Dielectric spectroscopy of concentrated colloidal suspensions

Frequency-Dependent Microelectrophoresis Study of Colloids with Tunable Surface Charge

Nonaqueous poly(methyl methacrylate) (PMMA) colloidal suspensions in a solvent that is simultaneously matched in both density and refractive index have been important for real-space studies of colloidal self-assembly, but their complex electrostatic character remains largely unexplored. Electrophoresis is a powerful tool for determining the surface potential and charge of the colloidal suspension; however, because of refractive index matching, standard electrophoresis measurements are not feasible. We carry out microscope-based microelectrophoresis measurements on PMMA colloids in cyclohexyl bromide and cis-trans decalin to measure particle charge as a function of salt concentration in both DC and frequency-variable AC fields. The colloid charge depends on salt concentration and reverses sign near 0.35 μM, providing evidence that solution ions are actively modifying the colloid surface. The frequency dependence of the electrophoretic mobility yields the characteristic time scale for electric double-layer polarization and provides intriguing evidence for Manning condensation and polyion formation.

AC Conductivity Measurements of Ultradilute Colloidal Suspensions in HEPES Buffer

Impedance spectroscopy was used to probe the AC conductivity of extremely dilute colloidal suspensions (2.5 × 10^-5 ≤ Φ_w/v ≤ 4.0 × 10^-2) comprising of polystyrene microspheres (PS; κa ≫ 1 and ζ = -65 mV), gold nanoparticles (Au NPs; κa > 1 and ζ = -26 mV), and Au-coated PS metallodielectric particles (Au-PS) in HEPES buffer. When AC electric fields of strength 10 mV and 1 MHz were applied via 100 μm gap interdigitated microelectrodes across 10 μL samples, a highly resistive (θ_capacitive < 1°) and nonmonotonic response was obtained with particle concentrations at steady state. While the suspensions were less resistive (than the buffer) below a critical concentration, they became more resistive above it. More interestingly, particle-particle interactions took place in suspensions with concentrations as low as 0.005% w/v. We believe this unique behavior is linked to the ion size asymmetry in the HEPES molecule that provides an ideal microenvironment for counterionic polarization around the particles. The exact mechanism of polarization in HEPES, however, still remains elusive as the current theoretical models for simple electrolytes fail to explain our data.

Measuring Nanoparticle Polarizability Using Fluorescence Microscopy

Using a novel method developed to quantify the polarizability of photoluminescent nanoparticles in water, we present experimental observations of the extraordinary polarizability exhibited by nanoparticles of commensurate size with the Debye screening length, confirming previously reported theory. Semiconductor quantum dots (QDs) are ideal model nanoparticles to demonstrate this assay, due to their tunable size and bright photoluminescence. This assay is based upon microfluidic chambers with microelectrodes that generate trapping potentials that are weaker than thermal energy. By comparing the local electric field strength and variations in QD concentration, their polarizability was computed and found to agree with estimates based upon the hydrodynamic diameter found using light scattering. Strikingly, the polarizability of the nanoparticles increased 30-fold in low salt conditions compared to high salt conditions due to the increased thickness of the Debye layer relative to the particle radius. In addition to providing evidence that corroborates theoretical work studying direct solutions to the Poisson-Nernst-Planck equations, these observations provide an explanation for the previously observed conductivity dependence of biomolecule polarizability. As the polarizability of nanoparticles is of high importance to the electrically directed assembly of particles, as well as their interactions with other materials in complex environments, we anticipate that these results will be highly relevant to ongoing efforts in materials by design and nanomedicine.

