Polarization and interactions of colloidal particles in ac electric fields

Micrometer-sized polystyrene particles form two-dimensional crystals in alternating current (ac) electric fields. The induced dipole-dipole interaction is the dominant force that drives this assembly. We report measurements of forces between colloidal particles in ac electric fields using optical tweezers and find good agreement with the point dipole model. The magnitude of the pair interaction forces depends strongly on the bulk solution conductivity and decreases as the ionic strength increases. The forces also decrease with increasing field frequency. The salt and frequency dependences are consistent with double layer polarization with a characteristic relaxation frequency omega(CD) approximately a(2)/D, where a is the particle radius and D is the ion diffusivity. This enables us to reinterpret the order-disorder transition reported for micrometer-sized polystyrene particles [Lumsdon et al., Langmuir 20, 2108 (2004)], including the dependence on particle size, frequency, and ionic strength. These results provide a rational framework for identifying assembly conditions of colloidal particles in ac fields over a wide range of parameters.     

A theoretical study on the frequency-dependent electric conductivity of electrolyte solutions

The theory on the ultrasonic absorption of electrolyte solutions we have proposed previously [T. Yamaguchi et al., J. Chem. Phys. 126, 144505 (2007)] is extended to calculate the frequency-dependent electric conductivity of the solution. The ionic contribution of the dielectric relaxation spectrum is obtained at the same time. The theory is able to handle the contributions of both the ion-pair dynamics and the relaxation of ionic atmosphere, as is the case of ultrasonic absorption. The effect of the barrier height between the contact and solvent-separated ion pairs is investigated in detail. It is clarified that the competition between the dissociation and reorientational relaxation rates of the contact ion pair is an important factor for the ion pair to be regarded as the ion pair in terms of ionic conductivity.     

Dielectric properties and frequency response of self-assembled monolayers of alkanethiols

This paper presents dielectric properties of alkanethiol self-assembled monolayers (SAMs) under an ac electric field. Using a Hg-SAM/SAM-Hg junction, we measured the ac impedance of alkanethiol SAMs using a sinusoidal perturbation of 30 mV (peak-to-peak) with frequency ranging from 1 Hz to 1 MHz at zero bias. Semicircles at higher frequencies and at middle frequencies along with Warburg lines at lower frequencies were observed in complex plane impedance plots, that is, Nyquist plots. The frequency response of SAMs was analyzed by modeling the junction using an equivalent circuit and fitting the Nyquist plots. The semicircles at higher frequencies are attributed to the effect of the SAM/SAM interfaces, and the ones at middle frequencies are attributed to the effect of alkanethiol SAMs. The comparison in the plots of the imaginary part of the impedance Z against frequency for the bare Hg electrodes (in pure ethanal) and the SAM-covered Hg electrodes (in alkanethiol solution) supports the analysis. The Warburg lines are attributed to a certain ionic impurity. The dielectric loss spectra are further analyzed. Chain-length-dependent peaks, which correspond to different relaxation mechanisms, at higher frequencies and middle frequencies were observed in the spectra of the dissipation factor (tan delta vs frequency). The peaks move to small frequency with the increase of chain length of alkanethiols. Using a correlation of peak position with the chain length, we then derived active energies of 39-99 meV for alkanethiol SAMs of C7-C18 under an ac electric field.     

From Molecule to Cluster to Bulk: Water OH Vibrations in Different Surroundings

Vibrational spectra for the O—H stretching motion of HDO molecules in different surroundings have been calculated by quantum mechanical ab initio methods and compared with experimental spectra. The free water molecule, water chains, and ion–water clusters are discussed. Solvent effects on OH vibrations in liquid water have been calculated as well as “in-crystal” OH frequencies in some ice and ionic crystalline hydrate structures. The importance of nonadditivity effects, electron correlation (at the mp 2 level), and long-range interactions for the total frequency downshift is demonstrated. It is shown that the inclusion of these effects, in conjunction with a variational quantum mechanical treatment of the anharmonic vibrational stretching motion (force constants up to the fourth order), yields vibrational frequencies in quantitative agreement with experiment for a wide range of aqueous systems.     

