Kinetics of Photochromic Conversion at the Solid State: Quantum Yield

ARTICLE pubs.acs.org/JPCA

Kinetics of Photochromic Conversion at the Solid State: Quantum Yield of Dithienylethene-Based Films Giorgio Pariani,*,†,‡ Andrea Bianco,‡ Rossella Castagna,†,§ and Chiara Bertarelli†,§ †

Dipartimento di Chimica, Materiali e Ingegneria Chimica “G. Natta”, Politecnico di Milano, piazza L. da Vinci 32, 20133 Milano, Italy Istituto Nazionale di Astrofisica - Osservatorio Astronomico di Brera, via E. Bianchi 46, 23807 Merate, Italy § Center for Nano Science and Technology @PoliMi, Istituto Italiano di Tecnologia, via G. Pascoli 70/3, 20133 Milano, Italy ‡

ABSTRACT: Quantum yield is one of the most important properties of photochromic systems. Unfortunately, a lack of data at the solid state exists, because measurements are intrinsically not straightforward. A kinetic model describing the conversion of the photoactive species is reported and both analytic and numeric solutions are provided according to relevant cases. The model is then applied to measure the quantum yield of dithienylethene-based polymers; the ring-opening quantum yield is measured for different laser beam profiles (i.e., Gaussian and uniform) and at different wavelengths, showing an increased value with increasing photon energy.

’ INTRODUCTION The possibility to reversibly light-trigger the physical and chemical properties of photochromic materials has attracted interest from the scientific community.1,2 The color change of such systems is the eye-sighted consequence of a molecular isomerization, which can also be accompanied by non-negligible modifications of polarizability, dipole moment and refractive index,37 red-ox potential,810 conductivity,11,12 luminescence,1,1315 wettability,16 solubility,17 etc. These switching properties can be exploited in new concept devices on condition that the photochromic molecules can be processed into suitable solid state materials. Incidentally, photochromic properties can be strongly affected by the aggregation state18 and preserving or even increasing19 the photochromic response is highly desirable. Photoreaction quantum yield, which is strictly related to the efficiency of the photoisomerization, is certainly one of the most important parameters used to characterize photochromic systems. Its determination in liquid solutions is a common task for photochromic molecules, and it is usually performed with classical methods, i.e., actinometry20 or pumpprobe techniques.21,22 Generally, the quantum yield of photochromic systems at the solid state has not been so far reported, except for some diarylethene single crystals.23 The main reason is that the model describing the photoconversion at the solid state represents a more complex analytical problem than in solution, because the photochromic conversion is not uniform across the film thickness, and the conversion rate depends on the local light intensity. Moreover, the experimental procedure is trickier than in solution, being dependent on the spatial distribution of the light intensity. It follows that the development of reliable methods to determine the quantum yield of photochromic systems at the solid state is a step forward in understanding the behavior of photochromic materials and gives the opportunity to test the r 2011 American Chemical Society

light-switching layers for real applications. We faced this problem starting from an AB(1ϕ) study case, e.g., thermally irreversible bistable systems,24 in which only one photoreaction is enabled at selected exposure wavelengths. Nevertheless, the numerical model is suited to thermally reversible systems or multiple reactions.

’ KINETIC MODEL A lot of attempts have been made in the past to give a mathematical description of the kinetics of photochromic systems, both in solution2426 and at the solid state.2732 In solution a good agreement between experimental and predicted data33,34 has been achieved, thus enabling, for example, diarylethenes to be employed as chemical actinometers; however, intrinsic practical problems have not allowed us to provide good results at the solid state. The first physical description of a bistable system (AB system) with a first-order kinetics was performed by Tomlinson27,28 about forty years ago. Unfortunately, the model can be analytically solved only in two particular cases, as will be discussed later on. An extended model was proposed by Rupp et al.,32 who determined the analytical solution for samples with a small residual absorbance at the saturation limit. Moreover, the relevant role of the shape of the light beam was pointed out by Caron et al.31,35 while performing irradiations at the solid state, because it apparently affects the photoconversion kinetics. The authors stated the importance of the light beam intensity distribution on the transmitted power, which has to be treated as an integral over the irradiated area. In particular, for thermally irreversible bistable systems, they extended the study to a relevant case, i.e., to Gaussian beams, which represent the most Received: July 28, 2011 Revised: September 19, 2011 Published: September 22, 2011 12184

dx.doi.org/10.1021/jp207210p | J. Phys. Chem. A 2011, 115, 12184–12193

The Journal of Physical Chemistry A

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Scheme 1. Progression of the Light-Triggered Conversion across the Film Thicknessa

