Automated process for permeability determinations of barrier resins

Permeability of structures consisting essentially of dispersions of barrier resins in permeable structural resins can be predicted by the application of near infrared spectroscopy, within the wavelength range of 600-2500 nm, especially 1100-2500 nm. The method requires establishing a correlation between base permeabilities of samples of a Training set and their near infrared spectra, developing from that correlation a predictive equation, verifying the accuracy of the predictive equation on samples of a Validation set, and applying the predictive equation to the determination of the permeabilities of unknown samples.

BACKGROUND OF THE INVENTION 
This invention relates to a process for quickly and reproducibly 
determining the permeability of structures made of certain barrier resin 
compositions. 
It is well known that certain resins such as, for example, polyamides, 
polyesters, polyvinyl alcohol, and ethylene/vinyl alcohol copolymers have 
low permeability to a variety of organic fluids, such as, for example, 
hydrocarbons and alcohols. Such resins, when used in applications where 
high permeability is undesirable, are often referred to as "barrier 
resins". In practical use, barrier resins are combined with resins having 
higher permeability to organic fluids but greater strength, especially 
greater impact strength, which in such applications are normally referred 
to as structural resins. Structures containing both a barrier resin and a 
structural resin are available in different forms. One such form is a 
laminar dispersion of barrier resin in a matrix of structural resin. 
Another is a composite containing at least one structural resin layer and 
at least one barrier resin layer, and which may in addition contain 
adhesive resin layers or layers of other materials. Barrier resin 
structures are very effective low permeability materials suitable for many 
uses, especially for containers such as bottles, paint cans, and gasoline 
tanks for automobiles. This last named use is growing very fast because 
substitution of plastic materials for metals effects weight savings, while 
at the same time eliminating gasoline tank corrosion. Additional 
advantages of gasoline tanks made of plastic materials are better 
utilization of available space, since such tanks can be molded in the 
exact desired shape, as well as the obvious superiority of blow molding 
plastic resins over bending and welding metal sheets. Many countries, 
including the United States, have approved in principle the use of 
synthetic materials in manufacturing gasoline tanks. 
A container which is to be used for storage or transportation of liquids 
evolving potentially hazardous or environmentally undesirable vapors must 
be manufactured from a very low permeability material; and, in fact, 
certain permeability criteria have been developed and are embodied in 
various government and industrial standards. Permeability is affected by 
even subtle changes in process variables, so that, contrary to the 
intuitive expectations, it is impossible to accurately predict in advance 
the permeability of a given barrier resin structure from the barrier resin 
content in such a structure and the nominal process conditions. It is, 
therefore, necessary to be able to ascertain on a regular basis whether 
container production runs produce products which satisfy such standards. 
This normally is done by placing a given liquid in a container, closing 
the container, leaving it for a specified period at a specified 
temperature, and weighing the container with the liquid at reasonable 
intervals until the end of the specified period. This method of 
determining the container's permeability is rather tedious and slow; it is 
not well suited for making quick production run determinations. 
It is, therefore, desirable to have available an automated, instrumental 
process for quickly and reliably determining container permeability, so 
that any departures from the standards can be readily recognized, and any 
necessary corrective action can be taken promptly. 
SUMMARY OF THE INVENTION 
According to this invention, there is provided a process for the 
determination of the permeability to organic fluids of a barrier resin 
structure comprising at least one barrier resin and at least one 
structural resin, said process involving the following steps: 
(a) establishing by independent means the permeability of each one of a 
statistically meaningful number of samples, divided into a Training set 
and a Validation set, of a particular barrier resin structure to a 
particular organic fluid, such permeability being designated base 
permeability; 
(b) making multiple scans at different locations of each sample of the 
Training set with a near infrared spectrometer operatively connected to a 
computer programmed to perform statistical analysis of data, to obtain by 
coaddition the spectral response of each sample--its transmittance, 
reflectance, or absorbance--at each wavelength within the range of about 
600-2500 nm; 
(c) statistically generating for the totality of the samples of the 
Training set a data matrix correlating their spectral responses at each 
wavelength with their base permeabilities previously established according 
to paragraph (a), to formulate a mathematical expression in the form of a 
predictive equation for calculating sample permeability from the spectral 
responses; 
(d) verifying the accuracy of the predictive equation obtained in step (c) 
by applying the equation to calculate the predicted permeabilities of the 
Training set; 
(e) measuring under the same conditions the spectral responses of the 
Validation set and applying the predictive equation obtained from the 
Training set to predict the permeability of each sample of the Validation 
set; 
(f) comparing the predicted permeability of each sample of the Validation 
set with its base permeability established according to paragraph (a); 
(g) if the results indicate that the predictive equation derived in step 
(c) does not predict the permeabilities of the Validation set at least as 
well as it predicts the permeabilities of the Training set, modifying the 
predictive equation in a statistically acceptable manner until it predicts 
the permeabilities of the Validation set at least to that degree; 
(h) if the predicted permeabilities of the samples of the Training set are 
not within a predetermined degree of error from their previously 
established base permeabilities, further modifying the predictive equation 
in a statistically acceptable manner until the resulting predictive 
equation predicts the permeability of the Training set within the 
predetermined degree of error; and 
(i) measuring under the same conditions the spectral response of a barrier 
resin structure of unknown permeability and applying the above predictive 
equation to its spectral response, to predict the permeability of said 
structure.

