The electroviscous effect in ethylcellulose latex suspensions. Effect of ionic strength and correlation between theory and experiments

 This article describes an experimental and theoretical investigation of the so-called primary electroviscous effect, i.e., the increase in suspension viscosity due to the existence of an electrical double layer around the particles. By measuring the viscosity of ethylcellulose latex suspensions, the electroviscous coefficient, the quantity measuring the effect, was estimated for different concentrations of 1-1 electrolyte in the dispersion medium. These data were compared with the predictions of Watterson and White's model, using the zeta potential of the particles deduced from electrophoretic mobility measurements. It was found that the theory considerably underestimates the effect. In an attempt to improve the agreement between data and predictions, the model was generalized to include the possibility (dynamic Stern layer) that ions in the inner part of the double layer have nonzero mobility. The general theory, however, predicts even lower values of the electroviscous coefficients, thus increasing the separation between calculated and measured electroviscous coefficients. A careful analysis of the ionic concentrations and velocity profiles with and without dynamic Stern layer corrections can account for this fact, but leaves unsolved the problem of the large discrepancies found in the theoretical explanation of the strength of the electroviscous effect. Received: 19 October 1999/Accepted: 17 December 1999     

An experimental test of Booth's primary electroviscous effect theory

The primary electroviscous effect has been investigated in dilute suspensions of titanium oxide (anatase), the viscosities of which were measured by means of a capillary viscometer with automatic timing. The linear relation between viscosity and solids volume fraction was first determined at the isoelectric point of the particles when the particles are uncharged, and the electroviscous contribution to the intrinsic viscosity was then determined at other values of pH. Booth's theory (Proc. R. Soc. London Ser. A203, 533 (1950)) agrees well with the experimental results when the particle zeta potential is small and the double layer is thin (kappa alpha approximately 7.3), but agreement is poor when the double layer is thick (kappa alpha approximately 0.6).     

Viscosity and electrophoretic mobility of cesium fullerenehexamalonate in aqueous solutions--comparing experiments and theories on nanometer-sized spherical polyelectrolyte

The viscosity of aqueous solutions of cesium fullerenehexamalonate T h -C 66(COOCs) 12, a rigid spherical nanometer-sized polyvalent salt, was measured by the Ubbelohde-type viscometer. The measurements were performed without added salt at 25 degrees C in the concentration range between 7 and 320 g/dm (3). THe concentration dependence of the obtained reduced viscosity was compared with the theoretical prediction, taking into account contributions stemming from the intrinsic viscosity, hydrodynamic perturbations of the hypothetically bare fullerenehexamalonate macroion, the primary electroviscous effect, and the secondary electroviscous effect. Using the geometric radius of the bare macroion from the previous measurements of the estimated effective charge of the macroion and from the small-angle X-ray scattering data of the estimated thickness of the compact shell of counterions electrostatically bound to the macroion, a good agreement between theory and the experiment was obtained in the range of the lowest and of the highest concentrations. Electrostatic interactions are identified as the main cause of the increased reduced viscosity at the lowest measured concentrations. At the highest concentrations, electrostatic interactions are effectively screened, and the influence of binary hydrodynamic interactions and perturbations of the hypothetical bare macroion prevails over electrostatic contributions to the increased viscosity. The electrophoretic mobility of the fullerenehexamalonate ion in aqueous salt-free medium was computed with the same value for the radius of the fullerenehexamalonate macroion as that used in the calculation of viscosity. The numerical solution of Ohshima's equation agreed well with the experimental values.     

Structure of colloid silica determined by viscosity measurements

The viscosity of nanosized colloid silica suspensions, used as binders in the investment casting, was determined as a function of their weight fraction reaching 52%. A new capillary viscometer was used whose construction eliminated sedimentation effects. The experiments have been carried out at fixed pH 10.0 and controlled ionic strength. It was found that for a low silica concentration range (weight fraction below 5%) the suspension viscosity increased more rapidly than the Einstein theory predicts. This anomalous behavior could not be explained in terms of the primary electroviscous effect predicted to be a few orders of magnitude smaller as observed. This discrepancy was accounted for by postulating a fuzzy, gel-like structure of colloid silicas used in our experiments. Hence, the apparent hydrodynamic radius of silica particles in aqueous suspensions was found to be larger than the primary particle size in accordance with previous observations. Based on this postulate, an apparent density of the silica sols was found to be 1.32-1.37 g/cm(3) instead of 2.2-2.32 g/cm(3) as determined from the suspension dilution method. This behavior was interpreted in terms of the core/shell model with high shell porosity, reaching 85%. Similarly, for higher concentration ranges, silica viscosity increased more rapidly with increased sol concentration than predicted by the Batchelor model derived for hard particles. The deviation was attributed to the secondary electroviscous effect stemming from the electrostatic interactions among silica particles in sheared suspensions. This effect has quantitatively been interpreted in terms of Russel's theory. On the other hand, for the high concentration range the experimental results were well accounted for by the Dougherty-Krieger model. By exploiting our experimental findings a sensitive method of determining the structure and apparent density of silica sols in aqueous media was proposed.     

