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Discrimination of polymers by laser induced breakdown spectroscopy together with the DFA method
Polymer Testing 31 (2012) 759–764
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Polymer Testing journal homepage: www.elsevier.com/locate/polytest
Analysis method
Discrimination of polymers by laser induced breakdown spectroscopy together with the DFA method M. Banaee, S.H. Tavassoli* Laser and Plasma Research Institute, Shahid Beheshti University, G. C., Evin, Tehran 1983963113, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 11 March 2012 Accepted 25 April 2012
Laser Induced Breakdown Spectroscopy (LIBS) is used to analyze and identify six kinds of the most important recyclable polymers i.e high density polyethylene (HDPE), low density polyethylene (LDPE), polyethylene terephthalate (PET), polypropylene (PP), polystyrene (PS) and polyvinyl chloride (PVC). Using a Nd:YAG laser with wavelength 1064, a plasma is created on the polymer surface. By analysis of spectral emission of plasma, some qualitative information about the plasma elements is obtained. The plasma spectra of polymers are similar and contain strong carbon and hydrogen spectral lines. Here, a statistical method called discriminant function analysis (DFA) is used to discriminate between the polymers by slight differences between the spectra. DFA establishes a model on the basis of input variables to predict group memberships of polymers. The spectral line ratios of C, CN, C2, N Cl, O and H are used as input variables in DFA. Results show that LIBS together with DFA has the ability to correctly classify 99% of the polymers. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: LIBS Laser-induced breakdown spectroscopy DFA Discriminant function analysis Polymers Plastics
1. Introduction Polymers and mixtures of them are used in manufacture and production of a large quantity of materials. A great number of packaging materials for consumer goods such as food and cosmetics and also bottles and boxes are made from polymers. The worst consequence of industrial development and material production to fulfill the needs of a growing world population is the deterioration of the environment due to pollution of air, soil and water. In recent years, salient growth is observed in the use of plastics in almost every aspect of modern life. Recovery of polymers (plastics) instead of dumping or incinerating them is one solution of this problem. Identification and classification of plastics are the first stages in recycling of plastic waste. Hence, we need suitable equipment for fast identification of plastics. The manual methods of separation and sorting based on physical and superficial
* Corresponding author. E-mail address: [email protected] (S.H. Tavassoli). 0142-9418/$ – see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.polymertesting.2012.04.010
differences of the polymers are costly and still don’t ensure high accuracy. Several techniques have been investigated for the fast recognition of plastic waste. Matsumoto et al. reported using near infrared (NIR) spectroscopy with an identification accuracy of 77% [1]. NIR reflectance spectroscopy was applied by Feldhoff et al. [2] and they achieved an overall performance of 97% accuracy in identification. Raman spectroscopy has also been evaluated for plastics discrimination by Allen et al. [3]. They reported improved results in comparison with NIR spectroscopy. Other techniques such as x-ray absorption spectroscopy, x-ray fluorescence spectroscopy, near-IR reflectance spectroscopy, sliding spark spectroscopy and thermo optical techniques have been investigated for plastics identification, and a review of them has been published by Bledzki and Kardasz [4]. Because of the superior potential for on-line, real-time analysis of recycled materials, which is really necessary for rapid separation of plastics, Laser Induced Breakdown Spectroscopy (LIBS) is one of the most common techniques that has been previously evaluated for plastics identification by Sattmann et al. [5]. Advantages of LIBS includes
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sample preparation is not compulsory, a small piece of the sample is sufficient, the state of the sample is not of importance and it is nearly non-destructive. LIBS has been used for compound identification together with different statistical methods such as: artificial neural networks (ANN) [5–8], statistical correlation methods including linear (parametric) and rank (nonparametric) correlations [9–16], ratio determination of a few emission lines and bands [17–21], method of normalized coordinates (MNC) [22,23], principal component analysis (PCA) [24–27], partial least squares (PLS) [28] and soft independent modeling of class analogy (SIMCA) [29]. Several multivariate techniques in LIBS have been studied by research groups. Principal component analysis (PCA) and cluster analysis (CA) were used by Amador-Hernández et al. [30]. Recently, Anzano et al. [31] applied PCA for identification and comparison of plastics with LIBS. PCA has also been applied together with LIBS in Refs. [24,32,33]. Partial leastsquares (PLS) regression was used to predict the composition of alloys used in jewellery manufacture [12]. PLS also was designed for quantitative characterization of a gold filled interface [34] and for characterization of jewellery products [35]. In Ref. [36] it is indicated that PLS can improve the quantitative analytical ability of LIBS for soil sample analysis compared with the univariate techniques. Laville et al. utilized a 2nd order polynomial multivariate inverse regression model to reduce the influence of the matrix effects in LIBS for solidified mineral melt samples [37]. Martin et al. [38] used PLS and PCA together with LIBS to identify preservative types and to predict elemental content in preservative-treated wood. In Ref. [39], partial least squares discriminant analysis (PLS-DA) was investigated for detection of explosives. In Ref. [40], PCA and PLS are proposed to resolve and extract useful information from the LIBS spectral data collected on biological materials. In this work, we apply a statistical method, discriminant function analysis (DFA), that has not previously been used for identification of recyclable polymers together with LIBS. It is a mathematically powerful multivariate statistical method. High accuracy, high speed, low cost and simplicity
are the reasons why we used this method; which have been explained more below.
