Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 158 (2016) 56–59
Contents lists available at ScienceDirect
Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy journal homepage: www.elsevier.com/locate/saa
Moles quantification in liquid samples by Raman spectroscopy R.Y. Sato-Berrú a,⁎, E.A. Araiza-Reyna b, A.R. Vazquéz-Olmos a a b
CCADET, Universidad Nacional Autónoma de México, Circuito Exterior S/N, Ciudad Universitaria, A.P. 70-186, Delegación Coyoacán, C.P. 04510, México D.F., México Facultad de Ciencias, Universidad Autónoma de San Luis Potosí, Av. Salvador Nava Martínez s/n, Zona Universitaria, C.P. 78290, San Luis Potosí, México
a r t i c l e
i n f o
Article history: Received 8 June 2015 Received in revised form 10 December 2015 Accepted 11 January 2016 Available online 14 January 2016 Keywords: Quantitative Raman Raman spectroscopy Raman technique Mole
a b s t r a c t The mole is a unit of measurement that expresses amounts of a chemical substance. Its importance lies in that the mass and the number of molecules of a substance can be determined with this value. In this work, we suggest a mathematical expression that relates the number of moles of the sample studied with the Raman signal and the experimental parameters used. In other words, with this mathematical expression it is possible to obtain quantitative information in a simple manner from Raman spectra. We have applied this method to different samples and we have observed an excellent correlation between the experimental and expected data. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Raman spectroscopy has proved to be an excellent non-destructive tool, not only for qualitative purposes but also for quantitative analysis [1,2]. The general spectrum profile (peak position and peak intensity) provides a unique chemical fingerprint which can be used to identify a substance and distinguish it from others. In addition, the intensity of a Raman signal in a spectrum is directly proportional to the sample concentration. Typically, a calibration procedure can be used to determine the relationship between peak intensity and sample concentration. Several quantitative Raman studies have been reported in different liquids or mixtures with two or more components. Unlike isotropic liquids, solid powder mixtures are more complicated systems. However, some studies have been conducted in this regard because of the several possible applications in the biology and pharmaceutical industries as well as in the quantitative analysis of drugs and other compounds [3–14]. The references provided of published quantitative Raman applications are by no means exhaustive. The instrumental factors that may affect the quantitative Raman analysis include variations in laser power or wavelength, optical train variations and irreproducible sample placement. The most common solution to the problem of instrumental variation is to use a standard sample, wherein the concentration of the sample is assumed to be proportional to the ratio of the sample peak height to the standard peak height. The instrumental variation affects the signal measured from the standard sample in the same way as the problem sample signal; this method can achieve excellent quantitative results as will be shown in this work. A simple mathematical relationship to get a ⁎ Corresponding author. E-mail address: [email protected] (R.Y. Sato-Berrú).
http://dx.doi.org/10.1016/j.saa.2016.01.017 1386-1425/© 2016 Elsevier B.V. All rights reserved.
quantitative value, as a first approximation for any sample studied, is proposed in this work. 2. Experiments Raman spectra were recorded with an Almega XR dispersive Raman spectrometer. These spectra were accumulated over 25 s with a resolution of ~ 4 cm−1 and an excitation source of 532 nm radiation from a Nd:YVO4 laser (frequency-doubled). All samples (ethanol—99.9%, methyl parathion—99.9%, pyridine—99% and rhodamine 6G—99%) used in this work were purchased from sigma Aldrich and used as received. The pure compounds and dilutions, prepared with triply distilled water, were stoked into well-sealed vessels. 2.1. Theoretical analysis It is well known that a concentrated solution should be diluted to obtain another solution of lower concentration. In this case, the volume of the solvent is increased to obtain the new concentration, which can be calculated by C1V1 = C2V2. In a similar manner, a mathematical expression can be adjusted to monitor the amount of sample mass that is transferred to a smaller volume. In other words, we studied the following relationship: CiVi → VH → vs, where Vi is the initial volume; Ci is the initial concentration; VH is the volume in a homogeneous configuration and vS is the volume of the laser spot used in the Raman experiment. Whereas a Gaussian beam, we determined the volume of the laser spot as vS = π2d4/4 λ. Here, we used d = 4 λf/π D as the diameter of a cylinder and L = π d2/λ as the height of the cylinder [15]; where the wavelength of laser was λ = 532 nm; the focal length of lens was f = 10 mm and the laser beam diameter was D = 1.9 mm.
