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

Article abstract of DOI:10.1021/ac8013059

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-1,2-bis(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 FT-NIR 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.

Full text of DOI:10.1021/ac8013059

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,
6
4
4
020 Innsbruck, Austria, Institute of Physical Chemistry, University Duisburg sEssen, Sch u¨ tzenbahn 70,
5117 Essen, Germany, and Institute of Technical Chemistry, University Duisburg sEssen, Universit a¨ tsstrasse 5,
5141 Essen, Germany
Fourier transform near-infrared (FT-NIR) diffuse reflec-
tion spectroscopy was used in combination with principal
component analysis and partial least-squares regression
to simultaneously determine the physical and the chemi-
cal parameters of a porous poly(p-methylstyrene-co-1,2-
bis(p-vinylphenyl)ethane) (MS/BVPE) monolithic poly-
mer. 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 chemi-
cal imaging was implemented as a tool to assess the
uniformity of the samples. The presented study sum-
marizes 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 (diam-
eter, 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
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 ingredi-
ents, particle size measurements, and determination of the
1-10
hardness and film coating of tablets.
In-line measurements
are frequently used to conduct kinetic studies in order to analyze
chemical reactions or to monitor emerging physical properties,
1
1,12
making particle or pore sizes visible.
a homemade polymer material, namely, poly(p-methylstyrene-co-
1
In the case of this study,
1
3
,2-bis(p-vinylphenyl)ethane) (MS/BVPE), that is used as a
stationary phase for micro-high-performance liquid chromatogra-
phy (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
.
1
.42-8.44%, and for pore area quantiles 0.38-1.45%,
.
respectively. The implication of these results is that FT-
NIR 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
.
(
.
(
(
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.
997, 359 (1), 74–77
.
1
.
*
To whom correspondence should be addressed. Tel.: +43 512 507 5195.
(12) Heigl, N.; Petter, C. H.; Rainer, M.; Najam-ul-Haq, M; Vallant, R. M.; Bakry,
Fax: +43 512 507 2965. E-mail: Christian.W.Huck@uibk.ac.at.
R.; Bonn, G. K.; Huck, C. W. J. Near Infrared Spectrosc. 2007, 15 (5), 269–
†
Leopold-Franzens University.
Institute of Physical Chemistry, University Duisburg sEssen.
282
(13) Trojer, L.; Lubbad, S. H.; Bisjak, C. P.; Bonn, G. K. J. Chromatogr., A 2006,
1117, 56–66
.
‡
§
Institute of Technical Chemistry, University Duisburg sEssen.
.
1
0.1021/ac8013059 CCC: $40.75  2008 American Chemical Society
Analytical Chemistry, Vol. 80, No. 22, November 15, 2008 8493
Published on Web 10/11/2008

14
chemical factors such as composition and surface derivatizations.
Scheme 1. Synthesis of
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
1,2-Bis(p-vinylphenyl)ethane (BVPE) Based on a
Grignard Dimerization of p-Vinylbenzyl Chloride
15
is absorbed or scattered by the sample. Changes in band shapes
and reflectance intensity are aroused by the specular reflectance
component that can be affected by morphological and physico-
1
6,17
chemical properties of the sample or combinations thereof.
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. 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:
smoothing, normalization, filters, and baseline- and multiplicative
1
8
2
5
correction methods. The fact that every material and surface
structure has its unique physicochemical fingerprint in the near-
infrared region makes NIRS, especially coupled to diffuse reflec-
tion 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.
2
2
S
(
[1 - R ] - T ) A (2 - A - 2R )
S
D
D
D
A(R, T) )
)
RS
RD
T
S
S
is the transmission fraction, and R denotes the measured
remission fraction. A is the absorbed light fraction, and subscript
1
9
D represents the thickness d of a layer.
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.
EXPERIMENTAL SECTION
Chemicals and Reagents. 1. Synthesis of 1,2-Bis(p-
vinylphenyl)ethane (BVPE). A Grignard dimerization of p-
vinylbenzyl 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. Increasing purity
of BVPE can be obtained by recrystallization from methanol. The
purity of the product was checked and confirmed by H and
For spectral data evaluation two methods, raw spectra inter-
pretation and chemometrics/multivariate data analysis (MVA), are
commonly used to elucidate the NIR spectra, which consist mainly
2
6
2
0
of overlapping, broad, and often low-absorption bands. Visual
spectra interpretations and absorption band assignments play an
important role, especially for the comparison of pure materials
1
13
C
NMR and GC/MS analysis.
2
1
and rather complex spectra mixes. 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
2. Monolithic Poly(p-methylstyrene-co-1,2-bis(p-vinylphe-
nyl)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 (macroporo-
gen; purity >98%), all purchased from Fluka (Buchs, Switzerland).
Before use, toluene was distilled over sodium. p-Methylstyrene
22-24
spectra.
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.
3 2 4
was extracted with 10% NaHCO and water, dried over Na SO ,
16) van de Hulst, H. C. Light Scattering by Small Particles; Dover Publications
Inc.: New York, 1981.
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, 1,2-
bis(p-vinylphenyl)ethane, R,R′-azoisobutyronitrile, toluene, 1-de-
canol) 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
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.
2
006, 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.
(24) Massart D. L.; Vandeginste B. G. M; Deming S. N.; Michotte Y; Kaufman
L. Chemometrics: a textbook; Elsevier: New York, 1988.
(22) Kowalski B. R. Chemometrics: Mathematics and Statistics in Chemistry; D.
Reidel: Dordrecht, Holland, 1984.
(25) Esbensen, K. H. An introduction to multivariate data analysis and experi-
mental design, 5th ed.; Camo: Oslo, Norway.
(23) Martens H.; Martens M. Multivariate Analysis of Quality; Wiley and Sons
Ltd.: Chichester, UK, 2001.
(26) Li, W. H.; Li, K.; St o¨ ver, H. D. H.; Hamielec, A. E. J. Polym. Sci., Part A
1994, 32 (11), 2023–2027
.
8494 Analytical Chemistry, Vol. 80, No. 22, November 15, 2008

