Highly Accurate Quantitative Analysis Of Enantiomeric Mixtures from

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Highly Accurate Quantitative Analysis Of Enantiomeric Mixtures From Spatially Frequency Encoded H NMR Spectra 1

Bertrand Plainchont, Daisy Pitoux, Mathieu Cyrille, and Nicolas Giraud Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.7b02411 • Publication Date (Web): 02 Jan 2018 Downloaded from http://pubs.acs.org on January 3, 2018

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Analytical Chemistry

Highly Accurate Quantitative Analysis Of Enantiomeric Mixtures From Spatially Frequency Encoded 1H NMR Spectra Bertrand Plainchont, Daisy Pitoux, Mathieu Cyrille and Nicolas Giraud*†

Université Paris Saclay, Institut de Chimie Moléculaire et des Matériaux d'Orsay, Equipe RMN en Milieu Orienté, UMR CNRS - UPS 8182, 91405 Orsay, France. ABSTRACT: We propose an original concept to measure accurately enantiomeric excesses on proton NMR spectra, which combines high resolution techniques based on a spatial encoding of the sample, with the use of optically active weakly orienting solvents. We show that it is possible to simulate accurately dipolar edited spectra of enantiomers dissolved in a chiral liquid crystalline phase, and to use these simulations to calibrate integrations that can be measured on experimental data, in order to perform a quantitative chiral analysis. This approach is demonstrated on a chemical intermediate for which optical purity is an essential criterion. We find that there is a very good correlation between the experimental and calculated integration ratios extracted from G-SERF spectra, which paves the way to a general method of determination of enantiomeric excesses based on the observation of 1H nuclei.

Quantitative analysis is a key challenge in all areas of chemistry, and the accurate determination of enantiomeric excesses (ee's) has been one of the major issues raised in this field over the last centuries. Since the pioneering work led by Louis Pasteur on molecular asymmetry, several approaches have been explored to analyze mixtures of enantiomers, in applications of prime interest such as the development of asymmetric catalysts, where the determination of ee's plays a crucial role.13 In this context, nuclear magnetic resonance (NMR) has shown to be a tool of choice for analyzing mixtures of enantiomers. Several methods developed in this field depend on the use of a chiral resolving agent.4 One of the most successful examples is the use of a chiral liquid crystal as an optically active orienting solvent to generate diastereoisomeric interactions with chiral solutes, yielding a different orientational order, and thus a different NMR spectrum for each enantiomer.5 This approach has paved the way for the measurement of a wide range of anisotropic spin interactions to probe the orientation and the structure of each enantiomer in the chiral solvent.6,7 If rare nuclei such as carbon-13 or deuterium have long been shown to give access to accurate determinations of ee's8,9, extracting a quantitative information from proton spectra of enantiomers dissolved in optically active orienting media has however long been challenging, despite the higher sensitivity of 1H nuclei. Indeed, the presence of homonuclear residual dipolar couplings (RDC’s) yields crowded spectra that are difficult to decipher. This issue is illustrated for the chemical intermediate β-lactone 1 (Fig. 1a). The 1H NMR spectrum of the racemate sample dissolved in a chiral liquid crystalline phase composed of PBLG is shown in Figure 1b. The complexity of the observed signals arises from the fact that this spectrum is the sum of the sub-spectra of both enantiomers, as it is highlighted by the simulated data shown in Figures 1c to 1d. Even for such a small compound, it is impossible to discriminate the lines arising from each enantiomer, which would prevent chemists from exploiting these data to measure an ee.

Figure 1. (a) The structure and atomic labeling of both enantiomers of 3-hydroxy-4,4,4-trichlorobutyric β-lactone 1. The experimental (b) and calculated (c) 1H NMR spectra of a racemate sample of 1 dissolved in a chiral liquid crystalline phase composed of PBLG and CD2Cl2. The simulated 1H spectra of enantiomers R and S are shown in (d) and (e), respectively.

