Coil-globule transition in two-dimensional polymer chains in an explicit solvent.

The structure of two-dimensional polymer chains in a solvent at different temperatures is still far from being fully understood. Computer simulations of high-density macromolecular systems require the use of appropriate algorithms, and therefore the simulations were carried out using the Cooperative Motion Algorithm. The polymer model studied was exactly two-dimensional, coarse-grained and based on a triangular lattice. The theta temperature and temperature of coil-to-globule transition, and critical exponents were determined. The differences between the structure of such a disk and that of a chain in a dense polymer liquid were shown.

The Influence of Constraints on Gelation in a Controlling/Living Copolymerization Process.

We developed a simple model of the copolymerization process in the formation of crosslinked macromolecular systems. A living copolymerization was carried out for free chains, in bulk and in a slit, as well as for grafted chains in a slit. In addition, polymer 2D brushes were placed in a slit with initiator molecules attached to one of the confining walls. Coarse-grained chains were embedded in the vertices of a face-centered cubic lattice with the excluded volume interactions. The simulations of the copolymerization processes were performed using the Dynamic Lattice Liquid algorithm, a version of the Monte Carlo method. The influence of the initial initiator to cross-linker ratio, slit width and grafting on the polymerization and on the gelation was examined. It was also shown that the influence of a confining slit was rather small, while the grafting of chains affected the location of the gel pint significantly.

Modelling Development in Radical (Co)Polymerization of Multivinyl Monomers.

Radical polymerization (RP) of multivinyl monomers (MVMs) provides a facile solution for manipulating polymer topology and has received increasing attention due to their industrial and academic significance. Continuous efforts have been made to understand their mechanism, which is the key to regulating materials structure. Modelling techniques have become a powerful tool that can provide detailed information on polymerization kinetics which is inaccessible by experiments. Many publications have reported the combination of experiments and modelling for free radical polymerization (FRP) and reversible-deactivation radical polymerizations (RDRP) of MVMs. Herein, a minireview is presented for the most important modelling techniques and their applications in FRP/RDRP of MVMs. This review hopes to illustrate that the combination of modelling and wet experiments can be a great asset to polymer researchers and inspire new thinking for the future MVMs experiment optimization and product design.

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.

The structure of polymer brushes: the transition from dilute to dense systems: a computer simulation study.

Monodisperse polymer brushes were studied by means of Monte Carlo simulations. A coarse-grained model of a polymer brush was designed and the Cooperative Motion Algorithm was employed to model the polymerization process 'grafted from' and to study the structure of a brush immersed in a good solvent. The structure of brushes was determined as a function of the chain length and the grafting density. The influence of these parameters on the scaling properties of the brush was presented and discussed. A thorough analysis of the distribution of concentrations of the polymer segments and the distribution of chain free ends was also carried out. The analysis of the depth of penetration of the low molecular weight solvent into the brush area showed that the main factor determining the penetration is the grafting density. Good agreement between the simulation results and theoretical predictions is observed, especially for longer chains and higher grafting density. The origin of small quantitative differences between the simulation and theoretical results is discussed.

Molecular transport in systems containing binding obstacles.

We studied the movement of particles in crowded environments by means of extensive Monte Carlo simulations. The dynamic lattice liquid model was employed for this purpose. It is based on the cooperative movement concept and allows the study of systems at high densities. The cooperative model of molecular transport is assumed: the motion of all moving particles is highly correlated. The model is supposed to mimic lateral motion in a membrane and therefore the system is two-dimensional with moving objects and traps placed on a triangular lattice. In our study the interaction (binding) of traps with moving particles was assumed. The conditions in which subdiffusive motion appeared in the system were analysed. The influence of the strength of binding on the dynamic percolation threshold was also shown. The differences in the dynamics compared to systems with impenetrable obstacles and with systems without correlation in motion were presented and discussed. It was shown that in the case of correlated motion the influence of deep traps is similar to that of impenetrable obstacles. If the traps are shallow a recovery to normal diffusion was observed for longer time periods.

Universal scaling behavior of polymer chains at the percolation threshold.

Two-dimensional macromolecular systems were studied by means of Monte Carlo simulations employing the Cooperative Motion Algorithm. The influence of chain length and internal architecture on the location of the percolation thresholds was shown. A universal behavior of chain size at these thresholds was presented.

Diffusion of small particles in polymer films.

