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Description  |
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BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates generally to the evaluation of the physical
properties of samples, and more specifically, to methods employing
near-infrared spectrophotometry to simultaneously quantify various
physical properties of a multicomponent sample, particularly hydrocarbons.
2. Description of the Prior Art
The need often arises to quantify the physical properties of different
gaseous or liquid samples used at various stages of industrial chemical
processes. For example, it is frequently required to measure the heats of
formation and molecular weights of hydrocarbons being used in petroleum
processing and refining.
In the past, the physical properties of samples have typically been
measured one property at a time, using testing methods which have been
developed to specifically evaluate one particular property. For example,
the heat of formation of a particular sample has been determined by
actually burning the sample in a calorimeter. Similarly, molecular weight
of a sample has been determined by inducing and measuring viscous flow of
the sample using a viscometer. In each of these examples, however, the
physical test methods measure, or quantify, the physical properties by
actually subjecting the sample to the conditions in question. To measure
more than one physical property of a particular sample, a plurality of
tests must be individually conducted on a plurality of samples. Such an
approach to measuring the physical properties of a sample is slow,
expensive, and univariate.
More recently, near-infrared spectrophotometric analysis has been used to
determine indirectly the qualitative properties of various samples. Such
methods are disclosed in Wetzel, D. L. Anal. Chem 1983, 55, 1165A to
1176A; Watson, C. A. Anal. Chem 1977, 49, 835A-840A, incorporated herein
by reference. For example, near-infrared spectrophotometric analysis has
been employed to determine the baking quality of flour as shown in Star,
S.; Smith, D. B.; Blackman, J. A.; Gill, A. A. Anal. Proc. (London) 1983,
20, 72-74; to determine digestibility of forages as shown in Winch, J. E.;
Helen, M. Can. J. Plant Sci. 1981,, 61, 45; Norris, K. H. Barns, R. F.;
Moore, J. E.; Shenk, J. S. Animal Sci. 1976, 43, 889-897; and to determine
the potencies of pharmaceutical drugs as shown in Rose, J. J. The
Pittsburgh Conference, Atlantic City, NJ, March, 1983; paper 707. Each of
the above references is incorporated herein by reference.
Use of near-infrared spectrophotometric analysis has many advantages over
other methods since it is rapid, relatively inexpensive, and multivariate
in that many properties can be tested for simultaneously. To date,
however, methods have not been available to use near-infrared
spectrophotometric analysis to directly quantify the physical properties
of samples, such as the molecular heat and weight of hydrocarbons.
The need existed to develop methods for using near-infrared
spectrophotometric analysis to effeciently and inexpensively quantify
various physical properties of samples.
SUMMARY OF THE INVENTION
Accordingly, it is an object of the present invention to provide efficient,
effective and inexpensive methods for quantifying various physical
properties of samples.
It is another object of the invention to provide methods using
near-infrared spectrophotometry to quantify a variety of physical
properties of different types of samples.
It is another object of the invention to provide methods for quantifying
physical properties of multicomponent samples without requiring
independent testing to determine the individual components or constituents
comprising the sample.
It is another object of the invention to provide such methods which are
statistically correlated with calibration data for the specific property
and type of sample tested.
It is another object of the invention to provide methods for simultaneously
quantifying a plurality of physical properties of a sample using
near-infrared spectrophotometry.
It is another object of the invention to provide methods for determining
the heat of formation, molecular weight and methyl groups per molecule of
hydrocarbon mixtures.
It is another object of the invention to provide methods for quantifying
any physical property of a solid, liquid or gaseous sample that is
correlated with chemical constituents that respond to near-infrared
radiation.
The above, and other objects are achieved by an improved method for
quantifying a physical property of a sample. The method comprises an
initial step of determining which wavelength or set of wavelengths in the
near-infrared spectrum is optimally correlated to the physical property
being quantified. Then, weighting, or correcting, constants are calculated
for absorbance or reflectance values measured at each of the determined
wavelengths. The absorbance or reflectance of the sample at each of the
determined wavelengths in the near-infrared spectrum is measured using a
spectrophotometer. A reference value for the physical property being
quantified is then calculated from the measured absorbance or reflectance
of the sample at each determined wavelength, as corrected by the
associated weighting constant.
