The possibility to extract velocity correlation quantities from fluctuation thermodynamic properties is explored in the case of macromolecule–solvent mixtures. Indeed, Kirkwood–Buff integrals, *G _{ij}*, together with self-diffusion and viscosity data can provide an approximation for distinct diffusion coefficients (DDCs),

**Kirkwood–Buff integrals together with self-diffusion and viscosity** provides an approximation for distinct diffusion coefficients, *D ^{d}_{ij}* in macromolecule–solvent mixture. Herein,

In this work, reactions between industrially relevant monomers (methyl acrylate, ethyl acrylate, methyl methacrylate, vinyl acetate, and isopropenyl acetate) and oxygen-centered radicals (^{•}OH and SO_{4}
^{•—}) are studied using a combination of quantum mechanics and transition state theory. These reactions may have a strong influence on polymer structure and properties. Thus, computational methodologies able to estimate reliably coefficients for these reactions are needed to improve the understanding of emulsion polymerization processes. In the case of reactions involving ^{•}OH, the computational approach is based on the SMD-water/M06-2X/6-311++G(3df, 2p)//B3LYP/6-31+G(d, p) DFT scheme. All calculated and experimental Gibbs free energy barriers, , are within 1 kcal mol^{−1}. In the case of reactions involving SO_{4}^{•—}, the SMD-water/M06-2X/6-311++G(3df, 2p)//CAM-B3LYP/6-31+G(d, p) DFT scheme is found to be more suitable than a similar scheme based on B3LYP. This proposed scheme works well for acrylates and methacrylates (errors within 1 kcal mol^{−1}), but it may overestimate the rate coefficients of acetates reacting with SO_{4}^{•}** ^{—}**.

**Rate coefficients for reaction between oxygen centered radicals and vinyl monomers** of industrial relevance are calculated. The methodology for the calculation is based on electronic structure calculations and on transition state theory. The figure represents the transition states for the abstraction of a hydrogen atom from a methyl methacrylate molecule by a sulfate radical.

A mathematical model is developed for the arborescent polyisobutylene system in a batch reactor, using multidimensional method of moments, to predict the concentrations of monomer and inimer as well as number and weight average molecular weight. This model is significantly efficient in computation, making parameter estimation practical. Simulation results agree with results obtained by Monte Carlo simulations. Parameter estimation results show that using the weight average molecular weight data provide better overall fit than leaving them out in the previous model.

**Multidimensional method of moments** is used to track molecular weight development and end groups in an arborescent polyisobutylene system. Simulation results agree with Monte Carlo simulations. The method enables parameter estimation using extra data to obtain improved model fit to data.

This study concerns the equilibrium geometric properties of a family of cyclic chains, referred to as the “bridged polycyclic rings,” which have *f* flexible subchains bridging two common branch points. By increasing the number of bridges, *f*, this family encompasses the usual linear chain (*f* = 1), monocyclic ring (*f* = 2), bicyclic θ-shaped polymer (*f* = 3), and multicyclic rings with increasing topological complexity. Results of their radius of gyration, mean span, and, consequently, geometric shrinking factors (also known as the *g*-factors) are obtained by three approaches—the Gaussian chain theory, simulations based on the Kremer–Grest bead-spring model, and a Flory-type mean-field approach. Using the confinement analysis from bulk structures method, the equilibrium partition coefficients (*K*) of several of those cyclic excluded volume chains in a cylindrical pore with inert surfaces are obtained, and the results fall onto a common curve on a graph of *K* versus the polymer-to-pore size ratio, using the mean span as the representative polymer size, in the range of *K* relevant to polymer separation in size exclusion chromatography (SEC) experiments. Applications of the results in predicting the SEC retention volume of such bridged polycyclic ring polymers are discussed in the framework of the equilibrium partition theory.

**Results on the equilibrium geometric properties of a family of cyclic polymers**, which includes ring-shaped, theta-shaped, and even more complex bridged polycyclic macromolecules, are presented. The calculated molecular parameters are compared with previous relevant theoretical results, as well as with available experimental data on the size exclusion chromatography of such polymers.

