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Accepted Manuscript
A comparative application of two-way and three-way analysis to
three-dimensional voltammetric dataset for the pKa determination
of vanillin
Zehra Yazan, Sevcan Erden, Erdal Dinç
PII:
DOI:
Reference:
S1572-6657(18)30519-8
doi:10.1016/j.jelechem.2018.07.047
JEAC 12529
To appear in:
Journal of Electroanalytical Chemistry
Received date:
Revised date:
Accepted date:
11 May 2018
23 July 2018
25 July 2018
Please cite this article as: Zehra Yazan, Sevcan Erden, Erdal Dinç , A comparative
application of two-way and three-way analysis to three-dimensional voltammetric dataset
for the pKa determination of vanillin. Jeac (2018), doi:10.1016/j.jelechem.2018.07.047
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ACCEPTED MANUSCRIPT
A comparative application of two-way and three-way analysis to three-dimensional
voltammetric dataset for the pKa determination of vanillin
Zehra Yazana, Sevcan Erdenb, Erdal Dinçc*
Faculty of Science, Department of Chemistry, Ankara University 06100, Ankara, Turkey
c
General Directorate of Mineral Research and Exploration, 06800 Ankara, Turkey
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b
Faculty of Pharmacy, Department of Analytical Chemistry, Ankara University, 06100 Ankara,
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a
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Turkey
ABSTRACT
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Two-way and three-way data analysis methods, multivariate curve resolution-alternating squares
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(MCR-ALS) and parallel factor analysis (PARAFAC) were applied to the potential-frequency
dataset to estimate the pKa value of vanillin, used as a flavoring agent in foods and
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pharmaceuticals. Three-dimensional (3-D) voltammetric plots of vanillin at 12 different pHs in
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the range of 1.3-12.0 and 8 different frequencies in the range of 5-120 Hz were recorded as a
function of potential (mV) and frequency (Hz) using square wave voltammetric (SWV)
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technique. The data matrix and data array of the 3D-voltammetric plots were processed by MCR-
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ALS and PARAFAC algorithms to predict the pKa values of the relevant flavor agent. In both
MCR-ALS and PARAFAC approaches, the relative concentration profiles with the used pH
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range were used for the determination of the pKa without using extra additional software. In the
MCR-ALS and PARAFAC applications, the numerical values for the pKa value of vanillin were
computed as 7.91 and 7.97, respectively. The experimental results showed that the SWV
technique coupled with the MCR-ALS and PARAFAC approaches have proved to be a quite
promising solution to the problem of the chemometric evaluation the pKa of the compound of
interest.
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Keywords: Multivariate curve resolution-alternating least squares; Parallel factor analysis;
Three-dimensional voltammogram; pKa determination; Vanillin
*Corresponding author. Tel.: +90 312 215 4886; Fax: + 90 312 213 1081;
e-mail: dinc@ankara.edu.tr
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1. Introduction
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Vanillin, chemically known as 4-hydroxy-3-methoxybenzaldehyde, has three different functional
groups consisting of aldehyde, hydroxyl and ether with the molecular formula C8H8O3 (Fig. 1).
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Vanillin, which is the main chemical component of the extract of the vanilla bean, is among the
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most consumed substances in the world. Natural vanillin has been widely used as flavoring in
foods (e.g. desserts, sweet foods, ice cream, chocolate, cake, chocolate and biscuit), beverages
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(e.g. tea, coffee, beer and milk etc.), pharmaceuticals (e.g. for the preparation of pharmaceutical
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drugs for Parkinson’s disease and in hypertension and many other drugs), health and personal
care products (e.g. in cosmetics), and other industries (e.g. in rubbers and plastics and tobacco,
Insert in Figure 1
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cigarette paper and its filter).
Artificial vanillin, instead of natural vanilla extract, is sometimes used as a flavoring agent for
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the above similar aims. Artificial vanillin is obtained from either guaiacol or from lignin, a
constituent of wood, which is a product of the paper industry.
As it was pointed out above, vanillin had been used in a wide range of food and pharmaceutical
sectors. Therefore, a research on the pKa determination of vanillin will provide a useful material
to uncover the acid-base equilibrium in terms of body system when taken together with either
foods or drugs.
