Prof. Dr. Gerhard Nägele
Institute of Biological Information Processing, IBI-4, Forschungszentrum Jülich, Germany

Theory and Simulation of Brownian Dispersions with competing Interactions: From three to quasi-two Dimensions
Dispersions of proteins (or colloids) with competing short-range attractive (SA) and long-range repulsive (LR) interactions exhibit a rich phase behavior with a variety of cluster phases. While these so-called SA-LR dispersions have been the subject of intense research over the past years, little is known to date about their dynamics, in particular under quasi-two-dimensional (Q2D) confinement. The unusual dynamics of SA-LR particles is influenced by solvent-mediated many-particles hydrodynamic interactions (HIs) which are ubiquitously present in fluid soft matter systems. Using mesoscale simulations and theoretical methods, we study the structure and dynamics of a generic model of SA-LR particles described as Brownian spheres interacting via short-range attractive generalized Lenard-Jones and long-range repulsive screened Coulomb forces. These interactions apply to protein solutions under low-salt conditions. Both three-dimensional and quasi-two-dimensional systems are considered. The particles of a Q2D dispersion form a planar monolayer embedded in the bulk fluid. Q2D confinement is realized, e.g., by particles trapped at a liquid interface or proteins attached to a cell membrane [1].

We discuss first the dynamics of three-dimensional dispersions of SA-LR particles, focusing on the so-called dispersed fluid and equilibrium cluster fluid phases [2-4]. The latter phase is characterized by flexible particle clusters of preferential size. The intra-cluster dynamics and lifetime is strongly affected by HIs, as we will show. There is an intermediate range order peak in the wavenumber-dependent hydrodynamic function, H(q), quantifying the influence of HIs on particle diffusion [2,3]. The theoretically predicted peak is observed indeed in neutron spin echo measurements for lyzosyme protein solutions [4]. Our theoretical methods are used to scrutinize the validity of generalized Stokes-Einstein relations between diffusion and viscelasticity properties.

Secondly, we analyze the structure and dynamics of Q2D dispersions of SA-LR particles. The phases in the Q2D state diagram resemble those in three dimensions, but are distinctly different in their microstructure invoking different levels of hexagonal ordering [5] We discuss indicators for the transition from the high-temperature dispersed fluid to the lower-temperature equilibrium cluster phase. Akin to three-dimensional systems, this transition is signalled by a low-wavenumber peak in the static structure factor whose height, however, is distinctly smaller than in three-dimensions. We uncover the self-diffusional particle motion with its non-Gaussian and non-Fickean statistics. The Q2D motion in conjunction with HIs causes anomalously enhanced collective diffusion, linked to out-of-plane fluid flow. Finally, we examine the spatio-temporal buildup of hydrodynamic interactions between particles, mediated by fluid vorticity diffusion and sound propagation [5].
[1] Z. Tan, V. Calandrini, J.K.G. Dhont, G. Nägele and R.G. Winkler, Soft Matter, 2021, 17, 7978.
[2] S. Das, J. Riest, R. Winkler, G. Gompper, J.K.G. Dhont and G. Nägele, Soft Matter, 2018, 14, 92.
[3] J. Riest and G. Nägele, Soft Matter, 2015, 11, 9273.
[4] J. Riest, G. Nägele, Y. Liu, N.J. Wagner and P.D. Godfrin, J. Chem. Phys., 2018, 148, 065101.
[5] Z. Tan, J.K.G. Dhont, V. Calandrini and G. Nägele, several papers in preparation, 2023.