On the importance of the "density per particle" (shape function) in the density functional theory

The central role of the shape function sigma(r) from the density functional theory (DFT), the ratio of the electron density rho(r) and the number of electrons N of the system (density per particle), is investigated. Moreover, its relationship with DFT based reactivity indices is established. In the first part, it is shown that an estimate for the chemical hardness can be obtained from the long range behavior of the shape function and its derivative with respect to the number of electrons at a fixed external potential. Next, the energy of the system is minimized with the constraint that the shape function should integrate to unity; the associated Lagrange multiplier is shown to be related to the electronic chemical potential micro of the system. Finally, the importance of the shape function for both molecular structure, reactivity, and similarity is outlined.     

Steady state energy distribution function of adatoms in reactive adsorption

The interplay between the energy distribution function of adatoms and the rate of diatom formation in catalytic reaction is studied by means of mean field rate equations. The recombination of adatoms is described as a multi-channel process where adatom desorption arises from several energy levels. It is shown that the distribution function can be computed, analytically, as a function of the ratio between recombination probability and rate constant for energy disposal to the solid. This parameter is the key quantity of the kinetics since it governs both reaction rate and the shape of the energy distribution function. It is found that, in order to obtain steady state conditions, the control parameter is constrained within a well defined interval of values which result lower than unity. It is shown that a kinetic transition takes place for the highest value of the parameter, which entails hyperthermal reaction rate.     

On the reduced moment in the transient regime of homogeneous nucleation

One of the parameters characterizing the evolution of nucleation in the transient regime is the so-called reduced moment, a dimensionless quantity. This parameter describes the steepness with which the nucleation rate approaches its steady state. Until recently, very little had been known about this parameter in real systems, although a widely quoted 1969 theory [D. Kashchiev, Surf. Sci. 14, 209 (1969)] existed that formally described nucleation in the transient regime. This theory has been shown to be incorrect in its implication about the reduced moment. Molecular dynamics simulations have recently greatly clarified what happens in the transient regime. It turns out that the reduced moment depends strongly on the size of the nucleus under consideration, and, for a rapidly quenched liquid, it substantially exceeds unity for small nuclei but approaches unity as nuclei increases in size. The objective of this paper is to illustrate the behavior of the reduced moment and to show how this behavior is a natural consequence of the kinetics of the nucleation process.     

Effect of the presence of an ordered micro-pillar array on the formation of silica monoliths

We report on the synthesis of siloxane-based monoliths in the presence of a two-dimensional, perfectly ordered array of micro-pillars. Both methyltrimethoxysilane- and tetramethoxysilane-based monoliths were considered. The obtained structures were analyzed using scanning-electron microscopy and can be explained from the general theory of surface-directed phase separation in confined spaces. The formed structures are to a large extent nearly exclusively determined by the ratio between the bulk domain size of the monolith on the one hand and the distance between the micro-pillars on the other hand. When this ratio is small, the presence of the pillars has nearly no effect on the morphology of the produced monoliths. However, when the ratio approaches unity and ascends above it, some new types of monolith morphologies are induced, two of which appear to have interesting properties for use as novel chromatographic supports. One of these structures (obtained when the domain size/inter-pillar distance ratio is around unity) is a 3D network of linear interconnections between the pillars, organized such that all skeleton branches are oriented perpendicular to the micro-pillar surface. A second interesting structure is obtained at even higher values of the domain size/inter-pillar distance ratio. In this case, each individual micro-pillar is uniformly coated with a mesoporous shell.     

Electronic structure and charge transfer in the ternary intercalated graphite beta-KS0.25C3

The electronic structure of the ternary intercalated graphite beta-KS(0.25)C3 is studied by means of a first-principles density functional theory approach. The nature of the partially filled bands is analyzed, and the K sublayers of the intercalate are shown to have an important contribution to the Fermi surface. This K-based contribution confers a sizable three-dimensional character to the conductivity even if considerably less than that for the related binary KC8. The electronic structure of beta-KS(0.25)C3 differs noticeably from that of the related ternary compound, KH(x)C4. The charge transfer is analyzed, and a way to evaluate it, which can be used in general for intercalated graphites, is proposed. The charge transfer per C atom in this ternary material is shown to be smaller than that in the KC8 binary compound despite a more favorable stoichiometry ratio between K and C.     

