Method to characterize curing of epoxy with aromatic diamines

A method for determining the extent of polymerization of an epoxy system consisting of adding a fluorescent label, the label having a reactivity similar to the reactivity of the curing agent, to the epoxy system and measuring the fluorescence intensity during polymerization. The fluorescence intensity of the label at its emission maximum increases sharply with polymerization, allowing one to follow cure reactions in a quantitative way by measuring fluorescence, especially in the later stages of cure beyond gelation. The composition, reactivity ratio, activation energy and weight-average molecular weight can also be determined by adding a label, such as p,p'-diaminoazobenzene (DAA) or trans diamine-stilbene (DAS), to mimic the reactivity of the curing agent, such as diaminodiphenyl sulfone (DDS) or methylene dianiline (MDA), and measuring the UV-VIS spectra in addition to the fluorescence intensity. Reaction of the label with the epoxide produces spectrophotometric shifts which are deconvoluted based on the band assignments of model compounds to obtain compositional analyses of cure products.

BACKGROUND OF THE INVENTION 
This invention relates generally to a method of chemical analysis and 
particularly to a method for characterizing the curing of an epoxy. 
The structure and properties of epoxies are known to strongly depend on the 
extent of cure and physical aging which has taken place after the cure 
cycle is completed. A number of physicochemical techniques have been used 
or developed toward a better characterization of cure and physical aging 
phenomena in epoxies. Among them are such techniques as FT-IR 
spectroscopy, described by M. K. Antoon et al. in Polym. Comp., 2, 81 
(1981); thermal analyses described by G. L. Hagnauer et al. in ASC Symp. 
Ser., 221, 229 (1983); GPC (size exclusion chromatography), described by 
G. L. Hagnauer et al. in ASC Symp. Ser., 227, 25 (1983) and ASC Symp. 
Ser., 221, 193 (1983); microdielectrometry, described by N. F. Sheppard et 
al. in Proc. of the 26th SAMPE Symposium, Los Angeles, 65, (1981); 
torsional braid analyses described by J. B. Enns et al. in ACS Symp. Ser., 
203, 27-63 (1983); .sup.13 C solid-state NMR, described by A. N. Garroway 
et al. in Macromolecules, 15, 1051 (1982); thermally stimulated current 
measuement, described by T. D. Chang et al. in Polym. Eng. Sci., 22, 1213 
(1982); fluorescence, described by R. L. Levy et al. in ACS Org. Coat. 
Appl. Polym. Sci. Proc., 48, 116 (1983) and Wang et al. in ACS Polym. 
Mater. Sci. Eng. Proc., 49, 138 (1983); and ESR spectroscopy, described by 
A. Gupta et al. in J. Appl. Polym. Sci., 28, 1011 (1983). 
While these experimental techniques provide useful information on the 
extent of cure and on epoxy structure, there are certain limitations and 
disadvantages associated with each technique. For example, FT-IR fails to 
monitor later stages of cure when the epoxy peak disappears. The use of 
GPC and of size exclusion chromatography is limited to the early stages of 
the curing reaction. The fluorescence techniques measure the emission of 
the epoxy as a function of increasing viscosity, not the formation of 
reaction products. ESR techniques also primarily measure decreasing 
mobilities of the label with increasing cure and viscosity but provide 
only limited information on the reaction products. For example, Brown and 
Sandreczki in Macromolecules, 16 1980 (1983) observed different ESR 
spectra which may allow spectroscopic monitoring of the initial addition 
products of the reaction of an epoxy with a nitroxide monoamine, if the 
reactivity of the nitroxide is similar to that of a diamine. 
.sup.13 C MAS-CP (magic angle spinning-cross polarized) solid-state NMR is 
another technique for the characterization of polymeric solids. As 
Garroway et al. demonstrated, it can provide information on certain 
molecular motions in epoxy. It is not easy, however, to obtain 
quantitative compositional information on the reaction products by .sup.13 
C NMR in cross-linked polymers due to such complications as line 
broadening and spinning side bands. The fact that the peak intensity is 
not generally representative of the concentration in crosspolarization 
experiments is another problem. .sup.15 N NMR, in principle, may be more 
useful, but its sensitivity is poor because of the low natural abundance. 
The article entitled "A New Method to Characterize Curing of Epoxy with 
Aromatic Diamines by Azochromophore Labeling" by In-Joo Chin and Chong 
Sook Paik Sung in Macromolecules 12, 2603-2607 (1984) describes a new 
method to obtain quantitative compositional information on the curing of 
epoxy with aromatic diamines by azochromophore labelling. In this 
technique, a small amount of an azochromophore, such as 
p,p'-diaminoazobenzene (DAA), which has reactivity similar to the curing 
agent, such as diaminodiphenyl sulfone (DDS), is used to provide an 
indication of the extent of cure. As the epoxy is cured, .lambda..sub.max 
of the .pi..fwdarw..pi.* transition corresponding to the azo bond of the 
curing agent is red-shifted in a way that provides spectral discrimination 
for the cure products (cross-linkers, branch points, linear chains, chain 
ends and unreacted diamines). The accuracy of the compositional analyses 
depends on the proper assignments of .lambda..sub.max positions and the 
determination of the extinction coefficients for the various cure 
products. 
Epoxies formed with aromatic diamines such as DGEBA-DDS (diglycidyl ether 
of bisphenol A-diaminodiphenyl sulfone) are important for high-temperature 
applications. In the DGEBA-DDS system, at the stoichiometric ratio, there 
are five major species during curing. This is because the amine groups are 
the major reactive species, and the hydroxyl groups do not initiate 
epoxy-polymerization in uncatalyzed epoxy cured with aromatic diamines at 
the stoichiometric ratio. 
In order to understand cure mechanisms, kinetics, and structure/property 
correlations, it is important to know the relative concentrations of the 
primary reaction products during the course of the curing process. 
It is therefore an object of the present invention to provide a means for 
determining the extent of cure in applications utilizing epoxies of 
varying thickness and in particular on metallic substrates in situ. 
It is another object of the present invention to provide a process for 
determining the relative concentrations of the primary reaction products 
produced during the curing of epoxies. 
It is yet another object of the invention to provide a sensitive method for 
determining the reactivity ratios, the activation energy, and the 
weight-average molecular weight of the reaction products produced during 
the polymerization of the epoxy. 
SUMMARY OF THE INVENTION 
The present invention is a method, and labelled epoxy system for use in the 
method, for monitoring polymerization of the epoxy system. The invention 
is based on the discovery that epoxy labelled with an azobenzene dye, an 
azonaphthalene dye, a benzylidene-dianiline dye or a conjugated stilbene 
dye exhibits very sensitive changes in fluorescence intensity 
corresponding to emission by the label as a function of cure extent. The 
label should be selected to have a reactivity similar to that of the 
curing agent. As shown by the following examples using three different 
epoxy systems, fluorescence intensity at the emission maximum of the label 
increases sharply after gelation, allowing for sensitive cure monitoring 
during the later stages of cure. 
By combining this method with the method of monitoring the relative 
composition of cure products utilizing the deconvolution of the UV-VIS 
spectra during polymerization of the epoxy system, parameters 
characteristic of cure kinetics and mechanisms such as cure product 
composition, reactivity ratio of primary amine versus secondary amine, 
initial rate constants and activation energy may be obtained.