In a preferred embodiment, a statistical algorithm is employed to evaluate
a field of test, or calibration, data in order to determine the
wavelengths in the near-infrared spectrum which optimally correlate to the
physical property to be quantified. Similarly, the statistical algorithm
is used to evaluate the field of test, or calibration, data to determine
the optimal value of the weighting constants for each of the determined
wavelengths. In this manner, the value for the physical property
quantified, such as the molecular heat of a hydrocarbon, is most likely to
be accurate.
In another embodiment of the invention, a plurality of physical properties
of a gaseous or liquid sample can be simultaneously quantified. In its
method form, the alternative embodiment of the invention again comprises
an initial step of selecting wavelengths, or sets of wavelengths in the
near-infrared spectrum which optimally correlate to each of the physical
properties to be quantified. For example, a first wavelength, or set of
wavelengths, is determined for measuring the molecular heat of a
hydrocarbon. Another wavelength, or set of wavelengths, is determined for
quantifying molecular weight of hydrocarbons. Similarly, weighting
constants corresponding to each of the selected wavelengths are
calculated. A spectrophotometer, based on multiple-filter,
wavelength-dispersive, or Fourier-transform technology is used to measure
the absorbance of the sample at each of the selected wavelengths. Each of
the physical properties is then quantified by calculating a reference
value from the absorbance measurements of the sample taken from the
wavelength or set of wavelengths corresponding to that physical property,
the absorbance measurement being corrected by the corresponding weighting
constant. In this manner, more than one physical property of a sample can
be simultaneously quantified.
In its preferred form, the invention comprises a method for quantifying the
molecular heat, or heat of formation, of a hydrocarbon or hydrocarbon
mixture. At least two optimal wavelengths are selected in the
near-infrared spectrum at which to test the hydrocarbon mixture. The
selected wavelengths are in the range of 750 to 2500 nanometers. Weighting
constants corresponding to each of the selected wavelengths are
determined. The absorbance or reflectance of the hydrocarbon or
hydrocarbon mixture at each of the selected wavelengths is measured with a
spectrophotometer. The measured absorbance at each selected wavelength is
then corrected with the corresponding weighting factor. From the corrected
group of absorbance measurements, a reference value corresponding to the
molecular heat of the hydrocarbon or hydrocarbon mixture is calculated.
In another preferred embodiment even greater accuracy is achieved by
selecting four optimal wavelengths in the near-infrared spectrum at which
to measure the absorbance of the sample. A row-reduction algorithm is used
to correlate the selected wavelengths with calibration data reflecting the
molecular heat values of a pre-tested field of hydrocarbon mixtures.
Similarly, a row-reduction algorithm is used to correlate the weighting
factors both with the selected wavelengths and with the calibration data
reflecting the molecular heat values of a pre-tested field of hydrocarbon
mixtures.
BRIEF DESCRIPTION OF THE DRAWINGS
The above and other objects of the invention may best be understood in
connection with the following description of the preferred embodiments
taken in conjunction with the accompanying drawings, in which:
FIG. 1 is a graph of the heat of formation of a series of hydrocarbon
mixtures as determined by the methods of the present invention.
FIG. 2 is a graph of the molecular weight of a series of hydrocarbon
mixtures as determined by the methods of the present invention.
FIG. 3 is a graph of the methyl groups per molecule for a series of
hydrocarbon mixtures as determined by the methods of the present
invention.
DESCRIPTION OF THE PREFERRED EMBODIMENT
The present invention provides methods for quantifying various physical
properties of samples. The samples tested may be solid, liquid or gaseous.
Nearly any physical property may be quantified, as long as the physical
property in question is correlated to some compositional or other feature
having significant near-infrared absorption or reflectance. It is not
necessary to know the actual components or constituents of the sample
being tested. In its preferred embodiment, the invention comprises methods
and devices employing near-infrared spectrophotometry to evaluate
absorbance characteristics to simultaneously quantify the molecular heat,
molecular weight, and methyl groups per molecule of hydrocarbon mixtures.