In the last years, a wide variety of approaches were explored to improve the resolution of 1H NMR spectra of enantiomeric mixtures dissolved in chiral liquid crystalline solvents.10 Among them, pulse sequences based on the concept of a spatial frequency encoding (SFE) have led to significant achievements.11,12 On the one hand, the Zangger-Sterk (ZS) method has triggered key developments in the field of pure

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shift NMR.13,14 1H experiments incorporating broadband homonuclear decoupling based on the ZS method were successfully applied to monitor small changes in chemical shift anisotropy, for enantiomeric mixtures dissolved in chiral liquid crystalline phases.15 These variations are however in general small in such weakly orienting media. For instance, no discrimination is achieved on the 1D pure shift spectra recorded on the samples investigated here, as it is illustrated in Figure S1 in Supporting Information. As a result, the most convincing results using a pure shift approach were rather reported for enantiomeric differentiations based on the use of shift reagents.15-17 On the other hand, spatial frequency encoded pulses were also successfully implemented in selective refocusing experiments.18-20 Among them, the G-SERF experiment21 has opened the way to a great simplification of 1H spectra of enantiomers dissolved in a chiral orienting solvent.22 This experiment has introduced the concept of J-edited spectra, the correlation pattern and the resolution of which are fully tailored to measure and assign 1H homonuclear coupling networks. G-SERF spectra have notably been shown to be an efficient way of discriminating enantiomers.23 Here we introduce a concept to extract a reliable estimate of ee's from T-edited spectra. It is based on the theoretical formalism that we have recently developed to simulate SFE experiments and calculate the resulting spatially encoded NMR spectra such as 2D G-SERF maps.11 We propose to use simulations to ascertain the quantitativity of such data by accounting for the influence of key features such as second order effects in fully coupled systems, or selectivity issues raised by the implementation of gradient encoded shaped pulses.

MATERIALS AND METHODS Sample Preparation. 3-hydroxy-4,4,4-trichlorobutyric βlactone 1 was chosen as a chiral model organic compound in order to illustrate the properties of the G-SERFph pulse sequence for determining enantiomeric excesses on molecules dissolved in a chiral liquid crystalline phase. A series of 5 gravimetrically prepared samples was obtained by diluting enantiomeric mixtures with varying enantiomeric excesses in a liquid-crystalline phase composed of poly-(γ-benzyl)-Lglutamate (PBLG, purchased from Sigma) and CD2Cl2, using standard procedure described elsewhere (see Table S1 in Supporting Information for details about the exact composition of each prepared sample).6 We remind that the enantiomeric excess in R is defined as follows:

ee = ( R − S ) ( R + S ) ×100

(1)

R and S are the molar fraction of enantiomers R and S respectively. The resulting 5 mm NMR tubes were then sealed in order to avoid solvent evaporation, and centrifuged back and forth until an optically homogeneous birefringent phase was obtained. NMR Spectroscopy. NMR spectra were acquired at 300 K on a Bruker AVANCE II NMR spectrometer operating at 14.1 T, equipped with a 5 mm 2H-1H/19F cryoprobe with z field gradient coil of maximum gradient strength 53.7 G.cm-1. We have implemented the G-SERFph pulse sequence that has been published elsewhere.21,22 An E-BURP-2 shape (resp. REBURP and Time reversal E-BURP-2) was used for the excitation (resp. refocusing and flip-back) pulse of duration 60 ms. The offset of the non-encoded soft π pulse was set at the desired resonance frequency of the proton spin whose coupling

