Digital image-based titrations

Analytica Chimica Acta 570 (2006) 283–290 Digital image-based titrations Edvaldo da Nobrega Gaiao, Valdomiro Lacerda Martins, Wellington da Silva Lyra, Luciano Farias de Almeida, Edvan Cirino da Silva, Mário César Ugulino Araújo ∗ Universidade Federal da Paraı́ba, CCEN, Departamento de Quı́mica, P. Box: 5093, 58051-970 João Pessoa, PB, Brazil Received 6 October 2005; received in revised form 8 April 2006; accepted 11 April 2006 Available online 29 April 2006 Abstract The exploitation of digital images obtained from a CCD camera (WebCam) as a novel instrumental detection technique for titration is proposed for the first time. Named of digital image-based (DIB) titration, it also requires, as a traditional titration (for example, spectrophotometric, potentiometric, conductimetric), a discontinuity in titration curves where there is an end point, which is associated to the chemical equivalence condition. The monitored signal in the DIB titration is a RGB-based value that is calculated, for each digital image, by using a proposed procedure based on the red, green, and blue colour system. The DIB titration was applied to determine HCl and H3 PO4 in aqueous solutions and total alkalinity in mineral and tap waters. Its results were compared to the spectrophotometric (SPEC) titration and, by applying the paired t-test, no statistic difference between the results of both methods was verified at the 95% confidence level. Identical standard deviations were obtained by both titrations in the determinations of HCl and H3 PO4 , with a slightly better precision for DIB titration in the determinations of total alkalinity. The DIB titration shows to be an efficient and promising tool for quantitative chemical analysis and, as it employs an inexpensive device (WebCam) as analytical detector, it offers an economically viable alternative to titrations that need instrumental detection. © 2006 Elsevier B.V. All rights reserved. Keywords: Digital images; RGB colour system; DIB titration; Alkalinity; Waters analysis 1. Introduction Several instrumental techniques have been widely used for implementing quantitative chemical analysis based on titration [1]. In order to find an end point, these titrations employ plots that are built by using the measured signal after the addition of each increment of titrant. The shape of the titration curves depend on some factors such as the reaction of titration, the monitored specie (indicator, titrant, analyte or formed product), as well as the chosen instrumental technique (spectrophotometry, conductimetry or potentiometry, for instance). Recent advances in digital image acquisition technology have offered video cameras (WebCam) based on charge-coupled devices (CCD), which are capable to capture digital images with up to 24 bits (16.7 million colours). In fact, by using the RGB colour system [2,3], the primary colours are combined in different intensities with values varying in the range 0–255 (8 bits) per colour. ∗ Corresponding author. Tel.: +55 83 32167438; fax: +55 83 3216 7437. E-mail address: laqa@quimica.ufpb.br (M.C.U. Araújo). 0003-2670/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.aca.2006.04.048 By using a CCD digital camera, the images obtained with high resolution have been exploited for different purposes, such as in studies involving multivariate image regression [4], classification of inhomogeneous food matrices [5], spectral image analysis for measuring ripeness of tomatoes [6], etc. However, the exploitation of digital images for the quantification of analyte concentrations has not been found in the literature, with exception of the work recently proposed by Maleki et al [7]. Maleki et al. [7] employed a digital camera as detection system for simultaneous determination of Al(III) and Fe(III) in alloys using the chrome azurol S (CAS) as chromogenic reagent. The RGB values associated to digital images from Al(III)-CAS and Fe(III)-CAS complexes were used in the construction of an artificial neural network (ANN) model. It should be also emphasized that due to the complex relationship between RGB values and analyte concentrations, the