Equilibrium Capillary Forces with Atomic Force Microscopy

Abstract

We present measurements of equilibrium forces resulting from capillary condensation. The results give access to the ultralow interfacial tensions between the capillary bridge and the coexisting bulk phase. We demonstrate this with solutions of associative polymers and an aqueous mixture of gelatin and dextran, with interfacial tensions around 10 N=m. The equilibrium nature of the capillary forces is attributed to the combination of a low interfacial tension and a microscopic confinement geometry, based on nucleation and growth arguments. DOI: 10.1103/PhysRevLett.99.104504 PACS numbers: 47.55.nk, 68.03.Cd, 68.37.Ps Interfaces are ubiquitous in soft matter and biological systems. The corresponding phase equilibria are often characterized by weak, tunable interactions and large length scales . As a result, the interfacial tensions, / k B T= 2 , are typically ultralow (i.e., 1 mN m ÿ1 ). Measurement of ultralow interfacial tensions is notoriously difficult. Many available techniques, such as drop shape [1] or interfacial profile analysis [2], rely on optical visualization. However, in weakly segregated and nearcritical systems, the optical contrast between the phases is generally small. Moreover, density differences are also small, because of which it is difficult to obtain accurate information from drop shape analysis under normal gravity. To induce larger deformations, the spinning drop method is commonly used [3]. However, it was recently reported that the centrifugal field that is applied in this method, significantly affects the compositions of coexisting liquid phases. Demixed systems can even be brought into the one-phase regime [4].The method that is presented in this Letter does not rely on optical contrast, density differences, or strong external fields. We use colloidal probe atomic force microscopy (CP-AFM), introduced independently by Ducker et al. [5] and Butt [6], to measure equilibrium forces originating from capillary, liquid bridges between two surfaces. We analyze the resulting force-separation profiles to extract ultralow interfacial tensions. In Fig. 1 we show a schematic representation of a capillary, liquid bridge between a sphere and a flat substrate, the characteristic configuration in the CP-AFM experiment.When a homogeneous phase, in which one of the components is near its saturation point, is confined between two surfaces, a new phase can be formed by either condensation or evaporation. It is well known that, e.g., water condenses between hydrophilic surfaces in humid air [7]. Between hydrophobic surfaces at close separation, immersed in pure water, a capillary bridge of water vapor is formed, a process known as capillary evaporation or cavitation [8]. Capillary condensation is also reported for systems that show liquid-liquid coexistence, e.g., demixed ternary polymer-solvent systems [9]. Because the curvature of the capillary bridge is negative with respect to the inner phase, a negative pressure difference is present across the interface, leading to an attractive force between the ...

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