Monitoring the polyamide 11 degradation by thermal properties and X-ray fluorescence spectrometry...

Research article

Received: 26 July 2012 Accepted: 30 October 2012 Published online in Wiley Online Library: 27 December 2012

(wileyonlinelibrary.com) DOI 10.1002/xrs.2436

Monitoring the polyamide 11 degradation bythermal properties and X-ray fluorescencespectrometry allied to chemometric methodsEloilson Domingos,a Thieres M. C. Pereira,a Paulo R. Filgueiras,a

Maria Izabel M. S. Bueno,b Eustáquio V. R. de Castro,a Regina C. L. Guimarães,c

Geovane L. de Sena,a Werickson F.C. Rochad and Wanderson Romãoa*

The influence of temperature (110 and 120 �C) on the ageing of piping made from polyamide 11 (PA-11) containing 10–12% ofplasticizer was studied using deionized water (pH� 7.0). A clean analytical methodology has been employed for quality controlof polymeric materials: energy-dispersive X-ray fluorescence spectrometry (ED-XRF). It provides a fast and suitable technique tocharacterize chemical elements because of its multielemental capability, good sensitivity, high precision, short analytical time,and nondestructive nature. Herein, the content of additive in PA-11 was monitored from ED-XRF measurements where theabundance of the S line is directly related to the ageing time, agreeing with the thermogravimetric analysis. The XRF data wereallied to chemometric treatment to classify PA-11 samples according to the amount of additive and weight average molar masschange, predicting the ageing time, and viscosity values of PA-11. Therefore, the XRF can be used as a clean analytical method-ology tomonitor the PA-11 degradation, thus eliminating the use of toxic organic solvents (necessary to viscosity measurements)and reducing the working time. Also, the effect of hydrolysis on the structure over time and the material morphology weremonitored through measurements of dynamic mechanical analysis and differential scanning calorimetry. Copyright © 2012 JohnWiley & Sons, Ltd.

Correspondence to: Wanderson Romão, Department of Chemistry, FederalUniversity of Espírito Santo - UFES 29075-910, Vitória, ES, Brazil. E-mail:[email protected]

Department of Chemistry, Federal University of Espírito Santo-UFES, 29075-910,Vitória, ES, Brazil

X-ray Spectroscopy Group, Institute of Chemistry, University of Campinas,UNICAMP, 13084-971, Campinas, SP, Brazil

Petróleo Brasileiro S/A-PETROBRAS, CENPES, Rio de Janeiro, RJ, Quadra 7,21949-900, Rio de Janeiro, Brazil

National Institute of Metrology, Quality and Technology (Inmetro), ChemicalMetrology Division (Dquim), 25250-020, Xerém/RJ, Brazil 7

9

Introduction

In offshore oil exploration, the technology of flexible pipelinesand risers is essential in the connection from the seafloor to plat-forms or among several platforms.[1] Flexible pipelines are multi-layer structures composed basically of metallic and/or polymericmaterials as shown in Fig. 1, being constituted by several concen-tric layers overlapped.[2] The internal polymeric layer has thefunction of sealing the line, preventing the direct contactbetween fluid and the steel layer. The polyamide 11 or PA-11 isthe main polymer used in the manufacture of flexible pipes,because of its good thermomechanical properties, suitable formanufacturing flexible pipe from extrusion processing.[3]

The PA-11 has the amide group (—CONH—) in their structure,improving desirable characteristics for offshore applications, suchas excellent mechanical properties (high fatigue resistance, lowfrictional coefficient, and excellent creep resistance) and goodchemical resistance, enabling the use of this semicrystallinethermoplastic material as a barrier during the transport of gas,water, and oil mixtures.[3,4] Generally, the PA-11 is plasticized withN-butyl-benzenesulfonamide in 12wt.% concentration to improveflexibility and to reduce hardness.[3,5,6] However, the PA-11 and otherpolyamides in the presence of water undergo hydrolytic degradationprocess,[3,5,7–9] being accelerated under high temperatures (>90 �C)and/or in acid medium (carbon dioxide, hydrogen sulfide, and or-ganic and inorganic acids), pH< 7. This degradation mechanismcauses mainly a decrease in weight average molar mass, Mw, andthe loss of plasticizer and mechanical properties of PA-11.[5]

