Composites equations for

Equations (7.40) and (7.41) suggest a second method, in addition to the copolymer composition equation, for the experimental determination of reactivity ratios. If the average sequence length can be determined for a feedstock of known composition, then rj and r2 can be evaluated. We shall return to this possibility in the next section. In anticipation of applying this idea, let us review the assumptions and limitation to which Eqs. (7.40) and (7.41) are subject ... 

Polymerization equilibria frequently observed in the polymerization of cyclic monomers may become important in copolymerization systems. The four propagation reactions assumed to be irreversible in the derivation of the Mayo-Lewis equation must be modified to include reversible processes. Lowry114,11S first derived a copolymer composition equation for the case in which some of the propagation reactions are reversible and it was applied to ring-opening copalymerization systems1 16, m. In the case of equilibrium copolymerization with complete reversibility, the following reactions must be considered. 

The derivation of fractional composition equations for a diprotic system follows the same pattern used for the monoprotic system. 

Step 1 Write a fractional composition equation for each acid or base that appears in the charge balance. 

A bigger nuisance when considering ion pairs is that the fractional composition equations for [H2T], [HT ], and [T2-] also are changed because the mass balance for H2T now has five species in it instead of three ... 

Our strategy is to substitute expressions into the charge balance to obtain an equation in which the only variable is [H+l. For this purpose, we use the fractional composition equations for the triprotic acid, H,P04, which we abbreviate as H3P ... 

Give a physical interpretation of Equations 23-6 and 23-7 in terms of the fractional composition equations for a monoprotic acid discussed in Section 10-5. 

Study of the composition equations for three-component cqiolymers. II. VysokomolekuL Soedin. 3. 14 (1961). 

COMBINATION OF SEPARATE CONTRIBUTIONS Summation of the expressions for each mechanism in accordance with Eq. (13-24) results in a composite equation for the effective thermal conductivity,... 

The composition equation for initial copolymer in terms of monomer group concentration [B]o becomes [cf. Eq. (7.11)] ... 

Local-composition equations for g arc resdily extended to multicomponent mixtures. The multicomponent expressions contain parameters obtainable in principle from binary data only they provide descriptions of g of acceptable accuracy for many engineering calculations of multicomponent vapor-liquid equilibria at subcriiical conditions. Listed below are the multicomponent versions of the Wilson. NRTL. aed UNIQUAC equations. 

Following a procedure similar to that used in deriving Eq. (7.11), the instantaneous copolymer composition equation for the penultimate model is then given (Hamielec et al., 1989) by... 

In this problem, we construct the fractional composition graph in Figure 11-1. From the mass balance and the equilibrium expressions, we can derive fractional composition equations for a diprotic system, H2A ... 

Consider the preparation of styrene-acrylonitrile and methyl methacrylate terpolymer in a CSTR. There can be 3x3 = 9 possible dyads formed. These are AA, AS, SA, SS, SM, MS, AM, MA, and MM. The reactivity ratios can be read from Chapter lO, Table 10.1 The terpolymer composition can be calculated using the terpolymerization composition equations for a CSTR given in Equations (10.23-10.25). The dyad probabilities were calculated using an MS Excel spreadsheet and listed in Table 11.3. Let AN be denoted as monomer 1, styrene as monomer 2, and methyl methacrylate as monomer 3. Assuming that the bond formation order does not influence the rate, that is. 

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