Electrokinetics of diffuse soft interfaces. 1. Limit of low Donnan potentials

The current theoretical approaches to electrokinetics of gels or polyelectrolyte layers are based on the assumption that the position of the very interface between the aqueous medium and the gel phase is well defined. Within this assumption, spatial profiles for the volume fraction of polymer segments (phi), the density of fixed charges in the porous layer (rho fix), and the coefficient modeling the friction to hydrodynamic flow (k) follow a step-function. In reality, the "fuzzy" nature of the charged soft layer is intrinsically incompatible with the concept of a sharp interface and therefore necessarily calls for more detailed spatial representations for phi, rho fix, and k. In this paper, the notion of diffuse interface is introduced. For the sake of illustration, linear spatial distributions for phi and rho fix are considered in the interfacial zone between the bulk of the porous charged layer and the bulk electrolyte solution. The corresponding distribution for k is inferred from the Brinkman equation, which for low phi reduces to Stokes' equation. Linear electrostatics, hydrodynamics, and electroosmosis issues are analytically solved within the context of streaming current and streaming potential of charged surface layers in a thin-layer cell. The hydrodynamic analysis clearly demonstrates the physical incorrectness of the concept of a discrete slip plane for diffuse interfaces. For moderate to low electrolyte concentrations and nanoscale spatial transition of phi from zero (bulk electrolyte) to phi o (bulk gel), the electrokinetic properties of the soft layer as predicted by the theory considerably deviate from those calculated on the basis of the discontinuous approximation by Ohshima.     

Series approach to modeling ion size effects for asymmetric electrolytes in the diffuse double layer

The theory of the diffuse layer for asymmetric electrolytes is reconsidered with emphasis on the effects of ion size on the diffuse layer potential drop and differential capacity. For asymmetric 2:1 and 1:2 electrolytes, this potential drop is expressed in terms of a polynomial with a linear, quadratic, and cubic term in the corresponding estimate in the Gouy-Chapman theory. Optimal polynomial coefficients and model validation for 2:1 electrolytes are provided by least-squares regression of Monte Carlo data obtained for a restricted electrolyte in a primitive solvent. These coefficients are then expressed as simple functions of the parameters commonly associated with the mean spherical approximation. The series approach accurately describes potential drops and differential capacities of the diffuse layer for 2:1 and 1:2 electrolytes for the chosen assumptions.     

Series approach to modeling ion size effects for symmetric electrolytes in the diffuse double layer

An analytical model is developed for the potential drop and differential capacity across the diffuse layer which considers the effects of ion size on these properties. For symmetric electrolytes, this potential drop is expressed in terms of a cubic polynomial in the corresponding estimate in the Gouy-Chapman theory. Optimal polynomial coefficients and model validation for 1:1 and 2:2 electrolytes are provided by fits of Monte Carlo data obtained for a restricted electrolyte in a primitive solvent. Simple relationships between these coefficients and parameters commonly associated with the mean spherical approximation are obtained. It is shown that the series approach accurately describes potential drops and differential capacities of the diffuse layer for 1:1 and 2:2 electrolytes for the chosen assumptions.     

Electrophoretic Mobility of Soft Particles in Concentrated Suspensions

A general theory is developed for the electrophoretic mobility of spherical soft particles (i.e., spherical hard colloidal particles of radius a coated with a layer of polyelectrolytes of thickness d) in concentrated suspensions in an electrolyte solution as a function of the particle volume fraction φ on the basis of Kuwabara's cell model. In the limit d-->0, the mobility expression obtained tends to that for spherical hard particles in concentrated suspensions, whereas in the limit a-->0, it becomes that for spherical polyelectrolytes (charged porous spheres with no particle core). Simple approximate analytic mobility expressions are derived for the case where relaxation effect is negligible. It is found that in practical cases, the φ dependence of the mobility is negligible for da, the mobility strongly decreases with increasing φ. Copyright 2000 Academic Press.     

Intercalation mechanism and interlayer structure of hexadecylamines in the confined space of layered alpha-zirconium phosphates

Well-defined hexadecylamine (HDA) intercalated structures, either interdigitated layers, bilayers, or hybrid layers of both, in a confined space of highly functionalized layered alpha-zirconium phosphates (alpha-ZrPs) have been prepared based on the two-step intercalation mechanism and these distinct intercalated structures can serve as a model system to investigate the interactions of two monolayers whose amphiphilic tails are adjacent to each other. At the first intercalation step, the electrostatic interaction between HDAs and alpha-ZrP is dominant and results in an interdigitated layer structure (d(001) = 3.0 nm) and the interdigitated layer is saturated at around phi = 50%, where phi is the weight fraction of intercalated HDAs in the intergallery of alpha-ZrP. For phi higher than 50%, the bilayer structure (d(001) = 4.3 nm) emerges due to further hydrophobic interaction between HDAs initially grafted to alpha-ZrP and unanchored HDAs and the relative fraction of the bilayer structure over the interdigitated layer increases with the increase in the intercalated amount of HDAs. The intriguing morphology of alpha-ZrP tactoids intercalated with HDAs in coexisting bilayers and interdigitated layers is observed by using microtomed TEM and the two-step intercalation has also been verified with TGA and FT-IR. Also, a structural transition from the bilayers to the interdigitated layers is monitored by using in situ synchrotron WAXS showing that the hydrophobically intercalated HDAs are selectively deintercalated at a relatively low decomposition temperature around 220 degrees C.     

