Stochastic Reaction Model Research Articles

Surface-Initiated Polymerization with an Initiator Gradient: A Monte Carlo Simulation.

Due to the difficulty of accurately characterizing properties such as the molecular weight (Mn) and grafting density (σ) of gradient brushes (GBs), these properties are traditionally assumed to be uniform in space to simplify analysis. Applying a stochastic reaction model (SRM) developed for heterogeneous polymerizations, we explored surface-initiated polymerizations (SIPs) with initiator gradients in lattice Monte Carlo simulations to examine this assumption. An initial exploration of SIPs with 'homogeneously' distributed initiators revealed that increasing σ slows down the polymerization process, resulting in polymers with lower molecular weight and larger dispersity (Đ) for a given reaction time. In SIPs with an initiator gradient, we observed that the properties of the polymers are position-dependent, with lower Mn and larger Đ in regions of higher σ, indicating the non-uniform properties of polymers in GBs. The results reveal a significant deviation in the scaling behavior of brush height with σ compared to experimental data and theoretical predictions, and this deviation is attributed to the non-uniform Mn and Đ.

Structural heterogeneity in tetra-armed gels revealed by computer simulation: Evidence from a graph theory assisted characterization.

Designing homogeneous networks is considered one typical strategy for solving the problem of strength and toughness conflict of polymer network materials. Experimentalists have proposed the hypothesis of obtaining a structurally homogeneous hydrogel by crosslinking tetra-armed polymers, whose homogeneity was claimed to be verified by scattering characterization and other methods. Nevertheless, it is highly desirable to further evaluate this issue from other perspectives. In this study, a coarse-grained molecular dynamics simulation coupled with a stochastic reaction model is applied to reveal the topological structure of a polymer network synthesized by tetra-armed monomers as precursors. Two different scenarios, distinguished by whether internal cross-linking is allowed, are considered. We introduce the Dijkstra algorithm from graph theory to precisely characterize the network structure. The microscopic features of the network structure, e.g., loop size, dispersity, and size distribution, are obtained via the Dijkstra algorithm. By comparing the two reaction scenarios, Scenario II exhibits an overall more idealized structure. Our results demonstrate the feasibility of the Dijkstra algorithm for precisely characterizing the polymer network structure. We expect this work will provide a new insight for the evaluation and description of gel networks and further help to reveal the dynamic process of network formation.

One-pot strategy for the preparation of nanoparticles grafted with bimodal polymers: An in-silico insight

Polymer nanocomposites composed of polymer-grafted nanoparticles (NPs) have garnered significant interest due to their diverse functional applications in various domains. The emerging concept of bimodal polymer brushes within the grafting-nanoparticle framework offers control over interfacial entropic and enthalpic interactions. Here, we introduce a novel one-pot strategy that integrates “grafting-to” and “grafting-from” methods to create polymer-grafted bimodal NPs. Utilizing coarse-grained molecular dynamics simulations with a stochastic reaction model, we explore the factors influencing grafting density and polydispersity in these NPs. Our findings demonstrate that this one-pot strategy achieves a polydispersity similar to the two-step “grafting-from then grafting-to” process, while attaining a moderate grafting density comparable to the “grafting-to then grafting-from” approach. Consequently, we analyze factors such as “grafting-from” reaction rates, and initial feeding ratios, step-addition techniques which collectively influence the final grafting density and polydispersity index within this one-pot strategy. This comprehensive investigation enhances our understanding of the kinetics behind synthesizing bimodal polymer-grafted NPs and offers insights for designing polymer-based nanocomposites with improved performance.

Simultaneous Bulk- and Surface-initiated Living Polymerization Studied with a Heterogeneous Stochastic Reaction Model

Simultaneous Bulk- and Surface-initiated Living Polymerization Studied with a Heterogeneous Stochastic Reaction Model

Molecular Dynamics Simulations of Ideal Living Polymerization: Terminal Model and Kinetic Aspects.