The photon flux at z position is the integral of the transmittance of the sample from the irradiated surface (z = 0) up to z: Iðz, tÞ ¼ I0 3 exp½

Z z 0

Aðz0 , tÞ dz0

ð6Þ

where A is the absorbance:36 Aðz0 , tÞ ¼ εA xA ðz0 , tÞC þ εB ½1 xA ðz0 , tÞC þ α

a

Notation Refers to the Ref 27.

common intensity distribution of laser beams. For AB(1ϕ) systems, all the above approaches provide the same result in the case of fading processes with no residual absorption and, in the approximation of a Gaussian intensity distribution, the exact equation of the transmittance can be easily integrated over the irradiated area to give the transmitted power as function of time. Starting from Tomlinson's work,27 we will give the reader the tools to apply the kinetics model to cases of photoconversion in film. The model that describes the uniform illumination of a photochromic film can be conveniently represented as the progression of the conversion profile through the thickness of the film, as sketched in Scheme 1. The fraction of molecules in each state varies along the z axis and with time t and can be defined as follows: xA ðz, tÞ ¼ NA ðz, tÞ=N

ð1Þ

xB ðz, tÞ ¼ NB ðz, tÞ=N

ð2Þ

We assume an uniform distribution of the chromophores in the film, with concentration C (molecules/m3), and at t = 0 all the molecules along the z axes are in state A, namely xA(z,0) = 1. The absorption of the polymer matrix is contained in the parameter α (1/m). The solution of the mathematical problem is complex and the explicit derivation can be performed only in two particular cases of interest: (i) in the region where one form is completely transparent (i.e., its absorption coefficient is zero), and (ii) where the absorption coefficient is constant, i.e., at the isosbestic point (if it possibly exist in the photochromic system). Regarding diarylethenes, the first case consists in the fading process, which follows the same equations, starting from xB(z,0) = 1, where state B is converted back to the colorless state A by means of visible light. The second case represents the coloration process induced by UV light, in which both forms absorb light with the same probability during the conversion process; usually, for diarylethenes, the isosbestic point occurs in the UV region. Case i: Fading Process. The fading process occurs when the colored B form is converted back to the colorless A form usually by means of visible light, and anytime the absorption coefficient of the A form is zero: εA = 0. If the chromophores are embedded in a not-absorbing matrix (α = 0) and only reflection losses are present, the photon flux along the film thickness becomes Iðz, tÞ ¼ I0 3 exp½

where NA and NB are the number of molecules in the colorless and colored forms, respectively, and xA þ xB ¼ 1

ð3Þ

It is worthwhile defining εA(λ) (m2/molecule) as the absorption cross section of species A and σA(λ) (m2/molecule) as the interaction cross section for molecules in state A to absorb a photon and promote the transition to state B. The ratio between the interaction cross section and the absorption cross section gives the well-known quantum yield of the photoreaction, which is the probability of the transition from A to B: ΦAfB ðλÞ ¼ σ A ðλÞ=εA ðλÞ

ð4Þ

Likewise, εB(λ), σB(λ), and ΦBfA(λ) are defined for the backward reaction. All these parameters are functions of the wavelength. The photon flux I = I(z,t) (photons/m2s) is assumed as uniform and equals to I(0,t) = I0 at the sample surface and it is constant for t > 0. In an arbitrary position along the z axis, the rate of conversion of the A form at a fixed wavelength λ is, in the case of a first-order kinetic rate, proportional to the population of A molecules: dxA ðz, tÞ ¼ Iðz, tÞ 3 εA ΦA f B 3 xA ðz, tÞ dt

ð7Þ

Z z 0

εB xB ðz0 , tÞC dz0

ð8Þ

The fraction of the B form can be analytically derived,27 as follows: xB ðz, tÞ ¼

1 1 þ

eεB Cz

kt 3 ðe 1Þ

ð9Þ

where k = I0 3 εBΦBfA is the conversion rate. From the previous equation and eq 7, integrating between 0 and the whole thickness D, the time dependent absorbance results in AðtÞ ¼ ln½1 þ ðeεB CD 1Þ 3 ekt

