Research
Research areas in our group cover
COMPLEX TRANSPORT SELF-PROPELLED PARTICLES GLASS TRANSITION THERMOPHORESIS POLYMER PHYSICS
Transport phenomena in crowded environments
Transport in heterogeneous media is found in many systems, such as molecular sieving, catalysis, ion-conductors and the interior of crowded cells. We study the fundamental features of this process through simplified model systems, where only the essential features are retained.
The random walk of a single tracer particle on a lattice with randomly distributed obstacles is known as a lattice Lorentz gas. A remarkable feature of this simple model is the existence of persistent memory in the form of long-time tails in the velocity autocorrelation function of the tracer. The fluctuation-dissipation-theorem can be used to monitor the response of the system under the influence of a small force pulling on the particle. This linear response result can be directly compared to an exact nonlinear response solution for any strength of the force, showing key features of nonlinear driving such as breakdown of persistent memory as well as nonanalytic behavior of the stationary state velocity.
- S. Leitmann and T. Franosch, Phys. Rev. Lett. 118 (2017)
In a simple extension to continuous space, known as the Lorentz model, a single particle explores the space between randomly distributed fixed obstacles. As the density of obstacles is increased, this model exhibits a localization transition, above which the particle is confined. Strikingly, from this simple model, subdiffusive motion is predicted at the transition point, in line with what is observed in the crowded environment of biological cells. The nature of this divergence from diffusive behavior is governed by the percolation transition of the geometry of the obstacles, and the specifics of the interaction dynamics between our moving particle and the obstacles.
- C. F. Petersen, T. Franosch, Soft Matter, 15, 3906 (2019)
- M. Spanner et. al. Phys. Rev. Lett. 116 (2016)
Non-equilibrium dynamics of active agents
Locomotion by swimming is a fundamental ingredient to optimize the survival strategies of a vast diversity of micro-organisms. Taking nature as a model, recently physicists have synthesized artificial self-propelled particles which are expected to play a pivotal role in the nano-technology of the 21st century. In striking contrast to their passive counterparts, these self-propelled particles are driven out of equilibrium and display peculiar transport properties at the single as well as the collective level.
Single-particle behavior. We investigate the spatiotemporal dynamics of various types of self-propelled agents in terms of exact solutions for the intermediate scattering function, which constitutes the Fourier transform of the probability density of the particle's displacements. In particular, we are interested in the dynamical behavior of catalytic Janus colloids, which can be completely characterized by the paradigmatic active Brownian particle model, and the run-and-tumble behavior of E. coli bacteria using renewal processes. We compare our theoretical predictions to observations of these synthetic and biological micro-swimmers measured by our experimental collaborators.
- C. Kurzthaler et al., Sci. Rep. 6 (2016), Soft Matter 13 (2017), Phys. Rev. Lett. 121 (2018)
Active transport in heterogeneous environments. The studies of active particles are usually performed in homogeneous clean spaces, yet in nature their motion is often obstructed by different obstacles. We focus on the different aspects of the interactions of particles with the environment and study their transport properties, which are very important in the context of biological and technological applications. Our goal is to develop a detailed understanding of the dynamics of micro-swimmers in different heterogeneous environments. We perform theoretical investigations of these intricate transport phenomena on the level of computer simulations and analytical analyses.
- W. Schirmacher et al., Phys. Rev. Lett. 115 (2015)
- O. Chepizhko, T. Franosch, Soft Matter, 15, 452-461 (2019), New J. Phys. 22 (2020)
Glass transition of confined liquids
Transport of liquids in nano-sized pores or narrow channels is crucial for most natural and industrial processes. It can exhibit a series of fascinating behaviors when the confinement length scale is comparable to the molecular size.
- C. F. Petersen et al., J. Stat. Mech. 083216 (2019)
We explore this regime of confinement by investigating hard spheres confined in a slit, wedge, or torus geometry in terms of a mode coupling theory and extensive computer simulations. Our studies suggest that the confinement length scale appears as another control parameter to the non-equilibrium phase diagram. In particular, we find that a wedge-like confinement with very small tilt angle can promote a liquid-glass coexistence. Since there is a growing interest for smaller systems in modern applications, these findings can be utilized for future technological advancements.
