This study considers step-growth polymerizing systems of general type “AfiBgi” whereby one or more of the reacting monomer species bear at least three reactive groups. The random polymerization process will lead to a population of polymer molecules in which the individual molecules may differ widely with respect to degree of polymerization and number of branch points. This study presents an algorithmic method to calculate the statistical distribution of weight over these two molecular properties. The method uses bivariate generating functions, recurrences, and integer arithmetic.

**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 straight to the bivariate (molecular size) × (number of branch points) weight distribution.

In this work, the combined iterative Boltzmann inversion/conditional reversible work scheme is extended with a little modifications to derive the systematically coarse-grained (CG) potentials for simulating two typical atactic polymer blends composed of poly(methyl methacrylate) (PMMA) and poly(vinyl chloride) (PVC) or polystyrene (PS). Molecular dynamics simulations are extensively performed on the two blends with a wide formulation range. It is revealed by these simulations that, throughout the entire composition range, the PMMA/PVC blend is homogeneous whereas the PMMA/PS blend undergoes phase separation, which agrees well with the experimental observation that the former exhibits strong interactions that are absent in the latter. Depending upon the formulation, the immiscible PMMA/PS blend presents one single- or double-continuous phase. It is further confirmed that intermolecular interactions play the key roles in forming the phase morphologies, which in turn can be inferred from only the three nonbonded CG potentials of one unlike pair and two like pairs.

**The systematically coarse-grained models** are employed for simulating the two binary polymer blends comprised of poly(methyl methacrylate) and poly(vinyl chloride) or polystyrene by the molecular dynamics simulation method, which reproduces the phase behaviors that can be predicted by only the features of the three pair potentials involved in the system since the intermolecular interactions play the key roles.

A Monte Carlo study has been performed for protonated and non-protonated coarse-grained PAMAM-EDA of generations (*G*) ranging from 2 to 6. This study calculates sizes, asphericities, and global and external dendrimer density profiles that confirm features previously found in other studies. It is shown that form factors do not change significantly with protonation. Diffusion coefficients, intrinsic viscosities, and Rouse relaxation times are computed as conformational averages. The hydrodynamic properties and their change with protonation are in good agreement with available experimental data. Some differences between the neutral and protonated molecules are noticeable in the case of the relaxation times corresponding to the higher generation numbers (*G* > 4). These features indicate that pH may play a role in the internal dynamics of dendrimers. The complex modulus curves have also been computed. When in reduced units to discount size effects, the protonation effect is seen to be very small.

**A Monte Carlo study** is performed for different properties of PAMAM-EDA dendrimers using a coarse-grained model. This study calculates different equilibrium properties and gives theoretically-based estimations of hydrodynamic and dynamic properties. A discussion of the influence of protonation is included together with a comparison with existing experimental data.

In this work, the structure of a strictly 2D dense polymer film for some model copolymer systems: diblock, triblock, and random copolymers is studied. An idealized model of these macromolecular systems is developed where positions of polymer beads are restricted to vertices of a simple cubic lattice and chains are under good solvent conditions (the excluded volume is the only interaction between beads of the chain and solvent molecules). The properties of the system are determined by means of Monte Carlo simulations with a sampling algorithm based on chain's local cooperative changes of conformation. Scaling of the chain size is studied and the influence of the polymer concentration on the chain's size and shape is discussed. The differences and similarities in the behavior of the percolation thresholds of one component in chains with different bead sequences are also shown and discussed. The percolation threshold is found to be weakly dependent on the chain length and more sensitive to the total polymer concentration.

**A model of 2D copolymer systems with explicit solvent molecules** is simulated and its structure is discussed. Percolation thresholds for different sequence in chain are determined.

In a recent paper, a new structural model of polyaniline (PANI) doped with camphorsulfonic acid (CSA) obtained by molecular dynamics simulations is proposed. This model is characterized by double layers of PANI separated by double layers of CSA. Here some new evidences for the correctness of the new model are shown, drawn from the comparison of its calculated diffraction patterns with experimental data. First, the powder diffraction patterns are calculated from the Debye formula and by a custom algorithm. This makes it possible to describe the anisotropy of all diffraction peaks by giving their pole figures. The orientations of all crystal planes and their indexations (obtained independently from the average orthorhombic unit cell proposed for the model structure) are consistent, and this description agrees well with already published results of experimental study of PANI/CSA thin films performed with the use of synchrotron radiation surface diffraction technique.

