Monte Carlo (MC) methods were applied to the complex kinetic model of butyl acrylate polymerizations. The MC simulator mcPolymer developed in house allows for handling chain-length-dependent termination kinetics. The simulations provide detailed information on the microstructure of each individual polymer chain. For example, the number of short chain branches (SCBs) on each polymer chain and the length of the monomer sequence between two short chain branches are captured. It is shown that the maximum of the branching density distribution is shifted to shorter chain lengths with reaction time. Variation of initiator concentration does not lead to significant changes in the sequence length distributions and branching distributions as long as the same monomer conversion is reached.

The Monte Carlo (MC) simulator mcPolymer is capable of handling of a large number of molecules, allowing for the implementation of a chain-length-dependent termination model. It was applied to the complex kinetic model of butyl acrylate polymerizations, being able to reproduce experimental findings. Furthermore, detailed information on the microstructure of each individual polymer chain was extracted.

The kinetic model of the amphiphilic copolymers with hyperbranched core and linear arms was developed for both semibatch and one-pot polymerization. The molecular size distribution functions of the species obtained and the various molecular parameters were analytically derived. The topological structures and molecular parameters of the products depend on initial mole feed ratios of the reactants. Under the same reaction conditions, the polydispersity index of the products resulted from semibatch is smaller than that of the one-pot process and there are more terminal units on the surface of hyperbranched macroinitiators from semibatch process. Accordingly, the topological structures of the amphiphilic hyperbranched copolymers and the successive self-assembly shapes can be designed by the suitable initial conditions of the polymerization.

**The kinetic model of the amphiphilic copolymers with hyperbranched core and linear arms was developed.** The molecular size distribution functions of the species obtained were analytically derived. Accordingly, the topological structures of the amphiphilic hyperbranched copolymers and the successive self-assembly shapes can be designed.

The generation of fully cross-linked structure is a central task in molecular dynamics simulations of thermosetting polymers. Several algorithms for generating such structures exist, but it is so far not clear what impact the choice of algorithm has on thermal and material properties one typically wants to use simulations to predict. We generated cross-linked systems comprised of stoichiometric amounts of diglycidyl ether of bisphenol A and poly(oxyproplylene) diamine using two methods: (1) a single-step approach, in which cross-link bonds are assigned based on a Monte-Carlo algorithm that minimizes aggregate bond lengths, and (2) a multi-step approach, which uses an incrementally increasing capture radius to identify bonding partners. The choice of cross-linking method has only a minimal impact on thermal and mechanical properties. The minimum nitrogen-to-nitrogen contour-length distributions are also insensitive to the method. However, significant differences were found in the molecular weight distribution of fragments formed by cutting each POP cross-linker between the amines: the single-step method results in fewer, larger fragments compared to the multi-step method. This indicates that the networks formed by the two methods are qualitatively different, and underscores the need for further studies to characterize the influence of polymer network connectivity both in simulations and experiments.

MD simulations with ad-hoc cross-linking algorithms have been used to generate molecular models of fully cross-linked epoxy materials. Two such algorithms are compared, and it is shown that glassy-state thermal and mechanical properties were not significantly influenced by the algorithm choice. This result notwithstanding, it is shown that the two algorithms result in very different network isomers, pointing toward a possible experimental method of structure validation in future work.

General step-growth polymerization systems of order 2 are considered, i.e. systems of type “AfiBgi”. We describe an algorithmic method to calculate the molecular size distribution (MSD). Input to the algorithm is the “recipe”: a list of the monomers involved stating their A and B functionalities and their molar amounts, and the degree of conversion. Output is the MSD and its moments. Three main steps lead from input to output: (i) setting up a polynomial equation for the generating function that generates the MSD, (ii) transforming this polynomial equation to a differential equation, and (iii) transforming the latter one further to a recurrence equation. The recurrence yields the MSD and is of constant order.

From the recipe straight to the MSD. For step-growth polymerized systems of general type “AfiBgi”, a computer algebra method is presented that leads via a few transformation steps from the recipe to the MSD.

A kinetic scheme describing Catalytic Chain Growth (CCG) polymerization was developed and implemented into the computer program PREDICI, by which experimental concentration versus time traces of the participating individual species obtained from online NMR spectroscopy as well as full molecular weight distributions could successfully be modeled. The obtained kinetic coefficients are of high statistical significance. The method was demonstrated on the CCG of styrene-*d*8 in toluene-*d*8 using Cp*_{2}ZrCl_{2} as the catalyst precursor and dibenzyl magnesium as the transfer agent. The quality of the modeling increased dramatically when assuming a chain-length dependent propagation. The extraordinarily good quality of the simulation for all participating species proves that the underlying kinetic model is very likely to be correct. The simulations also demonstrate that this CCG system is a controlled process and that increasing the concentration of the catalyst precursor may lead to a reduced overall polymerization rate.