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As it is known, according to the ratio of the unionized and ionized forms in the acid-base
equilibrium, a chemical substance exhibits different physicochemical characteristics e.g.
absorption solubility, partition coefficient, biological activity (or chemical reactivity) and
permeability of membrane, etc. Due to the mentioned reasons, the issue of determining the acid-
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base dissociation constants of active compounds used in foods and medicines still attracts the
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interest of scientists working in analytical chemistry and related research fields. This interest is
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to force scientists to develop new analytical techniques, methods, methodologies and approaches,
which are easier, faster, cheaper and more reliable, for the determination of the dissociation
In previous works, UV-Visible spectrophotometry and
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constants of acids or bases.
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potentiometric methods are two of the most commonly used methods for the studies on
dissociation equilibriums of weak acids and bases.
methodological
approaches
including
spectrophotometry
[1-3]
and
capillary
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some
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A literature survey indicated that the pKa value of vanillin in different media was determined by
electrophoresis [4]. On the other hand, in IUPAC chemical data series, it was observed that there
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is a study on the pKa value of vanillin in aqueous solution [5]. However, the application of
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chemometric two-way and three-way data analysis approaches with square wave voltammetric
technique to the vanillin’s pKa determination was not reported.
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In practice, a conventional strategy based on a graphical relationship between different pH values
and related parameter of instrumental measurement methods is a common approach to the
estimation of the acid dissociation constant (or pKa). However, the above mentioned methods
may not always allow to exactly determine the acidity constant (or pKa on a logarithmic scale)
for analyzed active compounds in related foods or pharmaceutical preparations because of
experimental
complexity,
unwanted
interference
and
methodological
disadvantages.
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Furthermore, these conventional methods do not provide any second order information related to
chemical species and their signals in acid-base equilibriums.
In recent years, MCR-ALS and PARAFAC approaches for multiway data analysis have received
more attention than other chemometric tools for providing useful and easy interpretable
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information for resolving complex data systems, which cannot be solve by using conventional
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analytical instrumental methods. Previously published papers on chemical equilibriums indicated
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that there were some studies on the applications of two-way and three-way data analysis methods
to the estimation of acid-base dissociation constants and reaction kinetics with pH-dependent
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photo-degradation [6-14].
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In chemometry, some of the most popular algorithms used in the analysis of three-way data
structures are parallel factor analysis (PARAFAC) [15,16], Tuker3 [17], direct trilinear
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decomposition (DTLD) [18], alternating trilinear decomposition (ATLD) [19], the generalized
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rank annihilation method (GRAM) [20] 20 and curve resolution-alternating least squares (MCRALS) [21]. In this research paper, new applications of three-way and two-way data analysis
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methods, PARAFAC and MCR-ALS to the potential-frequency dataset were demonstrated for
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monitoring the unionized and ionized species and their voltammograms in acid equilibrium of
vanillin and estimating the pKa value of vanillin. A good agreement was reported for the pKa
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values obtained from MCR-ALS and PARAFAC approaches.
1.1. Theoretical framework
If HA is a weak acid, the following general reaction for the acid dissociation in aqueous
solutions can be written as
HA ⇌ H + + A−
(1)
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Where HA is the weak acid and A- is its conjugate base. In the above expression, an equilibrium
is established between A- and HA forms, which are expressed as ionized and unionized species.
From the equilibrium reaction, the following acid dissociation constant would be obtained
[H+ ] [A− ]
(2)
[HA]
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 =
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according to the law of mass action.
[HA]
(3)
[A− ]
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[H + ] = 
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Equation (2) can be formulated as
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If the negative logarithm of both sides of equation (3) is taken, the following HendersonHasselbalch equation for the calculation of the pH value in chemical and biological systems is
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obtained as
[A− ]
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pH = pK a + log [HA]
(4)
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Here [HA] and [A−] are considered as coming from the acid and its salt in relevant system,
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respectively. In Equation (4), if [HA] = [A−], the pH value is equal to pKa (-log Ka). In order to
determine pKa value, an appropriate parameter of experimental methods is measured as a
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function of pH. In the implementation of instrumentation techniques in the pKa analysis, a graph
is obtained from the relationship between the responses of instrument and different pH values.
This graph is used for the pKa determination of weak acid. A similar way is utilized for the
application of multiway data analysis technique to get better pKa analysis results than that of
traditional instrumental techniques as in this study.
