Randomly branched Gaussian chains, including regular and random stars, were modeled. The chains were generated by repeated random movement of the end-point in a cubic grid. The radius-of-gyration- and viscosity-volume branching indexes, *g* and *g*′, were calculated for randomly branched molecules and compared with the data taken from the literature. The dependence of *g*′ on *g*, constructed from our data as well as from those by Kurata and Fukatsu, appears linear. The experimental data taken from the literature do not contradict this finding. On the other hand, the values of the branching exponent *ϵ* are highly scattered and a reliable average cannot be found. This findings support the value of the branching exponent of *ϵ* = 1, relating *g* and *g*′, proposed also by other authors.

**Numerically calculated values of hydrodynamic branching index in dependence of the radius-of-gyration branching index, g**

Theoretical considerations and Monte Carlo simulations prove that small size of droplets narrows dispersity of chains in both chain and step polymerizations. Equations describing the chains lengths distribution in living polymerization carried out in nano-droplets are derived, proving to be the binomial distribution function. The effect of lowering of polymer dispersity in irreversible polycondensation is predicted as well.

**Confining of the polymerization system into small droplets** results in narrowing of the chain-length distribution. When the number of growing chains in living polymerization equals to 2 then its variance is twice lower than of the Poisson distribution. When in irreversible step polymerization the number of remaining chains reaches 2 then polymer has a uniform (rectangle) distribution with dispersity equal to 1.33.

It is challenging to track explicit copolymer sequences and related measures using continuum kinetic models. We developed a generalized framework based on kinetic Monte Carlo (KMC) to model free radical polymerization of any number of monomers to obtain the explicit sequence and its distribution. The KMC framework was applied to copolymerization of butyl acrylate/methyl methacrylate (BA/MMA) and methyl acrylate/methyl methacrylate (MA/MMA), and the simulation output was compared with experimental results. Sequence characteristics that were not accessible via experiments were then predicted. Explicit monomer sequence information was used to construct operating diagrams to design a representative copolymer recipe with a specific sequence target as a function of molecular weight and monomer conversion.

**Kinetic Monte Carlo simulations allow sequence characteristics to be tallied and used in the design** of copolymers with specific sequence measures as dictated by the feasible operating diagram shown here.

Herein, a new coarse-grained methodology for modeling and simulations of polyelectrolyte systems using implicit solvent ionic strength (ISIS) with dissipative particle dynamics (DPD) is presented. This ISIS model is based on mean-field theory approximation and the soft repulsive potential is used to reproduce the effect of solvent ionic strength. The capability of the ISIS model is assessed via two test cases: dynamics of a single long polyelectrolyte chain and the self-assembly of polyelectrolyte diblock copolymers in aqueous solutions with variable ionic strength. The results are in good agreement with previous experimental observations and theoretical predictions, which indicates that our polyelectrolyte model can be used to effectively and efficiently capture salt-dependent conformational features of large-scale polyelectrolyte systems in aqueous solutions, especially at the salt-dominated regime.

**The newly developed ISIS DPD model with implicit representation of the effect of salt concentration is applied** to explore the structural conformations of a long polyelectrolyte and micellization of polyelectrolyte block copolymers in aqueous solution.

Structured polymers offer a means to tailor transport pathways within mechanically stable manifolds. The building block of such a membrane is examined, namely a single large pentablock co-polymer that consists of a center block of a randomly sulfonated polystyrene, designed for transport, tethered to poly-ethylene-*r*-propylene and end-capped by poly-*t*-butyl styrene, for mechanical stability, using molecular dynamics simulations. The polymer structure in a cyclohexane-heptane mixture, a technologically viable solvent, and in water, a poor solvent for all segments and a ubiquitous substance is extracted. In all solvents the pentablock collapsed into nearly spherical aggregates where the ionic block is segregated. In hydrophobic solvents, the ionic block resides in the center, surrounded by swollen intermix of flexible and end blocks. In water all blocks are collapsed with the sulfonated block residing on the surface. Our results demonstrate that solvents drive different local nano-segregation, providing a gateway to assemble membranes with controlled topology.

**The conformation of a structured pentablock ionic polymer** in a mixture of cyclohexane and heptane and in water is demonstrated. In the mixed solvent, the flexible and end blocks are swollen while the sulfonated polystyrene center block is collapsed. In water, all the blocks of the pentablock are collapsed into a nearly spherical shape.

The lattice density functional theory (LDFT) is used to describe the substrate effect on the phase behavior of polymer brush grafted on different substrates. The LDFT predicts that: both attractive and repulsive interactions between the substrate and the polymer chains have effects on the thickness of brushes; when the short-range monomer–substrate interaction is larger than a certain value, the thickness and density profiles of polymer brushes almost do not change. And also an attractive substrate can increase the critical grafting density of pancake to brush transition. For temperature responsive polymer brushes, the temperature transition points are almost the same with different substrates, however, an attractive substrate can increase the swelling ratio and a repulsive substrate can decrease the swelling ratio. We also find that an increasing grafting density can decrease the substrate effect on the swelling behavior of temperature responsive polymer brushes.

**The substrate effect on the phase behavior of polymer brush is studied by LDFT.** An attractive substrate increases the swelling ratio of thermally sensitive brushes, while a repulsive substrate decreases the swelling ratio. Additionally, the increasing grafting density decreases the substrate effect on polymer brushes.

A model for predicting the molecular weight distributions of mechanochemically degraded star polymers has been developed. The model was shown to be in good agreement with experimental distributions and average total molecular weights obtained from ultrasonically degraded three-arm star poly(methyl acrylate)s. Generalization of the model to four- and *n*-arm star polymers was also achieved. The models are straightforward to use, and thus, all calculations were completed in Microsoft Excel.

