Nano‐scaled intrachain ordering and dynamics in two‐dimensional orientational polymer domains1)

Statistical and local relaxation properties of two‐dimensional finite polymer systems (domains) are considered. The domains consist of a large number of semirigid chains with the finite contour length at free, half‐free and fixed boundary conditions for chain ends. The intermolecular orientational order at short distances between chains in the thick domains is similar to the order in infinite two‐dimensional systems. The correlations of orientation between sufficiently distant elements of different chains decay by the exponential law, but the effective constant of interchain interactions in the domain is proportional to the molecular weight of the chain. At the given intra‐and interchain interactions an elongtation of the chains leads to a local ordering of chains in the domain (at free boundary conditions) or, on the contrary, to the decreasing of the parameter of short‐range orientational order (at fixed and half‐free boundary conditions). Independently of type of boundary conditions the parameter of large‐range orientational order tends to zero with increasing of the chain contour length. Dynamical equations and relaxation spectrums for times of local motions are obtained. From time correlation functions of local relaxation the times of nano‐scaled mobility of chains were calculated in depending on the bending rigidity of chains, the parameter of interchain interactions, and the contour length of chains. At the given intra‐and interchain interactions an elongtation of chains forming the domain leads to to the slowing‐down of local mobility of chains in the domain. The comparison with experimental date obtained by dielectric relaxation and polarized luminescence methods on investigation of nano‐scaled mobility in the dilute melts of comb‐shaped polymers has been carried out.     

Thermal Marangoni Convection of a Fluid Film Coating a Deformable Membrane

The thermal Marangoni instability of a fluid film coating a deformable membrane has been investigated by taking into account the deformation of the fluid free surface. Numerical calculations for different thermal boundary conditions are presented. The prestressed membrane is supposed to be very thin and therefore its behavior is similar to that of an isothermal fluid free surface with a surface tension but with a different mechanical boundary condition; that is, the fluid should stick on its surface and thus the fluid velocity is zero. An important assumption is that the membrane has no temperature dependence and therefore that only one Marangoni number exists for the free surface of the fluid. Numerical results are presented for stationary and oscillatory thermocapillary instability in both the sinuous and the varicose modes. It is shown that membrane deformation has important implications on the Marangoni instability of the fluid layer for positive and negative Marangoni numbers. Copyright 2001 Academic Press.     

Use of a cell model for the evaluation of the dynamic mobility of spherical silica suspensions

In this paper we evaluate the validity of a cell model for the calculation of the dynamic mobility of concentrated suspensions of spheres. The key point is the consideration of the boundary conditions (electrical and hydrodynamic) at the boundary of the fluid cell surrounding a single probe particle. The model proposed is based on a universal criterion for the averages of fluid velocity, electric potential, pressure field or electrochemical properties in the cell. The calculations are checked against a wide set of experimental data on the dynamic mobility of silica suspensions with two different radii, several ionic strengths, and two particle concentrations. The comparison reveals an excellent agreement between theory and experiment, and the model appears to be extremely suitable for correctly predicting the behavior of the dynamic mobility, including the changes in the zeta potential, zeta, with ionic strength, the frequency and amplitude of the Maxwell-Wagner-O'Konski relaxation, and the inertial relaxation occurring at the top of the frequency range accessible to our experimental device.     

Influence of cell-model boundary conditions on the conductivity and electrophoretic mobility of concentrated suspensions

In the last few years, different theoretical models and analytical approximations have been developed addressing the problem of the electrical conductivity of a concentrated colloidal suspension. Most of them are based on the cell model concept, and coincide in using Kuwabara's hydrodynamic boundary conditions, but there are different possible approaches to the electrostatic boundary conditions. We will call them Levine-Neale's (LN, they are Neumann type, that is they specify the gradient of the electrical potential at the boundary), and Shilov-Zharkikh's (SZ, Dirichlet type). The important point in our paper is that we show by direct numerical calculation that both approaches lead to identical evaluations of the conductivity of the suspensions if each of them is associated to its corresponding evaluation of the macroscopic electric field. The same agreement between the two calculations is reached for the case of electrophoretic mobility. Interestingly, there is no way to reach such identity if two possible choices are considered for the boundary conditions imposed to the field-induced perturbations in ionic concentrations on the cell boundary (r = b), deltan(i) (r = b). It is demonstrated that the conditions deltan(i)(b) = 0 lead to consistently larger conductivities and mobilities. A qualitative explanation is offered to this fact, based on the plausibility of counter-ion diffusion fluxes favoring both the electrical conduction and the motion of the particles.     

