The effect of structural-kinetic features of hologram formation on holographic properties of photopolymers
A thermodynamic model of the holographic recording process in photopolymers have been developed. By the example of photopolymerizing compositions PPC-488 containing oligoetheracrylates and neutral components (NC) we have explored dependencies of holographic characteristics of medium on NC concentrat...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
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irk-123456789-1191342017-06-05T03:03:45Z The effect of structural-kinetic features of hologram formation on holographic properties of photopolymers Smirnova, T. Sakhno, O. Lozenko, S. A thermodynamic model of the holographic recording process in photopolymers have been developed. By the example of photopolymerizing compositions PPC-488 containing oligoetheracrylates and neutral components (NC) we have explored dependencies of holographic characteristics of medium on NC concentration and thermodynamic properties of polymer-NC system. The thermodynamic affinity of the polymer forming during recording and NC was evaluated using the difference of their solubility parameters ∆δP,NC. We have determined the feasible range of variation for ∆δP,NC and optimal concentration of NC ( 0 opt N ) that ensure high-performance recording. It was ascertained that excess in NC concentration over the optimal value leads to the increase of photoinduced light scattering in the layer. The efficiency of scattering depends on the size of microphase enriched by NC. We have determined the size of microphase particles and its dependence on kinetic parameters of polymerization. 2004 Article The effect of structural-kinetic features of hologram formation on holographic properties of photopolymers / T. Smirnova, O. Sakhno, S. Lozenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 3. — С. 326-331. — Бібліогр.: 19 назв. — англ. 1560-8034 PACS: 42.70.Ln http://dspace.nbuv.gov.ua/handle/123456789/119134 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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A thermodynamic model of the holographic recording process in photopolymers have been developed. By the example of photopolymerizing compositions PPC-488 containing oligoetheracrylates and neutral components (NC) we have explored dependencies of holographic characteristics of medium on NC concentration and thermodynamic properties of polymer-NC system. The thermodynamic affinity of the polymer forming during recording and NC was evaluated using the difference of their solubility parameters ∆δP,NC. We have determined the feasible range of variation for ∆δP,NC and optimal concentration of NC ( 0 opt N ) that ensure high-performance recording. It was ascertained that excess in NC concentration over the optimal value leads to the increase of photoinduced light scattering in the layer. The efficiency of scattering depends on the size of microphase enriched by NC. We have determined the size of microphase particles and its dependence on kinetic parameters of polymerization. |
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Smirnova, T. Sakhno, O. Lozenko, S. |
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Smirnova, T. Sakhno, O. Lozenko, S. The effect of structural-kinetic features of hologram formation on holographic properties of photopolymers Semiconductor Physics Quantum Electronics & Optoelectronics |
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Smirnova, T. Sakhno, O. Lozenko, S. |
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Smirnova, T. |
| title |
The effect of structural-kinetic features of hologram formation on holographic properties of photopolymers |
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The effect of structural-kinetic features of hologram formation on holographic properties of photopolymers |
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The effect of structural-kinetic features of hologram formation on holographic properties of photopolymers |
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The effect of structural-kinetic features of hologram formation on holographic properties of photopolymers |
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The effect of structural-kinetic features of hologram formation on holographic properties of photopolymers |
| title_sort |
effect of structural-kinetic features of hologram formation on holographic properties of photopolymers |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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2004 |
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http://dspace.nbuv.gov.ua/handle/123456789/119134 |
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The effect of structural-kinetic features of hologram formation on holographic properties of photopolymers / T. Smirnova, O. Sakhno, S. Lozenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 3. — С. 326-331. — Бібліогр.: 19 назв. — англ. |
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Semiconductor Physics Quantum Electronics & Optoelectronics |
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Semiconductor Physics, Quantum Electronics & Optoelectronics. 2004. V. 7, N 3. P. 326-331.
