It is well known since the seminal work by Asakura and Oosawa (AO) [1] that large colloidal

particles supended in a dilute polymer solution suffer an effective short-ranged

attractive interaction arising from the depletion of solutes between the colloidal particles,

provided they are sufficiently close to each other. In the analytically soluble AO model,

the colloidal particles are modeled as hard objects of arbitrary shape and the depletion

agent as an ideal gas, whose interaction with the colloids is of the excluded volume type.

A peculiar prediction of the AO model is that the strength of attraction increases with the

size of the colloidal particles, at fixed solute volume fraction, implying that macroscopic

objects should feel extremely large attractive forces at short distances. Surface roughness

contrasts this paradoxical consequences by inhibiting the depletion mechanism.

During the last decade, the interest in this topic has been revived since the surface morphology

of the colloid can be used to tune the effective interaction. Rough colloids with

different shapes have been produced experimentally in order to investigate the change in

the interaction: From particles decorated with spheres or litographycally shaped to lock

and key colloids.

Theoretical studies of the effects of roughness on depletion have been recently performed

by Monte Carlo simulations [2] coupled with liquid state theories [3], in the case of colloidal

particles decorated with smaller spheres immersed in a ideal gas. However, analytical

expressions able to capture the main effects of surface roughness on the shape of

the depletion interaction are still missing.

We developed a simple model, in the framework of the AO theory, able to describe the

effects of surface rughness for a significant range of parameters. The resulting explicit

expressions are easily computed for a large interval of all the relevant parameters of the

problem. Comparison with the available numerical simulations [2] shows an encouraging

aggreement and allows to predict the onset of colloidal aggregation in dilute suspensions

of rough particles.

[1] S. Asakura and F. Oosawa, J. Polym. Sci. 33, 183 (1958)

[2] M. Kamp, M. Hermes, C. M. Van Kats, D. J. Kraft, W. K. Kegel, M. Dijkstra and A. Van

Blaaderen, Langmuir 32, 1233 (2016)

[3] D. Banerjee, J. Yang and K. S. Schweizer, Soft Matter 11, 9086 (2015)