Electrophoresis of ionic microgel particles: from charged hard spheres to polyelectrolyte-like behavior

We perform electrophoretic mobility measurements of ionic microgel particles in the deswollen and swollen phases. The results show that microgels behave as charged hard spheres in the first case and as free-draining spherical polyelectrolytes in the latter. A unified theory for the electrophoresis of polyelectrolyte-coated particles [H. Ohshima, Adv. Colloid Interface Sci. 62, 189 (1995)] is shown to contain the essential physics for describing the experiments, upon adequate consideration of the particles swelling behavior and network-solvent friction variations.     

Shape analysis based critical Eotvos numbers for buoyancy induced partial detachment of oil drops from hydrophilic surfaces

Removal of oil drops from solid surfaces immersed in an aqueous medium is of interest in many applications. It has been shown that drop shape analysis can be used to predict conditions at which the stability limit of a lighter than water oil drop on a solid surface immersed in an aqueous bath is reached (Adv. Colloid Interface Sci. 98 (2002) 265). However the above analysis is restricted to cases where the contact angle made by the drop is below 90degrees and when the surface conditions result in a 'pinned' contact line. In this paper, it is shown that drop shape analysis can be used to predict the critical conditions at which drop stability limit is reached for drop contact angles of 90degrees and above, which is encountered with 'hydrophilic' surfaces. This critical condition can predict the occurrence of partial oil drop detachment, before complete removal due to 'roll-up', which occurs when the hydrophilic surface is adequately smooth which prevents 'pinning' of the contact line. The critical conditions at which partial drop detachment occurs can also be approximately predicted from simple force balances. It has been shown (Adv. Colloid Interface Sci. 98 (2002) 265) that for contact angles less than 90degrees, the critical limit based on shape analysis appears to resolve the differences that arise due to alternate expressions for capillary retention force. This paper shows that even for contact angles above 90degrees, the critical conditions predicted from the shape analysis resolves the differences in the predictions from the alternate force balances. Drop shape analysis used in this paper is based on the 'Arc-length' form of Young-Laplace or 'drop shape' equation, which is different from the 'Y vs X' form of the above equation that is used in Adv. Colloid Interface Sci. 98 (2002) 265. The above drop shape equation is solved by a fourth order Runge-Kutta technique and it is shown that for angles less than 90degrees, the two forms of the drop shape equation, predict almost identical values of the critical Eotvos number. This paper highlights the competing effects of interfacial tension lowering induced drop instability and 'roll-up', a term that is used to describe the retraction of the contact line of an oil drop on a surface, in being the primary c ause for drop detachment.     

On structural forces in thin fluid films at the critical point

Smooth approximations for structural force in thin fluid films near the critical point are presented to facilitate the usage of formulas derived in [J. Colloid Interface Sci. 278 (2004) 173-183] in experimental studies.     

pH-dependent surface charging and points of zero charge. III. Update

The recently published points of zero charge (PZC) of various materials are compiled to update previous compilations [M. Kosmulski, Chemical Properties of Material Surfaces, Dekker, New York, 2001; M. Kosmulski, J. Colloid Interface Sci. 253 (2002) 77; M. Kosmulski, J. Colloid Interface Sci. 275 (2004) 214]. The recent results corroborate the previously found PZC with a few exceptions. The PZC of alumina obtained from the second-harmonic generation response is substantially lower than the PZC obtained by means of standard methods, while for titania the difference is less significant. PZC of Tl2O3 at pH 7.9 was reported for the first time. A surprisingly insignificant temperature effect on the IEP of rutile was found. Recent model studies aimed at explanation of the effect of the nature of 1-1 electrolytes on the course of charging curves and of discrepancies in the PZC of different materials having the same chemical formula are summarized.     