1. The Inventive Methods
The inventive method is used to directly quantify the physical properties
of a sample. An initial step in the method is the determination of the
wavelength, or set of wavelengths, in the near-infrared spectrum which is
optimally correlated to the physical property being quantified. For
example, if the molecular heat of hydrocarbons is to be quantified, it is
ncessary to first determine the optimal wavelengths in the near-infrared
spectrum at which to measure the absorbance or reflectance of the
hydrocarbon samples in order to obtain the most accurate results. The
wavelengths which are optimal for quantifying the molecular heat of a
hydrocarbon may not be the same wavelengths at which absorbance would be
measured to most accurately quantify another physical property of a
hydrocarbon, such as its molecular weight.
In order to correlate the wavelengths in the near-infrared spectrum with
the physical property being quantified, a cross-section of test or
calibration samples, which is representative of the actual samples which
will be tested, must be fully evaluated. This generally entails measuring
and recording the absorbance spectra of each of the calibration samples at
a wide range of wavelengths in the near-infrared spectrum. In the test
samples, the value of the physical property of interest has already been
determined by an alternative technique.
The recorded spectra of the calibration samples are then statistically and
mathematically evaluated, to locate the particular wavelength, or set of
wavelengths, which optimally represents the physical property being
quantified. In its preferred form, a statistical analysis using, for
example, the row-reduction algorithm such as that disclosed in Honigs, D.
E.; Hieftje, G. M.; Hirschfeld, T. B. Appl. Spectrosc. 1983, 37, 491-497,
attached hereto as Exhibit A, is used to statistically evaluate the
spectra of the calibration samples in order to locate those wavelengths
which are best correlated to the physical property being quantified. This
article is reproduced in its entirety (except for the abstract and certain
figures which have been redacted) as Exhibit A below.
The row-reduction algorithm referred to above is described in full detail
in the article attached hereto as Exhibit A.
Briefly, this row-reduction algorithm presents a specific way of solving
(by reducing rows of) simultaneous equations such as:
2x+4y=8
1x+8y=10
The algorithm merely codifies the steps so that the solution is found in
the same manner every time. Using the above equations as an example, the
algorithm would first rewrite the equations so that the largest value
comes first:
8y+1x=10
4y+2x=8
Next, each row is normalized by its y coefficient:
y+1/8x=10/8
y+1/2x=2
Finally, a subtraction is made (of the first equation from the second) so
that the new equations are:
y+1/8x=10/8
0+3/8x=6/8
or:
x=2
y=1.
The importance of this order of solving the equations increases as more and
"noisier" (i.e., more complex to reflect actual, and not theoretical,
values) equations are added. By always selecting the largest value, the
solution will be least affected by such additional complexity.
With respect to the present invention, for example, if the sample is a
hydrocarbon mixture, and the physical property being quantified is the
molecular heat of the hydrocarbon mixture, then a representative field of
hydrocarbon mixture calibration samples must be fully evaluated to
determine which wavelengths in the near-infrared spectrum are optimally
suited for quantifying molecular heat. Each calibration sample would be
closely controlled and would be carefully prepared with hydrocarbon
mixtures which would be representative of the actual samples to be later
tested. Alternatively, the calibration samples could be natural and would
have the desired physical property determined by an alternative technique.
The absorbance spectra of each calibration sample is recorded by a
spectrophotometer. The recorded spectra are then statistically analyzed,
preferably by computer program, in accordance with the row-reduction
algorithm, to determine which wavelengths in the near-infrared spectrum
are optimally suited for quantifying molecular heat of any hydrocarbon
mixture.
