Simultaneous Determination of the Micro-, Meso-, and Macropore Size

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Anal. Chem. 2008, 80, 8493–8500

Simultaneous Determination of the Micro-, Meso-, and Macropore Size Fractions of Porous Polymers by a Combined Use of Fourier Transform Near-Infrared Diffuse Reflection Spectroscopy and Multivariate Techniques N. Heigl,† A. Greiderer,† C. H. Petter,† O. Kolomiets,‡ H. W. Siesler,‡ M. Ulbricht,§ G. K. Bonn,† and C. W. Huck*,† Institute of Analytical Chemistry and Radiochemistry, Leopold-Franzens University, Innrain 52a, 6020 Innsbruck, Austria, Institute of Physical Chemistry, University Duisburg sEssen, Schu¨tzenbahn 70, 45117 Essen, Germany, and Institute of Technical Chemistry, University Duisburg sEssen, Universita¨tsstrasse 5, 45141 Essen, Germany Fourier transform near-infrared (FT-NIR) diffuse reflection spectroscopy was used in combination with principal component analysis and partial least-squares regression to simultaneously determine the physical and the chemical parameters of a porous poly(p-methylstyrene-co-1,2bis(p-vinylphenyl)ethane) (MS/BVPE) monolithic polymer. Chemical variations during the synthesis of the polymer material can alter the pore volume and pore area distributions within the polymer scaffold. Furthermore, mid-infrared and near-infrared (NIR) spectroscopic chemical imaging was implemented as a tool to assess the uniformity of the samples. The presented study summarizes the comparative results derived from the spectral FT-NIR data combined with chemometric techniques. The relevance of the interrelation of physical and chemical parameters is highlighted whereas the amount of MS/ BVPE (%, v/v) and the quantity (%) of micropores (diameter, d < 6 nm), mesopores (6 nm < d < 50 nm), and macropores (50 nm < d < 200 nm) could be determined with one measurement. For comparison of the quantitative data, the standard error of prediction (SEP) was used. The SEP for determining the MS/BVPE amount in the samples showed 0.35%, for pore volume quantiles 1.42-8.44%, and for pore area quantiles 0.38-1.45%, respectively. The implication of these results is that FTNIR spectroscopy is a suitable technique for the screening of samples with varying physicochemical properties and to quantitatively determine the parameters simultaneously within a few seconds. Today near-infrared (NIR) diffuse reflection spectroscopy is a widely used and accepted technique for rapid and noninvasive analysis of solid samples. Especially the pharmaceutical industry * To whom correspondence should be addressed. Tel.: +43 512 507 5195. Fax: +43 512 507 2965. E-mail: [email protected]. † Leopold-Franzens University. ‡ Institute of Physical Chemistry, University Duisburg sEssen. § Institute of Technical Chemistry, University Duisburg sEssen. 10.1021/ac8013059 CCC: $40.75  2008 American Chemical Society Published on Web 10/11/2008

took advantage of conventional near-infrared spectroscopy (NIRS) and NIR chemical imaging to investigate the characteristics of the materials, mainly powders and tablets, such as for blend uniformity analysis, distribution of excipients and active ingredients, particle size measurements, and determination of the hardness and film coating of tablets.1-10 In-line measurements are frequently used to conduct kinetic studies in order to analyze chemical reactions or to monitor emerging physical properties, making particle or pore sizes visible.11,12 In the case of this study, a homemade polymer material, namely, poly(p-methylstyrene-co1,2-bis(p-vinylphenyl)ethane) (MS/BVPE),13 that is used as a stationary phase for micro-high-performance liquid chromatography (µ-HPLC), was investigated in respect to its chemical composition and pore size distributions. Many factors contribute to the materials properties, which can be separated into physical factors such as porosity, surface area, and particle size and

