J. Phys. Chem. B 2008, 112, 9883–9889
9883
Aggregation Behavior and Chromonic Liquid Crystal Phase of a Dye Derived from Naphthalenecarboxylic Acid Michelle R. Tomasik and Peter J. Collings* Department of Physics and Astronomy, Swarthmore College, Swarthmore, PennsylVania 19081 ReceiVed: April 25, 2008; ReVised Manuscript ReceiVed: May 28, 2008
Polarizing microscopy, X-ray scattering, and absorption spectroscopy are used to investigate the aggregation process and chromonic liquid crystal of the anionic compound Bordeaux dye, a product of the sulfonation of the dibenzimidazole derivative of naphthalenetetracarboxylic acid. Polarizing microscopy reveals that the liquid crystal phase forms at room temperature when the concentration is only about 6 wt%, a value lower than what is found in many aggregating systems. The X-ray results indicate that the aggregation is via columns, with a cross-sectional area about 2.5 times larger than the individual molecule. Absorption spectroscopy shows a significant change in the absorption spectrum due to aggregation, which is nicely explained by a simple theory of isodesmic aggregation and excitonic coupling between the molecules in an aggregate. The “stacking free energy change” for a molecule in an aggregate relative to a molecule in solution is estimated to be about 9 kBT, a larger value than that found in the one other system where it has been estimated. 1. Introduction Liquid crystals are fluids with orientational order and sometimes positional order as well. As such, they represent a type of complex fluid or soft matter. There are two main classes of liquid crystals, thermotropic and lyotropic. Thermotropic liquid crystals are composed of liquid-crystal-forming molecules and undergo phase transitions in response to temperature changes. Lyotropic liquid crystals are composed of liquidcrystal-forming molecules and a nonliquid-crystal-forming solvent. These systems undergo phase transitions in response to both concentration and temperature changes. Typical lyotropic liquid-crystal-forming molecules are rod-like and amphiphilic (containing both hydrophilic and hydrophobic groups). Orientational and positional order occurs in these systems mainly due to the segregation of the hydrophobic parts of the molecules away from the polar solvent. Hence, soaps form spherical micelles, and phospholipids form spherical vesicles in aqueous solutions at low concentration. Both form more highly ordered structures at higher concentration. Frequently, a critical micelle concentration (cmc) exists, below which no micelles form. Another type of lyotropic liquid crystal has been known for some time, but only recently has interest in it started to grow. These liquid-crystal-forming molecules are only weakly amphiphilic and are disk-like, with a polyaromatic central core and hydrophilic ionic groups on the outside. In a polar solvent, the molecules tend to aggregate into stacks due to both weak van der Waals interactions between the cores (π-π stacking) and the hydrophobic effect. Instead of exhibiting a critical micelle concentration, these systems show isodesmic aggregation. At all concentrations, there is some degree of aggregation. As the concentration increases, the distribution of aggregate size shifts to higher and higher numbers of molecules in the aggregates. If the concentration is high enough to form large and interacting rod-like aggregates, liquid crystal phases form. The stability of these phases depends on both temperature and concentration, and both a nematic phase with just orientational order and a * To whom correspondence should be addressed. E-mail: PCOLLIN1@ swarthmore.edu. Fax: 610-328-7895.
