Non-equilibrium theory of nucleation at first order phase transitions.
Final Report Abstract
Nucleation at first order phase transitions is a non-equilibrium process. It is also a collective process, which involves a very large number of microscopic degrees of freedom. Hence to predict nucleation rates, a coarse-grained, non-equilibrium description is required. Classical nucleation theory, which builds on a diffusion process in a free energy landscape, claims to give such an description. However, classical nucleation theory requires some assumptions (such as Markovianity) that seem questionable. In this project we used projection-operator techniques to derive exact coarsegrained equations of motion for systems out of thermal equilibrium. We showed how to obtain an effective equation of motion for the nucleation process that resembles classical nucleation theory in that it contains a derivative of a thermodynamic potential (or “potential of mean force”) as a driving force. However, the resulting equations are not Markovian. Further, even if the memory functions decayed rapidly, the resulting structure would still not resemble a simple diffusion process in a free-energy landscape. A numerical analysis of molecular dynamics simulation data of colloidal hard spheres showed that the temporal extent of the memory is of the same order as the duration of the nucleation process itself. Hence, we do not easily obtain a Markovian description in this situation. We also tackled the problem of the mismatch between experimentally measured nucleation rates and their theoretical predictions in colloidal hard spheres. This mismatch had been regarded as a shortcoming of the theory. In large scale molecular dynamics simulations of hard-sphere systems, however, we demonstrated that the mismatch is explained by a reinterpretation of the experimental data. If one allows for poly-crystalline nuclei due to twinning, the discrepancy between theory and experiment is resolved. Other results obtained in this research project comprise a method to generate new trajectories from the reduced non-equilibrium description yielding a route to rigorous coarse graining, an exact reduced formalism to describe driven systems with a formulation involving equilibrium memory functions, and an analysis of tracer dynamics within a membrane.
Publications
-
Comments on the validity of the non-stationary generalized Langevin equation as a coarse-grained evolution equation for microscopic stochastic dynamics. The Journal of Chemical Physics, 154(17).
Glatzel, Fabian & Schilling, Tanja
-
Evaluation of memory effects at phase transitions and during relaxation processes. Physical Review E, 103(2).
Meyer, Hugues; Glatzel, Fabian; Wöhler, Wilkin & Schilling, Tanja
-
Reversible heat production during electric double layer buildup depends sensitively on the electrolyte and its reservoir. The Journal of Chemical Physics, 154(6).
Glatzel, Fabian; Janssen, Mathijs & Härtel, Andreas
-
The interplay between memory and potentials of mean force: A discussion on the structure of equations of motion for coarse-grained observables. Europhysics Letters, 136(3), 36001.
Glatzel, Fabian & Schilling, Tanja
-
Extension of the primitive model by hydration shells and its impact on the reversible heat production during the buildup of the electric double layer. The Journal of Chemical Physics, 156(3).
Pelagejcev, Philipp; Glatzel, Fabian & Härtel, Andreas
-
Generalized Langevin dynamics simulation with non-stationary memory kernels: How to make noise. The Journal of Chemical Physics, 157(19).
Widder, Christoph; Koch, Fabian & Schilling, Tanja
-
Hard Sphere Crystal Nucleation Rates: Reconciliation of Simulation and Experiment. Physical Review Letters, 128(23).
Wöhler, Wilkin & Schilling, Tanja
-
Analysis of the Dynamics in Linear Chain Models by means of Generalized Langevin Equations. Journal of Statistical Physics, 191(5).
Koch, Fabian; Mandal, Suvendu & Schilling, Tanja
-
Nonequilibrium solvent response force: What happens if you push a Brownian particle. Physical Review Research, 6(1).
Koch, Fabian; Erle, Jona & Schilling, Tanja
-
Tracer dynamics in polymer networks: Generalized Langevin description. The Journal of Chemical Physics, 160(9).
Milster, Sebastian; Koch, Fabian; Widder, Christoph; Schilling, Tanja & Dzubiella, Joachim
