Multivariate Curve Resolution of Synchronous FluorescenceSpectra Matrices of Fulvic Acids Obtained as a Function of pH

JOAQUIM C. G. ESTEVES DA SILVA* and ROMA TAULERCentro de Investigacao em Quımica, Departamento de Quımica, Faculdade de Ciencias da Universidade do Porto, R. Campo Alegre 687,

4169-007 Porto, Portugal (J.C.G.E.d.S.); and Department of Environmental Chemistry, Institute of Chemical and Environmental Research,

CSIC, Jordi Girona 18-26, 08034, Barcelona, Spain (R.T.)

Synchronous fluorescence spectra (excitation wavelength range between

280 and 510 nm and wavelength interval of 25 nm) of three samples of

fulvic acids (FA) were obtained as a function of the pH, in the range from

2.0 to 10.5, and as a function of the FA concentration, in the range from 20

to 180 mg/L. FA were obtained from composted livestock materials (lsFA),

composted sewage sludge (csFA), and Laurentian soil (laFA). Three-

dimensional spectral matrices were obtained (wavelength, pH, and FA

concentration) and multivariate curve resolution (MCR) was used to

calculate spectra and fluorescence intensity profiles for the detected

components. Cluster analysis of the calculated spectra showed the

existence of similar and unique fluorescent properties in the three FA

samples. Some of the calculated fluorescence intensity profiles have a

shape compatible with acid–base species distribution diagrams, which

allowed pKa values to be estimated, namely, a well-defined acid–base

equilibrium with pKa 5.7 6 0.2 (lsFA), 6.9 6 0.4 (csFA), and 5.5 6 0.2

(laFA); and other acid–base systems not well defined with pKa at about 3.0

and 8.6. Other spectral variations revealed the existence of inner-filter

effects or self-quenching as the concentration of FA increases.

Index Headings: Synchronous fluorescence; Fulvic acids; Acid–base

equilibrium; Multivariate curve resolution; MCR; Alternating least

squares; ALS.

INTRODUCTION

Fulvic acids (FA) are among the most reactive structures ofsoil organic matter, participating in acid–base reactions andinteracting with metal ions and organic substances.1 Molecularsynchronous fluorescence (SyF) spectroscopy is a particularlyuseful technique for the study of the chemical equilibriumproperties of FA because it is a highly sensitive analyticaltechnique, allowing measurements to be made at naturalenvironmental concentrations, and measurements are nonde-structive.2–17 Moreover, SyF spectra of FA are characterized bya great amount of information,5,12,15–17 which is an importantproperty for FA studies because they are a complex mixture ofsubstances with somewhat similar properties.

The SyF spectra of FA are quite sensitive to the samplepH.6,8–16 The origin of these spectral variations with the pHwas attributed to different acid–base and spectroscopicproperties of the most important pH-reactive structures. Self-modeling curve resolution methods based on factor analysishave been proposed for the reduction of the SyF spectralvariations in the spectra and concentration profiles (from whichpKa values could be estimated) of a small number ofcomponents.8,10,13,15,16 These methods were based on thedecomposition of one two-way data matrix composed of SyFspectra (wavelength) collected as a function of the pH.

In order to increase the information about FA samples using

the pH-induced SyF spectra variations, a further experimentalfactor can be changed, namely the concentration of FA. Thismethodology originates three-way data structures for one FAsample (wavelength 3 pH 3 concentration). The increase in theconcentration of FA will originate modifications in the SyFspectra as a consequence of filter effects due to the relativelyhigh optical density of the organic matter.18,19

Multivariate curve resolution (MCR), which is a constrainedinteractive alternating least squares procedure, is suitable forthe analysis of these three-way data matrices that deviate fromthe true trilinear model.20–25 Indeed, the data matrices underanalysis in this work hardly follow a trilinear model, mainlybecause of the following points: although the spectra collectedas a function of the concentration show some distortions due tofilter effects, a high colinearity degree is expected; and exactpH value reproduction in different titrations is almostimpossible to achieve.

The objective of the work described in this paper is topropose a new methodology for the study of the acid–baseproperties of FA based on these three-way data matrices and inthe use of MCR to reduce the experimental data in the SyFspectra, pH, and FA concentration profiles of the detected acid–base systems. This paper shows the results of the proposedmethodology for three samples of FA: lsFA, FA extracted fromcompost livestock; csFA, FA extracted from composted sludgefrom a wastewater treatment plant; and laFA, a sample ofLaurentian FA.