2. Theoretical background DFA is a multivariate statistical technique that serves to establish a model to predict group memberships. The primary goal of DFA is to find the dimensions or directions along which the groups are best separated, and then to find discriminant functions to predict group membership. In reality, discriminant functions are based on a linear combination of predictive variables that provide the best discrimination between groups:
Z ¼ a1 x1 þa2 x2 þ. þ an xn þ c; where Z is what is known as a dependent variable (grouping variable), the x’s are independent variables (predictor variables), the a’s are discriminant coefficients and c is a constant. Each predictor variable in a discriminant function has a weight (a’s) indicating its contribution to distinguishing the groups on that dimension. These functions are derived from a sample whose group memberships are known. The number of possible dimensions (i.e., discriminant functions) is either one fewer than the number of groups or equal to the number of predictor variables, whichever is smaller. (So there is only one discriminant function for a discriminant analysis with only two groups.) For each function, DFA finds the set of weights that maximizes the ratio of the variance between groups (i.e., in the groups’ means of all of the independent variables) to the variance within groups (i.e., among the members of the same group). An optimal combination of variables is computed so that the first function provides the most overall discrimination between groups. The second function again maximizes the differences between groups, but this time controlling for the first factor, and so on. Moreover, the functions are independent (orthogonal), meaning that their contributions to the discrimination between groups do not overlap.
Fig. 1. Experimental set-up.
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Fig. 2. A typical LIBS spectrum of HDPE.
Discriminant function analysis is broken into a 2-step process: (1) an F test (Wilks’ Lambda) is used to determine whether the discriminant model (discriminant function) as a whole is significant, Lambda varies from 0 to 1, with 0 meaning group means differ (thus the more the variable differentiates the groups), and 1 meaning all group means are the same, and (2) if the F test is significant, then the independent variables are assessed to see which differ in mean by group, and these are used to classify the dependent variable. More details regarding DFA computational formula can be found in Refs. [41–49].
3. Experimental 3.1. Instrumental setup The LIBS set-up used in this work is shown in Fig. 1. We carried out the experiment with a Q-switched Nd:YAG laser (pulse energy 30 mJ at 1064 nm) operating at a pulse repetition rate of 10 Hz. The laser pulses were focused on the sample vertically by a convergent lens with focal length of 8 cm. The samples were fixed to a holder that had been erected on a motorized stage and was controlled with a computer. Its velocity and acceleration was adjusted (2 mm/s, 2 mm/s2) every time a new location of the sample was being irradiated. The light from the plasma spark was collected by a collimating lens which was placed at 45 with respect to the laser pulse and then is transferred to a spectrograph (spectral range from 200 to 900 nm) by an optical fiber cable. The spectrograph was coupled to an intensified charge coupled device (ICCD). The exposure time was 1 s, the pulse gate width was 20 ms and the MCP gain was fixed at 180. Pulse energy was 30 mJ which is suitable for small degree of ablation of samples. The highest signal to noise ratio was obtained at optimum delay time of 0.5 ms. In order to decrease the effects of shot to shot fluctuations, each spectrum was obtained by accumulation of 50 laser pulses. Background emission was subtracted from the spectral lines, and spectral line ratios were calculated. All
statistical calculations and computations were performed with SPSS 17.0 software. 3.2. Samples Six types of commercial plastics were used that have the highest application in industry and are also most recyclable. These polymers are polyethylene terephthalate (PET), high density polyethylene (HDPE), polyvinyl chloride (PVC), low density polyethylene (LDPE), polypropylene (PP) and polystyrene (PS) which are coded from 1 to 6, respectively. These plastic identification codes (PIC) appear inside a three-chasing arrow recycling symbol usually found at the base or at the side of plastic products, including food/ chemical packaging and containers. We obtained standard samples from Puya Polymer corporation (Iran, Tehran) and then cut them into 9 4 cm pieces in order to fasten them to the holder with clamps. All samples had flat surfaces and were oriented perpendicular to the laser beam. They were moved in horizontal lines by a motorized xyz stage at a constant velocity of 2 mm/s.