**The new structural model of polyaniline protonated with camphorsulfonic acid** is investigated using various methods. The Debye formula and a custom algorithm are applied to calculate the X-ray diffraction pattern. Pole figures are calculated using two different methods. All these various approaches are consistent with each other and with experimental data. This shows that the model exhibits very important features.

Dissipative particle dynamics simulation is employed to study the chain exchange kinetics between micelles of diblock copolymer in aqueous solution via in silico hybridization method. One focus is placed on the effect of chain flexibility on the dynamic behavior by varying the spring constant in the bead-spring model. The length ratio of hydrophilic to hydrophobic block is also varied. It is found that chain expulsion/insertion is the dominant mechanism in the chain exchange process. The most interesting finding is the multimodal relaxation behavior for the chain exchange and expulsion when the spring constant is small or the length ratio of hydrophilic to hydrophobic block is large. This phenomenon is due to an increase in size polydispersity of micelles with rising population of small aggregates/micelles, for which the exchange kinetics is faster. Micelles with larger aggregation numbers (>10) are found to follow single exponential relaxation kinetics.

**Multimodal relaxation arises when the spring constant in the bead-spring model** is low or the length ratio of hydrophilic to hydrophobic block is large enough. This phenomenon is attributed to the increased size polydispersity of micelles with rising population of small micelles/aggregates, for which the dynamics is faster as compared to the larger counterpart.

A Kinetic Monte Carlo (KMC) simulation approach has been adopted in this study to capture evolutionary events in the course of free radical copolymerization, through which batch and starved-feed semibatch processes are compared. The implementation of the KMC code developed in this work: (i) enables satisfactory control of the molecular weight of the copolymer by tracking the profiles of concentrations of macroradicals, monomers, and polymer as well as degree of polymerization, polydispersity, and chain length distribution; (ii) captures the bivariate distribution of chain length and copolymer composition; (iii) comprehensively tracks and analyzes detailed information on the molecular architecture of the growing chains, thus distinguishing between sequence length and polydispersity of chains produced in batch and starved-feed semibatch operations; (iv) makes possible the screening of products, based on such details as the number and weight fractions of products having different comonomer units located at various positions along the copolymer chains. The aforementioned characteristics are achieved by stochastic calculations through code developed in-house. This KMC simulator becomes a very useful tool for the development of tailored copolymers through free radical polymerization, with blocks separated with single units of a different type.

**This study shows how to manipulate molecular architecture** in a general free radical copolymerization. An advanced Kinetic Monte Carlo (KMC) approach is employed as the design tool. The KMC approach allows us to screen and evaluate different designs of copolymer chains with various targeted chain lengths and comonomer sequence arrangements.

For mesoscale structural studies of polymers, obtaining maximum level of coarse-graining that maintains the chemical specificity is highly desirable. Here we present a systematic coarse-graining study of sulfonated poly(ether ether ketone), sPEEK, and show that a 71:3 coarse-grained (CG) mapping is the maximum possible map within a CG bead-spring model. We perform single chain atomistic simulation on the system to collect various structural distributions, against which the CG potentials are optimized using iterative Boltzmann inversion technique. The potentials thus extracted are shown to reproduce the target distributions for larger single chains as well as for multiple chains. The structure at the atomistic level is shown to be preserved when we back-map the CG system to re-introduce the atomistic details. By using the same CG mapping for another repeat unit sequence of sPEEK, we show that the nature of the effective interaction at the CG level depends strongly on the polymer sequence and cannot be assumed based on the nature of the corresponding atomistic unit. These CG potentials will be the key to future mesoscopic simulations to study the structure of sPEEK based polymer electrolyte membranes.

**A systematic coarse-graining scheme** is devised for hydrated sulfonated poly(ether ether ketone), to study membrane microstructure in larger systems. The coarse-grained (CG) mapping is the highest possible, within a CG bead-spring model. CG simulation of larger systems followed by back-mapping gives a relatively faster route to equilibration as compared to a fully atomistic counterpart.

