Numerical calculation of the dielectric and electrokinetic properties of vesicle suspensions

The dielectric and electrokinetic properties of aqueous suspensions of vesicles (unilamellar liposomes) are numerically calculated in the 1 Hz to 1 GHz frequency range using a network simulation method. The model consists of a conducting internal medium surrounded by an insulating membrane with fixed surface charges on both sides. Without an applied field, the internal medium is in electric equilibrium with the external one, so that it also bears a net volume charge. Therefore, in the presence of an applied ac field, there is fluid flow both in the internal and in the external media. The obtained results are qualitatively different from those corresponding to suspensions of charged homogeneous particles, mainly due to the existence of an additional length scale (the membrane thickness) and the corresponding dispersion mechanism, charging of the membrane. Because of this dispersion, the shapes of the spectra change with the size of the particles (at constant zeta potential and particle radius to Debye length ratio) instead of merely shifting along the frequency axis. A comparison between the numerical results and those obtained using approximate analytical expressions shows deviations that are, in general, sufficiently large enough to show the necessity to use numerical results in order to interpret broad frequency range dielectric and electrokinetic measurements of vesicle suspensions.     

Electrokinetics in extremely bimodal suspensions

Prompted by the results obtained by Mantegazza et al. [Nature Physics 1 (2005) 103], where the electric birefringence of suspensions of elongated particles was strikingly affected by the presence of a sea of very small (size ratio lower than 10:1) colloidal spheres, we have undertaken an investigation of other electrokinetic phenomena in suspensions containing various relative concentrations of large (Teflon or polystyrene latex) and small (nanometer-sized silica spheres) colloids. We have determined the quantities that might be greatly affected by the size distribution of the particles, mainly in the presence of ac electric fields, since the response of the suspensions will show very characteristic relaxations, dominated in principle by the size of the particles. In this work, we report on measurements of the dielectric dispersion of mixed particles as a function of the concentration, ionic strength, and field frequency. The results indicate that the response is not just a simple combination of those obtained with suspensions of the individual particles, and in fact the presence of even small amounts of the small particles affects considerably the frequency response of the suspensions.     

Analysis of the dielectric permittivity of suspensions by means of the logarithmic derivative of its real part

Measurement of the dielectric permittivity of colloidal suspensions in the kilohertz frequency range (the so-called low-frequency dielectric dispersion) is a promising tool for the electrokinetic characterization of colloids. However, this technique is less used than would be desirable because of the difficulties associated with the measurements, the most important of which is the electrode polarization (EP). Recently (M. Wübbenhorst and J. Van Turnhout, Dielectrics Newsl. November (2000)) a method was proposed that appears capable of separating the unwanted electrode effects from the double-layer relaxation that we are interested in. The method, based on the logarithmic derivative of raw epsilon'(omega) data (epsilon'(omega) is the real part of the permittivity of the suspension for a frequency omega of the applied AC field), is first checked against the well-known theory of the AC permittivity of colloidal suspensions developed by DeLacey and White (E. H. B. DeLacey and L. R. White, J. Chem. Soc. Faraday Trans. 277, 2007 (1981)). We show that the derivative epsilon'(D)(omega)=-(pi/2)(partial differential epsilon'/partial differential ln omega) gives an excellent representation of the true imaginary part of the permittivity, epsilon'(omega). The technique is then applied to experimental data of the dielectric constant of polystyrene and ethylcellulose suspensions. We found that epsilon'(D) displays two separated behaviors when plotted against log omega in the frequency range 100 Hz-1 MHz: a monotonous decrease (associated with EP) followed by an absorption peak (associated with the double-layer relaxation, or alpha-relaxation). Interestingly, they are separated enough to make it possible to easily find the characteristic frequency of the alpha-relaxation. Fitting a relaxation function to epsilon'(D)(omega) after eliminating the part due to EP, we could calculate the real part epsilon'(omega) and compare it to the DeLacey and White (DW) theoretical predictions. A significantly better agreement between DW calculations and experimental epsilon'(omega) data is obtained when the logarithmic derivative method is used, as compared to the classical electrode-separation techniques.     

Transition from dilute to concentrated electrokinetic behavior in the dielectric spectra of a colloidal suspension

Dielectric spectroscopy is used to measure the complex permittivity of 200 and 100 nm diameter polystyrene latex suspended in potassium chloride (KCl) solutions over the frequency range 10(4)-10(7) Hz as a function of particle volume fraction (?) and ionic strength. Dilute suspension dielectric spectra are in excellent agreement with electrokinetic theory. A volume fraction dependence of the dielectric increment is observed for low electrolyte concentrations (0.01, 0.05, and 0.1 mM) above ? ≈ 0.02. This deviation from the dilute theory occurs at a critical frequency ω* that is a function of volume fraction, particle size, and ionic strength. The dielectric increment of suspensions at the highest salt concentration (1 mM) shows no volume fraction dependence up to ? = 0.09. Values of ω* are collapsed onto a master curve that accounts for the length and time scales of ion migration between neighboring particles. The measured conductivity increment is independent of volume fraction and agrees with theory after accounting for added counterions and nonspecific adsorption.     

