Copolymerization point, azeotropic

The heterogeneous copolymerization of styrene and acrylonitrile in various diluents as reported by Riess and Desvalois (22). Although the copolymer composition in these studies was not strongly influenced by the diluent choice, the preferential adsorption of acrylonitrile monomer onto the polymer particles shifted the azeotropic copolymerization point from the 38 mole % acrylonitrile observed in solution to 55 mole % acrylonitrile. 

The plots in Fig. 6-2 illustrate an interesting characteristic of copolymerizations with a tendency toward alternation. For values of r and r2 both less than unity, the F /f plots cross the line representing F — j. At these interesections or crossover points the copolymer and feed compositions are the same and copolymerization occurs without a change in the feed composition. Such copolymerizations are termed azeotropic copolymerizations. The condition under which azeotropic copolymerization occurs, obtained by combination of Eq. 6-12 with d[Mi]/ii[M2] = [Mi]/[M2], is... 

As seen from Figure 2.3.2, the composition of the polymer and that of the feed is usually different. As the reaction progresses, only by maintaining a constant composition of the feed is it possible to obtain a uniform copolymer. For rA and re less than unity, the variation of Fa as a function of fa has a point where (Fa)c = (fA)c. where the composition of the copolymer is identical to the concentration of the feed. The copolymerization at this concentration is known as azeotropic copolymerization. This is achieved when fA has the value given by rel. (2.3.24) ... 

Figure 7.2 shows curves for several nonideal cases, that is, where r T2 1. It is seen that when both r and T2 are less than 1 there exists some point on the i i-versus-/i curve where the copolymer composition equals the feed composition and at this point the curve crosses the line F = f (that is, the diagonal line). At this point of intersection, polymerization proceeds without change in either feed or copolymer composition. Distillation terminology is again borrowed for this instance. Azeotropic copolymerization is said to occur at such points and the resulting copolymers are called azeotropic copolymers. 

In those cases, where rj and V2 both either less or greater than unity, the curves of Figure 8.2 cross the line Fj = fj. The points of interception represent the occurrence of azeotropic oopolymerization that is, polymerization proceeds without a change in the composition of either the feed or the copolymer. For azeotropic copolymerization the solution to Equation 8.5 with d[M[]/d[M2] = [Mi]/[M2] gives the critical composition. 

Azeotropic copolymerization occurs when ta < 1 with ra < 1 (the situation defined by ta > 1 with ra > 1 is not observed in practice). The Fa vs. /a curves are characterized by their intersection of the Fa = /a line at one point which corresponds to the azeotropic composition (/A)azco. Substituting Fa = /a = (/A)azeo uito Equation (1.33) leads to... 

The curve does not intercept the ideal azeotrope line, either, in nonideal nonazeotropic copolymerization. But, in contrast to ideal nonazeotropic copolymerization, the curve is no longer symmetrical. In azeotropic nonideal copolymerizations, behavior depends on whether both copolymerization parameters are or are not of the same magnitude. If they are also equal, then, according to Equation (22-15), the azeotropic point must occur at a 1 1 composition ratio, that is, at a mole fraction of 0.5. If the molar fraction is less than 0.5 for monomer B, then the azeotropic ordinate point must be above the 45° ideal azeotropic line because of the tendency to alternate, but the point... 

During the investigation of the principles governing the process of copolymerization of AN with ISP in DMSO at 30 °C in the presence of ammonium persulfate, it was established that the anisotropic type of copolymerization is characteristic for this pair of monomers. The azeotropic point, as it is seen from Fig. 1 corresponds to a content of 60% of monomeric units of ISP in the monomer mixture. 

In such cases the polymerization can be taken to relatively high conversion without change in composition of the copolymer formed (see Example 3-37). In the copolymerization diagram the azeotrope corresponds to the intersection point of the copolymerization curve with the diagonal. For example, from Fig. 3.4 it may be seen that in the radical copolymerization of styrene and methyl methacrylate the azeotropic composition corresponds to 53 mol% of styrene. 

Note that the expressions (4.15) can be obtained even without the formulae (4.11), if we employ an algorithm similar to the one used for the derivation of formulae (4.11). Actually, the proper diverging from the point i directed tree corresponds to each of the items in the expression for Af. A weighting factor o ay corresponds to each of the arcs in there digraphs that leaves point i and enters point j. The sum of all so weighted trees directed from a root of type i directly gives an expression similar to expressions (4.15) for the value of Af, which is equal (when all coj are positive) within the accuracy of the normalizing factor A to the component xf = Xf = Af/A of azeotropic composition under the copolymerization of an arbitrary number (m) of monomers. 

In the systems (I) and (III) 2-simplex consists of a sole cell, all the trajectories inside which approach SP corresponding to homopolymer Ms where rs < 1. The systems (I) and (III) topologically are equivalent, since they differ from each other only by the inversion of the monomer indexes therefore their phase portraits are of the same type, too. In the systems (II) and (IV) the azeotropic point separates the simplex into the two cells. However, the system (IV), in which both parameters r, and r2 exceed unity practically is non-realizable [20-24]. That is why the stable binary azeotropes are excluded from the consideration, and the dynamics of the copolymerization of two monomers is exhaustively characterized by only two types (I) and (II) of phase portraits. 

The calculation of coefficients ak of equation (5.11) for SP located on m-simplex boundary is reduced to the analysis of the inner azeotropes in the systems with the less number of component Let us consider, for example, one of such boundary points x where xf > 0, xf > 0,..., x, > 0, x, +1 = 0,..., x = 0. This SP obviously is the inner azeotrope on 1-subsimplex (12. .. 1), where its location and corresponding characteristic equation of (1 — 1) degree are determined as a result of the consideration of copolymerization of following monomers Mt, M2,... Mj. The obtained solutions L2,. .. of the above equation are also the roots of the characteristic equation (5.11) of m-component system, and the rest (m — 1) roots are calculated by the following formula... 

Some copolymerization systems are not strictly alternating, but still they show a tendency toward alternation. This occurs when both and r2 < 1. The alternating trend increases as the reactivity ratios approach zero. An interesting feature of these systems is that they present the so-called azeotropic composition, at which Fj = /j. At this composition, the copolymer formed has the same composition as the monomers in the feed and, therefore, systems copolymerizing at this condition do not show compositional drift. It can be shown that a necessary condition that the reactivity ratios have to satisfy in order for a copolymerization system to show an azeotropic point is that either both and r2 < 1 or both and T2 > 1. 

Hint 1. Plot Fj versus /i in a batch copolymerization for different combinations of r and r2 and observe the composition drift. Is the direction of composition drift always the same Are azeotropic points stable or unstable to small perturbations in monomer concentration ... 

Such terpolymerizations can be represented quite well by a triangular plot. An arrow indicates how the composition of the initial monomer mixture changes with respect to the initial copolymer composition during copolymerization. The two compositions are equal for the azeotropic case the arrow shrinks to a point (Figure 22-6). 

Both reactivity ratios are smaller than unity ri < 1 and /-2 < 1 or Aril composition curve crosses the diagonal in an azeotropic point. In this azeotropic point the incorporation ratio of both monomers equals the monomer composition, so there is no preferential reaction of one of the monomers (curve b in Fig. 8.1). 

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