Energy Transfer between Colloids via Critical Interactions

Nanoalignment by critical Casimir torques

The manipulation of microscopic objects requires precise and controllable forces and torques. Recent advances have led to the use of critical Casimir forces as a powerful tool, which can be finely tuned through the temperature of the environment and the chemical properties of the involved objects. For example, these forces have been used to self-organize ensembles of particles and to counteract stiction caused by Casimir-Liftshitz forces. However, until now, the potential of critical Casimir torques has been largely unexplored. Here, we demonstrate that critical Casimir torques can efficiently control the alignment of microscopic objects on nanopatterned substrates. We show experimentally and corroborate with theoretical calculations and Monte Carlo simulations that circular patterns on a substrate can stabilize the position and orientation of microscopic disks. By making the patterns elliptical, such microdisks can be subject to a torque which flips them upright while simultaneously allowing for more accurate control of the microdisk position. More complex patterns can selectively trap 2D-chiral particles and generate particle motion similar to non-equilibrium Brownian ratchets. These findings provide new opportunities for nanotechnological applications requiring precise positioning and orientation of microscopic objects.

Critical Casimir forces in soft matter

We review recent advances in the theoretical, numerical, and experimental studies of critical Casimir forces in soft matter, with particular emphasis on their relevance for the structures of colloidal suspensions and on their dynamics. Distinct from other interactions which act in soft matter, such as electrostatic and van der Waals forces, critical Casimir forces are effective interactions characterised by the possibility to control reversibly their strength via minute temperature changes, while their attractive or repulsive character is conveniently determined via surface treatments or by structuring the involved surfaces. These features make critical Casimir forces excellent candidates for controlling the equilibrium and dynamical properties of individual colloids or colloidal dispersions as well as for possible applications in micro-mechanical systems. In the past 25 years a number of theoretical and experimental studies have been devoted to investigating these forces primarily under thermal equilibrium conditions, while their dynamical and non-equilibrium behaviour is a largely unexplored subject open for future investigations.

Phases of surface-confined trivalent colloidal particles

Patchy colloids promise the design and modelling of complex materials, but the realization of equilibrium patchy particle structures remains challenging. Here, we assemble pseudo-trivalent particles and elucidate their phase behaviour when confined to a plane. We observe the honeycomb phase, as well as more complex amorphous network and triangular phases. Structural analysis performed on the three condensed phases reveals their shared structural motifs. Using a combined experimental and simulation approach, we elucidate the energetics of these phases and construct the phase diagram of this system, using order parameters to determine the phase coexistence lines. Our results reveal the rich phase behaviour that a relatively simple patchy particle system can display, and open the door to a larger joined simulation and experimental exploration of the full patchy-particle phase space.

Inducing oscillations of trapped particles in a near-critical Gaussian field

We study the nonequilibrium dynamics of two particles confined in two spatially separated harmonic potentials and linearly coupled to the same thermally fluctuating scalar field, a cartoon for optically trapped colloids in contact with a medium close to a continuous phase transition. When an external periodic driving is applied to one of these particles, a nonequilibrium periodic state is eventually reached in which their motion synchronizes thanks to the field-mediated effective interaction, a phenomenon already observed in experiments. We fully characterize the nonlinear response of the second particle as a function of the driving frequency, in particular far from the adiabatic regime in which the field can be assumed to relax instantaneously. We compare the perturbative, analytic solution to its adiabatic approximation, thus determining the limits of validity of the latter, and we qualitatively test our predictions against numerical simulations.

Nonequilibrium relaxation of a trapped particle in a near-critical Gaussian field

We study the nonequilibrium relaxational dynamics of a probe particle linearly coupled to a thermally fluctuating scalar field and subject to a harmonic potential, which provides a cartoon for an optically trapped colloid immersed in a fluid close to its bulk critical point. The average position of the particle initially displaced from the position of mechanical equilibrium is shown to feature long-time algebraic tails as the critical point of the field is approached, the universal exponents of which are determined in arbitrary spatial dimensions. As expected, this behavior cannot be captured by adiabatic approaches which assumes fast field relaxation. The predictions of the analytic, perturbative approach are qualitatively confirmed by numerical simulations.

Critical Casimir interactions of colloids in micellar critical solutions

We study the temperature-dependence of critical Casimir interactions in a critical micellar solution of the nonionic surfactant C12E5 dissolved in water. Experimentally, this is achieved with total internal reflection microscopy (TIRM) which measures the interaction between a single particle and a flat wall. For comparison, we also studied the pair interactions of a two dimensional layer of colloidal particles in the identical micellar system which yields good agreement with the TIRM results. Although, at the surfactant concentration considered here, the fluid forms a dynamical network of wormlike micelles whose structure is considerably more complex than that of simple critical molecular fluids, the temperature-dependence of the measured interactions is - for surface-to-surface distances above 160 nm - in excellent quantitative agreement with theory. Below 160 nm, deviations arise which we attribute to the adsorption of micelles to the interacting surfaces.

