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  • Vol. 6, Iss. 3 — Mar. 18, 2011
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Improved detection sensitivity of D-mannitol crystalline phase content using differential spectral phase shift terahertz spectroscopy measurements

Jean-François Allard, Alain Cornet, Christophe Debacq, Marc Meurens, Daniel Houde, and Denis Morris  »View Author Affiliations


Optics Express, Vol. 19, Issue 5, pp. 4644-4652 (2011)
http://dx.doi.org/10.1364/OE.19.004644


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Abstract

We report quantitative measurement of the relative proportion of δ- and β- D-mannitol crystalline phases inserted into polyethylene powder pellets, obtained by time-domain terahertz spectroscopy. Nine absorption bands have been identified from 0.2 THz to 2.2 THz. The best quantification of the δ-phase proportion is made using the 1.01 THz absorption band. Coherent detection allows using the spectral phase shift of the transmitted THz waveform to improve the detection sensitivity of the relative δ-phase proportion. We argue that differential phase shift measurements are less sensitive to samples' defects. Using a linear phase shift compensation for pellets of slightly different thicknesses, we were able to distinguish a 0.5% variation in δ-phase proportion.

© 2011 OSA

1. Introduction

Process monitoring is used in the fabrication of a pharmaceutical product for quality and reproducibility control. Dehydration is used to increase shelf life-time and to reduce its weight for transportation: it is however a critical part of the overall fabrication process [1

1. S. Byrn, R. Pfeiffer, M. Ganey, C. Hoiberg, and G. Poochikian, “Pharmaceutical solids: a strategic approach to regulatory considerations,” Pharm. Res. 12(7), 945–954 (1995). [CrossRef] [PubMed]

]. Freeze drying or lyophilisation is widely used in the industry and D-mannitol is an alcohol sugar that is commonly used as an excipient. However, depending on the freeze drying conditions different crystalline phases of D-mannitol can be produced [2

2. A. I. Kim, M. J. Akers, and S. L. Nail, “The physical state of mannitol after freeze-drying: effects of mannitol concentration, freezing rate, and a noncrystallizing cosolute,” J. Pharm. Sci. 87(8), 931–935 (1998). [CrossRef] [PubMed]

, 3

3. L. Yu, N. Milton, E. G. Groleau, D. S. Mishra, and R. E. Vansickle, “Existence of a mannitol hydrate during freeze-drying and practical implications,” J. Pharm. Sci. 88(2), 196–198 (1999). [CrossRef] [PubMed]

] resulting in potentially different biological activities of the final product. Specific signatures of the different D-mannitol crystalline phases have already been revealed using techniques such as X-Ray powder diffraction (XRPD) [4

4. S. N. Campbell Roberts, A. C. Williams, I. M. Grimsey, and S. W. Booth, “Quantitative analysis of mannitol polymorphs. X-ray powder diffractometry - exploring preferred orientation effects,” J. Pharm. Biomed. Anal. 28(6), 1149–1159 (2002). [CrossRef] [PubMed]

], Raman spectroscopy [5

5. S. N. Campbell Roberts, A. C. Williams, I. M. Grimsey, and S. W. Booth, “Quantitative analysis of mannitol polymorphs. FT-raman spectroscopy,” J. Pharm. Biomed. Anal. 28(6), 1135–1147 (2002). [CrossRef] [PubMed]

], nuclear magnetic resonance (NMR) [6

6. T. Yoshinari, R. T. Forbes, P. York, and Y. Kawashima, “Moisture induced polymorphic transition of mannitol and its morphological transformation,” Int. J. Pharm. 247(1-2), 69–77 (2002). [CrossRef] [PubMed]

] and mid-infrared (MIR) spectroscopy [7

7. V. K. Sharma and D. S. Kalonia, “Effect of vacuum drying on protein-mannitol interactions: the physical state of mannitol and protein structure in the dried state,” AAPS PharmSci.Tech 5(1), E10 (2004). [CrossRef]