DETAILED DESCRIPTION OF THE INVENTION 
Fluorescence due to a chromophore label in an epoxy system increases 
sharply due to the increasing fluorescence quantum yield of cure products 
containing tertiary amines. Fluorescence intensity is therefore used to 
determine the extent of cure, as well as to estimate composition, based on 
kinetic differential equations. UV-VIS spectral deconvolution can also be 
used to determine cure extent. 
The method of determining the extent of curing of an epoxy system by adding 
a chromophore label to the system and measuring the fluorescence intensity 
is applicable to any multifunctional epoxy system. The chromophore label 
should be selected to have a reactivity similar to the reactivity of the 
epoxy curing agent. Fluorescence is determined at the emission maximum of 
the chromophore label. 
In examples utilizing DGEBA-DDS, DGEB-DDS and DGEB-MDA epoxy systems 
labelled with DAA or DAS, fluorescence was used to determine relative 
composition of cure products, the extent of cure, or for comparison with 
the theoretically predicted weight average molecular weight and soluble 
fractions. UV-VIS and IR techniques were also used to determine the extent 
of cure in the epoxy systems. Analysis of the UV-VIS spectra and the 
fluorescence spectra allows one to determine the cure product composition, 
reactivity ratio of primary amine versus secondary amines, initial rate 
constants and activation energy. Since IR and thermal analyses suggested 
that DAA reacts a little faster than DDS, a calibration curve is 
constructed to correct for differences in the reactivities between the 
label and the curing agent. 
Epoxy networks studied included DGEBA-DDS, DGEB-DDS, and DGEB-MDA epoxy. 
The first epoxy, DGEBA epoxy (diglycidyl ether of bisphenol A) has a 
maximum T.sub.g of 215.degree. C. which leads to a complete cure, subject 
to degradation. When cured below 215.degree. C., vitrification occurs some 
time after gelation (e.g., 150 minutes at a cure temperature of 
160.degree. C.) according to its T-T-T diagram. Since there is little 
progress in the cure reaction after vitrification, the extent of cure is 
limited. The second epoxy, DGEB epoxy (diglycidyl ether of butane diol), 
has a maximum T.sub.g of about 80.degree. C. The cure reaction of DGEB can 
progress much further at cure temperatures above 80.degree. C. due to the 
absence of vitrification. 
The polymerization of these epoxy systems were characterized as follows, 
although such characterization is not required to practice the method of 
determining the extent of cure by measuring the fluorescence intensity of 
the chromophore label. First, the quantitative composition of each product 
over a wide range of cure extents were obtained for each of the epoxy 
networks cured at three isothermal temperatures. The reactivity ratio of 
the primary amine and the secondary amine with the epoxy group were then 
determined from this experimental data. The reactivity ratio is predicted 
to have a strong effect on the cure process including parameters such as 
gel time, molecular weight and the elastically active network chains. The 
activation energy is estimated from the initial slopes of the rate 
constants of the epoxy-primary amine reaction. The data are then compared 
assuming the weight average molecular weight as a function of cure using 
Miller and Macosko's recursive theory for network, described in 
Macromolecules, 13, 1063 (1980). Predicted soluble fractions are also 
compared with the composition of cure products. 
The total fluorescence intensity by the DAA or DAS label at its emission 
maximum increases sharply as the cure proceeds. This behavior of DAA is 
not due to the viscosity change, but rather to the increasing fluorescence 
by the cure products. For DAS, fluorescence increase is due to viscosity 
as well as the cure reactions. The observed fluorescence intensities per 
mole of the model compounds representing each cure product in the DGEB-DAA 
and DGEBA-DAA epoxy system are in the following ratios when excited at 456 
nm: cross-linker (1400):branch point (1100):linear chain (18):chain end 
(9): DAA (1). Assuming the above ratios and using the known concentration 
of each cure product by deconvolution of UV-VIS spectra, the observed 
overall fluorescence intensity can be modeled as the sum of contributions 
from each cure product. Thus, fluorescence can be used to monitor cure 
reactions in DAA labelled epoxy. 
In the following examples, the extent of cure of DGEBA-DDA, DGEB-DDA and 
DGEB-DDS epoxy was determined by the fluorescence method. Using the ratio 
of the amine functionality estimated from UV-VIS data, the composition of 
cure products at a given fluorescence intensity value were also estimated. 
The results are compared with those obtained by UV-VIS spectral 
deconvolution, as described by the article entitled "A New Method to 
Characterize Curing of Epoxy with Aromatic Diamines by Azochromophore 
Labeling" by In-Joo Chin and Chong Sook Paik Sung in Macromolecules 12, 
2603-2607 (1984). 
EXAMPLE OF CHARACTERIZING THE POLYMERIZATION OF DGEBA-DDS AND DGEB-DDS 
LABELLED WITH DAA 
1. Synthesis of Model Compounds for determination of the quantitative 
composition over a wide range of cure extents 
p,p'-Diamino azobenzene (DAA) from Eastman Kodak Chemical, Rochester, NY 
was purified by passing it through basic alumina columns. This method of 
purification leaves little residue in a TLC plate in comparison to DAA 
recrystallized from toluene and acetone. Purified DAA has a melting point 
in the range of 238.degree. C. to 241.degree. C. 
1,2-Epoxy-3-phenoxypropane (glycidyl phenyl ether, GPE) from Aldrich 
Chemical Co., Milwaukee, WI was used without further purification. 
Model compounds were made by reacting DAA and GPE at 145.degree. C. under 
N.sub.2 with a varying excess of GPE. FIG. 1 shows the chemical structures 
of the major model compounds expected from this reaction. In order to 
obtain intermediate cure products, DAA and GPE were reacted in 1:4 molar 
ratio for 10 or 30 minutes at 145.degree. C. After the reaction products 
were developed with a mixture of benzene:acetone:diethyl amine (16:3:1) 
five times, three well-separated spots in a TLC plate were seen. The top 
spot corresponds to DAA and the two lower spots (Fraction A and B) were 
purified and their properties summarized in Table 1. 
In order to obtain products of the later stages of the reaction, DAA was 
reacted with a large excess of GPE (6, 8, or 30 fold excess) for periods 
up to 4 hrs. at 150.degree. C. under N.sub.2. The major reaction products 
(Fraction C and D) appeared between Fraction A and B after developing 4 
times with a 13:1:1 mixture of benzene:acetone:diethylamine. The reaction 
mixture was initially fractionated by flash chromatography using silica 
gel at a pressure of 25 lbs/in.sup.2 with the same solvent mixture 
described above. Out of the total fractions collected from flash 
chromatography, mother liquids of fractions 11 to 19 were combined after 
adding a 1:1 mixture of petroleum ether and ethanol to precipitate an 
orange powder. Preparatory TLC was used to separate Fraction C and D from 
this mother liquid by the same solvent mixture after developing 8 times. 
Their physical characteristics are also summarized in Table I. 
TABLE I 
__________________________________________________________________________ 
Physical Characteristics of the Fractions 
Obtained by Reaction of DAA and GPE 
Nitrogen 
Fraction 
Color M.P. Mass Spec 
(cal'd/obs) 
UV-VIS/.mu.m 
__________________________________________________________________________ 
A Brown &lt;70.degree. C. 
m.w. 362 obs. 
15.46/13/79 
420 
B Reddish 
185-6.degree. C. 
m.w. 512 obs. 