Electrophoresis of a spherical particle along the axis of a cylindrical pore: effect of electroosmotic flow

The electrophoresis of a spherical particle along the axis of a cylindrical pore is investigated under conditions of low surface potential and thick double layer. In particular, the effect of electroosmotic flow is taken into account. The results of numerical simulation reveal that if both particle and pore are positively charged, the variation of the mobility of a particle may have a local minimum as the thickness of the double layer varies, which is not reported in the literature. This is mainly due to the charge induced on the particle surface, which arises from the presence of the charged boundary. Depending upon the level of the surface potential of the pore, the presence of the local minima may lead to a reversal in the direction of particle movement as the thickness of the double layer surrounding it varies: if the surface potential is either too low or too high, reversal does not occur; if it has a medium level, reversal occurs twice. This interesting observation can play a role in electrophoresis measurements. Previous analysis predicts that reversal always occurs once, regardless of the level of the surface potential of the pore.     

Quantum yield of photoenhanced currents in crystalline tetracene

A study of photoenhanced currents (PEC) in crystalline tetracene has been made. Using the well-established theory of space-charge controlled currents in insulators, it is shown that the quantum yield for the release of trapped carriers by triplet excitons is less than unity.     

Surface excess free energy of simple fluids confined in cylindrical pores by isothermal-isobaric Monte Carlo: influence of pore size

Confined fluid properties are mainly determined by interfacial phenomena characterized by surface quantities. Based on a simple model of Lennard-Jones particles confined in a cylindrical pore, this study introduces a grand potential surface quantity to quantify the difference in the thermodynamic pressure between the bulk and the confined fluids. The usual surface tension gamma defined as this grand potential difference for the same chemical potential in both confined and bulk states is generally strongly dependent on both the chemical potential and temperature. It is proposed here to introduce another surface quantity zeta which measures the thermodynamic pressure difference between confined and bulk states for identical densities. It is shown that this quantity is much less dependent on confined fluid density or chemical potential. It is actually constant along the gas-like and liquid-like adsorption/desorption branches for an irreversible isotherm (hysteresis), with a different value for each branch. For reversible supercritical isotherms, zeta is shown to remain constant in the low and high density parts of the isotherm. This independence on chemical potential (or equivalently fluid density) is believed to be of great interest for practical applications when one desires to calculate thermodynamic quantities such as the usual surface tension gamma or the thermodynamic pressure of a confined fluid for any given chemical potential and temperature. Such calculations are required to determine fundamental properties such as metastability or coexistence. The effects of temperature, fluid/substrate interaction strength, and pore size are studied.     

Density-scaling and the Prigogine-Defay ratio in liquids

The term "strongly correlating liquids" refers to materials exhibiting near proportionality of fluctuations in the potential energy and the virial pressure, as seen in molecular dynamics simulations of liquids whose interactions are comprised primarily of van der Waals forces. Recently it was proposed that the Prigogine-Defay ratio, Π, of strongly correlating liquids should fall close to unity. We verify this prediction herein by showing that the degree to which relaxation times are a function T/ρ(γ), the ratio of temperature to density with the latter raised to a material constant (a property inherent to strongly correlating liquids) is reflected in values of Π closer to unity. We also show that the dynamics of strongly correlating liquids are governed more by density than by temperature. Thus, while Π may never strictly equal 1 for the glass transition, it is approximately unity for many materials, and thus can serve as a predictor of other dynamic behavior. For example, Π ? 1 is indicative of additional control parameters besides T/ρ(γ).     

Effect of formation temperature and roughness on surface potential of octadecyltrichlorosilane self-assembled monolayer on silicon surfaces

Kelvin probe force microscopy (KPFM) and atomic force microscopy (AFM) are employed to probe the surface potential and topography of octadecyltrichlorosilane [OTS, CH3(CH2)17SiCl3] self-assembled monolayers (SAMs) on oxidized Si(100) and polycrystalline silicon surfaces as a function of deposition temperature and substrate roughness with particular attention paid to the monitoring of SAM adsorption on highly rough surfaces. In these studies, it is found that the surface potential magnitude of the adsorbed layer is larger for monolayers formed in the liquid-condensed (LC) phase than for those formed in the liquid-expanded (LE) phase. Experiments on individual islands in the LC phase show that surface potential and monolayer thickness increase with increasing island size; islands larger than about 1.5 microm reach maximum potential and height values of 48+/-4 mV and 2.7+/-0.1 nm, with respect to the underlying oxidized surface. It is also shown that KPFM is suitable for the study of monolayer adsorption on polycrystalline surfaces, for which preexisting surface texture makes the use of traditional scanning probe techniques for molecular recognition difficult. In these scenarios it is shown that OTS growth occurs preferentially along grain boundaries in fingerlike patterns having a molecular arrangement comparable to that of LC phase islands on atomically smooth silicon. These findings indicate that surface potential measurements provide a highly accurate, local means of probing monolayer morphology on rough surfaces encountered in many applications.     

