The mechanisms of H-transfer in termination reactions, and the role of fluorine interactions to achieve the living polymerization of olefins, are investigated. Mecking's bis(enolatoimine)Ti catalysts are considered, with or without *ortho*-F substituents. DFT calculations are performed on a parallel platform. The stationary structures are localized and energy barriers of activation are determined. Normal mode analysis is carried out and free energies are calculated. Different mechanisms can be involved in the termination: in all cases, the presence of F atoms rise the energy barrier of activation, according to experimental observations of living polymerization. The stabilizing role of the fluorine *o*-F · · · H bonds in the equilibrium species, and destabilizing *o*-F · · · H and *o*-F · · · *o*-F interactions in the transition states, are discussed.

**H-transfer terminations during homogeneous olefin polymerization are of great importance** for the understanding of the living behavior, and for the design of new catalysts. Several pathways are possible for Mecking's catalysts, and the unpredicted transfer to the ligand is the most favorable one.

A polymer network consists of linear chains. Each chain is an alternant sequence of flexible and stiff parts. The stiff parts of all the networked chains interact via nematic potential interactions. The flexible parts do not interact with other parts (flexible or stiff) of the network system. Various concentrations of flexible and stiff parts lend various elastic properties to the network. The influence of these molecular mechanisms on the stress–strain relations of the polymer network near the isotropic–nematic transition is calculated and discussed.

**A polymer network consists of chains that comprise flexible and stiff parts.** The stress–strain relation for that system depends on the concentration of those parts within the network chain, in addition to the relative orientation between the system elongation and the nematic axes.

Cure depth of photo-polymerized gels is theoretically analyzed. The critical point in a frontally photo-polymerized sample is determined by the critical degree of polymerization, which is derived by the concentration ratio of monomer and initiator. While the total polymer depth or gel depth weighed by the monomer conversion depends on both radiation energy and light intensity, the averaged cure depth around the critical point depends on radiation energy only. The profile is consistent with experimental results. This is a practical formulation of the cure depth of photo-polymerized gels without any empirical parameter.

**A practical method to determine the cure depth of photo-polymerized gels is presented.** While the total polymer thickness or gel thickness depends on both radiation energy and light intensity, the averaged thickness depends on radiation energy only. The profile well supports experimental results.

The synthesis of high-order multiblock copolymers by one-pot sequential monomer addition RAFT polymerization is examined by use of modeling and simulations using PREDICI. The system is the previously experimentally investigated model multiblock homopolymer system comprising 10 blocks of *N,N*-dimethyl acrylamide with average degree of polymerization 10 for each block. The simulations show that despite 10 chain extensions to full conversion, the number of dead chains at the end of the process is only ≈7%. The number fraction of dead chains is known from the number of chains generated from the initiator, and the conditions can thus be tailored with regards to the livingness required.

**The synthesis of sequence-controlled polymers in the form of high-order multiblock copolymers** by one-pot sequential monomer addition RAFT polymerization is examined by use of modeling and simulations implemented with the software PREDICI.

The hydrolysis of almost ideal networks based on macrodiols of average molar mass about 2 kg mol^{−1}, with *L = *18 ester groups per chain is studied. Tensile testing is used to evaluate the crosslink density through the statistical theory of rubber elasticity at two temperatures and three values of relative humidity. A kinetic model for ester consumption including an autocatalysis term is proposed and combined with two original approaches for modeling the crosslink density changes. This allows kinetic parameters of hydrolysis to be determined, and very good predictions are obtained for the variations of crosslink density (or elastic modulus) in the three aging conditions considered. The initial curvature of elastic modulus versus time is predicted positive for weak autocatalysis and negative for strong autocatalysis. The obtained conversion ratio at degelation is found to decrease sharply with the number of esters per elastically active chain.

**The hydrolysis of poly(ethylene glycol adipate) based networks is studied at two temperatures and three values of relative humidity.** A kinetic model for ester consumption including an autocatalysis term is proposed and combined with two original approaches for modeling the crosslink density changes. The conversion ratio at degelation decreases sharply with the number of esters per EAC.