Electrokinetic fingerprinting of grafted polyelectrolyte layers--a theoretical approach

Electrokinetic fingerprinting (EF) was introduced by Marlow and Rowell [Marlow BJ, Rowel RL. Langmuir 1990;6:1088] for the comprehensive characterization of charged particle surfaces. Afterwards, EF was applied by many groups for the characterization of "hard" (i.e. non-swelling) surfaces. However, the advantages of EF could not yet utilized for the characterization of grafted polyelectrolyte layers (PL) since the theoretical background was not yet elaborated. A theory for the characterization of PL at complete dissociation of the functional groups was developed by Ohshima [Adv Colloid Interface Sci 1995;62:189] and later extended by Dukhin et al. [Dukhin S, Zimmermann R, Werner C. J Colloid Interface Sci 2005;286:761] for any degree of dissociation. Further progress in the characterization of soft surfaces may be achieved by combining EF and surface conductivity (SC) measurements. Both theory and experiment demonstrate that integrated measurements of SC and apparent zeta potential zeta(a) in broad ranges of pH and ionic strength provide information about Donnan potential Psi(D), surface charge, pK and surface potential Psi(0), while the interpretation is more uncertain, when only zeta(a) is measured. This advanced method of PL characterization is established for PL grafted on flat surfaces. When PL are formed on spherical particles, the SC may be measured by means of conductometry and/or dielectric spectroscopy. However, the current theories can only be applied within a rather narrow range of the practically relevant conditions. To overcome this limitation, an unified approach to the theory of electrophoresis for spherical particles with grafted PL was elaborated taking into account the existence of two different electrokinetic models for soft surfaces. While one model is focused on hydrodynamic permeability of soft surface and disregards surface current, another model considers the surface current and disregards electrokinetic water transport within the soft surface layer. Unification became possible through generalization of the capillary osmosis theory over soft surfaces.     

The validity of Cassie's law: a simple exercise using a simplified model

The contact angle of a macroscopic droplet on a heterogeneous but flat substrate is studied using the interface displacement model which can lead to the augmented Young-Laplace equation. Droplets under the condition of constant volume as well as constant vapor pressure are considered. By assuming a cylindrical liquid-vapor surface (meniscus) and minimizing the total free energy of the interface displacement model, we derive an equation which is similar but different from the well-known Cassie's law. Our modified Cassie's law is essentially the same as the formula obtained previously by Marmur [J. Colloid Interface Sci. 168 (1994) 40]. A few consequences from this modified Cassie's law are briefly described in the following sections of this paper. Several sets of recent experimental results seem to support the validity of our modified Cassie's law.     

Comment on "Two touching spherical drops in uniaxial extensional flow: analytic solution to the creeping flow problem"

From an analysis of tangent spherical drops in straining flow, Baldessari and Leal conclude that the drop-scale internal circulation, driven by the ambient flow, has a negligible influence on the drainage of the thin liquid film between drops under small-deformation conditions [F. Baldessari, L.G. Leal, J. Colloid Interface Sci. 289 (2005) 262]. However, their conclusion is incorrect as explained in this letter.     

Spectroscopic studies of solutes in aqueous solution

Absorption and fluorescence characteristics of aqueous solutions of salts, sugars, and amino acids were studied using UV-vis spectroscopy and spectrofluorometry. Motivation stemmed from unanticipated absorption spectral and fluorescence features of the "exclusion zone" seen adjacent to various hydrophilic surfaces. Those features implied a structure distinct from that of bulk water (Adv. Colloid Interface Sci. 2006, 127, 19). Absorption peaks at approximately 270 nm similar to those observed in the exclusion zone were seen in solutions of the following substances: salts, Nafion 117 solution/film, l-lysine, d-alanine, d-glucose and sucrose. To determine the fate of the absorbed energy, we studied the fluorescence properties of these solutions. The salts showed fluorescence emission around 480-490 nm under different excitation wavelengths. The fluorescence intensity of LiCl was higher than NaCl, which was in turn higher than KCl-the same ordering as the absorption intensities. Fluorescence of Nafion 117 solution/film, l-lysine, d-alanine, d-glucose and sucrose were observed as well, with multiple excitation wavelengths. Hence, at least some of the absorbed energy is released as fluorescence. The results show features closely similar to those observed in the exclusion zone, implying that the aqueous region around the solutes resembles the aqueous zone adjacent to hydrophilic surfaces. Both may be more extensively ordered than previously thought.     

