Steady Polydispersity, effect

The Curtiss-Bird theory has been extended to include polydispersity effects extensive data comparisons for the steady-state shear compliance and various nonlinear rheological properties further support the inclusion of the link-tension coefficient in the theory. 

The inlet monomer concentration was varied sinusoidally to determine the effect of these changes on Dp, the time-averaged polydispersity, when compared with the steady-state case. For the unsteady state CSTR, the pseudo steady-state assumption for active centres was used to simplify computations. In both of the mechanisms considered, D increases with respect to the steady-state value (for constant conversion and number average chain length y ) as the frequency of the oscillation in the monomer feed concentration is decreased. The maximum deviation in D thus occurs as lo 0. However, it was predicted that the value of D could only be increased by 10-325S with respect to the steady state depending on reaction mechanism and the amplitude of the oscillating feed. Laurence and Vasudevan (12) considered a reaction with combination termination and no chain transfer. 

Under periodic operation, the polydispersity is greater by between 15-30% and the wave form of the forcing function has little effect. There is a small increase in both R and with respect to their steady-state values and the conversion appears to be little affected by the mode of operation of the reactor. 

Comparison between Experimental Results and Model Predictions. As will be shown later, the important parameter e which represents the mechanism of radical entry into the micelles and particles in the water phase does not affect the steady-state values of monomer conversion and the number of polymer particles when the first reactor is operated at comparatively shorter or longer mean residence times, while the transient kinetic behavior at the start of polymerization or the steady-state values of monomer conversion and particle number at intermediate value of mean residence time depend on the form of e. However, the form of e influences significantly the polydispersity index M /M of the polymers produced at steady state. It is, therefore, preferable to determine the form of e from the examination of the experimental values of Mw/Mn The effect of radical capture mechanism on the value of M /M can be predicted theoretically as shown in Table II, provided that the polymers produced by chain transfer reaction to monomer molecules can be neglected compared to those formed by mutual termination. Degraff and Poehlein(2) reported that experimental values of M /M were between 2 and 3, rather close to 2, as shown in Figure 2. Comparing their experimental values with the theoretical values in Table II, it seems that the radicals in the water phase are not captured in proportion to the surface area of a micelle and a particle but are captured rather in proportion to the first power of the diameters of a micelle and a particle or less than the first power. This indicates that the form of e would be Case A or Case B. In this discussion, therefore, Case A will be used as the form of e for simplicity. 

Under ideal condition, when an isothermal CSTR is operating at steady state (SS) in a totally micro-mixing condition, the PS produced will be homogeneous having a perfect 2.0 polydispersity (the Schultz-Flory distribution). Deviations from ideality have been theoretically studied by operating CSTR processes under non-steady state conditions with forced periodic operation [70]. The effects of an independent sinusoidal forcing of the monomer and the initiator feed concentrations results in theoretical control of the polydispersity. 

These are identical for the limiting values for the batch reactor, except that they require only the assumption of perfect mixing. Thus, while polydispersi-ties of 2.0 and 1.5 for termination by disproportionation and combination respectively represent unattainable minima for batch polymerization, these same values represent feasible operation in a well-mixed CSTR. Thus, the CSTR will give a narrower dead polymer number chain length distribution since it is possible to maintain a constant reaction environment at steady state. The effect of residence time distribution on the polydispersity is negligible since the lifetime of a single radical is far less than the average residence time. Likewise, for a copolymerization in a CSTR at steady state, the constancy of... 

Separation occurs with each polymer component established in a condition very close to the steady-state distribution relative to the accumulation wall [14]. The greater the force exerted on a component by the field, the closer it is driven toward the wall under steady-state conditions. If the components of a mixture, such as the different molecular mass components of a polydisperse polymer, are driven toward the accumulation wall at different force levels, they will form steady-state layers next to the wall having different thicknesses. This is very similar in effect (but not in the mechanism for achieving it) to differential... 

There is also the case of reaction-controlled diffusion (briefly discussed in Section 1.2.4), closely associated with the Trommsdorff effect [55, 56], which leads to the loss of control even under isothermal conditions because the slow diffusion of radicals drastically decreases the rate of termination. This subsequently increases the concentration of radicals, as well as the rate of propagation relative to termination. Under these circumstances, polydispersity can increase significantly, easily reaching PDIs in excess of 10. In fact, the solutions found for polydispersity in a steady-state system in Section 1.2.7 generally underestimate the PDI values expected by a polymerization engineer due to various effects at high conversion and other deviations from steady-state conditions. It has also been recently shown that nanocon-fmement of a free radical polymerization can actually lower the polydispersity [57-59]. 

In this section, we present the molecular theory for the linear dynamic viscoelasticity of miscible polymer blends by Han and Kim (1989a, 1989b), which is based on the concept of the tube model presented in Chapter 4. Specifically, the reptation of two primitive chains of dissimilar chemical structures under an external potential will be considered, and the expressions for the linear viscoelastic properties of miscible polymer blends will be presented. We will first present the expressions for zero-shear viscosity ob. dynamic storage and loss moduli G co) and G " co), and steady-state compliance J° for binary miscible blends of monodisperse, entangled flexible homopolymers and then consider the effect of polydispersity. There are a few other molecular theories reported... 

For polydisperse materials the steady-state compliance is very sensitive to molecular weight distribution. This effect shows up even in so-called monodisperse samples. Fuchs ef al. [38] fitted the following empirical equation to their data for a series of PMMAs having polydispersity indices (M /M ) less than 1.15. 

In the course of NMP, the persistent radical effect (PRE) leads to a steady increase in excess nitroxide. This slows the polymerization rate down and leads to longer polymerization times. As shown by Matyjaszewski, Fukuda and Miura/ introduction of a conventional radical initiator which slowly decomposes under the reaction conditions considerably enhances the conversion rate. Even a low rate of external initiation ( 1% of the initial internal initiation, reaction 1, Scheme 4.5) leads to a considerable reduction in the polymerization time while the livingness, polydispersity and controlled degree of polymerization remain virtually unchanged. The extra radicals reduce the concentration of persistent nitroxides rather than initiating new chains. The kinetic aspects of additional initiation were studied by Fukuda et alP and Fischer et In summary, if the rate R of generation of additional... 

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