Electric properties of macromolecules. XIII. Transient electric birefringence of sodium polyethylenesulfonate solutions

The electric birefringence of sodium polyethylenesulfonate in water has been studied. For a low molecular weight fraction, the electric field dependence followed the Kerr law quite closely. For a higher molecular weight fraction, the specific Kerr constant was much larger, and pronounced saturation of the electric birefringence was observed in fields of 15 kv./cm. The specific Kerr constant increased with decreasing polyelectrolyte concentration in pure water. On the other hand, it decreased on isoionic dilution. The saturation effect was the more marked, the lower the polyelectrolyte concentration. The saturation behavior resembled that of permanent dipole orientation, but this mechanism was not supported by the build-up of the birefringence. The magnitudes of specific Kerr constants of various types of macromolecules in solution are tabulated and discussed.     

Frequency dependence of the dielectric and electro-optic response in suspensions of charged rod-like colloidal particles

We have performed an experimental investigation on the electrokinetic properties of charged rod-like fluorinated latex colloids. Systematic measurements of electrophoretic mobility, dielectric constant and electric birefringence have been performed as a function of the concentration of added nonionic surfactant and salt. In the investigated range of parameters, the zeta potential is a strongly decreasing function of the concentration of nonionic surfactant, while it is basically independent from ionic strength. We have obtained the frequency dependence of dielectric constant and Kerr constant as a function of zeta-potential and ionic strength. We observe the transition from a low frequency behavior, where both the dielectric constant and the Kerr constant are enhanced by the presence of the double layer, to a high frequency behavior, where both quantities take the value expected for unchanged particles in an insulating medium. The shape of the frequency dispersion of the Kerr constant coincides with that of the dielectric constant, but the cut-off frequencies are the same only when the zeta-potential of the particles is low.     

Proprietes dynamo-optiques du bromure de poly-N-butyl-4-vinylpyridinium dans differents solvants

Flow birefringence measurements on polybutylvinylpyridinium bromide have confirmed the change of the sign of the optical anisotropy previously observed by the electric birefringence method. The birefringence is negative in aqueous media, but positive in some organic solvents such as nitromethane. The estimation of the intrinsic optical anisotropy shows that this parameter is negative in water as well as in nitromethane; this is consistent with an orientation of the pyridinium lateral group perpendicular to the long axis of the particle. The positive sign of the birefringence displayed in nitromethane can be attributed both to an important contribution of form anisotropy, and to a pronounced decrease of the intrinsic optical anisotropy; the latter is explained by a conformational change of the polyelectrolyte which becomes more coiled and more flexible in solvents of lower dielectric constant.     

Electric birefringence of dispersions of platelets

This paper describes the electro-optic response of a suspension of disk-like colloids. We have considered aqueous suspensions of Gibbsite platelets and measured the electrically induced birefringence in the broad frequency range 10(2)-10(8) Hz. When simply dispersed in an electrolyte solution, these particles orient with their major axis parallel to the electric field at all frequencies. The spectral dependence of their Kerr coefficient features three regimes: an electrokinetic α-relaxation within the kHz range, a conductive Maxwell-Wagner-O'Konski (MWO) relaxation having characteristic frequency in the 1-10 MHz range, and a nonzero high frequency asymptote. We quantitatively analyze the MWO spectral component and the high-frequency asymptote on the basis of a model developed for oblate particles. This analysis enables us to obtain the relevant particle properties: surface conductivity, zeta potential, and intrinsic Gibbsite birefringence. When the particles are dispersed in a mixture that also contains smaller spherical particles that have a charge of the same sign, their electric birefringence becomes negative at low frequency. This anomalous orientation of the platelets is analogous to that observed in mixtures of prolate and spherical particles, and demonstrates the anomalous birefringence as a universal property of suspensions of nonspherical particles when surrounded by smaller charged particles.     

Kerr effect of low melting nematic liquid crystals with negative dielectric anisotropy

The two low melting nematic liquid crystals, 2-chloro-4-heptylphenyl 4-pentylbicyclo[2,2,2]octane-1-carboxylate (7CP5BOC) and 2-chloro-4-heptylphenyl 4-heptylbicyclo[2,2,2]octane-1-carboxylate (7CP7BOC) have been investigated to determine their electro-optical behaviour and third order non-linearity by the static Kerr effect method. Both liquid crystals are laterally substituted by a single chlorine atom located close to the ester linking group. The temperature dependence of the electric Kerr constant in the isotropic phase and the pretransitional behaviour have been investigated for these low birefringence nematic liquid crystals in the isotropic phase. Both the compounds, with negative dielectric anisotropy, have a positive Kerr constant. The Landau-de Gennes model was obeyed for these compounds.     