The motion of small probe molecules in a two-dimensional system containing frozen polymer chains was studied by means of Monte Carlo simulations. The model macromolecules were coarse-grained and restricted to vertices of a triangular lattice. The cooperative motion algorithm was used to generate representative configurations of macromolecular systems of different polymer concentrations. The remaining unoccupied lattice sites of the system were filled with small molecules. The structure of the polymer film, especially near the percolation threshold, was determined. The dynamic lattice liquid algorithm was then employed for studies of the dynamics of small objects in the polymer matrix. The influence of chain length and polymer concentration on the mobility and the character of motion of small molecules were studied. Short- and long-time dynamic behaviors of solvent molecules were also described. Conditions of anomalous diffusions' appearance in such systems are discussed. The influence of the structure of the matrix of obstacles on the molecular transport was discussed.

Simulation of diffusion in a crowded environment.

We performed extensive and systematic simulation studies of two-dimensional fluid motion in a complex crowded environment. In contrast to other studies we focused on cooperative phenomena that occurred if the motion of particles takes place in a dense crowded system, which can be considered as a crude model of a cellular membrane. Our main goal was to answer the following question: how do the fluid molecules move in an environment with a complex structure, taking into account the fact that motions of fluid molecules are highly correlated. The dynamic lattice liquid (DLL) model, which can work at the highest fluid density, was employed. Within the frame of the DLL model we considered cooperative motion of fluid particles in an environment that contained static obstacles. The dynamic properties of the system as a function of the concentration of obstacles were studied. The subdiffusive motion of particles was found in the crowded system. The influence of hydrodynamics on the motion was investigated via analysis of the displacement in closed cooperative loops. The simulation and the analysis emphasize the influence of the movement correlation between moving particles and obstacles.

Star Polymers vs. Dendrimers: Studies of the Synthesis Based on Computer Simulations.

A generic model was developed for studies of the polymerization process of regular branched macromolecules. Monte Carlo simulations were performed employing the Dynamic Lattice Liquid algorithm to study this process. A core-first methodology was used in a living polymerization of stars with up to 32 arms, and dendrimers consisted of 4-functional segments. The kinetics of the synthesis process for stars with different numbers of branches and dendrimers was compared. The size and structure of star-branched polymers and dendrimers during the synthesis were studied. The influence of the functionality of well-defined cores on the structure and on the dispersity of the system was also examined. The differences in the kinetics in the formation of both architectures, as well as changes to their structures, were described and discussed.

Dynamics of Opposing Polymer Brushes: A Computer Simulation Study.

Opposing polymer brush systems were synthesized and investigated by molecular modeling. Chains were restricted to a face-centered cubic lattice with the excluded volume interactions only. The system was confined between two parallel impenetrable walls, with the same number of chains grafted to each surface. The dynamic properties of such systems were studied by Monte Carlo simulations based on the dynamic lattice liquid model and using a highly efficient parallel machine ARUZ, which enabled the study of large systems and long timescales. The influence of the surface density and mean polymer length on the system dynamic was discussed. The self-diffusion coefficient of the solvent depended strongly on the degree of polymerization and on the polymer concentration. It was also shown that it is possible to capture changes in solvent mobility that can be attributed to the regions of different polymer densities.

Polymerization and Structure of Opposing Polymer Brushes Studied by Computer Simulations.

A model of the polymerization process during the formation of a pair of polymer brushes was designed and investigated. The obtained system consisted of two impenetrable parallel surfaces with the same number of chains grafted on both surfaces. Coarse-grained chains embedded in nodes of a face-centered cubic lattice with excluded volume interactions were obtained by a 'grafted from' procedure. The structure of synthesized macromolecular systems was also studied. Monte Carlo simulations using the dynamic lattice liquid model were employed using dedicated parallel machine ARUZ in a large size and time scale. The parameters of the polymerization process were found to be crucial for the proper structure of the brush. It was found that for high grafting densities, chains were increasingly compressed, and there is surprisingly little interpenetration of chains from opposite surfaces. It was predicted and confirmed that in a polydisperse sample, the longer chains have unique configurations consisting of a stretched stem and a coiled crown.

Percolation in polymer-solvent systems: a Monte Carlo study.

In this study we investigated the percolation in the system containing long flexible polymer chains. The system also contained explicit solvent molecules. The polymer chains were represented by linear sequences of lattice points restricted to a two-dimensional triangular lattice. The Monte Carlo simulations were performed applying the cooperative motion algorithm. The percolation thresholds and the critical exponents of chains and solvent molecules were determined. The influence of the chain length on the percolation was discussed. It was shown that the percolation threshold decreased strongly with the chain length, which is closely connected to changes in chains' structure with the decreasing polymer concentration. The critical exponent beta for all chains under consideration and for solvent molecules was found almost constant and close to the theoretical value 5/36.

Motion in a crowded environment: the influence of obstacles' size and shape and model of transport.