Response to the comment on [J. Colloid Interface Sci. 253 (2002) 196] by J. Eggers and R. Evans

We examine the comment on our paper [J. Colloid Interface Sci. 253 (2002) 196] by Eggers and Evans and show that the assertions made there have no foundation in fact nor in scientific substance.     

A numerical study of the effect of insoluble surfactants on the stability of a viscous drop translating in a Hele-Shaw cell

A circular drop is a linearly stable solution for the buoyancy-driven motion of drops in a Hele-Shaw cell [Gupta et al. J. Colloid Interface Sci.218(1), 338 (1999)]. In the absence of surface-active agents, an initially prolate drop always goes to a steady circular shape while initially oblate drops exhibit complex dynamics [Gupta et al. J. Colloid Interface Sci.222, 107 (2000)]. In this study, the effect of insoluble surfactant impurities on the critical conditions for drop breakup is explored by using the Langmuir adsorption framework in conjunction with a physically based expression for the depth-averaged tangential stress exerted on a two-phase interface in a Hele-Shaw cell. It is shown that the presence of surfactants can have both a stabilizing and a destabilizing effect on the shape of the drop, depending on the Bond number, the magnitude of the initial perturbation, and the strength of surface convection. Similar to the clean drop dynamics, two marginally stable branches are found. Increasing the surface Peclet number results in the stabilization of the main branch while the secondary branch shifts to higher Bond numbers. The mode of breakup is also found to be strongly influenced by the strength of surface convection.     

Excluded volume effect on the electrophoretic mobility of colloidal particles

In a recent work [J. Colloid Interface Sci. 316 (2007) 196] we studied the influence of the excluded volume effect on spatial distributions of ionic species and electrostatic potential in the neighborhood of a suspended spherical particle. It was shown that the excluded volume effect considerably increases the surface potential (for a given value of the particle charge) as compared to the case when ideal ion behavior is assumed. In the present work we extend our previous equilibrium results to the perturbed/nonequilibrium problem and analyze the effect of ion size constraints on the electrophoretic mobility of a rigid spherical particle immersed in a general electrolyte solution. We find that the electrophoretic mobility always increases with the excluded volume effect, which might broaden the range of experimental data that can be interpreted, including those cases where the measured mobility exceeded the theoretical maximum value predicted by the standard model.     

Studies on the Spontaneous Evolution of Small Particle Aggregations

On the basis of the criteria for spontaneous evolution of small particle aggregations, which are described by D. Zhaojing, L. Yiping, and L. Cunye [J. Colloid Interface Sci.173,79 (1995)], and according to the results of the experiments and simulations, the spontaneous evolution process of small particle aggregations is further discussed in detail.     

