Intensity, Wavelength, and Polarization Dependence of Nonphotochemical Laser-Induced Nucleation in Supersaturated Aqueous Urea Solutions Jelena Matic, Xiaoying Sun, and Bruce A. Garetz*
CRYSTAL GROWTH & DESIGN 2005 VOL. 5, NO. 4 1565-1567
Othmer Department of Chemical & Biological Sciences & Engineering, Polytechnic University, Brooklyn, NY 11201
Allan S. Myerson Department of Chemical Engineering, Illinois Institute of Technology, Chicago, IL 60616 Received January 31, 2005;
Revised Manuscript Received May 1, 2005
ABSTRACT: We have measured the intensity dependence of nonphotochemical laser-induced nucleation (NPLIN) in 11.9 M aqueous urea solutions at 532 and 1064 nm, using both linearly and circularly polarized light. In all cases, we observed a nonlinear intensity dependence of the nucleation efficiency with thresholds of approximately 0.02-0.06 GW/cm2. The threshold at the green wavelength is lower than the threshold at the near-infrared wavelength. Moreover, the green nucleation efficiency is greater than the near-infrared efficiency at the same intensity. We attribute these differences to the greater absorption coefficient of water at 1064 nm compared to that at 532 nm. At both 532 and 1064 nm, the threshold for NPLIN is lower, and the efficiency of NPLIN at a given intensity is higher for linear polarization than for circular polarization. These differences are consistent with an optical Kerr effect mechanism for NPLIN. Introduction Crystallization from supersaturated solutions is a process commonly used in the separation and purification of industrially important chemicals such as pharmaceuticals, dyes, pigments, and explosives.1 Control of crystallization has commanded considerable attention in recent years, in contexts ranging from biomineralization to crystallization on polymer surfaces and Langmuir-Blodgett films.2,3 Nucleation, the initial step in the process of crystallization involving the formation of a critical nucleus, is still poorly understood. There is growing evidence that it is a two-step process, first the formation of a nanoscale liquid-like solute cluster, followed by a second organizational step in which the cluster takes on a crystalline structure.4,5 The process of nucleation is further complicated when the material under study is polymorphic, that is, when the material has the possibility of crystallizing into more than one crystal structure. Different polymorphs of a substance may exhibit great differences in chemical and physical properties such as melting point, solubility, dissolution rate, bioavailability, and hardness.6,7 Living organisms are able to control morphology and polymorphism through biomineralization. The addition of certain impurity chemicals can inhibit or promote the growth of particular crystal surfaces. Such tailor-made additives operate through stereospecific interactions not unlike enzyme-substrate interactions.8 New polymorphs of organic molecules constitute novel materials that may have important industrial applications. About nine years ago, we accidentally discovered that intense near-infrared laser pulses could induce supersaturated aqueous urea solutions to nucleate.9 We called this phenomenon nonphotochemical laser-induced nucle* To whom correspondence should be addressed.
ation (NPLIN) to distinguish it from the better-known, century-old field of ultraviolet and visible light-induced nucleation in supersaturated vapors,10 the mechanism of which typically involves the photochemical generation of a nonvolatile product that acts as a nucleus for the growth of the condensed phase.11 Photochemical laser methods have been recently applied to the control of morphology in the crystallization of supersaturated solutions.12,13 More recently, we showed that supersaturated aqueous glycine could be induced to crystallize into either the R or γ polymorph depending on the polarization state of the laser beam.14 Spontaneous nucleation at these concentrations always produces R glycine, although γ glycine is the most stable polymorph. We attributed both the urea and glycine observations to the interaction of large preexisting solute clusters with the intense electric field of the light and consequent organization of the cluster through the electric field-induced alignment of molecules (i.e., the optical Kerr effect15) in the cluster. Linear and circular polarizations induce different types of alignment and thus induce the nucleation of different polymorphs. This “polarization switching” is the strongest evidence to date that the mechanism of NPLIN is not photochemical, since both linearly and circularly polarized light would populate the same electronically excited states in a photochemical excitation. One serious problem with our hypothesis is that the calculated induced-dipole interaction energy, 1/2(∆R)E2 ) 10-4kT, where E is the oscillating optical electric field, ∆R is the solute molecule polarizability anisotropy, k is the Boltzmann constant, and T is the kelvin temperature, is orders of magnitude too small to account for the observed reduction in nucleation time.16 Cooperative effects among many solute molecules in a large solute cluster might account for this discrepancy.17
