The equilibrium partition coefficients () are calculated for self-avoiding, semiflexible chains with the same finite contour length () and a variety of persistence length () values, partitioning between a macroscopic dilute solution phase and confined solution phases in cylindrical voids in the steric exclusion limit. It is found that, for the range of -values most relevant to polymer separation in size exclusion chromatograph (), the geometric mean of the radius of gyration () and the mean span () performs better than or alone in collapsing the partition curves of the various linear semiflexible chains onto a single curve. The dependence of the confinement free energy () on the persistence length is also examined. For those chains having the same , the pore diameter is found to be the necessary and sufficient condition for to decrease with the increase of .

**Two questions are answered:** (i) which size parameter correlates best with the equilibrium partition coefficients of linear semiflexible chains in the range relevant to polymer separation in GPC? (ii) For two chains with the same contour length but different persistence length in equilibrium with a cylindrical pore, which chain spends less free energy to get in.

Conditions for azeotropic copolymerization derived for irreversible systems are not satisfactory for reversible copolymerizations. The presented theoretical treatment leads to formulation of conditions for a terminal (dyad) model equilibrium copolymerization to form copolymer azeotropes. Numerical simulations of kinetics of copolymer formation confirm validity of the derived relationships between rate and equilibrium constants and comonomer concentrations.

**Reversible copolymerization can behave azeotropically** only when certain relationships, given in the paper, between the equilibrium and rate constants of homo- and cross-propagations are held. The main conditions for azeotropicity of the reversible copolymerization ensure that the compositions and microstructures of initially formed copolymer and of that at the system equilibrium are identical.

An important high-temperature polyimide, namely HFPE-30, has been coarse grained to three different levels of detail. It has been shown that while it is possible to successfully calibrate bonded and non-bonded forcefields and attain realistic densities with all levels of coarse graining, reproducing chain structures and dynamic properties requires an adequate level of atomistic detail to be retained. A model that coarse grains the HFPE-30 molecule into eight beads, approximates both chain structure and dynamic properties well. Alternately, the unrealistically fast dynamics in coarse-grained models can be slowed down by increasing the thermal coupling constant by a scaling factor that is estimated by comparing mean square displacements in detailed atomistic and coarse-grained simulations. In general, stress-strain responses of coarse-grained systems do not match those of the detailed atomic systems except when the coarse graining involves eight beads. In cases where lesser number of beads are used, slowing the dynamics down by the estimated scaling factor takes the stress-strain response of the coarse-grained system close to that of the detailed atomistic one.

**The figure shows three mapping schemes of molecular fragments in the backbone of the commercial polyimide HFPE-30**. A coarse-grained representation with large number of beads is necessary to predict static and configurational properties. However, with smaller number of beads and an appropriate amount of friction on the beads, we are able to predict glass transition temperature and stress–strain response.

Hierarchical lamellae self-assembled from linear multiblock copolymers in thin films are investigated by self-consistent field theory. The thin films are confined between two parallel substrates. The confinement strategy allows generating hierarchical microstructures with various numbers and different orientations of small-length-scale lamellae. Effects of film thickness and surface affinity on the structures are studied. It is found that not only the period of the large- and small-length-scale lamellae but also the orientation of small-length-scale lamellae relative to large-length-scale lamellae can be tuned by varying the film thickness. Moreover, the structures of the hierarchical lamellae can be tailored by changing the surface affinity. Through analyzing free energies of various lamellae, phase diagrams are mapped out. The present work could provide guidance for fabricating hierarchical microstructures in a controllable way.

**In thin films of linear multiblock copolymers**, not only the period of large- and small-length-scale lamellae but also the orientation of small-length-scale lamellae can be tuned by varying film thickness. Moreover, a reentrant phase transition of perpendicular lamellae-in-lamellae with increasing the film thickness is revealed.

A dynamic Monte Carlo method was employed to study regular as well as irregular dendrimers with up to *G* = 8 generations with functionality *F* = 3 under athermal conditions. The size of dendrimers showed the same scaling law with respect to chain-length *n* as linear chains, keeping *G* at a constant value. If *n* was varied via *G* at fixed spacer-length *m* its scaling behavior was similar to that of collapsed globules, at least for large values of *G*. Asphericity strongly decreased with an increase of *G*. The composition of irregular dendrimers remained unchanged with respect to *F* and *G* but the spacer-lengths were distributed according to several models. Quite generally, distributions became broader, size larger and shape less symmetric compared to the regular case. These effects increased with an increase of dispersity of the branches.