]. Each of these techniques has its own drawbacks [8

8. M. Otsuka, J.-I. Nishizawa, J. Shibata, and M. Ito, “Quantitative evaluation of mefenamic acid polymorphs by terahertz-chemometrics,” J. Pharm. Sci. 99(9), 4048–4053 (2010). [CrossRef] [PubMed]

] so the pharmaceutical industry is still looking for a high detection sensitivity technique for quantifying the polymorphic content of D-mannitol compounds. Such a technique can take advantage of the fact that D-mannitol has an extensive inter-molecular H-bond network [9

9. F. R. Fronczek, H. N. Kamel, and M. Slattery, “Three polymorphs (α, β, and δ) of D-mannitol at 100 K,” Acta Crystallogr. C 59(Pt 10), 567–570 (2003). [CrossRef]

]. Multi-molecular vibrational modes are very sensitive to molecular composition and crystalline phase: the energies and the intensities of these modes represent a precise molecular finger print. With the advent of reliable broad band THz radiation sources, a spectrum of the low-energy vibrational modes can now be measured. Recently, Chakkittakandy qualitatively measured 0.5 - 7 THz spectra of D-mannitol crystallized during freeze drying, using a quasi near-field setup [10

10. R. Chakkittakandy, J. A.W.M Corver, and P. C.M. Planken, “Terahertz spectroscopy to identify the polymorphs in freeze-dried Mannitol,” J. Pharm. Sci. 99(2), 932–940 (2010).

]. While the conventional far-field measurement with a semiconductor emitter and a ZnTe electro-optic detection is restricted to a maximum frequency of about 4 THz, its signal/noise ratio is much better than the one of a near-field measurement. On an industrial point of view, it is advantageous to measure the D-mannitol absorbance at 1 THz since this frequency falls below the inter-molecular and intra-molecular vibrational modes [11

11. B. M. Fischer, M. Walther, and P. U. Jepsen, “Far-infrared vibrational modes of DNA components studied by terahertz time-domain spectroscopy,” Phys. Med. Biol. 47(21), 3807–3814 (2002). [CrossRef] [PubMed]

] of most other excipients or growth ingredients. Far-field measurements are also more interesting for on-line quantification of different crystalline phases of a specific product.

The quantification of different crystalline phases of a molecule in a mixture sample has already been reported using time-domain terahertz spectroscopy [8

8. M. Otsuka, J.-I. Nishizawa, J. Shibata, and M. Ito, “Quantitative evaluation of mefenamic acid polymorphs by terahertz-chemometrics,” J. Pharm. Sci. 99(9), 4048–4053 (2010). [CrossRef] [PubMed]

, 10

10. R. Chakkittakandy, J. A.W.M Corver, and P. C.M. Planken, “Terahertz spectroscopy to identify the polymorphs in freeze-dried Mannitol,” J. Pharm. Sci. 99(2), 932–940 (2010).

14

14. H. Wu, E. J. Heilweil, A. S. Hussain, and M. A. Khan, “Process analytical technology (PAT): quantification approaches in terahertz spectroscopy for pharmaceutical application,” J. Pharm. Sci. 97(2), 970–984 (2008). [CrossRef]

]. The polymorphic content can be extracted from a chemometric analysis [13

13. M. Otsuka, J.-I. Nishizawa, J. Shibata, and M. Ito, “Quantitative evaluation of mefenamic acid polymorphs by terahertz-chemometrics,” J. Pharm. Sci. 99(9), 4048–4053 (2010). [CrossRef] [PubMed]

, 14

14. H. Wu, E. J. Heilweil, A. S. Hussain, and M. A. Khan, “Process analytical technology (PAT): quantification approaches in terahertz spectroscopy for pharmaceutical application,” J. Pharm. Sci. 97(2), 970–984 (2008). [CrossRef]