Dielectric relaxation behavior of colloidal suspensions of palladium nanoparticle chains dispersed in PVP/EG solution

Dielectric measurements were carried out on colloidal suspensions of palladium nanoparticle chains dispersed in poly(vinyl pyrrolidone)/ethylene glycol (PVP/EG) solution with different particle volume fractions, and dielectric relaxation with relaxation time distribution and small relaxation amplitude was observed in the frequency range from 10(5) to 10(7) Hz. By means of the method based on logarithmic derivative of the dielectric constant and a numerical Kramers-Kronig transform method, two dielectric relaxations were confirmed and dielectric parameters were determined from the dielectric spectra. The dielectric parameters showed a strong dependence on the volume fraction of palladium nanoparticle chain. Through analyzing limiting conductivity at low frequency, the authors found the conductance percolation phenomenon of the suspensions, and the threshold volume fraction is about 0.18. It was concluded from analyzing the dielectric parameters that the high frequency dielectric relaxation results from interfacial polarization and the low frequency dielectric relaxation is a consequence of counterion polarization. They also found that the dispersion state of the palladium nanoparticle chain in PVP/EG solution is dependent on the particle volume fraction, and this may shed some light on a better application of this kind of materials.     

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.     

Dielectric spectroscopy of Anabaena 7120 protoplast suspensions

The dielectric spectroscopy of Anabaena 7120 protoplast suspensions has been investigated over the frequency range of 40 Hz-110 MHz. The protoplast suspensions showed a complicated dielectric dispersion consisting of at least four distinct sub-dispersions with the increasing frequencies due to the Maxwell-Wagner interfacial polarization. The double-shell model, in which an equivalent shell of thylakoid was assumed inside the cytoplasm, was adopted to describe the special morphology of the protoplast. Under the assumption that the conductivity of plasmalemma was negligible and the conductivity of the equivalent shell was 0.1 microS/cm, we attempted to estimate the dielectric properties of various protoplast components by fitting theoretical curve to experimental data. The relative permittivity of the plasmalemma epsilon(mem) was estimated to be 6.5+/-0.5, and the permittivity of the equivalent shell of thylakoid epsilon(thy) was estimated to be about 3.2+/-0.2. The permittivity epsilon(cyt) and conductivity kappa(cyt) of the cytoplasm were estimated to be 60 and 0.88+/-0.11 mS/cm, respectively. The permittivity epsilon(nuc) and conductivity kappa(nuc) of the nucleoplasmic region were determined to be 100 and 0.13+/-0.02 mS/cm, respectively.     

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.     

沸石及核壳结构聚合物粒子分散系的介电解析── 粒子排列模式对体积分数的解释

在40 Hz～110 MHz频率范围对NaA沸石堆积体系和聚苯乙烯-聚吡咯悬浮液进行了介电测量. 两类体系分别在105和107 Hz表现出因界面极化产生的弛豫. 利用Hanai理论解析两类体系的介电谱, 发现解析体积分数与实测体积分数之间存在与体系的浓度相关的明显差异. 通过分析Wagner原始模型阐明了差异的原因, 指出了分散相粒子相互作用力与差异程度间的内在联系, 从介电角度为胶体分散系中粒子统计排列方式的确定提供了判定依据: 当分散系浓度高于临界值时, 其最可取粒子统计排列模式为六方最密型; 低于临界值后, 排列模式随浓度的降低逐渐向简单立方型转变.     

Dielectric analysis of a nanoscale particle in an aqueous solution of low electrolyte concentration

The dielectric spectra of aqueous suspensions of nanoscale silica particles (8 and 24 nm) with low electrolyte concentrations were investigated as a function of the particle concentration. Obvious dispersions observed in the frequency range of 10-10(5) kHz are explained by the multiple effects of the interfacial polarization and the polarization of counterions by using a two-step model and the corresponding dielectric analytical method arising from the combination of Hanai's method and O'Konski's theory. The phase parameters, which reflect the inner properties of constituent phases of the system, are calculated and discussed in detail. The validity of the two-step model was tested in terms of the standard electrokinetic model deduced from pure theories.     

