Class Note for CHEM 777 at UMass(5)
Class Note for CHEM 777 at UMass(5)
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Date Created: 02/06/15
Ch 777 Spring 03 page 33 16 Measuring kinetics of dynamic processes by NMR What is the quotNMR timescalequot What dynamic processes can be monitored a motion which enhances relaxation or averages an NMR parameter examples 1 Methyl group rotation at right frequency promotes T1 relaxation 2 Motion of lipid in different phases bilayer in gel vs liquid crystal vs vesicles averages lipid headgroup 31F spectrum in diagnostic ways when motional frequency is faster than frequency range of parameter being averaged b chemical exchange between 2 states which differ in 6 or J or T1 or T2 Compare the rate k11C of the dynamic process to the NMR parameter being averaged A8 or AJ or AT1 or AT2 timescale slow exchange intermediate exchange fast exchange I gtgt 4 t N 4 1 ltlt 4 5 I521 5839 ISA 5839 FA 68 kltlt6A 63 kml A BBI kgtgt6A 68 J 1 gtgt 1 1 1 1 ltlt 1 IJAJB IJAJB 6A6B T1 or T2 1 gtgt 1 etc etc Ch 777 Spring 03 page 34 McConnell equations Recall general Bloch equation foc Myj2 MZ M0 2 Mimly t Y X0Y X10 T2 T1 611 express E E0 310 then dM E y M X B relaxation terms EMyBZ MZBy XMXBZ MZBXZAMXBy MyBX FOI ED BZ and 51 B1 coswt c B1 sinwt This is an X pulse B1 on Larmor frequency starting on X in the laboratory frame fixed on x in the rotating frame M x y Mle0 MZBlsincut dt 7 d M y MB MBcosut y dt 4v x 0 z 1 7 Now consider exchange process d A d B 1 1 kA kB 1 1 MA MB dt dt dA dB E dt 1A 13 dt 11A 1 3 Then incorporate exchange into processes occuring to MX of A MAX MEX etc dAAx M M M M M MB MBsmwt Ax i MB MBsmwt B dt Y Ay 0 A2 1 T2 TA TB Y Ay 0 A2 1 A 18 d M M M M M Ay 39yMAZB1 sinmt MAXBOy Ay Ay By yMAZBlsincut MAXBO Ay By dt 2 TA TB TB and corresponding equations for MEX MBy Equation shows that exchange increases relaxation rate so broadens resonance 1 1 1 1 1 1 ETT ET 2A A 28 TB General equation is complex Evans pp 45746 a Ch 777 Spring 03 page 35 Look at special cases Let pA population in A state pB population in B state 1 1 1 1 1 1 and recall 39 2A Y39ZA TA 728 Z B I B Normal lineshape of absorption signal in high resolution spectra fa MoYB Z 172w0 oa2 Maximum at 0 0 0 half max when Lorentzian lineshape T22 u0 12 1 occurs at 2 points with u0 D2 i2 2 2 AmlZ 2wo m y 2 Au 1 AV 2 17 2 MOYBIEAPA 1 Slow exchange fmm Like normal equation but replace T2A with T392A so see linewidth increase Same equations for B If know T2A and TZB use broadening to measure rates k1 and kl As T decreases 1 increases reach limit T392A T2A 4 Fast exchange limit where no further changes as increase T M Bquot 39 0y 1 ZPA 2 17pAmi meB m Gives an averaged signal with averaged linewidth 1 p p wavgz pAmA meB and F TA TB 3 Approaching fast exchange averaged resonance but still broadened by exchange 1 1 F2quot 5 pApBwA 03f TA 173 Approach to very fast exchange T increase 2 k increase 2 TA TB decrease 7 until last term negligible 2 Intermediate exchange use general solution equation Moy117QR 131178 1 where39c andP R Tu m c f IATB Q f2 A BpApB See Evans p 46 for PQR equations
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