This paper presents a mathematical model to describe the evolution of the molecular weight distribution (MWD) in vinyl chloride (VCM) free-radical suspension polymerizations performed with a bifunctional initiator, 1,3-di(2-neodecanoylperoxyisopropyl) (DIPND). The model yields, as a function of time, the mass balances for the distinct phases, the monomer conversion, the number- and mass-average molecular weights and the complete MWD of both the growing and dead polymer chains. In order to describe the MWD, the model uses probability generating functions (pgf) to transform the mass balance equations into a reduced and finite set of model equations. As shown throughout many examples, the MWD's of the final polymer resin is little sensitive to the presence of the linear symmetrical bifunctional initiator.

**The molecular weight distributions of different macromolecular species are illustrated formed during** vinyl chloride polymerizations performed with a bifunctional initiator, as calculated with the proposed pgf (probability generating function) model.

A novel hybrid simulation approach is developed, which combines the advantages of deterministic and stochastic modeling of complex polymerization networks. The fast deterministic simulation solves the heat and pressure balances and generates position-dependent event frequency profiles. The detailed stochastic simulation is used as add-on and offers a deep insight into the polymeric microstructure of each macromolecule. Our hybrid simulation approach is applied to high-pressure ethylene polymerization in industrial tubular and continuous autoclave reactors with peroxide initiation. But in general, the presented approach can be used for all types of polymerization reactions in ideal and non-ideal reactors of any kind.

**A novel hybrid simulation approach is developed, which combines the advantages of deterministic and stochastic modeling of complex polymerization networks.** The algorithm is applied to high-pressure ethylene polymerization in industrial tubular and continuous autoclave reactors with peroxide initiation. But in general, the presented approach can be used for all types of polymerization reactions in ideal and non-ideal reactors of any kind.

We estimate the comonomer content in random copolymers, through the use of semi-empirical models. We extend the model of Anantawaraskul et al. by expanding the number of model parameters from 4 to 9. Using available data on well-characterized ethylene/1-hexene copolymers, we randomly select a subset to train the model, and regress model parameters. We test the ability of the parametrized model to infer comonomer content on the rest of the data. We quantify the predictive ability by exploring the effect of the quantity and quality of the training data. The accuracy and precision of the inference improve as the amount of training data increases, and as datasets span the domain more evenly.

**Uncertainty in the estimation of comonomer content (CCD)** is characterized in random copolymers using Crystaf. We ask questions such as: (i) how often is the estimated CCD within a specified range of the true value? (ii) what is the variability in the inferred CCD? (iii) how does model parameterization affect the predictions?

Self-assembly behaviors of rod–coil–rod triblock copolymers in the selective solvent are systematically investigated by dissipative particle dynamic simulations. Three selective solvents are considered: the pure coil-selective solvent, the pure rod-selective solvent, and the mixed solvent. The concentration-induced morphologies and morphological transition affected by the rod and coil length are examined. The micelle adopts the overall shape of sphere, nematic bundle, worm, cylinder, lamella, coil-, and rod-aggregated hollow cylinders, and network. In the coil-selective solvent, increasing coil length can defer the phase transition from sphere to other morphologies while increasing rod length can advance the transition. In the rod-selective solvent, an opposite influence rule is found.

**The interesting morphologies from the self-assembly of rod–coil–rod triblock copolymers in solvents are investigated and the rules of phase transition driven by the concentration are obtained.** The findings have the possible relevance for the design and fabrication of optoelectronic materials.

A hierarchy of models for self-avoiding polymer chains on the tetrahedral lattice is introduced. The chain comprises a concatenation of identical atoms. The models (SAW_{n}), are characterized by the degree of self-avoidance (specified by the integer *n*), which is controlled by systematic variation of the closest distance allowed between atom pairs that are not covalently bonded. SAW_{1}, possessing the lowest degree of self-avoidance, is the simple self-avoidance model (i.e., no two atoms of the chain occupy the same site) that has been routinely employed in studies of fundamental phenomena. The results of Monte Carlo calculations are presented that show the influence of *n* on such properties of the chain as Flory radius, distribution of dihedral angles, and entropy loss due to self avoidance. Algorithms are developed that allow the efficient generation of large ensembles of chain conformations, which are necessary especially for a reliable calculation of the entropy loss induced by self-avoidance.