DETAILED DESCRIPTION OF THE INVENTION 
The term "structure" means a shaped article, which may be, for example, a 
container, a film, or a sheet. The term "container" is used in its 
broadest sense, to include any container that may be suitable for the 
storage or transport of fluids such as liquids or gases. In particular, 
this term will encompass, i.a., in addition to automobile gasoline tanks, 
such containers as bottles, cans, bags, pouches, tubes and pipes, tanks, 
and reservoirs. Films and sheets, of course, can be formed into 
containers. The structure of the highest importance is the container, but 
permeability determination need not be made on the whole container; it can 
be made on a fragment of a wall of the container, or of the film or sheet 
from which it was made. A whole container also can be subjected to its 
permeability determination according to this invention. In normal use, the 
container will be sealed or at least will be used in a manner which will 
minimize loss of fluid by simple evaporation, but this is neither a 
requirement nor a critical limitation of this invention. 
The base permeability of a container can be most conveniently determined by 
weight loss under some standar time, temperature, and pressure conditions. 
The permeability of a film or sheet can be determined, e.g., by forming 
the film or sheet into a sealed container or by instrumentally analyzing 
the concentration of fluid in a chamber separated from the source of the 
fluid by a partition formed of the film or sheet. 
Various barrier resin structures are known. Those include, i.a., laminar 
dispersions in structural resins and laminated or coextruded composite 
structures in which the barrier resin and the structural resin form 
separate layers, or a dispersion of barrier resin in structural resin 
which is laminated to a layer of the same or similar structural resin. 
Dispersions of barrier resins in permeable (structural) resins are known, 
for example, from U.S. Pat. Nos. 4,410,842 and 4,444,817 to P. M. 
Subramanian. Coextruded composite structures can be made, for example, as 
taught in U.S. Pat. Nos. 4,824,618 to Strum et al. and 4,800,129 to Deak. 
This near infrared spectroscopy technique, although particularly suitable 
for the determination of permeability to fluids of barrier resins 
associated with structural resins, would not be normally applied to the 
determination of permeability of barrier resins alone or of structural 
resins alone. While the near infrared spectroscopic technique could be 
utilized for the measurement of the permeabilities of barrier resins 
alone, or of structural resins along, other, less expensive but reasonably 
fast techniques are available for that purpose. 
Near infrared spectroscopy, however, is sensitive to the concentration and 
morphology of the barrier resin contained within the structural resin as 
well as to process conditions. It thus is commonplace to obtain different 
permeability values for compositionally identical barrier resin structures 
fabricated under slightly different conditions. 
It is, therefore, a unique and outstanding characteristic of the process of 
this invention that it can quickly and accurately predict permeabilities 
of barrier resin structures under any process conditions and detect 
departures from the standards, thus making it possible to immediately 
adjust the process conditions to attain the desired permeability levels. 
Typical barrier resins include, for example, polyesters such as 
poly(ethylene terephthalate) and poly(tetramethylene terephthalate), 
polyamides such as poly(hexamethylene adipamide), 
poly(epsilon-caprolactam), and copolymers of hexamethylene adipamide with 
epsilon-caprolactam, polyvinyl alcohol, copolymers of ethylene with vinyl 
alcohol, polyvinyl chloride, polyvinylidene chloride, and blends of two or 
more of the above resins; for example, blends of polyvinyl alcohol with a 
polyamide and of ethylene/vinyl alcohol copolymer with a polyamide. 