Surfactant solutions and porous substrates: spreading and imbibition

In Section 1, spreading of small liquid drops over thin dry porous layers is investigated from both theoretical and experimental points of view [V.M. Starov, S.R. Kosvintsev, V.D. Sobolev, M.G. Velarde, S.A. Zhdanov, J. Colloid Interface Sci. 252 (2002) 397]. Drop motion over a porous layer is caused by an interplay of two processes: (a) the spreading of the drop over already saturated parts of the porous layer, which results in an expanding of the drop base, and (b) the imbibition of the liquid from the drop into the porous substrate, which results in a shrinkage of the drop base and an expanding of the wetted region inside the porous layer. As a result of these two competing processes, the radius of the drop goes through a maximum value over time. A system of two differential equations has been derived to describe the evolution with time of radii of both the drop base and the wetted region inside the porous layer. This system includes two parameters, one accounts for the effective lubrication coefficient of the liquid over the wetted porous substrate, and the other is a combination of permeability and effective capillary pressure inside the porous layer. Two additional experiments were used for an independent determination of these two parameters. The system of differential equations does not include any fitting parameter after these two parameters are determined. Experiments were carried out on the spreading of silicone oil drops over various dry microfiltration membranes (permeable in both normal and tangential directions). The time evolution of the radii of both the drop base and the wetted region inside the porous layer were monitored. All experimental data fell on two universal curves if appropriate scales are used with a plot of the dimensionless radii of the drop base and of the wetted region inside the porous layer on dimensionless time. The predicted theoretical relationships are two universal curves accounting quite satisfactory for the experimental data. According to theory predictions [1]: (i) the dynamic contact angle dependence on the same dimensionless time as before should be a universal function, and (ii) the dynamic contact angle should change rapidly over an initial short stage of spreading and should remain a constant value over the duration of the rest of the spreading process. The constancy of the contact angle on this stage has nothing to do with hysteresis of the contact angle: there is no hysteresis in the system under investigation. These conclusions again are in good agreement with experimental observations [V.M. Starov, S.R. Kosvintsev, V.D. Sobolev, M.G. Velarde, S.A. Zhdanov, J. Colloid Interface Sci. 252 (2002) 397]. In Section 2, experimental investigations are reviewed on the spreading of small drops of aqueous SDS solutions over dry thin porous substrates (nitrocellulose membranes) in the case of partial wetting [S. Zhdanov, V. Starov, V. Sobolev, M. Velarde, Spreading of aqueous SDS solutions over nitrocellulose membranes. J. Colloid Interface Sci. 264 (2003) 481-489]. The time evolution was monitored of the radii of both the drop base and the wetted area inside the porous substrate. The total duration of the spreading process was subdivided into three stages-the first stage: the drop base expands until the maximum value of the drop base is reached; the contact angle rapidly decreases during this stage; the second stage: the radius of the drop base remains constant and the contact angle decreases linearly with time; the third stage: the drop base shrinks and the contact angle remains constant. The wetted area inside the porous substrate expends during the whole spreading process. Appropriate scales were used with a plot of the dimensionless radii of the drop base, of the wetted area inside the porous substrate, and the dynamic contact angle on the dimensionless time. Experimental data showed [S. Zhdanov, V. Starov, V. Sobolev, M. Velarde, Spreading of aqueous SDS solutions over nitrocellulose membranes. J. Colloid Interface Sci. 264 (2003) 481-489]: the overall time of the spreading of drops of SDS solution over dry thin porous substrates decreases with the increase of surfactant concentration; the difference between advancing and hydrodynamic receding contact angles decreases with the surfactant concentration increase; the constancy of the contact angle during the third stage of spreading has nothing to do with the hysteresis of contact angle, but determined by the hydrodynamic reasons. It is shown using independent spreading experiments of the same drops on nonporous nitrocellulose substrate that the static receding contact angle is equal to zero, which supports the conclusion on the hydrodynamic nature of the hydrodynamic receding contact angle on porous substrates. In Section 3, a theory is developed to describe a spontaneous imbibition of surfactant solutions into hydrophobic capillaries, which takes into account the micelle disintegration and the concentration decreasing close to the moving meniscus as a result of adsorption, as well as the surface diffusion of surfactant molecules [N.V. Churaev, G.A. Martynov, V.M. Starov, Z.M. Zorin, Colloid Polym. Sci. 259 (1981) 747]. The theory predictions are in good agreement with the experimental investigations on the spontaneous imbibition of the nonionic aqueous surfactant solution, Syntamide-5, into hydrophobized quartz capillaries. A theory of the spontaneous capillary rise of surfactant solutions in hydrophobic capillaries is presented, which connects the experimental observations with the adsorption of surfactant molecules in front of the moving meniscus on the bare hydrophobic interface [V.J. Starov, Colloid Interface Sci. 270 (2003)]. In Section 4, capillary imbibition of aqueous surfactant solutions into dry porous substrates is investigated from both theoretical and experimental points of view in the case of partial wetting [V. Straov, S. Zhdanov, M. Velarde, J. Colloid Interface Sci. 273 (2004) 589]. Cylindrical capillaries are used as a model of porous media for theoretical treatment of the problem. It is shown that if an averaged pore size of the porous medium is below a critical value, then the permeability of the porous medium is not influenced by the presence of surfactants at any concentration: the imbibition front moves exactly in the same way as in the case of the imbibition of the pure water. The critical radius is determined by the adsorption of the surfactant molecules on the inner surface of the pores. If an averaged pore size is bigger than the critical value, then the permeability increases with surfactant concentration. These theoretical conclusions are in agreement with experimental observations. In Section 5, the spreading of surfactant solutions over hydrophobic surfaces is considered from both theoretical and experimental points of view [V.M. Starov, S.R. Kosvintsev, M.G. Velarde, J. Colloid Interface Sci. 227 (2000) 185]. Water droplets do not wet a virgin solid hydrophobic substrate. It is shown that the transfer of surfactant molecules from the water droplet onto the hydrophobic surface changes the wetting characteristics in front of the drop on the three-phase contact line. The surfactant molecules increase the solid-vapor interfacial tension and hydrophilise the initially hydrophobic solid substrate just in front of the spreading drop. This process causes water drops to spread over time. The time of evolution of the spreading of a water droplet is predicted and compared with experimental observations. The assumption that surfactant transfer from the drop surface onto the solid hydrophobic substrate controls the rate of spreading is confirmed by experimental observations. In Section 6, the process of the spontaneous spreading of a droplet of a polar liquid over solid substrate is analyzed in the case when amphiphilic molecules (or their amphiphilic fragments) of the substrate surface layer are capable of overturning, resulting in a partial hydrophilisation of the surface [V.M. Starov, V.M. Rudoy, V.I. Ivanov, Colloid J. (Russian Academy of Sciences English Transaction) 61 (3) (1999) 374]. Such a situation may take place, for example, during contact of an aqueous droplet with the surface of a polymer whose macromolecules have hydrophilic side groups capable of rotating around the backbone and during the wetting of polymers containing surface-active additives or Langmuir-Blodgett films composed of amphiphilic molecules. It was shown that droplet spreading is possible only if the lateral interaction between neighbouring amphiphilic molecules (or groups) takes place. This interaction results in the tangential transfer of "the overturning state" to some distance in front of the advancing three-phase contact line making it partially hydrophilic. The quantitative theory describing the kinetics of droplet spreading is developed with allowance for this mechanism of self-organization of the surface layer of a substrate in the contact with a droplet.     