ð10Þ

Figure 1 shows the xB profile during the light exposure: the conversion profile maintains the same shape during time, moving toward the back side of the film. This means that, except for a short initial transient, the conversion depth moves with constant speed along the film thickness, and the absorbance of the film, starting from A0 = A(0) = εBCD, decreases almost linearly with time. The description of the fading process is quite simple: the longer the exposure time, the larger the conversion depth. When time approaches zero, eq 10 can be approximated as a linear function of time, where the slope is the conversion rate:

ð5Þ

Aðt f 0Þ ≈ A0 kt 12185

ð11Þ

dx.doi.org/10.1021/jp207210p |J. Phys. Chem. A 2011, 115, 12184–12193


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Figure 1. Fading irradiation conditions. Top: conversion profiles along the film thickness for different exposure times. Bottom left: film transmittance at exposure wavelength. Bottom right: normalized absorbance of the film at exposure wavelength.

Therefore, also the film transmittance is constant during irradiation. Equation 5 then becomes

The transmittance can be easily derived from eq 10: TðtÞ ¼

1 1 þ ðeεB CD 1Þ 3 ekt 1 1 1 3 ekt T0

¼ 1 þ

dxA ðz, tÞ ¼ I0 3 exp½ðεC þ αÞz 3 εΦA f B 3 xA ðz, tÞ dt

which can be easily solved by separation of variables:

where T0 = eεBCD. The analysis of the transmittance function can be useful to fit experimental data (see Results and Discussion) when a specimen is illuminated with a uniform light beam. By studying the first and second derivative of eq 12, we find that T(t) is symmetric with respect to the inflection point F (Figure 1), where kt = ln((1/T0) 1), T = 1/2 and dT/dt = k/4. Moreover, the function preserves the same shape by increasing initial transmittance, shifting backward on the time axes. The symmetry of the transmittance function is the self-evident marker of uniform illumination and gives the first indication on the actual experimental conditions. Case ii: Isosbestic Point. The cyclization process from the A to the B form of diarylethenes is usually induced by UV light (250400 nm); in this spectral region both forms absorb light. Here we state the hypothesis that the light absorbed by the A form induces the photoreaction, whereas the light absorbed by the B form promotes the molecule into excited states, which decay following photophysical processes; i.e., the backward reaction from B to A does not take place. At the isosbestic point, εA = εB = ε and the photon flux through the thickness becomes independent of time: Iðz, tÞ ¼ IðzÞ ¼ I0 3 exp½

Z z 0

ð14Þ

ð12Þ

ðεC þ αÞ dz0

¼ I0 3 exp½ðεC þ αÞz

ð13Þ

dxA ðz, tÞ ¼ f ðzÞ dt xA ðz, tÞ

ð15Þ

The fraction of the A form results: xA ðz, tÞ ¼ exp½eðεC þ αÞz 3 kt

ð16Þ

where k = I0εΦAfB. Figure 2 shows the xA profile during the light exposure: in this case, because the B form absorbs the light beam too, the conversion depth grows with a logarithmic law in time. Therefore, the complete conversion can be achieved only for infinite exposure times. Depending on the film thickness and on the content of the chromophore into the film, a finite conversion depth exists: if the absorbance is larger than 3, the inner region of the film remains in the A form, also when both sides of the substrate are irradiated. The knowledge of this limit is of crucial importance for practical applications. Obviously, the conversion cannot be followed at the irradiation wavelength, because the transmittance of the film is constant during the exposure. The best monitoring wavelength corresponds to the absorption maximum of the B form in the visible region. Other Cases: A Numerical Approach. When the system differs from the two particular cases above-discussed, no analytic solution exists. Such a case mainly regards the coloration reaction, which is triggered by photons with a wavelength that hardly ever corresponds to the isosobestic point. For this reason, a numerical model based on the finite difference method has been 12186



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Figure 2. Irradiation at the isosbestic point. Top: conversion profiles along the film thickness for different exposure times. Bottom left: film transmittance at monitoring wavelength. Bottom right: normalized absorbance of the film at exposure wavelength; conversion of the A form (dashed line) and B form (solid line).