A new generalization of the standard electrokinetic model

We present a new generalization of the standard electrokinetic model based on the assumption that there is a thin layer surrounding the suspended particle where the equilibrium ion density is not determined by the Gouy-Chapman distribution, while the standard model applies outside this layer. Our approach differs from existing models in that we consider that the surface layer is made both of free ions (mostly counterions) and of the fixed ions that constitute the charge of the particle. Furthermore, the free ion density is determined by appropriate boundary conditions without considering any adsorption isotherms. Finally, the fluid is allowed to freely flow inside the layer, only hindered by the presence of the fixed charges and the adhesion condition on the surface of the particle. We show that this generalization leads to results that qualitatively differ from those obtained using existing models: instead of always decreasing, the electrophoretic mobility can actually increase with the anomalous surface conductivity. This could make it possible to use our model for the interpretation of a broader set of experimental data, including those cases when the measured mobility is higher than predicted by the standard model.     

Effects of double-layer polarization and electroosmotic flow on the electrophoresis of an ellipsoid in a spherical cavity

The electrophoresis of a rigid, positively charged ellipsoidal particle at the center of a spherical cavity is investigated theoretically under the conditions where the effects of double-layer polarization and the presence of an electroosmotic flow can be important. The equations governing the problem under consideration and the associated boundary conditions are solved numerically, and the influences of the key parameters on the electrophoretic mobility of the particle are discussed. We show that if the cavity is uncharged, the effect of double-layer polarization yields a local minimum in the electrophoretic mobility as the thickness of the double layer varies. This local minimum disappears if the cavity is also positively charged. In addition to reducing the scaled mobility of an ellipsoid, the presence of the boundary is also capable of influencing the relative magnitudes of the scaled mobility for particles of various shapes. For instance, if the volume of an ellipsoid is fixed, the scaled mobility ranks as prolate > sphere > oblate if the boundary effect is unimportant, but that order is reversed if the boundary effect is important.     

Dynamic electrophoresis of a droplet in a spherical cavity

The electrophoretic behavior of a droplet in a spherical cavity subject to an alternating electric field is analyzed theoretically under the conditions of an arbitrary level of surface potential and double-layer thickness. The influences of the thickness of the double layer, the level of surface potential, the size of a droplet, the viscosity of the droplet fluid, and the frequency of the applied electric field on the electrophoretic behavior of a droplet are examined through numerical simulations. We show that, because of the effect of double-layer deformation, the magnitude of the electrophoretic mobility of a droplet could have a local maximum and the phase angle could have a negative (phase lead) local minimum as the frequency of the applied electric field varies. In general, the lower the surface potential, the thicker the double layer and the larger the viscosity of the droplet fluid, and the more significant the boundary effect, the smaller the magnitude of the electrophoretic mobility of a droplet.     

The Electrophoretic Mobility and Electric Conductivity of a Concentrated Suspension of Colloidal Spheres with Arbitrary Double-Layer Thickness

The electrophoresis in a monodisperse suspension of dielectric spheres with an arbitrary thickness of the electric double layers is analytically studied. The effects of particle interactions are taken into account by employing a unit cell model, and the overlap of the double layers of adjacent particles is allowed. The electrokinetic equations, which govern the ionic concentration distributions, the electric potential profile, and the fluid flow field in the electrolyte solution surrounding the charged sphere in a unit cell, are linearized assuming that the system is only slightly distorted from equilibrium. Using a perturbation method, these linearized equations are solved with the surface charge density (or zeta potential) of the particle as the small perturbation parameter. Analytical expressions for the electrophoretic mobility of the colloidal sphere in closed form correct to O(zeta) are obtained. Based on the solution of the electrokinetic equations in a cell, a closed-form formula for the electric conductivity of the suspension up to O(zeta(2)) is derived from the average electric current density. Comparisons of the results of the cell model with different conditions at the outer boundary of the cell are made for both the electrophoretic mobility and the electric conductivity. Copyright 2001 Academic Press.     