columnar phase with hexagonal packing have been observed. These systems have been named chromonic liquid crystals due to the fact that often the molecules are dyes. Further background information on chromonic liquid crystals is available in the review article by Lydon.1 The properties of chromonic liquid crystals differ markedly from other lyotropic liquid crystals. This means that there is a great deal to be explained as far as the science of these systems is concerned, but it also indicates that new applications are possible. As a result, some recent investigations sought to synthesize new molecules2 or study fundamental properties such as the fluctuations associated with the liquid crystal to isotropic liquid transition.3 This was followed by work on the oriented monolayers that could be formed with these materials4 and the phase changes induced by adding various salts to the solution.5 Further investigations utilized both optical and X-ray measurements on aligned liquid crystal samples.6,7 Finally, there have been reports of worm-like micellar formation in one chromonic liquid crystal,8 an X-ray microscopy study of the textures in the dried films formed by these systems,9 and an effort to immobilize the chromonic liquid crystal structure with a sol-gel process.10 Theoretical investigations relevant to chromonic liquid crystals started with the consideration of uniform rods or spherocylinders that interact through the excluded volume effect.11,12 Also germane was the conventional theory of linear aggregation due to pairwise attraction.13 Later, theorists considered the aggregates to be self-assembling systems, calculating hard-core potentials, short-range repulsions, and an energy contribution for each pair of molecules.14,15 A distribution of aggregate size was predicted, along with a transition from the isotropic to nematic phase at high concentration. More recently, a Monte Carlo simulation of a mixture of model chromonic and water molecules has been performed.16 As the volume fraction of chromonic molecules increased, the average number of molecules per aggregate increased, reaching about 10 for a volume fraction of 0.1. One model for the chromonic molecule produced a columnar phase, while another model did not. Very recently, a chromonic liquid crystal system has been examined theoreti-
10.1021/jp803648g CCC: $40.75 2008 American Chemical Society Published on Web 07/23/2008
9884 J. Phys. Chem. B, Vol. 112, No. 32, 2008 cally, showing that aggregation can cause a strong enhancement of light-induced director orientation, a phenomenon that has been observed in a number of dye-doped liquid crystal systems.17,18 Applied work has generally been in two areas, the fabrication of thin films that can be used as optical polarizers and retarders and utilizing the nematic phase to facilitate the detection of immune complexes. The thin film work has the longest history since it has been known for awhile that the orientation of the nematic phase can be maintained in a thin dry film on a solid substrate.19 As polarizers, these films allow the polarization parallel to the optic axis to pass and are therefore called E-type polarizers, as opposed to conventional O-type polarizers that absorb the polarization parallel to the optic axis.20–22 These films also achieve high retardation in the neighborhood of the absorption and therefore can be used as optical retarders.23,24 The work on immune complex detection is based on the fact that chromonic liquid crystals are aqueous solutions and that the growth of an immune complex disrupts the orientational order of the nematic phase. If a well-ordered nematic phase is placed between crossed polarizers, the perturbation of the orientational order due to the growth of the immune complex is detected by increased light transmission in the neighborhood of the complex.25,26 There are many aspects of chromonic liquid crystal systems worthy of study, but two of the most important are the structure of the aggregates and the nature of the aggregation process. While phase diagrams and optical parameters have been studied in a number of different systems, information on the aggregate structure and aggregation process is extremely scarce. X-ray studies have been carried out on a number of dye systems, and a peak corresponding to the 0.34 nm repeat distance between molecular planes is always present. This separation is similar to the distance between planes in graphite and base pairs in DNA. X-ray measurements on a more limited number of chromonic liquid crystals have revealed that the stacking is columnar, with a cross-sectional area approximately equal to the area of a single molecule 6,27,28 or larger than the area of a single molecule.29,30 Investigations into the nature of the aggregation process are extremely few in number. The behavior of the disodium chromoglygate system was also examined through the addition of salt to the solution, revealing some general aspects of the aggregation process.5 Investigations of the dependence of the absorption spectrum on concentration have been useful in verifying the isodesmic nature of the aggregation process in C. I. Direct Blue 67,28 Sunset Yellow FCF,6 and Blue 27 and Violet 20.7 In the case of Sunset Yellow FCF, the spectral changes were analyzed in order to estimate the “stacking free energy change”, that is, the difference in free energy of a single molecule in solution relative to that of a molecule in an aggregate.6 Clearly, more experimental work aimed at uncovering the structure of the aggregates and the nature of the aggregation process is called for. In particular, a worthwhile goal is to understand how the molecular structure influences the aggregation process, the structure of the aggregates, and the liquid crystal phase diagram. With this in mind, polarizing microscopy, X-ray measurements, and absorption spectroscopy similar to what was done with Sunset Yellow FCF were performed on a dye with a very different structure. While Sunset Yellow FCF has a benzene and napthalene ring linked by an azo group, Bordeaux dye27 possesses a much larger polyaromatic ring structure with no linking groups. The difference in molecular structure reveals itself in several ways. The liquid crystal phase of Bordeaux dye forms at a much lower dye concentration, the
Tomasik and Collings aggregation process is characterized by a larger “stacking free energy change”, and the cross-sectional area of the aggregates contains two or three molecules instead of one. In addition, in this report, the analysis leading to a determination of the “stacking free energy change” has been improved to include more rigorous formulations of both the statistical mechanics of aggregation and the changes in the absorption spectrum due to aggregation. 2. Theoretical Considerations. 2.1. Aggregation Theory. Conventional theories that describe molecular aggregation assume that there is no interaction between the aggregates and start with a determination of the partition function Q
Q)
∏i
qini ni !
