On-line prediction of crystallinity spatial distribution across polymer films using NIR spectral imaging and chemometrics methods.
The global moulded plastics market was estimated to exceed 156 million tons in 2005, a large portion of which was taken up by common semi-crystalline polymers. Of this total, the consumption of low-density polyethylene (LDPE), high-density polyethylene (HDPE) and polypropylene (PP) reached 18, 29, and 40 million tons, respectively (Murphy, 2003). These materials are very sensitive to the conditions in which they are produced, especially geometry, pressure and cooling rates are known to influence their degree of crystallinity, which in turn strongly affects their mechanical, optical and barrier properties (Rastogi et al., 1991; Apichartpattanasiri et al., 2001; Albano et al., 2003; Pantani et al., 2005; Shepherd et al., 2006; Dusunceli and Colak, in press). Controlling the amount of crystallinity is thus essential when working with semi-crystalline polymers (Albano et al., 2003). However, theoretically establishing a relationship between the processing conditions and the final microstructure of a polymer is complex and time consuming (Pantani et al., 2005). On-line quality control of plastic film, either cast or blown, is typically limited to shape and clarity monitoring as well as detecting other irregularities like impurities, holes and scratches. While efficiently detecting macroscopic defects, these methods are ineffective at identifying smaller characteristics such as crystallinity variations, leading to film yields typically falling between 90% and 95% (Osborn and Jenkins, 1992). Rapid and non-intrusive tools for on-line crystallinity measurement would help improve quality control of thin polymer products.
Several methods are currently used to determine polymer crystallinity, but most of these measurements are performed off-line, are destructive, and provide single point measurements. They often rely on small sample size and require significant handling time. The most common off-line method is differential scanning calorimetry (DSC), which relies on the heat associated with melting of small samples, typically less than 20 mg. DSC has been widely used in polymer analysis (Batur et al., 1999; Saeki et al., 2003; Sato et al., 2003; Albano et al., 2003; Watanabe et al., 2006; Pelsoci, 2007). Numerous microscopy methods also exist. Of these, atomic force microscopy (AFM), scanning electron microscopy (SEM) and optical microscopy have all been used in micro-structural characterization of polymers (Kantz et al., 1972; Butler et al., 1995; Pantani et al., 2005). These methods have a slow acquisition time and may require surfacing and/or vacuum conditions. Nuclear magnetic resonance (NMR) spectroscopy has also been used to obtain physical, chemical and structural information about polymer phases (Bergmann, 1981; Pelsoci, 2007). Application of this method is typically expensive, time consuming and destructive (Vailaya et al., 2001; Saeki et al., 2003). X-ray scattering methods are a family of non-destructive methods based on the scattered intensity of a beam hitting a sample and providing information about the average structure and composition (Brown et al., 1973; Polizzi et al., 1991; Albano et al., 2003; Pantani et al., 2005; Pelsoci, 2007; Briskman, 2007). As these methods depend on the incident and scattering angles, as well as the polarization and wavelengths of the beams, they are not easily adapted to 2D surface scans.
Various vibrational spectroscopic techniques, such as near-infrared (NIR), have also been proposed for estimating polymer crystallinity since they are rapid and non-intrusive, they require little or no sample preparation, and provide a wealth of information (Lachenal, 1995). However, most of the methods published in the past are based on single point measurements (i.e., using probes), and separate calibration models were typically built for each type of polymer to be monitored. Estimating crystallinity over a larger area using these approaches require either moving the sample or the probe, which is difficult to perform on a high-speed production line or using probe arrays, which generally results in coarse spatial coverage of the surface. However, fine spatial measurements are key in identifying local crystallinity gradients that may compromise the material overall quality. The mechanical, optical and barrier properties of an entire sample may fall below specifications because of local weaknesses that may be overlooked by a coarser spatial analysis. Furthermore, rich spatial data would also be useful for precise diagnostic of operational problems in the production line, such as non-uniform cooling of the polymer products.
