Monomer diffusion rates in photopolymer material. Part II. High-frequency
gratings and bulk diffusion

C. E. Close; M. R. Gleeson; D. A. Mooney; J. T. Sheridan

doi:10.1364/JOSAB.28.000842

Journal of the Optical Society of America B
Vol. 28,
Issue 4,
pp. 842-850
(2011)
•https://doi.org/10.1364/JOSAB.28.000842

Monomer diffusion rates in photopolymer material. Part II. High-frequency gratings and bulk diffusion

C. E. Close, M. R. Gleeson, D. A. Mooney, and J. T. Sheridan

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C. E. Close, M. R. Gleeson, D. A. Mooney, and J. T. Sheridan, "Monomer diffusion rates in photopolymer material. Part II. High-frequency gratings and bulk diffusion," J. Opt. Soc. Am. B 28, 842-850 (2011)

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Abstract

Photosensitive polymers are of practical importance, and mass transport within such materials plays a critical role in their behavior. Building on the work in Part I [J. Opt. Soc. Am. B doc. ID 136413 (posted 5 January 2011, in press)], the diffusion constants of a number of materials (i.e., acrylamide, polyacrylamide, water, propanol, and acetone) within a photosensitive layer are measured. A combination of optical and physical chemistry techniques is applied under different conditions. Determining the rates of diffusion is beneficial as it: (i) indicates material stability over time and (ii) supports material characterization, modeling, and performance optimization.

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	IC	BC1	BC2
Position condition	$0 \leq x \leq ℓ$	$x = ℓ$	$x = 0$
Concentration condition	$C = C_{0}$	$C = C_{1}$	$\partial C / \partial x = 0$
Time condition	$t = 0$	$t \geq 0$	$t \geq 0$
Resulting equation	$D \frac{\partial^{2} \bar{C}}{\partial x^{2}} = p \bar{C} - C_{0}$	$\bar{C} = C_{0} / p$	$\partial \bar{C} / \partial x = 0$

	Water	Propanol	Acetone	Acrylamide
Chemical formula	$H_{2} O$	$C_{3} H_{8} O$	$C_{3} H_{6} O$	$C_{3} H_{5} O$
Chemical structure
Molecular weight ( $g / mol$ )	18 [48]	60.09 [48]	58.09 [48]	71.08 [48]
Melting point/boiling point, ( $° C$ )	0/100 [48]	$- 126.5$ /97.1 [48]	$- 94.9$ /56.3 [48]	84.5/125 [48]
Dielectric constant/dipole moment (D)	80.1/1.85 [49, 50]	20.1/1.68 [51, 52]	20.7/2.91 [52, 53]	2.8/0.12–3.42 [40, 41]
Molecular radius (Å)	2.78 [54]	6.19 [55]	$\sim 6$ [56]	Not available, but $\sim 7$ [57]^a

PA, $D_{PA}$	Average $D \pm Δ D$ , ${cm}^{2} / s$
With $0.8 g / 100 ml$ BA crosslinker	$(7.77 \pm 4.47) \times 10^{- 15}$
With $0.4 g / 100 ml$ BA crosslinker	$(3.36 \pm 0.75) \times 10^{- 14}$
With $0.2 g / 100 ml$ BA crosslinker	$(8.41 \pm 2.68) \times 10^{- 14}$
Without BA crosslinker	$(1.49 \pm 0.82) \times 10^{- 13}$
Short-exposure diffusion rate (no BA crosslinker), $D_{PA}$
$1 s$ exposure	$(4.56 \pm 0.86) \times 10^{- 11}$
$3 s$ exposure	$(3.27 \pm 0.45) \times 10^{- 11}$
$6 s$ exposure	$(2.33 \pm 0.24) \times 10^{- 11}$
$9 s$ exposure	$(1.80 \pm 0.11) \times 10^{- 11}$
Water (diffusion both in and out of the layer), $D_{W}$
$Thickness = 100 μm$	$(1.22 \pm 0.62) \times 10^{- 8}$
$Thickness = 220 μm$	$(5.90 \pm 3.00) \times 10^{- 8}$
Propanol (diffusion out of the layer), $D_{Prop}$
$Thickness = 100 μm$	$(1.86 \pm 0.52) \times 10^{- 8}$
$Thickness = 220 μm$	$(9.00 \pm 2.52) \times 10^{- 8}$
Acetone (diffusion out of the layer), $D_{Ace}$
$Thickness = 100 μm$	$(1.76 \pm 0.47) \times 10^{- 8}$
$Thickness = 220 μm$	$(8.52 \pm 2.27) \times 10^{- 8}$

	IC	BC1	BC2
Position condition	$0 \leq x \leq ℓ$	$x = ℓ$	$x = 0$
Concentration condition	$C = C_{0}$	$C = C_{1}$	$\partial C / \partial x = 0$
Time condition	$t = 0$	$t \geq 0$	$t \geq 0$
Resulting equation	$D \frac{\partial^{2} \bar{C}}{\partial x^{2}} = p \bar{C} - C_{0}$	$\bar{C} = C_{0} / p$	$\partial \bar{C} / \partial x = 0$

	Water	Propanol	Acetone	Acrylamide
Chemical formula	$H_{2} O$	$C_{3} H_{8} O$	$C_{3} H_{6} O$	$C_{3} H_{5} O$
Chemical structure
Molecular weight ( $g / mol$ )	18 [48]	60.09 [48]	58.09 [48]	71.08 [48]
Melting point/boiling point, ( $° C$ )	0/100 [48]	$- 126.5$ /97.1 [48]	$- 94.9$ /56.3 [48]	84.5/125 [48]
Dielectric constant/dipole moment (D)	80.1/1.85 [49, 50]	20.1/1.68 [51, 52]	20.7/2.91 [52, 53]	2.8/0.12–3.42 [40, 41]
Molecular radius (Å)	2.78 [54]	6.19 [55]	$\sim 6$ [56]	Not available, but $\sim 7$ [57]^a

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Equations (6)

Journal of the Optical Society of America B