Colloid vibration potential and ion vibration potential in a dilute suspension of spherical colloidal particles

A general electroacoustic theory is presented for the macroscopic electric field in a dilute suspension of spherical colloidal particles in an electrolyte solution, which consists of the colloid vibration potential (CVP) and the ion vibration potential (IVP), induced by an oscillating pressure gradient field due to an applied sound wave. This is a unified theory that unites previous theories for CVP and those for IVP. Approximate analytic expressions are derived for CVP and IVP. The obtained IVP expression agrees with Debye's formula that is corrected by taking into account the force acting on the electrolyte ions as a result of the pressure gradient in the sound wave. The obtained CVP expression is correct to the first order of the particle zeta potential and applicable for arbitrary kappaalpha, where kappa is the Debye-Hückel parameter and alpha is the particle radius. It is found that an Onsager relation holds between CVP and dynamic electrophoretic mobility. It is also shown that the CVP from particles with very small kappaalpha approaches IVP; that is, in the limit of very small kappaalpha a particle behaves like an ion.     

Sedimentation velocity and potential in a concentrated suspension of charged liquid drops

The sedimentation behavior of a concentrated suspension of charged liquid drops is analyzed theoretically at arbitrary surface potential and arbitrary double-layer thickness; that is, the effects of double-layer polarization and double-layer overlapping are taken into account. Kuwabara's unit cell model is employed to model the suspension system, and a pseudospectral method based on the Chebyshev polynomial is adopted to solve the governing electrokinetic equations numerically. Several interesting phenomena, which are of significant influence if the internal flow inside a liquid drop is taken into account, are observed. Key factors are examined such as the thickness of the electric double layer, the magnitude of the surface potential, the volume fraction of liquid drops, and the viscosity of the internal fluid. The results presented here add another dimension to the previous studies, which include concentrated suspensions of rigid particles and mercury drops under low zeta potential, with the consideration of the internal flow of liquid drops and double-layer polarization, characterized by its viscosity and the zeta potential respectively. It is found, among other things, that the smaller the viscosity of the internal fluid is, the higher the sedimentation velocity of liquid drops. The higher the zeta potential is, the larger the decrease in sedimentation velocity. In particular, the sedimentation velocity of an inviscid drop (gas bubble) is about three times higher than that of a rigid one. The decrease in sedimentation velocity resulting from the effect of double-layer polarization achieves about 50% if the zeta potential is sufficiently high.     

Sedimentation Velocity and Potential in Concentrated Suspensions of Charged Spheres with Arbitrary Double-Layer Thickness

The sedimentation in a homogeneous suspension of charged spherical particles 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. Overlap of the double layers of adjacent particles is allowed, and the polarization effect in the double layer surrounding each particle is considered. The electrokinetic equations that govern the ionic concentration distributions, the electric potential profile, and the fluid flow field in the electrolyte solution 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 for a symmetrically charged electrolyte with the surface charge density (or zeta potential) of the particle as the small perturbation parameter. An analytical expression for the settling velocity of the charged sphere in closed form is obtained from a balance among its gravitational, electrostatic, and hydrodynamic forces. A closed-form formula for the sedimentation potential in a suspension of identical charged spheres is also derived by using the requirement of zero net electric current. Our results demonstrate that the effects of overlapping double layers are quite significant, even for the case of thin double layers. Copyright 2000 Academic Press.     

Effect of a Dynamic Stern Layer on the Sedimentation Velocity and Potential in a Dilute Suspension of Colloidal Particles

In this paper the theory of the sedimentation velocity and potential (gradient) in a dilute suspension of charged spherical colloidal particles developed by Ohshima et al. (H. Ohshima, T. W. Healy, L. R. White, and R. W. O'Brien, J. Chem. Soc., Faraday Trans. 2, 80, 1299 (1984)) has been modified to include the presence of a dynamic Stern layer on the particle surfaces. The starting point has been the theory that Mangelsdorf and White (C. S. Mangelsdorf, and L. R. White, J. Chem. Soc., Faraday Trans. 86, 2859 (1990)) developed to calculate the electrophoretic mobility of a colloidal particle allowing for the lateral motion of ions in the inner region of the double layer (dynamic Stern layer). The effects of varying the different Stern layer parameters on the sedimentation velocity and potential are discussed and compared to the case when a Stern layer is absent. The influence of electrolyte concentration and zeta potential of the particles is also analyzed. The results show that regardless of the chosen set of Stern layer and solution parameters, the presence of a dynamic Stern layer causes the sedimentation velocity to increase and the sedimentation potential to decrease, in comparison with the standard case (no Stern layer present). These changes are almost negligible when sedimentation velocity is concerned, but they are very important when it comes to the sedimentation potential. A justification for this fact can be given in terms of an Onsager reciprocal relation, connecting the magnitudes of the sedimentation potential and the electrophoretic mobility. As previously reported, the presence of a dynamic Stern layer exerts a great influence on the electrophoretic mobility of a colloidal particle, and by means of the Onsager relation, the same is confirmed to occur when the sedimentation potential is concerned. Copyright 2000 Academic Press.     

