The Debye length and anionic transport properties of composite membranes based on supported ionic liquid-like phases (SILLPS).

An analysis of the ionic transport properties of BMIM [NTf2] in supported ionic-liquid-like phase (SILLP)-based membranes has been carried out based on experimental impedance spectroscopy measurements. The direct current (dc)-conductivity was analyzed to determine the temperature and frequency dependence. The fit of the loss tangent curve data with the Cole-Cole approximation of the electrode polarization model provides the conductivity, diffusivity, and density of charge carriers. Among these quantities, a significant increase in conductivity is observed when an ionic liquid is added to the polymeric matrix containing imidazolium fragments. The use of a recent generalization of Eyring's absolute rate theory allowed the elucidation of how the local entropy restrictions, due to the porosity of the polymeric matrix, control the conductive process. The fit of the conductivity data as a function of temperature manifests the behavior of the excess entropy with respect to the temperature. The activation entropy and enthalpy were also determined. Our results correlate the Debye length (LD) with the experimental values of conductivity, electrode polarization relaxation time, and sample relaxation time involved. Our work provides novel insights into the description of ionic transport in membranes as the diffusivity, mobility, and free charge density depend on the LD. Moreover, we discuss the behavior of the polarization relaxation time, the sample relaxation time, and the static permittivity as a function of the temperature.

Scaling Planck's law: a unified approach to the Casimir effect and radiative heat-conductance in nanogaps.

Using Planck's law from an innovative point of view brings about the possibility to understand the common origin of the repulsive Casimir thermal pressure and the heat exchange in nanogaps. Based on a scale transformation, a procedure that removes divergences of the energy density, we prove the validity of Planck's law to describe confined thermal radiation properties in nanoscale gaps. This scaling involves a configurational temperature obtained from Wien's displacement law and having an entropic origin. We derive analytical expressions for the Casimir thermal pressure as well as for the heat conductance. Comparison of our results with experimental data shows a remarkable agreement.

A Theoretical Perspective of the Photochemical Potential in the Spectral Performance of Photovoltaic Cells.

We present a novel theoretical approach to the problem of light energy conversion in thermostated semiconductor junctions. Using the classical model of a two-level atom, we deduced formulas for the spectral response and the quantum efficiency in terms of the input photons' non-zero chemical potential. We also calculated the spectral entropy production and the global efficiency parameter in the thermodynamic limit. The heat transferred to the thermostat results in a dissipative loss that appreciably controls the spectral quantities' behavior and, therefore, the cell's performance. The application of the obtained formulas to data extracted from photovoltaic cells enabled us to accurately interpolate experimental data for the spectral response and the quantum efficiency of cells based on Si-, GaAs, and CdTe, among others.

Correction: Temperature dependence of anomalous protonic and superprotonic transport properties in mixed salts based on CsH2PO4.

Correction for 'Temperature dependence of anomalous protonic and superprotonic transport properties in mixed salts based on CsH2PO4' by Andreu Andrio et al., Phys. Chem. Chem. Phys., 2019, 21, 12948-12960, DOI: 10.1039/C8CP07472K.

Eckhaus selection: The mechanism of pattern persistence in a reaction-diffusion system.

In this work, we show theoretically and numerically that a one-dimensional reaction-diffusion system, near the Turing bifurcation, produces different number of stripes when, in addition to random noise, the Fourier mode of a prepattern used to initialize the system changes. We also show that the Fourier modes that persist are inside the Eckhaus stability regions, while those outside this region follow a wave number selection process not predicted by the linear analysis. To test our results, we use the Brusselator reaction-diffusion system obtaining an excellent agreement between the weakly nonlinear predictions of the real Ginzburg-Landau equations and the numerical solutions near the bifurcation. Although the persistence of patterns is not relevant as a simple generating mechanism of self-organization, it is crucial to understand the formation of patterns that occurs in multiple stages. In this work, we discuss the relevance of our results on the robustness and diversity of solutions in multiple-steps mechanisms of biological pattern formation and auto-organization in growing domains.

Entropic restrictions control the electric conductance of superprotonic ionic solids.

