The microphase separation in the bulk, in the strong segregation limit, of model conetworks based on end-linked ABA triblock copolymers was investigated by calculating and minimizing the total Gibbs free energy for the various possible morphologies. The results of this study comprise a phase diagram with the prevailing morphologies mapped against junction functionality and conetwork composition, and the various geometrical parameters of the system at equilibrium, including the domain sizes and the aspect ratios. In the free-energy calculations for the assembly of the anisotropic morphologies, cylinders and lamellae, two important characteristics of the system were taken into consideration: core crowding at high core functionality, and topological loop formation upon self-assembly. The former leads to an increase in the elastic energy of the core-forming chains, whereas the latter results in a reduction in the stretching energy of the chains. The results of this study suggest that spheres are favored by a high core functionality (100–200) and a low volume fraction (≤0.15) of the A end-block, whereas lamellae are promoted by an intermediate core functionality (20–100) and a relatively high A-block volume fraction (≥0.30).

The microphase separation in the bulk, in the strong segregation limit, of model conetworks based on end-linked ABA triblock copolymers is investigated by calculating and minimizing the total Gibbs free energy for the various possible morphologies. Two important characteristics of the system are taken into consideration: core crowding at high core functionality, and topological loop formation upon self-assembly.

Cover: Using dilatometry combined with shear flow at conditions comparable to realistic processing conditions, a flow induced crystallization model is employed for the kinetics of quiescent nucleation, flow enhanced nucleation, fibrillar growth, and the time evolution of the dimensions of the resulting crystalline structures. Three important model parameters are determined over a broad range of temperatures, pressures, and shear rates; pre-factors to the creation rate of nucleation and to the shish growth rate and a critical molecular stretch defining the transition between flow-enhanced nucleation and oriented structures. Further details can be found in the article by Tim B. van Erp, Peter C. Roozemond, and Gerrit W. M. Peters* on page 309.

Model-based design of experiments using the error-in-variables model (EVM) is explored. The fundamental differences between DOE in the traditional nonlinear regression versus the EVM context are discussed, and it is pointed out that for cases where there are errors in all variables, using the EVM design criterion is the only appropriate approach. In addition, the implementation of the EVM design criterion and its characteristics for both initial and sequential design schemes are discussed. The main application is the implementation of the EVM criterion to design optimal trials for reliable estimating reactivity ratios for typical copolymerization systems, along with prescriptions for the practitioner.

A detailed investigation of model-based DOE under the EVM context shows that for cases where there are errors in all variables the EVM design criterion is the only appropriate approach. The implementation of the EVM design criterion is discussed, along with its application for designing optimal trials for estimating reactivity ratios for a typical copolymerization.

This is the second of two works presenting a new mathematical method for modeling bivariate distributions of polymer properties. It is based on the transformation of population balances using 2D probability generating functions (pgf) and a posteriori recovery of the distribution from the transform domain by numerical inversion. Part I of this work was devoted to the numerical inversion step. Here the transformation of the population balances to the pgf domain is analyzed. A 2D pgf transform table is developed, which allows a simple transformation of any typical polymer balance equation. Three copolymerization examples are used to show the application of the complete procedure of this modeling technique.

The 2D pgf technique is a powerful method for modeling bivariate distributions of polymer properties. We study the transformation of the polymer balance equations into the pgf domain in order to develop a pgf transform table that allows a quick transformation of most balance equations. This simplifies the transformation process and makes the pgf method more useful to a non-expert user.

Using dilatometry combined with shear flow at conditions comparable to realistic processing conditions, the flow-induced crystallization of polymers is modelled. The model describes the kinetics of quiescent nucleation, flow-enhanced point nucleation, fibrillar growth, and the time evolution of the dimensions of the resulting crystalline structures. The growth rate of nuclei is coupled to the backbone stretch of a mode with a relaxation time representative of the average of the molecular weight distribution. The eXtended Pom-Pom (XPP) model is used to calculate the backbone stretches from flow conditions. Three important model parameters are determined over a broad range of temperatures, pressures, and shear rates for a fixed shear time; a prefactor to the creation rate of flow-induced nucleation, a prefactor to the shish growth rate, and the critical molecular stretch defining the transition between flow-enhanced nucleation and flow-induced crystallization of oriented fibrilar structures. Excellent agreement is obtained between calculated and experimentally determined crystallization kinetics of iPP. Moreover, the extended experimental dataset leads to an important adaption of the model, i.e., a new criterion for the initiation of shish growth.

A flow-induced crystallization model is employed for the kinetics of quiescent nucleation, flow-enhanced nucleation, and shish formation. Three important model parameters are determined over a broad range of temperatures, pressures, and shear rates; pre-factors to the creation rate of nucleation and to the shish growth rate and a critical molecular stretch defining the transition between flow-enhanced nucleation and oriented structures.