Article pubs.acs.org/JPCA
Chiroptical Spectroscopy of Surfactants Prasad L. Polavarapu* and R. Vijay Department of Chemistry, Vanderbilt University, Nashville, Tennessee 37235, United States S Supporting Information *
ABSTRACT: Three different chiroptical spectroscopic methods, namely, optical rotation, electronic circular dichroism (ECD), and vibrational circular dichroism (VCD) have been evaluated for studying the aggregation of sodium dodecylsulfate (SDS), an achiral surfactant, using garcinia acid disodium salt (GADNa) as a chiral probe. The specific rotation and ECD of GADNa are found to be altered by the aggregation of SDS, suggesting for the first time that achiral surfactants can be characterized with chiroptical spectroscopy using appropriate chiral probes. In addition, a chiral compound, fluorenyl methyloxy carbonyl L-leucine sodium salt (FLNa) is found for the first time to behave as a surfactant in water, with 205 Å2 surface area per molecule at the air−water interface, critical micelle concentration (CMC) of 0.18 M, and Gibbs energy of micellization of −14 kJ/mol. The specific rotation of FLNa in water is found to increase with concentration beyond CMC, suggesting the formation of chiral aggregates. Different conformations of FLNa amenable to micellization have been identified using quantum chemical conformational analysis and their specific rotations calculated. The formation of lamellar aggregates of FLNa in water is suggested to be the cause for increase in specific rotation with concentration beyond CMC.
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INTRODUCTION For surfactants, the estimation of concentration that represents the onset of adsorption at the air−solution interface and the critical micelle concentration (CMC) is routinely achieved with tensiometry.1 However, tensiometry is not sensitive to chirality and is not useful for studying the chiral molecular properties. Chiroptical spectroscopy, which includes optical rotatory dispersion (ORD),2,3 electronic circular dichroism (ECD),2,3 vibrational circular dichroism (VCD),2,4 and vibrational Raman optical activity (VROA),2,5 is widely used for characterization and structural determination of optically active compounds. Therefore, for studying the chiral surfactants, it is natural to consider the commonly used chiroptical spectroscopic methods. While several ECD investigations are known for studying the chiral surfactants,6 only a limited number of sporadic optical rotation (OR) investigations have appeared in the literature. The slope in the plot of observed optical rotation vs concentration for the chiral surfactants (β-D-octyl glucoside, N-decyl-N,N-dimethylalanine, and morphine sulfate) was reported to change by a small extent upon the formation of aggregates.7−11 Numerous developments have taken place, since the seventies, in the instrumentation for optical rotation measurements,12,13 and modern optical rotation instruments have not yet been applied to chiral surfactants. VCD studies on chiral molecules entrapped in achiral surfactants have been reported,14 but VCD and VROA studies on chiral surfactants themselves have not been. In studying the surfactants, it is not clear which of the chiroptical spectroscopic methods will be more sensitive/ appropriate to determine their molecular properties. To understand the related issues, we undertook simultaneous investigations using multiple chiroptical spectroscopic methods, © 2012 American Chemical Society
supplemented with tensiometry, on the following: (a) aggregates of achiral surfactant, sodium dodecylsulfate (SDS), in the absence and presence of garcinia acid disodium salt (GADNa)15 as a chiral probe. To the best of our knowledge, the formation of achiral aggregates has not been monitored before using the changes in optical activity of a chiral probe; (b) aggregation and chiroptical properties of fluorenyl methyloxy carbonyl (FMOC)-L-leucine sodium salt (FLNa), in water. To the best of our knowledge, the surfactant properties of FLNa have not been reported to date. The area per molecule at the air−water interface, critical micellar concentration (CMC), and standard free energy change of micellization are determined for FLNa for the first time. Using quantum chemical conformational analysis, the possible conformations of FLNa surfactant have been determined and their specific rotations calculated. Some of these conformations are amenable for the formation of lamellar aggregates, and these aggregates appear to be responsible for the increase in observed specific rotation at concentrations above CMC.