The authors have introduced and extended the sequential Bayesian Monte Carlo model discrimination (SBMCMD) method described in previous studies by Masoumi et al. for the purpose of discriminating between mechanistic models via designed experiments. The features of the Markov Chain Monte Carlo methods utilized in SBMCMD allow this method to work with a wide range of nonlinear models. Here, SBMCMD has been applied to simulated copolymerization systems to compare its performance with other statistical discrimination methods used in previous studies by Burke et al. In addition, the Hsiang and Reilly method has been reapplied to the same copolymerization systems to address questions arising from previous work on this subject. The results of applying the SBMCMD method show that it is possible to choose the best model correctly with fewer experiments compared to the previously studied methods. Results also confirm that copolymer composition data do not provide enough information to discriminate between terminal and penultimate data.

**A sequential Bayesian and Monte Carlo based procedure** is utilized to discriminate between simulated copolymerization systems. Performance of this approach is compared with that of other statistical discrimination methods and the benefits of the utilized method are discussed.

To provide a faster calculation of the block copolymer phase diagrams a simplified version of the self-consistent field theory (SCFT) is proposed. Multi-component block copolymers with interactions between repeated units described by the *χ*-parameters satisfying the Hildebrand conditions are studied. This case is shown to correspond to a degeneration within the framework of the general SCFT approach. Remarkably, the degenerated thus multi-component block copolymers admit two-component only SCFT description. The procedure presented is applied to gradient copolymers considered as a limiting case of multi-component copolymers obeying Hildebrand conditions, the lengths of the blocks vanishing and the number of different kinds of repeated monomers tending to infinity. Finally, a melt of symmetric triblock copolymers blurred into a gradient copolymer is studied and corresponding phase diagrams are calculated.

**Multi-component block copolymers** with *χ*-parameters obeying the Hildebrand conditions are studied. Such copolymers include gradient copolymers as a limiting case and correspond to a degeneration in the framework of the self-consistent field theory with effective two-component description. Phase diagrams are calculated for a melt of symmetric triblock copolymers specially blurred into a gradient copolymer.

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**: In this work, a modeling pathway and software tool for linking entangled linear polymer molecular properties to linear viscoelasticity and melt index (MI) values is presented. A reptation model links molecular properties to the flow curve, and then, an ANSYS Polyflow model calculates MI values based on the flow curve predicted. The method is thoroughly tested and validated for uni-and bi-modal, low- and high-density polyethylene grades. An overall accuracy level in the range of 90% on average is exhibited, considering both model prediction steps: (i) MWD to flow curve and (ii) flow curve to MI. These promising results offer a valuable tool to enhance product development toward the direction of end-use polymer bulk properties prediction. Further details can be found in the article by Vasileios Touloupidis,* Christof Wurnitsch, Alexandra Albunia and Girish Galgali on page 392.

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.

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.

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 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.

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.

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 modeling pathway and software tool for linking entangled linear polymer molecular properties to linear viscoelasticity and melt index (MI) values is presented. A reptation model links molecular properties to the flow curve, and then, an ANSYS Polyflow model calculates MI values based on the flow curve predicted. The method is thoroughly tested and validated for uni- and bimodal, low- and high-density polyethylene grades. An overall accuracy level in the range of 90% on average is exhibited, considering both model prediction steps: (i) molecular weight distribution to flow curve and (ii) flow curve to MI.

**A modeling pathway and software tool** for linking entangled linear polymer molecular properties to linear viscoelasticity and melt index (MI) values is presented. A reptation model links molecular properties to the flow curve, and then, an ANSYS Polyflow model calculates MI values based on the flow curve predicted.

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.

The general concept for nitroxide-mediated radical terpolymerization is advanced. This concept is based on activation-deactivation equilibria for terminal polymer-nitroxide adducts. Depending on monomer activity and the stability of terminal nitroxide adducts, terpolymerization can be equilibrium living, quasi-equilibrium (gradient) living, decaying living, decaying gradient, or non-living. Expressions for the effective activation-deactivation equilibrium constant, *K _{ef}*, and the rate of terpolymerization are derived from theoretical speculations on equilibrium living and decaying living terpolymerization. For quasi-equilibrium living terpolymerization, various types of gradient terpolymers are predicted. When activity of the active monomer M

**The general concept of living radical nitroxide-mediated terpolymerization** is suggested. According to the activity of monomers and polymer-nitroxide adducts, terpolymerization can be living equilibrium, living quasi-equilibrium, living decaying, or non-living radical terpolymerization. The general concept is experimentally proven using the results of TEMPO and SG1 nitroxide-mediated terpolymerization in the styrene−MMA−acrylonitrile system.