Dependence of the dielectric properties of suspensions on the volume fraction of suspended particles

It is shown that the fundamental expression for the complex permittivity epsilons* of a dilute suspension of monodispersed, spherical particles, epsilons*=epsilone*(1+3phid*), where epsilone* is the complex permittivity of the suspending medium and d* the dipolar coefficient, is strictly valid for any value of the volume fraction phi of particles in the suspension, provided that d* is interpreted as the ensemble average value of the dipolar coefficient of the particles and is defined in terms of the macroscopic electric field in the suspension.     

Augmented Gaussian basis set of quintuple zeta valence quality for H and from Li to Ar: Applications in DFT calculations of molecular electric properties

Augmented Gaussian basis set of quintuple zeta valence quality plus polarization functions (A5ZP) for H and Li–Ar is presented. It was determined from the 5ZP basis set by addition of diffuse (s and p symmetries) and polarization (p, d, f, g, and h symmetries) functions that were optimized for the anion at the Hartree–Fock and Mller–Plesset second-order levels, respectively. It was shown that in general this basis set in combination with the density functional theory can be used with success to predict electric properties for a sample of molecules. Comparison with theoretical and experimental values available in the literature is done.     

The conditions governing the specific adsorption of counter-ions in the interaction of two parallel plate-like colloidal particles

Frens and Overbeek have proposed that during the Brownian collision of two colloidal particles in a hydrophobic sol, the surface charge density due to potential-determining (p.d.) ions remains virtually unchanged. It is argued here that the cause of this behaviour is the low concentration of p.d. ions in the diffuse layer. However, equilibrium can be maintained with respect to counter-ions adsorbed into the Stern region from the supporting electrolyte, because the concentration of such electrolyte in the dispersion medium is considerably greater than that of p.d. ions.A general expression is quoted from earlier work for the electric double layer interaction between two parallel plate-like particles in the case where surface charge due to p.d. ions is fixed, but where counter-ions adsorbed into the Stern region can equilibrate with ions of the same species in the diffuse layer. Incorporating discreteness-of-charge and ion-size effects into the adsorption isotherm of the counter-ions, the double layer interaction energy of the two plates is calculated at contact of the two outer Helmholtz planes (o.h.p.'s). It is shown that although this energy exceeds the classical expression obtained by assuming the potential at the o.h.p. to be independent of plate separation, it remains finite.     

Spin contamination for Hartree-Fock, optimized effective potential, and density functional approximations

In an earlier paper [S. Thanos and A. K. Theophilou J. Chem. Phys. 124, 204109 (2006)], we found an explicit formula for the expansion of a Slater determinant |Phi(M)> in terms of eigenstates of S(2). In this paper, we use the same formula to determine the spin contamination S(con) of the unrestricted single determinant approximations, i.e., Hartree-Fock, optimized effective potential, and density functional theory. We derived an expression which gives S(con) in terms of the overlap of the spatial parts of the spin up and spin down "corresponding" orbitals. It was found that S(con) does not depend on M, the eigenvalue of S(z), at least for the lower order approximations, i.e., when || is large. In this case, the predominant coefficient of the expansion assumes its maximum value when S=M. However, for the class of solutions that || is small, the spin L of the largest coefficient increases with the number of unpaired electrons. We also derived the explicit form of the expansion states.     

Chlorination-methylation of the hydrogen-terminated silicon(111) surface can induce a stacking fault in the presence of etch pits

Recently, we reported STM images of the methylated Si(111) surface [prepared through chlorination-alkylation of the Si(111)-H surface] taken at 4.7 K, indicating that the torsion angle of the methyl group with respect to the subsurface silicon layer is phi = 23 +/- 3 degrees . Repulsions between H atoms in adjacent methyl groups are minimized at 30 degrees , while repulsions between H atoms and second layer Si atoms are minimized at 60 degrees . The experimental result of 23 degrees is surprising because it suggests a tendency of the methyl group toward the eclipsed configuration (0 degrees ) rather than staggered (60 degrees ). In contrast, extensive fully periodic quantum mechanical Density Functional Theory studies of this surface give an equilibrium torsion angle of 37.5 degrees , indicating a tendency toward the staggered configuration. This discrepancy can be resolved by showing that the CH3 on the step edges and etch pits interacts repulsively with the CH3 on the surface terraces unless a stacking fault is introduced between the first and second silicon layers of the Si(111)-CH3 surface terraces. We propose that this could occur during the chlorination-alkylation of the Si(111)-H surface. This stacking fault model predicted phi = 22.5 degrees measured with respect to the bulk (corresponding to phi = 37.5 degrees with respect to the second layer Si atoms). This model can be tested by measuring the orientation of the CH3 within the etch pits, which should have phi = 37.5 degrees , or by making a surface without etch pits, which should have phi = 37.5 degrees .     

