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.

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.

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.

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.

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.

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**

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.

**Front Cover:** A model that can predict the evolving molecular weight distributions of star polymers undergoing mechanochemical degradation is developed. In the foreground of the cover image, a 3D plot shows the distributions obtained with this model for a theoretical four-arm star polymer. In the background, the equations pertaining to the model are presented. Further details can be found in the article by G. I. Peterson and A. J. Boydston* on page 555.

Structured polymers offer a means to tailor transport pathways within mechanically stable manifolds. The building block of such a membrane is examined, namely a single large pentablock co-polymer that consists of a center block of a randomly sulfonated polystyrene, designed for transport, tethered to poly-ethylene-*r*-propylene and end-capped by poly-*t*-butyl styrene, for mechanical stability, using molecular dynamics simulations. The polymer structure in a cyclohexane-heptane mixture, a technologically viable solvent, and in water, a poor solvent for all segments and a ubiquitous substance is extracted. In all solvents the pentablock collapsed into nearly spherical aggregates where the ionic block is segregated. In hydrophobic solvents, the ionic block resides in the center, surrounded by swollen intermix of flexible and end blocks. In water all blocks are collapsed with the sulfonated block residing on the surface. Our results demonstrate that solvents drive different local nano-segregation, providing a gateway to assemble membranes with controlled topology.

**The conformation of a structured pentablock ionic polymer** in a mixture of cyclohexane and heptane and in water is demonstrated. In the mixed solvent, the flexible and end blocks are swollen while the sulfonated polystyrene center block is collapsed. In water, all the blocks of the pentablock are collapsed into a nearly spherical shape.

Theoretical considerations and Monte Carlo simulations prove that small size of droplets narrows dispersity of chains in both chain and step polymerizations. Equations describing the chains lengths distribution in living polymerization carried out in nano-droplets are derived, proving to be the binomial distribution function. The effect of lowering of polymer dispersity in irreversible polycondensation is predicted as well.

**Confining of the polymerization system into small droplets** results in narrowing of the chain-length distribution. When the number of growing chains in living polymerization equals to 2 then its variance is twice lower than of the Poisson distribution. When in irreversible step polymerization the number of remaining chains reaches 2 then polymer has a uniform (rectangle) distribution with dispersity equal to 1.33.

A model for predicting the molecular weight distributions of mechanochemically degraded star polymers has been developed. The model was shown to be in good agreement with experimental distributions and average total molecular weights obtained from ultrasonically degraded three-arm star poly(methyl acrylate)s. Generalization of the model to four- and *n*-arm star polymers was also achieved. The models are straightforward to use, and thus, all calculations were completed in Microsoft Excel.

**A predictive model for the evolution of molecular weight distributions of star polymers during mechanochemical degradation has been developed.** The predicted distributions are in good agreement with experimental results for three-arm star polymers.

It is challenging to track explicit copolymer sequences and related measures using continuum kinetic models. We developed a generalized framework based on kinetic Monte Carlo (KMC) to model free radical polymerization of any number of monomers to obtain the explicit sequence and its distribution. The KMC framework was applied to copolymerization of butyl acrylate/methyl methacrylate (BA/MMA) and methyl acrylate/methyl methacrylate (MA/MMA), and the simulation output was compared with experimental results. Sequence characteristics that were not accessible via experiments were then predicted. Explicit monomer sequence information was used to construct operating diagrams to design a representative copolymer recipe with a specific sequence target as a function of molecular weight and monomer conversion.

**Kinetic Monte Carlo simulations allow sequence characteristics to be tallied and used in the design** of copolymers with specific sequence measures as dictated by the feasible operating diagram shown here.

The lattice density functional theory (LDFT) is used to describe the substrate effect on the phase behavior of polymer brush grafted on different substrates. The LDFT predicts that: both attractive and repulsive interactions between the substrate and the polymer chains have effects on the thickness of brushes; when the short-range monomer–substrate interaction is larger than a certain value, the thickness and density profiles of polymer brushes almost do not change. And also an attractive substrate can increase the critical grafting density of pancake to brush transition. For temperature responsive polymer brushes, the temperature transition points are almost the same with different substrates, however, an attractive substrate can increase the swelling ratio and a repulsive substrate can decrease the swelling ratio. We also find that an increasing grafting density can decrease the substrate effect on the swelling behavior of temperature responsive polymer brushes.

**The substrate effect on the phase behavior of polymer brush is studied by LDFT.** An attractive substrate increases the swelling ratio of thermally sensitive brushes, while a repulsive substrate decreases the swelling ratio. Additionally, the increasing grafting density decreases the substrate effect on polymer brushes.