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To test our hypothesis about the optical Kerr mechanism of NPLIN, we have measured the intensity dependence of NPLIN in supersaturated aqueous urea solutions at 532 and 1064 nm, using both linearly and circularly polarized light. Experimental Section The urea was obtained from Fluka Biochemika and was used without further purification, and the water was obtained from Fisher (environmental grade). For each of the four experiments, 30 identical 11.9 M urea solutions were prepared by dissolving 3.150 ( 0.002 g of urea in 2.00 ( 0.01 g of water in identical 1.3-cm diameter Pyrex test tubes with screw-on caps. Solutions were placed in an ultrasonic heating bath to dissolve at 50 °C. After all the solute was dissolved (2-3 days), the solutions were allowed to slowly reach room-temperature overnight. Solutions were aged from 2 to 4 days before exposure to laser light at 21 °C. Solutions that did not nucleate during the cooling period typically lasted longer than two weeks without spontaneously nucleating. There were sufficient samples that did not nucleate spontaneously to expose 18-20 samples to laser pulses in each of the four experiments. The solubility of urea at 20 °C is 105 g in 100 g water,18 and saturated solutions have a concentration of 9.7 M. An annular laser light beam is generated by a Quanta-ray DCR-1A Q-switched Nd:YAG laser, producing a 10 pulse per second train of linearly-polarized 9-ns laser pulses at 1064 nm. The annular laser beam was sent through a 1.85-mm diameter circular ceramic aperture to select a small circular portion of the beam with roughly constant intensity. The output of this laser can be sent through a KD*P frequency-doubling crystal to generate a train of linearly-polarized 7-ns pulses of light at 532 nm. The linearly polarized light is converted to circular polarization by sending it through a Glan-Thompson prism polarizer followed by a quartz zero-order quarter-wave retardation plate, cut for either 1064 or 532 nm. The laser power was measured with a Coherent LM30-V power meter, designed for high intensity use. The test tubes used have curved walls, and therefore each behaves as a cylindrical lens for the incident laser beam. Based on ray tracing calculations, we estimate that the focusing caused by this curvature increases the laser intensity in the solution by a factor of 2 at both 532 and 1064 nm. The most straightforward method of determining the dependence of nucleation efficiency on laser intensity is to prepare a large number of identical samples, to expose N samples to a given laser intensity, and to note how many samples nucleate at that intensity. If n samples nucleate, then the nucleation probability is n/N. We tried such a procedure and rejected it because random sample-to-sample variations masked the effect of the laser-sample interaction. Instead, we have employed a procedure that is less sensitive to random sample variations but makes several assumptions about the behavior of supersaturated solutions exposed to laser pulses: (1) a sample that nucleates at a given intensity would have also nucleated at higher intensities and (2) a sample that has not nucleated is unaffected by any earlier history of laser exposure.14 We believe that these assumptions are reasonable and are consistent with the solution behavior that we have observed. Each solution was exposed to 1-min trains of laser pulses of increasing intensity of either linearly or circularly polarized light at 1064 or 632 nm, with 20-s pauses between trains. (In developing this procedure, we tried pauses as long as 5 min; no significant differences in nucleation behavior were observed.) The intensity at which each solution nucleated was noted. The observed dependence is illustrated in Figure 1, where we show the nucleation efficiency, that is, the percentage of solutions that nucleated at or below a given intensity, assuming that a solution that nucleated at a low intensity would also have nucleated at higher intensities. It is possible to calculate statistical error limits based on the procedure employed. The analysis is based on a binomial distribution, since a nucleation experiment has only two