© 2004, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine326
PACS: 42.70.Ln
The effect of structural-kinetic features
of hologram formation
on holographic properties of photopolymers
T. Smirnova, O. Sakhno*, S. Lozenko
Institute of Physics NAS of Ukraine, 46, prospect Nauky, 03028 Kiev, Ukraine
Phone: +380 (44) 265 12 20, fax: +380 (44) 265 17 52
*Fraunhofer Institute AG Polymerphotochemie Geiselbergstr. 69, D-14476 Golm
Phone: 0331 568 1259, fax: 0331 568 3259, E-mail smirnova@iop.kiev.ua
Abstract. A thermodynamic model of the holographic recording process in photopolymers
have been developed. By the example of photopolymerizing compositions PPC-488 contain-
ing oligoetheracrylates and neutral components (NC) we have explored dependencies of ho-
lographic characteristics of medium on NC concentration and thermodynamic properties of
polymer-NC system. The thermodynamic affinity of the polymer forming during recording
and NC was evaluated using the difference of their solubility parameters ∆δP,NC. We have
determined the feasible range of variation for ∆δP,NC and optimal concentration of NC ( 0
optN )
that ensure high-performance recording. It was ascertained that excess in NC concentration
over the optimal value leads to the increase of photoinduced light scattering in the layer. The
efficiency of scattering depends on the size of microphase enriched by NC. We have deter-
mined the size of microphase particles and its dependence on kinetic parameters of polymeri-
zation.
Keywords: photopolymer holographic materials, holographic recording, holographic grat-
ing, thermodynamic model.
Paper received 23.04.04; accepted for publication 21.10.04.
1. Introduction
Photopolymer systems possess many advantages as at-
tractive recording materials for 3D holography. Origi-
nally two approaches to the creation of photopolymer
recording materials were proposed: 1) a holographic film
that is a neutral polymer matrix containing polymerizable
compounds [1], or 2) a liquid mixture of components that
is cured during the recording [2]. Holograms recorded in
solid films, as a rule, require optical or thermal develop-
ment and fixing. Liquid compositions are so-called self-
developing media. They ensure the formation of holo-
grams during recording and are characterized by the sim-
plest production process of the medium and recording
layer. Nowadays liquid compositions are widely used for
creation of polymer-liquid crystal [3,4], and polymer-
nanoparticle [5,6] periodical structures.
Liquid photopolymerizable compositions (PPC) in-
clude two monomers that differ in reactivity and refrac-
tive indices and initiator of radical photopolymerization.
Stable holograms in photopolymers are formed as a re-
sult of the diffusive redistribution of components in the
course of inhomogeneous polymerization in the interfer-
ence pattern. In liquid compositions both monomers must
take part in diffusion process to create stable hologram.
In the limiting case the monomer with lower reactivity
can be substituted by a neutral component (NC), which
does not take part in the chemical reaction but is involved
in the diffusion.
The present article studies liquid PPC developed in
the Institute of Physics NAS Ukraine [7�9] containing
oligomers and neutral components. We have shown that
phase separation of the initial mixture plays significant
role in hologram formation [10�12]. We have also pro-
posed a thermodynamic model of recording process. The
purpose of the present work is the development of ther-
modynamic approach to holographic recording in PPC.
We analyze dependence of holographic characteristics
of PPC on thermodynamic properties of system and con-
sider influence of microstructure of medium on its holo-
graphic properties. It should be noted that in media con-
taining two monomers, the low-reactive monomer polym-
T. Smirnova et al.: The effect of structural-kinetic features of hologram formation on ...
327SQO, 7(3), 2004
erizes when diffusive separation of components is fin-
ished. Therefore, displacement of this monomer with NC
does not influence on generality of results.
