High-Modulation-Depth Surface Relief Gratings Using s–s Polarization

Article pubs.acs.org/JPCC

High-Modulation-Depth Surface Relief Gratings Using s−s Polarization Configuration in Supramolecular Polymer−Azobenzene Complexes A. Sobolewska,*,† S. Bartkiewicz,† and A. Priimagi‡,# †

Institute of Physical and Theoretical Chemistry, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50−370 Wroclaw, Poland ‡ Department of Applied Physics, Aalto University, P.O. Box 13500, 00076 Aalto, Finland ABSTRACT: The formation of the surface relief gratings (SRG) in azo-polymers strongly depends on the polarization configuration of the writing beams. So far the s−s polarization configuration has been considered as ineffective in terms of SRG formation. Here, we report that very high-amplitude SRGs can be recorded when using the s−s inscription geometry in supramolecular polymer−azobenzene complexes and that the efficiency of the process strongly depends on the molecular weight of the polymer. Furthermore, a single holographic irradiation leads to the formation of the surface relief grating (primary grating) and, unexpectedly, to the formation of the secondary fine-structure grating with a considerable modulation depth in the direction perpendicular to the primary grating. The detailed analysis of holographic recording has been performed on the basis of the proposed phenomenological model. A new aspect of the phenomenon of the SRG formation has been indicated by demonstrating that the SRG can be inscribed for the s−s polarization configuration. Since the SRG formation is considered as an important new tool in micro/ nanofabrication technologies, both the formation of the SRG for s−s geometry and the formation of the fine-structure grating open new possibilities in photonic applications.

1. INTRODUCTION Azobenzene-containing polymers are a class of holographic materials extensively investigated in the past decade due to potential applications in optical information storage and processing, polarization holography, and photonics.1−6 Holographic recording in these types of materials is inseparably connected with the phenomenon of the photoinduced mass transport and the formation of surface relief gratings (SRGs).7,8 The creation of large-amplitude SRGs in azo-materials has become essential because of the very high diffraction efficiency easily obtained using a one-step inscription process, and the possibility to erase and reconfigure the gratings at will. Therefore, independently from the studies on holographic recording, the SRG formation itself has attained a lot of attention as an important new tool in photonics and micro/ nanofabrication technologies.9−14 Several models have been suggested as possible mechanisms for the SRG formation, trying to explain the origin of the driving force responsible for the mass transport.15−21 Despite such theoretical efforts, none of them delivers a suitable explanation for all experimental observations. The fundamental nature of the driving force remains still unsolved, which however does not prevent the development of possible applications of the SRGs in, e.g., photonics and nanostructuring. Among many different aspects of the SRG formation in amorphous azo-materials, one thing that seems to be established is the strong dependence of the inscription efficiency on the polarization of the writing beams.22−29 © 2014 American Chemical Society

Many literature reports have shown that the SRG formation is efficient when applying the polarization geometries p−p, +45°/−45°, or RCP-LCP (right-/left-circular polarization), whereas gratings with small or nonexisting amplitude are produced when using the combinations s−s, +45°/+45° (−45°/−45°), or RCP-RCP (LCP-LCP). The influence of the polarization on the efficiency of SRG formation has been reasonably explained by the Tripathy/Kumar group who proposed a model based on electric-field gradient.16,22,23,30 According to this model, the presence of the electric-field gradient along the grating vector is necessary and responsible for the large-scale migration of the polymer chains ensuring the formation of high-amplitude SRGs. Therefore, for polarization configurations for which there is no electric-field gradient along the grating vector, only a weak SRG can be formed, or no grating will be formed at all. In the present paper, we want to refocus our attention to the SRG formation in the s−s geometry, generally considered as ineffective as explained above. We recently observed that the SRG inscription using s-polarized interference irradiation is sensitive to the length of polymer main chains: by shortening the chains via ultrasonic treatment, the SRG formation efficiency increased significantly.31 Although our study highlighted the dependence of the SRG formation on the length of Received: July 25, 2014 Revised: September 3, 2014 Published: September 12, 2014 23279