An iterative procedure can start when the intensity distribution on the film surface I(0,j) and the initial fraction of each species xξ(i,0) are known, where

Scheme 2. Numerical Calculation Procedure

∑ξ xξði, jÞ ¼ 1

developed to analyze the photon induced conversion in all spectral ranges. If the space and time vectors are created, eqs 57 will be numerically solved. Fixed a position index i inside the film thickness, the fraction of the specie ξ as function of the time index j becomes xξ ði, j þ 1Þ ¼ xξ ði, jÞ 3 ½1 þ kξ Δt

ð17Þ

where kξ is the kinetic constant, which is negative when the species is consumed and positive when produced: kξ ¼ kΔ kξ ¼ Iði, jÞεξ Φξ f ξ0

for thermal reactions for photochromic reactions

ð18Þ

The photons reaching the position i + 1 can be estimated using the LambertBeer law, where the total absorbance is the sum of the partial absorbances over the species ξ: Iði þ 1, jÞ ¼ Iði, jÞ 3 exp½ Aξ ði, jÞ ¼ εξ xξ ði, jÞCΔz

∑ξ Aξ ði, jÞ

ð19Þ ð20Þ

ð21Þ

Equation 17 is applied on the film surface, where i = 0 and I(i,j) = I(0,j), and vectors xξ(0,j) are calculated. Then, moving through the film to i = 1, and applying eq 19eq 20, I(1,j) is obtained. Equation 17 is then used to calculate xξ(1,j) with the light intensity reaching the position i = 1 inside the film I(1,j), and the procedure continues until covering the overall thickness of the sample D, as sketched in Scheme 2. Actually, we applied this approach to AB(1ϕ) systems, where the chromophore is embedded in a polymer matrix with non-null absorbance. The 1D model with the light intensity function of thickness and time has been extended to 2D and 3D with I = I(x, y,z,t), to study complex illumination conditions. The model has been applied to planar and Gaussian light distributions to verify the goodness of the sampling, by comparing our results with those published in ref 31.

’ MATERIALS In diarylethene derivatives, the photoreaction consists of a conrotatory 4n + 2 electrocyclization toward a more conjugated species, which can be converted back by suitable illumination, as sketched in Figure 3. Photons in the ultraviolet region usually induce the photoreaction between the colorless A form and the colored B form (A f B), whereas photons in the visible region cause the backward reaction (B f A). The two isomers are usually thermally stable, so the backward reaction is light triggered at room temperature.1 Diarylethenes are often representative of AB(1ϕ) systems in all the UVvis spectral range, although in some cases it can occur 12187



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Figure 3. (a) Open (1A) and closed (1B) forms of dithienylethenes. (b) UVvis absorption spectra of molecule 1 with R1 = CH3, R2 = H, R3 = p-methoxyphenyl, and R4 = p-cyanophenyl in hexane in the open and closed forms at different illumination times (λexc = 290 nm).

that a partial superposition of the actinic bands of A and B forms in the UV region takes place and the excited B* state decays into the A form following photochemical paths. Accordingly, both the forward and backward reactions are simultaneously driven, and a photochemical equilibrium between A and B forms is accomplished at the photostationary (PS) state: the diarylethene derivative behaves like an AB(2ϕ) system. The measurement of the conversion at the PS state, as reported in literature,37,38 allows us to discriminate between the two cases. Although a partial conversion at the PS state has been observed in benzothiopheneperfluorocyclopentene derivatives,39 an almost complete conversion is obtained in 550 substituted dithienylethenes38 (i.e., phenyl-substituted dithienylethenes37,40), making them representative of AB(1ϕ) systems in the ultraviolet region. In the visible region, where the backward reaction takes place, the A form of diarylethenes is usually completely transparent, and only the B f A photoreaction is active at each wavelength. It means that the system belongs to the AB(1ϕ) class, and a fading process occurs under illumination. In the work herein discussed only AB(1ϕ) systems are considered and experimental measurements have been carried out using a diarylethene derivative that meets this condition. In the past, both theoretical and experimental studies have been performed on diarylethene based systems to investigate the reaction mechanism and hence the difference between the forward and backward processes.21,22,41 The absorption of a photon promotes the transition of a molecule from the ground to the excited state; in photochromic systems the interconversion is enabled due to the presence of a conical intersection (CI) between the excited states of the two forms, without involving triplet states. Calculations on hexatrienecyclohexadiene (HTCHD) based systems41 showed that (i) the ring-closure reaction is very efficient, as any energy barrier has to be overcome, thus resulting in a fast decay to the ground state of CHD, and (ii) the ring-opening reaction is limited by the presence of a potential energy barrier in the excited state, and hence it is temperature dependent. In diarylethenes, this behavior is confirmed by quantum yield data.18,23,37,42,43 Cyclization quantum yield can approach unity, according to the relative population of antiparallel conformers, and it is almost thermally independent. At opposite, cycloreversion quantum yield is usually smaller, and increases with increasing temperature.18 It has also been shown that the cycloreversion quantum yield strongly lowers while the conjugation of the B form of the molecule increases,37,42 and it is affected by the nature of the substituents in the 220 position of the thiophene rings.39,44 Furthermore, time-resolved absorption