Figure 1. Intensity, wavelength and polarization dependence of NPLIN in supersaturated aqueous urea. Red symbols correspond to 1064-nm wavelength; green symbols correspond to 532-nm wavelength. Line symbols are for linear polarization; circles are for circular polarization. Uncertainties in nucleation efficiencies are 10%. possible outcomes: nucleation or no nucleation. For each wavelength/polarization experiment, we irradiate N (18-20) samples at various intensity levels and observe that n of them nucleate at or below a given level. The probability of nucleation at that intensity level is p ) n/N, and its standard deviation is given by σ ) xNp(1-p).19
Discussion The data are a bit noisy because of the relatively small number of solutions per experiment, but the overall trends are clear. In all cases, we observed a nonlinear intensity dependence, with thresholds of about 0.020.06 GW/cm2. At the highest intensities, all induced nucleation efficiencies seem to be converging, indicating that there may be a saturation intensity above which all solutions that are capable of nucleating (i.e., that contain clusters suitable for NPLIN) have nucleated. The 532-nm threshold is lower than the 1064-nm threshold, and the 532-nm nucleation efficiencies at a given intensity are higher than the 1064-nm efficiencies at the same intensity. The optical Kerr effect alone (i.e., the intensity-dependent refractive index) exhibits a quadratic intensity dependence with no intensity threshold;22 however, when coupled to the induction of nucleation, the optical Kerr effect could give rise to a nucleation phenomenon with an intensity threshold. An optical Kerr mechanism for NPLIN predicts equal thresholds and efficiencies at two different wavelengths because the electric field strength of light depends only on intensity and is independent of wavelength. We attribute the observed differences in nucleation efficiency and threshold to the greater absorption coefficient of water in the near-infrared at 1064 nm (0.1 cm-1) compared to that in the green at 532 nm (5 × 10-4 cm-1).20 The greater absorption in the nearinfrared would give rise to greater sample heating, thus reducing the supersaturation, making NPLIN more difficult. Our experiments also suggest that future NPLIN studies of aqueous solutions at 1064 nm should be avoided to reduce solution heating. The thresholds for linearly and circularly polarized light are different at 532 nm and at 1064 nm; the
Intensity, Wavelength and Polarization Dependence
threshold is lower for linear polarization than for circular polarization at both wavelengths. In addition, the nucleation efficiency is significantly higher for linearly polarized light than for circularly polarized light at a given laser intensity at both wavelengths. These differences are consistent with an optical Kerr effect mechanism, since the optical Kerr effect is more effective at aligning rodlike molecules or n-mers with linear polarization than with circular polarization. Urea is known to form rodlike, linear head-to-tail dimers, trimers, and n-mers with parallel CdO bonds and enhanced polarizabilities in the stacking direction.21 For simplicity, we consider the case of a molecule or n-mer of which the polarizability tensor is represented by a prolate ellipsoid of revolution, where ∆R ) Ra - Rb > 0, where a is the ellipsoid rotation axis and b is perpendicular to a. An applied linearly or circularly polarized optical field partially aligns such ellipsoids, resulting in a uniaxial distribution in a laboratory z direction, where z is parallel to a linearly-polarized electric field and perpendicular to a circularly polarized field (i.e., the electric field of linear polarization points in the z direction, while the electric field of circular polarization rotates in the xy plane). An order parameter Kz ) 〈cos2θ〉 describes the extent of this z-alignment, where the polar angle θ is defined as the angle between the molecular a axis and the laboratory z axis. To order E2, Kz is given by 1 2 KLP z ) /3 + (E /(45kT))∆R and 1 2 KCP z ) /3 - (E /(90kT))∆R (1)