Retention factor and retention index of homologous series compounds in microemulsion electrokinetic chromatography employing suppressed electroosmosis

The retention factor (k) and retention index (I) of homologous series compounds such as alkylbenzenes (BZ), alkylaryl ketones, alkylbenzoates, and alkylparabens in microemulsion electrokinetic chromatography (MEEKC) with suppressed electroosmosis were investigated in a wide range of SDS concentrations ([SDS]), temperatures, and concentrations of organic cosolvents (phi). Using BZ as standards, the retention indices of other homologous series compounds were determined and they were found to be independent of [SDS] and temperature, while are dependent on the types and concentrations of organic cosolvents. The retention factor linearly increases with increasing [SDS], while linearly decreases with increasing temperature. The value of log k linearly decreases with increasing phi for methanol, ethanol, or ACN, while decreases by a second-degree polynomial with increasing phi for 2-propanol. Excellent agreement was found between the observed and predicted values of log k of analytes in MEEKC at given [SDS] and phi, where the predicted values were obtained from modified equations of the linear relationship of log k as functions of [SDS], the number of carbons, and phi. Therefore, both k and I can be used for peak identification of homologous series compounds.     

Preparation of highly concentrated nanostructured dispersions of controlled size

This article presents the use of a shearing procedure for the preparation of stable nanostructured dispersions of lipid mesophases. This new application of the shearing technique is compared with the well-established ultrasonication method for the emulsification of these mesophases in water in terms of particle size, particle size distribution and available concentration range. With a laboratory-built shear device based on a Couette cell, it was possible to produce high quantities of internally self-assembled emulsion particles of controlled size at concentrated hydrophobic phase contents (_o) of up to 70 wt%. The concentration limit of 70 wt% could be reached however, the maximum attainable concentration depended on the internal structure type of the particles. The limit was thus easily attained for emulsified microemulsions (EME) as well as for the emulsified inverse hexagonal phase (H₂), whereas it was found to be lower for emulsified discontinuous (Fd3m) and bicontinuous (Pn3m) cubic phases. Moreover, by shearing, it was possible to keep the size of the particles relatively constant when increasing _o, whereas the particle size significantly increased with _o when ultrasonication was employed. By means of ultrasonication, the hydrodynamic radius of the particles could be tuned linearly between 85 to 180 nm as a function of _o up to a maximum of 20 to 30 wt%. Below the maximum concentration limit, particles displayed a well-controlled size.     

Critical phenomenon of nonaqueous microemulsion (AOT/DMA/decane)

The critical phenomenon of nonaqueous microemulsion was studied for the first time. The coexistence curves of (T,n), (T,phi), and (T,psi) (n and phi are refractive index and volume fraction, respectively; psi is defined as psi=phi/[phi+phi(c)(1-phi)/(1-phi(c))]) for a ternary microemulsion [phi (AOT-DMA)+(1-phi) decane] at constant pressure and a constant molar ratio (omega=2.86) of DMA to AOT have been determined within about 7 K from the critical temperature T(c) by measurements of refractive index. The critical exponent beta has been deduced from (T,n), (T,phi), and (T,psi) coexistence curves within 1 K below T(c). They all were 0.329+/-0.005 and were consistent with the 3D Ising value. The experimental results in a temperature range of (T(c)-T)<7 K also have been analyzed to obtain critical amplitudes and the Wegner correction terms, to examine the diameters of the coexistence curves.     

Application of the hypernetted chain approximation to the electrical double layer for 2:1 and 1:2 electrolytes

The equations needed to estimate the potential drop across the diffuse layer according to the hypernetted chain approximation (HNCA) are derived in this paper for 2:1 and 1:2 electrolytes at the restricted primitive level. It is shown that HNCA results can be expressed in the same format as the corresponding Gouy-Chapman equations with inclusion of two modifying functions. One function depends on the fraction of the solution volume occupied by the ions, and the other depends on the reciprocal thickness of the ionic atmosphere surrounding each ion. In addition, an expression for the potential profile in the diffuse layer for 2:1 and 1:2 electrolyte solutions is derived according to Gouy-Chapman theory. The modifying functions in the HNCA are then estimated using the Henderson-Blum approach for solutions containing ions with diameters of 300 and 400 pm for concentrations in the range from 0.1 to 2 M. It is shown that the Henderson-Blum approach is inadequate for systems with multivalent ions except for charge densities very close to the point of zero charge.     

