Effect of Dimer Formation on the Growth Cessation ... - ACS Publications

CRYSTAL GROWTH & DESIGN

Effect of Dimer Formation on the Growth Cessation of Polar Organic Crystals Jae Woo

Park,†

Hyung-ki

Hong,†

Kwang-Sup

Lee,‡

and Choon Sup

Yoon*,†

Department of Physics, KAIST, Daeduck Science Town, Daejon 305-701, Korea, and Department of Polymer Science & Engineering, Hannam UniVersity, Daejon 306-791, Korea

2006 VOL. 6, NO. 9 2011-2020

ReceiVed June 14, 2004; ReVised Manuscript ReceiVed December 7, 2005

ABSTRACT: Despite their excellent nonlinear optical, electrooptic, piezoelectric, pyroelectric, photorefractive, and triboluminescent properties, the growth of polar organic crystals of large size and high quality has been hindered by growth cessation phenomena that occur in solution growth. Investigation of the crystal growth behavior of a highly polar organic nonlinear optical material, 3-methyl4-methoxy-4′-nitrostilbene (MMONS), reveals that there exists an upper limit for the solution concentration, above which the crystals stop growing. Electric field induced second harmonic generation measurements show that the solution consists of two species, monomers and dimers of MMONS molecules, at room temperature and that the dimer concentration increases significantly as the solution concentration increases, while the monomer concentration decreases. The corresponding equilibrium constant of a dimer, K, is 0.61 (mol/L)-1. The analysis of UV-visible absorption spectra also confirms the EFISH results. Analysis of the crystal structure shows that dimers attached on the crystal surface may cause a gradual degradation of crystal transparency and a buildup of lattice strain as the solution temperature increases from ∼16-40 °C and may cause the growth cessation at solution temperatures above ∼40 °C. 1. Introduction Because delocalized π-electrons in organic molecules are responsible for very large induced electric polarization, organic materials exhibit much larger nonlinear optical (NLO) responses and faster response time than their inorganic counterparts.1 Most organic chromophores that have a large first-order molecular hyperpolarizability β also have a large ground state dipole moment. When crystallized, NLO molecules are arranged in such a way that the total internal energy of the system is at a minimum. This frequently results in centrosymmetric crystal structures, in which the dipole moments of adjacent molecules cancel each other out, leading to a vanishing macroscopic polarization. However, to observe second-order NLO effects, one must have noncentrosymmetric crystal structures and, as a consequence, most organic NLO crystals have polar structures. The organic crystals of noncentrosymmetric structures also possess interesting physical properties, such as electrooptic, piezoelectric, pyroelectric, photorefractive, and triboluminescent properties.2 To explore and utilize such properties, it is necessary to grow polar organic crystals of large size and high quality. Despite much effort, however, little progress has been made. The difficulty lies in the following: (i) the crystals grow only in one polar direction in solutions of low solute concentration and (ii) they cease to grow at even a moderate concentration. The overall effect is the growth of crystals of very small size. Such unidirectional growth and growth cessation seem to occur frequently in polar organic crystals and have been reported in a number of polar organic NLO crystals, including m-nitroaniline (mNA),3 2-(N-cyclooctylamino)-5-nitropyridine (COANP),4 N-(4nitrophenyl)-L-prolinol (NPP),5 (-)-2-(2-methylbenzylamino)5-nitropyridine (MBANP),6 4-nitro-4′-methylbenzylideneaniline (NMBA),7 and 3-methoxy-4-hydroxybenzaldehyde (MHBA).8 The unidirectional growth9 of MMONS crystals can be explained by the molecular recognition concept suggested by * To whom correspondence should be addressed. Phone: +82-(42)-8692532. Fax: +82-(42)-869-5532. E-mail: [email protected]. † KAIST. ‡ Hannam University.

Figure 1. ORTEP diagram of a MMONS molecule. Hydrogen atoms are omitted for simplicity.

