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44953-G5
Direct Measurement of Casimir Force in Critical Films of Binary Liquid Mixtures

Ashis Mukhopadhyay, Wayne State University

We performed preliminary experiments in measuring the critical Casimir force of a binary liquid mixture. We are using a home-built atomic force microscope (AFM) for this purpose. Previously we used a single component liquid, a nearly spherical, nonpolar molecule tetrakis(2-ethylhexoxy)silane (TEHOS) as a test for the set-up. Our results indicated oscillations in the stiffness with a period of ~ 1 nm, which is consistent with the molecular dimension of TEHOS (Fig. 1a). For the measurement of the Casimir force, we are using a mixture of water and 2, 6 lutidine, which constitutes similar (+,+) boundary condition. This system has a convenient critical temperature, T_c » 32 ⁰C. Expectedly, we found that the oscillation disappears because of the incommensurate size of water and lutidine. Currently, we are taking measurements as a function of temperature. To measure the Casimir force (or energy) form this data, we require to develop a suitable mechanical model, which is currently underway. Also, please note that horizontal axis in Fig. 1 is not the film thickness. Measuring the absolute film thickness is a notoriously difficult problem in AFM experiments. In our new design, we are implementing two interferometers: one to monitor & control AFM-sample distance and one as deflection sensor for the cantilever. Using the sample interferometer, we cross-correlate the distance measured by the interferometer with the distance measured by withdrawing the tip from a gentle ‘crash' with the surface. With an interferometer sensitivity of better than 50 mV/Å, we expect to determine the distance at better than Å scale.

Fig. 1: Stiffness of (a) TEHOS and (b) water + 2, 6 lutidine film as a function of displacement. The surface is located to the right.

            In parallel, the support from the PRF grant had helped us to pursue other experiments in parallel. We have used the method of fluorescence correlation spectroscopy (FCS) to measure the center-of-mass diffusion coefficient of fluorescently labeled polystyrene (M_W=8100 g/mol) dissolved in polymer/toluene solutions above the overlap concentration (Fig. 2). The diffusion coefficient was found to decrease by two orders of magnitude for a concentration change of 0.17 g/cm³ to 0.6 g/cm³ at 34 °C. Less dramatic changes were observed at higher temperatures. The results are compared with the diffusion of free dyes in similar concentrated solutions. Vrentas-Duda free volume theory can explain the data reasonably well, from which the unit size of transport for the labeled macromolecule and the dye relative to the solvent is determined. The activation energy of diffusion was found to increase significantly as a function of concentration.

Figure 2. Temperature dependence of the diffusion coefficient for the free dye coumarin (top) and fluorescein-labeled PS (bottom), dissolved in varying concentrations of PS in toluene. In the temperature regime investigated, the data obey the Arrhenius equation (straight line fits).

            The PI has also coauthored a book chapter, titled “Interfacial Forces and Spectroscopy of Confined Fluids”. The chapter is a part of Springer Handbook of Nanotechnology (3^rd ed., Springer Verlag, editor: Bharat Bhusan). Here, we discussed current issues which are relevant for thin liquid film in intimate contact with solid surfaces. This chapter will be included in the second edition of Nanotribology and Nanomechanics, which is used in many universities as a text book.

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