(1) Ciurczak, E. W.; Drennen, J. K. Pharmazeutical Assays. In Pharmaceutical and Medical Applications of Near-Infrared Spectroscopy; Marcel Dekker: New York, 2002. (2) Lyon, R. C.; Lester, D. S.; Lewis, E. N.; Lee, E.; Yu, L. X.; Jefferson, E. H.; Hussain, A. S. AAPS PharmSciTech 2002, 3 (3), 1–15. (3) Dubois, J.; Wolff, J.-C.; Warrack, J. K.; Schoppelrei, J.; Lewis, E. N. Spectroscopy 2007, 22 (2), 40–50. (4) Lee, E.; Huang, W. X.; Chen, P.; Lewis, E. N.; Vivilecchia, R. V. Spectroscopy 2006, 21 (11), 24–32. (5) Li, W.; Woldu, A.; Kelly, R.; McCool, J.; Bruce, R.; Rasmussen, H.; Cunningham, J.; Winstead, D. Int. J. Pharm. 2008, 350 (1-2), 369–373. (6) Lewis, E. N.; Schoppelrei, J. W.; Lee, E.; Kidder, L. H. Process Anal. Technol. 2005, 187–225. (7) Reich, G. Adv. Drug Delivery Rev. 2005, 57 (8), 1109–1143. (8) Koehler, F. W.; Lee, E.; Kidder, L. H.; Lewis, E. N. Spectrosc. Eur. 2002, 14 (3), 12–19. (9) Tran, C. D. J. Near Infrared Spectrosc. 2000, 8 (2), 87–99. (10) Tanabe, H.; Otsuka, K.; Otsuka, M. Anal. Sci. 2007, 23, 857–862. (11) Fischer, D.; Bayer, T.; Eichhorn, K. J.; Otto, M. Fresenius’ J. Anal. Chem. 1997, 359 (1), 74–77. (12) Heigl, N.; Petter, C. H.; Rainer, M.; Najam-ul-Haq, M; Vallant, R. M.; Bakry, R.; Bonn, G. K.; Huck, C. W. J. Near Infrared Spectrosc. 2007, 15 (5), 269– 282. (13) Trojer, L.; Lubbad, S. H.; Bisjak, C. P.; Bonn, G. K. J. Chromatogr., A 2006, 1117, 56–66.

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chemical factors such as composition and surface derivatizations.14 Generally, in NIR diffuse reflection spectroscopy, the spectrometer beam is reflected, scattered, or transmitted through a sample whereas the diffusely scattered light is reflected back and directed to the detector. The other part of the electromagnetic radiation is absorbed or scattered by the sample.15 Changes in band shapes and reflectance intensity are aroused by the specular reflectance component that can be affected by morphological and physicochemical properties of the sample or combinations thereof.16,17 It is a fact that the absorption fraction of a particle is related to the volume of the particle; in other words, the larger the volume of a particle the more of the incident light is absorbed. In contrast, reflectance is related to the particle’s surface area, which in turn is related to the material’s porosity.18 The absorption/remission function is related to the fraction of absorbed light, the fraction of remitted (or back scattered) light, and the fraction of light transmitted by a representative layer as follows:

A(R, T) )