R.Y. Sato-Berrú et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 158 (2016) 56–59
57
Fig. 1. Expected (line) and experimental (circles) data for the ethanol sample (A) and deviation values of data (B).
However, we noted that the number of moles “n” does not remain constant (ninitial N nHomogeneous N nspot), it changes as the volume of study decreases. Based on these considerations, a mathematical expression can be obtained for the number of moles that exist within the laser spot (volume): ns ¼ A C V
ð1Þ
where A = vs/VH, is the ratio between the volume of the laser spot and the homogeneous volume considered in the experiment. C is the concentration of the sample in Molarity and V is the volume of study in liters. If the number of moles in a system is known, the number of molecules and the sample mass can be determined with the following relationship: Nmolecules = ns ∗ NAvog and g = ns ∗ W; where, NAvog is the Avogadro's number (6.022 × 1023 mol− 1) and W is the molecular weight of the studied sample. On the other hand, Raman intensity is proportional to the intensity of the excitation source and to the number of molecules in the sample volume being probed with the Raman instrument [16,17]. Experimentally, it is known that the intensity of a Raman spectrum is directly proportional to the concentration. In this paper, considering the previous premises and our experience, we propose that the Raman signal is proportional to the number of molecules by using the following simple correlation: IR ¼ M i
ð2Þ
where M represents the number of elementary entities and i represents the Raman emission of each entities, which is representative of the material of study and under our experimental conditions. If we assume that M = ns, where ns represents the number of moles present within the laser spot (mathematical expression 1), the unitary intensity can be expressed as: i = IR/ns. Similarly, it can be assumed that it also satisfies the relationship: Ir = n ∗ i, where Ir represents an arbitrary Raman signal. Therefore, the number of moles can be determined in an arbitrary Raman signal with the following equation: n ¼ I ns
ð3Þ
where, I = Ir/IR is the ratio between the arbitrary and reference Raman intensity. We observed that I varies between 0 ≤ I ≤1. For pure and diluted substances, we have used the following mathematical expressions: A = vs/VH ; C = Ci = ni/Vi ; ni = m/W ;ρ = m/Vi ; V = VH, in Eqs. (1) and (3); then, we were able to obtain two particular expressions by quantitative Raman analysis of the liquid samples, in which we know the density “ρ” or initial concentration “Ci” of the reference sample. We implemented all these expressions in an excel worksheet. n ¼ I vs
ρ W
n ¼ I vs C i :
Fig. 2. Expected (line) and experimental (circles) data for the methyl parathion sample (A) and deviation values of data (B).
ð4Þ ð5Þ
58
R.Y. Sato-Berrú et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 158 (2016) 56–59
Fig. 3. Expected (circles) and experimental (stars) data for the pyridine sample for normal Raman (A) and for SERS (B).
