Study on PQ/PMMA Photopolymer Films Fabricated by Solvent Casting.

PQ/PMMA photopolymer films fabricated by solvent casting are realized using tetrahydrofuran (THF) as the solvent. The corresponding photochemical reaction model is established with material parameters numerically studied based on 57 samples recorded with a 532 nm laser. The fabrication and the recording time are noticeably reduced. A 2-fold increase in the average refractive index variation is achieved compared with the two-step thermal polymerization method with the same PQ initial concentration.

Introduction

PQ (9,10-phenanthrenequinone)-doped PMMA (polymethyl methacrylate), PQ/PMMA, was first reported by Steckman et al. in 1998[1] as the easy-to-make holographic recording material with low shrinkage and low cost.[1−7] In 2000, Lin et al. developed the method of two-step thermal polymerization and fabricated the bulk material of PQ/PMMA with large dimensions.[2] In 2008, Luo et. al exposed PQ/PMMA to a periodic light field to make a transmission volume Bragg grating (VBG) of 90% diffraction efficiency for a spectral-spatial imaging filter.[8] In 2014, a reflective PQ/PMMA VBG serving as the laser mirror of a 976 nm tapered amplifier successfully achieved a high-power single-mode laser.[9] In 2011, Liu et al. proposed the photochemical reaction mechanisms and model of the recording process of PQ/PMMA. The corresponding rate equations were established.[10] In 2016, Shih et al. simplified the model by assuming that MMA monomers are abundant and the change of MMA concentration can be neglected during the recording process.[11]

However, the previous models for the two-step thermal polymerization method requiring the assumption of a constant concentration of residual MMA monomers throughout the recording process might be inadequate to estimate the actual amount of the photoproduct. Also, the time-consuming fabrication process of the two-step thermal polymerization method usually takes up to 36 h before the sample can be recorded.

This work utilizes the solvent casting method frequently adopted in fabricating organic semiconductor thin films[12] for PQ/PMMA fabrication. Dissolving ready-made PMMA and PQ with tetrahydrofuran (THF), practically no MMA monomers are left in the sample. The corresponding photochemical reaction model and the reaction rate and diffusion equations are proposed. A series of simulations and experiments were performed to evaluate the unknown material parameters of different fabrication and recording conditions.

Modeling

The photochemical reaction model utilizing differential equations to evaluate molecular concentrations as a function of space and time describes the dynamic behavior of PQ molecules excited by photons, the diffusion through the PMMA matrix, and the reactions with PMMA molecules. By applying the Lorentz–Lorenz formulation, the refractive index distribution can be evaluated with the knowledge of molecular concentrations. With a periodic recording pattern, the diffraction efficiency can then be obtained by the coupled-wave theory.

Reaction Rate and Diffusion Equations

PQ molecules can be excited by blue-green photons, and the corresponding reaction[10] can be written aswhere hν represents the absorbed photon, kPQ indicates the excitation rate of PQ to 1PQ*, and k is the transfer rate of 1PQ* to 3PQ*. kPQ can be expressed aswhere σPQ is the effective absorption cross section of PQ in the PMMA matrix. I and ν are the intensity and frequency of the recording light, respectively. The singlet state 1PQ* promptly turns into the triplet state 3PQ* that has an extremely long lifetime; therefore, 1PQ* can be neglected in the reaction rate and diffusion equations. 3PQ* can react with a hydrogen atom on a PMMA chain and attaches to the chain at the same site.[10] The reactions are described bywhere k and k are the corresponding reaction rates, R represents the rest of the PMMA chain, and HPQR is known as the PQ/PMMA molecule. The second reaction happens much faster than the first one;[10] therefore, eqs and 4 can be reduced to

Note that 3PQ* molecules travel freely through the openings inside the PMMA matrix; therefore, only the hydrogen atoms exposed to the void of the PMMA matrix that can make contact with 3PQ* are able to participate in the reactions. As a result, PMMA in eq will be referred to as react-able hydrogen, Hreact, in the following paragraphs. Also, the large molecular weights of PMMA and PQ/PMMA, which are more than a million, along with the tangled PMMA chains make the diffusion of PMMA and PQ/PMMA negligible. Therefore, the reaction rate and diffusion equations can be written by simplifying the model in ref (10) aswhere t is the time, x stands for the x-coordinate of the space, square parentheses represent the molarity of each kind of molecule enclosed, and D is the diffusion coefficient. With the above equations, the numerical method can be applied to model the dynamic spatial behaviors of the chemical reactions.