([1 - RS]2 - TS2) AD(2 - AD - 2RD) ) RS RD

TS is the transmission fraction, and RS denotes the measured remission fraction. A is the absorbed light fraction, and subscript D represents the thickness d of a layer.19 Moreover, the surface of a particle or composite behaves not like one mirror, but many, so for each reflecting surface at a different angle to the light, reflectance signal changes. Thus, the reflections send light back in many directions; as a result, diffuse reflectance occurs. For spectral data evaluation two methods, raw spectra interpretation and chemometrics/multivariate data analysis (MVA), are commonly used to elucidate the NIR spectra, which consist mainly of overlapping, broad, and often low-absorption bands.20 Visual spectra interpretations and absorption band assignments play an important role, especially for the comparison of pure materials and rather complex spectra mixes.21 Multivariate data analysis based calibration techniques are applied to combine the spectral data with target parameters transferred from reference techniques or to expose similarities and hidden data structures in the spectra.22-24 A couple of useful spectra pretreatments are available that help to increase the quality of calibrations, namely, derivatives, (14) Siesler, H. W.; Ozaki, Y.; Kawata, S.; Heise, H. M., Near-Infrared SpectroscopysPrinciples, Instruments, Applications; Wiley-VCH: Weinheim, Germany, 2002. (15) Dahm, D. J.; Dahm, K. D.; Norris, K. H. J. Near Infrared Spectrosc. 2002, 10 (1), 1–13. (16) van de Hulst, H. C. Light Scattering by Small Particles; Dover Publications Inc.: New York, 1981. (17) Berne, B. J.; Pecora, R. Dynamic Light Scattering; Dover Publications Inc.: New York, 2000. (18) Huck, C. W.; Ohmacht, R.; Szabo, Z.; Bonn, G. K. J. Near Infrared Spectrosc. 2006, 14, 51–57. (19) Dahm, D. J.; Dahm, K. D. Interpreting Diffuse Reflectance and Transmittance; IM Publications: Chichester, 2007. (20) Workman, J.; Weyer, L., Practical Guide to Interpretive Near-infrared Spectroscopy; Taylor & Francis: Boca Raton, FL, 2007. (21) Weyer, L. G.; Lo, S.-C. Spectra-Structure Correlations in the Near-infrared. In Handbook of Vibrational Spectroscopy Chalmers, J. M., Griffiths P. R., Eds.; Wiley: Chichester, 2002; Vol. 3. (22) Kowalski B. R. Chemometrics: Mathematics and Statistics in Chemistry; D. Reidel: Dordrecht, Holland, 1984. (23) Martens H.; Martens M. Multivariate Analysis of Quality; Wiley and Sons Ltd.: Chichester, UK, 2001.

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Scheme 1. Synthesis of 1,2-Bis(p-vinylphenyl)ethane (BVPE) Based on a Grignard Dimerization of p-Vinylbenzyl Chloride

smoothing, normalization, filters, and baseline- and multiplicative correction methods.25 The fact that every material and surface structure has its unique physicochemical fingerprint in the nearinfrared region makes NIRS, especially coupled to diffuse reflection devices and combined with MVA, a powerful tool in the field of material science and in particular for the expression of chemical and physical parameters within one measurement. To sum up, the main objective of this work is to set up a noninvasive and rapid screening method for simultaneously determining the chemical (monomer fraction + cross-linker fraction + porogen content ) 100%) and the physical (pore size quantiles (%)) properties of a monolithic MS/BVPE polymer scaffold. EXPERIMENTAL SECTION Chemicals and Reagents. 1. Synthesis of 1,2-Bis(pvinylphenyl)ethane (BVPE). A Grignard dimerization of pvinylbenzyl chloride (Aldrich, Milwaukee, WI, 90% purity) was employed to yield the cross-linker BVPE (Scheme 1). Magnesia was purchased from Aldrich. A detailed protocol of the BVPE synthesis can be found in the cited literature.26 Increasing purity of BVPE can be obtained by recrystallization from methanol. The purity of the product was checked and confirmed by 1H and 13C NMR and GC/MS analysis. 2. Monolithic Poly(p-methylstyrene-co-1,2-bis(p-vinylphenyl)ethane) (MS/BVPE) Polymers. All monolithic MS/BVPE composites were prepared by thermally initiated free radical copolymerization of p-methylstyrene (MS; purity g96%), purchased from Aldrich, and BVPE (Scheme 2). The polymerization was performed in the presence of R,R′-azoisobutyronitrile (AIBN; purity g98%) and a binary mixture of inert diluents (porogens), namely, toluene (microporogen; purity g99%) and 1-decanol (macroporogen; purity >98%), all purchased from Fluka (Buchs, Switzerland). Before use, toluene was distilled over sodium. p-Methylstyrene was extracted with 10% NaHCO3 and water, dried over Na2SO4, and finally distilled under vacuum. AIBN was recrystallized from MeOH (Aldrich, purity g99.9%). 1-Decanol was used as received. Before polymerization, the polymer mixture (p-methylstyrene, 1,2bis(p-vinylphenyl)ethane, R,R′-azoisobutyronitrile, toluene, 1-decanol) was sonicated for 5 min at 60 °C to solve the components and to remove gas. Polymerization was carried out in 1.0-mL glass vials in a water bath at 65 °C for 24 h. Monomer conversion is (24) Massart D. L.; Vandeginste B. G. M; Deming S. N.; Michotte Y; Kaufman L. Chemometrics: a textbook; Elsevier: New York, 1988. (25) Esbensen, K. H. An introduction to multivariate data analysis and experimental design, 5th ed.; Camo: Oslo, Norway. (26) Li, W. H.; Li, K.; Sto ¨ver, H. D. H.; Hamielec, A. E. J. Polym. Sci., Part A 1994, 32 (11), 2023–2027.