The crystallographic structure of solid electrolytes and other materials determines the protonic conductivity in devices such as fuel cells, ionic-conductors, and supercapacitors. Experiments show that a rise of the temperature in a narrow interval may lead to a sudden increase of several orders of magnitude of the conductivity of some materials, a process called a superprotonic transition. Here, we use a novel macro-transport theory for irregular domains to show that the change of entropic restrictions associated with solid-solid phase or structural transitions controls the sudden change of the ionic conductivity when the superprotonic transition takes place. Specifically, we deduce a general formula for the temperature dependence on the ionic conductivity that fits remarkably well experimental data of superprotonic transitions in doped cesium phosphates and other materials reported in the literature.

Temperature dependence of anomalous protonic and superprotonic transport properties in mixed salts based on CsH2PO4.

We present an experimental study and a theoretical interpretation of the temperature dependence of the transport properties of doped CsH2PO4 salts in both protonic and superprotonic phases. Cesium phosphate based solid electrolytes are technologically relevant because their operational temperature range is about 100 to 300 °C in which a superprotonic transition may manifest depending on its mixed composition. The experimental study was carried out using impedance spectroscopy at the temperature range of 150-230 °C, and the protonic and superprotonic transport properties and proton concentrations were calculated and analyzed by using the electrode polarization, and the Debye and Cole-Cole models for the dielectric constant. We have shown that the transport properties predicted by the Cole-Cole model are consistent with the conductivity measurements whereas the Debye model shows some inconsistencies. We attribute this to the fact that the Cole-Cole model incorporates the effects of interactions among charge carriers better than the more commonly used Debye model. In this way, our work shows a more consistent approach to determine the transport properties of solid electrolytes and, therefore, provides a more reliable tool to analyze the transport properties of heterogeneous solid electrolytes that can be used in electrochemical devices, including fuel cells and supercapacitors.

The interplay between phenotypic and ontogenetic plasticities can be assessed using reaction-diffusion models : The case of Pseudoplatystoma fishes.

Every morphological, behavioral, or even developmental character expression of living beings is coded in its genotype and is expressed in its phenotype. Nevertheless, the interplay between phenotypic and ontogenetic plasticities, that is, the capability to manifest trait variations, is a current field of research that needs morphometric, numerical, or even mathematical modeling investigations. In the present work, we are searching for a phenotypic index able to identify the underlying correlation among phenotypic, ontogenetic, and geographic distribution of the evolutionary development of species of the same genus. By studying the case of Pseudoplatystoma fishes, we use their skin patterns as an auxiliary trait that can be reproduced by means of a reaction diffusion (RD) model. From this model, we infer the phenotypic index in terms of one of the parameters appearing in the mathematical equations. To achieve this objective, we perform extensive numerical simulations and analysis of the model equations and link the parameter variations with different environmental and physicochemical conditions in which the individuals develop, and which may be regulated by the ontogenetic plasticity of the species. Our numerical study indicates that the patterns predicted by a set of reaction diffusion equations are not uniquely determined by the value of the parameters of the equation, but also depend on how the process is initiated and on the spatial distribution of values of these parameters. These factors are therefore significant, since they show that an individual's growth dynamics and apparent secondary transport processes, like advection, can be determinant for the alignment of motifs in a skin pattern. Our results allow us to discern the correlation between phenotypic, ontogenetic, and geographic distribution of the different species of Pseudoplatystoma fishes, thus indicating that RD models represent a useful taxonomic tool able to quantify evolutionary indexes.

Relation between the porosity and tortuosity of a membrane formed by disconnected irregular pores and the spatial diffusion coefficient of the Fick-Jacobs model.

In this work, we provide a theoretical relationship between the spatial-dependent diffusion coefficient derived in the Fick-Jacobs (FJ) approximation and the macroscopic diffusion coefficient of a membrane that depends on the porosity, tortuosity, and the constriction factors. Based on simple mass conservation arguments under equilibrium as well as in nonequilibrium conditions, we generalize previous expressions for the effective diffusion coefficient of an irregular pore, originally obtained by Festa and d'Agliano for horizontal and periodic pores, and then extended by Bradley for tortuous periodic pores, to the case of pores with arbitrary geometry. Through a formal definition of the constrictivity factor in terms of the geometry of the pore, our results provide very clear physical interpretation of experimental measurements since they link the local properties of the flow with macroscopic quantities of experimental relevance in the design and optimization of porous materials. The macroscopic diffusion coefficient as well as the spatiotemporal evolution of the concentration profiles inside a pore have been recently measured by using pulse field gradient NMR techniques. The advantage of using the FJ approach is that the spatiotemporal concentration profile inside a pore of irregular geometry is directly related to the pore's shape and, therefore, that the macroscopic diffusion coefficient can be obtained by comparing the spatiotemporal concentration profiles from such experiments with those of the theoretical model. Hence, the present study is relevant for the understanding of the transport properties of porous materials where the shape and arrangement of pores can be controlled at will.