Nuclear magnetic resonance investigation of dynamics in poly(ethylene oxide)-based lithium polyether-ester-sulfonate ionomers

Nuclear magnetic resonance spectroscopy has been utilized to investigate the dynamics of poly(ethylene oxide)-based lithium sulfonate ionomer samples that have low glass transition temperatures. (1)H and (7)Li spin-lattice relaxation times (T(1)) of the bulk polymer and lithium ions, respectively, were measured and analyzed in samples with a range of ion contents. The temperature dependence of T(1) values along with the presence of minima in T(1) as a function of temperature enabled correlation times and activation energies to be obtained for both the segmental motion of the polymer backbone and the hopping motion of lithium cations. Similar activation energies for motion of both the polymer and lithium ions in the samples with lower ion content indicate that the polymer segmental motion and lithium ion hopping motion are correlated in these samples, even though lithium hopping is about ten times slower than the segmental motion. A divergent trend is observed for correlation times and activation energies of the highest ion content sample with 100% lithium sulfonation due to the presence of ionic aggregation. Details of the polymer and cation dynamics on the nanosecond timescale are discussed and complement the findings of X-ray scattering and quasi-elastic neutron scattering experiments.     

Effects of ion atmosphere relaxation on dipole isomerization reactions in electrolyte solutions

A theoretical study of the effects of ion atmosphere relaxation on the rate of a model dipole isomerization reaction in electrolyte solutions is presented. The time-dependent ion atmosphere friction is calculated by using a molecular hydrodynamic theory which properly includes the static and dynamic interionic correlations through ionic structure factors and van Hove functions. The rate constant is determined by employing the well-known Grote-Hynes theory. Numerical results are obtained for the time-dependent ion atmosphere friction and for the rate of isomerization reaction in electrolyte solutions of varying ion concentration and dielectric constant. It is found that the ion atmosphere friction can have significant effects in reducing the rate of isomerization below the prediction of equilibrium solvation transition state theory.     

Segmental Dynamics and Ionic Conduction in Poly(vinyl methyl ether)-Lithium Perchlorate Complexes

Broadband dielectric spectroscopy was used to investigate the segmental dynamics and ionic conduction in LiClO4/PVME complexes with Li/O from 0.1/100 to 10/100, at temperatures from Tg to approximately Tg + 80 degrees C. Although no microphase separation is observed via DSC, dielectric experiments reveal two segmental relaxations and one localized ion motion process. The fastest process is attributed to relaxations of segments in ion-depleted domains and it slows down with increasing salt content, as does the ion motion. The segmental relaxation of PVME chains in ion-rich domains is even slower than the ion motion process, and about 104 times slower than the fast segmental process in the 0.5/100 complex. This process becomes faster with increasing LiClO4 content, despite the concurrent increase in the bulk Tg. Maximum molar conductivity is obtained in the 2/100 complex and the ionic conduction is about 10-9 S/cm at 30 degrees C. By using the dynamic bond percolation model, it was found that the ions move about 0.8 nm for the 0.5/100 complex at 25 degrees C at the time scale of the slow segmental relaxation, assuming that structural renewal is realized by the latter. This size, together with the strong correlation between the ionic conduction and the slow segmental relaxation, supports the idea that hopping from one segment to another one is probably the effective fundamental step giving rise to macroscopic conduction.     

Influence of cellulose gel matrix on BMIMCl ionic liquid dynamics and conductivity

Fast field-recycling magnetic resonance relaxometry (FFC NMR) was applied to measure the spin-lattice relaxation time, T ₁, of protons in pure ionic liquid (IL) 1-butyl-3-methylimidazolium chloride (BMIMCl) and when confined in cellulose (Cell) ion gel (Cell/BMIMCl) at different temperatures and different Larmor frequencies. The rotational and translational contributions were taken to interpret the relaxation data of neat BMIMCl and were described by Woessner’s and Torrey’s theoretical models, respectively. The ionic liquid–cellulose matrix interaction detected in 10 wt% polymer-ion gel was interpreted on the basis of a dynamical process called reorientation mediated by translational displacements (RMTD), which allow explanation of the significant slowing of the dynamics of IL cations at cellulose surfaces. Two types of cation diffusion were identified in this gel: a long-range translational diffusion within large cavities of the Cell matrix and diffusion occurring at the polymer surface. The correlational time constants and self-diffusion coefficients of the BMIMCl ionic liquid in bulk-like state and interaction with the cellulose matrix surface were determined. The conductivity measurements performed for pure IL and that confined in the Cell/BMIMCl ion gel show that the gelation only results in a small decrease of the ionic conductivity.     

