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The Theoretical Foundation of Spin-Echo Small-Angle Neutron

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The Theoretical Foundation of Spin-Echo Small-Angle Neutron The Theoretical Foundation of Spin‐Echo Small‐Angle Neutron Scattering (SESANS) Applied in Colloidal System Wei‐Ren Chen, Gregory S. Smith, and Kenneth W. Herwig (NSSD ORNL) Yun Liu (NCNR NIST & Chemistry, University of Delaware) Li (Emily) Liu (Nuclear Engineering, RPI) Xin Li, Roger Pynn (Physics, Indiana University) Chwen‐Yang Shew (Chemistry, CUNY) UCANS‐II Indiana University July 08th 2011 Bloomington, IN Outline 1. Motivation — why Spin-Echo Small-Angle Neutron Scattering (SESANS)? 2. Basic Theory — what does SESANS measure? 3. Results and Discussions — what can SESANS do? (1). Straightforward observation of potential (2). Sensitivity to the local structure (3). Sensitivity to the structural heterogeneity 4. Summary Outline 1. Motivation — why Spin-Echo Small-Angle Neutron Scattering (SESANS)? 2. Basic Theory — what does SESANS measure? 3. Results and Discussions — what can SESANS do? (1). Straightforward observation of potential (2). Sensitivity to the local structure (3). Sensitivity to the structural heterogeneity 4. Summary Neutron Scattering Structure (Elastic Scatt.) Dynamics (Inelastic Scatt.) Small‐Angle Neutron Quasi‐Elastic Neutron Unpolarized Scattering (SANS), Scattering (QENS), beam Neutron Diffraction, Inelastic Neutron Scattering Neutron Reflectometry (INS) Polarized Spin‐Echo Small‐Angle Neutron Spin‐Echo (NSE) beam Neutron Scattering (SESANS) Neutron Scattering Structure (Elastic Scatt.) Dynamics (Inelastic Scatt.) Small‐Angle Neutron Quasi‐Elastic Neutron Unpolarized Scattering (SANS), Scattering (QENS), beam Neutron Diffraction, Inelastic Neutron Scattering Neutron Reflectometry (INS) Polarized Spin‐Echo Small‐Angle Neutron Spin‐Echo (NSE) beam Neutron Scattering (SESANS) Length scale probed by SESANS Comparison to other investigation tools Comparison to Light Scattering • Extended length scale range • Multiple scattering • Transparent samples Comparison to Ultra‐Small Angle Neutron Scattering (USANS) • Much higher flux Comparison to Transmission Electron Microscope (TEM) • Non‐destructive nature Comparison to Confocal Microscopy • EblEnsemble average iifnforma tion Examples for SESANS •Highly concentrated systems such as colloidal glass (e.g. PMMA/PS binary glass) •Large scale structure (polyelectrolyte aggregation) observed in the polyelectrolyte systems (protein, DNA, ionic polymers) •Optoelectronic soft matters such as polymeric solutions of PLED/OLED •Precipitate‐strengthening superalloy Outline 1. Motivation — why Spin-Echo Small-Angle Neutron Scattering (SESANS)? 2. Basic Theory — what does SESANS measure? 3. Results and Discussions — what can SESANS do? (1). Straightforward observation of potential (2). Sensitivity to the local structure (3). Sensitivity to the structural heterogeneity 4. Summary Small Angle Neutron Scattering (SANS) —measure the structure d d d area A Intensity I polar axis d density N I(Q) (Q) x d Ax azithliimuthal axis 4 Wave vector Q Q sin I A (Momentum transfer) 2 Scattering cross section Roger Pynn Small Angle Neutron Scattering (http://www.iub.edu/~neutron/) Neutron Spin Echo (NSE) —measure the dynamics +B ‐B I II I II Polarizer Analyzer Detector P S Q, cos d S Q, cos d S(Q, ) II I cBL3m where the "spin echo time" 2 c 4.63681014T 1m2 Mezei, in Neutron Spin Echo, Ed. Mezei, Springer 1980 Spin‐Echo Small‐Angle Neutron Scattering (SESANS) —measure the structure I II 2 1 +B I ‐B II L L Polarizer Analyzer Detector d 3 d 3 P Qcos d Q QcoszQ d Q Gz d II I d z cBL2 cot where the "spin echo length" z 2 14 1 2 c 4.636810 T m Pynn, Lecture 11, Neutron Physics and Scattering Indiana University (http://www.iub.edu/~neutron/) Length scale probed by SESANS Density Profile Debye Correlation Function 1 r γ(r) ρ(r')ρ(r' r )d 3 r' V V r d 2 Gz 2 r dr IQ (Q) 4 rJ0 Qrr dr 2 2 z r z d 0 Fourier z axis Abel y axis r Density Profile Debye Correlation Function 1 r γ(r) ρ(r')ρ(r' r )d 3 r' V V r d 2 Gz 2 r dr IQ (Q) 4 rJ0 Qrr dr 2 2 z r z d 0 IQ nP(Q)S(Q) G(z) Gauto (z) nGexcl (z) nGstruct (z) Interaction in concentrated hard colloidal system Liu et al. PRL 95 118102 2005 Chen et al. Macromolecules 40 5887 2007 Chen et al. Science 300 619 2003 Likos et al. PRE 58 6229 1998 Huang et al. APL 93 161904 2008 Outline 1. Motivation — why Spin-Echo Small-Angle Neutron Scattering (SESANS)? 2. Basic Theory — what does SESANS measure? 