Leiserowitz et al.10,11 However, the cause of the growth cessation remains unknown and the problem poses a major obstacle for the growth of polar organic crystals. MMONS crystals are highly polar and show extremely large second-order NLO effects, the second harmonic powder efficiency of which is about 1250 times larger than that of urea.12 The second-order NLO coefficients of MMONS are d31 ) 16.6 pm/V, d32 ) 42.4 pm/V, and d33 ) 173 pm/V at 1064 nm.13 In this paper, we investigate the cause of the growth cessation in a polar organic crystal, 3-methyl-4-methoxy-4′-nitrostilbene (MMONS), using the electric field induced second harmonic (EFISH) generation method14-16 and UV-visible absorption spectroscopy17 based on the singular value decomposition (SVD) method.18,19 2. Crystal Growth of MMONS Figure 1 shows the molecular structure of MMONS, which is almost planar. The ground-state dipole moment lies along the line joining the electron-acceptor nitro functionality to the electron-donor methoxy functionality, and its magnitude is 5.2 D in p-dioxane.20 The molecular polarizability and first- and second-order molecular hyperpolarizabilities are 3.7 × 10-23, 26 × 10-30, and 96 × 10-36 esu, respectively, at a wavelength of 1.91 µm.20 MMONS crystals have an orthorhombic structure and belong to the point group mm2 and space group Aba2 (No.

10.1021/cg0498103 CCC: $33.50 © 2006 American Chemical Society Published on Web 08/08/2006

2012 Crystal Growth & Design, Vol. 6, No. 9, 2006

Figure 2. Solubility curve of a MMONS solution in MEK and the number ratio of MEK to MMONS molecules in the saturated solution.

41). The unit cell parameters are a ) 15.750 Å, b ) 13.470 Å, c ) 13.356 Å, and V ) 2833 Å3, with Z ) 8 and F ) 1.262 g/cm3.21 MMONS was synthesized by the Wittig reaction of diethyl p-nitrobenzylphosphonate and 3-methyl-p-anisaldehyde and purified by fivefold recrystallization, followed by liquid column chromatography using silica gel as a stationary phase. The purity of the end product was 99.9%, checked by gas chromatography and mass spectroscopy. MMONS crystals were grown from various solvents by slow solvent evaporation at room temperature, and details of the growth characteristics are reported by the authors in ref 9. Among the 10 solvents used, including polar and nonpolar solvents, only methyl ethyl ketone (MEK), ethyl acetate, and acetone yielded unidirectional growth. The observed unidirectional growth of MMONS crystals in the three solvents was well explained by the solvent-poisoning mechanism on the (001h) face,9 using the molecular recognition concept, which was suggested by Leiserowitz et al.10,11 In Figure 2, the solubility of MMONS in MEK solution is shown by the solid line, and the number ratio of MEK to MMONS molecules in the saturated solution is indicated by the dotted line. Figure 3a shows a MMONS crystal that was grown in MEK solution using a low-temperature solution growth method. The initial and final growth temperatures were 26.8 and 16.7 °C, respectively, and the temperature lowering rate ranged from 0.07 to 0.3 °C/day, depending on the stage of the growth. The growth period was about 37 days in all. The as-

Park et al.

grown crystal was large (38 × 33 × 30 mm3) and was of excellent quality (Figure 3a), as evidenced by X-ray topography.9 Below ∼40 °C, MMONS crystals grew unidirectionally in the +c direction (Figure 3b), which can be explained by the concept of molecular recognition.10,11 As the solution temperature increased, the transparency of the as-grown MMONS crystals gradually became degraded, from transparent (∼1627 °C) to translucent (∼28-35 °C) to opaque (∼36-40 °C), but the crystals maintained unidirectional growth. However, above ∼40 °C, MMONS crystals did not grow at all, even if a high degree of supersaturation was established. As the supersaturation increased above 4.9%, polycrystalline aggregates of a coral reef shape started to attach on the seed crystal. Such growth cessation was also observed in the bulk growth of 2-(R-methylbenzylamino)-5-nitropyridine22 (MBANP) crystals. No study has yet been reported on the fundamental causes of the growth cessation in polar nonlinear organic crystals. As shown in Figure 2, as the temperature increases, the number of MEK molecules per MMONS molecule falls. The number of MEK molecules available for surrounding a MMONS molecule is about 26 at 20 °C and decreases to about 12 at 40 °C. Therefore, there may not be sufficient MEK molecules to surround a MMONS molecule above 40 °C and the chances of forming dipole pairs (dimers) and trimers become increasingly high because of the large dipole moment. Once the dimers and trimers are formed in the solution and they are attached at growth sites on the crystal surface, MMONS molecules can no longer attach at the growth sites, and this may lead to the observed growth cessation in MMONS crystals at high concentration. In this paper, we investigate the cause of the growth cessation in MMONS crystals using the dimer model by the EFISH method and UV-visible absorption spectroscopy. 3. Electric Field Induced Second Harmonic (EFISH) Measurements The EFISH method14-16 was used to probe the existence of dimers of MMONS molecules and to monitor their concentration as a function of temperature. Although a MMONS molecule has a large value of first-order molecular hyperpolarizability β, MMONS solution does not show second harmonic generation (SHG) because the second-order nonlinear susceptibility χ(2) vanishes in a centrosymmetric medium. However, if an external

