In this work, we investigate the impact of geometric confinement on the process of ring-closing of a single chain. To do so we assume that the probability of a ring-closing event is linearly related to the probability that the two ends of a chain are located within a center-to-center distance between zero and some reaction length λ. We start out by analyzing the end-to-end distance distribution for ideal Gaussian chains, and for molecular dynamic simulations of an atomistic representation of 18and 28-monomer long alkane oligomers, where one of the end monomers is fixed in space, and located a distance d away from a reflecting, that is, inert and impenetrable, surface. This setup is motivated by the idea that a possible catalyst can be attached to a confining wall via molecular linker groups of various lengths at a certain distance. The comparison between the ideal chain and the atomistic oligomers is performed by mapping the oligomer conformational properties to an equivalent freely-jointed chain, whose statistical properties can be calculated analytically via classic polymer theory. [9] Previous analytic work on RCM for bulk systems has been done, for example, in refs. [10, 11]. Our analysis of this model suggests that the ring-closing probability of a tethered ideal chain is always enhanced compared to a free ideal chain, and that the two investigated united atom oligomers can show both an enhancement, and a diminishing, of the ringclosing probability, which depends on the tether distance d. This article is organized as follows: First we describe the polymer theory and the notation for our setup. In Section 3, we describe the investigated atomistic oligomer model, followed by the results in Section 4. We finish our article with the conclusions and outlook for further studies. 2. Theory The theory of ideal Gaussian polymer chains (or classical random walks) is well understood, [9] and is summarized in the following section. Starting the random walk (RW) at the origin, a displacement of fixed length b, in one of the Cartesian directions is chosen randomly. Starting again from this point in space, the procedure is repeated N times. If the probability to take a step in any direction is equally likely, the distribution of walks of a certain length (i.e., the end-to-end distance of the ideal polymer) is given by the binomial distribution. For long RWs, N ≫ 1, the central limit theorem can be applied, and the The probability distribution of chain ends meeting when one end of the polymer is fixed to a certain distance to a reflecting wall is investigated. For an ideal polymer chain the probability distribution can be evaluated analytically via classic polymer theory. These analytical predictions are compared to atomistic MD simulations of one tethered alkane chain close to the wall. The results demonstrate that a confining wall can lead to a significant increase in the return probability for the chain ends, and thus, can increase the occurrence of ring-closing reactions. It is further demonstrated that the excess retur...
We introduce a scheme to simulate the spatial and temporal evolution of the densities of charged species, taking into account diffusion, thermal fluctuations, coupling to a carrier fluid, and chemical reactions. To this end, the diffusive fluxes in the electrokinetic model by Capuani et al. [1] are supplemented with thermal fluctuations. Chemical reactions are included via an additional source term in the mass balance equation. The diffusion-reaction model is then coupled to a solver for fluctuating hydrodynamics based on the lattice Boltzmann method. We describe our implementations, one based on the automatic code generation tools using pystencils and lbmpy, and another one contained as in the molecular dynamics package ESPResSo which allows the coupling of particles to the density fields. We validate our implementations by demonstrating that the expected influence of density fluctuations on the reaction rate for chemical reactions of order > 1 is reproduced. Our novel algorithm will be applicable to coarse-grained catalysis problems as well as to many other multi-scale problems that require the coupling of explicit-particle simulations with flow fields, diffusion, and reaction problems in arbitrary geometries.
We introduce a scheme to simulate the spatial and temporal evolution of the densities of charged species, taking into account diffusion, thermal fluctuations, coupling to a carrier fluid, and chemical reactions. To this end, the diffusive fluxes in the electrokinetic model by Capuani et al. [1] are supplemented with thermal fluctuations. Chemical reactions are included via an additional source term in the mass balance equation. The diffusion-reaction model is then coupled to a solver for fluctuating hydrodynamics based on the lattice Boltzmann method. We describe our implementations, one based on the automatic code generation tools using pystencils and lbmpy, and another one contained as in the molecular dynamics package ESPResSo which allows the coupling of particles to the density fields. We validate our implementations by demonstrating that the expected influence of density fluctuations on the reaction rate for chemical reactions of order > 1 is reproduced. Our novel algorithm will be applicable to coarse-grained catalysis problems as well as to many other multi-scale problems that require the coupling of explicit-particle simulations with flow fields, diffusion, and reaction problems in arbitrary geometries.
We introduce a scheme to simulate the spatial and temporal evolution of the densities of charged species, taking into account diffusion, thermal fluctuations, coupling to a carrier fluid, and chemical reactions. To this end, the diffusive fluxes in the electrokinetic model by Capuani et al. [1] are supplemented with thermal fluctuations. Chemical reactions are included via an additional source term in the mass balance equation. The diffusion-reaction model is then coupled to a solver for fluctuating hydrodynamics based on the lattice Boltzmann method. This combination is particularly useful for soft matter simulations, due to the ability to couple particles to the lattice-Boltzmann fluid. These could, e.g., be charged colloids or polymers, which then interact with an ion distribution. We describe one implementations based on the automatic code generation tools pystencils and lbmpy, and another one that is contained in the molecular dynamics package ESPResSo and that allows for an easy coupling of particles to the density fields. We validate our implementations by comparing to several known analytic results. Our method can be applied to coarse-grained catalysis problems as well as to many other multi-scale problems that require the coupling of explicit-particle simulations to flow fields, diffusion, and reaction problems in arbitrary geometries.
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