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were of high quality, amorphous, and their thickness was ca. 2 μm. 2.2. Holographic Technique. Holographic recording and thereby the inscription of SRGs was performed with a standard degenerate two-wave mixing (DTWM) technique.29,40 The experimental setup for DTWM is shown in Figure 2. Two

the polymer chains, ultrasonication provides no control over the molecular-weight distribution, and the overall massmigration efficiency of the polymer used was rather low. To address these deficiencies, we utilize a supramolecular approach and attach the azobenzene units to the polymer backbone via hydrogen bonding. The strength of such polymer−azobenzene complexes lies in their modular tunability:32 length of the polymer backbone as well as the concentration and chemical composition of the azobenzene units can be separately optimized for a specific purpose without laborious synthesis work. Since the first reports in 2007,33,34 several supramolecular polymeric complexes have been shown to exhibit efficient SRG formation.35−38 Herein, we show that hydrogen-bonded polymer-azobenzene complexes between 4-hydroxy-4′-dimethylaminoazobenzene (OH-DMA) and poly(4-vinylpyridine) (P4VP) (see Figure 1

Figure 2. Experimental setup of degenerate two-wave mixing: L, lasers; BS, beam splitter; M, mirrors; PF, polymer film; D, detector; C, computer (marked the polarization state of the beams, s−s polarization configuration).

Figure 1. Chemical structure of the hydrogen-bonded P4VP(OHDMA) complex.

for the chemical structures) yield gratings with modulation depth as high as 600 nm even when using s−s inscription geometry, given that the molecular weight of P4VP is sufficiently low. The SRG formation is analyzed by taking into account that upon holographic interference irradiation, not only the SRG but also two other gratings, driven by the geometrical and the orientational changes of the azobenzene groups and the motions of the polymer main chains, are simultaneously formed.29,39 Therefore, we report not only the efficient SRG formation in the s−s geometry but also study in detail holographic recording in supramolecular polymer− azobenzene complexes, which may result in a better understanding of the phenomenon of the SRG formation.

linearly s-polarized beams from an Ar+ ion laser (476.5 nm, Innova 90, Coherent) were used for the grating recording. The intensity of the recording beams was 140 mW/cm2 and the crossing angle θ = 4.6°, resulting in a grating period Λ = 6 μm. The recording time was fixed to ca. 70 min for all the samples. The grating inscription was monitored with a low-power spolarized probe beam from a He−Ne laser (633 nm). The power of the probing light diffracted into first-order was measured as a function of time and was used for the determination of the dynamics of the diffraction efficiency [η(t)]. The topography of the polymer surface and estimation of the amplitude of the SRGs were determined after holographic recording with an atomic force microscope (AFM, Dimension V Scanning Probe Microscopy, Veeco) working in tapping mode.

2. EXPERIMENTAL SECTION 2.1. Materials and Sample Preparation. The polymer− azobenzene complexes were prepared by complexing 4hydroxy-4′-dimethylaminoazobenzene (OH-DMA; 241 g/ mol; TCI Europe) and poly(4-vinylpyridine) (P4VP; Polymer Source) through phenol-pyridine hydrogen bonding as shown in Figure 1. Five different molecular weights (Mw) of P4VP were used: 1000, 3200, 7000, 19 000, and 50 000 g/mol. Given that the molar mass of the vinylpyridine repeat unit is 105 g/ mol, the range of polymer chain lengths extends from ca. 10 to ca. 500 repeat units. All compounds were used as received without further purification. P4VP and OH-DMA were separately dissolved in dimethylformamide at concentrations of 15 wt % (P4VP) and 6 wt % (OH-DMA). The solutions were stirred for at least 4 h, filtered through 200 nm syringe filters, and mixed in a proportion P4VP:OH-DMA 1:0.33. The resulting complexes are denoted as P4VPx(OH-DMA)0.33, indicating that every third polymer repeat unit carries an azobenzene unit. x refers to the molecular weight of the polymer. Thin-film samples were prepared by drop casting the complex solutions onto clean microscope slides (washed by successive sonication in acetone, isopropanol, and deionized water), allowing majority of the solvent to evaporate, and subsequently drying at 80 °C overnight. The resulting films

3. THEORETICAL APPROACH Holographic light irradiation onto an azopolymer thin film induces a spatially modulated optical anisotropy into the bulk of the material, i.e., changes the refractive index (Δn) and the absorption coefficient (Δκ) with the periodicity determined by the light interference pattern. These changes are accompanied by a periodic surface corrugation (Δd) at the free surface of the film, known as the surface relief grating. By measuring the power of light diffracting from the grating into the first order, temporal evolution of the grating build-up process can be monitored. Diffraction efficiency, defined as the ratio between the power of the first-order diffracted beam to the power of the incident beam, is a sum of the light diffracted by the refractive index and the absorption gratings: η(t ) = ηΔn(t ) + ηΔκ (t )

(1)

