The Presence of a Wall Enhances the Probability for Ring‐Closing Metathesis: Insights from Classical Polymer Theory and Atomistic Simulations

Abstract

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...

Disentanglement of Surface and Confinement Effects for Diene Metathesis in Mesoporous Confinement

“…Using this model, we performed an extensive investigation of the effects of the presence of a wall near the catalysts. In accordance with our previous analytical work, 25 we also found with our simulational approach that the presence of a wall enhances the excess return probability of chain ends, which leads to a corresponding change in the ring-closing probability due to the wall constraint. For all systems investigated in the present work, we could measure an increase in the ring-closing selectivity compared to the selectivity measured in a homogeneous system at the same substrate reservoir density.…”

“…The centers of the active sites are spaced d cat = 0.7 nm from the wall. According to a previous study, 25 this should maximize the probability that the end of the molecule returns to its origin, increasing the probability of ring closure. The catalyst model has many parameters that could potentially influence the selectivity.…”

“…In an earlier study, 25 we could show via random walk theory and molecular dynamics (MD) simulations that the presence of a flat wall near the catalyst has positive feedback on the ringclosing probability. Here, we study the confined ring-closing metathesis reaction on a coarse-grained level.…”