Circular- and Linear Dichroism with Photoelastic Modulator Spectrometers John Sutherland Physics...

Circular- and Linear Dichroism with Photoelastic Modulator Spectrometers

John SutherlandPhysics Department, East Carolina University

Biology Department, Brookhaven National Laboratory

2011 CIRCULAR AND LINEAR DICHROISM WORKSHOP: 6–8 December, 2011 at University of Warwick

Warwick Winter Workshop 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

2010-12-5


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 LD2010-12-5


The 12 Subsystems of a PEM SpectrometerPlus Supports and Enclosures: the “Bakers Dozen”

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A Minimal PEM Spectrometer for CD and LD

2010-12-5 Warwick Winter Workshop 5


A Typical Laboratory Instrument

2011-12-8


Xenon Arc

2010-12-5

Warwick Winter Workshop

Synchrotron Radiation CD

2010-12-58


An SRCD Experiment

2010-12-5


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 Experiments2010-12-5


Incident Light Linearly Polarized

• Can be resolved into a sum of Left- and right circularly polarized components,

Or• A sum of vertical and

horizontal components

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€

rE V

€

rE H = 0


PEM Shifts Phase of relative to

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€

rE ||

€

rE ⊥


Beam Transmitted by PEM(and incident on sample)

• Let intensity of incident beam be Io • Intensity if described as sum of circular

components • Intensity if described as sum of linear

components – Where δ is the phase shift at time t

• For a PEM,– δo is the maximum phase shift– f is frequency of oscillation of the PEM (~ 50 kHz)– and ω= 2πf is the angular frequency of the PEM (~314

krad/s)2010-12-5

€

IL / R =I0

21± sinδ[t]( )

€

IV / H =I0

21 ± cosδ[t]( )

€

δ[t] = δ 0 sin 2π f t[ ] = δ 0 sin ω t[ ]


sin[δ0 sinωt] & cos[δ0 sinωt]

• Fourier series expansion in Bessel Function

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€

sin δ 0 sinω t[ ] = 2J1 δ 0[ ]sinω t + 2J3 δ 0[ ]sin 3ω t + ...

€

cos δ 0 sinω t[ ] = J0 δ 0[ ]+ 2J2 δ 0[ ]cos2ω t + 2J4 δ 0[ ]cos4ω t...

J0 J1 J2


Absorbance: Decadic and Eulerian

• Transmission T= I/I0

• Intensity of incident beam is I0 and • Intensity of transmitted beam is I

• Decadic absorbance I = I0 10−A

• Good for routine use

• Eulerian absorbance I = I0 e−a

• aka “Napierian” absorbance• Good for derivations• a = A ln[10]

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sample

I0 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 ΔACD=AL-AR LD ΔALD=AV –AH (?)

• Eulerian CD ΔaCD=aL-aR LD ΔaLD=aV -aH

• Useful definitions:

2010-12-5

€

aL / R = a ±ΔaCD

2

€

aV / H = a ±ΔaLD

2


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

2010-12-5


Differential Absorption by Sample Modulates the Beam

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sample

l

PEM

I0 I[t] Detector

€

I[t] = IL[t] + IR[t]

€

I[t] =I0

21+ sin δ o sinω t[ ]( )e−aL +

I0

21− sin δ o sinω t[ ]( )e−aR


CD

2010-12-5

€

I[t] = IL[t] + IR[t]

€

I[t] =I0

21+ sin δ 0 sinω t[ ]1 2 4 4 3 4 4

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟e−aL

}

+I0

21− sin δ 0 sinω t[ ]1 2 4 4 3 4 4

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟e−aR

}

€

a +ΔaCD

2

€

a −ΔaCD

2

€

2J1 δ 0[ ]sinω t + 2J3 δ 0[ ] sin 3ω t + ...

€

I t[ ] = I0 e−a e+

ΔaCD

2 + e−

ΔaCD

2 − 2J1[δ 0] e+

ΔaCD

2 − e−

ΔaCD

2 ⎛

⎝ ⎜ ⎞

⎠ ⎟sinω t + ... ⎛

⎝ ⎜ ⎞

⎠ ⎟

€

I[t] = I + ΔIω sin ω t[ ] + ...

€

I0 e−a e+

ΔaCD

2 + e−

ΔaCD

2 ⎛

⎝ ⎜ ⎞

⎠ ⎟

6 7 4 4 4 8 4 4 4

€

−I0 e−a 2J1[δ 0] e+

ΔaCD

2 − e−

ΔaCD

2 ⎛

⎝ ⎜ ⎞

⎠ ⎟

6 7 4 4 4 4 4 8 4 4 4 4 4


CD continued

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€

ΔIω

I =

−I0 e−a 2J1[δ 0 ] e+

ΔaCD

2 − e−

ΔaCD

2 ⎛

⎝ ⎜ ⎞

⎠ ⎟

I0 e−a e+

ΔaCD

2 + e−

ΔaCD

2 ⎛

⎝ ⎜ ⎞

⎠ ⎟

→ − 2 J1 δ 0[ ] tanhΔaCD

2 ⎡ ⎣ ⎢

⎤ ⎦ ⎥ ≈ − J1 δ 0[ ] ΔaCD

€

ΔACD ≈−1

ln10 J1 δ 0[ ]

ΔIω

I


What Value of

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€

δ0 ?

