Replica Field Theory for a Generalized Franz-Parisi Potential of Inhomogeneous Glassy Systems: New Closure and the Associated Self-Consistent Equation.

On approaching the dynamical transition temperature, supercooled liquids show heterogeneity over space and time. Static replica theory investigates the dynamical crossover in terms of the free energy landscape (FEL). Two kinds of static approaches have provided a self-consistent equation for determining this crossover, similar to the mode coupling theory for glassy dynamics. One uses the Morita-Hiroike formalism of the liquid state theory, whereas the other relies on the density functional theory (DFT). Each of the two approaches has advantages in terms of perturbative field theory. Here, we develop a replica field theory that has the benefits from both formulations. We introduce the generalized Franz-Parisi potential to formulate a correlation functional. Considering fluctuations around an inhomogeneous density determined by the Ramakrishnan-Yussouf DFT, we find a new closure as the stability condition of the correlation functional. The closure leads to the self-consistent equation involving the triplet direct correlation function. The present field theory further helps us study the FEL beyond the mean-field approximation.

Electric-field-induced oscillations in ionic fluids: a unified formulation of modified Poisson-Nernst-Planck models and its relevance to correlation function analysis.

We theoretically investigate an electric-field-driven system of charged spheres as a primitive model of concentrated electrolytes under an applied electric field. First, we provide a unified formulation for the stochastic charge and density dynamics of the electric-field-driven primitive model using the stochastic density functional theory (DFT). The stochastic DFT integrates the four frameworks (the equilibrium and dynamic DFTs, the liquid state theory and the field-theoretic approach), which allows us to justify in a unified manner various modifications previously made for the Poisson-Nernst-Planck model. Next, we consider stationary density-density and charge-charge correlation functions of the primitive model with a static electric field. We predict an electric-field-induced synchronization between emergences of density and charge oscillations. We are mainly concerned with the emergence of stripe states formed by segregation bands transverse to the external field, thereby demonstrating the following: (i) the electric-field-induced crossover occurs prior to the conventional Kirkwood crossover without an applied electric field, and (ii) the ion concentration dependence of the decay lengths at the onset of oscillations bears a similarity to the underscreening behavior found by recent simulation and theoretical studies on equilibrium electrolytes. Also, the 2D inverse Fourier transform of the correlation function illustrates the existence of stripe states beyond the electric-field-induced Kirkwood crossover.

Stochastic Density Functional Theory on Lane Formation in Electric-Field-Driven Ionic Mixtures: Flow-Kernel-Based Formulation.

Simulation and experimental studies have demonstrated non-equilibrium ordering in driven colloidal suspensions: with increasing driving force, a uniform colloidal mixture transforms into a locally demixed state characterized by the lane formation or the emergence of strongly anisotropic stripe-like domains. Theoretically, we have found that a linear stability analysis of density dynamics can explain the non-equilibrium ordering by adding a non-trivial advection term. This advection arises from fluctuating flows due to non-Coulombic interactions associated with oppositely driven migrations. Recent studies based on the dynamical density functional theory (DFT) without multiplicative noise have introduced the flow kernel for providing a general description of the fluctuating velocity. Here, we assess and extend the above deterministic DFT by treating electric-field-driven binary ionic mixtures as the primitive model. First, we develop the stochastic DFT with multiplicative noise for the laning phenomena. The stochastic DFT considering the fluctuating flows allows us to determine correlation functions in a steady state. In particular, asymptotic analysis on the stationary charge-charge correlation function reveals that the above dispersion relation for linear stability analysis is equivalent to the pole equation for determining the oscillatory wavelength of charge-charge correlations. Next, the appearance of stripe-like domains is demonstrated not only by using the pole equation but also by performing the 2D inverse Fourier transform of the charge-charge correlation function without the premise of anisotropic homogeneity in the electric field direction.

Non-hyperuniform metastable states around a disordered hyperuniform state of densely packed spheres: stochastic density functional theory at strong coupling.