The following example will illustrate how the appropriate wavelengths are
selected by the row-reduction algorithm disclosed in Exhibit A. This
problem is solved by establishing an equation such as
(B.sub.1 *W.sub.1)+(B.sub.2 *W.sub.2)+(B.sub.3 *W.sub.3) . . . =C,
where C is the physical property in question, the B values are unknown
variables (just like x and y in the previous example), and W is the
absorbance or some other spectral response of the sample. This equation is
in the same form as the first example and can be solved in the same
manner. The only difference is that there is potentially hundreds of
wavelengths which might need to be evaluated, and accordingly hundreds of
"rows" which might need to be reduced. In practice, equations similar to
the above example are created based upon the spectra of many characterized
samples. Using the row-reduction algorithm, the largest absorbance value
is then selected. This sample will be least affected by noise. The
selected sample and wavelength are used to reduce the problem one rank,
just as the first row was subtracted from the second one in the previous
example. This entire procedure is then repeated with the remaining "rows"
until the residuals of the physical or chemical property values are
reduced. A simple example is set forth below:
______________________________________
Wavelengths
a b c d
______________________________________
Hydrocarbon
A 3 6 2 1 = 6 Physical Property
Spectra B 4 3 1 1 = 5 (e.g., Octane
C 2 2 2 3 = 11 Number)
D 6 4 6 1 = 7
______________________________________
The value of sample spectrum "D", wavelength "c" is among the largest, and
thus is the first wavelength selected by the row-reduction algorithm. This
value also is used to solve the first part of the problem, in the manner
set forth above, so that additional optimal wavelengths may be determined:
______________________________________
c a b d
______________________________________
D 6 6 4 1 = 7
A 2 3 6 1 = 6
B 1 1 3 4 = 5
C 2 2 2 3 = 11
______________________________________
Thereafter, the data is reduced as described above:
______________________________________
c a b d
______________________________________
D 1 1 2/3 1/6 = 7/6
A 0 1/2 7/3 1/3 = 11/6
B 0 3 7/3 5/6 = 23/6
C 0 0 1/3 4/3 = 13/3
______________________________________
The next wavelength choice is sample spectrum "B", wavelength "a", because
it is the largest residual. This procedure is continued until the residual
values in the physical property column become insignificant, and all of
the equations essentially are solved. Again, this row-reduction algorithm
is only one of many possible methods to perform such a statistical
analysis.
Once the optimal wavelengths at which to evaluate the actual samples are
selected, weighting or correction constants must be determined. The
weighting constants are used to statistically correct the actual
absorbance measurements which are taken at the selected wavelengths in
order to quantify the physical properties. The row-reduction algorithm
techniques disclosed in Honigs, D. E.; Hieftje, G. M.; Hirschfeld, T. B.
Appl. Spectrosc. 1983, 37, 491-497 may again be used to statistically
evaluate the pre-tested calibration samples in order to determine the
values of the weighting constants which, when used to correct the actual
absorbance measurements at the previously selected wavelengths, result in
an acceptably accurate reference value for the physical property being
quantified. Specifically, such weighting (or correction) constants are
represented by the solutions to the equations which have been solved in
the manner illustrated above (e.g., the previously unknown x and y
values).
Having determined the optimal wavelengths at which to make absorbance
measurements and the corresponding weighting constants in order to most
accurately quantify the physical property of the sample being evaluated,
the following relation results:
Ref=(WC(a).times.ABS(a))+(WC(a+1).times.ABS(a+1))+ . . .
+(WC(b).times.ABS(b)) (1)
where Ref is the reference value of the physical property being quantified,
WC(a) is a weighting constant determined by the statistical analysis to
best correlate to a selected wavelength, ABS(a) is the measured absorbance
of the sample at the same selected wavelength, and b is the number of
wavelengths determined by the statistical analysis to best quantify the
particular physical property of the sample. Equation (1) can be rewritten
follows:
##EQU1##
A spectrophotometer is used to record the absorbance spectra of an actual
sample for which the physical property in question is being quantified.
The absorbance values of the sample at each of the wavelengths previously
determined to best correlate with the data from the calibration samples
are then inserted in equation (1) or (2), corrected by the corresponding
weighting constants, and added together to result in a numerical reference
value representing the quantity of the desired physical property.
In sum, a basic embodiment of the invention is a method for quantifying a
physical property of a sample comprising the steps of (a) using a
statistical algorithm to determine which wavelengths in the near-infrared
spectrum optimally correlate to the particular physical property being
quantified; (b) using a statistical algorithm to determine numerical
weighting constants which are optimally correlated to the determined
wavelengths; (c) measuring with a spectrophotometer the absorbance of a
sample at each of the determined wavelengths; and (d) calculating
according to equation (1) or (2) a reference value for the physical
property of the sample.