There are several typical analytical techniques to monitor theMw of polymeric materials such as osmometry, ebulliometry,

X-Ray Spectrom. 2013, 42, 79–86

viscometry (corrected inherent viscosity, CIV), and size exclusionchromatography. Among them, the American Petroleum Instituterecommends the use of CIV and size exclusion chromatographyas routine methodology.[10] However, the main disadvantage ofthese methods is the necessity of one step of sample preparationsuch as dissolution, extraction, or chromatographic separationincreasing, as consequence, the time of analysis.

Recently, a clean analytical methodology has been employedfor quality control of polymeric materials: energy-dispersive X-rayfluorescence spectrometry, ED-XRF. It can provide a fast andsuitable technique to characterize chemical elements because ofits multielemental capability, good sensitivity, high precision, shortanalytical time, and nondestructive nature.[11–15] For PA-11, theX-ray spectrum can be associated with light elements (C, H, O,among others) and sulfur from polymeric matrix, proving powerful

*

a

b

c

d

Copyright © 2012 John Wiley & Sons, Ltd.

Figure 1. Flexible piping applied to petroleum production in which sevenlayers are lighted: polyamide 11 is utilized mainly as internal plastic layer.

E. Domingos et al.

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properties for qualitative or even quantitative determination of Mw

and of amount of additives in PA-11.Multivariate methods can help to extract relevant qualitative

or quantitative information from the spectra because thesemethods can be used to derive rapid analysis for polymersquality control.[16,17] Gregoire et al.[16] used chemometric tools todifferentiate several organic materials, particularly polymers, bylaser-induced breakdown spectroscopy. Camacho et al.[17] deter-mined moisture content in nylon 6,6 by near-infrared spectroscopyand chemometrics. Ortiz et al.[15] performed inorganic fingerprint-ing of Sildenafil and Tadalafil tablets in commercial pharmaceuticalsamples via X-ray fluorescence spectrometry and multivariatemethods. From this, the use of chemometric methods to interpretmultivariate data has been increased, specially, in the polymericmaterials field.In the present work, the degradation process was monitored

by CIV measurements. As this thermoplastic contains additives,it was necessary to correct the inherent viscosity (IV). The deter-mination of the additive content was made through thermogra-vimetric analysis and ED-XRF. Both results were compared. Theeffect of hydrolysis over time on the material structure andmorphology was studied through measurements of dynamicmechanical analysis (DMA) and differential scanning calorimetry(DSC). Moreover, ED-XRF allied to principal component analysis(PCA), partial least squares (PLS), and support vector machines(SVM) were used to classify PA-11 samples and to correlate spec-tral information with CIV values and ageing time of PA-11. Thechemometric tools used in this study are briefly described inthe following paragraphs.

PCA

Principal component analysis is a technique that, quite literally,takes a different viewpoint of multivariate data.[18] In fact, PCAdefines new variables, consisting of linear combinations of theoriginal ones, in such a way that the first axis is in the directioncontaining most variation. Every subsequent new variable isorthogonal to previous variables, but again in the directioncontaining most of the remaining variation.

PLS

Most of the linear regression methods estimate a set of coefficientsusing only the information contained in the dataset (X matrix) topredict the information contained in responses (y vector), that is,the decomposition of the X is made fully independent of the y. Inthe PLSmethod, the information in y is inserted into the estimationprocedure of the coefficients that are now called latent variables

wileyonlinelibrary.com/journal/xrs Copyright © 2012 J

(LVs).[19] The criterion for the acquisition of LVs is to maximize thecovariance between X and y. PLS is recommended when thenumber of variables is greater than the number of samples andwhen there is multicollinearity in the X matrix.