Simulations of motion in a complex crowded environment were performed. We employed the dynamic lattice liquid model, which was based on the cooperative movement concept. This algorithm is capable of working at very high densities, and the motion of all objects was highly correlated. The so-called motion of a single agent, where the motion of molecules is considered as a random walk without any correlation with other moving objects, was also calculated as the state of reference. Immobilized chains embedded in a two-dimensional triangular lattice modeled the crowded environment. The dynamic behavior of movable objects was studied and the influence of the structure of the matrix of obstacles on the molecular transport was discussed. It was shown that the type of transport has an impact on the dynamics of the system. The appearance and properties of subdiffusive motion were analyzed and referred to the structure of polymer systems.

Monte Carlo studies of two-dimensional polymer-solvent systems.

The static properties of two-dimensional athermal polymer solutions were studied by performing Monte Carlo lattice simulations using the cooperative motion algorithm (CMA) and taking into account the presence of explicit solvent molecules. The simulations were performed for a wide range of polymer chain lengths N (16-1024) and concentrations φ (0.0156-1). The results obtained for short chains (N < 256) were in good agreement with those given by previous simulations. For the longest chains (512 or 1024 beads), some unexpected behavior was observed in the dilute and semidilute regimes. A pronounced change in the concentration dependence of chain size and shape was observed below a certain critical concentration (0.6 for the longest chains under consideration, consisting of 1024 beads). Longer chains became more extended below this concentration. The behavior of the single-chain structure factor confirmed these changes in the fractal dimension of the chain as a function of the concentration. The observed phenomena are related to the excluded volume of solvent molecules, which causes the chain statistics to be modified in the vicinity of other chains; this effect is important in strictly 2D systems. Graphical abstract Extended long chains at moderate density with solvent molecules inside coils.

Reaction-diffusion fronts in systems with concentration-dependent diffusivities.

We examine properties of a reaction front that forms in irreversible reaction-diffusion systems with concentration-dependent diffusivities. We study two different models of such systems and find that in the limit of a vanishingly small diffusivity of the reaction product, the reaction front dynamics enters a separate universality class, with the front width asymptotically tending to a constant value, and the reaction rate at the reaction front center diminishing with time t as t(-1/2). This behavior can be also observed in systems with nonvanishing (but small) diffusivity of the reaction product at intermediate times.

Simulation of Molecular Transport in Systems Containing Mobile Obstacles.

In this paper, we investigate the movement of molecules in crowded environments with obstacles undergoing Brownian motion by means of extensive Monte Carlo simulations. Our investigations were performed using the dynamic lattice liquid model, which was based on the cooperative movement concept and allowed to mimic systems at high densities where the motion of all elements (obstacles as well as moving particles) were highly correlated. The crowded environments are modeled on a two-dimensional triangular lattice containing obstacles (particles whose mobility was significantly reduced) moving by a Brownian motion. The subdiffusive motion of both elements in the system was analyzed. It was shown that the percolation transition does not exist in such systems in spite of the cooperative character of the particles' motion. The reduction of the obstacle mobility leads to the longer caging of liquid particles by mobile obstacles.

The structure of percolated polymer systems: a computer simulation study.

We studied the percolation process in a system consisting of long flexible polymer chains and solvent molecules. The polymer chains were approximated by linear sequences of beads on a two-dimensional triangular lattice. The system was athermal and the excluded volume was the only potential. The properties of the model system across the entire range of polymer concentrations were determined by Monte Carlo simulations employing a cooperative motion algorithm (CMA). The scaling behavior and the structure of the percolation clusters are presented and discussed.

Microphase separation in two-dimensional athermal polymer solutions on a triangular lattice.

The results of Monte Carlo simulations of 2D polymer solutions are presented. The simulations were performed under athermal conditions for long chains (up to 1024 beads) over a full range of polymer concentration phi, explicitly taking into account the solvent molecules. The results obtained for short chains (N < or = 256) are in good agreement with previous simulations whereas for long chains microphase separation is observed below phi = 0.6. This phenomenon is attributed to strong excluded volume interactions in 2D systems. A sort of interpenetration of the coils is also observed.

Simulation of polymer--polymer interdiffusion using the dynamic lattice liquid model.

In this paper, we present computer simulation results concerning interdiffusion of fully compatible components in symmetric binary (AB) polymer mixtures in solutions. The simulation is performed in two dimensions using the algorithm based on the dynamic lattice liquid model. The solvent molecules are taken into account explicitly. The evolution of the concentration profiles in time at an interface is studied for chain lengths N=2,4,8,16 for three polymer concentrations phi=0.1,0.5,0.9. The tracer diffusion coefficients for polymer chains and for the solvent are obtained by monitoring the mean square displacements of their center of mass. The relationships between coefficients of interdiffusion and self-diffusion are tested.