spectroscopy determined that, for one-photon transitions, both cyclization and cycloreversion reactions usually take place in a few picoseconds.21,22 At the solid state, Nakamura et al.45 reported the dependency of both cyclization and cycloreversion quantum yield of a fluorescent diarylethene embedded in polymer matrices on their glass transition temperatures. Indeed, the quantum yield of the photoreaction is affected by the presence of multiple minima in the potential energies both of the ground and of the excited states, which causes the absorption of more than one photon before the photoreaction takes place. This phenomenon occurs in high Tg polymers (PMMA, having a Tg of 105 °C, Zeonex, with a Tg of about 130 °C, and a modified Arton-amorphous polyolefin, having an extremely high Tg of 300 °C) and not in low Tg matrices, such as poly(n-buthylmethacrylate) with a Tg of 21 °C, where the photoreactions follow the classical kinetics.45 The developed model has been herein applied to photochromic solid samples to determine the quantum yield values at the solid state. Among the possible choices, we selected polymer films and, specifically, a polyurethane with diarylethene units in the main chain.46,47 The motivations of this choice are related to (i) the very high content of photochromic units that can be introduced in the backbone, thus resulting in an intense photochromic response, (ii) the good optical quality of the polymer films, which are obtained directly by an in situ polymerization, and (iii) the low Tg of the polymer (about 25 °C).47

’ RESULTS AND DISCUSSION The full description of the photochromic film can be performed knowing (i) the concentration of the active unit C (molecules/m3), (ii) the film thickness D, (iii) the absorption coefficients ε(λ) (m2/molecule) of the two forms, and (iv) the quantum yields of the possible photoreactions at the exposure wavelength Φ(λ). These parameters are determined as follows: (i) The concentration C in molecules/m3 can be determined by C¼

w% FNA Mph

where w% is the weight amount of active units on all components, F (g/m3) is the density of the photochromic polymer film, NA is Avogadro’s number, and Mph is the molar mass of the photochromic unit (g/mol), namely the dye in dyepolymer dispersions, where the matrix density is not strongly affected by the addiction of the small 12188


The Journal of Physical Chemistry A Scheme 3. Uniform Illumination Exposure: Experimental Setup

amount of chromophores (usually less than 68% to avoid aggregations). When the photochromic unit is polymerized with other components to give a backbone photochromic polymer, the identification of the active unit may be not straightforward. The molar mass of the photochromic monomer is used as a good approximation in the case herein considered of diarylethene-based photochromic polyurethanes, because the monomer is totally incorporated in the growing chain (the polymerization that affords polyurethanes is a step-growth reaction) and the conjugation of π electrons responsible for the coloration of the B form is confined all over the photochromic monomer unit. (ii) The film thickness can be measured by means of common techniques (spectral reflectance, profilometry, or ellipsometry) with errors less than 1%. (iii) The absorption coefficient can be evaluated by UVvis spectroscopy, in a way similar to that for the solutions, i.e., applying a linear fitting on the absorbance of films of different thicknesses: AðλÞ ¼ eðλÞ 3 D where e is expressed in 1/m and D is the film thickness (m). Then ε (m2/molecule) is εðλÞ ¼

eðλÞ C

For practical interests, multiplying ε (m2/molecule) by Avogadro’s number gives ε in m2/mol. The absorption coefficient of the photochromic specimens studied in this work in the two different forms is reported in Figure 6. (iv) Because diarylethenes belong to AB(1ϕ) systems, quantum yields are ΦAfB(λ) or ΦBfA(λ). Photoreaction quantum yield can be conveniently obtained as explained hereafter. The kinetic constants of the photoconversion will be monitored by following the transmittance change of photochromic films under illumination. In particular, different light distributions and consequently different test configurations will be described, giving an overview of the main advantages and disadvantages. Examples and a comparison between the techniques are shown later on. Uniform Illumination. An uniform illumination is achieved by using the configuration sketched in Scheme 3. The laser beam is expanded by means of a spatial filter or a simple diverging lens, to obtain a quasi-uniform beam on a suitable aperture. The sample is illuminated by the whole beam and a hole of known diameter is placed between the sample and the detector, to measure only the power transmitted by the central region of the sample. In this configuration most of the light power is not measured, and high intensities are

