Molecular weight predicted evolution

Figure 9.1 Predicted evolution of molecular weight (arbitrary units) with monomer conversion for a conventional radical polymerization with a constant rate of initiation (---------------) and a living polymerization (--).

This paper presents the physical mechanism and the structure of a comprehensive dynamic Emulsion Polymerization Model (EPM). EPM combines the theory of coagulative nucleation of homogeneously nucleated precursors with detailed species material and energy balances to calculate the time evolution of the concentration, size, and colloidal characteristics of latex particles, the monomer conversions, the copolymer composition, and molecular weight in an emulsion system. The capabilities of EPM are demonstrated by comparisons of its predictions with experimental data from the literature covering styrene and styrene/methyl methacrylate polymerizations. EPM can successfully simulate continuous and batch reactors over a wide range of initiator and added surfactant concentrations. 

There is an extensive amount of data in the literature on the effect of many factors (e.g. temperature, monomer and surfactant concentration and types, ionic strength, reactor configuration) on the time evolution of quantities such as conversions, particle number and size, molecular weight, composition. In this section, EPM predictions are compared with the following limited but useful cross section of isothermal experimental data ... 

This theoretical model allows to predict the variation of complexation degree 6 and the molecular weight of the complex versus PAA concentration, molecular weight of the primary chains (PAA, polybase), concentration ratio r - [polybase]/[PAA], acrylate ratio p, and the minimvim chain length 1 (27). The theoretical predictions about the evolution of the system are confirmed by experimental results. For instance, in figure 12 (DP ). - which is the num-... 

The experimental data obtained at low surface densities, for end grafted chains, are in very good agreement with these theoretical predictions, not only for the overall evolution of the slip velocity vs the shear rate or of the slip length vs the slip velocity as shown in Fig. 19, but also for the molecular weight dependence of the critical velocity V which do follow exactly the laws implied by... 

The basic objective of the theoretical analyses is to obtain the effective rate constant for bimolecular reaction between rodlike polymers when the reaction is limited by slow diffusion, in terms of the polymer diffiisivities. The latter are dependent on the concentration and polymer length, and consequently the rate constant is obtained as a function of these variables. This is then useful for predicting the time evolution of the molecular weight distribution using a population balance analysis [48-50]. 

The model equations (Eqs. (60) and (61)) were solved numerically using an implicit finite difference technique. Typical profiles for the solvent volume fraction as a function of position and time in the rubber and the polymer volume fraction in the diffusion boundary layer are shown in Figs. 31 and 32 respectively. Other features of the simulation are the prediction of the temporal evolution of the rubbery-solvent interface and the mass fraction of the polymer dissolved as a function of time (Figs. 33 and 34). The simulations showed that the dissolution could be either disentanglement or diffusion controlled depending on the polymer molecular weight and the thickness of the diffusion boundary layer. 

The experimental data were compared to the model predictions for all three molecular weights studied. The model presented earlier was modified (since PEG is rubbery) and used to predict the temporsd evolution of the gel layer thiclmess for PEG dissolution in water at 21 C. Figures 14-16 show Ae comparison between the model predictions and the experimental data for PEG (Mn = 10,000 20,000 and 35,000) dissolution in deionized water. It is seen that there is good agreement between the predictions and the data within experimental error. This indicated that the model for rubbery polymer dissolution was able to correctly predict dissolution behavior of such polymers. 

Only the results for ATRP are shown here. Figure 8.1.B-1 deals with the polymerization of styrene at 110 °C with 1-phenlylethylbromide as an initiator and addition of a Cu-complex. The model prediction and experimental results are in reasonable agreement. The number average molecular weight increases with the conversion of the monomer and the polydispersity Pw/Pn drops to a value close to one from a relativity low conversion onwards. The evolution of the Cu-concentration is also shown. 

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