Another embodiment of the invention comprises a method for simultaneously
quantifying a plurality of physical properties of a sample. In this
embodiment, the row-reduction algorithm is employed to evaluate a
representative field of calibration samples to determine which
wavelengths, or different sets of wavelengths, are optimally correlated to
each of the physical properties being quantified. Thus, for example, if
three physical properties of a sample are to be simultaneously quantified,
there may be three different wavelengths, or sets of wavelengths, in the
near-infrared spectrum at which absorbance measurements will be taken in
order to optimally quantify each physical property. The row-reduction
algorithm is also used to evaluate the field of calibration samples to
determine the values for weighting constants which optimally correlate to
each of the selected wavelengths in order to obtain statistically
acceptable or valid results.
Having determined the wavelengths, or sets of wavelengths for each physical
property at which to measure absorbance of the sample and the
corresponding weighting constants, the following relationships are used to
quantify the physical properties:
##EQU2##
where: Ref(1), Ref(2) and Ref(n) each represent reference values for
different physical properties being quantified; n is the number of
physical properties being quantified; WC(1), WC(2) and WC(n) each
represent the weighting constants determined to correlate to the
wavelengths, or sets of wavelengths used to quantify the associated
physical property; b, c and d represent the number of selected wavelengths
within the sets determined to optimally correlate to a particular physical
property; and ABS(1), ABS(2) and ABS(n) represent the measured absorbance
of the sample at each selected wavelength, or set of wavelengths,
correlated to particular physical properties. Equations (3), (4) and (5)
can be simplified as follows:
##EQU3##
A spectrophotometer is used to measure and record the absorbance spectra of
the actual sample for which the plurality of physical properties are being
quantified. The absorbance values of the sample at each of the selected
wavelengths, or set of wavelengths, corresponding to a first physical
property are then inserted in equation (6), corrected by the corresponding
weighting constants, and added together to result in a numerical reference
value representing the quantity of the first physical property. The
procedure is repeated for each of the physical properties being
quantified.
Thus, a second basic embodiment of the invention is a method for
quantifying a plurality of physical properties comprising the steps of:
(a) using a statistical algorithm, such as the row-reduction algorithm, to
select sets of wavelengths in the near-infrared spectrum which optimally
correlate to each of the physical properties being quantified; (b) using a
statistical algorithm, such as the row-reduction algorithm, to determine a
weighting factor corresponding to each of the selected wavelengths; (c)
measuring with a spectrophotometer the absorbance of the sample at each of
the selected wavelengths; and (d) calculating for each physical property
being quantified a reference value, the reference value depending upon the
measured absorbance of the actual sample at each wavelength within the
corresponding correlated set of wavelengths, the measured absorbance at
each wavelength being corrected by the corresponding weighting constant.
EXAMPLE
The methods and devices of the present invention were used to
simultaneously quantify the molecular heat, molecular weight and the
number of methyl groups per molecule in a variety of hydrocarbon mixtures.
Calibrations accurate to 1.2 kcal/mole for determining heats of formation,
1.5 g/mole for determining mean molecular weight, and 0.057
groups/molecule for determining methyl groups per molecule were obtained.
1. The Calibration Samples
Hydrocarbon mixtures were synthetically prepared by weighing aliquots of
reagent-grade benzene (Mallinckrodt) and cyclohexane (MC&B), and
spectroanalyzed iso-octane and n-heptane (Fisher) into gas-tight vials.
Ninety of the hydrocarbon mixtures, ranging from 0% to 100% concentration
of each hydrocarbon, were prepared as calibration samples for this
example. The error in each standard concentration was approximately 0.05%,
estimated by propagation of an error in weighing of 0.01 g.
The absorbance spectra of each of the calibration samples was recorded by a
Digilab FTS-15C Fourier-transform spectrophotometer equipped with a Si
beam splitter, a PbSe detector operated at 300.degree. K., and a CaF.sub.2
flow-through cell. The instrumental resolution was nominally 4 cm.sup.-1
and boxcar apodization was employed. Throughout the data collection, the
calibration cell holding the hydrocarbon mixture was fixed in position in
order to minimize any pathlength errors.
