Polymer phase modeling

Lamellar morphology variables in semicrystalline polymers can be estimated from the correlation and interface distribution fiinctions using a two-phase model. The analysis of a correlation function by the two-phase model has been demonstrated in detail before [30,11] The thicknesses of the two constituent phases (crystal and amorphous) can be extracted by several approaches described by Strobl and Schneider [32]. For example, one approach is based on the following relationship ... 

As suggested by Barrett (2), it is assumed that following the particle nucleation stage, the polymerization proceeds in the particle (monomer/polymer) phase with no mass transfer limitation. Therefore, the dispersion polymerization is similar to a mass or suspension polymerization, and kj can not be assumed to be constant even at isothermal conditions, since kp and even kp are dependent on the degree of polymerization because of a gel effect. (2., ,D However, since the application of the model is for a finishing step, with polymer molecular weight and viscosity fairly well established, further changes in kp and kp should be minimal. 

Usually, reactions 1 and 2 take place in the aqueous jiiase, yttiile all the other kinetic events can occur both in the aqueous and in the polymer phases. Note that Pj,n indicates the concentration of active polymer chains with nTronaner units and tenninal unit of type j (i. e. of monomer j) Hi is the concentration of monomer i and T is the concentration of the chain transfer agent. Reactions 4 and 5 are responsible for chain desorption from the polymer pjarticles reactions 6 and 7 describe bimolecular temination by conJoination and disproportionation, respiectively. All the kinetic constants are depsendent upon the last monomer unit in the chain, i. e. terminal model is assumed. 

Two macromolecular computational problems are considered (i) the atomistic modeling of bulk condensed polymer phases and their inherent non-vectorizability, and (ii) the determination of the partition coefficient of polymer chains between bulk solution and cylindrical pores. In connection with the atomistic modeling problem, an algorithm is introduced and discussed (Modified Superbox Algorithm) for the efficient determination of significantly interacting atom pairs in systems with spatially periodic boundaries of the shape of a general parallelepiped (triclinic systems). 

Volume and mass-based expressions for the degree of crystallinity are easily derived from the experimentally measured density (p) of a semi-crystalline polymer. The method is based on an ideal crystalline and liquid-like two-phase model and assumes additivity of the volume corresponding to each phase... 

In this review, we focus on the effect of anisotropic interactions, in particular parallel attractions, and demonstrate that the inclusion of such interactions in a model leads to a great richness in possible polymer phase behavior. From a practical point of view, the model that we describe has the advantage that it is computationally very cheap—although this advantage comes at the price of sacrificing the greater realism of an off-lattice model. 

Figure 3a shows the mean-field predictions for the polymer phase diagram for a range of values for Ep/Ec and B/Ec. The corresponding simulation results are shown in Fig. 3b. As can be seen from the figure, the mean-field theory captures the essential features of the polymer phase diagram and provides even fair quantitative agreement with the numerical results. A qualitative flaw of the mean-field model is that it fails to reproduce the crossing of the melting curves at 0 = 0.73. It is likely that this discrepancy is due to the neglect of the concentration dependence of XeS Improved estimates for Xeff at high densities can be obtained from series expansions based on the lattice-cluster theory [68,69].

For the development of an appropriate strategy for cleavage from the novel syringaldehyde resin, the authors adapted a previously elaborated solution-phase model study on intramolecular Diels-Alder reactions for the solid-phase procedure (Scheme 7.60). The resulting pyridines could be easily separated from the polymer-bound by-products by employing a simple filtration step and subsequent evaporation of the solvent. The remaining resins were each washed and dried. After drying,... 

Rate Constants of Peroxyl Radicals Reactions with C—H bonds of Polymers and Model Compounds in Liquid Phase... 

It should be taken into account that the reaction of chain propagation occurs in polymer more slowly than in the liquid phase also. The ratios of rate constants kjlkq, which are so important for inhibition (see Chapter 14), are close for polymers and model hydrocarbon compounds (see Table 19.7). The effectiveness of the inhibiting action of phenols depends not only on their reactivity, but also on the reactivity of the formed phenoxyls (see Chapter 15). Reaction 8 (In + R02 ) leads to chain termination and occurs rapidly in hydrocarbons (see Chapter 15). Since this reaction is limited by the diffusion of reactants it occurs in polymers much more slowly (see earlier). Quinolide peroxides produced in this reaction in the case of sterically hindered phenoxyls are unstable at elevated temperatures. The rate constants of their decay are described in Chapter 15. The reaction of sterically hindered phenoxyls with hydroperoxide groups occurs more slowly in the polymer matrix in comparison with hydrocarbon (see Table 19.8). 

The non-random two-liquid segment activity coefficient model is a recent development of Chen and Song at Aspen Technology, Inc., [1], It is derived from the polymer NRTL model of Chen [26], which in turn is developed from the original NRTL model of Renon and Prausznitz [27]. The NRTL-SAC model is proposed in support of pharmaceutical and fine chemicals process and product design, for the qualitative tasks of solvent selection and the first approximation of phase equilibrium behavior in vapour liquid and liquid systems, where dissolved or solid phase pharmaceutical solutes are present. The application of NRTL-SAC is demonstrated here with a case study on the active pharmaceutical intermediate Cimetidine, and the design of a suitable crystallization process. 

The observed catalytic effect of the crown ether appears to be dependent on the nucleophile employed in both polymerization and corresponding model reactions. Not surprisingly, it appears that the stronger the nucleophile employed, the smaller the catalytic influence of the crown ether. For example, with potassium thiophen-oxide yields of polymer or model products were almost quantitative with or without catalyst. By contrast, the reaction of PFB with potassium phthalimide, a considerably weaker nucleophile, affords 6 in 50% with catalyst and in 2-3% without catalyst under identical conditions. However, it may be that this qualitative difference in rates is, in fact, an artifact of different solubilities of the crown complexed nucleophiles in the organic liquid phase. A careful kinetic study of nucleophilicity in catalyzed versus non-catalyzed reactions study is presently underway. 

Surface interactions between water and polymer networks have a profound effect on the water structure. The properties of water in these and other heterogeneous systems are sensitive to the size of the network pores and have been described by the two-phase model which assumes partition of the water between the "bulk and the "bound water phases" Evidence for this partition has been obtained in several proton NMR studies and also in ESR studies of paramagnetic probes in zeolites, silica gels and in water containing polymers. ... 

The only revision of the model which has been incorporated here is the formal description of the functional group concentration in the polymer rich phases. In our work with the dendrimer, nominally containing 128 terminal functional groups, we calculated the total ligand concentration within the polymer phase 1 to be... 

The existence of a l.c. polymer phase requires that in the polymer melt above Tg the side chains are ordered anisotropically. In order to realize systematically such systems, a simple model consideration can be used 24> (Fig. 2). 

Gray and McCrum735 used the Hashin-Shtrikman theory to explain the origin of the y relaxation in PE and PTFE, Maeda et al.745 have given exact analyses of several two phase models for semi-crystalline polymers and Buckley755 represented a biaxially oriented sheet of linear polyethylene by a two phase composite model. 

We have developed a detailed two-phase model for the UNIPOtr process. This model was used to investigate the steady and dynamic characteristics of this important industrial process that creates polymers directly from gaseous components. The reader should develop MATLAB programs to solve for the steady state and the unsteady-state equations of this model. This will enable him or her to investigate... 

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