A kinetic scheme describing Catalytic Chain Growth (CCG) polymerization was developed and implemented into the computer program PREDICI, by which experimental concentration versus time traces of the participating individual species obtained from online NMR spectroscopy as well as full molecular weight distributions could successfully be modeled. The method was demonstrated on the CCG of styrene-d8 in toluene-d8 using Cp*_{2}ZrCl_{2} as the catalyst precursor and dibenzyl magnesium as the transfer agent.

In this study propagation kinetics of free radical polymerization of N-methylacrylamide (NMAAm) is studied with density functional theory calculations. The propagation rate constant ratio of N,N-dimethylacrylamide (DMAAm) and NMAAm (k_{NMAAm}/k_{DMAAm}) is evaluated via model reactions at dimeric stage. The most favorable modes of addition is shown to be determined by the steric effects and hydrogen bonding interactions between the reactive fragments. Gauche and trans orientations are preferred as the least energetic additions in pro-meso and pro-racemo attacks, respectively. Benchmark studies with various density functionals (M05-2X, M06-2X, MPWB1K, BMK) combined with 6-311 + G(3df,2p) basis set assess the calculations. The k_{NMAAm}/k_{DMAAm} ratio obtained in this study is in line with the experimental value. The addition reaction barrier via dimeric associates in case of NMAAm does not yield significant difference than the barrier via monomeric species.

Propagation kinetics in free radical polymerization of N,N-dimethylacrylamide and N-methylacrylamide is modeled with quantum chemical calculations at dimeric model stage. The propagation rate constant ratio of these monomers is calculated with various density functionals. Calculations shed light on the electronic and steric effects and hydrogen bonding interactions within the reactive species that co-play a role in determining the favorable modes of additions.

The linear rheology of unentangled Maxwellian transient networks formed from reversibly associating telechelic polymers can be characterized by a plateau modulus and a shear relaxation time. The concentration dependences of both these properties have been modeled using a variety of theories. An expression is introduced here that allows the concentration dependence of shear relaxation time to be determined (to within a constant, the microscopic chain lifetime) directly from the concentration dependence of the plateau modulus, subject to some approximations. This prediction is tested against experimental results for hydrophobic ethoxylated urethane (HEUR) and against results of simple-model simulations. The nature of the approximations needed to derive this relationship and the scope of its applicability are discussed.

**A simple equation relating the microscopic lifetime of associating chains in a transient network to the shear stress relaxation time,** in terms of the concentration dependence of the plateau modulus, is proposed and tested against published experimental data on associating polymers near the gelation transition and against simulated networks well above the gelation transition.

The statistical description of a polymer chain within the nematic system of many chains is considered. The chain entropy and free energy are numerically calculated on the basis of fundamental definitions. No constraints are imposed on the elongation of the chain end-to-end distance, which can change from zero to a value for maximally stretched chains, or on the strength of the internal nematic interactions within the system. Obtained results are compared with those calculated by approximate formulas for varying strength of interactions and length of chains.

Numerical exact calculations show that for long chains the chain end-to-end probability can be Gaussian or non-Gaussian. It depends on the intensity of the orienting interactions inside the system of chains. That result verifies often accepted assumption that long chains are always Gaussian.

Reactive blending of PET and PEN has been simulated by numerical integration of kinetic differential equations and Monte Carlo (MC) approaches. Accurate modeling of transesterification reaction at different temperatures, times, and PET/PEN feed compositions assured precise control of architecture of PET–PEN copolymer chains. Microstructural features like the number and weight distribution of ethylene terephthalate and ethylene naphthalate segments, molecular weight distribution, and polydispersity were monitored. The developed MC code can satisfactorily capture the extent of reaction, the randomness coefficient of PET–PEN copolymers, and compositional variations as found by ^{1}H-NMR.

**A detailed information on microstructural evolutions during reactive blending of PET and PEN based on fitting of results of numerical integration of differential equations and Kinetic Monte Carlo simulations** to experimental data is reported. A broad understanding of transesterification kinetics which enables precise control of architecture of PET-PEN copolymer chains during reactive blending is provided.