The disordered and hyperuniform structures of densely packed spheres near and at jamming are characterized by vanishing of long-wavelength density fluctuations, or equivalently by long-range power-law decay of the direct correlation function (DCF). We focus on previous simulation results that exhibit the degradation of hyperuniformity in jammed structures while maintaining the long-range nature of the DCF to a certain length scale. Here we demonstrate that the field-theoretic formulation of stochastic density functional theory is relevant to explore the degradation mechanism. The strong-coupling expansion method of stochastic density functional theory is developed to obtain the metastable chemical potential considering the intermittent fluctuations in dense packings. The metastable chemical potential yields the analytical form of the metastable DCF that has a short-range cutoff inside the sphere while retaining the long-range power-law behavior. It is confirmed that the metastable DCF provides the zero-wavevector limit of the structure factor in quantitative agreement with the previous simulation results of degraded hyperuniformity. We can also predict the emergence of soft modes localized at the particle scale by plugging this metastable DCF into the linearized Dean-Kawasaki equation, a stochastic density functional equation.

Free-energy functional of instantaneous correlation field in liquids: Field-theoretic derivation of the closures.

This paper presents a unified method for formulating a field-theoretic perturbation theory that encompasses the conventional liquid state theory. First, the free-energy functional of an instantaneous correlation field is obtained from the functional-integral representation of the grand potential. Next, we demonstrate that the instantaneous free-energy functional yields a closure relation between the correlation functions in the mean-field approximation. Notably, the obtained closure relation covers a variety of approximate closures introduced in the liquid state theory.

Electrostatic contribution to colloidal solvation in terms of the self-energy-modified Boltzmann distribution.

Electrostatic interactions make a large contribution to solvation free energy in ionic fluids such as electrolytes and colloidal dispersions. The electrostatic contribution to solvation free energy has been ascribed to the self-energy of a charged particle. Here we apply a variational field theory based on lower bound inequality to the inhomogeneous fluids of one-component charged hard-spheres, thereby verifying that the self-energy is given by the difference between the total correlation function and direct correlation function. Based on the knowledge of the liquid state theory, the self-energy specified in this study not only relates a direct correlation function to the Gaussian smearing of each charged sphere, but also provides the electrostatic contribution to solvation free energy that shows good agreement with simulation results. Furthermore, the Ornstein-Zernike equation leads to a set of generalized Debye-Hückel equations reflecting the Gaussian distributed charges.

Transverse Density Fluctuations around the Ground State Distribution of Counterions near One Charged Plate: Stochastic Density Functional View.

We consider the Dean-Kawasaki (DK) equation of overdamped Brownian particles that forms the basis of the stochastic density functional theory. Recently, the linearized DK equation has successfully reproduced the full Onsager theory of symmetric electrolyte conductivity. In this paper, the linear DK equation is applied to investigate density fluctuations around the ground state distribution of strongly coupled counterions near a charged plate, focusing especially on the transverse dynamics along the plate surface. Consequently, we find a crossover scale above which the transverse density dynamics appears frozen and below which diffusive behavior of counterions can be observed on the charged plate. The linear DK equation provides a characteristic length of the dynamical crossover that is similar to the Wigner-Seitz radius used in equilibrium theory for the 2D one-component plasma, which is our main result. Incidentally, general representations of longitudinal dynamics vertical to the plate further suggest the existence of advective and electrical reverse-flows; these effects remain to be quantitatively investigated.

Frequency-Modulated Wave Dielectrophoresis of Vesicles And Cells: Periodic U-Turns at the Crossover Frequency.