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required. It follows that a laser light source is preferred to the light coming out from a monochromator. If a reliable uniform illumination is obtained, a nice symmetric curve of the transmitted power is measured. Equation 12 gives the following expression, which allows us to better evaluate the transmitted power: 1 1 1 ¼ ln 1 kt ð22Þ ln TðtÞ T0 Accordingly, a straight line with slope k results from the plot of ln(1/T1) as a function of time. As an example, the experimental results obtained on photochromic polyurethane films are shown in Figure 4. Several exposures at 488 nm have been carried out at different light powers on films with 50% of photochromic units, and the power passing through a 600 μm diameter hole was monitored during exposure. Kinetic constants and quantum yield values obtained by fitting the function ln((1/T(t)) 1) are reported in Table 1. ΦBfA at 488 nm have been determined to be 1.5 ( 0.1% for εB = 575 m2/mol. Gaussian Illumination. The configuration set to expose the sample with a Gaussian intensity profile is shown Scheme 4. The sample is directly exposed to the laser beam, which usually has a Gaussian profile. The diameter of the beam is adjustable with a converging or diverging lens, not altering the power distribution of the beam. The beam diameter can be easily measured by means of a beam profiler or with the well-known knife-edge test.48 The experimental setup is simple and low light powers are required to obtain conversions in reasonable time. The curve of the transmitted power is no longer symmetrical, but a mathematical closed form exists, derived by Caron, 35 that allows us to obtain the quantum yield value free from the error of the absorption coefficient value. For a fading process in AB(1ϕ) systems, the transmitted power is expressed by eq 12, where the transmittance is a function of the distribution of light intensity on the sample surface:

Tðx, y, tÞ ¼ 1 þ

1 1 1 3 eIðx, yÞ 3 εB ΦB f A t T0

ð23Þ

and, if the intensity has an axial-symmetrical distribution along the z axis:

TðF, tÞ ¼ 1 þ

1 1 1 3 eIðFÞ 3 εB ΦB f A t T0

ð24Þ

where F is the distance from the z axis. For a Gaussian beam the light intensity I(F) is 2 F IðFÞ ¼ Ic 3 exp42 F0

!2 3 5

ð25Þ

The total power P(t) collected by the detector is the integral over the plane, perpendicular to the z axis, of the transmission function multiplied by the light intensity distribution PðtÞ ¼ 12189

Z ∞ 0

2πFTðF, tÞ IðFÞ dF

ð26Þ



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Figure 4. Data analysis for a photochromic film under uniform illumination at 532 nm; measured P0 = 7.4 μW. (a) Film transmittance: experimental and best fitting curve. (b) Film absorbance: ln(1/T 1) function and best fitting line.

Table 1. Quantum Yield Values for Photochromic Polyurethane Films Containing 50% of Diarylethene Units under Uniform Illumination Exposure at 488 nm sample

D (μm)

P0 (W/m2)

k (103 s1)

ΦBfA (%)

1

0.62

220

8.1

1.54

2

0.62

140

4.2

1.65

3 4

0.90 0.90

220 140

8.5 5.0

1.62 1.50

5

1.28

220

8.3

1.58

6

1.28

290

9.5

1.41

The integration is quite easy with a Gaussian intensity distribution (after a change of variables) and gives 1 1 kc t ln T 1 þ 1 e PðtÞ ¼ P0 3 1 þ 0 3 3 kc t 3 T0 ð27Þ where kc = Ic 3 εBΦBfA and P0 ¼

Z ∞ 0

2πFIðFÞ dF ¼

π Ic F 2 2 0

ð28Þ

is the total light power measured on the detector plane.35 For long time exposures, the transmitted power can be approximated as ln T0 PðtÞ ≈ P0 3 1 þ ð29Þ kc t thus, plotting P versus 1/t gives a straight line with slope m: ln T0 A π εB CD m ¼ P0 3 ¼ P0 3 ¼ F0 2 kc 2 εB ΦB f A kc

ð30Þ

Accordingly, it is possible to obtain the quantum yield ΦBfA free from the nominal light power P0 and from the absorption coefficient εB: π CD ΦB f A ¼ F0 2 ð1 RÞ 3 2 m

