Unconstrained depth photopolymerization is emerging as a promising technique for fabrication of several polymer microstructures such as self propagating waveguides, 3D freeform structures by bulk lithography, and polymer nanoparticles by flash exposure. Experimental observations reveal governing physics beyond Beer Lambert's law and scattering effects. This paper seeks to model unconstrained depth photopolymerization using classical nonlinear Schrödinger equation coupled with transient diffusion phenomenon. The beam propagation part of the proposed model considers scattering effects induced due to spatial variation of the refractive index as a function of the beam intensity. The critical curing energy model is used to further predict profile of polymerized voxel. Profiles of photopolymerized voxel simulated using proposed model are compared with the corresponding experimental results for several cases of exposure dose and duration. The comparison shows close match leading to conclusion that the experimentally observed deviation from Beer Lambert's law is indeed due to combined effect of diffusion of photoinitiator and scattering of light because of change in the refractive index.

1.
S.
Shoji
and
S.
Kawata
,
Appl. Phys. Lett.
75
,
737
(
1999
).
2.
M.
Kagami
,
T.
Yamashita
, and
H.
Ito
,
Appl. Phys. Lett.
79
,
1079
(
2001
).
3.
H.-B.
Sun
,
S.
Matsuo
, and
H.
Misawa
,
Appl. Phys. Lett.
74
,
786
(
1999
).
4.
S.
Yang
,
M.
Megens
,
J.
Aizenberg
,
P.
Wiltzius
,
P. M.
Chaikin
, and
W. B.
Russel
,
Chem. Mater.
14
,
2831
(
2002
).
5.
S.
Jeon
,
J.-U.
Park
,
R.
Cirelli
,
S.
Yang
,
C. E.
Heitzman
,
P. V.
Braun
,
P. J. A.
Kenis
, and
J. A.
Rogers
, “
Fabricating complex three-dimensional nanostructures with high-resolution conformable phase masks
,”
Proc. Natl. Acad. Sci. U.S.A.
101
,
12428
12433
(
2004
).
6.
J.-H.
Jang
,
C. K.
Ullal
,
M.
Maldovan
,
T.
Gorishnyy
,
S.
Kooi
,
C.
Koh
, and
E. L.
Thomas
,
Adv. Funct. Mater.
17
,
3027
(
2007
).
7.
J. P.
Singer
,
S. E.
Kooi
, and
E. L.
Thomas
,
Nanoscale
3
,
2730
(
2011
).
8.
D.
Dendukuri
,
S. S.
Gu
,
D. C.
Pregibon
,
T. A.
Hatton
, and
P. S.
Doyle
,
Lab Chip
7
,
818
(
2007
).
9.
D.
Dendukuri
,
D. C.
Pregibon
,
J.
Collins
,
T. A.
Hatton
, and
P. S.
Doyle
,
Nature Mater.
5
,
365
(
2006
).
10.
A. S.
Jariwala
,
F.
Ding
,
A.
Boddapati
,
V.
Breedveld
,
M. A.
Grover
,
C. L.
Henderson
, and
D. W.
Rosen
,
Rapid Prototyping J.
17
,
168
(
2011
).
11.
A. S.
Jariwala
,
R. E.
Schwerzel
,
H. A.
Nikoue
, and
D. W.
Rosen
, “
Exposure controlled projection lithography for microlens fabrication
,”
Proc. SPIE
8249
,
824917
(
2012
).
12.
P. S.
Gandhi
and
K. S.
Bhole
,
J. Micro Nano-Manuf.
1
,
041002
(
2013
).
13.
A. J.
Jacobsen
,
W.
Barvosa-Carter
, and
S.
Nutt
,
Adv. Mater.
19
,
3892
(
2007
).
14.
A. J.
Jacobsen
,
W.
Barvosa-Carter
, and
S.
Nutt
,
Acta Mater.
56
,
1209
(
2008
).
15.
A. J.
Jacobsen
,
W.
Barvosa-Carter
, and
S.
Nutt
,
Acta Mater.
56
,
2540
(
2008
).
16.
T. A.
Schaedle
,
A. J.
Jacobsen
,
A.
Torrents
,
A. E.
Sorensen
,
J.
Lian
,
J. R.
Greer
,
L.
Valdevit
, and
W. B.
Carter
,
Science
334
,
962
(
2011
).
17.
A. S.
Kewitsch
and
A.
Yariv
,
Opt. Lett.
21
,
24
(
1996
).
18.
A. S.
Kewitsch
and
A.
Yariv
,
Appl. Phys. Lett.
68
,
455
(
1996
).
19.
K.
Kasala
and
K.
Saravanamuttu
,
Appl. Phys. Lett.
93
,
051111
(
2008
).
20.
J.
Zhang
and
K.
Saravanamuttu
,
J. Am. Chem. Soc.
128
,
14913
(
2006
).
21.
I. H.
Lee
and
D.-W.
Cho
,
Int. J. Adv. Manuf. Tech.
22
,
410
(
2003
).
22.
S.-J.
Lee
,
H.
WookKang
,
T.-Y.
Kang
,
G.
Lim
,
J.
-
WonRhie
,
B.
Kim
, and
D.-W.
Cho
,
J. Micromech. Microeng.
17
,
147
(
2007