海藻酸钠在KCl水溶液中的粘度行为

通过测定海藻酸钠水溶液的特性粘数及在低高于强度的条件下其浓度与比浓粘度关系曲线上的峰值，系统地研究了KCl浓度在2×10（－5）－0.5mol·L（-1）范围内对海藻酸钠溶液粘度行为的影响．根据Odijk－Skolnick－Fixman理论和Rinaudo的处理方法，从理论上对海藻酸钠溶液的粘度行为进行了探讨．研究结果表明：聚电解质溶液的电粘滞效应可使用静电相关长度得到合理解释     

A STUDY OF THE PRIMARY ELECTROVISCOUS EFFECT IN PYREX GLASS SUSPENSIONS.

An experimental investigation on the electrokinetic phenomenon known as primary electroviscous effect is described for suspensions of Pyrex glass, a highly charged and well known material. By means of an automatic method, the viscosity of the suspensions is measured for different volume fractions of solids, at various electrolyte concentrations and pH values. These measurements allow the estimation of the electroviscous coefficient, p. The electrophoretic mobility was determined for the same systems and zeta potential calculated from these experimental data in order to carry out the comparison between the measured values of p and different theoretical predictions. A qualitative agreement between theory and experiment was found in many cases, but the rigorous theories seem to systemmatically underestimate the experimental p values. The reasons for this disagreement are discussed in addition to the general trends of the electrokinetic behaviour of Pyrex glass.     

Intrinsic viscosity of aqueous suspensions of cellulose nanofibrils

Cellulose nanofibrils (CNF) from wood fibers are of increasing interest to industry because they are from renewable sources and are biodegradable. Owing to their high aspect ratio, they produce viscous suspensions and stiff gels that are strengthened by interfibrillar hydrogen bonds. In this study, the viscosity of aqueous CNF suspensions, at dilute concentrations ( \(nL^{3}<1\) ), was measured at various pH values by addition of HCl, and at various ionic strengths by addition of NaCl and \(\hbox {CaCl}_{2}\) . The results show that the primary electroviscous effect significantly increases the intrinsic viscosity. The intrinsic viscosity under conditions where the surface charge of nanofibrils is fully screened is in good agreement with the predictions of classical theory for dispersions of rodlike particles at low shear rates. Increasing the ionic strength up to \(\kappa d\approx 1\) decreases the intrinsic viscosity; at \(\kappa d>1\) , the intrinsic viscosity increases because of fibril aggregation and increase of the effective volume fraction.     

Protonation of Lysozymes and Its Consequences for the Adsorption onto a Mica Surface

Several physicochemical properties of chicken egg white lysozyme (LSZ) in electrolyte solutions were determined. The hydrodynamic diameter of LSZ at an ionic strength of 0.15 M was found to be 4.0 nm. Using the determined parameters, the number of uncompensated (electrokinetic) charges, N(c), on the molecule surface was calculated from the electrophoretic mobility data. It was found that the N(c) = 2.8 at pH = 3.0 and an ionic strength of I = 0.15 M. At the lower ionic strength, I = 1 × 10(-3) M, this positive charge increased to N(c) = 5.6 at a pH = 3.0 The physicochemical characteristics were supplemented by the dynamic viscosity measurements. The intrinsic viscosity and the hydrodynamic diameter results were compared with theoretical predictions from Brenner's model. Using this approach, it was found that the effective molecule length of LSZ is equal to L(ef) = 5.6 nm. Additional information on the LSZ adsorbed films was obtained by the contact angle measurements. The notably large contact angles were measured on LSZ films formed under the conditions where both the LSZ and the mica were oppositely charged. The higher the positive zeta potential of LSZ, the greater the contact angle measured, which indicates that LSZ affinity for the adsorption on mica increases with its uncompensated charge. The adsorption dependence on the zeta potential of LSZ was explained, assuming a roughly uniform distribution of the net charge on the molecule surface. This assumption is supported by the results of depositing negatively charged, fluorescent latex particles onto the mica surface, which had been modified by LSZ adsorption. The highest latex coverage was formed on mica surfaces that had first been coated with LSZ solutions of lower pH, as a result of the increasing charge of LSZ monolayers in this condition.     