Figure 3. (a) MMONS crystal grown from methyl ethyl ketone solution. The fine scale indicates 2.5 mm. (b) Schematic diagram of the morphology of the MMONS crystal in (a).

Growth Cessation of Polar Organic Crystals

Crystal Growth & Design, Vol. 6, No. 9, 2006 2013

between the two linear media 1 and 3. The electric field of the second harmonic wave in medium 3 was obtained using the method of Kajzar et al.24 In the plane wave approximation, the electric field of the second harmonic wave in medium 3 is expressed as (3)

E2ω,t Figure 4. Schematic illustration of EFISH for the low- and highconcentration solutions: (a) dilute solution containing only monomers without applying a field; (b) dilute solution containing only monomers with an applied field; (c) high-concentration solution containing monomers and dimers with an applied field.

(2) (2) (2) (2) eiφfE(2) b nω cos θ2ω + nω cos θω [ei(φb-φf) - 1] (1) ) -HC

where

[

]

RL BD exp exp[2iRe{φf}] (2) AC cos θ2ω

H)1-

(2)

The phase factors of the free and bound waves, φf and φb, are

φf )

(2) 2ωn2ω R L (2) L cos θ2ω +i c 2 cos θ(2)

2ω

φb )

2ωn(2) ω L cos θ(2) ω c

where R is the absorption coefficient of the free and reflected waves in medium 2. The coefficients A-D in eq 2 are expressed, respectively, as (1) (2) (2) (1) A ) n2ω cos θ2ω + n2ω cos θ2ω (1) (2) (2) (1) B ) -n2ω cos θ2ω + n2ω cos θ2ω

Figure 5. Second harmonic wave propagation in a nonlinear medium between two linear media.

(3) (2) (2) (3) C ) -(n2ω cos θ2ω + n2ω cos θ2ω ) (3) (2) (2) (3) D ) n2ω cos θ2ω - n2ω cos θ2ω

electric field is applied to the MMONS solution, the dipole moment of the MMONS molecules tends to align with the direction of the field to minimize the potential energy, and the medium becomes noncentrosymmetric and, therefore, can produce SHG. Using the EFISH technique, the hyperpolarizability of organic molecules can be determined by analyzing Maker fringes that are formed by the interference of bound and free second harmonic waves.23 In general, the EFISH measurement is performed in a dilute solution in which no molecular aggregation exists. The higher the concentration of the solution, the stronger the SHG signal is expected to be, because there are more polarized sources. However, as the concentration of the solution increases further, the number of solvent molecules becomes less than the minimum number of the solvent molecules required for complete surrounding of a solute molecule and, therefore, molecular aggregations, such as dimer, trimer, etc., start to form. As the concentration of the solution increases, the probability of forming dimers is much higher than that for trimers or higher-order aggregations. When highly polar molecules, such as MMONS, form dimers, they tend to assemble a dipole pair with the direction of the two dipoles being opposite to each other, which is the lowest energy state. Therefore, the ground-state dipole moment of the dimers vanishes and the dimers become almost inactive in response to an external field. If dimers exist in the solution, the SHG signal from a solution of higher concentration will be weaker than that from one of lower concentration, because the dimers do not participate in the SHG due to their symmetric structure, as shown in Figure 4. As shown in Figure 5, the fundamental beam of p polarization, (1) E,ωi , is incident upon nonlinear medium 2, which is placed