In the case of thin sinusoidal gratings, the diffraction efficiency of the phase grating [ηΔn(t)] is described by the square of the first-order Bessel function J1, whereas for the 23280

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subsequent reorientation, and is formed with the recording time constant τA. As the azobenzene molecules are attached to the polymer main chains, in the present case via hydrogen bonding, their rearrangement affects the spatial reorganization of the polymer main chains, which is the origin of the gratings ΔΦC(t) and ΔΦD(t). The former is a result of the polymer mass flow in the bulk of the material, while the latter corresponds to the polymer mass flow expressed as the surface corrugation. The bulk diffusion grating, or density grating,41,42 and surface relief grating are formed with the recording time constants τB and τC, respectively. These three gratings are strongly interrelated and affect one another.29,31,39 The amplitude grating (ΔΦY(t)) can be described by two consecutive processes driven by the photoisomerization and subsequent thermal relaxation:

absorption grating [ηΔκ(t)] it can be expressed by the square of a sinusoidal function: η(t ) = J12 [ΔΦ(t )] + sin 2[ΔΦY (t )]

(2)

where ΔΦ(t) and ΔΦY(t) are arguments of the phase and amplitude gratings, respectively.29,31,39 The phase grating (ΔΦ(t)), formed in azobenzene-based materials, results from the formation of three coupled gratings which can be described as a complex reaction consisting of three consecutive processes: kA

kB

kC

(3)

A→B→C→D

Proper description of the formation of ΔΦ(t) should also include the mutual phase shifts between the gratings; therefore, the vectorial grating approach is applied:29,31,39 ΔΦ(t ) = ⎡⎣ΔΦB 2(t ) + ΔΦC 2(t ) + ΔΦD2(t )

kX

+ 2ΔΦB(t )ΔΦC(t )cos ϕBC + 2ΔΦC(t )ΔΦD(t ) cos ϕCD + 2ΔΦB(t )ΔΦD(t )cos ϕBD⎤⎦

1/2

(4)

ΔΦY (t ) = ΦY

kA (e−kAt − e−kBt ) kB − kA

⎡ ⎧ kA ΔΦD(t ) = ΦD⎢1 − ⎨kA e−kAt + (e−kAt − e−kBt ) ⎢⎣ kB − kA ⎩ kA ·kB + (e−kAt − e−kCt ) (kB − kA )(k C − kA ) ⎫⎤ kAkB − (e−kBt − e−kCt )⎬⎥ (kB − kA )(k C − kB) ⎭⎥⎦ (5)

where ki (i = A, B, C) are the rate constants for the phase gratings and (ki = (1/τi)), τi are their recording time constants. ΦB, ΦC, and ΦD are the maximal amplitudes of the respective gratings defined as

ΦD =

;

λ 2πneff ΔdD,max λ

ΦC =

2π ΔnC,max d λ

(8)

4. RESULTS AND DISCUSSION The aim of this work is to deepen our previous study on SRG formation using the s−s inscription geometry,31 in particular the dependence of the grating formation efficiency on the length of the polymer backbone. Supramolecular complexes provide a perfect tool for performing this task, due to the wide range of monodisperse polymers available from commercial sources. Herein, we limit ourselves to five P4VPx(OH-DMA)0.33 complexes with P4VP molecular weights of 1000, 3200, 7000, 19 000, and 50 000 g/mol. Figure 3 depicts the diffraction efficiency measured as a function of the recording time for all five complexes. The experimental results are indicated by symbols whereas the solid lines are theoretical fits into the experimental data. Next to the dynamics curves, Figure 3 also presents the AFM scans of the film surfaces after the inscription process. It is clearly evident that the efficiency and the dynamics of the holographic recording and the inscription of SRGs depend crucially on the P4VP molecular weight, being significantly more effective for the low-molecular-weight complexes (1000, 3200 g/mol) than for those with high molecular weight (7000, 19 000, 50 000 g/ mol). The AFM scans of P4VP1000(OH-DMA)0.33 and P4VP3200(OH-DMA)0.33 reveal SRGs modulation depths of 400 and 600 nm, respectively, as shown in Figure 4 for P4VP1000(OH-DMA)0.33. In addition to the relief grating with a period defined by the light interference pattern (ca. 6 μm), a fine-grating with a different periodicity (ca. 1 μm), dependent on the wavelength of the writing beams, was formed in the direction perpendicular to the grating wave vector for both complexes. As seen from Figure 4, this fine grating is rather

and

2π ΔnB,max d

kX (e−kXt − e−kYt ) k Y − kX

where kj = (1/τj) (j = X,Y) are the rate constants of the amplitude grating, τj being the recording (τX) and erasure (τY) time constants, and ΦY is the maximum amplitude of the absorption grating related to the maximum absorption coefficient changes. The contribution of the absorption grating to the diffraction efficiency is typically negligible in comparison to the phase grating. However, since we study relatively thick drop-cast films, we decided to include also the absorption grating into the analysis.