3. Results and discussions The ethanol sample (molecular weight 46.058 g/mol and density 0.789 g/ml) was prepared in the range from 99.9 to 1% (v/v) with triply distilled water [5]. The intensity of a characteristic peak (882 cm−1) was used for the analysis. Then, when using vS =8 × 10−10 cm3 and mathematical expression 4, we observed that the experimental and expected values presented an excellent correlation, see Fig. 1A. Moreover, we have used and found the deviation values (Fig. 1B) through the following relation: s = ((experiment − expected)/expected) ∗ 100. This equation can give negative or positive values. A zero deviation indicates that the expected values perfectly correlate with the experimental values. A positive deviation indicates that the experimental values are higher than expected and, if the deviation is negative, the experimental values are lower than expected. The methyl parathion sample (molecular weight 263.21 g/mol) was prepared in the range from 1.5 M to 6.3 mM with triply distilled water [5] which is an organophosphate pesticide and harmful to health. The intensity of a characteristic peak (1345 cm−1) was used for the analysis. The same, when using vS = 8 ×10−10cm3 and mathematical expression 5, we observed that the experimental and expected values presented an excellent correlation (see Fig. 2A). Fig. 2B illustrates the deviation values. A pyridine sample (molecular weight 79.1 g/mol) was prepared in the range from 0.284 M to 6.3 mM with triply distilled water [18].The intensity of a characteristic peak (999 cm−1) was used for the analysis. The same, when using vS = 8 ×10−10cm3 and mathematical expression 5, we observed that the experimental and expected values presented an excellent correlation, see Fig. 3A. In this sample, the detection limit was found to be 6.3 mM and into the laser spot volume, the detection was of 5 × 10−13 g or 4 × 109 molecules. However, applying this mathematical expression to SERS experiments (Surface Enhanced Raman Spectroscopy) posed a challenge. In this regard, mixtures of spherical Ag nanoparticles colloids (0.25 ml), NaCl (0.05 ml: 8.5 mM) and 0.25 ml of the test molecule (pyridine or rhodamine 6G) were carried out [19]. Pyridine dissolutions were prepared in the range from 6.3 to 0.63 mM with triply distilled water [18]. The same, when using vS = 8 ×10−10cm3 and mathematical expression 5, we observed that the experimental and expected values presented an excellent correlation (see Fig. 3B). We must emphasize that, for these experiments, we have considered a homogeneous distribution and, as a first approximation, we have considered neither the particles number, nor the size of the silver nanoparticles. Therefore, in SERS analysis of pyridine, the detection limit was found to be 0.63 mM and into the laser spot volume, the detection was of 3 × 10−14 g or 2 × 108 molecules.
Likewise in SERS experiments, with rhodamine 6G dissolutions in water, the detection limit was found to be 10−10 M and into the laser spot volume, the detection was of 5 × 10−20 g or 60 molecules. Finally, these equations help predict that in 10−12 M, we should detect a single molecule. This range of concentration can be observed in different works [20–22]. The experimental data show that our quantification proposal is viable and very easy to implement. With regard to the problem of heterogeneity of some experimental arrangements, especially in micro-Raman experiments, we observed that they can be minimized by having a good point of reference or adequate initial concentration. 4. Conclusions In this work, we demonstrated and applied a simple mathematical route that relates the number of moles in the studied sample with the Raman signal and the experimental parameters. In general, this approach helped us to assign quantitative values to the Raman intensity. In addition, we have shown that it is feasible to consider a homogeneous distribution for quantitative analysis. In summary, we showed a general equation that can help us to quantify any type of specimen using the macro-Raman configuration. Acknowledgments The authors acknowledge PAPIIT:IA100813-2 (UNAM) project and Fondo de Fomento a la Investigación Científica y Tecnológica del Gobierno del D.F. (ICyTDF 90/2010) for their financial support. References [1] M.J. Pelletier, Quantitative analysis using Raman spectrometry, Appl. Spectrosc. 