Molecular weight averages, prediction

Anionic polymerization Narrow molecular weight distribution Limited chain transfer reactions Predictable molecular weight average Possibility of forming living polymers End groups can be tailored for further reactivity Solvent-sensitive due to the possibility of chain transfer to the solvent Can be slow Sensitive to trace impurities Narrow molecular weight distribution... 

Observed dispersions e1 for four sized fractions with average molecular weights M from 0.44 to 1.85 x 106 Dalton at concentrations C 8 to 9 x 10 5 are shown in Figure 1(b). Within experimental Error, the values of Ae /C, where Ac is the increment of static permittivity for added solute, were independent of concentration but increased linearly with molecular weight, as predicted by the McTague-Gibbs theory for molecular weights below about 106 Dalton. 

A mathematical model for styrene polymerization, based on free-radical kinetics, accounts for changes in termination coefficient with increasing conversion by an empirical function of viscosity at the polymerization temperature. Solution of the differential equations results in an expression that calculates the weight fraction of polymer of selected chain lengths. Conversions, and number, weight, and Z molecular-weight averages are also predicted as a function of time. The model was tested on peroxide-initiated suspension polymerizations and also on batch and continuous thermally initiated bulk polymerizations. 

The dynamic model developed by Kiparissides et al M,2] and subsequently modified by Chiang and Thompson [ J] can predict the conversion, number of particles, particle diameters, etc., for the continuous emulsion polymerization of vinyl acetate. In this paper, the model is extended to predict molecular weight averages and long chain branching as well. 

In research and development the characterization of polymers, as regards to molecular weight averages and distribution, is essential in order to predict... 

An optimal predictive controller was developed and implemented to allow for maximization of monomer conversion and minimization of batch times in a styrene emulsion polymerization reactor, using calorimetric measiuements for observation and manipulation of monomer feed rates for attainment of control objectives [31]. Increase of 13% in monomer conversion and reduction of 28% in batch time were reported. On-line reoptimization of the reference temperature trajectories was performed to allow for removal of heater disturbances in batch bulk MMA polymerizations [64]. Temperature trajectories were manipulated to minimize the batch time, while keeping the final conversion and molecular weight averages at desired levels. A reoptimization procediue was implemented to remove disturbances caused by the presence of unknown amounts of inhibitors in the feed charge [196]. In this case, temperatiue trajectories were manipulated to allow for attainment of specified monomer conversion and molecular weight averages in minimum time. 

An optimum model-based predictive controller was developed to allow for control of molecular weight averages (intrinsic viscosities) and reactor temperatures in solid-state PET polymerizations, through manipulation of the inert gas temperatures and flowrates [ 199]. Simulation studies also showed that predictive controllers might lead to significant improvement of process operation in PVC suspension reactors, when temperatures are allowed to vary along the batch time [200]. Simulation studies performed for continuous styrene solution polymerizations showed that the closed-loop predictive control can also be used to stabilize the reactor operation at unstable open-loop steady-state conditions [201]. 

Polymers having a predictable molecular weight average, from simple stoichiometry. 

Number and weight average molecular weights were predicted for the runs with using the expressions below and the effective conversions described in equation 6. 

It is very important to mention that the structure of caUbra-tion models used to predict the weight-average molecular weight of the final polymers were not reported by Cherfi et al. [138]. Based on the authors analysis, it seans that the initial feed compositions and feed profiles were used for model cahbration. Therefore, it seans that the calibration model developed for was actually replacing the detailed process model required for prediction of molecular weight averages, as discussed previously. This means that the model developed for would be unable to respond to process perturbations not included in the input data set and that independent evaluation of based solely on the NIR spectra was not possible. 

Prediction and control of molecular weight averages, the number of short-and long-chain branches, and termimal double bonds per polymer molecule is of... 

The first quantitative model, which appeared in 1971, also accounted for possible charge-transfer complex formation (45). Deviation from the terminal model for bulk polymerization was shown to be due to antepenultimate effects (46). Mote recent work with numerical computation and C-nmr spectroscopy data on SAN sequence distributions indicates that the penultimate model is the most appropriate for bulk SAN copolymerization (47,48). A kinetic model for azeotropic SAN copolymerization in toluene has been developed that successfully predicts conversion, rate, and average molecular weight for conversions up to 50% (49). 

If critical pressure and critical temperature are given in Pa and K, respectively, viscosities in centipoise result. The variable Io is either the low pressure pure component or mixture viscosity according to whether a pure component or mixture is being considered. For mixtures, simple molar average pseiidocritical temperature (Kay s rule), pressure, and density, and molar average molecular weight are used. The vapor density can be predicted by the methods previously discussed. Errors of above 5 percent are common for hydrocarbons and their mixtures. Experimental densities will reduce the errors slightly. 

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