Theoretical study of the acid-base properties of the montmorillonite/electrolyte interface: influence of the surface heterogeneity and ionic strength on the potentiometric titration curves

The parallel shape of the potentiometric titration curves for montmorillonite suspension is explained using the surface complexation model and taking into account the surface heterogeneity. The homogeneous models give accurate predictions only if they assume unphysically large values of the equilibrium constants for the exchange process occurring on the basal plane. However, the assumption that the basal plane is energetically heterogeneous allows to fit the experimental data (reported by Avena and De Pauli [M. Avena, C.P. De Pauli, J. Colloid Interface Sci. 202 (1998) 195-204]) for reasonable values of exchange equilibrium constant equal to 1.26 (suggested by Fletcher and Sposito [P. Fletcher, G. Sposito, Clay Miner. 24 (1989) 375-391]). Moreover, we observed the typical behavior of point of zero net proton charge (pznpc) as a function of logarithm of the electrolyte concentration (log[C]). We showed that the slope of the linear dependence, pznpc=f(log[C]), is proportional to the number of isomorphic substitutions in the crystal phase, which was also observed in the experimental studies.     

Thermodynamics of aqueous carbohydrate surfactant solutions

The paper deals with the application of the micelle formation theory, developed by Nagarajan and Ruckenstein [R. Nagarajan, E. Ruckenstein, Langmuir 7 (1991) 2934–2969] and Nagarajan [R. Nagarajan, in: K. Esumi (Ed.), Structure–Performance Relationships in Surfactants, Dekker, New York, 1997, pp. 1–81; R. Nagarajan, Adv. Colloid Interface Sci. 26 (1986) 205-264] to various n-alkyl-β-d-glucopyranoside surfactants, differing in the surfactant tail length (n-octyl-β-d-glucopyranoside C₈G₁, n-decyl-β-d-glucopyranoside C₁₀G₁ and dodecyl-β-d-glucopyranoside C₁₂G₁). The model predicts that the carbohydrate surfactant molecules assemble for energetic reasons in spherical bilayer vesicles. The critical micellar concentration as function of the temperature shows a minimum value. The formed micellar aggregates exhibit a broad distribution of sizes. It is demonstrated in this study that the thermodynamic theory in combination with phase separation thermodynamics can be used successfully to described the phase separation, which occurs for the system C₁₀G₁+water and C₁₂G₁+water at low surfactant concentrations.     