SVM

The SVM algorithm is based on the statistical learning theory andon the Vapnik–Chervonenkis dimension introduced by VladimirVapnik and Alexey Chervonenkis.[20] In this method, the data ismapped into a higher dimensional input space, and an optimalseparating hyperplane is constructed in this space. This basicallyinvolves solving a quadratic programming problem, whereasgradient-based training methods for neural network arc-hitectures, on the other hand, suffer from the existence of manylocal minima.[21–23] Kernel functions and parameters are chosensuch that a bound on the Vapnik–Chervonenkis dimension isminimized.

Ageing test

The PA-11 samples containing 10% to 12% of n-butyl-benzene-sulfonamide plasticizer used for the construction of flexible pipe-lines were provided by PETROBRAS S.A./CENPES. The sampleswere cut to 13.0� 34.5� 5.5mm3 in size, set in stainless steelbrackets, and submerged in the ageing fluid inside a 2-L reactorwith a removable lid. To prevent accidents caused by the liquidexpansion, 75% of the total volume was used.[5] Ageing testswere performed in deionized water (pH 7). In addition, oxygenwas removed from the system by bubbling argon (quality99.999%) for 2 h in the reactor before the ageing experimentsto prevent the overlay between oxidative and thermal degrada-tion processes. The tests were performed at two differenttemperatures, 110 and 120 �C, during a total immersion time of50 days.[5] After, thermal properties [thermogravimetry and differ-ential thermal analysis (TG/DTA), DSC, and DMA] and multiele-mental analyses (ED-XRF) were used in PA-11 characterizationaccording to the ageing time: 0, 3, 5, 7, 13, 16, 19, 21, 25, 30,35, 42, and 50 days (for 110 �C); and 0, 3, 5, 7, 9, 13, 16, 19, 22,25, 30, 35, 42, and 50 days (for 120 �C).

Characterization

CIV and TG/DTA

Measurements of IV were performed according to ISO-307 (1994)for PA-11 using m-cresol as solvent from semiautomatic viscom-eter model D15KP-LAUDA at 20 �C. Values of IV for each solutionwere calculated according to Eqn (1) where to, t, and c are theflow time for m-cresol, the flow time of the solution (in seconds),and the concentration (g dL�1), respectively.[5]

IV ¼In�tt0

� �c

(1)

The IV of the PA-11 solution is affected by the presence ofn-butyl-benzenesulfonamide plasticizer. Hence, it was necessaryto quantify the presence of low molar mass substances in thesample, calculating thus, the IV corrected (CIV). The content ofadditives was determined by TG/DTA in a Shimadzu thermalanalysis apparatus, operating from 25 to 800 �C, with a heatingrate of 10 �Cmin�1 under a nitrogen atmosphere. The CIV was

ohn Wiley & Sons, Ltd. X-Ray Spectrom. 2013, 42, 79–86

Monitoring the PA-11 degradation by thermal properties and XRF

calculated with the corrected weight of polymer according toEqn (2), where the content of additives is expressed in weightpercent.[5]

CIV ¼ IV � 100

100� additives

� �(2)

DSC and DMA

The DSC experiments were performed according to ASTM D3417-99 in a thermogravimetric analysis calorimeter, modelMDSCQ200. The heating and cooling rate was 10 �Cmin�1. Inthe first heating scan, the samples were heated from ambienttemperature to 220 �C. The crystallization process was recordedfrom 220 to 120 �C, and the values of the enthalpy of crystalliza-tion (ΔHc) and crystallization temperature (Tc) were calculated.The second heating was performed from 120 to 220 �C; the melt-ing temperature (Tm) and enthalpy of fusion (ΔHm) werecalculated.

Dynamic mechanical analyses were performed on a DMA 8000model (PerkinElmer) at 1 and 10Hz. The heating temperatureranged from �40 to 100 �C, and heating rate of 2 �Cmin�1 undernitrogen atmosphere (sample area and thickness were about44mm2 and 1–2mm, respectively). Storage modulus (E0) andmechanical loss factor (tan d) values were reported for the twofrequencies used. Therefore, the glass transition temperature,Tg, was estimated from these values.

