Tunable Nonlinear Optical Pattern Formation and Microstructure in

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Tunable Nonlinear Optical Pattern Formation and Microstructure in Crosslinking Acrylate Systems during Free-Radical Polymerization Saeid Biria, Philip Patrick Anthony Malley, Tara F Kahan, and Ian Dean Hosein J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b11377 • Publication Date (Web): 16 Feb 2016 Downloaded from http://pubs.acs.org on February 17, 2016

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The Journal of Physical Chemistry

Tunable Nonlinear Optical Pattern Formation and Microstructure in Crosslinking Acrylate Systems during Free-Radical Polymerization

Saeid Biria1, Philip P.A. Malley2, Tara F. Kahan2, Ian D. Hosein1

1. Department of Biomedical and Chemical Engineering, Syracuse University, Syracuse, NY, 13244, United States 2. Department of Chemistry, Syracuse University, Syracuse, NY, 13244, United States

1 ACS Paragon Plus Environment


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ABSTRACT We report crosslink-tunable, nonlinear optical pattern formation of transmitted light in a photopolymer undergoing free-radical polymerization. Photopolymerization induces microscale filamentation of a uniform, broad transmitted beam, which corresponds to a concurrent spatial evolution in crosslinked morphology in the photopolymer. As the photopolymerization is permanent, the ensemble of filaments imprint a microstructure comprising a crosslink gradient pattern. Tuning the system’s capability to crosslink and branch changes the magnitude of the refractive index change (∆n), which both induces nonlinear conditions, and also changes the strength of the optical nonlinearity. Only a monomer with sufficient functionality shows stable optical pattern formation, and its nonlinear regime exists for a specific range of exposure intensities. A monomer of lower functionality can be pushed into the nonlinear regime by formulating it with higher functional monomers, whereby ∆n is increased to provide a stronger response to light. In such formulations, the strength of the nonlinearity, as evidenced by changes in light confinement in the optical pattern, is tuned by varying this monomer’s functionality or its relative weight fraction. The strong correlation among polymerization-induced refractive index change, optical pattern feature size, and crosslinked morphology demonstrates tunable optical nonlinearity through variations in the inherent polymer structure.


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INTRODUCTION Coupling polymeric systems to nonlinear dynamics offers opportunities for creating materials with tailored morphology and function via pattern forming processes. Examples include periodic striations from travelling fronts in thermal polymerization, coalescence of polymer films during dewetting, oscillatory gels, and morphology evolution in phase separation.1,2 Particularly, optical pattern formation due to nonlinear optical dynamics, observed in materials such as liquid crystals3 or photorefractive crystals,4-11 is attractive for potential lightdirect synthesis of patterned soft matter. Burgess and coworkers12 discovered that through photopolymerization, polymer morphology can be coupled to the nonlinear dynamics of incoherent, polychromatic, transmitted optical fields, and a new light-driven, nonlinear mechanism of polymer pattern formation proceeds. Mechanistically, weak spatial noise always present in an input beam seeds a spatially varying polymerization rate, however infinitesimally small. As changes in refractive index (∆n) is proportional to the degree of polymerization, the nascent morphology establishes a non-homogenous refractive index profile. Light is drawn into the spatially local regions of greater degree of polymerization, due to its higher refractive index. This initiates a positive feedback between optical field dynamics and polymer morphology evolution, whereby both the uniformity of the beam and homogeneity of the photopolymer medium become unstable, and pattern formation occurs. The optical beam undergoes spontaneous division into a densely packed population of identical filaments, a “self-trapped” beam,13 characterized by divergence-free propagation, traversing the medium in its own selfinduced waveguide.14 In the field of nonlinear optics, this filamentation process is referred to as Modulation Instability (MI). In terms of polymer morphology, the photopolymerizable system is



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permanently transformed from a liquid solution to a solid medium imprinted with an arrangement of microscale “channels”, each of which operate as a polychromatic, cylindrical waveguide. The continuous, auto-accelerated, off-equilibrium evolution of polymer morphology, self-regulated via photopolymerization, offer enormous potential for controlling soft matter structure at the microscale. Conversely, the self-organized polymer morphology offers a pathway to permanent, large-scale light self-organization, whereby a transmitted optical field may be concentrated at the micron to submillimeter length-scale in waveguide architectures. This transformation into densely packed, microscale subunits is especially attractive for light delivery systems in microscale solar cell arrays,15,16 for which waveguide arrangements can ensure complete capture of light, its division among solar cells, and lossless transfer to their surfaces. One critical issue is how to control this patterning process through a fundamental understanding and tuning of the associated polymer evolution. Optical pattern formation in photopolymers is described by the nonlinear paraxial wave equation,17

ik 0 n0

∂ε 1 2 i + ∇ t ε + k 02 n0 ∆nε + k 0 n0αε = 0 , 2 ∂z 2

(1)

which describes the dynamic competition between (1) the natural tendency of a light beam to diverge in the directions orthogonal to its propagation path (transverse Laplacian) and (2) the self-focusing nonlinearity due to self-induced refractive index changes, ∆n. This competition leads to instability of the transverse profile of the beam and consequent optical pattern formation. The increase in ∆n of a photopolymer system under exposure to light is described by:14

  1 t −τ  ∆n(x, y, z,t) = ∆ns 1− exp− ∫ | E(t' ) |2 dt'  Uo 0  

(2)