(1)
where i is the number of molecules in an aggregate, qi is the partition function for an aggregate with i molecules, and ni is the number of aggregates with i molecules. The partition function for an aggregate qi is further broken down into a product of the partition functions describing the external and internal degrees of freedom
qi )
( )(
( )
V ∆µ(i-1) V ( ) e kBT ) 3 (eR i-1 ) L3 L
)
(2)
where V/L3 is the partition function describing the external degrees of freedom (the sample volume V divided by the cube of an appropriate length L), ∆µ is the free energy of a single molecule in solution relative to a molecule in an aggregate (the “stacking free energy change”), kB is the Boltzmann constant, T is the absolute temperature, and R is the “stacking free energy change” in units of kBT. The Helmholtz free energy of the system F can be obtained from the partition function and simplified using Stirling’s approximation
F ) -kBT ln Q ) -kBT
∑ [ni ln(qi) - ln(ni ! )] ≈ i
kBT
∑ i
[(
ni ln
)]
ni -1 qi
(3)
The chemical potential of an aggregate of size i is therefore
µi ) kBT
∂ (F/kBT) ni ) kBT ln ∂ni qi
(4)
At equilibrium, the chemical potential of each molecule, whether in solution as a single molecule or part of an aggregate of any size, must be the same. Equating µi/i and µ1, one obtains a relationship between the number of aggregates of size i and the number of single molecules in solution n1
ni )
( ) L3 R e V
i-1
ni1
(5)
Since the volume fraction for aggregates of size i is simply iVni/V, where V is the volume of a single molecule, the last relationship can be written in terms of the volume fraction Xi
( )
Xi ) i
L3 R e V
i-1
Xi1
(6)
However, the volume fraction of single molecules X1 can be written in terms of the total volume fraction for all molecules φ
A Dye Derived from Naphthalenecarboxylic Acid ∞
φ)
∑
∞
Xi )
i)1
∑ i)1
[( i
) ]
L3 R e X1 V
i-1
X1 )
(
X1
J. Phys. Chem. B, Vol. 112, No. 32, 2008 9885
)
L3 1 - eRX1 V
2
(7)
This results in an expression for the volume fraction of single molecules in terms of the total volume fraction for all molecules
X1 )
(1 + 2φz) - √1 + 4φz
2φz2
(8)
where z ) L3eR/V. Thus knowing the total volume fraction, the volume of a single molecule, and the “stacking free energy change”, the distribution of aggregate sizes can be calculated using eqs 6 and 8. In addition, the average aggregation number 〈i〉 is given by ∞
〈i 〉
)
∑ i(Xi/i) i)1 ∞
∑ (Xi/i)
)
2φz
√1 + 4φz - 1
(9)
i)1
If 4φz . 1, then eq 9 reduces to a relationship similar to the Flory-Huggens result31 〈i 〉 ≈
√(L3/V)φeR/2
(10)
There has been considerable discussion on what to use for the partition function that describes the external degrees of freedom. Theories that treat aggregation as a chemical reaction with activity coefficients equal to one are equivalent to setting V/L3 equal to V/V.13 In other theories, the volume divided by the cube of the thermal wavelength, Λ ) h/(2πmkBT)1/2, is used.14,15 However, the former may not be completely applicable to the aggregation of ionized molecules in solution at the concentrations used, and the quantum nature of the latter is inconsistent with classical statistical mechanics, which should describe the aggregation of molecules in solution. Some researchers have approached this problem by solving a model aggregating system exactly and then determining what V/L3 must equal for the method described above to give the same results. In one example, the proper assignment for L was 2.9(kBT/k)1/2, where k is the force constant describing the interaction between molecules.32 Using the parameters of the Lennard-Jones potential for polycyclic aromatic hydrocarbons in the gas phase,33 one obtains L ≈ 0.03 nm at room temperature. Clearly, using the interaction between polycyclic aromatic hydrocarbons may not be appropriate for ionized molecules in solution. Therefore, for the sake of simplicity, V/V is used for the partition function describing the external degrees of freedom in the calculations that follow. The determination of the “stacking free energy change” is sensitive to this choice; therefore, it should be kept in mind that the “stacking free energy change” may be larger than what is reported (by up to a factor of 2 if L ) 0.03 nm is used). However, if this calculation is used to analyze data from different chromonic systems, comparison of the resulting “stacking free energy changes” reveals important differences between the aggregation processes in the two systems. Figure 1 shows the ni and Xi distributions for two total volume fractions according to the theory, using V/V as the partition function describing the external degrees of freedom and parameter values appropriate for Bordeaux dye. Figure 2 illustrates how the average aggregation number depends on the “stacking free energy change” and the total volume fraction for the same set of parameters.