Fig. 3. Chlorine spectral line in PVC sample.
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Table 1 Variables that are useda,b in the analysis at each step. Step
Entered
Wilts’ Lambda Statistic
1 2 3 4 5 6 7 8 9 10
Cl(837.59)/C(247.85) C2(563.5)/C(247.85) H(656.28)/C(247.85) 0(777.4)/C(247.85) C,N(388.3)/C(247.85) N(746.8 þ 744.2 þ 742.4)/C(247.85) CN(421.6)/C(247.85) N(868.03)/C(247.85) N(746.8 þ 744.2 þ 742.4)/O(777.4) C2(512.9)/C(247.85)
.136 .017 .005 .001 .000 .000 .000 .000 .000 .000
df1
1 2 3 4 5 6 7 8 9 10
df2
5 5 5 5 5 5 5 5 5 5
df3
294.000 294.000 294.000 294.000 294.000 294.000 294.000 294.000 294.000 294.000
Exact F
Approximate F
Statistic
df1
df2
Sig.
374.815 384.960
5 10
294.000 586.000
.000 .000
Statistic
df1
df2
Sig.
313.895 349.573 314.625 270.497 227.534 198.830 178.423 157.280
15 20 25 30 35 40 45 50
806.485 966.088 1078.804 1158.000 1213.936 1253.798 1282.450 1303.164
.000 .000 .000 .000 .000 .000 .000 .000
At each step, the variable that minimizes the overall Wilks’ Lambda is entered. a Maximum significance of F to enter is .15. b Minimum significance of F to remove is .20.
4. Results and discussion 4.1. Selection of emission lines and bands for analysis A typical HDPE spectrum is shown in Fig. 2. As expected, carbon and hydrogen have strong spectral lines. Also, the molecular bands of C2 and CN are observed clearly. The other lines are related to N, O, Ca, Na, Mg. Other polymers have similar spectra but with slight differences. PVC contains chlorine and so the spectral line of Cl at 837.59 nm is observed only in the PVC spectrum (see Fig. 3). To select the least number of predictors that most reliably distinguish between the six polymeric groups, stepwise DFA was performed and Wilks’ l was calculated at each step to assess the improvement in the classification. At each step, the variable that minimizes the overall Wilks’ lambda is entered into the analysis. In Table 1, we see that ten steps were taken, with each one including another variable. This Table 1 reveals that all the predictors add some predictive power to the discriminant function as all are significant with p < 0.000. 4.2. Discriminant functions As mentioned above, the number of discriminant functions obtained by the DFA procedure is the minimum amount between (g1), where ‘g’ is the number of groups, and the number of predictors. In our study the number of groups and predictors were six and ten respectively. So, the number of discriminant functions obtained was five and all were significant (p < 0.000). The relative discriminating power of the discriminant functions is shown in Table 2. Table 2 First 5 canonical discriminant functions are used in the analysis. Function
Eigenvalue
% of variance
Cumulative %
Canonical correlation
1 2 3 4 5
19.089 12.661 7.273 1.488 .294
46.8 31.0 17.8 3.6 .7
46.8 77.8 95.6 99.3 100.0
.975 .963 .938 .773 .477
Although all functions were significant, we restricted our interpretation to the first three functions since they reflect the highest percentages of variance. As shown in Table 2, accumulation of the first three variance is 95.6%. Moreover the large amounts of the canonical correlation of the first three functions show a high correlation between the discriminant scores and group numbers (a canonical correlation of 1.0 indicates that all of the variability in the discriminant scores can be accounted by that dimension). Hence, the first discriminant function is the most important in explanatory power, the second is the next most important, and so on. Table 3 provides an index of the importance of each predictor for each dimension represented by the function. We used this Table 3 to assess the importance of each independent variable’s unique contribution to the discriminant functions. The sign indicates the direction of the relationship. According to Table 3, CN(388.3)/C(247.85), H(656.28)/C(247.85) and Cl(837.59)/C(247.85) scores were the strongest predictors in the first function (dimension), H(656.28)/C(247.85) and N(746.8 þ 744.2 þ 742.4)/ C(247.85) were the strongest predictors in the second function and CN(388.3)/C(247.85) was the strongest in the third function, while N(868.03)/C(247.85) and C2(512.9)/ C(247.85) scores were the weakest predictors in each of the first three functions. In general, it seems that the H(656.28)/ C(247.85) ratio is the strongest factor in separation of these polymers, as we had expected. Table 3 Standardized canonical discriminant function coefficients. Function