Dielectric response of a concentrated colloidal suspension in a salt-free medium

In this paper the complex dielectric constant of a concentrated colloidal suspension in a salt-free medium is theoretically evaluated using a cell model approximation. To our knowledge this is the first cell model in the literature addressing the dielectric response of a salt-free concentrated suspension. For this reason, we extensively study the influence of all the parameters relevant for such a dielectric response: the particle surface charge, radius, and volume fraction, the counterion properties, and the frequency of the applied electric field (subgigahertz range). Our results display the so-called counterion condensation effect for high particle charge, previously described in the literature for the electrophoretic mobility, and also the relaxation processes occurring in a wide frequency range and their consequences on the complex electric dipole moment induced on the particles by the oscillating electric field. As we already pointed out in a recent paper regarding the dynamic electrophoretic mobility of a colloidal particle in a salt-free concentrated suspension, the competition between these relaxation processes is decisive for the dielectric response throughout the frequency range of interest. Finally, we examine the dielectric response of highly charged particles in more depth, because some singular electrokinetic behaviors of salt-free suspensions have been reported for such cases that have not been predicted for salt-containing suspensions.     

Electric dipole moments of particle aggregates in magnetite colloidal solutions in liquid dielectrics

The permanent electric moments and the electric polarizability anisotropy of particle aggregates are determined from the results of measuring the birefringence of a magnetite colloidal solution in kerosene subjected to constant and pulsed electric fields. A possible mechanism of generating an induced dipole moment in the aggregates is analyzed. The moment is characterized by a long relaxation time and, according to the results of optical experiments, is interpreted as permanent. The calculated dipole moments are consistent with the experimental data in the order of magnitude.     

Electrical and dynamooptical properties of Frechet dendron-modified polystyrene molecules in solutions

The electrooptical, dynamic, and dielectric characteristics of polystyrene modified by the Frechet dendrons of 1–4 generations have been studied in benzene, chloroform, and THF solutions. It has been shown that the Kerr constant and the shear optical coefficient for all the studied polymers coincide in sign and their absolute values increase with the dendron generation number. The intrinsic optical anisotropy of the repeating unit of dendronized polystyrene molecules is negative in sign, and its absolute value tends to grow with an increase in the generation number of dendrons. The frequency dispersions of the Kerr constand and of the dielectric polarization have been discovered for solutions of the modified polymer. The ratio between the times of relaxation characterizing the dispersion of dielectric permittivity and of the Kerr constant of solutions and the times of a rise and decay of electric birefringence measured on the onset and termination of the rectangular-pulsed field does not obey the longitudinal relaxation theory for polar macromolecules. The relaxation times of dielectric polarization and of electric birefringence tend to increase with the dendron generation number.     

Polarizability and Kerr constant of proteins by boundary element methods

A precise implementation of the boundary element method has been applied to the computation of the polarizability and the Kerr constant of eight soluble proteins. The method is demonstrated to be accurate and precise by comparison with analytical values for spheroids. Two different integral equations have been solved: (1) an exact equation with explicit dielectric constant dependence, and (2) an exact equation for a metallic body. The dielectric dependence for the metallic body case is built in with a generalization of the ellipsoid formula. Both methods agree quantitatively with each other for low relative dielectric constants. A full tensor expression for the Kerr constant yields perfect agreement with experiment for some proteins and badly under reports for the rest. The protein structure is obtained from a crystallographic database and is assumed rigid throughout the TEB measurement. Electrolyte effects are neglected. The Kerr constant is dominated by the protein dipole moment and is quite sensitive to the orientation of the dipole moment relative to the principal axes of the polarizability tensor. Several possible reasons for the large discrepancy between some computed and measured values are discussed.     

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.     

