Phase-field modeling of wetting on structured surfaces

We study the dynamics and equilibrium profile shapes of contact lines for wetting in the case of a spatially inhomogeneous solid wall with stripe defects. Using a phase-field model with conserved dynamics, we first numerically determine the contact line behavior in the case of a stripe defect of varying widths. For narrow defects, we find that the maximum distortion of the contact line and the healing length is related to the defect width, while for wide defects, it saturates to constant values. This behavior is in quantitative agreement with the experimental data. In addition, we examine the shape of the contact line between two stripe defects as a function of their separation. Using the phase-field model, we also analytically estimate the contact line configuration and find good qualitative agreement with the numerical results.     

Properties of combustion waves in the model with competitive exo- and endothermic reactions

In this paper we investigate the properties of the travelling combustion wave solutions in a diffusion-thermal model with a two-step competitive exo–endothermic reaction mechanism in one spatial dimension under adiabatic conditions. The model is analysed both numerically and analytically using asymptotic analysis. It is demonstrated that depending on the parameter values, the flame speed as a function of parameters is either a single-valued monotonic function or a double-valued c-shaped function with the turning point type of behaviour. For the case of single-valued flame speed, two flame regimes are identified: the regime with exo- and endothermic reaction domination. Two different routes to extinction are found as well as regions of the existence of combustion waves in the parameter space. Prospects of further work are also discussed.     

Three-dimensional square water in the presence of an external electric field

In this work we study a tridimensional statistical model for the hydrogen-bond (HB) network formed in liquid water in the presence of an external electric field. This model is analogous to the so-called square water, whose ground state gives a good estimate for the residual entropy of the ice. In our case, each water molecule occupies one site of a cubic lattice, and no hole is allowed. The hydrogen atoms of water molecules are disposed at the lines connecting nearest-neighbor sites, in a way that each water can be found in 15 different states. We say that there is a hydrogen bond between two neighboring molecules when only one hydrogen is in the line connecting both molecules. Through Monte Carlo simulations with Metropolis and entropic sampling algorithms, and by exact calculations for small lattices, we determined the dependence of the number of molecules aligned to the field and the number of hydrogen bonds per molecule as a function of temperature and the intensity of the external field. The results for both approaches showed that, different of the two-dimensional case, there is no maximum in the number of HBs as a function of the electric field. However, we observed nonmonotonic behaviors as a function of the temperature of the quantities of interest. We also found the dependence of the entropy on the external electric field at very low temperatures. In this case, the entropy vanishes for the value of the external field for which the contributions to the total energy coming from the HBs and the field become the same.     

Stationary points on the aminomethanol potential energy surface

Summary In this work we study surface fitting equations for a rigid rotor model of aminomethanol. The energies were obtained from the GAUSSIAN88 package using 3-21G bases and fitted on a least square equation, thus generating a Fourier series expansion of the energy as a function of two dihedral angles. The dihedral angles chosen are those that represent rotation around the C-O and N-C axes in the first case, and rotation around C-O and inversion around the amino group in the second case. Results indicate that the hydroxyl hydrogen is subject to almost free rotation around the C-O axis. Further fully relaxed 6-31G* calculations were performed in order to qualify the results obtained for the rigid rotor model.     

Entropy of polydisperse chains: solution on the Bethe lattice

We consider the entropy of polydisperse chains placed on a lattice. In particular, we study a model for equilibrium polymerization, where the polydispersivity is determined by two activities, for internal and endpoint monomers of a chain. We solve the problem exactly on a Bethe lattice with arbitrary coordination number, obtaining an expression for the entropy as a function of the density of monomers and mean molecular weight of the chains. We compare this entropy with the one for the monodisperse case and find that the excess of entropy due to polydispersivity is identical to the one obtained for the one-dimensional case. Finally, we obtain an exponential distribution of molecular weights.     

