How to Upscale The Kinetics of Complex Microsystems

The rate constants of chemical reactions are typically inferred from slopes and intersection points of observed concentration curves. In small systems that operate far below the thermodynamic limit, these concentration profiles become stochastic and such an inference is less straightforward. By using elements of queuing theory, we introduce a procedure for inferring (time dependent) kinetic parameters from microscopic observations that are given by molecular simulations of many simultaneously reacting species. We demonstrate that with this procedure it is possible to assimilate the results of molecular simulations in such a way that the latter become descriptive on the macroscopic scale. As an example, we upscale the kinetics of a molecular dynamics system that forms a complex molecular network. Incidentally, we report that the kinetic parameters of this system feature a peculiar time and temperature dependences, whereas the probability of a network strand to close a cycle follows a universal distribution

On the inner workings of Monte Carlo codes

We review state-of-the-art Monte Carlo (MC) techniques for computing fluid coexistence properties (Gibbs simulations) and adsorption simulations in nanoporous materials such as zeolites and metal-organic frameworks. Conventional MC is discussed and compared to advanced techniques such as reactive MC, configurational-bias Monte Carlo and continuous fractional MC. The latter technique overcomes the problem of low insertion probabilities in open systems. Other modern methods are (hyper-)parallel tempering, Wang-Landau sampling and nested sampling. Details on the techniques and acceptance rules as well as to what systems these techniques can be applied are provided. We highlight consistency tests to help validate and debug MC codes

Molecular modeling of free radical polymerization of diacrylates

Photocurable systems have become very popular in the last years, however, little is known on the molecular structure of the formed polymer networks and its influence in the ultimate properties of the materials. During photopolymerization the liquid monomer polymerizes in a few seconds via strongly branched polymers to a solid polymer network. Description of the kinetics is a challenging task as the rates of the reaction decrease by orders of magnitude due to increasing diffusion limitation. Still mathematical modeling is required to predict the network topology and the associated properties. In order to obtain better understanding of this extremely complex reaction process and to describe the evolution and the final characteristics of the polymer network, we use molecular simulations to generate several polymer networks at an atomic level for different diacrylate monomers (1,6-hexanediol diacrylate, 1,4-butanediol diacrylate, 1,10-decanediol diacrylate and 1,6-hexanediol dimethacrylate). Furthermore, we use graph theory tools to analyze the topological properties of the networks and their influence in the thermo-physical properties of the polymer network. The simulations are successfully compared with both, experimental and mathematical modeling results. The results highlight the influence of the monomer flexibility and functionality in the network topologies and properties. Please click Additional Files below to see the full abstract

Living apart together: On graph theory and polymer chemistry

Graph theory and chemistry has always been bound by intricate relationships. This theory centers its attention on the connectivity between atoms but not their spatial configurations. Graph theory is attractive not just due to pure convenience of representing a molecule as a diagram made of nodes and sticks. On many occasions such reduction revealed a deep connection between the structure and the properties, that is to say, a connection between the chemistry and the physics. Notably, differences in boiling temperatures of isomers, formation heats of conjugated hydrocarbons, and vibrational potential energy of proteins has been successfully explained by graph theory. Please click Additional Files below to see the full abstract

Effect of different monomer precursors with identical functionality on the properties of the polymer network

Thermo-mechanical properties of polymer networks depend on functionality of the monomer precursors -- an association that is frequently exploited in materials science. We use molecular simulations to generate spatial networks from chemically different monomers with identical functionality and show that such networks have several universal graph-theoretical properties as well as near universal Young's modulus. The vitrification temperature is shown to be universal only up to a certain density of the network, as measured by the bond conversion. The latter observation is explained by the fact that monomer's tendency to coil enhances formation of topological holes, which, when accumulated in the network, amount to a percolating cell complex restricting network's mobility. This higher-order percolation occurs late after gelation and is shown to coincide with the onset of brittleness, as indicated by a sudden increase in the glass transition temperature. This phenomenon may signify a new type of phase transition in polymer materials