where LP and CP indicate linear and circular polarization, respectively. Kz is equal to 1 for perfect z alignment, 0 for perfect x-y alignment, and 1/3 for an isotropic distribution.14,22 In the limit of infinite electric field, linearly polarized light would create perfect z-alignment, in which all ellipsoids would have their a-axes parallel to the z-axis. Circularly polarized light would induce perfect xyalignment, in which all ellipsoids would lie in the xy plane with their a-axes at random azimuthal angles within the xy plane. Alignment with circularly polarized light is thus is a much weaker kind of alignment compared to alignment with linearly polarized light, and this difference remains even for finite electric fields. This optical Kerr picture is consistent with the observed differences in NPLIN thresholds for linearly and circularly polarized light. Summary We have measured the intensity dependence of NPLIN in supersaturated aqueous urea solutions. The higher threshold and lower efficiency in the nearinfrared is attributed to the greater absorption of water at this wavelength. The higher threshold and lower efficiency for circular polarization is consistent with an optical Kerr mechanism of NPLIN in which the optical electric field induces the alignment of solute molecules in a prenucleating cluster. This polarization behavior also provides further evidence that the mechanism of NPLIN is not photochemical. Acknowledgment. Financial support from the National Science Foundation (Grant No. CTS-0210065)
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is gratefully acknowledged. We wish to thank Janice Aber for her advice and helpful discussions. References (1) Myerson, A. S.; Ginde, R. In Handbook of Industrial Crystallization; Myerson, A. S., Ed.; Butterworths: Montvale, MA, 1992. (2) D’Souza, S. M.; Alexander, C.; Carr, S. W.; Waller, A. M.; Whitcombe, M. J.; Vulfson, E. N. Directed nucleation of calcite at a crystal-imprinted polymer surface. Nature 1999, 398, 312-316. (3) Aizenberg, J.; Muller, D. A.; Grazul, J. L.; Hamann, D. R. Direct Fabrication of Large Micropatterned Single Crystals. Science 2003, 299, 1205-1211. (4) Shore, J. D.; Perchak, D.; Shnidman, Y. Simulations of the nucleation of AgBr from solution. J. Chem. Phys. 2000, 113, 6276-6284. (5) Vekilov, P. G. Dense Liquid Precursor for the Nucleation of Ordered Solid Phases from Solution. Cryst. Growth Des. 2004, 4, 671-685. (6) Weissbuch, I.; Popovitz-Biro, R.; Lahav, M.; Leiserowitz, L. Understanding and Control of Nucleation, Growth, Habit, Dissolution and Structure of Two- and Three-Dimensional Crystals Using ‘Tailor-Made’ Auxiliaries. Acta Crystallogr. 1995, B51, 115-148. (7) Leusen, F. J. J. Ab initio prediction of polymorphs. J. Cryst. Growth 1996, 166, 900-903. (8) Weissbuch, I.; Leiserowitz, L.; Lahav, M. Tailor-made and charge-transfer auxiliaries for the control of the crystal polymorphism of glycine. Adv. Mater. 1994, 6, 952-956. (9) Garetz, B. A.; Aber, J. E.; Goddard, N. L.; Young, R. G.; Myerson, A. S. Non-photochemical, polarization-dependent, laser-induced nucleation in supersaturated aqueous urea solutions. Phys. Rev. Lett. 1996, 77, 3475-3476. (10) Tyndall, J. On the Blue Color of the Sky, the Polarization of Skylight and on the Polarization of Light by Cloudy Matter Generally. Philos. Mag. 1869, 37, 384-394. (11) Wen, F. C.; McLaughlin, T.; Katz, J. L. Photo-induced nucleation of supersaturated vapors in the presence of carbon disulfide. Phys. Rev. A 1982, 26, 2235-2242. (12) Okutsu, T.; Isomura, K.; Kakinuma, N.; Horiuchi, H.; Unno, M.; Matsumoto, H.; Hiratsuka, H. Laser-Induced Morphology Control and Epitaxy of Dipara-anthracene Produced from the Photochemical Reaction of Anthracene. Cryst. Growth Des., 2005, 5, 461-475. (13) Okutsu, T.; Nakamura, K.; Haneda, H.; Hiratsuka, H. Laser-Induced Crystal Growth and Morphology Control of Benzopinacol Produced from Benzophenone in Ethanol/ Water Mixed Solution. Cryst. Growth Des. 2004, 4, 113115. (14) Garetz, B. A.; Matic, J.; Myerson, A. S. Polarization switching of crystal structure in the non-photochemical laserinduced nucleation of supersaturated aqueous glycine solutions. Phys. Rev. Lett. 2002, 89, 175501:1-4. (15) Reintjes, J. F. Nonlinear Optical Parametric Processes in Liquids and Gases; Academic Press: New York, 1984. (16) Zaccaro, J.; Matic, J.; Myerson, A. S.; Garetz, B. A. Nonphotochemical, laser-induced nucleation of supersaturated glycine produces unexpected γ-polymorph. Cryst. Growth Des. 2001, 1, 5-8. (17) Oxtoby, D. W. Crystals in a flash. Nature 2002, 420, 207208. (18) Mullin, J. W. Crystallization, 3rd ed.; Butterworth-Heinemann Ltd: Oxford, U.K., 1993. (19) Kennedy, J. B.; Neville, A. M. Basic Statistical Methods for Engineers & Scientists, 3rd ed.; Harper & Row: New York, 1986. (20) Hale, G. M.; Querry, M. R. Optical constants of water in the 200 nm to 200 µm wavelength region. Appl. Opt. 1973, 12, 555-563. (21) Jensen, L.; Astrand, P.-O.; Osted, A.; Kongsted, J.; Mikkelsen, K. V. Polarizability of molecular clusters as calculated by a dipole interaction model. J. Chem. Phys. 2002, 116, 4001-4010. (22) Boyd, R. W. Nonlinear Optics; Academic Press: Boston, MA, 1992.
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