.] based on a multi-parameters fitting procedure that sets the best calibration model relating each THz absorption feature to one or several crystalline forms of the molecule. By choosing an appropriate reference sample, it is sometime possible to simplify drastically the analysis by obtaining absorbance spectra with well resolved absorption bands over a given spectral range. In these circumstances, one can verify that the amplitude of each chosen absorption band scales almost linearity with the crystalline phase content. The detection sensitivity of one particular crystalline phase depends on the experimental considerations such as the signal to noise ratio of the measurements and the reproducibility of the fabrication process used for making the set of calibration samples. Thickness variations resulting from the inevitable loss of material during the pellet's compression and fluctuations in the density of defects from sample to sample have a direct impact on the amplitude of a given THz absorbance peak. In this paper, we show that it is advantageous to use the spectral phase shift of the transmitted THz waveform to improve the polymorphic content detection sensitivity. We argue that differential spectral phase shift measurements are less sensitive to samples' defects.

We report room temperature quantitative measurements of relative crystalline phases of a mixture of δ- and β-phase D-mannitol inserted into a polyethylene powder pellet, with far-field Time-Domain THz Spectroscopy (TDS). Multiple absorption bands spectra of a series of D-mannitol samples are obtained and reproduced using Voigt functions that account for homogeneous and inhomogeneous spectral broadening mechanisms. The quantitative measurement of the δ-phase proportion is obtained using specific absorption bands. Differential phase shift spectra of the transmitted THz waveform are also obtained for the different samples. We calculate a series of differential phase shift data curves by subtracting measurements obtained for the x% δ-phase samples with the one obtained for the 100% β-phase sample, and compensate for the linear behavior resulting from any slight variation in thickness between two given pellets. We then compare the quantification methods of D-mannitol crystalline phases using either the amplitude of one particular absorbance band or the maximum variation of the differential phase shift values around the same absorption band.

2. Experiment

The time-domain THz spectroscopy (THz-TDS) setup uses a conventional 4 parabolic mirrors configuration. A photoconductive low-aperture antenna was used for the generation of short THz pulses. The THz emitter was fabricated on a multi energy H-bombarded high resistivity GaAs substrate [15

15. B. Salem, D. Morris, V. Aimez, J. Beerens, J. Beauvais, and D. Houde, “‘Pulsed photoconductive antenna terahertz sources made on ion-implanted GaAs substrates,” J. Phys. Condens. Matter 17(46), 7327–7333 (2005). [CrossRef]

]. A 60 fs mode-locked Ti:sapphire oscillator was used as the excitation laser source. A home-made frequency chirping pulse apparatus allows minimizing the pulse duration at the position of the THz emitter. A 4 mm hemispherical silicon lens was fixed on the backside of the emitter. The terahertz radiation was collected over a large solid angle and refocused on our sample using a pair of off-axis parabolic mirrors. The transmitted THz beam was collected and refocused on our detector using a second set of parabolic mirrors. The THz traces were detected using a 40-ps delay line and electro-optic sampling in a 0.5 mm-thick <110> ZnTe crystal. The intensity of the pump beam was modulated at a frequency of 3 kHz using a mechanical chopper and a lock-in amplifier was used to retrieve the THz signal. The spectra of the THz traces were then obtained using numerical Fourier transforms.The samples were mounted on a rotating wheel and the entire setup is enclosed in a vacuum chamber. A turbo-molecular pump was used to quickly reduce the pressure (< 10−3 Torr) inside the chamber and measurements were carried out after filling the chamber with dry nitrogen.

The ACS Reagent D-mannitol and the ultra high molecular weight 53-75 μm polyethylene powder were purchased from Sigma-Aldrich. As received, the D-mannitol was in the β-phase and consists in coarse polycrystalline particles. The protocol described by L. Walther –Lévy [16

16. L. Walter-Lévy, “Sur les variétés cristallines du D-mannitol,” C. R. Acad. Sc. Paris 267, 1779–1782 (1968).

] was followed to crystallized a part of the D-mannitol in its δ-phase and separate each phase in order to obtain pure polycrystalline samples. We have verified the purity of each phase by comparing the X-ray powder diffraction pattern (XRDP) with the International Center Diffraction Data (ICDD) table. To insure a correct interpretation from XRDP data, the polycrystalline D-Mannitol powder were carefully ground with a mortar and pestle until a very fine powder is obtained.