The crosspropagation of 1-ethylcyclopentyl methacrylate (ECPMA) and methyl methacrylate (MMA) has been studied using a combination of quantum chemistry calculations and experiment. Our computational work utilizes a trimer-to-tetramer reaction model, coupled with an ONIOM (B3LYP/6-31G(2df,p): B3LYP/6-31G(d)) method for geometry optimization and an M06-2X/6-311+G(2df,p) method plus SMD solvation model for single point energy calculations. The results show several trends: the identity of the ultimate unit of a trimer radical affects not only the preferred conformation of the region where the reaction takes place, but also the reactivity of the radical; the addition of an ECPMA monomer to the radicals is generally favored compared to an MMA monomer; the pen-penultimate unit of a trimer radical shows a nonnegligible entropic effect; the penultimate unit effect is implicit for the ECPMA–MMA copolymer system. Finally, terminal model reactivity ratios fitted based on the explicit rate coefficients calculated from the quantum chemical results are compared with those from experimental measurements. The computations not only agree qualitatively with experimentally derived results in terms of the selectivity of ECPMA–MMA crosspropagation, but also give reasonable quantitative predictions of reactivity ratios.

**Understanding the kinetics of copolymerization of different methacrylates** is crucial for the development of their industrial applications. Quantum chemistry and a trimer-to-tetramer model is used to reveal the details of crosspropagation kinetics of 1-ethylcyclopentyl methacrylate and methyl methacrylate. Predicted terminal model reactivity ratios fitted from the calculations agree well with experimental data.

**Front Cover**: The glass transition behaviors and mechanical properties of the π-conjugated polymers, polyacetylene (PA) and poly(*para*-phenylene vinylene) (PPV), are predicted using atomistic simulations and compared with experimental measurements. The cover shows a molecular dynamics simulation box consisting of PPV molecules. The box, each side of which is about 7.4 nm, is filled with 60 polymer chains that are 40 monomer units long. The stresses generated upon subjecting the simulation box to small deformations are calculated employing force field parameters, and then used to determine the Young's modulus and the Poisson's ratio of the polymer. Also shown are representative data from nanoindentation measurements of PA and PPV at room temperature. Further details, including the temperature variations of the specific volumes, the cohesive energy densities, the torsion angle distributions, and the characteristic ratios of the two polymers, can be found in the article by Ramaswamy I. Venkatanarayanan, Sitaraman Krishnan,* Arvind Sreeram, Philip A. Yuya, Nimitt G. Patel, Adama Tandia, and John B. McLaughlin on page 238.

In surface-initiated atom transfer radical polymerization, knowledge of grafting density is of significant interest because it is one of the determining properties of grafted polymer. It is well known that not all of the immobilized initiators can grow into polymer chains. However, little is known about why this happens and what affects the grafting efficiency. The lack of information is partly due to the difficulty in experimental determination of grafting density on flat substrates. To circumvent the problem, Monte Carlo simulation with bond fluctuation model is used in this study to investigate the effects of various reaction conditions on the grafting density. The simulation results show lower grafting density when less deactivator is present. In systems with lower deactivator concentration, the number of monomer added per activation cycle is higher. Coupling this with close proximity of immobilized initiators results in chains initiated at earlier time to shield their neighboring initiator moieties from adding monomers, thus lowering the grafting density in such a system. These simulation results also provide an explanation to the seemingly conflicting trend reported in the literatures.

**Various factors affecting grafting density in surface-initiated atom transfer radical polymerization** are investigated through simulation approach. It is found that the final grafting density decreased as more monomer is added between one activation and deactivation cycle due to shielding. The results can be used in conjunction with termination theory to explain the conflicting experiment trends reported in the literature.

Eosin, a photosensitizer dye that can exist in multiple oxidation states, has been shown to initiate visible-light photopolymerizations of acrylates in open air when used in combination with tertiary amines. The exact mechanism behind this reactivity with micromolar concentrations of eosin in aqueous monomer solutions initially containing millimolar concentrations of oxygen has not been conclusively established, although pathways for regeneration of eosin in the presence of oxygen certainly play a role. In this work, a reaction–diffusion model incorporating a peroxy-mediated eosin-regeneration mechanism is built to explore the effects of oxygen diffusing into the system as the light-activated reaction proceeds. An oxygen concentration-dependent flux boundary condition is used to model the continuous replenishment of oxygen at the surface open to air as it is consumed by reaction. The model predicts the formation of a free radical concentration front that initially forms closer to the open surface and gradually moves toward the closed surface, with polymer film thickness increasing and the time required for polymerization to begin decreasing as the initial eosin concentration is increased. These results suggest that oxygen's dual role as both a free radical inhibitor and a precursor of the oxidizing species required for regeneration of eosin brings about interesting spatial variations when the reaction is carried out in a thin film geometry that is exposed to open air. In this case, an assumption of a well-mixed system is not appropriate and the kinetics of the reaction and conversion as a function of position are likely to depend on the geometry of the system.