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1.2. Multivariate curve resolution-alternating squares
MCR-ALS is a very powerful mathematical tool for the bilinear decomposition of data matrices
to get individual pure contributions of analytes in a complex mixture. In practice, MCR-ALS
approach has been used in chemistry and related branches of science and industry. The bilinear
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decomposition of experimental responses (data matrix, X) into pure component contributions can
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be given as
X = P FT + E
(5)
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Where P (n x k) is the potential profile (or voltammetric profile) of the k components on n
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potential points, F (m x k) is the frequency profile of the k components on m frequency points,
and E (n x m) is the residual data matrix which is related to model error or random noise.
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Decomposition of data matrix X is performed by iterative least squares minimization of ‖E‖
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under suitable constraining conditions i.e. non-negativity and unimodality in related profiles.
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More explanations and all theoretical details concerning the mathematical apparatus of the MCR-
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ALS iterative procedure can be found in the literature [21-23].
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1.3. Parallel Factor Analysis
PARAFAC is a mathematical generalization of principal component analysis (PCA) to higher
order arrays. Parallel Factor Analysis (PARAFAC) is one of decomposition methods of threeway data (or N-way data) into trilinear components, which are defined by three loading matrices
A, B, C with the elements aif, bjf and ckf, respectively. The PARAFAC approach is based on the
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minimization of the sum of squares of the residues, eijk in the fitting model [24, 25], which is
expressed as follows:
X = ∑    + 
(6)
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here af, bf and cf denote the f th columns of the loading matrices A, B and C, respectively. In
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practice, the alternate least squares (ALS) algorithm is used to fit the PARAFAC model of higher
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order data. In the PARAFAC decomposition of three-way dataset, the use of some constraints
such as orthogonality and non-negativity, etc. may be necessary for the resolution of the
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component profiles of the analyzed mixtures. In some cases, constraining the PARAFAC model
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can be beneficial in terms of the interpretability or the accuracy of the model. In order to identify
the optimal number of components, the criteria of core consistency diagnostic tool is described in
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the literature [26]. An optimum condition for a PARAFAC fit to obtain unique parameter
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assessment is proposed by Kruskal [27] and then elaborated by Sidiropoulos and Bro [28].
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2. Materials and Methods
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2.1. Instrument and software
Voltammetric potential-frequency data were collected on a CH Instruments Model 660C
connected C4 Cell Stand with working electrode consisting of sepiolite clay, TiO2 nanoparticles
and multi-walled carbon nanotubes (SC/TiO2/MWCN) based on use of a carbon paste electrode,
which was firstly used in the literature [29], auxiliary electrode consisting of Pt wire (CHI 115)
and reference electrode consisting of Ag/AgCl (CHI 111). Square wave voltammetry was used
for the oxidation of vanillin on the related modified electrode system.
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pH adjustments were performed using a Hanna HI 2211 pH/ORP meter calibrated with buffer
solutions (Thermo Scientific).
Doubly-distilled and de-ionized water supplied from Human Power I+ Ultra pure water system
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was used throughout in this work.
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All data were converted to Microsoft EXCEL files and imported into Matlab by means of a
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special m-file program written in-house in Matlab. The MCR-ALS algorithm written in-house in
MATLAB (Math. Works, Natick, MA) was implemented for the deconvolution of potential-
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frequency dataset into pure contributions of the analyzed profiles for the evaluation of the pKa
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values of vanillin.
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2.2. Chemicals, reagents and solutions
Graphite powder, mineral oil, sepiolite clay, TiO2 nanoparticules, Multiwalled carbon nanotubes
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(MWCNTs) and all solvents were purchased from Sigma. All the reagents were analytical grade
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and used without any further purification. All solutions were freshly prepared with triply distilled
water. Britton-Robinson (BR) buffer solutions were prepared by mixing appropriate amounts of
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0.04 molL-1CH3COOH, 0.04 molL-1 H3BO3 and 0.04molL-1 H3PO4 and then, the buffer solutions
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at 12 different pHs (1.3, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0 and 12.0) were adjusted
with additions of 0.1 M NaOH and 0.1 M HCl to stock buffer solutions.
For the solution of 1.0x10-3 M vanillin dissolved in ethanol, the voltammograms at 12 different
pH values between 1.3-12.0 and at 8 different frequencies between 5.0-120.0 Hz were recorded
between -200.0–1400.0 mV. In the experimental applications, each sample solution containing
vanillin (1.0x10-3 M, 1 mL) and 9.0 mL of BR buffer solution for each pH in the working pH
ranges was pipetted into a voltammetric cell.