Samples were made from a mixture of polyethylene powder and D-mannitol crystallites in a proportion of 3:1. A set of 14 samples has been prepared with the D-mannitol portion containing a mixture of δ- and β-crystalline phases: the δ-phase content in the D-mannitol portion is respectively 0.5%, 1%, 2.5%, 5%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90% and 100%. To insure a good homogeneity, the polyethylene + D-mannitol preparation was mixed thoroughly with the mortar and pestle. Pellets were then made from 500 mg of this powder compressed at 7000 lbs/cm2. A 500 mg of polyethylene powder pellet was also made as a reference. Another XRDP analysis on the compressed pellet confirms that humidity or pressure did not cause any phase transformation. Samples were kept into a desiccators’ chamber after each manipulation. All results presented in this article were measured on the same set of samples.

3. Results

Absorbance=α(ω)d2=ln(E(ω)E0(ω)).
(1)

Equation (1) is the absorbance with ∝(ω) being the coefficient of absorption at a given wavelength, d is the pellet thickness, E(ω) and E0(ω) are the electric field of the transmitted THz pulses through the sample and reference, respectively. A zero padding procedure with a quenching window is applied to the THz traces. The instrumental spectral resolution is about 0.03 THz. Figure 1(a)
Fig. 1 (color online) (a) Transmitted THz electric field amplitude measured between 0.7 and 2.2 THz for different 4.2 mm thick pellets containing a mixture of δ- and β- crystalline phase D-mannitol combined with polyethylene powder. The reference sample is the polyethylene only pellet. The δ-phase proportion varies from 10% (bottom curve) to 100% (top curve), by increment of 10%. The curves are displaced vertically for clarity. (b) Corrected data points between 0.9 to 1.3 THz for the 50% δ-phase – 50% β-phase mixture pellet (full squares) and 100% β-phase (full circles). The best fit (solid line) of the 50% δ-phase data points is obtained using three Voigt functions (dashed lines) centered at the δ1, M1 and δ2 peaks. (c) Integrated amplitude corresponding to the area under the fitted absorption peak plotted as a function of the δ-phase proportion, for the δ1 (full squares) and the δ2 (full circles) bands. The R-square values of the best linear fits (solid lines) passing through the data points are 0.9997 and 0.9908 for the δ1 and δ2 bands, respectively.
shows the absorbance spectra of D-mannitol samples as the δ-phase content is increased from 0% (top) to 100% (bottom) by 10% increments. The reference is the polyethylene only pellet. The β-phase absorbance spectrum (pellet with 0% δ-phase – 100% β-phase) shows two main absorption bands at 1.11 THz (M1) and 1.49 THz (M2). Other absorption bands appear as the δ-phase proportion increases: the main one being at 1.01 THz (δ1). The M1 and M2 bands seem to undergo a frequency shift as the δ-phase proportion increases. Fitting the absorbance using specific and non-specific δ-phase absorption bands reveals that this apparent shift results from a change in the relative importance of two closely separated absorption bands when the δ-phase proportion increases.

The central frequencies of all absorption bands are listed in Table 1

Table 1. Absorption bands of δ and β phase D-mannitol between 0.2 and 2.2 THz.

table-icon
View This Table
. The frequencies of the δ1 to δ5 absorption bands are determined from the fit of the absorbance spectrum of D-mannitol 100% δ-phase sample using the 100% β-phase sample as a reference, see Fig. 2(a). The fitting procedure consists in using one Voigt function per absorption band. The error bars on these frequencies are estimated by comparing the frequency values obtained using the same fitting procedure for at least three other spectra corresponding to samples with different δ-phase contents. The central peak frequencies of δ6 and δ7 bands are evaluated using the low δ-phase proportion absorbance curves before the onset of the saturation regime. Finally, the central frequencies of the M1 and M2 absorption bands are determined using the 100% β-phase absorbance curve obtained using the polyethylene only sample as a reference.