ED-XRF and chemometric analysis

The ED-XRF experiments were performed using an X-ray spec-trometer from ShimadzuW, EDX 700 model (Kyoto, Japan). Themeasurements were performed under air, with a beam collima-tion of 3mm, 25% of detector dead time, with the current auto-matically adjusted during spectrum acquisition to keep thedetector dead time of 25%. The Shimadzu EDX 700 also presentsthe following characteristics: (1) an Rh X-ray generator, with tubevoltage ranging from 5 to 50 kV, and tube current from 1 to1000mA, (2) a semiconductor detector, Si(Li), with detection areaof 10mm2 and resolution of <155 eV.[12,13]

Table 1. Thermal data for virgin and aged polyamide 11 at 110 �C, calculaanalysis curves and corrected inherent viscosity (CIV) measurements (dL g�

Ageing time (days) CIV (dLg�1) Tg (�C)* Tm,on (�C) Tm1 (�C

0 1.79 12 170 183

3 1.62 21 172 182

5 1.55 31 174 184

7 1.45 42 176 185

13 1.42 45 177 187

16 1.35 42 177 189

19 1.31 43 178 188

21 1.25 45 178 188

25 1.21 44 178 189

30 1.21 45 178 189

35 1.21 45 179 189

42 1.19 44 178 191

50 1.19 45 179 189

* Tg estimated from maximum point of tan d curve at 1Hz.

X-Ray Spectrom. 2013, 42, 79–86 Copyright © 2012 John W

For spectral acquisition, PA-11 samples (dimensions of13.0� 34.5� 5.5mm3) were placed into XRF cells, and the mea-surement time was 300 s. In all the cases, the spectra wererecorded from 0 to 40 keV, with an energy step of 0.02 keV, result-ing in 2048 points for each spectrum. After the acquisition, XRFspectral data were mean-centered. Then, to classify the samplesaccording to the amount of plasticizer and CIV values in PA-11,PCA was applied to the XRF data using the software Pirouettev.3.11 (Infometrix, Woodinville, WA, USA). The entire spectra wereused in PCA analysis (0 to 40 keV), resulting in 2048 points(variables) and 26 samples. Then, PLS and SVM models wereconstructed to predict the ageing time and CIV values in PA-11.The computer program Matlab version R2007b and PLS Toolboxversion 6.2, from Eigenvector Research, were used to build thePLS and SVM models.

Results

The glass transition temperature (Tg), storage modulus (E0), andmechanical loss factor (tan d) were obtained from DMA curve.Maximum (Tm, and Tc) and onset (Tm,on and Tc,on) of meltingand crystallization temperatures, melting enthalpy (ΔHm), andcrystallization enthalpy (ΔHc) were obtained from the DSC curve.All the results are shown together with the intrinsic CIV in Tables 1and 2 for virgin and aged PA-11 at 110 and 120 �C as function ofageing time, respectively.

The variation of the CIV regarding ageing time in deionizedwater at 110 and 120 �C changes exponential over time until aplateau is reached, where there is an equilibrium process. The ini-tial rate of decreasing in viscosity is faster at higher temperatures.After a certain time, the viscosity essentially has reached a con-stant value indicating that the degradation reaction has reachedthe equilibrium process.[5] Viscosity plateau values for curves at120 �C (Table 2) are lower than those observed in 110 �C (Table 1),suggesting that the PA-11 degradation process is more severe athigher temperatures.[5] Therefore, if the pH remains constant, thetemperature controls the initial rate of decrease and the plateauof viscosity, simultaneously.

