2] DEUTERIUM EXCHANGE 29 



for the rate constant assigned to the two bonds situated i places from the 

 ends. The quantity y is e'^^ri^'^ and i may assume values from 1 to 13, 

 the two halves of the helix being considered symmetrical (/2i=2), The cal- 

 culations leading to Eq. (10) are rather trivial and will be given in greater 

 detail elsewhere. The terms involving ßi for the seven deuterium atoms 

 which are not hydrogen-bonded were assumed to be negligible. 



It will appear from Eq. (10) that the more positive AVr, the more the 

 ßi will decrease toward the middle of the helix (/=13). It was therefore 

 tempting to apply Eq. (10) to our results and see whether reasonable values 

 for A¥r and k^y^ [QH] could be obtained on the basis of these very simple 

 assumptions. It became immediately clear that it was impossible to fit this 

 theory to the experimental data in an acceptable way. In order to satisfy 

 the condition that deuterium atoms fully exposed to water (7 in our case) 

 should exchange with a half-time too small to be measured, A¥r has to be 

 given a high positive value so that hydrogen bonds only a few places away 

 from the ends are suitably inhibited in their exchange. This choice of zlFr 

 caused, however, the ßi of bonds nearer to the middle of the helix to become 

 too small so that the calculated rate curves fell off too rapidly. 



This negative result led us to consider the possibiUty of breaks in the 

 interior of the helix as a means to increase the value of the internal ßi, 

 and we have adopted the treatment of Schellman,^^ p. 236, Eq. (9), putting 



(A) breafc = Ä:2[QH] . 3 . g-^^öreafc/^^ (1 1) 



and taking into account that a particular hydrogen atom becomes exposed 

 in three different breaks and that breaks occur not only in completely folded 

 helices, but also in partly unfolded ones. Formula (11) is correct only if 

 AY'r is large so that the concentration of intact helices is high, and even then 

 it is a crude approximation. A more exact expression could be derived, but 

 it is hardly worth the effort to introduce these highly complex corrections. 



The possibility that deuterium ions are pulled out one by one from the 

 middle of the hehx and replaced by protium ions cannot be excluded entirely. 

 Since, however, the mechanism of this process is not clear to us — except 

 for the belief that it may lead to a term of the same type as Eq. (1 1), i.e. 

 to ßi values which are approximately independent of i — we shall postpone 

 the discussion of this point to a later publication. 



The curves in Figs. 1 and 2 are calculated on the basis of Eqs. (11) and 

 (10) combined, viz., 



Bi={e-iàP,lRTj^2>. e-^^6rea*/^^}Ä:2[QH] (12) 



or 



i3ï={(0-376)»+000572}A:2[QH] (13) 



neglecting higher powers of y in Eq. (10). The numerical value introduced 

 for A¥r was +530 cal. and for ^F&reaÄ; = +3400 cal., a somewhat lower 

 value than that adopted by Schellman (4500), who neglected the entropy 

 increase in the process of breaking. The calculation is in any case uncertain 