The index of refraction increases with frequency below and above the absorption band (normal dispersion regime) and the variation in the index of refraction suffers a sign change at the resonant frequency (abnormal dispersion regime). The amplitude of the frequency dependent phase shift profile around a specific absorption band depends on the oscillator strength of the vibrational mode; this amplitude is proportional to the crystalline phase content in the linear regime of oscillation. The δ-phase quantification can then be obtained using a differential phase shift measurement which consists in subtracting the THz phase spectrum of a x% δ-phase sample to the one of a 100% β-phase D-mannitol reference sample. Figure 3
Fig. 3 (color online) Differential phase shift values of the THz waveform transmitted through the β-phase (0% δ-100% β) and the 10% δ-phase (10% δ-90% β) D-mannitol pellets plotted as a function of the frequency (full square symbol). The corrected data points (empty circle symbol) are obtained by subtracting a linear curve fit (solid line) to the experimental data points.
shows the differential phase shift plot of the 10% δ-phase D-mannitol sample.

The experimental data curve (full square symbol) presents several absorption band features superimposed on a linear function of the phase characterized by a positive slope and a negative intercept. This linear frequency-dependent behavior is attributed to a difference in the pellet thickness of the two samples. Corrected data curve (empty circle symbol) is obtained by subtracting a simple linear interpolation that passes through the experimental data points. Since no absorption band is observed between 0.2 and 0.8 THz, we have used this frequency range (dotted box region shown in Fig. 3) to evaluate the standard deviation between the fitted and the experimental data points.

4. Conclusion

Acknowledgments

This work was supported financially by NSERC, CFI, FQRNT (Québec), Nano-Québec and coopération Wallonie-Québéc. The authors would like to thank M. Lacerte, G. Laliberté, F. Francoeur, and K. Truong for their technical support.

References and links

1.

S. Byrn, R. Pfeiffer, M. Ganey, C. Hoiberg, and G. Poochikian, “Pharmaceutical solids: a strategic approach to regulatory considerations,” Pharm. Res. 12(7), 945–954 (1995). [CrossRef] [PubMed]

2.

A. I. Kim, M. J. Akers, and S. L. Nail, “The physical state of mannitol after freeze-drying: effects of mannitol concentration, freezing rate, and a noncrystallizing cosolute,” J. Pharm. Sci. 87(8), 931–935 (1998). [CrossRef] [PubMed]

3.

L. Yu, N. Milton, E. G. Groleau, D. S. Mishra, and R. E. Vansickle, “Existence of a mannitol hydrate during freeze-drying and practical implications,” J. Pharm. Sci. 88(2), 196–198 (1999). [CrossRef] [PubMed]

4.

S. N. Campbell Roberts, A. C. Williams, I. M. Grimsey, and S. W. Booth, “Quantitative analysis of mannitol polymorphs. X-ray powder diffractometry - exploring preferred orientation effects,” J. Pharm. Biomed. Anal. 28(6), 1149–1159 (2002). [CrossRef] [PubMed]

5.

S. N. Campbell Roberts, A. C. Williams, I. M. Grimsey, and S. W. Booth, “Quantitative analysis of mannitol polymorphs. FT-raman spectroscopy,” J. Pharm. Biomed. Anal. 28(6), 1135–1147 (2002). [CrossRef] [PubMed]

6.

T. Yoshinari, R. T. Forbes, P. York, and Y. Kawashima, “Moisture induced polymorphic transition of mannitol and its morphological transformation,” Int. J. Pharm. 247(1-2), 69–77 (2002). [CrossRef] [PubMed]

7.