Tm,on, Tm, Tc,on, Tc, ΔHm, and ΔHc values were obtained fromthe typical DSC curves (Fig. 2) and are shown in Tables 1 and 2,

ted from the differential scanning calorimetry and dynamic mechanical1)

) Tm2 (�C) Tc,on (�C) Tc (�C) ΔHm (J g�1) ΔHc (J g�1)

// 158 153 33 29

178 161 159 33 28

180 162 160 35 30

181 164 160 39 32

182 165 162 39 33

183 166 162 39 34

182 166 162 40 33

183 166 163 44 34

183 166 164 47 36

183 166 164 48 37

183 166 164 48 37

183 165 163 45 35

183 166 163 45 36

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Table 2. Thermal data for virgin and aged polyamide 11 at 120 �C, calculated from the differential scanning calorimetry and dynamic mechanicalanalysis curves and corrected inherent viscosity measurements (dL g�1)

Ageing time (days) CIV (dL g�1) Tg (�C)* Tm,on (�C) Tm1 (�C) Tm2 (�C) Tc,on (�C) Tc (�C) ΔHm (J g�1) ΔHc (J g�1)

0 1.79 12 170 183 // 158 153 33 29

3 1.53 31 171 183 177 160 158 35 31

5 1.45 37 172 183 177 160 158 34 30

7 1.35 37 175 185 179 163 160 37 33

9 1.24 45 175 185 179 162 160 37 33

13 1.19 45 176 187 181 164 161 39 36

16 1.18 46 178 188 182 165 162 38 34

19 1.12 47 178 189 183 165 162 38 33

22 1.09 46 178 188 182 166 163 41 37

25 1.11 45 182 189 183 166 164 44 38

30 1.07 46 179 189 183 166 163 39 34

35 1.05 47 179 189 183 166 163 42 37

42 1.06 43 183 189 183 167 164 43 36

50 1.06 50 183 190 183 167 164 44 38

* Tg estimated from maximum point of tan d curve at 1Hz.

Figure 2. (a) Differential scanning calorimetry cooling and (b) seconddifferential scanning calorimetry heating scans for virgin and aged poly-amide 11 (7 and 50 days) in deionized water, pH 7 at 110 �C.

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respectively. The first cooling of PA-11 is displayed in Fig. 2(a),where low Tc,on and Tc values for virgin PA-11, 158 and 153 �C, re-spectively, are observed. A broad increase in Tc,on and Tc togetherwith a narrow crystallization peak was observed for the agedPA-11 samples for 7 and 50 days at 110 �C, respectively. Theseshifts are mainly due to the increase in the amount of low molarmass compounds (oligomers) that give a higher mobility in theaged PA-11 chains.[5] Oligomers are formed mainly from amor-phous phase, migrating to crystalline phase. The changing in Tcand crystallization rate is assigned to the decrease in CIV valuescaused by chain scission reactions in the hydrolytic degradationprocess.[24,25] In Fig. 2(b) (second melting of PA-11), the curvefor the sample aged for 7 days shows a shoulder indicating asecond melting temperature (Tm2). This bimodal behavior (Tm1+Tm2)suggests the presence of oligomers, where a higher ageing timecontributes to define this shoulder, shifting both (Tm1 and Tm2) tohigher temperatures.[26] This behavior is due to different sizedcrystallite formations that are dispersed and homogenized in thesecond heating crystallization rate of PA-11. Consequently, theΔHm and ΔHc values are also affected.

The effect of hydrolytic degradation process on the amorphousphase is shown in the temperature dependences of the E0 and ofthe tan d, at two different frequencies, 1 and 10Hz, respectively,Fig. 3. The step of curve from �40 to 100 �C of E0 and the corre-spond tan d peak indicate a relaxation or first-order relaxation thatis connected with the Tg.

