Weight fraction of polymer

Weight fraction of polymer of length j Monomer conversion... 

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W Gog M) d log M = weight fraction of polymer with log(molecular weight)... 

If the units of primary molecules of uniform length are subjected to cross-linking at random, the weight fraction of polymer molecules comprised of z primary molecules is ... 

The exact form of 7p. the number of bubbles nucleated per unit volume per unit time, is not known since there appears to be no published scientific studies which deal with nucleation rates in concentrated polymeric solutions at pressures below the equilibrium partial pressure. Blander and Katz (1975) have studied nucleation rates of pure liquids as a function of temperature at atmospheric pressure and Prud homme (1982) has studied nucleation rates of polymeric solutions containing up to 0.60 weight fraction of polymer as a function of temperature, concentration, and polymer molecular weight at atmospheric pressure. Both sets of investigators concluded that nucleation rates seem to follow the equation... 

Fig. 3-12 Plots of w(log M) (solid plot) and dw(log M)ld log M (dotted plot) versus log M for dodecyl acrylate polymerization at —4°C and 200 bar in 36 wt% CO2. w is the weight fraction of polymer having molecular weight M. After Beuermann and Buback [2002] by permission of Elsevier, Oxford an original plot, from which this figure was drawn, was kindly supplied by Dr. S. Beuermann.

It can be shown that the volume fraction of polymer in solution, vg, can be related to the weight fraction of polymer in solution, as follows ... 

The solubility of polymers decreases slightly as the molecular weight increases. This difference is sufficient to permit the separation of high-mo-lecular-wcight fractions of polymers by the addition of small amounts of a poor solvent to a polymer solution. It is also sufficient to permit preferential extraction of low-molecular-weight fractions of polymers. When a solution of a polymer is cooled, the first fraction to precipitate is the highest-molecular-weight fraction. It is customary to separate a solution of a polydisperse polymer into about five fractions and then to separate each of these fractions into three subtractions. 

Criticize or defend the following proposition As proof that no low molecular weight fractions of polymer have passed through the membrane in an osmotic pressure experiment, the following test may be performed. A quantity of poor solvent is added to an aliquot taken from the solvent side of the membrane. The absence of precipitate proves that no low molecular weight polymer passed through the membrane. 

In SAS, a compressed gas is added to a polymer solution. The upper critical solution temperature (UCST) and lower critical solution temperature (LCST) of that solution are shifted to higher and lower temperatures respectively until they finally merge to one region of immiscibilty over the whole temperature range. This process can be used for solvent recovery in solution polymerisation processes as well as for molecular weight fractionation of polymers. 

Figure 19, which represents GPC curves of the polystyrene prepared in concentrated emulsions of various surfactant concentrations, shows that the amount of bulk phase decreases with increasing surfactant concentration. As the surfactant concentration increases, the weight fraction of polymer formed in the droplets of the gel increases first (Fig. 20) and then levels off, while the conversion shows a linear increase through the entire range of surfactant concentration. Obviously the stability of the gel cells depends on the surfactant concentration. The molecular weight of polymer produced in the gel phase... 

The bulk phase, reflected in the tail of the GPC curves, increased with NaCl concentration because the double-layer repulsion between the emulsion cells becomes weaker with increasing salt concentration. As a result, the conversion and the weight fraction of polymer formed in the gel phase decrease with increasing NaCl concentration (Fig. 23). 

Temperature in kelvins Weight fraction of polymer in phase A Weight fraction of component 2 in phase A Weight fraction of polymer in phase B Weight fraction of component 2 in phase B... 

Assuming that classical chemical kinetics are valid and that the crosslinking reaction rate is proportional to the concentrations of polymer radicals and pendant double bonds, it was shown theoretically that the crosslinked polymer formation in emulsion polymerization differs significantly from that in corresponding bulk systems [270,316]. To simplify the discussion, it is assumed here that the comonomer composition in the polymer particles is the same as the overall composition in the reactor, and that the weight fraction of polymer in the polymer particle is constant as long as the monomer droplets exist. These conditions may be considered a reasonable approximation to many systems, as shown both theoretically [316] and experimentally [271, 317]. First, consider Flory s simplifying assumptions for vinyl/divinyl copolymerization [318] that (1) the reactivities of all types of double bonds are equal, (2) all double bonds... 

Quantitatively, the weight fraction of polymer with j structural units as a function of fractional conversion of functional groups is given by... 

Given the Schulz-Flory distribution, the mole and weight fractions of polymer with j monomer units (based on polymer) as a function of that number j are... 

It is also easy to calculate how much polymer has been made at a given degree of conversion. Defining polymer as any species with i > 2, the weight fraction of polymer must be equal to the total weight fraction of all species minus the weight... 

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