Electro-optic characteristics of optically interacting beta-FeOOH particles

In this article the influence of multiple light scattering on the basic electro-optic parameters of optically dense colloidal particles is analyzed. The model system is an aqueous suspension of monodisperse ellipsoidal beta-FeOOH particles that displays large electric light scattering variations, including sign reversal, at very low particle volume fractions (two orders of magnitude below the critical concentration of particle electric interactions). The scaling method permits the relative variations in particle electric polarizability to be followed and its relaxation frequency to be determined. Particle rotational relaxation frequency and the phase shift of the responses at this frequency are obtained by the alternating component of the effects. Characteristic field intensity curves in the low-frequency range are used to follow the relative changes induced by the slow electrokinetic effect. The experimental results show that, despite the drastic variations in the effects with volume fraction, the basic electro-optic parameters are independent of multiple scattering and can be adequately determined for any particle concentration, excluding a narrow range in the vicinity of the electro-optic sign reversal. The investigation demonstrates that the dependence of the frequency behavior of aqueous beta-FeOOH on particle volume fraction reported in the literature is due not to optical interactions but to variation of particle surface electric state in the process of dilution.     

Anomalous low-frequency electro-optic behavior of ferric oxide particles in the presence of poly(ethylene oxide)

Electro-optic techniques were used to investigate the influence of poly(ethylene oxide) (PEO) on the surface electric state of positively charged oxide particles. The variations in particle electrophoretic mobility of beta-FeOOH particles in the presence of PEO indicate significant changes in the surface electric state of the particles in the concentration interval of PEO 10(-2)-10(-1) g dm(-3). The electro-optic results for the same conditions were unexpected: no significant difference is observed in the value and the relaxation frequency of particle electric polarizability in the frequency domain of the alpha-relaxation (detected in the kilohertz range); particle rotational relaxation time also remains unchanged; considerable changes are detected only in the relaxation interval of particle rotation (detected in the hertz range). The obtained results reject the possibility of the formation on the particle surface of a thick polymer layer. A thin adsorption layer cannot explain the significant decrease in particle electrophoretic mobility. The variations in electrophoretic mobility are well correlated with the effects in the domain of particle rotation. A possible explanation of the observed effects is proposed, based on our previous investigations of the effects in the low-frequency domain. The presented results demonstrate that the important information on the electrokinetic charge distribution is not found in the domain of the alpha-dispersion, but in the domain of particle rotation.     

Steady electro-optic characteristics of noninteracting colloidal particles

In previous papers on the electro-optic effects of beta-FeOOH particles we proposed a new procedure for analysis of the low frequency behavior of charged particles. The procedure is based on comparison of characteristic field intensity curves on an appropriate scale and helps to test the dependence of the slow effects on particle surface electric polarizability (relaxing in the kilohertz domain). The results stimulated us to test the applicability of the method to other samples and to reconsider the literature data on the electro-optic behavior of charged colloids in the hydrodynamic domain. The aim of the present paper is to demonstrate on a series of samples similar features of the electro-optic responses of charged particles in the relaxation interval of particle rotation. The analysis leads to a new hypothesis for explanation of the complicated low frequency behavior of charged particles. The superposition of two slow effects (linear and quadratic with field intensity), relaxing in the relaxation interval of particle rotation, can explain the complicated frequency curves in this domain. One of the slow effects is observed for all polarizable particles. It is of negative sign and displays the features of an induced dipole effect dependent on the "kilohertz" induced moment. It corresponds to a slow stage of the surface polarization process related to electrokinetic charge. The linear slow effect shows permanent dipole like behavior and appears only at certain ionic content of the medium. It shows no direct dependence on counterion mobility and on the "kilohertz" induced moment and is probably due to surface charge nonuniformity.     

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.     

