Adsorption of weakly charged polyelectrolytes onto oppositely charged spherical colloids

The adsorption of a long weakly charged flexible polyelectrolyte in a salt solution onto an oppositely charged spherical surface is investigated. An analytical solution for Green's function is derived, which is valid for any sphere radius and consistently recovers the result of a planar surface in the limit of large sphere radii, by substituting the Debye-Hückel potential via the Hulthén potential. Expressions for critical quantities like the critical radius and the critical surface charge density are provided. In particular, we find a universal critical line for the sphere radius as a function of the screening length separating adsorbed from desorbed states. Moreover, results for the monomer density distribution, adsorbed layer thickness, and the radius of gyration are presented. A comparison of our theoretical results with experiments and computer simulations yields remarkably good agreement.     

Use of the concentration dependences of hydration numbers for calculating the gibbs energies and activities of strong electrolytes

The expression for the Gibbs energy (G) of electrolytes derived in terms of the Debye-Hückel theory is modified so as to describe the experimentally observed dependence of the hydration numbers of electrolyte ions on their concentration by minimizing G. It is shown that the activity coefficients of electrolyte solutions determined from this expression are in good agreement with experimental data over a wide concentration range.     

The Debye-Hückel approximation: its use in describing electroosmotic flow in micro- and nanochannels

In this work we consider the electroosmotic flow in a rectangular channel. We consider a mixture of water or other neutral solvent and a salt compound, such as sodium chloride, and other buffers for which the ionic species are entirely dissociated. Results are produced for the case where the channel height is much greater than the width of the electric double layer (EDL) (microchannel) and for the case where the channel height is of the order or slightly greater than the width of the EDL (nanochannel). At small cation, anion concentration differences the Debye-Hückel approximation is appropriate; at larger concentration differences, the Gouy-Chapman picture of the electric double emerges naturally. In the symmetric case, the velocity field and the potential are identical. We specifically focus in this paper on the limits of the Debye-Hückel approximation for a simplified version of a phosphate-buffered saline (PBS) mixture. The fluid is assumed to behave as a continuum and the volume flow rate is observed to vary linearly with channel height for electrically driven flow in contrast to pressure-driven flow which varies as height cubed. This means that very large pressure drops are required to drive flows in small channels. However, useful volume flow rates may be obtained at a very low driving voltage. In the course of the solution, we establish the relationship between the wall mole fractions of the electrolytes and the zeta potential. Multivalent electrolyte mixtures are also considered.     

Electrical double layer interactions for spherical charge regulating colloidal particles

A new way of linearising the Poisson-Boltzmann equation is presented which is capable of producing accurate answers for moderately high surface charge and surface potentials. Unlike the Debye-Hückel approximation, the linearisation is based on the fact that electric potential variation, rather than the magnitude of the potential itself, remains small between two charged plates at close separation. The method can be applied quite generally to any type of surface. The cases of constant surface charge, the constant surfaceppotential and charge regulating systems are considered as examples. The results for constant charge and potentials as high as 5 μC/cm² and 200 mV are within 7% of the exact answers for plate separations of one Debye length or less. In contrast, the Debye-Hückel approximation produces answers that are at least an order of magnitude too large, for the same problems. The application of the method to the problem of calculating the electrostatic forces between charge regulated spherical particles is also addressed in some detail.     

Investigation of fundamental transport properties and thermodynamics in diglyme-salt solutions

Ionic mobility, the thermodynamics of ionic association, and the structure of associated species are studied in solutions of diglyme containing either lithium triflate or tetrabutylammonium triflate. Infrared spectroscopic, PFG NMR, thermodynamic, and crystallographic data suggest that the solute species existing in diglyme-lithium triflate are "free" ions, contact ion pairs, and dimers. Equilibrium constants, S(o), deltaH(o), and deltaG(o) are calculated for processes occurring between these species. In particular, the equilibrium constant, corrected for nonideality using a modified Debye-Hückel expression, is calculated for the dissociation of contact ion pairs into "free" cations and anions. A second equilibrium constant for the formation of dimers from contact ion pairs is also calculated; these constants do not significantly vary with salt concentration up to about 1.3 x 10(-3) mol cm(-3). The measured temperature dependence of equilibrium constants was used to calculate deltaH(o) and deltaS(o) for the two processes. The value of deltaS(o) = -102 J mol(-1) K(-1) for the dissociation of contact ion pairs shows that the large entropy decrease due to cation solvation outweighs the entropy increase due to dissociation of a contact ion pair. Ionic mobilities are calculated in lithium triflate-diglyme solutions using conductivity data in conjunction with information about the nature and concentrations of solute species obtained from IR spectroscopy. Mobilities in tetrabutlyammonium triflate-diglyme solutions are calculated directly from conductivity data. It was concluded that the concentration dependence of the molar conductivity is due in large part to the variation of the ion mobilities with concentration.     