ð31Þ

Scheme 4. Gaussian Illumination Exposure: Experimental Setup

where the factor 1 R accounts for the reflections on the first surface of the sample. Figure 5a shows the transmittance curve and the best fitting curve for a photochromic polymer film containing 50% diarylethene units in the main chain, 1.3 μm thick, under Gaussian illumination at 488 nm (P0 = 1.38 ( 0.02 mW, F0 = 0.48 ( 0.01 mm, and R = 0.0438). In Figure 5b the light power is reported as a function of the inverse of time and, according to eq 29, follows a straight line for long time exposures. The measurements have been repeated for samples with different thicknesses. The resulting slope m and quantum yield values are reported in Table 2. The quantum yield of cycloreversion at 488 nm is ΦBfA = 1.5 ( 0.1%, in good agreement with the preceding obtained value. Wavelength Dependency of the Quantum Yield. Quantum yield values at 488 nm are in good agreement with the one published in refs 18 and 40 for similar molecules at 492 nm in hexane solution and in the crystalline phase. Exposures under Gaussian illumination have been carried out at different wavelengths in the visible region, and data at long exposure times have been analyzed by means of eq 29. Results are shown in Table 3. The lowering of the ring-opening quantum yield while increasing the wavelength of the exposure light has been already reported for diarylethene derivatives in solutions,33,34,49 but the results shown herein represent the first evidence that the same behavior is maintained at the solid state. Two explanations have been proposed for this dependency. The first one is related to the excess of vibrational energy in the excited state given by more energetic photons, which is necessary to induce the cycloreversion reaction, thus allowing more molecules to overcome the 12190



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Figure 5. Data analysis for a photochromic film (50% of diarylethene units, 1.28 μm thick) under Gaussian illumination. Measured P0 = 1.38 μW at 488 nm, F0 = 0.48 ( 0.01 mm. (a) Film transmittance: experimental and best fitting curve. (b) P as a function of 1/t; experimental and best fitting line.

Table 2. Quantum Yield Values for Photochromic Polyurethane Films with a Content of 50% of Diarylethene Units under Gaussian Illumination Exposure at 488 nm

Table 3. Quantum Yield Values for the Ring-Opening of Photochromic Polyurethane Films with 50% of Diarylethene Units

sample

D (μm)

m (mJ)

ΦBfA (%)

λ (nm)

ΦAfB(%)

1

0.62

3.4

1.46

456.9

3.4 ( 0.3

2

0.62

3.1

1.60

488.0

1.5 ( 0.2

3

0.90

4.6

1.57

514.0

1.2 ( 0.1

4

0.90

4.8

1.51

532.0

0.9 ( 0.1

5

0.90

4.5

1.60

632.8

0.5 ( 0.1

6

1.28

8.0

1.28

687.9

0.3 ( 0.1

7

1.28

6.7

1.53

8

1.28

6.1

1.68

energy barrier.49 The second mechanism is ascribed to the possible presence of two actinic bands in the visible region, with different quantum yield values.43 The existence of two different conformations is supported by the asymmetry of the absorption band in the visible region and confirmed by UVvis absorption spectroscopy at low temperatures.43 Accordingly, the superimposition of two or more actinic bands can explain the temperature dependency of the quantum yield. Nevertheless, the linear behavior shown in Figure 6 between ln(1/ΦAfB) and photon energies, which is typical of an energy activated reactions, may suggest the first mechanism.

’ CONCLUSIONS The kinetic model describing the photoconversion of thermally irreversible bistable systems, i.e., AB(1ϕ) systems, at the solid state has been herein highlighted, and reliable methods to determine the photoconversion quantum yield at the solid state have been presented, focusing the attention on the practical procedure. As a specific study case, the described techniques have been applied to dithienylethene-based backbone photochromic polyurethanes for the determination of the cycloreversion quantum yield, and consistent results have been obtained with different illumination intensity profiles. The ring-opening quantum yield of the photochromic polymer has been measured at different wavelengths in the visible

region (from 456.9 to 687.9) by means of a Gaussian intensity beam profile showing, for the first time at the solid state, an increased value with increasing photon energy.

