Absorption changes under UV illumination in doped PMMA

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Oct 5, 2000 - Time-resolved measurements of the kinetics of the absorption ... molecules decay into free radicals and trigger polymerization reactions of the ...

Appl. Phys. B 72, 201–205 (2001) / Digital Object Identifier (DOI) 10.1007/s003400000438

Applied Physics B Lasers and Optics

Absorption changes under UV illumination in doped PMMA F. Havermeyer1,3,∗ , C. Pruner2 , R.A. Rupp2 , D.W. Schubert3 , E. Krätzig1 1 University of Osnabrück, 49069 Osnabrück, Germany 2 University of Vienna, 1090 Wien, Austria 3 GKSS Research Centre, 21502 Geesthacht, Germany

Received: 17 July 2000/Published online: 5 October 2000 –  Springer-Verlag 2000

Abstract. The absorption spectra of poly(methyl methacrylate) (PMMA) doped with the photoinitiator 2,2-dimethoxy2-phenylacetophenone (DMPA) change under illumination with UV light. Time-resolved measurements of the kinetics of the absorption changes at 352 nm prove the existence of a second light-induced reaction besides the expected light-induced decay of the photoinitiator. We propose a model for this second process which is in good agreement with the observed experimental facts. PACS: 82.50; 42.70.Ln Poly(methyl methacrylate) (PMMA) containing residual monomer and doped with the photoinitiator 2,2-dimethoxy-2phenylacetophenone (DMPA) is a photosensitive system for light in the ultraviolet (UV) range. For production of holographic gratings of high spatial frequency, polymer sheets of this material are illuminated by the interference pattern of two coherent light beams. In the illuminated regions DMPA molecules decay into free radicals and trigger polymerization reactions of the residual monomer. This permits us to record volume phase gratings with refractive-index amplitudes up to 10−4 and spatial frequencies up to 10 000 lines/mm [1]. A complete model of the photorefractive effect in PMMA, i.e. of the light-induced refractive-index changes, must describe two processes: the light-induced generation of radicals and the polymerization reactions induced by these radicals. This paper deals with the first step of the photorefractive effect: the decay of the photoinitiator molecules under illumination with UV light.

C5 O2 H8 , by vacuum distillation. An amount of 0.50 g/l = 3.0 mol/l azobisisobutyronitrile (AIBN) and up to 0.81 g/l = 3.2 mol/l DMPA are dissolved in the cleaned monomer. The solution is then prepolymerized for 48 h at 45 ◦ C in a reaction chamber formed by two glass plates. These plates are spaced about 3-mm apart from each other by a flexible tube of 3-cm diameter. During prepolymerization the AIBN molecules decay into radicals which start a free-radical polymerization of the monomer, while the photoinitiator DMPA is stable under these conditions. The residual monomer content of the produced polymer blocks depends mainly on the temperature during the prepolymerization and amounts to 10 to 20%. 1.2 Experimental set-up Light-induced absorption changes were investigated with the set-up shown in Fig. 1. The expanded light beam of an argon– ion laser (operating at λ = 352 nm) is split into an activation beam and a test beam. The activation beam impinges nearly perpendicularly onto the surface of the sample and illuminates the whole sample homogeneously. The diameter of the test beam is limited by an aperture to 2 mm. Its intensity, reduced by an absorption filter, is at least 100 times smaller

absorption filter mirror

aperture beam splitter expansion system


1 Experimental

sample 1.1 Sample preparation Preparation of the polymer blocks begins with the purification of the commercially available monomer methyl methacrylate, ∗ Corresponding

author. Present address: GKSS Research Centre, Max-Planck-Strasse, 21502 Geesthacht, Germany (E-mail: [email protected])