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where ∆ns is the maximum achievable index change (between fully cured and uncured photopolymer media), U0 is the critical energy required to initiate polymerization, τ is the monomer radical lifetime (which is negligibly small), and E(t) is the electric field amplitude of the optical field. Equation 2 describes the strength of the nonlinearity, ∆n, as dependent specifically on the light intensity and the polymer structure associated with ∆ns. Hence, we anticipate that tuning polymer structure in general is a means to tune both nonlinear optical pattern formation and corresponding polymer morphology. The three requisite conditions for self-trapping of spatially and temporally incoherent light,18 including white light, can be satisfied by photoinitiated polymer systems.12,13 The first condition is a noninstantaneous photoresponse. Owing to the inherently slow rate of the chemical reaction, the refractive index response, regardless of optical intensity, is always noninstantenous.14 The response to light intensity is averaged over milliseconds to seconds, and the random, femtosecond-scale phase fluctuations characteristic of incoherent light cancel out.4 Furthermore, the greater refractive index changes found in polymer systems is capable of countering the stronger divergence found in incoherent beams. The second condition is that waveguides formed in polymer systems are multimoded, such that they support the optical modes of an incoherent beam. The third condition is self-consistency, namely the multimode beam can guide itself in its own self-induced waveguide. In other words, the time-averaged intensity of the beam corresponds to the superposition of time-averaged populations of guided modes in the waveguide, which are themselves induced by the total time-averaged intensity of the beam. The motivation of our present study herein is to explore nonlinear optical pattern formation in crosslinking systems, whose ∆ns depends on the crosslinking density and degree of



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branching,19 which vary with the kinetics of photoinitiation20 (e.g., light intensity) and the functionality of the monomer. Crosslinked structure is shown to drive free radical polymerization into a nonlinear regime as evidenced by the clear onset of optical pattern formation: both MIbased filamentation and, specifically studied herein, the simultaneous self-trapping of multiple, incandescent beams. Tuning the phenomenon by varying either the photoinitiation rate or crosslinking degree is demonstrated by direct correlations to the emerging optical pattern and underlying polymer morphology. This is the first demonstration of tuning the nonlinearity, resultant pattern, and microstructure by specifically tuning the crosslinking in neat, photoinitiated monomer formulations, and this work emphasizes the importance of considering the evolving morphological properties of polymer systems in their nonlinear optical response. This route is attractive as it elicits intrinsic variations of polymer structure, as opposed to other approaches such as surface plasmon resonances of embedded metal nanoparticles,21 or the use of chromophore and sensitizing additives in photorefractive polymers.22,23 As refractive index changes in polymer systems can be upwards of 0.15,24 the optical response is stronger than in conventional Kerr and photorefractive media (∆n ~ 10-3), and only requires optical intensities on the order of milliWatts rather than Watts. The process is also attractive, because it can be elicited by incoherent light sources, such as incandescent lamps, LEDs, or even sunlight. Furthermore, as the refractive index change is irreversible, polymerizable systems do not compete with any inherent relaxation mechanisms, thereby allowing stronger, sustained pattern formation and morphology evolution.

EXPERIMENTAL SECTION


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Materials. Methyl methacrylate, 1,6-hexanediol dimethacrylate (HDDMA), Trimethylolpropane triacrylate (TMPTA), and pentaerythritol tetraacrylate (PETA) were purchased from Sigma Aldrich (MO, USA). Dipentaerythritol pentaacrylate (DPEPA) was donated by Sartomer (PA, USA). Bis (.eta.5-2,4-cyclopentadien-1-yl)-bis(2,6-difluoro-3-(1H-pyrrol-1-yl)- phenyl) titanium (Irgacure 784) was donated by the M.F. Cachat Company. All chemicals were used as received.

Preparation of Photopolymerizable Media. Mixtures of acrylate monomer and photoinitiator (fixed at 0.1 wt% for all experiments) were placed in a vial on a magnetic stirrer for 24 hours, protected from exposure to ambient light. Prior to experiments, the mixtures were filtered using a polytetrafluoroethylene (PTFE) membrane with 0.2 µm pore size (Pall Corporation). The filtered mixtures were injected into a homemade “ring cell” consisting of a Teflon ring (17 mm inner diameter) sandwiched between two plastic cover slips. The thickness of the ring for all experiments was fixed to 3 mm, which specifies the optical path length of light propagation in the sample. For precuring of samples, mixtures were loaded into a vial and placed in oven (80 °C), before loading into the cell.

Photopolymerization of Acrylate Media. Photopolymer media were exposed to collimated (1” diameter lens, focal length = 25 cm) incandescent light emitted from a Quartz-Tungsten-Halogen (QTH) lamp (300-2500 nm), and exposure intensities from 2-30 mW/cm2 were explored. The light was first passed through a photomask (Photosciences Inc.) consisting of an array of squareshaped chrome patterns (width = 40 µm, spacing = 80 µm), which in turn weakly modulates the beam into the form of a bright grid pattern. The mask spacing was selected based on filament measurements performed elsewhere.12 The transmitted light was passed through imaging optics



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and then focused onto a Charge-Coupled Device (CCD) camera with pixel resolution of 3.2 × 3.2 µm (Dataray, WinCAMD-XHR). The imaging setup captured the spatial intensity profile of the transmitted beam at the “exit” surface of the cell. Filament full width at half maximum (FWHM) values were determined by fitting in Matlab the spatial intensity profiles of their cross sections to a 2D Gaussian function. Optical Microscopy. Optical microscope images of the photopolymerized samples were acquired with a Zeiss Axioscope equipped with an Axiocam 105 color camera operated by Zeiss imaging software. Images were captured under transmission mode.

