Microscopic diffusion coefficients of dumbbell- and spherocylinder-shaped colloids and their application in simulations of crowded monolayers

Abstract

We explore the diffusion properties of colloidal particles with dumbbell and spherocylinder shapes using a hydrodynamic bead-shell approach and additional Brownian dynamics (BD) simulations. By applying the bead-shell method, we determine empirical formulas for the microscopic diffusion coefficients. A comparison of these formulas and established experimental and theoretical results shows remarkable agreement. For example, the maximum relative discrepancy found for dumbbells is less than 5%. As an application example of the empirical formulas, we perform two-dimensional (2D) BD simulations based on a single dumbbell or spherocylinder in a suspension of spheres and calculate the resulting effective long-time diffusion coefficients. The performed BD simulations can be compared to quasi-2D systems such as colloids confined at the interface of two fluids. We find that the effective diffusion coefficient of translation mostly depends on the sphere area fraction ϕ, while the effective diffusion coefficient of rotation is influenced by the aspect ratio and ϕ. Furthermore, the effective rotational diffusion constant seems to depend on the particle shape with the corresponding implementation of the interactions. In the resolution limit of our methods, the shape-dependent differences of the microscopic diffusion coefficients and the long-time diffusion constant of translation are negligible in the first approximation. The determined empirical formulas for the microscopic diffusion coefficients add to the knowledge of the diffusion of anisotropic particles, and they can be used in countless future studies.

Rotational and translational microrheology from shape-anisotropic particles

“…Analogously, the so obtained rotational diffusion coefficient of the confined dimers in water is 0.5035 rad 2 s −1 , 1.85 times smaller than the bulk rotational diffusion coefficient of the dimer. The bulk values are theoretical values obtained from [29][30][31][32][33]. In this way, the values used to rescale the measured mean squared displacements under confinement are 2.22 for the translation of the sphere, 4.76 for the translation of the dimer and 1.85 for the rotation of the dimer.…”

“…D Tras,⊥ d , and rotational D Rot d , diffusion coefficients of dumbbells, obtained by Lüders et al[31] by using the bead-shell model, which deviates only about 2% from exact solutions[29][30][31][32][33]. The expressions for those quantities are given by:…”

Optogenetic Control of Bacterial Cell‐Cell Adhesion Dynamics: Unraveling the Influence on Biofilm Architecture and Functionality

“…A suitable value for σ bf was chosen by first, estimating the diffusion coefficient for a spherical particle of the same diameter, suspended in PBS buffer. Correcting for the fact that the diffusion takes place near a wall, [ 57 ] and that the particles are spherocylindrical with an aspect ratio of three, [ 58 ] gave us a diffusion constant of D particle = 0.024 µm 2 s −1 . Measuring the MSD after one hour for 2000 particles we find that σ bf = 10 −3 gives us an MSD of the expected ≈500 µm 2 (Figure S3, Supporting Information).…”

Capture and transport of rod-shaped cargo via programmable active particles

“…To describe the motion of the passive rod, we use and the formulas of Ref. 38 for the diffusion coefficients of spherocylinders. For the quasi-2D spherical APs, the diffusion coefficients are set to and .…”