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EXPERIMENTAL METHODS SDS was purchased from Aldrich (purity >98%) and Fluka (purity >99%). Fluorenyl methyloxy carbonyl L-leucine (FMOC-L-Leu) (purity >98%) was obtained from Ezbiolab. Sodium methoxide (purity >99%), methanol (from Aldrich), CD3OD (from Cambridge Isotope Laboratories), and NaOD (from Aldrich) used in these experiments have purity >99%. The solutions of FMOC-L-Leu in water (D2O for VCD Received: February 6, 2012 Revised: April 16, 2012 Published: May 4, 2012 5112
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experiments) were prepared by converting FMOC-L-Leu to its sodium salt by titrating with one equivalence of sodium hydroxide (99% NaOD for D2O solutions). To prepare solutions of FLNa in methanol, FMOC-L-leucine was reacted with one equivalence of sodium methoxide in methanol. For VCD experiments, FLNa solution in methanol was evaporated under vacuum using a rotatory evaporator and redissolved in CD3OD. Precautions for, and observations made during, the preparation of FLNa solutions are provided as Supporting Information. Garcinia acid disodium salt (GADNa) was obtained from Professor Ibrahim Ibnusaud.15 Surface tension measurements were performed on a Fisher Scientific tensiometer (Model 21), employing a platinum du Nuoy ring as the probe. The surface tension values reported here are the averages of at least three measurements and represent the equilibrium values. Since surface tension has weak dependence1 on temperature and pressure, all measurements were made at room temperature and pressure only. The optical rotation measurements were made at 25 °C using an Autopol IV polarimeter (Rudolph Research Analytical, Flanders, NJ, USA), with reproducibility of 0.002°, using either a 2 dm or 0.5 dm cylindrical cell with quartz windows. Optical rotation measurements for FLNa were performed using a 0.5 dm cylindrical quartz cell for concentrations in the range of 3.5 × 10−4− 0.2827 g/mL. The reported observed rotations are in degrees and specific rotations are in deg cm3 g−1 dm−1. ECD measurements were made using a JASCO 720 spectrometer using a 0.1 mm, 1 mm, or 1 cm quartz cell. VCD measurements were made using ChiralIR spectrometer using fixed path length (100 or 50 μm) cells with BaF2 windows. Computational Methods. The conformations of FLNa were investigated using CONFLEX16 and Gaussian0917 programs. Since CONFLEX program does not handle the ionic species properly,18 a molecular model of FMOC-L-leucine was input into the CONFLEX program and conformational search was undertaken using MMFF94S molecular mechanics force field. A total of 2360 conformations were found within 20 kcal/mol. The hydrogen atom of COOH group in these conformers was then replaced with Na atom and the fifty lowest energy conformers were subjected to geometry optimizations using B3LYP functional, 6-31G* basis set, and polarizable continuum model (PCM)17,19 for water solvent environment. The optimized structures were found to be within 4.4 kcal/mol, and after discarding the duplicate structures, 19 of the distinct conformers within 1 kcal/mol are used for analyzing their structures. Specific rotations at six different wavelengths, 633, 589, 546, 436, 405, and 365 nm, were calculated for these 19 conformations at B3LYP/6-31G*/PCM level, using the Gaussian09 program.
Figure 1. Surface tension (A) and optical rotation (B) of SDS in water at 25 οC as a function of its logarithmic concentration (M).