Characterization of globular protein solutions by dynamic light scattering, electrophoretic mobility, and viscosity measurements

In this work, physicochemical properties of two globular proteinsbovine serum albumin (BSA) having a molecular weight of 67 kDa and human serum albumin (HSA) having a molecular weight of 69 kDawere characterized. The bulk characteristics of these proteins involved the diffusion coefficient (hydrodynamic radius), electrophoretic mobility, and dynamic viscosity as a function of protein solution concentration for various pH values. The hydrodynamic radius data suggested an association of protein molecules, most probably forming compact dimers. Using the hydrodynamic diameter and the electropheretic mobility data allowed the determination of the number of uncompensated (electrokinetic) charges on protein surfaces. The electrophoretic mobility data were converted to zeta potential values, which allowed one to determine the isoelectric point (iep) of these proteins. It was found to be at pH 5.1 for both proteins, in accordance with previous experimental data and theoretical estimations derived from amino acid composition and p K values. To determine further the stability of protein solutions, dynamic viscosity measurements were carried out as a function of their bulk volume concentration for various pH values. The intrinsic viscosity derived from these measurements was interpreted in terms of the Brenner model, which is applicable to hard spheroidal particles. It was found that the experimental values of the intrinsic viscosity of these proteins were in good agreement with this model when assuming protein dimensions of 9.5 x 5 x 5 nm3 (prolate spheroid). The possibility of forming linear aggregates of association degree higher than 2 was excluded by these measurements. It was concluded that the combination of dynamic viscosity and dynamic light scattering can be exploited as a convenient tool for detecting not only the onset of protein aggregation in suspensions but also the form and composition of these aggregates.     

Primary electroviscous effect in a dilute suspension of charged mercury drops

The standard theory of the primary electroviscous effect in a dilute suspension of charged spherical rigid particles in an electrolyte solution (Watterson, I. G.; White, L. R. J. Chem. Soc., Faraday Trans. 2 1981, 77, 1115) is extended to cover the case of a dilute suspension of charged mercury drops of viscosity eta(d). A general expression for the effective viscosity or the electroviscous coefficient p of the suspension is derived. This expression tends to that for the case of rigid particles in the limit of eta(d) --> infinity. We also derive an approximate analytical viscosity expressions applicable to mercury drops carrying low zeta potentials at arbitrary kappaa (where kappa is the Debye-Hückel parameter and a is the drop radius) and to mercury drops as well as rigid spheres with arbitrary zeta potentials at large kappaa. It is shown that the large-kappaa expression of p for rigid particles predicts a maximum when plotted as a function of zeta potential. This result for rigid particles agrees with the exact numerical results of Watterson and White. It is also shown that in the limit of high zeta potential the effective viscosity of a suspension of mercury drops tends to that of uncharged rigid spheres given by Einstein's formula (Einstein, A. Ann. Phys. 1906, 19, 289), whereas in the opposite limit of low zeta potential the effective viscosity approaches that of a suspension of uncharged liquid drops derived by Taylor (Taylor, G. I. Proc. R. Soc. London, Ser. A 1932, 138, 41).     

Electroviscous Effect in Dilute Suspensions of Alumina

A study on the electroviscous effect of alumina suspensions has been made. At the low volume fraction of the particles studied here only a first-order effect was detected. Ubbelohde-type capillary viscometers have been used. A simple method to determine the hydrodynamic constant k(1) has been proposed. The experimental primary electroviscous coefficients corresponding to different electrolyte concentrations have been compared with two different theoretical approachs (I. G. Watterson, and L. R. White, J. Chem. Soc. Faraday Trans. 2 77, 1115 (1981); F. J. Rubio-Hernández, E. Ruiz-Reina, and A. I. Gómez-Merino, J. Colloid Interface Sci. 206, 334 (1998)) and the results suggest that the presence of a dynamic Stern layer plays a certain role in this effect. Copyright 2000 Academic Press.     