2. Formation of the phase structure
The PPC-488 and its modifications are binary composi-
tions containing oligomers, which form a three-dimen-
sional polymer network. Since the polymer network
swells to some extent in its own monomer and different
solvents, polymer formation gives rise to the displace-
ment of solvent from the network. Therefore polymeriza-
tion of monomer-NC mixture under uniform illumina-
tion results in formation of two-phase structure: the dis-
persion of microdrops of NC with polymer molecules dis-
solved (β-phase) in a polymer matrix with equilibrium
content of NC (α-phase). Polymerization in an interfer-
ence pattern has additional features (Fig. 1). Initially,
monomer polymerizes in the regions of maximum illumi-
nation. The polymer being formed has limited thermody-
namic compatibility with the NC. For this reason NC is
forced out of high intensity regions and forms microdrop
structure mainly in low intensity zones. Fig. 1 shows a
two-phase structure obtained when polymer does not swell
in the NC and the latter is completely displaced out of the
polymer network. Relatively low concentration of NC in
the α-phase and, accordingly, a low concentration of poly-
mer molecules in the β-phase enriched by NC are typical
for a three-dimensional polymer network. A microscopic
picture of grating with period Λ = 50 µm confirms the
two-phase structure of holograms in PPC (Fig. 2). When
polymerization is relatively slow and inter-diffusion be-
tween the nuclei of new phases has time to restore the
equilibrium, the �pathway� of phase separation in co-
ordinates γP versus ϕNC (depth of polymer conversion
versus normalized concentration of NC) can be described
by a binodal curve [13]. If the properties of a polymer
network depend on intensity, phase diagrams for the mix-
ture in illuminated and dark zones will be different.
Within this framework the hologram in a binary me-
dium may be treated as a spatially organized heteroge-
neous structure with periodic distribution of phases. Such
two-phase system is thermodynamically at quasi-equilib-
rium and diffusion of components between phases is for-
bidden, thus establishing a permanently stable hologram.
3. Dependence of holographic characteristics
on thermodynamic properties of mixture
As it was shown in [11,12], the amplitude of the refractive
index modulation in a holographic grating that is a two-
phase structure can be described by the equation:
)()(
2
1
)()(
2
1
minmax
minmax
1
ββ
βββα
υυ
υυ
−⋅−→
→−⋅−=
NCP nn
nnn
(1)
where nα, nβ, nP, nNC, are the refractive indices of corre-
sponding phases, polymer and NC; minmax, ββ υυ are vol-
ume fractions of the β-phase in the light and dark zones,
respectively.
The value of n1 increases with increase of segregation
of the polymer and the NC. The degree of segregation is
determined by thermodynamic affinity of components,
kinetic parameters of polymerization reaction and by
their diffusive separation. The value of )( βα nn − rea-
ches its maximum, if the interdiffusion rate allows trans-
fer of components over a distance that is equal to the av-
erage distance between nuclei of α and β phases. When
segregation of components is large, )( βα nn − appro-
aches the difference between refractive indices of the poly-
mer and the NC ( NCPn ,∆ ). The second term in equation
(1) is determined by concentration of NC (N0) in the mix-
ture and also by the interdiffusion rate. It reaches the
maximum value, if the system allows the mass-transfer
over a distance of Λ/2. Thus, when diffusion does not
limit the material redistribution, holographic properties
of PPC are determined by thermodynamic compatibility
of the polymer � NC system.
Fig. 1. Principal scheme of two-phase structure formation in the
course of polymerization within the interference pattern.
, � molecules of monomer and NC; � polymer net-
work.
Fig. 2. Microscopic image of the grating with Λ = 50 µm. (An
arrow indicates the decrease of field intensity)
b � phase a � phase
Initial mixture
Redistribution of phases
in the interference field
328
SQO, 7(3), 2004
T. Smirnova et al.: The effect of structural-kinetic features of hologram formation on ...
Research of the recording kinetics of gratings with
Λ ≤ 2 µm [14] has shown that while using the low-molecu-
lar NC diffusive redistribution of components finishes be-
fore the layer is fully polymerized. In this case, the diffu-
sion process does not limit the recording rate that is de-
termined by the rate of polymerization.
The thermodynamic affinity of polymer and NC can
be determined by the difference between their solubility
parameters (∆δ = |δP � δNC|) [15, 16]. The solubility pa-
rameter, 2/1)( iiE υδ ∆= , where iiE υ∆ is the density of
cohesion energy (the evaporation energy per mole). The
equality PS δδ = implies that the S- and P-components
are mutually soluble. Because cross-linked polymers are
not soluble, this condition corresponds to the maximum
possible swelling of polymer network in a solvent. Since
this equality implies an athermic dilution, it is gener-
ally assumed that the solvent is suitable, if |δS � δP| <
< 2.5 �3 MPa1/2. Ability to form hydrogen bonds widens
this region. The solubility parameter, δ, is available in
literature for the large number of polymers and organic
liquids. It also can be calculated or measured by simple
methods. It is evident from this model that for effective
recording NC should not be a �good solvent� for the
polymer.
