Abstract

A holographic characterization technique is developed in accordance with a general photopolymerization model. The technique allows detailed quantification of the chemical parameters, including their variation from the Trommsdorff effect. The holographic procedure is especially suited for studying the diffusion of the chemical reactants.

© 1999 Optical Society of America

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References

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  1. A. S. Kewitsch and A. Yariv, “Nonlinear-optical properties of photoresists for projection lithography,” Appl. Phys. Lett. 68, 455–457 (1996); A. S. Kewitsch and A. Yariv, “Self-focusing and self-trapping of optical beams upon photopolymerization,” Opt. Lett. 21, 24–26 (1996).
    [CrossRef] [PubMed]
  2. C. Decker and K. Moussa, “Real-time kinetic study of laser-induced polymerization,” Macromolecules 22, 4455–4462 (1989); C. Decker, “Photoinitiated curing of multifunctional monomers,” Chimia 47(10), 378–382 (1993); C. Decker, “Recent advances in laser-induced curing,” Radiation Curing 58IPA2 182 (4310), 383–386 (1992).
    [CrossRef]
  3. V. V. Krongauz, in Processes in Photoreactive Polymers, V. V. Krongauz and A. D. Trifunac, eds. (Chapman and Hall, New York, 1995), Chaps. 2–5; S. Piazzolla and B. K. Jenkins, “Holographic grating formation in photopolymers,” Opt. Lett. 21, 1075–1077 (1996).
    [CrossRef] [PubMed]
  4. C. Decker, in Handbook of Polymer Science and Technology, N. P. Cheremisinoff, ed. (Marcel Dekker, New York, 1989).
  5. C. Decker, “Real-time monitoring of polymerization quantum yields,” Macromolecules 23, 5217–5220 (1990).
    [CrossRef]
  6. G. Odion, Principles of Polymerization (Wiley, New York, 1981), Chap. 3.
  7. C. Decker, in Processes in Photoreactive Polymers, V. V. Krongauz and A. D. Trifunac, eds. (Chapman and Hall, New York, 1995), Chaps. 1 and 2.

1990 (1)

C. Decker, “Real-time monitoring of polymerization quantum yields,” Macromolecules 23, 5217–5220 (1990).
[CrossRef]

Decker, C.

C. Decker, “Real-time monitoring of polymerization quantum yields,” Macromolecules 23, 5217–5220 (1990).
[CrossRef]

Macromolecules (1)

C. Decker, “Real-time monitoring of polymerization quantum yields,” Macromolecules 23, 5217–5220 (1990).
[CrossRef]

Other (6)

G. Odion, Principles of Polymerization (Wiley, New York, 1981), Chap. 3.

C. Decker, in Processes in Photoreactive Polymers, V. V. Krongauz and A. D. Trifunac, eds. (Chapman and Hall, New York, 1995), Chaps. 1 and 2.

A. S. Kewitsch and A. Yariv, “Nonlinear-optical properties of photoresists for projection lithography,” Appl. Phys. Lett. 68, 455–457 (1996); A. S. Kewitsch and A. Yariv, “Self-focusing and self-trapping of optical beams upon photopolymerization,” Opt. Lett. 21, 24–26 (1996).
[CrossRef] [PubMed]

C. Decker and K. Moussa, “Real-time kinetic study of laser-induced polymerization,” Macromolecules 22, 4455–4462 (1989); C. Decker, “Photoinitiated curing of multifunctional monomers,” Chimia 47(10), 378–382 (1993); C. Decker, “Recent advances in laser-induced curing,” Radiation Curing 58IPA2 182 (4310), 383–386 (1992).
[CrossRef]

V. V. Krongauz, in Processes in Photoreactive Polymers, V. V. Krongauz and A. D. Trifunac, eds. (Chapman and Hall, New York, 1995), Chaps. 2–5; S. Piazzolla and B. K. Jenkins, “Holographic grating formation in photopolymers,” Opt. Lett. 21, 1075–1077 (1996).
[CrossRef] [PubMed]

C. Decker, in Handbook of Polymer Science and Technology, N. P. Cheremisinoff, ed. (Marcel Dekker, New York, 1989).

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Figures (9)

Fig. 1
Fig. 1

Slow dynamics exhibited by (a) the average monomer concentration, (b) the spatially varying monomer concentration, and (c) the grating amplitude. The grating is gradually erased under constant illumination. The decay deviates from a simple exponential behavior because of the Trommsdorff effect.

Fig. 2
Fig. 2

Fast dynamics exhibited by the spatially varying amplitudes of (a) radical concentration, (b) monomer concentration, and (c) refractive-index change during and immediately after the grating writing stage. Grating writing is stopped at time τon, and the grating amplitude peaks after a time of τr.

Fig. 3
Fig. 3

Comparison of the constructed (solid curve) and actual (dashed curve) chemical parameters: (a) average monomer concentration dynamics (log-linear); (b) monomer concentration dependence of the polymerization rate (log-log). The constructions are expected to be accurate for m0l<m0<m0u.

Fig. 4
Fig. 4

Dynamics in the diffusion-dominated regime: (a) spatially varying monomer concentration quickly decays owing to diffusion; (b) at the same rate the grating amplitude, Δn1, achieves a steady, fixed amplitude.

Fig. 5
Fig. 5

Setup for the holography experiments: PD, photodiode; ICF, chromatic filter; BS, beam splitter; LP Filt., low-pass filter; D/A, digital-to-analog; A/D, analog-to-digital.

Fig. 6
Fig. 6

Dynamics exhibited by the grating amplitude in the experiments: (a) during and immediately after the grating writing (timeτon);(b) gradual decay of the grating under constant illumination. The decay does not follow an exponential law.

Fig. 7
Fig. 7

Constructions of (a) average monomer concentration dynamics and (b) average monomer concentration dependence of the polymerization rate. Constructions are carried out with the experimental data shown in Fig. 6. The results are expected to be accurate for 0.4m00.8.

Fig. 8
Fig. 8

Scaling of (a) the radical dynamics and (b) the monomer dynamics. The plots are shown in log-linear format.

Fig. 9
Fig. 9

Simple procedure to determine the order of magnitude of monomer diffusion is carried out in three different multifunctional acrylates: (a) TMTA, (b) butyle ethylene and (c) HDODA with 0.1 wt.% initiator concentration (Irgacure 369). The dark waiting period is 30 minutes. Complete decay of the gratings after the dark period implies an exceptionally low diffusion constant.

Tables (1)

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Table 1 Values and Functional Forms of Kinetic Parameters Used in Numerical Simulations

Equations (13)

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drd t=ΦIs(0)-2kt(m)r2,
dmd t-Dm(m)d2mdx2=-kp(m)mr,
dΔnd t=βkp(m)mr,
r0s(m0)=s0(0)I0ϕ2kt(m0),
dm0dt=-kp(m0)r0s(m0)m0,
Δn0=β(m0(0)-m0),
dr1dt=-4kt(m0)r0s(m0)r1+ΦI1s0(0),
dm1dt=-Dm(m0)κ2+kp(m0)r0s(m0)+d[kp(m0)r0s(m0)]dm0m1-kp(m0)r1m0,
dΔn1dt=βkp(m0)r0s(m0)+d[kp(m0)r0s(m0)]dm0×m1+βkp(m0)r1m0,
r=r0s+r1 exp(iκx)+c.c.,
m=m0+m1 exp(iκx)+c.c.,
m0(t)=m0(0)tΔn1(t)dt0Δn1(t)dt,
1τp[m0(t)]=Δn1(t)tΔn1(t)dt.

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