Raúl A. Rica

Brownian Carnot engine

The Carnot cycle imposes a fundamental upper limit to the efficiency of a macroscopic motor operating between two thermal baths1. However, this bound needs to be reinterpreted at microscopic scales, where molecular bio-motors2 and some artificial micro-engines3–5 operate. As described by stochastic thermodynamics6,7, energy transfers in microscopic systems are random and thermal fluctuations induce transient decreases of entropy, allowing for possible violations of the Carnot limit8. Here we report an experimental realization of a Carnot engine with a single optically trapped Brownian particle as the working substance. We present an exhaustive study of the energetics of the engine and analyse the fluctuations of the finite-time efficiency, showing that the Carnot bound can be surpassed for a small number of non-equilibrium cycles. As its macroscopic counterpart, the energetics of our Carnot device exhibits basic properties that one would expect to observe in any microscopic energy transducer operating with baths at different temperatures9–11. Our results characterize the sources of irreversibility in the engine and the statistical properties of the efficiency—an insight that could inspire new strategies in the design of efficient nano-motors.

Adiabatic processes realized with a trapped Brownian particle.

The ability to implement adiabatic processes in the mesoscale is of key importance in the study of artificial or biological micro- and nanoengines. Microadiabatic processes have been elusive to experimental implementation due to the difficulty in isolating Brownian particles from their fluctuating environment. Here we report on the experimental realization of a microscopic quasistatic adiabatic process employing a trapped Brownian particle. We circumvent the complete isolation of the Brownian particle by designing a protocol where both characteristic volume and temperature of the system are changed in such a way that the entropy of the system is conserved along the process. We compare the protocols that follow from either the overdamped or underdamped descriptions, demonstrating that the latter is mandatory in order to obtain a vanishing average heat flux to the particle. We provide analytical expressions for the distributions of the fluctuating heat and entropy and verify them experimentally. Our protocols could serve to implement the first microscopic engine that is able to attain the fundamental limit for the efficiency set by Carnot.

Electric permittivity of concentrated suspensions of elongated goethite particles

This paper describes an investigation on the electric permittivity of concentrated suspensions of non-spherical particles, specifically prolate spheroids. It is first discussed how the determination of the frequency (omega) dependence of the electric permittivity (a phenomenon traditionally known as LFDD or low-frequency dielectric dispersion) can provide ample information on the properties of the dispersed material (shape, size, state of aggregation, conductivity) and of its interface with the (typically aqueous) medium. The basic quantities are the strength and frequency dependence of the dipole moment induced by the applied field, and its dimensionless counterpart, the dipole coefficient, C(*)(omega). It is explicitly shown how the (complex) relative permittivity of the suspension, epsilon(r)(*)(omega), can be calculated from it. Two theoretical models on the polarizability of spheroidal colloidal particles will be used as theoretical starting point; one of them (Model I) explicitly considers two relaxations of the permittivity, each associated to one of the particle axes. The other (Model II) is a semi-analytical theory that yields an LFDD practically independent of the axial ratio of the particles. Both models are aimed to be used if the suspensions are dilute (low volume fraction of solids, phi), and here they are generalized to concentrated systems by means of a previously published approximate evaluation of the permittivity of concentrated suspensions. Experiments are performed in the 1 kHz-1 MHz frequency range on suspensions of elongated goethite particles; the effects of ionic strength, pH, and volume fraction are investigated, and the two models are fitted to the data. In reality, taking into account that the particles are non-uniformly charged (a fact that contributes to their instability), two zeta potentials (roughly representing the lateral surface and the tip of the spheroid) are used as parameters. The results indicate that, when experimental conditions are optimal (high ionic strength and low zeta potential), the suspensions do indeed display two relaxations, that we ascribe to the long axis (and to flocs likely present in suspension) and to the short one. The permittivity increases with ionic strength, a result found with other systems, and compatible with a zeta potential that, on the average, decreases with ionic strength, an equally well known result, consequence of electric double layer compression. Another reasonable finding is the increase of estimated average dimensions and the decrease of electrokinetic potentials when the pH is close to the isoelectric point of goethite (around pH 9). The increase in volume fraction, finally, produces an overall increase in the permittivity, and the approximate model used for the evaluation of volume fraction variations can describe properly these effects, with basically constant zeta potentials and dimensions.

Optically levitated nanoparticle as a model system for stochastic bistable dynamics.

Nano-mechanical resonators have gained an increasing importance in nanotechnology owing to their contributions to both fundamental and applied science. Yet, their small dimensions and mass raises some challenges as their dynamics gets dominated by nonlinearities that degrade their performance, for instance in sensing applications. Here, we report on the precise control of the nonlinear and stochastic bistable dynamics of a levitated nanoparticle in high vacuum. We demonstrate how it can lead to efficient signal amplification schemes, including stochastic resonance. This work contributes to showing the use of levitated nanoparticles as a model system for stochastic bistable dynamics, with applications to a wide variety of fields.

Realization of nonequilibrium thermodynamic processes using external colored noise.