Nevertheless, NIR spectroscopy has been used to analyze the extent of crystallization (Lachenal, 1995; Stuart, 1996; Sato et al., 2003; Pantani et al., 2005; Pelsoci, 2007), orientation (Buffeteau et al., 1995), and density (Saeki et al., 2003; Watanabe et al., 2006) of semi-crystalline polymers. Since these spectroscopic techniques are based on surface reflectance or absorbance, they are usually applied to films or thin samples (less than 2 mm) for which surface crystallinity is known to be representative across sample thickness (Pantani et al., 2005). While different methods have been reported, FTIR transmission spectroscopy remains the standard technique when studying polymer crystallinity when applied to microtome slices (Pantani et al., 2005), blown films (Buffeteau et al., 1995) or thicker samples (0.5-2 mm) (Lachenal, 1995). Infrared reflection spectroscopy has also been used to study polymer crystallinity; Sato et al. (2003) collected the diffuse reflectance spectra of plastic pellets placed on a rotating cell and used the average spectra for predicting pellet crystallinity. Work has also been reported on real-time crystallinity estimation by single-point laser Raman spectroscopy (Batur et al., 1999; Cherukupalli and Ogale, 2004).
The objective of this work is to develop a non-intrusive online sensor for monitoring spatio-temporal crystallinity variations across the surface of thin polymer materials. While single point NIR vibrational spectroscopy has proven useful in the study of polymer crystallinity, this work focuses on combining NIR imaging spectroscopy and multivariate image analysis and regression (MIA and MIR) methods to efficiently obtain the crystallinity spatial distribution of a sample. The proposed methodology is illustrated using thin polyolefin samples produced via compression moulding under different cooling conditions. Non-isothermal cooling rates throughout the cooling circuit ensure local crystallinity variations within a single sample. A total of four different methods are compared in this study: PLS regression between the full averaged NIR spectra or second order spectra derivatives, and crystallinity measurements (methods 1 and 2), and MIA applied to the NIR spectra or second order spectra derivatives followed by regression (methods 3 and 4). The results obtained for three polymers (HDPE, LDPE, and PP) are incorporated into a single model, rather than building a model for each, in order to highlight their ability to cope with complex datasets as may be encountered with polymer blends or composites. Local crystallinity estimates may be used in process monitoring, fault detection and diagnosis (i.e., identification of non-uniform cooling rates) or for predicting both the local and overall polymer properties (i.e., mechanical, optical, orientation, etc.) of thin samples (<2 mm) for automatic process and quality control applications. As with any surface analysis, it may also be used with caution on thicker samples.
Materials and Processes
The polymers used in this study were commercial polypropylene (PP) (Pro-fax PF-814, [rho]=0.902 g/[cm.sup.3]; MFI = 3.0 g/10 min) supplied by Basell (Wilmington, DE), high-density polyethylene (HDPE) (HDPE 3000, [rho] = 0.965 g/[cm.sup.3]; MFI = 8.8 g/10 min) supplied by Petromont (Varennes, QC) and low-density polyethylene (LDPE) (Novapol LA-0219-A, [rho] = 0.919 g/[cm.sup.3]; MFI = 2.3 g/10 min) supplied by Nova Chemicals (Calgary, AB).
A compression press was used to mould the polymers into thin films (100 mm x 40 mm x 1.5 mm). The batch process consists of moulding 6 g of resin at 180[degrees]C under 3 tons of pressure for 10 min, long enough to remove any previous thermal history (Chew et al., 1989; Albano et al., 2003). The mould was then water-cooled to release the sample. A total of 18 samples were produced, 6 for each polymer using average cooling rates of 1, 2, 4, 5, 8, and 16[degrees]C/min. These changes in cooling rates produced samples of different overall crystallinity. Moreover, the water-cooling circuit introduced within-sample variability in each film. In other words, while each sample is characterized by its own average crystallinity, it also presents crystallinity patterns, or mosaics, across its surface (i.e., crystallinity is a distributed property).
