Theoretical Approach to the Measurement of the Induced Linear Dichroism of Rigid Macromolecules

A. R. Foweraker; B. R. Jennings

doi:10.1364/AO.12.001983

Applied Optics
Vol. 12,
Issue 8,
pp. 1983-1991
(1973)
•https://doi.org/10.1364/AO.12.001983

Theoretical Approach to the Measurement of the Induced Linear Dichroism of Rigid Macromolecules

A. R. Foweraker and B. R. Jennings

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A. R. Foweraker and B. R. Jennings, "Theoretical Approach to the Measurement of the Induced Linear Dichroism of Rigid Macromolecules," Appl. Opt. 12, 1983-1991 (1973)

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Abstract

A comprehensive theory is developed in terms of the principal molar extinction coefficients (∊_ii) of rigid, isolated, rodlike macromolecules when subjected to orienting force fields. The theory embraces the conventional transverse parallel and perpendicular arrangements and the novel longitudinal dichroism method where the light beam and applied field traverse the system concomitantly. Both transverse and longitudinal measurements are considered when the initial light beam is unpolarized. It is shown that unpolarized light yields as much molecular information as the polarized methods used hitherto. Equations also are given in terms of a single repeating chromophore (∊₀) as if at a specific direction (α) to the molecular backbone.

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Refs.	Factor	Definition	In terms of ∊_ii and Φ	In terms of ∊₀, α, and Φ	As a function of ∊^L and ∊_u
	Δ∊	(∊^‖−∊^⊥)	(∊₃₃− ∊₁₁)Φ	$\frac{∊_{0} (3 {cos}^{2} α - 1) Φ}{2}$	3(∊_u − ∊^L)
13–16, 25	Δ∊/∊_u	$\frac{(∊^{‖} - ∊^{⊥})}{∊_{u}}$	$\frac{3 (∊_{33} - ∊_{11}) Φ}{(∊_{33} + 2 ∊_{11})}$	$\frac{3 (3 {cos}^{2} α - 1) Φ}{2}$	$\frac{3 (∊_{u} - ∊^{L})}{∊_{u}}$
12, 22	R	∊^‖/∊^⊥	$\frac{(∊_{33} + 2 ∊_{11}) + 2 (∊_{33} - ∊_{11}) Φ}{(∊_{33} + 2 ∊_{11}) - (∊_{33} - ∊_{11}) Φ}$	$\frac{2 + 2 (3 {cos}^{2} α - 1) Φ}{2 - (3 {cos}^{2} α - 1) Φ}$	$\frac{3 ∊_{u} - 2 ∊^{L}}{∊^{L}}$
11, 12	D^⊥	$\frac{a^{‖} - a}{a} = \frac{∊^{‖} - ∊_{u}}{∊_{u}}$	$\frac{2 (∊_{33} - ∊_{11}) Φ}{(∊_{33} + 2 ∊_{11})}$	(3 cos²α − 1)Φ	$\frac{2 (∊_{u} - ∊^{L})}{∊_{u}}$
11, 12	D^‖	$\frac{a^{⊥} - a}{a} = \frac{∊^{⊥} - ∊_{u}}{∊_{u}}$	$\frac{(∊_{11} - ∊_{33}) Φ}{(∊_{33} + 2 ∊_{11})}$	$\frac{(1 - 3 {cos}^{2} α) Φ}{2}$	$\frac{(∊^{L} - ∊_{u})}{∊_{u}}$
26, 27	D	$\frac{(∊^{‖} - ∊^{⊥})}{(∊^{‖} + ∊^{⊥})}$	$\frac{3 (∊_{33} - ∊_{11}) Φ}{2 (∊_{33} + 2 ∊_{11}) + (∊_{33} - ∊_{11}) Φ}$	$\frac{3 (3 {cos}^{2} α - 1) Φ}{4 + (3 {cos}^{2} α - 1) Φ}$	$\frac{3 (∊_{u} - ∊^{L})}{3 ∊_{u} - ∊^{L}}$
10	D	$\frac{a^{‖}}{a^{⊥}} = \frac{∊^{‖}}{∊^{⊥}} for {\begin{array}{l} ∊^{‖} & > ∊^{⊥} \\ a^{‖} & > a^{⊥} \end{array}$	$\frac{(∊_{33} + 2 ∊_{11}) + 2 (∊_{33} - ∊_{11}) Φ}{(∊_{33} + 2 ∊_{11}) - (∊_{33} - ∊_{11}) Φ}$	$\frac{2 + 2 (3 {cos}^{2} α - 1) Φ}{2 - (3 {cos}^{2} α - 1) Φ}$	$\frac{3 ∊_{u} - 2 ∊^{L}}{e^{L}}$
10	D	$- \frac{a^{⊥}}{a^{‖}} = \frac{∊^{⊥}}{∊^{‖}} for {\begin{array}{l} a^{⊥} > a^{‖} \\ ∊^{⊥} > ∊^{‖} \end{array}$	$\frac{- (∊_{33} + 2 ∊_{11}) + (∊_{33} - ∊_{11}) Φ}{(∊_{33} + 2 ∊_{11}) + 2 (∊_{33} - ∊_{11}) Φ}$	$\frac{- 2 + (3 {cos}^{2} α - 1) Φ}{2 + 2 (3 {cos}^{2} α - 1) Φ}$	$\frac{∊^{L}}{(2 ∊^{L} - 3 ∊_{u})}$
11	Δa	a^‖ − a^⊥	(∊₃₃ − ∊₁₁)Φcl log₁₀e	0.22∊₀(3 cos²α − 1)Φcl	1.30(∊_u − ∊_L)cl

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Applied Optics