57 (2003) 20A–42A. [2] C.J. Strachan, T. Rades, K.C. Gordon, J. Rantanen, Raman spectroscopy for quantitative analysis of pharmaceutical solids, J. Pharm. Pharmacol. 59 (2007) 179–192. [3] A.O. Izolani, M.T. de Moraes, C.A. Tellez, Fourier transform Raman spectroscopy of drugs: quantitative analysis of 1-phenyl-2,3-dimethyl-5-pyrazolone-4methylaminomethane sodium sulfonate: (dipyrone), J. Raman Spectrosc. 34 (2003) 837–843. [4] A. Szep, G. Marosi, B. Marosfoi, P. Anna, I. Mohammed-Ziegler, M. Viragh, Quantitative analysis of mixtures of drug delivery system components by Raman microscopy, Polym. Adv. Technol. 14 (2003) 784–789. [5] R.Y. Sato-Berrú, J. Medina-Valtierra, C. Medina-Gutiérrez, C. Frausto-Reyes, Quantitative NIR Raman analysis in liquid mixtures, Spectrochim. Acta A Mol. Biomol. Spectrosc. 60 (2004) 2225–2229. [6] J. Johansson, S. Pettersson, S. Folestad, Characterization of different laser irradiation methods for quantitative Raman tablet assessment, J. Pharm. Biomed. Anal. 39 (2005) 510–516. [7] M. Kim, H. Chung, Y.A. Woo, M.S. Kemper, New reliable Raman collection system using the wide area illumination (WAI) scheme combined with the synchronous
R.Y. Sato-Berrú et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 158 (2016) 56–59
[8]
[9]
[10]
[11]
[12] [13] [14]
intensity correction standard for the analysis of pharmaceutical tablets, Anal. Chim. Acta 579 (2006) 209–216. S.C. Park, M. Kim, J. Noh, H. Chung, Y. Woo, J. Lee, M.S. Kemper, Reliable and fast quantitative analysis of active ingredient in pharmaceutical suspension using Raman spectroscopy, Anal. Chim. Acta 593 (2007) 46–53. M. Kim, H. Chung, Y.A. Woo, M.S. Kemper, A new non-invasive, quantitative Raman technique for the determination of an active ingredient in pharmaceutical liquids by direct measurement through a plastic bottle, Anal. Chim. Acta 587 (2007) 200–207. C. Eliasson, N.A. Macleod, L.C. Jayes, F.C. Clarke, S.V. Hammond, M.R. Smith, P. Matousek, Non-invasive quantitative assessment of the content of pharmaceutical capsules using transmission Raman spectroscopy, J. Pharm. Biomed. Anal. 47 (2008) 221. S. Laing, A. Hernandez-Santana, J. Sassmannshausen, D.L. Asquith, I.B. McInnes, K. Faulds, D. Graham, Quantitative detection of human tumor necrosis factor α by a resonance Raman enzyme-linked immunosorbent assay, Anal. Chem. 83 (2011) 297–302. N.K. Budhavaram, J.R. Barone, Quantifying amino acid and protein substitution using Raman spectroscopy, J. Raman Spectrosc. 42 (2011) 355–362. K.P. Matousek, Recent advances in the application of transmission Raman spectroscopy to pharmaceutical analysis, J. Pharm. Biomed. Anal. 55 (2011) 645–652. C.A. Roach, J.V. Simpson, R.D. JiJi, Evolution of quantitative methods in protein secondary structure determination via deep-ultraviolet resonance Raman spectroscopy, Analyst 137 (2012) 555–562.
59
[15] G. Turrell, J. Corset, “Raman Microscopy: Developments and applications”, Elsevier, San Diego California, USA, (ISBN 0-12-189690-0), pp 51–57. [16] G. Placzek, “Rayleigh-Streuung und Raman- Effekt in Handbuch der Radiologie”, in Acadeische-Verlag, E. Marx, Ed. (Leipzig, 1934), vol. VI.2, pp. 205. (Translation: The Rayleigh and Raman Scattering (University of California Radiation Laboratory (UCRL), trans 526(L), 1962)). [17] D.A. Long, Raman Spectroscopy, Mc- Graw-Hill, New York, 1977. [18] R.Y. Sato Berrú, J.M. Saniger, Comparación de la señal Raman de la piridina en disolución y en dispersiones coloidales de plata, SOMI XXI Congreso de Instrumentación, 55-RSB, Octubre – 2006, Ensenada, Baja California – México, 2006. [19] R. Sato-Berrú, R. Redón, A. Vázquez-Olmos, J.M. Saniger, Silver nanoparticles synthesized by direct photoreduction of metal salts. Application in surface enhanced Raman spectroscopy, J. Raman Spectrosc. 40 (2009) 376–380. [20] S. Lee, J. Choi, L. Chen, B. Park, J.B. Kyong, G.H. Seong, J. Choo, Y. Lee, K.H. Shin, E.K. Lee, S.W. Joo, K.H. Lee, Fast and sensitive trace analysis of malachite green using a surface-enhanced Raman microfluidic sensor, Anal. Chim. Acta 590 (2007) 139–144. [21] Y. Xie, X. Wang, X. Han, W. Song, W. Ruan, J. Liu, B. Zhao, Y. Ozaki, Selective SERS detection of each polycyclic aromatic hydrocarbon (PAH) in a mixture of five kinds of PAHs, J. Raman Spectrosc. 42 (2011) 945–950. [22] Y. Numata, H. Tanaka, Quantitative analysis of quercetin using Raman spectroscopy, Food Chem. 126 (2011) 751–755.