Selectivity effects and hydrocarbon-chain growth during Fischer–Tropsch synthesis

It is well known that if the formation of hydrocarbons during Fischer–Tropsch synthesis occurs via the condensation polymerization mechanism, there is little hope for selectivity enhancement in the desired range of products. Recent data on low surface area model catalysts, where readsorption is unlikely, have shown that at low conversions, the product distribution obeys the condensation polymerization mechanism and the distribution of products is shifted to lower-molecular-weight hydrocarbons. We have used a computer simulation of the growth of hydrocarbon chains to obtain a picture of the catalyst surface under synthesis conditions. Such an approach could prove useful in distinguishing between various theoretical models. We have applied the simulation to compare the changes in selectivity when readsorption occurs and when it does not. The dynamic behavior of the reacting system which is obtained from the computer results has shown that selectivity to lower-molecular-weight hydrocarbons is a stronger function of the extent of reaction than the incorporation of readsorption into the chain growth mechanism.     

Near-quantitative internal quantum efficiency in a light-emitting electrochemical cell

A green-light-emitting iridium(III) complex was prepared that has a photoluminescence quantum yield in a thin-film configuration of almost unity. When used in a simple solid-state single-layer light-emitting electrochemical cell, it yielded an external quantum efficiency of nearly 15% and a power efficiency of 38 Lm/W. We argue that these high external efficiencies are only possible if near-quantitative internal electron-to-photon conversion occurs. This shows that the limiting factor for the efficiency of these devices is the photoluminescence quantum yield in a solid film configuration. The observed efficiencies show the prospect of these simple electroluminescent devices for lighting and signage applications.     

Fundamental global model for the structures and energetics of nanocrystalline ionic solids

This paper presents a general theory elucidating the relationships between the structures and cohesive energetics of alkali halide nanocrystals consisting of small sections of bulk rocksalt structures with m(1) and m(2) rows but infinite along the z axis. The theory introduces the electrostatic interactions between the ions treated as point charges and the short-range repulsions between the closest ion neighbors with the latter terms written in the Born form Ar(-)(n). Minimum energy structures are defined by the distances a(e) and b(e) separating the closest ions perpendicular and parallel to the z direction. The ratio a(e)/b(e), defining the crystal shape, is independent of the strength A of the short-range repulsion, greater than the bulk value of unity, and increases with decrease of the crystal cross section or n. This ratio tends toward unity in the hard sphere limit of infinite n. Both b(e)/R(6:6)(e) and a(e)/R(6:6)(e), with the bulk separation R(6:6)(e), are less than one, increase with increase of the crystal cross section or n, and are independent of A if this is independent of structure. The structural dependence of A increases its value with a decreasing crystal cross section rendering closer to unity the ratios a(e)/b(e), b(e)/R(6:6)(e), and a(e)/R(6:6)(e). Energy gains on relaxing the crystal toward equilibrium from its bulk separations decrease with increase of the crystal cross section or n, being about 60 kJ/mol for a one-dimensional chain with n = 6 but 0.5 kJ/mol for m(1) = m(2) = 4 with n = 12. The energy gained on relaxing to a structure with a(e)/b(e) constrained at unity is about 10 times greater than the further energy gains consequent on removing this constraint. The present theory neglecting the interaction between ions and the encapsulating nanotube explains the experimentally measured b(e)/R(6:6)(e) ratios. The observation that the a(e)/R(6:6)(e) values are greater than one shows that ion-wall interactions are important in determining the values of a(e).     