Refractive Index Variation and Diffraction Efficiency

The refractive indices of PQ, PMMA, and PQ/PMMA are 1.701, 1.493, and 1.497, respectively. With the above photochemical reactions, the exposed part of PQ/PMMA can lead to localized refractive index reduction.[2,10,11,13,14] Therefore, the periodic refractive index variation within PQ/PMMA can be achieved by the two-beam interference recording scheme.

PQ, 3PQ*, and PQ/PMMA are the chemical compounds responsible for the refractive index distribution in this system. With the initial chemical concentrations and the recording intensity distribution, the reaction rate and diffusion equations give the spatial distributions of the chemical compounds at any given time. Similar to ref (11), the first-order Fourier coefficients of the chemical compound concentrations and Lorentz–Lorenz formulation[15] are applied. The overall refractive index variation of the first Fourier order can be written aswhere γ is the proportionality constant of each chemical compound concentration and the corresponding contribution to the local refractive index of PQ/PMMA. A represents the first-order Fourier coefficients of each chemical compound concentration. With Δn1(t), the diffraction efficiency, η(t), can be obtained by the coupled-wave theory.[16]

Simulations

Material and Recording Parameters

The simulation parameters fall into two categories, the material parameters and the recording parameters. Table lists the material parameters. The lower case after the square parentheses indicates the initial concentration of the corresponding molecules; n is the average refractive index of PQ/PMMA; [PQ] and the grating thickness d are set to match the experimental conditions that will be discussed later; σPQ and DPQ are set to the values in accordance with refs (11, 14, 17); and D, [Hreact], k, and γ cannot be obtained directly and will be determined by experimental results.

Table 1

Material Parameters

parameter	value (unit)	parameter	value (unit)
[PQ]i	5.61 × 10–5 mol/cm3	[Hreact]i	1 × 10–4 mol/cm3
d	120 μm	ki	20 cm3/(mol·s)
σPQ	7.5 × 10–21 cm2	γPQ	14 cm3/mol
DPQ	1.24 × 10–18 m2/s	γ3PQ*	16 cm3/mol
D3PQ*	1.24 × 10–18 m2/s	γPQ/PMMA	37 cm3/mol
n	1.493

The recording parameters include the wavelength λ0, the average intensity I0 of the light source, the angle between the two recording beams θ, and the exposure time tex. Note that diffusion is a slow process; therefore, the simulation time is much longer than tex to reach equilibrium. The values listed in Table are based on the experimental configurations. The recorded grating period in the sample is then determined to be 251.96 nm.

Table 2

Recording Parameters

parameter	value (unit)
I0	1.6 W/cm2
λ0	532 nm
θr	90°
tex	∼50 s

Dynamic Behaviors of Molecular Concentrations and Refractive Index Variations

Using the RK4 (Runge–Kutta) method, the time development of the reaction and diffusion equations can be evaluated. The temporal and spatial distributions of [PQ], [3PQ*], and [PQ/PMMA] with tex = 50 s are shown in Figure . The corresponding first-order Fourier coefficients of these molecular concentrations as a function of t can be calculated, as shown in Figure a. Δn1(t), shown in Figure b, and η(t) can then be obtained by means of the Lorentz–Lorenz formulation and the coupled-wave theory.

Figure 1

Simulation of the time-varying (a) [PQ], (b) [3PQ*], and (c) [PQ/PMMA] concentration distributions of tex = 50 s recording.

Figure 2

(a) First-order Fourier coefficient of each chemical compound concentration distribution and (b) Δn1(t) with tex = 50 s recording.

The diffusion of PQ and 3PQ* and the reaction of 3PQ* and Hreact are responsible for the development of Δn1 after the exposure stops. Δn is defined as the final value of Δn1 when diffusion and all reactions cease. By varying tex, Δnf can be obtained, as shown in Figure . The peak of Δnf located at about tex = 40 s is marked by the dashed line in the inset of Figure . When tex is less than 40 s, there are not enough PQ molecules that can be excited to form 3PQ*, which leads to a smaller number of PQ/PMMA as well as a lower Δnf. On the other hand, when tex is over 40 s, the first-order Fourier coefficient of [PQ/PMMA] gradually becomes smaller as discussed in ref (12) and results in a lower Δnf. To ensure that the sample reaches the maximum diffraction efficiency, tex is chosen to be 60 s in the following simulations as well as the experiments. With the given laser intensity of 1.6 W/cm2, the exposure fluence is 96 J/cm2.

Figure 3

Δnf as a function of tex.