H(656.28)/C(247.85) Cl(837.59)/C(247.85) CN(388.3)/C(247.85) CN(421.6)/C(247.85) N(868.03)/C(247.85) N(746.8 þ 744.2 þ 742.4)/C(247.85) N(746.8 þ 744.2 þ 742.4)/O(777.4) C2(563.5)/C(247.85) C2(512.9)/C(247.85) O(777.4)/C(247.85)
1
2
3
4
5
1.050 1.029 1.092 .158 .111 .755
1.210 .892 .169 .516 .111 1.157
.049 .236 .947 .396 .182 .634
.234 .290 .644 .440 .522 .887
.248 .071 .512 1.284 .691 .456
.338
.544
.104
.488
.253
.268 .185 .255
.075 .055 .016
.825 .207 .693
.399 .063 1.350
.916 .039 .327
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Table 4 Classification results.b,c ID
Original
Count
%
Cross-validateda
Count
%
PET HDPE PVC LDPE PP PS PET HDPE PVC LDPE PP PS PET HDPE PVC LDPE PP PS PET HDPE PVC LDPE PP PS
Predicted group membership PET
HDPE
PVC
LDPE
PP
PS
Total
50 0 0 0 0 0 100.0 .0 .0 .0 .0 .0 50 0 0 0 0 0 100.0 .0 .0 .0 .0 .0
0 50 0 0 2 0 .0 100.0 .0 .0 4.0 .0 0 50 0 0 2 0 .0 100.0 .0 .0 4.0 .0
0 0 50 0 0 0 .0 .0 100.0 .0 .0 .0 0 0 50 0 0 0 .0 .0 100.0 .0 .0 .0
0 0 0 50 0 0 .0 .0 .0 100.0 .0 .0 0 0 0 50 1 0 .0 .0 .0 100.0 2.0 .0
0 0 0 0 48 0 .0 .0 .0 .0 96.0 .0 0 0 0 0 47 0 .0 .0 .0 .0 94.0 .0
0 0 0 0 0 50 .0 .0 .0 .0 .0 100.0 0 0 0 0 0 50 .0 .0 .0 .0 .0 100.0
50 50 50 50 50 50 100.0 100.0 100.0 100.0 100.0 100.0 50 50 50 50 50 50 100.0 100.0 100.0 100.0 100.0 100.0
a Cross validation is done only for those cases in the analysis. In cross validation, each case is classified by the functions derived from all cases other than that case. b 99.3% of original grouped cases correctly classified. c 99.0% of cross-validated grouped cases correctly classified.
4.3. Classification of polymers The classification results based on DFA are presented in Table 4. It gives information about actual group membership versus predicted group membership. DFA revealed that 99.3% of the original grouped cases were successfully classified into their polymeric groups. In addition, we used a leave-one-out (also known as jackknife [50,51]) method to cross-validate the discrimination functions derived above. In other words, we obtained an estimated accuracy for prediction of group membership of an unknown recyclable polymer by this method. The leave-one-out method involves removing 1 observation (testing set) from the data
set and building a DFA model from the remaining data (training set) and then classifying that observation based on the DFA to test it. This procedure was repeated for all the observations, leaving out one observation at each time and, in the end, the ratio of misclassified cases to the whole of the observations gives us the actual prediction error rate and, subsequently, gives the prediction accuracy. In this work, overall correct classification ratio that was obtained using the leave-one-out method was 99.0%. For each case, three discriminant scores according to each of the three discriminant functions were calculated. These discriminant score values constitute a threedimensional DFA matrix for our cases. In reality, the three functions are corresponding to the three dimensions, and discriminant scores were used for plotting a scatter diagram in this three-dimensional space. Fig. 4 shows three-dimensional canonical discriminant function plot. Each group is depicted as one shape and the group centroids have been displayed with an astral shape. As we see in this figure, the PVC sample due to own chlorine spectral line has been separated completely from the other samples and the HDPE and LDPE samples that have the same monomers are very close to each other in the figure. 5. Conclusions
Fig. 4. Three-dimensional canonical discriminant function.