Differential Scanning Calorimetry (DSC)
DSC is a thermo-analytical technique measuring heat flow into a material as a function of temperature. The degree of crystallinity ([phi]) of a semi-crystalline polymer can be determined from the endothermic heat flow due to melting ([DELTA][H.sub.m]), the exothermic heat flow due to crystallization ([DELTA][H.sub.c]) and the heat of fusion of the 100% crystalline phase ([DELTA][H.sub.[infinity]]):
[FIGURE 1 OMITTED]
[phi] = [DELTA][H.sub.m] - [DELTA][H.sub.c]/[DELTA][H.sub.[infinity]] (1)
DSC thermograms were obtained using temperature ramps from 30 to 200[degrees]C at a rate of 10[degrees]C/min under a nitrogen atmosphere. The weight of the samples was approximately 7.5 mg and the tests were performed on a Perkin Elmer DSC 6. The fusion peaks were found to be located at 110[degrees]C (LDPE), 138[degrees]C (HDPE), and 160[degrees]C (PP) and range respectively between 60 and 125[degrees]C, 90-155[degrees]C, and 100-180[degrees]C. The heats of fusion ([DELTA][H.sub.[infinity]]) of the crystalline phases were found to be 290 J/g (LDPE), 293 J/g (HDPE), or 207 J/g (PP).
The line scan NIR imaging system used in this work is composed of a XenICs XEVA-USB-FPA camera (256 x 320 pixels) coupled with a Specim ImSpector N17E grating spectroscope (slit: 30 [micro]m x 14.3 mm) sensing between 900 and 1700 nm. Each scanned line on the sample is captured by the CCD array as a spatial/spectral image (Figure 1) consisting of 256 x 320 pixels, providing a 0.5 mm/pixel spatial resolution and 2 nm/pixel spectral resolution. A hyperspectral image ([R.bar]) of the entire sample is achieved by repeatedly moving the sample perpendicularly to the spectroscope slit (along the y-axis). Each hyperspectral image consists of 500 juxtaposed line scans, at 0.25 mm intervals.
Diffuse light from a tungsten-halogen lamp was used as the light source. The raw signals of each spectral-spatial image ([R.bar]) were transformed into reflectance units according to Equation (2) using a flat black image ([B.bar]) and a true white image ([W.bar]). The flat black and true white images were obtained by collecting a spatial-spectral image leaving the lens cap in place (i.e., dark current), and by imaging a 99% reflectance standard sheet (Gigahertz-Optik, Newburyport, ME), respectively
[i.sub.xy[lambda]] = [r.sub.xy[lambda]] - [b.sub.x[lambda]]/[w.sub.x[lambda]] - [b.sub.x[lambda]] (2)
In Equation (2), [r.sub.xy[lambda]] is an element of the raw signal image, [b.sub.x[lambda]] and [w.sub.x[lambda]] are elements of the black and white calibration images, and [i.sub.xy[lambda]] is an element of the standardized reflectance image ([I.bar]). This simple calibration scheme was used since it successfully removed all the linear discrepancies encountered in the NIR images collected in this work. All images were captured using a single imaging system, under controlled lighting conditions, and over a short period of time. More advanced calibration techniques should be considered for long-term, industrial applications (Geladi et al., 2004; Burger and Geladi, 2005; Liu et al., 2007). Data acquisition was performed using a LabView 8.0 interface (National Instruments (Austin, TX)) and data analysis was performed using custom scripts developed within the Matlab R14 (MathWorks (Natick, MA)) environment.
Predicting the polymer crystallinity spatial distribution requires building a regression model (i.e., correlations) between features contained within NIR spectral images of the samples (X) and analytical crystallinity measurements (y) obtained using DSC. A total of four different methods were tested and compared in this work, differing mainly in the way NIR spectra are processed before applying appropriate regression techniques. Conventional NIR calibration methods involving averaged spectra (method 1) or second order derivatives (method 2) and PLS regression were first tested, followed by a multivariate image regression (MIR) approach involving either the raw spectra (method 3) or its second order derivatives (method 4).