**Regular and irregular dendritic polymers, the latter realized for several types of branch-length distributions**, are simulated and their properties are compared. In addition, for the regular case emphasis is given to parameters in the limit of infinite branch length (spacer length) in order to obtain model independent results.

Polymers can be used in diverse applications in daily life because of their various microstructures. Molecular weight distribution and chemical composition distribution are the two most important microstructural indices for many copolymers. Monte Carlo simulation is an efficient method to obtain those specific distributions that cannot be easily determined via traditional equation-based methods. However, this method requires long computation time. In this project, a parallel method is proposed for Monte Carlo simulation on a graphics processing unit platform. Both steady state and dynamic state cases are presented to show the accuracy and efficiency of the proposed method. The computation time of the proposed method is greatly decreased by at least 30-fold compared with the time required by CPU platform.

**Monte Carlo method is suitable to simulate the microstructural distributions**, but it normally requires a long time for the computation. By decomposing the conventional Monte Carlo simulation of all chains into millions of threads, the calculation is parallelized on a GPU platform and more than 30-fold speedup ratio is obtained.

Topological constraints due to chain connectivity and uncrossability greatly impact the long time dynamics and rheology of high molecular weight polymer melts. Computer simulations to study properties of such melts are very advantageous, since perfect control of molecular conformation and melt morphology is available. We present a methodology to prepare well-equilibrated polymer melts which only requires local relaxation. The approach efficiently leads to equilibrated ensembles of bead-spring polymer melts of 1 000 chains of up to 2 000 beads, which correspond to 24 (fully flexible) and 45 entanglement lengths (semi-flexible chains). Entanglements are identified by a primitive path analysis and a master curve of the entanglement lengths for different chain and persistence lengths is presented.

**Excluded volume and topological constraints (entanglements)** lead to difficulties for polymer melt equilibration in computer simulations. To avoid long equilibration runs, an improved feedback loop methodology is introduced, which only needs relaxation on short length scales. The analysis shows that a homogeneous density and perfect internal distances along the chain backbone can be reached for melts of chains of up to about 45 entanglement lengths.

In this paper, we employ a molecular theory to study HCl gas-adsorption/desorption properties of PNIPAM brushes. Here, PNIPAM–HCl hydrogen bonds and theirs explicit coupling to the PNIPAM conformations are considered. We find that hydrogen bonding becomes a key element in determining HCl gas-adsorption/desorption behaviors of PNIPAM brushes. Our results indicate that, when at moderate grafting densities, the association of PNIPAM–HCl hydrogen bonds can result in a dependence of PNIPAM brush-height on HCl concentration, and the morphology of PNIPAM brushes may have a significant effect on the HCl gas-adsorption/desorption properties.

**HCl gas adsorption capacity of poly( N-isopropylacrylamide) (PNIPAM)** brushes is described by PNIPAM–HCl hydrogen bonds. Hydrogen bonding becomes a key element in determining HCl adsorption/desorption behaviors of PNIPAM brushes. The morphology of PNIPAM brushes may have a significant effect on the HCl adsorption/desorption properties.

Extensive fully-atomistic molecular dynamics simulations have been performed for the *G* = 4 generation of the dendrimer PAMAM-EDA in water, with fully protonated and non-protonated amine groups. Some parameters from these results have been incorporated into a coarse-grained model suitable for Monte Carlo simulations. Satisfactory agreement is found between the dendrimer density profiles obtained from the Monte Carlo and the molecular dynamics simulations, both for the protonated and neutral molecules. The Monte Carlo and molecular dynamics trajectories have also been employed to calculate binary interactions between pairs of dendrimers. The interactions between *G* = 4 PAMAM-EDA dendrimers can be satisfactorily described by a theoretically proposed Gaussian potential.

**Extended molecular dynamics simulations for protonated and neutral** *G* = 4 PAMAM-EDA in water permit an accurate analysis of conformational properties. The trajectories are used to compute binary interactions between dendrimer molecules. These interactions are shown to obey the theoretically predicted Gaussian behavior.

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.