Structural resins, as contemplated by this invention, are permeable to 
organic fluids, especially to hydrocarbon liquids and vapors. Typical 
structural resins are homopolymers and copolymers of alpha-olefins and of 
1,3-dienes, and blends of two or more of the above resins as well as other 
hydrocarbon and chlorinated hydrocarbon resins having an alpha-olefinic 
unsaturation; for example, polyethylene, polypropylene, polyisobutylene, 
polychloroprene, polybutadiene, polystyrene, ethylene/propylene 
copolymers, and ethylene/propylene/1,3-butadiene terpolymers. All the 
typical structural resins and barrier resins are commercially available. 
Near infrared (NIR) spectroscopy is conducted with specialized computerized 
equipment known as the near infrared (NIR) spectrometer. There are several 
suppliers of such equipment, including NIRSystems, Silver Spring, Md; L. 
T. Industries, Inc., Rockville, Md.; and Bran+Luebbe Analyzing 
Technologies, Elmsford, N.Y. The equipment vendors normally supply with 
their equipment operating software, which permits the user to operate his 
or her NIR spectrometer and to analyze the data. However, for the purpose 
of this invention, the computer program needs to be adapted or amplified 
to satisfy the requirements of this process, and this can be done in 
several ways. 
The NIR spectrometer normally will be operated in either its transmittance 
or its reflectance mode. The former occurs when the source of near 
infrared radiation and the near infrared detector are located on the 
opposite sides of the sample, while the latter occurs when both the source 
and the detector are located on the same side of the sample. The 
transmittance mode may not be practical for thick or opaque samples or 
samples of filled or pigmented material. For these purposes, the so-called 
transflectance mode of operation, wherein a separate or integral reflector 
is employed, is considered to be a variant of the reflectance mode. 
Therefore, the reflectance mode will have potentially broader 
applications. The resulting response at each wavelength can be expressed 
in transmittance (T), reflectance, or absorbance (A) units, A being equal 
to log (1/T). When T=1, no absorption occurs; while, when T=0, infinite 
absorption occurs. 
FIGS. 1 and 2 are typical NIR plots (usually referred to as NIR scans) of 
absorbance vs. wavelength. These particular scans were obtained for a 
structure made of a barrier resin composition consisting of a laminar 
dispersion prepared from a pelletized blend of 45.7 weight percent of 
polyamide and 54.3 weight percent of compatibilizer in polyethylene 
structural resin. The polyamide was made by condensing 
hexamethylenediamine, adipic acid, and epsilon-caprolactam in such weight 
ratios that the product contained 80% of poly(hexamethylene adipamide) and 
20% of polycaproamide. The compatibilizer was high density polyethylene 
grafted with about 0.9 weight percent of fumaric acid. The dispersion 
contained 4 weight percent of the above barrier resin blend in 96 weight 
percent of high density polyethylene. The test structures were gasoline 
tanks, which were made by dry blending particles of the barrier resin 
blend and the structural resin and blow-molding at a melt temperature of 
225.degree.-230.degree. C. The test fluid was xylene, and the permeability 
of the container to this fluid, determined by weight loss, was 33.4 grams 
per mm of sample thickness per day per 1 square meter of sample surface at 
50.degree. C. These gasoline tanks contained no pigment. 
FIG. 1 represents the complete NIR scan over the wavelength range of less 
than 600 to 2500 nm, while FIG. 2 represents the preferred portion of the 
NIR scan from 1100 to 2500 nm. Absorbance is expressed in FIGS. 1-4 in 
Absorbance Units. One Absorbance Unit corresponds to a tenfold change in 
the transmittance of the sample relative to the reference signal. 
Transmittance is defined as the ratio of the radiant power transmitted by 
the sample to the radiant power incident on the sample. It is noted that 
absorbance exhibits over the indicated ranges several peaks and shoulders. 
The barrier resin structure in these scans was not pigmented and, 
therefore, is referred to as a natural color barrier resin structure. 
FIG. 3 again represents the complete NIR scan over the wavelength range of 
less than 600 to 2500 nm, while FIG. 4 represents the preferred portion of 
the NIR scan from 1100 to 2500 nm for a so-called "black" barrier resin 
structure, which was pigmented with carbon black. In this case, the scan 
of FIG. 3 appears to have considerably fewer peaks and valleys than the 
scan of FIG. 1, but this is due only to the scale of the plot, which also 
includes the very sharp minimum below 600 nm. When the 1100-2500 nm range 
is scaled up, as shown in FIG. 4, again numerous peaks and shoulders are 
observed. The particular barrier resin structure used in this experiment 
was the same as that used for the natural color samples shown in FIGS. 1 
and 2. 