ANN modelling was chosen by Maleki et al. [7] for multivariate calibration because there is no need to know the exact form of the analytical function on which the model should be built. On the other hand, such modelling requires training and testing procedure of the network, which can be considered laborious and time consuming 284 E. da Nobrega Gaiao et al. / Analytica Chimica Acta 570 (2006) 283–290 especially when optimized parameters for ANN modelling are aimed. A titration technique based on digital image exploitation is proposed in this paper for the first time. Similarly, to spectrophotometric, condutimetric or potentiometric titrations, for instance, the DIB titrations were always accomplished in order to make sure the titrant was added in excess, yielding a discontinuity in the titration curve where there is an end point, which is associated to the chemical equivalence condition. However, as it can be observed in fundamentals of analytical chemistry text books, end points are not so precisely determined in original titration curves. This problem has been minimized by using derivative titration curves [8,9]. Initially, two model titrations (HCl/NaOH and H3 PO4 /NaOH) were studied to evaluate the performance of the DIB titrations. Thereafter, an analytical application involving the determination of the total alkalinity in mineral and tap waters was carried out. 2. Experimental 2.1. Reagents, samples, and solutions All solutions were prepared with freshly distilled-deionised water and analytical grade chemicals. About 100.0 mmol l−1 NaOH was used for titrations of HCl and H3 PO4 , whereas for determination of total alkalinity in mineral and tap water samples was employed 10.0 mmol l−1 H2 SO4 as titrant. These titrant solutions were standardised employing conventional methodologies [10,11]. About 0.1% (w/v) phenol red, 0.1% (w/v) bromocresol green and 0.2% (w/v) methyl orange were used as indicators in the titrations of HCl, H3 PO4 and total alkalinity in mineral and tap water samples, respectively. Mineral water samples were purchased in a local supermarket and the tap water samples were collected from three points in the city of João Pessoa, Paraı́ba, Brazil. All samples were analyzed without any further treatment. 2.2. Apparatus A schematic diagram and a photograph of the system assembled for digital images acquisition is depicted in Fig. 1. A model CTWCII Creative WebCam (WC) [12], which was positioned in front of the model QS 137 Hellma flow cell (FC) with inner volume 2.6 ml and optical path 1.0 cm, was used for digital images acquisition. The coloured solutions were only illuminated by light from a 5 W Avante fluorescent lamp. In order to avoid interferences of ambient light, the WebCam and the flow cell were put into a plastic box with approximately 11 cm × 14 cm × 9 cm. To provide a uniform illumination and to reduce glare and specular reflection the internal walls of the box were covered with a layer of white paper. The WebCam was connected to the parallel port of a Pentium III 650 MHz microcomputer (PC) and configured to capture 24-bits digital images (16.7 million colours) at a rate of 7.5 images/s with a sensitivity of 15 lx (luminance unit) and a Fig. 1. Schematic diagram (a) and photograph (b) of the system for digital images acquisition. B: burette, SB: stirring bar; MS: magnetic stirrer; PP: peristaltic pump; WC: WebCam, SPEC: spectrophotometer; PC: microcomputer; FC: flow cell and PS: power supply. Arrows indicate directions of pumping. For further details, see the text. 320 pixels × 240 pixels spatial resolution [12]. The images were captured and stored as “jpg” compressed files using the software provided by manufacturer of the WebCam. A model 8453 Hewlett-Packard (HP) diode array UV–vis spectrophotometer, equipped with a model QS 178.010 Hellma flow cell (inner volume 100 ␮l and optical path 1.0 cm) was used for spectrophotometric measurements. A model 190M Hanna Instruments magnetic stirrer (MS) driven a stirring bar (SB) inside the Erlenmeyer. An 8 channel-12 rolls Gilson, peristaltic pump, model Miniplus 3, employing Tygon® pumping tubes, and Teflon® line tubes of 1.85 and 0.8 mm inner diameter was used to propel the solutions. 