Direct Measurement of Thermodynamic Properties of Colloidal Hard Spheres

R P.A Dullens,D G.A.L Aarts,W K Kegel

doi:10.2516/ogst:2008015

R P.A Dullens, D G.A.L Aarts + Show 1 more

Open Access

https://doi.org/10.2516/ogst:2008015

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Abstract

Recently, we have shown how to measure thermodynamic properties of colloidal hard sphere suspensions by microscopy [Dullens et al. (2006) PNAS 103, 529]. Here, we give full experimental details on how to acquire three dimensional snapshots of a colloidal hard sphere suspension over a wide range of densities by means of confocal laser scanning microscopy. Furthermore, we elaborate on the analysis of the data sets, in which we measure the available volume to insert an additional sphere and the surface area of that volume. These geometrical properties are related to key thermodynamic quantities by statistical geometry. This enables us to measure in a direct and non-interfering way the pressure, the chemical potential and the free energy density of a hard sphere suspension, which are in good agreement with theoretical predictions.

Highlights

The intimate relation between colloids and statistical mechanics was pioneered by Perrin in his determination of Boltzmann’s constant kB from microscopy images of sedimenting colloids at low densities [1]
The available volume to insert an additional sphere and the surface area of that volume are geometric quantities that are directly related to important thermodynamic quantities [3, 5, 6]
The mass density of the particles is almost matched by the mass density of the solvent, we have to rule out that gravity induces a gradient in the concentration within the imaged volume

Summary

INTRODUCTION

The intimate relation between colloids and statistical mechanics was pioneered by Perrin in his determination of Boltzmann’s constant kB from microscopy images of sedimenting colloids at low densities [1]. Geometry provides a microscopic and straightforward route to the equation of state, the chemical potential and the free energy of the hard sphere system. Issues like crystallization and glass formation in concentrated colloidal suspensions have been addressed in great detail using confocal microscopy [14,15,16,17,18,19] It is non-trivial to measure accurate hard sphere configurations in more diluted suspensions. We combine fast confocal microscopy and model colloids to obtain three dimensional hard sphere configurations throughout almost the whole fluid region of the hard sphere phase diagram From these snapshots the available volume to insert an additional sphere and the surface area of that volume are determined.

STATISTICAL GEOMETRY OF HARD SPHERES

EXPERIMENTAL SECTION

RESULTS AND DISCUSSION

CONCLUSIONS