1. Circular- and Linear Dichroism with Photoelastic Modulator Spectrometers John Sutherland Physics Department, East Carolina University Biology Department, Brookhaven National Laboratory 2011 CIRCULAR AND LINEAR DICHROISM WORKSHOP: 6–8 December, 2011 at University of Warwick

2. Agenda Components of a CD/LD Spectrometer Photoelastic Modulators Photoelastic Modulators and Extraction of CD Photoelastic Modulators and Extraction of LD Related Experiments: the DichroFluoroSpectroPhotometer 2010-12-5Warwick Winter Workshop2

3. Agenda Components of a CD/LD Spectrometer – Subsystems: a bakers dozen – Classes of CD spectrometers Simple (similar to fluorometer) Classical laboratory Synchrotron source – Light Sources {xenon arc, synchrotron} Photoelastic Modulators Photoelastic Modulators and Extraction of CD Photoelastic Modulators and Extraction of LD 2010-12-5Warwick Winter Workshop3

4. The 12 Subsystems of a PEM Spectrometer Plus Supports and Enclosures:  the “Bakers Dozen” 2010-12-5Warwick Winter Workshop4

5. A Minimal PEM Spectrometer for CD and LD 2010-12-5 Warwick Winter Workshop 5

6. A Typical Laboratory Instrument 2011-12-8Warwick Winter Workshop6

7. Xenon Arc 2010-12-5Warwick Winter Workshop7

8. Synchrotron Radiation CD 2010-12-5Warwick Winter Workshop

9. An SRCD Experiment 2010-12-5Warwick Winter Workshop9

10. Agenda Components of a CD/LD Spectrometer Photoelastic Modulators – Superposition: alternate ways of describing a polarized beam – Electric fields vs. Intensity – You sine of a sine and other profanities – Absorbance: decadic and Eularian – From total absorbances to averages and differentials Photoelastic Modulators and Extraction of CD Photoelastic Modulators and Extraction of LD Related Experiments 2010-12-5Warwick Winter Workshop10

11. Incident Light Linearly Polarized Can be resolved into a sum of Left- and right circularly polarized components, Can be resolved into a sum of Left- and right circularly polarized components,Or A sum of vertical and horizontal components A sum of vertical and horizontal components 2010-12-5Warwick Winter Workshop11

12. PEM Shifts Phase of relative to 2010-12-5Warwick Winter Workshop12

13. Beam Transmitted by PEM (and incident on sample) Let intensity of incident beam be Let intensity of incident beam be I o Intensity if described as sum of circular components Intensity if described as sum of circular components Intensity if described as sum of linear components Intensity if described as sum of linear components – Where is the phase shift at time – Where  is the phase shift at time t For a PEM, For a PEM, is the maximum phase shift – δ o is the maximum phase shift is frequency of oscillation of the PEM (~ 50 kHz) – f is frequency of oscillation of the PEM (~ 50 kHz) – and is the angular frequency of the PEM (~314 krad/s) – and ω= 2πf is the angular frequency of the PEM (~314 krad/s) 2010-12-5Warwick Winter Workshop13

14. sin[δ 0 sinωt] & cos[δ 0 sinωt] Fourier series expansion in Bessel Function 2010-12-5Warwick Winter Workshop14 J0J0 J1J1 J2J2

15. Absorbance: Decadic and Eulerian Transmission Transmission T= I/I 0 Intensity of incident beam is and Intensity of incident beam is I 0 and Intensity of transmitted beam is Intensity of transmitted beam is I Decadic absorbance Decadic absorbance I = I 0 10 −A Good for routine use Good for routine use Eulerian absorbance Eulerian absorbance I = I 0 e −a aka “Napierian” absorbance aka “Napierian” absorbance Good for derivations Good for derivations a = A ln[10] 2010-12-5Warwick Winter Workshop15 sample I0I0 I0I0 I I

16. Absorbances: From Absolute to Average and Differential The difference in the absorption of left- and right circularly polarized light or vertical and horizontal linearly polarized light Decadic CD ΔA CD =A L -A R LD ΔA LD =A V –A H (?) Eulerian CD Δa CD =a L -a R LD Δa LD =a V -a H Useful definitions: 2010-12-5Warwick Winter Workshop16

17. Agenda Components of a CD/LD Spectrometer Photoelastic Modulators Photoelastic Modulators and Extraction of CD – A PEM modulates the polarization of the beam – A dichroic sample modulates the amplitude beam – Electronics detect the amplitude modulation Photoelastic Modulators and Extraction of LD Related Experiments 2010-12-5Warwick Winter Workshop17

18. Differential Absorption by Sample Modulates the Beam 2010-12-5Warwick Winter Workshop18 sample l PEMPEM PEMPEM I0I0 I0I0 I[t]I[t] I[t]I[t] Detector

19. CD 2010-12-5Warwick Winter Workshop19

20. CD continued 2010-12-5Warwick Winter Workshop20

21. What Value of 2010-12-5Warwick Winter Workshop21

22. Hyperbolic Tangent 2010-12-5Warwick Winter Workshop22 x x tanh[x]

23. Electronics for CD & LD 2010-12-5Warwick Winter Workshop23

24. Ellipticity 2010-12-5Warwick Winter Workshop24 Sample

25. Agenda Components of a CD/LD Spectrometer Photoelastic Modulators Photoelastic Modulators and Extraction of CD Photoelastic Modulators and Extraction of LD – Without a quarter wave plate – With a quarter wave plate Related Experiments 2010-12-5Warwick Winter Workshop25

26. Linear Dichroism with a CD Spectrometer: no QWP 2010-12-5Warwick Winter Workshop26 δ 0 = π/2 δ 0 = π

27. LD 2010-12-5Warwick Winter Workshop27

28. LD (continued) 2010-12-5Warwick Winter Workshop28

29. LD: for ΔA LD ≥ 0.2 2010-12-5Warwick Winter Workshop29

30. Linear Dichroism with a CD Spectrometer: with QWP 2010-12-5Warwick Winter Workshop30

31. Agenda Components of a CD/LD Spectrometer Photoelastic Modulators Photoelastic Modulators and Extraction of CD Photoelastic Modulators and Extraction of LD Related Experiments: the DichroFluoroSpectroPhotometer 2010-12-5Warwick Winter Workshop31

32. Magnetic CD Place sample in a magnetic field Provides information on electronic structure and spectra Spectrum is sum of CD and MCD 2010-12-5Warwick Winter Workshop32 H

33. MCD Recently become easier and more affordable due to very strong permanent magents Few uses in Biochemistry: quantitation of trytophan 2010-12-5Warwick Winter Workshop33 MCD of indole: Data from OLIS

34. Optical Rotary Dispersion (ORD) The rotational angle vs wavelength CD is preferable, but may be historical standards expressed in ORD 2010-12-5Warwick Winter Workshop34

35. Fluorescence Polarization Anisotropy Linear polarization Does not require orientation Usually done with dedicated fluorometer Can be done on a modified CD 2010-12-5Warwick Winter Workshop35

36. Fluorescence Polarization Anisotropy Must set the PEM differently 2010-12-5Warwick Winter Workshop36

37. Review CD/LD spectrometers can be built using either conventional (xenon arc) of synchrotron sources. – Conceptually similar (12 subsystems) – Practically very different CD and LD found from ratio of AC to DC signals For CD, small AC signal at frequency of the PEM For LD, small AC signal at frequency of – the PEM (without a quarter wave plate) – twice the PEM (with a quarter wave plate) With basic CD spectrometer can also measure MCD, LD, ORD, Fluorescence polarization Anisotrophy and absorption 2010-12-5Warwick Winter Workshop37

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