2.3. The procedure for the RGB-based value calculation Initially, the user selects, with the computer mouse, the region of the first titration image that is used for the RGB-based value calculation. This region must be selected where the light beam crosses the flow cell (Fig. 2). Right after, the software performs a scan (column by column) of the pixels on the delimited region, calculates the RGB-based value of each pixel and then the average of all RGB-based values. This average value is used to build the DIB titration curves. The software written in Kylix (version 3.0) automatically uses the same coordinates of the delimited E. da Nobrega Gaiao et al. / Analytica Chimica Acta 570 (2006) 283–290 285 2.4. DIB and SPEC titrations Fig. 2. Delimited region of a first digital image with n × m pixels that is captured during the DIB titration. x1 , x2 , y1 and y2 are the coordinates of the delimited region. The titrations of HCl and H3 PO4 in aqueous solutions and total alkalinity in tap and mineral waters were carried out using the WebCam and spectrophotometer (Fig. 1) and standardized NaOH (for HCl or H3 PO4 ) or H2 SO4 (for the total alkalinity). H2 SO4 was used as titrant because all water samples analyzed presented very low hardness (<10.0 mg l−1 of CaCO3 ). Aliquots of 20, 25 or 100 ml (HCl, H3 PO4 or water samples) and three drops of indicator (phenol red, bromocresol green or methyl orange), respectively, were transferred to the Erlenmeyer. During the titration, the solution inside Erlenmeyer was always kept under stirring and a closed-loop pumping between the detectors (WebCam and spectrophotometer) and the Erlenmeyer. The measurements of RGB-based values and absorbance signals were always carried out with the stopped flow (peristaltic pump off) and stored in the microcomputer for posterior treatment. The absorbance measurements were carried out at 558, 617 and 480 nm for titration of HCl, H3 PO4 and total alkalinity in water samples, respectively. 3. Results and discussion region (Fig. 2) to calculate RGB-based values of all images of the titration. The computer code is available as supplementary information. Each sampled image has been a matrix with 320 pixels × 240 pixels and the delimited region by the user has been a matrix with about 40 pixels × 50 pixels. The pixel resolution has been 87 × 87 dots/in. The RGB-based value calculations are based on the product 2R .2G .2B , where R, G and B are the red, green and blue colour components, respectively. These components may assume integer values in a range from 0 to 7, reaching up to 16,777,216 colours. 3.1. Digital images and visible spectra of the HCl, H3 PO4 and total alkalinity titrations To simplify and to make clear the discussions bellow, only 10 digital images and its corresponding visible spectra of HCl, H3 PO4 and total alkalinity titrations are shown in Figs. 3 and 4, respectively. As can be seen in Figs. 3a and 4a, the colours and the corresponding spectral profiles of the images 1–6 and 7–10 are different. Thus, it is feasible to state that between the images 6 Fig. 3. Sequence of the digital images captured during the titration of HCl/NaOH (a), H3 PO4 /NaOH (b) and total alkalinity in a mineral water sample (c) (for interpretation of the references to colour in this figure legend, the reader is referred to the web version of the article). 286 E. da Nobrega Gaiao et al. / Analytica Chimica Acta 570 (2006) 283–290 colours; the yellow and magenta are secondary colours (resulting from the mixture of primary colours green + red and blue + red, respectively); and the orange is a tertiary colour (resulting from the mixture of the red + yellow) [2,3]. In H3 PO4 /NaOH titration, the images 1–5 in Fig. 3b are yellow because the indicator in its acid form absorbs predominantly blue radiation (see the spectra 1–5 in Fig. 4b), while the images 6–10 in Fig. 3b present the cyan secondary colour (mixture of green + blue) due to the absorption of red light by the indicator in its basic form (see the spectra 6–10 in Fig. 4b). As the spectra and the images 5 and 6 are different, it