V. K. Sharma and D. S. Kalonia, “Effect of vacuum drying on protein-mannitol interactions: the physical state of mannitol and protein structure in the dried state,” AAPS PharmSci.Tech 5(1), E10 (2004). [CrossRef]

8.

M. Otsuka, J.-I. Nishizawa, J. Shibata, and M. Ito, “Quantitative evaluation of mefenamic acid polymorphs by terahertz-chemometrics,” J. Pharm. Sci. 99(9), 4048–4053 (2010). [CrossRef] [PubMed]

9.

F. R. Fronczek, H. N. Kamel, and M. Slattery, “Three polymorphs (α, β, and δ) of D-mannitol at 100 K,” Acta Crystallogr. C 59(Pt 10), 567–570 (2003). [CrossRef]

10.

R. Chakkittakandy, J. A.W.M Corver, and P. C.M. Planken, “Terahertz spectroscopy to identify the polymorphs in freeze-dried Mannitol,” J. Pharm. Sci. 99(2), 932–940 (2010).

11.

B. M. Fischer, M. Walther, and P. U. Jepsen, “Far-infrared vibrational modes of DNA components studied by terahertz time-domain spectroscopy,” Phys. Med. Biol. 47(21), 3807–3814 (2002). [CrossRef] [PubMed]

12.

M. Yamaguchi, F. Miyamaru, K. Yamamoto, M. Tani, and M. Hangyo, “Terahertz absorption spectra of L-, D-, and DL-alanine and their application to determination of enantiometric composition,” Appl. Phys. Lett. 86(5), 053903 (2005). [CrossRef]

13.

M. Otsuka, J.-I. Nishizawa, J. Shibata, and M. Ito, “Quantitative evaluation of mefenamic acid polymorphs by terahertz-chemometrics,” J. Pharm. Sci. 99(9), 4048–4053 (2010). [CrossRef] [PubMed]

14.

H. Wu, E. J. Heilweil, A. S. Hussain, and M. A. Khan, “Process analytical technology (PAT): quantification approaches in terahertz spectroscopy for pharmaceutical application,” J. Pharm. Sci. 97(2), 970–984 (2008). [CrossRef]

15.

B. Salem, D. Morris, V. Aimez, J. Beerens, J. Beauvais, and D. Houde, “‘Pulsed photoconductive antenna terahertz sources made on ion-implanted GaAs substrates,” J. Phys. Condens. Matter 17(46), 7327–7333 (2005). [CrossRef]

16.

L. Walter-Lévy, “Sur les variétés cristallines du D-mannitol,” C. R. Acad. Sc. Paris 267, 1779–1782 (1968).

17.

M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100-μm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282(7), 1304–1306 (2009). [CrossRef]

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(170.0170) Medical optics and biotechnology : Medical optics and biotechnology
(300.6495) Spectroscopy : Spectroscopy, teraherz

ToC Category:
Spectroscopy

History
Original Manuscript: December 15, 2010
Revised Manuscript: February 3, 2011
Manuscript Accepted: February 9, 2011
Published: February 24, 2011

Virtual Issues
Vol. 6, Iss. 3 Virtual Journal for Biomedical Optics

Citation
Jean-François Allard, Alain Cornet, Christophe Debacq, Marc Meurens, Daniel Houde, and Denis Morris, "Improved detection sensitivity of D-mannitol crystalline phase content using differential spectral phase shift terahertz spectroscopy measurements," Opt. Express 19, 4644-4652 (2011)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-19-5-4644