Collection of a Training Data Set
Initially, each of the 18 samples was fully scanned and the raw image was calibrated into a reflectance image [[I.bar].sub.k] according to Equation (2), where k is the sample number (k = 1, 2, ..., 18). A training data set was obtained by selecting a smaller region of interest (2.5 mm x 5 mm or 10 x 10 pixels) for each polymer sample as shown in Figure 2. These regions correspond to a multivariate sub-image [I.sub.k] of size (10 x 10 x [lambda]), where [lambda] is the number of spectral channels ([lambda] = 256 in this work). These arrays were then unfolded into matrices [[??].sub.k] of size (100 x [lambda]) by simply storing each spectrum row-wise. The [[??].sub.k] matrices are the common input of all four methods described in this section.
Finally, each region of interest corresponding to the [[??].sub.k] subimages were cut off the samples and sent for DSC analysis. The resulting crystallinity measurements ([y.sub.k]) were stored in a response matrix y (18 x 1).
PLS Models Based on Average Spectra or Second Order Derivatives
Method 1: averaged NIR spectra
The first method simply consists of averaging all available reflectance spectra obtained from the region of interest of a sample (i.e., column-wise averaging of each [[??].sub.k] matrix) and collecting the averaged spectra of each sample in a matrix of regressors X (18 x [lambda]), as shown in Figure 2. A latent variable PLS regression model was then built between the averaged spectra matrix X and the corresponding crystallinity measurements y as:
[FIGURE 2 OMITTED]
X = [A.summation over (a=1)] [t.sub.a][p.sup.T.sub.a] + E = T [P.sup.T] + E
y = [A.summation over (a=1)] [t.sub.a][q.sup.T.sub.a] + F = T [Q.sup.T] + F
T = XW (3)
where the P and Q matrices contain the loading vectors that best represent the X and y spaces, respectively, whereas W contain the loading vectors defining the common latent variable space T relating X to y. The E and F matrices contain the PLS model residuals (i.e., projection distance from the latent variable space of the model). The number of PLS components or latent variables (A) was selected using a standard leave-one-out cross-validation procedure (Wold, 1978). PLS was selected in this case since the columns of X are highly collinear.
Method 2: second order derivative of the NIR spectra
Method 2 uses the second order derivative of the spectra [[??].sub.k] rather than the spectra themselves. The spectra derivatives were also averaged over the region of interest and then collected in a regressor matrix X (18 x ([lambda] - 2)) for each sample before building a PLS regression model with y (Figure 2). Taking second order derivatives is a commonly used pre-treatment applied to NIR spectra (Chan et al., 1990). This offers a distinct advantage when sharp absorption bands are present in the spectrum (Whitbeck, 1981). It is preferred over the 1st derivative because it does not shift the peaks, allowing better interpretability. While the second order derivative emphasizes spectral transitions, it remains insensitive to systematic shifts in spectra intensity. This can be seen in Figure 3 with the three spectral bands emphasized in the original spectrum (centred on 1100, 1300, and 1600 nm). Numerical approximation of the second order derivative were used (Gerald and Wheatley, 1994) after smoothing of the line scans in the spectral direction using a window of 5 pixels in order to reduce the effect of bad pixels (Savitzky and Golay, 1964). Numerical differentiation leads to the loss of two columns (i.e., spectral channels) in matrix X compared to using the spectra directly.
[FIGURE 3 OMITTED]
Multivariate Image Regression Applied to Spectra or Second Order Derivatives
Multivariate Image Regression (MIR) consists of a family of latent variable techniques used for regressing quality or response variables onto features extracted from a set of digital images. Image regression problems can be formulated in several ways, depending on the nature of the features extracted from the images, ranging from simple statistics computed for each spectral channel (i.e., mean, variance, etc.) to distribution features. The reader is referred to Esbensen et al. (1992) and Yu and MacGregor (2003) for more details on MIR problem formulation and methods. In this work, distribution features were extracted from NIR spectral images. These were obtained through a decomposition of spectral image data cubes (i.e., reflectance spectra - method 3, or second order derivatives--method 4, see Figure 2) using Multi-Way Principal Component Analysis (MPCA), which is the first step of a method known as Multivariate Image Analysis (MIA) (Geladi and Grahn, 1996).