Scheme 2. Thermally Initiated Free Radical
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
Copolymerization of p-Methylstyrene (MS) and
1,2-Bis(p-vinylphenyl)ethane (BVPE)
“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 (v-
set). 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), respec-
tively. 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 test-
set 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
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 instru-
ment offers a signal-to-noise ratio of >12000:1, a spectra collection
(PRESS) that shows the sum of squares of deviation between
predicted (y ) and reference values (x ).
n
n
2
PRESS )
(x - y )
n n
∑
-
1
speed of 160 spectra/s at 16 cm , and a maximum number of
Selection of the best quantitative regression model is based
on the following calculated values.
spectra per image of >260 000. Spectra were collected over a
-
1
wavenumber range from 7800 to 748 cm . 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
(1) BIAS: i.e., the average deviation between predicted values
(y
n
) and actual values (x
n
), in the calibration set.
-
1
scanned at 8 cm spectral resolution and 50-µm pixel size. The
1
N
recorded image consists of 38 416 singe IR spectra. In the case
Bias )
(x - y )
n n
∑
of NIR imaging (CaF
2
beam splitter), each pixel represents the
average of two scans and the analyzed area (1000 × 1000 µm)
(
2) Standard error of estimation (SEE): the standard deviation
-1
was scanned at 16 cm 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. Spectru-
mIMAGE-Spotlight R 1.6.0. was used for spectral data processing.
Measurements were carried out at room temperature (23 °C).
of differences between reference values and NIRS results in the
calibration set.
1
N
2
SEE )
(x - y - Bias)
n n
∑
ꢀ
2. FT-NIR Spectroscopy. NIR spectra were recorded with
(3) Standard error of prediction (SEP): the standard deviation
a Bruker Vector 22/N Fourier transform NIR spectrometer (FT-
NIR) (Bruker Optik GmbH, Ettlingen, Germany) equipped with
a tungsten-halogen lamp and a germanium electronic semicon-
ductor detector. The instrument offers a spectral resolution of
of differences between reference values and NIRS-results in the
validation set.
-1
1
N
2
8
.0-2.0 cm (0.3-1.2 nm) and an absolute wavelength accuracy
SEP )
(x - y - Bias)
n n
∑
-1
ꢀ
of >0.01 nm between 4000 and 12500 cm (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
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 )
4.21 (B u¨ chi, Flawil, Switzerland) was used for creating the models.
∑
n n
N
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),
r )
2
2
(
(x - ¯x )
(y - ¯y ) )
n
∑
n
∑
ꢀ
N
N
Analytical Chemistry, Vol. 80, No. 22, November 15, 2008 8495