Mean-square displacement of particles in slightly interconnected polymer networks.

Structural and viscoelastic properties of slightly interconnected polymer networks immersed in a solvent have been studied in two cases: when the polymer network is building up and when the polymer network is shrinking stepwise in a controlled way. To accomplish this goal, the mean square displacement (MSD) of embedded microspheres in the polymer network was measured as a function of time, with diffusive wave spectroscopy. Particle motion was analyzed in terms of a model, based on a Fokker-Planck type equation, developed for describing particles in Brownian motion within a network that constrain their movement. The model reproduces well the experimental features observed in the MSD vs t curves. The variation of the parameters describing the structure of the network can be understood as the polymerization comes about, and also after the successive volume contractions. In addition, from the MSD curves, the complex shear moduli were obtained in a wide range of frequencies when the network is building up, and at the different shrinking states of the network. Our microrheological results give an insight about the dynamics of embedded particles in slightly interconnected networks, which were also compared with similar results for polymers without interconnections and polymer gels.

Some conceptual thoughts toward nanoscale oriented friction in a model of articular cartilage.

This work presents a conceptual framework as to how a deficit in the synovial-fluid content, exemplified by hyaluronan or any other amphiphilic species, is capable of decisively altering the complex lubrication and wear conditions observed clinically in articular cartilage. The effect is revealed in (non)stationary regimes if the cartilage is subjected to some normal periodic load, revealing over its exploitation time increasingly dissipative, in general entropy-addressing, characteristics. It can be hypothesized that a Grotthuss-type proton transport physiology-concerning mechanism in channel-like, phospholipid-water cartilage's articulating nanospaces will be responsible for the expression of the lubrication mode. The corresponding wear involving overall change is then manifested adequately in the stationary regime, and in a viable system-parametric correlation with its lubrication counterpart. Certain analytic formulae for the nanoscale oriented coefficient of friction, involving generically H-bonds breaking mechanism, and pointing to some local-viscosity context, have been proposed for fitting the experimental data and clinical observations involving proton management at articular cartilage surfaces.

Biophysics of active vesicle transport, an intermediate step that couples excitation and exocytosis of serotonin in the neuronal soma.

Transmitter exocytosis from the neuronal soma is evoked by brief trains of high frequency electrical activity and continues for several minutes. Here we studied how active vesicle transport towards the plasma membrane contributes to this slow phenomenon in serotonergic leech Retzius neurons, by combining electron microscopy, the kinetics of exocytosis obtained from FM1-43 dye fluorescence as vesicles fuse with the plasma membrane, and a diffusion equation incorporating the forces of local confinement and molecular motors. Electron micrographs of neurons at rest or after stimulation with 1 Hz trains showed cytoplasmic clusters of dense core vesicles at 1.5±0.2 and 3.7±0.3 µm distances from the plasma membrane, to which they were bound through microtubule bundles. By contrast, after 20 Hz stimulation vesicle clusters were apposed to the plasma membrane, suggesting that transport was induced by electrical stimulation. Consistently, 20 Hz stimulation of cultured neurons induced spotted FM1-43 fluorescence increases with one or two slow sigmoidal kinetics, suggesting exocytosis from an equal number of vesicle clusters. These fluorescence increases were prevented by colchicine, which suggested microtubule-dependent vesicle transport. Model fitting to the fluorescence kinetics predicted that 52-951 vesicles/cluster were transported along 0.60-6.18 µm distances at average 11-95 nms(-1) velocities. The ATP cost per vesicle fused (0.4-72.0), calculated from the ratio of the ΔG(process)/ΔG(ATP), depended on the ratio of the traveling velocity and the number of vesicles in the cluster. Interestingly, the distance-dependence of the ATP cost per vesicle was bistable, with low energy values at 1.4 and 3.3 µm, similar to the average resting distances of the vesicle clusters, and a high energy barrier at 1.6-2.0 µm. Our study confirms that active vesicle transport is an intermediate step for somatic serotonin exocytosis by Retzius neurons and provides a quantitative method for analyzing similar phenomena in other cell types.

Reconstructing the free-energy landscape associated to molecular motors processivity.