€

ΔACD ≈−1

ln10 J1 δ 0[ ]

ΔIω

I


Hyperbolic Tangent

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€

tanh x[ ] ≈ x for x << 1

x

xtanh[x]


Electronics for CD & LD

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€

v t[ ] = v + Δvω sin[ωt] + Δv2ω cos[2ωt] + ...


Ellipticity

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€

θdeg =360

2πθ rad →

45

πln[10]ΔACD ≈ 32.98 ΔACD

€

E→

R + E→

L

€

E→

R − E→

L€

θ

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

2010-12-5


Linear Dichroism with a CD Spectrometer: no QWP

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δ0 = π/2δ0 = π

LD

2010-12-5 Warwick Winter Workshop 27

€

I[t] = IV [t] + IH [t]

€

I[t] =I0

21+ cos δ 0 sinω t[ ]1 2 4 4 3 4 4

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟e−aV

}

+I0

21− cos δ 0 sinω t[ ]1 2 4 4 3 4 4

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟e−aH

}

€

a +ΔaLD

2

€

a −ΔaLD

2

€

I = I0 e−a e+

ΔaLD

2 + e−

ΔaLD

2 − J0 δ o[ ] e+

ΔaLD

2 − e−

ΔaLD

2 ⎛

⎝ ⎜ ⎞

⎠ ⎟ ⎛

⎝ ⎜ ⎞

⎠ ⎟

€

ΔI2ω = −I0 e−a 2J2[δ 0] e+

ΔaCD

2 − e−

ΔaCD

2 ⎛

⎝ ⎜ ⎞

⎠ ⎟

€

J0 δ 0[ ]+ 2J2 δ 0[ ]cos2ω t +...6 7 4 4 4 4 8 4 4 4 4

€

I[t] = I + ΔI2ω cos 2ω t[ ] + ...


LD (continued)

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€

ΔI2ω

I =

−2J2[δ 0]e

+ΔaLD

2 − e−

ΔaLD

2

e+

ΔaLD

2 + e−

ΔaLD

2

⎛

⎝

⎜ ⎜

⎞

⎠

⎟ ⎟

1− J0 δ 0[ ]e

+ΔaLD

2 − e−

ΔaLD

2

e+

ΔaLD

2 + e−

ΔaLD

2

⎛

⎝

⎜ ⎜

⎞

⎠

⎟ ⎟

→−2J2[δ 0] tanh

ΔaLD

2 ⎡ ⎣ ⎢

⎤ ⎦ ⎥

1− J0 δ 0[ ]tanhΔaLD

2 ⎡ ⎣ ⎢

⎤ ⎦ ⎥

€

ΔALD ≈−1

ln10 J2[π ]

ΔI2ω

I

for ΔALD ≤0.2

Note assymmetry

€

I = I0 e−a e+

ΔaLD

2 + e−

ΔaLD

2 − J0 δ o[ ] e+

ΔaLD

2 − e−

ΔaLD

2 ⎛

⎝ ⎜ ⎞

⎠ ⎟ ⎛

⎝ ⎜ ⎞

⎠ ⎟

€

ΔI2ω = −I0 e−a 2J2[δ 0] e+

ΔaCD

2 − e−

ΔaCD

2 ⎛

⎝ ⎜ ⎞

⎠ ⎟

€

δ0 = π 180o( )


LD: for ΔALD ≥ 0.2

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€

Fix Denominator

Choose δ 0 such that J0 δ 0*

[ ] = 0

δ 0* =0.765π (138o ), δ 0

* ="magic phase"€

ΔI2ω

I =

−2J2[δ 0 ] tanhΔaLD

2 ⎡ ⎣ ⎢

⎤ ⎦ ⎥

1− J0 δ 0[ ]tanhΔaLD

2 ⎡ ⎣ ⎢

⎤ ⎦ ⎥

€

ΔALD =−1

ln 10[ ] Jo δ o*

[ ]

ΔI2ω

I

€

δ0*


Linear Dichroism with a CD Spectrometer: with QWP

2010-12-5


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

2010-12-5


Magnetic CD

• Place sample in a magnetic field• Provides information on electronic structure and spectra• Spectrum is sum of CD and MCD

2010-12-5

H


MCD• Recently become easier and more affordable due to very strong permanent

magents• Few uses in Biochemistry: quantitation of trytophan

2010-12-5

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

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Fluorescence Polarization Anisotropy

• Linear polarization• Does not require

orientation• Usually done with

dedicated fluorometer• Can be done on a

modified CD

2010-12-5


Fluorescence Polarization Anisotropy

• Must set the PEM differently

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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

2010-12-5

Warwick Winter Workshop 382010-12-5

Circular- and Linear Dichroism with Photoelastic Modulator Spectrometers John Sutherland Physics...

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