Copolymerization of Partly Incompatible Monomers: An Insight from Computer Simulations

The explicit bonding reaction ensemble Monte Carlo method

We present the explicit bonding Reaction ensemble Monte Carlo (eb-RxMC) method, designed to sample reversible bonding reactions in macromolecular systems in thermodynamic equilibrium. Our eb-RxMC method is based on the reaction ensemble method; however, its implementation differs from the latter by the representation of the reaction. In the eb-RxMC implementation, we are adding or deleting bonds between existing particles, instead of inserting or deleting particles with different chemical identities. This new implementation makes the eb-RxMC method suitable for simulating the formation of reversible linkages between macromolecules, which would not be feasible with the original implementation. To enable coupling of our eb-RxMC algorithm with molecular dynamics algorithm for the sampling of the configuration space, we biased the sampling of reactions only within a certain inclusion radius. We validated our algorithm using a set of ideally behaving systems undergoing dimerization and polycondensation reactions, for which analytical results are available. For dimerization reactions with various equilibrium constants and initial compositions, the degree of conversion measured in our simulations perfectly matched the reference values given by the analytical equations. We also showed that this agreement is not affected by the arbitrary choice of the inclusion radius or the stiffness of the harmonic bond potential. Next, we showed that our simulations can correctly match the analytical results for the distribution of the degree of polymerization and end-to-end distance of ideal chains in polycondensation reactions. Altogether, we demonstrated that our eb-RxMC simulations correctly sample both reaction and configuration spaces of these reference systems, opening the door to future simulations of more complex interacting macromolecular systems.

Reaction-induced morphological transitions in a blend of diblock copolymers and reactive monomers: dissipative particle dynamics simulation

The dissipative particle dynamics (DPD) method is applied to the morphological transitions of microphase-separated domains in a mixture of symmetric AB-diblock copolymers and reactive C-monomers, where polymerization and cross-linking reactions take place among C-monomers. The initial structure for the DPD simulation is an equilibrated cylindrical domain structure prepared by the density-biased Monte Carlo method with density profiles obtained from the self-consistent field theory. By introducing a cross-linking reaction among reactive C-monomers, we confirmed that the DPD simulation reproduces the morphological transitions observed in experiments, where the domain morphology changes due to segregation between A-blocks of diblock copolymers and cross-linking networks of C-monomers. When the cross-linking reaction of C-monomers is sufficiently fast compared to the deformation of the domains, the initial cylindrical domains are preserved, while the distance between the domains increases. On the other hand, when the formation of the cross-linking network is slow, the domains can deform and reconnect with each other in the developing cross-linking network. In this case, we observe morphological transitions from the initial domain morphology with a large-curvature interface to another domain morphology with a smaller-curvature interface, such as the transition from the cylindrical phase to the lamellar phase. We calculated the spatial correlations in the microphase-separated domains and found that such correlations are affected by the speed of the formation of the cross-linking network depending on whether the bridging between microphase-separated domains occurs in a nucleation and growth process or in a spinodal decomposition process.

Phase Diagrams of Polymerization-Induced Self-Assembly Are Largely Determined by Polymer Recombination

In the current work, atom transfer radical polymerization-induced self-assembly (ATRP PISA) phase diagrams were obtained by the means of dissipative particle dynamics simulations. A fast algorithm for determining the equilibrium morphology of block copolymer aggregates was developed. Our goal was to assess how the chemical nature of ATRP affects the self-assembly of diblock copolymers in the course of PISA. We discovered that the chain growth termination via recombination played a key role in determining the ATRP PISA phase diagrams. In particular, ATRP with turned off recombination yielded a PISA phase diagram very similar to that obtained for a simple ideal living polymerization process. However, an increase in the recombination probability led to a significant change of the phase diagram: the transition between cylindrical micelles and vesicles was strongly shifted, and a dependence of the aggregate morphology on the concentration was observed. We speculate that this effect occurred due to the simultaneous action of two factors: the triblock copolymer architecture of the terminated chains and the dispersity of the solvophobic blocks. We showed that these two factors affected the phase diagram weakly if they acted separately; however, their combination, which naturally occurs during ATRP, affected the ATRP PISA phase diagram strongly. We suggest that the recombination reaction is a key factor leading to the complexity of experimental PISA phase diagrams.

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.