Systematic Dielectric and NMR Study of the Ionic Liquid 1‐Alkyl‐3‐Methyl Imidazolium

The dynamic behaviors of ionic liquid samples consisting of a series of 1‐alkyl‐3‐methylimidazolium cations and various counteranionic species are investigated systematically over a wide frequency range from 1 MHz to 20 GHz at room temperature using dielectric relaxation (DR) and nuclear magnetic resonance (NMR) spectroscopies. DR spectra for the ionic liquids are reasonably deconvoluted into two or three relaxation modes. The slowest relaxation times are strongly dependent upon sample viscosity and cation size, whereas the relaxation times of other modes are almost independent of these factors. We attribute the two slower relaxation modes to the rotational relaxation modes of the dipolar cations because the correlation times of the cations evaluated using longitudinal relaxation time (T₁ ¹³C NMR) measurements corresponded to the dielectric relaxation times. On the other hand, the fastest relaxation mode is presumably related to the inter‐ion motions of ion‐pairs formed between cationic and anionic species. In the case of the ionic liquid bis(trifluoromethanesulfonyl)imide, the system shows marked dielectric relaxation behavior due to rotational motion of dipolar anionic species in addition to the relaxation modes attributed to the dipolar cations.     

Explanation of spin-lattice relaxation rates of spin labels obtained with multifrequency saturation recovery EPR

Electron paramagnetic resonance (EPR) pulsed saturation recovery (pSR) measurements of spin-lattice relaxation rates have been made on nitroxide-containing fatty acids embedded in lipid bilayers by Hyde and co-workers. The data have been collected for a number of spin-labeled fatty acids at several microwave spectrometer frequencies (from 2 to 35 GHz). We compare these spin-lattice relaxation rates to those predicted by the Redfield theory incorporating several mechanisms. The dominant relaxation mechanism at low spectrometer frequencies is the electron-nuclear dipolar (END) process, with spin rotation (SR), chemical shift anisotropy (CSA), and a generalized spin diffusion (GSD) mechanism all contributing. The use of a wide range of spectrometer frequencies makes clear that the dynamics cannot be modeled adequately by rigid-body isotropic rotational motion. The dynamics of rigid-body anisotropic rotational motion is sufficient to explain the experimental relaxation rates within the experimental error. More refined models of the motion could have been considered, and our analysis does not rule them out. However, the results demonstrate that measurements at only two suitably chosen spectrometer frequencies are sufficient to distinguish anisotropic from isotropic motion. The results presented demonstrate that the principal mechanisms responsible for anisotropically driven spin-lattice relaxation are well understood in the liquids regime.     

Microphase separation and ion‐conduction mechanisms in polypropylene oxide/lithium perchlorate (LiClO4) complexes

Broadband dielectric spectroscopy was used to examine ion‐conduction mechanisms in polypropylene oxide (PPO) with a molecular weight of 4000 complexed with LiClO₄. Two distinct conduction mechanisms were proposed with respect to high and low salt concentration regions. In a concentrated regime (Li/O >10%), the segmental motion of PPO molecules is significantly slowed down by enhanced cation coordination that results in a marked decrease in molar conductivity. We found a linear relationship between the ionic diffusion coefficient and the relaxation frequency of slowed segmental motion over broad temperature and salt‐concentration ranges. The use of a random walk scheme revealed that ions hop around at the same rate as slowed segmental motion for a monomer length. In a dilute regime (Li/O <0.1%), ions are temporarily localized in a limited domain. The direct current conductivity is achieved by structural renewal that releases ions from such localization and provides a diffusional character. At intermediate salt concentrations, microphase separation into ion‐depleted and ion‐rich regions was evidenced by the coexistence of fast and slow segmental processes. The molar conductivity revealed a maximum at Li/O = 3%. Its decrease at higher salt concentrations was attributed to the slowing down of segmental motion, and that at lower salt concentrations was attributed to localization of ionic motion. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 613–622, 2002; DOI 10.1002/polb.10123     

Electroosmosis through a Cation-Exchange Membrane: Effect of an ac Perturbation on the Electroosmotic Flow

Electroosmosis experiments through a cation-exchange membrane have been performed using NaCl solutions in different experimental situations. The influence of an alternating (ac) sinusoidal perturbation, of known angular frequency and small amplitude, superimposed to the usual applied continuous (dc) signal on the electroosmotic flow has been studied. The experimental results show that the presence of the ac perturbation affects the electroosmotic flow value, depending on the frequency of the ac signal and on the solution stirring conditions. In the frequency range studied, two regions have been observed where the electroosmotic flow reaches a maximum value: one at low frequencies (Hz); and another at frequencies of the order of kHz. These regions could be related to membrane relaxation phenomena.     

