RESUMEN

Temperature, particle number and volume are the independent variables of the Helmholtz free energy for a bulk fluid. For a fluid confined in a slit pore between two walls, they are usually complemented by the surface area. However, an alternative choice is possible with the volume replaced by the pore width. Although the formulations with such two sets of independent variables are different, we show they are equivalent and present their relations. Corresponding general statistical-mechanics results are also presented. When the pore width becomes very small, the system behaves rather like a two-dimensional (2D) fluid and one can wonder if thermodynamics still holds. We find it remains valid even in the limit of vanishing pore width and show how to treat the divergences in the normal pressure and the chemical potential so that the corresponding 2D results can be obtained. Thus, we show that the Gibbs surface thermodynamics is perfectly capable of describing small systems.

RESUMEN

Molecular building blocks interacting at the nanoscale organize spontaneously into stable monolayers that display intriguing long-range ordering motifs on the surface of atomic substrates. The patterning process, if appropriately controlled, represents a viable route to manufacture practical nanodevices. With this goal in mind, we seek to capture the salient features of the self-assembly process by means of an interaction-site model. The geometry of the building blocks, the symmetry of the underlying substrate, and the strength and range of interactions encode the self-assembly process. By means of Monte Carlo simulations, we have predicted an ample variety of ordering motifs which nicely reproduce the experimental results. Here, we explore in detail the phase behavior of the system in terms of the temperature and the lattice constant of the underlying substrate.

RESUMEN

We discuss the dynamic behavior of a tagged particle close to a classical localization transition in the framework of the mode-coupling theory of the glass transition. Asymptotic results are derived for the order parameter as well as the dynamic correlation functions and the mean-squared displacement close to the transition. The influence of an infrared cutoff is discussed.

RESUMEN

Scanning tunneling microscopy (STM) images of self-organized monolayers of Frechet dendrons display a variety of two-dimensional ordering motifs, which are influenced by engineering the molecular interactions. An interaction-site model condenses the essential molecular properties determined by molecular mechanics modeling, which in a Monte Carlo approach successfully predicts the various ordering motifs. This confirms that geometry as well as a few salient weak interaction sites encode these structural motifs.

Asunto(s)

RESUMEN

We investigate the delocalization transition appearing in an exclusion process with two internal states, respectively on two parallel lanes. At the transition, delocalized domain walls form in the density profiles of both internal states, in agreement with a mean-field approach. Remarkably, the topology of the system's phase diagram allows for the delocalization of a (localized) domain wall when approaching the transition. We quantify the domain wall's delocalization close to the transition by analytic results obtained within the framework of the domain wall picture. Power law dependences of the domain wall width on the distance to the delocalization transition as well as on the system size are uncovered, they agree with numerical results.

Asunto(s)

RESUMEN

The phase behavior of a two-dimensional colloidal system subject to a commensurate triangular potential is investigated. We consider the integer number of colloids in each potential minimum as rigid composite objects with effective discrete degrees of freedom. It is shown that there is a rich variety of phases including "herringbone" and "Japanese 6 in 1" phases. The ensuing phase diagram and phase transitions are analyzed analytically within variational mean-field theory and supplemented by Monte Carlo simulations. Consequences for experiments are discussed.

RESUMEN

We discuss a class of driven lattice gas obtained by coupling the one-dimensional totally asymmetric simple exclusion process to Langmuir kinetics. In the limit where these dynamics are competing, the resulting nonconserved flow of particles on the lattice leads to stationary regimes for large but finite systems. We observe unexpected properties such as localized boundaries (domain walls) that separate coexisting regions of low and high density of particles (phase coexistence). A rich phase diagram, with high and low density phases, two and three phase coexistence regions, and a boundary independent "Meissner" phase is found. We rationalize the average density and current profiles obtained from simulations within a mean-field approach in the continuum limit. The ensuing analytic solution is expressed in terms of Lambert W functions. It allows one to fully describe the phase diagram and extract unusual mean-field exponents that characterize critical properties of the domain wall. Based on the same approach, we provide an explanation of the localization phenomenon. Finally, we elucidate phenomena that go beyond mean-field such as the scaling properties of the domain wall.

RESUMEN

We study a one-dimensional totally asymmetric exclusion process with random particle attachments and detachments in the bulk. The resulting dynamics leads to unexpected stationary regimes for large but finite systems. Such regimes are characterized by a phase coexistence of low and high density regions separated by domain walls. We use a mean-field approach to interpret the numerical results obtained by Monte Carlo simulations, and we predict the phase diagram of this nonconserved dynamics in the thermodynamic limit.

RESUMEN

The light-scattering spectra of molecular liquids are derived within a generalized hydrodynamics. The wave-vector and scattering-angle dependencies are given in the most general case and the change of the spectral features from liquid to solidlike is discussed without phenomenological model assumptions for (general) dielectric systems without long-ranged order. Exact microscopic expressions are derived for the frequency dependent transport kernels, generalized thermodynamic derivatives, and the background spectra.

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The response of a field-stabilized two-dimensional smectic liquid crystal to shear stress is discussed. Below a critical temperature the smectic film exhibits elastic response to an infinitesimal shear stress normal to the layering. At finite stresses free dislocations nucleate and relax the applied stress. The coupling of the dislocation current to the stress results in non-Newtonian viscous flow. The flow profile in a channel geometry is shown to change qualitatively from a power-law dependence to a Poiseuille-like profile upon increasing the pressure head.

RESUMEN

The hydrodynamics of smectic films at an air-water interface is discussed, with particular focus on the viscous response of the film under flow normal to the layers. The corrections to the response functions of the smectic phase, arising from the coupling between the flow and the smectic order parameter, are calculated. The results for the effective viscosity are illustrated by analyzing smectic film flow in a channel geometry. Two limiting cases of the flow, namely, motion dominated by dislocation-induced shear-softening and dislocation-free motion dominated by the permeation mode of mass transfer, are studied. The effect of drag from a finite depth liquid subphase is considered. The results are compared to those for hexatic and liquid films.