Synthesis of Shape-Memory Polyurethanes: Combined Experimental and Simulation Studies

The presented research focuses on the synthesis and structure-properties relationship of poly(carbonate-urea-urethane) (PCUU) systems including investigations on shape-memory effect capability. Furthermore, we approached the topic from a broader perspective by conducting extensive analysis of the relationship between the synthesized compounds and the results of computer simulations by means of the Monte Carlo method. For the first time, by using a unique simulation tool, the dynamic lattice liquid model (DLL), all steps of multi-step synthesis of these materials were covered by the simulations. Furthermore, broad thermal, mechanical, and thermomechanical characterization of synthesized PCUUs was performed, as well as determining the shape-memory properties. PCUUs exhibited good mechanical properties with a tensile strength above 20 MPa, elongation at break around 800%, and an exhibited shape-memory effect with shape fixity and shape recovery ratios above 94% and 99%, respectively. The dynamic lattice liquid model was employed to show the products and their molar mass distribution, as well as monomer conversion or the dispersity index for individual reaction steps. The results obtained in the following manuscript allow the planning of syntheses for the PCUUs of various structures, including crosslinked and soluble systems, which can provide a broad variety of applications of these materials, as well as a better understanding of the composition-properties relationship.

Selective solvent conditions influence sequence development and supramolecular assembly in step-growth copolymerization

Sequence control in synthetic copolymers remains a tantalizing objective in polymer science due to the influence of sequence on material properties and self-organization. A greater understanding of sequence development throughout the polymerization process will aid the design of simple, generalizable methods to control sequence and tune supramolecular assembly. In previous simulations of solution-based step-growth copolymerizations, we have shown that weak, non-bonding attractions between monomers of the same type can produce a microphase separation among the lengthening nascent oligomers and thereby alter sequence. This work explores the phenomenon further, examining how effective attractive interactions, mediated by a solvent selective for one of the reacting species, impact the development of sequence and the supramolecular assembly in a simple A-B copolymerization. We find that as the effective attractions between monomers increase, an emergent self-organization of the reactants causes a shift in reaction kinetics and sequence development. When the solvent-mediated interactions are selective enough, the simple mixture of A and B monomers oligomerize and self-assemble into structures characteristic of amphiphilic copolymers. The composition and morphology of these structures and the sequences of their chains are sensitive to the relative balance of affinities between the comonomer species. Our results demonstrate the impact of differing A-B monomer-solvent affinities on sequence development in solution-based copolymerizations and are of consequence to the informed design of synthetic methods for sequence controlled amphiphilic copolymers and their aggregates.

Simulation of the RAFT polymerization in 3D: steric restrictions and incompatibility between species

In this work we developed a RAFT polymerization model taking into account the main reactions of the experimental RAFT process and implemented that model in dissipative particle dynamics (DPD). With...

Computer simulation of zwitterionic polymer brush grafted silica nanoparticles to modify polyvinylidene fluoride membrane

Dissipative particle dynamics (DPD) simulations was adopted to investigate the modification of polyvinylidene fluoride (PVDF) membrane by adding zwitterionic polymer brush poly(sulfobetaine methacrylate)- tetraethyl orthosilicate (PSBMA-TEOS) grafted silicon nanoparticles (SNPs) to the casting solution. The effects of polymer concentration and grafting architecture (PSBMA length and SNPs grafting ratio) on membrane morphology are discussed. When the polymer concentration reaches 40%, part of the SNPs is embedded in the membrane; the optimal polymer concentration is around 25-30%. In the SNPs system with the grafting ratio of 1, some SNPs are eluted into solution during phase separation. Compared with different grafting architectures, M_8-5, M_10-5 and M_12-5 system (M_x-y, where x represents the length of the zwitterionic polymer brush and y represents the grafting ratio of the silica nanoparticles) exhibited stable membrane morphologies. This work can provide guidance for the design and modification of organic-inorganic composite membrane and help understand the distribution of modified materials on the membrane surface.

Polymerization-Induced Microphase Separation with Long-Range Order in Melts of Gradient Copolymers

In this work, we studied the question of whether it is possible to develop a one-step approach for the creation of microphase-separated materials with long-range order with the help of spontaneous gradient copolymers, i.e., formed during controlled copolymerization solely due to the large difference in the reactivity ratios. To that end, we studied the polymerization-induced microphase separation in bulk on the example of a monomer pair with realistic parameters based on styrene (S) and vinylpirrolydone (VP) by means of computer simulation. We showed that for experimentally reasonable chain lengths, the structures with long-range order start to appear at the conversion degree as low as 76%; a full phase diagram in coordinates (fraction of VP-conversion degree) was constructed. Rather rich phase behavior was obtained; moreover, at some VP fractions, order-order transitions were observed. Finally, we studied how the conversion degree at which the order-disorder transition occurs changes upon varying the maximum average chain length in the system.