).
23.
P. S.
Gandhi
,
S.
Deshmukh
,
R.
Ramtekkar
,
K.
Bhole
, and
A.
Baraki
,
J. Adv. Manuf. Syst.
12
,
43
(
2013
).
24.
K.-S.
Lee
,
R. H.
Kim
,
D.-Y.
Yang
, and
S. H.
Park
,
Prog. Polym. Sci.
33
,
631
(
2008
).
25.
J. Y.
Kim
,
J. W.
Lee
,
S.-J.
Lee
,
E. K.
Park
,
S.-Y.
Kim
, and
D.-W.
Cho
,
Microelectron. Eng.
84
1762
(
2007
).
26.
C.
Sun
,
N.
Fang
,
D. M.
Wu
, and
X.
Zhang
,
Sens. Actuators, A
121
,
113
(
2005
).
27.
S.
Maruo
and
K.
Ikuta
,
Sens. Actuators, A
100
,
70
(
2002
).
28.
S.
Nagamori
and
T.
Yoshizawa
, “
Research on solidification of resin in stereolithography
,” in
Optical Engineering, Society of Photo-Optical Instrumentation Engineers
(
2003
), Vol.
42
, pp.
2096
2103
.
29.
M.
Farsari
,
F.
Claret-Tournier
,
S.
Huang
,
C. R.
Chatwin
,
D. M.
Budgett
,
P. M.
Birch
,
R. C. D.
Young
, and
J. D.
Richardson
,
J. Mater. Process Tech.
107
,
167
(
2000
).
30.
A.
Goswami
,
A.
Phani
,
A. M.
Umarji
, and
G.
Madras
,
Rev. Sci. Instrum.
83
,
095003
(
2012
).
31.
J.-W.
Choi
,
E.
MacDonald
, and
R.
Wicker
,
Int. J. Adv. Manuf. Technol.
49
,
543
(
2010
).
32.
V. K.
Varadan
,
X.
Jiang
, and
V. V.
Varadan
,
Microstereolithography and Other Fabrication Techniques for 3D MEMS
(
John Wiley Sons
,
New York
,
2001
).
33.
M. F.
Perry
and
G. W.
Young
,
Macromol. Theor. Simul.
14
,
26
(
2005
).
34.
N.
Fang
,
C.
Sun
, and
X.
Zhang
,
Appl. Phys. A
79
,
1839
(
2004
).
35.
A. K.
O'Brien
and
C. N.
Bowman
,
Macromolecules
39
,
2501
(
2006
).
36.
M. D.
Goodner
and
C. N.
Bowmana
,
Chem. Eng. Sci.
57
,
887
(
2002
).
37.
J.
Zhang
,
K.
Kasala
,
A.
Rewari
, and
K.
Saravanamuttu
,
J. Am. Chem. Soc.
128
,
406
(
2006
).
38.
I. B.
Burgess
,
W. E.
Shimmell
, and
K.
Saravanamuttu
,
J. Am. Chem. Soc.
129
,
4738
(
2007
).
39.
A. B.
Villafranca
and
K.
Saravanamuttu
,
Opt. Express
19
,
15560
(
2011
).
40.
C.
Decker
and
A. D.
Jenkins
,
Macromolecules
18
,
1241
(
1985
).
41.
See supplementary material at http://dx.doi.org/10.1063/1.4891109 for the chemical reactions involved in the radical photopolymerization.
42.
M. A.
Hadis
,
P. H.
Tomlins
,
A. C.
Shortall
, and
W. M.
Palin
,
Dent. Mater.
26
,
1106
(
2010
).
43.
T.
Babeva
,
I.
Naydenova
,
S.
Martin
, and
V.
Toal
,
Opt. Express
16
,
8487
(
2008
).
44.
D. S.
Achilias
,
Macromol. Theory Simul.
16
,
319
(
2007
).
45.
E.
Andrzejewska
,
Prog. Polym. Sci.
26
,
605
(
2001
).
46.
Y.
Tang
, “
Stereolithography cure process modeling
,” Ph.D. dissertation (
School of Chemical and Biomolecular Engineering, Georgia Institute of Technology
, Atlanta, Georgia,
2005
), see http://smartech.gatech.edu/handle/1853/7235.
47.
A.
Boddapati
, “
Modeling cure depth during photopolymerization of multifunctional acrylates
,” M.S. thesis (
School of Chemical and Biomolecular Engineering, Georgia Institute of Technology
, Atlanta, Georgia,
2010
).
48.
Newport Optics, UV optics, mirrors, lenses,
2007
, see http://www.newport.com.
49.
T. C.
Poon
and
T.
Kim
,
Engineering Optics with MATLAB
(
World Scientific
,
Singapore
,
2006
).
50.
Sigma Aldrich, HDDA monomer and BEE photoinitiator,
2007
, see http://www.sigmaaldrich.com/.
51.
Coherent Inc. Ar+ ion laser system
,
2007
, see http://www.coherent.com.
52.
Holmarc, Optomechanical translational stages,
2007
, see http://www.holmarc.com/optomechanics.html.
53.
Neos Technologies
, Acousto-optic modulators,
2007
, see http://www.neostech.com.
54.
dSPACE, dSPACE DS1104 micro-controller,
2007
, see http://www.dspace.de.
55.
Olympus, Optical microscope,
2012
, see http://www.olympus-ims.com/en/microscope/mx51/.

Supplementary Material

You do not currently have access to this content.