Living polymerization is an important synthetic approach to achieving precise control of synthesized polymers, which is crucial for their applications. The molecular weight distribution (MWD) prescribes the macroscopic properties of polymers and hence is a key feature to characterize polymerization. In this work, we present a systematic molecular dynamics simulation study of ideal living polymerization in bulk and surface-initiated systems based on a terminal stochastic reaction model. The evolution of polymer dispersity and MWD along with the polymerization process is examined. We demonstrate that MWD is generally well captured by the Schulz-Zimm distribution for bulk and surface-initiated systems with low grafting densities. However, as the grafting density in the surface-initiated case increases, heterogeneity in chain growth emerges due to the kinetic trapping of reactive sites, which causes the starving of short chains and the thriving of minority long chains such that a shoulder region shows up in MWD. This effect can be enhanced by kinetic compressing induced by polymerization. In addition, the interplay of bonding reaction kinetics and other kinetic properties (e.g., mass transfer and polymer relaxation) is further explored, alongside the influences of bonding probability and reactant concentration. We expect that this investigation will aid in our understanding of typical kinetic aspects of living polymerization.

A Simple Stochastic Reaction Model for Heterogeneous Polymerizations.

The stochastic reaction model (SRM) treats polymerization as a pure probability‐based issue, which is widely applied to simulate various polymerization processes. However, in many studies, active centers were assumed to react with the same probability, which cannot reflect the heterogeneous reaction microenvironment in heterogeneous polymerizations. Recently, we have proposed a simple SRM, in which the reaction probability of an active center is directly determined by the local reaction microenvironment. In this paper, we compared this simple SRM with other SRMs by examining living polymerizations with randomly dispersed and spatially localized initiators. The results confirmed that the reaction microenvironment plays an important role in heterogeneous polymerizations. This simple SRM provides a good choice to simulate various polymerizations.

Preparation of nanoparticles grafted with bimodal-bidisperse polymers in nanocomposite

Because of the important application in nanocomposite materials, the preparation of nanoparticles (NPs) tethered with bimodal bidispersed polymer chains via grafting-from strategy is studied by coarse-grained molecular dynamics simulations combined with the stochastic reaction model. We design three conventional scenarios for preparing these NPs, i.e., a two-step grafting-from process with the long chains grow first followed by the short chains, a similar two-step grafting-from process with the short chains grow first followed by the long chains, and a one-step scenario to graft both chains concurrently. We find the priority of chain growth greatly influences the grafting density of the finally prepared nanoparticles. The simulations strongly suggest that for obtaining a medium and comparable grafting density of both short and long chains in experiment, an ideal strategy is activating both the initiators simultaneously or grafting the long chains firstly. We also find that in the one-step scenario, the simultaneously growing short and long chains have complicated mutual effects on each other. Our study helps to better understand the kinetics during the preparation of bimodal bidisperse-polymer grafted NP and could act as a guide to better design and improve the performance of polymer nanocomposites.

Insight into the Polymerization-Induced Self-Assembly via a Realistic Computer Simulation Strategy

The dynamic process of polymerization-induced self-assembly (PISA) is simulated by the dissipative particle dynamics method coupled with the stochastic reaction model. Meaningful comparisons betwee...

Polymer-grafted nanoparticles prepared via a grafting-from strategy: a computer simulation study.

Nanoparticles (NPs) grafted with polymer chains prepared via a grafting-from strategy are studied through coarse-grained molecular dynamics simulations combined with our stochastic reaction model. A system involving multiple individual NPs, with grafting-from processes for all the NPs induced simultaneously, is simulated, so that chain growth competition on the same NP, as well as between neighbouring NPs, are both naturally considered. Our results imply that there should be an optimized range of NP sizes, as compared to monomer size, in which initiator sites are most easily induced. Besides, when the initiator density is high, a shielding effect from the sparse long chains on the most short chains or initiators evidently yields an extremely unbiased distribution of chains. We also adopt a representative polymer-tethered NP prepared via a grafting-from strategy to study the potential of mean force between NPs, so that the dispersion and stabilization abilities of such polymer-grafted NPs in a polymer matrix can be generally predicted during the preparation of polymer nanocomposite materials. Our study helps to elucidate the cause of chain dispersity during the grafting-from process and could act as a guide for better design and to improve the performance of polymer nanocomposites.

Polymerization-induced polymer aggregation or polymer aggregation-enhanced polymerization? A computer simulation study.