Fig. 1. Schematic drawing of the set-up used for the time-resolved measurements of the light-induced absorption changes. The different path lengths of the activation beam (thick) and of the test beam (thin) are adjusted to suppress beam coupling


where α(t) is the absorption coefficient at time t, IT the intensity of the test beam transmitted through the sample and d the geometric path length of the test beam through the sample (taking into account the angle of incidence of 33 ◦ ). 2 Results Samples with different concentrations NS0 of the photoinitiator DMPA were first characterized by absorption spectroscopy. As shown in Fig. 2, DMPA gives rise to an absorption band with a maximum at λmax = 345 nm. The maximum increases linearly with NS0 according to α(λmax ) = 120 m2 kg−1 NS0 + 18 m−1 . After illumination with UV light this absorption band vanishes. Instead a shift of the edge of the fundamental absorption from about 300 to 320 nm is observed. The typical kinetics of the absorption under constant and homogeneous illumination (wavelength of the activation light and the test light is 352 nm) is exemplarily shown in Fig. 3 for three different concentrations N S0 of the initial photoinitiator and different light intensities IP . As described in [2] for similar experimental conditions, the absorption coefficient increases at the beginning of the illumination. But after some time it passes a maximum and then slowly decays towards a final value below the initial absorption coefficient α(0). The final absorption is nearly equal to the absorption of the undoped (NS0 = 0) polymer (cf. Fig. 2). The difference between the maximum value and the final value of the absorption change depends on NS0 . In particular, for NS0 = 0 no absorption changes are observed. During, and also after the illumination with the activation beam, noise holograms build up. The profile of the transmitted activation beam becomes strongly distorted by the



NSO[g 1-1] IP[W m-2] 0.0 112 0.4 40 0.4 80 38 0.8 0.8 70

0.10 0.05 0.00 -0.05 -0.10 0


2000 t [s]


Fig. 3. Time dependence of the absorption changes ∆α for different initial DMPA concentrations NS0 and illumination intensities IP with light of wavelength λP = 352 nm. Symbols represent measured data, while solid lines result from fits according to (5)

interaction with these noise holograms and the two-ring scattering phenomena [3] can nicely be observed. The intensity of the test beam is too small to induce significant holographic gratings within the typical time period (up to 2 h) of our experiments. Furthermore, the test beam does not match the Bragg condition for read-out of most of the noise holograms induced by the activation beam. Therefore intensity losses due to diffraction are small and will be neglected in the further discussion. The key observation is that the evolution of the absorption changes can be stopped at any time by turning off the activation light (Fig. 4): during dark periods of less then 1 h, ∆α is constant within the experimental error. (Only for very long interruptions of the illumination of several hours does the absorption coefficient slightly decrease in the dark.) When the activation light is turned on again ∆α follows the same kinetics as for the non-interrupted case. This effect was used to corroborate that beam-coupling effects can be excluded. For that purpose the shutter for the activation beam was opened only when the shutter for the test beam was closed, and vice versa. No difference was obtained

NS0 [g l-1] 0 0.3 0.4 0.5 0.8 0.8 (illuminated)




∆α [mm-1]

than the intensity IP of the activation beam. The path-length difference between the two beams is adjusted such that no beam coupling is observed, i.e. for minimum coherence of both beams. Starting the illumination with the activation beam at time t = 0 the induced absorption change is given by   1 IT (0) , (1) ∆α(t) := α(t) − α(0) = ln d IT (t)






Fig. 2. Absorption spectra of PMMA samples with different concentrations NS0 of the initial photoinitiator. For the sample with NS0 = 0.8 g/l the spectrum after illumination (10 h at 400 W/m2 , light wavelength λP = 352 nm) is also shown

Fig. 4. Time dependence of the absorption changes ∆α. At t = 0 the activation light (intensity IP = (16 ± 2) W/m2 ) is turned on for the time tL (open symbols). Then the light is turned off for 1900 s (filled symbols) and afterwards turned on again for the rest of the observation time (open symbols). Solid lines result from fits according to (5)


in comparison with measurements where both shutters where open at the same time. Several measurements like the ones exemplarily shown in Figs. 3 and 4 were performed for a variety of initial photoinitiator concentrations NS0 and for step-like constant functions IP (t) of the light intensity. By plotting ∆α/NS0 versus the irradiation t Q(t) =

