Efficient simulation protocol for determining the density of states: Combination of replica-exchange Wang-Landau method and multicanonical replica-exchange method

Predicting Ion Sequestration in Charged Polymers with the Steepest-Entropy-Ascent Quantum Thermodynamic Framework

The steepest-entropy-ascent quantum thermodynamic framework is used to investigate the effectiveness of multi-chain polyethyleneimine-methylenephosphonic acid in sequestering rare-earth ions (Eu3+) from aqueous solutions. The framework applies a thermodynamic equation of motion to a discrete energy eigenstructure to model the binding kinetics of europium ions to reactive sites of the polymer chains. The energy eigenstructure is generated using a non-Markovian Monte Carlo model that estimates energy level degeneracies. The equation of motion is used to determine the occupation probability of each energy level, describing the unique path through thermodynamic state space by which the polymer system sequesters rare-earth ions from solution. A second Monte Carlo simulation is conducted to relate the kinetic path in state space to physical descriptors associated with the polymer, including the radius of gyration, tortuosity, and Eu-neighbor distribution functions. These descriptors are used to visualize the evolution of the polymer during the sequestration process. The fraction of sequestered Eu3+ ions depends upon the total energy of the system, with lower energy resulting in greater sequestration. The kinetics of the overall sequestration are dependent on the steepest-entropy-ascent principle used by the equation of motion to generate a unique kinetic path from an initial non-equilibrium state.

Predicting Polymer Brush Behavior in Solvents Using the Steepest-Entropy-Ascent Quantum Thermodynamic Framework

The steepest-entropy-ascent quantum thermodynamic (SEAQT) framework is utilized to study the effects of temperature on polymer brushes. The brushes are represented by a discrete energy spectrum, and energy degeneracies obtained through the replica-exchange Wang-Landau algorithm. The SEAQT equation of motion is applied to the density of states to establish a unique kinetic path from an initial thermodynamic state to a stable equilibrium state. The kinetic path describes the brush's evolution in state space, as it interacts with a thermal reservoir. The predicted occupation probabilities along the kinetic path are used to determine the expected thermodynamic and structural properties. The polymer density profile of a polystyrene brush in cyclohexane solvent is predicted using the equation of motion, and it agrees qualitatively with the experimental density profiles. The Flory-Huggins parameter chosen to describe brush-solvent interactions affects the solvent distribution in the brush but has a minimal impact on the polymer density profile. Three types of nonequilibrium kinetic paths with differing amounts of entropy production are considered: a heating path, a cooling path, and a heating-cooling path. Properties such as tortuosity, radius of gyration, brush density, solvent density, and brush chain conformations are calculated for each path.

Calculation of the residual entropy of Ice Ih by Monte Carlo simulation with the combination of the replica-exchange Wang-Landau algorithm and multicanonical replica-exchange method

We estimated the residual entropy of Ice Ih by the recently developed simulation protocol, namely, the combination of the replica-exchange Wang-Landau algorithm and multicanonical replica-exchange method. We employed a model with the nearest neighbor interactions on the three-dimensional hexagonal lattice, which satisfied the ice rules in the ground state. The results showed that our estimate of the residual entropy is in accordance with various previous results. In this article, we not only give our latest estimate of the residual entropy of Ice Ih but also discuss the importance of the uniformity of a random number generator in Monte Carlo simulations.