The equipment used to generate the scan shown in FIG. 1 was NIR 
spectrometer Model 6500, supplied by NIRSystems, operatively connected to 
an IBM desktop computer PS/2 Model 50 loaded with software known as NSAS, 
also supplied by NIRSystems. 
There are many well known mathematical techniques for correlation of NIR 
spectral responses to accomplish development of quantitative chemical 
analyses. They include, for example, "Single-Term Linear Regression", 
"Multiterm Linear Regression", "Component Spectrum Reconstruction", and 
"Discriminant Analysis" methods explained in an article by W. R. Hruschka 
at pp. 35-55 of Near-Infrared Technology In The Agricultural And Food 
Industries, P. C. Williams et al., Editors, American Association of Cereal 
Chemists, Inc., St. Paul, Minn., 1987 ("Williams"). Other techniques 
include, for example, "Hruschka Regression", "Fourier Transform 
Regression", "Principal Component Regression", and "Partial Least Squares 
Regression" methods explained in detail in an article by H. Martens et al. 
at pp. 57-87 of Williams. In Chapter 3 of Multivariate Calibration, H. 
Martens et al., John Wiley & Sons, Ltd., Chichester, U.K., 1989, more 
techniques, including for example, "Univariate Calibration", "Bilinear 
Modelling", "Self Deconvolution", "Target Transformation Factor Analysis", 
"Rank Annihilation Method", "Stepwise Multiple Linear Regression", "Ridge 
Regression", "Nonlinear Regression", and "Nonparametric Regression" are 
taught. The "Neural Network" technique explained in D. E. Rumelhart et al. 
in Parallel Distributed Processing--Explorations in the Microconstruction 
of Cognition, Vol. 1. Foundations 1986; Vol. 2. Psychological and 
Biological Models, 1986; and Vol. 3. A Handbook of Models, Programs and 
Exercises, 1988, MIT Press, Cambridge, Mass., may also be applied. 
Although it is possible for a mathematician, scientist, or engineer to 
generate predictive equations for calculating permeability from NIR 
spectral scans of sample containers by applying the above mathematical 
techniques, either manually or by employing a self-contained computer 
program, it usually is simpler to employ computer programs supplied by 
manufacturers of NIR spectroscopy equipment. These programs provide data 
storage and retrieval as well as various data regression and report 
capabilities directly suited to the development of predictive equations 
from NIR spectral responses. Some commercially available software packages 
include, for example, "Near-Infrared Spectral Analysis Software" (NSAS) by 
NIRSystems, Inc., Silver Spring, Md.; "Unscrambler" by Camo A/S, 
Trondheim, Norway; "SpectraMetrix", "LightCal", and "LightCal Plus" by L. 
T. Industries, Inc., Rockville, Md.; "Spectra Calc" by Galactic Industries 
Corporation, Salem, N.H.; and "InfraAnalyzer Data Analysis System" (IDAS) 
and "Principal Component Analysis Program" (PCA-pc) by Bran+Luebbe 
Analyzing Technologies, Inc., Elmsford, N.Y. 
The preferred procedure for generating the permeability predictive equation 
uses the Partial Least Squares Regression (PLS) algorithms contained in 
NSAS version 3.07. FIGS. 5A and 5B represent a block diagram for this 
procedure, where the computer algorithm is enclosed within the broken 
lines. 
Barrier resin structure samples expected to have permeabilities within a 
predetermined range (as estimated, for example, from known permeabilities 
of barrier resin structures having similar compositions) are divided into 
"Training" and "Validation" sets in such a way that each set contains a 
statistically valid number of samples the permeabilities of which span the 
entire range. 
Base permeabilities, respectively, P.sub.bT and P.sub.bV, of a 
representative number of Training set and Validation set samples are 
determined by conventional means, as shown in Blocks 1-4 in FIG. 5A. 
Obviously, it is immaterial to the success of this invention whether the 
samples are divided into the Training set and the Validation set before or 
after their base permeabilities have been determined. 
All samples in these sets are scanned by NIR spectrometry within the 
selected range, either the full 600-2500 nm range or a smaller portion of 
the spectrum, usually 1100-2500 nm, as shown in Blocks 5 and 6 of FIG. 5B. 
In the preferred practice of this invention, each scan over the NIR 
wavelength range is replicated, usually 32 times, once per second, and the 
average spectral response at each wavelength is recorded. The particular 
number of replicates and the scan repetition rate are largely dependent on 
the particular spectrometer employed and are not a critical limitation of 
this preferred practice. It is recommended that both the Training and 
Validation sets be scanned at several locations in order to reduce the 
importance of morphology and gross reflectivity variations caused by the 
shape of the container. 