[FIGURE 4 OMITTED]
Multivariate image analysis (MIA)
Originally introduced by Esbensen and Geladi (1989), it has been widely used in fields ranging from flame analysis (Yu and MacGregor, 2004; Szatvanyi et al., 2006) to flotation froth (Liu et al., 2005), snack food (Yu and MacGregor, 2003; Yu et al., 2003) as well as softwood lumber grading (Bharati et al., 2003). A complete overview of MIA can be found in Geladi and Grahn (1996). MIA relies on the basis that local intensity variations can be extracted by classifying each image pixel according to its spectral characteristics regardless of its spatial location within the image. In combination with regression techniques, MIA can be used to extract the relevant features from digital images that are the most highly correlated with corresponding response variables, such a sample quality measurements.
The unfolded spectra matrices [[??].sub.k] corresponding to the regions of interest selected for each polymer sample were first collected together in a single matrix [??] of size (1800 x [lambda]) (18 samples x 100 spectrum/sample). Principal Component Analysis was then used to decompose the image information into a set of A orthogonal loadings vectors [p.sub.a] (1 x [lambda]) and score vectors [t.sub.a] (1800 x 1) as shown in Equation (4) and in Figure 4:
[??] = [A.summation over (a=1)] [t.sub.a] x [p.sup.T.sub.a] + E (4)
where E (1800 x [lambda]) contains the projection residuals (non zero when A < [lambda]). The loadings vectors ([p.sub.a]) are usually obtained using singular value decomposition (SVD) of kernel matrix [[??].sup.T][??] (Geladi and Grahn, 1996) of much smaller dimensions (i.e., 256 x 256). The score vectors are computed from [t.sub.a] = [??] [p.sub.a]. The first score vector [t.sub.1], is the linear combination of the 256 spectral channels (defined by the loadings vectors [p.sub.1]) capturing the largest possible variance within the spectral matrix [??], while the second score vector [t.sub.2] represents the second largest source of variance, and so on. The score vectors can therefore be viewed as a multivariate summary of each spectrum.
A small number of components (A) are often found sufficient in practice to extract most of the relevant information within multivariate image data. The few score vectors can therefore be used as representative distribution features of the multivariate image. These are typically displayed using scatter plots of score vectors as shown in Figure 4 ([t.sub.1]-[t.sub.2] score plot is illustrated) or as 2-D density histograms (Geladi and Grahn, 1996; Yu and MacGregor, 2003; Szatvanyi et al., 2006).
Multivariate image regression (MIR)
Formulating a regression problem between such score scatter plot (or 2-D density histograms) and response variables was investigated by Yu and MacGregor (2003). It involves extracting a certain number of features (n) from the score plots (or histograms) obtained from each of the K images, collecting them in a regressor matrix X (K x n), and building a regression model with the response variable of interest (i.e., crystallinity) y (K x 1), as shown in Figure 2.
The formulation used specifically for relating NIR spectral images to polymer crystallinity measurements is based on observing the clustering pattern of the NIR spectra of the three polymer types shown in Figure 5A. This [t.sub.1]-[t.sub.2] scatter plot was obtained by PCA decomposition of the spectral matrix I (1800 x 256). The first two score vectors explained respectively 95.8% and 3.2% of the variance of [??] when using method 3, and 77.7% and 11.1% when using method 4. The spectra corresponding to each of the three polymers appear as very distinct clusters as expected; NIR spectroscopy is often used for polymer identification. Furthermore, the spectral data corresponding to each polymer type also cluster according to cooling rates with a clear spatial orientation (Figure 5A, HDPE cluster zoom-in). To capture the crystallinity-relevant information a new vector [t.sub.12] was computed by projecting the spectral data shown in Figure 5A onto a linear combination of the first two score vectors (Figure 5B). A simple linear regression model was then built between [t.sub.12] and y using ordinary least squares:
[t.sub.12] = r[t.sub.1] + (1 - r)[t.sub.2] y = [[beta].sub.0] + [[beta].sub.1][t.sub.12] + [epsilon] (5)
The linear combination (r) or, alternatively, the angle of the [t.sub.12] vector was selected to maximize the correlation between [t.sub.12] and y. A similar approach was discussed in Yu and MacGregor (2003) for score density histogram segmentation as one of the possible formulation of MIR problems.
