University of Ljubljana, FMF, and Institute „Jožef Stefan“, Ljubljana, Slovenia

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Evolution of molecular translational dynamics in complex-fluids studied by MGSE spectroscopy Aleš Mohorič, Janez Stepišnik, Igor Serša and Franci Bajd University of Ljubljana, FMF, and Institute „Jožef Stefan“, Ljubljana, Slovenia

Modulated gradient spin echo Frequency-temporal 3D plot of VAS The NMR method of modulated gradient The apparent timeline of VAS spin echo (MGSE) directly probes the  1  k 2 velocity autocorrelation spectrum (VAS) of D (w,t) =     / k = D w  k D 2 w t  D3 w t 3  ... 1,2 a         spin bearing particles  T2  2  D w = v t v 0 cos w t dt , shows the evolution of VAS dispersion after the excitation    x   x     0 by RF pulse for a variety of fluids: where vx(t) is the molecular velocity fluctuation in the direction of the applied magnetic field gradient. CPMG train of p- Ethanol radiofrequency (RF) pulses applied together with the fixed gradient, G,

휋 휋 휋 휋 휋 휋 휋 휋 휋/2

rf +G(t)

q(t) 2t

which periodically modulates the spin Water Coupled Langevine equations phases discordance, q(t), is the MGSE Unusual spectra of water, mixtures of sequence that gives the spin echo decay water and glycerol and other liquids with the attenuation of N-th echo3 may be explained by a simple model of Langevin equations, where the molecule t 8 2G 2 is coupled with its neighbors by a  t,wm  =  Dwm  2 2 t ; t = Nt. harmonic force: T2 wm  p wm d 2 x dx Here, T is the spin relaxation, t is the m  γ  κ(x-X)  ... = f t 2 dt 2 1 dt spacing between RF-pulses and wm =p/t is d 2 X dX the modulation frequency. The m  γ  κ(x-X)  ... = dt measurements with and without gradient dt 2 2 dt field discards the relaxation part of Water/glycerol:    attenuation. By changing t , we obtain 10 v% glycerol The solution of equations is the D(w) at different modulation frequencies. 50 v% glycerol spectrum D D w 2t 2 D w = bond free . Analysis of VAS dispersion by MGSE x 1  w 2t 2 The observed nonlinear time dependence of that fits well to the experimentally the echo attenuation can be explained by a observed results: dispersion of molecular motional properties in the fluid.

Toluene

The echo attenuation, which is due to a sum References of exponential contributions, can be expanded in Taylor series [1] J. Stepišnik, Analysis of NMR self-diffusion measurements by density matrix calculation, t  k D t t Physica 104B (1981) 350- 361. d logE d i 8 2 = log e T2 k = Gt  dt dt  p 4 [2] P.T. Callaghan, J. Stepišnik, Generalized i analysis of motion using magnetic field 1 k 3 gradients, Advances in Magnetic and Optical =  k Dt   k 2 D 2 t  t  D3 t  t 3  ... T 2 Resonance ed. Waren S. Waren, Vol. 19, p. 2 Contact giving 324-397, (1996), Academic Press Aleš Mohorič and Janez Stepišnik, University [3] J. Stepišnik, S. Lasič, A. Mohorič, I. Serša, n A. Sepe, Spectral characterization of diffusion n 1 n of Ljubljana, FMF, Jadranska 19, 1000 D = Di  D  central moments; D = mean in porous media by the modulated gradient n i=1 Ljubljana, Slovenia, [email protected], spin echo with CPMG sequence, J. Magn. as the parameters of instantaneous D(w) Reson., 182, 195-199 (2006). dispersion. [email protected]