Contents lists available at ScienceDirect
Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy journal homepage: www.elsevier.com/locate/saa
Moles quantification in liquid samples by Raman spectroscopy R.Y. Sato-Berrú a,⁎, E.A. Araiza-Reyna b, A.R. Vazquéz-Olmos a a b
CCADET, Universidad Nacional Autónoma de México, Circuito Exterior S/N, Ciudad Universitaria, A.P. 70-186, Delegación Coyoacán, C.P. 04510, México D.F., México Facultad de Ciencias, Universidad Autónoma de San Luis Potosí, Av. Salvador Nava Martínez s/n, Zona Universitaria, C.P. 78290, San Luis Potosí, México
a r t i c l e
i n f o
Article history: Received 8 June 2015 Received in revised form 10 December 2015 Accepted 11 January 2016 Available online 14 January 2016 Keywords: Quantitative Raman Raman spectroscopy Raman technique Mole
a b s t r a c t The mole is a unit of measurement that expresses amounts of a chemical substance. Its importance lies in that the mass and the number of molecules of a substance can be determined with this value. In this work, we suggest a mathematical expression that relates the number of moles of the sample studied with the Raman signal and the experimental parameters used. In other words, with this mathematical expression it is possible to obtain quantitative information in a simple manner from Raman spectra. We have applied this method to different samples and we have observed an excellent correlation between the experimental and expected data. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Raman spectroscopy has proved to be an excellent non-destructive tool, not only for qualitative purposes but also for quantitative analysis [1,2]. The general spectrum profile (peak position and peak intensity) provides a unique chemical fingerprint which can be used to identify a substance and distinguish it from others. In addition, the intensity of a Raman signal in a spectrum is directly proportional to the sample concentration. Typically, a calibration procedure can be used to determine the relationship between peak intensity and sample concentration. Several quantitative Raman studies have been reported in different liquids or mixtures with two or more components. Unlike isotropic liquids, solid powder mixtures are more complicated systems. However, some studies have been conducted in this regard because of the several possible applications in the biology and pharmaceutical industries as well as in the quantitative analysis of drugs and other compounds [3–14]. The references provided of published quantitative Raman applications are by no means exhaustive. The instrumental factors that may affect the quantitative Raman analysis include variations in laser power or wavelength, optical train variations and irreproducible sample placement. The most common solution to the problem of instrumental variation is to use a standard sample, wherein the concentration of the sample is assumed to be proportional to the ratio of the sample peak height to the standard peak height. The instrumental variation affects the signal measured from the standard sample in the same way as the problem sample signal; this method can achieve excellent quantitative results as will be shown in this work. A simple mathematical relationship to get a ⁎ Corresponding author. E-mail address: [email protected] (R.Y. Sato-Berrú).
http://dx.doi.org/10.1016/j.saa.2016.01.017 1386-1425/© 2016 Elsevier B.V. All rights reserved.
quantitative value, as a first approximation for any sample studied, is proposed in this work. 2. Experiments Raman spectra were recorded with an Almega XR dispersive Raman spectrometer. These spectra were accumulated over 25 s with a resolution of ~ 4 cm−1 and an excitation source of 532 nm radiation from a Nd:YVO4 laser (frequency-doubled). All samples (ethanol—99.9%, methyl parathion—99.9%, pyridine—99% and rhodamine 6G—99%) used in this work were purchased from sigma Aldrich and used as received. The pure compounds and dilutions, prepared with triply distilled water, were stoked into well-sealed vessels. 2.1. Theoretical analysis It is well known that a concentrated solution should be diluted to obtain another solution of lower concentration. In this case, the volume of the solvent is increased to obtain the new concentration, which can be calculated by C1V1 = C2V2. In a similar manner, a mathematical expression can be adjusted to monitor the amount of sample mass that is transferred to a smaller volume. In other words, we studied the following relationship: CiVi → VH → vs, where Vi is the initial volume; Ci is the initial concentration; VH is the volume in a homogeneous configuration and vS is the volume of the laser spot used in the Raman experiment. Whereas a Gaussian beam, we determined the volume of the laser spot as vS = π2d4/4 λ. Here, we used d = 4 λf/π D as the diameter of a cylinder and L = π d2/λ as the height of the cylinder [15]; where the wavelength of laser was λ = 532 nm; the focal length of lens was f = 10 mm and the laser beam diameter was D = 1.9 mm.