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
1
2
3
4
5
6
7
8
9
monomer (MS) (%)
17.5
17.5
9
18
18
9
18.5
18.5
9
19
19
9
19.5
19.5
9
20
20
9
20.5
20.5
9
21
21
9
21.5
21.5
9
cross-linker (BVPE) (%)
microporogen (toluene) (%)
makroporogen (decanol) (%)
56
55
54
53
52
51
50
49
48
Where x
n
represents the true values y
n
the predicted values, ¯x
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
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 com-
pared 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
-1
at 4047 cm is probably the second overtone of the δ (CH
3
) band,
whereas the bands in the range of 4200-4400 cm are the ν
(CH /CH ) + δ (CH /CH ) combination bands. A pair of ν (dCH)
+ δ (CdC) combination bands emerge at 4601 and 4664 cm .The
-1
3
2
3
2
-1
-
1
intense absorption bands in the range from 5500 to 6200 cm
27
(
BET) model. The pore size distribution, in the range up to 200-
nm diameter, was calculated using the Barrett-Joyner-Halenda
BJH) model. The BJH method for calculating pore size
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.
2
8
(
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 well-
defined surface tension. For this study, samples were outgassed
for 10 h at 50 °C to remove any moisture or adsorbed contami-
nants 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.
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
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. 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
3
0
Viklund et al. Calibration wavenumbers were set from 4000 to
2
9
-1
8994 cm 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
1
b 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
(
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
-
1
4
000 cm , 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
1
3
suited for using it as a stationary phase for µ-HPLC, but that we
(
(
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,
73–380
29) Tran, C. D.; Cui, Y.; Smirnov, S. Anal. Chem. 1998, 70, 4701–4708
.
3
.
(30) Viklund, C.; Svec, F.; Frechet, J. M. J.; Irgum, K. Chem. Mater. 1996, 8,
(
.
744–750.
8496 Analytical Chemistry, Vol. 80, No. 22, November 15, 2008

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
-
1
to 4000 cm , 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).
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
Quantitative Analysis. 1. Monomer (MS)/Cross-Linker
(
1,2-Bis(p-vinylphenyl)ethane (BVPE)) Content. For data
-1
acquisition, a spectral resolution of 8 cm was selected and one
spectrum represents the average of 64 scans from 4000 to 12000
cm . Partial least-squares regression (PLSR) calibration was
-
1
4000-8994 cm region in combination with 3 factors. A suitable
-
1
wavenumber range for the calibration was chosen by the property/
Analytical Chemistry, Vol. 80, No. 22, November 15, 2008 8497

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
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
-
1
cm . The calculated PRESS function showed a minimum and
the v-set regression coefficient a maximum at 3 factors, respec-
tively. 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 Analytical Chemistry, Vol. 80, No. 22, November 15, 2008