Electrokinetic flow in a planar slit covered by an ion-penetrable charged membrane

The electrokinetic flow of an electrolyte solution in a planar slit covered by an ion-penetrable charged membrane layer is analyzed theoretically. An approximate analytical expression for the spatial variation in the electrical potential is derived, and the electroosmotic velocity, the total electric current, and the streaming potential of the system under consideration are evaluated. The effects of epsilon' (relative permittivity of liquid phase/relative permittivity of membrane layer), eta' (viscosity of liquid phase/viscosity of membrane layer) and the valence of anions (coions) on the volumetric flow rate and total current are examined. We show that the effect of the valence of cations (counterions) on the volumetric flow rate is less significant than that of epsilon' and that of eta'. However, the effect of epsilon' on the total current is less significant than that of the valence of cations and that of eta'. The variation of total current as a function of ionic strength is found to have a local minimum, regardless of whether a pressure gradient is applied or not. The absolute streaming potential has a local maximum as the concentration of fixed charge varies, which was not found in previous studies.     

Sedimentation velocity and potential in concentrated suspensions of charged porous spheres

The body-force-driven migration in a homogeneous suspension of polyelectrolyte molecules or charged flocs in an electrolyte solution is analyzed. The model used for the particle is a porous sphere in which the density of the hydrodynamic frictional segments, and therefore also that of the fixed charges, is constant. The effects of particle interactions are taken into account by employing a unit cell model. The overlap of the electric double layers of adjacent particles is allowed and the relaxation effect in the double layer surrounding each particle is considered. The electrokinetic equations which govern the electrostatic potential profile, the ionic concentration (or electrochemical potential energy) distributions, and the fluid velocity field inside and outside the porous particle in a unit cell are linearized by assuming that the system is only slightly distorted from equilibrium. Using a regular perturbation method, these linearized equations are solved for a symmetrically charged electrolyte with the density of the fixed charges as the small perturbation parameter. An analytical expression for the settling velocity of the charged porous sphere is obtained from a balance among its gravitational, electrostatic, and hydrodynamic forces. A closed-form formula for the sedimentation potential in a suspension of identical charged porous spheres is also derived by using the requirement of zero net electric current. The dependence of the sedimentation velocity and potential of the suspension on the particle volume fraction and other properties of the particle-solution system is found to be quite complicated.     

毛细管电泳中的温度效应和温度梯度技术

对毛细管电泳中的温度效应及温度梯度的应用作了较为详尽的论述,５１篇。     

表面Zeta电位与表面吸附—聚沉规则的理论解释

本文系统地研究了α-Fe_2O_3悬浮体在三种不同价态电解质(KCl,CuCl_2 CrCl_3)的不同浓度中,粒子表面双电层的ζ电位和表面的吸附性质。通过实验总结出一、二、三价正离子影响α-Fe_2O_3悬浮体沉降值的规律性,并以此为根据,结合吸附理论论证了沉降值与被吸附电解质价态之间的反比关系,该结论与叔采—哈迪(Schulze-Hardy)经验规则相似。并对溶胶的聚沉规则提出有独到见解的理论解释。     

The Effect of Protein Concentration on Electrophoretic Mobility

A theory of sedimentation in a concentrated suspension of spherical soft particles (i.e., polyelectrolyte-coated particles) is developed to obtain general expressions for sedimentation velocity of soft particles and sedimentation potential in the suspension. An Onsager relation between sedimentation potential and electrophoretic mobility of spherical soft particles in concentrated suspensions is derived for the case of low potentials and nonoverlapping electrical double layers of adjacent particles. Copyright 2000 Academic Press.     

Sedimentation of DNA supercoils and bacterial nucleoids

The sedimentation of DNA supercoils and bacterial nucleoids is discussed in terms of an asymptotic expression for the size of branched supercoils exhibiting an excluded-volume effect between superhelical segments. A Kirkwood–Riseman approximation is adopted for the sedimentation coefficient. The theory predicts the sedimentation of DNA supercoils fairly well despite their relatively small size in current simulations and experiments. We introduce a crosslinked supercoil model for bacterial nucleoids that are known to contain a variety of adsorbed proteins. Sedimentation experiments of the 1970s are discussed.     

