Weight fraction distributions

The simplest way computationally of obtaining a sedimentation coefficient distribution is from time derivative analysis of the evolving concentration distribution profile across the cell [40,41]. The time derivative at each radial position r is d c r,t)/co /dt)r where cq is the initial loading concentration. Assuming that a sufficiently small time integral of scans are chosen so that Ac r t)/At= dc r t)ldt the apparent weight fraction distribution function g (s) n.b. sometimes written as (s ) can be calculated... 

Figure 5. Weight fraction distributions for polymer Seeds I ( ), 11 (A),...

Calculated Molecular Weight Distributions. The calculated weight fraction distributions for the micro-mixed, segregated, and micro-mixed reactor with dead-polymer models for Runs 2, 5,... 

Figure 8. Comparison of experimental and calculated weight fraction distributions for Run 2 ((0) Exp (---------) Micro- D (---) Micro (---) Seg)...

Fig. 52.—Weight fraction distributions of chain molecules in linear condensation polymers for several extents of reaction p.

Fig. 55.—Weight fraction distribution of cyclic polymers for a type ii polymer with B Mo/c = 0.01 (g./cc.) as calculated from Eq. (16) for p =0.95 and 1.00 (solid curves) only even integral values of x apply. The chain distribution for p =0.95 is shown for comparison by the broken curve calculated from Eq. (3 ), p. 330.

Weight fraction distributions according to Eq. (33) for three values... 

With the aid of these results, the following are readily obtained. For the weight fraction distribution ... 

It will be observed that both of the distribution equations, (19) and (27) for the mole and weight fraction distributions, respectively, contain factors cox and Since a is limited to values less than Q c = l/(/— 1), is always much less than unity (for/=3 the maximum value of is j3c = l/4), and the factors o x and change in opposite directions as x increases. The decrease of the latter outweighs the increase of the former for all permissible values of see p. 366,... 

Fig. 69.—Weight fraction distribution for a branched polymer prepared from a simple trifunctional monomer at the a s indicated. ...

For the purpose of deriving the weight fraction distribution, attention is directed to the fact that a molecule containing n /-functional branches is composed oi fn—n+1 chains. The average size of a chain being independent of the location of the chain in a branched structure, the quantity fn — n + 1 may be taken as a measure of the average weight of an n-chain polymer. It follows that... 

Equation 2.8 relating the weight fraction distribution with the extent of reaction can also be used for determining the extent of reaction that should be attained to get a maximum yield of a particular Molecular weight species. Thus, from eq. (2.8) we can derive ... 

Fig Weight-fraction distribution of chain molecules at different extents of reaction in polycondensation... 

Around 1970 computer simulations of the branching processes on a lattice started to become a common technique. In bond percolation the following assessment is made [7] whenever two units come to lie on adjacent lattice sites a bond between the two units is formed. The simulation was made by throwing at random n units on a lattice with ISP lattice sites. Clusters of various size and shape were obtained from which, among others, the weight fraction distribution could be derived. The results could be cast in a form of [7]... 

The area of the chromatogram for the unknown sample can also be utilized to generate a weight fraction distribution, but as a function of eluent volume, i (see Figure 4). At a constant mass fraction, the two distributions are equal and can be utilized to generate a calibration curve to check the validity of the semi-logarithmic calibration constraint. Equation 1. Figure 5 pre-... 

Fig. 2-10 Weight fraction distribution plot for linear polymerization. Plot 1, p = 0.9600 plot 2, p = 0.9875 plot 3, p = 0.9950. After Howard [1961] (by permission of Iliffe Books, London and Elsevier, Oxford).

Fig. 2-14 Weight fraction distribution plot for multichain polymerization. Plot I. / 1 plot 2, / = 2 ...

Using the same approach as in Secs. 2-7a and 2-7b, the following equations are derived for the weight-fraction distribution, number- and weight-average degrees of polymerization,... 

Granular beds may consist of mixtures of particles of several sizes. In flow problems, the mean surface diameter is the appropriate mean, given in terms of the weight fraction distribution, x by... 

The distribution of molecules (trees) according to their degree of polymerization is obtained by so-called cascade substitution, in which the variable z is substituted by a generating function. Thus, the weight fraction distribution function W(z) is given by... 

In our illustrative calculated results, chain transfer reactions are neglected in order to highlight unique characteristics of emulsion polymerization. However, the radical entry rate into a polymer particle is often much smaller than the chain transfer frequency in emulsion polymerization usually. In such cases, dead polymer chain formation is dominated by chain transfer reactions, and the instantaneous weight fraction distribution is given by the following most probable distribution ... 

Figure 14 shows the development of the weight fraction distribution with and without TDBP [263]. 

Fig. 14 Accumulated weight fraction distribution development with and without terminal double bond polymerization...

Fig. 18 Comparison of the calculated weight fraction distribution with Cf=Cfp=5xlO and Xc=0.5. For the emulsion polymerization model, the total number of polymerized monomeric units in a polymer particle Hp=4x 10, which is equal to the size of a dried polymer particle...

Fig. 5-5. (a) Mole fraction disiribiition of reaction mixture in linear step-growth polyinerizalion for several extents of reaction, (b) Weight fraction distribution of reaction mixture in linear step-growth polymerization for several extents of leaction [2],... 

Wesslau MWD. The model based on the Wesslau MWD has been described previously (JS). The weight fraction distribution of x-mer, where X is the degree of polymerization (DP), measured as a function of the logarithm of the degree of polymerization, is given by... 

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