Energetics Solvent-Separated and Contact Ion Pairs

2 kJ mol-1 in tetrahydrofuran. Similarly, the effect of / on K in more polar solvents is greater for the smaller, better-solvated ions (Na+) compared to the larger, more poorly solvated ions (Cs+). 

The observed ion-pair propagation constant kj is an apparent rate constant, kj is a composite of the rate constants for the contact ion pair (kc) and solvent-separated ion pair (ks) according to 

The variation of kj with temperature depends on the interplay of the separate variations of kc, ks, and Kcs on temperature according to 

Experimental data of kj versus 1 /T can be fitted to the preceding equations to yield values of the various activation and thermodynamic parameters pertinent to ion-pair propagation (Table 5-12). Corresponding values of the parameters for free-ion propagation are included in Table 5-12 for comparison. The solvent-separated ion pair is approximately half as reactive as the free ion, while the contact ion pair is more than 3 orders of magnitude 

The reactivity of the solvent-separated ion pair is hardly affected by the counterion. This can be observed from the kj values in THF (Table 5-11). Most of the observed propagation in THF is due to solvent-separated ion pairs and kj is a good indication of ks. The variation in kj from Li+ to Cs+ is relatively small and is probably due more to differences in the fractions of solvent-separated ion pairs than to differences in ks. The reactivity of contact ion pairs is more sensitive to the counterion. The variation of kj in dioxane is by a factor of 25 between the different counterions. Since the fraction of solvent-separated ion pairs is extremely small in dioxane, kj is indicative of kc. The larger, more loosely held cesium counterion results in a higher reactivity for the contact ion pair. The variation of kc and ks with solvating power of the reaction medium is not established. Some data indicate that ks is insensitive to solvent while kc increases with increasing solvating power, but these results are limited to ether solvents. 

The initiation and propagation reactions typically show fractional orders of dependence of rate on aikyiiithium. The situation is quite complex. The fractional orders for initiation and propagation are seldom the same and often vary depending on the monomer, solvent, and initiator and their absolute as well as relative concentrations. For styrene polymerization by n-butyllithium in aromatic solvents, the initiation and propagation rates are proportional to only the and -powers of n-butyllithium concentration, respectively. These results have been interpreted in terms of the following association equilibria 

---