The omega function for the lithium atom

The omega model is reviewed in the case of a three-electron function and the omega function determined for the lithium atom ground state by using a procedure based on Brillouin' theorem. The resulting function is analyzed in terms of natural configurations, and the correlation coefficient determined as a function of the distance to the nucleus. It is found that the omega function is essentially equivalent to two configurations built up with the occupied NO' and that the model introduces mainly correlation at large distance. These results contrast with those obtained for the beryllium atom using the same model.     

Reliable phase stability analysis for asymmetric models

A deterministic technique for reliable phase stability analysis is described for the case in which asymmetric modeling (different models for vapor and liquid phases) is used. In comparison to the symmetric modeling case, the use of multiple thermodynamic models in the asymmetric case adds an additional layer of complexity to the phase stability problem. To deal with this additional complexity we formulate the phase stability problem in terms of a new type of tangent plane distance function, which uses a binary variable to account for the presence of different liquid and vapor phase models. To then solve the problem deterministically, we use an approach based on interval analysis, which provides a mathematical and computational guarantee that the phase stability problem is correctly solved, and that thus the global minimum in the total Gibbs energy is found in the phase equilibrium problem. The new methodology is tested using several examples, involving as many as eight components, with NRTL as the liquid phase model and a cubic equation of state as the vapor phase model. In two cases, published phase equilibrium computations were found to be incorrect (not stable).     

Structural relaxation in the hydrogen-bonding liquids N-methylacetamide and water studied by optical Kerr effect spectroscopy

Structural relaxation in the peptide model N-methylacetamide (NMA) is studied experimentally by ultrafast optical Kerr effect spectroscopy over the normal-liquid temperature range and compared to the relaxation measured in water at room temperature. It is seen that in both hydrogen-bonding liquids, beta relaxation is present, and in each case, it is found that this can be described by the Cole-Cole function. For NMA in this temperature range, the alpha and beta relaxations are each found to have an Arrhenius temperature dependence with indistinguishable activation energies. It is known that the variations on the Debye function, including the Cole-Cole function, are unphysical, and we introduce two general modifications: One allows for the initial rise of the function, determined by the librational frequencies, and the second allows the function to be terminated in the alpha relaxation.     

Dynamics of macromolecular chains. V. Interpretation of the dielectric relaxation data

The autocorrelation function of orientations, derived for the model of conformational jumps in a chain described in a tetrahedral lattice, has been tentatively applied to dielectric relaxation data. The complex dielectric relaxation of polymers can be interpreted by the aid of only two relaxation processes. In the case of poly(p-chlorostyrene) in solution, the characteristic times that we have calculated agree favorably with the fluorescence-depolarization results. The model has been shown to be consistent with the empirical decay function exp[? (t/τ)^β] proposed by Williams.     

FORMATION OF METAL-SEMICONDUCTOR BARRIERS FOR GaAs-INTERFACES IN THE LOW METAL COVERAGE LIMIT

The early stages in the formation of the Schottky barrier in alkali metal-semiconductor interfaces is analyzed theoretically for the prototypical cases of GaAs(110) and GaAs(100) surfaces. We concentrate in describing the metal-insulator transition taking place as a function of the alkali metal coverage. For each of the cases analyzed we identify two different mechanisms driving this transition: for the GaAs(110) case we find a typical Mott-transition which can be described by an effective half-filled Hubbard model; for the GaAs(100) case the non-local Coulomb interactions play an important role, leading for low coverages to a charge density wave insulating phase.     

Analysis of the half-projected Hartree–Fock function: Density matrix,natural orbitals,and configuration interaction equivalence

The half-projected Hartree–Fock function for singlet states (HPHF ) is analysed in terms of natural electronic configurations. For this purpose the HPHF spinless density matrix and its natural orbitals are first deduced. It is found that the HPHF function does not contain any contribution from odd-times excited configurations. It is seen in addition, in the case of the singlet ground states, this function is approximately equivalent to two closed-shell configurations, although the nature of the excited one depends on the nuclear geometry. An example is given in the case of the LiH ground state. Finally, the application of this model for studying systems of more that two atoms is criticized.     