Spin thermoelectric properties of different lengths of polythiophene in molecular junction are investigated using Green function in linear response regime. An extended Su-Schrieffer-Heeger model is used to describe the Hamiltonian of the molecule. The coupling of molecular chain to three-dimensional ferromagnetic electrodes is studied by a tight-binding model for both parallel and antiparallel configurations. The decrease of HOMO-LUMO gap and magnetothermopower and increase of oscillation of the spin thermopower and spin figure of merit are the most important phenomena observed by increasing the molecular length. In addition, results show that the spin thermoelectric coefficients are strongly related to the integral exchange energy.

**The spin figure of merit ( Z**

The validity of the Mayo-Lewis (ML) terminal model for copolymer composition in nitroxide mediated copolymerization is systematically tested by simulation. Significant deviations in copolymer composition from ML behavior occur under various parameter combinations before the nitroxide quasi-equilibrium condition (QEC) is reached. Maximum deviations are usually below 5 pp, and absent at conversions higher than 3%, but after 10% in some cases. High reactivity ratios lead to larger deviations; low reactivity ratios (faster cross-propagation) produce near ML behavior. An additional continuous radical source leads to faster attainment of the QEC and reduces the deviations from ML behavior.

**An issue of practical and theoretical interest in controlled radical copolymerization is whether or not the reactivity ratios measured in conventional** free radical copolymerization, based on the terminal model, can be applied in the controlled case as well. This paper tries to answer this question for nitroxide-mediated copolymerization.

Equilibrium morphologies and mechanical properties of copolymers with hydrophobic segments are explored using Langevin dynamics simulations. The interplay between different length scales, namely, persistence length *ℓ*_{p}, and disorder correlation length *p*, in addition to the fraction of hydrophobic patches *f*, determines the equilibrium morphology and in turn their mechanical response. Globular and coil phases for flexible chains and core-shell and looped morphologies for semi-flexible ones are reported. Consequently, a force induced globule-coil transition for flexible chains is observed for all disorder realizations, with *p* dictating the force vs. extension curves. Semi-flexible chains with same *ℓ*_{p} and *f* but different *p*, show different sequences of force-induced conformational transitions on account of their differing equilibrium conformations.

**Langevin dynamics simulations are used to investigate equilibrium morphologies and mechanical properties of copolymers** with hydrophobic segments. In addition to the fraction of the hydrophobic groups, the equilibrium morphologies and the mechanical behavior of the polymers depend on the interplay between different length scales.

By the use of a dynamic Monte Carlo method, three-generation dendrimers of type *F*_{1}*F*_{2}*F*_{2} with functionalities *F*_{1} = 3 to 6 and *F*_{2} = 2 to *F*_{1}–1 are simulated and investigated as functions of spacer lengths, with a total chain length up to 200 000 segments. Highly diluted athermal and theta solutions are studied as well as properties of non-reversal random walk dendrimers for comparison. For athermal conditions mean square dimensions obey the same scaling law regarding the total number of bonds as linear chains, irrespective of functionality and complexity. Likewise the theta parameter is the same for all systems investigated. Dimensions of theta systems are slightly expanded as compared to non-reversal random walk data, the effect increasing with increasing *F*_{1} and *F*_{2} while shape data near to theta conditions fairly well coincide with those of non-reversal random walks.

**Several quantities characteristic of the size and shape of dendrimers are studied**. Monte Carlos calculations are performed making use of a cubic lattice; however, by careful extrapolation to infinite chain length short chain effects are eliminated. Thus, only the theta parameter – found to be independent of functionality – is specific for the actual lattice used.