Electric birefringence in solutions of cellulose carbanilate as a function of molecular weight

Electro-optical, dynamo-optical and hydrodynamic properties of solutions of some fractions of cellulose carbanilate (CC) in dioxan have been investigated. In a variable electric field, strong dispersion of the Kerr effect is observed, indicating the dipole-orientational mechanism of electrical birefringence and its relaxation. A comparison of relaxation times of fractions with their molecular weights and intrinsic viscosities indicates that the mechanism responsible for the Kerr effect is the rotation of the molecule as a whole in an electric field (a kinetically rigid molecule). The dependence of relaxation time on molecular weight (M) shows that, with increase in M, the conformation of the CC molecule changes from a slightly curved rod to a rigid Gaussian coil. The same conclusion may be drawn from a study on the dependence of the equilibrium value of the Kerr constant on M. In the Gaussian range (high M), the Kerr effect depends on the longitudinal (with respect to the chain) component of the dipole moment formed by the CO bonds in the glucoside ring. At low M, the transverse components of the monomer dipoles begin to play an important part in birefringence.     

Electrooptics of beta-FeOOH Particles in Aqueous Media

Reversing-pulse electric birefringence (RPEB) of a nearly monodisperse iron(III) hydroxide oxide sample in the beta-form (beta-FeOOH) was measured at 25 degrees C and at a wavelength of 633 nm in aqueous media in the presence of NaCl. The concentrations of beta-FeOOH and added NaCl varied between 0.00111 and 0.0555 g/L and 0.03 and 2.0 mM, respectively. Except for the suspensions with high salt concentrations, each RPEB signal showed a dip or minimum in the reverse process upon electric field reversal, together with a smooth rise in the buildup and a fall in the decay process. The observed signals were analyzed with a new RPEB theory, which takes into account not only the permanent electric dipole moment (μ) but also the root-mean-square ionic dipole moment ((1/2)) due to the ion fluctuation in ion atmosphere, in addition to the field-induced electronic (covalent) dipole moment Deltaalpha' E. The results showed that the slowly fluctuating moment of (1/2) is by far the most predominant one for the field orientation of the beta-FeOOH particle, though the permanent dipole moment μ may not be completely excluded. The rotational relaxation time of the whole particle was evaluated from the decay signal, while the relaxation time for fluctuating ions was estimated from RPEB signal fitting. The sign of the steady-state birefringence for beta-FeOOH suspensions was positive without exception under the present conditions. The birefringence signals in the steady state (delta/d) were proportional to the second power of the applied field strength (E) in the low field region; thus, the Kerr law was verified to hold for beta-FeOOH suspensions. The specific Kerr constant was evaluated for each suspension by extrapolating the values of delta/d to zero field (E-->0). Copyright 2000 Academic Press.     

On the electrical polarization of polymer single crystals in suspension

A model is proposed for the electrical polarization that causes the orientation and, hence, the electric birefringence of a suspension containing single crystals of a poly(ethylene oxide)–polystyrene diblock copolymer or a poly(ethylene oxide) homopolymer. It serves to describe how an electric dipole moment lying in the plane of the single crystal can be induced by protons migrating in poly-(ethylene oxide). The resulting Kerr effect is calculated up to saturating fields, and the observed dispersion of the polarization in high frequency fields is explained as a space charge relaxation phenomenon. The estimated relaxation time agrees satisfactorily with published experimental data.     

The magnitude and temperature dependence of the Kerr constant in liquid crystal blue phases and the dark conglomerate phase

A new method of evaluating the Kerr constant in liquid crystals (LCs) is used to determine the temperature dependence of the Kerr effect in blue phases I and II (BPI and BPII) and to investigate the Kerr constant of the isotropic dark conglomerate (DC) phase. This method employs relatively small driving voltages and a vertical field switching (VFS) device geometry. An unusually large Kerr constant, K, is determined in the BPs of a non-polymer-stabilised material, ～3×10^?9 mV^?2 (BPI). The large value of K is attributed to significant pre-transitional values of the dielectric anisotropy and birefringence. K follows an inverse dependence on temperature and we consequently suggest that BPI demonstrates properties best suited to electro-optic devices. The new methodology has the advantage of revealing the dispersion of K in a single measurement. It is also possible to deconvolute the influence of the Kerr effect from measurements of electrostriction of the BP lattice. Finally, the Kerr effect has been measured for the first time in the DC phase of an oxadiazole bent-core liquid crystalline material, and is found to take rather low values, ～1×10^?11 mV^?2, which can be understood in the context of the physical properties of the material.     