10.93/10.75 
445 
C Yellowish 
177.degree. C. 
m.w. 662 not enough for 
458 
(small peak) obs. 
analysis 
D Orange 
172.degree. C. 
not available 
6.39/6.49 
460 
__________________________________________________________________________ 
*Calculated based on the assumption that the Fraction A, B, and D 
correspond to the Model compounds 1, 2, (or 3) and 5, respectively. 
**The main .lambda..sub.max is indicated while there were shoulders 
present in some fractions. The extinction coefficient at the main peak wa 
approximately 4 .times. 10.sup.4 moles/cm, independent of the fractions. 
Fractions A, B, C and D obtained from model reactions were further analyzed 
by reverse phase HPLC using a Waters Associate, Milford, MA analytical 
system interfaced with a Spectra Physics data system. Reverse phase 
(Bondapak C.sub.18) columns were employed, using a solvent programmer 
gradient and a varying amount of acetonitrile in water. An ultraviolet 
detector set at 280 nm was used. 
2. Cure composition from analysis of the UV-VIS spectra 
DGEBA was recrystallized from saturated methyl ethyl ketone solution by 
seeding it with purified DGEBA crystals and leaving it in the freezer 
(-15.degree. C.) for one to two weeks. DAA was recrystallized from toluene 
and acetone. DDS and DGEB were purchased from Aldrich and used without 
purification. 
In typical cure monitoring studies, a small amount of DAA (approximately 5 
to 7 mg or about 0.1% by weight for UV-VIS studies and 0.01% by weight in 
most fluorescence studies) was mixed with a stoichiometric mixture of 
DGEBA (5.0 g) or DGEB (2.98 g). DDS (1.825 g) was then added and the 
mixture heated with a magnetic stirrer at 120.degree. C. for 5 minutes. 
Two circular quartz plates were clamped together with two thin Mylar films 
(1.5 mil) on the edges leaving a center space for sample. The clamped 
quartz plate with Mylar spacers were dipped into epoxy heated to 
100.degree. C. The sample enters the center space by capillary action. 
UV-VIS spectra and fluorescence spectra were measured after curing the 
epoxy in an oven for a specific time and cooling the sample to room 
temperature. Fluorescence was measured with a 1 nm wide excitation slit 
and a 10 nm wide emission slit using a Perkin-Elmer MPF-66 spectrometer 
with a Model 7500 Data Station. UV-VIS spectra were obtained with a 
Perkin-Elmer Diode Array (Model 3840) System with a Model 7500 Data 
Station. The area under the UV-VIS peak was used to calibrate for 
concentration and thickness changes during cure to obtain the relative 
fluorescence intensity. UV-VIS spectra were deconvoluted with a computer 
program assuming a Gaussian distribution curve for each cure species. The 
.lambda..sub.max 's of the various cure products were assigned 410, 420, 
445, 460 and 470 nm, respectively. 
The model compounds were analyzed as follows: Table 1 shows the physical 
characteristics of Model Compounds, Fractions A to D, which were purified 
by thin layer chromatography after reactions of DAA and GPE (in varying 
excess) at 145.degree. C. under N.sub.2. There is a distinct color change 
as the fractions change from A to D. Fraction A is brownish as is DAA 
itself, while Fraction B is reddish. Fractions C and D are yellow and 
orange, respectively. Results of nitrogen analyses are close to the 
calculated results assuming that Fraction A, B, or D corresponds to the 
Model compound 1, 2 or 5, respectively, as shown in FIG. 1. The UV-VIS 
spectrum shows shoulders in addition to the main absorption peak. 
In order to ascertain if Fractions A to D are pure, reverse phase high 
pressure liquid chromatography using mixtures of acetonitrile and water as 
the mobile phase was carried out. A starting gradient of 
acetonitrile:water of 50:50 was used. DAA appears at 3.52 (76%) while GPE 
appears at 3.80. Fraction A shows a main peak at 5.72 (91%) and several 
small impurity peaks &lt;2% each). Fraction B shows its main peak at 7.26 
(95%). Fraction C shows four peaks between 7 to 9, with two major peaks at 
7.80 (68%) and 8.48 (16%). Fraction D shows a main peak at 7.20 (81%) and 
a small peak at 8.44 (7%). 
While Fractions A and B are relatively pure, Fractions C and D are 
certainly mixtures. Closely-overlapping peaks for Fractions C and D were 
spread out by using a different starting gradient (80/20 ratio of 
acetonitrile to water). After the major peak was separated, the UV-VIS 
scan was taken in the HPLC instrument by switching the UV-VIS detector to 
the scanning mode. The maximum absorption for the major peak for the 
Fractions C and D is about 460 nm and 470 nm, respectively. For Fractions 
A and B, the absorption maxima were 420 nm and 445 nm, respectively. Since 
Fraction B is quite pure, it could be either model compound 2 or 3. These 
.lambda..sub.max positions, as summarized in Table II, were used in the 
deconvolution of the peaks obtained in the epoxy system. The extinction 
coefficient of about 4.times.10.sup.5 mole/cm was measured regardless of 
the fractions so that an equal extinction coefficient was assumed in the 
deconvolution of the curves. 
TABLE II 
______________________________________ 
Positions of .lambda..sub.max for Model Compounds 
Positions of DAA and GPE 
Model Compound .lambda.max (nm) 
.DELTA..lambda. 
______________________________________ 
DAA/(PP) 410 0 
1st (PS) 420 10 
2nd (SS) 445 35 
3rd (PT) 
4th (ST) 460 50 
5th (TT) 470 60 
______________________________________ 
*refer to FIG. 1 for chemical structure. Designation in parentheses: P is 
primary amine, S is secondary amine and T is tertiary amine. 
FIG. 2 compares UV-VIS spectra obtained as a function of cure time in 
DGEBA-DDS (FIG. 2a) and DGEB-DDS (FIG. 2b) at 160.degree. C. In both sets 
of sepctra, significant red shifts are observed with increasing cure time. 
In DGEBA-DDS epoxy, the matrix gels after about 50 minutes of cure and 
vitrifies after 150 minutes of cure. The cure reaction is quenched after 
vitrification. As a consequence, UV-VIS spectra in DGEBA-DDS matrix does 
not show much change after vitrification, as shown by "e" in FIG. 2a 
corresponding to 300 min. cure time. In contrast, no vitrification occurs 
at 160.degree. C. in DGEB-DDS epoxy since its maximum T.sub.g is only 
about 80.degree. C. The cure reaction for the DGEB-DDS epoxy has been 
pushed further, as indicated by additional red shifts shown in "e" of FIG. 
2b. 
In order to insure that these spectral shifts are due to cure reactions and 
not to the changes in the matrix (e.g., polarity change as a function of 
cure), UV-VIS spectra of the model compound representing cross-linkers in 
DGEBA-DDS epoxy were run as a function of cure at 160.degree. C. Any 
spectral shift in this case would be due to the matrix change since the 
cross-linkers cannot react any further. Only a negligible (&lt;5 nm) spectral 
shift was observed. The spectral shifts obtained in DAA labelled epoxy 
were therefore interpreted as arising from cure reactions only. 
Table III summarizes the results on the composition of cure products by 
deconvolution of UV-VIS spectra with a computer program by assuming 
.lambda..sub.max positions of the model cure products according to Table 
II and a Gaussian distribution curve for each species. The error in 
resolving closely overlapping peaks in the spectra can be significant, 
especially when the cure is intermediate, for example, as with "b" and "c" 
in FIGS. 2a and 2b, however, the curve is fitted until tthe overall error 
calculated by the program is below two percent. The error in the 
composition of each cure product can still be as large as several percent, 
since the composition, given in Table III, corresponding to a certain cure 
time may not be an unique solution to the particular spectrum. 
