Reactivity principle of equal

As pointed out by Flory [16], the principle of equal reactivity, according to which the opportunity for reaction (fusion or scission) is independent of the size of the participating polymers, implies an exponential decay of the number of polymers of size / as a function of /. Indeed, at the level of mean-field approximation in the absence of closed rings, one can write the free energy for a system of linear chains [11] as... 

A kinetic study for the polymerization of styrene, initiated with n BuLi, was designed to explore the Trommsdorff effect on rate constants of initiation and propagation and polystyryl anion association. Initiator association, initiation rate and propagation rates are essentially independent of solution viscosity, Polystyryl anion association is dependent on media viscosity. Temperature dependency correlates as an Arrhenius relationship. Observations were restricted to viscosities less than 200 centipoise. Population density distribution analysis indicates that rate constants are also independent of degree of polymerization, which is consistent with Flory s principle of equal reactivity. 

SUMMARY AND CONCLUSIONS THE PRINCIPLE OF EQUAL REACTIVITY OF ALL FUNCTIONAL GROUPS... 

The principle of equal reactivity as enunciated above asserts merely that all like functional groups remaining unreacted at any given stage of the process enjoy equal opportunities for reaction. It has not been stated that the level of reactivity (i.e., the velocity coefficient) necessarily remains constant as the reaction progresses. Indeed, the velocity coefficient for polyesterification has been shown to change as the reaction progresses from 0 to 80 percent conversion. Since monoesterifications exhibit a similar perturbance, it has been concluded that the size of the polymer molecules formed does not alter the course of the reaction hence the principle of equal reactivity is not violated. 

The size distribution equations rest squarely on the validity of the principle of equal reactivity. Should they be proved appreciably in error in a given instance, this principle would have to be modified, or abandoned, for the polymerization process concerned. Since the principle seems well established, the likelihood of need for such qualifications seems remote. 

In 1959 and 1960, Challa published the first results of quantitative experiments on the poly condensation equilibrium in PET [22, 41, 42], He determined the polycondensation equilibrium constant K at different temperatures and average degrees of polycondensation and found that this parameter depends only slightly on temperature, but increases significantly with increasing degree of polycondensation. The monomer BHET was found not to follow the principle of equal reactivity. 

Polymer chemistry shows that the larger the various polymers become, the more their reactivity becomes independent of the length of the polymer chains. This fact, known as the principle of equal reactivity of cocondensing functional groups, has been verified in fused polyphosphate systems (which, for several properties, may be considered as analogous to silicate melts cf Fraser, 1977) with polymeric chains longer than 3 units (Meadowcroft and Richardson, 1965 Cripps-Clark et ah, 1974). Assuming this principle to be valid, the equilibrium constant of reaction 6.4 ... 

The constants of equations 6.16 and 6.17 are identical, on the basis of the principle of equal reactivity of cocondensing functional groups. Adopting Temkin s model for fused salts, and thus assuming that molar fractions represent activities over the appropriate matrix, we obtain... 

The linearity in the standard partial molal properties of the aqueous polymers as a function of the length of the chain (in terms of C atoms) observed by Shock and Helgeson (1990) is the result of the principle of equal reactivity of cocondensing functional groups (which, as we have already seen in section 6.1.2, also holds for silica polymers). This principle is, however, strictly valid only when the length of the chain is sufficiently elevated and small departures are observed for chains with one or two carbon atoms (cf figure 8.28). 

Thus, it is assumed that the reactivity is independent of molecular weight. This principle of equal reactivity holds true for both condensation and stepwise addition polymerizations. It means that there is no difference in the reactivity of the end groups of monomer, dimer, etc. and, therefore, that the rate constant is independent of the degree of polymerization over the total duration of reaction. 

Assuming that the principle of equal reactivity applies even for the amino acid, then... 

In several instances, discussed in more detail later in this section, experimental evidence strongly indicates that the principle of equal reactivity of functional groups is not obeyed for all chain lengths, and that the equilibrium constant may itself be a function of the degree of polycondensation. 

The derivations given in the previous Section for A—B type polycondensation (type I) hold also for A—A plus B —B types of polycondensation (type II) reactions when there are precisely equivalent proportions of A—A and B — B reactants and the principle of equal reactivity of all functional groups of the same chemical type is applicable. Now, however, x represents the combined number of both types of units in the polymer chain. Therefore, in place of Mo in Eq. (5.38) one has to use the average weight of units... 

Applying the principle of equal reactivities one can write a more generalized expression for K2 , , , ... 

In isodesmic polymerizations, the individual monomers associate with an association constant that is independent of the polymer size. This is comparable to the simplest description of a step-growth polycondensation given by Flory s principle of equal reactivity [10]. The mechanism gives rise to a PDI of 2 in the high-concentration regime. 

The principle of equal reactivity is no longer valid when the reacting groups are only formally independent of each other, so that in actual fact they influence each other strongly. After the reaction of the first vinyl group in divinyl benzene the second group has a quite different reactivity to the first. The reactivity similarly decreases on the formation of conjugated systems... 

The principle of equal reactivity states that all functional groups of the same species are equivalent, that is, the reactivity of all functional groups on the polymers is the same irrespective of their molecular weight and structure [1]. In other words, there is an intrinsic reactivity of the polycondensation. We shall derive the molecular weight distribution function of nonlinear polymers under the assumption of equal reactivity. 

The propagation constant kp and the termination constants for combination and disproportionation, k,c and k,d, are independent of the size of the chains. This is called the principle of equal reactivity. 

Polymerization equUibiium. Consider the process of polymerization and assume the principle of equal reactivity, that each monomer adds with the same equilibrium constant as the previous one ... 

The Principle of Equal Reactivity and the Prediction of the Evolution of Functional Croup Concentrations... 

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