Chain length dependent determination

While many data are suggestive of chain length dependence, the data are not usually suitable for or have not been tested with respect to model discrimination. Values of ,u have been determined for a variety of small monomeric radicals to be ca I09 M s 1.4 Taking kt0 as Jk,lj and a as 1.0 in the geometric expression yields values of ,iJ as shown in Figure 5.4a.49 Use of the Smoluchowski mean or the harmonic mean approximation prediets a shallower dependence of k 1 on the chain length (Figure 5.4b). All expressions yield the same dependence for j=i. 

The parameters indexed with a are connected with the nucleation step or other effects occurring only once per triple helix. Parameters denoted by s are related with the equilibrium constants of the propagation steps and are ordered to be independent of the position of the reacting chain segment. This implies that end effects are neglected. Since the same dependences are valid for AH° and AS, with the help of their chain length dependence we can determine AG by extrapolation up to 3 n - 2 = 0, and thus, a can be estimated it depends neither on temperature nor on the chain length. 

Engel et al.92) have estimated the nucleation parameter for H(Pro-Pro-Gly) OH by computing AG° and AS° with Eq. (5) and reported melting temperatures Tm and AH0 values determined calorimetrically. Utilizing the chain length dependence, they obtained the following parameters (in diluted acetic acid at 25 °C n = 5, 10, 14.15) ... 

The nucleation parameters have to be determined with the help of the chain length dependence of Tm, since no calorimetric data are available. Using Eqs. (2, 7, 8) we obtain... 

The traditional method of determining the monomer transfer constant is the Mayo method [294,295], where the inverse of the number average chain length Pn is extrapolated to zero polymerization rate. To obtain reliable values, one needs to measure rather large P values to high precision that can then be extrapolated to zero polymerization rate. In addition, linear extrapolation is not guaranteed if bimolecular termination reactions are chain-length-dependent [296]. 

K above their glass transitions. All linear polymer melts have viscosity proportional to molar mass (ry M) for sufficiently short chains, when the data are determined at a constant friction coefficient as opposed to isothermal data. Longer chains have entanglement effects (discussed in Chapter 9) and have The full chain length dependence of... 

The chain length dependence of termination rate constants (Section 5.2.1.4) should not be ignored when considering copolymerization kinetics. It has been pointed out that average chain lengths in copolymerization will be a function of the monomer feed composition especially in copolymerizations with disparate propagation rate constants. Factors determining the rate of copolymerizalion are not fully resolved and copolymerization kinetics remains a topic of discussion and an area in need of further study. 

Equation 4.19 is a plausible first approximation when miceUes are small and spherical and solubilization is relatively low. Indeed, King (1995) showed that the dependence predicted by this model of on both and surfactant chain length, which determines r, is in quantitative agreement with experimental data for pure gases of low molecular weight solubilized in ionic surfactant micelles. 

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