Weight chain length distribution function

In the two-site model, it is assumed that the catalytic sites have the same polymerization activity (propagation activity) but they differ in their chain transfer capabilities. The two-site model is the simplest of the multisite model and its main advantage is that the number of adjustable parameters is minimal. The weight chain length distribution function of the two-site model takes the following form ... 

The length and the distribution of chain lengths are functions of the temperature, pressure, residence time, catalyst characteristics, and the proportion of ethylene present in the reaction, A measure of this is the mole ratio of ethylene, which measures the weight of ethylene compared to the weight of triethyl aluminum in scales related to their atomic weights. As an example, Table 15-2 shows how the distribution of chain lengths can vary, using different mole ratios of ethylene to triethyl aluminum. 

Henry constant for absorption of gas in liquid Free energy change Heat of reaction Initiator for polymerization, modified Bessel functions, electric current Electric current density Adsorption constant Chemical equilibrium constant Specific rate constant of reaction, mass-transfer coefficient Length of path in reactor Lack of fit sum of squares Average molecular weight in polymers, dead polymer species, monomer Number of moles in electrochemical reaction Molar flow rate, molar flux Number chain length distribution Number molecular weight distribution... 

Wcxun(r) weight-fraction distribution of cumulative chains Wp(r) chain length distribution of primary chains u>s sol fraction X monomer conversion Xa functional group A conversion Xb functional group B conversion Vf free-voltune fraction a stoichiometric imbalance ratio... 

Figure 1 (a) Number-fraction chain length distribution n i) and (b) weight-fraction chain length distribution w i) of the polymers at different functional group conversions in condensation polymerization. 

Applying the SSH to eqn [92], we obtain the number-fraction chain length distribution for the cationic chains, /i (r) = [P f]/[P ] =exp(-it). Substituting this function into eqn ]93] gives the weight-fraction chain length distribution of the total polymer ... 

The chain length distribution of the polymer formed under conditions of chain transfer to monomer was calculated in a number of papers [2, 34, 36]. However, the continuum approximation was not used and the results are represented in the form of very complicated sums over the chain length. This complexity was the reason for erroneous MWD curves of the polymer formed in the presence of chain transfer to monomer for the case of initiator of functionality m= 3, calculated in Ref. [34] by a graphical method. Using the continuum approximation, and neglecting k jkp, one can obtain [35] a fairly simple expression for the weight fraction of macromolecules of... 

We wish to compute as functions of 0 < /> < 1 the chain length distribution [P ], the number (DP ) and weight (DP ) averaged chain lengths, and their ratio (thepolydispersity T disp), which is a measme of the breadth of the distribution. If Edisp = 1, all chains are of the same length, and if Pdisp 1 there is considerable variation in chain length. 

Fig. 7. Interrelation between molecular weight and retention volume for macromolecules of different functionality at chromatography in the exclusion (1-3), the critical (4), and the adsorption (5) separation modes 59). In the general case, the distribution coefficient Kd is a function of the pore size D, the chain length N, the interaction energy with the pore wall of the backbone segments 0 and the terminal segment 0f containing the functional group (zones 1,2 and 3 correspond to the cases shown in Fig. 2)...

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