Alignment of cylindrical colloids near chemically patterned substrates induced by critical Casimir torques

Abstract

Recent experiments have demonstrated a fluctuation-induced lateral trapping of spherical colloidal particles immersed in a binary liquid mixture near its critical demixing point and exposed to chemically patterned substrates. Inspired by these experiments, we study this kind of effective interaction, known as the critical Casimir effect, for elongated colloids of cylindrical shape. This adds orientational degrees of freedom. When the colloidal particles are close to a chemically structured substrate, a critical Casimir torque acting on the colloids emerges. We calculate this torque on the basis of the Derjaguin approximation. The range of validity of the latter is assessed via mean-field theory. This assessment shows that the Derjaguin approximation is reliable in experimentally relevant regimes, so that we extend it to Janus particles endowed with opposing adsorption preferences. Our analysis indicates that critical Casimir interactions are capable of achieving well-defined, reversible alignments both of chemically homogeneous and of Janus cylinders.

Three-body critical Casimir forces

“…In view of future experimental and theoretical studies of the phase behavior of nonspherical colloids in near-critical solvents we emphasize that the isotropic colloidal liquid phase is stabilized by the repulsive three-body CCF, while nematic colloidal liquids and smectic phases are disfavored, similar to results of earlier studies concerning the influence of interaction potentials on phase diagrams of fluids consisting of nonspherical particles [65], On the basis of our earlier theoretical studies on the alignment of elongated nonspherical colloids near homogeneous [41] or chemically patterned substrates [56] we conclude that the attractive two-body CCF favors colloidal nematic liquid and smectic phases.…”

“…8(b) one can see that even for a surface-to-surface distance between the colloids (1) and (3) which is 2 times larger than the radius of the particles (i.e., for A |3 = 2), close to Tc there remains a significant deviation from the pairwise force between the colloids (1) and (2). We attribute this behavior to the fact that the ratio of the strengths of the two-body CCFs for ( + ,-) and (+ ,+ ) BCs varies as a function of temperature [56]. Whereas close to Tc the CCF for ( + ,-) BCs is much stronger than the attractive CCF for (+ ,+ ) BCs, both become comparable in strength for ©i2 » 1 • Therefore, even for A )3 = 2 the repulsive interaction between the colloids (1) and (3) significantly contributes to the force + _) on the colloid (1) shown in Fig.…”

Critical Casimir force in the presence of random local adsorption preference

“…Beside surfaces with a homogeneous adsorption preference [14,15], the critical Casimir force has been investigated in the presence of a chem ically structured substrate [16], leading to a laterally varying adsorption preference, as well as in the presence of a substrate with a gradient in the adsorption preference [17]. Theoretical investigations of the critical Casimir force for inhomogeneous BC have considered the film geometry in the presence of a chemically striped substrate, studied within mean-field theory [46], within Gaussian approximation [47,48], and recently by MC simulations [8,39,44], The critical Casimir force in the presence of a chemically structured substrate has also been studied within the Derjaguin approximation for a sphere [49] and a cylindrical colloid [50] close to a planar wall. Inhomogeneous BC have been also considered within Gaussian approximation in Refs.…”

Critical Casimir forces between planar and crenellated surfaces

“…are displaced such that the minimum of A as a function of τ is located closer to the critical point at τ = 0. For comparison we note that the functional shape of the amplitude of the step contribution is very close to the numerically obtained MFT scaling function of the attractive critical Casimir force acting between a thin cylinder and a planar substrate, where the symmetry axis of the cylinder is parallel to the substrate [31]. Indeed, the lower white contour line in Fig.…”

“…[19][20][21][22][23]). Critical Casimir forces for chemically structured confinements have been studied theoretically [24][25][26][27][28][29][30][31] as well as in experiments with colloidal particles [32,33]. It has been demonstrated that such patterns induce lateral critical Casimir forces which can be used to trap particles reversibly along the lateral direction in a designated way [32,33].…”