Boundary Effects on Diffusiophoresis of Cylindrical Particles in Nonelectrolyte Gradients

The diffusiophoretic motion of a long circular cylinder in a transversely imposed gradient of a nonionic solute near a large plane wall parallel to its axis is analyzed. The range of the interaction between the solute and the solid surfaces is assumed to be small relative to the particle radius and to the gap width between the particle and the wall, but the polarization effect of the mobile solute in the thin diffuse layers adjacent to the solid surfaces caused by the strong adsorption of the solute is incorporated. A normal flux of the solute and a slip velocity of the fluid at the outer edge of the diffuse layers are used as the boundary conditions for the fluid domain outside the diffuse layers. Through the use of cylindrical bipolar coordinates along with these boundary conditions, a set of transport equations governing this problem is solved in the quasisteady situation and the wall effects on the diffusiophoresis of the cylinder are computed for various cases. For the diffusiophoretic motion of a cylinder normal to a plane, the particle mobility decreases monotonically with the decrease of the distance of the particle axis from the wall. The stronger the polarization effect in the diffuse layer, the weaker the wall effect on the diffusiophoresis. The effect of the normal plane on the diffusiophoresis of a cylinder is much more significant than that for a sphere at the same separation. For the diffusiophoresis of a cylinder parallel to a plane, the boundary effect is a complicated function of the relevant parameters (not necessarily varies monotonically with the extent of separation) mainly due to the existence of a diffusio-osmotic flow caused by the tangential fluid velocity at the plane wall. Copyright 2000 Academic Press.     

Electrophoresis of a toroid along the axis of a cylindrical pore

The electrophoresis of a toroid (doughnut-shaped entity) along the axis of a long cylindrical pore is analyzed under the conditions of low surface potential and weak applied electric field. The system under consideration is capable of modeling the electrophoretic behavior of various types of biocolloid such as bacterial DNA, plasmid DNA, and anabaenopsis, in a confined space. The influences of the key parameters of the problem, including the sizes of a toroid, the radius of a pore, and the thickness of the double layer, on the electrophoretic mobility of a toroid are discussed. We show that the electrophoretic behavior of a toroid under typical conditions can be different from that of an integrated entity. For instance, although the presence of the pore wall has the effect of retarding the movement of a particle, it becomes advantageous if a toroid is sufficiently close to the boundary. Several interesting behaviors are also observed, for example, the mobility of a toroid when the boundary effect is significant can be larger than that when it is insignificant.     

Electrophoresis of a spherical particle along the axis of a cylindrical pore filled with a Carreau fluid

The electrophoresis of a spherical particle along the axis of a cylindrical pore filled with a Carreau fluid is investigated theoretically. In addition to the boundary effect due to the presence of the pore, the influences of the thickness of double layer surrounding a particle and the properties of the fluid on the electrophoretic behavior of the particle are also examined. We show that, in general, the presence of the pore has the effect of retarding the movement of a particle. On the other hand, the shear-thinning nature of the liquid phase is advantageous to its movement. For both Newtonian and Carreau fluids, the mobility of a particle increases monotonically with the decrease in the thickness of double layer, but the mobility is more sensitive to the variation of the thickness of double layer in the latter. The mobility of a particle in a Carreau fluid is larger than that in the corresponding Newtonian fluid, and the difference between the two increases with the decrease in double-layer thickness; in addition, depending upon the values of the parameters assumed, the percentage difference can be in the order of 50%.     

High-pressure reactivity of propene

The phase diagram of propene has been investigated at high pressure by using the diamond anvil cell technique and Fourier transform infrared spectroscopy. The pressure conditions necessary to induce a spontaneous reaction of the sample have been found at different temperatures, allowing the stability boundary of propene to be drawn. The reaction is diffusion controlled and seems to occur only in the fluid phase, implying a slope inversion of the stability boundary at about 250 K. The product of the reaction is a mixture of linear oligomers independently of the P-T conditions. The activation volume and energy of the process have been obtained from the kinetic data. Also the activation of the reaction by laser absorption has been carefully studied. A high proton mobility has been identified as the likely reason that limits the lengthening of the chain up to six to eight monomeric units preventing the polymer formation.     