We investigate the dynamics of single microparticles immersed in water that are driven out of equilibrium in the presence of an additional external colored noise. As a case study, we trap a single polystyrene particle in water with optical tweezers and apply an external electric field with flat spectrum but a finite bandwidth of the order of kHz. The intensity of the external noise controls the amplitude of the fluctuations of the position of the particle and therefore of its effective temperature. Here we show, in two different nonequilibrium experiments, that the fluctuations of the work done on the particle obey the Crooks fluctuation theorem at the equilibrium effective temperature, given that the sampling frequency and the noise cutoff frequency are properly chosen.

Thermodynamics at the microscale: from effective heating to the Brownian Carnot engine

We review a series of experimental studies of the thermodynamics of nonequilibrium processes at the microscale. In particular, in these experiments we studied the fluctuations of the thermodynamic properties of a single optically-trapped microparticle immersed in water and in the presence of external random forces. In equilibrium, the fluctuations of the position of the particle can be described by an effective temperature that can be tuned up to thousands of Kelvins. Isothermal and non-isothermal thermodynamic processes that also involve changes in a control parameter were implemented by controlling the effective temperature of the particle and the stiffness of the optical trap. Since truly adiabatic processes are unfeasible in colloidal systems, mean adiabatic protocols where no average heat is exchanged between the particle and the environment are discussed and implemented. By concatenating isothermal and adiabatic protocols, it is shown how a single-particle Carnot engine can be constructed. Finally, we provide an in-depth study of the fluctuations of the energetics and of the efficiency of the cycle.

Modeling the patterns of visual field loss in glaucoma.

Purpose. A computer model was developed to test the assumption that diffuse neural loss can result in the field loss pattern characteristic of glaucoma. Methods. The anterior visual pathways comprised the retinal ganglion cells, and their axons up to the optic nerve head (ONH) were modeled in a computer program. Axon resistance to stress was accounted for depending on the location on the ONH, taking into consideration the presence or absence of vessels in the area. Damage patterns were applied to the axons at the ONH, and the corresponding dendritic fields were removed accordingly. A visual field was extracted and represented on a gray scale after a predetermined stage of damage was reached. Two patterns of damage were considered, a diffuse damage produced by randomly removing fibers and an ordered anteroposterior elimination. Results. Random damage never rendered a pattern loss. Ordered centrifugal fiber loss may produce a radial pattern more conspicuous when the vessels are endowed with a protective role. In both cases, scotomas tend to be detectable earlier in more peripheral locations, attributable to the increasing size of the receptive fields with eccentricity. Conclusions. The model shows that pattern loss typical of glaucoma cannot be solely the result of a random loss of fibers. Anteroposterior damage of the ONH can explain radial progression of scotomas if a protective role is introduced for the central vessels.

Trapping and manipulation of individual nanoparticles in a planar Paul trap

Visualisation and manipulation of nanoscale matter is one of the main and current challenges in nanosciences. To this aim, different techniques have been recently developed to non-invasively trap and manipulate nano-specimens, like nanoparticles or molecules. However, operating in air or vacuum still remains very challenging since most approaches are limited to a liquid environment. In this letter, we design and characterise a planar Paul trap optimised to trap and manipulate individual charged nanoparticles. This configuration offers competitive capabilities to manipulate nano-specimens in air or vacuum, including in-plane integration, high trap confinement along with dynamical trap reconfiguration, pointing towards applications in the field of levitated optomechanics.

Measuring kinetic energy changes in the mesoscale with low acquisition rates

We report on the measurement of the average kinetic energy changes in isothermal and non-isothermal quasistatic processes in the mesoscale, realized with a Brownian particle trapped with optical tweezers. Our estimation of the kinetic energy change allows to access to the full energetic description of the Brownian particle. Kinetic energy estimates are obtained from measurements of the mean square velocity of the trapped bead sampled at frequencies several orders of magnitude smaller than the momentum relaxation frequency. The velocity is tuned applying a noisy electric field that modulates the amplitude of the fluctuations of the position and velocity of the Brownian particle, whose motion is equivalent to that of a particle in a higher temperature reservoir. Additionally, we show that the dependence of the variance of the time-averaged velocity on the sampling frequency can be used to quantify properties of the electrophoretic mobility of a charged colloid. Our method could be applied to detect temperature gradients in inhomogeneous media and to characterize the complete thermodynamics of biological motors and of artificial micro and nanoscopic heat engines.

Effect of the volume fraction of solids on the concentration polarization around spheroidal hematite particles

We present the first experimental results on the effect of the particles content (up to ϕ = 20% volume fraction of solids) in the low frequency dielectric dispersion (LFDD) of suspensions of hematite (α-Fe2O3) prolate spheroidal colloids. Two α-relaxations, each one associated to a characteristic dimension of the particles, are clearly observed, but they present different dependencies with volume fraction. Accounting for particle–particle interactions, in terms of models for spheres, allows a comprehensive interpretation of the mechanisms involved, suggesting the presence of a nematic phase in our suspensions.