THEORY

For each titration, all the SyF spectra measured after eachaddition of titrant were arranged in a data matrix D. This matrixD has m rows (number of SyF spectra recorded as function ofthe pH) and n columns (number of wavelengths of the SyFspectra: in this work n was always equal to 47).

At a determined pH value the SyF spectra of FA is the sumof the individual SyF spectra of the fluorescent constituents ofFA multiplied by the correspondent concentration. If thefluorescent constituent has no acid–base properties its concen-tration is constant throughout the titration. On the contrary, ifthe constituent undergoes ionization in the pH window underanalysis, its concentration profile has the shape of an acid–basespecies distribution diagram. The bilinear decomposition of thematrix D can be described by the following equation:

D ¼ CST þ E ð1Þ

where C is the matrix describing the concentration (orfluorescence intensity) profiles of every detected component,ST is the matrix describing the individual ‘‘pure’’ SyF spectrum

Received 7 June 2006; accepted 1 September 2006.* Author to whom correspondence should be sent. E-mail: jcsilva@fc.up.pt

Volume 60, Number 11, 2006 APPLIED SPECTROSCOPY 13150003-7028/06/6011-1315$2.00/0

� 2006 Society for Applied Spectroscopy

of these components, and E is the residual matrix describingthe variance not explained by CST.

In this work, several D matrices were obtained for eachsample of the three FA samples under analysis by independenttitration of different concentration solutions (ns) of the FA (sixor seven solutions in the range 20 to 180 mg/L): matrices D1,D2,. . ., Dns. These matrices were arranged in an augmentedcolumn-wise data matrix. This augmented data matrix has anumber of rows equal to the total number of acquired SyFspectra (m 3 ns) and it has a number of columns equal to thenumber of wavelengths of the SyF spectra (n ¼ 47). Thiscolumn-wise data matrix augmentation assumes that commonvectors span the column vector spaces of the differentindividual data matrices, i.e., that common SyF spectra arepresent in the four data sets. The linear model given by Eq. 1can be easily extended to the augmented data matrix as follows:

Daug ¼ CaugST þ E ð2Þ

In this work three augmented column-wise data matrices areobtained, D1

aug, D2aug, and D3

aug, one for each FA sample(lsFA, csFA, and laFA).

The resolution power of the MCR–alternating least squares(ALS) method improves considerably if several experiments,giving data matrices obtained for the same chemical systemunder different experimental conditions, are simultaneouslyanalyzed. Moreover, interrelations between different FAsamples can be obtained.

In order to evaluate the fitting error in the reproduction of theoriginal matrix using the solutions found either by principalcomponents analysis (PCA) or by MCR-ALS, a percentage oflack of fit (lof) value was calculated using the followingequation:

lofð%Þ ¼ 100 3

ffiffiffiffiffiffiffiffiffiffiffiffiffiXi; j

e2ij

Xi; j

d2ij

vuuuuut ð3Þ

where eij are the elements of the residuals matrix E and dij arethe elements of the data set (D or Daug).

EXPERIMENTAL

Reagents. Anthropogenic FA were extracted from twosamples of livestock waste (mixed with vegetable residues)(lsFA) and composted solid wastes derived from sewage sludge(csFA). FA were isolated by a procedure recommended by theInternational Humic Substances Society.26 The characterizationof the anthropogenic FA samples has been done previous-ly.15,16 A commercial FA sample extracted from a Laurentiansoil (Laurentian FA, laFA) was obtained from FredriksResearch Products (The Netherlands).

Solutions of FA ranging from 20 to 180 mg/L were preparedin 0.1 M potassium nitrate. The initial pH of the FA solutionswas adjusted to pH¼ 2.0 with a standard solution of nitric acid(0.1 M). A solution of decarbonated potassium hydroxide(about 0.05 M) was used as the titrant and the total amountadded at the end of the titration did not cause significantdilution of the FA solution (less than 5%).