A predictive equation of the following form is assumed: 
EQU P.sub.p =a.sub.0 +a.sub.1 .multidot.r.sub.1 +a.sub.2 .multidot.r.sub.2 + . 
. . +a.sub.n .multidot.r.sub.n (1) 
where 
P.sub.p =predicted permeability of test fluid through the sample material; 
r.sub.1, r.sub.2, . . . r.sub.n =spectral responses at wavelengths 1, 2, . 
. . n; 
a.sub.0, a.sub.1, a.sub.2 . . . a.sub.n =constant coefficients. 
This equation is the starting point of the algorithm employed by the 
computer; Block 7, FIG. 5A. 
The PLS algorithm begins by presuming the existence of one loading factor; 
Block 8, FIG. 5A. Loading factors are related to the physical phenomena 
which contribute to production of error between the predicted permeability 
and base permeability. The PLS algorithm calculates the constant 
coefficients of the predictive equation (1) accounting for only one 
error-producing loading factor; Block 9, FIG. 5A. The predicted 
permeabilities for the Training set, P.sub.pT, are calculated from the 
predictive equation (1); Block 10, FIG. 5A. 
These P.sub.pT permeabilities are then compared with the respective base 
permeabilities, P.sub.bT, of the same samples. Ideally, the relationship 
between the predicted and base permeabilities, when the pairs are ordered 
numerically from smallest to largest, is linear. Therefore, predicted and 
base permeabilities can be correlated by any standard statistical method, 
including linear least squares regression, and the quality of the 
correlation can be determined by numerical evaluation of one or more 
appropriate statistical parameters, such as, for example, the correlation 
coefficient and sum of the squares of the residuals. Although different 
techniques can be used for this correlation, comparison of correlation 
coefficients has been found very satisfactory and is recommended. 
The correlation coefficient, R.sub.T, of the Training set is first 
evaluated, as shown in Block 11 of FIG. 5A. By the term "correlation 
coefficient" is meant the Pearson product moment correlation coefficient, 
R, which is a well known statistical value for measuring the association 
between two variables and which is calculated according to the following 
equation (2): 
##EQU1## 
where R=correlation coefficient 
m=number of samples 
X.sub.j =j-th value of variable X 
Y.sub.j =j-th value of variable Y 
As applied to this invention, X is the predicted permeability, P.sub.p ; Y 
is the base permeability, P.sub.b ; and m is the number of averaged scans. 
Similarly, predicted permeabilities, P.sub.pV, for the Validation set 
samples are obtained from Equation (1), as in Block 12, FIG. 5B. They are 
then statistically correlated with the respective base permeabilities of 
this set, the correlation coefficient for the validation set, R.sub.V, 
being calculated from the above Equation (2). This is shown in Block 13 of 
FIG. 5B. 
The statistical quality parameters for the correlation of base and 
predicted Training set permeabilities are compared to the similarly 
obtained parameters of the Validation set. In the particular case 
illustrated in FIGS. 5A and 5B, the correlation coefficients R.sub.T and 
R.sub.V are compared; see Block 14, FIG. 5B. If the Validation set 
correlation is not at least as good as the Training sample set correlation 
(that is, if the absolute value of R.sub.V is smaller than the absolute 
value of R.sub.T), either the system operator or the computer program 
itself instructs the PLS algorithm to add a further loading factor and 
repeat the numerical procedure for calculating new predictive equation 
constant coefficients (Block 14A, FIG. 5B). This process is repeated until 
the correlation between the predicted and base permeabilities of the 
Validation set is at least as good as the correlation of the Training set, 
from which it was derived. 
The correlation coefficient of the Training set, R.sub.T, is next evaluated 
to determine whether the quality of the predictive equation is 
satisfactory for the intended application, Block 15 of FIG. 5B. It is a 
well understood principle of statistics that the absolute value of the 
correlation coefficient will increase and approach unity as the quality of 
the predictive equation improves. It is the preferred practice to test 
whether the predictive equation produces a correlation coefficient at 
least equal to 0.9. If not, either the system operator or the computer 
program itself instructs the PLS algorithm to add a further loading factor 
and repeat the numerical procedure for calculating new predictive equation 
constant coefficients. When the correlation coefficient is at least 0.9, 
the calibration procedure is complete. Unknown samples can now be scanned, 
as shown in Block 16 of FIG. 5B, and the predictive equation can be used 
to calculate permeability. 