Raman Analysis. Raman compositional images were acquired with a confocal Raman microscope (Renishaw, InVia) using a 532 nm continuous wave (CW) diode laser. The images were acquired just below the surface (~10 µm) on the exit side of the medium. Light passed through a collimator onto a series of mirrors that guided the light through a 5× magnified objective. Scattered light was collected through the microscope objective and imaged onto a CCD camera. Spectra were acquired between 506 and 2198 cm-1. Area maps were performed by acquiring spectra at multiple positions on the sample (with 1 µm step sizes) using an automated x, y, z translation stage. Spectra were analyzed using Matlab for mapping the integrated peak intensities. Peaks were fit to a Gaussian function to determine their integrated areas.

Thermal Analysis. Dynamic scanning calorimetry (DSC) plots of the samples were obtained using a DSC Q200 DSC system (TA Instruments). Approximately 7 mg of sample was heated between 50 to 300°C at a rate of 10°C.min-1 under a 50 mL.min-1 flow rate of nitrogen. The degree of crosslinking (X) of the cured samples was determined from the total heat calculated


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from the exothermic peak (found between 150 to 250 °C) for samples and their liquid mixtures (i.e., uncured) using the equation:25

X =

∆H ( S 0 ) − ∆H ( Sx )

(3)

∆H ( S 0 )

Where ∆H(S0) and ∆H(Sx) are the reaction enthalpies of the uncured liquid formulation and photopolymerized sample, respectively.

Refractive Index Measurements. Refractive indices of liquid (uncured) mixtures and solid (cured) samples were measured with an Abbe Refractometer (Atago, NAR-1T SOLID). Solid samples are required to have a rectangular prism geometry for accurate measurements; therefore, cured slabs 3 mm thick, 22 mm in length, and 8 mm in width were prepared in a homemade glass cell. Refractive indices were measured to an accuracy of ±0.001.

RESULTS AND DISCUSSION The importance of a crosslinked structure to stable pattern formation is shown in Figure 1 for photopolymerized media consisting of monomers with different functionality. A monofunctional monomer, methyl methacrylate, showed no pattern formation, and significant shrinkage during polymerization disrupted the medium over the exposure duration. A difunctional monomer, HDDMA, showed no pattern formation for the same exposure intensity and duration. The appearance of a weak, 1D lamellae pattern could be observed in some instances (for example, see Figure S1 in the Supporting Information); however, no filamentation occurred regardless of the exposure time or intensity.

The difunctional system, although

displaying no shrinkage, remained in a low viscous state, rendering the medium easily disrupted. 9 ACS Paragon Plus Environment


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In contrast, a clear pattern forms (Figure 1c) with a trifunctional monomer, TMPTA, the medium of which gels within the first 25 minutes. Hence, a medium consisting of a monomer with sufficient functionality demonstrates a strong nonlinear response to light. This transformation to a stable medium that shows nonlinear optical pattern formation is attributed to both the inherent network formation possible with a multifunction monomer, as well as the enhanced reactivity of its double bonds due to their large concentration in close proximity to free radical sites.26 This in turn enables a stronger nonlinear response to light via photopolymerization-induced refractive index changes. Importantly, the bright intensity spots in the spatial intensity profile in Figure 1c correspond to the filament cross sections, and their positions indicate the highly crosslinked regions to which they are confined. As light confinement is proportional to refractive index, which is proportional to degree of polymerization, the optical intensity profile is a faithful replica of the profile of the crosslinked morphology (vida infra).

Modulation instability could be achieved in TMPTA both under the conditions of no modulation and a 1D periodic modulation to the input beam (See Figure S2 in Supporting Information). In the former case, MI is evidenced by the emergence of randomly positioned filaments. In the latter case, the 1D pattern modulates the beam into the form of a periodic array of bright “stripes”, which each spontaneously break up into a multitude of filaments in an arrangement completely distinct from the 1D pattern used to induce it. Modulating the beam to some extent is often required to seed process, and this may be provided deliberately with a photomask,27,28 or surreptitiously through noise induced from the experiment setup.12 Whereas, the 2D mask modulates the beam into the form of two arrays of bright stripes arranged perpendicular to one another (i.e., a “light grid”). In this case, the self-trapped beam


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positions in TMPTA are commensurate with the 2D square symmetry and spacing of the spatial modulation applied on the input beam by the mask. This ordered arrangement of self-trapped beams, as opposed to random locations observed with no modulation or a 1D modulation, indicates that the 2D mask is seeding the specific locations for their emergence, and the process is not strictly MI, but rather the simultaneous self-trapping of multiple, incandescent beams. This is indicated by the fact that the initial spatial intensity profile of the beam at the exit face of the medium shows a uniform spatial intensity distribution, as does the individual stripes when the 1D mask is employed; however, for the 2D mask a greater intensity is observed at the positions where the stripes intersect (See Figure S3 in the Supporting Information for the images of the initial spatial intensity profiles). Therefore, for a 2D modulation we can infer that at the entrance of the sample, the light intensity is marginally greater at these specific positions, and that the mask seeds the formation of self-trapped beams at these locations. Having noted that MI is possible for TMPTA media, as well as two-component formulations (vida infra), the nonlinear optical phenomenon specifically studied herein is with regards to tuning the self-trapping of light, and the 2D mask employed for all studies hereon is sufficient.