**Atomistic self-avoiding tetrahedral-lattice based polymer models are introduced, featuring bond and torsion angles suitable for chemical polymer backbone architecture.** The self-avoidance is generalized to mimic realistic non-bonded atom distances. Efficient Monte Carlo algorithms are developed to generate polymers of several hundred atoms.

Analytic solution for the weight-average chain length in a matrix formula, , is derived for free-radical polymerization with simultaneous long-chain branching and scission. Illustrative calculations are conducted for a batch polymerization. With bimolecular termination by combination, gelation could be observed. Assuming the same polymerization kinetics for branching and scission in the post-gel period, the formed gel molecule could be degenerated into sol molecules again, i.e., degelation might occur. Both the gelation and degelation points are defined as the point when the largest eigenvalue of **M** is unity. The matrix formula is suitable to determine accurate values, while the Monte-Carlo simulation can give much more detailed information. These two approaches are nicely complementary.

**Analytic solution for the weight-average chain length in a matrix formula,** , is derived for free-radical polymerization with simultaneous long-chain branching and scission. Illustrative calculations are conducted for a batch polymerization, which agree with the Monte Carlo simulation results. With a particular set of parameters that involves combination termination, both gelation and degelation were observed during the course of polymerization.

The phase behavior of blends of A-b-B and A-b-C diblock copolymers with opposite self-assembly tendencies are studied, where the former exhibits the assembly upon heating and the latter shows the assembly upon cooling. A compressible random-phase approximation (RPA) theory and a Ginzburg–Landau simulation based on the RPA are first extended to such copolymer blends. It is shown that a delicate balance in self and cross interactions between constituent monomers can yield various phase behaviors covering the assembly upon heating, loop-type assembly, and assembly upon cooling by varying the blend composition. In particular, the loop-forming blend reveals the tremendously enhanced pressure sensitivity of the ordering temperatures, which can prove useful in pressure-related nanofabrication.

**Theoretical analysis is performed on the stability and equilibrium morphologies of blends of A-b-B copolymer exhibiting self-assembly upon heating and A-b-C copolymer exhibiting reverse assembly upon cooling.** The A-b-B/A-b-C blends reveal all possible self-assembly behavior spanning from self-assembly upon heating to a closed loop, and then to self-assembly upon cooling. The loop-forming blend shows tremendously enhanced pressure sensitivity.

A mathematical model for the kinetics of copolymerization with crosslinking of vinyl/divinyl monomers in the presence of ARGET ATRP controllers is developed. A reaction scheme considering multifunctional polymer molecules, which results in a tridimensional problem, is proposed. Molecular weight development during the pre-gelation period is calculated using the method of moments. Flory-Stockmayer's theory is used for the post-gelation period. The ATRP solution copolymerization of methyl acrylate (MA) and ethylene glycol diacrylate (EGDA) is used as a case study and test of the model. Good agreement between predicted profiles and experimental data from the literature is obtained.

**Polymer network formation by ATRP of vinyl/divinyl monomers is adequately described using a multifunctional polymer molecule approach.** The model is validated with experimental data for ATRP of MA/EGDA at 60 °C. The evolution of living and dormant radical distribution indices (LRDI and DRDI) shows the importance of using a multifunctional modeling approach.

**Cover:** Molecular modeling and molecular dynamics simulations are shown to be capable of predicting the thermal degradation temperature of crosslinked thermosetting polymers and nanocomposites produced therefrom. Further details can be found in the article by A. Baggott, J. R. Bass, S. A. Hall, I. Hamerton, B. J. Howlin,* L. Mooring, and D. Sparks on page 369.