High frequency electric polarizability of bacteria E. coli: dependence on the medium ionic strength

There are two main kinds of electric polarizability of bacteria: surface charge dependent (SChD) and Maxwell-Wagner (MW) polarizability. The aim of this article is to distinguish SChD and MW components on the external bacteria surface. An electro-optic method (electric turbidity) was used to study the polarizability of E. coli fixed by formaldehyde at the frequency range 20kHz to 20MHz. According to the literature the SChD polarization disappears at such high frequencies and MW one gives the main contribution. However we found unexpected dependence on the outer medium electrolyte concentration, which cannot be explained by MW polarization. The results show that the polarizability decreases by ionic strength increasing in the same way as the double electric layer thickness does. Such behaviour is a characteristic for SChD polarizability, which allows us to conclude that this component has the main contribution on the external bacteria surface at the experimental frequencies mentioned.     

Dielectrophoretic assembly of metallodielectric Janus particles in AC electric fields

"Janus" particles with two hemispheres of different polarizability or charge demonstrate a multitude of interesting effects in external electric fields. We reported earlier how particles with one metallic hemisphere and one dielectric hemisphere self-propel in low-frequency alternating current (AC) electric fields. Here, we demonstrate the assembly of such Janus particles driven by AC electric fields at frequencies above 10 kHz. We investigated the relation between field-induced dielectrophoretic force, field distribution, and structure of the assemblies. The phase space for electric field intensity and frequency was explored for particle concentrations large enough to form a monolayer on a glass surface between two gold electrodes. A rich variety of metallodielectric particle structures and dynamics were uncovered, which are very different from those obtained from directed assembly of plain dielectric or plain conductive particles under the action of fields of similar frequency and intensity. The metallodielectric particles assemble into new types of chain structures, where the metallized halves of neighboring particles align into lanes along the direction of the electric field, while the dielectric halves face in alternating direction. The staggered chains may assemble in various orientations to form different types of two-dimensional metallodielectric crystals. The experimental results on the formation of staggered chains are interpreted by means of numerical simulations of the electric energy of the system. The assembly of Janus metallodielectric particles may find applications in liquid-borne microcircuits and materials with directional electric and heat transfer.     

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.     

Polarizability and complex conductivity of dilute suspensions of spherical colloidal particles with uncharged (neutral) polymer coatings

The polarizability of polymer-coated colloidal particles, as measured via dielectric relaxation spectroscopy, reflects on the degree to which convection, diffusion, and electromigration deform the equilibrium double layer. With a polymer coating, convection and electro-osmosis are resisted by hydrodynamic drag on the polymer segments. The electro-osmotic flow near the underlying bare surface is therefore diminished. Characteristics of the particles and the adsorbed polymer can, in principle, be inferred by measuring the frequency-dependent polarizability. In this work, "exact" numerical solutions of the electrokinetic equations are used to examine how adsorbed polymer changes the particle polarizability and, hence, the conductivity and dielectric constant increments of dilute suspensions. For neutral polymer coatings, the conductivity and dielectric constant increments are found to be very similar to those of the underlying bare particles, so the response depends mostly on the underlying bare particles. These observations suggest that dielectric spectroscopy is best used to determine the underlying surface charge, with characteristics of the coating inferred from the electrophoretic or dynamic mobility, together with the hydrodynamic radius obtained from sedimentation or dynamic light scattering. Addressed briefly are the effects of added counterions and nonspecific adsorption. The electrokinetic model explored in this work can be used to guide experiments (frequency and ionic strength, for example) to either minimize or maximize the sensitivity of the complex conductivity to the coating thickness or permeability.     

Dynamic electrophoretic mobility of spherical colloidal particles in salt-free concentrated suspensions

In this contribution, the dynamic electrophoretic mobility of spherical colloidal particles in a salt-free concentrated suspension subjected to an oscillating electric field is studied theoretically using a cell model approach. Previous calculations focusing the analysis on cases of very low or very high particle surface charge are analyzed and extended to arbitrary conditions regarding particle surface charge, particle radius, volume fraction, counterion properties, and frequency of the applied electric field (sub-GHz range). Because no limit is imposed on the volume fractions of solids considered, the overlap of double layers of adjacent particles is accounted for. Our results display not only the so-called counterion condensation effect for high particle charge, previously described in the literature, but also its relative influence on the dynamic electrophoretic mobility throughout the whole frequency spectrum. Furthermore, we observe a competition between different relaxation processes related to the complex electric dipole moment induced on the particles by the field, as well as the influence of particle inertia at the high-frequency range. In addition, the influences of volume fraction, particle charge, particle radius, and ionic drag coefficient on the dynamic electrophoretic mobility as a function of frequency are extensively analyzed.     