[26] Maximum tan d values for virgin PA-11are observed from12 to 20 �C for the two frequencies studied, Fig. 3(a). These values increase with the ageing time, Fig. 3(b), where amaximum value is reached at 42–50 �C for PA-11 aged during50days at 110 �C, Fig. 3(b). The shift in Tg is directly dependenton the decrease of additive amount in the polymeric matrix ofvirgin PA-11 during the hydrolytic degradation process.[5]

The values of PA-11 thermal properties (Tg, Tc, Tc,on, Tm1, andTm,on) as function of time at 110 and 120 �C, shown in Tables 1and 2, are better visualized and explained when plotting thethermal properties changes versus time at 110 and 120 �C, Fig. 4(a) and (b). In all cases, an exponential increase of thermal prop-erties values is observed until a plateau is reached. The influenceof temperature under the initial rate of curve is better observed


Figure 3. Storage modulus and mechanical loss factor against tempera-ture at frequencies of 1 and 10Hz for (a) virgin polyamide 11 and (b) agedpolyamide 11 in deionized water, pH 7, during 50 days at 110 �C.

Figure 5. Energy-dispersive X-ray fluorescence spectrometry spectrumof virgin polyamide 11.


for Tg [Fig. 4(a)] Tc, and Tc,on [Fig. 4(b)] curves. For Tm1 and Tm,on

curves, these values are similar. However, the dependence of tem-perature under the plateau affects uniquely the Tg curve, Fig. 4(a).

Generally, the clear effect of temperature under the PA-11physical–chemical properties in hydrolytic degradation process isbetter observed for viscosity (Tables 1 and 2), and for Tg, Fig. 4(a).These properties are affected because of the molar mass reductionand, consequently, formation of low molar mass compounds(oligomers) during hydrolytic degradation process; and loss ofadditives and, therefore, elasticity changes in morphology.

Figure 4. Thermal properties changes [(a) Tg, and (b) Tm1, Tm,on, Tc,on, and(white symbol) and 120 �C (black symbol).


Figure 5 shows an example of ED-XRF spectrum of a virginPA-11 sample, where the presence of Ka characteristic lines forS (2.28 keV), Rh (2.68 keV), Fe (6.36 keV), Cu (8.02 keV), and Zn(8.60 keV) are observed, being the S-Ka line because of the pres-ence of S element in the structure of n-butyl-benzenesulfonamideplasticizer. The region of high intensity lines is related to theCompton [Ka (19.20 keV) and Kb (21.56 keV) lines] and Rayleigh[Ka (20.16 keV) and Kb (22.74 keV) lines] effects. The Compton(incoherent scatter) and Rayleigh (coherent scatter) effects contrib-ute significantly to quantitative organic ED-XRF analysis. Thescattering region from the X-ray spectrum is mainly associated withlight elements (C, H, O, among others) from the matrix, andthe characteristic lines for these elements are not visualized onED-XRF spectra; however, this region can present powerful proper-ties for qualitative or even quantitative determination of lightelements when treated by chemometrics.[11–13]

Figure 6(a) and (b) shows the combined ED-XRF spectra forthe ten and 14 PA-11 samples according to the ageing time indeionized water, pH 7, at 110 �C [Fig. 6(a)] and 120 �C [Fig. 6(b)],respectively. An S line expansion in the 2–3 keV region of theED-XRF spectra [inserts shown in Fig. 6(a) and (b)] shows theabundance of the S line to be directly related to the ageing timeof PA-11. This comportment is related to an additive amount

Tc] against ageing time for polyamide 11 in deionized water, at 110 �C


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Figure 6. Energy-dispersive X-ray fluorescence spectrometry spectra of polyamide 11 in different ageing time in deionized water, pH 7 at (a) 110 �Cand (b) 120 �C.