IP (t  ) dt 



it turns out that all data can be described in good approximation by one universal curve f(Q). This is shown in Fig. 5 for the data already presented in Fig. 3. Hence we have ∆α(t) = NS0 f(Q(t))


and obtain

 ∂ f  ∆α(t) ˙ = NS0 IP (t) ∂Q t


for the general form of the absorption rate. The observed function f(Q) is well described by the sum of two exponential functions (cf. solid lines in Fig. 3, 4 and 5):     (5) f(Q) = ai 1 − e−ki Q + ad e−kd Q − 1 . Here ai and ad are the amplitudes of the fast increase (index i) and slow decrease (index d), respectively. The pertinent proportionality constants are denoted by k i and k d . These four parameters are determined by a least square fit of (5) to the experimental data for each individual measurement. For the investigated initial photoinitiator concentrations between NS0 = 0 and 0.81 g/l and for light intensities between I P = 4 and 300 W/m2 these four parameters neither depend on N S0 nor on IP . The average parameter set determined from all measurements is given in Table 1. Similar results can be obtained for activation and test light of wavelength λ = 364 nm. However, the absorption changes ∆α(t) for this wavelength are nearly one order of magnitude smaller than those for light with λ = 352 nm. Absorption changes for test light with λ = 478 and 543 nm are too small to be detected within our experimental error of ∆α/α = 5%.

Table 1. Average amplitudes ai and ad of the fast increase and slow decrease, and pertinent proportionality constants ki and kd , respectively (cf. (5)). The wavelength of the activation light and the test light is λ = 352 nm Parameter Value





0.22 m2 /g

0.37 m2 /g

7.8 × 10−4 m2 /J

1.4 × 10−5 m2 /J

Most measurements were done with samples which were removed from their reaction chambers after prepolymerization and cut into blocks with dimensions of about 2 mm × 4 mm × 4 mm. If necessary these blocks were stored for the time between preparation and experiment under an argon atmosphere at −32 ◦ C. In addition, some samples were kept in their reaction chambers during the whole measurements, as this reduces the evaporation rate of the residual monomer and minimizes the contact between polymer and air. Regardless of all these different kinds of sample treatments we obtained the same results. 3 Model From the absorption spectra of the non-illuminated samples in Fig. 2 two contributions can be distinguished: the ground absorption αG of the pure polymer and the contribution α S0 of the photoinitiator which is proportional to its concentration NS0 . For long illumination times the absorption caused by the photoinitiator vanishes and the low absorption of the pure polymer is approximately reached for the wavelength λ = 352 nm. These observations can be explained by the known decay kS IP

S −→ 2R∗ + X

of the photoinitiator molecules S into two radicals R ∗ and chemically inactive molecules X [4]. The rate constant k S IP for this reaction is proportional to the light intensity I P . For constant light intensity the DMPA concentration decays exponentially according to NS (t) = NS0 e−kS IP t .


Since the absorption for λ = 352 nm does not decay monotonically but increases in the first stage of illumination (see Fig. 3), at least a third contribution, αR , must be taken into account. Assuming that αR is proportional to a substance with concentration NR , the total absorption is then given by α(t) = αG + f S NS (t) + f R NR (t) .

Fig. 5. Normalized absorption changes ∆α/NS0 versus irradiation Q = IP t for the data presented in Fig. 3. The solid line represents the best fit for the universal curve f according to (5)



Here f S and f R are the proportionality constants for the contributions of the photoinitiator molecules and the reaction products, respectively. From (3) we see that the contribution αR must be related to the light-induced decay of the photoinitiator S: because of ∆α ∝ NS0 the contribution αR must be proportional to (at least) one of the products of the reaction chain which begins with the decay of S. From these products we can exclude all products like the chemically inactive residues X. These stable products would lead to constant, non-vanishing absorption