The LIBS technique together with discriminant function analysis was utilized for identification and classification of six groups of the most used polymers in manufacturing and packaging of materials. The most effective factors in discriminating the polymers are CN(388.3)/C(247.85), H(656.28)/C(247.85) and Cl(837.59)/C(247.85) intensity
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Analysis method
Discrimination of polymers by laser induced breakdown spectroscopy together with the DFA method M. Banaee, S.H. Tavassoli* Laser and Plasma Research Institute, Shahid Beheshti University, G. C., Evin, Tehran 1983963113, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 11 March 2012 Accepted 25 April 2012
Laser Induced Breakdown Spectroscopy (LIBS) is used to analyze and identify six kinds of the most important recyclable polymers i.e high density polyethylene (HDPE), low density polyethylene (LDPE), polyethylene terephthalate (PET), polypropylene (PP), polystyrene (PS) and polyvinyl chloride (PVC). Using a Nd:YAG laser with wavelength 1064, a plasma is created on the polymer surface. By analysis of spectral emission of plasma, some qualitative information about the plasma elements is obtained. The plasma spectra of polymers are similar and contain strong carbon and hydrogen spectral lines. Here, a statistical method called discriminant function analysis (DFA) is used to discriminate between the polymers by slight differences between the spectra. DFA establishes a model on the basis of input variables to predict group memberships of polymers. The spectral line ratios of C, CN, C2, N Cl, O and H are used as input variables in DFA. Results show that LIBS together with DFA has the ability to correctly classify 99% of the polymers. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: LIBS Laser-induced breakdown spectroscopy DFA Discriminant function analysis Polymers Plastics
1. Introduction Polymers and mixtures of them are used in manufacture and production of a large quantity of materials. A great number of packaging materials for consumer goods such as food and cosmetics and also bottles and boxes are made from polymers. The worst consequence of industrial development and material production to fulfill the needs of a growing world population is the deterioration of the environment due to pollution of air, soil and water. In recent years, salient growth is observed in the use of plastics in almost every aspect of modern life. Recovery of polymers (plastics) instead of dumping or incinerating them is one solution of this problem. Identification and classification of plastics are the first stages in recycling of plastic waste. Hence, we need suitable equipment for fast identification of plastics. The manual methods of separation and sorting based on physical and superficial
* Corresponding author. E-mail address: [email protected] (S.H. Tavassoli). 0142-9418/$ – see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.polymertesting.2012.04.010
differences of the polymers are costly and still don’t ensure high accuracy. Several techniques have been investigated for the fast recognition of plastic waste. Matsumoto et al. reported using near infrared (NIR) spectroscopy with an identification accuracy of 77% [1]. NIR reflectance spectroscopy was applied by Feldhoff et al. [2] and they achieved an overall performance of 97% accuracy in identification. Raman spectroscopy has also been evaluated for plastics discrimination by Allen et al. [3]. They reported improved results in comparison with NIR spectroscopy. Other techniques such as x-ray absorption spectroscopy, x-ray fluorescence spectroscopy, near-IR reflectance spectroscopy, sliding spark spectroscopy and thermo optical techniques have been investigated for plastics identification, and a review of them has been published by Bledzki and Kardasz [4]. Because of the superior potential for on-line, real-time analysis of recycled materials, which is really necessary for rapid separation of plastics, Laser Induced Breakdown Spectroscopy (LIBS) is one of the most common techniques that has been previously evaluated for plastics identification by Sattmann et al. [5]. Advantages of LIBS includes
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sample preparation is not compulsory, a small piece of the sample is sufficient, the state of the sample is not of importance and it is nearly non-destructive. LIBS has been used for compound identification together with different statistical methods such as: artificial neural networks (ANN) [5–8], statistical correlation methods including linear (parametric) and rank (nonparametric) correlations [9–16], ratio determination of a few emission lines and bands [17–21], method of normalized coordinates (MNC) [22,23], principal component analysis (PCA) [24–27], partial least squares (PLS) [28] and soft independent modeling of class analogy (SIMCA) [29]. Several multivariate techniques in LIBS have been studied by research groups. Principal component analysis (PCA) and cluster analysis (CA) were used by Amador-Hernández et al. [30]. Recently, Anzano et al. [31] applied PCA for identification and comparison of plastics with LIBS. PCA has also been applied together with LIBS in Refs. [24,32,33]. Partial leastsquares (PLS) regression was used to predict the composition of alloys used in jewellery manufacture [12]. PLS also was designed for quantitative characterization of a gold filled interface [34] and for characterization of jewellery products [35]. In Ref. [36] it is indicated that PLS can improve the quantitative analytical ability of LIBS for soil sample analysis compared with the univariate techniques. Laville et al. utilized a 2nd order polynomial multivariate inverse regression model to reduce the influence of the matrix effects in LIBS for solidified mineral melt samples [37]. Martin et al. [38] used PLS and PCA together with LIBS to identify preservative types and to predict elemental content in preservative-treated wood. In Ref. [39], partial least squares discriminant analysis (PLS-DA) was investigated for detection of explosives. In Ref. [40], PCA and PLS are proposed to resolve and extract useful information from the LIBS spectral data collected on biological materials. In this work, we apply a statistical method, discriminant function analysis (DFA), that has not previously been used for identification of recyclable polymers together with LIBS. It is a mathematically powerful multivariate statistical method. High accuracy, high speed, low cost and simplicity
are the reasons why we used this method; which have been explained more below.
