Steady-state nucleation rate and flux of composite nucleus at saddle point

The steady-state nucleation rate and flux of composite nucleus at the saddle point is studied by extending the theory of binary nucleation. The Fokker-Planck equation that describes the nucleation flux is derived using the Master equation for the growth of the composite nucleus, which consists of the core of the final stable phase surrounded by a wetting layer of the intermediate metastable phase nucleated from a metastable parent phase recently evaluated by the author [J. Chem. Phys. {\bf 134}, 164508 (2011)]. The Fokker-Planck equation is similar to that used in the theory of binary nucleation, but the non-diagonal elements exist in the reaction rate matrix. First, the general solution for the steady-state nucleation rate and the direction of nucleation flux is derived. Next, this information is then used to study the nucleation of composite nucleus at the saddle point. The dependence of steady-state nucleation rate as well as the direction of nucleation flux on the reaction rate in addition to the free-energy surface is studied using a model free-energy surface. The direction of nucleation current deviates from the steepest-descent direction of the free-energy surface. The results show the importance of two reaction rate constants: one from the metastable environment to the intermediate metastable phase and the other from the metastable intermediate phase to the stable new phase. On the other hand, the gradient of the potential $\Phi$ or the Kramers crossover function (the commitment or splitting probability) is relatively insensitive to reaction rates or free-energy surface.Comment: 12 pages, 6 figures, to be published in Journal of Chemical Physic

The stability of a crystal with diamond structure for patchy particles with tetrahedral symmetry

The phase diagram of model anisotropic particles with four attractive patches in a tetrahedral arrangement has been computed at two different values for the range of the potential, with the aim of investigating the conditions under which a diamond crystal can be formed. We find that the diamond phase is never stable for our longer-ranged potential. At low temperatures and pressures, the fluid freezes into a body-centred-cubic solid that can be viewed as two interpenetrating diamond lattices with a weak interaction between the two sublattices. Upon compression, an orientationally ordered face-centred-cubic crystal becomes more stable than the body-centred-cubic crystal, and at higher temperatures a plastic face-centered-cubic phase is stabilized by the increased entropy due to orientational disorder. A similar phase diagram is found for the shorter-ranged potential, but at low temperatures and pressures, we also find a region over which the diamond phase is thermodynamically favored over the body-centred-cubic phase. The higher vibrational entropy of the diamond structure with respect to the body-centred-cubic solid explains why it is stable even though the enthalpy of the latter phase is lower. Some preliminary studies on the growth of the diamond structure starting from a crystal seed were performed. Even though the diamond phase is never thermodynamically stable for the longer-ranged model, direct coexistence simulations of the interface between the fluid and the body-centred-cubic crystal and between the fluid and the diamond crystal show that, at sufficiently low pressures, it is quite probable that in both cases the solid grows into a diamond crystal, albeit involving some defects. These results highlight the importance of kinetic effects in the formation of diamond crystals in systems of patchy particles.Comment: 15 pages, 13 figure

On the action potential as a propagating density pulse and the role of anesthetics

The Hodgkin-Huxley model of nerve pulse propagation relies on ion currents through specific resistors called ion channels. We discuss a number of classical thermodynamic findings on nerves that are not contained in this classical theory. Particularly striking is the finding of reversible heat changes, thickness and phase changes of the membrane during the action potential. Data on various nerves rather suggest that a reversible density pulse accompanies the action potential of nerves. Here, we attempted to explain these phenomena by propagating solitons that depend on the presence of cooperative phase transitions in the nerve membrane. These transitions are, however, strongly influenced by the presence of anesthetics. Therefore, the thermodynamic theory of nerve pulses suggests a explanation for the famous Meyer-Overton rule that states that the critical anesthetic dose is linearly related to the solubility of the drug in the membranes.Comment: 13 pages, 8 figure

3D characterization of CdSe nanoparticles attached to carbon nanotubes

The crystallographic structure of CdSe nanoparticles attached to carbon nanotubes has been elucidated by means of high resolution transmission electron microscopy and high angle annular dark field scanning transmission electron microscopy tomography. CdSe rod-like nanoparticles, grown in solution together with carbon nanotubes, undergo a morphological transformation and become attached to the carbon surface. Electron tomography reveals that the nanoparticles are hexagonal-based with the (001) planes epitaxially matched to the outer graphene layer.Comment: 7 pages, 8 figure