of well-defined symmetric spherical micelles.20−22 Using a home-assembled instrument with laser source, Rusanov and coworkers reported21 a specific rotation of ∼25° (we presumed the units to be deg cm3 g−1 dm−1) at 450 nm, for ∼8 mM (∼2.3 × 10−3 g/mL) SDS in 0.8 dm path length beaker. This reported specific rotation corresponds to an observed rotation of ∼0.046°, a magnitude that should be easily measurable on modern commercial polarimeters. Therefore, we first measured the optical rotation of SDS as a function of concentration (0.01−200 mM), using a cylindrical cell with 2 dm path length. The measured rotations for SDS in water are within the instrumental noise (0.002°) in the concentration range of 0.01−200 mM and at five different wavelengths, 405, 436, 546, 589, and 633 nm (see Figure 1 for data at 405 nm). To ensure that the commercial source of samples did not have any influence on the results, SDS samples obtained from two different manufacturers were investigated and found all measurements to be within the instrumental noise. We conclude therefore that either the reported magnitudes of specific rotation of SDS in water are in error or magnitudes are so small that they cannot be recorded on commercial polarimeters (with a reproducibility of 0.002°). It should be added that the formation of bubbles and/or colloidal particles in solution do give erroneous optical rotation results, and artifacts in optical rotation measurements are not uncommon.23 If the reported optical rotations of SDS aggregates are in fact real, then there is a possibility that SDS aggregates may also exhibit ECD, as ECD and ORD are related through the Kramers−Kronig (KK) transform.24 This possibility led us to measure the ECD spectra of SDS as a function of concentration in water (see Figure S1 in Supporting Information). No measurable ECD was found in the 190−300 nm region for SDS in the 10−7−0.2 M concentration range. The presence/absence of ECD in the wavelength region below 190 nm could not be verified, however, as this region is inaccessible with the commercial ECD instrument used here. Monitoring the Aggregation of Achiral Surfactant Using a Chiral Probe. Establishing that the aggregation of SDS cannot be detected (Figure 1) both on a commercial
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RESULTS AND DISCUSSION Monitoring the Aggregation of SDS in Water. Tensiometry was performed to ascertain if the CMC of SDS used in the present study is in line with the reported literature values (see Figure 1). From the surface tension data in Figure 1, CMC of SDS used is inferred to be 8 mM, which is in good agreement with the reported literature values.1 Since SDS is an achiral surfactant, one would not expect SDS to exhibit chiroptical properties. However, it was reported recently that nonchiral surfactants exhibit optical activity at a concentration around CMC, probably due to the formation of poorly defined asymmetric aggregates, and that this optical activity disappears at a concentration above CMC, possibly due to the formation 5113
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concentration used, did not perturb the aggregation of SDS to a significant extent. The specific rotation of GADNa, as the concentration of SDS is varied from 1 × 10−7 to 0.163 M, is shown in Figure 2b, where data points from two independent measurements and their average values are displayed. The specific rotation of GADNa changed from ∼150 (for SDS concentrations in the 10−6−10−5 M range, which corresponds to that before the start of SDS aggregation), to ∼166 (for SDS concentration of 10−4 M, which corresponds to the onset of adsorption of the surfactant at the air−solution interface in the presence of GADNa), and then to ∼130 (for SDS concentration of 8 mM, which corresponds to the CMC). The specific rotation of GADNa remained almost unchanged with further increase in the concentration of the SDS beyond CMC. It should be added that the changes in observed optical rotation of GADNa, as the concentration of SDS is varied, are not very large (a swing of 0.01° among the data points shown in Figure 2) but are reproducible. The ECD and absorbance spectra of GADNa at a concentration of 6 × 10−4 M and in the presence of varying SDS concentrations (1 × 10−7−0.2 M) are provided in the Supporting Information (Figures S2 and S3). It should be added that, due to the low concentration of GADNa used, these spectra in the 240−190 nm region were obtained as averages of 12 scans (∼1 h data collection for each spectrum) to achieve better signal-to-noise ratio. GADNa, by itself, in water shows a positive ECD band at ∼202 nm (Figure S2, Supporting Information). The normalized area of ECD from 190 to 230 nm does show (see Figure 2c) a slight change in the presence of varying SDS concentrations (1 × 10−7−0.2 M; premicellar to postmicellar concentration range). The trend seen for the changes in the area of ECD closely follows that seen for specific rotation (except for the highest concentration point). Same trend is also seen when the normalized peak ECD intensity at 202 nm, in place of band area, was used (Figure 2c), but band area data are considered to be better representatives of the chiral probe. VCD spectroscopic studies on SDS in the presence of GADNa are not feasible in H2O or D2O solutions because, at the desired low concentrations of GADNa and shorter path lengths of 6 and 50 μm mandated by strong solvent absorptions of H2O and D2O, respectively, sufficient absorbance for vibrational bands to measure VCD above the noise