Phase behavior of polarizable spherocylinders in external fields

Applied electric fields are known to induce significant changes in the properties of systems of polarizable molecules or particles. For rod-shaped molecules, the field-induced behavior can be rather surprising, as in the case of the negative electric birefringence of concentrated solutions of rodlike polyelectrolytes. We have investigated the interplay of shape anisotropy and field-induced anisotropy in molecular dynamics simulations of systems of polarizable soft spherocylinders in an electric field, in the limit of infinitely anisotropic polarizability, taking full account of mutual induction effects. We find a novel crystalline structure (K(2)) in the high-field limit, whose formation is driven by interactions between induced dipoles. For high pressures, the phase diagram exhibits a polar nematic phase between the hexagonal close-packed crystal phase and the K(2) phase. We also compare this system with an analogous system of spherocylinders with permanent electric dipoles and find that qualitatively similar behavior is obtained in the limit of strong coupling of the permanent dipoles to the external field.     

Effect of the microphase separation on the electro-optical properties of isotropic melts of thermotropic liquid crystals

An analytical expression for the free energy of the isotropic melt of a mesogen under the conditions of the microphase separation is obtained on the basis of the Landau-de Gennes approach. The temperature dependence of the orientation and translational order parameters of the parameter characterizing microstructuring and the Kerr constant of a melt is calculated. The theoretical calculations are compared with the results from studying electric birefringence in isotropic melts of comb polymers. It is revealed that the break in the temperature dependence of the inverse Kerr constant can occur at the temperature of microphase separation for phase transitions of the first and second kind.     

AC electrokinetics of conducting microparticles: A review

This paper reviews both theory and experimental observation of the AC electrokinetic properties of conducting microparticles suspended in an aqueous electrolyte. Applied AC electric fields interact with the induced charge in the electrical double layer at the metal particle–electrolyte interface. In general, particle motion is governed by both the electric field interacting with the induced dipole on the particle and also the induced-charge electro-osmotic (ICEO) flow around the particle. The importance of the RC time for charging the double layer is highlighted. Experimental measurements of the AC electrokinetic behaviour of conducting particles (dielectrophoresis, electro-rotation and electro-orientation) are compared with theory, providing a comprehensive review of the relative importance of particle motion due to forces on the induced dipole compared with motion arising from induced-charge electro-osmotic flow. In addition, the electric-field driven assembly of conducting particles is reviewed in relation to their AC electrokinetic properties and behaviour.     

Dielectric spectroscopy and electrophoretic mobility measurements interpreted with the standard electrokinetic model

We report results from complementary electrokinetic measurements-dielectric relaxation and electrophoretic mobility-undertaken to test the applicability of the standard electrokinetic theory with a model system. Dielectric spectra were obtained at frequencies between 1 kHz and 40 MHz with a new, two-electrode cell design [Hollingsworth and Saville, J. Colloid Interface Sci. 257 (2003) 65-76]; mobility data were acquired with an electrophoretic light scattering instrument. Data from the two-electrode cell were collected at different electrode separations and interpreted with newly developed procedures to remove the influence of electrode polarization. Methodology A employs extrapolation to infinite electrode separation to compute the dielectric constant and conductivity as functions of frequency. The contributions from suspended particles are reported in terms of dielectric constant and conductivity increments. Methodology B uses a theoretical model of electrode polarization and the standard electrokinetic model in a nonlinear regression scheme. Results are presented in several forms: frequency-dependent dielectric constant and conductivity increments, frequency-dependent dielectric constants and conductivities, and the complex dipole coefficient. It is shown that the standard model provides a consistent methodology for interpreting particle behavior; zeta-potentials inferred from mobility and dielectric relaxation agree to within experimental error. Moreover, the cell design and interpretation are straightforward and provide relatively simple ways to obtain complementary measurements over a wide frequency range. The results unambiguously show that electrokinetic character of this dispersion follows the standard model.     

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

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

Electrophoretic mobility of cylindrical soft particles

 A general theory for the electrophoresis of a cylindrical soft particle (i.e., a cylindrical hard colloidal particle coated with a layer of ion-penetrable polyelectrolytes) in an electrolyte solution in an applied transverse or tangential electric field is proposed. This theory unites two different electrophoresis theories for cylindrical hard particles and for cylindrical polyelectrolytes. That is, the general mobility expression obtained in this paper tends to the mobility expression for a cylindrical hard particle for the case where the polyelectrolyte layer is absent or the frictional coefficient in the poly-electrolyte layer becomes infinity, whereas it tends to that for a cylin-drical polyelectrolyte in the absence of the particle core. Simple approximate analytic mobility expressions are also presented. Received: 29 August 1996 Accepted: 7 November 1996