Scheme 2. Thermally Initiated Free Radical Copolymerization of p-Methylstyrene (MS) and 1,2-Bis(p-vinylphenyl)ethane (BVPE)

considered to be >99%. After polymerization, the polymer was refluxed in a 50-mL flask with MeOH for 5 h in order to remove the porogens. Finally, the material was dried overnight in an oven at 85 °C. All chemical quantiles in the text are given in % (v/v). Instrumentation. 1. IR/NIR Chemical Imaging. The image data sets of the monolithic MS/BVPE composites were collected on a Spectrum Spotlight 400 combined with a Spectrum GX IR/NIR spectrometer (Perkin-Elmer, Rodgau, Germany). The imaging system consists of a dual MCT detector device, a 16 × 1 narrow-band (NBMCT) photoconductive array and single-point MBMCT on the same substrate in the same dewar. The instrument offers a signal-to-noise ratio of >12000:1, a spectra collection speed of 160 spectra/s at 16 cm-1, and a maximum number of spectra per image of >260 000. Spectra were collected over a wavenumber range from 7800 to 748 cm-1. In the case of IR imaging (KBr beam splitter), each pixel represents the average of two scans whereas the analyzed area (1000 × 1000 µm) was scanned at 8 cm-1 spectral resolution and 50-µm pixel size. The recorded image consists of 38 416 singe IR spectra. In the case of NIR imaging (CaF2 beam splitter), each pixel represents the average of two scans and the analyzed area (1000 × 1000 µm) was scanned at 16 cm-1 spectral resolution and 25-µm pixel size. The resulting image is assembled of 109 392 single NIR spectra. All spectra were recorded in diffuse reflection mode whereas a gold surface was scanned as a background spectrum. SpectrumIMAGE-Spotlight R 1.6.0. was used for spectral data processing. Measurements were carried out at room temperature (23 °C). 2. FT-NIR Spectroscopy. NIR spectra were recorded with a Bruker Vector 22/N Fourier transform NIR spectrometer (FTNIR) (Bruker Optik GmbH, Ettlingen, Germany) equipped with a tungsten-halogen lamp and a germanium electronic semiconductor detector. The instrument offers a spectral resolution of 8.0-2.0 cm-1 (0.3-1.2 nm) and an absolute wavelength accuracy of >0.01 nm between 4000 and 12500 cm-1 (2500-800 nm). The signal-to-noise ratio is >1000:1 within a 5-s measurement. For reflection spectra recording, a light fiber optic (N261, i.d. ) 4.0 mm) was utilized. Software package OPUS 5.0 was used for spectral data processing. NIR spectra of nine monolithic polymer composites varying in physicochemical properties were recorded on the upper side and rear side resulting in a total of 18 spectra. Measurements were carried out at room temperature (23 °C). Multivariate Data Analysis. Chemometric software NirCal 4.21 (Bu¨chi, Flawil, Switzerland) was used for creating the models. The Unscrambler 9.6 software package (CAMO Software AS., Oslo, Norway) was drawn for comparison. Qualitative analysis was performed by using a principal component analysis (PCA),