The computer program used in these examples is attached as part of the 
specification. Similar programs for deconvolution of the spectra are 
commercially available. 
TABLE III 
__________________________________________________________________________ 
Composition of Cure Products in DGEB-DDS and DGEBA-DDS 
Epoxy as a Function of Cure Time at 160.degree. C. 
Extent of Amine 
Cure Time 
Cure Products (%) Reaction 
Epoxy (min.) 
A.sub.PP 
A.sub.PS 
A.sub.SS + A.sub.PT 
A.sub.ST 
A.sub.TT 
(.epsilon.a) 
__________________________________________________________________________ 
DEGB-DDS 
0 78 20 2 0 0 .059 
5 44 34 14 6 2 .219 
10 33 33 16 11 7 .318 
20 13 20 32 22 14 .510 
30 6 12 20 31 31 .676 
45 2 8 18 33 40 .750 
70 2 4 17 36 41 .775 
100 1 5 13 30 52 .815 
150 1 5 11 21 62 .848 
300 1 3 10 37 47 .814 
800 1 3 13 34 49 .813 
DEGBA-DDS 
0 75 25 0 0 0 .063 
5 61 20 9 6 5 .183 
10 35 41 9 9 5 .270 
15 25 28 36 5 5 .343 
30 10 17 17 23 34 .636 
45 8 10 23 25 33 .653 
60 9 15 19 25 33 .646 
100 10 15 26 25 23 .667 
150 10 15 15 29 27 .675 
300 8 14 23 29 27 .638 
140 7 20 12 20 42 .680 
__________________________________________________________________________ 
The last column of Table III lists the extent of amine reaction 
(.epsilon..sub.a) as defined by the following equation: 
EQU .epsilon..sub.a =[A.sub.ps +2(A.sub.ss +A.sub.pt)+3A.sub.st +4A.sub.tt ]/4 
(1) 
where A.sub.ps, A.sub.ss, A.sub.st or A.sub.tt corresponds to the 
fractional amount of cure products, namely chain ends, linear chains, 
branch points or cross-linkers, respectively. The cure products are shown 
in FIG. 3. A.sub.pp is the fraction of unreacted diamine. 
As demonstrated by Table III: the fractions of branch points and 
cross-linkers increase with cure time for both epoxy matrices, as 
predicted by the spectral shifts of FIG. 2, and the cure reaction of 
DGEBA-DDS epoxy seems somewhat slower than DGEB-DDS, expecially at long 
cure times, as shown by the values of the cure products as well as by 
comparing the overall extent of amine reaction (.epsilon..sub.a) versus 
cure time (minutes) for both epoxy systems DGEB-DDS and DGEBA-DDS when 
cured at 160.degree. C. In DGEBA-DDS, the maximum .epsilon..sub.a is only 
about 70%, presumably due to quenching by vitrification. Even in DGEB-DDS 
where vitrification does not occur at the cure temperatures, 
.epsilon..sub.a only reaches about 85% at this temperature. 
The extent of amine cure for both epoxy systems is temperature dependent, 
as shown by a graph of .epsilon..sub.a versus time of curing (minutes) at 
140.degree. C., 160.degree. C., and 180.degree. C. At early stages of the 
cure, the effect of higher temperature is quite pronounced, leading to 
greater cure extent. However, at later stages of cure, the temperature 
does not have much effect, especially for DGEBA epoxy, leading to a 
plateau in the overall extent of reaction. This phenomenon is undoubtedly 
due to the vitrification occurring in DGEBA epoxy in comparison to the 
absence of vitrification of DGEB epoxy. The maximum .epsilon..sub.a 
obtained for DGEB-DDS when cured at 180.degree. C. is about 95%. 
3. Analysis of the cure kinetics and mechanisms 
Since epoxy homopolymerization may be neglected in the absence of 
catalysts, the major cure reactions can be assumed to be the reactions 
between epoxide and amine groups, as shown in FIG. 3. The kinetic scheme 
defines the rate constant k.sub.1 as due to the conversion of primary 
amine to the secondary amine while k.sub.2 is due to the conversion of 
secondary amine to the tertiary amine. 
Based on FIG. 3, one can write a series of kinetic differential equations, 
as described by Dusek et al in J. Polym. Sci., Symp. No. 53, 29 (1975), as 
follows: 
##EQU1## 
where [b] is the concentration of unreacted epoxy groups. 
Solving the above equations, one can obtain the fraction of each cure 
species only as a function of the reactivity ratio of k.sub.2 /k.sub.1 and 
the fraction of unreacted diamine (A.sub.pp): 
##EQU2## 
where r=k.sub.2 /k.sub.1, p=1/(1-r/2) and q=(1+r/2)2. 
The overall extent of amine reaction (.epsilon..sub.a) written in terms of 
App and r only, is as follows: 
EQU .epsilon..sub.a =1-[1/(2-r)][(1-r)A.sub.pp 1/2+A.sub.pp r/4](13) 
A calculated fraction of each cure product and of the unreacted diamine is 
plotted as a function of .epsilon..sub.a, as shown in FIG. 4. The 
reactivity ratio, r, is assumed to be 0.1 in FIG. 4(a) and 2 in FIG. 4(b). 
Comparing these two figures, it becomes obvious that the smaller the r 
value, the greater the magnitude of A.sub.ps, A.sub.ss and A.sub.st. When 
r=2, A.sub.pt becomes noticable while it is negligible when r is less than 
one. At smaller value of r, A.sub.pp also decreases faster while A.sub.tt 
increases slower than at greater value of r. 
The r value has a strong effect on many structural parameters of the epoxy 
network. The fraction of each cure product is deconvoluted from the UV-VIS 
spectra obtained at three cure temperatures (140.degree., 160.degree. and 
180.degree. C.) and plotted as a function of the extent of amine reaction 
in FIGS. 5a and 5b. As shown in FIG. 5a, experimental data are only 
available up to about 75% reaction due to vitrification occurring in 
DGEBA-DDS epoxy. In contrast, experimental data are available up to 95% 
reaction in DGEB-DDS epoxy. Comparing the theoretical prediction of the 
composition of cure species as a function of amine reaction according to 
equations 8-12 for a reactivity ratio of 0.1 with the experimental 
composition of cure species as a function of extent of amine reaction, 
shown in FIGS. 5a and 5b, allows one to determine the best fit r, or 
reactivity ratio to be used to deconvolute the spectra. The theoretical 
curves according to the equations 8-12, corresponding to r of 0.5 or 2, 
are plotted. The r value which seems to describe the experimental points 
best, in view of the range of experimental error, is then determined. As 
demonstrated, this is a r value close to unity. Thus, reaction rates of 
primary amine-epoxy and secondary amine-epoxy are practically 
indistinguishable in this system. 
k.sub.1 is then calculated from the kinetic equation (2). In order to 
integrate Eqn. (2), [b] (concentration of unreacted epoxy) and [A.sub.pp ] 
are expressed in terms of .epsilon..sub.a. 