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Electrochemical experiments were performed by using SWV technique with suitable
voltammetric conditions consisting of supporting electrolyte Britton-Robinson (BR) buffer, pulse
amplitude of 0.05 V, scan increment of 0.008 V, frequencies of 5, 10, 20, 40, 60, 80, 100, 120
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Hz.
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3. Results and Discussion
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As it is well known, electroactive compounds (weak acidic compound in our case) in different
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pH media give different electrochemical behaviors with diverse wave forms when applying some
electrochemical techniques such as cyclic voltammetry, square wave voltammetry (SWV) and
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differential plus voltammetry, etc. In a similar manner, the change of the frequency in the
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implementation of the mentioned techniques for the analysis of the relevant compounds in
samples exhibits different electrochemical peak forms with varying peak currents. Among the
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electrochemical parameters, pH and frequency are very important particularly to monitor
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electrochemical characteristics of a weak acid (or a weak base) on the working electrode surface.
In our research paper, it was observed from preliminary experiments that pH and frequency of
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the substance was influential on the variation of the peak current and waveform (or wave
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potential) of the voltammograms obtained from the oxidation of vanillin on the SC/TiO2/MWCN
electrode applying square wave voltammetry.
In the following experiments, the peak current of the related weak acid i.e., vanillin at 12
different pHs in the range of 1.3-12.0 and 8 different frequencies in the range of 5-120 Hz at the
mentioned working electrode was plotted as a function of potential in the potential range of -2001400 mV.
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In order to get three dimensional (3-D) voltammograms (potential x frequency), one-dimensional
peak currents obtained from 8 different frequencies (Hz) were collected in a voltammetric twoway data matrix, for each pH medium. Figure 2 shows the 3D-voltammograms of vanillin at 12
different pH values.
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Insert in Figure 2
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Recorded 3D-voltammograms were converted into Microsoft Excel files. Two-way matrices of
the voltammetric 3D-plots were imported from Microsoft Excel files into Matlab domain and
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then they arranged in a three-way array , also named as a tensor, with dimensions 200x8x12
(potential x frequency x pH) as indicated in Figure 3a. In three-way dataset, the columns denote
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peak current measurements that change with potentials and the rows represent intensity
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measurements that change with frequency, and the frontal slices correspond to the pH values.
Insert in Figure 2
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were illustrated in Figure 3b.
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The sub-structures (frontal slices, horizontal slices and vertical slices) in three-way data array 
3.1. Application of MCR-ALS model
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In this application, the augmented data matrices (or two-way data matrices) obtained unfolding
voltammetric three-way array  were processed using MCR-ALS algorithm providing pure
voltammetric profile, frequency profile and relative concentration profile to predict the pKa
value of vanillin. Before performing the MCR-ALS application to the analysis of three-way data
array, the tensor , which has a 200812 dimension with potential x frequency x pH was
unfolded in three different directions, along the row in first mode, along the column in second
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mode and along a third direction of the cubic data. As it can be seen in Figure 3c, it is possible to
obtain three different unfolding structures, which correspond to two-way data matrices 1 with
the dimension potential x (frequency x pH),  2 with dimension frequency x (potential x pH) and
 3 with dimension pH x (potential x frequency). In our study, the two-way data matrices  2 and
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 3 were considered as augmented matrices for the evaluation of electrochemical behavior and
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pKa value of vanillin. For the deconvolution of data matrix, the MCR-ALS algorithm was
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separately applied to the augmented matrices  2 and  3 matrices, which correspond to 2-D data
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matrices, frequency x (potential x pH) and pH x (potential x frequency), respectively. In MCRALS models, the  2 and  3 , matrices were iteratively decomposed into a set of voltammetric
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profile and relative concentration for the unionized (or acid) and ionized (or congregated base)
species. In case of the application of MCR-ALS with a non-negativity constraint to the two-way
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were illustrated in Figure 4a and b.