**Eosin/tertiary amine-initiated photopolymerization in open air** using micromolar concentrations of eosin is simulated using a reaction–diffusion model. A peroxy-mediated eosin regeneration reaction is included into the reaction scheme and its effects on the temporal and spatial profiles of various pertinent species during polymerization are studied as oxygen diffuses into the reacting system.

Thermophysical and mechanical properties of two conjugated polymers, poly(*p*-phenylene vinylene) (PPV) and polyacetylene (PA), are predicted using molecular dynamics simulations and compared with results obtained from differential scanning calorimetry, nanoindentation, and dynamic mechanical analysis experiments. Glass transition temperature (*T*_{g}) is calculated from the changes in the slopes of the specific volume versus temperature and cohesive energy density versus temperature plots, obtained from constant pressure and constant temperature simulations (NPT ensemble). The effects of temperature on the torsion angle distributions and characteristic ratio are analyzed. PPV is found to have a *T*_{g} of 416 ± 8 K. PA does not exhibit a glass transition in the temperature range of 120 to 500 K. Using the static deformation method, the values of Young's modulus are calculated to be 1.81 ± 0.34 GPa for PA and 9.20 ± 0.57 GPa for PPV at 298 K. These values are in good agreement with the experimental measurements, validating the suitability of these techniques in the prediction of the polymer properties.

**Predictions of glass transition temperature** and Young's modulus of polyacetylene and poly(*para*-phenylene vinylene) from atomistic molecular dynamics simulations are compared with results from empirical measurements. Good agreement with differential scanning calorimetry and nanoindentation experiments are found.

The coil-globule transition of short hydrophobic-polar (HP) chains, composed of 24 hydrophilic monomers and 24 polar monomers, in solution and on hydrophobic surface and the adsorption of the HP chain on hydrophobic surface are simulated. The coil-globule transition point of the HP chain is dependent on sequence of chain but is roughly independent of the surface adsorption strength. Whereas the critical adsorption point of the HP chain is roughly independent of sequence. In addition, the lowest energy states can be obtained for the HP chain in solution or on surface by Monte Carlo simulated annealing method. Results show that the statistical conformation is strongly dependent on the intrachain H-H attraction strength and the surface adsorption strength.

**The coil-globule transition of short hydrophobic-polar (HP) chains,** composed of 24 hydrophilic monomers and 24 polar monomers, on hydrophobic surface is simulated by using Monte Carlo simulated annealing method. The coil-globule transition point is dependent on sequence of chain but is roughly independent of the surface adsorption strength. The lowest energy states can be obtained for the HP chain even on surface.

The crosspropagation of 1-ethylcyclopentyl methacrylate (ECPMA) and methyl methacrylate (MMA) has been studied using a combination of quantum chemistry calculations and experiment. Our computational work utilizes a trimer-to-tetramer reaction model, coupled with an ONIOM (B3LYP/6-31G(2df,p): B3LYP/6-31G(d)) method for geometry optimization and an M06-2X/6-311+G(2df,p) method plus SMD solvation model for single point energy calculations. The results show several trends: the identity of the ultimate unit of a trimer radical affects not only the preferred conformation of the region where the reaction takes place, but also the reactivity of the radical; the addition of an ECPMA monomer to the radicals is generally favored compared to an MMA monomer; the pen-penultimate unit of a trimer radical shows a nonnegligible entropic effect; the penultimate unit effect is implicit for the ECPMA–MMA copolymer system. Finally, terminal model reactivity ratios fitted based on the explicit rate coefficients calculated from the quantum chemical results are compared with those from experimental measurements. The computations not only agree qualitatively with experimentally derived results in terms of the selectivity of ECPMA–MMA crosspropagation, but also give reasonable quantitative predictions of reactivity ratios.

**Understanding the kinetics of copolymerization of different methacrylates** is crucial for the development of their industrial applications. Quantum chemistry and a trimer-to-tetramer model is used to reveal the details of crosspropagation kinetics of 1-ethylcyclopentyl methacrylate and methyl methacrylate. Predicted terminal model reactivity ratios fitted from the calculations agree well with experimental data.