Line Defects in Molybdenum Disulfide Layers

Layered molecular materials and especially MoS2 are already accepted as promising candidates for nanoelectronics. In contrast to the bulk material, the observed electron mobility in single-layer MoS2 is unexpectedly low. Here we reveal the occurrence of intrinsic defects in MoS2 layers, known as inversion domains, where the layer changes its direction through a line defect. The line defects are observed experimentally by atomic resolution TEM. The structures were modeled and the stability and electronic properties of the defects were calculated using quantum-mechanical calculations based on the Density-Functional Tight-Binding method. The results of these calculations indicate the occurrence of new states within the band gap of the semiconducting MoS2. The most stable non-stoichiometric defect structures are observed experimentally, one of which contains metallic Mo-Mo bonds and another one bridging S atoms

Diffusive Evolution of Stable and Metastable Phases II: Theory of Non-Equilibrium Behaviour in Colloid-Polymer Mixtures

By analytically solving some simple models of phase-ordering kinetics, we suggest a mechanism for the onset of non-equilibrium behaviour in colloid-polymer mixtures. These mixtures can function as models of atomic systems; their physics therefore impinges on many areas of thermodynamics and phase-ordering. An exact solution is found for the motion of a single, planar interface separating a growing phase of uniform high density from a supersaturated low density phase, whose diffusive depletion drives the interfacial motion. In addition, an approximate solution is found for the one-dimensional evolution of two interfaces, separated by a slab of a metastable phase at intermediate density. The theory predicts a critical supersaturation of the low-density phase, above which the two interfaces become unbound and the metastable phase grows ad infinitum. The growth of the stable phase is suppressed in this regime.Comment: 27 pages, Latex, eps

Equilibrium shapes and energies of coherent strained InP islands

The equilibrium shapes and energies of coherent strained InP islands grown on GaP have been investigated with a hybrid approach that has been previously applied to InAs islands on GaAs. This combines calculations of the surface energies by density functional theory and the bulk deformation energies by continuum elasticity theory. The calculated equilibrium shapes for different chemical environments exhibit the {101}, {111}, {\=1\=1\=1} facets and a (001) top surface. They compare quite well with recent atomic-force microscopy data. Thus in the InP/GaInP-system a considerable equilibration of the individual islands with respect to their shapes can be achieved. We discuss the implications of our results for the Ostwald ripening of the coherent InP islands. In addition we compare strain fields in uncapped and capped islands.Comment: 10 pages including 6 figures. Submitted to Phys. Rev. B. Related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm

EEG-fMRI Based Information Theoretic Characterization of the Human Perceptual Decision System

The modern metaphor of the brain is that of a dynamic information processing device. In the current study we investigate how a core cognitive network of the human brain, the perceptual decision system, can be characterized regarding its spatiotemporal representation of task-relevant information. We capitalize on a recently developed information theoretic framework for the analysis of simultaneously acquired electroencephalography (EEG) and functional magnetic resonance imaging data (fMRI) (Ostwald et al. (2010), NeuroImage 49: 498–516). We show how this framework naturally extends from previous validations in the sensory to the cognitive domain and how it enables the economic description of neural spatiotemporal information encoding. Specifically, based on simultaneous EEG-fMRI data features from n = 13 observers performing a visual perceptual decision task, we demonstrate how the information theoretic framework is able to reproduce earlier findings on the neurobiological underpinnings of perceptual decisions from the response signal features' marginal distributions. Furthermore, using the joint EEG-fMRI feature distribution, we provide novel evidence for a highly distributed and dynamic encoding of task-relevant information in the human brain

Controlling crystallization and its absence: Proteins, colloids and patchy models

The ability to control the crystallization behaviour (including its absence) of particles, be they biomolecules such as globular proteins, inorganic colloids, nanoparticles, or metal atoms in an alloy, is of both fundamental and technological importance. Much can be learnt from the exquisite control that biological systems exert over the behaviour of proteins, where protein crystallization and aggregation are generally suppressed, but where in particular instances complex crystalline assemblies can be formed that have a functional purpose. We also explore the insights that can be obtained from computational modelling, focussing on the subtle interplay between the interparticle interactions, the preferred local order and the resulting crystallization kinetics. In particular, we highlight the role played by ``frustration'', where there is an incompatibility between the preferred local order and the global crystalline order, using examples from atomic glass formers and model anisotropic particles.Comment: 11 pages, 7 figure