We propose a biochemical model providing the kinetic and energetic descriptions of the processivity dynamics of kinesin and dinein molecular motors. Our approach is a modified version of a well known model describing kinesin dynamics and considers the presence of a competitive inhibition reaction by ADP. We first reconstruct a continuous free-energy landscape of the cycle catalyst process that allows us to calculate the number of steps given by a single molecular motor. Then, we calculate an analytical expression associated to the translational velocity and the stopping time of the molecular motor in terms of time and ATP concentration. An energetic interpretation of motor processivity is discussed in quantitative form by using experimental data. We also predict a time duration of collective processes that agrees with experimental reports.

Pattern formation from consistent dynamical closures of uniaxial nematic liquid crystals.

Pattern formation in uniaxial polymeric liquid crystals is studied for different dynamic closure approximations. Using the principles of mesoscopic non-equilibrium thermodynamics in a mean-field approach, we derive a Fokker-Planck equation for the single-particle non-homogeneous distribution function of particle orientations and the evolution equations for the second and fourth order orientational tensor parameters. Afterwards, two dynamic closure approximations are discussed, one of them considering the relaxation of the fourth order orientational parameter and leading to a novel expression for the free-energy like function in terms of the scalar order parameter. Considering the evolution equation of the density of the system and values of the interaction parameter for which isotropic and nematic phases coexist, our analysis predicts that patterns and traveling waves can be produced in lyotropic uniaxial nematics even in the absence of external driving.

On morphological selection rule of noisy character applied to model (dis)orderly protein formations.

We propose that the main mechanism controlling the selection rule of model (dis)orderly protein formations, such as non-Kossel crystal growth and aggregation of lysozyme from aqueous solution, is an ion-channeling filter having flicker-noise properties. This filter is originated at the interfaces between growing solidlike object and its external liquid-type phase, and it can be considered as a series of voltage gated ion subchannels. The dynamics of each channel is studied by using both simulation and analytic argumentation lines, and represents a novel thought on how to utilize the presence of constructive-noise sources in protein formation, a field of utmost experimental and technological interest.

Mesoscopic nonequilibrium thermodynamics approach to non-Debye dielectric relaxation.

Mesoscopic nonequilibrium thermodynamics is used to formulate a model describing nonhomogeneous and non-Debye dielectric relaxation. The model is presented in terms of a Fokker-Planck equation for the probability distribution of noninteracting polar molecules in contact with a heat bath and in the presence of an external time-dependent electric field. Memory effects are introduced in the Fokker-Planck description through integral relations containing memory kernels, which in turn are used to establish a connection with fractional Fokker-Planck descriptions. The model is developed in terms of the evolution equations for the first two moments of the distribution function. These equations are solved by following a perturbative method from which the expressions for the complex susceptibilities are obtained as a function of the frequency and the wave number. Different memory kernels are considered and used to compare with experiments of dielectric relaxation in glassy systems. For the case of Cole-Cole relaxation, we infer the distribution of relaxation times and its relation with an effective distribution of dipolar moments that can be attributed to different segmental motions of the polymer chains in a melt.

Thermodynamics and dynamics of the formation of spherical lipid vesicles.

We propose a free energy expression accounting for the formation of spherical vesicles from planar lipid membranes and derive a Fokker-Planck equation for the probability distribution describing the dynamics of vesicle formation. We find that formation may occur as an activated process for small membranes and as a transport process for sufficiently large membranes. We give explicit expressions for the transition rates and the characteristic time of vesicle formation in terms of the relevant physical parameters.

On the protein crystal formation as an interface-controlled process with prototype ion-channeling effect.

A superdiffusive random-walk action in the depletion zone around a growing protein crystal is considered. It stands for a dynamic boundary condition of the growth process and competes steadily with a quasistatic, curvature-involving (thermodynamic) free boundary condition, both of them contributing to interpret the (mainly late-stage) growth process in terms of a prototype ion-channeling effect. An overall diffusion function contains quantitative signatures of both boundary conditions mentioned and indicates whether the new phase grows as an orderly phase or a converse scenario occurs. This situation can be treated in a quite versatile way both numerically and analytically, within a generalized Smoluchowski framework. This study can help in (1) elucidating some dynamic puzzles of a complex crystal formation vs biomolecular aggregation, also those concerning ion-channel formation, and (2) seeing how ion-channel-type dynamics of non-Markovian nature may set properly the pace of model (dis)ordered protein aggregation.