Using systematic coarse-grained (CG) techniques such as iterative Boltzmann inversion (IBI) is an efficient means to simulate high molecular weight polymer melts within reasonable computational time. One drawback of such an approach is however the need to carry out extensive atomistic simulations in order to extrapolate the necessary distributions to derive the inter and intrabead force field parameters. Here it is shown that it is possible to use atomistic simulations of relative short oligomers to develop the CG model for high molecular weight polymers. In particular for the specific case of polycarbonates, it is found that the structural properties (end-to-end distance, radius of gyration and their distributions) are similar irrespective of whether the CG potentials are derived from 5-mer or 10-mer melt systems. Dynamical properties of the CG systems are smoother and faster than the atomistic ones. Scaling factor, derived by overlapping the CG mean square displacement curves (obtained from different CG IBI potentials) over the atomistic ones, also scales the autocorrelation functions. A prediction of the dynamical scaling factor in the case of the unavailability of atomistic simulations is also discussed. The dynamical properties of the CG melts are modeled reasonably well by all the CG potentials derived from atomistic simulations of short oligomers.

**Structure based coarse graining (CG) approach** are used to simulate different molecular weights of Bisphenol-A-polycarbonate. The CG potentials are derived using the iterative Boltzmann inversion methodology for the polymer with different molecular weights. Here it is shown that it is possible to use atomistic simulations of relative short oligomers to develop the CG model for high molecular weight polymers. Also the dynamical properties of the CG melts are modeled reasonably well by the CG potentials.

Dissipative particle dynamics (DPD) models of orientation of weakly-interacting silicate particles in a polymer matrix are presented. To examine the DPD models, the evolution of orientation under shear flow is compared with the predictions of the standard orientation models, namely, the Folgar–Tucker (FT) and the strain reduction factor (SRF) models. While the orientation patterns are the same in all models, the slow orientation kinetics observed in previous experiments is only predicted in the DPD and SRF models. Since the coefficients of the SRF model are in good agreement with the experiments, the good tally between the DPD and SRF models supports the capability of DPD to successfully simulate the orientation process. The orientation in a large cell constructed from unit cells with various averaged initial orientation angles is evaluated from evolutions in the unit cells based on the affine deformation assumption. The good agreement between such calculations and SRF model predictions supports that the affine deformation assumption in the large cell is reasonable. It is argued that the nonaffine deformation originated from the particle-based nature of DPD models at the lower scale could be combined with the affine deformation at the upper scale to yield appropriate estimations of the orientation state.

**Dissipative particle dynamics (DPD) models** of orientation of weakly-interacting silicate particles embedded in a polymer matrix are presented. The good tally between the DPD and the standard orientation models supports the capability of DPD to simulate the orientation process. Furthermore, a multiscale strategy is developed by combining nonaffine and affine deformations at different scales to estimate the orientation state.

Influences of branch content (BC) and branch length (BL) on isothermal crystallization of precisely branched polyethylene are studied by molecular dynamics simulation. Branch acts as a defect both in nucleation and crystal growth process. BC affects not only crystallization kinetics but also final morphologies. Crystallization rate and crystallinity decrease as BC increases. Morphology Regimes change from lamellae crystal to bundle crystal at critical BC (20/1000 C) because of different folding pattern. 50 CH_{2} is the critical methyl sequence length to form lamellae crystal. Lamellae thicknesses of final morphologies decrease in gradient corresponding to Morphologies Regimes. BL has no influence on the crystallization kinetics, and only affects the final morphologies when more branches inclusion happens with BL increasing. *Trans*-rich phenomenon in pre-crystalline state is observed. Crystallization process begins at the end of induction stage when *trans* state population reaches a critical value, and this value is independent of BC and BL.

**Effects of branch length and content on polyethylene crystallization** are investigated by molecular dynamics simulation. Branch content greatly influences both crystallization kinetics and morphologies. Final morphologies change from lamellae crystal to bundle crystal as branch content increases. Branch length mainly affects conformational changes as branch inclusion happens. *Trans*-rich phenomenon in pre-crystalline state is observed by using logarithm scale of time.

This study presents a molecular model for the amplitude-dependent dynamic moduli of polymer melts reinforced with nanoparticles. This study shows that intense strain-thinning reported in experimental studies of polymer nanocomposites can be attributed to disentanglement of bulk polymer chains from those strongly adsorbed to the surface of nanoparticles. This flow-induced relaxation is what is frequently termed as convective constraint release and is similar to the cohesive slip of polymer melt at solid interfaces.

**A molecular model** is used to examine the effect of flow-induced disentanglement on the viscoelastic nonlinearity and strain-thinning of polymer nanocomposites. The major relaxation mechanism of adsorbed chains is assumed to be the tube dilation. This study shows that the disentanglement of bulk polymer chains from those strongly adsorbed to the surface of nanoparticles leads to strain-thinning.