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Download NMR of Chemically Exchanging Systems by Jerome I. Kaplan PDF

By Jerome I. Kaplan

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T h e result is that p A B ( )/ ( 5 _ 1 2) - e ^ » + ^ y<-0~ p r coh = The probability that after a time t collision is t’ AB will not suffer an exchange -(/-OA ab — ( 5 - 1 3) T AB A B and therefore the ensemble average p ( / ) is the weighted probability of all AB molecules created at t’ which survive until time / J - ~ AB We next differentiate (5-14) to obtain the differential form of the p ^ equation. This is done using the result from calculus that for y(t) = Jf’g(t, t’) dt’, (5-15) A % = J^(s(’,n)dt’ (5-16) + g(t,t).

4-180) b y 3C An = Σ («ο/ ~ P N O " + P, 'Po -] ] ^ . («)3Γ(«). (4-188) T o be specific, consider + A B $1 = ( / , ) " ( / / ) " . (4-189) In (4-187) we thus will have one term of the form + > . [˘ˆ/y- . ´ æ Γ>ˇ " + B A P. "Po -]] * — 00 (4-190) which using the high temperature approximation p£W^l /NMB) (4-191) becomes upon substituting into (4-178) -KB)/ " + 0 + °e—c2 (r, .

L . Gordon , J. Chem. Phys. 59, 4569 (1973). 21. A. Abraga m an d R. V. Pound , Phys. Rev. 92, 943 (1953). GENERA L REFERENCE S A. G . Redfield , IBM Res. Dev. 1, 19 (1957); H . G . Redfield , Adv. Magn. Reson. 1, 1 (1965). Redfiel d relaxatio n theory . A. Abragam , "Th e Principle s of Nuclea r Magnetism, " Chap . VIII . Oxfor d Univ . Press , Londo n an d N e w York , 1961. C . P. Slichter , "Principle s of Magneti c Resonance, " Chaps . 5 an d 6. Harper , N e w York , 1964. R. K . Wangnes s an d F .

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