Determination of thermodynamic acidity constants and limiting ionic mobilities of weak electrolytes by capillary electrophoresis using a new free software AnglerFish

Thermodynamic acidity constants (acid or acid-base dissociation constants, sometimes called also as ionization constants) and limiting ionic mobilities (both of them at defined temperature, usually 25°C) are the fundamental physicochemical characteristics of a weak electrolyte, that is, weak acid or weak base or ampholyte. We introduce a novel method for determining the data of a weak electrolyte by the nonlinear regression of effective electrophoretic mobility versus buffer composition dependence when measured in a set of BGEs with various pH. To correct the experimental data for zero ionic strength we use the extended Debye-Hückel model and Onsager-Fuoss law with no simplifications. Contrary to contemporary approaches, the nonlinear regression is performed on limiting mobility data calculated by PeakMaster's correction engine, not on the raw experimental mobility data. Therefore, there is no requirement to perform all measurements at a constant ionic strength of the set of BGEs. We devised the computer program AnglerFish that performs the necessary calculations in a user-friendly fashion. All thermodynamic pKa values and limiting electrophoretic mobilities for arbitrarily charged substances having any number of ionic forms are calculated by one fit. The user input consists of the buffer composition of the set of BGEs and experimentally measured effective mobilities of the inspected weak electrolyte.     

Electrophoretic mobilities of cationic analytes in non-aqueous methanol, acetonitrile and their mixtures. Influence of ionic strength and ion-pair formation

The mobilities of cationic analytes in organic solvents and water are compared, and the reasons for differences in the mobilities are discussed in detail. Actual mobilities (at background electrolyte concentration 10 mmol/l) of anilinium ions were determined by capillary zone electrophoresis in water, methanol, acetonitrile and mixtures of methanol and acetonitrile (in volume ratios 1:1, 1:3 and 3:1). The actual mobilities correlated with the viscosity of the organic solvent: the products of actual mobility and viscosity were constant within 7%. However, these products were significantly larger in water. Larger products of mobility and viscosity in water were also found for unsubstituted anilinium when the absolute mobility (at zero ionic strength) was taken into consideration. Thus, ion-solvent interactions must be responsible for the seemingly high mobility in water compared with that in organic solvents. This finding can be explained by the effect of the ion on the water structure. Based on equilibrium constant for ion-pair formation given in the literature, about 20% of the main background electrolyte constituent (tetrapropylammonium perchlorate) is associated at 10 mmol/l concentration in acetonitrile. Comparison of the plot of the measured mobilities of the analytes vs. the square root of the corrected ionic strength of the background electrolyte in acetonitrile with the prediction based on the Debye-Hückel-Onsager theory showed the measured mobilities deviate negatively from the theoretical line. This is apparently due to ion pairing, which takes place for the analytes as well.     

Primary electroviscous effect in a dilute suspension of soft particles

A theory for the primary electroviscous effect in a dilute suspension of soft particles (i.e., particles coated with an ion-penetrable surface layer of polyelectrolytes) in an electrolyte solution is presented. The general expression for the effective viscosity eta s of the suspension and the primary electroviscous coefficient p, which is further expressed in terms of a function L, is given. On the basis of the general expressions, we derive approximate analytic expressions for eta s and p, which are applicable when the density of the fixed charges distributed within the surface layer is low. Further we obtain a simple approximate analytic expression (without involving numerical integrations) for p applicable for most practical cases. It is found that the function L exhibits a minimum when plotted as a function of kappa a (kappa is the Debye-Hückel parameter and a is the particle core radius), unlike the case of a suspension of hard particles, in which case L decreases as kappa a increases, exhibiting no minimum. The presence of a minimum for the case of a suspension of soft particles is due to the fact that L is proportional to 1/kappa 2 at small kappa a and to kappa 2 at large kappa a. Because of the presence of this minimum, the difference in L between soft and hard particles becomes very large for large kappa a.     

Effect of hydroacoustic treatment on the state of aqueous solutions of sodium alginate

Effect of a hydroacoustic treatment in a rotary-pulsed apparatus on the properties of sodium alginate solutions: dynamic viscosity, intrinsic viscosity, surface tension, and optical density, was studied. The contribution of the mechanical degradation of macromolecules to the observed decrease in the viscosity of alginate solutions was determined. The effect of the ionic strength of the solutions on their stability against hydroacoustic degradation was analyzed.     

Determination of stability constants of complexes of neutral analytes with charged cyclodextrins by affinity capillary electrophoresis

A novel procedure for the determination of stability constants in systems with neutral analytes and charged complexation agents by affinity capillary electrophoresis was established. This procedure involves all necessary corrections to achieve precise and reliable data. Temperature, ionic strength, and viscosity corrections were applied. Based on the conductivity measurements, the average temperature of the background electrolyte in the capillary was kept at the constant value of 25°C by decreasing the temperature of the cooling medium. The viscosity correction was performed using the viscosity ratio determined by an external viscosimeter. The electrophoretical measurements were performed, at first, at constant ionic strength. In this case, the increase of ionic strength caused by increasing complexation agent concentration was compensated by changing of the running buffer concentration. Subsequently the dependence of the analyte effective mobility on the complexation agent concentration was measured without the ionic strength compensation (at variable ionic strength). The new procedure for determination of the stability constants even from such data was established. These stability constants are in a very good agreement with those obtained at the constant ionic strength. The established procedure was applied for determination of the thermodynamic stability constants of (R, R)-(+)- and (S, S)-(-)-hydrobenzoin and R- and S-(3-bromo-2-methylpropan-1-ol) complexing with 6-monodeoxy-6-mono(3-hydroxy)propylamino-β-cyclodextrin hydrochloride.     