The universal electro-optic response of charged colloids in low electrolyte suspensions

The large dielectric dispersion of colloids in the low-frequency range, related to polarization of the particle surface electric layer (the alpha-relaxation), has been a subject of scientific interest for decades. In recent papers we advanced the idea that the process of particle surface polarization is partially detected by a second low-frequency relaxation displayed in the frequency domain of particle rotation. The aim of the present paper is to argument this view more consistently. The second low-frequency relaxation is as universal as alpha-relaxation and closely related to it. It is more sensitive to variations in particle electrophoretic mobility than the alpha-relaxation. The paper discusses several aspects concerning the phenomenon: the reasons for its difficult identification as a universal effect; the procedures helping its analysis; and the basic features and the origin of the phenomenon.     

Rheological and Electrokinetic Properties of Sodium Montmorillonite Suspensions

Because of their particular electric surface properties and crystal structure, most clay minerals possess a very high ion exchange capacity. Furthermore, the surface charge distribution is anisotropic: while faces of the laminar clay particles have a negative, pH-independent charge, edges may be positive or negative, depending on pH. In this work, we propose to contribute new data on particle-particle interaction and charge distribution, by means of measurements of the low-frequency dielectric dispersion (LFDD) of the clay suspensions. Because of the nonspherical shape of clay particles, there are no theoretical models capable of explaining the experimental relaxation spectra. Hence, we limit ourselves to obtaining indirect information by comparing LFDD spectra in different experimental conditions. The quantities of interest in LFDD are the value of the low-frequency dielectric constant, epsilon'(r)(0), and the characteristic or relaxation frequency, omega(cr). These two parameters were measured varying the weight fraction, straight phi, of clay (0.5, 1, and 1.5% w/v) and the pH of the dispersion medium (5, 7, and 9), while maintaining the ionic strength constant ([NaCl]=10(-4) M). It was found that the characteristic relaxation frequency of the dielectric constant was pH-dependent, with a significant minimum at pH 7 in all cases. The results are interpreted as the superposition of two independent relaxation phenomena, associated with edges and faces. With respect to the weight fraction influence, we have found a linear behavior of epsilon'(r)(0) with straight phi at pH 9, indicating the existence of no significant interaction between particles. However, at pH 7 a slight deviation of linearity is observed, and at pH 5 we observe a clearly nonlinear behavior, indicating a stronger degree of interaction between particles. This is in good agreement with the initial assumption that at acid pH values, the electric surface charge of faces is negative, whereas the edges possess a positive charge, thus favoring attractive face-to-edge interaction. Copyright 2000 Academic Press.     

PS-PBA粒子分散系的介电弛豫谱解析——同、反离子对弛豫的影响及表界面电参数的计算

制备了近纳米级的聚苯乙烯-丙烯酸丁酯(PS-PBA)复合微球粒子,并在40Hz～110×106Hz的宽频范围测量了该粒子分散在9种电解质中时的介电弛豫谱,发现了与PS微球粒子分散系不同的特异介电弛豫:低频弛豫对反离子种类具有敏感性而高频弛豫则与电解质种类几乎无关;根据Shilov-Dukhin模型和M-W-O模型分别分析了高、低频率的弛豫机制,并通过对介电谱的Cole-Cole拟合获得了各体系的介电参数.进一步利用Hanai方法由介电参数计算获得了所有体系的相参数;详细分析了体系的内部参数受PS-PBA微球自身结构以及电解质种类影响的原因;讨论了离子扩散系数对介电参数的影响,从而得出了低、高频的弛豫特征时间分别由同离子的扩散系数和反离子的扩散系数所决定之结论.最后,结合Grosse宽频介电理论计算了粒子表面的以及双电层的主要电参数,并分析了电解质种类差异对这些电参数的影响.     

