A statistical theory of the photoluminescence determination of the band gap energy in nano-crystals and layered materials.

Semiconductor nano-crystals as well as two-dimensional nanostructures manifest an abnormal dependence of the optical band gap energy on the temperature. In contrast to bulk systems, in the present case the optical band gap energy increases with temperature or may show a non-monotonic blueshift-redshift behavior. It was suggested that this abnormal temperature behavior is associated with the recombination of excitons and free electron-hole pairs under conditions of quantum confinement. Here, we show that the presence of nanometer lengths and anharmonic interactions makes it necessary to rescale the energy and thermal energy of the material according to the invariance of statistical mechanics on the energy/thermal-energy ratio. In addition, considering the effects of the thermal expansion of the material, we managed to derive a formula for the optical band gap energy. Using this formula, the photoluminescence spectra are accounted for by emphasizing that the exciton and free electron-hole pair recombination is a non-thermal statistical process following a Poisson distribution in which the average value of the energy and the full width at half maximum are both directly related to the optical band gap energy. Our results account remarkably well for several experimental data reported in recent literature.

Adiabatic limit collapse and local interaction effects in non-linear active microrheology molecular simulations of two-dimensional fluids.

Nonlinear active microrheology molecular dynamics simulations of high-density two-dimensional fluids show that the presence of strong confining forces and an external pulling force induces a correlation between the velocity and position dynamics of the tracer particle. This correlation manifests in the form of an effective temperature and an effective mobility of the tracer particle, which is responsible for the breaking of the equilibrium fluctuation-dissipation theorem. This fact is shown by measuring the tracer particle's temperature and mobility directly from the first two moments of the velocity distribution of a tracer particle and by formulating a diffusion theory in which effective thermal and transport properties are decoupled from the velocity dynamics. Furthermore, the flexibility of the attractive and repulsive forces in the tested interaction potentials allowed us to relate the temperature and mobility behaviors to the nature of the interactions and the structure of the surrounding fluid as a function of the pulling force. These results provide a refreshing physical interpretation of the phenomena observed in non-linear active microrheology.

Size and surface-energy dependence of the adsorption/desorption equilibrium in ethanol electro-oxidation by Pd-nanoparticles. Theory and experiment.

The relation between current and voltage in the electro-oxidation of ethanol by metal nanoparticles depends on experimental parameters like the applied potential, peak potential, temperature, the electron-transfer coefficient, and the number of molecules adsorbed at active sites on the nanoparticle surface. In this form, the oxidation current depends on the ability of the nanoparticles to adsorb the ethanol molecules. Though the Laviron model well describes this phenomenology, few studies focus on the dependence of the oxidation current on the size and surface properties of the metal nanoparticles. Here, we present an experimental and theoretical study that comprises the synthesis of palladium-based nanoparticles and the generalization of the Laviron model that allows determining the dependence of the oxidation current on the size, surface energy, and adsorption-desorption properties of the nanoparticles for the ethanol oxidation. The determination of the adsorption-desorption equilibrium and the electro-oxidation current dependence with the physicochemical properties of the materials was carried out by electrochemical characterization.

Eyring equation and fluctuation-dissipation far away from equilibrium.

Understanding and managing the influence that either external forces or non-equilibrated environments may have on chemical processes is essential for the current and future development of theoretical chemistry. One of the central questions to solve is how to generalize the transition state theory in order to make it applicable in far from equilibrium situations. In this sense, here we propose a way to generalize Eyring's equation based on the definition of an effective thermal energy (temperature) emerging from the coupling of both fast and slow dynamic variables analyzed within the generalized Langevin dynamics scheme. This coupling makes the energy distribution of the fast degrees of freedom not equilibrate because they have been enslaved to the dynamics of the corresponding slow degrees. However, the introduction of the effective thermal energy enables us to restore an effective adiabatic separation of timescales leading to a renormalization of the generalized fluctuation-dissipation theorem. Hence, this procedure opens the possibility to deal with systems far away from equilibrium. A significant consequence of our results is that Eyring's equation is generalized to treat systems under the influence of strong external forces.

Possible fates of the spread of SARS-CoV-2 in the Mexican context.

The determination of the adequate time for house confinement and when social distancing restrictions should end are now two of the main challenges that any country has to face in an ongoing battle against SARS-CoV-2. The possibility of a new outbreak of the pandemic and how to avoid it is, nowadays, one of the primary objectives of epidemiological research. In this work, we present an innovative compartmental model that explicitly introduces the number of active cases, and employ it as a conceptual tool to explore the possible fates of the spread of SARS-CoV-2 in the Mexican context. We incorporated the impact of starting, inattention and end of restrictive social policies on the pandemic's time evolution via time-dependent corrections to the infection rates. The magnitude and impact on the epidemic due to post-social restrictive policies are also studied. The scenarios generated by the model could help authorities determine an adequate time and population load that may be allowed to reassume normal activities.

Entropy production and energy dissipation in symmetric redox supercapacitors.