The dependence of the holographic characteristics on
the thermodynamic properties has been determined by
measuring the dependence of n1 on N0 for NC with differ-
ent δNC (Table 1). For this purpose, transmission gratings
with Λ = 0.8 µm and d = 25 µm were recorded. Recording
was carried out using Ar laser (λr = 0.488 mm) with I =
= 1 mW/cm2. Note that for the sample with this thickness
the dynamic range max
1n ≅ 0.01 ensures the diffraction effi-
ciency of η ≅ 1.
The following regularities were obtained. Stable
gratings are formed, if the concentration of NC in initial
mixture, N0, exceeds the NC equilibrium content of poly-
mer 0
0N . An optimum NC concentration, optN0 , exists that
ensures the maximum dynamic range of recording. The
decrease of n1 with increase of N0 above the optimum
value is the result of increased light scattering in holo-
gram due to the growth of the size of β-phase particles
(see sec. 4). In Fig. 3, the change of optN0 is plotted versus
δNC for NC, listed in Table 1. The neutral components
No.8-12 can create hydrogen bonds. The value of δP is
about 20.5 MPa1/2. Since optN0 depends on the size of
microstructure, the curves in Fig. 3 depict only a general
trend of optN0 (δ) change. The optimum concentration de-
creases with a decrease in thermodynamic affinity be-
tween the polymer and NC (∆δP,NC increases). This is
obvious from the equation (1). The enhancement of com-
ponent segregation due to the decrease of their compati-
bility causes the growth of the difference between the re-
fractive indices of α and β phases. As a result, the maxi-
mum value of n1 can be achieved for smaller differences
in the volume fraction of the β-phase in the �fringes� of
the grating and, accordingly, at a smaller initial concen-
Fig. 3. Dependence of NC optimal concentration on its solubility
parameter.
15 20 25 30 35
10
20
30
40
50
d, MPa
N
,
v
o
l.
%
0o
p
t
1/2
Table 1. NC characteristics and diffraction efficiency of gratings at the optimal concentration of NC.
No NC nNC nP � nNC δNC, MPa1/2 optN0 , vol.% η
1 Acetonitrile 1.344 0.176 24.3 25 0.95
2 α-Naphthalenebromide 1.66 �0.140 21.7 45 0.98
3 Pentachlorodiphenyl 1.636 �0.116 21.5 40 0.90
4 Quinoline 1.627 �0.107 21.3 40 0.85
5 Toluene 1.467 0.023 18.2 35 0.42
6 n-Heptane 1.387 0.133 15.5 15 0.95
7 n-Hexane 1.375 0.145 14.9 12 0.95
8 Ethylene glycol 1.432 0.089 29.9 7 0.35
9 Methanol 1.328 0.193 29.7 25 0.80
10 Ethanol 1.362 0.159 26 40 0.881)
11 Butanol-1 1.399 0.122 23.3 35 0.951)
12 Triethylene glycol 1.456 0.065 21.9 45 0.80
1) The strength of grating, πn1d/λtcosθB > π/2.
T. Smirnova et al.: The effect of structural-kinetic features of hologram formation on ...
329SQO, 7(3), 2004
tration of NC. The value of optN0 is maximized when
NC Pδ δ≅ , because at this condition the equilibrium NC
content in the polymer network is also a maximum.
Equation (1) can be used to estimate the minimum
value of N0 that provides a required dynamic range. If
the neutral component is assumed to be completely dis-
placed into dark regions,
optN min0 ~ NCP nnn −1 . (2)
For max
1 0.01n ≥ and 1.0≅− NCP nn the minimum op-
timal concentration is about 0.1.
Hence, for effective holographic recording ( max
1n ≥
0.01≥ ) the values of ∆δP,NC and ∆nP,NC should sa-
tisfy the following conditions:
∆nP,NC ≥ 0.1;
∆δP,NC ≤ 5 MPa1/2, if hydrogen bonds
are not formed,
(3)
∆δP,NC ≤ 12 MPa1/2if hydrogen bonds can be formed.
Note that variations in δNC should not result in a vio-
lation of condition δNC ≅ δM. Otherwise phase separation
will take place in the initial mixture.