Figure 1. Distribution of aggregate size for two dye concentrations according to the theory and using parameter values appropriate for Bordeaux dye. The main plot displays the fraction of aggregates of each size. The inset shows the relative volume fraction of each aggregate size. The average aggregate size 〈i〉 is also given for each distribution.
Figure 2. Characteristics of a typical distribution of aggregates according to the theory. The large graph shows the variation of the average aggregate size 〈i〉 with the “stacking free energy change” R assuming a fixed total volume fraction of dye. The dashed line is the Flory-Huggens relationship, eq 10 with L3/V ) 1. The dependence of the average aggregate size 〈i〉 on the total volume fraction φ assuming a fixed “stacking free energy change” R is displayed in the inset.
2.2. Exciton Theory. In all chromonic liquid crystal systems, the absorption spectrum changes as aggregation occurs. The most pronounced change is a decrease in the absorption coefficient with increasing aggregation. In many cases, the wavelength of the absorption maximum shifts as the dye concentration is increased. The absorption spectra are usually complicated, making it extremely difficult to model them theoretically. However, the decrease in the absorption coefficient
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and shift in the wavelength of the absorption maximum can be explained by relatively simple theories. One class of theories utilizes exciton coupling to model absorption changes with aggregation. For example, coupling between the molecules is taken into account by introducing off-diagonal elements in the Hamiltonian for the aggregate.34 If a constant amount of coupling β is restricted to neighboring molecules, then the energies and dipole moments of the eigenstates of the excited aggregate can be calculated. If E1 and p1 are the energy and dipole moment of the single-molecule excited state, respectively, then the excited-state energies and dipole moments for an aggregate of i molecules are given by
( i +jπ1 ) p) i +2 1 ∑ p sin(ijkπ + 1) Ej ) E1 + 2β cos
(11)
i
j
1
(12)
k)1
where j is the index for the excited states of an aggregate of i molecules. As the number of molecules in an aggregate increases, more eigenstates of the excited aggregate are present, and they have energies deviating more from the excited-state energy of a single molecule. This tends to broaden the absorption coefficient spectrum and lower the peak absorption coefficient. In addition, the dipole moments of these additional excited states are not equal; the sign of the coupling term in the Hamiltonian determines whether the excited eigenstates with higher or lower energies have the larger dipole moment. This tends to shift the absorption spectrum to either higher or lower energy. These changes are greatest in going from a single molecule to a dimer, becoming less and less as the number of molecules in an aggregate gets larger. If a Lorentzian line shape with the appropriate width is attributed to each eigenstate of the excited aggregate, then the result is that the maximum absorption coefficient shifts in wavelength and decreases in magnitude as the number of molecules in an aggregate increases. Figure 3 shows the result of a calculation in which such Lorentzian line shapes are used, where the width of the Lorentzian and β (negative in this case) have been chosen so that the change is readily apparent. Notice that both the maximum absorption coefficient and the absorption coefficient at the wavelength of maximum absorption of the single molecule strongly decrease in going from monomer to dimer to trimer, but the decrease slows as the aggregation number increases. Since the absorption spectra are so much more complicated then what is predicted by the coupled exciton theory, it is impossible to fit the data to the theory. However, the theory does predict a decrease in the absorption coefficient at the wavelength of maximum absorption and a decrease in the absorption at the wavelength of the single-molecule absorption maximum, which are measured experimentally. As the inset in Figure 3 demonstrates, both of these decreases can be modeled by a fairly simple function if the absorption coefficient for very large aggregates a∞ is considered a fitting parameter in the following relationship for the absorption coefficient of an aggregate with i molecules
( i +π 1 )
ai ) a1 + (a∞ - a1)cos
(13)
where a1 is the absorption coefficient for a single molecule. 3. Experimental Procedures and Results Bordeaux dye is the product of the sulfonation of the cisdibenzimidolazole derivative of naphthalenetetracarboxylic
Figure 3. Absorption spectra of aggregates of different sizes according to exciton theory as described in the text. The inset shows how the absorption maximum and the absorption at the wavelength of maximum absorption of the single molecule depend on the size of the aggregate. The lines in the inset are fits of eq 12 to the exciton absorption coefficients.