2. Theoretical background DFA is a multivariate statistical technique that serves to establish a model to predict group memberships. The primary goal of DFA is to find the dimensions or directions along which the groups are best separated, and then to find discriminant functions to predict group membership. In reality, discriminant functions are based on a linear combination of predictive variables that provide the best discrimination between groups:
Z ¼ a1 x1 þa2 x2 þ. þ an xn þ c; where Z is what is known as a dependent variable (grouping variable), the x’s are independent variables (predictor variables), the a’s are discriminant coefficients and c is a constant. Each predictor variable in a discriminant function has a weight (a’s) indicating its contribution to distinguishing the groups on that dimension. These functions are derived from a sample whose group memberships are known. The number of possible dimensions (i.e., discriminant functions) is either one fewer than the number of groups or equal to the number of predictor variables, whichever is smaller. (So there is only one discriminant function for a discriminant analysis with only two groups.) For each function, DFA finds the set of weights that maximizes the ratio of the variance between groups (i.e., in the groups’ means of all of the independent variables) to the variance within groups (i.e., among the members of the same group). An optimal combination of variables is computed so that the first function provides the most overall discrimination between groups. The second function again maximizes the differences between groups, but this time controlling for the first factor, and so on. Moreover, the functions are independent (orthogonal), meaning that their contributions to the discrimination between groups do not overlap.
Fig. 1. Experimental set-up.
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Fig. 2. A typical LIBS spectrum of HDPE.
Discriminant function analysis is broken into a 2-step process: (1) an F test (Wilks’ Lambda) is used to determine whether the discriminant model (discriminant function) as a whole is significant, Lambda varies from 0 to 1, with 0 meaning group means differ (thus the more the variable differentiates the groups), and 1 meaning all group means are the same, and (2) if the F test is significant, then the independent variables are assessed to see which differ in mean by group, and these are used to classify the dependent variable. More details regarding DFA computational formula can be found in Refs. [41–49].
3. Experimental 3.1. Instrumental setup The LIBS set-up used in this work is shown in Fig. 1. We carried out the experiment with a Q-switched Nd:YAG laser (pulse energy 30 mJ at 1064 nm) operating at a pulse repetition rate of 10 Hz. The laser pulses were focused on the sample vertically by a convergent lens with focal length of 8 cm. The samples were fixed to a holder that had been erected on a motorized stage and was controlled with a computer. Its velocity and acceleration was adjusted (2 mm/s, 2 mm/s2) every time a new location of the sample was being irradiated. The light from the plasma spark was collected by a collimating lens which was placed at 45 with respect to the laser pulse and then is transferred to a spectrograph (spectral range from 200 to 900 nm) by an optical fiber cable. The spectrograph was coupled to an intensified charge coupled device (ICCD). The exposure time was 1 s, the pulse gate width was 20 ms and the MCP gain was fixed at 180. Pulse energy was 30 mJ which is suitable for small degree of ablation of samples. The highest signal to noise ratio was obtained at optimum delay time of 0.5 ms. In order to decrease the effects of shot to shot fluctuations, each spectrum was obtained by accumulation of 50 laser pulses. Background emission was subtracted from the spectral lines, and spectral line ratios were calculated. All
statistical calculations and computations were performed with SPSS 17.0 software. 3.2. Samples Six types of commercial plastics were used that have the highest application in industry and are also most recyclable. These polymers are polyethylene terephthalate (PET), high density polyethylene (HDPE), polyvinyl chloride (PVC), low density polyethylene (LDPE), polypropylene (PP) and polystyrene (PS) which are coded from 1 to 6, respectively. These plastic identification codes (PIC) appear inside a three-chasing arrow recycling symbol usually found at the base or at the side of plastic products, including food/ chemical packaging and containers. We obtained standard samples from Puya Polymer corporation (Iran, Tehran) and then cut them into 9 4 cm pieces in order to fasten them to the holder with clamps. All samples had flat surfaces and were oriented perpendicular to the laser beam. They were moved in horizontal lines by a motorized xyz stage at a constant velocity of 2 mm/s.