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matrix  2 , the resulting profiles for unionized and ionized species of the analyzed compound
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Insert in Figure 4
The normalized voltammograms of unionized and ionized species of vanillin were extracted
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from the voltammetric profile presented in Figure 4a and then they were shown in Figure 5. At
12 different pH media, the electrochemical behaviors of unionized and ionized forms obtained
with the oxidation of vanillin on the SC/TiO2/MWCN electrode were observed from the
normalized voltammograms displayed in Figure5. These normalized voltammograms indicated
that the MCR-ALS deconvolution was suitable way to uncover the electrochemical
characteristics of vanillin in diverse pH media for considering chemical and biological systems.
The relative concentration profile of unionized and ionized of the analyzed substance at eight
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different frequencies was given in Figure 4b. It can be seen from this figure that the relative
concentration ratio of two species is equal to the frequency of 58 Hz.
Insert in Figure 5
In similar manner, MCR-ALS method with a non-negativity constraint was iteratively applied to
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the deconvolution of the two-way data matrix  3 with dimension pH x (potential x frequency) to
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get voltammetric profile and relative concentration profile for the unionized and ionized (also
named as acid and congregated base) forms. Figures 6a and b show the voltammetric profile and
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relative concentration profile of both the acid (unionized) and the base (ionized) species,
obtained by the MCR-ALS deconvolution of the matrix  3 . In Figure 6a, the electrochemical
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behavior of vanillin can be observed from the normalized voltammograms of two species of the
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related compound at eight different frequencies. In the relative concentration, profile of two
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species at 12 different pH values was depicted in Figure 6b.
Insert in Figure 6
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As can be seen from this figure, the fraction of the acid (unionized) and the base (ionized) forms
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was equal when the pH was 7.91± 0.14. In the MCR-ALS implementation, this pH value
corresponds to the vanillin’s pKa value, which corresponds to the negative logarithm of the acid
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dissociation constant, Ka (see Table 1).
Insert in Table 1
Figure 7 shows the normalized voltammograms extracted from Figure 6a obtained by the
application of MCR-ALS model to  3 data matrix. As it was pointed out above, the pKa value
obtained from the intersection point of concentration profiles was given in Table 1.
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Insert in Figure 7
3.2. Application of PARAFAC model
For the demonstration of the electrochemical characteristics and the pKa estimation of vanillin
with the PARAFAC method, the peak currents of the vanillin’s oxidation on the
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SC/TiO2/MWCN electrode were measured as a function of potential, mV and frequency, Hz to
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record the voltammetric 3-D plots in the potential range of -200-1400 mV applying SWV
technique (see Figure 2). As explained above, the data sets of two-way matrices obtained from
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voltammetric 3-D plots were arranged in three-way array  with dimensions 200x8x12 (potential
x frequency x pH). The structure of the three-way array (or tensor) with potential in columns
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frequency in rows, and pH in frontal slices was schematized in Figure 3a. In order to estimate the
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electrochemical behavior and pKa value of vanillin, some two component PRAFAC models with
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different constraints were iteratively tested for the decomposition of three-way data array into
individual contributions of the unionized and ionized forms of the relevant substance using
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alternating least squares (ALS) computation. Then, it was reported from the mentioned
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preliminary test results that un-constraining PARAFAC deconvolution of three-way array was
very useful approach for the assessment of the potential profile of voltammograms, the frequency
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profile and relative concentration profile of the unionized (acidic) and ionized (conjugate basic)
species of vanillin. In the PARAFAC approach, no pre-treatment processes e.g., centering or
scaling, was used for the data analysis. Three loadings were obtained by the PARAFAC
decomposition of the tensor  into trilinear components. The related loadings correspond to the
potential profile of voltammograms, the frequency profile and relative concentration profile for
both chemical forms (unionized and ionized species of vanilin), respectively as shown in Figure
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8a-c. In this implementation, the fit of PARAFAC model with two components was done and
then the explained variance was found to be 99.98% of the change in three-way data.
Insert in Figure 8
In the PARAFAC deconvolution of three-way array, core consistency was reported as 100.0 %.
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Experimental results indicated that PARAFAC model was satisfactory for the demonstration of
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electrochemical characterization of vanillin and for the prediction of the pKa value of the
subjected substance. In Figure 8c, it can be seen the pH point when the ratio of two chemical
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species of vanillin in the relative concentration profile was equal in acid-base equilibrium. In this
pH point, the pKa value and its corresponding standard deviation for the analyzed compound was
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listed in Table 1. This pKa value was obtained from the average of three replicate experiments.