RESULTS AND DISCUSSION
Model Building Using the Training Data Set
Summary statistics for the PLS models built on the training set are shown in Table 1 for methods 1 and 2. The number of PLS components (A) of each model were selected by a standard leave-one-out cross-validation procedure using the SIMCA-P + V10 software (Umetrics, Inc., Kinnelon, NJ). Three cumulative multiple correlation coefficients were computed for quantifying the model predictive ability: [R.sup.2.sub.X,cum] is the cumulative percentage of the total variance in X used to explain y, [R.sup.2.sub.X,cum] gives the cumulative percentage of the total variance of y explained by the model, and [Q.sup.2.sub.cum] is the cumulative percentage of the total variance of y that can be predicted by the models using the cross-validation procedure. A total of 2 components for each model were selected through cross-validation. Model 2 based on second order derivatives seems to provide a better fit of the data compared to using the averaged spectra (i.e., method 1).
[FIGURE 5 OMITTED]
The results obtained for methods 3 and 4 are presented in Table 2 and Figure 6. The linear combination of the first two score vectors obtained using MIA ([t.sub.12]) was selected to maximize the predictive ability (i.e., [Q.sup.2.sub.cum]) of the models as shown in Figure 6. A r-ratio of 0.8 provides the best results for method 3 ([R.sup.2.sub.cum] = 0.991 and [Q.sup.2.sub.cum] = 0.923). For method 4, a r-ratio of 0.1 was found to provide the best MIR model using second order derivatives ([R.sup.2.sub.y,cum] = 0.861 and [Q.sup.2.sub.cum] = 0.252). The lower predictive power ([Q.sup.2.sub.cum]) of this model may be explained by the fact that a low r-ratio implies that crystallinity is hardly related to the first score ([t.sub.1]) and much more to the second ([t.sub.2]). Since [t.sub.1], represents the largest source of variation in the data (77.7%), it appears that the bulk of the information contained in the second order derivatives hardly correlate to crystallinity. Additional score vectors (i.e., [t.sub.3], [t.sub.4], and [t.sub.5]) were investigated for model 4, but these were found to be uncorrelated to crystallinity.
[FIGURE 6 OMITTED]
Fitting quality of the four methods is compared in Figure 7. This figure shows the experimentally measured crystallinity by DSC compared to model predictions obtained by cross-validation. The original reflectance spectrum (method 1) provides the largest errors (root mean square error of estimation RMSEE = 9.31) while the second order derivatives (method 2) provides much better results (RMSEE = 3.88). The MIR methods applied to the reflectance spectra (method 3) and to the second order derivatives (method 4) provided RMSEE values of 1.78 and 6.83, respectively. It is therefore clear that performing MIA on the image data in order to extract the relevant features does improve predictive ability when applied to the spectra directly, but is detrimental when using second order derivatives.
Generally speaking, this may be explained by the degree of correlation between the image data (spectrum or second derivative) and the quality parameter to be predicted (crystallinity). In method 3, crystallinity is mainly correlated with [t.sub.1], which represents 95.8% of the variance of I whereas in method 4, it is essentially correlated with [t.sub.2] which explains only 11.1% of the variance of [??]. In other words, method 3 relies on nearly all the spectral data while method 4 only relies on a small fraction since most of the spectral data contained in the second derivatives is irrelevant to the prediction of polymer crystallinity. This characteristic of the second derivative may explain the relative inability of methods 2 and 4 to explain fine surface variations. This will be further discussed and illustrated in the next section.
[FIGURE 7 OMITTED]
Model Validation and Crystallinity Spatial Distributions
Previous discussions (See Model Building Using the Training Data Set Section) were centred on the predictive capabilities of the four methods on the training data set. In the present section they will be used to predict the remaining areas of the samples that were not used to construct the models. As previously mentioned, the cooling system design is known to produce localized gradients in the cooling rates resulting in crystallinity patterns across the surface of the samples. These methods should extract such patterns.