- S. Mandal et al., Nature. Comun. 5 (2014), Phys. Rev. Lett. 118 (2017), Soft Matter 13 (2017)
- G. Jung, C. F. Petersen, Phys. Rev. Res. 2 (2020)
Thermophoresis of a colloidal particle
Thermophoresis is referred to the response of particles to temperature gradients. This phenomenon can be exploited for microfluidic applications and has also been argued to be one of the key mechanisms for the origin of life.
We are interested in the description of a single charged colloid immersed in an electrolyte. In the presence of a temperature gradient, electrical body forces are no longer counter balanced by pressure gradients, thereby, inducing solvent flow and the directed motion of the colloidal particle. We solve numerically the associated field equations including the non-linear Poisson Boltzman equation for the electrical potential and the steady Stokes equation governing the fluid flow. Ultimately, we aim to extract transport properties, such as the Soret coefficient, of experimental systems.
Physics of semiflexible polymers & the needle in a haystack
Semiflexible polymers are ubiquitous in nature and include biopolymers such as filamentous actin, microtubules, or DNA strands. These represent the fundamental building blocks of cells and dictate their elastic properties and shape, intracellular transport processes, and mitosis. In particular, polymers often form entangled meshworks, which display remarkable mechanical response and complex dynamics behavior. Understanding these intricate many-body physics relies on a profound knowledge of the underlying physical mechanisms at different levels of coarse-graining:
We aim to understand the response of single semiflexible polymers to compression forces in terms of the celebrated wormlike chain model. We derive analytic solutions for the experimentally accessible force-extension relations and elucidate the elastic behavior with respect to the classical Euler buckling instability of a rigid rod. Moreover, we characterize the buckling behavior by computing the associated probability densities.
- C. Kurzthaler, T. Franosch, Phys. Rev. E 95 (2017), Soft Matter 14 (2018)
We study dynamically crowded solutions of stiff fibers, which have the remarkable property that their static properties are that of an ideal gas, yet their dynamics is governed by a complex behavior since any two needles are not allowed to cross each other. We elaborate analytic expressions for the intermediate scattering function to characterize the spatiotemporal dynamics of a single needle. We use these predictions to elucidate the intricate transport properties of solutions of stiff fibers in the semidilute regime, where the motion of a single needle becomes confined to a narrow tube. This effective description is obtained by inserting the long-time diffusion coefficients obtained from simulations into the analytic theory of a single needle.
- S. Leitmann et al., Phys. Rev. Lett. 114 (2016), Phys. Rev. E 96 (2017)
Mode coupling theory of the glass transition
We use Mode-Coupling Theory (MCT) of the glass transition as an analytical framework to study and understand the glassy dynamics in dense colloidal suspensions. Using this approach, we can predict the glass transition packing fraction and describe the system's dynamics over several orders of magnitude in time, based solely on static input quantities such as the particle density and the static structure factor*.
Currently, we are extending MCT to inhomogeneous systems under external modulation and are also focusing on MCT applications to size-polydisperse systems. Introducing external fields and polydispersity provides additional control over particle caging within the system. External modulations can strongly influence the configuration of particles in colloidal liquids, while polydispersity is often employed to stabilize supercooled liquids against crystallization in computational studies of the glass transition.
Reference:
*Gotze, W. (2009), Complex Dynamics of Glass-Forming Liquids: A Mode-Coupling Theory, Oxford University Press.
Brownian Particles in Periodic Potentials
Brownian motion - the random movement of microscopic particles suspended in a fluid - serves as a fundamental model for processes ranging from diffusion to intracellular transport, and it also plays a role in active matter such as bacterial motility. Our research focuses on Brownian particles in periodic energy landscapes, providing insights into ratchet effects, hopping dynamics, and non-equilibrium statistical physics, with applications in biophysics and nanotechnology.
We investigate periodic systems such as ratchets, sinusoidal, tilted washboard, and barrier potentials and extend our analysis to active Brownian motion, including gravitaxis in circle swimmers. A key observable is the intermediate scattering function (ISF), the Fourier transform of the probability density of particle displacements, which captures the spatiotemporal dynamics of the system. By employing spectral theory, Bloch's theorem, and perturbative methods, we derive exact analytical solutions to the Fokker–Planck equation, which are validated through both simulations and experimental collaborations.
Reference: R. Rusch, Y. Mohebi Satalsari, A. B. Zuccolotto-Bernez, M.A. Escobedo-Sánchez and T. Franosch, Soft Matter 21 (2025)
Link: Intermediate scattering function of colloids in a periodic laser field