Fluorescence Spectroscopy

Transcription

1 Fluorescence Spectroscopy Raleigh light scattering light all freqs Fluorescence emission

2 Raleigh Scattering 10 nm Raleigh light scattering Fluorescence emission 400 nm

3 Scattering - TWO particle 10 nm Particle Pair Diffraction Pattern Constructive & Destructive Interference Thomas Young - Royal Society, 1803

4 Scattering - MANY particles Diffraction Pattern Many uniformly spaced sin waves Constructive & Destructive Interference Constructive & Destructive Interference Thomas Young - Royal Society, 1803

5 Scattering - MANY particles Many pairwise groups of constructive & destructive interferences But no coherent additivity Scattering but no pattern Constructive & Destructive Interference Thomas Young - Royal Society, 1803

6 Pair of molecules yields scattering at a specific angle and magnitude Constructive & Destructive Interference Thomas Young - Royal Society, 1803

7 Pair of molecules yields scattering at a specific angle and magnitude Constructive & Destructive Interference Thomas Young - Royal Society, 1803

8 Pair of molecules yields scattering at a specific angle and magnitude Different sizes - a new angle & magnitude Constructive & Destructive Interference Thomas Young - Royal Society, 1803

9 Constructive & Destructive Interference Thomas Young - Royal Society, 1803

10 Volume empty - no scattering Constructive & Destructive Interference Thomas Young - Royal Society, 1803

11 Volume empty - no scattering Constructive & Destructive Interference Thomas Young - Royal Society, 1803

12 Smaller molecule scattering - angle 1 Constructive & Destructive Interference Thomas Young - Royal Society, 1803

13 Volume empty - no scattering Constructive & Destructive Interference Thomas Young - Royal Society, 1803

14 Larger molecule scattering - angle 2 Constructive & Destructive Interference Thomas Young - Royal Society, 1803

15 Larger molecule scattering - angle 2 Constructive & Destructive Interference Thomas Young - Royal Society, 1803

16 Volume empty - no scattering Constructive & Destructive Interference Thomas Young - Royal Society, 1803

17 g 2 ( q, t) = I ( t ) I( t + τ ) I( t) 2 f ( t) = time average of f ( t)

18 Autocorrelation function g 2 ( q, t) = I ( t ) I( t + τ ) I( t) 2 f ( t) = time average of f ( t)

19 Autocorrelation function g 2 ( q, t) = I ( t ) I( t + τ ) I( t) 2 Specific wave vector f ( t) = time average of f ( t)

20 Autocorrelation function g 2 ( q, t) = I ( t ) I( t + τ ) I( t) 2 Specific wave vector time f ( t) = time average of f ( t)

21 Autocorrelation function g 2 ( q, t) = I ( t ) I( t + τ ) I( t) 2 Specific wave vector time Intensity of scattered light f ( t) = time average of f ( t)

22 Autocorrelation function small time interval g 2 ( q, t) = I ( t ) I( t + τ ) I( t) 2 Specific wave vector time Intensity of scattered light f ( t) = time average of f ( t)

23 Autocorrelation function small time interval g 2 Specific wave vector ( q, t) = I ( t ) I( t + τ ) time I( t) 2 Intensity of scattered light non-zero only when particles stick around in time τ f ( t) = time average of f ( t)

24 g 2 ( q, t) = I ( t ) I( t + τ ) I( t) 2 non-zero only when particles stick around in time τ Relates to probability distribution function P( r,t 0,0) = ( 4πDt) 3 2 e r 2 4Dt

25 g 2 ( q, t) = I ( t ) I( t + τ ) I( t) 2 non-zero only when particles stick around in time τ Relates to probability distribution function P( r,t 0,0) = ( 4πDt) 3 2 e r 2 4Dt Assumes random (Brownian) motion

26 g 2 ( q, t) = I ( t ) I( t + τ ) I( t) 2 non-zero only when particles stick around in time τ Diffusion relates to size D = kt 6πηR

27 g 2 ( q, t) = I ( t ) I( t + τ ) I( t) 2 non-zero only when particles stick around in time τ Diffusion relates to size D = kt 6πηR Assumes spherical particles of radius R

28 g 2 ( q, t) = I ( t ) I( t + τ ) I( t) 2 non-zero only when particles stick around in time τ Diffusion relates to size D = kt 6πηR Assumes spherical particles of radius R Calibrate with particles of known size

29 g 2 q, t ( ) = I t ( ) I t + τ ( ) I t ( ) 2

30 Assumptions and Caveats D = kt 6πηR Assumes Brownian motion non-interacting billiard balls Spherical scatterers Proper calibration for viscosity, etc Properly dilute solution No interference from other scatterers

31 Magnetic Resonance Electron/Nuclear Magnetic Moment Nuclei g β µ = n n m L = γ n L β n = 5.05x10 24 erg gauss 1 γ n/e = gyromagnetic ratio Bohr magneton β e = 9.27x10 21 erg gauss 1 Electrons g β µ = e e m L = γ e L

32 Magnetic Resonance Quantization of angular momentum ( ) Nuclei µ m = γ n I I Nuclear magnetic moments can interact with an external magnetic field Torque = τ = µ m H H

33 Magnetic Resonance Quantization of angular momentum ( ) Nuclei µ m = γ n I I Nuclear magnetic moments can interact with an external magnetic field Torque = τ = µ m H H µ m

34 Magnetic Resonance Quantization of angular momentum ( ) Nuclei µ m = γ n I I Nuclear magnetic moments can interact with an external magnetic field Torque = τ = µ m H H µ m τ

35 Magnetic Resonance Quantization of angular momentum ( ) Nuclei µ m = γ n I I Nuclear magnetic moments can interact with an external magnetic field Torque = τ = µ m H H µ m τ µ m = γ n L Torque induces change in angular momentum L