Effect of pH on the electrophoretic mobility of a particle with a charge-regulated membrane in a general electrolyte solution

The electrophoretic motion of an entity comprised of a rigid, uncharged core covered by a charge-regulated membrane which simulates a biological cell, in a general a:b electrolyte solution is analyzed. The membrane carries a fixed charge which arises from the dissociation of the acidic functional group HA. We show that the higher the concentration of cations in the bulk liquid phase, the lower the absolute Donnan potential, _D, and the lower the concentration of functional group, N₀, the lower the _D. Also, the higher the pH, the higher the absolute electrical potential, and the greater the N₀, the lower the pH. The absolute mobility of a cell, μ, increases with pH, but decreases with the increase in the friction coefficient of the membrane phase, γ. For a fixed total number of HA, if γ is large, μ/μ_s is less than unity, μ_s being the mobility of the corresponding rigid particle, and it decreases with the thickness of membrane d, and the inverse is true if γ is small. For a medium γ, the variation of μ/μ_s as a function of d has a local maximum, and depending upon d, it can be either greater or less than unity.     

Interaction between an ion-penetrable particle and a solid particle. 1. Electrical double-layer interaction

Expressions are derived for the force and potential energy of the electrical double layer interaction between two parallel plates of different nature, i. e., an ion-penetrable plate and an ion-impenetrable plate. The latter may have either constant surface potential or constant surface charge density. It is shown that when the ion-impenetrable plate has a constant surface potential, the interaction force may, under certain conditions, become attractive even if the surface potentials of the two plates at infinite separation are of the same sign. In contrast, when the ion-impenetrable plate has a constant surface charge density, the interaction force may, under certain conditions, become repulsive even if the two plates at infinite separation are of opposite sign. This means that an ion-penetrable plate shows a dual behavior. That is, under certain conditions, it behaves like a solid plate with constant surface potential or surface charge density, depending on whether it interacts with a solid plate having a constant surface potential or a constant surface charge density.     

Melt crystallized polyamide 6.6 and its copolymers, Part II. Crystallization mechanisms in the homopolymer

The crystallization kinetics of polyamide 66 have been studied using polarized optical microscopy. The growth rate data for positively birefringent spherulites in polyamide 66 show a distinct change of slope, which would be identified as a regime I/II transition based on secondary nucleation theory. However, recent data for the same specimens crystallized isothermally, from small angle X-ray scattering found the lamellar thickness to be constant at approximately 2.0 chemical repeat units, but with an internal crystalline core and a substantial innerlayer. The crystal core increases in size to 2 chemical repeat units with both time and temperature at the expense of the inner layer. This evidence is totally inconsistent with secondary nucleation theory, where a lamellar thickness which varies significantly with supercooling is an integral part of the derivations.A calculation of the dimensions of the critical nucleus is reported here, using surface free energies, which found it to be impossibly large at a value between 14 and 360 stems in size, further suggesting that another crystallization mechanism is operating. Calculations of the surface free energy of the hydrogen-bonded surface suggest that it is the high energy surface, rather than the folded surface, which normally occurs as the high energy surface in polymers. As the high energy surface, the hydrogen-bonded surface would be expected to be the growth face, as occurs in non-polymeric materials. An earlier model of Lovinger, which placed the fold direction into the melt, generating a rough surface, is consistent with these results.It is suggested that crystallization in polyamide 66, if not in all polyamides, occurs through a surface roughening mode of growth. This is a natural consequence of the presence of H-bonding in the direction of growth. In one sense, polyamide 66 is conventional in its growth behavior, relative to non-polymeric materials, as the growth face is the highest energy surface. As such, the lamellar thickness would no longer be a morphological variable related to the supercooling in any direct way as an essential part of any crystallization theory for polymers. Such behavior is impossible in other polymeric systems as the fold surface is the highest energy surface and the presence of folds prohibits growth on that surface. However, models of surface roughening, which were developed as an alternative explanation for the behavior of, principally, polyethylene, predict the conventional lamellar thickness - supercooling relation to exist, which is inconsistent with the observed existence of a constant lamellar thickness with variable crystal core dimensions.It is suggested that polyamide 66 be taken as a paradigm for a different kind of polymer crystallization than that normally encountered. That is crystallization in which the growth face is the highest energy surface, not the folded chain surface, having much in common with the behavior of non-polymeric materials. The energetic changes occurring in this case, however, are governed by a combination of entropic and enthalpic barriers to crystallization, rather than being dominated by enthalpic considerations, as in metals. This is a direct result of the entropic effects of the long chain nature of polymers combined with the enthalpic effects of the hydrogen-bonding.     