Coulson function and Hosoya index: extension of the relationship to polycyclic graphs and to new types of matching polynomials

Gutman et al. [Chem. Phys. Lett. 355 (2002) 378–382] established a relationship between the Coulson function, , where \phi is the characteristic polynomial, and the Hosoya index Z, which is the sum over all k of the counts of all k-matchings. Like the original Coulson function, this relationship was postulated only for trees. The present study shows that the relationship can be extended to (poly)cyclic graphs by substituting the matching, or acyclic, polynomial for the characteristic polynomial. In addition, the relationship is extended to new types of matching polynomials that match cycles larger than edges (2-cyc1es). Finally, this presentation demonstrates a rigorous mathematical relationship between the graph adjacency matrices and the coefficients of these polynomials and describes computational algorithms for calculating them.     

Dynamic Mobility of Particles with Thick Double Layers in a Nondilute Suspension

The dynamic mobility of a nondilute suspension of spherical particles is investigated in the case where the thickness of the electrical double layer around each particle is comparable to the particle radius. A formula is obtained for the O(φ) correction in a random suspension of particles with volume fraction φ, involving an integral over the dynamic mobility of a pair of spheres. This formula is then evaluated using both analytical approximations and numerical results previously obtained for the pair mobilities and valid for low surface potentials. The effect of double-layer thickness on the O(φ) coefficient is most pronounced at low frequencies, and lessens once the hydrodynamic penetration depth is smaller than the particle radius. Various approximations are considered that use the O(φ) result to predict the dynamic mobility in concentrated suspensions, and at high frequencies these approximations are shown to give results qualitatively different from those of recent cell models. Copyright 2000 Academic Press.     

Adsorption behavior of oxyethylated surfactants at the air/water interface

The low-shear viscosity eta(0) of colloidal suspensions of acrylic latex or silica in aqueous gelatin has been measured at a temperature above the sol-gel transition. Measurements were made on dilution of a concentrated suspension with water or a gelatin solution. Thus, either the gelatin : colloid ratio was maintained or it was varied at constant aqueous gelatin concentration. Systems were studied with four lime-processed gelatins of different molecular weights at two concentrations of added salt. In addition, the latex particle size and the thickness of the adsorbed gelatin layer were measured by photon correlation spectroscopy (PCS) under dilute conditions. The dependence of the low-shear viscosity eta(0) on particle concentration was exponential and did not follow the well-established Krieger-Dougherty model for simple hard-sphere suspensions over the concentration range studied. A simple phenomenological model, eta(0)=eta(o)10(phi(e)/phi(s)), was found to predict the behavior well. Here, eta(o) is the viscosity of a gelatin solution of the corresponding solution concentration, phi(e) is proportional to the volume fraction of the particles, and phi(s) is a scaling factor, which was determined to have a value of 0.85. With this value of phi(s), the dimensions determined from PCS could be used to predict the viscosity values.     

Novel BrФnsted Acidic Ionic Liquid Based on a Cyclic Guanidinium Cation： a Green, Efficient, and Recyclable Dual Slovent-catalyst System for Fisher Esterification

A novel Brфnsted acidic ionic liquid(IL)based on the cyclic guanidinium cation has been synthesized.This IL,as a strong Brфnsted acid catalyst or solvent,shows high catalytic activity and biphsaic behavor in the esterifications of carboxylic acids and alcohols.The produced esters as a separate phase can be conveniently decanted out from the IL and the IL is recyclable without any loss of catalytic activity.     

Static electrification of solid oxide in liquid metal and electrical double layer at the interface

Static electrification of a solid oxide, say a semiconducting oxide in liquid metal, is mainly due to electron transfer between two phases. Excess electrons in the liquid metal phase provided by the oxide give rise to an electrical double layer at the interface. The electrical double layer may be divided into three parts, an immobile inner layer, a compressed diffuse layer, and a flat layer extending into the bulk liquid metal. Differential potential analysis and the induced emf method were used to measure the potential of the compressed diffuse layer and the excess electron density of the flat layer, respectively. Results show that most oxides in liquid metals carry positive charges on their surfaces and the potentials of the compressed diffuse layer are in the range of 3 to 42 microV. Such a low potential implies that the diffuse layer is considerably compressed. The excess electron densities of the flat layer are on the order of 10(22) electrons/m(3) of Hg and their contributions to surface charges of oxide are in the range of 10(17) to 10(18) charges/m(2) for the oxide/mercury systems with a solid density of 0.3 wt% at room temperature.