’ EXPERIMENTAL SECTION The general procedure to synthesize the diarylethene-based photochromic polyurethane consists of the reaction between the 1,2-bis(5-(p-(hydroxymethyl)phenyl)-2-methyl-3-thienyl)hexafluorocyclopentene,50 polyols, and the 4,40 -diisocyanate dicyclohexylmethane (H12 MDI) in butyl acetate, as described in ref 47. The relative quantity between diarylethene units and other alcohols was 50 wt % on all components. The solution batch was filtered (0.20 μm PTFE) and spin coated (LAURELL WS-400 B-6NPP Lite) on borosilicate glass substrates (Borofloat-Schott AG), 1.10 mm thick. Polymerization was carried out at 130 °C for 8 h. Film thickness was measured with the spectral refractometer F20-EXR by Filmetrics Inc. (spectral range 3801700 mm). Films with thicknesses ranging from 0.60 to 1.50 μm were obtained. UVvis absorption spectra were recorded with a JASCO V-570 spectrophotometer. Different laser sources were used to shine samples at different wavelengths. Lines at 456.9, 488, and 514 nm were generated by a 5490A air cooled ion argon laser from Ion Laser Technology Inc. (maximum power 200 mW, beam diameter 0.65 mm, linearly polarized); the different lines were separated with a low angle diffraction grating (600 lines/ mm). Emission at 532 was stimulated by a Torus single frequency 12191



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Figure 6. On the left: molar absorption coefficient of photochromic films in the open form (gray line) and at the photostationary state (blue line); dots represents the values obtained from the kinetic measurements, calculated from film transmittances at t = 0. On the right: ring-opening quantum yield of photochromic films (50% content of diarylethene units) as function of the photon energy.

CW DPSS laser from Laser Quantum Ltd. (maximum power 400 mW, beam diameter 1.7 mm, linearly polarized), at 632.8 nm by a OEM06XR HeNe laser from Aerotech Inc. (1 mW, linearly polarized), and at 687.9 nm by a Toshiba TOLD 9140 laser diode (20 mW). Power measurements were carried out with calibrated silicon photodiodes: Ophir Optronics Ltd. PD300-UV (aperture 10 10 mm, spectral range 2001100 nm, resolution 0.001 nW in the range 20 pW to 3 mW, 100 nW in the range 2 μW to 300 mW); Newport Co. 918D-UV-OD3 (active area 1 cm2, spectral range 2001100 nm, NEP 0.45 pW/(Hz)1/2).

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT This work was partly funded by the UE through Opticon (Optical Infrared Coordination Network for Astronomy) Project-FP7 Framework and by Regione Lombardia through the MITO - Materiali Innovativi per oTtiche Olografiche project. ’ REFERENCES (1) Irie, M. Chem. Rev. 2000, 100, 1685–1716. (2) Ercole, F.; Davis, T. P.; Evans, R. A. Polym. Chem. 2010, 1, 37. (3) Biteau, J.; Chaput, F.; Lahlil, K.; Boilot, J. P.; Tsivgoulis, G. M.; Lehn, J. M.; Darracq, B.; Marois, C.; Levy, Y. Chem. Mater. 1998, 10, 1945–1950. (4) Bertarelli, C.; Bianco, A.; D’Amore, F.; Gallazzi, M. C.; Zerbi, G. Adv. Funct. Mater. 2004, 14, 357–363. (5) Pu, S.; Yang, T.; Yao, B.; Wang, Y.; Lei, M.; Xu, J. Mater. Lett. 2007, 61, 855–859. (6) Chen, L.; Yao, B.; Han, J.; Gao, P.; Chen, Y.; Wang, Y.; Lei, M. Opt. Commun. 2009, 282, 568–573. (7) Bertarelli, C.; Bianco, A.; Castagna, R.; Pariani, G. J. Photochem. Photobiol. C 2011, 12, 106–125. (8) Kawai, S. H.; Gilat, S. L.; Ponsinet, R.; Lehn, J. M. Chem.—Eur. J. 1995, 1, 285–293. (9) Peters, A.; Branda, N. R. Chem. Commun. 2003, 954–955. (10) Gorodetsky, B.; Branda, N. R. Adv. Funct. Mater. 2007, 17, 786–796. (11) van der Molen, S. J.; Liao, J.; Kudernac, T.; Agustsson, J. S.; Bernard, L.; Calame, M.; van Wees, B. J.; Feringa, B. L.; Sch€onenberger, C. Nano Lett. 2009, 9, 76–80.

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Kinetics of Photochromic Conversion at the Solid State: Quantum Yield

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