whereas for creating a quantitative model, the partial least-squares (PLS) regression method was employed. All models tested were subjected to internal cross-validation or test-set validation with “leave-one-out”. In case of the test-set validation, samples 1, 3, 4, 5, 7, and 9 were subjected to the calibration-set (c-set), whereas samples 2, 6, and 8 (Table 1) consisted to the validation-set (vset). For the leave-one-out approach, at a given time samples 2, 6, and 8 were consecutively taken out of the v-set and were treated as unknown samples. For testing the calibrations prediction ability, samples 2, 6, and 8 were predicted by the established model regarding its chemical composition and pore size distributions. Preliminary studies have shown only low deviations for both, the software (The Unscrambler 9.6 and NIRCal 4.21) and the different validation methods (cross-validation, test-set validation), respectively. In order to make results comparable and to keep evaluation conditions constant, the presented models were all calculated with the NirCal 4.21 software in combination with a leave-one-out testset validation. All spectral data were mean-centered prior to calibration. The number of factors to be used in each case was determined by the predicted residual error sum of squares (PRESS) that shows the sum of squares of deviation between predicted (yn) and reference values (xn). PRESS )

∑ (x

2 n - yn)

Selection of the best quantitative regression model is based on the following calculated values. (1) BIAS: i.e., the average deviation between predicted values (yn) and actual values (xn), in the calibration set. Bias )

1 N

∑ (x

n - yn)

(2) Standard error of estimation (SEE): the standard deviation of differences between reference values and NIRS results in the calibration set.

SEE )

N1 ∑ (x - y - Bias)

2

n

n

(3) Standard error of prediction (SEP): the standard deviation of differences between reference values and NIRS-results in the validation set.

SEP )

N1 ∑ (x - y - Bias)

2

n

n

N is the number of spectra in the c-set and v-set, respectively. (4) (SEE/SEP) × 100: i.e., can be used for selection of calibration factors svalues above 100 indicate that the calibration tends to overfit (too many factors are used for creating the model). (5) The quality of quantitative calibration data is described by the regression coefficient (r) defined as

∑ (x -x¯) - (y -y¯) n

r)

n

N

∑ (

N

(xn -x¯)2

∑ (y -y¯) ) 2

n

N

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Table 1. Compositions of the Reaction Mixtures (“Chemical Parameter”) for Synthesis of Poly(p-methylstyrene-co-1,2-bis(p-vinylphenyl)ethane) Polymers sample number monomer (MS) (%) cross-linker (BVPE) (%) microporogen (toluene) (%) makroporogen (decanol) (%)