Dielectric analysis of macroporous anion-exchange resin beads suspensions

Dielectric measurements were carried out for suspensions of D354 anion-exchange beads dispersed in electrolyte solutions at different concentrations, and distinct Maxwell-Wagner dielectric relaxations were observed around 10(6) Hz. Through fitting the experimental data we obtained the dielectric parameters of the suspensions, and then we calculated the phase parameters from the dielectric parameters and the measured volume fractions by Hanai's method. In light of the present understanding of the interfacial properties, and with the information obtained from the phase parameters, we satisfactorily interpreted the concentration dependences of the dielectric parameters. It is concluded that Hanai's method is an effective tool for obtaining the properties of dispersed particles; the properties of the electrical double layer, which are mainly decided by the properties of the electrolyte solution, predict the dielectric behavior of suspensions with conducting particles. The dielectric relaxation spectroscopy (DRS), based on the M-W mechanism, is also a very sensitive tool for probing the properties of the liquid/solid interface.     

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.     

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.     

离子交换树脂悬浊液的介电弛豫谱研究

研究了D354阴离子交换树脂分散在不同浓度KCl溶液中的悬浊液的频率域介电谱,发现在测量频率为106～107 Hz处出现了显著的介电弛豫现象,得出了介电常数、电导率以及弛豫时间随KCl溶液浓度的特异的变化关系,理论分析表明,该弛豫是一个以界面极化为主的非单一极化机制的弛豫过程,进而利用Maxwell-Wagner界面极化理论和双电层性质解释了该体系的特异介电行为,得到了树脂悬浊液在外加交变电场下的离子迁移和聚集信息,并确定了该树脂在静态平衡下双电层中对离子的相对离子强度.     

Dielectric and electrical properties of electrorheological carbon suspensions

Measurements of electrorheological (ER) effects, dielectric properties, and electrical conductivity are made on an ER suspension composed of carbonaceous particles and silicone oil to understand the mechanism which governs the ER effect. In the frequency dependence of the dielectric permittivities, a dielectric dispersion is observed in the first-order dielectric permittivity, while in the third-order dielectric permittivity a resonance peak, which is due to shear-induced particle rotation, is recognized, showing that such dielectric properties are closely related to ER properties of the suspension. An electrical conduction mechanism, which is responsible for the ER effect, is also investigated from the dependence of dc electrical conductivity on electric-field strength and temperature.     

The use of dielectric spectroscopy for the characterization of polymer-induced flocculation of polystyrene particles

The flocculation of colloidal suspensions is an important unit operation in many industries, as it greatly improves the performance of solid separation processes. The number of available techniques for evaluating flocculation processes on line is limited, and most of these are only functional in dilute suspensions. Thus, techniques usable for flocculation characterization in high-solids suspensions are desirable. This study investigates the use of dielectric spectroscopy to monitor the flocculation of polystyrene particles with a cationic polymer. The frequency-dependent permittivity is modeled and the model parameters are used to describe the particle aggregation. The results show a peak in the modeled time constants of the dielectric relaxation at the onset of flocculation. Further, the adsorption of polymeric flocculant onto the particle surface results in a reduction in particle charge, evident as a decrease in the magnitude of the dielectric dispersion. The use of dielectric spectroscopy is found to be valuable for assessing flocculation processes in high-solids suspensions, as changes in parameters such as floc size and charge can be detected.     

Temperature Dependent Dielectric Relaxation in Solvent Mixtures at Microwave Frequencies

By the use of time domain reflectometry method, dielectric measurements were carried out on dimethylformamide‐2‐nitrotoluene solvent mixtures in the frequency range 10 MHz‐20 GHz, at various temperatures from 15 °C to 45 °C. These solvent mixtures as well as pure solvents display a Debye type dispersion. Their frequency dependent dielectric properties can be summarized by the three parameters in the Debye equation: a static permittivity, permittivity at high frequency and a dielectric relaxation time constant. The free energy of activation for dipolar relaxation process and the Kirkwood correlation factor were determined using these fitting parameters for these solvent mixtures at various concentrations and temperatures. By using these dielectric parameters, the excess permittivity and excess inverse relaxation time is obtained. The excess permittivity is found to be positive for all concentrations and temperatures whereas the excess inverse relaxation time is negative.     

Dielectric properties of aqueous zwitterionic liposome suspensions

The dielectric spectra of aqueous suspensions of unilamellar liposomial vesicles built up by zwitterionic phospholipids (dipalmitoylphosphatidyl-choline, DPPC) were measured over the frequency range extending from 1 kHz to 10 MHz, where the interfacial polarization effects, due to the highly heterogeneous properties of the system, prevail. The dielectric parameters, i.e., the permittivity epsilon'(omega) and the electrical conductivity sigma(omega), have been analyzed in terms of dielectric models based on the effective medium approximation theory, considering the contribution associated with the bulk ion diffusion on both sides of the aqueous interfaces. The zwitterionic character of the lipidic bilayer has been modeled by introducing an "apparent" surface charge density at both the inner and outer aqueous interface, which causes a tangential ion diffusion similar to the one occurring in charged colloidal particle suspensions. A good agreement with the experimental results has been found for all the liposomes investigated, with size ranging from 100 to 1000 nm in diameter, and the most relevant parameters have briefly discussed in the light of the effective medium approximation theory.