Science Record

However, we may furthermore make a detailed analysis of the experimental data; it is spontaneously found that the curves in Fig. 6 show somewhat a saddle tendency. This phenomenon may be explained as follows: Because the length of the chain in the succinic acid or in the glutaric acid is rather short, the carboxyl groups at the two ends of the chain slightly interact with each other, and therefore, their velocity constants are a little greater than those of the adipic acid, pimelic acid, suberic acid and azelaic acid. As the length of the chain is further increased, due to its flexibility, the carboxyl groups at the end of the chain may interact again, so the velocity constant is also slightly increased. But the velocity constant will not vary too much as the length of the chain increases indefinitely, because the average distance (/?? between the two end carbon atoms for long molecules obeys the following formula:

= , 1+ cosB 1+ <cos$) Ne Ne 1 — cosB 1 — Ccos$>” @

where N is the number of links in the chain, b the carbon-carbon bond distance, B the valence angle, and <cos $) 1s defined as

is e VPVET cosh db — Jo

€ cos > = = 2 (3) \, e VP V/RT dp

here V(#) being the potential function of the internal rotation. The average distance between two carboxyl groups is obviously proportional to the square root of (2), i.e. proportional to»/N 6. Hence, when the length of the chain is rather long, the interaction between the two end carboxyl groups tends toward zero, and therefore the velocity constant approaches a definite value.

-From Table 1 and Fig. 7 we may find two phenomena: First, when one hydrogen atom in the chain of the ethylene glycol is substituted by the methyl group in the formation of 1,2-propylene glycol, its velocity constant is decreased; secondly, when the length of the chain becomes longer such as 1,4-butylene glycol and 1,6-hexamethylene glycol in comparison with ethylene glycol, the velocity constant is increased. These two phenomena may be explained by the theory of the molecular structures and the mechanism of polyesterification reaction supposed by us. One of the important steps in the hydrogen ion catalysis in polyesterification is

OH OH

| ; | —Ct + :0—(CH2),—-O—C— == —C—0—(CH.),—O—c— —> ll

i OH H O OH,H+ O wey —o—0~(CHi)x—0—C— + HO + Ht. 4) I O oO