The optical nonlinear regime, as indicated by the optical pattern in TMPTA (Figure 2), is observed in a specific range of exposure intensities (~4-20 mW/cm2). Patterns do not form below this range, regardless of exposure time, and the medium remains in low viscosity state. Pattern formation does occur beyond 20 mW/cm2; however, the arrangement is no longer commensurate with the mask pattern, but rather random in position, and filaments appear larger in size (vida infra). As ∆ns is fixed for single monomer media (0.007 for TMPTA), optical pattern formation is driven by the underlying polymerization growth mechanisms, and their dependence on



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exposure intensity, i.e., |E(t)|2. At low exposure intensities, only a few acrylate functions initiate over time, and chain growth predominates, resulting in a low viscosity medium consisting of long linear chains with relatively low crosslinking. Consequently, any associated refractive index change in the medium will be small and slow in evolving (i.e., low responsiveness), inhibiting the medium from providing any significant modulation to the beam that could lead to spatial variation in polymerization. A slow, uniform cure is the consequence, yet with no gelling of the medium. At moderate exposure intensities, the rate of chain initiation increases, and additional acrylate functions on monomers begin to polymerize. Long chain backbones are now drawn together through crosslinks, achieving a higher degree of densification, and greater refractive index. The rate of change of ∆n in this intensity range is sufficient to yield a positive feedback, whereby leakage of light into local regions of higher refractive index increases their polymerization rate,29 leading to accelerated crosslinking, and larger refractive index changes. This is characteristic of the optical nonlinear regime. This transition with increased intensity is supported by the observed increase in the degree of crosslinking induced by exposure intensities associated with the onset of system nonlinearity (See crosslinking results in Figure S4(a) in the Supporting Information).

The speed of pattern formation is itself intensity dependent, via increased photoinitiation, and appears earlier (i.e., within the first 25 minutes) at higher exposure intensities within the regime, compared to lower intensities. i.e., 50 min for 4 mW/cm2. At high exposure intensities, the high rate of initiation causes large scale crosslinking. A significant amount of free-radical formation is also expected with higher exposure intensities, such that the diffusion of freeradicals beyond the illuminated region can further contribute to the increase in waveguide


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diameter and the self-trapped beam. This would also eventually move the system towards a uniform cure, due to sufficient polymerization in the unexposed and low intensity regions, thereby pushing the system out of the nonlinear regime. Yet, once the system has gelled, the impact of diffusion will be significantly reduced. Furthermore, at such higher intensities, the high photoinitiation rate increases the likelihood of multiple acrylates initiated on a single monomer, and consequent polymerization of these groups with other such monomers, which will lead to a tighter crosslink (i.e., shorter distance between crosslink points). In this case, both chain propagation incorporating monomers with multiple acrylates initiated, and also termination mechanisms such as combination (i.e., two chain ends couple together to form one long chain) will contribute to stronger crosslinking. Consequently, with increased exposure intensity, the combination of free-radical diffusion and faster, tighter crosslinking makes the system tend towards larger self-trapped beam sizes, rather than tighter confinement of light, and eventually a uniform cure, as neighboring high-intensity, self-trapping regions begin to overlap. These effects are indicated by the change in the self-trapped beam size with increased exposure intensity (vida infra). Similar regimes in which pattern formation is, and is not, observed have been identified with increased photoinitiator content.30 These results point to the crucial role of crosslinking, and its intensity dependence, in determining the optical nonlinearity and consequent optical pattern in a photopolymer medium.

The difunctional monomer medium could be pushed into an optical nonlinear regime by the addition of monomers of higher functionality, such as monomers that consist of three, four, and five acrylate groups (Figure 3): TMPTA, PETA and DPEPA, respectively. Pattern formation occurred within the first 25 minutes of exposure. Even modest additions (5 wt%) were sufficient



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to stabilize the medium (i.e., gelling) and to induce complete filamentation of the beam. Increased weight fraction of any one of the three higher functional monomers showed tighter confinement of light, i.e., smaller filaments as indicated visually by their smaller cross section profiles. Modulation instability was also achieved in these formulations both in a broad uniform beam and by using a 1D mask to seed the filamentation (see Figure S5 in Supporting Information). The strong confinement of light, as shown in the intensity profiles in Figure 3, is attributed to both the filamentation of the input beam, and also to the subsequent, sustained photopolymerization in the high intensity regions over the duration of exposure (for example, see pattern variation over time in Figure S6 of the Supporting Information). Formulations of methyl methacrylate and TMPTA (5 wt%) also showed pattern formation; however, samples remained in a low viscous state, and the patterns were not commensurate with the mask due to shrinkage. Shrinkage also appeared to compress the filaments, as evidence by their elliptical cross sections. By preheating the sample their circular cross sections were retained, but the arrangement was not commensurate with the mask, nor did the medium gel. For the results of methyl methacrylate with TMPTA, see Figure S7 in the Supporting Information. The optical patterns consisting of a periodic arrangement of filaments permanently inscribes a periodic microstructure into the photopolymer medium (Figure 4). The samples consist of cylindrical channels arranged with same spacing and symmetry as the mask. This periodic array of channels corresponds to a spatially periodic crosslinked morphology.

For two component formulations under fixed exposure intensity (12 mW/cm2), the optical nonlinearity in this case varies with the magnitude of ∆ns. Relative to pure HDDMA (∆ns = 0.044), formulations from 10-30 wt% show a monotonic increase in the ∆ns (Figure 5). For such


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weight fractions, the contribution to the crosslink made by HDDMA and any one of these monomers is approximately equal to the percent of (meth)acrylate functions they contribute to the medium,31 which can explain this positive trend. Yet, network formation with multifunctional monomers depends strongly on the molecular structure, reactivity, diffusion, and concentration,26 and may still vary significantly with variations in relative weight fractions, especially at very low weight fractions for either component. For example, polymer networks from different multifunctional monomers are significantly different in their spacing and symmetry.31 Consequently, formulations may induce transformations in the network with changes in the relative weight fraction, and this may account for the increase in ∆ns at 5 wt%, relative to pure HDDMA, and lowest ∆ns values at 10 wt% for all formulations. Nevertheless, Figure 5 confirms that the addition of higher functional monomers increases ∆ns, and this is attributed to higher crosslinking density and a tighter crosslink.32 This fact is corroborated by the increase in the degree of crosslinking in samples with increase weight fraction of higher functional monomers (see Figure S4(b) in the Supporting Information). Hence, nonlinear optical pattern formation is enabled by the increase in a medium’s ∆ns, as well as providing stabilization, via formulating with higher functional monomers.