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network was probed. The gradient amplitude used to generate the spatial frequency encoding was 0.54 G.cm-1. A sine-shaped gradient pulse of duration 1 ms and 5.4 G.cm-1, followed by a recovery delay of 150 µs was used in the z filter. For each of the 128 increments in t1, a free induction decay of 4096 points was acquired, with 4 scans and recycle delays between scans of 2.0 s. The spectral windows were set to 2500 Hz in the direct domain and 60 Hz in the indirect domain. A phasable 2D map was obtained using the Quadrature Sequential Mode in 36 minutes. Data were processed by using zero-filling up to 256 points in t1 and 8192 points in t2, apodization with an exponential function using a line broadening of 1.0 Hz and 0.3 Hz, and automatic baseline correction in the direct and indirect dimension, respectively. NMR Simulations. Simulations were performed using the SpinDynamica program24 under Mathematica 9.025 on a computer equipped with 8 Intel Xeon processors E5-2609v2 2.5GHz and 32 Go DDR3 memory. To simulate the action of the G-SERFph pulse sequence on a given enantiomer of 1, the encoding gradient strength was set so as to encode the entire spectral width of the compound under study. The spatial frequency encoding gradient was modeled by dividing the sample into virtual slices, and the local density operator ρ(z,t1,t2) has been computed for selected virtual slices at positions z.11 Only the virtual slices around positions encoded at δA, δB and δX were computed. It was checked that the resulting spectrum is similar to the one obtained by computing the whole virtual sample when a reduced swept width of 410 Hz (resp. 205 Hz) is considered around δA and δB (resp. δX). The computation time needed to simulate the signal for one enantiomer was 2 days and 6 hours. The time- and position-dependent Hamiltonian used to solve in each slice the corresponding LiouvilleVon Neumann equation accounts for all the spin interactions mainly the chemical shift, the scalar and dipolar couplings, and the interaction with the radiofrequency (rf) field- acting on ρ(z,t1,t2). The chemical shifts and homonuclear total couplings values that were used to describe the spin system of 1 are summarized for each enantiomer in Table S2 in Supporting Information. We remind that these values are slightly different for each anisotropic sample, because the weak alignment induced by the chiral liquid crystalline phase on each enantiomer is known to be slightly different from one sample to another. The overall NMR signal S(z,t1,t2) issued from these calculations was digitized following the desired quadrature scheme and the resulting real and imaginary parts of the FID were injected into a dataset that is compatible with further processing using the ©Bruker's TopSpin™ software. The simulated 2D data were then processed with zero-filling and apodization with an exponential function in the direct and indirect dimensions to adjust the lineshape to corresponding experimental spectra.

RESULTS AND DISCUSSION Figure 2a shows the G-SERF spectrum recorded on 1 dissolved in PBLG, to probe the coupling network around HA. As expected, two series of multiplets -one per enantiomer- are observed at the chemical shift of each coupling partner HX and HB, whose splitting along the indirect domain is the total coupling TAX and TAB. The relative sensitivity induced by the spatial encoding was found to be ~ 5 % of that of a standard 1H spectrum. This lower sensitivity11,26 allowed us, though, for recording this spectrum in half an hour, on a sample at routine concentration for industrial or academic laboratories.


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Analytical Chemistry modern spectrometers, and notably cryogenically cooled probes. The proposed protocol for determining accurately ee’s is summarized in Figure 3. It aims at simulating G-SERF experiments on each enantiomer R and S, and calculating their 2D NMR signals SRcalc(t1, t2) and SScalc(t1, t2), where t1 and t2 correspond to the direct and indirect time domain. Beforehand, the acquisition of a complete set of experimental G-SERF spectra allows for measuring and assigning straightforwardly all the total couplings that are needed for each enantiomer to simulate their spin system. We adjust the chemical shifts (including chemical shift anisotropy) by fitting directly the 1H 1D spectrum of the sample, as it is illustrated in Figures 1b-e. Then, we generate the overall signal Scalc(t1, t2) of our virtual sample by adding the weighted signals of each enantiomer according to the desired ee:

 100 + ee  calc  100 − ee  calc S calc ( t1, t2 ) =   SR (t1, t2 ) +   SS ( t1, t2 )  2 ×100   2 ×100  (2) We account for the contribution of sample inhomogeneity and 1 H relaxation to the observed linewidth by adjusting the apodization in each dimension of the spectrum. Figure 2c shows for instance the G-SERF spectrum calculated for the racemate sample. We observe that the simulated spectrum reproduces faithfully the main features of the experimental one, notably the second order effect observed for HB. Third, we perform the projection of each set of correlations arising from each total coupling TAX and TAB. We integrate the doublets corresponding to each enantiomer, and we calculate the integration ratio between R and S:

(I

(R)

− I (S) ) ( I (R) + I (S) ) ×100

(3)

I(R) and I(S) are the integrations of the doublets that can be assigned to enantiomers R and S, respectively (see details in SI).

Figure 2. (a) The experimental G-SERF spectrum recorded on the racemate sample of 1. The offset of the non-encoded refocusing pulses was set so as to edit the coupling network involving HA. The experimental (b) and calculated (c) expansions of the regions where the couplings involving HA are edited. In (c) the subspectra corresponding to the enantiomers S and R are displayed in red and blue, respectively. (d) The total couplings that can be measured using this spectrum are shown on the structure of each enantiomer.