Surface-initiated controlled radical polymerization, such as ATRP, has been proven to be a powerful method for preparation of well-controlled functional grafted polymers. There are thousands of experimental works published, by varying polymers, surfaces, and applications. In comparison, theoretical developments are very lacking. Many fundamental questions still remain to be answered. These questions include, but not limited to: What determine the surface initiator efficiency? How many chains per square nanometer can be fully grown? What is the maximum thickness can polymer grow to? If chains are simultaneously grown from surface and solution, which has higher molecular weight? Answers to these questions are most helpful for innovation and further development in this important area. In this work, we employed recently developed theories to explain experimentally observed kinetic profiles of polymer layer thickness growth. What limits the growth of surface chains? Is it the monomer starvation in grafting layer that slow down propagation? Or is it the termination of radicals that stop the chain growth? It was found that no existing models could fully explain the often contradictory experimental observations. It is our hope that this work will provoke further discussions and inspire more effort in resolving the fundamental issues of this area.

This paper discusses a fundamental question: how thick can a polymer layer grow to in surface-initiated ATRP (SI-ATRP)? or equivalently, what limits the growing of chains from surface? Two models developed from existing theories are compared to experiment trends from literature. It is shown that the current understanding of the mechanism behind SI-ATRP is still incomplete and requires further investigations.

Star polymers with arms of two different homopolymers with a weak mutual attraction have been investigated using a coarse grained polymer model and Monte Carlo (MC) simulations. The effect of the polymer architecture on the complexation behavior has been studied for various numbers of arms (up to 8) starting from a diblock copolymer and compared to diblock copolymers as well as alternating linear copolymers. It was found that the star architecture promotes an internal complexation, which is indicated by a reduction of the end-to-end distance of the polymer chains. The local concentration of the weakly attractive partners is important to promote their interaction and to harvest the attraction. The results were compared to experimental data.

**Polymeric systems consisting of two different weakly attractive components are investigated using Monte Carlo simulations, comparing various architectures.** When arranged in a miktoarm star polymer, complexation is promoted compared to a linear block copolymer and a strictly alternating copolymer.

Influence of size and shape of simulation box on lamellar morphology in DPD simulation is systematically studied. The 3D Voronoi Tessellation and cluster analysis is employed. It is shown that orientation and number of lamellar planes determines the value of lamellar spacing in box with periodic boundary conditions. The role of initial conditions and relaxation scenario on lamellar morphology is also studied. Scaling the box dimensions and equalizing the diagonal pressure tensor components is used to obtain natural lamellar spacing. Where the estimation of natural lamellar spacing is unclear, the intersection of the off-diagonal components of the pressure tensor is used. Finally, examples where maximum lamellar spacing achieved by scaling of the box is smaller than the natural lamellar spacing are presented.

**Commensuration of lamellar morphology and simulation box** is studied by means of dissipative particle dynamics. The lamellar spacing is found to be influenced by incommensurability effect even for large cubic simulation boxes. The adjusted box dimensions and components of pressure tensor are used for estimating the natural lamellar spacing for generally oriented lamellar planes.

We examine the simplest relevant molecular model for large-amplitude oscillatory shear flow of a polymeric liquid: The dilute suspension of rigid dumbbells in a Newtonian solvent. We find explicit analytical expressions for the orientation distribution, and specifically for test conditions of frequency and shear rate amplitude that generate higher harmonics in the shear stress and normal stress difference responses. We solve the diffusion equation analytically to explore molecular orientation induced by oscillatory shear flow. We see that the orientation distribution is neither even nor odd. We find zeroth, first, second, third, and fourth harmonics of the orientation distribution, and we have derived explicit analytical expressions for these. We provide a clear visualization of the orientation distribution in large-amplitude oscillatory shear flow in spherical coordinates all the way around one full alternant cycle. The Newtonian distribution is nearly isotropic, the linearly viscoelastic, only slightly anisotropic, and the nonlinear viscoelastic, highly anisotropic.

**We examine the simplest relevant molecular model for large-amplitude oscillatory shear flow of a polymeric liquid: the dilute suspension of rigid dumbbells in a Newtonian solvent.** We find explicit analytical expressions for the orientation distribution, and use these expressions to examine the detailed shape of the orientation distribution with detailed visualizations all the way around one full alternant cycle.

A Markovian model is proposed to investigate the complex molecular buildup processes during the self-condensing vinyl polymerization. The weight-average chain length is represented by the analytic formula, . By application of the Markovian model to the Monte Carlo method, one can investigate the structure of the polymer formed one by one, and the full distributions of chain lengths, degrees of branching, and molecular dimensions are investigated. When the polymer molecules are fractionated by the chain length, the universal curves for the degree of branching, and the molecular dimension, which do not change during the course of polymerization were discovered.