Fibrinogen conformations and charge in electrolyte solutions derived from DLS and dynamic viscosity measurements

Hydrodynamic properties of fibrinogen molecules were theoretically calculated. Their shape was approximated by the bead model, considering the presence of flexible side chains of various length and orientation relative to the main body of the molecule. Using the bead model, and the precise many-multipole method of solving the Stokes equations, the mobility coefficients for the fibrinogen molecule were calculated for arbitrary orientations of the arms whose length was varied between 12 and 18nm. Orientation averaged hydrodynamic radii and intrinsic viscosities were also calculated by considering interactions between the side arms and the core of the fibrinogen molecule. Whereas the hydrodynamic radii changed little with the interaction magnitude, the intrinsic viscosity exhibited considerable variation from 30 to 60 for attractive and repulsive interactions, respectively. These theoretical results were used for the interpretation of experimental data derived from sedimentation and diffusion coefficient measurements as well as dynamic viscosity measurements. Optimum dimensions of the fibrinogen molecule derived in this way were the following: the contour length 84.7nm, the side arm length 18nm, and the total volume 470nm(3), which gives 16% hydration (by volume). Our calculations enabled one to distinguish various conformational states of the fibrinogen molecule, especially the expanded conformation, prevailing for pH<4 and lower ionic strength, characterized by high intrinsic viscosity of 50 and the hydrodynamic radius of 10.6nm. On the other hand, for the physiological condition, that is, pH=7.4 and the ionic strength of 0.15M NaCl, the semi-collapsed conformation dominates. It is characterized by the average angle equal to <φ>=55°, intrinsic viscosity of 35, and the hydrodynamic radius of 10nm. Additionally, the interaction energy between the arms and the body of the molecule was predicted to be -4kT units, confirming that they are oppositely charged than the central nodule. Results obtained in our work confirm an essential role of the side chains responsible for a highly anisotropic charge distribution in the fibrinogen molecule. These finding can be exploited to explain anomalous adsorption of fibrinogen on various surfaces.     

Estimation of aspect ratio of cellulose nanocrystals by viscosity measurement: influence of surface charge density and NaCl concentration

Cellulose nanocrystals (CNCs) with similar size and various surface charge densities were prepared by sulfuric acid hydrolysis and NaOH desulfation. The influence of surface charge density and NaCl concentration on the intrinsic viscosity of CNC suspensions and predicted aspect ratio were investigated by Ubbelohde viscometer. With decreased CNC surface charge density, the intrinsic viscosity initially decreased due to the electric double layers on the CNC surface and subsequently increased due to CNC aggregation. To screen electroviscous effect, NaCl was added into CNC suspensions. With increased NaCl concentration, the intrinsic viscosity of CNC suspensions first decreased and then increased. The aspect ratios of CNCs predicted by Batchelor equation from the minimum intrinsic viscosity were consistent with that measured by transmission electron microscopy. Suspensions of CNCs with higher surface charge density needed less NaCl to obtain minimum intrinsic viscosity. The NaCl content that should be added to the suspension to predict the actual physical aspect ratio of CNC can be estimated by Debye–Hückel theory, assuming that the Debye length is equal to the CNC diameter.     

Cell models for the primary electroviscous effect

The primary electroviscous effect in a nondilute suspension of charged spherical particles is studied by means of cell models. The governing equations are derived, and then analytic results are obtained by restricting attention to the limit of thin double layers, small Hartmann and Peclet numbers, and small potentials. Previous work has assumed that the velocity at the outer boundary of the cell is identical to the imposed flow, as proposed by Simha (J. Appl. Phys. 1952, 23, 1020). Results with this boundary condition are compared against those predicted when the tangential shear stress on the outer boundary is assumed to be unperturbed, as proposed by Happel (J. Appl. Phys. 1957, 28, 1288). Both the hydrodynamic and electroviscous contributions to the effective viscosity are smaller with the Happel boundary condition, showing that such cell models offer a range of predictions and should be used with caution.