Instruments and Procedures. Potentiometric titrations withpH measurement were conducted with a PC-controlled system,assembled with a Crison MicropH 2002 pHmeter and a Crison

MicroBu 2030 microburette. The experiments were done undernitrogen at 25 6 0.2 8C. The cell was calibrated with threebuffer solutions with ionic strength adjusted to 0.1 M.27

Synchronous fluorescence measurements were made with aPerkin-Elmer LS-50 luminescence spectrometer with a flowcell. A Gilson Minipuls 2 peristaltic pump forced thedisplacement of the titrated solution into the flow cell aftereach addition of potassium hydroxide. During pH and SyFspectra measurements the pump was turned off. The spectrawere recorded with the following settings: between 280 and510 nm; 0.5 nm acquisition interval between points; 7.5 nmexcitation and emission slit widths; wavelength difference of25 nm; and scan rate of 200 nm min�1. The resolution of theraw spectra was reduced to 5 nm before data analysis (47points per spectrum) by eliminating intermediate raw spectraldata points.

Programs. The calculations associated with the MCR-ALSmethod were performed using several programs implementedin MATLAB and obtained from http://www.ub.es/gesq/mcr/mcr.htm. Hierarchical cluster analysis was performed withSPSS (Statistical Package for the Social Sciences) using thesingle linkage and Ward methods, and Euclidean distanceswere calculated.

Multivariate Curve Resolution–Alternating LeastSquares Constraints. The MCR-ALS interactive procedurecan be subjected to several constraints according to thephysico-chemical properties of the data structure underanalysis.20–25 In this work, non-negativity and equalityconstraints were tested.

Non-negativity constraints on both the spectra and theconcentration profiles (fluorescent intensity profiles) resultedfrom the physical meaning of a fluorescence spectrum becausethe intensity must always be positive.

Equality constraints were applied when the fluorescenceintensity profile of a component has the shape of a speciesdistribution diagram as function of the pH (S or Z curves).15

This shape can be observed by evolving factor analy-sis8,10,11,15,16,28,29 or by the MCR-ALS unconstrained solution.If the fluorescence intensity profile corresponds to an ionizationof the acid species (decreasing trend), then the concentration atthe end of the titration is zero (at this point the acid iscompleted ionized). If the fluorescence intensity profilecorresponds to the formation of the conjugate base species(increasing trend), then the concentration at the beginning ofthe titration is zero. If the fluorescence intensity profilecorresponds to the conjugate base (first ionization) and acidspecies (second ionization) of a diprotic acid (increasingfollowed by a decreasing trend), then the concentration of thisspecies is zero at the beginning and at the end of the titration. Inthis work a harder equality constraint (equal to practically zero)and a softer equality (unequality) constraint (equal to or lowerthan a threshold value equal to one) were tested.

RESULTS AND DISCUSSION

Preliminary Analysis of the Synchronous FluorescenceMatrices. Some typical SyF spectra of the three FA samplesand the effect of varying pH on their intensities are shown inFig. 1. The comparative analysis of these spectra shows that thepH induces marked spectral variations on the SyF spectra ofcsFA and minor variations on the SyF spectra of lsFA and laFAsamples. However, the pH-induced variation of these twosamples apparently is more complex because the intensity of

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several overlapped bands oscillates, particularly for the naturalFA sample (laFA).

The shape of the SyF spectra of FA may be affected by theconcentration because of inner-filter effects due to the strongabsorption of these substances.30–33 A red shift is observedwhen humic substance concentration increases as a conse-quence of the attenuation of the fluorescence of thefluorescence emission in the shorter wavelength region.30

Indeed, several fluorophores present in the FA samples showdifferent concentration dependence as a consequence of theinner-filter effects.33

Figure 2 shows typical SyF spectra of the three FA samplesat pH¼ 3 at four concentrations. The analysis of these spectrashows that spectral distortions and nonlinearities are observedin the low wavelength range, around 300 nm. This effect is

particularly marked for the lsFA and laFA samples because theglobal spectral intensity of these samples is smaller than thatobserved for csFA.

Principal Components Analysis of the SynchronousFluorescence Matrices. The three sets of SyF spectra weresubjected to PCA, either the individual concentration matricesor the augmented data matrices, in order to obtain an estimationof the intrinsic number of components of each FA sample. Inthis case, each component represents a fluorophore present inthe FA sample whose fluorescent properties vary with the pH.Acid–base chemical reactions and physical processes (forexample, quenching and inner-filter effects) may be responsiblefor these spectral variations.