(4)

24 The electric field of the bound wave, E(2) b , is given by

E(2) b )

4πPNL eff (2) 2 2 (n(2) ω ) - (n2ω)

(5)

16 The effective nonlinear polarization, PNL eff , is given as

(2) 2 (2) PNL eff ) 3ΓE0(Eω ) sin θω

(6)

where E0 is the applied electric field, Γ is the macroscopic thirdorder susceptibility of the solution, 3 is the degeneracy factor, and θ(2) ω is the angle between the direction of the beam path and that of the electric field. The third-order susceptibility, Γ, is given as14

Γ ) f(NMMONSγMMONS + NMEKγMEK)

(7)

where NMMONS and NMEK are the numbers of MMONS and MEK molecules per unit volume, and γMMONS and γMEK are the molecular hyperpolarizabilities of MMONS and MEK molecules, respectively. f is the local field factor of the solution, which is represented as15

f)

(

)

nω2 + 2 2n2ω2 + 2 (∞ + 2) ‚ 3 3 ∞ + 2

(8)

The first two terms are the Lorentz correction factors for the optical fields at ω and 2ω, respectively, and the last is the Onsager field factor. and ∞ are the dielectric constants of the solution at low frequency and optical frequency, respectively.


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Table 1. Physical Parameters of MMONS-MEK Solutions of Several Concentrations MMONS concn (mol/L) 0 0.0462 0.217 0.414 0.535 0.649 0.757

saturation temp (°C)

refractive index at 1064 nm

abs coeff at 532 nm (cm-1)

dielectric constant at 10 kHz

20.5 29.5 34.5 39.5

1.373 78 1.377 18 1.389 73 1.404 25 1.413 18 1.421 59 1.429 55

0 0.002 0.064 0.182 0.288 0.408 0.536

21.2 24.0 18.0 17.8 17.7 18.1 18.6

We used nω2 for ∞ in the estimation of the Onsager field factor. The second-order molecular hyperpolarizability, γ, is given as20

γ ) γe + γv +

µβ 5kT

(9)

where γe and γvdenote the electronic and vibrational contributions, respectively, and µβ/5kT represents the dipolar orientational contributions. The magnitude of the electronic and vibrational contributions is about 13% of the total contribution to γ in MMONS.20 The rest comes from the dipolar orientational contributions. From eqs 1, 5, and 6, it can be seen that the electric field of the second harmonic wave in medium 3 is proportional to the third-order susceptibility, Γ, from which the number of MMONS molecules, NMMONS, can be derived using eqs 7 and 8. If we measure the second harmonic signal from the MMONS solution of various concentrations, we can quantify the MMONS dimers by fitting the experimental data as a function of solution concentration. The physical parameters of the MMONS solutions in MEK are summarized in Table 1. The refractive index at 1064 nm and the absorption coefficient at 532 nm were measured using a Mach-Zender interferometer method25 and a UV-visible spectrometer (JASCO inc., V-530), respectively. The dielectric constant was measured at 10 kHz using an impedance analyzer (HP4192A). We designed a sample cell for EFISH measurements by modifying that of Uemiya et al.,16 with the particular purpose of keeping MEK from evaporating, as shown in Figure 6a. Figure 6b shows the schematic diagram of the cell, where θt is the angle between the wall of the cell and the plane of ITO glasses. The solution between the two ITO glasses acts as a nonlinear medium on which the fundamental wave is incident with an angle of θω. The thickness of ITO glasses, the spacers between ITO glasses, and the wall of the cell were 1.1, 1.0, and 1.175 mm, respectively. The path length of the cell was 10 mm. The temperature of the cell was controlled within (0.5 °C. The overall experimental setup for EFISH measurements is shown in Figure 7. A Q-switched Nd:YAG laser (Spectron Laser Systems, SL854G) of 15.8 ns pulse width and 10 Hz repetition rate was used as a fundamental light source, which operated at a wavelength of 1.064 µm. The SHG signal was detected by a photomultiplier tube and a boxcar integrator. A half-wave plate and a polarizer were used to control the polarization and intensity of the fundamental beam. Filter 1 was used for blocking the visible light from flash lamps of the Nd:YAG laser. A collimated Gaussian beam of 1.7 mm diameter and 33 MW/ cm2 peak intensity was obtained using a combination of a planoconvex lens and a plano-concave lens. Filter 2 was used to cut the fundamental beam completely, and filter 3 allowed only the SHG signal to pass. For the EFISH measurements, a pulsed electric field of a width ranging from a few microseconds to a few milliseconds was applied to prevent current flow in the

Figure 6. (a) Sample cell and (b) schematic diagram of the cell.