Figure 4. The chemical structure of Bordeaux dye and its phase diagram.
acid.27 It was obtained from Optiva, Inc. as an 8.6 wt% aqueous solution with ammonium counterions. The chemical structure of Bordeaux dye is shown in Figure 4. Samples were diluted using Millipore water, with concentrations determined with an analytical balance. For the phase diagram and X-ray measurements, the Bordeaux dye solution was contained in sealed capillary tubes. Either sealed cuvettes or sealed coverslip-slide arrangements were used for the absorption measurements. The density of Bordeaux dye was measured with a small pycnometer. The pycnometer was first calibrated using Millipore water. Then, the density of the 8.6 wt% solution of Bordeaux
A Dye Derived from Naphthalenecarboxylic Acid
J. Phys. Chem. B, Vol. 112, No. 32, 2008 9887
Figure 5. X-ray scattering intensity as a function of scattering wavevector for four concentrations of Bordeaux dye at room temperature. The lines are fits to the data of a Lorentzian function with a linear background. The X-ray scattering from the highest three concentrations showed evidence of some alignment.
dye was measured. The density of the pure dye was estimated to be 1.38 g/cm3 by linear extrapolation to a 100 wt% solution. The phase diagram was determined by observing with a polarizing microscope sealed capillary tubes containing various concentrations of Bordeaux dye. The capillary tubes were heated at a rate of 1 °C/min in an Instec thermal stage, noting the temperature at which the first isotropic region formed and the temperature at which the last region of nematic liquid crystal disappeared. The results of this investigation are shown in Figure 4, where a wide coexistence region, about 20 °C, is evident. The X-ray diffraction measurements utilized the Cu KR radiation from a Bruker-Nonius FR591 generator with mirror monochromator optics and a multiwire detector. As has been observed in other chromonic liquid crystals, a broad concentration-dependent peak was present at very low angles, and a sharper concentration-independent peak occurred at a higher angle. In partially aligned liquid crystalline samples, these peaks were separated by 90° in χ scans. The concentration-dependent peak has been assigned to the average distance between columnar aggregates, while the concentration-independent peak is due to the 0.34 nm repeat distance between molecules in the aggregate. The concentration-dependent peaks for various concentrations of Bordeaux dye are shown in Figure 5. The horizontal axis is the scattering wave vector q
q)
4π sin θ λ
(14)
where λ is the wavelength of the X-rays and θ is the Bragg angle (half of the scattering angle). The lines in the figure represent fits to the data of a Lorentzian line shape with a linear background. An indication of the dimension of the aggregates can be obtained by graphing the peak scattering wave vector q0 versus the volume fraction of the dye φ on a log-log plot. As can be seen from the inset in Figure 6, the slope is 0.51 ( 0.03, consistent with one-half, as is expected for columnar aggregates. The cross-sectional area of the columns can be determined from the slope of the q20 versus φ graph if a packing
Figure 6. Dependence of the peak X-ray scattering wavevector q0 on volume fraction φ. The inset is a log-log plot, while the full graph is a plot of the square of the peak X-ray scattering wavevector versus volume fraction. The slope of 0.5 for the log-log plot indicates that the aggregates grow in one dimension.