That a greater achievable ∆n enhances the medium nonlinearity is manifested by stronger self-focusing of light, which can counter the greater divergence of a smaller beam. Hence, one visually observable effect of this enhancement is the formation of filaments with smaller cross sections. Figure 6 shows the mean FWHM of the filaments for TMPTA as a function of exposure intensity and for diacrylate formulations as a function of weight fraction of the higher functional monomers. In the former case (Figure 6a), a decrease in the FWHM values with



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increased exposure intensity corresponds to the onset of the nonlinear regime. Within the nonlinear regime, the filament sizes remain relatively the same; variations are only observed at the upper boundary. This increase in the FWHM at higher exposure intensities (≥ 20mW/cm2) can be understood as follows: at higher exposure intensity the index change at the center of the selftrapped beams saturates, and the waveguide develops of step-index refractive index profile. The strength of the self-focusing is diminished, and the optical intensity is now distributed over the entire cross-section of the waveguide. As the tails of the optical field of the waveguide extend beyond its core, the polymerization is initiated at the boundaries, which broadens both the waveguide and self-trapped beam. A gradual increase in beam width results in a corresponding decrease in the intensity of these tails, which eventually no longer extend far into the surrounding medium. Further photoinitation at the periphery is slow and the self-trapped beam reaches a stable, but larger diameter than achieved at lower exposure intensities. For very large intensities, this growth of the waveguide may persist until neighboring waveguides “fuse”, and the medium becomes essentially uniform. Heat produced by the exothermic reaction and consequent increase in temperature result in higher degrees of polymerization,29 which will also affect the final, stable self-trapped beam diameter. With regards to the exposed and unexposed regions, in the case of using either a 1D or 2D mask, heat dissipation into the unexposed regions, combined with free-radical diffusion, will increase gelation kinetics; that is, a faster rate of photopolymerization yields more heat dissipation, which leads to earlier gelling, enabling self-trapped beams to evolve to confine light more tightly (i.e., smaller FWHM). Furthermore, as the 2D mask yields a marginally higher intensity at the intersections of bright stripes, and we infer that these local spots will yield the


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highest heat evolution. In other words, the regions in which the self-trapped beams form are highest in local temperature. The heat produced within a self-trapped beam can contribute not only to the entire system gelling faster, but also enhance lateral growth of the waveguide, as heat enhancement by the reaction leads to the peripheries of the self-written waveguides to have higher polymerization rates than dictated solely by optical intensity. As photopolymerization is proportional to intensity, heat evolution will be greatest in the center of the self-trapped beams. However, as polymerization saturates, first at the center of the self-trapped beams, the heat production will decrease. Furthermore, as a broader waveguide results in lower intensity tails at the boundaries of the waveguide, eventually both the light intensity and the consequent heat created will become reduced, and a stable crosslinked profile is reached. However, as observed at higher exposure intensities with TMPTA, should this heat production become significant, it may disrupt the self-trapping and confinement of light. This is because the broadening effect due to rapidly evolving heat, may itself now contribute to a uniform cure of the sample, before any significant light modulation has occurred. Therefore, the heat evolved from the reaction may also account for the upper boundary in intensity of the nonlinear regime. In the latter case (Figure 6b), the FWHM values show a strong negative correlation with ∆ns for formulations with any of the three higher functional monomers (r values: -0.958, -0.917, -0.840 for TMPTA, PETA, DPEPA, respectively), and a stronger correlation if only 10-30 wt% formulations are considered (-0.968, -0.996, -0.961 for TMPTA, PETA, DPEPA, respectively). As formulations with PETA yielded the largest values of ∆ns, but the largest FWHM values, no strong correlation was found between filament size and the number of acrylate groups on the higher functional monomers.



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Raman spectral maps of the transverse cross section of photopolymerized, twocomponent microstructured samples reveal the variation in the evolving morphology associated with the optical pattern (Figure 7). Area maps of composition, as opposed to volume maps, were sufficient for analysis, owing to the 2D nature of the pattern (i.e., congruent 2D patterns can be observed along the propagation axis of light). After 25 minutes of exposure, formulating with monomers of higher functionality achieves higher degrees of densification, as indicated in the maps by the spatially tighter intensity spots for the carbonyl peak (C=O), which was chosen to indicate densification, because it is common among all monomers. Although FTIR and NMR studies31 have inferred phase separation in mixtures of dimethacrylates with higher functional monomers, the length scale is 20 mW/cm2) are deleterious to the process. The mechanism of nonlinear pattern formation and the role of crosslinking can thus be described as follows. During beam propagation, filamentation begins almost immediately upon exposure to light. It is these nascent filaments that form within the first 25 minutes of exposure that most likely correlate well with increased functionality of the higher functional monomer in the two-component formulations. The continuous initiation of acrylate groups eventually causes the medium to undergo large scale gelling. Thereafter, tighter confinement of light continues as the polymerization proceeds in the regions of the self-trapped beams. Sustained polymerization induced by filaments causes tighter confinement of light over time. This occurs over a specific



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range of exposure intensities for a medium consisting of a single monomer. Higher functional monomers in greater formulating quantities enables photopolymerization to achieve greater refractive index changes, yielding smaller filaments. Crosslinking thus serves two purposes: 1) to stabilize the medium, inhibiting heat convection or flow that would disrupt the spatial locations of the nascent filaments, and 2) to facilitate crosslink-associated refractive index changes in the medium.