can be inferred that there is an end point between them and that it was originated due to the addition of titrant in excess and the change of the indicator from its acid to basic form. A method recommended by the American Public Health Association [11] to determine total alkalinity of water samples with very low hardness is acid-base titration using the H2 SO4 titrant, the methyl orange indicator and the visual detection. In general, the analyst may have difficulty to determine the end point with good precision when this method is used. This fact is corroborated by the visual examination of the images 1–10 (Fig. 3c). As this titration was surely accomplished with the addition of titrant excess, there must be an end point among the images 1–10. However, it is not visually located because a colour change is not easily realized among these images. On the other hand, taking into account that the spectra 1–5 (Fig. 4c) are different of the spectra 6–10, it may be inferred that there is an end point between the images 5 and 6. 3.2. DIB and SPEC titration curves To a more accurate evaluation of the variations observed both in the RGB-based and in the absorbance values and, consequently, to a better comparison of the DIB and SPEC titrations (Figs. 3–7), a collection of points with a greater number of added titrant volumes, especially close to the end point, are shown in Table 1. The following equations are used by the data treatment software to build the second-derivative curves. • Equations for the calculation of the first derivatives: Fig. 4. Absorption spectra in the visible region obtained during the titration of HCl/NaOH (a) H3 PO4 /NaOH (b) and total alkalinity in a mineral water sample (c). and 7 there is an end point and that such fact happens when the titrant is added in excess and the indicator changes from acid to basic form. It is worth pointing out that the images 1–6 are of orange colour because the indicator in its acid form absorbs the blue and green-blue lights (see the spectra 1–6 in Fig. 4a), while the images 7–10 present the magenta colour due to the yellow-green light absorption (see the spectra 7–10 in Fig. 4a) by the indicator in its basic form. In order to understand the complementary colours of the images obtained during DIB titrations (Fig. 3), it is worth reminding that the red, green and blue are considered primary
R R(i+1) − Ri =
V V(i+1) − Vi and Vaverage = V(i+1) + Vi 2 • Equations for the calculation of the second derivatives:
2 R
((
R)/(
V )) =
Vaverage
Vaverage = V̄average = ((
R)/(
V ))i+1 − ((
R)/(
V ))i (Vaverage )i+1 − (Vaverage )i and (Vaverage )i+1 + (Vaverage )i 2 where R is the analytical response and V is the added titrant volume. i = 0, 1, 2, . . ., n, and n is the number of titration 287 E. da Nobrega Gaiao et al. / Analytica Chimica Acta 570 (2006) 283–290 points that were used in derivative calculations. The secondderivative curves were built by using V̄average . Initially, it is worth arguing that an abrupt variation of the RGB-based value does not necessarily imply in a association with a region of the DIB titration curve where the end point may be located. For example, in the HCl/NaOH titration, the abrupt variation of the RGB-based value between the points 6–7 (Fig. 5a) is associated with a region where an end point can be found. This fact is corroborated by the difference of colour (Fig. 3a) and of the corresponding spectral profile (Fig. 4a) between these images. In addition, an abrupt variation of absorbance between the points 6 and 7 is also observed in the SPEC titration curve (Fig. 5c). On the other hand, according to the SPEC titration curve (Fig. 6c) and the differences of colour (Fig. 3b) and of corresponding spectral profile (Fig. 4b), Table 1 A collection of points of three DIB and SPEC titrations with a greater number of added titrant volumes close to the end point
2 absorbance
Vaverage
2 RGB−based value
