Competition and Response: from Active Matter to Electrolytes under Confinement

Abstract

Most systems in Nature manifest complex transport phenomena arising from the interplay of multiple time and length scales, be them intrinsic in the system’s dynamics or externally enforced. It is the case, for instance, of a colony of migrating cells whose competing mechanisms of self-propulsion and interaction allow for the reorganization into different tissues. Or, by ‘zooming in’ and looking at the same system on a different scale, it is the case of the ionic channels located in the membranes of the aforesaid cells. These channels typically exhibit extraordinary ion selectivity and water permeability due to the interplay between geometric confinement, surface properties and external drivings. Whether to investigate the collective structures of the former system, or the nanofluidic properties of the latter one rests on the interests of the reader. In any case, she will find some food for thought in this thesis.

Here we aim at the study of the transport properties of two very different classes of systems: active matter and electrolytes under confinement. In the examples above drawn from biology, cell tissues belongs to the class of active matter and protein channels are the archetype nanometric ionic systems. We tackle the problem from a purely statistical physics viewpoint by constructing minimal models to study the system’s response to outside influences and, by doing so, learn something about its internal properties. In the case of active matter, the challenge resides in the intrinsically out-of-equilibrium nature of its constituents, having the ability to self-propel by consuming fuel stored in the environment. In Part I of the manuscript, we study how the interplay between self-propulsion and steric interactions affects the linear response of active systems. First, we construct a very general theoretical framework which allows to derive general constraints that arbitrarily out-of-equilibrium systems must fulfilled. Then, we apply it to two different minimal models of active systems to derive generalized fluctuation-dissipation relations and Green-Kubo expressions. In Part II of the manuscript we investigate the surface-dominated transport of electrolytes in (i) a nanofluidic diode and (ii) a scanning ionic conductance microscopy configuration. In both cases, we develop a theory of ionic conductivity that rationalizes previous experimental results. By doing so, we shed light on the importance of the surface versus bulk competition in controlling ionic transport and we propose a new approach to exploit it for the imaging of surface charge with nanometric resolution.

La mayoría de los sistemas en la Naturaleza manifiestan fenómenos de transporte complejos que surgen de la interacción de múltiples escalas de tiempo y longitud, ya sean intrínsecas en la dinámica del sistema o forzadas externamente. Es el caso, por ejemplo, de una colonia de células migratorias cuyos mecanismos competitivos de autopropulsión e interacción permiten la reorganización en diferentes tejidos; o, al "acercar" y mirar el mismo sistema en una escala diferente, es el caso de los canales iónicos ubicados en las membranas de las células mencionadas. Estos canales exhiben típicamente una selectividad de iones extraordinaria y permeabilidad al agua debido a la interacción entre el confinamiento geométrico, las propiedades de la superficie y los conductos externos. Ya sea para investigar las estructuras colectivas del primer sistema, o las propiedades nanofluídicas del último, se basa en los intereses del lector. En cualquier caso, encontrará algo de reflexión en esta tesis.