Correlation hole and physical properties: A model calculation

The correlation hole of Coulson and Nielson and its extension to momentum space by Banyard and Reed is studied by using an exactly solvable model. For this model all relevant quantities pertaining to the correlation hole have been calculated exactly. We use this model to study the relationship between the fit to the correlation hole for an approximate wave function and the closeness of the approximate energies to the exact ones. We show that, although in general the better the fit the closer are the approximate physical quantities to the exact ones, there are exceptions where that is not the case. Also, we present a convenient method for the calculation of the two particle distribution in momentum space and generalize the concept of the correlation hole by defining it in the pseudophase space of position and momentum.     

Fractal growth of rotating DLA‐clusters

A theoretical model for fractal growth of DLA‐clusters in two‐ and three‐dimensional Euclidean space is proposed. This model allows to study some statistical properties of growing clusters in two different situations: in the static case (the cluster is fixed), and in the case when the growing structure has a nonzero rotation around its germ. By the direct computer simulation the growth of rotating clusters is investigated. The fractal dimension of such clusters as a function of the rotation velocity is found. It is shown that for small enough velocities the fractal dimension is growing, but then, with increasing rotation velocity, it tends to the unity.     

A polarizable continuum model for molecules at diffuse interfaces

In this work we illustrate an extension of the polarizable continuum model to describe solvation effects on molecules at the interface between two fluid phases (liquid/liquid, liquid/vapor). This extension goes beyond the naive picture of the interface as a plane dividing two distinct dielectrics, commonly employed in continuum models. The main feature of the model is the use of a diffuse interface with an electric permittivity depending on the position. This characteristic clearly allows the study of simple interfaces as well as more complex membrane or multilayer structures. Moreover the smooth variation of the permittivity in the diffuse interface, in contrast to the sharp boundary between two regions, overcomes the numerical divergences due to charges placed at the boundary. The implementation of the model relies on the integral equation formalism, which allows one to calculate the reaction field acting on a molecule immersed in a dielectric environment once the proper Green's function is known. In the present case, such a Green's function is obtained numerically, allowing a large flexibility in the choice of the dielectric permittivity profile. The applications have been selected with the aim of illustrating the capabilities of the model; its present limitations are also discussed.     

Possibility of different time scales in the capillary rise around a fiber

By molecular modeling simulations, we study the dynamics of the rise of a meniscus on the outside of a fiber. We develop methods to measure simultaneously the height of the liquid interface and the contact angle versus time. We observe that in the complete wetting case (with an equilibrium contact angle equal to zero), the dynamic contact angle theta(t) behaves asymptotically as t(-1) contrary to some experimental results where one observes t(-1/2) instead. Using the combined model describing the dynamics of wetting, we predict that there are two different time scale behaviors within this process related to the two dissipation channels: friction between the liquid and the solid, leading to t(-1), and hydrodynamics, leading to t(-1/2). Using this approach, we find that the maximal speed of spreading on a fiber is a nonmonotonic function of the equilibrium contact angle.     

The asymptotic behavior of a Chemostat model with Crowley–Martin type functional response and time delays

In this paper, we introduce an improved Chemostat model with Crowley–Martin type functional response and time delays. By constructing Lyapunov functionals, the global asymptotic stability of the equilibria is shown in the case of a single species. The conditions for the global asymptotical stability of the model with time delays are obtained via monotone dynamical systems in the case of two species. Our results demonstrate that the effects of predator interference may result in coexistence of two species.     