By definition 
EQU 1-.epsilon..sub.b =[b/4] 
Rearranging, the above equation becomes 
EQU [b]=4-4.epsilon..sub.b (14) 
In a stoichiometric mixture, .epsilon..sub.a =.epsilon..sub.b. For the case 
of r=1, Eqn. (13) is reduced to 
EQU .epsilon..sub.a =1-[A.sub.pp ].sup.1/4 (15) 
Rearranging Eqn. (15) leads to 
EQU [A.sub.pp ]=(1-.epsilon..sub.a).sup.4 (16) 
Substituting Eqns. (14) and (16) into Eqn. (2), 
##EQU3## 
Rearrangement of Eqn. (17) leads to 
##EQU4## 
Plotting .epsilon..sub.a /(.epsilon..sub.a -1) versus time for DGEBA-DDS 
epoxy at three cure temperatures demonstrates that at cure times beyond 
gelation, the reaction rate constant which is proportional to the slope of 
these curves is clearly reduced. By drawing a straight line through the 
first few data point for the slope, k.sub.1 is estimated to be 
5.4.times.10.sup.-3, 1.3.times.10.sup.-2 and 3.1.times.10.sup.-2 
min.sup.-1 at 140.degree. C., 160.degree. C., and 180.degree. C., 
respectively. 
An activation energy of 15.7 Kcal/mole and a pre-exponential factor of 
1.2.times.10.sup.6 min.sup.-1 were estimated from an Arrhenius plot 
combining the data for both epoxy matrices. 
4. Fluorescence Studies 
The inherent fluorescence of the epoxy matrix itself is not useful to 
monitor cure reactions, as shown by the following: When excited at around 
320 nm, both DGEBA-DDS and DGEB-DDS are highly fluorescent with an 
emission maximum around 370 to 380 nm. However, when the fluorescence 
intensity is calibrated for thickness fluctuations, the fluorescence 
intensity is constant with the extent of cure. 
In contrast, when the DAA label is excited, for example at 456 nm, a 
strongly cure dependent behavior of fluorescence intensity is observed. 
FIGS. 6a and 6b shows such fluorescence spectra for DGEBA-DDS-DAA and 
DGEB-DDS-DAA epoxy matrices respectively in the spectral range of 450 nm 
to 800 nm. In both epoxy matrices, at zero cure time, hardly any 
fluorescence is observed. But with increasing cure time, fluorescence with 
a broad emission peak around 560 nm increases. At long cure times, the 
emission peak seems to have red-shifted slightly, by 5 to 10 nm. This 
small red shift is in sharp contrast to much larger red shifts observed in 
UV-VIS spectra, shown in FIGS. 2a and 2b. Changes of polarity in the 
solvent medium is known to cause large shifts in emission spectra. 
Therefore, one can conclude that polarity did not change much as the epoxy 
cured. This trend was also suggested by small shifts in UV-VIS spectra by 
the model compound representing a cross-linker. 
In order to quantify the fluorescence intensity changes, relative 
fluorescence intensity at 560 nm (after dividing by the UV-VIS peak area 
of the label) is plotted as a function of cure time at three cure 
temperatures for both epoxies. Fluorescence intensity for DGEB epoxy is 
about the same as for DGEBA epoxy up to gelation time. However, 
fluorescence increases continuously beyond gelation for DGEB but levels 
off in DGEBA epoxy. This is due to the vitrification which only occurs in 
DGEBA epoxy, but not in DGEB epoxy. In DGEBA epoxy, the increase in 
fluorescence originates from the cure products alone rather than from the 
viscosity changes. Thus the total fluorescence intensity can be written as 
I.sub.F =c.SIGMA.F.sub.i A.sub.i where F.sub.i is the fluorescence 
intensity ratio obtained for each cure product under the same experimetal 
conditions, A.sub.i is their concentration and c is the experimental 
constant. The fluorescence intensity ratio for the cross-linker model 
compound is found to be independent of cure. Using the concentration 
values obtained by deconvolution of UV-VIS spectra, shown in Table III, 
the predicted I.sub.F agrees well with the experimental points. Much 
greater values of I.sub.F for DGEB are thus a direct consequence of 
further cure reactions, as also indicated by UV-VIS results as well as by 
IR monitoring of epoxy ring disappearance. 
The extent of cure reaction is estimated from the fluorescence intensity 
values. As described before, the total fluorescence intensity is 
attributed to by the fluorescence of each cure product. 
EQU I.sub.F =c(F.sub.pp A.sub.pp +F.sub.ps A.sub.ps +F.sub.ss A.sub.ss 
+F.sub.pt A.sub.pt +F.sub.st A.sub.st +F.sub.tt A.sub.tt) (20) 
From the model compound studies, the following fluorescence intensity ratio 
was estimated. 
EQU F.sub.pp :F.sub.ps :F.sub.ss :F.sub.pt :F.sub.st :F.sub.tt 
=1:9:18:700:1100:1400 (21) 
Thus 
EQU i.sub.F =c(A.sub.pp +9A.sub.ps +18A.sub.ss +700A.sub.pt +1100A.sub.st 
+1400A.sub.tt) (22) 
Substituting A.sub.ps, A.sub.ss, A.sub.pt, A.sub.st and A.sub.tt by 
A.sub.pp and the amine reactivity ratio, r, according to Eqns. (8-12), one 
obtains 
##EQU5## 
Eqn. (22) shows that I.sub.F is a function of only A.sub.pp for a given r. 
Using r=1 as determined from the extensive data in the previous section, 
and the experimental constant c, estimated from a few sets of known 
compositions to be on the order of 0.01, App is determined for a given 
I.sub.F using Eqn. (22). 
Once A.sub.pp values are calculated, the concentration of other cure 
products can be calculated according to Eqn. (8-12). FIG. 7 shows a 
graphical representation of the data in comparison to the results obtained 
by UV-VIS deconvolution. As can be seen, the cure composition obtained 
from fluorescence is in reasonable agreement with the data obtained by 
deconvolution of UV-visible spectra. 
In order to correlate fluorescence intensity at 565 nm with the overall 
extent of amine reaction, I.sub.F versus .epsilon..sub.a is plotted for 
both epoxies cured at three isothermal cure temperatures, 140.degree. C., 
160.degree. C., and 180.degree. C., shown in FIG. 8. In this figure, 
.epsilon..sub.a is estimated from deconvolution of UV-visible spectra. All 
the data fall on a single smooth curve whose slope is much sharper at 
later stages of cure, especially after gelation. In other words, this 
fluorescence is a very sensitive monitoring technique for cure beyond 
gelation, because its intensity comes mostly from tertiary amine products. 
5. Molecular Weight and Soluble Fractions as a Function of Cure 
By extending a recursive approach developed for ideal networks, Miller and 
Macosko in Macromolecules 13, 1063 (1980) derived molecular average 
properties of polymer networks in systems with first-shell substitution 
effects. This applies in the epoxy-diamine system where the primary amine 
may have a different reactivity as compared with the secondary amine. 
According to their theory, the weight average molecular weight, M.sub.w can 
be written for a stoichiometric mixture of epoxy-diamine as follows: 
##EQU6## 
where .epsilon..sub.a is the overall extent of cure reaction as defined by 
Eqn. (1), M.sub.A and M.sub.B are the molecular weight of the diamine and 
the diepoxide, respectively and .mu. is the weight average extent of 
reaction as defined by: 
##EQU7## 
Using M.sub.A =212 (DAA) and M.sub.B =202 (DGEB) or 340 (DGEBA), the 
molecular weight and soluble fractions as a function of cure can be 
determined. According to Eq. (8-12), expected values of A.sub.ps, 
A.sub.ss, A.sub.pt, A.sub.st and A.sub.tt can be generated as a function 
A.sub.pp if r is known. For a given r value (for example, 1 or 1.5), a 
.epsilon..sub.a, according to Eqn. 1, and a corresponding .mu. value, 
according to Eqn. 25, is obtained from each set of expected values of cure 
products. 
