Mass fractions, of polymers

The GPC traces in Fig. 24 reveal a broad molecular weight distribution, MJMn = 4.42, for the dual reactor blend sample. On the other hand, the diblock OBC displays an overall MJMn of 1.67. The narrowing of the distribution indicates that the polymerization has CCTP characteristics. The theoretical molecular weight distribution from an ideal living polymerization in a series of two CSTR reactors is given by the following equation, where/j and/2 are the mass fractions of polymer comprising the two blocks [11] ... 

The mass fraction of polymer with a chain length j within a certain interval dj is given by yjdj. The chain-termination probability, q, can be estimated from Mayo s equation ... 

Wa and Wb mass fraction of polymer (B) and solvent (A) (definition see below)... 

Using the terminology of Schmidt and Biddison [20], the weight or mass fraction of polymer, Ms, below the selected diameter remsdning in the suspension can be calculated from the equation ... 

Figure 5-30. Specific volume of methyl methacrylate-poly(methyl methacrylate) mixtures as function of mass fraction of polymer at 25° C. vim = 0.842 cmVg, v° = 0.820 cmVg (after D. Panke and W. Wunderlich).

It is also interesting to calculate the mass fraction of polymer populations containing i LCB per chain, niucBi-... 

In the simplest case, the mass CLD of a heterogeneous polymerization, which is defined as the mass fraction of polymer molecules with a given chain length i, is represented by a weighted sum over different Flory distributions (Flory, 1953), each corresponding to one type of catalyst site ... 

Equation 17 can be solved numerically for any specified temperature history. However, the mesophase temperature history is a function of both time and position (see Fig. 4), and so the transient temperature distribution T(x, t) must be specified in order to obtain an analytic solution for equation 17. If the temperature distribution is static during steady burning of a thick sample as the surface x = 0 recedes at constant velocity v = (dx/df)r and the mesophase is a thin surface layer, then the rate of temperature rise of the mesophase is constant, (dT/df)a =o = -v(dT/dx)t = The assumption of a constant heating rate for the mesophase transforms the independent variable in equation 17 from time to temperature and allows for a solution in terms of the mass fraction of polymer remaining at temperature T... 

G (sx,Sa), G (sx,Sa) pgf of trees starting, respectively, vith a prescribed monomer unit X , an unreacted group A , or a half-bond Z pgf of mass fractions of polymer molecules in a sol acceleration due to gravity [m s ] ratio niA/bA [m moffi ]... 

It is usually straightforward to detect the presence of multiple-site types on a coordination catalyst because these catalysts will produce polymer with polydispersity higher than 2 even under invariant polymerization conditions. The simplest way to visualize this phenomenon is to assume that every different site type on a multiple-site catalyst produces polymers that follow a distinct Flory s distribution that is, those with a distinct number-average chain length, [38]. In this way, the chain length distribution for the whole polymer is a combination of distinct Flory s distributions weighted by the mass fraction of polymer made on each site type, mj [Eq. (24)]. 

Under some circumstances, such as when the bubble size is very small and low gas flow rates are used, the concentrations of the VOCs in all phases are at thermodynamic equilibrium. In this case, the removal kinetics of the VOCs is given by Eq. (11) [82-84], where t is the removal time and k is the apparent removal rate constant, given by Eq. (12) [84]. is the water molecular weight, E is the mass of latex in the devolatilizer, and X is the mass fraction of polymer in the latex. 

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