1

2

3

4

5

6

7

8

9

17.5 17.5 9 56

18 18 9 55

18.5 18.5 9 54

19 19 9 53

19.5 19.5 9 52

20 20 9 51

20.5 20.5 9 50

21 21 9 49

21.5 21.5 9 48

Where xn represents the true values yn the predicted values, ¯x and ¯y are the mean values, and N is the number of spectra in the c-set and v-set. The results provided by the different calibrations were compared via the SEP. Reference Analysis: Porosity Measurements. Nitrogen adsorption experiments were performed with each sample using a Beckman Coulter SA 3100 gas adsorption analyzer, and specific surface area was calculated using the Bunauer-Emmett-Teller (BET) model.27 The pore size distribution, in the range up to 200nm diameter, was calculated using the Barrett-Joyner-Halenda (BJH) model.28 The BJH method for calculating pore size distributions is based on a model of the adsorbent as a collection of cylindrical pores. The theory accounts for capillary condensation in the pores using the classical Kelvin equation, which in turn assumes a hemispherical liquid-vapor meniscus and a welldefined surface tension. For this study, samples were outgassed for 10 h at 50 °C to remove any moisture or adsorbed contaminants that may have been present on the sample surface. The analyzed pore size range is from 3 to 200 nm. The pore volume/ area accessible by gas adsorption was further evaluated by summation of micro-, meso-, and macroporous volumes/areas and calculating the respective quantiles. RESULTS AND DISCUSSION First, representative MIR and NIR spectral images of the total MS/BVPE polymer surface were generated. The reason behind this was potentially inhomogenously distributed amounts of MS and BVPE in the samples.29 Figure 1a shows the optical image of the cylindrically shaped polymer sample (sample 9) that was clamped into an orifice during the measurements. The bright part at the upper left side indicates a disruption of the sample. Figure 1b depicts the MIR imaged area (1000 × 1000 µm) whereas the upper left side, or red area, can be clearly differentiated from the sample as all incident radiation is lost or no signal is reflected from the sample surface. The green area is the polymer sample, and the blue area represents the orifice made of steel. The contrast of the full spectrum image is a function of the intensity of the NIR/IR spectrum associated with each pixel at a specified wavelength. Panels c and d in Figure 1 illustrate the averaged NIR and MIR absorbance spectra from 4000 to 7800 and 478 to 4000 cm-1, respectively. The MIR and NIR chemical images indicated homogeneous distributions of the p-methylstyrene and the 1,2-bis(p-vinylphenyl)ethane and morphological factors like irregularly dense packed areas, respectively. Moreover, no O-H (27) Brunauer, S.; Emmett, P. H.; Teller, E. J. Am. Chem. Soc. 1938, 60, 309. (28) Barrett, E. P.; Joyner, L. G.; Halenda, P. P. J. Am. Chem. Soc. 1951, 73, 373–380. (29) Tran, C. D.; Cui, Y.; Smirnov, S. Anal. Chem. 1998, 70, 4701–4708.

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absorptions occurred, which would be an indicator for water adsorbed onto the polymer surface. Especially the NIR spectra show well-resolved absorption bands that can be attributed to characteristic molecular vibrations. The absorption band observed at 4047 cm-1 is probably the second overtone of the δ (CH3) band, whereas the bands in the range of 4200-4400 cm-1 are the ν (CH3/CH2) + δ (CH3/CH2) combination bands. A pair of ν (dCH) + δ (CdC) combination bands emerge at 4601 and 4664 cm-1.The intense absorption bands in the range from 5500 to 6200 cm-1 are characteristic for the first overtones of the aliphatic and aromatic ν (CH) vibrations. NIR provides more intense radiation compared to the MIR and thus penetrates deeper into the sample. The interaction of the incident light with the material in deeper sample layers provides important information about the physical characteristics of a sample. In contrast, MIR only interacts with the sample surface (specular reflectance). As a consequence, further analyses were exclusively conducted by NIR diffuse reflection spectroscopy. Qualitative Analysis. The collected FT-NIR absorbance spectra, depicted in Figure 2, were subjected to PCA. As seen from Table 1, the compositions of the reaction mixture are changed gradually. The porosity of the resulting materials should decrease with reduced total content of porogen. However, the ratio between “macroporogen” and “microporogen” was changed simultaneously, so that the pore size distribution should also change. More details on the influence of the used porogens in a very similar system (styrene/divinylbenzene) can be found in Viklund et al.30 Calibration wavenumbers were set from 4000 to 8994 cm-1 whereas three factors were sufficient to describe >99% of the variance. The three-dimensional factor plot, depicted in Figure 3, shows a clear separation of samples one, two, and three, along principal component (PC) 2 and PC 3 into one quadrant, whereas samples 4, 5, and 6 are placed into the opposite quadrant. The other samples are clustered between PC 1, PC 2 at low score values of PC 3. This score plot correlates well with the data obtained by BET nitrogen adsorption regarding the pore volumes (mL/g) accessible by gas adsorption of the polymer scaffolds. Samples 1, 2, and 3 (Table 1) all possess low pore volumes, namely, 0.0112, 0.0082, and 0.008 mL/g, which makes the incisive difference among samples 1, 2, and 3 and the other samples by means of PC 1. The remaining samples all show a linear increase of pore volumes with increasing MS/BVPE content from 0.0123 to 0.0183 to 0.0422 to 0.0703 to 0.0937 to 0.118 mL/g indicated by PC 2 and PC 3. It should be kept in mind that the overall porosity of the materials is much larger, therefore making them suited for using it as a stationary phase for µ-HPLC,13 but that we (30) Viklund, C.; Svec, F.; Frechet, J. M. J.; Irgum, K. Chem. Mater. 1996, 8, 744–750.

