The penultimate model of copolymerization taking into account the dependence of the reactivity of a macroradical on the type of the unit preceding the ultimate one is well-known in polymer chemistry. All types of chemical structure of multiblock copolymers capable to form during copolymerization processes described by such a model are revealed in the present work. Phase diagrams of copolymers of all these types specifying the regions of thermodynamic stability of spatially periodic mesophases differing in morphology are constructed in the framework of the weak segregation theory. Besides, the periods and amplitudes of the variation of different type densities of units in mesophases as well as volume fractions of these latter within the regions of their coexistence are calculated.

**Finding of the dependence of the phase behavior of heteropolymer liquids on the chemical structure of their macromolecules is of utmost importance**. Theoretical consideration of such a behavior of multiblock copolymers whose architectures are describable by the extended Markov chain has been undertaken in this paper. Our analysis reveals the possibility of the existence in their melts of phase diagrams of nontraditional appearance.

The translocation of hexa-arginine peptides across the asymmetric lipid bilayer in both random and bundled state was studied by coarse-grained molecular dynamics simulations. It was found that the peptides pass through the membrane by a pore-mediated mechanism when their concentration exceeds a critical value. However, the translocation efficiency of the bundled peptides is much higher than that of the random case at the same concentration. The pore formation results from the cumulative effects of each peptide in random case, while the bundled ones disturb the membrane locally. Furthermore, we show that the role of the hydrophobic group of peptide amphiphiles is facilitating the formation of aggregation for improving their penetration efficiency.

**The translocation of hexa-arginine peptides across membrane is investigated by computer simulations.** It is found the translocation efficiency of the bundled peptides is much higher than that of the random case. Further, the primary role of the hydrophobic group of peptide amphiphiles is facilitating the formation of aggregation for improving their penetration efficiency. We propose that peptides with high charge density and proper hydrophobic tails will be the candidates in designing drug carriers.

By means of computer simulation, we have investigated self-organization of a single macromolecule being amphiphilic on the level of an individual monomer unit. It was demonstrated first, that in selective solvent such macromolecules are able to form spontaneously spherical vesicle-like globules having empty cavity in their center and dense shell on their surface.

**Spontaneous formation of a vesicle-like capsule by a collapsed macromolecule with amphiphilic monomer units** is demonstrated for the first time by means of molecular dynamics computer simulation. Such vesicle-like globules are formed by long macromolecules with solvophilic backbone and short solvophobic side groups and could be prospective for practical applications as nanocapsules and nanocarriers.

In this work, a novel approach, based on the population balance equation (PBE), is presented and applied for the first time to the simulation of expanding polyurethane foams. The solution of the PBE allows to determine the evolution of the bubble size distribution (BSD) of the foam, which in turn defines the mechanical and thermal properties. The approach includes a kinetic model for the polymerization and blowing reactions, accounts for the presence of a physical blowing and for the total energy balance. Model predictions are compared with experiments from the literature for 12 different chemical recipes, highlighting acceptable agreement.

**This manuscript describes a new mathematical model for the simulation of polyurethane foams**, which for the first time employs a population balance model for describing the evolution of the bubble (or cell) size distribution of the foam. The model is here validated against experiments from the literature and will be further developed in our future work.

When polymeric liquids undergo large-amplitude shearing oscillations, the shear stress responds as a Fourier series, the higher harmonics of which are caused by fluid nonlinearity. Previous work on large-amplitude oscillatory shear flow has produced analytical solutions for the first few harmonics of a Fourier series for the shear stress response (none beyond the fifth) or for the normal stress difference responses (none beyond the fourth) [*JNNFM*, **166**, 1081 (2011)], but this growing subdiscipline of macromolecular physics has yet to produce an exact solution. Here, we derive what we believe to be the first exact analytical solution for the response of the extra stress tensor in large-amplitude oscillatory shear flow. Our solution, unique and in closed form, includes both the normal stress differences and the shear stress for both startup and alternance. We solve the corotational Maxwell model as a pair of nonlinear-coupled ordinary differential equations, simultaneously. We choose the corotational Maxwell model because this two-parameter model (*η*_{0} and *λ*) is the simplest constitutive model relevant to large-amplitude oscillatory shear flow, and because it has previously been found to be accurate for molten plastics (when multiple relaxation times are used). By *relevant* we mean that the model predicts higher harmonics. We find good agreement between the first few harmonics of our exact solution, and of our previous approximate expressions (obtained using the Goddard integral transform). Our exact solution agrees closely with the measured behavior for molten plastics, not only at alternance, but also in startup.

**We derive the first exact analytical solution for the extra stress tensor in LAOS flow for both the normal stress differences and the shear stress responses.** Our exact solution agrees with the measured behaviors for three molten plastics, not only for alternance, but also for startup.

Improving the high-temperature long-term thermo-oxidative stability of high-performance polymers is crucial for their applications in aerospace industry. For designing novel polymers with improved oxidative stability, it is vital to identify the most reactive moiety of the polyimide toward oxidation and understand the mechanism of oxidation. Quantum chemical calculations and microkinetic analysis have been carried out here to obtain the molecular level details of the oxidative degradation of a commercially important polyimide, PMR-15, at high temperatures. This study identifies the most vulnerable moiety of PMR-15 toward oxidation. Moreover, the rate-determining step in the oxidative degradation is also scrutinized. Mechanistic understanding of the reaction leads us to propose new modifications of PMR-15 with a better thermo-oxidative stability.

**Quantum mechanical calculations combined with microkinetic analysis are used to explore the oxidative degradation of a commercially important polyimide**, PMR-15, at high temperatures. The most vulnerable moiety of this polyimide and the rate determining step of the oxidative degradation are scrutinized. Possible modifications on PMR-15 to improve its thermo-oxidative stability are thereby proposed.