Effective pair interaction of patchy particles in critical fluids

We study the critical Casimir interaction between two spherical colloids immersed in a binary liquid mixture close to its critical demixing point. The surface of each colloid prefers one species of the mixture with the exception of a circular patch of arbitrary size, where the other species is preferred. For such objects, we calculate, within the Derjaguin approximation, the scaling function describing the critical Casimir potential, and we use it to derive the scaling functions for all components of the forces and torques acting on both colloids. The results are compared with available experimental data. Moreover, the general relation between the scaling function for the potential and the scaling functions for the force and the torque is derived.

Controlling the dynamics of colloidal particles by critical Casimir forces

Critical Casimir forces can play an important role for applications in nano-science and nano-technology, owing to their piconewton strength, nanometric action range, fine tunability as a function of temperature, and exquisite dependence on the surface properties of the involved objects. Here, we investigate the effects of critical Casimir forces on the free dynamics of a pair of colloidal particles dispersed in the bulk of a near-critical binary liquid solvent, using blinking optical tweezers. In particular, we measure the time evolution of the distance between the two colloids to determine their relative diffusion and drift velocity. Furthermore, we show how critical Casimir forces change the dynamic properties of this two-colloid system by studying the temperature dependence of the distribution of the so-called first-passage time, i.e., of the time necessary for the particles to reach for the first time a certain separation, starting from an initially assigned one. These data are in good agreement with theoretical results obtained from Monte Carlo simulations and Langevin dynamics.

Motile bacteria in a critical fluid mixture

We studied the swimming of Escherichia coli bacteria in the vicinity of the critical point in a solution of the nonionic surfactant C_{12}E_{5} in buffer solution. In phase-contrast microscopy, each swimming cell produces a transient trail behind itself lasting several seconds. Comparing quantitative image analysis with simulations show that these trails are due to local phase reorganization triggered by differential adsorption. This contrasts with similar trails seen in bacteria swimming in liquid crystals, which are due to shear effects. We show how our trails are controlled, and use them to probe the structure and dynamics of critical fluctuations in the fluid medium.

Nonisotropic Self-Assembly of Nanoparticles: From Compact Packing to Functional Aggregates

Quantum strongly correlated systems that exhibit interesting features in condensed matter physics often need an unachievable temperature or pressure range in classical materials. One solution is to introduce a scaling factor, namely, the lattice parameter. Synthetic heterostructures named superlattices or supracrystals are synthesized by the assembling of colloidal atoms. These include semiconductors, metals, and insulators for the exploitation of their unique properties. Most of them are currently limited to dense packing. However, some of desired properties need to adjust the colloidal atoms neighboring number. Here, the current state of research in nondense packing is summarized, discussing the benefits, outlining possible scenarios and methodologies, describing examples reported in the literature, briefly discussing the challenges, and offering preliminary conclusions. Penetrating such new and intriguing research fields demands a multidisciplinary approach accounting for the coupling of statistic physics, solid state and quantum physics, chemistry, computational science, and mathematics. Standard interactions between colloidal atoms and emerging fields, such as the use of Casimir forces, are reported. In particular, the focus is on the novelty of patchy colloidal atoms to meet this challenge.

Tuning Patchy Bonds Induced by Critical Casimir Forces

Experimental control of patchy interactions promises new routes for the assembly of complex colloidal structures, but remains challenging. Here, we investigate the role of patch width in the assembly of patchy colloidal particles assembled by critical Casimir forces. The particles are composed of a hydrophobic dumbbell with an equatorial hydrophilic polymer shell, and are synthesized to have well-defined patch-to-shell area ratios. Patch-to-patch binding is achieved in near-critical binary solvents, in which the particle interaction strength and range are controlled by the temperature-dependent solvent correlation length. Upon decreasing the patch-to-shell area ratio, we observe a pronounced change of the bonding morphology towards directed single-bonded configurations, as clearly reflected in the formation of chain-like structures. Computer simulations using an effective critical Casimir pair potential for the patches show that the morphology change results from the geometric exclusion of the increasingly thick hydrophilic particle shells. These results highlight the experimental control of patchy interactions through the engineering of the building blocks on the way towards rationally designed colloidal superstructures.

Effective potentials induced by self-assembly of patchy particles

Effective colloid-colloid interactions can be tailored through the addition of a complex cosolute. Here we investigate the case of a cosolute made by self-assembling patchy particles. Depending on the valence, these particles can form either polymer chains or branched structures. We numerically calculate the effective potential Veff between two colloids immersed in a suspension of reversible patchy particles, exploring a wide region of the cosolute phase diagram and the role of valence. In addition to well-known excluded volume and depletion effects, we find that, under appropriate conditions, Veff is completely attractive but shows an oscillatory character. In the case of polymerizing cosolute, this results from the fact that chains are efficiently confined by the colloids through the onset of local order. This argument is then generalized to the case of particles with higher valence, under the condition that they are still able to maintain a fully bonded organization upon confinement. The resulting effective potentials are relevant for understanding the behavior of complex mixtures in crowded environments, but may also be exploited for tuning colloidal self-assembly at preferred target distances in order to build desired superstructures.