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

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

NetSquid, a NETwork Simulator for QUantum Information using Discrete events

In order to bring quantum networks into the real world, we would like to determine the requirements of quantum network protocols including the underlying quantum hardware. Because detailed architecture proposals are generally too complex for mathematical analysis, it is natural to employ numerical simulation. Here we introduce NetSquid, the NETwork Simulator for QUantum Information using Discrete events, a discrete-event based platform for simulating all aspects of quantum networks and modular quantum computing systems, ranging from the physical layer and its control plane up to the application level. We study several use cases to showcase NetSquid's power, including detailed physical layer simulations of repeater chains based on nitrogen vacancy centres in diamond as well as atomic ensembles. We also study the control plane of a quantum switch beyond its analytically known regime, and showcase NetSquid's ability to investigate large networks by simulating entanglement distribution over a chain of up to one thousand nodes.Comment: NetSquid is freely available at https://netsquid.org; refined main text section

Learning heterogenous reaction rates from stochastic simulations

Reaction rate equations are ordinary differential equations that are frequently used to describe deterministic chemical kinetics at the macroscopic scale. At the microscopic scale, the chemical kinetics is stochastic and can be captured by complex dynamical systems reproducing spatial movements of molecules and their collisions. Such molecular dynamics systems may implicitly capture intricate phenomena that affect reaction rates but are not accounted for in the macroscopic models. In this work we present a data assimilation procedure for learning nonhomogeneous kinetic parameters from molecular simulations with many simultaneously reacting species. The learned parameters can then be plugged into the deterministic reaction rate equations to predict long time evolution of the macroscopic system. In this way, our procedure discovers an effective differential equation for reaction kinetics. To demonstrate the procedure, we upscale the kinetics of a molecular system that forms a complex covalently bonded network severely interfering with the reaction rates. Incidentally, we report that the kinetic parameters of this system feature peculiar time and temperature dependences, whereas the probability of a network strand to close a cycle follows a universal distribution

Learning heterogenous reaction rates from stochastic simulations

Reaction rate equations are ordinary differential equations that are frequently used to describe deterministic chemical kinetics at the macroscopic scale. At the microscopic scale, the chemical kinetics is stochastic and can be captured by complex dynamical systems reproducing spatial movements of molecules and their collisions. Such molecular dynamics systems may implicitly capture intricate phenomena that affect reaction rates but are not accounted for in the macroscopic models. In this work we present a data assimilation procedure for learning nonhomogeneous kinetic parameters from molecular simulations with many simultaneously reacting species. The learned parameters can then be plugged into the deterministic reaction rate equations to predict long time evolution of the macroscopic system. In this way, our procedure discovers an effective differential equation for reaction kinetics. To demonstrate the procedure, we upscale the kinetics of a molecular system that forms a complex covalently bonded network severely interfering with the reaction rates. Incidentally, we report that the kinetic parameters of this system feature peculiar time and temperature dependences, whereas the probability of a network strand to close a cycle follows a universal distribution

HASTAC Image 65

Images from HASTAC 2017, hosted by the Florida Digital Humanities Consortium in Orlando, Florida, November 3-4, 2017.https://stars.library.ucf.edu/hastac2017-photos/1064/thumbnail.jp

Modeling the free-radical polymerization of hexanediol diacrylate (HDDA) : A molecular dynamics and graph theory approach

In the printing, coating and ink industries, photocurable systems are becoming increasingly popular and multi-functional acrylates are one of the most commonly used monomers due to their high reactivity (fast curing). In this paper, we use molecular dynamics and graph theory tools to investigate the thermo-mechanical properties and topology of hexanediol diacrylate (HDDA) polymer networks. The gel point was determined as the point where a giant component was formed. For the conditions of our simulations, we found the gel point to be around 0.18 bond conversion. A detailed analysis of the network topology showed, unexpectedly, that the flexibility of the HDDA molecules plays an important role in increasing the conversion of double bonds, while delaying the gel point. This is due to a back-biting type of reaction mechanism that promotes the formation of small cycles. The glass transition temperature for several degrees of curing was obtained from the change in the thermal expansion coefficient. For a bond conversion close to experimental values we obtained a glass transition temperature around 400 K. For the same bond conversion we estimate a Young's modulus of 3 GPa. Both of these values are in good agreement with experiments

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

The association between thermo-mechanical properties in polymers and functionality ofmonomer precursors is frequently exploited in the materials science. However, it is notknown if there are more variables beyond monomer functionality that have a similar link.Here, by using simulations to generate spatial networks from chemically different monomerswith identical functionality we show that such networks have universal graph-theoreticalproperties as well as a near-universal elastic modulus. The vitrification temperature wasfound to be universal only up to a certain network density, as measured by the bond con-version. The latter observation is explained by the fact that monomer’s tendency to coilenhances formation of topological holes, which, when accumulated, amount to a percolatingcell complex restricting network’s mobility. This higher-order percolation occurs late aftergelation and is shown to coincide with the onset of brittleness, as indicated by a suddenincrease in the glass transition temperature