Describing colloidal soft matter systems with microscopic continuum models

In this thesis we explore two different theories for modelling soft matter systems. We start by discussing density functional theory (DFT) and dynamical density functional theory (DDFT) and consider the thermodynamics underpinning these theories as well as showing how the main results may be derived from the microscopic properties of soft matter. We use this theory to set up a model for the evaporation of the solvent from a thin film of a colloidal suspension. The general background for such systems is discussed and we display some of the striking nanostructures which self-assemble during the evaporation process. We show that our theory successfully reproduces some of these patterns and deduce the various mechanisms and transport processes behind the formation of the different structures. In the second part of this thesis we discuss results for a second model; the phase field crystal (PFC) model. The model equations are discussed, showing how they may be derived from DDFT as well as discussing the general background of PFC models. We present some results for the PFC model in its most commonly used form before going on to introduce a modified PFC model. We show how the changes in the model equations are reflected in the thermodynamics of the model. We then proceed by demonstrating how this modified PFC model may be used to qualitatively describe colloidal systems. A two component generalisation of the modified PFC model is introduced and used to investigate the transition between hexagonal and square ordering in crystalline structures. We conclude by discussing the similarities and connections between the two models presented in the thesis

Localized states in the conserved Swift-Hohenberg equation with cubic nonlinearity

The conserved Swift-Hohenberg equation with cubic nonlinearity provides the simplest microscopic description of the thermodynamic transition from a fluid state to a crystalline state. The resulting phase field crystal model describes a variety of spatially localized structures, in addition to different spatially extended periodic structures. The location of these structures in the temperature versus mean order parameter plane is determined using a combination of numerical continuation in one dimension and direct numerical simulation in two and three dimensions. Localized states are found in the region of thermodynamic coexistence between the homogeneous and structured phases, and may lie outside of the binodal for these states. The results are related to the phenomenon of slanted snaking but take the form of standard homoclinic snaking when the mean order parameter is plotted as a function of the chemical potential, and are expected to carry over to related models with a conserved order parameter.Comment: 40 pages, 13 figure

Extensive Protein Similarity of the Hybridizing Chickadees Parus atricapillus and P. carolinensis

This is the published version. Copyright Central Ornithology Publication OfficeStarch gel electrophoresis of proteins was used to assess genetic differentiation and introgression across a contact zone between Parus atricapillus and P. carolinensis. Little or no differentiation was found at 35 presumed genetic loci, even between distantly allopatric population samples. Nei's (1978) genetic distance (D) was <O.001 for all comparisons. In contrast, Parus gambeli, another chickadee known to hybridize with atricapillus, was well differentiated at 3 loci (D - 0.065). While the data suggest that atricapillus and carolinensis are closely related, they do not allow conclusions on the extent of introgression across the contact zone. The implications of these data are discussed in the light of the emerging pattern of isozyme variation in birds. Received 26 August 1985, accepted 28 March 1986

Contact area of rough spheres: Large scale simulations and simple scaling laws

We use molecular simulations to study the nonadhesive and adhesive atomic-scale contact of rough spheres with radii ranging from nanometers to micrometers over more than ten orders of magnitude in applied normal load. At the lowest loads, the interfacial mechanics is governed by the contact mechanics of the first asperity that touches. The dependence of contact area on normal force becomes linear at intermediate loads and crosses over to Hertzian at the largest loads. By combining theories for the limiting cases of nominally flat rough surfaces and smooth spheres, we provide parameter-free analytical expressions for contact area over the whole range of loads. Our results establish a range of validity for common approximations that neglect curvature or roughness in modeling objects on scales from atomic force microscope tips to ball bearings.Comment: 2 figures + Supporting Materia

Finite-size scaling in the interfacial stiffness of rough elastic contacts

The total elastic stiffness of two contacting bodies with a microscopically rough interface has an interfacial contribution K that is entirely attributable to surface roughness. A quantitative understanding of K is important because it can dominate the total mechanical response and because it is proportional to the interfacial contributions to electrical and thermal conductivity in continuum theory. Numerical simulations of the dependence of K on the applied squeezing pressure p are presented for nominally flat elastic solids with a range of surface roughnesses. Over a wide range of p, K rises linearly with p. Sublinear power-law scaling is observed at small p, but the simulations reveal that this is a finite-size effect. We derive accurate, analytical expressions for the exponents and prefactors of this low-pressure scaling of K by extending the contact mechanics theory of Persson to systems of finite size. In agreement with our simulations, these expressions show that the onset of the low-pressure scaling regime moves to lower pressure as the system size increases.Comment: Supplementary material is available at arXiv:1210.4255, 5 pages, 3 figure

Unified Description of Aging and Rate Effects in Yield of Glassy Solids

The competing effects of slow structural relaxations (aging) and deformation at constant strain rate on the shear yield stress $\tau^y$ of simple model glasses are examined using molecular simulations. At long times, aging leads to a logarithmic increase in density and $\tau^y$. The yield stress also rises logarithmically with rate, but shows a sharp transition in slope at a rate that decreases with increasing age. We present a simple phenomenological model that includes both intrinsic rate dependence and the change in properties with the total age of the system at yield. As predicted by the model, all data for each temperature collapse onto a universal curve.Comment: 4 pages, 3 figure

Morphological and Vocal Variation across a Contact Zone between the Chickadees Parus atricapillus and P. carolinensis

This is the published version. Copyright Central Ornithology Publication OfficeA contact zone between Black-capped and Carolina chickadees (Parus atricapillus and P. carolinensis) exists in southwestern Missouri. It was less than 15 km wide and paralleled the interface between the relatively treeless Great Plains and the forested Ozark Plateau. Many birds in this zone were intermediate in morphology or vocalizations or both. Moreover, both morphological and vocal discriminant analysis scores of contact zone birds were unimodally distributed and there was no correlation between morphological discriminant scores of mated males and females in the contact zone, indicating little or no assortative mating. Playback experiments demonstrated that birds to the north or south of the contact zone responded aggressively only to their own song type, while contact zone birds responded to either song type. We believe that southwestern Missouri contact zone populations are derived from extensive hybridization between atricapillus and carolinensis. Received 26 August 1985, accepted 28 March 1986