These values (.epsilon..sub.a and .mu.) are substituted in Eqn. 23 to 
generate theoretical predictions of M.sub.w as a function of 
.epsilon..sub.a. M.sub.w does not change much whether it is 1 or 1.5, as 
shown by the closeness of two solid lines. 
One can determine concentration of each of the cure products by comparing 
these theoretical predictions with the experimental data from the UV-VIS 
curve deconvolution assuming at the early stages of cure, before gelation, 
only one side of diepoxide is reacted with diamine, leaving the other side 
unreacted in all cure products. This is a reasonable assumption when there 
are many unreacted diamines present, thus making molecular weight 
calculation of the cure species easy. In order to experimentally determine 
the molecular weight of the whole system, one needs to know the molecular 
weight of each cure species. With the molecular weight values of cure 
species (e.g., A.sub.st =M.sub.A +3M.sub.B) and compositional analyses 
(Table III), M.sub.w of the epoxy system as a function of .epsilon..sub.a 
is easily estimated. The experimental values closely follow the 
theoretical prediction in the early stages of cure for both DGEBA and DGEB 
epoxy. However, as the cure approaches gelation, experimental points are 
much smaller than predicted, since the assumption is not valid at higher 
conversion. 
Up to the gel point, all molecules are finite and therefore soluble. After 
the gel point, the weight soluble fraction, W.sub.s, drops sharply. At 
100% reaction, one expects to have an infinite network with no soluble 
species. Theoretical curves are derived as described in Miller & Macosko's 
paper in Macromolecules, 9, 206 (1976) and extended by Charlesworth in J. 
Polym. Sci. Polym. Phys., 17, 1557 (1979). Part of the derivation as it 
applies to the present system is shown below: 
EQU W.sub.s =W.sub.Af P(F.sub.A.sup.out).sup.4 +W.sub.B 
P(F.sub.B.sup.out).sup.2 (25) 
where 
W.sub.AF =wt. fraction of amine molecules 
W.sub.B =wt. fraction of epoxy molecules 
P(F.sub.A.sup.out)=probability that, looking out from an amine molecule, 
leads to a finite or dangling chain 
P(F.sub.B.sup.out)=probability that, looking out from an epoxy molecule, 
leads to a finite or dangling chain 
P(F.sub.A.sup.out) and P(F.sub.B.sup.out) can be expressed in terms of the 
extent of reaction, .epsilon..sub.a, for f=4: 
##EQU8## 
P(F.sub.B.sup.out) is then defined as: 
##EQU9## 
substituting Eqn. (26) and (27), 
##EQU10## 
The dotted line in FIG. 9 shows the predicted weight fraction soluble, 
W.sub.s as a function of .epsilon..sub.a, according to Eqn. (28). Some 
cure product compositions are also indicated in FIG. 9. At high cure 
conversion (.epsilon..sub.a &gt;0.8 for example), W.sub.s is only comparable 
to the unreacted DAA concentration (A.sub.pp). This is quite reasonable 
since other cure products are expected to be incorporated into the 
network. At somewhat lower conversion (.epsilon..sub.a approximately 0.7), 
the soluble fraction seems close to the added fractions of unreacted DAA 
(A.sub.pp) and A.sub.ps, the first product of the cure. This result 
illustrates estimating the soluble fraction from cure product composition 
rather than from tedious and destructive solvent extraction studies. 
6. IR Studies and Comparison with UV-VIS Studies 
IR spectroscopy can be used to monitor the cure from the epoxide 
functionality simultaneously with UV-VIS and fluorescence studies 
following the cure reactions from the amine functionality of DAA. The 
extent of the epoxy reaction, .epsilon..sub.b for DGEBA-DDS epxoy, as 
defined by the following equation, 
##EQU11## 
where A.sub.915 cm.sup.-1 is the IR absorption due to epoxy ring and 
A.sub.1184 cm.sup.-1 is the absorption due to C--C stretching of the 
bridge carbon atom in DGEBA can be plotted. For DGEB-DDS, A.sub.1610 
cm.sup.-1 is used to calibrate for thickness fluctuation during cure, due 
to the phenyl ring in DDS, instead of A.sub.1184 cm.sup.-1. The curves are 
s-shaped, showing strong cure temperature effects, especially in the early 
stages of cure. The extent of epoxy cure, .epsilon..sub.b reaches about 
80% maximum in DGEBA-DDS epoxy, and about 95% at 180.degree. C. cure in 
DGEB-DDS epoxy. In DGEBA-DDS epoxy, a leveling-off at high conversion due 
to vitrification is observed. When compared at the same temperature, 
160.degree. C., greater cure is observed in DGEB-DDS than in DGEBA-DDS 
which is consistent with UV-VIS and fluorescence results. 
In order to compare the extent of amine reactions of DAA and epoxide 
reactions, .epsilon..sub.a by UV-VIS deconvolution versus .epsilon..sub.b 
for three cure temperatures for DGEB-DDS epoxy, where the reaction is 
almost complete, is plotted. The straight line shows the slope of one 
which corresponds to the .epsilon..sub.a =.epsilon..sub.b case. The data 
in general indicate that .epsilon..sub.a is somewhat greater than 
.epsilon..sub.b meaning faster consumption of DAA amine than overall 
epoxide. Since most of the epoxide reacts with DDS, this type of behavior 
is an indication that DAA may react a little faster than DDS. In order to 
confirm such differences in the reactivity between DDS and DDA, a scanning 
differential thermogram of a stoichiometric mixture of DGEB-DDS is 
compared with that of DGEB-DAA. Even though the areas under the exotherm 
are not very different, DGEB-DAA epoxy has an exotherm at a lower 
temperature, about 20.degree. lower, indicating a faster cure reaction by 
DAA than DDS. Therefore, a calibration curve should be used in order to 
correlate the extent of reaction monitored by DAA with the extent of 
overall reaction in DDS containing epoxy. 
EXAMPLE OF MEASURING THE EXTENT OF CURE BY DGEB-MDA LABELLED WITH DAS 
p,p'-diamino stilbene (DAS) is used as a reactive label in another 
important epoxy amine resin, DGEB-MDS. DAS is selected since it is 
expected to have a reactivity similar to the curing agent, methylene 
dianiline (MDA), according to the Hammet constant reported by O. Exner in 
"A Critical Compilation at Substitute Constants" in Correlation Analysis 
in Chemistry by N. B. Chapman and J. Shorter, p.457 (Plenum Press, NY 
1978). Unlike DAA, DAS is highly fluorescent even when the amine groups 
are primary, providing a greater sensitivity at early stages of cure. The 
photophysical behavior of trans stilbene and some of its derivatives are 
known to be sensitive to environmental viscosity. Thus, one can expect to 
see the effects on photophysical behavior from both the increasing 
viscosity and the chemical reaction as cure proceeds. DGEB was chosen 
since the cure reaction can progress much further at cure temperatures 
above 80.degree. C. due to the absence of vitrification. 