Fig. 3. Chlorine spectral line in PVC sample.
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Table 1 Variables that are useda,b in the analysis at each step. Step
Entered
Wilts’ Lambda Statistic
1 2 3 4 5 6 7 8 9 10
Cl(837.59)/C(247.85) C2(563.5)/C(247.85) H(656.28)/C(247.85) 0(777.4)/C(247.85) C,N(388.3)/C(247.85) N(746.8 þ 744.2 þ 742.4)/C(247.85) CN(421.6)/C(247.85) N(868.03)/C(247.85) N(746.8 þ 744.2 þ 742.4)/O(777.4) C2(512.9)/C(247.85)
.136 .017 .005 .001 .000 .000 .000 .000 .000 .000
df1
1 2 3 4 5 6 7 8 9 10
df2
5 5 5 5 5 5 5 5 5 5
df3
294.000 294.000 294.000 294.000 294.000 294.000 294.000 294.000 294.000 294.000
Exact F
Approximate F
Statistic
df1
df2
Sig.
374.815 384.960
5 10
294.000 586.000
.000 .000
Statistic
df1
df2
Sig.
313.895 349.573 314.625 270.497 227.534 198.830 178.423 157.280
15 20 25 30 35 40 45 50
806.485 966.088 1078.804 1158.000 1213.936 1253.798 1282.450 1303.164
.000 .000 .000 .000 .000 .000 .000 .000
At each step, the variable that minimizes the overall Wilks’ Lambda is entered. a Maximum significance of F to enter is .15. b Minimum significance of F to remove is .20.
4. Results and discussion 4.1. Selection of emission lines and bands for analysis A typical HDPE spectrum is shown in Fig. 2. As expected, carbon and hydrogen have strong spectral lines. Also, the molecular bands of C2 and CN are observed clearly. The other lines are related to N, O, Ca, Na, Mg. Other polymers have similar spectra but with slight differences. PVC contains chlorine and so the spectral line of Cl at 837.59 nm is observed only in the PVC spectrum (see Fig. 3). To select the least number of predictors that most reliably distinguish between the six polymeric groups, stepwise DFA was performed and Wilks’ l was calculated at each step to assess the improvement in the classification. At each step, the variable that minimizes the overall Wilks’ lambda is entered into the analysis. In Table 1, we see that ten steps were taken, with each one including another variable. This Table 1 reveals that all the predictors add some predictive power to the discriminant function as all are significant with p < 0.000. 4.2. Discriminant functions As mentioned above, the number of discriminant functions obtained by the DFA procedure is the minimum amount between (g1), where ‘g’ is the number of groups, and the number of predictors. In our study the number of groups and predictors were six and ten respectively. So, the number of discriminant functions obtained was five and all were significant (p < 0.000). The relative discriminating power of the discriminant functions is shown in Table 2. Table 2 First 5 canonical discriminant functions are used in the analysis. Function
Eigenvalue
% of variance
Cumulative %
Canonical correlation
1 2 3 4 5
19.089 12.661 7.273 1.488 .294
46.8 31.0 17.8 3.6 .7
46.8 77.8 95.6 99.3 100.0
.975 .963 .938 .773 .477
Although all functions were significant, we restricted our interpretation to the first three functions since they reflect the highest percentages of variance. As shown in Table 2, accumulation of the first three variance is 95.6%. Moreover the large amounts of the canonical correlation of the first three functions show a high correlation between the discriminant scores and group numbers (a canonical correlation of 1.0 indicates that all of the variability in the discriminant scores can be accounted by that dimension). Hence, the first discriminant function is the most important in explanatory power, the second is the next most important, and so on. Table 3 provides an index of the importance of each predictor for each dimension represented by the function. We used this Table 3 to assess the importance of each independent variable’s unique contribution to the discriminant functions. The sign indicates the direction of the relationship. According to Table 3, CN(388.3)/C(247.85), H(656.28)/C(247.85) and Cl(837.59)/C(247.85) scores were the strongest predictors in the first function (dimension), H(656.28)/C(247.85) and N(746.8 þ 744.2 þ 742.4)/ C(247.85) were the strongest predictors in the second function and CN(388.3)/C(247.85) was the strongest in the third function, while N(868.03)/C(247.85) and C2(512.9)/ C(247.85) scores were the weakest predictors in each of the first three functions. In general, it seems that the H(656.28)/ C(247.85) ratio is the strongest factor in separation of these polymers, as we had expected. Table 3 Standardized canonical discriminant function coefficients. Function