Vaverage Volume (ml) Absorbance RGB-based value (×107 ) HCl/NaOH titration 0 4.0 8.0 12.0 16.0 19.4 19.6 19.7 19.8 19.9 20.0 20.1 20.2 22.0 24.0 26.0 0.0053 0.0003 0.0012 0.0031 0.0011 0.0007 0.0028 0.0005 0.3658 0.3503 0.3914 0.3875 0.3901 0.3554 0.3539 0.3529 1.4994 1.5308 1.5842 1.6294 1.7031 1.7449 1.7531 1.8695 1.8753 1.5988 1.5984 1.5971 1.5964 1.5869 1.5816 1.5646 – 0.0045 0.0023 −0.0014 0.0008 0.0700 −0.4364 36.7572 −38.0781 −5.6680 −4.5110 −2.4580 −1.7090 −0.0002 −0.0009 – – 0.0246 −0.0164 −0.0148 −0.0008 0.2505 −5.8260 −11.0670 −28.2220 27.6030 −0.0820 0.0550 −0.0390 0.0067 0.0004 – H3 PO4 /NaOH titration 0 2.0 3.0 5.0 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.6 7.0 8.0 10.0 0.0023 0.0061 0.0079 0.0150 0.0719 0.2384 0.4049 0.8221 0.8987 0.9753 0.9875 0.9966 1.0893 1.0825 1.0457 1.5382 1.5991 1.6028 1.6234 1.6308 1.6327 1.6346 1.6272 1.5632 1.4991 1.5314 1.5637 1.8600 1.8778 1.9174 – 0.0016 −0.0005 0.0430 15.7190 20.1200 25.0710 34.0630 −16.0100 −6.4310 −0.3170 0.3150 −0.2563 −0.0095 – – −0.0178 0.0075 −0.0099 0.0010 −0.0010 −0.0926 −0.5668 −0.0006 0.9640 0.9219 0.8798 0.3714 −0.0093 –
2 absorbance
Vaverage Alkalinity titration 0 2.0 4.0 6.0 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5 8.6 8.8 9.0 0.1435 0.1438 0.1483 0.1470 0.1529 0.1613 0.1691 0.1807 0.1850 0.1967 0.2049 0.2128 0.2314 0.2369 0.2289 8.7500 8.6400 8.6900 8.7100 8.7600 8.9600 9.0600 8.8500 8.7600 8.6600 8.5500 8.4400 8.3800 8.2300 8.1700 – 0.0130 −0.0017 0.0015 0.0004 0.0938 0.3220 −0.0650 −0.3820 −0.7340 0.7460 0.3510 0.0310 0.1072 –
2 RGB−based value
Vaverage – 0.0600 0.1400 0.0500 0.0100 1.2000 26.0000 −10.0000 −8.8000 −0.7000 −0.6000 −0.5000 −0.2000 −0.1000 – 288 E. da Nobrega Gaiao et al. / Analytica Chimica Acta 570 (2006) 283–290 Fig. 5. Zero-order and second-derivative curves of the HCl/NaOH model titration with WebCam (a and b) and spectrophotometer (c and d) detectors. the end point of the H3 PO4 /NaOH titration is located between the points 5 and 6. However, the variation of the RGB-based value is much greater between the points 7 and 8 (Fig. 6a). This abrupt change of RGB-based value between these points occurs due to the abrupt increase of the contribution of the blue emerging component (B) regarding to the red (R) and green (G) components, resulting from the increase (in the red spectral region) and decrease (in the blue and green region) of the absorption by the indicator in its basic form. In contrast, the change of RGB-based value between points 5 and 6 occurs due to the decrease of the contribution of R component, regarding to G and B components. The volume of titrant associated to the end point (Vep ) has always been determined by the data treatment software adopting the zero crossing criteria in the second-derivative curves. Independent of the particular titration considered, the software uses all points of titration (points 20–30) to build such curves. About 10 points with increments of 0.1 ml of titrant have always been measured around the end point. As in a traditional SPEC titration, the increment of 0.1 ml of titrant in DIB titration has been started when the RGB-based value (displayed on computer screen by the software) presented a significant change. It can be noted that the zero crossing, indicated by an arrow in the second-derivative curves of HCl, H3 PO4 and total alkalinity Fig. 6. Zero-order and second-derivative curves of the H3 PO4 /NaOH model titration with WebCam (a and b) and spectrophotometer (c and d) detectors. E. da Nobrega Gaiao et al. / Analytica Chimica Acta 570 (2006) 283–290 289 Fig. 7. Zero-order and second-derivative curves of the total alkalinity/H2 SO4 titration of a mineral water sample with WebCam (a and b) and spectrophotometer (c and d) detectors. (Figs. 5b and d, 6b and d, 7b and d), provides Vep values very close for both DIB and SPEC titrations. Table 2 displays the results of HCl and H3 PO4 in aqueous solutions and of total alkalinity in mineral and tap waters as determined by the DIB and SPEC titration. They show a good agreement between the obtained values by both methods. Actually, no statistic difference at the 95% confidence level has been verified between the results by applying the paired t-test. Table 2 Results of HCl (in mmol l−1 ) and H3 PO4 (in mmol l−1 ) in aqueous solutions and of total alkalinity (in mg CaCO3 l−1 ) in mineral and tap waters as determined by the