Polymerization constant

Table 6.2 Relationship between field strength of dissolved cation and polymerization constant in M0-Si02 melts (data from Hess, 1971).

It is obvious that the acid-base property of a dissolved oxide may markedly affect the structure of a silicate melt. A dissolved acidic oxide associates the free oxygen, thus displacing reaction 6.4 toward the right, resulting in a marked correlation between the field strength of the dissolved cation and the polymerization constant of the melt. This correlation is shown in the values listed in table 6.2. 

Fig. 18. The polymerization constants kp, for sodium methoxide initiated polymerizations of y-benzyl-i-.glutamate-N-carboxyanhydride in dioxane solution (4 g/100 ml) as a function of mole per cent. D-anhydride isomer X, polymers made with m.-NCA and optically active NCA o, polymers made with mixtures of pure o- and pure t-NCA. [Reprinted from paper by Idelson and Blovi J. Am. Chem. Soc. 80, 2387 (1958)...

Reservoir Diffusion through a polymeric Constant drug release with time Zero-order release M t ... 

The equilibrium constant Kg, is considered to be equal to the product of a polymerization constant Kp and an Ionization constant... 

Polymerization constant. The polymerization constant k corresponds to the following equilibrium ... 

Further, the polymerization constant ks (referring to the formation of a siloxane bond) and the ionization constant Ki are assumed not to be modified by the presence of aluminum atoms. The ka value, corresponding to the formation of a Si-O-Al bond, aas estimated by iteration according to values originating from a semi-quantitative experimental study (29) and aas found to be 35. The follo-aing results are based upon an example from this study. 

Polymerization Constants for Several Monomers Conmonly Prepared by Emulsion Polymerization (15)... 

Table 9. Number of active centers and some polymerization constants as a function of reaction parameters for propylene... 

It is known that conversion of syngas to hydrocarbons by FTS is largely dependent on the kinetics of reaction [4,5]. Decrease in space velocity, temperature of reaction and H2/CO ratio increases the formation of high molecular weight fraction (higher carbon number) of the product. For middle distillate selectivity, it is required that the polymerization constant a 1 in the Ci-Cj2 product range and product polymerization should preferably be avoided beyond C20-1-... 

Table 18-1. Anionic Polymerization Constants for Styrene and Isoprene with Butyl Lithium (Initiation) or Metal Alkyls (Propagation) at 3(PC...

Equilibrium constant of polymerization Constant in the Mark-Houwink-Sakurada equation... 

The product of the polymerization constants, riT2, is very frequently used as an index for evaluating the alternating tendency in binary copolymeriz-ation/" In fact, the reciprocal of the product rir2 is often called the alternation tendency index. The ideal (random) copolymerization condition exists for the case / i/ 2 = Where ri and r2 are very low and the rir2 product tends to zero the alternating tendency increases.The product r r2 can be zero in two cases—where one or both reactivity ratios are zero. Where r — 0, the copolymer chain is built of isolated Mi units separated by sequences of M2 monomer units. Strictly alternating copolymer would be obtained when both / i and V2 are zero. The second condition is often found for MA copolymerizations, as described in Chapter 10. Where ri > 1, the polymer is richer in Ml monomers than the monomer feed. For ri < 1, the opposite holds. 

One can easily observe that the cyclization equilibrium constants are in fact reciprocals of the equilibrium polymerization constants of macrocycles, regarded as monomers of linear homopolymerization. 

Polymer models of the type described above have been used with considerable success to interpret the mixing properties of certain binary silicate melts. Althoiagh the polymerization constants for melts of geological complexity are as yet unknown and the... 

Tljius the equilibrium water content ( 0 ) increases with (fH2o) Exact values of the polymerization constants for oxygen species in melts of albite composition are inknown. However the results of Burnham and Davies (197 ) on albite-H20 may be expressed by the simple equilibrium relation (19) if it is assumed that one mole of NaAlSi308 melt contains eight moles of 0. Values of InK calc ilated from (19) for different pressures are plotted against l/T in Fig. 10. 

The curves shown in Fig. 11 are of some interest because the cation effect is the opposite of that which might be predicted from studies of the effects of cation polarizing power on the polymerization constants (Hess, 1971). Hess has pointed out that values of K tend to increase as the polarizing power of the cation (Z/r2) increases. Referring to the polymerization reactions ... 

The Masson and Toop and Samis mixing models assume complete dissociation of the basic oxide components. Thus, while these models may allow the calculation of oxide activities within any binary, activities in different binary systems cannot be compared since they relate to different standard states. The magnitude of the polymerization constant for a system is a measure of the shape of the titration curve not its absolute position. Thus with decreasing K the curves become steeper, or more sharply inflected, reflecting strong interactions between 02- and 0° or Si-O-Si. As pointed out by Hess (l97l) values of K decrease as Z/r decreases. So the activity curves for Ca2+ systems should be more steeply inflected than in the case of the equivalent Mg2+ compositions and these effects are shown in Fig. 11. 

In attempting to use the polymer or quasi-chemical models to calculate the mixing properties of ternary and more complex melts, the differences in the standard state values of X 2- assumed for the end-member oxide components may be very important. In the absence of any additional cross-interactions the polymerization constants in a multicomponent system containing a mols of AO, b mols BO etc. will be given by... 

The variation of polymerization constants with temperature is known for the system FeO - Si02 (Distin et al., 1971 Masson, 1972). The proportions of different structons can thus be cal-ciilated at different temperatures using the combinatorial formulae in Table 1. Activities of fayalite in the melt can therefore be calciilated from the expression ... 

This can he compared with the value calciolated from equation Taking the data of Distin et al. (l97l) and Masson (1972) a value of the polymerization constant for Fe0-Si02 melts can he obtained at li 55°K from a regression of InK versus l/T. From this, K = 0.57 - Using this value the activity of Fe2Si01 in the melt calculated from equation is... 

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