Analysis of the Material Parameters, k and [Hreact]

In practice, higher Δn1 and Δn are preferred. The influences of k and [Hreact] to Δn1 can be simulated, as shown in Figure . Since [3PQ*] distribution matches the recording light pattern and higher k allows 3PQ* to react locally, [PQ/PMMA] matches better with the recording light pattern with higher k, which gives higher Δn, as shown in Figure a. On the other hand, higher [Hreact] increases the opportunity of 3PQ* being intercepted by Hreact during diffusion. Consequently, [PQ/PMMA] distribution also matches better with the recording light pattern. Higher Δn is thus achievable, as indicated in Figure b.

Figure 4

Δn1 of 60 s recording: (a) k varies from 5 to 60 cm3/(mol·s) and [Hreact] is set to 1 × 10–4 mol/cm3. (b) [Hreact] varies from 0.2 × 10–4 to 1 × 10–4 mol/cm3 and k is set to 60 cm3/(mol·s). The insets are the final Δn1 versus k and [Hreact], respectively.

Fabrication and Recording Configurations

Fabrication of a PQ/PMMA Film by Solvent Casting

The method of solvent casting involves three major procedures that include preparation of the casting solution, coating process, and evaporation. The casting solution consisted of 23.02 wt% PMMA powder (Merck & Co., average molecular weight of 120,000) as the host material and 0.23 wt% PQ (Tokyo Chemical Industry) as the additive that were dissolved by 76.75 wt% tetrahydrofuran (THF, Chung Yuan Chemicals). The mixture was stirred at a rate of 180 rpm at 45 °C for 120 min using a heating magnetic stirrer (Thermo Fisher Scientific, SP131325Q). The doctor blade coating method[12] was utilized to fabricate the film. About 2.5 mL of casting solution was spread by a doctor blade coater (KTQ-II) to form a 400 μm wet film on a BK7 substrate. The wet film was then placed inside a temperature-controlled environment for a 90 min evaporation process. The evaporation temperatures, Tevap, were chosen to be 60, 40, 25, or 5 °C, which may affect the morphology and characteristics of the film.[18−21] As shown in Figure , a solid film formed after THF evaporated, and the thickness of the film was measured to be 120 ± 10 μm. The absorption at the recording wavelength is about 4%. Regardless of the Tevap, the films showed excellent transparency with no noticeable scattering or surface roughness. The PQ/PMMA solid film and the BK7 substrate will be referred to as the sample in the following paragraphs.

Figure 5

PQ/PMMA solid film after the evaporation process.

The entire fabrication process can be completed within 4 h, which is greatly reduced compared to the method of two-step thermal polymerization.[2] Furthermore, ready-made PMMA powder is used instead, and the difficulty of estimating the residual MMA monomer concentration is thus avoided.

Two-Beam Interference Recording Configuration

The recording configuration is shown in Figure . A single longitudinal mode 532 nm laser (Coherent, Verdi) was chosen to be the recording light source. A Faraday isolator (Optics for Research, IO-5-532-LP) was used to prevent optical feedback. The polarization was then adjusted by a half-wave plate to TE polarization with respect to the surface of the sample. To increase the spatial coherence, a spatial filter composed of a 20 × objective (Thorlabs, RMS20X) and a 10 μm pinhole (Thorlabs, P10H) was mounted before a collimation lens (Thorlabs, C330TME). The laser beam was split with a 50:50 beamsplitter (Thorlabs, BS013). M5 and M6 redirect the two recording beams to the sample. The angle between the two recording beams was set to be 90°. The sample was clamped by two BK7 right-angle prisms (Thorlabs, PS912) whose refractive indices are 1.52. Silicone oil (Kuen Min Tech) of refractive index 1.52 was applied to both surfaces of the sample for refractive index matching.

Figure 6

Two-beam interference recording configuration.

The diffraction efficiency of the sample during the recording process was monitored and measured by blocking one of the recording beams with an optical shutter (Thorlabs, SHB1T), as shown in Figure . The other recording beam was partly diffracted and partly transmitted through the sample with the corresponding powers of P1 and P2 measured using a power meter (Ophir, PD300-3W). The diffraction efficiency η can thus be obtained by

Figure 7

Measurement of the diffraction efficiency of the sample during the recording process.

Experimental Results

Parameters Fitted by the Photochemical Reaction Model

By measuring η every 30 s during a recording/developing process, Δn1 can also be obtained by the coupled-wave theory. The data of Δn1(t) can then be fitted by the reaction rate and diffusion equations, thereby determining the unknown material parameters, namely, D, [Hreact], k, and γ.