Table I shows the PCA results of the 140 mg/L individualconcentration matrix and of the augmented data matrices.Although the analysis of these results is not straightforward,three types of information can be obtained: (1) three or fourcomponents are necessary to describe the data set variance; (2)the lsFA and laFA samples require a higher number ofcomponents than the csFA sample; and (3) the augmented data

FIG. 1. SyF spectra of 140 mg/L solutions of (top) lsFA, (middle) csFA, and(bottom) laFA at four pH values: (�) 2.0; (3) 5.3; (&) 7.5; and (m) 10.5.

FIG. 2. SyF spectra of (top) lsFA, (middle) csFA, and (bottom) laFA at pH 3and at four concentrations: (�) 20 mg/L; (3) 80 mg/L; (m) 110 mg/L; and (&)140 mg/L.

APPLIED SPECTROSCOPY 1317

matrices require more components than the single concentra-tion matrices. This last result supports our previous discussionabout the deviations of the trilinear model of the three-way datastructures under investigation as a consequence of spectraldistortions due to inner-filter effects and to the impossibility ofexact pH value reproduction in different experiments.

Multivariate Curve Resolution–Alternating LeastSquares of the Synchronous Fluorescence Matrices. Thethree augmented data matrices were analyzed by MCR-ALSforcing the number of components between three and five andusing non-negativity constraints (concentrations and spectra)and equality constraints (concentration or fluorescent intensityprofiles).

From the analysis of the MCR-ALS results, the SyF data setof the lsFA, csFA, and laFA samples are best described usingfour, three, and four components, respectively. Table II showsthe fitting quality parameters of the best MCR-ALS modelobserved; only non-negativity in both the spectra andconcentration were used.

When equality (equal to practically zero) or unequality(equal to or lower than one) constraints were used, the worstfittings were found. Nevertheless, the calculated spectra andfluorescence intensity profiles show a global shape similar tothat obtained when only non-negativity constraints were used.Consequently, equality constraints were not considered infurther analysis.

Figures 3, 4, and 5 show the calculated spectra andfluorescence intensity profiles (concentration and pH) for thethree FA samples.

Analysis of the Multivariate Curve Resolution–Alter-nating Least Squares Results. All the calculated spectra

(Figs. 3a, 4a, and 5a) have a shape compatible with a SyF

spectrum, i.e., the spectral peaks are not too narrow or as largeas a typical emission spectrum. The analysis of the fluorescence

intensity profiles of the lsFA sample (Fig. 3a) shows three

different types of fluorescence intensity variation with the

concentration and pH.

Type i. The component represented by (3) shows no marked

relative variation either by the concentration or the pH. This

component probably corresponds to a background signal

common to all individual concentration data sets. This

TABLE I. PCA results of SyF matrices corresponding to 140 mg/L and augmented data matrices.a

Nc

lsFA csFA laFA

EV %V %CV EV %V %CV EV %V %CV

140 mg/L matrices

1 3.8 3 104 99.90 99.90 4.1 3 104 99.12 99.12 1.5 3 104 99.71 99.712 2.9 3 101 0.08 99.98 3.5 3 102 0.83 99.95 3.2 3 101 0.21 99.923 5.2 3 100 0.01 99.99 1.5 3 101 0.01 99.99 1.0 3 101 0.07 99.994 2.2 3 100 0.01 100.00 1.9 3 100 0.00 100.00 5.0 3 10�1 0.00 99.995 7.5 3 10�1 0.00 100.00 9.5 3 10�1 0.00 100.00 3.1 3 10�1 0.00 99.99

Augmented matrices

1 4.0 3 10 85.94 85.94 3.2 3 10 67.23 67.23 3.5 3 10 74.94 74.942 5.3 11.21 87.15 1.1 3 10 24.24 91.46 8.5 18.17 93.113 9.2 3 10�1 1.97 99.11 3.3 6.96 98.43 2.3 4.88 97.984 1.2 3 10�1 0.25 99.37 3.5 3 10�1 0.75 99.18 4.8 3 10�1 1.03 99.015 6.2 3 10�2 0.13 99.50 1.1 3 10�1 0.24 99.42 9.9 3 10�2 0.21 99.22

a Nc: number of eigenvalues; EV: eigenvalue; %V: percentage of variance of each eigenvalue; %CV: cumulative percentage of variance.