Ion size effects on the electrokinetics of salt-free concentrated suspensions in ac fields

We analyze the influence of finite ion size effects in the response of a salt-free concentrated suspension of spherical particles to an oscillating electric field. Salt-free suspensions are just composed of charged colloidal particles and the added counterions released by the particles to the solution that counterbalance their surface charge. In the frequency domain, we study the dynamic electrophoretic mobility of the particles and the dielectric response of the suspension. We find that the Maxwell-Wagner-O’Konski process associated with the counterions condensation layer is enhanced for moderate to high particle charges, yielding an increment of the mobility for such frequencies. We also find that the increment of the mobility grows with ion size and particle charge. All these facts show the importance of including ion size effects in any extension attempting to improve standard electrokinetic models.     

Vertical motion of a charged colloidal particle near an AC polarized electrode with a nonuniform potential distribution: theory and experimental evidence

Electroosmotic flow in the vicinity of a colloidal particle suspended over an electrode accounts for observed changes in the average height of the particle when the electrode passes alternating current at 100 Hz. The main findings are (1) electroosmotic flow provides sufficient force to move the particle and (2) a phase shift between the purely electrical force on the particle and the particle's motion provides evidence of an E2 force acting on the particle. The electroosmotic force in this case arises from the boundary condition applied when faradaic reactions occur on the electrode. The presence of a potential-dependent electrode reaction moves the likely distribution of electrical current at the electrode surface toward uniform current density around the particle. In the presence of a particle the uniform current density is associated with a nonuniform potential; thus, the electric field around the particle has a nonzero radial component along the electrode surface, which interacts with unbalanced charge in the diffuse double layer on the electrode to create a flow pattern and impose an electroosmotic-flow-based force on the particle. Numerical solutions are presented for these additional height-dependent forces on the particle as a function of the current distribution on the electrode and for the time-dependent probability density of a charged colloidal particle near a planar electrode with a nonuniform electrical potential boundary condition. The electrical potential distribution on the electrode, combined with a phase difference between the electric field in solution and the electrode potential, can account for the experimentally observed motion of particles in ac electric fields in the frequency range from approximately 10 to 200 Hz.     

The effect of the concentration of dispersed particles on the mechanisms of low-frequency dielectric dispersion (LFDD) in colloidal suspensions

There are two mechanisms which are currently used to explain the low-frequency (kHz range) dispersion of the dielectric permittivity of suspensions in electrolyte solutions (LFDD). The first, the surface diffusion mechanism (SDM), associates the LFDD with the diffusion of bound ions along the particle surface caused by the applied electric field. The second, the volume diffusion mechanism (VDM), follows from the generalization for alternating fields of the classical theory of the relaxation effect in electrophoresis and associates the LFDD with the diffusion of free ions in the diffuse double layer. It has been found that VDM is much more strongly dependent on particle concentration than SDM, opening new possibilities for the investigation of each of these two mechanisms separately. The reason is that when the concentration of particles in suspension increases, the characteristic length for the propagation of volume diffusion processes decreases together with the decrease of the free electrolyte volume, whereas the characteristic length for the surface diffusion remains constant. Correspondingly, when particle concentration is raised, the relaxation time of the VDM effect must decrease, whereas it must remain constant for the SDM mechanism. Thus, by varying the concentration of particles in suspension, one can separate the dispersion curves of SDM and VDM. A simple model is elaborated which can be useful to predict the volume fraction dependence of the parameters of LFDD; in particular, its amplitude and critical frequency. The results are compared with experimental data obtained with polymer latex dispersions of volume fractions ranging from 3 to 16%. It is found that the dielectric behaviour (the volume fraction dependence of both the amplitude and critical frequency of LFDD) of the dispersions is reasonably well explained with our model, thus demonstrating that VDM prevails in the systems studied. Experimental data previously found by other authors are also discussed in the light of the model presented.     

Complexation of ferric oxide particles with pectins of different charge density

The effect of polyelectrolyte charge density on the electrical properties and stability of suspensions of oppositely charged oxide particles is followed by means of electro-optics and electrophoresis. Variations in the electro-optical effect and the electrophoretic mobility are examined at conditions where fully ionized pectins of different charge density adsorb onto particles with ionizable surfaces. The charge neutralization point coincides with the maximum of particle aggregation in all suspensions. We find that the concentration of polyelectrolyte, needed to neutralize the particle charge, decreases with increasing charge density of the pectin. The most highly charged pectin presents an exception to this order, which is explained with a reduction of the effective charge density of this pectin due to condensation of counterions. The presence of condensed counterions, remaining bound to the pectin during its adsorption on the particle surface, is proved by investigation of the frequency behavior of the electro-optical effect at charge reversal of the particle surface.     