level could not be realized (see Supporting Information). These experimental observations indicate that specific rotation and ECD of an appropriate chiral probe can indicate the onset of adsorption of achiral surfactant at the air−solution interface when proper precautions are taken. This observation reveals that polarimetry and ECD can be sensitive methods for studying the aggregation of achiral surfactants using appropriate chiral probes. Monitoring the Aggregation of FLNa. The properties of several amino acid surfactants have been reported in the literature,25 but all those surfactants were synthesized with long alkyl side chains. There was no report in the literature suggesting that the salts of native FMOC amino acids can behave as surfactants. During the course of VCD measurements in our laboratory, we discovered that FLNa can behave like a surfactant and aggregate in water. As a result, there is a need for determining the concentration that represents the onset of adsorption of FLNa at the air−water interface and the CMC. Tensiometry experiments were performed first on FLNa (see
polarimeter (even with a 2 dm cell) and a ECD spectrometer, we sought to use a chiral probe to study the aggregation of SDS. An ideal probe to monitor the aggregation of achiral surfactants using chiroptical spectroscopy should (a) be chiral, (b) exhibit optical activity above the instrumental noise at very low concentrations, (c) have the same polarity as that of achiral surfactant, and (d) not significantly perturb the CMC of achiral surfactant. GADNa (see Figure S2 in Supporting Information for the chemical structure) is chiral with the same polarity as that of SDS and exhibited optical rotation of 0.049° at 405 nm in a 2 dm cell, at a concentration of 6 × 10−4 M (or ∼1.4 × 10 −4 g/mL). Our goal here is to use GADNa as a nonperturbing probe and the role of GADNa as a surfactant/ cosurfactant has not been investigated (it may be noted that surfactant properties of GADNa, by itself, are not known). Tensiometry was performed (see Figure 2a) to estimate the CMC of SDS in the presence of GADNa at 6 × 10−4 M. From the surface tension data as a function of concentration, for SDS in the presence of fixed concentration (6 × 10−4 M) of GADNa, the CMC of SDS remained at ∼8 mM. This observation leads us to believe that GADNa, at the
Figure 2. Surface tension (A), specific rotation (B), and ECD (C) as a function of logarithmic SDS concentration (M) in water in the presence of fixed GADNa concentration (6 × 10−4 M or 1.4 × 10−4g/ mL). The inset displays specific rotation of GADNa at fixed concentration (6 × 10−4 M), as a function of concentration of SDS, from premicellar concentration (0.056 mM) to CMC (8 mM). ECD band areas (190−230 nm), normalized with corresponding absorption area, are displayed as filled squares, and peak intensities at 202 nm, normalized with corresponding peak absorption intensities, are displayed as open circles. 5114
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Figure 3a), in the concentration range of 10−7 to 0.2827 g/mL (or ∼2.6 × 10−7−0.75 M). Note that, even though the
methanol unchanged at 22.5 mN/m (see Figure 3a), which indicates complete solubilization of FLNa in methanol and the absence of adsorption of FLNa at the air−solution interface.26 From the surface tension (γ) versus concentration data for FLNa in water, the Gibbs energy of micellization can be determined using the following equation:1 ° = 2.303RT log10 xcmc ΔGmic
(1)
where xCMC is the mole fraction of FLNa in solution at CMC. At CMC, xcmc ≈ 3.3 × 10−3, which yields −14 kJ/mol for ΔGmic of FLNa at 25 °C. In addition, the surface area per molecule, as1 in Å2 units, of FLNa at the air−water interface can be determined from1
a1s =
1023 N Γ1
(2a)
⎛ ⎞ ∂γ −1 ⎟ × ⎜⎜ 2.303(1 + α)RT ⎝ ∂ log10 C1 ⎟⎠
(2b)
where Γ1 =
with Γ1 in units of (mol 10−3 m−2), N representing Avogadro number, C1 the concentration of FLNa in solution, and α the fractional dissociation of ionic surfactant. For sodium salts, α = 1. The slope of γ vs log10 C1 (from data in Figure 3) is −9.26 mN/m, which yields a surface area per molecule of FLNa, at the air−water interface, of as1 = 205 Å2. The specific rotation of FLNa in water (Figure 3b) remained approximately constant (increased only slightly from −24 to −23 deg cm3 g−1 dm−1) in the low concentration range of 3.5 × 10−4−3.5 × 10−2 g/mL (or ∼9.3 × 10−4−9.3 × 10−2 M). Then the specific rotation increased from −21 to −7 deg cm3 g−1 dm−1 with increasing concentration of FLNa from 0.0707 to 0.2827 g/mL (∼0.18 to 0.75 M). It is to be noted that a large increase in the specific rotation beyond CMC has not been reported previously for any chiral surfactant. The specific rotation of FLNa in methanol, however, remained almost constant (decreased only slightly from −22 to −23 (see Figure 3b) in a wide concentration range of 3.5 × 10−4−0.2827 g/mL, which can be correlated with the absence of aggregation in methanol as deduced from tensiometry data (Figure 3a). It is known that specific rotations of chiral organic compounds can vary with concentration in situations where molecular aggregation occurs in solution,27−29 but the variation of specific rotation with concentration of chiral surfactants has not been reported, or dealt with, to date. An explanation for the increase
Figure 3. Surface tension (A) and specific rotation (B) of FLNa in water and methanol at 25 οC, as a function of its logarithmic concentration (M). The inset displays specific rotation as a function of FLNa concentration (mg/mL).
