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

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 Warwick Winter Workshop2

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 Warwick Winter Workshop3

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

A Minimal PEM Spectrometer for CD and LD Warwick Winter Workshop 5

A Typical Laboratory Instrument Warwick Winter Workshop6

Xenon Arc Warwick Winter Workshop7

Synchrotron Radiation CD Warwick Winter Workshop

An SRCD Experiment Warwick Winter Workshop9

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 Warwick Winter Workshop10

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 Warwick Winter Workshop11

PEM Shifts Phase of relative to Warwick Winter Workshop12

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) Warwick Winter Workshop13

sin[δ 0 sinωt] & cos[δ 0 sinωt] Fourier series expansion in Bessel Function Warwick Winter Workshop14 J0J0 J1J1 J2J2

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] Warwick Winter Workshop15 sample I0I0 I0I0 I I

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: Warwick Winter Workshop16

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 Warwick Winter Workshop17

Differential Absorption by Sample Modulates the Beam Warwick Winter Workshop18 sample l PEMPEM PEMPEM I0I0 I0I0 I[t]I[t] I[t]I[t] Detector

CD Warwick Winter Workshop19

CD continued Warwick Winter Workshop20

What Value of Warwick Winter Workshop21

Hyperbolic Tangent Warwick Winter Workshop22 x x tanh[x]

Electronics for CD & LD Warwick Winter Workshop23

Ellipticity Warwick Winter Workshop24 Sample

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 Warwick Winter Workshop25

Linear Dichroism with a CD Spectrometer: no QWP Warwick Winter Workshop26 δ 0 = π/2 δ 0 = π

LD Warwick Winter Workshop27

LD (continued) Warwick Winter Workshop28

LD: for ΔA LD ≥ Warwick Winter Workshop29

Linear Dichroism with a CD Spectrometer: with QWP Warwick Winter Workshop30

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 Warwick Winter Workshop31

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

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

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

Fluorescence Polarization Anisotropy Linear polarization Does not require orientation Usually done with dedicated fluorometer Can be done on a modified CD Warwick Winter Workshop35

Fluorescence Polarization Anisotropy Must set the PEM differently Warwick Winter Workshop36

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 Warwick Winter Workshop37

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