We have formulated the dielectrophoretic force exerted on micro/nanoparticles upon the application of frequency-modulated (FM) electric fields. By adjusting the frequency range of an FM wave to cover the crossover frequency f X in the real part of the Clausius-Mossotti factor, our theory predicts the reversal of the dielectrophoretic force each time the instantaneous frequency periodically traverses f X . In fact, we observed periodic U-turns of vesicles, leukemia cells, and red blood cells that undergo FM wave dielectrophoresis (FM-DEP). It is also suggested by our theory that the video tracking of the U-turns due to FM-DEP is available for the agile and accurate measurement of f X . The FM-DEP method requires a short duration, less than 30 s, while applying the FM wave to observe several U-turns, and the agility in measuring f X is of much use for not only salty cell suspensions but also nanoparticles because the electric-field-induced solvent flow is suppressed as much as possible. The accuracy of f X has been verified using two types of experiment. First, we measured the attractive force exerted on a single vesicle experiencing alternating-current dielectrophoresis (AC-DEP) at various frequencies of sinusoidal electric fields. The frequency dependence of the dielectrophoretic force yields f X as a characteristic frequency at which the force vanishes. Comparing the AC-DEP result of f X with that obtained from the FM-DEP method, both results of f X were found to coincide with each other. Second, we investigated the conductivity dependencies of f X for three kinds of cell by changing the surrounding electrolytes. From the experimental results, we evaluated simultaneously both of the cytoplasmic conductivities and the membrane capacitances using an elaborate theory on the single-shell model of biological cells. While the cytoplasmic conductivities, similar for these cells, were slightly lower than the range of previous reports, the membrane capacitances obtained were in good agreement with those previously reported in the literature.

Anisotropic micro-cloths fabricated from DNA-stabilized carbon nanotubes: one-stop manufacturing with electrode needles.

Among a variety of solution-based approaches to fabricate anisotropic films of aligned carbon nanotubes (CNTs), we focus on the dielectrophoretic assembly method using AC electric fields in DNA-stabilized CNT suspensions. We demonstrate that a one-stop manufacturing system using electrode needles can draw anisotropic DNA-CNT hybrid films of 10 to 100 µm in size (i.e., free-standing DNA-CNT micro-cloths) from the remaining suspension into the atmosphere while maintaining structural order. It has been found that a maximal degree of polarization (ca. 40%) can be achieved by micro-cloths fabricated from a variety of DNA-CNT mixtures. Our results suggest that the one-stop method can impart biocompatibility to the downsized CNT films and that the DNA-stabilized CNT micro-cloths directly connected to an electrode could be useful for biofuel cells in terms of electron transfer and/or enzymatic activity.

Microscopic Characterization of Individual Submicron Bubbles during the Layer-by-Layer Deposition: Towards Creating Smart Agents.

We investigated the individual properties of various polyion-coated bubbles with a mean diameter ranging from 300 to 500 nm. Dark field microscopy allows one to track the individual particles of the submicron bubbles (SBs) encapsulated by the layer-by-layer (LbL) deposition of cationic and anionic polyelectrolytes (PEs). Our focus is on the two-step charge reversals of PE-SB complexes: the first is a reversal from negatively charged bare SBs with no PEs added to positive SBs encapsulated by polycations (monolayer deposition), and the second is overcharging into negatively charged PE-SB complexes due to the subsequent addition of polyanions (double-layer deposition). The details of these phenomena have been clarified through the analysis of a number of trajectories of various PE-SB complexes that experience either Brownian motion or electrophoresis. The contrasted results obtained from the analysis were as follows: an amount in excess of the stoichiometric ratio of the cationic polymers was required for the first charge-reversal, whereas the stoichiometric addition of the polyanions lead to the electrical neutralization of the PE-SB complex particles. The recovery of the stoichiometry in the double-layer deposition paves the way for fabricating multi-layered SBs encapsulated solely with anionic and cationic PEs, which provides a simple protocol to create smart agents for either drug delivery or ultrasound contrast imaging.

Tuning the size and configuration of nanocarbon microcapsules: aqueous method using optical tweezers.