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decrease from virgin PA-11 to aged PA-11 as reported by Romãoet al.[5] Using TG/DTA analysis, the authors showed a decreasein the additive percentage (wt.%) from 12 to 3.5wt.% when thePA-11 is aged in deionized water for 9 days at 110 �C.The curves obtained by the loss of additives in the polymer

matrix as a function of time are shown in Fig. 7(a) and (b) at ]110 �C [Fig. 7(a)] and 120 �C [Fig. 7(b)]. This changing ismonitored from TG/DTA (in wt.% of additives, dark circle) andED-XRF (intensity S Ka lines, white circle) measurements, simulta-neously. Both techniques show good agreement in the initial lossof additives, but over time, it is faster at higher temperatures,Fig. 7(a) and (b). This rapid loss of additives in aqueous media isdue mainly to an increase in solubility of the low molar masscompounds as a function of temperature. Therefore, ED-XRFalso seems efficient as an analytical methodology to additivesquantification in polymeric materials.[11,12,27,28]

Energy-dispersive X-ray fluorescence spectrometry data weresubjected to chemometric treatment via PCA, Fig. 8(a) and (b). Itwas used to statistically evaluate the performance of ED-XRFspectra in classifying PA-11 samples for quality control purposes.Figure 8(a) and (b) shows PC1 � PC2 scores and loading plots,where the two first PCs account for ~87.8% of total variance. InPC1 � PC2 scores plot, in general, a separation into five groups(A–E) is observed, Fig. 8(a). The A, B, and C groups present higherCIV values (>1.20 dLg�1) than the D and E groups (<1.20 dLg�1).

Figure 7. Intensity of S Ka lines (○) and percentage of additive (●) against110 �C and (b) 120 �C.


Figure 8(b) shows PC1� PC2 loading plot, where most informationis located in the S Ka lines (2.2–2.4 keV) and in the Rh scatteringregion (17–20 keV). Both are responsible for indicating somechanging in the PA-11 structure such as amount of additive andMw, respectively. The variations of CIV values and amount of addi-tive decreases over time in the respective order: A>B>C>D> E.

After the classification of several PA-11 samples, chemometricmethods were used to predict the ageing time and CIV values.For this objective, PLS and SVM models were constructed forPA-11 samples and then compared.

To quantify the ageing time and CIV values in PA-11 samples, 16samples were used for calibration resulting in an Xcalibration matrix(16� 2048) and a ycalibration vector (16� 1), whereas eight sampleswere employed for validation resulting in an Xvalidation matrix(8� 2048) and a yvalidation vector (8� 1). Several preprocessingtechniques and their combinations were tested. The best resultswere obtained from autoscaling. For the separation of samples inthese groups, the Kennard–Stone algorithm was used.[29]

Figure 9 shows the predicted values according to PLS [Fig. 9(A)and (B)] and SVM [Fig. 9(C) and (D)] models against the measuredvalues. In all the graphs, validation samples are represented bywhite circles, whereas calibration samples are indicated by blackcircles. The distribution pattern in most of the data points is verynear to the 45-degree solid line, demonstrating a good agree-ment between the predicted and measured values.

ageing time (days) for aged polyamide 11 in deionized water, pH 7, at (a)


Figure 8. (a) PC1 � PC2 scores and (b) loading plots for all energy-dispersive X-ray fluorescence spectrometry data: (○) virgin and aged polyamide 11in deionized water at (○) 110 �C and (●) 120 �C.

Figure 9. Calibration curves obtained by the partial least squares (A–B) and support vector machines (C–D) models for corrected inherent viscosityvalues (dL g�1) and ageing time (days) where the validation samples are represented by white circles and calibration samples by black circles.


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Quantification models evaluation

Some statistical parameters were calculated to compare PLS andSVMmodels (Table 3), namely root mean square error of calibration(RMSEC), root mean square error of cross-validation (RMSECV),root mean square error of validation (RMSEP), Pearson’s correla-tion coefficient between the real and predicted concentrationsduring the validation (rVal), and Pearson’s correlation coefficientbetween real and predicted concentrations (calibration) (rCal).For the PLS model, the number of LVs was chosen by leave-one-out cross-validation, in which all calibration samples werevalidated one by one. The number of LVs chosen for each modelwas based on the lowest RMSECV values obtained. To constructthe SVM model, it is very important to select a proper Kernelfunction and determine its optimal parameters for the construc-tion of the best SVM model, that is, the model that has a lowerRMSECV value. In this work, we optimized the parametersepsilon (2), cost (C), and gamma (g) as reported.[30]

As shown in Table 3, the RMSEC and RMSEP values for the PLSand SVM models presented in Fig. 9 were lower than 0.08 g/dLand 12.9 days for CIV values and ageing time, respectively.Additionally, these values were quite similar for both models


(PLS and SVM), which makes both of them suitable for quantifica-tion of CIV values and ageing time.