**A predictive model for the evolution of molecular weight distributions of star polymers during mechanochemical degradation has been developed.** The predicted distributions are in good agreement with experimental results for three-arm star polymers.

**Cover:** An analytic equation for the weight-average chain length in a matrix formula is proposed for free-radical polymerization with simultaneous long-chain branching and scission. With combination termination, the illustrative calculation shows that both gelation and degelation may occur during the course of polymerization. Further details can be found in the article by H. Tobita* on page 477.

**Cover:** The concentration-induced morphologies and morphological transitions for the solvent-state self-assembly of rod-coil-rod triblock copolymers are investigated, and the rules of phase transition driven by the concentration are obtained. Further details can be found in the article by Y. Zhou,* S. Song, X.-P. Long, C.-Y. Zhang, and Y.-M. Chen on page 490.

Analytic solution for the weight-average chain length in a matrix formula, , is derived for free-radical polymerization with simultaneous long-chain branching and scission. Illustrative calculations are conducted for a batch polymerization. With bimolecular termination by combination, gelation could be observed. Assuming the same polymerization kinetics for branching and scission in the post-gel period, the formed gel molecule could be degenerated into sol molecules again, i.e., degelation might occur. Both the gelation and degelation points are defined as the point when the largest eigenvalue of **M** is unity. The matrix formula is suitable to determine accurate values, while the Monte-Carlo simulation can give much more detailed information. These two approaches are nicely complementary.

**Analytic solution for the weight-average chain length in a matrix formula,** , is derived for free-radical polymerization with simultaneous long-chain branching and scission. Illustrative calculations are conducted for a batch polymerization, which agree with the Monte Carlo simulation results. With a particular set of parameters that involves combination termination, both gelation and degelation were observed during the course of polymerization.

Self-assembly behaviors of rod–coil–rod triblock copolymers in the selective solvent are systematically investigated by dissipative particle dynamic simulations. Three selective solvents are considered: the pure coil-selective solvent, the pure rod-selective solvent, and the mixed solvent. The concentration-induced morphologies and morphological transition affected by the rod and coil length are examined. The micelle adopts the overall shape of sphere, nematic bundle, worm, cylinder, lamella, coil-, and rod-aggregated hollow cylinders, and network. In the coil-selective solvent, increasing coil length can defer the phase transition from sphere to other morphologies while increasing rod length can advance the transition. In the rod-selective solvent, an opposite influence rule is found.

**The interesting morphologies from the self-assembly of rod–coil–rod triblock copolymers in solvents** are investigated and the rules of phase transition driven by the concentration are obtained. The findings have the possible relevance for the design and fabrication of optoelectronic materials.

This paper presents a mathematical model to describe the evolution of the molecular weight distribution (MWD) in vinyl chloride (VCM) free-radical suspension polymerizations performed with a bifunctional initiator, 1,3-di(2-neodecanoylperoxyisopropyl) (DIPND). The model yields, as a function of time, the mass balances for the distinct phases, the monomer conversion, the number- and mass-average molecular weights and the complete MWD of both the growing and dead polymer chains. In order to describe the MWD, the model uses probability generating functions (pgf) to transform the mass balance equations into a reduced and finite set of model equations. As shown throughout many examples, the MWD's of the final polymer resin is little sensitive to the presence of the linear symmetrical bifunctional initiator.

**The molecular weight distributions of different macromolecular species are illustrated formed during** vinyl chloride polymerizations performed with a bifunctional initiator, as calculated with the proposed pgf (probability generating function) model.

Differential scanning calorimetry (DSC) analysis for ethylene/propylene copolymers synthesized in the whole composition range with a supported metallocene catalyst has been carried out. The melting/crystallization process can be determined both in the ethylene and propylene rich regions covering a comonomer composition range of up to 20%. Two peaks are detected showing two different transitions (*T*_{m1} and *T*_{m2}). A procedure is developed for modeling DSC melting curves by using a model previously reported by Kissin. Two contributions are considered for the copolymer crystallization in connection with a random comonomer distribution. Such model favourably describes experimental DSC curves and *T*_{m1} and *T*_{m2} values. The obtained parameters follow a regular trend in accordance with its physical meaning. Standard deviation for melting temperatures reveals accurate calculated values. The analysis of the parameter trend allows a fit against composition and predicting melting temperatures, yielding also accurate values.

**A rigorous thermodynamic model enables the DSC curve description** of ethylene/propylene copolymers in a wide temperature range. Accurate calculation of the first melting temperature is achieved for copolymers in a wide composition range. Model parameters are well correlated with the copolymer composition. Prediction of melting temperatures is possible exclusively from copolymer composition.

Coarse-grained molecular dynamics simulations are performed to investigate the effects of dendrimer size and lipid phase on the dendrimer–membrane interactions. It is found that the low-generation dendrimer flattens on the gel-phase bilayer without any disturbance of lipids, while dendrimers with immediate generation can fluidize the upper leaflet of the membrane. High-generation dendrimers can induce the gel–fluid phase transition of lipids in the vicinity of the dendrimer and the significant bending of membranes. The phase transition is companied by membrane thinning and facilitates a domain formation on the membrane. The findings suggest that high-generation dendrimers are much more effective in disturbing membranes not only at high temperature but also at low temperature. This work is helpful to understand the binding and internalization mechanisms of cationic nanoparticles into cells involving lipid rafts and endocytosis.

**High-generation PAMAM dendrimers can fluidize gelled lipids in their vicinity.** This facilitates the bending of the gelled bilayers and the formation of DMPG-rich microdomains. However, the projected area of the membrane is not changed during the fluidization process. Molecular dynamics simulations suggest that high-generation dendrimers thin the gelled membrane locally, supporting experimental observations on the interactions between cationic nanoparticles and gel-phase membranes.