In this study, using dissipative particle dynamics simulations coupled with the stochastic reaction model, we investigate the polymerization-induced polymer aggregation process and the polymer aggregation-enhanced polymerization process in a binary solution, by simply tuning the solubility of the solvent to one species of copolymerization. Our simulations indicate that it is a complicated interplay of the copolymerization on the formation of aggregates, namely, on one hand the polymerization may induce the aggregation of one species; on the other hand it has an effect of mixing the two species together. We also find that the polymerization process basically follows the first order reaction kinetics. With the increase of insolubility of B species in the solution, it continuously deviates from the first order reaction kinetics. In the symmetric copolymerization system, we find that the dispersity of copolymers monotonically decreases with the increase of reaction probability. This counterintuitive result can be understood via the comparison of diffusion-controlled kinetics and reaction-controlled kinetics. In the asymmetric system, for systems with preferential copolymerization, the mass distribution shapes are Gaussian-like with certain peaks. For comparison, for systems with preferential homopolymerization, the mass distribution shape shows an obviously bimodal form. This study helps to better understand the cooperative competition between the reaction dynamics and the diffusion dynamics during the preparation of copolymer materials, and could act as a guide to better design and improve the copolymerization technologies in laboratories and in industry.

Single-Nanocrystal Reaction Trajectories Reveal Sharp Cooperative Transitions

Whereas pathways of chemical reactions involving small molecules are well-understood, the dynamics of reactions in extended solids remain difficult to elucidate. Frequently, kinetic studies on bulk materials provide a picture averaged over multiple domains or grains, smearing out interesting dynamics such as critical nucleation phenomena or sharp phase transitions occurring within individual, often nanoscale, grains, or domains. By optically monitoring a solid-state reaction with single nanocrystal resolution, we directly identified a unique, previously unknown, reaction pathway. Reaction trajectories of single cadmium selenide nanocrystals undergoing ion exchange with silver reveal that each individual nanocrystal waits a unique amount of time before making an abrupt switch to the silver selenide phase on a few hundred millisecond time scale. The gradual reaction progress of ensemble-scale cation exchange is actually comprised of these sharp single-nanocrystal switching events. Statistical distributions of waiting times suggest that the reaction is a cooperative transition rather than a diffusion-limited cation-by-cation exchange, which is confirmed by a stochastic reaction model. Such insight, achievable from single nanocrystal reaction studies, furthers mechanistic understanding of heterogeneous reactions, solid-state catalysis, bottom-up nanostructure growth, and materials' transformations and degradation in reactive environments.

Polymer-grafted nanoparticles prepared by surface-initiated polymerization: the characterization of polymer chain conformation, grafting density and polydispersity correlated to the grafting surface curvature

The polymer-grafted nanoparticles prepared by the surface-initiated polymerization induced from the spherical surface is studied by coarse-grained molecular dynamics simulations combined with the stochastic reaction model. The coupling effect of the initiator density and the grafting surface curvature is mainly investigated. The confinement degree greatly changes with the grafting surface curvature, thus the initiation efficiency, the grafted chain polydispersity, as well as the chain mass distribution show great dependence on the surface curvature. The results reveal that preparing the nanoparticle with desired size (i.e., grafting surface curvature) is crucial for control of the grafted chain polydispersity and even its dispersion in the polymer matrix. Our studies shed light on better design of grafted nanoparticles and better control of dispersion in polymer matrices for improving the performance of polymer nanocomposite materials.

SmartCell, a framework to simulate cellular processes that combines stochastic approximation with diffusion and localisation: analysis of simple networks

SmartCell has been developed to be a general framework for modelling and simulation of diffusion-reaction networks in a whole-cell context. It supports localisation and diffusion by using a mesoscopic stochastic reaction model. The SmartCell package can handle any cell geometry, considers different cell compartments, allows localisation of species, supports DNA transcription and translation, membrane diffusion and multistep reactions, as well as cell growth. Moreover, different temporal and spatial constraints can be applied to the model. A GUI interface that facilitates model making is also available. In this work we discuss limitations and advantages arising from the approach used in SmartCell and determine the impact of localisation on the behaviour of simple well-defined networks, previously analysed with differential equations. Our results show that this factor might play an important role in the response of networks and cannot be neglected in cell simulations.