Micro-structural evolution of polyethylene (PE) across the glass transition temperature (*T*_{g}) is investigated by full atom molecular dynamic (MD) simulation. The specific volume as a function of temperature for PE is obtained, through which the volumetric glass transition temperature was determined. The dihedral distribution of the overall bonds of the amorphous polyethylene chain system keeps consistent with the rotational isomeric state scheme. The dependence of isomer probability of skeletal bonds and average radius of gyration on temperature also can be used to estimate the glass temperature. The micro-structural information obtained from MD simulation should be helpful to understand glass transition mechanism of polymer system.

**Micro-structural evolution of polyethylene across the glass transition temperature is investigated by full atom molecular dynamic simulation.** The relationship between the specific volume and the temperature can be used to determine glass temperature of amorphous polyethylene system. The dihedral distribution of the overall bonds of the amorphous polyethylene chain system keeps consistent with the rotational isomeric state scheme. The dependence of isomer probability of skeletal bonds and average radius of gyration on temperature also can be used to estimate the glass temperature.

The present study concerns analysis of advective–diffusive transport in prototypical industrial mixing devices by the diffusive mapping method. The latter is a recent extension of the conventional mapping method for distributive mixing and enables application of this efficient technique to mixing flows, including molecular diffusion. Primary challenge is detailed numerical analysis of flow and mixing properties inside realistic systems with complex geometries. This is performed by combining the diffusive mapping method with a sophisticated computational scheme for flow simulations in domains with complex (moving) boundaries: the eXtended Finite Element Method (XFEM). The mixing properties are investigated through spectral analysis of the advective–diffusive transport by way of eigenmode decomposition of the mapping matrix. Key topic is the correlation between the evolution of concentration fields and invariant Lagrangian structures in the flow field.

**Mixing in realistic industrial devices is of great relevance.** The diffusive mapping method is a flexible technique for mixing simulations inside complex geometries. This study applies this method to advective–diffusive transport in two prototypical 3D industrial mixers. It is combined with the extended finite element method (XFEM), enabling reliable and efficient computation of evolving concentration fields.

Structural properties of polyaniline (PANI) protonated with camphorsulfonic acid (CSA) have been investigated by means of molecular dynamics simulations. New OPLS-AA based force field has been applied to calculations done within the Gromacs package. All partial charges were derived from DFT quantum calculations using NWChem package. After testing the force field applied to the simulated macromolecules and ions, we have performed a series of long calculations for the system containing (at least) 42 PANI chains of 7 monomers each, doped with 294 CSA ions (equal amounts of both enantiomers). Our calculations show that the only stable and highly ordered structure of the system studied is characterized by double layers of PANI separated by double layers of CSA. The most important conclusion is that identical final result is reached while starting from several quite different initial arrangements. Here the new model is discussed and justified.

**The structure of polyaniline protonated with camphorsulfonic acid has been modeled by molecular dynamics simulations.** All partial charges have been derived from DFT quantum calculations and a new force field has been applied. The resulting stable structure is characterized by double layers of PANI separated by double layers of CSA. The new model is in good agreement with several experimental data.

Olefin block copolymers (OBCs) are new class of thermoplastic elastomers having low glass transition temperature soft blocks and highly crystalline hard blocks synthesized by reversible chain shuttling between two catalysts with considerably different comonomer responses through a chain transfer agent. Theoretical representation of kinetics and microstructure evolution in chain shuttling polymerization (CSP) is of vital importance especially since the existing characterization tools have severe limitations in retrieving the blocky nature of OBCs. In this work, we correspondingly develop an effective model to represent CSP in practical conditions and compare our predictions to the existing experimental data. We illuminate kinetics and microstructure development in both OBC chains and individual blocks. We specifically clarify the effect of varying the reversibility of transfer reactions through tuning chain shuttling agent and hydrogen concentrations on OBC chains and blocks in terms of their corresponding molecular weight and chemical composition distribution and draw guidelines for achieving OBCs with desired properties.

**An effective model is developed for representation of kinetics and microstructure evolution in the** course of chain shuttling polymerization in the view of both OBC chains and individual hard and soft blocks.

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.

**Cover:** The orientation of suspended rigid dumbbells in the large-amplitude oscillatory shear flow of a polymeric liquid is evolved and visualized. These orientations explain the observed nonlinearity in viscoelastic fluids. Further details can be found in the article by A. M. Schmalzer and A. J. Giacomin* on page 181.

This work presents a mathematical model for the cross-linking copolymerization of styrene-divinylbenzene comprising the phase separation and cyclization kinetics. The gelation dynamics was modeled through the Numerical Fractionation technique, and the phase separation was taken into account through modified Flory's equations. A balance of sequences was used in order to ensure cyclization reactions in the model. The present approach tends to predict the copolymerization's main variables and it was compared with porosity data from literature. The cyclization reactions effect on the phase separation behavior could also be assessed. The cyclization rate coefficient was found to be a function of the solvents system used in the reaction. Further details can be provided by the model through the Numerical Fractionation method which allows one to calculate the concentration of chains from different generations, and their effect upon the polymer particle porosity.

**The gelation dynamics is modeled through the Numerical Fractionation technique, which is applied for gel and sol phases (the numbers represent the chain generations).** The cyclization reactions' rate depends on the degree of polymerization and on the good/poor solvent mixture's composition. These reactions are responsible for delaying the gelation process, affecting the porosity of the polymer particle, as shown in simulation results.

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.

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.

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.

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.

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.

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.

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.