The rate of recording also depends on the thermody-
namic affinity of the components. For materials of PPC-
type, a reduction of this affinity allows to decrease the
concentration of NC that increases both the polymeriza-
tion and recording rates.
Finally it should be noted that these concepts are not
only valid for materials of PPC-type. Phase separation
occurs during holographic recording in compositions
containing liquid crystals and nanoparticles.
4. Influence of micro-heterogeneity
of the photopolymer composition
on its holographic properties
It was noted above that the values optN0 and, correspon-
dingly, 1n are bounded by the size of β-phase particles.
In this section experimental results are considered, that
confirm this assumption. Light scattering was measured
in PPC layers that contain different NC. Also, the size of
β-phase particles was determined using microscopic mea-
surements.
Integral variation of light scattering in a recording
layer was estimated by the change of transmission for the
probing He-Ne laser beam in the course of photopolyme-
rization of PPC layer by incoherent spatially-homoge-
neous UV-radiation. The use of incoherent radiation ex-
cludes the recording of noise holograms [17]. Transmis-
sion of the layer was calculated as T(t) = Ptr(t) / P0(t),
where Ptr is the power of the passing beam, 0P is the power
of the falling beam.
Kinetics of transmission change was measured dur-
ing polymerization for PPC with various NC concentra-
tions. The results for two NC α-bromnaphthalene which
demonstrates high affinity to a polymer and n-hexane
with low affinity are shown in Figs 4, 5. To exclude re-
flection and light scattering losses in substrate, the data
was normalized so that the transmission of the initial liq-
uid layer was 100%. The error in kinetic curve measure-
ment is less than 0.2%.
In both cases, the transmission of the layer decreases
with the increase of the NC concentration. However, when
concentrations are equal, the terminal transmission sub-
stantially depends on the nature of NC. Thus, if for a-
bromnaphthalene the increase of concentration up to 40%
leads to decrease in transmission by 1% while injection
of n-heptane decreases the layer transmission up to 35%.
The similar behavior was obtained for NC that form hy-
drogen bonds.
Examination of the structure of polymer layers with
microscope Polam I-411 (1000x magnification) allowed
determining the following behaviour. The structure of
polymer composition contains discrete microinhomo-
geneities, which size increase with the increase of NC
concentration. The size differs greatly for PPC with diffe-
0 500 1000 1500 2000 2500 3000 3500
0.86
0.88
0.90
0.92
0.94
0.96
0.98
1.00
a
2
4
3
1
t, s
T
0 500 1000 1500
0.98
0.99
1.00
2
aT
t, s
Fig. 4. The change of transmission of PPC layer with α-brom-
napthalene during polymerization by UV-radiation at concen-
tration of NC 0 (1), 40 (2), 60 (3) and 80 vol.% (4).
200 300 400 500 600
0.0
0.2
0.4
0.6
0.8
1.0
3
2
1
a
t, s
T
200 400 600
0.980
0.990
1.000
1
a
T
t, s
Fig. 5. The change of transmission of PPC layer with n-heptane
during polymerization by UV-radiation at concentration of NC
12 (1), 20 (2) and 40 vol.% (3).
330
SQO, 7(3), 2004
T. Smirnova et al.: The effect of structural-kinetic features of hologram formation on ...
rent NC. When employing α-bromnaphthalene the struc-
ture becomes distinguishable at N0 ≅ 60 vol.%. We can
mark out the particles of two characteristic sizes: the sepa-
rate micro-inhomogeneities with the diameter D ≈ 10 µm
and a substantial number of particles with D < 1 µm.
When employing n-hexane as NC, the large-scale drops
of emerging phase with characteristic diameters 5 and
100 µm become visible at N0 = 20 vol.% They merge in
some areas forming tree-type structures.
To determine the size of inhomogeneities in PPC that
contains α-bromnaphthalene, the turbidity spectrum me-
thod was used [10]. It was shown that at N0 ≅ 60 vol. %
the radius of the scattering particle is nearly 0.75±0.2 µm.