**A Markovian model is proposed for the self-condensing vinyl polymerization (SCVP), to investigate the full distributions of chain lengths, degrees of branching, and molecular dimensions.** When the polymer molecules are fractionated by the chain length, the universal curves for the degree of branching, and the molecular dimension, which are invariant during the course of polymerization were discovered.

Within the broad class of hyperbranched polymers, highly symmetrical objects (such as dendrimers and Vicsek fractals) are of special theoretical interest. Here we study, using the MARTINI force-field, polyamidoamine Vicsek fractals (PVF) in silico, focusing on their structure and dynamics in dilute solution. Our extensive microsecond-long simulations show that the radius of gyration of PVF scales with the molecular weight as *N*^{0.54}, behavior rather close to that of stars and considerably distinct from that of dendrimers. The study of the radial density profiles indicates that different parts of the PVF interpenetrate significantly, fact which stresses the soft and sparse character of PVF. These results are also supported by our findings for the rotational autocorrelation functions.

**Highly symmetrical, deterministic structures are important representatives for hyperbranched macromolecules; in particular, fractal structures cover a broad class of model polymeric systems.** Here, polyamidoamine Vicsek fractals are studied by employing extensive molecular dynamics simulations along with the coarse-grained MARTINI force-field to unravel their structural and dynamic characteristics in dilute solution.

For the simple ABC linear terpolymer composed of a solvophilic A block and two solvophobic B and C blocks, the solution-state self-assembly is systematically investigated by dissipative particle dynamics (DPD) simulations, and several complex multicompartment micelles beyond the conventional wisdom, such as helix-on-sphere, cage, ring, bowl, raspberry-onion and so on, are predicted from the simulations. The detailed phase diagrams clearly point out the regions of building these complex multicompartment micelles. Thus, the complex multicompartment micelles can be obtained from the simple linear ABC terpolymers. This work advances the molecular-level understanding of multicompartment micelles from the simple linear ABC terpolymers, which will be useful for the future application of novel micelles.

**Rich multicompartment micelles,** such as raspberry-onion, helix-on-sphere, cage, ring, worm, bowl, can be formed by the self-assembly of the simplest linear ABC terpolymers in solutions, which is beyond the traditional understanding.

Randomly branched Gaussian chains, including regular and random stars, were modeled. The chains were generated by repeated random movement of the end-point in a cubic grid. The radius-of-gyration- and viscosity-volume branching indexes, *g* and *g*′, were calculated for randomly branched molecules and compared with the data taken from the literature. The dependence of *g*′ on *g*, constructed from our data as well as from those by Kurata and Fukatsu, appears linear. The experimental data taken from the literature do not contradict this finding. On the other hand, the values of the branching exponent *ϵ* are highly scattered and a reliable average cannot be found. This findings support the value of the branching exponent of *ϵ* = 1, relating *g* and *g*′, proposed also by other authors.

**Numerically calculated values of hydrodynamic branching index in dependence of the radius-of-gyration branching index, g**

**Cover:** Morphological transformations of polyelectrolyte self-assembled structures in aqueous solutions are identified in response to the change in solvent ionic strength, through the application of a newly developed implicit solvent ionic strength (ISIS) model for a dissipative particle dynamics (DPD) method. Further details can be found in the article by N. K. Li, W. H. Fuss, and Y. G. Yingling* on page 7.

Herein, a new coarse-grained methodology for modeling and simulations of polyelectrolyte systems using implicit solvent ionic strength (ISIS) with dissipative particle dynamics (DPD) is presented. This ISIS model is based on mean-field theory approximation and the soft repulsive potential is used to reproduce the effect of solvent ionic strength. The capability of the ISIS model is assessed via two test cases: dynamics of a single long polyelectrolyte chain and the self-assembly of polyelectrolyte diblock copolymers in aqueous solutions with variable ionic strength. The results are in good agreement with previous experimental observations and theoretical predictions, which indicates that our polyelectrolyte model can be used to effectively and efficiently capture salt-dependent conformational features of large-scale polyelectrolyte systems in aqueous solutions, especially at the salt-dominated regime.

**The newly developed ISIS DPD model with implicit representation of the effect of salt concentration is applied** to explore the structural conformations of a long polyelectrolyte and micellization of polyelectrolyte block copolymers in aqueous solution.

