Trapping colloids near chemical stripes via critical Casimir forces

Abstract

We study theoretically and experimentally the solvent-mediated critical Casimir force acting on colloidal particles immersed in a binary liquid mixture of water and 2,6-lutidine and close to substrates which are chemically patterned with periodically alternating stripes of antagonistic adsorption preferences. These patterns are experimentally realized via microcontact printing. Upon approaching the critical demixing point of the solvent, normal and lateral critical Casimir forces generate laterally confining effective potentials for the colloids. We analyse in detail the rich behaviour of the spherical colloids close to such substrates. For all patterned substrates we investigated, our measurements of these effective potentials agree with the corresponding theoretical predictions. Since both the directions and the strengths of the critical Casimir forces can be tuned by minute temperature changes, this provides a new mechanism for controlling colloids as model systems, opening encouraging perspectives for applications.

Keywords:

• solvation forces
• critical Casimir effect
• colloidal suspension
• chemically patterned substrates

Acknowledgements

It is a great pleasure for the authors to dedicate this paper to Bob Evans on the occasion of his 65th birthday in view of his long lasting inspiration and encouragement across many fields of statistical physics.

Notes

Notes

1. Here we quote the value of ν within the Ising universality class, which is relevant for the interpretation of experimental data concerning classical binary liquid mixtures.

2. Note that the Derjaguin approximation holds only for distances which are small on the scale of the particle size (a detailed analysis of its applicability for the system under consideration is given in 16). However, in Equation (13) also large values of z occur. But at these large particle–wall distances the critical Casimir force as well as the electrostatic force are negligibly small compared to the gravitational force, so that using this approximation is nonetheless not detrimental. In principle, the integration in Equation (13) is limited by the vertical extension of the experimental sample cell of around 200 µm. However, due to the gravitational contribution to the potential, de facto no colloidal particle moves out of the vertical field of view of the imaging objective. Thus the integration in Equation (13) can be taken to run up to infinity without quantitatively relevant consequences because contributions from large z are strongly suppressed.