contributions, which is in contradiction to the observation that αR and αS practically vanish for long illumination times. The contribution αR can only be caused by transient photoproducts. Equations (7), (8) and (4) state that these transient products must decay with a rate which is (at least) a linear function of IP and are stable in the dark (at least in the time intervals investigated). According to (6) and (7) initial radicals build up with the rate −2 N˙ S (t). On the one hand these initial radicals undergo reactions with the residual monomer and form oligomer and then polymer radicals. This reaction finally leads to permanent changes of the density and the refractive index of the material and is responsible for the photorefractive effect. On the other hand initial radicals and/or polymer radicals undergo bimolecular termination reactions. Both reactions, polymerization and termination, are characteristic for free-radical polymerization (cf. [5]). Their kinetics does not depend on the illumination and will continue even in the absence of light. Since the evolution of the absorption changes can be temporarily stopped by turning off the activation beam, they cannot be the dominant processes responsible for the observed time and intensity dependence of ∆α. Moreover, there seems to be no need to distinguish between initial radicals and polymer radicals. The simplest hypothesis in accordance with the observed time dependence of ∆α is to introduce a light-induced termination reaction for radicals. The complete rate equation for radical concentration NR is then N˙ R (t) = −2 N˙ S (t) − kR IP NR (t) ,


where kR IP is the rate constant for the termination of radicals under the influence of light. Solving (9) with N R (0) = 0 gives   NR (t) = NS0 κ e−kR IP t − e−kS IP t

set with f S = f S , f R = [ f S + (2 f R − f S )kS /kR ] /2 kS = kR , kR = kS


which leads to the same time dependence for ∆α. Table 2 gives the values for both parameter sets calculated from the experimental results in Table 1. 4 Discussion The model for light-induced absorption changes described in the previous sections enables us to calculate the time evolutions of the photoinitiator and of the radical concentration. The experimental findings are in good agreement with the predictions from the model. However, there are two sets of parameters which cannot be distinguished from our measurements so far. Although both sets result in identical ∆α(t) dependences, they predict quite different time dependences for NS (t) and NR (t) as shown in Fig. 6. In this figure and in the following discussion all quantities referring to the second parameter set are indicated by a prime. For the first parameter set the light-induced dissociation rate is much larger than the light-induced termination rate for radicals (k S kR ). Since every DMPA molecule decays into two radicals, the maximum molar radical concentration reaches nearly twice the value of the initial DMPA concentration. For the second parameter set we have the reverse case kR kS : the photoinitiator decays slowly while the light-induced termination of radicals is fast. Therefore the radical concentration always remains smaller than for


with κ = 2kS /(kS − kR ). For the absorption changes we finally derive   ∆α(t) = NS0 ( f S − κ f R ) e−kS IP t + κ f R e−kR IP t − f S . (11) It can easily be seen that this equation can be rewritten in the form of our empirical (3) and (5). Without any further assumptions it fulfills the conditions that the amplitudes of the exponential functions are proportional to N S0 while the inverse time constants are proportional to I P . With (11) the condition ∆α(0) > 0 is equivalent to f R > ˙ f S /2. This, however, does not remove the ambiguity that for each set of parameters ( f S , fR , kS , kR ) there exists a second


Table 2. Proportionality constants fS(R) for the contribution of the photoinitiator (radicals) to the absorption coefficient (8) and rate constants kS(R) of the light-induced dissociation (termination) rate for the photoinitiator (radical) molecules ((6) and (9)) Parameter

First set Second set

fS fR kS kR 10−4 m2 mol−1 10−4 m2 mol−1 10−4 m2 J−1 10−4 m2 J−1 5.5 5.5

7.0 234

7.8 0.14

0.14 7.8

b Fig. 6a,b. Photoinitiator NS , NS and radical NR , NR concentration versus irradiation Q = IP t. Calculated according to (7) and (10) by using a the first and b the second parameter set of Table 2


the first case. From (10) and (12) we find that the ratio NR (t)/NR (t) = kS /kR is constant. Using the values in Table 2 this constant is 56. In conclusion, we found strong experimental evidence that the dynamics of light-induced reactions in DMPA-doped PMMA is not only determined by the dissociation of DMPA molecules. The time dependence of the absorption coefficient for UV light under illumination with UV light indicates that the products of the DMPA dissociation also undergo lightinduced reactions. The results can be explained by assuming a light-induced termination reaction for free radicals. The model permits two different parameter sets for the time dependence of the radical concentration, which cannot be distinguished from each other by our measurements up to now.

Time-resolved absorption spectroscopy and/or spectroscopy with thermally induced radicals in PMMA could give a more detailed understanding of the nature of these additional lightinduced reactions.

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