Figure 7. Absorption coefficient as a function of wavelength for three representative concentrations of Bordeaux dye. The inset shows the dependence of the maximum absorption coefficient on concentration. The line is a fit to the theory as explained in the text, yielding a value for the “stacking free energy change” of (9.2 ( 0.4)kBT.
symmetry is assumed.35 Since hexagonal packing of the columns provides the most space for the columns to explore, it is the appropriate choice since it maximizes the entropy. However, this assumption is not critical since an assumption of square packing only changes the results by 13%. The graph is shown in Figure 6, yielding a value of the cross-sectional area of 3.24 ( 0.04 nm2 if hexagonal packing is assumed. Absorption measurements were made with a Jasco UV-vis spectrophotometer on dilute solutions of Bordeaux dye (well below the concentration where the liquid crystal phase forms at room temperature). The path length of the cuvette or sample
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Figure 8. Possible arrangements of Bordeaux dye molecules in the aggregate. There are two molecules in each layer, but the two molecules are rotated by 90° in neighboring layers. The molecules in the lower layer are drawn in red, and the molecules in the upper layer are drawn in blue. In arrangement (a), the two molecules in a layer are rotated by 180° relative to one another; in arrangement (b), the two molecules have the same orientation. For both arrangements, the cross-sectional area is roughly 2.5 times the molecular area, in agreement with the experimental results.
cell was chosen to keep the absorbance within the range that the spectrophotometer can measure accurately. The results for three representative concentrations are displayed in Figure 7, where a significant decrease in the absorption coefficient and a slight shift of the wavelength of maximum absorption are evident. The inset of Figure 7 shows the variation of the maximum absorption coefficient with concentration. 4. Discussion The phase diagram for Bordeaux dye is similar to other aggregating dye systems, showing a wide coexistence region between the nematic and isotropic phases. The slopes of the phase transition lines are about 4 °C/wt%. Typical slopes in other systems are about 3 °C/wt% for disodium chromoglyate5 and about 6 °C/wt% for Blue 27.7 The width of the coexistence region is wider than what is found in Sunset Yellow FCF6 but close to the width of the coexistence region in Violet 20,7 a molecule similar to Bordeaux dye. Also, as observed in other systems,7 nonspherical droplets of one phase in the other phase (tactoids) are present in the coexistence region. At room temperature, the liquid crystal phase appears at about 6 wt%, which is considerably lower than that in Sunset Yellow FCF where it appears at about 30 wt%6 but not too much different from what is observed in some other chromonic liquid crystal systems.5,7 One of the more interesting findings is the cross-sectional area of the aggregates as revealed by the X-ray measurements. Using the software package Gaussian to model the Bordeaux dye molecule, one obtains an area of about 1.28 nm2. This indicates that unlike Sunset Yellow FCF, the structure of the aggregate is not a simple stack of molecules. One way this can be understood is to realize that there are only two sulfate groups. This means that it is possible for two molecules to be side-byside in the same plane with the sulfate groups far apart. This would allow two more molecules to stack on top of these two molecules in a way that would provide considerable overlap of the π orbitals of the multiple aromatic rings. Two such models are shown in Figure 8, with the difference between the two arrangements being the orientation of the two molecules in the layer. Both arrangements have a cross-sectional area about 2.5 times that of a single molecule, in agreement with the X-ray results. The change in the absorption coefficient with concentration is very similar to what is found in Sunset Yellow FCF. If exciton theory is used to describe the decrease as a function of concentration, as outlined in the section 2.2, the “stacking free