3. Results and Discussions — what can SESANS do? (1). Straightforward observation of potential (2). Sensitivity to the local structure (3). Sensitivity to the structural heterogeneity 4. Summary Example I: Hard Sphere Potential r D V (r) 0 r D V(r) D Li et al., J. Chem. Phys. 132 174509 2010 Example II: Attractive Potential r D V (r) u D r D(1 ) 0 r D(1 ) V(r) u D Li et al., J. Chem. Phys. 132 174509 2010 Example III: Screened Coulomb Repulsion Potential r D V (r) exp- Z r D K 1 r D 1 r K1 V(r) D Li et al., J. Chem. Phys. 132 174509 2010 Outline 1. Motivation — why Spin-Echo Small-Angle Neutron Scattering (SESANS)? 2. Basic Theory — what does SESANS measure? 3. Results and Discussions — what can SESANS do? (1). Straightforward observation of potential (2). Sensitivity to the local structure (3). Sensitivity to the structural heterogeneity 4. Summary Sensitivity to the local structure 1.6 HS 1.4 Phenomenological Model L 1.2 101.0 100 S(Q) 0.8 10-1 0.6 Phenomenological Model 10-2 0.4 I(Q) 10-3 0.2 10-4 0.0 10-5 0 5 10 15 20 25 30 2QR -0.2 0 5 10 15 20 25 30 L 2QR Huang et al. APL 93 161904 2008 Li et al., J. Chem. Phys. 132 174509 2010 Sensitivity to the local structure L Phenomenological Model L Huang et al. APL 93 161904 2008 Li et al., J. Chem. Phys. 132 174509 2010 Outline 1. Motivation — why Spin-Echo Small-Angle Neutron Scattering (SESANS)? 2. Basic Theory — what does SESANS measure? 3. Results and Discussions — what can SESANS do? (1). Straightforward observation of potential (2). Sensitivity to the local structure (3). Sensitivity to the structural heterogeneity 4. Summary Sensitivity to the geometric shape n D2O n n D2O H 2O Li et al., J. Phys.: Condens Matter (submitted) Outline 1. Motivation — why Spin-Echo Small-Angle Neutron Scattering (SESANS)? 2. Basic Theory — what does SESANS measure? 3. Results and Discussions — what can SESANS do? (1). Straightforward observation of potential (2). Sensitivity to the local structure (3). Sensitivity to the geometric shape 4. Summary Summary • SESANS length scale: from tens of nm up to several m • SESANS correlation function G(z): real space projection • SESANS advantages: direct observation of the spatial distribution sensitivit y to lllocal stttructure sensitivity to geometric shape high concentrated case… Acknowledgement LDRD of ORNL 05272 DOE NERI‐C Award No. DE‐FG07‐07ID14889 NRC Award No. NRC‐38‐08‐950 Thank you for your attention! Backscattering —measure the dynamics How about probing much ħ = Ei ‐ Ef slower dynamics (characteristic time > 1 ns)? Neutron Spin Echo —measure the dynamics +B ‐B I II I II Polarizer Analyzer Detector Mezei, in Neutron Spin Echo, Ed. Mezei, Springer 1980 What does SESANS measure? 2 1 +B ‐B PADI II z x Pynn,Lecture 11, Neutron Physics and Scattering Indiana University (http://www.iub.edu/~neutron/) What does SESANS measure? 2 1 +B ‐B PADI II z Final Polarization P cos(II I ) x F. Mezei, Z. Physik, 255 (1972) 145 Pynn,Lecture 11, Neutron Physics and Scattering Indiana University (http://www.iub.edu/~neutron/) What does SESANS measure? 2 1 +B ‐B PADI II z Final Polarization P cos(II I ) x F. Mezei, Z. Physik, 255 (1972) 145 cos(II I ) cos(cBL cot ) cos(zQz ) Pynn,Lecture 11, Neutron Physics and Scattering Indiana University (http://www.iub.edu/~neutron/) What does SESANS measure? 2 1 +B ‐B PADI II z Final Polarization P cos(II I ) x F. Mezei, Z. Physik, 255 (1972) 145 cos(II I ) cos(cBL cot ) cos(zQz ) spin-echo length cBL2 cot z 2 Pynn,Lecture 11, Neutron Physics and Scattering Indiana University (http://www.iub.edu/~neutron/) What does SESANS measure? 2 1 +B ‐B PADI II z Final Polarization P cos(II I ) x F. Mezei, Z. Physik, 255 (1972) 145 cos(II I ) cos(cBL cot ) cos(zQz ) spin-echo length 2 d d cBL cot P (Q)cos( )d 3 Q (Q)cos(zQ )d 3 Q z d II I d z 2 Pynn,Lecture 11, Neutron Physics and Scattering Indiana University (http://www.iub.edu/~neutron/) What does SESANS measure? SANS SESANS d d I (Q) (Q) G(z) (Q)cos(zQ )d 3Q d d z O. Spalla, in Neutron, X-rays and Light: Scattering Methods Applied to Soft Condensed Matter, edited by P. Linder and Th. Zemb (North-Holland, Amsterdam, 2002), pp. 49–71. What does SESANS measure? SANS SESANS d 3 d I(Q) (Q) (r)exp(iQ r)d r G(z) (Q)cos(zQ )d 3Q z d V d O. Spalla, in Neutron, X-rays and Light: Scattering Methods Applied to Soft Condensed Matter, edited by P. Linder and Th. Zemb (North-Holland, Amsterdam, 2002), pp. 49–71. What does SESANS measure? SANS SESANS d 3 d I(Q) (Q) (r)exp(iQ r)d r G(z) (Q)cos(zQ )d 3Q z d V d Debye Correlation Function 1 γ( r ) ρ( r' )ρ(r' r )d 3 r' V V O. Spalla, in Neutron, X-rays and Light: Scattering Methods Applied to Soft Condensed Matter, edited by P. Linder and Th.
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