The linear viscoelastic response, usually described through the moduli *G*′(*ω*) and *G*″(*ω*), is widely employed to investigate the material properties because it is strictly related to the microstructure of thermoplastics. In a semi-crystalline polymeric material both the amount (degree of crystallinity) and the morphology of the crystalline phase strongly influence the polymer rheological behavior. In order to obtain information about the effect of crystallinity on the linear viscoelastic functions, the parameters of the linear multi-mode Maxwell equation have been determined by fitting literature data of *G*′(*ω*) and *G*″(*ω*) collected at different crystallinity degrees. The analysis of the resulting spectra, at least in the considered frequency and crystallinity range, clearly shows that the relaxation times of all modes increase with crystallinity in the same way. On the other hand, the parameters *G*_{i} of faster modes do not depend upon the crystallinity, whereas the parameters *G*_{i} increase with crystallinity only for the slowest modes. These results are very relevant to the rheology evolution during solidification: it is not sufficient to analyze only one viscoelastic function during crystallization, the relaxation time for instance; also the moduli change, and their increase seems concentrated to the modes having the largest relaxation times.

**The parameters of a linear multi-mode Maxwell equation are determined by fitting literature data of G**

The kinetics of butyl acrylate (BA) atom-transfer radical polymerization (ATRP) up to 2 000 bar has been modeled via PREDICI. A novel software package has been used in conjunction with PREDICI to perform automatic simulation and data processing within an extended range of polymerization conditions. The polymerization rate is enhanced with pressure, although to a weaker extent than in the ATRP of styrene and methyl methacrylate. Modeling suggests that intramolecular chain-transfer in BA polymerization is significantly accelerated at high pressure.

**Butyl acrylate (BA) atom-transfer radical polymerization (ATRP)** has been modeled within an extended range of polymerization conditions. Polymerization rate is enhanced with pressure, although to a weaker extent than in the ATRP of styrene and methyl methacrylate. Modeling of experimental data suggests that backbiting in BA polymerization is significantly accelerated towards higher pressure.

**Cover:** Theoretically-predicted polymerization rate acceleration by a decrease in miniemulsion droplet size in RAFT polymerization is nicely demonstrated by the experimental results which show the validity of intermediate termination model, rather than the slow fragmentation model, in the dithiobenzoate-mediated styrene polymerization. Further details can be found in the article by K. Suzuki,* Y. Kanematsu, T. Miura, M. Minami, S. Satoh, and H. Tobita on page 136.

A mathematical model is presented to describe a micro-dispersive suspension polymerization (MDSP) that yields pomegranate-like polymer micro-particles by inducing a local phase separation within suspended monomer micro-droplets. A modular approach is applied to theoretically understand the morphological development. It is proposed that two distinctive polymerization regions develop within a suspended droplet: (i) an outer region close to the droplet interface where a pseudo-homogeneous polymerization takes place to build the peel of the pomegranate-like structure and (ii) an inner region at the particle core where a starved dispersion polymerization takes place to generate the “arils” of the pomegranate-like structure. The model simulations agree reasonably well with the experimental results.

**A mathematical model is presented to describe the production of pomegranate-like micro-polymer particles.** It considers thermodynamic, kinetic, and morphological aspects of the polymerization under the basic assumption that two distinct polymerization regions coexist within a suspended monomer droplet. The model can predict not only global variables, such as monomer conversion and molecular weight distribution but also the evolution of particle morphology.

Experimental evidence and a simple model for a special segregation effect in hydrophobically initiated emulsion polymerization are presented. This effect is controlled by the size ratio between the droplets and the perfectly mixed volume of the growing chains. It leads within a certain range of droplet size to a drastic retardation of the polymerization reaction. For reaction loci outside this critical range, the monomer conversion is, at given polymerization time, drastically enhanced. The higher conversion for droplets that are smaller than the critical value can be explained by the effective segregation of growing radicals as typical for emulsion polymerization. Increasing conversion in bigger sized droplets happens as soon as the droplet volume exceeds the corresponding perfectly mixed volume. The limiting case of the latter situation is been experimentally observed for the corresponding bulk polymerization. Mathematical simulations with a simple model taking into account imperfectly mixed conditions inside the droplets describe the essential experimental data astonishingly well.