⎡ kAkB ΔΦC(t ) = ΦC⎢ (e−kAt − e−kCt ) ⎣ (kB − kA )(k C − kA ) ⎤ kAkB − (e−kBt − e−kCt )⎥ (kB − kA )(k C − kB) ⎦

ΦB =

(7)

and as a result it can be expressed as

where ΔΦB(t), ΔΦC(t), and ΔΦD(t) express the dynamics of the formation of each grating, and ϕBC(t), ϕCD(t), and ϕBD(t) are the phase shifts between the gratings. The dynamics of the individual gratings can be described as follows: ΔΦB(t ) = ΦB

kY

X→Y→Z

;

(6)

where ΔnB,max, ΔnC,max , and ΔdB,max are the maximum refractive index and thickness modulations, respectively, d is the polymer film thickness, and neff is the effective refractive index of the corrugated layer. For azopolymers, the gratings ΔΦB(t), ΔΦC(t), and ΔΦD(t) arise from the molecular reorientation, bulk polymer diffusion, and the surface corrugation, respectively. ΔΦB(t) is linked with the volume-geometrical changes of the azobenzene molecules, arising from the trans−cis−trans photoisomerization cycles and 23281

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regular and its modulation depth is as high as 200 nm. The origin of the fine-structure formation is not clear yet and will be the subject of a separate paper, here we note that related observations have been made by several research groups.43−47 The results shown in Figures 3 and 4 bring out three essential things. First, holographic recording and the inscription of high-modulation-depth SRGs can be performed with success using the s−s polarization geometry of the writing beams. Second, the efficiency of the process and the amplitude of the SRGs strongly depend on the molecular weight of the polymer. Hence, these results confirm our earlier observations31 with a better-defined, supramolecular material system that undergoes very efficient SRG formation. Third, in low-molecular-weight polymer−azobenzene complexes, a fine-grating structure with a different period and significant amplitude is inscribed together with the formation of the expected SRG, such that the two gratings are perpendicular to each other. In order to go deeper into the mechanism of the grating formation and understand what are the reasons for the drastic molecular-weight dependence, the experimental curves of the diffraction efficiency dynamics shown in Figure 3 were simulated on the basis of the above-described theoretical approach assuming the formation of three phase gratings. The results of the calculations are presented in Figure 3 by the solid lines, and the fitting parameters are gathered in Table 1. The phase shifts between the gratings were as follows: ϕBC = π, ϕBD = 0, and ϕCD = π, meaning that the reorientation grating and the surface relief grating are in phase with each other, but the bulk diffusion grating is out of phase with respect to these two. The results of Table 1 reveal several important details on the grating formation process in complexes with different molecular weights. The influence of molecular weight is clearly reflected in the formation efficiency of the bulk-diffusion grating and the surface-relief grating. The amplitude of the former decreases systematically with increasing molecular weight, suggesting that it is more difficult for long chains to diffuse and pack. The latter, on the other hand, seems to exhibit an optimum Mw, in the present case 3200 g/mol, and falls off drastically when the Mw further increases. The recording time constants of the gratings ΔΦC(t) and ΔΦD(t) also increase with Mw, especially drastically for the SRG. Independently from the simulation results, the influence of molecular weight on the SRG formation is demonstrated by the modulation depth Δd directly measured with AFM (cf. Table 1). It is also evident that the contribution of the reorientation grating is small (1000 g/mol) or negligible (other Mw’s) for all the complexes. The formation of the absorption grating and its erasure takes place with the same time constants for all complexes, however, the amplitude of the absorption grating decreases when the Mw increases. One can also notice that the main contribution in the diffraction efficiency in low Mw complexes comes from the surface relief grating and due to its significant amplitude the diffraction efficiency has reached high values. On the other side, for high Mw complexes the main contribution in the diffracted signal comes from the bulk diffusion grating, resulting from spatial density changes of the polymer chains, which along with the formation of the SRG with very low amplitude leads to low diffraction efficiency. Our analysis implies that both the SRG formation and the diffusion of the polymer in the bulk are strongly affected by the Mw of the migrating polymer chains. In a nutshell, in the case of the s−s polarization configuration, considered generally as ineffective in terms of SRG formation, the process strongly depends on the molecular weight of the

Figure 3. Diffraction efficiency as a function of time in the P4VPx(OH-DMA)0.33 complexes, as measured during the holographic recording process using the s−s polarization configuration. (a) 1000 and 3200 g/mol; (b) 7000, 19 000, and 50 000 g/mol. The symbols represent the experimental data points and the solid lines are theoretical fits. Insets: Atomic force microscopy scans (2D view) of the surface relief gratings.