R.Y. Sato-Berrú et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 158 (2016) 56–59
57
Fig. 1. Expected (line) and experimental (circles) data for the ethanol sample (A) and deviation values of data (B).
However, we noted that the number of moles “n” does not remain constant (ninitial N nHomogeneous N nspot), it changes as the volume of study decreases. Based on these considerations, a mathematical expression can be obtained for the number of moles that exist within the laser spot (volume): ns ¼ A C V
ð1Þ
where A = vs/VH, is the ratio between the volume of the laser spot and the homogeneous volume considered in the experiment. C is the concentration of the sample in Molarity and V is the volume of study in liters. If the number of moles in a system is known, the number of molecules and the sample mass can be determined with the following relationship: Nmolecules = ns ∗ NAvog and g = ns ∗ W; where, NAvog is the Avogadro's number (6.022 × 1023 mol− 1) and W is the molecular weight of the studied sample. On the other hand, Raman intensity is proportional to the intensity of the excitation source and to the number of molecules in the sample volume being probed with the Raman instrument [16,17]. Experimentally, it is known that the intensity of a Raman spectrum is directly proportional to the concentration. In this paper, considering the previous premises and our experience, we propose that the Raman signal is proportional to the number of molecules by using the following simple correlation: IR ¼ M i
ð2Þ
where M represents the number of elementary entities and i represents the Raman emission of each entities, which is representative of the material of study and under our experimental conditions. If we assume that M = ns, where ns represents the number of moles present within the laser spot (mathematical expression 1), the unitary intensity can be expressed as: i = IR/ns. Similarly, it can be assumed that it also satisfies the relationship: Ir = n ∗ i, where Ir represents an arbitrary Raman signal. Therefore, the number of moles can be determined in an arbitrary Raman signal with the following equation: n ¼ I ns
ð3Þ
where, I = Ir/IR is the ratio between the arbitrary and reference Raman intensity. We observed that I varies between 0 ≤ I ≤1. For pure and diluted substances, we have used the following mathematical expressions: A = vs/VH ; C = Ci = ni/Vi ; ni = m/W ;ρ = m/Vi ; V = VH, in Eqs. (1) and (3); then, we were able to obtain two particular expressions by quantitative Raman analysis of the liquid samples, in which we know the density “ρ” or initial concentration “Ci” of the reference sample. We implemented all these expressions in an excel worksheet. n ¼ I vs
ρ W
n ¼ I vs C i :
Fig. 2. Expected (line) and experimental (circles) data for the methyl parathion sample (A) and deviation values of data (B).
ð4Þ ð5Þ
58
R.Y. Sato-Berrú et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 158 (2016) 56–59
Fig. 3. Expected (circles) and experimental (stars) data for the pyridine sample for normal Raman (A) and for SERS (B).
3. Results and discussions The ethanol sample (molecular weight 46.058 g/mol and density 0.789 g/ml) was prepared in the range from 99.9 to 1% (v/v) with triply distilled water [5]. The intensity of a characteristic peak (882 cm−1) was used for the analysis. Then, when using vS =8 × 10−10 cm3 and mathematical expression 4, we observed that the experimental and expected values presented an excellent correlation, see Fig. 1A. Moreover, we have used and found the deviation values (Fig. 1B) through the following relation: s = ((experiment − expected)/expected) ∗ 100. This equation can give negative or positive values. A zero deviation indicates that the expected values perfectly correlate with the experimental values. A positive deviation indicates that the experimental values are higher than expected and, if the deviation is negative, the experimental values are lower than expected. The methyl parathion sample (molecular weight 263.21 g/mol) was prepared in the range from 1.5 M to 6.3 mM with triply distilled water [5] which is an organophosphate pesticide and harmful to health. The intensity of a characteristic peak (1345 cm−1) was used for the analysis. The same, when using vS = 8 ×10−10cm3 and mathematical expression 5, we observed that the experimental and expected values presented an excellent correlation (see Fig. 2A). Fig. 2B illustrates the deviation values. A pyridine sample (molecular weight 79.1 g/mol) was prepared in the range from 0.284 M to 6.3 mM with triply distilled water [18].The intensity of a characteristic peak (999 cm−1) was used for the analysis. The same, when using vS = 8 ×10−10cm3 and mathematical expression 5, we observed that the experimental and expected values presented an excellent correlation, see Fig. 3A. In this sample, the detection limit was found to be 6.3 mM and into the laser spot volume, the detection was of 5 × 10−13 g or 4 × 109 molecules. However, applying this mathematical expression to SERS experiments (Surface Enhanced Raman Spectroscopy) posed a challenge. In this regard, mixtures of spherical Ag nanoparticles colloids (0.25 ml), NaCl (0.05 ml: 8.5 mM) and 0.25 ml of the test molecule (pyridine or rhodamine 6G) were carried out [19]. Pyridine dissolutions were prepared in the range from 6.3 to 0.63 mM with triply distilled water [18]. The same, when using vS = 8 ×10−10cm3 and mathematical expression 5, we observed that the experimental and expected values presented an excellent correlation (see Fig. 3B). We must emphasize that, for these experiments, we have considered a homogeneous distribution and, as a first approximation, we have considered neither the particles number, nor the size of the silver nanoparticles. Therefore, in SERS analysis of pyridine, the detection limit was found to be 0.63 mM and into the laser spot volume, the detection was of 3 × 10−14 g or 2 × 108 molecules.
Likewise in SERS experiments, with rhodamine 6G dissolutions in water, the detection limit was found to be 10−10 M and into the laser spot volume, the detection was of 5 × 10−20 g or 60 molecules. Finally, these equations help predict that in 10−12 M, we should detect a single molecule. This range of concentration can be observed in different works [20–22]. The experimental data show that our quantification proposal is viable and very easy to implement. With regard to the problem of heterogeneity of some experimental arrangements, especially in micro-Raman experiments, we observed that they can be minimized by having a good point of reference or adequate initial concentration. 4. Conclusions In this work, we demonstrated and applied a simple mathematical route that relates the number of moles in the studied sample with the Raman signal and the experimental parameters. In general, this approach helped us to assign quantitative values to the Raman intensity. In addition, we have shown that it is feasible to consider a homogeneous distribution for quantitative analysis. In summary, we showed a general equation that can help us to quantify any type of specimen using the macro-Raman configuration. Acknowledgments The authors acknowledge PAPIIT:IA100813-2 (UNAM) project and Fondo de Fomento a la Investigación Científica y Tecnológica del Gobierno del D.F. (ICyTDF 90/2010) for their financial support. References [1] M.J. Pelletier, Quantitative analysis using Raman spectrometry, Appl. Spectrosc. 57 (2003) 20A–42A. [2] C.J. Strachan, T. Rades, K.C. Gordon, J. Rantanen, Raman spectroscopy for quantitative analysis of pharmaceutical solids, J. Pharm. Pharmacol. 59 (2007) 179–192. [3] A.O. Izolani, M.T. de Moraes, C.A. Tellez, Fourier transform Raman spectroscopy of drugs: quantitative analysis of 1-phenyl-2,3-dimethyl-5-pyrazolone-4methylaminomethane sodium sulfonate: (dipyrone), J. Raman Spectrosc. 34 (2003) 837–843. [4] A. Szep, G. Marosi, B. Marosfoi, P. Anna, I. Mohammed-Ziegler, M. Viragh, Quantitative analysis of mixtures of drug delivery system components by Raman microscopy, Polym. Adv. Technol. 14 (2003) 784–789. [5] R.Y. Sato-Berrú, J. Medina-Valtierra, C. Medina-Gutiérrez, C. Frausto-Reyes, Quantitative NIR Raman analysis in liquid mixtures, Spectrochim. Acta A Mol. Biomol. Spectrosc. 60 (2004) 2225–2229. [6] J. Johansson, S. Pettersson, S. Folestad, Characterization of different laser irradiation methods for quantitative Raman tablet assessment, J. Pharm. Biomed. Anal. 39 (2005) 510–516. [7] M. Kim, H. Chung, Y.A. Woo, M.S. Kemper, New reliable Raman collection system using the wide area illumination (WAI) scheme combined with the synchronous
R.Y. Sato-Berrú et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 158 (2016) 56–59
[8]
[9]
[10]
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