Phase Diagram of Solvophilic Nanodiscs in a Polymer Solution: Depletion Attraction

Aggregation of discoidal particles due to depletion interaction

Depletion interactions between colloids of discoidal shape can induce their self-assembly into columnar aggregates. This is an effect of entropic origin with important implications in a range of colloidal systems, particularly in the clustering of erythrocytes that determine the rheological properties of blood. Here, we investigate the equilibrium state reached by discoidal colloids in a solution of smaller depletant particles. We develop a thermodynamic model of depletion-induced aggregation based on self-assembly theory and solve it analytically. We test the validity of the model by using Langevin simulations of a system of discs and depletant particles in which the depletion interaction emerges naturally. In addition, we consider the effect of an attractive interaction between depletant and discoidal particles, which we show induces a re-entrant dependence of aggregation with temperature.

Non-affinity adsorption of nanorods onto smooth walls via an entropy driven mechanism

Preferential adsorption of nanorods onto smooth walls is investigated using dissipative particle dynamics in the absence of specific attraction and a depletant. Although the translational and rotational entropy of nanorods is significantly reduced after adsorption, the effective attraction between the nanorod and wall is clearly identified based on the distribution profile of rods. As the rod length increases, the attractive interaction grows stronger and clusters of aligned nanorods can emerge on the smooth wall. However, the presence of a depletion zone of nanorods adjacent to the adsorbed layer gives zero surface excess. These two regions correspond to the primary minimum and maximum mean force potentials observed. Since adsorbed nanorods lose their rotational and translational entropy, the strong adsorption of long nanorods has to be attributed to the entropy gain associated with the increase in free volume for the solvent in this athermal system. Nonetheless, as the surface roughness is present, entropy-driven attraction is lessened, similar to the depletion force between colloids.

Self-Assembly of Microscopic Rods Due to Depletion Interaction

In this article, using numerical simulations we investigate the self-assembly of rod-like particles in suspension due to depletion forces which naturally emerge due to the presence of smaller spherical depletant particles. We characterize the type of clusters that are formed and the evolution of aggregation departing from a random initial configuration. We show that eventually the system reaches a thermodynamic equilibrium state in which the aggregates break and reform dynamically. We investigate the equilibrium state of aggregation, which exhibits a strong dependence on depletant concentration. In addition, we provide a simple thermodynamic model inspired on the theory of self-assembly of amphiphilic molecules which allows us to understand qualitatively the equilibrium aggregate size distributions that we obtain in simulation.

Surface Segregation and Bulk Aggregation in an Athermal Thin Film of Polymer-Nanoparticle Blends: Strategies of Controlling Phase Behavior

The phase behavior of an athermal film of a polymer-nanoparticle blend (PNB) driven by depletion attraction is investigated by dissipative particle dynamics for nanospheres and nanocubes. Surface segregation is observed at low nanoparticle concentrations, while bulk aggregation is seen at high concentrations. Surface excess and the aggregation number can be controlled by tuning the nanoparticle concentration. As surface-roughened or polymer-grafted nanoparticles are used, uniform PNBs are acquired due to the lack of depletion. Thus, addition of surface-roughened nanoparticles into PNBs of smooth nanoparticles can be employed to tune the phase characteristics. It is found that bulk aggregation is suppressed for both polymer-nanosphere and polymer-nanocube blends. However, surface segregation is impeded for polymer-nanosphere blend but enhanced for polymer-nanocube blend owing to the distinct influence of the nanoparticle shape on depletion.

Assembly of Lock-and-Key Colloids Mediated by Polymeric Depletant

Polymer-mediated lock-and-key assembly via depletion attraction is purely a shape-recognition process without any molecular bonding. Since the depletion attraction relates to osmotic pressure and excluded volume, the binding tendency in a dispersion of lock-and-key colloids can be controlled by adjusting the characteristics of polymeric depletants. In this work, dissipative particle dynamics accounting for explicit solvents, polymers, and multiple lock-key pairs are performed to investigate the influences of the polymer concentration, chain length, solvent quality, and chain stiffness. As the polymer concentration associated with osmotic pressure is increased, the binding free energy (E(b)) between a lock-key pair rises linearly and the binding fraction (θ(LK)) in the dispersion grows sigmoidally. Moreover, the increases in the chain length, solvent quality, and chain stiffness lead to the expansion of the polymer size associated with excluded volume and thus both E(b) and θ(LK) rise accordingly. However, E(b) and θ(LK) grow to be insensitive to the chain length for long enough polymer coils but still can be enhanced if the polymer becomes rod-like. As the solvent quality is varied, θ(LK) can be dramatically altered, although the radius of gyration of polymers is slightly changed.

Diffusion, sedimentation equilibrium, and harmonic trapping of run-and-tumble nanoswimmers

The diffusion of self-propelling nanoswimmers is explored by dissipative particle dynamics in which a nanoswimmer swims by forming an instantaneous force dipole with one of its nearest neighboring solvent beads. Our simulations mimic run-and-tumble behavior by letting the swimmer run for a time τ, then it randomly changes its direction for the next run period. Our simulations show that the swimming speed (ν(a)) of a nanoswimmer is proportional to the propulsion force and the mobility of a pusher is the same as that of a puller. The effective diffusivity is determined by three methods: mean squared displacement, velocity autocorrelation function, and sedimentation equilibrium. The active colloid undergoes directed propulsion at short time scales but changes to random motion at long time scales. The velocity autocorrelation function decreases with time and becomes zero beyond the run time. Under gravity, the concentration profile of active colloids follows Boltzmann distribution with a sedimentation length consistent with that acquired from the drift-diffusion equation. In our simulation, all three methods yield the same result, the effective diffusivity of an active colloid is the sum of the diffusivity of a passive colloid and ν(a)²τ/6. When the active colloids are confined by a harmonic well, they are trapped within a confinement length defined by the balance between the swimmer active force and restoring force of the well. When the confinement length is large compared to the run length, the stationary density profile follows the Boltzmann distribution. However, when the run length exceeds the confinement length, the density distribution is no longer described by Boltzmann distribution, instead we found a bimodal distribution.