Enthalpies and heat capacities of dissolution for calcium chloride and sodium oxalate

The heats of solution at 25 and 40°C in water are measured for various concentrations of calcium chloride and sodium oxalate. The standard enthalpies of solution are determined using the Debye-Hückel second approximation. The heat capacity change upon dissolution and the partial molal heat capacities of electrolytes at infinite dilution are calculated.     

An improved procedure for the construction of ion-pair distribution functions within the Debye-Hückel framework

A recently proposed scheme for the construction of physically realistic pair functions for the distribution of ions about a central reference ion within the framework of the Debye-Hückel model is assessed and extended to include the effects of different distances of closest approach for like and unlike ions within the screening cloud around the central ion. Improved values for the mean configurational energy per ion are predicted when compared to the results of Monte Carlo simulation studies.     

Approximate analytic expression for the dynamic electrophoretic mobility of a spherical colloidal particle in an oscillating electric field

An approximate analytic expression is derived for the dynamic electrophoretic mobility of a spherical charged colloidal particle in an electrolyte solution in an applied oscillating electric field. This expression, which takes into account the relaxation effects, is applicable for all values of zeta potential at large kappa a (kappa a > or = ca. 30) and omega/2pi < or = ca. 10 MHz, where kappa is the Debye-Hückel parameter, a is the particle radius, and omega is the frequency of the electric field. It is shown that the obtained mobility expression is in excellent agreement with the exact numerical results of Mangelsdorf and White (J. Chem. Soc., Faraday Trans. 1992, 88, 3567).     

Electrophoretic mobility of a soft particle in a salt-free medium

A theory is presented for the electrophoretic mobility mu of dilute spherical soft particles (i.e., polyelectrolyte-coated particles) in salt-free media containing only counterions. As in the case of other types of particles (rigid particles and liquid drops) in salt-free media, there is a certain critical value of the particle charge separating two cases, the low-surface-charge case and the high-surface-charge case. For the low-charge case, the mobility is proportional to the particle charge and coincides with that of a soft particle in an electrolyte solution in the limit of very low electrolyte concentrations kappa-->0 (Hückel's limit), where kappa is the Debye-Hückel parameter. For the high-charge case, however, mu becomes essentially constant, independent of the particle charge, due to the counterion condensation effect.     

Ionic strength dependence of heavy metal tartrate complex stabilities

Summary Ion chromatography and potentiometry were used for the determination of the stability constants Pb, Zn, Co, Ni, Mn tartrate complexes at different ionic strengths. An extrapolation function based on the Debye-Hückel equation was applied to obtain the thermodynamic stability constants.     

Thermodiffusion of charged colloids: single-particle diffusion

An expression for the single-particle thermal diffusion coefficient of a charged colloidal sphere is derived on the basis of force balance on the Brownian time scale in combination with thermodynamics. It is shown that the single-particle thermal diffusion coefficient is related to the temperature dependence of the reversible work necessary to build the colloidal particle, including the core, the solvation layer, and the electrical double layer. From this general expression, an explicit expression for the contribution of the electrical double layer to the single-particle thermal diffusion coefficient is derived in terms of the surface charge density of the colloidal sphere, the electrostatic screening length, and its core radius, to within the Debye-Hückel approximation. This result is shown to explain experimental data, for both thin and thick double layers. In addition, a comparison with other theories is made.     

Simple approximate analytic expression for the electrophoretic mobility of a spherical colloidal particle in a mixed solution of 1:1 and 2:1 electrolytes

Simple approximate analytic expressions are derived for the electrophoretic mobility of a spherical colloidal particle of radius a and zeta potential ζ in a mixed solution of 1:1 and 2:1 electrolytes with common anions on the basis of the general mobility expression previously derived by Ohshima (Colloids Surf A Physicochem Eng Asp 267:50, 2005). The obtained expressions, which are applicable for spheres of any ζ and large radii such that κa ≥ ca. 30 (where κ is the Debye-Hückel parameter), consist of Smoluchowski’s equation and the correction term taking into account the relaxation effect.     