Using the four models developed on the training set, one can predict crystallinity for any point on the surface of any sample (i.e., for every pixel or groups of pixels of spectral images [[I.bar].sub.k]). One sample of each polymer type was selected for this purpose. Figure 8 shows the predicted crystallinity distribution for one such sample (HDPE: 4[degrees]C/min). To validate these predictions four regions of interest dispersed across the samples were removed, analyzed using DSC in triplicate, and compared to the predicted values. The location of these regions is also shown in Figure 8.
As illustrated in Figure 8, the predicted crystallinity differs greatly according to the method used. The prediction made by method 1 seems to show an area of slightly lower crystallinity in the lower right section of the sample. Method 2 predicts a vertical gradient while method 4 predicts a homogeneous surface. Method 3 predicts a complex pattern in which the right hand side is significantly less crystalline. Comparing these predictions to measured crystallinity values (see DSC measurements on top of Figure 8), it can be seen that method 1 slightly overestimates crystallinity, and that both models based on second order derivatives (methods 2 and 4) predict an average value across the sample. Only method 3 based on MIR of the reflectance spectra provides a reasonable map of crystallinity distribution.
[FIGURE 8 OMITTED]
[FIGURE 9 OMITTED]
Together, Table 3 and Figure 9 illustrate all the results for the three tested samples (one for each polymer type) including the predicted crystallinity and the absolute mean prediction error. DSC standard deviations are based on triplicate tests. Model predictions were averaged over the region sent for DSC analyses (equivalent surface area of 20 x 20 pixels since more material was necessary for triplicates). These results show that the averaged experimental error associated with DSC measurements is 0.7%, independently of the polymer tested. Method 3 provided the lowest mean prediction errors (0.8%), falling practically within the DSC experimental error (i.e., method 3 yields a statistically adequate model). Finally, method 3 and 4 (MIR models) provide more consistent prediction errors for all polymer species since the angle (i.e., linear combination r) of vector t1Z was selected to maximize correlation with crystallinity, irrespectively of polymer type. This may be useful for analyzing more complex materials such as polymer blends or composites.
Since prediction results for both methods 2 and 3 on the training set (i.e., see Figure 7) containing all three polymer species are quite similar, although method 3 has a slightly better fit (i.e., less scatter around the parity line), it may seem surprising that both methods predict such a different crystallinity distribution across the surface of a particular polymer type as shown in Figure 8. This may be explained by recognizing that the variance of the crystallinity vector (y) has two main sources: (1) each polymer type has a different mean crystallinity, and (2) changes introduced by the cooling rate (i.e., scattering around the mean crystallinity of each polymer type). The y-variance explained by methods 2 and 3 is different. Indeed, by enhancing spectral transitions (i.e., peaks in the spectra), the method based on second order derivatives (method 2) seems better at predicting the mean crystallinity of each polymer specie or, alternatively, at identifying polymer type, than predicting more subtle variations in crystallinity due to changes in cooling rates, what is interesting from a process operation perspective. To confirm this, crystallinity measurements within the training set (y) were recalculated in deviation from the mean crystallinity values of each polymer type: 63.8% (HDPE), 35.9% (PP), and 24.7% (LDPE). Removing the mean crystallinity of each polymer type should enhance crystallinity variations caused by changes in the cooling rates. Prediction results shown in Figure 10 were obtained after building new regression models for methods 2 and 3 using the new centred crystallinity vector ([y.sup.c]). In accordance with previous results, method 3 explains a greater amount of the local crystallinity variations ([R.sup.2.sub.y,cum] = 0.757) compared to method 2 ([R.sup.2.sub.y,cum] = 0.542). This confirms the higher predictive power of the MIR model based on the original reflectance spectrum. Note that this method could also be used for polymer type identification by segmenting vector [t.sub.12] according to the mean crystallinity of each polymer type.
Finally, Figure 11 illustrates the predictions obtained for the LDPE and PP samples (both cooled at a rate of 4[degrees]C/min) using methods 2 and 3. The general patterns and conclusions concur with those previously discussed with the HDPE sample. The second derivatives efficiently predict the average crystallinity of the sample but remain insensitive to local variations. On the other hand, method 3 adequately predicts both local and global variations in crystallinity.