Charging and swelling of cellulose films

Charging and swelling of cellulose in aqueous environments are of highest interest with respect to the performance of cellulose based products and applications. To unravel the interplay between ionization and structural features of the biopolymer hydrogel we compared non-crosslinked and crosslinked cellulose thin films based on a determination of the Donnan potential [S.S. Dukhin, R. Zimmermann, C. Werner, J. Colloid Interface Sci. 274 (2004) 309] from microslit electrokinetic (streaming potential/streaming current) experiments and layer thicknesses from ellipsometry in aqueous electrolyte solutions. The pH dependence of the Donnan potential, reflecting the ionization of carboxylic acid groups within the cellulose films, was found to be significantly different from the related trend of the streaming current which reflects the characteristics of the topmost surface of the layers: While carboxylic acid groups on the surface of the films dissociate as isolated functionalities, the electrostatic interactions of ionized groups within the cellulose layers cause an incomplete dissociation (pK shift) of the carboxylic acid and a layer expansion (swelling) in the alkaline pH range. The system was found to restrict its volume charge density even after structural restrictions (crosslinking) of the layer and at lower ionic strength of the solutions through a further decrease of the degree of dissociation of the carboxylic acid functions. These findings were attributed to the local accumulation of the carboxylic acid groups caused by preferential oxidation of the amorphous regions of the cellulose and to the ordered water structure within the layer.     

Forces between a rigid probe particle and a liquid interface. II. The general case

The semianalytic theory developed previously (Chan, D. Y. C., Dagastine, R. R., and White, L. R., J. Colloid Interface Sci. 236, 141 (2001)) to predict the force curve of an AFM measurement at a liquid interface using a colloidal probe has been expanded to incorporate a general force law with both attractive and repulsive forces. Expressions for the gradient of the force curve are developed to calculate the point at which the probe particle on the cantilever will spontaneously jump in toward the liquid interface. The calculation of the jump instability is reduced to a straightforward embroidery of the simple algorithms presented in Chan et al. In a variety of sample calculations using force laws including van der Waals, electrostatic, and hydrophobic forces for both oil/water and bubble/water interfaces, we have duplicated the general behaviors observed in several AFM investigations at liquid interfaces. The behavior of the drop as a Hookean spring and the numerical difficulties of a full numerical calculation of F(deltaX) are also discussed.     

Parameter identifiability in application of soft particle electrokinetic theory to determine polymer and polyelectrolyte coating thicknesses on colloids

Soft particle electrokinetic models have been used to determine adsorbed nonionic polymer and polyelectrolyte layer properties on nanoparticles or colloids by fitting electrophoretic mobility data. Ohshima first established the formalism for these models and provided analytical approximations ( Ohshima, H. Adv. Colloid Interface Sci.1995, 62, 189 ). More recently, exact numerical solutions have been developed, which account for polarization and relaxation effects and require fewer assumptions on the particle and soft layer properties. This paper characterizes statistical uncertainty in the polyelectrolyte layer charge density, layer thickness, and permeability (Brinkman screening length) obtained from fitting data to either the analytical or numerical electrokinetic models. Various combinations of particle core and polymer layer properties are investigated to determine the range of systems for which this analysis can provide a solution with reasonably small uncertainty bounds, particularly for layer thickness. Identifiability of layer thickness in the analytical model ranges from poor confidence for cases with thick, highly charged coatings, to good confidence for cases with thin, low-charged coatings. Identifiability is similar for the numerical model, except that sensitivity is improved at very high charge and permeability, where polarization and relaxation effects are significant. For some poorly identifiable cases, parameter reduction can reduce collinearity to improve identifiability. Analysis of experimental data yielded results consistent with expectations from the simulated theoretical cases. Identifiability of layer charge density and permeability is also evaluated. Guidelines are suggested for evaluation of statistical confidence in polymer and polyelectrolyte layer parameters determined by application of the soft particle electrokinetic theory.