Figure 1. Optical (a) and MIR chemical image (b) of the whole poly(p-methylstyrene-co-1,2-bis(p-vinylphenyl)ethane) polymer sample with the marked region of averaged spectra. (c) and (d) show the averaged NIR and MIR absorbance spectra in the range from 4000 to 7800 and 748 to 4000 cm-1, respectively.

Figure 2. FT-NIR absorbance spectra of MS/BVPE polymers marked with varying amounts of MS/BVPE.

focus here on a method which is able to distinguish between different pore size fractions (see below). Quantitative Analysis. 1. Monomer (MS)/Cross-Linker (1,2-Bis(p-vinylphenyl)ethane (BVPE)) Content. For data acquisition, a spectral resolution of 8 cm-1 was selected and one spectrum represents the average of 64 scans from 4000 to 12000 cm-1. Partial least-squares regression (PLSR) calibration was

computed over the 35-43% MS/BVPE and the 56-48% decanol content, but keeping the amount of toluene constant at 9%. As a reference technique, nitrogen adsorption according to the BET and BJH theorems was drawn to build the PLS models. The best results were obtained by employing untreated spectra in the 4000-8994 cm-1 region in combination with 3 factors. A suitable wavenumber range for the calibration was chosen by the property/ Analytical Chemistry, Vol. 80, No. 22, November 15, 2008

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Figure 3. Three-dimensional score plot representing PC 1, 2, and 3.

Figure 4. PLS regression model for determining the MS/BVPE amount in the samples.

wavenumber regression that shows the regression coefficient of the spectra over the whole measurement range from 4000 to 8994 cm-1. The calculated PRESS function showed a minimum and the v-set regression coefficient a maximum at 3 factors, respectively. An adequate data description by 3 factors was also confirmed by the eigenvalues showing values close to zero above factors 3. The slopes and intercepts were close to 1 and 0, as pointed out in Figure 4. Predictions of the v-set samples 2, 6, and 8498

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8 by the leave-one-out approach showed good prediction abilities of the PLS model. The predicted values for the upper and lower surface of sample 2 showed 36.01 and 36.00% (reference 36.00%), for sample 6 39.64 and 39.42% (reference 40.00%), and for sample 8 42.02 and 42.44% (reference 42.00%) for the MS/BVPE content. Applying a multiplicative scatter correction (MSC) to the raw spectra resulted in an increase of the SEP from 0.35 to 1.02%. MSC is generally used to eliminate the baseline fluctuations and

Figure 5. Resulting pore volume and pore area distributions by gradually increasing the MS/BVPE content. Note that not the entire macropore range can be assessed with nitrogen adsorption (up to d ∼ 200 nm). Table 2. Estimated Values for Predicting the Pore Volume Distributions by PLSR (Calibration: 4000-8994, Raw Data, 3 Factors, PLS) quantile micropores (50 nm) (%)

predicted

SEP SEE/SEP × 100 leave 1 out (40)

quantile mesopores (>6 nm 6 nm