Dielectrophoresis force spectroscopy for colloidal clusters

Optical trapping-based force spectroscopy was used to measure the frequency-dependent DEP forces and DEP crossover frequencies of colloidal polymethyl methacrylate spheres and clusters. A single sphere or cluster, held by an optical tweezer, was positioned near the center of a pair of gold-film electrodes where alternating current elecroosmosis flow was negligible. Use of amplitude modulation and phase-sensitive lock-in detection for accurate measurement of the DEP force yielded new insight into dielectric relaxation mechanisms near the crossover frequencies. On one hand, the size dependence of the DEP force near the crossover frequencies indicates that the dominant polarization mechanism is a volume effect. On the other hand, the power-law dependence of the crossover frequency on the particle radius with an exponent of -2 indicates the dielectric relaxation is more likely because of ionic diffusion across the particle surface, suggesting the dominant polarization mechanism may be a surface polarization effect. Better theories are needed to explain the experiment. Nevertheless, the strong size dependence of the crossover frequencies suggests the use of DEP for size sorting of micron-sized particles.     

Electrostatic relaxation and hydrodynamic interactions for self-diffusion of ions in electrolyte solutions

The concentration dependence of self-diffusion of ions in solutions at large concentrations has remained an interesting yet unsolved problem. Here we develop a self-consistent microscopic approach based on the ideas of mode-coupling theory. It allows us to calculate both contributions which influence the friction of a moving ion: the ion atmosphere relaxation and hydrodynamic interactions. The resulting theory provides an excellent agreement with known experimental results over a wide concentration range. Interestingly, the mode-coupling self-consistent calculation of friction reveal a nonlinear coupling between the hydrodynamic interactions and the ion atmosphere relaxation which enhances ion diffusion by reducing friction, particularly at intermediate ion concentrations. This rather striking result has its origin in the similar time scales of the relaxation of the ion atmosphere relaxation and the hydrodynamic term, which are essentially given by the Debye relaxation time. The results are also in agreement with computer simulations, with and without hydrodynamic interactions.     

Conductivity dispersion in supercooled calcium potassium nitrate: caged ionic motion viewed as part of standard behaviour

Conductivity spectra of ionic materials with disordered structures are usually thought to consist of several parts, i.e., the DC conductivity, a power-law component, a nearly-constant-loss feature (if identified) and the (far-)infrared conductivity caused by vibrational motion. Such a decomposition may, however, easily lead to a misinterpretation of the underlying dynamics. Here, we discuss broad-band conductivity data of the supercooled glass-forming melt calcium potassium nitrate, of composition 0.4 Ca(NO(3))(2).0.6 KNO(3), often abbreviated as CKN. Data have been taken at frequencies up to the far infrared. We show that the frequency-dependent conductivity is very well reproduced by a superposition of only two components. One of them is due to vibrations, the other is caused by displacements of the mobile ions. The latter component, which does not follow a power law, is described in terms of a physical model called the MIGRATION concept. This model treatment has been found to apply in many solid electrolytes as well and is, therefore, considered to provide a "standard" formulation of the ion dynamics. The gradual transition from a correlated forward-backward ("caged") ionic motion to a stepwise translational motion may be regarded as the main feature of the MIGRATION concept.     

Charge and momentum transfer in supercooled melts: why should their relaxation times differ?

The steady-state values of the viscosity and the intrinsic ionic conductivity of quenched melts are computed, in terms of independently measurable quantities. The frequency dependence of the ac dielectric response is estimated. The discrepancy between the corresponding characteristic relaxation times is only apparent; it does not imply distinct mechanisms, but stems from the intrinsic barrier distribution for alpha-relaxation in supercooled fluids and glasses. This type of intrinsic "decoupling" is argued not to exceed four orders in magnitude for known glassformers. The origin of the discrepancy between the stretching exponent beta, as extracted from epsilon(omega) and the dielectric modulus data, is explained. The actual width of the barrier distribution always grows with lowering the temperature. The contrary is an artifact of the large contribution of the dc-conductivity component to the modulus data. The methodology allows one to single out other contributions to the conductivity, as in "superionic" liquids or when charge carriers are delocalized, implying that in those systems, charge transfer does not require structural reconfiguration.     