Interaction Between Fine Diamond Particles in Electroless Nickel Solutions

The classical DLVO theory was applied to calculate the interaction potential energy between diamond particles in electroless nickel (EN) solution and its diluted solutions with deionized (DI) water to predict their dispersion and sedimentation rates. Sedimentation tests and particle size distribution for all particle dispersions were measured to verify the DLVO calculations. Results show that the curve features of interaction potential energy vary with the dilution ratio of dispersions. The energy barrier in the curves requires the minimum 1:100 dilution of the EN solution. A sufficient energy barrier results in an extremely slow sedimentation rate of particles by keeping them separate. Otherwise, they settle down quickly due to the agglomeration resulting from their attractive forces at any separation distance. The prediction results are in good agreement with the measurement of sedimentation tests and particle size distribution. The classical DLVO theory is applicable to the field of electroless plating.     

Effect of the Ar-Ni(s) potential on the cross section for Ar+CH4/Ni{111} collision-induced desorption and the need for a more accurate CH4/Ni{111} potential

In a previous paper [L. Sun, P. de Sainte Claire, O. Meroueh, and W. L Hase, J. Chem. Phys. 114, 535 (2001)], a classical trajectory simulation was reported of CH(4) desorption from Ni{111} by Ar-atom collisions. At an incident angle theta(i) of 60 degrees (with respect to the surface normal), the calculated collision-induced desorption (CID) cross sections are in excellent agreement with experiment. However, for smaller incident angles the calculated cross sections are larger than the experimental values and for normal collisions, theta(i)=0 degrees , the calculated cross sections are approximately a factor of 2 larger. This trajectory study used an analytic function for the Ar+Ni(s) intermolecular potential which gives an Ar-Ni{111} potential energy minimum which is an order of magnitude too deep. In the work reported here, the previous trajectory study is repeated with an Ar+Ni(s) analytic intermolecular potential which gives an accurate Ar-Ni{111} potential energy minimum and also has a different surface corrugation than the previous potential. Though there are significant differences between the two Ar+Ni(s) analytic potentials, they have no important effects on the CID dynamics and the cross sections reported here are nearly identical to the previous values. Zero-point energy motions of the surface and the CH(4)-Ni(s) intermolecular modes are considered in the simulation and they are found to have a negligible effect on the CID cross sections. Calculations of the intermolecular potential between CH(4) and a Ni atom, at various levels of theory, suggest that there are substantial approximations in the ab initio calculation used to develop the CH(4)+Ni{111} potential. The implication is that the differences between the trajectory and experimental CID cross sections may arise from an inaccurate CH(4)+Ni{111} potential used in the trajectory simulation.     

Double-layer interaction between two plates with hairy surfaces

In most theoretical treatments of colloidal particles with hairy surfaces, only the steric effect is taken into account. The steric force is a short-range interaction and acts only when the chains on different particles begin to interpenetrate each other. However, since the hairy chains are extended into the continuous phase, they constrain the orientation of the water molecules near the surface and, as a result, the dielectric constant in that region can become very different from that in the bulk. The low dielectric constant affects the distributions of ion concentrations and the gradient of the electric field. Therefore, the double-layer interactions between two plates with hairy surfaces cannot be calculated on the basis of the classical Gouy-Chapman theory, which involves a uniform dielectric constant in the Poisson-Boltzmann equation. A model which accounts for the difference in dielectric constants in the hairy region and outside that region is therefore proposed. The ion specificity is also taken into account by using Born's expression for the free energy of hydration of ions. The repulsive forces calculated via the Gouy-Chapman theory and via the new model are compared. The hairy region can have a long range effect on the repulsive double-layer interactions.     

Temperature effect on the stability of bentonite colloids in water

The stability of natural bentonite suspensions has been investigated as a function of temperature at pH 9 and ionic strength 10(-3) M. The sedimentation rate of the particles is directly related to their stability. The sedimentation kinetics was determined by examining the variation of particle concentration in solution with time. The observed kinetics for sedimentation is discussed quantitatively in terms of the potential energy between particles. The zeta-potential of the particles was measured and the DLVO theory was used to calculate attractive and repulsive potentials. Experimental observations are consistent with DLVO model predictions and show that the stability of bentonite colloids increases with temperature. Differences with other colloidal systems can be attributed to the temperature dependence of the surface charge of bentonite particles.     

The concentration dependence of the diffusion and permeability in a homogeneous membrane

For the sorption and diffusion coefficient dependence on the concentration of the penetrant the transport properties of a homogeneous medium are calculated. The diffusion current is assumed to be proportional to the negative gradient of the chemical potential. This is in contrast with the first Fick's law that assumes this current to be proportional to the negative gradient of the concentration of the penetrant. The difference between the two cases depends on the concentration dependence of the sorption coefficient. In a homogeneous membrane the chemical potential formulation leads to an equation which is very similar to the Fickian expression. The apparent diffusion coefficient, however, depends not onlly on the transport resistance but also on the deviation of the sorption coefficient from constancy.     