Finally, an F-test[31] was performed with 95% confidence level(p= 0.05), considering the null hypothesis that there is no signif-icant difference in errors for the determination of CIV valuesand ageing time in PA-11 given by the two models (PLS andSVM). For the F-test, the following expression was used:

F ¼ RMSEPið Þ2RMSEPj� �2 (3)

where RMSEP is the root mean square error of prediction(validation), and the subscripts i and j represent the models thathave the largest and lowest RMSEP values, respectively. Thedegree of freedom in the F-test was 7 for both models. The F-testresults were 1.01 and 1.05 for CIV values and ageing time,respectively. Both calculated F-values were lower than 3.79,which is the critical F-value (with confidence level of 95%). Theseresults confirmed again the equivalence between both models(PLS and SVM).


Table 3. Performance comparison results between partial leastsquares (PLS) and support vector machines (SVM) calibration models

VIC values Ageing time

PLS SVM PLS SVM

RMSEC a 0.0104 0.0019 0.9826 0.1312

RMSECV b 0.0953 0.0972 10.1337 8.5126

RMSEP c 0.0779 0.0789 12.8022 12.2322

rVald 0.9711 0.8833 0.8792 0.9679

rCale 0.9985 0.9999 0.9970 0.9999

LVs f 3 — 3 —

C g— 100 — 10

2 h— 0.01 — 0.01

g i— 0.001 — 0.0001

aRoot mean square error of calibration in g/dL for VIC values and indays for ageing time;

bRoot mean square error of cross-validated prediction in g/dL for VIC

values and in days for ageing time;cRoot mean square error of validation in g/dL for VIC values and in

days for ageing time;dPearson’s correlation coefficient between real and predicted

concentrations (validation);ePearson’s correlation coefficient between real and predicted

concentrations (calibration);fNumber of latent variables;gCost;hEpsilon;iGamma.

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Conclusion

Differential scanning calorimetry results show that the crystalliza-tion rate, maximum (Tm and Tc) and onset (Tm,on and Tc,on) ofmelting, and crystallization temperatures were affected whenPA-11 was subjected to hydrolytic degradation process. For Tm,a bimodal behavior, and consequently, increase in meltingenthalpy, is observed, suggesting the presence of compoundswith lower Mw in the polymeric matrix. They are formed fromrandom chain scission reactions where a higher ageing timecontributes to define this observed shoulder. Similarly, the Tc wasalso affected; a narrowing and a shift to higher temperatures wereobserved. Consequently, melting and crystallization enthalpyvalues were also influenced.The effect of hydrolytic degradation process on the amorphous

phase showed that the glass transition temperature, Tg, increasesexponential until a plateau is reached. The temperature controlsthe initial rate and the plateau of Tg curve. This behavior is directlydependent on the additive amount decrease in the polymericmatrix during the hydrolytic degradation process.Energy-dispersive X-ray fluorescence spectrometry data provide

relatively simple, fast, and suitable tools in polymeric materialsinvestigations. The X-ray spectrum mainly showed the presenceof S and scattering regions in PA-11 polymeric matrix that aremainly associated to n-butyl-benzenesulfonamide plasticizer andlight elements (C, H, and O). Therefore, the content of additive inPA-11 can be monitored from XRF measurements. Additionally,when the XRF data are allied to PCA, it is possible to classifyPA-11 samples according to the additive amount and weightaverage molar mass changing, thus predicting from PLS and SVMmodels, the ageing time and viscosity values of PA-11.


Acknowledgements

This research has also been generously funded by PETROBRAS/CENPES, CNPq, CAPES, and FINEP.

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