Electrical phenomena of soft particles. A soft step function model

Simple analytic expressions are derived for the electrophoretic mobility of a soft particle consisting of the hard particle core covered with an ion-penetrable surface layer of polyelectrolyte for the case where the electric potential is low. The effect of the distribution of the polymer segments is taken into account by modeling the surface layer as a soft step function with the inhomogeneous distribution width δ. It is shown that the electrophoretic mobility becomes lower than that for the hard step function model and that the maximum deviation of the soft step function model from the hard step function model, which is a function of λδ (where 1/λ is the softness parameter) and κ/λ (where κ is the Debye-Hückel parameter), is 2.7% at λδ = 0.1, 5.1% at λδ = 0.2, and 11% at λδ = 0.5. In the limit of very high electrolyte concentrations, the obtained mobility expression tends to the result derived from the conventional hard step function model. In addition, an analytic expression for the interaction energy between two similar soft plates is derived on the basis of the present soft step function model. The magnitude of the interaction energy is shown to decrease by a factor 1/(1 + κδ)(2). Approximate analytic expressions for the interaction energies between two similar soft spheres and between two similar soft cylinders are also derived with the help of Derjaguin's approximation.     

Aging correlation functions for blinking nanocrystals, and other on-off stochastic processes

Following recent experiments on power law blinking behavior of single nanocrystals, we calculate two-time intensity correlation functions I(t)I(t+t') for these systems. We use a simple two state (on and off) stochastic model to describe the dynamics. We classify possible behaviors of the correlation function and show that aging, e.g., dependence of the correlation function on age of process t, is obtained for classes of the on time and off time distributions relevant to experimental situation. Analytical asymptotic scaling behaviors of the intensity correlation in the double time t and t' domain are obtained. In the scaling limit I(t)I(t+t('))-->h(x), where four classes of behaviors are found: (i) finite averaged on and off times x=t' (standard behavior); (ii) on and off times with identical power law behaviors x=t/t' (case relevant for capped nanocrystals); (iii) exponential on times and power law off times x=tt' (case relevant for uncapped nanocrystals); (iv) for defected off time distribution we also find x=t+t'. Origin of aging behavior is explained based on simple diffusion model. We argue that the diffusion controlled reaction A+B <==>AB, when followed on a single particle level exhibits aging behavior.     

Measuring raft size as a function of membrane composition in PC-based systems: Part II--ternary systems

The heterogeneity of cell membranes, specifically the presence of lipid rafts, has been hypothesized to play a role in a large number of cellular processes. Although extensive work has been carried out to show the function of lipid rafts in these processes, the characterization of lipid rafts has proven to be extremely difficult. It is known that raft size is relevant to the function of cellular processes and that raft coalescence may be a driving factor for these processes; however, it remains unclear what factors influence raft size and coalescence in natural cell membranes. In this work, we study two ternary model phospholipid and cholesterol systems using two steady-state fluorescent techniques to detect and characterize membrane domains. Domain size is determined through the use of a model to relate experimental F?rster resonance energy transfer (FRET) measurements to domain size. Domains in the range of 3-15 nm were detected in a dioleoylphosphatidylcholine-dipalmitoylphosphatidylcholine-cholesterol (DOPC-DPPC-Chol) system, while only a very small region containing domains was detected in a 1-palmitoyl-2-oleoyl-phosphatidylcholine-dipamitoylphosphatidylcholine-cholesterol (POPC-DPPC-Chol) system. In addition, the polarity-dependent emission maximum shift of the acceptor 1-myristoyl-2-[12-[(5-dimethylamino-1-naphthalenesulfonyl)amino]dodecanoyl]-sn-glycero-3-phosphocholine (DAN-PC) was used to detect the type of liquid phase(s) present in the membrane. It was found that, even in the case in which no two-phase coexistence was observed (POPC-DPPC-Chol), two liquid phases are present, although not necessarily in coexistence. These steady-state fluorescent techniques provide a method for detecting the presence of very small domains in model membranes and provide previously inaccessible detail about the phase behavior of these two systems.     

Influence of the Screening Function on Theoretical Calculations of the Structure Factor of Liquid Aluminum

Abstract

The structure factor S(k) of liquid aluminum is calculated using the Metropolis Monte Carlo method. The effective two-body ion-ion interaction used in the calculations are the Shaw optimized model and the local approximation suggested by Harrison calculated using two screening function in each case, the screening function of Vashishta and Singwi and that of Utsumi and Ichimaru. The calculated structure factors from each case are compared with experiment.