Figure 7. Setup for EFISH measurements. Legend: PH, pinhole; M, mirror; HWP, half-wave plate; P, polarizer; F1, IR pass filter; S, sample; RS, rotational stage; F2, IR cut filter; F3, 532 nm narrow pass filter; PMT, photomultiplier tube.

solution.26 A function generator (Tektronix, AFG310) that was synchronized with the pump laser produced a square pulse of 0.4 V height and 500 µs duration, followed by amplification using a high-voltage amplifier (Trek, 20/20b) to 800 V to supply an electric field of 800 V/mm. Maker fringes for a solution concentration of 0.414 mol/L are shown in Figure 8. The solid circles represent experimental data. Because the position of the center of the Maker fringes, the interval between the fringes, and the envelope of the fringes are related to θt, n2ω, and Γ, respectively, the solid line was obtained by adjusting θt, n2ω, and Γ and taking into consideration the transmission of the fundamental and SHG beams at the interfaces so that |E2ω|2 in eq 1 may fit the experimental data well. The fitted parameters and the related values for various concentrations are summarized in Table 2.



Figure 8. Maker fringes for a solution concentration of 0.414 mol/L.

Figure 9. Dependence of Γ/f on the concentration of MMONS. The solid circles represent experimental data. The dashed and solid lines are the fitted curves according to eqs 7 and 13, respectively.

Table 2. Fitted Parameters and Related Values MMONS concn (mol/L)

Γ (au)

0 0.0462 0.217 0.414 0.535 0.649 0.757

1.1 × 10-3 2.0 × 10-3 4.8 × 10-3 7.8 × 10-3 9.4 × 10-3 1.1 × 10-2 1.3 × 10-2

n2ω

local field factor, f

Γ/f (au)

NMEK (mol/L)

1.383 66 1.389 92 1.408 61 1.427 65 1.439 94 1.451 98 1.461 99

4.08 4.14 4.25 4.44 4.56 4.68 4.80

2.70 × 10-4 4.83 × 10-4 1.13 × 10-3 1.76 × 10-3 2.05 × 10-3 2.33 × 10-3 2.60 × 10-3

11.2 11.1 10.9 10.4 10.1 9.76 9.49

γMEK was calculated from the values of Γ/f and NMEK for pure MEK using eq 7. Γ/f is plotted as a function of MMONS concentration in Figure 9, in which the solid circles represent experimental data. Assuming that all the MMONS molecules in the solution exist in the monomer state, eq 7 was fitted to the experimental data, which is represented by a dashed curve in Figure 9. The fitting result shows an almost linear dependence, because the contribution of the MMONS molecules to SHG is dominant over that of MEK. However, the dashed curve shows a significant difference from the experimental data, which indicates that the assumption of all the MMONS molecules being in the monomer state may fail. If some of the MMONS molecules should exist in the dimer state, the number of MMONS monomers per unit volume, Nmonomer (mol/L), and the number of MMONS dimers per unit volume, Ndimer (mol/L), satisfy the relationship

NMMONS ) Nmonomer + 2Ndimer

(10)

and, at thermodynamic equilibrium between the monomers and dimers, the equilibrium association constant,17 K, is defined as

K)

Ndimer N2monomer

(11)

From eqs 10 and 11, Nmonomer is expressed as

Nmonomer )

-1 + x1 + 8KNMMONS 4K

(12)

On the basis of the earlier assumption that the MMONS dimers form dipole pairs and, therefore, do not contribute to SHG, the dependence of Γ/f on the solution concentration can be fitted by

Γ ) (Nmonomerγmonomer + NMEKγMEK) f

(13)

Figure 10. Fraction of MMONS molecules in the monomer state and those in the dimer state as a function of concentration and saturation temperature.