Phase Diagram for Ideal Diblock-Copolymer Micelles Compared to Polymerization-Induced Self Assembly

In this work we constructed a detailed phase diagram for the solutions of ideal diblock-copolymers and compared such diagram with that obtained during polymerization-induced self-assembly (PISA); a wide range of polymer concentrations as well as chain compositions was studied. As the length of the solvophobic block nB increases (the length of the solvophilic block nA was fixed), the transition from spherical micelles to cylinders and further to vesicles (lamellae) occurs. We observed a rather wide transition region between the spherical and cylindrical morphology in which the system contains a mixture of spheres and short cylinders, which appear to be in dynamic equilibrium; the transition between the cylinders and vesicles was found to be rather sharp. Next, upon increasing the polymer concentration in the system, the transition region between the spheres and cylinders shifts towards lower nB/nA values; a similar shift but with less magnitude was observed for the transition between the cylinders and vesicles. Such behavior was attributed to the increased number of contacts between the micelles at higher polymer volume concentrations. We also found that the width of the stability region of the cylindrical micelles for small polymer volume concentrations is in good quantitative agreement with the predictions of analytical theory. The obtained phase diagram for PISA was similar to the case of presynthesized diblock copolymer; however, the positions of the transition lines for PISA are slightly shifted towards higher nB/nA values in comparison to the presynthesized diblock copolymers, which is more pronounced for the case of the cylinders-to-vesicles transition. We believe that the reason for such behavior is the polydispersity of the core-forming blocks: The presence of the short and long blocks being located at the micelle interface and in its center, respectively, helps to reduce the entropy losses due to the insoluble block stretching, which leads to the increased stability of more curved micelles.

Zwitterionic Membrane via Nonsolvent Induced Phase Separation: A Computer Simulation Study

Dissipative particle dynamics (DPD) was adopted to study the nonsolvent induced phase separation (NIPS) process during a pH-responsive poly(ether sulfone) membrane preparation with a zwitterionic copolymer poly(ether sulfone)- block-polycarboxybetaine methacrylate (PES-b-PCBMA) as the blending additive. The membrane formation process and final morphology were analyzed. Simulation results show that the hydrophilic PCBMA segments enrich on the membrane surface by surface segregation and exhibit pH-responsive behavior, which is attributed to the deprotonation of the carboxylic acid group. With the polymer concentration increasing, both the shrinkage of the membrane and the flexibility of the system decrease, which also reduce the effect of surface segregation. By adjusting the blend ratio of PES-b-PCBMA with PES from 5% to 15%, the surface coverage of PCBMA segments on the membrane can be regulated. This work contributes to a better understanding on the mechanism of NIPS and can serve as a guide for the design of the polymer blend membrane.

Micellar polymerization: Computer simulations by dissipative particle dynamics

Nowadays, micellar polymerization is widely used in different fields of industry and research, including modern living polymerization technique. However, this process has many variables and there is no comprehensive model to describe all features. This research presents simulation methodology which describes key properties of such reactions to take a guide through a variety of their modifications. Dissipative particle dynamics is used in addition to Monte Carlo scheme to simulate initiation, propagation, and termination events. Influence of initiation probability and different termination processes on final conversion and molecular-weight distribution are presented. We demonstrate that prolonged initiation leads to increasing in polymer average molecular weight, and surface termination events play major role in conversion limitation, in comparison with recombination. © 2018 Wiley Periodicals, Inc.

One-pot production of porous assemblies by PISA of star architecture copolymers: a simulation study

Porous vesicles can be produced in one-pot by the PISA of star architecture copolymers.

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.

Copolymerization on Selective Substrates: Experimental Test and Computer Simulations

We explore the influence of a selective substrate on the composition and sequence statistics during the free radical copolymerization. In particular, we study the radical copolymerization of styrene and acrylic acid in bulk and in silica pores of different sizes. We show that the substrate affects both polymer composition and sequence statistics. We use dissipative particle dynamics simulations to study the polymerization process in detail, trying to pinpoint the parameters responsible for the observed differences in the polymer chain composition and sequences. The magnitude of the observed effect depends on the fraction of adsorbed monomer units, which cannot be described in the framework of the copolymerization theories based on the terminal unit model.