Ion atmosphere relaxation controlled electron transfers in cobaltocenium polyether molten salts

A room-temperature redox molten salt for the study of electron transfers in semisolid media, based on combining bis(cyclopentadienyl)cobalt with oligomeric polyether counterions, [Cp2Co](MePEG350SO3), is reported. The transport properties of the new molten salt can be varied (plasticized) by varying the polyether content. The charge transport rate during voltammetric reduction of the ionically conductive [Cp2Co](MePEG350SO3) molten salt exceeds the actual physical diffusivity of [Cp2Co]+ because of rapid [Cp2Co](+/0) electron self-exchanges. The measured [Cp2Co](+/0) electron self-exchange rate constants (k(EX)) are proportional to the diffusion coefficients (D(CION)) of the counterions in the melt. The electron-transfer activation barrier energies are also close to those of ionic diffusion but are larger than those derived from optical intervalent charge-transfer results. Additionally, the [Cp2Co](+/0) rate constant results are close to those of dissimilar redox moieties in molten salts where D(CION) values are similar. All of these characteristics are consistent with the rates of electron transfers of [Cp2Co](+/0) (and the other donor-acceptor pairs) being controlled not by the intrinsic electron-transfer rates but by the rate of relaxation of the ion atmosphere around the reacting pair. In the low driving force regime of mixed-valent concentration gradients, the ion atmosphere relaxation is competitive with electron transfer. The results support the generality of the recently proposed model of ionic atmosphere relaxation control of electron transfers in ionically conductive, semisolid materials.     

Anharmonic effects in ammonium nitrate and hydroxylammonium nitrate clusters

The covalent and ionic clusters of ammonium nitrate and hydroxyl ammonium nitrate are characterized using density functional theory and second-order vibrational perturbation theory. The most stable structures are covalent acid-base pairs for the monomers and ionic acid-base pairs for the dimers. The hydrogen-bonding distances are greater in the ionic dimers than in the covalent monomers, and the stretching frequencies are significantly different in the covalent and ionic clusters. The anharmonicity of the potential energy surfaces is found to influence the geometries, frequencies, and nuclear magnetic shielding constants for these systems. The inclusion of anharmonic effects significantly decreases many of the calculated vibrational frequencies in these clusters and improves the agreement of the calculated frequencies with the experimental data available for the isolated neutral species. The calculations of nuclear magnetic shielding constants for all nuclei in these clusters illustrate that quantitatively accurate predictions of nuclear magnetic shieldings for comparison to experimental data require the inclusion of anharmonic effects. These calculations of geometries, frequencies, and shielding constants provide insight into the significance of anharmonic effects in ionic materials and provide data that will be useful for the parametrization of molecular mechanical force fields for ionic liquids. Anharmonic effects will be particularly important for the study of proton transfer reactions in ionic materials.     

Fundamentals of ionic conductivity relaxation gained from study of procaine hydrochloride and procainamide hydrochloride at ambient and elevated pressure

The pharmaceuticals, procaine hydrochloride and procainamide hydrochloride, are glass-forming as well as ionically conducting materials. We have made dielectric measurements at ambient and elevated pressures to characterize the dynamics of the ion conductivity relaxation in these pharmaceuticals, and calorimetric measurements for the structural relaxation. Perhaps due to their special chemical and physical structures, novel features are found in the ionic conductivity relaxation of these pharmaceuticals. Data of conductivity relaxation in most ionic conductors when represented by the electric loss modulus usually show a single resolved peak in the electric modulus loss M(")(f) spectra. However, in procaine hydrochloride and procainamide hydrochloride we find in addition another resolved loss peak at higher frequencies over a temperature range spanning across T(g). The situation is analogous to many non-ionic glass-formers showing the presence of the structural α-relaxation together with the Johari-Goldstein (JG) β-relaxation. Naturally the analogy leads us to name the slower and faster processes resolved in procaine hydrochloride and procainamide hydrochloride as the primary α-conductivity relaxation and the secondary β-conductivity relaxation, respectively. The analogy of the β-conductivity relaxation in procaine HCl and procainamide HCl with JG β-relaxation in non-ionic glass-formers goes further by the finding that the β-conductivity is strongly related to the α-conductivity relaxation at temperatures above and below T(g). At elevated pressure but compensated by raising temperature to maintain α-conductivity relaxation time constant, the data show invariance of the ratio between the β- and the α-conductivity relaxation times to changes of thermodynamic condition. This property indicates that the β-conductivity relaxation has fundamental importance and is indispensable as the precursor of the α-conductivity relaxation, analogous to the relation found between the Johari-Goldstein β-relaxation and the structural α-relaxation in non-ionic glass-forming systems. The novel features of the ionic conductivity relaxation are brought out by presenting the measurements in terms of the electric modulus or permittivity. If presented in terms of conductivity, the novel features are lost. This warns against insisting that a log-log plot of conductivity vs. frequency is optimal to reveal and interpret the dynamics of ionic conductors.