It should be noted that the duration of this experiment is first of all imposed by the high number of increments recorded in the indirect domain to achieve a sufficient resolution. The lower sensitivity induced by the spatial frequency encoding is nowadays compatible with the range of sensitivity achieved by

Figure 3. Flowchart describing the steps for determining ee’s from T-edited spectra (here G-SERF).



We have carried out a series of G-SERF experiments on five samples with increasing ee in R (the corresponding data are shown in SI), and we have applied the protocol described above to simulate and process these spectra. Figure 4a shows the correlation between the simulated and experimental integration ratios that were determined for each total coupling TAX and TAB, for each prepared enantiomeric excess. The high coefficients of determination (R2) obtained for the data extracted from the AX and AB series, of respectively 0.9978 and 0.9985, highlight the goodness of the linear regression performed on these datasets. Interestingly, we observe that the integration ratios that are determined for each sample (with a given prepared ee) are systematically different for the total couplings TAX and TAB. In particular, Figure 4b shows that the ratios calculated for the AX series are close to the values of the prepared ee’s, whereas there is a strong deviation between the integration ratios and the prepared ee's for the AB series (Fig. 4b - see Table S3 in SI). This deviation is expected for SFE experiments. It arises on the one hand from the difficulty to implement a sufficiently selective refocusing block to encode each proton in a spatially resolved region of the sample. On the other hand, a partial overlap of the correlations of each enantiomer may also cause a bias. This suggests that any SFEbased method relying on T-edited or pure shift experiments to perform a chiral analysis does not allow for interpreting integration ratios as being directly equal to the prepared ee, because it may be prone to significant bias.9,16,27 The good correlation between the calculated and experimental integration ratios reported here opens the way to a reliable determination of the ee of an unknown sample, by fitting the simulated projections of a G-SERF spectrum to their experimental counterpart. In other words, we propose to calibrate the experimentally determined integration ratios by using simulated spectra in order to account rigorously for the deviations from the prepared ee. For the present samples, it appeared that the two main parameters to be adjusted are the ee and the apparent linewidth along the indirect domain of the G-SERF spectrum, for each proton site. We have thus evaluated the ability of this method to converge to the true value of the prepared ee, by calculating a reliability factor Rproj when these two parameters are adjusted:

∑( S [ n] − S [ n]) calc proj

Rproj =

n

exp proj

∑( S [ n ] ) exp proj

n

2

2

(4)

n corresponds to the nth point from the calculated or experimental projection Sproj[n]. Figure 5 shows an overview of the evolution of Rproj for two samples (ee = 0 % and 85.7 %), for the AX series. The simulation converges unambiguously toward a unique best fit in both cases, which corresponds to the true value of the ee. Finally, we note that the precision with which the best fit can be determined, which is known to depend on the value of the ee, varies as expected from one sample to another. In conclusion, we have introduced a concept for determining accurately ee's from 1H NMR spectra, which combines the properties of chiral liquid crystalline solvents and the high resolution that can be achieved using SFE techniques.

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Figure 4. a) Correlation between the simulated and experimental integration ratios for five different samples of 1. Dashed lines correspond to the linear regressions performed on the integration ratios calculated for the total couplings AX and AB, respectively. The prepared ee is indicated for each point. b) Correlation between the prepared enantiomeric excess (%) and the experimentally determined integration ratio (%). The dashed line represents the linear trend corresponding to quantitativity. The error bars correspond to the standard deviation on ee's evaluated through a Monte Carlo method, and reflect the fact that the experimental uncertainty is dominated by the accuracy on the weighing of each enantiomer (see Table S1).

It relies on the simulation of T-edited spectra to fit experimental data while accounting for the complexity of the anisotropic sample under study, and the key features of spatially encoded spectra. This approach is robust, simple to implement, and is demonstrated here on a chiral anisotropic sample for which the enantiomeric differentiation is monitored through the observation of RDC’s. The good correlation that is observed between experimental and simulated data is achieved here by adjusting a reduced number of parameters to fit projections.


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Figure 5. The evolution of the reliability factor Rproj against the ee and the 1H linewidth in the indirect domain is shown for the AX series, (a) for the racemate sample, and (b) for the sample with ee = 85.7 %.