Remarks on the theory of diffusion in electrolyte solutions

The assumptions usually made that the ionic atmosphere has spherical symmetry in the diffusion of binary electrolytes and that the electrophoretic effect is negligible in the tracer diffusion of ions are pointed out to be incorrect when terms up to order κ² ln κ (κ is the Debye-Hückel parameter) are considered.     

Osmotic and Activity Coefficients of Trimethyloctylammonium Bromide and Decyltrimethylammonium Bromide in Aqueous Solutions as a Function of Temperature

Osmotic coefficients of aqueous solutions of trimethyloctylammonium bromide and decyltrimethylammonium bromide were measured by the isopiestic method at the following temperatures: 298.15, 293.15, 288.15 and 283.15 K. Activity coefficients of the solutes were calculated from the osmotic coefficients. The results were compared with the Debye-Hückel limiting law and analyzed according to their variation with the alkyl chain length of the cation and with the change in temperature.     

Oscillating laminar electrokinetic flow in infinitely extended rectangular microchannels

This paper has addressed analytically the problem of laminar flow in microchannels with rectangular cross-section subjected to a time-dependent sinusoidal pressure gradient and a sinusoidal electric field. The analytical solution has been determined based on the Debye-Hückel approximation of a low surface potential at the channel wall. We have demonstrated that Onsager's principle of reciprocity is valid for this problem. Parametric studies of streaming potential have shown the dependence of the electroviscous effect not only on the Debye length, but also on the oscillation frequency and the microchannel width. Parametric studies of electroosmosis demonstrate that the flow rate decreases due to an increase in frequency. The obtained solutions for both the streaming potential and electroosmotic flows become those for flow between two parallel plates in the limit of a large aspect ratio.     

The apparent molal volumes of 1:1 electrolytes in urea solution. II. Variation of apparent molal volume with salt concentration

The apparent molal volumes of NaCl, NaBr, KCl, KBr, LiCl, and CsCl were measured as a function of salt concentration in 1m and 8m aqueous urea at 25°C. It was found that equations of the form $$\phi = \phi _0 + S\prime \surd \bar C + b\prime C$$ where the limiting slopeS′ is the same for all the salts in a given concentration of urea, accurately describe the data for salt concentrations less than 1M. The values found forS′ were 1.52 in 1m urea and 1.00 in 8m urea. These are in good agreement with estimated values of the Debye-Hückel limiting slope.     

Enthalpies and heat capacities of reaction between calcium chloride and sodium oxalate in water

The heats of mixing at 25 and 40°C of dilute aqueous solutions of calcium chloride and sodium oxalate are measured. The heats of dilution of aqueous calcium chloride solutions are measured. Both processes are exothermic. However, the dilution exothermicity increases with temperature elevation in full accordance with the Debye-Hückel theory, while the mixing exothermicity noticeably decreases. The enthalpies of precipitation of calcium oxalate and the heat capacity change upon precipitation from dilute aqueous solutions are calculated for the first time.     

Corrected Debye-Hückel analysis of surface complexation; III. Spherical particle charging including ion condensation

Statistical mechanics has been used to derive a model for the charging of a spherical particle in a salt solution to complement our experimental studies and gain a deeper understanding of the processes involved in surface complexation. Our chosen model goes beyond the equilibrium constants and the Gouy-Chapmann theory currently used in surface complexation models. The proton adsorption is taken to occur at a harmonic potential well on the surface characterized by a frequency v and a well depth u(0). Outside the particle surface there is a capacitor layer of width w(c) which is impenetrable to the salt ions. The diffuse screening of the charged particle is described by a corrected Debye-Hückel analysis accounting for ion size in the ion-ion interactions. To account also for nonlinear electrostatic response a layer of condensed counterions has been introduced. The criterion for the onset of ion condensation is that the electrostatic field exceeds a linear response criterion. Ion size effects are accounted for in terms of hole-corrected electrostatic energies and excluded volume. The model has been applied to titrated surface charge data on goethite (alpha-FeOOH) at various background concentrations and good agreement between the experimental data and the model was obtained. Both the size of the screening ions and the central particle size were shown to be of importance for the surface charge.