Figure 4. (a) SRG inscribed on P4VP1000(OH-DMA)0.33 (2D AFM scan, 30 × 30 μm) together with surface profiles: (b) along the grating wave-vector (x-direction) and (c) in the direction perpendicular to the grating wave-vector (z-direction). (d) 3D view of the structure shown in (a).

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Table 1. Fitting Parameters (± 5%) of the Experimental Curves of the Diffraction Efficiency Dynamics Measured in Supramolecular P4VPx(OH-DMA)0.33 Complexes of Different Molecular Weight (x) of the Polymer and the Amplitude of the Surface Relief Grating Measured by AFM polymer code P4VPx(OH-DMA)0.33 low Mw

high Mw

a

P4VP1000(OHDMA)0.33 P4VP3200(OHDMA)0.33 P4VP7000(OHDMA)0.33 P4VP19000(OHDMA)0.33 P4VP50000(OHDMA)0.33

phase grating recording time constants [s]

maximum phase grating amplitudes

SRG amplitude [nm]

amplitude grating recording time constants [s]

maximum absorption grating amplitude

τA = (1/kA)

τB = (1/kB)

τC = (1/kC)

ΦB

ΦC

ΦDa

Δd

τX = (1/kX)

τY = (1/kY)

ΦY

400

410

580

0.24

1.00

1.05

410

400

1000

0.19

400

410

950

0

0.85

1.57

590

400

1000

0.12

400

1400

3700

0

0.46

0.10

40

400

1000

0.10

400

2000

46000

0

0.40

0.05

20

400

1000

0.08

400

3500

90000

0

0.38

0.04

16

400

1000

0.07

Assuming neff = 0.25.

■

polymer: SRGs with very high amplitude can be recoded given that the polymer chains are sufficiently short. Hence the results reported here confirm the observations of ref 31, with the important difference that herein we used a supramolecular polymer−azobenzene complex instead of a covalently functionalized azopolymer. Such complexes are inherently dynamic, which may result in the formation of large-size superstructures especially when short oligomeric chains are used. Before conclusive statements can be made, this issue warrants further investigations that are currently in progress. However, we can already say that micron-scale crystalline domains seem to appear in the low-Mw complexes, whereas such domains are less evident in the complexes based on long, entangled chains, the ones that do not form SRGs. How this affects the efficiency, polarization dependence and fine-structure formation of the surface patterning process is a subject of future study. The fact that we also observe a high-amplitude fine-grating (>100 nm) in the direction perpendicular to the grating grooves is also rather unique and clearly distinct from our previous observations.31 All this points to the direction that instead of simply providing a facile preparation method for SRG-forming materials, supramolecular complexes may have much more to offer, and their light-responsive behavior is truly unique.

AUTHOR INFORMATION

Corresponding Author

*Phone: (048) 71 320 39 24. Fax: (048) 71 320 33 64. E-mail: [email protected]. Present Address #

Department of Chemistry and Bioengineering, Tampere University of Technology, P.O. Box 541, FI-33101 Tampere, Finland.

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The work performed under Grant No. 2011/03/B/ST5/01021 from the Polish National Science Centre.

■

REFERENCES

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5. CONCLUSION We have demonstrated that high-amplitude surface relief gratings can be inscribed successfully using the s−s polarization configuration in supramolecular polymer−azobenzene complexes, given that the molecular weight of the host polymer is sufficiently low. The high-modulation depth “primary” surface relief grating is accompanied by a secondary fine-structure grating with a considerable modulation depth in the direction perpendicular to the primary grating. The grating formation was analyzed through three-coupled-gratings method, which is universal and can be applied to any material/inscription geometry. The analysis revealed that both polymer bulk diffusion and surface corrugation diminish rapidly upon increasing molecular weight, whereas chromophore reorientation within the polymer matrix is much less affected by the length of the polymer chains. 23283

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