It can be further improved if the complexity of the observed anisotropic lineshapes require that a higher number of spectral parameters be adjusted. We also note that a single G-SERF spectrum provides several correlations on which integration ratios can be calculated independently, which can contribute to enhance the quality of the analysis. This concept can of course be extended to other sequences designed for editing 1H-1H homonuclear couplings, and offering potentially higher resolution and sensitivity. Several pulse sequences were introduced in the recent years to acquire Jedited spectra with a better performance than the original GSERF pulse sequence.26,28-34 Among them, the pushGSERF35 and the PSYCHEDELIC experiments36 allow for acquiring J-edited spectra with broadband homonuclear decoupling in the direct dimension. For all these sequences however, the robustness of each pulse sequence regarding the analysis of anisotropic samples should be evaluated, and adequate simulation tools have to be developed. In particular their ability to account faithfully for the artifacts generated by the PSYCHE element needs to be addressed. The use of simulation tools to describe accurately the key features of complex pulse sequences and address the possible quantitativity issues that may arise from their implementation can also be applied to other fields of enantiomeric discrimination. On the one hand, several 1D and 2D experiments incorporating broadband

or band-selective homonuclear decoupling have been successfully shown to allow for leading to the determination of enantiomeric or even diastereomeric excesses.37-39 In all these cases, it is obvious that the resulting spectra should be analyzed using the approach described in this paper to account for imperfections of the pulse sequences, and the complexity of the sample. We remark however that the pure shift approach is less general because 1H chemical shift anisotropy is known to be rather weak, except for particular cases. On the other hand, an interesting approach has been introduced recently to overcome the problem raised by the overlap of 1H signals, which consists in recording heteronuclear pure shift HSQC spectra in order to benefit from the higher chemical shift dispersion of another nucleus such as 13C.40 This latter approach combines spectral aliasing, homonuclear decoupling in the 1H dimension, and linear prediction. In summary, the present study paves the way for an accurate determination of ee's by 1H NMR. It can be applied to a wide variety of compounds ranging from chemical intermediates such as β-lactone derivatives for which optical purity is a key feature41, to larger chiral molecules where spectral resolution is critical. In this latter case, two size-dependent issues need to be considered. On the one hand, there will be a higher number of proton signals on the spectrum, hence leading to the acquisition of crowded spectra. Experiments implementing pure shift evolutions such as push-GSERF35 or PSYCHEDELIC36 may be of great use to solve this problem. On the other hand, a higher number of residual dipolar couplings will contribute to the multiplicity of each proton NMR signal. T-edited experiments were shown to be potentially well suited for addressing this issue for chiral compounds interacting with weakly orienting media.22 The implementation of SFE simulations into a more efficient code to perform rapid calculations is under progress in our group to address this challenging application.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Details about gravimetrically prepared NMR samples, experiments and simulations. Pure shift 1D 1H NMR spectra. Experimental and simulated G-SERF spectra recorded on 1. Integration ratios determined on experimental and simulated GSERF spectra.

AUTHOR INFORMATION Corresponding Author * E-mail: [email protected]

Present Address † Université Paris Descartes, Laboratoire de Chimie et Biochimie Pharmacologiques et Toxicologiques, UMR 8601 CNRS, Paris, France.

Author Contributions NG designed the project, analyzed the data and wrote the paper. DP and MC prepared the samples. BP, DP and MC ran the NMR experiments. BP ran the simulations.

Funding Sources The authors declare no competing financial interest.



ACKNOWLEDGMENT This work was supported by the French Research Agency (ANR2011-JS08-009-01).

