Fluctuations and correlations in soft matter surfaces

Resumen

A liquid-vapor interface is the region of the space where coexists the liquid and vapor phase of a given element or molecule. The liquid-vapor interface can be described as a uctuating bidimensional region (a surface) or a quasibidimensional region, and both points of view have associated a magnitude that characterizes both of them, the surface tension. Historically, these di erent visions gave birth to the theories known nowadays as: Capillary Wave Theory (bidimensional vision) and Density Functional Theory, whose precursors were Madlestam and van der Waals respectively. Both theories were developed in parallel and despite the e ort and the work performed to connect them, their link has been puzzling and is not clear yet. In the rst part of this thesis, we will focus on how to connect both descriptions through the magnitude that relate them, which is a generalized version of the surface tension that describes the interface at the mesoscopic level. We will obtain this magnitude by di erent routes to ensure that it is well de ned for each system, something questioned recently. And we will study di erent systems which could be described as "interfaces", such as: 2D suspended material (chapter 3), liquid-vapor interfaces (chapters 4 and 6) and lipid bilayers (chapter 5). In chapter 1, we will introduce the topic and the previous state of art, and in chapter 2 the theoretical techniques developed in this thesis to analyze 2D suspended materials and liquid-vapor interfaces. In the second part of this thesis, we will analyze, within the DFT, the novel experimental technique 3D-AFM, which allows to scan a uid in contact with a solid surface (substrate) and allows to measure the in uence of the uid on the movement of the tip. This in uence is observed in the AFM observables, from which we can obtain the normal force (respect to the substrate) over the tip at each position. This normal force should be related to the structure of the uid close to the substrate, but since it is a recent technique the way to connect them is not yet clear. For this reason along chapters 7- 9 we will analyze this system from a theoretical point of view and we will obtain some predictions, that we will check with experiments in chapter 10. The last part is a direct collaboration with an experimental group, they observed a huge enhancement in the water adsorption isotherm of a novel composite (MOF@COF), which should be regarded as a complex network of interconnected pores. In chapter 11, we will analyze the adsorption isotherms, we will hypothesize a cooperative e ect and we will check (theoretically) if this e ect takes place under the experimental conditions