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4. Conclusions
A comparative application of the MCR-ALS and PARAFAC algorithms to two-way data array
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and three-way data array of 3D-voltammograms brings new opportunity different approaches for
the pKa prediction of vanillin used in foods and pharmaceuticals. In the MCR-ALS and
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PARAFAC deconvolutions of 2-D voltammetric dataset and 3-D voltammetric dataset,
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respectively, the voltammetric profiles in different frequencies and different pH media made it
possible to monitor the unionized and ionized forms of vanillin in its dissociation equilibrium
and relative concentration profiles giving the fraction of two chemical species against pH values
made it possible to predict the pKa value of the analyzed compound without using additional
software and chemical treatment e.g. titration. It was concluded that easy interpretable results
obtained from SWV combined with MCR-ALS and PARAFAC were due to second order
advantage of multiway data analysis methods over traditional pKa determination methods.
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Although MCR-ALS and PARAFAC methodologies have different mathematical algorithms,
they gave comparable pKa results. This study indicated that the proposed MCR-ALS and
PARAFAC were alternative tools to demonstrate the electrochemical behavior of vanillin against
frequency and pH changes in chemical and biological systems with small number of experiments
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to leads to more accurate results.
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Acknowledgments
This study was performed at the Chemometrics Laboratory of Faculty of Pharmacy, which was
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supported by the scientific research fund of Ankara University (Project Number 10A3336001).
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The authors would like to thank Ankara University for their support regarding Chemometrics
Laboratory. Electrochemical part of the experiments was done at Faculty of Science, Department
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of Chemistry and it was supported by the scientific research fund of Ankara University (Project
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Number 2005-07-05-094).
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Table 1. Experimental pKa determination results of vanillin obtained by
the application of MCR-ALS and PRAFAC methods to the
voltammetric dataset
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: Standard deviation
RSD : Relative standard deviation
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CI : Confidence interval at 95 % confidence level
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SD
Literature methods
[1]
[2]
[3]
[4]
7.75 7.40 7.15 7.36
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Mean
SD
RSD
CI
Proposed methods
MCR-ALS
PARAFAC
7.91
7.97
0.12
0.10
1.40
1.19
0.14
0.12
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Figure 1. Chemical structure of vanillin
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Figure 2. Three-dimensional voltammograms as a function of the potential and
frequency (from pH=1.3 to pH =12.0)
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(c)
Frequency x pH (8 x 12)
1
2
3
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Potential
(b)
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198
199
200
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(a)
Two-way data matrix, 1
Frontal slices
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Frequency
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Frequency
1
2
3
4
5
6
7
8
Two-way data matrix,  2
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Horizontal slices
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Three-way data array, 
Potential x Frequency (200 x 8)
pH
Potential
Potential x pH (200 x 12)
1
2
3
4
5
6
7
8
9
10
11
12
Two-way data matrix,  3
Vertical slices
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Figure 3. a) Three-way array, b) the substructures (frontal slices, horizontal slices and
vertical slices) in three-way array and c) the representation of unfolding threeway data array  into two-way data matrices 1 ,  2 and  3 .
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Figure 4. a) Normalized voltammetric profiles and b) relative concentration profiles
obtained by applying the MCR-ALS method to the 2-D matrix  2 .
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Figure 5. Normalized voltammograms of unionized (acid) and ionized (conjugate base)
forms of vanillin in 12 different pH media, obtained by the extraction from the
voltamometric profiles given in Figure 3a.
Figure 6. a) Voltammetric profile and b) relative concentration profile obtained by
applying the MCR-ALS method to the 2-D matrix,  3 .
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Figure 7. Normalized voltammograms of unionized (acid) and ionized (conjugate base)
forms of vanillin in eight different frequencies (Hz), obtained by the extraction
from the voltamometric profiles given in Figure 5a.
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Figure 8. a) Voltammetric profile, b) Frequency profile and c) Relative concentration
profile obtained by PARAFAC decomposition of the potential-frequency
tensor.
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Figure: Graphical abstract
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Highlights
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3D-voltammograms were obtained as a function of different frequencies and pHs.
Multiway analysis of 3D-voltammograms was used for the estimation of vanillin’s pKa.
Multiway analysis methods are PARAFAC and MCR-ALS deconvolutions.
This study indicates possible to monitor acid and base species of vanillin in its
dissociation equilibrium.
MCR-ALS and PARAFAC were alternative tools to quantify pKa.
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