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References

  1. S. Byrn, R. Pfeiffer, M. Ganey, C. Hoiberg, and G. Poochikian, “Pharmaceutical solids: a strategic approach to regulatory considerations,” Pharm. Res. 12(7), 945–954 (1995). [CrossRef] [PubMed]
  2. A. I. Kim, M. J. Akers, and S. L. Nail, “The physical state of mannitol after freeze-drying: effects of mannitol concentration, freezing rate, and a noncrystallizing cosolute,” J. Pharm. Sci. 87(8), 931–935 (1998). [CrossRef] [PubMed]
  3. L. Yu, N. Milton, E. G. Groleau, D. S. Mishra, and R. E. Vansickle, “Existence of a mannitol hydrate during freeze-drying and practical implications,” J. Pharm. Sci. 88(2), 196–198 (1999). [CrossRef] [PubMed]
  4. S. N. Campbell Roberts, A. C. Williams, I. M. Grimsey, and S. W. Booth, “Quantitative analysis of mannitol polymorphs. X-ray powder diffractometry - exploring preferred orientation effects,” J. Pharm. Biomed. Anal. 28(6), 1149–1159 (2002). [CrossRef] [PubMed]
  5. S. N. Campbell Roberts, A. C. Williams, I. M. Grimsey, and S. W. Booth, “Quantitative analysis of mannitol polymorphs. FT-raman spectroscopy,” J. Pharm. Biomed. Anal. 28(6), 1135–1147 (2002). [CrossRef] [PubMed]
  6. T. Yoshinari, R. T. Forbes, P. York, and Y. Kawashima, “Moisture induced polymorphic transition of mannitol and its morphological transformation,” Int. J. Pharm. 247(1-2), 69–77 (2002). [CrossRef] [PubMed]
  7. V. K. Sharma and D. S. Kalonia, “Effect of vacuum drying on protein-mannitol interactions: the physical state of mannitol and protein structure in the dried state,” AAPS PharmSci.Tech 5(1), E10 (2004). [CrossRef]
  8. M. Otsuka, J.-I. Nishizawa, J. Shibata, and M. Ito, “Quantitative evaluation of mefenamic acid polymorphs by terahertz-chemometrics,” J. Pharm. Sci. 99(9), 4048–4053 (2010). [CrossRef] [PubMed]
  9. F. R. Fronczek, H. N. Kamel, and M. Slattery, “Three polymorphs (α, β, and δ) of D-mannitol at 100 K,” Acta Crystallogr. C 59(Pt 10), 567–570 (2003). [CrossRef]
  10. R. Chakkittakandy, J. A.W.M Corver, and P. C.M. Planken, “Terahertz spectroscopy to identify the polymorphs in freeze-dried Mannitol,” J. Pharm. Sci. 99(2), 932–940 (2010).
  11. B. M. Fischer, M. Walther, and P. U. Jepsen, “Far-infrared vibrational modes of DNA components studied by terahertz time-domain spectroscopy,” Phys. Med. Biol. 47(21), 3807–3814 (2002). [CrossRef] [PubMed]
  12. M. Yamaguchi, F. Miyamaru, K. Yamamoto, M. Tani, and M. Hangyo, “Terahertz absorption spectra of L-, D-, and DL-alanine and their application to determination of enantiometric composition,” Appl. Phys. Lett. 86(5), 053903 (2005). [CrossRef]
  13. M. Otsuka, J.-I. Nishizawa, J. Shibata, and M. Ito, “Quantitative evaluation of mefenamic acid polymorphs by terahertz-chemometrics,” J. Pharm. Sci. 99(9), 4048–4053 (2010). [CrossRef] [PubMed]
  14. H. Wu, E. J. Heilweil, A. S. Hussain, and M. A. Khan, “Process analytical technology (PAT): quantification approaches in terahertz spectroscopy for pharmaceutical application,” J. Pharm. Sci. 97(2), 970–984 (2008). [CrossRef]
  15. B. Salem, D. Morris, V. Aimez, J. Beerens, J. Beauvais, and D. Houde, “‘Pulsed photoconductive antenna terahertz sources made on ion-implanted GaAs substrates,” J. Phys. Condens. Matter 17(46), 7327–7333 (2005). [CrossRef]
  16. L. Walter-Lévy, “Sur les variétés cristallines du D-mannitol,” C. R. Acad. Sc. Paris 267, 1779–1782 (1968).
  17. M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100-μm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282(7), 1304–1306 (2009). [CrossRef]

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