Martin Grant

Modeling Elasticity in Crystal Growth

A new model of crystal growth is presented that describes the phenomena on atomic length and diffusive time scales. The former incorporates elastic and plastic deformation in a natural manner, and the latter enables access to time scales much larger than conventional atomic methods. The model is shown to be consistent with the predictions of Read and Shockley for grain boundary energy, and Matthews and Blakeslee for misfit dislocations in epitaxial growth.

Modeling elastic and plastic deformations in nonequilibrium processing using phase field crystals.

A continuum field theory approach is presented for modeling elastic and plastic deformation, free surfaces, and multiple crystal orientations in nonequilibrium processing phenomena. Many basic properties of the model are calculated analytically, and numerical simulations are presented for a number of important applications including, epitaxial growth, material hardness, grain growth, reconstructive phase transitions, and crack propagation.

Thermal effects on atomic friction.

We model friction acting on the tip of an atomic force microscope as it is dragged across a surface at nonzero temperatures. We find that stick-slip motion occurs and that the average frictional force follows (absolute value lnv)(2/3), where v is the tip velocity. This compares well to recent experimental work, permitting the quantitative extraction of all microscopic parameters. We calculate the scaled form of the average frictional forces dependence on both temperature and tip speed as well as the form of the friction-force distribution function.

The hydrophobic effect and its role in cold denaturation

The hydrophobic effect is considered the main driving force for protein folding and plays an important role in the stability of those biomolecules. Cold denaturation, where the native state of the protein loses its stability upon cooling, is also attributed to this effect. It is therefore not surprising that a lot of effort has been spent in understanding this phenomenon. Despite these efforts, many unresolved fundamental aspects remain. In this paper we review and summarize the thermodynamics of proteins, the hydrophobic effect and cold denaturation. We start by accounting for these phenomena macroscopically then move to their atomic-level description. We hope this review will help the reader gain insights into the role played by the hydrophobic effect in cold denaturation.

Diffusive Atomistic Dynamics of Edge Dislocations in Two Dimensions

The fundamental dislocation processes of glide, climb, and annihilation are studied on diffusive time scales within the framework of a continuum field theory, the phase field crystal model. Glide and climb are examined for single edge dislocations subjected to shear and compressive strain, respectively, in a two-dimensional hexagonal lattice. It is shown that the natural features of these processes are reproduced without any explicit consideration of elasticity theory or ad hoc construction of microscopic Peierls potentials. Particular attention is paid to the Peierls barrier for dislocation glide or climb and the ensuing dynamic behavior as functions of strain rate, temperature, and dislocation density. It is shown that the dynamics are accurately described by simple viscous motion equations for an overdamped point mass, where the dislocation mobility is the only adjustable parameter. The critical distance for the annihilation of two edge dislocations as a function of separation angle is also presented.

Microscopic mechanism for cold denaturation

We elucidate the mechanism of cold denaturation through constant-pressure simulations for a model of hydrophobic molecules in an explicit solvent. We find that the temperature dependence of the hydrophobic effect induces, facilitates, and is the driving force for cold denaturation. The physical mechanism underlying this phenomenon is identified as the destabilization of hydrophobic contact in favor of solvent-separated configurations, the same mechanism seen in pressure-induced denaturation. A phenomenological explanation proposed for the mechanism is suggested as being responsible for cold denaturation in real proteins.

Model for calcium dependent oscillatory growth in pollen tubes

Experiments have shown that pollen tubes grow in an oscillatory mode, the mechanism of which is poorly understood. We propose a theoretical growth model of pollen tubes exhibiting such oscillatory behaviour. The pollen tube and the surrounding medium are represented by two immiscible fluids separated by an interface. The physical variables are pressure, surface tension, density and viscosity, which depend on relevant biological quantities, namely calcium concentration and thickness of the cell wall. The essential features generally believed to control oscillating growth are included in the model, namely a turgor pressure, a viscous cell wall which yields under pressure, stretch-activated calcium channels which transport calcium ions into the cytoplasm and an exocytosis rate dependent on the cytosolic calcium concentration in the apex of the cell. We find that a calcium dependent vesicle recycling mechanism is necessary to obtain an oscillating growth rate in our model. We study the variation in the frequency of the growth rate by changing the extracellular calcium concentration and the density of ion channels in the membrane. We compare the predictions of our model with experimental data on the frequency of oscillation versus growth speed, calcium concentration and density of calcium channels.

MODEL OF SURFACE INSTABILITIES INDUCED BY STRESS

We propose a model based on a Ginzburg-Landau approach to study a strain relief mechanism at a free interface of a non-hydrostatically stressed solid, commonly observed in thin-film growth. The evolving instability, known as the Grinfeld instability, is studied numerically in two and three dimensions. Inherent in the description is the proper treatment of nonlinearities. We find these nonlinearities can lead to competitive coarsening of interfacial structures, corresponding to different wavenumbers, as strain is relieved. We suggest ways to experimentally measure this coarsening.

Microfilament Orientation Constrains Vesicle Flow and Spatial Distribution in Growing Pollen Tubes

The dynamics of cellular organelles reveals important information about their functioning. The spatio-temporal movement patterns of vesicles in growing pollen tubes are controlled by the actin cytoskeleton. Vesicle flow is crucial for morphogenesis in these cells as it ensures targeted delivery of cell wall polysaccharides. Remarkably, the target region does not contain much filamentous actin. We model the vesicular trafficking in this area using as boundary conditions the expanding cell wall and the actin array forming the apical actin fringe. The shape of the fringe was obtained by imposing a steady state and constant polymerization rate of the actin filaments. Letting vesicle flux into and out of the apical region be determined by the orientation of the actin microfilaments and by exocytosis was sufficient to generate a flux that corresponds in magnitude and orientation to that observed experimentally. This model explains how the cytoplasmic streaming pattern in the apical region of the pollen tube can be generated without the presence of actin microfilaments.

Melting at dislocations and grain boundaries: A Phase Field Crystal study

Dislocation and grain boundary melting are studied in three dimensions using the Phase Field Crystal method. Isolated dislocations are found to melt radially outward from their core, as the localized excess elastic energy drives a power law divergence in the melt radius. Dislocations within low-to-mid angle grain boundaries melt similarly until an angle-dependent first order wetting transition occurs when neighboring melted regions coalesce. High angle boundaries are treated within a screening approximation, and issues related to ensembles, metastability, and grain size are discussed.