Antonio Faraone. Dept. of Nuclear Engineering, UMD NIST Center for Neutron Research

Transcription

1 Antonio Faraone Dept. of Nuclear Engineering, UMD NIST Center for Neutron Research What a user (you!!!) need to know to propose and perform a successful NSE experiment. How a NSE measurement is performed. The data reduction: Exercise. Typical examples of data analysis. Shape Fluctuations in a microemulsion. Determination of the bending modulus of the membrane in a lipid vesicle. 1

2 The preparation is often the most important part of a QENS experiment. NSE characteristics. NSE technical concept. NSE science. NSE measurements details. 2

3 It is the QENS technique with the highest energy resolution. The accessible Q range extends to a portion of the small-angle region. It works in the time domain. - The instrumental resolution can be simply divided out. It can cover up to ~4 orders of magnitude in time. ϕ = B0dl B1dl γ γ v v f ( λ ) Echo Condition: J 0 = J1 ϕ = 0 P x = 1 3

4 B0dl γ v( λ) v( λ) 2 3 B1dl m λ m ϕ = γ γ J 0ω + γ ( J 0 J1)λ 2 + δv 2πh h 2 3 m λ m P x = cos( ϕ) = f ( λ) S( Q, ω) cosγ J 0 ω + γ ( J 0 J 1 ) λdλdω Dynamics of Soft Condensed Matter ACNS 2πh Santa h Fe, NM May 10 th m m λ = cos( ϕ) = f ( λ) cos γ ( J 0 J1) λ dλ S( Q, ω) cosγ J ωdω h 2πh 2 P x 0 FT of the wavelength distribution FT of the Dynamic Structure Factor P x phi phi ( ) ( ) J, Q, t = P J s S ( Q, ω) cos[ ωt] S( Q, ω) dω dω NSE measures the Fourier Transform of the Dynamic Structure Factor 4

5 Diffusion. Collective diffusion: Effects of S(Q) and H(Q). Shape Fluctuations. Microemulsion. Membranes. Worm-Like Micelles. Glasses. Polymer. Collective Diffusion Apoferritin Solutions!" # ( Q, t) S( Q,0) 2 S( Q, t) ( ) = exp[ D Q t] exp[ 2 D ] = exp 0Q th Q D Q t S 2 0 = eff S( Q,0) S( Q) Haußler W. and Farago B., J. Phys.: Condens. Matter, 15, S197 (2003) 5

6 Protein Internal Dynamics Taq Polimerase!" # Bu Z., Biehl R., Monkenbusch M., Richter D., and Callaway D.J.E., Proceedings of the National Academy of Sciences, 102, (2005)!" #$ % Reptation PolyEthylene Schleger P., Farago B., Lartigue C., Kollmar A. and D. Richter, Phys. Rev. Lett., 81, 124 (1998) 6

7 !" #$ %% Rouse Dynamics PDMS Zimm Dynamics PS/d-Octane Richter D., Ewen B., Farago B., and Wagner T., Phys. Rev. Lett., 62, 2140 (1989)!" # Corona Dynamics in Pluronic Triblock Copolymer Micelles F gr/cm 3 Yardimci H., Chung B., Harden J.L., and Leheny R.L., J. Chem. Phys., 123, (2005). 7

8 !" # Corona Dynamics in Pluronic Triblock Copolymer Micelles F gr/cm 3 β t exp τ PPO β t t A s exp + Af exp τ PPO τ PEO Yardimci H., Chung B., Harden J.L., and Leheny R.L., J. Chem. Phys., 123, (2005). & ' (() 8

9 * + ( The Q-t range accessible to NSE is broad and is best for the investigation of slow processes on largemedium length scales. The High Energy Resolution of NSE is achieved by encoding the neutron velocity into its Spin state. NSE is the instrument of choice for studying coherent (collective) dynamics in Soft Condensed Matter. - Collective Diffusion, Shape Fluctuation, + What does NSE measure? Polarization vs Phase and F t. How to Eliminate Instrument Dependent Signals. How using a 2D detector complicates things? How DAVE helps us out. 9

10 P x phi phi ( ) ( ) J, Q, t = P J s $,% - S ( Q, ω) cos[ ωt] S( Q, ω) dω dω $,%- 10

11 I 0 Average Intensity A Amplitude, related to I(Q,t) ph 0 Echo point σ Echo width, function of f(λ) width distribution ( T Period, function of λ Static measurements (Up and Down) t=0 (J=0): S(Q,ω)dω I p ( ph ph ) + Aexp 2 2σ 360 cos T 2 0 = I0 0 ( ph ph ) $%!! I I ( Q, t) 2A ( Q) Up Dwn Incidentally, in this way, both polarization and detector efficiency effects are taken care off. 11

12 $,%-., I( Q, t) 2A = R I( Q,0) 2 A ( Up Dwn) R R ( Up Dwn ) 12

13 2 A I Q t (, ) = I( Q) / * T BKG T BKG BKG ( 1 φ) A ( Up Dwn) ( ) ( Up Dwn ) BKG BKG T 1 φ T R R R 2A ( Up Dwn ) + * + ( The Physical Information is in the Echo Amplitude. But You Have to Accurately Fit the Echo to get the Amplitude right. The Resolution can be simply divided out. 13

14 Questions: 0 (/ (& + * ( What are the advantages of using a 2D detector? What are the problems that a 2D detector gives for the reduction of NSE data? 1&& Total Data=32 32 N phase N Ft

15 ) %% What are those thin blue lines? Does the polarized intensity change with the pixel position? Why? Up and Down I 0 A T Ph 0 Yes. Efficiency, Polarization. Yes. Yes. Q-dependence. No. No. Yes. Field Integral: Bdl. 1&&! The echoes at each detector pixel have to be fitted individually. 15

16 $+ The Phase Map should be a smoothly varying function of the position on the detector and of the Fourier time..( &!2 1. Mask low intensity areas. 2. Fit the resolution. 3. Make sure the phase map is correct. 4. Remove poor resolution points. 5. Check the 2. 16

17 % ( The phase map is sample independent. To fit your sample and background data just 1. Import the phase map from the resolution. 2. Check the 2. 2 A I Q t (, ) = I( Q) %3) 45 T BKG T BKG BKG ( 1 φ) A ( Up Dwn) ( ) ( Up Dwn ) BKG BKG T 1 φ T R R R 2A ( Up Dwn ) The Intermediate Scattering function values are calculated pixel by pixel and averaged, according to their weight, by Q areas. 17

18 At the end of the reduction process the I(Q,t) contains information about your sample only. 18