Non-equilibrium steady-state colloidal assembly dynamics

Abstract

Simulations and experiments are reported for nonequilibrium steady-state assembly of small colloidal crystal clusters in rotating magnetic fields vs frequency and amplitude. High-dimensional trajectories of particle coordinates from image analysis of experiments and from Stokesian Dynamic computer simulations are fit to low-dimensional reaction coordinate based Fokker-Planck and Langevin equations. The coefficients of these equations are effective energy and diffusivity landscapes that capture configuration-dependent energy and friction for nonequilibrium steady-state dynamics. Two reaction coordinates that capture condensation and anisotropy of dipolar chains folding into crystals are sufficient to capture high-dimensional experimental and simulated dynamics in terms of first passage time distributions. Our findings illustrate how field-mediated nonequilibrium steady-state colloidal assembly dynamics can be modeled to interpret and design pathways toward target microstructures and morphologies.

Coiling of semiflexible paramagnetic colloidal chains

“…The first loop is defined in the simulation when a bead gets in contact with a particle that is not one of its neighbors in the linear configuration. To characterize the geometric features of the first loop formed during the coiling dynamics, the gyration tensor is computed 50,64 where ν is the number of beads that make up the loop and x i n is the n -th component of the position of the i -th particle. Note that ν < N /2 because coiling occurs on both ends of the chain anti-symmetrically.…”

“…48 Similar wrapping behavior has also been reported for paramagnetic chains in the absence of macromolecular linkers, where the CRMF induces the formation of triangular clusters at both ends that then grow by rotating and consuming the backbone of the chain until both ends merge into a 2D cluster with crystalline arrangement of the colloids. 49–51 These magnetically induced coiling dynamics are also reminiscent of the self-entanglement of long filaments, like nylon, when subjected to very high shear rates, which start as curling ends that wrap several times to form tight loops. 8,10,11…”

On the Time Transition Between Short- and Long-Time Regimes of Colloidal Particles in External Periodic Potentials

“…For all displayed values, the escape time τ escape produced by the Lifson-Jackson equation displays an excellent agreement with the data obtained from the Brownian dynamics simulations. On the other hand, it is interesting to note that the histograms of the FTP displayed in Figure 12 resemble the distribution of first passage times in complex geometries [46][47][48][49], or in energy landscapes [50][51][52][53], and are actually closely related. Here, we focus the discussion on the relationship between the histograms of escape times and a more simple statistical quantity such as the MSD.…”

Controlling colloidal crystals via morphing energy landscapes and reinforcement learning

“…These elements, in the terminology of colloid science (and control science), include capabilities to (i) quantify microstructures (sense states), (ii) tune interactions (actuate state changes), (iii) model nonequilibrium microstructure evolution (dynamic models), and (iv) determine how to choose colloidal interactions (control policy) based on current and desired states (objective). Some aspects have been previously developed, such as quantifying microstructures and their dynamic evolution between states for tunable depletion- (30), magnetic field- (31), and electric field-(32) mediated assembly processes. In addition, field-mediated colloidal assembly dynamic models have been used to implement feedback control in experiments (33) and simulations (34,35) to assemble defect-free colloidal crystals.…”