Naturally, one may elect to accept predictive equations which produce lower 
correlation coefficients than 0.9 for less critical applications, but even 
in that case the same general procedure would be used. 
The relative order in which the operations of Blocks 14 and 15 of FIG. 5B 
are performed is not critical; one may prefer to first determine whether 
R.sub.T is at least 0.9; if it is not, add further load factors until this 
result is obtained, and only then compare the absolute values of R.sub.T 
and R.sub.V. Likewise, Block 15 may be placed between Blocks 11 and 12, if 
desired, instead of following Block 14 or 13. 
Since Training set samples are preferably scanned at multiple locations, 
the PLS technique can minimize the prediction error attributed to scanning 
at different locations on samples by adding sufficient loading factors. 
Therefore, it is sufficient to scan unknown samples at only one location, 
thus making application of this invention to on-line production quality 
control simple, quick, and economical. 
Another technique for defining a predictive equation for calculating 
permeability from NIR measurements uses the Stepwise Multiple Regression 
(SMR) method implemented by the "Standard Regression" algorithm of the 
NSAS computer software. A block flow diagram for this procedure is shown 
in FIGS. 6A, 6B, 7A, and 7B, where the computer algorithm is enclosed by 
broken lines. 
In the SMR technique, the initial steps of selecting Training and 
Validation set samples and establishing their base permeabilities, 
P.sub.b, are the same as in the PLS technique and as shown in Blocks 1-4 
of FIG. 6A. Each Training set sample is scanned by the NIR spectrometer 
(Block 5, FIG. 6B). Preferably each NIR wavelength range scan is repeated 
multiple times, most preferably 32 times, once per second, and the average 
spectral response at each wavelength is recorded. It is a further 
preferred practice to scan sample structures at multiple positions. The 
coadded average spectral response for each Training sample structure is 
calculated (Block 6, FIG. 6B) by computing the sum of the recorded 
spectral responses at each wavelength obtained from the scans at each 
structure position and dividing the sum by the number of positions 
scanned. For example, assume that a sample structure in the form of a 
cube-shaped container is scanned at six positions, (that is, its top, 
bottom, and four sides); then the six recorded spectral responses at 600 
nm would be summed and divided by 6 to obtain the coadded average spectral 
response at 600 nm; the six recorded spectral responses at 601 nm would be 
summed and divided by 6 to obtain the coadded average spectral response 
at 601 nm, etc. 
Validation set sample structures are each similarly scanned at multiple 
positions and multiple times at each position, and the coadded average for 
each sample structure is calculated, as shown in Blocks 7-8 of FIG. 6B. 
The SMR method may be applied to the coadded average spectral responses 
directly. Practice has shown that the spectral responses when plotted 
against wavelength, as shown in FIGS. 1-4, for typical barrier resin 
structures, produce plots having shifting baselines (that is, the baseline 
from which the peaks rise, appears to shift across the wavelength range). 
It is a preferred practice of the SMR method to minimize or eliminate the 
error introduced by shifting baselines by correlating permeability to the 
first and second derivatives of coadded spectral response. Many derivative 
calculation techniques are available in numerical analysis literature to 
calculate derivatives of the plot of coadded spectral response versus 
wavelength. The method implemented by the NSAS version 3.07 "Standard 
Regression" algorithm requires selection of "gap" and "segment" 
parameters. The algorithm automatically selects an initial set of "gap" 
and "segment" parameters by default (Block 9 of FIG. 6A), from which the 
first and second derivatives of the plots of spectral response versus 
wavelength are calculated (Blocks 10-12, FIG. 6A; Block 13, FIG. 6B). 
As shown in Block 14 of FIG. 6B, the SMR method initially postulates a 
predictive equation of the form: 
EQU P.sub.p =a.sub.0 +a.sub.1 .multidot.r.sub.1 (3) 
where 
P.sub.p =permeability of test fluid through barrier resin structure; 
r.sub.1 =second derivative of spectral response at wavelength 1; 
a.sub.0 and a.sub.1 =constant coefficients. 
Values for constant coefficients are calculated by standard regression 
analysis of the data matrix consisting of the base permeabilities and 
second derivative spectral responses at each wavelength for each Training 
set sample; see Block 15 of FIG. 6B. All the Training set base 
permeabilities, P.sub.bT, thus are paired with the corresponding second 
derivative spectral responses at the first wavelength of the scanned 
range, and standard regression methods, such as linear least squares 
regression, are used to calculate the constant coefficients. Predicted 
permeability for each Training set sample, P.sub.pT, can be calculated 
from equation (3). All the predicted permeabilities and corresponding base 
permeabilities of Training set samples can be processed according to 
equation (2) to obtain a correlation coefficient, R.sub.T. This regression 
procedure is repeated for each wavelength of the scanned range, in turn. 
