Stochastic dynamics of penetrable rods in one dimension: Occupied volume and spatial order

Lagrangian descriptors of driven chemical reaction manifolds

The persistence of a transition state structure in systems driven by time-dependent environments allows the application of modern reaction rate theories to solution-phase and nonequilibrium chemical reactions. However, identifying this structure is problematic in driven systems and has been limited by theories built on series expansion about a saddle point. Recently, it has been shown that to obtain formally exact rates for reactions in thermal environments, a transition state trajectory must be constructed. Here, using optimized Lagrangian descriptors [G. T. Craven and R. Hernandez, Phys. Rev. Lett. 115, 148301 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.148301], we obtain this so-called distinguished trajectory and the associated moving reaction manifolds on model energy surfaces subject to various driving and dissipative conditions. In particular, we demonstrate that this is exact for harmonic barriers in one dimension and this verification gives impetus to the application of Lagrangian descriptor-based methods in diverse classes of chemical reactions. The development of these objects is paramount in the theory of reaction dynamics as the transition state structure and its underlying network of manifolds directly dictate reactivity and selectivity.

Nonequilibrium structure in sequential assembly

The assembly of monomeric constituents into molecular superstructures through sequential-arrival processes has been simulated and theoretically characterized. When the energetic interactions allow for complete overlap of the particles, the model is equivalent to that of the sequential absorption of soft particles on a surface. In the present work, we consider more general cases by including arbitrary aggregating geometries and varying prescriptions of the connectivity network. The resulting theory accounts for the evolution and final-state configurations through a system of equations governing structural generation. We find that particle geometries differ significantly from those in equilibrium. In particular, variations of structural rigidity and morphology tune particle energetics and result in significant variation in the nonequilibrium distributions of the assembly in comparison to the corresponding equilibrium case.

Structure of a tractable stochastic mimic of soft particles

The structure and assembly of soft particles is difficult to characterize because their interpenetrability allows them to be packed at ever higher density albeit with an increasing penalty in energy and/or pressure. Alternatively, the use of impenetrable particles (such as hard spheres) as a reference model for soft particles can fail because the packing densities are limited by the impossibility of complete space filling. We recently introduced the stochastic penetration algorithm (SPA) so as to allow for the computationally efficient integration of hard sphere models while including overlaps seen in soft interactions [Craven et al., J. Chem. Phys., 2013, 138, 244901]. Moving beyond the initial one-dimensional case studied earlier, we now consider the spatial properties of systems of stochastically penetrable spheres in dimensions d≤ 3 through the use of molecular dynamics simulations and analytic methods. The stochastic potential allows spheres to either interpenetrate with a probability δ or collide elastically otherwise. For δ > 0 the particles interpenetrate (overlap), reducing the effective volume occupied by the particles in the system. We find that the occupied volume can be accurately predicted using analytic expressions derived from mean field arguments for the particle overlap probabilities with the exception of an observed clustering regime. This anomalous clustering behavior occurs at high densities and small δ. We find that this regime is coincident with that observed in deterministic penetrable models. The behavior of the stochastic penetrable particles also indicates that soft particles would be characterizable through a single reduced parameter that captures their overlap probability.