Sedimentation of a concentrated dispersion of composite colloidal particles

The sedimentation of a concentrated spherical dispersion of composite particles, where a particle comprises a rigid core and a membrane layer containing fixed charge, is investigated theoretically. The dispersion is simulated by a unit cell model, and a pseudo-spectral method based on Chebyshev polynomials is adopted to solve the problem numerically. The influences of the thickness of double layer, the concentration of particles, the surface potential of the rigid core of a particle, and the amount of fixed charge in the membrane layer on both the sedimentation potential and the sedimentation velocity are discussed. Several interesting results are observed; for example, depending upon the charged conditions on the rigid core and in the membrane layer of a particle, the sedimentation potential might have both a local maximum and a local minimum and the sedimentation velocity can have a local minimum as the thickness of double layer varies. Also, the sedimentation velocity can have a local maximum as the surface potential varies. We show that the sedimentation potential increases with the concentration of particles. The relation between the sedimentation velocity and the concentration of particles, however, depends upon the thickness of double layer.     

Colloid Vibration Potential in a Concentrated Suspension of Spherical Colloidal Particles

A relation between the dynamic electrophoretic mobility of spherical colloidal particles in a concentrated suspension and the colloid vibration potential (CVP) generated in the suspension by a sound wave is obtained from the analogy with the corresponding Onsager relation between electrophoretic mobility and sedimentation potential in concentrated suspensions previously derived on the basis of Kuwabara's cell model. The obtained expression for CVP is applicable to the case where the particle zeta potential is low, the particle relative permittivity is very small, and the overlapping of the electrical double layers of adjacent particles is negligible. It is found that CVP shows much stronger dependence on the particle volume fraction φ than predicted from the φ dependence of the dynamic electrophoretic mobility. It is also suggested that the same relation holds between the electrokinetic sonic amplitude of a concentrated suspension of spherical colloidal particles and the dynamic electrophoretic mobility. Copyright 1999 Academic Press.     

Size distribution of superparamagnetic particles determined by magnetic sedimentation

We report on the use of magnetic sedimentation as a means to determine the size distribution of dispersed magnetic particles. The particles investigated here are (i) single anionic and cationic nanoparticles of diameter D approximately 7 nm and (ii) nanoparticle clusters resulting from electrostatic complexation with polyelectrolytes and polyelectrolyte-neutral copolymers. A theoretical expression of the sedimentation concentration profiles at the steady state is proposed, and it is found to accurately describe the experimental data. When compared to dynamic light scattering, vibrating sample magnetometry, and cryogenic transmission electron microscopy, magnetic sedimentation exhibits a unique property: it provides the core size and core size distribution of nanoparticle aggregates.     

Computer simulation studies of anisotropic systems. XI. Second- and fourth-rank molecular interactions

The Maier-Saupe theory for nematic liquid crystals provides a reasonable account of their orientational order and its temperature dependence. The theory is based on second-rank anisotropic interactions and its predictions can be improved by the introduction of higher-rank terms as in the Humphries-James-Luckhurst theory. However comparison with the properties of real nematogens does not allow an unambiguous test of the theory because the form of the pair potential is unknown. This is not the case for computer simulations where the intermolecular potential is defined. We have therefore undertaken a Monte Carlo study of the influence fourth-rank interactions on nematic behaviour and report the results of our simulations here. The model nematogen used as a reference is that developed by Lebwohl and Lasher in which the particles are confined to the sites of a simple cubic lattice and interact via a second-rank anisotropic potential. The simulation gives the internal energy, the heat capacity at constant volume and the second-rank order parameter as a function of temperature, as well as the nematic-isotropic transition temperature. These results are used to provide the first unambiguous test of the Humphries-James-Luckhurst theory. We also discuss the changes in the transition temperature which are caused by the introduction of the fourth-rank term in the pair potential using thermodynamic perturbation theory for the Helmoltz free energy.     

Sedimentation of concentrated spherical particles with a charge-regulated surface

The sedimentation of a concentrated colloidal dispersion is examined for the case of an arbitrary double-layer thickness. Here, a general mixed-type condition on particle surface is assumed, and the classic models, which assume constant surface properties, can be recovered as the special cases of the present analysis. In particular, the behavior of biological cells, which carry dissociable functional groups on their surfaces, and particles, which are capable of exchanging ions with the surrounding medium, can be simulated by the present model. The mixed-type boundary condition leads to several interesting results in both sedimentation velocity and sedimentation potential as double-layer thickness and the concentration of particles vary.