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 (<6 nm) (%)
quantile mesopores (>6 nm <50 nm) (%)
quantile macropores (>50 nm) (%)
reference
predicted
reference
predicted
reference
predicted
3
3
3.40
3.40
33.38
33.39
59.64
59.64
59.05
59.06
6.96
6.96
7.57
7.55
leave 1 out (36)
SEP
SEE/SEP × 100
2.58
5.98
8.44
31.98
15.70
20.77
1
1
4.35
4.35
18.54
19.08
40.34
40.34
48.77
48.91
45.31
45.31
32.69
32.01
leave 1 out (40)
SEP
SEE/SEP × 100
1.42
58.10
1.71
54.76
2.85
61.41
8
8
.21
.21
9.88
7.64
41.41
41.41
37.64
36.78
50.38
50.38
54.72
56.89
leave 1 out (42)
SEP
SEE/SEP × 100
2.02
40.85
4.92
19.03
6.77
25.88
unwanted offset due to scatter effects in the sample. The increase
of the SEP, by applying MSC to suppress the influence of physical
properties, explicitly shows the interrelation of the physical and
chemical properties of the polymer material.
physical properties and the porosity of the polymers. In order to
confirm the previous results, the same strategy as for determining
the amount of MS/BVPE was applied to quantitatively ascertain
the quantiles of micro-, meso-, and macropores in the samples.
To simultaneously determine the chemical and the physical
parameters, the same PLS model was used for the MS/BVPE
determination (Figure 4). Table 2 gives the estimated values for
the pore volume of the v-set samples 2, 6, and 8, each representing
low, middle, and high amounts of MS/BVPE, obtained by the
leave-one-out PLS approach. Table 3 shows the values for the pore
areas in the same manner. Samples 2 (36% MS/BVPE) and 8 (42%
MS/BVPE) show a good correlation of the predicted to the
reference values, while sample 6 (40% MS/BVPE) shows relatively
high deviating predicted values from the reference values. This
may be due to the abrupt rise of the macropore fraction as can
be gathered from Figure 5. The fact that the (SEE/SEP) × 100
values show relatively high values for the macropores of sample
6 (134.55) and micropores of sample 8 (133.25) makes clear that
for a more precise prediction of the pore quantiles separate, more
specific PLS models could be used. In case of the described
method, one’s attention should be turned on the simultaneous
determination of the pore size fractions; therefore, the same PLS
model has to be used for predicting all unknown samples. It should
be kept in mind that the accuracy for determining the macropore
fraction (including its percentile) accessible gas adsorption is
2. Pore Size Distributions. The emerged quantiles (%) and
pore size distributions regulated by the amount of MS/BVPE can
be gathered from Figure 5. For example, the sample that contains
35% MS/BVPE shows the greatest fraction of emerged pore
volume in the mesopore range (59.0%), whereas the quantile of
micropore volume shows 33.7%, and for the macropore volume
quantile 7.3%. That means 59% of the pore volume is in the
mesopore range, 33.7% in the micropore range, and 7.3% in the
macropore range. The sum of the micro-, meso-, and macro-
pore volumes and pore areas always yields 100.0%. In other words,
the computed lines in each graph represent the pore volume and
pore area fractions by increasing the MS/BVPE content. The
dashed connection lines give the sum of the quantiles (%) for the
pore volume and pore area for each sample, here only marked
for samples representing the 35 and 43% monomer + cross-linker
amounts. In particular, the micropore size distributions and the
macropore size distributions show good coherence, meaning the
micropore quantile decreases and the macropore quantile in-
creases with increasing the MS/BVPE content. This makes clear
that, as expected, the variation of chemical parameters, here the
composition of reaction mixture can be drawn to regulate the
Analytical Chemistry, Vol. 80, No. 22, November 15, 2008 8499

Table 3. Estimated Values for Predicting the Pore Area Distributions by PLSR (Calibration: 4000-8994, Raw Data, 3
Factors, PLS)
quantile micropores (<6 nm) (%)
quantile mesopores (>6 nm <50 nm) (%)
quantile macropores (>50 nm) (%)
reference
predicted
reference
predicted
reference
predicted
5
5
8.37
8.37
58.30
58.30
40.98
40.98
40.50
40.49
0.65
0.65
1.21
1.21
leave 1 out (36)
SEP
SEE/SEP × 100
0.977
77.00
1.41
7.10
1.40
57.64
4
4
9.46
9.46
58.30
58.30
42.73
42.73
40.50
40.49
7.81
7.81
1.21
1.21
leave 1 out (40)
SEP
SEE/SEP × 100
0.97
77.25
0.38
25.90
0.60
134.55
3
3
9.01
9.01
38.20
37.31
48.79
48.79
48.43
48.77
12.20
12.20
13.37
13.92
leave 1 out (42)
SEP
SEE/SEP * 100
0.56
133.25
1.45
6.90
1.05
76.43
lower than for meso- and micropores because of the upper limit
of this method (∼200 nm). The SEPs ranging from 1.42 to 8.44%
are within an acceptable limit. The same characteristic was
observed for estimating the pore area distributions. As the pore
volume and the pore area are closely related, the SEPs showed
analogical values. Here too, sample 6 (40% MS/BVPE) showed
the largest deviation from the reference values (Table 3). In the
case of the pore area distributions, the SEP range from minimum
spectra of polymeric samples varying in physicochemical char-
acteristics allows obtaining quantitative information about the
chemical composition and the pore volume/area distributions. By
applying the same calibration model for both, the determination
of the chemical factors and the physical factors, the whole
information is available with only one measurement.
ACKNOWLEDGMENT
0.38% to maximum 1.45%.
The authors thank Dipl.-Ing. Chem. Inge Danielzik from the
Institute of Technical Chemistry, University of DuisburgsEssen
for conducting the BET measurements.
CONCLUSIONS
By analyzing the calibration models theoretically based on
geometrical structural factors, the results obtained by the PCA
and PLS models suggest that the regression vector involves both
physical and chemical factors, which are strongly interrelated. The
application of multivariate data analysis methodology to the NIR
Received for review June 26, 2008. Accepted September
8, 2008.
AC8013059
8500 Analytical Chemistry, Vol. 80, No. 22, November 15, 2008