Counterion release from adsorbed highly charged polyelectrolyte: an electrooptical study

The adsorption of sodium poly(4-styrene sulfonate) on oppositely charged beta-FeOOH particles is studied by electrooptics. The focus of this paper is on the release of condensed counterions from adsorbed polyelectrolyte upon surface charge overcompensation. The fraction of condensed Na+ counterions on the adsorbed polyion surface is estimated according to the theory of Sens and Joanny and it is compared with the fraction of condensed counterions on nonadsorbed polyelectrolyte. The relaxation frequency of the electrooptical effect from the polymer-coated particle is found to depend on the polyelectrolyte molecular weight. This is attributed to polarization of the layer from condensed counterions on the polyion surface, being responsible for creation of the effect from particles covered with highly charged polyelectrolyte. The number of the adsorbed chains is calculated also assuming counterion condensation on the adsorbed polyelectrolyte and semiquantative agreement is found with the result obtained from the condensed counterion polarizability of the polymer-coated particle. Our findings are in line with theoretical predictions that the fraction of condensed counterions remains unchanged due to the adsorption of highly charged polyelectrolyte onto weakly charged substrate.     

Electrooptic Study of Colloid Dispersions Stabilized by Polyelectrolyte Adsorption

Several electrooptic parameters can be used to follow the stages of polyelectrolyte adsorption on colloid particle surfaces. The process of electrostatic stabilization, achieved by polyelectrolyte surface recharging, is investigated for a series of samples and the results are compared to those obtained for low molecular surfactant stabilization. The results indicate a significant decrease of the relaxation frequency of particle electric polarizability in the presence of polyelectrolyte coverage. Evidence is given for the direct relation of the electrooptic relaxation frequency to the type of the adsorbed polymer molecule.     

Polarization behavior of polystyrene particles under direct current and low‐frequency (<1 kHz) electric fields in dielectrophoretic systems

The relative polarization behavior of micron and submicron polystyrene particles was investigated under direct current and very low frequency (<1 kHz) alternating current electric fields. Relative polarization of particles with respect to the suspending medium is expressed in terms of the Clausius–Mossotti factor, a parameter of crucial importance in dielectrophoretic‐based operations. Particle relative polarization was studied by employing insulator‐based dielectrophoretic (iDEP) devices. The effects of particle size, medium conductivity, and frequency (10–1000 Hz) of the applied electric potential on particle response were assessed through experiments and mathematical modeling with COMSOL Multiphysics^®. Particles of different sizes (100–1000 nm diameters) were introduced into iDEP devices fabricated from polydimethylsiloxane (PDMS) and their dielectrophoretic responses under direct and alternating current electric fields were recorded and analyzed in the form of images and videos. The results illustrated that particle polarizability and dielectrophoretic response depend greatly on particle size and the frequency of the electric field. Small particles tend to exhibit positive DEP at higher frequencies (200–1000 Hz), while large particles exhibit negative DEP at lower frequencies (20–200 Hz). These differences in relative polarization can be used for the design of iDEP‐based separations and analysis of particle mixtures.     

非导电球型粒子悬浮液宽频介电谱——薄双电层理论的计算机模拟

以Shilov等提出的带有紧密层表面电导率的非导电球型粒子悬浮液宽频介电弛豫的薄双电层理论为基础, 从电动力学角度解释了粒子分散系两种典型介电弛豫(高频和低频弛豫)的机制. 在此基础上, 利用Mathcad程序将该理论定量程序化并建立了粒子/水相分散系介电谱参数与体系内部相参数的关系. 进而利用该程序模拟了溶液浓度、Zeta电位以及分散粒子半径等内相参数对两种弛豫的影响, 结合该理论阐述了不同环境下这两种弛豫的变化规律, 从而为今后更好地利用这两种弛豫表征纳米至毫米级球形粒子分散系的各相电及界面性质提供了有价值的参考.