H(656.28)/C(247.85) Cl(837.59)/C(247.85) CN(388.3)/C(247.85) CN(421.6)/C(247.85) N(868.03)/C(247.85) N(746.8 þ 744.2 þ 742.4)/C(247.85) N(746.8 þ 744.2 þ 742.4)/O(777.4) C2(563.5)/C(247.85) C2(512.9)/C(247.85) O(777.4)/C(247.85)
1
2
3
4
5
1.050 1.029 1.092 .158 .111 .755
1.210 .892 .169 .516 .111 1.157
.049 .236 .947 .396 .182 .634
.234 .290 .644 .440 .522 .887
.248 .071 .512 1.284 .691 .456
.338
.544
.104
.488
.253
.268 .185 .255
.075 .055 .016
.825 .207 .693
.399 .063 1.350
.916 .039 .327
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Table 4 Classification results.b,c ID
Original
Count
%
Cross-validateda
Count
%
PET HDPE PVC LDPE PP PS PET HDPE PVC LDPE PP PS PET HDPE PVC LDPE PP PS PET HDPE PVC LDPE PP PS
Predicted group membership PET
HDPE
PVC
LDPE
PP
PS
Total
50 0 0 0 0 0 100.0 .0 .0 .0 .0 .0 50 0 0 0 0 0 100.0 .0 .0 .0 .0 .0
0 50 0 0 2 0 .0 100.0 .0 .0 4.0 .0 0 50 0 0 2 0 .0 100.0 .0 .0 4.0 .0
0 0 50 0 0 0 .0 .0 100.0 .0 .0 .0 0 0 50 0 0 0 .0 .0 100.0 .0 .0 .0
0 0 0 50 0 0 .0 .0 .0 100.0 .0 .0 0 0 0 50 1 0 .0 .0 .0 100.0 2.0 .0
0 0 0 0 48 0 .0 .0 .0 .0 96.0 .0 0 0 0 0 47 0 .0 .0 .0 .0 94.0 .0
0 0 0 0 0 50 .0 .0 .0 .0 .0 100.0 0 0 0 0 0 50 .0 .0 .0 .0 .0 100.0
50 50 50 50 50 50 100.0 100.0 100.0 100.0 100.0 100.0 50 50 50 50 50 50 100.0 100.0 100.0 100.0 100.0 100.0
a Cross validation is done only for those cases in the analysis. In cross validation, each case is classified by the functions derived from all cases other than that case. b 99.3% of original grouped cases correctly classified. c 99.0% of cross-validated grouped cases correctly classified.
4.3. Classification of polymers The classification results based on DFA are presented in Table 4. It gives information about actual group membership versus predicted group membership. DFA revealed that 99.3% of the original grouped cases were successfully classified into their polymeric groups. In addition, we used a leave-one-out (also known as jackknife [50,51]) method to cross-validate the discrimination functions derived above. In other words, we obtained an estimated accuracy for prediction of group membership of an unknown recyclable polymer by this method. The leave-one-out method involves removing 1 observation (testing set) from the data
set and building a DFA model from the remaining data (training set) and then classifying that observation based on the DFA to test it. This procedure was repeated for all the observations, leaving out one observation at each time and, in the end, the ratio of misclassified cases to the whole of the observations gives us the actual prediction error rate and, subsequently, gives the prediction accuracy. In this work, overall correct classification ratio that was obtained using the leave-one-out method was 99.0%. For each case, three discriminant scores according to each of the three discriminant functions were calculated. These discriminant score values constitute a threedimensional DFA matrix for our cases. In reality, the three functions are corresponding to the three dimensions, and discriminant scores were used for plotting a scatter diagram in this three-dimensional space. Fig. 4 shows three-dimensional canonical discriminant function plot. Each group is depicted as one shape and the group centroids have been displayed with an astral shape. As we see in this figure, the PVC sample due to own chlorine spectral line has been separated completely from the other samples and the HDPE and LDPE samples that have the same monomers are very close to each other in the figure. 5. Conclusions
Fig. 4. Three-dimensional canonical discriminant function.
The LIBS technique together with discriminant function analysis was utilized for identification and classification of six groups of the most used polymers in manufacturing and packaging of materials. The most effective factors in discriminating the polymers are CN(388.3)/C(247.85), H(656.28)/C(247.85) and Cl(837.59)/C(247.85) intensity
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