The Δn1(t) of the three PQ/PMMA samples fabricated at T = 40 °C with tex chosen to be 60 s was calculated and plotted in Figure . D, γPQ, γ, and γPQ/PMMA of sample 1 were obtained by fitting eqs –9 as 3.2 × 10–18 m2/s, 14.1, 16.8, and 37.5 cm3/mol, respectively. D and γ are both assumed to be identical under the same fabrication and recording conditions. [Hreact] and k listed in Table are the parameters distinguishing different samples. With these values, the fitted Δn1(t) curves agree well with the experimental data of all three samples, as shown in Figure . Therefore, under a constant Tevap, the assumption of identical values of D and γ under the same fabrication and recording conditions is credible.

Figure 8

Δn1(t) and the corresponding fitting curves of the three identical PQ/PMMA samples fabricated at Tevap = 40 °C with tex chosen to be 60 s.

Table 3

Parameter Values of the Fitting Curves of Samples 1, 2, and 3

sample	[Hreact]i (mol/cm3)	ki (cm3/(mol·s))
sample 1	6.0 × 10–5	93.9
sample 2	6.7 × 10–5	56.6
sample 3	6.3 × 10–5	35.7

Effects of the Evaporation Temperature, Tevap

The effects of Tevap are analyzed similarly. Totally 57 samples are fabricated at Tevap = 60, 40, 25, or 5 °C with the identical recording conditions. Δn1(t) is then obtained and fitted to estimate the material parameters. The recorded samples showed similar weak bleaching at the recording spots, which have no significant difference among different Tevap values.

The average D is plotted against Tevap in Figure . The trend shows that a lower evaporation temperature leads to a higher value of D. Tevap determines the solvent evaporation rate and the kinetic energy of PMMA, which in turn affects the final morphology of the PMMA matrix. A higher value of D implies that the matrix contains more openings that allow easier diffusion of PQ and 3PQ* molecules. Therefore, according to Figure , lower Tevap may tend to result in a more porous PMMA matrix due to the lack of stretching of PMMA molecules during the process of evaporation.

Figure 9

Average D of a total of 57 PQ/PMMA samples fabricated at different Tevap values.

The calculated k versus [Hreact] and [Hreact] versus Tevap of all 57 samples are shown in Figure a,b, respectively. Most of the samples have [Hreact] lower than 1 × 10–4 mol/cm3. However, there are samples with [Hreact] noticeably higher and can even reach 5.3 × 10–4 mol/cm3. On the other hand, k does not show a clear trend and distributes from 3 to 300 cm3/(mol·s). The data showing higher [Hreact] only appear for Tevap = 25 and 40 °C. Though the fabrication and recording conditions are identical, the data of Tevap = 25 °C fall into two distinct groups on this plot. About 37% of the samples have high [Hreact] but with low k, whereas the other 63% take on lower [Hreact] with relatively high k. On the other hand, no conspicuous groups can be found among the data of Tevap = 40 °C. Unlike the previous cases, the data of Tevap = 5 and 60 °C are confined to relatively small regions with low [Hreact]. While [Hreact] almost remains fixed, k varies largely.

Figure 10

(a) k and [Hreact] and (b) average [Hreact] of a total of 57 PQ/PMMA samples fabricated at different Tevap values.

From the grating fabrication perspective, reaching the highest possible Δn and η is the goal. As discussed in Section , both higher k and [Hreact] allow reaching higher Δn and η. With Tevap = 5 and 60 °C, the samples have low [Hreact] and result in low Δn. Though with a minority of the samples fabricated at Tevap = 25 °C that have unusually high [Hreact], the fabrication at Tevap = 40 °C gives the largest average [Hreact] and Δn among the four evaporation temperatures. The average Δnf of the VBG fabricated at Tevap = 40 °C with the previously mentioned recording conditions reached 3.6 × 10–4. With the same [PQ], this value is more than 2 times higher than those of the samples fabricated by the method of two-step thermal polymerization in ref (14), which reached only 1.5 × 10–4.

At higher Tevap, the PMMA matrix may have a chance to settle with fewer pores for PQ to move and less react-able H is exposed. At lower Tevap, PQ molecules may tend to cluster. Therefore, PQ may be harder to react. However, the detailed mechanism requires further investigation.

Conclusions

Solvent-cast PQ/PMMA photopolymer films using THF as the solvent are realized with the benefits of fast fabrication, efficient recording, and high refractive index variation. The corresponding photochemical reaction model and the reaction and diffusion equations recorded with a 532 nm laser are established. The fabrication and recording processes can be completed within 4 h. The material parameters D, [Hreact], k, and γ are numerically obtained and analyzed based on 57 samples. With a 40 °C evaporation temperature, 96 J/cm2 recording fluence, and 60 s exposure time, the average Δnf of such PQ/PMMA films can reach 3.6 × 10–4.