**During heterophase polymerization with initiation inside monomer drops of broad size distribution,** various kinetic events happen simultaneously in droplets of different size leading to a pronounced influence of the average drop size on the rate of polymerization.

A simple model discrimination method for RAFT polymerization mechanism, proposed on a theoretical basis, is applied to the polystyryl dithiobenzoate-mediated styrene polymerization. It is confirmed that the intermediate termination (IT) is the major reason for the rate retardation. The method utilizes the theoretical finding that the IT model shows a significantly larger polymerization rate in miniemulsion compared with the corresponding bulk polymerization, while the slow fragmentation model does not change the polymerization rate. The miniemulsion polymerization rate increases as the droplet size is made smaller, which agrees reasonably well with the theoretical prediction. The present model discrimination method is easy to apply, and would provide great insight into both basic and applied research in RAFT polymerization.

**In the dithiobenzoate-mediated RAFT miniemulsion polymerization of styrene, the polymerization rate increases drastically by making the droplet size smaller, as shown in the figure.** On the basis of the present result, the intermediate termination model, rather than the slow fragmentation model can be concluded, which applies to the present RAFT polymerization system.

A mathematical model for the kinetics of copolymerization with crosslinking of vinyl/divinyl monomers in the presence of RAFT controllers is developed. A reaction scheme considering multifunctional polymer molecules, which results in a multidimensional problem, is proposed. Molecular weight development during the pre-gelation period was calculated using the method of moments. Flory–Stockmayer's theory is used for the post-gelation period. The case of RAFT homopolymerization is also studied, as an example of model reduction, with identical results as those obtained with an existing model based on a simplifying premise. Good agreement between predicted profiles, our own experimental data, and data from other groups is obtained in most of the analyzed cases despite the occasional use of certain simplifying assumptions.

**A mathematical model for RAFT copolymerization kinetics of vinyl/divinyl monomers using a multifunctional macromolecule approach has been developed**. Polymer species are allowed to hold several active, intermediate free radical, and dormant radical centers at the same time, which results in a multidimensional problem. Model performance is good and in agreement with available experimental data.

A complex interplay between aggregation and coalescence occurs in many colloidal polymeric systems and determines the morphology of the final clusters of primary particles. To describe this process, a 2D population balance equation (PBE) based on cluster mass and fractal dimension is solved, employing a discretization method based on Gaussian basis functions. To prove the general reliability of the model and to show its potential, parametric simulations are performed employing both diffusion-limited-cluster aggregation (DLCA) and reaction-limited-cluster-aggregation (RLCA) kernels and different coalescence rates. It turns out that in both DLCA and RLCA regimes, a faster coalescence leads to smaller sized and more compact clusters, whereas a slow coalescence promotes the formation of highly reactive fractals, resulting in larger aggregates.

**The particle size distribution of a stagnant colloidal system undergoing aggregation and coalescence is evaluated by solving a 2D population balance equation.** It turns out that a fast coalescence leads primary particles to organizing in rather compact and small clusters, whereas for slow coalescence larger, open cluster are being formed. The latter conclusion holds for both the DLCA and the RLCA regimes.

Free-radical polymerization that involves the polymer transfer reactions, leading to both long-chain branching and scission, as in the cases of high-pressure ethylene polymerization, is considered for a tanks-in-series model. In a tanks-in-series model, the residence time distribution (RTD) becomes narrower to approach that for a plug flow reactor (PFR), as the number of tanks, *N* increases. The molecular weight distribution approaches rather quickly to that for a PFR, as the *N*-value increases. On the other hand, the branching density and the radius of gyration of highly branched polymers may show clear differences from that for a PFR, even when *N*-value is as large as 20. The present theoretical approach would provide great insight into the continuous production processes having complex RTDs.

**The branched structure formed in free-radical polymerization that involves both long-chain branching and scission**, as in the case of LDPE, is much different depending on the reactor types used. The figure shows how the mean-square radii of gyration of formed polymers change with the number of tanks, *N* in a tanks-in-series model.