concentrations are generally expressed in mol/L for surface tension measurements, we used g/mL here due to the need for these units in the calculation of specific rotation. As the concentration of FLNa in water is increased from 10−7 to 0.0707 g/mL, the surface tension of the solution is reduced from 72 to 47 mN/m. In the concentration range of 0.0707− 0.2827 g/mL in water, the surface tension remained almost constant at 47 mN/m, which is indicative of the complete coverage of the air−water interface with a monolayer of FLNa. From tensiometry data in Figure 3a, the concentration that represents the onset of adsorption of FLNa surfactant at the air−water interface and CMC can be deduced to be ∼10−4 g/ mL (∼2.6 × 10−4 M) and ∼70 mg/mL (∼0.18 M), respectively. Note that in methanol, however, a progressive increase in the concentration of FLNa in the concentration range of 10−7 to 0.2827 g/mL leaves the surface tension of
Figure 4. Three selected conformations of FLNa optimized at the B3LYP/6-31G* level using PCM for water solvent. All 19 optimized conformations, their structural parameters, and calculated specific rotations can be found in the Supporting Information. 5115
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is unusual because of the presence of one very short alkyl side chain and one rigid aromatic side chain. Because of this unusual nature, the widely used models30 for micellization need not apply for FLNa. Nevertheless, the aggregation of surfactants with one hydrophilic headgroup and two hydrophobic side chains is known30 to lead to the formation of lamellar structures (bilayers or vesicles). Since compact organization is likely to dominate during aggregation, several of the 19 conformers (including 3 and 19 in Figure 4) of FLNa (see Supporting Information) are likely to be present in the aggregated structures. It should be added that many more investigations, including molecular modeling and further quantum chemical calculations, are needed to fully characterize the structure of FLNa aggregates. In the absence of molecular aggregation (or strong intermolecular interactions), specific rotation is expected to be independent of concentration. In the light of possible formation of lamellar aggregates, the increase in observed specific rotation of FLNa as a function of concentration beyond CMC can now be understood. In the concentration range from ∼0 to CMC, specific rotation is attributed to individual surfactant molecules at the air−solution interface and specific rotation is expected to be concentration independent in this region, as experimentally observed. At concentration above CMC, specific rotation is determined by aggregates in the bulk solution and is expected to be influenced by the intermolecular interactions within the aggregates. The experimentally observed concentration dependence of specific rotation confirms this hypothesis and indicates that observed optical rotation has nonlinear dependence on concentration29 and that this nonlinear dependence may be correlated with the size of aggregates. As the concentration increases, the number and size of the aggregates are expected to increase, which leads to varying intermolecular interactions and hence to varying specific rotation as a function of concentration. To quantify these interactions, quantum chemical calculations of specific rotation as a function of aggregate size are required, and we hope to undertake these studies in the near future. It should be useful to note that tensiometry, being a surface property, is extremely useful for determining the CMC, but it does not reveal any bulk property of the chiral surfactant solution. Once CMC is reached, tensiometry provides no further information. On the contrary, specific rotation, being sensitive to the intermolecular interactions in the bulk medium, can reveal new information above CMC on the nature of chiral aggregates in the bulk medium, as is transparent in the experimental data of Figure 3.
