussian pair potentials that exhibits phase separation, we study the dynamics of the fluid one body density profiles on breaking the symmetry of the external potentials, using the dynamical density functional theory of Marconi and Tarazona [{\it J. Chem. Phys.}, {\bf 110}, 8032 (1999)]. On breaking the symmetry we see that the fluid one body density profiles can then show the phase separation that is present.Comment: 7 pages, 4 figures. Accepted for the proceedings of the Liquid Matter conference 2005, to be publication in J. Phys.: Condens. Matte

Dynamical density functional theory for molecular and colloidal fluids: a microscopic approach to fluid mechanics

In recent years, a number of dynamical density functional theories (DDFTs) have been developed for describing the dynamics of the one-body density of both colloidal and atomic fluids. In the colloidal case, the particles are assumed to have stochastic equations of motion and theories exist for both the case when the particle motion is over-damped and also in the regime where inertial effects are relevant. In this paper we extend the theory and explore the connections between the microscopic DDFT and the equations of motion from continuum fluid mechanics. In particular, starting from the Kramers equation which governs the dynamics of the phase space probability distribution function for the system, we show that one may obtain an approximate DDFT that is a generalisation of the Euler equation. This DDFT is capable of describing the dynamics of the fluid density profile down to the scale of the individual particles. As with previous DDFTs, the dynamical equations require as input the Helmholtz free energy functional from equilibrium density functional theory (DFT). For an equilibrium system, the theory predicts the same fluid one-body density profile as one would obtain from DFT. Making further approximations, we show that the theory may be used to obtain the mode coupling theory that is widely used for describing the transition from a liquid to a glassy state.Comment: 11 pages, accepted for publication in J. Chem. Phy

Dynamical density functional theory and its application to spinodal decomposition

We present an alternative derivation of the dynamical density functional theory for the one body density profile of a classical fluid developed by Marconi and Tarazona [J. Chem. Phys., 110, 8032 (1999)]. Our derivation elucidates further some of the physical assumptions inherent in the theory and shows that it is not restricted to fluids composed of particles interacting solely via pair potentials; rather it applies to general, multi-body interactions. The starting point for our derivation is the Smoluchowski equation and the theory is therefore one for Brownian particles and as such is applicable to colloidal fluids. In the second part of this paper we use the dynamical density functional theory to derive a theory for spinodal decomposition that is applicable at both early and intermediate times. For early stages of spinodal decomposition our non-linear theory is equivalent to the (generalised) linear Cahn-Hilliard theory, but for later times it incorporates coupling between different Fourier components of the density fluctuations (modes) and therefore goes beyond Cahn-Hilliard theory. We describe the results of calculations for a model (Yukawa) fluid which show that the coupling leads to the growth of a second maximum in the density fluctuations, at a wavenumber larger than that of the main peak.Comment: 23 pages, 3 figure

Phase stability and dynamics of entangled polymer-nanoparticle composites.

Nanoparticle-polymer composites, or polymer-nanoparticle composites (PNCs), exhibit unusual mechanical and dynamical features when the particle size approaches the random coil dimensions of the host polymer. Here, we harness favourable enthalpic interactions between particle-tethered and free, host polymer chains to create model PNCs, in which spherical nanoparticles are uniformly dispersed in high molecular weight entangled polymers. Investigation of the mechanical properties of these model PNCs reveals that the nanoparticles have profound effects on the host polymer motions on all timescales. On short timescales, nanoparticles slow-down local dynamics of the host polymer segments and lower the glass transition temperature. On intermediate timescales, where polymer chain motion is typically constrained by entanglements with surrounding molecules, nanoparticles provide additional constraints, which lead to an early onset of entangled polymer dynamics. Finally, on long timescales, nanoparticles produce an apparent speeding up of relaxation of their polymer host

Pair correlation functions and phase separation in a two component point Yukawa fluid

We investigate the structure of a binary mixture of particles interacting via purely repulsive (point) Yukawa pair potentials with a common inverse screening length $\lambda$. Using the hyper-netted chain closure to the Ornstein-Zernike equations, we find that for a system with `ideal' (Berthelot mixing rule) pair potential parameters for the interaction between unlike species, the asymptotic decay of the total correlation functions crosses over from monotonic to damped oscillatory on increasing the fluid total density at fixed composition. This gives rise to a Kirkwood line in the phase diagram. We also consider a `non-ideal' system, in which the Berthelot mixing rule is multiplied by a factor $(1+\delta)$. For any $\delta>0$ the system exhibits fluid-fluid phase separation and remarkably the ultimate decay of the correlation functions is now monotonic for all (mixture) state points. Only in the limit of vanishing concentration of either species does one find oscillatory decay extending to $r = \infty$. In the non-ideal case the simple random phase approximation provides a good description of the phase separation and the accompanying Lifshitz line.Comment: 11 pages, 6 figures. Accepted for publication in J. Chem. Phy

User community development for the space transportation system/Skylab

The New User Function plan for identifying beneficial uses of space is described. Critical issues such as funding, manpower, and protection of user proprietary rights are discussed along with common barriers which impede the development of a user community. Studies for developing methodologies of identifying new users and uses of the space transportation system are included

Modelling the evaporation of nanoparticle suspensions from heterogeneous surfaces

We present a Monte Carlo (MC) grid-based model for the drying of drops of a nanoparticle suspension upon a heterogeneous surface. The model consists of a generalised lattice-gas in which the interaction parameters in the Hamiltonian can be varied to model different properties of the materials involved. We show how to choose correctly the interactions, to minimise the effects of the underlying grid so that hemispherical droplets form. We also include the effects of surface roughness to examine the effects of contact-line pinning on the dynamics. When there is a `lid' above the system, which prevents evaporation, equilibrium drops form on the surface, which we use to determine the contact angle and how it varies as the parameters of the model are changed. This enables us to relate the interaction parameters to the materials used in applications. The model has also been applied to drying on heterogeneous surfaces, in particular to the case where the suspension is deposited on a surface consisting of a pair of hydrophilic conducting metal surfaces that are either side of a band of hydrophobic insulating polymer. This situation occurs when using inkjet printing to manufacture electrical connections between the metallic parts of the surface. The process is not always without problems, since the liquid can dewet from the hydrophobic part of the surface, breaking the bridge before the drying process is complete. The MC model reproduces the observed dewetting, allowing the parameters to be varied so that the conditions for the best connection can be established. We show that if the hydrophobic portion of the surface is located at a step below the height of the neighbouring metal, the chance of dewetting of the liquid during the drying process is significantly reduced.Comment: 14 pages, 14 figure

Solvent mediated interactions close to fluid-fluid phase separation: microscopic treatment of bridging in a soft core fluid

Using density functional theory we calculate the density profiles of a binary solvent adsorbed around a pair of big solute particles. All species interact via repulsive Gaussian potentials. The solvent exhibits fluid-fluid phase separation and for thermodynamic states near to coexistence the big particles can be surrounded by a thick adsorbed `wetting' film of the coexisting solvent phase. On reducing the separation between the two big particles we find there can be a `bridging' transition as the wetting films join to form a fluid bridge. The potential between the two big particles becomes long ranged and strongly attractive in the bridged configuration. Within our mean-field treatment the bridging transition results in a discontinuity in the solvent mediated force. We demonstrate that accounting for the phenomenon of bridging requires the presence of a non-zero bridge function in the correlations between the solute particles when our model fluid is described within a full mixture theory based upon the Ornstein-Zernike equations.Comment: 28 pages, 8 figure