H NMR Studies of Molecular Dynamics. Basis Seminar on June 25th by Cornelius Friedrichs

Transcription

1 2 H NMR Studies of Molecular Dynamics Basis Seminar on June 25th by Cornelius Friedrichs

2 Outline 1. IntroducDon to 2 H nuclei 2. MoDons 3. SimulaDon of 2 H spectra 4. Line shape analysis in 1D spectra 5. 2D spectra of deuterium 2

3 Comparing 1 H and 2 H proper%es 1 H 2 H atomic composidon atomic weight natural abundance spin u u % 0.015% gyromagnedc rado! 1 H = "107 rad s#t! 2 H = "107 rad s#t 3

4 Spin ProperDes Nuclei with spin possess an assymmetric charge I > 1 2 distribudon quadrupolar moment, which is Q = 2.8!10 "31 m 2 very small compared to other nuclei! Q = 140 " 220kHz for other nuclei the quadrupolar frequency is in the range of MHz 4

5 GyromagneDc RaDo Dipole dipole interacdons are propordonal to the product of the gammas for interacdng nuclei:! DD " # I # S dipole dipole interacdon very small for two 2 H (range of 100Hz) Quadrupolar interacdons are much stronger than dipole dipole interacdons 2 H solid state spectra are governed by quadrupolar interacdons 5

6 2 H for dynamic Studies Advantages: 1. quadrupolar interacdon endrely intramolecular 2. deuterons give very unique informadon 3. depending on the applied technique, the dynamic range is 10MHz to 1Hz 4. low natural abundance opens the possibility of selecdvity 6

7 How to describe MoDon? Markov model: hopping or exchange between N discrete sites!"#$$%&'!(%)*! +*,%-*&.*!(%)* hopping between very sharp and deep potendal wells no diffusion within the wells MoDons in solids are best described by an autocorreladon funcdon G: # & G (! ) = f ( t) f ( t +! ) G! $ % ' (!! c : "#$$%&'()#*!()+% ( ) = exp "!! c 7

8 SimulaDon of MoDons To analyse a concrete spectrum one has to know what modons occure within the spectrum Comparing experimental to simulated data is a common pracdce to calculate modonal parameters 8

9 Theory Stuff The Dme evoludon of the transversal magnedsadon M is given by a differendal equadon: +!,",t ( ) dm + dt = M + ( $1 i! (",#) + T ) 2 To include modons one has to add the exchange magne DzaDon between the N sites as a result of molecular hopping:! ij = " -1 c, ij p j! p : "#$%$&'(#)!#*!+'&', j j 9

10 Theory Stuff The equadon becomes then: dm + dt = M + ( i! + T "1 2 + #) The soludon of this equadon is averaged over all possible molecular orientadons: 2! $ 0! $ 0 M + = 1 M + 8! 2 0 (",#)L (",#,t )sin(" )d"d# ( ) = exp i#!," L!,",t ( )t + T 2 $1 t + % ( ) 10

11 Theory Stuff The FID is propordonal to the Dme dependent transversal magnedsadon: FID t N! i ( ) = M + i ( t) Combining the two equadons leads to: FID( t) = 1 2! & 0! & 0 ( ) ij sin (# ) % p 8! 2 j " L #,$,t d#d$ i, j 11

12 MoDonal Regimes DefiniDon of the rate constant: k = 1! c Assuming two hopping sites with frequency difference,!" one can disdnguish three kinds of modons 1. fast exchange limit: k!!" 2. intermediate exchange region: k! "# 3. slow exchange limit: k!!" 12

13 2 H Solid Echo In solids it is useful to apply the solid echo puls sequence 13

14 Factors Spectra depend on the orientadon (anisotropy parameter) and the shape (asymmetry parameter) of the spin interacdon tensors η Q = V yy V xx V zz! Q = 3 4 eqeq!! = 0.0! = 0.3! =

15 WebLab for 1D Spectra WebLab is an internet based simuladon socware where one can calculate spectra with different modon sites. Screen shots from WebLab 15

16 Cone Angle Dependence Two site hopping! = 40! = 60! = 80 16

17 Rate Constant Dependence Two site hopping k = 10kHz k = 10 3 khz k = 10 5 khz 17

18 Echo Time Dependence Two site hopping in the intermediate regime at 1000kHz! = 10µs! = 50µs! = 100µs 18

19 LimitaDons Line shape analysis has some limitadons 1. usually there are several fits 2. in complex systems there may be distribudons of correladon Dmes 3. Markov model is not sufficient for broad and shallow wells (no descrete sites) 19

20 2 H 2D NMR To get more informadon about slow modons (range of ms and slower) one can apply mulddimensional exchange experiments. 20

21 The Puls Sequence To obtain pure absorpdon spectra one has to record two datasets (quadrature detecdon) The transversal magnedzadon acer the sequence is then for both datasets: "#!!M + = M + 0 sin (! 1 )sin(! 2 )sin(! 3 )cos(" 1 t 1 )cos(" 2 t ) 2! $#!!M = M sin (! 0 4 1)sin( 2! 2 )sin( 2! 3 )sin(" 1 t 1 )sin " 2 t 2 sin (! 2 )sin(! ) 3 = 3 sin ( 2! 4 2 )sin( 2! ) 3 ( ) for! 2 =! 3 =

22 MoDons in 2D Spectra If a spin with frequency performs a modon, the! 1 frequencyacer the mixing Dme will change to a new! m value.! 2! 1 "! 2 for! c <! m This means that cross peaks appear in the spectrum If is much greater than there will be no exchange! c! m and all intensity is located on the diagonal! 1 =!! 2 for!! c m 22

23 Further Feature In 1D Spektra one only sees modons reladve to the Principal Axis Frame which is not known. 2D Spektra contain informadons about the Euler Angles ( ) for the transformadon of the modon.!!"!""!# The shape of the correlated spectrum gives informadon about the Euler Angels of the modon 23

24 WebLab for 2D Spectra WebLab can also calculate 2D spectra Screen shot from WebLab 24

25 Line Shapes in 2D Spectra If the asymmetry parameter there are simple! = 0 shapes that define the modon angle.! = 0! = 20! = 45! = 70! = 90 25

26 Asymmetry Dependence The asymmetry parameter may be and the spectra! > 0 change their shapes. is constant during a reorientadon. η! = 0! = 0.2! = 0.4! = 0.6! = 0.8! = 1 26

27 Angle Dependence For the asymmetry parameters the angles and! > 0 α γ become important! 1 =! 2 = 0.2! = 45! = 0! = 20! = 45! = 70! = 90 27

28 Conclusions The big goal of 2 H NMR for modons is the wide frequency range Line shape analyses are sufficient for simple systems For more complex systems one has to use other models Other techiques (not mendoned here) give further informadon about modon 2D NMR is a good tool to get the geometries of modons 28

29 Literature IntroducDon to Solid State NMR Spectroscopy by M. Duer, 1st EdiDon, Blackwell, 2004 MulDdimensional Solid State NMR by H. W. Spiess and K. Schmidt Rohr, 1st EdiDon, Academic Press, 1994 H. W. Spiess, Advances in Polymer Science, 1985, 66, hip://weblab.mpip mainz.mpg.de/weblab41/ weblab.html 29

30 Thanks for your aiendon!... my guess: 3 : 1 30