To date, optical manipulation techniques for aqueous dispersions have been developed that deposit and/or transport nanoparticles not only for fundamental studies of colloidal dynamics, but also for either creating photonic devices or allowing accurate control of liquids on micron scales. Here, we report that optical tweezers (OT) system is able to direct three-dimensional assembly of graphene, graphite, and carbon nanotubes (CNT) into microcapsules of hollow spheres. The OT technique facilitates both to visualize the elasticity of a CNT microcapsule and to arrange a triplet of identical graphene microcapsules in aqueous media. Furthermore, the similarity of swelling courses has been found over a range of experimental parameters such as nanocarbon species, the power of the incident light, and the suspension density. Thanks to the universality in evolutions of rescaled capsule size, we can precisely control the size of various nanocarbon microcapsules by adjusting the duration time of laser emission.

Electric moulding of dispersed lipid nanotubes into a nanofluidic device.

Hydrophilic nanotubes formed by lipid molecules have potential applications as platforms for chemical or biological events occurring in an attolitre volume inside a hollow cylinder. Here, we have integrated the lipid nanotubes (LNTs) by applying an AC electric field via plug-in electrode needles placed above a substrate. The off-chip assembly method has the on-demand adjustability of an electrode configuration, enabling the dispersed LNT to be electrically moulded into a separate film of parallel LNT arrays in one-step. The fluorescence resonance energy transfer technique as well as the digital microscopy visualised the overall filling of gold nanoparticles up to the inner capacity of an LNT film by capillary action, thereby showing the potential of this flexible film for use as a high-throughput nanofluidic device where not only is the endo-signalling and product in each LNT multiplied but also the encapsulated objects are efficiently transported and reacted.

Precise switching control of liquid crystalline microgears driven by circularly polarized light.

Liquid crystalline molecules carrying photopolymerizable end groups absorb photon energy via a two-photon process, enabling the photofabrication of 3D structures. In this work, we prepared microgears with different heights and tooth lengths. These birefringent microgears can be induced to rotate by circularly polarized light. Here, we demonstrate that the use of phase plate for switching between left- and right-handed polarization reverses the optically induced rotation while maintaining the same rotational frequency. Due to the precise switching control, these birefringent microgears have advantages over previous microrotors that are fabricated from non-birefringent light-curing resins.

Measuring the length distribution of self-assembled lipid nanotubes by orientation control with a high-frequency alternating current electric field in aqueous solutions.

The present work addresses the length distribution of self-assembled lipid nanotubes (LNTs) by controlling the orientation of the LNTs using an alternating current (ac) electric field in aqueous solutions. The effect of the ac field on the orientation and rotation of individual LNTs was examined to evaluate the optimum orientation frequency by visualizing the individual LNTs in real time. By using the high-frequency ac field, we have successfully measured the length distribution for two different types of LNTs and have quantitatively analyzed the maximum occurrences of the length distribution as well as the extension of the longer length region.

A functional-integral formulation for polymer colloids: Pagonabarraga-Cates free energy revisited.

We have formulated a new functional-integral representation with respect to both polymer and monomer densities, along the lines of the current picture treating polymers as soft colloids. Comparison between the resulting form and a model free energy functional of Pagonabarraga and Cates (PC 2001 Europhys. Lett. 55 348) indicates that the PC relation between monomer and polymer concentrations is to be modified, and that further insertion of the order parameter defined by the square of monomer density is indispensable for regularizing a divergent term absent in the PC functional. Moreover, the saddle-point approximation to our functional integral leads to a self-consistent equation which efficiently preincludes the minimum of the Flory-Huggins-type local free energy as input.

Merging of alpha and slow beta relaxation in supercooled liquids.

Dielectric relaxation spectroscopy (1 Hz - 20 GHz) has been performed on supercooled glass-formers from the temperature of glass transition (T(g)) up to that of melting. Precise measurements particularly in the frequencies of MHz order have revealed that the temperature dependences of secondary beta relaxation times in well above T(g) deviate from the Arrhenius relation below T(g): the beta process does not merge with the alpha process around the dynamical crossover temperature in contradiction to previously speculated extrapolations.