DGEB (98% purity) was purchased from Aldrich and used without further 
purification. MDA was recrystallized from toluene. DAS-dihydrochloride 
from Aldrich was neutralized with sodium carbonate and recrystallized from 
methanol to obtain the free amine. 
A stoichiometric mixture of DGEB and MDA was used with 0.1% of DAS as a 
label. Sample preparation method was the same as in the previous example. 
A Perkin-Elmer UV-VIS Diode Array (Model 3840) and Fluorescence 
Spectrometer (MPF-66) with a Model 7500 Data Station were used to record 
the spectra. UV-VIS and fluorescence spectra were obtained after cooling 
the sample to room temperature following cure in an oven for a specific 
time. Fully substituted DAS (tt-DAS) was synthesized by reacting DAS with 
a large excess of phenyl glycidyl ether (PGE) at 140.degree. C. for 12 
hrs., followed by removal of the excess PGE under vacuum. A UV-VIS 
absorption peak at 372 nm was observed for tt-Das. The extent of reaction 
based on epoxy ring disappearance was estimated by monitoring IR 
absorption at 915 cm.sup.-1 (epoxy ring) corrected with the absorption at 
1610 cm.sup.-1 (MDA internal standard). 
1. Uv-visible absorption spectra 
FIG. 10h shows the UV-VIS spectra of DGEB-MDA-DAS (0.1%) following cure at 
140.degree. C. Before cure, DAS absorption maxima is at 352 nm. DAS in 
DGEB shows another absorption peak at 327 nm, which is hidden under MDA 
absorption in DGEB-MDA epoxy. As cure proceeds, red shifts of the peak at 
352 nm occur. After 300 minutes of cure at 140.degree. C., the DAS 
absorption peak is shifted to 371 nm. Further curing, even at high 
temperatures, does not increase this absorption beyond 372 nm. 
Red shifts in DAA and DAS are caused by the electron donating effect of the 
tertiary amines as compared to the primary amines. Assuming that such 
electronic effects are of similar magnitude for DAA and DAS, one would 
expect smaller red shifts in DAS compared to DAA. This is due to the fact 
that it requires greater energy to produce the same shifts in the uv 
region where DAS absorbs as compared to the visible region where DAA 
absorbs. Due to such small shifts in DAS labelled epoxy, it is not 
possible to deconvolute the absorption spectra. 
2. Fluorescence Spectra 
FIG. 10b shows fluorescence spectra as a function of cure time at 
140.degree. C. At zero cure time, the emission maximum is at 418 nm and a 
shoulder at 403 nm. As cure time increases, enhancement of emission as 
well as splitting into two peaks (at 418 nm and 430 nm) occur, as shown in 
FIG. 10b. The emission spectra of tt-DAS in dilute solution of PGE shows 
the same two peaks, apparently red shifted as in UV-VIS spectra. The ratio 
of fluorescence quantum yield of tt-DAS to DAS in dilute solution is found 
to be about 2.4 at 418 nm. 
FIG. 11 shows the s-shaped curves of the emission intensity at 418 nm as a 
function of cure time at two cure temperatures, 140.degree. and 
120.degree. C., respectively. At these temperatures, the gel time for 
DGEBA-MDA epoxy is known to be about 8 min. and 16 min., respectively. One 
may assume that the gel times are similar for DGEB-MDA epoxy. After 
gelation, fluorescence emission increases sharply at the respective curve 
temperature. Also, it is noted that the overall increase in emission 
intensity is usually about 3 to 3.5 times greater as compared to zero cure 
time at longer cure times. 
Emission intensity of tt-DAS in DGEB-MDA epoxy is relatively constant until 
the later stages of cure. From this behavior, one can conclude that the 
chemical reaction, substitution on DAS amine groups, is the main cause for 
the emission enhancement near gelation but that the viscosity effect 
begins to contribute to the enhancement of the emission at later stages of 
cure. 
A plot of fluorescence intensity at 418 mn as a function of cure based on 
the epoxy ring disappearance shows that the fluorescence intensity 
increases sharply after gelation, thus allowing for sensitive cure 
monitoring during the later stages of cure. 
__________________________________________________________________________ 
FILE: 
SSDECONV FORTRAN UCONN CMS REL3 SL302 4/86 
C THIS PROGRAM DECONVOLUTES A COMPOSITE CURVE USING GAUSSIAN 
SSD00010 
C BUTION FUNCTIONS: CURVE USING ONLY 80 CH/LINE. SSD00020 
DIMENSION Y(2000), P(10), S(10), XM(10), G(2000), A(10) 
SSD00030 
DIMENSION JXY(10), XMEAN(10), R(10), (10), XY(1000,4) 
SSD00040 
F1=3.1415926 SSD00050 
XD=1. SSD00060 
READ (01,7) XL,XU,XXL,XXU,YYL,YYU SSD00070 
NX=1+(XU-XL)/XC SSD00080 
C SSD00090 
DO 15 I=1,NX SSD00100 
READ(01,7) Y(I) SSD00110 
7 FORMAT(F5.0) SSD00120 
15 CONTINUE SSD00130 
C SSD00140 
10 PRINT *, ` ASSUME NUMBER OF COMPONENTS, N?` SSD00150 
READ *, N SSD00160 
C SSD00170 
17 PRINT *, ` WANT TO ASSUME S(I)=40. FOR ALL I? (YES=2/NO=1)` 