Bayesian design of experiments can be very useful for complex polymerizations and other chemical engineering processes. The technique has many practical benefits; it incorporates prior information, allows for adjustment of design levels, increases the information content, and optimizes experimental resources. In this work, Bayesian design is applied to the simulated emulsion copolymerization of NBR in a series of CSTRs. Statistical comparisons show that the Bayesian design is as good as (or better than) standard design techniques. This makes the Bayesian design superior overall, as it provides the extra flexibility of designing sequences of fewer trials and an increased information content.

**Bayesian design of experiments is a sequential, iterative, optimal and versatile technique that can be applied to complex polymerizations.** In this work, it is applied to a simulated emulsion acrylonitrile butadiene rubber production in a series of CSTRs. Bayesian design results can reduce the experimental effort considerably, and are in tune with process understanding and reaction fundamentals.

The effect of fragmentation rate of a catalyst/polymer particle and diffusivity ratio inside cracks to fragments on reaction rate and molecular weight distribution are studied. A split algorithm is developed to reduce the computational cost and make it possible to simulate fragmentation on a normal PC computer. The simulation results show that the fragmentation rate and diffusivity ratio have a considerable effect on the polymerization rate and molecular properties of the polymer. In fragmentation process, the radial cracks play an important role to feed monomer into the particle to increase the reaction rate. To evaluate the accuracy of split algorithm, its results are compared with a normal method of solution for sample cases. The developed 2D model is also validated on a benchmark problem.

**The effect of fragmentation rate of a catalyst/polymer particle and diffusivity ratio inside cracks to fragments on reaction rate and molecular weight distribution are studied.** A split algorithm is developed to reduce the computational cost. In fragmentation process, the radial cracks play an important role to feed monomer into the particle to increase the reaction rate.

A combined study of experimental and molecular dynamics (MD) simulation methods is presented for hindered phenol AO-80/nitrile-butadiene rubber/poly(vinyl chloride) (AO-80/NBR/PVC) composites with different AO-80 contents to establish the microstructure-damping property relations. MD simulation found that the AO-80/NBR/PVC composite (abbreviated as AO-80/NBVC) with an AO-80 content of 99 phr had the largest hydrogen bonds (H-bonds) and highest binding energy, indicating a good compatibility between NBR and AO-80 and good damping performance of AO-80/NBVC composites. Experimental results from SEM, DSC, and DMA were in good agreement with the MD simulation results. The tensile test results showed that the AO-80/NBVC composite with an AO-80 content of 99 phr had high tensile strength because of the strong H-bonds of the composites and the disintegration and reintegration of the H-bonds. The MD simulation technique proves to be a promising tool for the design and prediction of high damping properties of advanced composites in a microscopic view.

**By combining molecular dynamics simulations and experiment, hydrogen bonds interaction and microstructures are investigated** in AO-80/NBVC composites. An attempt is made to establish microstructure-property relationships for elucidating the damping mechanism by experimental and MD simulation methods.

Monte Carlo simulation methods are suitable for free radical polymerizations (FRP) even when there is significant chain length dependence of the reactions. For each simulation step the probability of each possible reaction is determined at that point in time. In FRP modeling most of the computation time is spent on radical propagation. We demonstrate a hybrid simulation method where the propagation reaction is treated using differential equations and other reactions (e.g. termination and initiation reactions) are treated stochastically. This allows significant reductions in simulation time while maintaining the features of complete Monte Carlo methods. This approach can be applied to more complex polymerization reactions like branching and crosslinking using Monte Carlo methods within manageable times.

**An hybrid stochastic simulation approach for free-radical polymerization reaction is demonstrated which is** significantly faster than complete Monte Carlo simulation methods while maintaining all the features of complete Monte Carlo apprach. Also, appropriate simulation volume for the simulation of free-radical polymerization is derived.

The creep-tensile fatigue relationship is investigated using MD simulations for amorphous polyethylene, by stepwise increasing the *R*-ratio from 0.3 for fatigue to an *R*-ratio = 1 for creep. The simulations can produce similar behavior as observed in experiments, for instances strain-softening behavior and hysteresis loops in the stress-strain curves. The simulations predict the molecular mechanisms of creep and fatigue are the same. Fatigue and creep cause significant changes of the van der Waals and dihedral potential energies. These changes are caused by movements of the polymer chains, creating more un-twisted dihedral angles and the unfolding of polymer chains along the loading direction.

**The creep–tensile fatigue relationship is investigated using MD simulations for amorphous polyethylene.** Increasing *R*-ratio of fatigue reduces mean strain while creep produces the lowest mean strain. Fatigue and creep cause significant changes of the van der Waals and dihedral potential energies. Polymer chains move creating more un-twisted dihedral angles and the unfolding of polymer chains along the loading direction.