CONCLUSION The mutual interaction between transmitted optical field and evolving polymer morphology facilitates spontaneous pattern formation of a beam and the permanent inscription of a microstructure. The phenomenon is clearest in a strongly crosslinked system, due to the stabilizing nature of the polymerizing matrix and greater achievable refractive index changes. The phenomenon may be tuned by changing the inherent crosslinking capability of the evolving polymer structure during photopolymerization. This is achieved in single monomer media by varying the exposure intensity. Likewise, in a weakly crosslinking system now formulated with higher functional monomers, the higher attainable degrees of crosslinking and branching over the duration of photopolymerization can also tune the phenomenon. Changes in the strength of the nonlinearity is evidenced by the changes in sizes of the filaments, and its tuning with polymer morphology is confirmed by the strong correlations both between the refractive index change at saturation and the filament size, and also between the filament sizes and their corresponding, localized density gradient in the photopolymerized media. Tuning optical pattern formation through the addition of higher functional monomers may be applied to a wide range of freeradical, cationic, and anionic systems, enabling a range of polymer materials to be explored as


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thin-films to control the transmission properties of light. Coupling optical pattern formation with crosslink-based morphology may also be used to control polymer gradient materials36 at fine scales, to tune local electronic properties of conducting polymers,37 to attain microscale precision in controlled free-radical polymerization for tuning contact lenses,38 to enhance hydrogel properties,39 and to control swelling properties via spatially controlled crosslink gradients.40

ACKNOWLEDGEMENT We thank Dr. Arthur J. Stipanovic for assistance with the DSC measurements.

Supporting Information Available: (1) Optical pattern formation under other conditions, (2) DSC crosslinking degree, (3) Optical microscopy, (4) Raman spectral maps, and (5) Filament FWHM for extended photopolymerization time. This information is available free of charge via the internet at http://pubs.acs.org.

Corresponding Authors *Correspondence to: Ian D. Hosein, Department of Biomedical and Chemical Engineering, Syracuse University. E-mail: [email protected]



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REFERENCES

(1) John, A. P.; Qui, Tran-Cong-Miyata, Q. Nonlinear Dynamics in Polymeric Systems; American Chemical Society, 2003; Vol. 869. (2) Epstein, I. R.; Pojman, J. A. Overview: Nonlinear Dynamics Related to Polymeric Systems Chaos 1999, 9, 255-259. (3) Peccianti, M.; Conti, C.; Assanto, G.; De Luca, A.; Umeton, C. Routing of Anisotropic Spatial Solitons and Modulational Instability in Liquid Crystals Nature 2004, 432, 733-737. (4) Streppel, U.; Michaelis, D.; Kowarschik, R.; Bräuer, A. Modulational Instability in Systems with Integrating Nonlinearity Phys. Rev. Lett. 2005, 95, 073901. (5) Centurion, M.; Pu, Y.; Psaltis, D. Self-Organization of Spatial Solitons Opt. Express 2005, 13, 6202-6211. (6) Shih, M.-F.; Jeng, C.-C.; Sheu, F.-W.; Lin, C.-Y. Spatiotemporal Optical Modulation Instability of Coherent Light in Noninstantaneous Nonlinear Media Phys. Rev. Lett. 2002, 88, 133902. (7) Saffman, M.; Glen, M.; Wieslaw, K. Two-Dimensional Modulational Instability in Photorefractive Media J. Opt. B: Quantum Semiclassical Opt. 2004, 6, S397-S403. (8) Kip, D.; Soljacic, M.; Segev, M.; Eugenieva, E.; Christodoulides, D. N. Modulation Instability and Pattern Formation in Spatially Incoherent Light Beams Science 2000, 290, 495498. (9) Kip, D.; Soljačić, M.; Segev, M.; Sears, S. M.; Christodoulides, D. N. (1+1)-Dimensional Modulation Instability of Spatially Incoherent Light J. Opt. Soc. Am. B 2002, 19, 502-512. (10) Chen, Z.; McCarthy, K. Spatial Soliton Pixels from Partially Incoherent Light Opt. Lett. 2002, 27, 2019-2021. (11) Klinger, J.; Martin, H.; Chen, Z. Experiments on Induced Modulational Instability of an Incoherent Optical Beam Opt. Lett. 2001, 26, 271-273. (12) Burgess, I. B.; Shimmell, W. E.; Saravanamuttu, K. Spontaneous Pattern Formation due to Modulation Instability of Incoherent White Light in a Photopolymerizable Medium J. Am. Chem. Soc. 2007, 129, 4738-4746. (13) Zhang, J. H.; Kasala, K.; Rewari, A.; Saravanamuttu, K. Self-Trapping of Spatially and Temporally Incoherent White Light in a Photochemical Medium J. Am. Chem. Soc. 2006, 128, 406-407. (14) Kewitsch, A. S.; Yariv, A. Self-Focusing and Self-Trapping of Optical Beams upon Photopolymerization Opt. Lett. 1996, 21, 24-26. (15) Sheng, X.; Bower, C. A.; Bonafede, S.; Wilson, J. W.; Fisher, B.; Meitl, M.; Yuen, H.; Wang, S.; Shen, L.; Banks, et. al. Printing-Based Assembly of Quadruple-Junction FourTerminal Microscale Solar Cells and Their Use in High-Efficiency Modules Nat. Mater. 2014, 13, 593-598. (16) Yoon, J.; Li, L.; Semichaevsky, A. V.; Ryu, J. H.; Johnson, H. T.; Nuzzo, R. G.; Rogers, J. A. Flexible Concentrator Photovoltaics based on Microscale Silicon Solar Cells Embedded in Luminescent Waveguides Nat. Commun. 2011, 2, 343. (17) Monro, T. M.; De Sterke, C. M.; Poladian, L. Catching Light in Its Own Trap J. Mod. Opt. 2001, 48, 191-238. (18) Trillo, S., Torruellas, W., Eds. Spatial Solitons; Springer: New York, 2001; pp. 87−125. 26 ACS Paragon Plus Environment