The correlation between a desired physical property and the near-infrared
spectrum was generated by the row-reduction algorithm disclosed in Honigs,
D. E.; Freelin, J. M.; Hieftje, G. M.; Hirschfeld, T. B. Appl. Spectrosc.
1983, 37, 491-497 set forth below as Exhibit a. Briefly, the row-reduction
algorithm is used to statistically evaluate the spectrum of each sample at
a large number of wavelength combinations until a particular combinations
reached which quantifies the desired physical property within an
acceptable degree of error. Each correlation was developed by dividing the
90 samples into calibration sets of 42 samples and
performance-verification sets of 48 samples.
Since in this example there are four chemical components or constituents
which sum to 100 percent of the sample and since three of the components
can vary independently, three wavelengths are enough to quantify the
physical properties of the hydrocarbon samples. However, one additional
wavelength is necessary to account for instrumental errors.
Initially, the calibration sets were evaluated for the best four analytical
wavelengths in the range of 750-2500 nm. 2000 wavelengths within this
range were searched. This initial evaluation of the calibration test
samples provided adequate results for quantifying molecular weight and
heats of formation, but unsatisfactory results for the determination of
methyl groups per molecule. It was determined empirically that increasing
the number of analytical wavelengths to six resulted in an improved
calibration for quantifying methyl groups per molecule.
The physical properties of the performance verification samples were then
quantified in accordance with equation (6) above. Reference values for
heat of formation, mean molecular weight, and methyl groups per molecule
were obtained by multiplying the absorbance value at the correlated
wavelengths of each hydrocarbon verification sample by the associated
weighting constant, and then adding the contributions from each component.
The reference values can be compared to the true heats of formations and
molecular weights of each of the pure hydrocarbons obtained from Neast, R.
C., Astle, M. J., Eds. "CRC Handbood of Chemistry and Physics", 60th
Edition, CRC Press; Boca Ratan, Fl 1979, incorporated herein by reference.
By propagation-of-error calculations the error of the reference values was
approximately 0.1%.
2. Results
The results of the spectrophotometric quantifications for heat of
formation, mean molecular weight, and the number of methyl groups per mole
are shown in FIGS. 1 through 3. Correlated analytical wavelengths and
weighting factors for the calibration samples are listed in Table I below.
TABLE I
______________________________________
Wavelengths and Weighting Coefficients used to
Spectrophotometrically Determine Heat of Formation, Mean
Molecular Weight, and Methyl Groups per Mole in a Series of
Hydrocarbon Mixtures.
Mean Methyl
Heat of Formation
Molecular Weight
Groups/Molecule
Wave- Wave- Wave-
length,
Weighting length, Weighting
length,
Weighting
nm Factors nm Factor nm Factors
______________________________________
2181 -3.8 2472 6.2 2346 -0.012
2150 9.4 2440 14.5 2323 -0.104
1958 -2.7 2319 -2.7 2319 0.097
1701 -2.9 1352 -10.8 2305 0.034
1753 -0.023
1671 0.002
______________________________________
The coefficients for mean molecular weight listed in Table 1 above
determine the mean number of micrograms per molecule in the sample. The
mean molecular weight is determined by dividing 1000 by the calculated
number of micrograms/gram. The verification statistics are summarized in
Table II, below.
TABLE II
______________________________________
Calibration results for the Spectrophotometric Determination
of Heat of Formation, Mean Molecular Weight, and Methyl
Groups per Molecule in a Series of Hydrocarbon Mixtures.
Range
Calibrated
Standard Error
Standard Error
of Samples
Property of Calibration
of Performance
Analyzed
______________________________________
Heat of 0.8 kcal/mole
2.0 kcal/mole
-51.5 to 19.8
Formation kcal/mole
including
pure benzene
Heat of 0.8 kcal/mole
1.2 kcal/mole
-51.5 to 2.3
Formation kcal/mole
excluding
pure benzene
Mean Molecu-
1.1 g/mole 1.5 g/mole 78 to 114
lar weight g/mole
Methyl 0.053 groups
0.057 groups
0 to 3 groups
Groups per
molecule molecule molecule
Molecule
______________________________________
From Table I one can quantify the physical property of a hydrocarbon sample
in a manner analogus to that illustrated in Eq 7:
##EQU4##
where Abs(x) is the sample absorbance at x nm. Similar equations derive
from Table I for determining mean molecular weight and methyl groups per
molecule.