The wavelength which produces the largest absolute value of the 
correlation coefficient, .vertline.R.sub.T .vertline., is chosen as 
wavelength No. 1 of equation (3), as shown in Block 16 of FIG. 6B. 
According to Blocks 17-18 of FIG. 6A and 19 of FIG. 6B, the Validation set 
samples are used to evaluate the quality of the predictive equation. 
Having identified wavelength No. 1 and constant coefficients, the 
predicted permeabilities of the Validation set samples, P.sub.pV, can be 
evaluated from equation (3). Validation set predicted and base 
permeabilities are processed using equation (2) to obtain the correlation 
coefficient, R.sub.V. If the Validation set correlation is not at least as 
good as the Training sample set correlation (that is, if the absolute 
value of R.sub.V is smaller than the absolute value of R.sub.T), then the 
initial selection of wavelength No. 1 was not appropriate. The system 
operator must select from among the wavelengths considered in Block 16 the 
wavelength which provides the next largest absolute value of the Training 
set correlation coefficient, .vertline.R.sub.T .vertline., for the 
Training set, as shown in Block 20 of FIG. 6A. The procedure of Blocks 20 
and 17-19 is repeated until a wavelength is found at which the correlation 
between the predicted and base permeabilities of the Validation set is at 
least as good as the correlation of the Training set, from which it was 
derived. 
The correlation coefficient of the Training set, R.sub.T, is next evaluated 
to determine whether the quality of the predictive equation is 
satisfactory for the intended application (Block 21 of FIG. 6B). As in the 
PLS method, it is the preferred practice to test whether the predictive 
equation produces a correlation coefficient having an absolute value of at 
least 0.9. If it does, the predictive equation is deemed sufficiently 
accurate to be applied to unknown samples. The system operator can proceed 
to steps, represented by Blocks 32-34 of FIG. 7A and 35-36 of FIG. 7B, in 
which unknown samples are scanned; the coadded spectral responses and 
second derivative responses are calculated; and permeabilities are 
determined from the predictive equation. 
If the absolute value of the correlation coefficient for the predicted and 
base permeabilities of the Training set, .vertline.R.sub.T .vertline., is 
smaller than 0.9, as shown in Block 21 of FIG. 6B, a statistical technique 
is employed to determine whether addition of a term to the predictive 
equation (3) (that is, addition of a contribution from spectral response 
at another wavelength) is justified; see Block 22 of FIG. 6B. One such 
statistical test is based upon the weighted sums of squared residuals for 
each prospective model and is described in Statistical Treatment of 
Experimental Data, Chapter 15, pp. 332-341, by J. R. Green et al., 
Elsevier Scientific Publishing Company, New York, 1978. If addition of 
another term is not justified, new "gap" and "segment" parameters are 
selected by the system operator (Block 23, FIG. 6A), and the entire 
process of Blocks 10-21 is repeated. If statistical analysis justifies 
adding a term to the predictive equation, SMR postulates an equation with 
one additional term (Block 24 of FIG. 7A) of the form of equation (4): 
EQU P.sub.p =a.sub.0 +a.sub.1 .multidot.r.sub.1 +a.sub.2 .multidot.r.sub.2 +. . 
. +a.sub.k .multidot.r.sub.k (4) 
where 
P.sub.p =permeability of fluid through barrier resin structure; 
r.sub.1, r.sub.2, . . . r.sub.k =derivative (usually, second derivative) 
spectral responses at wavelength number k; 
a.sub.0, a.sub.1, a.sub.2, . . . a.sub.k =constant coefficients; 
k=k-th numbered term of the equation. 
When a k-th term is added to the predictive equation, previous, lower 
numbered wavelength selections, (that is, wavelengths numbered 1, 2, . . . 
, k-1) are retained. Standard multivariable linear regression techniques 
are applied to the matrix data arrays of the Training set base 
permeabilities and corresponding second derivative spectral responses at k 
wavelengths to calculate new constant coefficients a.sub.0, . . . , 
a.sub.k for predictive equation (4). The matrix data arrays are: 
##EQU2## 
where P.sub.bTm =base permeability of the m-th Training set sample, and 
r.sub.mk =second derivative spectral response of the m-th Training set 
sample at the k-th wavelength. 