Page 27 of 40

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(19) Askadskii, A. A. Influence of Crosslinking Density on the Properties of Polymer Networks Polymer Science U.S.S.R. 1990, 32, 2061-2069. (20 Fouassier, J.-P. Photoinitiation, Photopolymerization, and Photocuring: Fundamentals and Applications; Hanser: Munich; Cincinnati; New York;, 1995. (21) Liqun, Q.; Kalaichelvi, S. Modulation Instability of Incandescent Light in a Photopolymer Doped with Ag Nanoparticles J. Opt. (Bristol, U. K.) 2012, 14, 125202. (22) Tolstik, E.; Romanov, O.; Matusevich, V.; Tolstik, A.; Kowarschik, R. Formation of SelfTrapping Waveguides in Bulk PMMA Media Doped with Phenanthrenequinone Opt. Express 2014, 22, 3228-3233. (23) Ostroverkhova, O.; Moerner, W. E. Organic Photorefractives: Mechanisms, Materials, and Applications Chem. Rev. 2004, 104, 3267-3314. (24) Odian, G. G. Principles of Polymerization; Wiley: New York, 1991; Vol. 3rd. (25) Hirschl, C.; Biebl–Rydlo, M.; DeBiasio, M.; Mühleisen, W.; Neumaier, L.; Scherf, W.; Oreski, G.; Eder, G.; Chernev, B.; Schwab, W. et. al. Determining the Degree of Crosslinking of Ethylene Vinyl Acetate Photovoltaic Module Encapsulants—A Comparative Study Sol. Energy Mater. Sol. Cells, 2013, 116, 203-218. (26) Andrzejewska, E. Photopolymerization Kinetics of Multifunctional Monomers Prog. Polym. Sci. 2001, 26, 605-665. (27) Burgess, I. B.; Ponte, M. R.; Saravanamuttu, K. Spontaneous Formation of 3-D Optical and Structural Lattices from Two Orthogonal and Mutually Incoherent Beams of White Light Propagating in a Photopolymerisable Material J. Mater. Chem. 2008, 18, 4133-4139. (28) Kasala, K.; Saravanamuttu, K. Optochemical Self-Organisation of White Light in a Photopolymerisable Gel: A Single-Step Route to Intersecting and Interleaving 3-D Optical and Waveguide Lattices J. Mater. Chem. 2012, 22, 12281-12287. (29) Decker, C. The Use of UV Irradiation in Polymerization Polym. Int. 1998, 45, 133-141. (30) Basker, D. K.; Brook, M. A.; Saravanamuttu, K. Spontaneous Emergence of Nonlinear Light Waves and Self-Inscribed Waveguide Microstructure during the Cationic Polymerization of Epoxides J. Phys. Chem. C 2015, 119, 20606-20617. (31) Jager, W. F.; Lungu, A.; Chen, D. Y.; Neckers, D. C. Photopolymerization of Polyfunctional Acrylates and Methacrylate Mixtures: Characterization of Polymeric Networks by a Combination of Fluorescence Spectroscopy and Solid State Nuclear Magnetic Resonance Macromolecules 1997, 30, 780-791. (32) Fouassier, J.-P.; Lalevée, J. Photoinitiators for Polymer Synthesis: Scope, Reactivity and Efficiency; Wiley-VCH: Weinheim, Germany, 2012; Vol. 1. (33) Kammer, S.; Albinsky, K.; Sandner, B.; Wartewig, S. Polymerization of Hydroxyalkyl Methacrylates Characterized by Combination of FT-Raman and Step-Scan FT-I.R. Photoacoustic Spectroscopy Polymer 1999, 40, 1131-1137. (34) Sandner, B.; Kammer, S. Crosslinking Copolymerization of Epoxy Methacrylates as Studied by Fourier Transform Raman Spectroscopy Polymer 1996, 37, 4705-4712 (35) De Santis, A. Photo-polymerisation Effects on the Carbonyl C=O Bands of Composite Resins Measured by Micro-Raman Spectroscopy Polymer 2005, 46, 5001-5004. (36) Claussen, K. U.; Giesa, R.; Schmidt, H.-W. Longitudinal Polymer Gradient Materials based on Crosslinked Polymers Polymer 2014, 55, 29-38. (37) Lee, S. H.; Gleason, K. K. Enhanced Optical Property with Tunable Band Gap of CrossLinked PEDOT Copolymers via Oxidative Chemical Vapor Deposition Adv. Funct. Mater. 2015, 25, 85-93. 27 ACS Paragon Plus Environment


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(38) Scott, A. J.; Nabifar, A.; Hernandez-Ortiz, J. C.; McManus, N. T.; Vivaldo-Lima, E.; Penlidis, A. Crosslinking Nitroxide-Mediated Radical Copolymerization of Styrene with Divinylbenzene Eur. Polym. J. 2014, 51, 87-111. (39) Lai, Y. C. A Novel Crosslinker for UV Copolymerization of N-Vinyl Pyrrolidone and Methacrylates to Give Hydrogels J. Polym. Sci., Part A-1: Polym. Chem. 1997, 35, 1039-1046. (40) Chen, C.-M.; Reed, J. C.; Yang, S. Guided Wrinkling in Swollen, Pre-Patterned Photoresist Thin Films with a Crosslinking Gradient Soft Matter 2013, 9, 11007-11013.