with the fitting parameters, γmonomer and K. The solid line in Figure 9 represents the fitted curve, and K was estimated to be 0.61 (mol/L)-1. As shown in Figure 9, the solid line agrees very well with the experimental data, which provides strong evidence for the existence of MMONS molecules in the dimer state. Nmonomer and Ndimer were calculated from eqs 10 and 11 using the K value. In Figure 10, the upper and lower curves represent the fractions of MMONS molecules in monomer and dimer states, respectively, as a function of concentration and saturation temperature. At a solution temperature of 20 °C, below which temperature MMONS crystals are grown normally, only 27% of the MMONS molecules exist in the dimer state. However, the fraction of MMONS molecules in the dimer state increases to 37% at 40 °C, above which growth cessation of the MMONS crystal starts to occur. The present study shows clearly that the dimer concentration increases as the concentration of MMONS in the solution increases and suggests strongly that the observed growth behavior of MMONS crystals may be related to the dimer concentration of MMONS molecules in the solution. Figure 11 shows the number ratio of dimer to monomer per unit volume, Ndimer/Nmonomer. When the dimer concentration was low at temperatures below ∼25 °C, the MMONS crystal grew to be highly transparent and maintained the unidirectional growth. As the dimer concentration increased due to the temperature of the solution being raised above ∼25 °C, the unidirectional growth behavior of polar morphology was maintained, but the transparency of the grown crystal gradually became degraded to be translucent in the solution temperature range of ∼28-35 °C and to be opaque in the solution temperature range of ∼36-40


Figure 11. Number ratio of MMONS dimer to monomer per unit volume, Ndimer/Nmonomer.

Figure 12. Schematic view of the layer structure of MMONS molecules. Carbon atoms are shown in blue, oxygen in red, and nitrogen in green. Hydrogen atoms are omitted for simplicity. Numbers indicate the relative positions of the layers.

°C. As the dimer concentration increased above a certain level at temperatures higher than ∼40 °C, the MMONS crystals stopped growing. The observed degradation of transparency below ∼40 °C and growth cessation behavior above ∼40 °C may be explained by incorporating the MMONS dimers onto the crystal lattice. Figure 12 shows a layer structure of the MMONS crystals, where the numbers indicate the relative position of the layers. The planar MMONS molecules are arranged in such a manner that they are almost parallel to each other. When they are viewed along the line bisecting the a and b axes (Figure 13a), the methoxy (electron donor) and nitro (electron acceptor) groups of MMONS molecules are placed in the order of methoxy-nitro-nitromethoxy in the region marked by an oval. If the c axis is raised from the plane of the paper by ∼45°, the relative positions of MMONS molecules may be identified more clearly, as shown in Figures 13b,c, where an MMONS molecule is represented by an arrow that denotes the direction and position of the dipole moment of the molecule. Because an MMONS molecule lies over two sites marked by an oval, the dipole moment starts from one oval and ends at the other neighboring oval. The colors stand for the relative position of a MMONS molecule along