For example, assume that 1250 nm, 900 nm, 2200 nm, and 1500 nm had been 
selected as wavelengths 1-4 and it was required to add a term to 
predictive equation (4). The second derivative spectral response at 600 nm 
is tentatively substituted for r.sub.mk. Linear regression is applied to 
the data matrices to identify constant coefficients a.sub.0 -a.sub.5. The 
predicted permeabilities, P.sub.pT, for each Training set sample are 
calculated from equation (4). All the predicted permeabilities and 
corresponding base permeabilities of the Training set samples can be 
processed according to equation (2) to obtain a correlation coefficient, 
R.sub.T. This regression procedure (Block 25, FIG. 7A) is repeated 
substituting 601 nm and each wavelength of the scanned range except 1250 
nm, 900 nm, 2200 nm, and 1500 nm, in turn, for wavelength k=5. 
The wavelength which produces the largest absolute value of the correlation 
coefficient, R.sub.T, is chosen as wavelength number k of equation (4), as 
shown in Block 26 of FIG. 7A. 
After the constant coefficients have been calculated for equation (4) that 
provides the highest R.sub.T for second derivative spectral responses at k 
specified wavelengths, the predicted permeabilities for the Validation set 
samples can be calculated (Block 27, FIG. 7B). Predicted and base 
permeabilities of the Validation set are processed using equation (2) to 
obtain the correlation coefficient, R.sub.V (Block 28, FIG. 7B). If the 
Validation set correlation is not at least as good as the Training set 
correlation (that is, if the absolute value of R.sub.V is smaller than the 
absolute value of R.sub.T), then the initial selection of wavelength k was 
not appropriate (Block 29, FIG. 7B). Another, previously unselected 
wavelength, which provides the next highest correlation coefficient for 
Training set predicted and baseline permeabilities is selected as 
wavelength k (Block 30, FIG. 7B). The steps represented by Blocks 27-29 
and 30 in FIG. 7B are repeated until predictive equation constant 
coefficients, a.sub.0 . . . a.sub.k, are found which cause the equation to 
predict Validation set sample permeability at least as well as Training 
set sample permeability. 
The correlation coefficient of the Training set, R.sub.T, is next evaluated 
to determine whether the quality of the predictive equation is 
satisfactory for the intended application; Block 31, FIG. 7B. As before, 
it is the preferred practice to test whether the predictive equation 
produces a correlation coefficient having an absolute value of at least 
0.9. If it does, the predictive equation is deemed sufficiently accurate 
to be applied to unknown samples. The system operator can proceed to the 
steps of Blocks 32-34 of FIG. 7A and 36--36 of FIG. 7B, in which unknown 
samples are scanned; the coadded spectral responses and second derivative 
responses are calculated; and permeabilities are determined from the 
predictive equation (4). 
If, however, the absolute value of the Training set correlation coefficient 
is less than 0.9, the predictive equation (4) must be further redefined by 
returning to the step of Block 22 of FIG. 6B. 
When using the SMR method, it is possible to scan unknown samples at single 
positions; however, it is preferred to employ the multiple-position 
scanning and coadded averaging procedures for unknown samples in the same 
way as done for the Training and Validation set samples. 
FIG. 8 is a plot of barrier resin structure permeability calculated for 
experimental gasoline tanks from NIR spectra according to the present 
invention vs. the independently established base permeability of samples 
of a natural color laminar dispersion of 7 weight percent of the same 
barrier resin blend in 93 weight percent of high density polyethylene as 
was used earlier for the purpose of FIGS. 1 and 2. The permeability data 
are expressed in grams of fluid per gasoline tank per day at 40.degree. C. 
Each X in this plot corresponds to a run in which some process variable 
was changed. 
Barrier properties depend not only on the amount of barrier resin in the 
dispersion but also on the degree to which the proper fabricating 
conditions have been attained. The extrusion/blow-molding conditions must 
result in a proper lamellar barrier structure. Variations in process 
temperature, shear conditions, extruder operating parameters, etc., lead 
to markedly different barrier properties. This is why a good quality 
control method is required. The data presented in FIG. 8 represent a run 
where extruder/blow-molding conditions were either deliberately or 
unintentionally varied, so that the samples would have varying 
permeabilities despite a constant barrier resin content in the dispersion. 
It can be seen that the plot, extrapolated by the least squares method, is 
a straight line, starting at the origin of the system of coordinates and 
bisecting the system of coordinates at a 45.degree. angle. This confirms 
the applicability of the process of the present invention to the 
prediction of permeabilities of compositionally identical samples 
fabricated under different conditions.