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Figures

Figure 1. Spatial profiles of the transmitted optical field intensity during free radical photopolymerization with incandescent light (20 mW/cm2, 25 minutes) of media consisting of a single acrylate monomer. (a) Methyl methacrylate. (b) HDDMA. (c) TMPTA. Spontaneous pattern formation in the form of microscale filaments are observed only in TMPTA. A close up of the large-scale pattern (~10×10 filaments) is shown in (c). Scale bars = 280 µm, 320 µm, 160 µm, for (a) to (c), respectively.



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Figure 2. Spatial profiles of the transmitted optical field intensity during the photopolymerization of TMPTA for exposure durations of (a-e) 25 min., (f-j) 50 min., and (k-o) 75 min. Pattern formation is observed at specific ranges of intensity and duration. At low exposure intensities of ≤2 mW/cm2 (a, f, k) no pattern formation is observed and the medium remains in a liquid state, for all exposure durations explored. Above a threshold intensity of ~4 mW/cm2 (b, g, l) pattern formation emergences over time. Over a range of intensities of ~6-20 mW/cm2 clear, stable pattern formation occurs within 25 minutes (c-d) and persist for long exposure durations of 50 minutes (h-i) and 75 minutes (m-n). At higher intensities of ≥20 mW/cm2 (e, j, o) a random pattern forms. All samples polymerized with intensities ≥4mW/cm2 gel within 25 minutes. Scale bars for each column = 160 µm.


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Figure 3. Optical pattern formation during the photopolymerization of media consisting of HDDMA formulated with acrylates of different functionality, n: TMPTA, n=3 (a-d), PETA, n=4 (e-h), and DPEPA, n=5 (i-l), and with systematically varied weight fractions of 5, 10, 20 and 30 wt% shown in columns left to right, respectively. Exposure intensity was 12 mW/cm2 for a duration of 75 min. Scale bars for each column = 160 µm.



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Figure 4. (a-c) Optical micrographs of the transverse cross section of the photopolymerized microstructure showing permanent inscription of a periodic arrangement of channels in formulations of HDDMA with 30 wt% TMPTA, PETA, DPEPA, respectively. Exposure intensity: 12 mW/cm2. Exposure time: 75 min. Scale bars = 160 µm.


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Figure 5. Measured refractive index difference at saturation (∆ns) for cured formulations of HDDMA with systematically varied weight fractions of TMPTA (●), PETA (■), DPEPA (▲). Respective red, green, and blue lines are to guide the eye.



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Figure 6. Mean FWHM of the filaments measured using their spatial intensity profile at the exit surface of media. Calculated values had coefficient of variances of ~2%. (a) TMPTA cured at different intensities for 75 min. (b) HDDMA formulated with systematically varied weight fractions of TMPTA (●), PETA (■), DPEPA (▲). Exposure was 12 mW/cm2 for 75 min. for all three formulations. Respective red, green, and blue lines are to guide the eye.


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.

Figure 7. (a-c) Raman images of the transverse cross section of an array (5×5) of channels inscribed in media of HDDMA formulated with 5 wt% (a) TMPTA, (b) PETA, and (c) DPEPA. Images map the integrated peak intensity for the C=O group of the acrylate (1720 cm-1). Exposure intensity: 12 mW/cm2. Exposure time: 25 min. Scale bars = 80 µm. (d) Intensity line scans over locations indicated in a through c, colored in red, green, and blue, respectively.



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Figure 8. Spatial map of the ratio of the integrated peak intensity for the C=C bond (1636 cm-1) to that for the C=O group, for media consisting of HDDMA formulated with 5 wt% (a) TMPTA, (b) PETA, and (c) DPEPA. Exposure intensity: 12 mW/cm2. Exposure time: 25 min. Scale bars = 80 µm. The maps indicate that in the PETA formulation the area surrounding the channels has the highest concentration of uncured acrylates, relative to TMPTA and DPEPA. A TMPTA formulation shows a spatially uniform distribution. (d-f) Frequency distributions of the calculated ratio values for their maps (a) to (c), respectively.


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Figure 9. Spatial map of the integrated peak intensity for the C=O bond (1720 cm-1) for media consisting of HDDMA formulated with 5 wt% (a) TMPTA, (b) PETA, and (c) DPEPA. Exposure intensity: 12 mW/cm2. Exposure time: 75 min. Scale bars = 80 µm.



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Figure 10. Gel points for photopolymerizing media during nonlinear optical pattern formation. (a) TMPTA as a function of exposure intensity. Note: media exposed to 2 mW/cm2 did not show gelling within the 75 total time examined. (b) HDDMA formulated with systematically varied weight fractions of TMPTA (●), PETA (■), DPEPA (▲). Exposure intensity was 12 mW/cm2 for all three formulations. Respective red, green, and blue lines are to guide the eye.


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Table 1. Calculated FWHM values of the Raman spatial cross sections of the channels and corresponding filaments in different formulated media. Exposure intensity: 12 mW/cm2. Exposure time: 25 min. Sample

Raman Peak FWHM (µ µm)

Filament FWHM (µ µm)

HDDMA+ 5 wt% TMPTA

61

49

HDDMA+ 5 wt% PETA

42

47

HDDMA+ 5 wt% DPEPA

31

35



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TABLE OF CONTENTS


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Tunable Nonlinear Optical Pattern Formation and Microstructure in

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