Pairs of linear chains – the end segment of one of each fixed at a surface – are analyzed for the relative probability of mutual contact formation between particularly specified segments *i* and *j* belonging to different chains within these pairs. Several positions are of general interest only, while other portray specific experimental conditions, e.g., the basic step in surface initiated Z-RAFT polymerization (contact of the end of the free chain with the anchored segment of the fixed one). Contact probabilities are calculated for athermal cubic lattice chains by means of exact enumeration. Basic results are chain-length dependences of shielding factors *K*_{ij} in form of scaling laws and changes of size and shape properties of the involved molecules while approaching and penetration as functions of chain separation.

**Shielding of contacts due to the presence of a surface and the involved chain segments is studied for one chain anchored to the surface and a freely movable one.** Emphasis is given to the interaction between the anchor of the fixed and the end of the free chain modeling the central step of surface initiated RAFT polymerizations.

The distribution of functional groups in polymer chains produced in radical copolymerization by starved-feed semibatch operation is simulated using three different methodologies. Even under perfect control of the overall copolymer composition, a significant fraction of the polymer chains produced contain no functionality. A deterministic model is formulated to separately track the homopolymer chains that are produced without the desired functionality, a Monte Carlo (MC) model is written to represent the system, and a hybrid deterministic/MC approach is taken using new capabilities within the software package PREDICI. The advantages and disadvantages of each approach are discussed.

**Simulations show that a significant fraction of the polymer does not contain the desired functionality during semibatch production of low MW copolymer for use as a reactive dispersant,** even though perfect control of the overall composition is maintained. The distribution of functional groups is modeled using both deterministic and stochastic methodologies, as well as with a new hybrid formulation that combines both approaches.

The average mean-square radii of gyration for the products of the linear polymerization, the star-shaped polymerization, and the hyperbranched polymerization of AB_{2}-type monomer in the absence or presence of a multifunctional core initiator are investigated using the Dobson-Gordon's method. The dependence relationships between the average radii of gyration and the average degree of polymerization calculated using the Dobson-Gordon's method for the linear polymerization products are in good agreement with those obtained from the matrix algebra method of the rotational isomeric state model. The radii of gyration of the star-shaped and hyperbranched polymers are much smaller than those of the linear polymers if their average degrees of polymerization are equal. The conversion of groups, the core/monomer feed ratio, and the core functionality affect the average radius of gyration of the products. However, compared with the other factors, the degree of polymerization is the most influential factor on the average radii of gyration for the hyperbranched polymer system.

**The average mean-square radii of gyration for the products** of linear polymerization, star-shaped polymerization, and hyperbranched polymerization of AB_{2}-type monomer in the absence/presence of a multifunctional core initiator are investigated by means of the Dobson-Gordon's method. The conversion of groups, the core/monomer feed ratio, and the core functionality affect the average radius of gyration of the products. However, the degree of polymerization is the most influential factor on the average radii of gyration for the hyperbranched polymer system.

In a previous work, a model of full molecular weight distribution (MWD) for atom transfer radical polymerization with radical termination has been developed, using analogy to a series of continuous stirred tank reactors. This model assumes constant reaction rates, which is applicable to low conversion batches or steady-state continuous processes. In this work, the model is generalized to any polymerization condition, which provides variations of the reaction rates with conversion are known. Using this extended model, the effect of monomer conversion on the MWD is demonstrated, for the cases with and without radical termination. The conversion dependence of MWD is found to be significant. The broadening of distribution is correlated to the lack of control and/or the loss of livingness. Both control and livingness are necessary conditions for narrow MWD. It is also found that the effects of these two factors are very different, yielding different distribution shapes, even with similar average chain lengths (*r*_{N}) and polydispersity indexes (PDI).

**The existing model for chain length distribution (CLD) of ATRP is extended to account for the conversion effect.** By using the extended model, the effects of loss of control and lack of livingness on the broadening of CLD are investigated separately. Livingness and control are both necessary conditions to obtain narrowly distributed polymer chains.