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(22) Merlet, D.; Beguin, L.; Courtieu, J.; Giraud, N. J. Magn. Reson. 2011, 209, 315-322. (23) Beguin, L.; Giraud, N.; Ouvrard, J. M.; Courtieu, J.; Merlet, D. J. Magn. Reson. 2009, 199, 41-47. (24) SpinDynamica code for Mathematica, programmed by Malcolm H. Levitt, with contributions by Jyrki Rantaharju, Andreas Brinkmann, and Soumya Singha Roy, available at http://www.spindynamica.soton.ac.uk/. (25) Wolfram Research, I.; Wolfram Research, Inc. : Champaign, Illinois, 2012. (26) Lokesh; Suryaprakash, N. Chem. Commun. 2014, 50, 85508553. (27) Nath, N.; Kumari, D.; Suryaprakash, N. Chem. Phys. Lett. 2011, 508, 149-154. (28) Lokesh, N.; Chaudhari, S. R.; Suryaprakash, N. Chem. Commun. 2014, 50, 15597-15600. (29) Chaudhari, S. R.; Suryaprakash, N. ChemPhysChem 2015, 16, 1079-1082. (30) Lin, L.; Wei, Z.; Lin, Y.; Chen, Z. J. Magn. Reson. 2016, 272, 20-24. (31) Mishra, S. K.; Suryaprakash, N. J. Magn. Reson. 2017, 279, 74-80. (32) Zeng, Q.; Lin, L.; Chen, J.; Lin, Y.; Barker, P. B.; Chen, Z. J. Magn. Reson. 2017, 282, 27-31. (33) Fredi, A.; Nolis, P.; Parella, T. Magn. Reson. Chem. 2017, 55, 525-529. (34) Mishra, S. K.; Lokesh, N.; Suryaprakash, N. RSC Advances 2017, 7, 735-741. (35) Pitoux, D.; Plainchont, B.; Merlet, D.; Hu, Z.; Bonnaffé, D.; Farjon, J.; Giraud, N. Chem. Eur. J. 2015, 21, 9044-9047. (36) Sinnaeve, D.; Foroozandeh, M.; Nilsson, M.; Morris, G. A. Angew. Chem. Int. Ed. 2016, 55, 1090-1093. (37) Castañar, L.; Pérez-Trujillo, M.; Nolis, P.; Monteagudo, E.; Virgili, A.; Parella, T. ChemPhysChem 2014, 15, 854-857. (38) Nath, N.; Verma, A.; Baishya, B.; Khetrapal, C. L. Magn. Reson. Chem. 2017, 55, 553-558. (39) Rachineni, K.; Kakita, V. M. R.; Hosur, R. V. Magn. Reson. Chem., n/a-n/a. (40) Perez-Trujillo, M.; Castanar, L.; Monteagudo, E.; Kuhn, L. T.; Nolis, P.; Virgili, A.; Williamson, R. T.; Parella, T. Chem. Commun. 2014, 50, 10214-10217. (41) Getzler, Y. D. Y. L.; Mahadevan, V.; Lobkovsky, E. B.; Coates, G. W. J. Am. Chem. Soc. 2002, 124, 1174-1175.


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Figure 1. (a) The structure and atomic labeling of both enantiomers of 3-hydroxy-4,4,4-trichlorobutyric βlactone 1. The experimental (b) and calculated (c) 1H NMR spectra of a racemate sample of 1 dissolved in a chiral liquid crystalline phase composed of PBLG and CD2Cl2. The simulated 1H spectra of enantiomers R and S are shown in (d) and (e), respectively. 82x96mm (300 x 300 DPI)


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Figure 2. (a) The experimental G-SERF spectrum recorded on the racemate sample of 1. The offset of the non-encoded refocusing pulses was set so as to edit the coupling network involving HA. The experimental (b) and calculated (c) expansions of the regions where the couplings involving HA are edited. In (c) the subspectra corresponding to the enantiomers S and R are displayed in red and blue, respectively. (d) The total couplings that can be measured using this spectrum are shown on the structure of each enantiomer. 84x203mm (300 x 300 DPI)



Figure 3. Flowchart describing the steps for determining ee’s from T-edited spectra (here G-SERF). 97x93mm (300 x 300 DPI)


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Figure 4. a) Correlation between the simulated and experimental integration ratios for five different samples of 1. Dashed lines correspond to the linear regressions performed on the integration ratios calculated for the total couplings AX and AB, respectively. The prepared ee is indicated for each point. b) Correlation between the prepared enantiomeric excess (%) and the experimentally determined integration ratio (%). The dashed line represents the linear trend corresponding to quantitativity. The error bars correspond to the standard deviation on ee's evaluated through a Monte Carlo method, and reflect the fact that the experimental uncertainty is dominated by the accuracy on the weighing of each enantiomer (see Table S1). 84x161mm (300 x 300 DPI)



Figure 5. The evolution of the reliability factor Rproj against the ee and the 1H linewidth in the indirect domain is shown for the AX series, (a) for the racemate sample, and (b) for the sample with ee = 85.7 %. 85x145mm (300 x 300 DPI)


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Highly Accurate Quantitative Analysis Of Enantiomeric Mixtures from

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