in specific rotation with concentration in water, beyond CMC, is provided in the next section. ECD spectra for FLNa in water at 10, 1, and 0.1 mM in water did not show any ECD bands (see Figure S4 in Supporting Information) in the 190−350 nm region, and these measurements at concentrations below 0.1 mM are not feasible. VCD spectra for FLNa, feasible only at high concentration (200 mM), did not show much difference in D2O and CD3OD (see Figure S5, Supporting Information). ROA measurements are only feasible for neat liquids or near saturated solutions. Thus, there is no hope for using ECD, VCD, or ROA for studying the aggregation of FLNa at low concentrations, such as those were possible with optical rotation measurements (Figure 3). Structure of FLNa Surfactant. Surfactants are known to aggregate at concentrations above CMC, but the type of aggregation (micelles, vesicles, bilayers, etc.) depends on the structural properties of the surfactant.30 To gain insight into the possible structure of FLNa aggregates, we undertook quantum chemical analysis of the conformations of FLNa. Among the structures optimized with B3LYP functional (using 6-31G* basis set with PCM for water solvent), the 19 lowest energy structures within 1 kcal/mol have been used for specific rotation calculations. These conformations are displayed in the Supporting Information, along with a table containing their structural parameters and wavelength dependent specific rotations. Three representative conformations, #1, #3, and #19, spanning the 1 kcal/mol energy range are shown in Figure 4. Conformations 1 and 3 differ in energy by 0.01 kcal/mol, while conformation 19 is higher in energy by 1.04 kcal/mol. In the assumption that a circular area of πr2 is needed for each molecule at the air−solution interface, the molecular dimensions of the structures shown in Figure 4 yield the surface area per molecule as 154, 155, and 104 Å2, respectively, for conformers 1, 3, and 19. The actual area could be greater than these numbers because of van der Waals and steric interactions between neighboring molecules. The experimentally determined area of 205 Å2 is closer to that for conformers 1 and 3. Nevertheless, conformer 1 is unlikely to self-assemble in water because the relative orientations of hydrophilic and hydrophobic groups do not provide a distinct spatial isolation from each other. This conclusion is also supported by the calculated specific rotations. The predicted [α]405 for conformers 1, 3, and 19 are, respectively, 249, −220, and −569 deg cc g−1 dm−1. Since the observed specific rotation for FLNA is negative, conformer 1 is an unlikely candidate for representing FLNa aggregates. Conformer 3, based on its low energy and negative specific rotation, appears to be the most likely candidate for representing FLNa aggregates. There are several conformers of FLNa, among the 19 conformers investigated (see Supporting Information), that have negative specific rotations as in the experimental data, and some have positive specific rotations as well. While the calculated specific rotations for different conformations (see Supporting Information) provide guidance as to the suitability of predicted conformations, the predicted specific rotations of individual conformers should not be given undue importance because one needs to use Boltzmann population weighted specific rotations to compare with experimental specific rotation. Both the populations and specific rotations derived at the B3LYP/6-31G*/PCM level can have significant uncertainties. Most of the surfactants discussed in the literature1,25,30 are associated with long alkyl chains. From that perspective, FLNa
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CONCLUSIONS The aggregation of SDS could be followed using optical rotation and ECD spectroscopic methods by employing an appropriate chiral probe. FLNa is found to behave like a surfactant in water, and its surfactant properties are determined for the first time. The surface area per molecule at the air− water interface is 205 Å2, CMC is 0.18 M, and Gibbs energy of micellization is −14 kJ/mol. The conformers amenable to micellization are determined using quantum chemical conformational analysis and their specific rotations calculated. On the basis of these data, the possible aggregate structures for FLNa are suggested. These structures help understand the observed increase in specific rotation of FLNa as a function of concentration beyond CMC. 5116
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ASSOCIATED CONTENT
S Supporting Information *
Sample preparation; EA and ECD spectra of SDS as a function of concentration, in the absence and presence of GADNa at 6 × 10−4 M in water; EA and ECD spectra of FLNa in water as a function of concentration; VA and VCD spectra of FLNa at 200 mM in D2O and CD3OD; 19 lowest energy conformations, their structural parameters, and specific rotations. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*Phone: (615)322-2836. Fax: (615)322-4936. E-mail: Prasad.L.
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank Dr. E. Castiglioni (Jasco Europe) for communications regarding artifacts in optical rotation measurements, Professor Ibrahim Ibnusaud (MG University, Kottayam, India) for the sample of GADNa, and Professor A. V. Anilkumar (Vanderbilt University) for the use of tensiometer. Funding from NSF (CHE-0804301) is gratefully acknowledged. This work was conducted in part using the resources of the Advanced Computing Center for Research and Education at Vanderbilt University, Nashville, TN.
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REFERENCES
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