[FIGURE 10 OMITTED]
[FIGURE 11 OMITTED]
The objective of this work was to develop a rapid and non-intrusive on-line NIR imaging sensor for monitoring spatio-temporal variations in crystallinity across the surface of thin polymer materials. Although NIR spectroscopy has already been investigated in the past for estimating polymer crystallinity, most methods were based on probes, hence providing measurements for a single point (or line) on a sample. Since most of the overall end-user properties of thin polymer materials, such as mechanical, optical and barrier properties, depend upon the local microstructure (i.e., weakest point on the sample), fine spatial measurements are the key in identifying local crystallinity gradients that may compromise overall material quality. Furthermore, rich spatial data would also be useful for precise diagnostic of operational problems in the production line, such as non-uniform cooling.
Thin samples of LDPE, HDPE, and PP were produced via compression moulding and cooled at six different rates in order to introduce a wide range of crystallinity levels. Each sample was then imaged using an NIR spectroscope and a certain number of regions of interest were selected for each sample, cut-off, and sent for analytical measurement of crystallinity using DSC. Four methods were tested and compared for extracting features from the NIR images that are correlated to polymer crystallinity obtained by DSC: (1) a conventional NIR calibration methods involving averaged spectra and PLS regression with crystallinity; this approach was used by Sato et al. (2003) for estimating crystallinity of polymer pellets, (2) a similar approach but using second order spectra derivatives for calibration against crystallinity (i.e., a standard pre-treatment used in spectroscopy for peak enhancement), (3) an MIA/MIR approach using either the raw reflectance spectra, or (4) its second order derivatives.
The results show that the models obtained using methods 2 and 3 provide the best fit of crystallinity measurements when predicting over a wide range of crystallinity, such as the one obtained using the three polymer species (LDPE, HDPE, and PP). However, only method 3 based on MIA/MIR analysis of the original NIR spectra was successful at predicting the more subtle variations in crystallinity introduced by changes in cooling rates, with prediction errors falling practically within DSC experimental errors. It was also shown that this method provides predictions of crystallinity spatial distribution that are consistent with processing conditions, and partially validated using additional DSC measurements. Finally, such predictive power was also consistently high for all three polymer species using a single model. This feature of the proposed approach shows an interesting potential for application to more complex materials such as polymer blends or composites.
Financial support from the National Science and Engineering Research Council of Canada (NSERC) is acknowledged.
Manuscript received February 28, 2008; revised manuscript received June 16, 2008; accepted for publication June 17, 2008.
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Ryan Gosselin, Denis Rodrigue and Carl Duchesne *
Department of Chemical Engineering, Universite Laval, Quebec City, Canada G1K 7P4
* Author to whom correspondence may be addressed. E-mail address: email@example.com
Table 1. Summary statistics of the predictive ability of methods 1 and 2 Method A [R.sup.2.sub.X,cum] (%) [R.sup.2.sub.y,cum] (%) 1 1 0.907 0.640 2 0.967 0.756 2 1 0.631 0.512 2 0.764 0.957 A [Q.sup.2.sub.cum] (%) 1 0.605 2 0.681 1 0.472 2 0.932 Table 2. Model parameters and predictive ability of methods 3 and 4 Method r [[??].sub.0] [[??].sub.1] 3 0.8 -64.41 0.90 4 0.1 -8.13 0.40 Method [R.sup.2.sub.y,cum] (%) [Q.sup.2.sub.cum] (%) cum (%) 3 0.991 0.923 4 0.861 0.252 Table 3. Experimental (DSC) and model prediction errors for all three polymer species HDPE PP LDPE Mean DSC 0.6 0.7 0.7 0.7 Method 1 2.6 1.8 1.2 1.8 Method 2 1.7 1.0 0.9 1.1 Method 3 0.8 0.9 0.7 0.8 Method 4 1.5 1.3 1.6 1.5 Experimental errors are reported as one standard deviation. Prediction errors are reported in absolute values (i.e., % crystallinity).
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|Author:||Gosselin, Ryan; Rodrigue, Denis; Duchesne, Carl|
|Publication:||Canadian Journal of Chemical Engineering|
|Date:||Oct 1, 2008|
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