Effect of a charged boundary on electrophoresis in a Carreau fluid: a sphere at an arbitrary position in a spherical cavity

The influence of a charged boundary on the electrophoretic behavior of an entity in a non-Newtonian fluid is studied by considering a sphere at an arbitrary position in a spherical cavity filled with a Carreau fluid under the conditions of low surface potential and weak applied electric field. The dependence of the mobility of a sphere on its position in a cavity, the size of a cavity, the thickness of a double layer, and the nature of a fluid is investigated. In addition to the fact that the effect of shear-thinning is advantageous to the movement of a sphere, several other interesting results are also observed. For instance, if an uncharged sphere is in a positively charged cavity, where the electroosmotic flow and the induced charge on the sphere surface play a role, the effect of shear-thinning is important only if the thickness of the double layer is either sufficiently thin or sufficiently thick. However, this might not be the case if a positively charged sphere is in an uncharged cavity.     

Mechanism and Kinetics of Hexamethyldisilazane Reaction with a Fumed Silica Surface

An analytical study is presented on the thermocapillary migration of a fluid sphere within a constant applied temperature gradient in an arbitrary direction with respect to a plane surface. The Peclet and Reynolds numbers are assumed to be small so that the Laplace and Stokes equations, respectively, govern the temperature distributions and fluid velocities inside and outside the droplet. The asymptotic formulas for the temperature and the velocity fields in the quasi-steady situation are obtained by using a method of reflections. The plane surface can be a no-slip solid wall and/or a perfect-slip free surface. The boundary effect on the thermocapillary migration is found to be weaker than that on the motion driven by a body force. Even so, the interaction between the plane and the droplet can be very significant when the gap thickness approaches zero. For the motion of a droplet normal to a solid wall, the effect of the plane surface reduces the translational velocity of the droplet; however, this solid wall can be an enhancement factor on the particle migration as it is translating parallel to the wall. On the other hand, in case of a droplet migrating close to a free surface due to thermocapillarity, the droplet velocity can be either greater or smaller than that which would exist in the absence of the plane surface, depending on the relative thermal conductivity and the surface properties of the particle and its relative distance from the plane. Furthermore, the interacting thickness of the affected region by the presence of the plane is discussed by considering the droplet mobility. Generally speaking, a free surface exerts less influence on the particle movement than does a solid surface. Copyright 2000 Academic Press.     

Cell model of the direct current electrokinetics in salt-free concentrated suspensions: the role of boundary conditions

In this paper, a general electrokinetic theory for concentrated suspensions in salt-free media is derived. Our model predicts the electrical conductivity and the electrophoretic mobility of spherical particles in salt-free suspensions for arbitrary conditions regarding particle charge, volume fraction, counterion properties, and overlapping of double layers of adjacent particles. For brevity, hydrolysis effects and parasitic effects from dissolved carbon dioxide, which are present to some extent in more "realistic" salt-free suspensions, will not be addressed in this paper. These issues will be analyzed in a forthcoming extension. However, previous models are revised, and different sets of boundary conditions, frequently found in the literature, are extensively analyzed. Our results confirm the so-called counterion condensation effect and clearly display its influence on electrokinetic properties such as electrical conductivity and electrophoretic mobility for different theoretical conditions. We show that the electrophoretic mobility increases as particle charge increases for a given particle volume fraction until the charge region where counterion condensation takes place is attained, for the above-mentioned sets of boundary conditions. However, it decreases as particle volume fraction increases for a given particle charge. Instead, the electrical conductivity always increases with either particle charge for fixed particle volume fraction or volume fraction for fixed particle charge, whatever the set of boundary conditions previously referred. In addition, the influence of the electric permittivity of the particles on their electrokinetic properties in salt-free media is examined for those frames of boundary conditions.     