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the c axis with red, blue, green, and pink indicating the order of higher position, respectively. The numbers indicate the relative position of the molecular layers to which the molecules belong, as indicated in Figure 12. The higher the dimer concentration, the greater the probability that the dimers will attach to the crystal surface. If a dimer, represented by a dipole pair in orange in Figure 13c, attaches over sites B and C, the MMONS molecule in green, which is placed over sites B and D in Figure 13b, cannot attach because the dimer occupies a part of the space of the second layer at site B. For the same reason, the MMONS molecule in pink in the second layer at site C in Figure 13b cannot attach either. Therefore, two MMONS vacancies are generated for a single dimer being attached, apart from the thermodynamic vacancies. At very low dimer concentration with low supersaturation, the slow crystal growth process at the crystal-solution interface is able to reject the dimers as impurities. Hence, the MMONS crystals grow unidirectionally with high crystal transparency, and this was observed in growth at temperatures below ∼27 °C. As the dimer concentration increases from low to moderate, the dimers become increasingly incorporated onto the crystal lattice, which causes severe lattice distortion, with the generation of vacancies amounting to twice the number of the dimers attached. The dimers and vacancies in the crystal can act as scattering centers of light. As a consequence, a gradual degradation of the crystal transparency and a buildup of lattice strain result, but still the unidirectional growth behavior and polar morphology are maintained, as observed in the solution temperature range of ∼28-40 °C. The MMONS crystal grown in the temperature range of ∼28-35 °C from methyl ethyl ketone solution was translucent, and the crystal grown in the temperature range of ∼36-40 °C was opaque (Figure 14). The lattice strain can be probed by the X-ray topography technique. Figure 15 shows a transmission X-ray topograph of the 002 reflection using the (100) plane of the MMONS crystal that was grown in the temperature range of ∼30-35 °C. Although the X-ray topograph reveals a number of mixed-type dislocations and a growth sector boundary that runs from top to bottom, herringbone shape features on both sides of the growth sector boundary indicate clearly that the lattice is highly strained, which contrast with the lower degree of strain observed in the topograph of the MMONS crystal that was grown at temperatures below 30 °C.9 Similar results were reported for an MBANP crystal that was grown at ∼35 °C, but no explanation was given for why the crystal was so strained.22 If the dimer concentration becomes high, a significant number of the dimers incorporate onto the growth sites of the crystal surface and will eventually poison all the crystal faces. This process resulted in the cessation of growth in the MMONS crystals observed at solution temperatures above ∼40 °C. 4. UV-Visible Absorption Spectroscopy To confirm the EFISH results, UV-visible absorption spectra were measured and analyzed using the molecular exciton model27 and the Beer-Lambert law.28 The molecular exciton model shows that the UV-visible absorption spectrum of a dimer is different from that of a monomer, because of their distinct excited states. The absorption coefficient in a solution satisfies the Beer-Lambert law

log

Iin ) εCL ≡ A Iout

(14)

where Iin and Iout are the intensities of the input and output



Figure 13. (a) MMONS crystal structure. The c axis lies in the plane of the paper, and the a and b axes lie above the plane of the paper, making an angle of 45° with the plane. (b) Schematic diagram of the MMONS crystal structure. An MMONS molecule is represented by an arrow, which denotes the direction and position of the dipole moment of the molecule. The colors stand for the relative position of a MMONS molecule along the c axis, with red, blue, green, and pink representing the order of higher position, respectively. The numbers indicate the relative position of the molecular layers to which the molecules belong, as indicated in Figure 12. (c) If a dimer, represented by a dipole pair in orange, attaches over sites B and C, the MMONS molecule in green, which is placed over sites B and D in Figure 13b, cannot attach because the dimer occupies a part of the space of the second layer at site B. For the same reason, the MMONS molecule in pink in the second layer at site C in Figure 13b also cannot attach.

beams, ε is the molar extinction coefficient, C is the concentration of the solution, L is the beam path length, and A is the

optical density. If there exists only one species among monomer, dimer, and trimer in the solution, ε is constant even if the


Park et al.

Figure 17. UV-visible absorption spectra for various concentrations. Squares, circles, triangles, and spades represent experimental data, and solid curves represent calculated values. Figure 14. MMONS crystal grown in the temperature range of ∼3640 °C from methyl ethyl ketone solution. The fine scale mark indicates 1 mm.

Figure 18. Spectral singular vectors in the wavelength range 505518 nm. The numbers indicate the corresponding singular values. Figure 15. Transmission X-ray topograph for the 002 reflection using the (100) plane of an MMONS crystal that was grown in the temperature range of ∼30-35 °C in methyl ethyl ketone solution. g ) diffraction vector.

Figure 16. UV-visible absorption spectrum of MMONS in an MEK solution of very low concentration, 4.65 × 10-5 mol/L.