proposed DIB and SPEC titration Samples Titrations DIB 4. Conclusions SPEC (1) HCl (2) HCl (3) HCl (4) HCl (5) HCl (6) HCl 98.8 50.1 72.6 147.7 198.8 258.7 ± ± ± ± ± ± 0.1 0.1 0.1 0.1 0.1 0.1 99.1 50.0 72.6 147.6 199.0 258.5 ± ± ± ± ± ± 0.1 0.1 0.1 0.1 0.1 0.1 (1) H3 PO4 (2) H3 PO4 (3) H3 PO4 (4) H3 PO4 (5) H3 PO4 (6) H3 PO4 24.8 64.6 99.8 127.1 175.8 208.6 ± ± ± ± ± ± 0.1 0.1 0.1 0.2 0.1 0.1 24.7 64.5 99.8 127.1 175.8 208.7 ± ± ± ± ± ± 0.1 0.1 0.1 0.2 0.1 0.1 (1) Mineral water (2) Mineral water (3) Mineral water (1) Tap water (2) Tap water (3) Tap water In terms of precision, the obtained values by the proposed and SPEC methods are identical for the HCl and H3 PO4 determinations and both values are better than the total alkalinity determinations. This finding may be ascribed to a clearer identification and determination of the end point for the HCl and H3 PO4 titrations than total alkalinity titrations. On the other hand, the slightly better precision of the DIB titration regarding to SPEC titration may be credited to the “multivariate advantage” [13]. In fact, the monitored signal in the DIB titration is of multivariate nature (variation of three RGB components), while the SPEC titration is univariate (variation of absorbance in 480 nm). 82.4 ± 0.4 82.7 ± 0.2 16.0 ± 0.1 82.5 ± 0.5 82.7 ± 0.3 15.9 ± 0.2 144.8 ± 0.5 6.0 ± 0.1 4.0 ± 0.1 144.7 ± 0.6 6.0 ± 0.2 4.0 ± 0.2 The feasibility of the exploitation of digital images obtained from a WebCam as novel instrumental detection technique for titration was demonstrated. To attain such a goal, the proposed technique requires a variation of the RGB image components from the analytical system and a discontinuity in titration curves where there is an end point that is associated to the chemical equivalence condition. The DIB titration can be considered a promising analytical tool for accomplishing quantitative chemical analysis, as well as it offers an economically viable alternative to titrations with a difficult visualization of the end point. By exploring the spatial-resolution-related advantages inherent to digital images, it is expected to increase considerably sampling throughput carrying out several DIB titrations at a same time, by acquiring contemporarily in a single image information on more analytical samples. The DIB titration speed can also be increased by using the Flow-Batch automatic system [14,15]. 290 E. da Nobrega Gaiao et al. / Analytica Chimica Acta 570 (2006) 283–290 It also aims at investigating the use of higher resolution CCD cameras and/or other colour system, such as HIS (hue, saturation and intensity system), which has already provided quite satisfactory results in colour image analysis [5], to improve precision on titrations with difficult visualization (as seen in the determinations of total alkalinity). In order to build parsimonious and robust models of multivariate analysis the use of variable and sample selection algorithms [16–18] or a wavelet transform-based strategy [19] in RGB space will also be investigated, especially when inhomogeneous matrices are involved as exploited by Antonelli et al. [5]. It is worth noting that the proposed approach was applied in a homogeneous analytical system (titration of samples in solution). Acknowledgement E.N. Gaião, V.L. Martins, L.F. Almeida, and M.C.U. Araujo thank the Brazilian agency CNPq for scholarship. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.aca.2006.04.048. References [1] D.A. Skoog, J.J. Leary, Principles of Instrumental Analysis, 4th ed., Saunders College Publishing, New York, 1992. [2] P. Geladi, H. Grahn, Multivariate Image Analysis, 2nd ed., Wiley, New York, 1996. [3] R.S. Berns, Principles of Color Technology, 3rd ed., Wiley, New York, 2000. [4] T.T. Lied, K.H. Esbensen, Chemom. Intell. Lab. Syst. 58 (2001) 213. [5] A. Antonelli, M. Cocchi, P. Fava, G. Foca, G.C. Franchini, D. Manzini, A. Ulrici, Anal. Chim. Acta 515 (2004) 3. [6] G. Polder, G.W.A.M. Van der Heijden, I.T. Young, Trans. ASAE 45 (2002) 1155. [7] N. Maleki, A. Safavi, F. Sedaghatpour, Talanta 64 (2004) 830. [8] D.A. Skoog, D.M. West, F.J. 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