The mechanisms of H-transfer in termination reactions, and the role of fluorine interactions to achieve the living polymerization of olefins, are investigated. Mecking's bis(enolatoimine)Ti catalysts are considered, with or without *ortho*-F substituents. DFT calculations are performed on a parallel platform. The stationary structures are localized and energy barriers of activation are determined. Normal mode analysis is carried out and free energies are calculated. Different mechanisms can be involved in the termination: in all cases, the presence of F atoms rise the energy barrier of activation, according to experimental observations of living polymerization. The stabilizing role of the fluorine *o*-F · · · H bonds in the equilibrium species, and destabilizing *o*-F · · · H and *o*-F · · · *o*-F interactions in the transition states, are discussed.

**H-transfer terminations during homogeneous olefin polymerization are of great importance** for the understanding of the living behavior, and for the design of new catalysts. Several pathways are possible for Mecking's catalysts, and the unpredicted transfer to the ligand is the most favorable one.

Despite their inability to model bond breaking molecular dynamics simulations are shown to predict thermal degradation temperatures of polycyanurate (cyanate ester) homopolymers and nanocomposites in very close agreement with experimental data. Simulated polymer density, used to predict *T*_{g} also shows a reduction within the same temperature range as experimental values for the thermal degradation.

**The thermal degradation temperatures ( T**

We extend a previously introduced coarse-grained computer model for the simulation of the amplitude and frequency dependence of dynamic moduli in filled elastomers. An algorithm is developed, which allows the generation of close to realistic filler structures. The latter significantly influences the compounds mechanical properties, in particular above a certain threshold concentration, where the mixing process causes the formation of a spanning filler network. Its basic units are “unbreakable” aggregates consisting of primary filler particles. The aggregates form, by comparison, loosely bound agglomerates, which in turn form the network largely responsible for the final compound's mechanical properties. We study the breakup of the network on the level of the agglomerates under mechanical stress and the attendant reduction of the storage modulus including its relation to the network structure.

**A coarse-grained model for the simulation of dynamic moduli in filled elastomers is developed, allowing the generation of close to realistic filler structures.** The breakup of the network on the level of the agglomerates under mechanical stress and the attendant reduction of the storage modulus including its relation to the network structure are studied.

An advanced Monte Carlo (MC) model is developed to predict the molecular weight distribution and branching level for arborescent polyisobutylene produced in a batch reactor via carbocationic copolymerization of isobutylene and an inimer. This new MC model uses differential equations and random numbers to determine the detailed structure of dendritic polymer molecules. Results agree with those from a traditional MC model for the same system, but the proposed model requires considerably less computational effort. The proposed MC model is also used to obtain information about polymer segments between branch points and dangling polymer segments.

**An Advanced Monte Carlo (MC) model is developed to predict branching and molecular weight development when isobutylene is copolymerized with an inimer**. This MC model combines differential equations and random numbers to determine the detailed structure of arborescent polymer molecules. Results agree with those from a traditional MC model and are generated using considerably less computational effort.

A simulation strategy for the creation of equilibrated nanostructured copolymer melt morphologies is proposed. Molecular dynamics simulations of bead-spring chains with a soft pair potential are used for efficient modeling of phase separation, while preserving Gaussian chain statistics and chain conformations of an underlying microscopic model. In a second step, hard excluded volume interactions are reintroduced that match the copolymer segregation strength but only require reequilibration of local packing structure. We show that substantial computational gains can be achieved for equilibrating moderately entangled bead-spring polymers. The resultant configurations can be used for further studies of structural and mechanical properties in melts or glasses.

**Block copolymer morphologies are simulated efficiently in a multiscale approach that utilizes soft interactions for fast** equilibration of entangled chains, followed by reinsertion of a microscopic model while preserving chain conformations and statistics.