concentration changes. However, if more than two species coexist in the solution, ε varies as a function of solution concentration, because each species has a different molar extinction coefficient and different molar fraction as the concentration changes. UV-visible absorption spectra of the MMONS-MEK solution were measured using a spectrophotometer (JASCO, V-530) and a fused quartz cell with a 10 mm path length. Figure 16 shows the absorption spectrum of MMONS in a MEK solution

of very low concentration, 4.65 × 10-5 mol/L. The absorption spectra of medium and high concentrations are shown in Figure 17 in the wavelength range of 505-518 nm. Squares, circles, triangles, and spades represent experimental data, and solid lines represent theoretical values. The absorption was too high to detect the transmitted signal at wavelengths shorter than 505 nm, even with ∼100 µm path length. The number of species that contribute to the absorption spectra was determined by the singular value decomposition (SVD) method.18,19 A 14 × 6 matrix (14 wavelengths in the wavelength range of 505-518 nm and 6 concentrations) was set up for the SVD of the absorption spectra, as shown in Figure 16, and six singular values were obtained: 4.94, 0.107, 7.11 × 10-3, 1.80 × 10-4, 1.48 × 10-4, and 7.28 × 10-5. The spectral singular vectors corresponding to the six singular values are depicted in Figure 18. The first two singular vectors in parts a and b are noise-free. The third singular vector in part c comprises a degree of noise but still contains significant spectral information. Parts d-f are regarded as pure noise. Therefore, the three species corresponding to the singular vectors (parts a-c) are regarded as being responsible for the absorption spectra in Figure 17. The experimental data for the molar extinction coefficient, ε0, at 505 nm as a function of solution concentration also confirm the existence of more than one species. In Figure 19, the solid circles and the solid line represent the experimental data and fitted curve, respectively. If only one species exists in the solution, ε0 is constant even if the solution concentration varies. However, as shown in the figure, the significant departure of ε0 from a constant value indicates the existence of more than one species.



solid curves in Figure 17. As shown in Figure 17, the theoretical curves are in good agreement with the experimental data, which strongly supports the monomer-dimer model on the basis of the EFISH measurements. 5. Conclusions

Figure 19. Concentration dependence of the extinction coefficient, 0, at 505 nm.

We chose a highly polar organic nonlinear optical material, 3-methyl-4-methoxy-4′-nitrostilbene, for the investigation of growth cessation that occurs in high-concentration solution. The results of EFISH measurements, on the basis of the monomerdimer equilibrium model, show that as the solution concentration increases, the fraction of MMONS molecules in the dimer state increases from 27% at 20 °C to 37% at 40 °C, while that in the monomer state decreases. The corresponding equilibrium constant of a dimer, K, is 0.61 (mol/L)-1. An analysis of UVvisible absorption spectra, using the singular value decomposition method, also confirms the EFISH results. The degradation of crystal transparency in the low- and medium-concentration solution was explained by incorporation of the dimers onto the crystal lattice as impurities, and the growth cessation in the highconcentration solution was by poisoning of the crystal surface by the dimers. The information presented here may be of considerable relevance to the growth of other polar organic crystals. Acknowledgment. This work was supported by the basic research fund of KAIST. References

Figure 20. Molar extinction coefficients of the MMONS monomer and dimer.

Considering that the third singular value is only 1/695 of the first one and 1/15 of the second one, the third singular vector may be neglected without much loss of spectral information. If we take into account only two species, monomer and dimer, the optical density is represented as17

A ) L(ε1Nmonomer + ε2Ndimer) ) ε0NMMONSL

(15)

where ε1 and ε2 are the molar extinction coefficients of the monomer and dimer, respectively, and NMMONS is the total number of MMONS molecules per unit volume in the unit of mol/L. Using eqs 10 and 11, 0 is obtained from eq 15 as

0 )

1 NMMONS

{

-1 + x1 + 8KNMMONS + 4K

1

(

)}

- 1 + x1 + 8KNMMONS 1 ε2 NMMONS 2 4K

(16)

The fitted curve in Figure 19 was obtained using eq 16 by adjusting the parameters, 1 and 2, and using the equilibrium constant K ) 0.61 (mol/L)-1, which was estimated for the monomer and dimer of MMONS molecules in part 3. The fact that the solid curve agrees very well with the experimental data demonstrates that the model of the dimer is adequate for the description of the MMONS solution structure. The fitting parameters, 1 and 2, are shown in Figure 20 in the wavelength range of 505-518 nm. Knowing the values of 1, 2, and the equilibrium constant K, the absorption coefficients of the solution in the wavelength range of 505-518 nm were calculated using eq 15, and the absorption spectra are drawn as

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Effect of Dimer Formation on the Growth Cessation ... - ACS Publications

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