A density of states-based approach to determine temperature-dependent aggregation rates L. F. Trugilho, S. Auer, L. G. Rizzi Journal of Chemical Physics, 2024 Here, we establish an approach to determine temperature-dependent aggregation rates in terms of thermostatistical quantities, which can be obtained directly from flat-histogram and statistical temperature algorithms considering the density of states of the system. Our approach is validated through simulations of an Ising-like model with anisotropically interacting particles at temperatures close to its first-order phase transition. Quantitative comparisons between the numerically obtained forward and reverse rates to approximate analytical expressions corroborate its use as a model-independent approach.
Shape-free theory for the self-assembly kinetics in macromolecular systems L. F. Trugilho, L. G. Rizzi Epl, 2022 Although temperature-dependent self-assembly kinetics is usually described by approaches which assume that the macromolecular aggregates have a definite shape, sometimes that assumption might be inappropriate, as in the case of several colloidal and biopolymeric systems. Here we consider a simple model for particle aggregation which displays a first-order phase transition in order to illustrate a rate theory based on microcanonical thermostatistics that allows one to obtain a shape-free description of its thermally induced self-assembly kinetics. Stochastic simulations are performed to validate our approach and demonstrate how the equilibrium thermostatistics properties of the system can be related to the temperature-dependent rate constants. As a model-independent kinetic approach, it may provide experimentalists with a reliable method to extract information about free-energy profiles and microcanonical entropies from kinetic data.
Microcanonical thermostatistics of aggregation transition in a system with anisotropically interacting molecules L. F. Trugilho, L. G. Rizzi Journal of Physics Conference Series, 2020 Microcanonical thermostatistics analysis has been introduced as an important method in the study of phase transitions observed in intrinsically small systems, such as folding transitions in proteins and surface adsorption transitions of polymeric chains. Here we consider a lattice model and apply microcanonical analysis to investigate the aggregation transition of a system with anisotropically interacting molecules. By performing multicanonical Monte Carlo simulations we are able to obtain free-energy profiles from where we extract physical quantities related to the aggregation transition such as its transition temperature, latent heat, and free-energy barriers. Our results confirms that the aggregation transition is a first-order type of transition and that it is related to the nucleation of molecules into elongated aggregates. Also, our analysis revealed an unexpected non-monotonic behavior for the free-energy barrier as a function of the anisotropic ratio ξ between strong and weak interactions of the molecules, indicating that the nucleation kinetics might be also influenced by ξ.