For the determination of the heats of formation of the hydrocarbon mixtures
there are two results reported in Table II, one including and one
excluding pure benzene. This comparison was made because the calibration
sample with the largest heat of formation (0.95 Kcal/mole) was
considerably below the heat of formation of pure benzene (19.82
Kcal/mole). For the other physical properties the disparity between the
calibration samples and benzene was much smaller and the calibration was
therefore more reliable.
FIGS. 1-3 and Table II indicate clearly that the inventive methods and
devices can be used to accurately quantify the physical properties of
samples.
3. Discussion
It is noted that different wavelengths, or sets of wavelengths, were chosen
to determine each of the different physical properties. However, any one
of these wavelength sets could, if desired, be used to determine all of
the physical properties and chemical-constituent concentrations. However,
because the different physical properties place different emphasis on the
four components of the sample, the error of each must be weighted
differently in the overall optimization. This is better done by selecting
a different set of optimal analytical wavelengths for each physical
property being quantified.
In the case of the determination of methyl groups per molecule the optimal
wavelengths determined by the row-reduction algorithm include a pair that
are closely spaced (2323 and 2319 nm) with equal but opposite multipliers:
essentially a derivative. This type of measurement is particularly
efficient for small-peak-shift resolution, as is found often in the
severely overlapped carbon-hydrogen (C-H) stretch bands. The use of a
derivative as an adaptive response by the row-reduction algorithm solves
the measurement problem but increases the number of wavelengths required.
In addition to identifying the chemical nature of many samples, a
near-infrared spectrum contains quantitative information about the sample
constituents. Since it is possible with the inventive methods to quantify
the chemical constituents, it is also possible to determine any physical
property that has a first-order dependence on their concentration. The
heat of formation or mean molecular weight of a sample, for example, could
be independently determined by a near-infrared method calibrated for the
concentration of each of the sample constituents and by then substituting
those concentration values into the proper equation. The
multiple-linear-regression mathematics employed by the inventive methods
make a separate substitution step unnecessary; the invention deduces
automatically the exact relationship between the sample constituents and
the physical property of interest. This feature makes near-infrared
spectrophotometry extremely useful not only for quantifying physical
properties, but also for evaluating physical properties which are related
to the chemical constituents in an unknown manner, such as the "baking
quality" of flour.
If the present invention is used to measure the near-infrared spectrum of a
sample by diffuse reflectance, it is also possible to determine additional
information about the physical properties of that sample. For example,
changes in macroscopic texture and microscopic crystal structure will
change the albedo of the sample. This type of information allows
near-infrared reflectance methods to locate material defects and determine
the "hardness" of a sample.
In general, any sample property that is a second-order of higher function
of concentration cannot be directly determined by the above-disclosed
embodiments of the inventive methods and devices since the correlation
step employs only first-order mathematics. The exceptions to this rule are
properties which have a first-order relationship to a spectrum, even if
this relationship to concentration is different, such as that in hydrogen
bonding. Second-order functions can be accommodated in the present
invention by using a series of linear approximations or higher-order
regression mathematics. The present invention is thus able to determine
any physical property that is correlated with those chemical constituents
that respond to near-infrared radiation, as long as the property in
question is correlated to some compositional or other feature having a
significant near-infrared absorption.
While the above example describes certain methods of the present invention,
they are not to be construed as limitations. For example, the methods
described above may employ the evaluation of reflectance characteristics
as well as absorption characteristics. Further, if the precise wavelengths
as which to quantify the physical property of the sample are known, a
fixed wavelength photometer can be employed, instead of the more complex
spectrophotometers, to measure the absorbance or reflectance of the
sample. In addition, the inventive methods may be employed outside the
near-infrared region if appropriate for the types of samples being
examined. Thus, as one skilled in the art would recognize, many
modifications may be made in the methods of the present invention without
departing from its spirit or scope.
EXHIBIT A
[Title and Abstract Redacted]
INTRODUCTION
A. Overview. The application of near-infrared reflectance analysis (NIRA)
as an analytical technique has been concentrated mainly in the
agricultural area where it originated..sup.1-4 These agricultural
applications are characterized by the need to determine a limited number
of constituents in a very large number of individual but similar samples.
In contrast to this situation, samples encountered in most industrial
analytical laboratories are widely varied in kind and the number of ver | | |