Asymmetric rectified electric fields between parallel electrodes: Numerical and scaling analyses

Recent computational and experimental work has established the existence of asymmetric rectified electric fields (AREFs), a type of steady electric field that occurs in liquids in response to an applied oscillatory potential, provided the ions present have different mobilities [Hashemi Amrei et al., Phys. Rev. Lett. 121, 185504 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.185504]. Here we use scaling analyses and numerical calculations to elaborate the nature of one-dimensional AREFs between parallel electrodes. The AREF magnitude is shown to increase quadratically with applied potential at low potentials, increase nonlinearly at intermediate potentials, then increase with a constant rate slower than quadratically at sufficiently high potentials, with no impact at any potential on the spatial structure of the AREF. In contrast, the AREF peak location increases linearly with a frequency-dependent diffusive length scale for all conditions tested, with corresponding decreases in both the magnitude and number of sign changes in the directionality of AREF. Furthermore, both the magnitude and spatial structure of the AREF depend sensitively on the ionic mobilities, valencies, and concentrations, with a potential-dependent peak AREF magnitude occurring at an ionic mobility ratio of D_{-}/D_{+}⪅5. The results are summarized with approximate scaling expressions that will facilitate interpretation of the steady component for oscillatory fields in liquid systems.

Oscillating Electric Fields in Liquids Create a Long-Range Steady Field

We demonstrate that application of an oscillatory electric field to a liquid yields a long-range steady field, provided the ions present have unequal mobilities. The main physics is illustrated by a two-ion harmonic oscillator, yielding an asymmetric rectified field whose time average scales as the square of the applied field strength. Computations of the fully nonlinear electrokinetic model corroborate the two-ion model and further demonstrate that steady fields extend over large distances between two electrodes. Experimental measurements of the levitation height of micron-scale colloids versus applied frequency accord with the numerical predictions. The heretofore unsuspected existence of a long-range steady field helps explain several long-standing questions regarding the behavior of particles and electrically induced fluid flows in response to oscillatory potentials.

Frequency-Dependent Solvent Impedance and Colloid Microelectrophoresis Measurements in Partially Polar Solvents

We carry out frequency-dependent solvent impedance measurements and alternating current (ac) colloid microelectrophoresis experiments in partially polar solvents in the low-frequency regime (0.25 Hz ≤ f ≤ 10 Hz). Solvent electrode polarization effects are quantified first in partially polar solvent mixtures containing bromocyclohexane (CHB). We find that the polarization capacitance from electrode polarization exhibits a clear power law behavior C_p = C_p0 f^-m with power law exponent m = 0.25 ± 0.04. Once we account for electrode polarization effects, we are able to obtain quantitative mobilities in the low-frequency regime from our ac microelectrophoresis measurements; for these measurements, we use poly(methyl methacrylate colloids that are gravitationally confined to a plane while suspended in a low-polar solvent mixture of cis-trans decahydronapthalene and CHB. We find that the dimensionless electrophoretic mobility is constant, consistent with expectations for frequencies below the ion-diffusion frequency, and has a value E = 1.6 ± 0.4.

Dielectric spectroscopy of ionic microgel suspensions

The determination of the net charge and size of microgel particles as a function of their concentration, as well as the degree of association of ions to the microgel backbone, has been pursued in earlier studies mainly by scattering and rheology. These methods suffer from contributions due to inter-particle interactions that interfere with the characterization of single-particle properties. Here we introduce dielectric spectroscopy as an alternative experimental method to characterize microgel systems. The advantage of dielectric spectroscopy over other experimental methods is that the polarization due to mobile charges within a microgel particle is only weakly affected by inter-particle interactions. Apart from electrode polarization effects, experimental spectra on PNIPAM-co-AA [poly(N-isopropylacrylamide-co-acrylic acid)] ionic microgel particles suspended in de-ionized water exhibit three well-separated relaxation modes, which are due to the polarization of the mobile charges within the microgel particles, the diffuse double layer around the particles, and the polymer backbone. Expressions for the full frequency dependence of the electrode-polarization contribution to the measured dielectric response are derived, and a theory is proposed for the polarization resulting from the mobile charges within the microgel. Relaxation of the diffuse double layer is modeled within the realm of a cell model. The net charge and the size of the microgel particles are found to be strongly varying with concentration. A very small value of the diffusion coefficient of ions within the microgel is found, due to a large degree of chemical association of protons to the polymer backbone.

Effect of surface modification of SiO2@TiO2core–shell particles on the structural colour under an electric field

Surface modified colloidal SiO₂@TiO₂core–shell particles were chosen to study their responsive photonic properties and the effect of surface on structural colour under low electric field.