TABLE II. Statistical quality parameters of the best MCR-ALS model.a

Matrix Nc PCA (%lof) ALS (%lof) R2

Daug (lsFA) 4 0.004570 0.7740 99.994Daug (csFA) 3 0.001593 1.4494 99.979Daug (laFA) 4 0.002518 1.0424 99.989

a Nc: number of components; PCA (%lof): percentage of lack of fit valuesbetween the experimental data matrix and the reproduced data matrices byPCA and ALS; ALS (%lof) percentage lack of fit values between theexperimental data and ALS fitting; R2: percentage of variance explained at theoptimum.

FIG. 3. SyF (a) spectra and (b) concentration profiles obtained by MCR-ALSfor the lsFA sample: (m) first, (&) second, (*) third, and (3) fourth component.

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background signal is probably due to an instrumental artifactusually present in the fluorescent spectra of humic substanc-es.33

Type ii. The component represented by (m) shows a slightvariation with the pH and its intensity decreases with theconcentration of the FA sample. The variation (increase offluorescence intensity) with the pH, observed in the most acidpH region (beginning of the titration), corresponds to an acid–base fluorophore. The decrease of the intensity with theconcentration must be due to an inner-filter effect resultingfrom the increase of the FA concentration. Indeed, themaximum of the SyF spectra corresponding to this componentfalls in the ultraviolet (UV) spectral region (at about 320 nm),which is most attenuated by inner-filter effects.30

Type iii. The components represented by (*) and (&) show atypical variation of a monoprotic acid species (&) and thecorresponding conjugated base species (*).

The analysis of the fluorescence intensity profiles of thecsFA sample (Fig. 4b) shows marked similarities with thosecalculated for the lsFA sample, namely, with the previouslymentioned Types (ii) and (iii).

However, the component represented by (m) shows nodecrease in intensity with the increase of the concentration ofthe FA but its intensity remains constant (Fig. 4b). Also,besides the increase of intensity due to an acid ionization in thebeginning of the titration, this increase is followed by adecrease of the intensity, probably due to an acid ionization.

The fluorescence intensity profiles obtained for the laFAsample are more complex to analyze and are shown in Figs. 5band 5c. Indeed, besides the existence of fluorescence intensityprofiles with marked similarities with those calculated for thelsFA and csFA sample, namely, with the previously mentionedTypes (ii) and (iii), there is a fourth fluorescence intensityprofile with a particular type of variation (represented by L inFig. 5c).

Type iv. This type is characterized by a marked increase ofintensity, beginning at a zero value, followed by a decrease tozero intensity. This type of component probably corresponds toan acid fluorophore that becomes fluorescent upon ionizationbut turns into a non-fluorescent species when it undergoes thesecond ionization.

Acid Ionization Constants. The analysis of the calculatedfluorescent intensity profiles (Figs. 3b, 4b, 5b, and 5c) showsthe existence of several variations compatible with acidionizations. The variations corresponding to Type (iii) (* and

FIG. 4. SyF (a) spectra and (b) concentration profiles obtained by MCR-ALSfor the csFA sample: (m) first, (&) second, and (*) third component.

FIG. 5. SyF (a) spectra and (b, c) concentration profiles obtained by MCR-ALS for the laFA sample: (m) first, (&) second, (*) third, and (L) fourthcomponent.

APPLIED SPECTROSCOPY 1319

&) clearly have the shape of a species distribution diagram of amonoprotic acid. From the graphical observation of the plotscrossover of two conjugated systems at about 50% ionization(one plot for each FA concentration under analysis), the pKa ofthis acid–base system can be estimated. The pKa for this acid–base system for the three FA samples are (average of the pKavalues calculated for each concentration and respectivestandard deviation): lsFA, 5.7 6 0.2; csFA, 6.9 6 0.4; andlaFA, 5.5 6 0.2. This result shows that this component of thelsFA and laFA samples has similar acid–base properties andthat of csFA is a weaker acid than the other two FA. No trendwas detected in the calculated pKa induced by the increasefrom 20 to 180 mg/L in the FA concentration.