In this work we propose a theoretical model that accounts for the main features of the loading-unloading process of a symmetric redox MnO_{2}-based supercapacitor dominated by fast electrochemical reactions at the electrodes. The model is formulated on the basis of nonequilibrium thermodynamics from which we are able to deduce generalized expressions for the electrochemical affinity, the load-voltage and the current-voltage equations that constitute generalizations of the current-overpotential and Butler-Volmer equations, and that are used to describe experimental voltagram data with good agreement. These equations allowed us to derive the behavior of the energy dissipated per cycle showing that it has a nonmonotonic behavior and that in the operation regime it follows a power-law behavior as a function of the frequency. The existence of a maximum for the energy dissipated as a function of the frequency suggests the that the corresponding optimal operation frequency should be similar in value to ω_{max}.

Origin of the effective mobility in non-linear active micro-rheology.

The distinction between the damping coefficient and the effective non-linear mobility of driven particles in active micro-rheology of supercooled liquids is explained in terms of individual and collective dynamics. The effective mobility arises as a collective effect which gives insight into the energy landscape of the system. On the other hand, the damping coefficient is a constant that modulates the effect of external forces over the thermal energy which particles have at their disposition to perform Brownian motion. For long times, these thermal fluctuations become characterized in terms of an effective temperature that is a consequence of the dynamic coupling between kinetic and configurational degrees of freedom induced by the presence of the strong external force. The interplay between collective mobility and effective temperature allows to formulate a generalized Stokes-Einstein relation that may be used to determine the collective diffusion coefficient. The explicit relations we deduce reproduce simulation data remarkably well.

Effective temperatures and the breakdown of the Stokes-Einstein relation for particle suspensions.

The short- and long-time breakdown of the classical Stokes-Einstein relation for colloidal suspensions at arbitrary volume fractions is explained here by examining the role that confinement and attractive interactions play in the intra- and inter-cage dynamics executed by the colloidal particles. We show that the measured short-time diffusion coefficient is larger than the one predicted by the classical Stokes-Einstein relation due to a non-equilibrated energy transfer between kinetic and configuration degrees of freedom. This transfer can be incorporated in an effective kinetic temperature that is higher than the temperature of the heat bath. We propose a Generalized Stokes-Einstein relation (GSER) in which the effective temperature replaces the temperature of the heat bath. This relation then allows to obtain the diffusion coefficient once the viscosity and the effective temperature are known. On the other hand, the temporary cluster formation induced by confinement and attractive interactions of hydrodynamic nature makes the long-time diffusion coefficient to be smaller than the corresponding one obtained from the classical Stokes-Einstein relation. Then, the use of the GSER allows to obtain an effective temperature that is smaller than the temperature of the heat bath. Additionally, we provide a simple expression based on a differential effective medium theory that allows to calculate the diffusion coefficient at short and long times. Comparison of our results with experiments and simulations for suspensions of hard and porous spheres shows an excellent agreement in all cases.

Nonlinear irreversible thermodynamics of single-molecule experiments.

Irreversible thermodynamics of single-molecule experiments subject to external constraining forces of a mechanical nature is presented. Extending Onsager's formalism to the nonlinear case of systems under nonequilibrium external constraints, we are able to calculate the entropy production and the general nonlinear kinetic equations for the variables involved. In particular, we analyze the case of RNA stretching protocols obtaining critical oscillations between different configurational states when forced by external means to remain in the unstable region of its free-energy landscape, as observed in experiments. We also calculate the entropy produced during these hopping events and show how resonant phenomena in stretching experiments of single RNA macromolecules may arise. We also calculate the hopping rates using Kramer's approach obtaining a good comparison with experiments.

Onsager's irreversible thermodynamics of the dynamics of transient pores in spherical lipid vesicles.

Onsager's irreversible thermodynamics is used to perform a systematic deduction of the kinetic equations governing the opening and collapse of transient pores in spherical vesicles. We show that the edge tension has to be determined from the initial stage of the pore relaxation and that in the final state the vesicle membrane is not completely relaxed, since the surface tension and the pressure difference are about 25% of its initial value. We also show that the pore life-time is controlled by the solution viscosity and its opening is driven by the solution leak-out and the surface tension drop. The final collapse is due to a non-linear interplay between the edge and the surface tensions together with the pressure difference. We also discuss the connection with previous models.

Effect of elastic colored noise in the hopping dynamics of single molecules in stretching experiments.

The influence of colored noise induced by elastic fluctuations in single-molecule stretching experiments is theoretically and numerically studied. Unlike in the thermal white noise case currently considered in the literature, elastically induced hopping dynamics between folded and unfolded states is manifested through critical oscillations showing smaller end-to-end distance fluctuations (δx∼1.25nm) within the free energy wells corresponding to both states. Our results are derived by analyzing the elastic coupling between the Handle-Molecule-Handle system and the laser optical tweezers (LOT) array. It is shown that an Ornstein-Uhlenbeck process related to this elastic coupling may trigger the hopping transitions via a colored noise with an intensity proportional to the elastic constant of the LOT array. Evolution equations of the variables of the system were derived by using the irreversible thermodynamics of small systems recently proposed. Theoretical expressions for the corresponding stationary probability densities are provided and the viability of inferring the shape of the free energy from direct measurements is discussed.