energy change” can be determined by combining this dependence with the distributions described in section 2.1 and fitting the resulting theoretical description to the absorption coefficient data. This fit is displayed in the inset of Figure 7, with the result that the “stacking free energy change” is about 9.2kBT, larger than what is found for Sunset Yellow FCF (7.2kBT). This is not a surprising finding as Bordeaux dye forms a liquid crystal at considerably lower concentration, indicating that the aggregation process proceeds at lower concentration. These last two results allow for some speculation concerning the relationship between aggregate structure and the nature of the aggregation process. Is the higher “stacking free energy change” in Bordeaux dye due to the fact that the cross section of the aggregate is composed of more than one molecule? There are hints in past work that this might be the case. For example, more complicated structures than a simple stack of molecules have been suggested in other aggregating systems that form a chromonic liquid crystal phase at concentrations similar to what is found for Bordeaux dye. Obviously, X-ray and optical experiments on more systems need to be performed before this connection can be verified. It should also be noted that these results on Bordeaux dye provide additional evidence that chromonic systems depart from simple hard rod theories such as the one due to Onsager.11 The order parameter in the nematic phase is high (0.7-0.8) as predicted by these theories,6,7,36 and for one system, the lengthto-width ratio seems to be about 10,3 which is the beginning of the range where the theory should be applicable. However, the applicability of the theory depends on the volume fraction and the length-to-width ratio (the product of these should be about 4 at the nematic-isotropic transition). If eq 10 is used to estimate the length of the aggregates and the cross-sectional area is obtained from X-ray data, the product of the volume fraction and the length-to-width ratio is about 1 for disodium chromoglycate, 1.3 for Sunset Yellow FCF, and 0.2 for Bordeaux dye. The fact that all of these are well below 4 is probably a sign that the charged groups on the periphery of the aggregates contribute a repulsive force quite different from the hard rod repulsion assumed in the theory. 5. Conclusions These measurements are part of a continuing investigation into chromonic liquid crystals, with the hope of understanding both the aggregate structures that spontaneously form and the nature of the aggregation processes. Although Bordeaux dye is only the second system to be studied using a combination of
A Dye Derived from Naphthalenecarboxylic Acid optical microscopy, X-ray scattering, and absorption spectroscopy, possible connections are starting to reveal themselves. Qualitative similarities among the different systems show up in the phase diagrams, diffuse X-ray reflections, and absorption coefficient changes that are observed. However, quantitative analysis reveals that aggregate structures differ and the freeenergy changes driving aggregation vary. A combination of experimental data on additional materials, perhaps utilizing sophisticated NMR or imaging techniques, and theoretical work specifically directed toward these aggregating systems should, in the future, elucidate the connection between the structure of the aggregates and the dynamics of the aggregation process. Acknowledgment. The partial support of this work by the Petroleum Research Fund of the American Chemical Society is acknowledged as is additional support from the Howard Hughes Medical Institute and the Research Experiences for Undergraduates Program at the Laboratory for Research in the Structure of Matter at the University of Pennsylvania. The authors would like to thank Michael Pauksho of Optiva, Inc. for supplying the sample of Bordeaux dye, the University of Pennsylvania for allowing the use of its X-ray facility, and Oleg Lavrentovich, Andrea Liu and Thomas Stephenson for many useful discussions. References and Notes (1) Lydon, J. Curr. Opin. Colloid Interface Sci. 2004, 8, 480. (2) Tam-Chang, S. W.; Iverson, I. K.; Helbley, K. Langmuir 2004, 20, 342. (3) Nastishin, Y. A.; Liu, H.; Shiyanovskii, S. V.; Lavrentovich, O. D.; Kostko, A. F.; Anisimov, M. A. Phys. ReV. E 2004, 70, 051706. (4) Schneider, T.; Artyushkova, K.; Fulghum, J. E.; Broadwater, L.; Smith, A.; Lavrentovich, O. D. Langmuir 2005, 21, 2300. (5) Kostko, A. F.; Cipriano, B. H.; Pinchuk, O. A.; Ziserman, L.; Anisimov, M. A.; Danino, D.; Raghavan, S. R. J. Phys. Chem. B 2005, 109, 19126. (6) Horowitz, V. R.; Janowitz, L. A.; Modic, A. L.; Heiney, P. A.; Collings, P. J. Phys. ReV. E 2005, 72, 041710. (7) Nastishin, Y. A.; Liu, H.; Schneider, T.; Nazarenko, V.; Vasyuta, R.; Shiyanovskii, S. V.; Lavrentovich, O. D. Phys. ReV. E 2005, 72, 041711. (8) Prasad, S. K.; Nair, G. G.; Hegde, G.; Jayalakshmi, V. J. Phys. Chem. B 2007, 111, 9741. (9) Kaznatcheev, K. V.; Dudin, P.; Lavrentovich, O. D.; Hitchcock, A. P. Phys. ReV. E 2007, 76, 061703.
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