If the concentration of NC decreased to the optimal value
of 45 vol.%, precision of the method was insufficient to
determine the size of the particles. These results coincide
with the data of microscopic analysis and verify that pre-
vailing size of the particles is ≤1 µm, when concentration
of NC is about 60%. The size of the scattering centers is
much smaller than 1 µm, when concentration of α-brom-
naphthalene is optimal. This conclusion is confirmed by
the fact of recording of high-effective reflective gratings
with N = 6000 mm�1 [18]. Maximum diffraction efficiency
η ≅ 1 can be accomplished when the size of phase struc-
ture is less than Λ/2 ≅ 0.08 µm.
So the investigation carried out reveals that the de-
crease of the recording efficiency with the increase of N0
starts at the same values of N0 as the increase of light
scattering caused by enlargement of heterostructure par-
ticles. The increase of light scattering during recording
leads to amplification of noise holograms that forms as a
result of interference between recording and scattered
waves. Amplification of noise hologram results in de-
crease of grating diffraction efficiency.
With the increase of compatibility of components, the
decrease of n1 is observed under a more excess of N0 over
the optimal value. This makes for an increase in the mate-
rial dynamic range. In most of considered cases, the ten-
dency to increase in optN0 with the increase of thermodyna-
mic compatibility of components takes place. However,
the values optN0 for different NC with the same solubility
parameters can differ significantly. To illustrate this, let
us compare these values for α-bromnaphthalene and bu-
tanol-1. For α-bromnaphthalene δNC =21.7 MPa1/2,
0
0N ≈ 12 vol.%, optN0 ≈ 45 vol.%; for butanol-1 δNC =
= 23.3 MPa1/2, 0
0N ≈ 16 vol.%, optN0 ≈ 30 vol.%. Increase
in the equilibrium content of NC for α-bromnaphthalene
in comparison with butanol-1 can be explained by spe-
cific interaction of polymer and NC, because butanol-1
can form hydrogen bonds. The decrease of the optimal
concentration is a result of enlargement of β-phase parti-
cles. It is confirmed by measurements of light-scattering
in a layer. Thus, transmission of 50 µm thick polymer
layer obtained as a result of polymerization of the com-
position with 40 vol. % of α-bromnaphthalene exceeds
99%, whereas for the layer with the same concentration
of butanol-1 it is about 92%. On the other hand, injec-
tion of ethanol with ∆δP,NC higher than that of butanol-1
lowers 0
0N down to 14 vol.% and rises the optimal con-
centration up to 40 vol.%. Transition of the layer also
increases up to 99%.
It is known that the size of β-phase microdrops de-
pends significantly on the polymerization rate. It was
shown for oligoetheracylates that slowing of polymeri-
zation is accompanied by enlargement of phase particles
and could be followed by full separation of a system [19].
We do not consider the influence of polymerization rate
in details. However, while examining the microstructure
of the gratings with Λ = 50 µm recorded with gaussian
beam, the increase of microdrops in size was observed at
the periphery of gratings where the intensity of the re-
cording field is lower (Fig. 2).
Thus, if the entire volume of β-phase displaced from
the polymer is determined by thermodynamic compat-
ibility of polymer and NC as well as the initial concen-
tration of NC, the characteristic size of β-phase particles
depends on the total volume of displaced phase, polym-
erization rate and interphase tension forces.
Since microphase structure of polymer determines the
resolution of PPC and noise characteristics of holograms,
the possibility to control the size of microphase particles
is quite important.
5. Conclusions
Thermodynamic approach to holographic recording in
PPC allows determining the following regularities. If the
characteristic time of polymerization is greater than char-
acteristic time of component diffusion, the dynamic range
and light sensitivity of medium (recording rate) are deter-
mined by thermodynamic properties of the system. In-
equalities (2) are the criterion of efficient recording in
media with phase separation. They can be used to choose
optimal composition components.
The microstructure that is formed during recording
influences significantly the dynamic range and resolu-
tion of material. The size of dispersed phase depends on
thermodynamic properties of medium, kinetic parameters
of polymerization and interphase interaction forces. To
control microphase structure parameters is important for
the improvement of optical and holographic characteris-
tics of photopolymers and needs further development.
Results obtained may be a basis for the development
of the thermodynamic model for polymer-liquid crystal
and polymer-nanoparticles structures.
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