Electrokinetic flow through an elliptical microchannel: effects of aspect ratio and electrical boundary conditions

The electrokinetic flow of an electrolyte solution through an elliptical microchannel is studied theoretically. The system under consideration simulates the flow of a fluid, for example, in vein. We show that, for a constant cross-sectional area, both the electroosmotic volumetric flow rate and the streaming potential increase monotonically with an increase in the aspect ratio, and both the total electric current and the electroviscous effect may exhibit a local minimum as the aspect ratio varies. Also, for a constant average potential on the channel wall, the difference between the results based on three kinds of boundary conditions, which include constant surface charge, constant surface potential, and charge-regulated surface, is inappreciable if the hydraulic diameter is larger than 1 mum.     

Criteria for diffusion limitation in coordination polymerization

The following criteria are proposed to judge whether a coordination polymerization may be diffusion controlled or not: (1) If the number-average molecular weight and polydispersity of the polymer calculated from kinetic rate constants as a function of time agree with the experimental values, the polymerization is not diffusion controlled. (2) The polymerization may be diffusion controlled if the Thiele modulus, the ratio of the characteristic diffusion time to the characteristic reaction time, is much greater than unity; if it is much smaller than unity, the polymerization is reaction controlled. (3) If an initial linear dependence of rate of polymerization on catalyst concentration changes over to a square-root dependence, the polymerization may be diffusion limited. (4) The polymerization is likely to be diffusion limited if the instantaneous rate of polymerization is proportional to the rate of particle growth when the proportionality coefficient is the surface area of the particle. Criterion (1) is a necessary and sufficient condition as stated, as its converse is not true. All the other criteria are merely necessary but not sufficient conditions. The established Ziegler–Natta catalysts have activities too low to cause diffusion limitation; the Phillips catalyst system is likely to be diffusion limited. The polydispersity of polyolefins produced with Ziegler–Natta catalysts are not the consequence of diffusion control but are the characteristics of the catalysts in their kinetics of initiation, propagation, chain transfer, and termination.     

Thermodynamics of epitaxial calcite nucleation on self-assembled monolayers

Classical heterogeneous nucleation theory is used to describe the epitaxial nucleation of calcite on self-assembled monolayers (SAMs). Both spherical and faceted clusters are considered. The use of faceted clusters reveals a useful relation between the shape of very small crystals and the ratio of the heterogeneous and homogeneous nucleation barriers. The experimental approach of this paper concerns the measurement of the threshold driving forces for both homogeneous and heterogeneous nucleation of calcite. This is accomplished by preparing solutions with well-defined driving forces and by measuring the resulting types of nucleation that are observed after a fixed experimental time. The results of the experiments and the theoretical shape analysis are compared, and it is shown that in the experiments no homogeneous nucleation of calcite occurs for driving forces up to at least Deltamu/k(B)T approximately equal to 6.0. A calculation of the critical cluster size for heterogeneous nucleation results in a range of 2-28 growth units and faceted critical clusters from 3-28 growth units, depending on the value of the surface free energy of calcite. These sizes are 50-100 times smaller than the crystalline domain sizes of SAMs and therefore small enough to explain the promoting effect of the substrate.     

Thermodynamic pressure of simple fluids confined in cylindrical nanopores by isothermal-isobaric Monte Carlo: influence of fluid/substrate interactions

The thermodynamic pressure or grand potential density is calculated by isobaric-isothermal Monte Carlo algorithm for simple Lennard-Jones fluid confined in cylindrical pores presenting chemical heterogeneities along their axis. Heuristic arguments and simulation results show that the thermodynamic pressure of the confined fluid contains two contributions. The first term is the usual pressure of the bulk fluid for a density equal to the confined fluid density defined as the total number of confined particles divided by the accessible volume due to thermal agitation. A second term has to be added, which is empirically shown to be proportional to the fluid/wall interface area and almost constant along the adsorption and desorption branches. This interfacial contribution, calculated for various pore models, has small variations reminiscent of the fluid adsorption/desorption properties calculated in the various pores. In particular, it is shown that this interfacial quantity is maximum for a fluid/substrate interaction intensity of the same order as the fluid/fluid one, while the thermodynamic pressure at which rapid desorption occurs presents a minimum. Stronger or weaker fluid/wall affinity favors gas state nucleation on the desorption of confined fluids.