Thermostatistical description of small systems in nonequilibrium conditions: energy conversion and harvesting.

Hysteresis cycles are very important features of energy conversion and harvesting devices, such as batteries. The efficiency of these may be strongly affected by the physical size of the system. Here, we show that in systems which are small enough, the existence of physical boundaries which produce nonhomogeneities of the interaction potential gives rise to inflections and barriers in the associated free energy. This in turn brings on irreversible processes which can be triggered under suitable external conditions imposed by a heat bath. As an example, by controlling the temperature, the state of a small system may be impelled to oscillate between two different structural configurations or aggregation states avoiding equilibrium coexistence and therefore dissipating energy. This cyclical behavior associated with a hysteresis cycle may be prototypical of energy conversion, storage, or generating nanodevices, as exemplified by Li-ion insertion batteries.

Mean-field "temperature" in far from equilibrium systems.

We calculate the nonequilibrium mean-field "temperature" of a brownian system in contact with a heat bath. We consider two different cases: an equilibrium bath in the presence of strong external forces, and a nonequilibrium bath. By proving the existence of a generalized fluctuation-dissipation relation, this mean-field "temperature" can be used to describe a nonequilibrium system as is if it were in thermal equilibrium with a thermal bath at the mean-field "temperature" mentioned above. We apply our results to chemical reactions in the presence of external forces showing how chemical equilibrium and Kramers rate constants are modified by the presence of these forces.

The rheology of concentrated suspensions of arbitrarily-shaped particles.

We propose an improved effective-medium theory to obtain the concentration dependence of the viscosity of particle suspensions at arbitrary volume fractions. Our methodology can be applied, in principle, to any particle shape as long as the intrinsic viscosity is known in the dilute limit and the particles are not too elongated. The procedure allows to construct a continuum-medium model in which correlations between the particles are introduced through an effective volume fraction. We have tested the procedure using spheres, ellipsoids, cylinders, dumbells, and other complex shapes. In the case of hard spherical particles, our expression improves considerably previous models like the widely used Krieger-Dougherty relation. The final expressions obtained for the viscosity scale with the effective volume fraction and show remarkable agreement with experiments and numerical simulations at a large variety of situations.

Transition to irreversibility in sheared suspensions: an analysis based on a mesoscopic entropy production.

We study the shear-induced diffusion effect and the transition to irreversibility in suspensions under oscillatory shear flow by performing an analysis of the entropy production associated with the motion of the particles. We show that the Onsager coupling between different contributions to the entropy production is responsible for the scaling of the mean square displacement on particle diameter and applied strain. We also show that the shear-induced effective diffusion coefficient depends on the volume fraction, and use lattice-Boltzmann simulations to characterize the effect through the power spectrum of particle positions for different Reynolds numbers and volume fractions. Our study gives a thermodynamic explanation of the transition to irreversibility through a pertinent analysis of the second law of thermodynamics.

Fluctuation theorems for systems under Fokker-Planck dynamics.

We study Brownian motion driven with both conservative and nonconservative external forces. By using the thermodynamic approach of the theory of Brownian motion we obtain the Fokker-Planck equation and derive expressions for the fluctuation theorem in local equilibrium and in quasiequilibrium. In local equilibrium the expressions we obtain coincide with previous results.

The rheology of hard sphere suspensions at arbitrary volume fractions: An improved differential viscosity model.

We propose a simple and general model accounting for the dependence of the viscosity of a hard sphere suspension at arbitrary volume fractions. The model constitutes a continuum-medium description based on a recursive-differential method where correlations between the spheres are introduced through an effective volume fraction. In contrast to other differential methods, the introduction of the effective volume fraction as the integration variable implicitly considers interactions between the spheres of the same recursive stage. The final expression for the viscosity scales with this effective volume fraction, which allows constructing a master curve that contains all the experimental situations considered. The agreement of our expression for the viscosity with experiments at low- and high-shear rates and in the high-frequency limit is remarkable for all volume fractions.

Thermokinetic approach of single particles and clusters involving anomalous diffusion under viscoelastic response.

We present a thermokinetic description of anomalous diffusion of single particles and clusters in a viscoelastic medium in terms of a non-Markovian diffusion equation involving memory functions. The scaling behavior of these functions is analyzed by considering hydrodynamics and cluster-size space random walk arguments. We explain experimental results on diffusion of Brownian particles in the cytoskeleton, in cluster-cluster aggregation, and in a suspension of micelles.

Finite-size effects in microrheology.

We propose a model to explain finite-size effects in intracellular microrheology observed in experiments. The constrained dynamics of the particles in the intracellular medium, treated as a viscoelastic medium, is described by means of a diffusion equation in which interactions of the particles with the cytoskeleton are modeled by a harmonic force. The model reproduces the observed power law behavior of the mean square displacement in which the exponent depends on the ratio between particle-to-cytoskeleton-network sizes.