Other variations compatible with acid ionizations can bedetected in the calculated fluorescent intensity profiles but theassignment of the corresponding pKa is somewhat fuzzy and,consequently, their values should be understood as roughestimations: the variations corresponding to Type (ii) (m), andpresent in the three FA samples, correspond to the conjugatedbase of an acid–base system with a pKa about 2.8; thevariations corresponding to Type (iv) (L) of the laFA samplereveal a fluorophore with two pKas at about 3.1 and 8.6.

Similarity Analysis of the Calculated SynchronousFluorescence Spectra. From the above discussion about the

fluorescence intensity profiles calculated for the three FAsamples several similarities were detected. The next step was toverify whether the spectra of the components detected in theFA samples have similarities. Figure 6 shows the dendogramsobtained by cluster analysis of the calculated spectra of thecomponents (four spectra for lsFA, three spectra for csFA, andfour spectra for laFA).

The analysis of Fig. 6 clearly shows the existence of twoclusters: (1) Cluster A composed of the spectra cs3, la1, andls1; and (2) Cluster B composed of the spectra ls2, ls3, la2, andla3. The other four spectra (cs1, cs2, la4, and ls4) do notcluster.

Cluster A correspond to the similar fluorescence intensityprofiles calculated for the three FA samples [Type (i) above]and represented by the symbol (m) in Figs. 3b, 4b, and 5c.Cluster B corresponds to the similar fluorescence intensityprofiles detected in the lsFA and laFA samples of Type (ii) (*

and & in Figs. 3b and 5b), which also have similar acid–baseproperties (pKa about 5.6). This result shows that the samefluorophores having acid–base properties exist in the lsFA andlaFA samples; indeed, as discussed above, these fluorophoreshave similar acid–base properties with a pKa about 5.6. Two ofthese fluorophores have similar SyF spectra characterized bytwo overlapped bands with maxima at about 340 and 400 nm

FIG. 6. Dendrograms obtained by hierarchical cluster analysis of the spectra of the FA samples calculated by MCR-ALS. The calculated SyF spectra of thecomponents are designated by: LS1, LS2, LS3, and LS4: lsFA sample; CS1, CS2, and CS3: csFA sample; and LA1, LA2, LA3, and LA4: laFA sample.

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and the third fluorophore has a SyF spectrum with a maximumat 320 nm. This last fluorophore is also present in the csFAsample.

The other four spectra that do not cluster contain particularfluorescent properties of the three FA samples, revealing theirdifferent origins. The ls4 spectrum corresponds to the above-defined Type (i) component that was only detected asbackground fluorescence of the lsFA sample. The la4 SyFspectrum has a maximum at 460 nm and corresponds to theabove defined Type (iv) component that was only detected inthe laFA sample. The cs1 and cs2 spectra correspond to thefluorescence intensity profiles of the Type (iii) component butare different from the spectra of Cluster B. The maindifferences are a pronounced maximum at 350 nm (cs1) andthe band at 420 nm (cs2) besides the two characteristic bandsof the Cluster B spectra (340 and 400 nm).

CONCLUSION

Multivariate curve resolution–alternating least squares is aparticularly useful soft-modeling data analysis technique forthe interpretation of complex spectroscopic data matrices.Indeed, in the case of three-way data with small deviationsfrom trilinearity, MCR-ALS succeeded in the resolution of thespectroscopic information.

The SyF spectra of the FA from different origins collected asa function of the pH and concentration of FA were successfullyresolved in the spectra and corresponding fluorescent intensityprofiles (as a function of the pH and concentration) of a smallnumber of components. Different spectral variations, inducedby varying the concentration of FA or pH, and resulting fromdifferent physico-chemical mechanisms, were detected, forexample, quenching, inner-filter effects, and acid–base reac-tion.

Although the FA samples under analysis have quite differentorigins, similarities among the samples were detected as well asparticularities. Indeed, either similar spectra or fluorescenceintensity profiles were detected in the three FA samples understudy, suggesting that similar chemical constituents wereresponsible for the fluorescent and acid–base properties.However, all three samples contain some components havingunique fluorescent properties, revealing their different origins.

ACKNOWLEDGMENTS

Integrated Actions Portugal-Spain E26/01 has financially supported thiswork. Sandra L.R.R.S. Bastos is acknowledged for performing some of theexperimental work.

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