On the General Expression for the Electrophoretic Mobility of a Soft Particle

Electrokinetic equations for electrophoresis of a soft particle (that is, a hard particle covered with a layer of polyelectrolytes) have been solved previously under the conditions that the net force acting on the soft particle as a whole (the particle core plus the polyelectrolyte layer) must be zero and that the electrical force acting on the polymer segment is balanced with a frictional force exerted by the liquid flow (J. Colloid Interface Sci. 163, 474 (1994)). In the present work we replaced the latter condition by the alternative and more appropriate condition that pressure is continuous at the boundary between the surface layer and the surrounding electrolyte solution to solve the electrokinetic equations and obtained the general mobility expression for the electrophoretic mobility of a spherical soft particle. It is found that the general mobility expression thus obtained reproduces all of the approximate mobility expressions derived previously and, in addition, that the continuous pressure condition leads to the correct limiting behavior of the electrophoretic mobility in the case where the frictional coefficient tends to zero (this behavior cannot be derived from the force balance condition for the polyelectrolyte layer). Copyright 2000 Academic Press.     

Computation of methodology-independent ionic solvation free energies from molecular simulations. II. The hydration free energy of the sodium cation

The raw ionic solvation free energies computed from atomistic (explicit-solvent) simulations are extremely sensitive to the boundary conditions (finite or periodic system, system shape, and size) and treatment of electrostatic interactions (Coulombic, lattice sum, or cutoff based) used during these simulations. In the present article, it is shown that correction terms can be derived for the effect of (A) an incorrect solvent polarization around the ion due to the use of an approximate (not strictly Coulombic) electrostatic scheme; (B) the finite size or artificial periodicity of the simulated system; (C) an improper summation scheme to evaluate the potential at the ion site and the possible presence of a liquid-vacuum interface in the simulated system. Taking the hydration free energy of the sodium cation as a test case, it is shown that the raw solvation free energies obtained using seven different types of boundary conditions and electrostatic schemes commonly used in explicit-solvent simulations (for a total of 72 simulations differing in the corresponding simulation parameters) can be corrected so as to obtain a consistent value for this quantity.     

Sieving of ionic constituents across moving boundaries in gel electrophoresis

The representative beta-hydroxyethylmorpholinium-chloride-bicinate moving boundary with a trailing ion net mobility relative to Na+ of 0.41, detected by precipitation of chloride with silver nitrate, exhibits a decreasing chloride mobility at increasing polyacrylamide gel concentrations from 3.5 to 45%T, 5%CBis. This decrease, largely due to an increase of field strength at constant current, is described by a convex* plot of log (mobility) vs. %T (Ferguson plot) and signifies that chloride/bicinate are sieved by the gel. In agarose gels, the same plot of mobility vs. gel concentration is constant below 7% gel concentration, since in those gels field strength and migration rate remain the same within that gel concentration range. Both in polyacrylamide and in agarose gels the displacement rate of the chloride-bicinate boundary as a function of the time of electrophoresis or distance migrated remains invariant within 15%. The plot of log (mobility) vs. gel concentration extrapolated to 0%T is 5.85 and 5.41 (10(-5) cm2s-1V-1) for polyacrylamide and for agarose (SeaKem HGT-P,FMC) gels, respectively. The slightly decreased mobility intercept at 0%T for agarose is presumably due either to the electroendosmotic properties of agarose HGT-P and/or failure to Sufficiently take into account the flattening of the Ferguson plot in the polyacrylamide concentration range below 3% in which a transition from a gel to a fluid (sol) medium takes place.     

Structural Anisotropy in Polar Fluids Subjected to Periodic Boundary Conditions

A heuristic model based on dielectric continuum theory for the long-range solvation free energy of a dipolar system possessing periodic boundary conditions (PBCs) is presented. The predictions of the model are compared to simulation results for Stockmayer fluids simulated using three different cell geometries. The boundary effects induced by the PBCs are shown to lead to anisotropies in the apparent dielectric constant and the long-range solvation free energy of as much as 50%. However, the sum of all of the anisotropic energy contributions yields a value that is very close to the isotropic one derived from dielectric continuum theory, leading to a total system energy close to the dielectric value. It is finally shown that the leading-order contribution to the energetic and structural anisotropy is significantly smaller in the noncubic simulation cell geometries compared to when using a cubic simulation cell.