SSD00180 
READ *, ITEM SSD00190 
IF(ITEM.EQ.1) GO TO 30 SSD00200 
DO 20 I=1,N SSD00210 
S(I)=40. SSD00220 
20 CONTINUE SSD00230 
C SSD00240 
DO 25 I=1,N SSD00250 
WRITE(6,27) I,I SSD00260 
27 FORMAT(` ASSUME XMEAN(`,I1,`), P(`,I1,`).`) SSD00270 
READ *, XMEAN(I),P(I) SSD00280 
XM(I)=1.+(XMEAN(I)-XL)/XD SSD00290 
25 CONTINUE SSD00300 
DO 55 I=1,N SSD00310 
WRITE(6,57) XMEAN(I), S(I), P(I) SSD00320 
57 FORMAT(3F10.1) SSD00330 
55 CONTINUE SSD00340 
PRINT *, ` IS THAT ASSUMPTION REASONABLE ? (YES=2/NO=1)` 
SSD00350 
READ *, ITEM SSD00360 
IF(ITEM.EQ.1) GO TO 17 SSD00370 
GO TO 43 SSD00380 
C SSD00390 
30 DO 40 I=1,N SSD00400 
WRITE(6,31) I,I,I SSD00410 
31 FORMAT(` ASSUME XMEAN(`,I1,`), S(`,I1,`), P(`,I1,`).`) 
SSD00420 
READ *, XMEAN(I), S(I), P(I) SSD00430 
XM(I)=1.+(XMEAN(I)-XL)/XD SSD00440 
40 CONTINUE SSD00450 
C SSD00460 
DO 49 I=1,N SSD00470 
WRITE(6,41) XMEAN(I), S(I), P(I) SSD00480 
41 FORMAT(3F10.1) SSD00490 
49 CONTINUE SSD00500 
PRINT *, ` IS THAT ASSUMPTION REASONABLE ? (YES=2/NO=1)` 
SSD00510 
READ *, ITEM SSD00520 
IF(ITEM.EQ.1) GO TO 17 SSD00530 
C SSD00540 
43 DO 50 I=1,NX SSD00550 
FILE: 
SSDECONV FORTRAN A UCONN CMS REL3 SL302 4/86 
FTEM=0. SSD00560 
DO 45 J=1,N SSD00570 
XTEM=FLOAT(I) SSD00580 
FTEM=FTEM+F(XTEM,P(J),S(J),XM(J)) SSD00590 
45 CONTINUE SSD00600 
G(I)=FTEM SSD00610 
50 CONTINUE SSD00620 
PRINT *, ` WANT GRAPH? (YES=2/NO=1)` SSD00630 
READ *, ITEM SSD00640 
IF(ITEM.EQ.1) GO TO 67 SSD00650 
C SSD00660 
NPLOT=500 SSD00670 
NAUTO=1 SSD00680 
60 DO 61 I=1,NX SSD00690 
XY(I,1)=XL+XD*(I-1.) SSD00700 
XY(I,2)=Y(I) SSD00710 
XY(I,3)=XY(I,1) SSD00720 
XY(I,4)=G(I) SSD00730 
61 CONTINUE SSD00740 
DO 62 J=1,4 SSD00750 
JXY(J)=J SSD00760 
62 CONTINUE SSD00770 
65 CALL VPLOT(XY,JXY,NPLOT,1000,2,NAUTO,XXL,XXU,YYL,YYU) 
SSD00780 
PRINT *, ` WANT PREVIOUS GRAPH AGAIN? (YES=2/NO=1)` 
SSD00790 
READ *, ITEM SSD00800 
IF(ITEM.EQ.2) GO TO 65 SSD00810 
C SSD00820 
67 PRINT *, ` WANT ERROR ESTIMATION? (YES=2/NO=1) SSD00830 
READ *, ITEM SSD00840 
IF(ITEM.EQ.1) GO TO 90 SSD00850 
PRINT *, ` CALCULATE ERROR FROM XLL TO XUU.` SSD00860 
READ *, XLL,XUU SSD00870 
NXLL=(XLL-XL)/XD+1 SSD00880 
NXUU=(XUU-XL)/XD+1 SSD00890 
70 ATEM=0. SSD00900 
BTEM=0. SSD00910 
DO 80 I=NXLL,NXUU SSD00920 
ATEM=ATEM+(Y(I)-G(I))**2 SSD00930 
BTEM=BTEM+Y(I) SSD00940 
80 CONTINUE SSD00950 
STDV=100.*(ATEM**(0.5))/BTEM SSD00960 
WRITE(6,81) XLL,XUU,STDV SSD00970 
81 FORMAT(` ERROR OF ESTIMATION FROM (`, F5.1 ,`) TO (`, F5.1 ,`) 
SSD00980 
$ `, F7.3, ` %`) SSD00990 
C SSD01000 
PRINT *, ` WANT GRAPH ONE MORE TIME? (YES=2/NO=1)` 
SSD01010 
READ *, ITEM SSD01020 
IF(ITEM.EQ.1) GO TO 90 SSD01030 
CALL VPLOT(XY,JXY,NPLOT,1000,2,NAUTO,XXL,XXU,YYL,YYU) 
SSD01040 
90 DO 100 I=1,N SSD01050 
A(I)=(P(I)*S(I))*((PI*2.)**0.5) SSD01060 
WRITE(6,91) I,XMEAN(I),I,S(I),I,P(I),I,A(I) SSD01070 
91 FORMAT(` XMEAN(`,I1,`) = `, F6.1,2X,` S(`,I1,`) = `, F5.1,2X,` 
SSD01080 
$(`,I1,`)= `, F7.1,2X,`; AREA(`,I1,`) = `, F12.1) 
SSD01090 
100 CONTINUE SSD01100 
FILE: 
SSDECONV FORTRAN A UCONN CMS REL3 SL302 4/86 
C SSD01110 
AR=0. SSD01120 
DO 99 I=1,N SSD01130 
AR=AR+A(I) SSD01140 
99 CONTINUE SSD01150 
DO 96 I=1,N SSD01160 
R(I)=A(I)/A(1) SSD01170 
(I)=100.*A(I)/AR SSD01180 
WRITE (6,94) I,R(I),I,(I) SSD01190 
94 FORMAT(/` R(`,I1,`)= `, F5.2, 5X, `(`,I1,`)= `, F7.2, 
SSD01200 
96 CONTINUE SSD01210 
C SSD01220 
PRINT *, ` WANT TO REPEAT? (YES=2/NO=1)` SSD01230 
READ *, ITEM SSD01240 
IF(ITEM.EQ.2) GO TO 10 SSD01250 
STOP SSD01260 
END SSD01270 
C SSD01280 
FUNCTION F(X,P,S,XM) SSD01290 
XTEM=(X-XM)**2/(2.*S**2) SSD01300 
F=0. SSD01310 
IF(XTEM.LT.100) F=P/EXP(XTEM) SSD01320 
RETURN SSD01330 
END SSD01340 
C SSD01350 
SUBROUTINE VPLOT(XY,JXY,N,NDIM,NCUR,ISCALE,XL,XU,YL,YU) 
SSD01360 
DIMENSION IGRID(61),XS(11),YS(13),ICHAR(7),XY(5000),JXY(10) 
SSD01370 
DATA ICHAR/1H+,1H*,1H-,1H$,1H=,1H.,1H / SSD01380 
XS(1)=XL SSD01390 
XMAX=XU SSD01400 
YMIN=YL SSD01410 
YS(1)=YU SSD01420 
IF(ISCALE.NE.0) GO TO 36 SSD01430 
XMAX=-1.0E 20 SSD01440 
XS(1)=-XMAX SSD01450 
YS(1)=XMAX SSD01460 
YMIN=XS(1) SSD01470 
J2=0 SSD01480 
DO 35 J=1,NCUR SSD01490 
J2=J2+2 SSD01500 
JIX=(JXY(J2-1)-1)*NDIM SSD01510 
JIY=(JXY(J2)-1)*NDIM SSD01520 
DO 35 I=1,N SSD01530 
IJX=JIX+I SSD01540 
IJY=JIY+I SSD01550 
IF(XY(IJX).GT.XMAX)XMAX=XY(IJX) SSD01560 
IF(XY(IJX).LT.XS(1))XS(1)=XY(IJX) SSD01570 
IF(XY(IJY).GT.YS(1))YS(1)=XY(IJY) SSD01580 
IF(XY(IJY).LT.YMIN)YMIN=XY(IJY) SSD01590 
35 CONTINUE SSD01600 
36 XR=XMAX-XS(1) SSD01610 
IF(XR.EQ.C.0)XR=1.0E-20 SSD01620 
YR=YS(1)-YMIN SSD01630 
IF(YR.EQ.0.0)YR=1.0E-20 SSD01640 
XT=XMAX*XS(1) SSD01650 
FILE: 
SSDECONV FORTRAN A UCONN CMS REL3 SL302 4/86 
YT=YMIN*YS(1) SSD01660 
IF(XT.LT.0.0)IYAX=60.0*(-XS(1))/XR+1.5 SSD01670 
IF(YT.LE.0.0)IXAX=48.0*YS(1)/YR+1.5 SSD01680 
XMAX=XR/10. SSD01690 
DO 46 I=2,11 SSD01700 
46 XS(I)=XS(I-1)+XMAX SSD01710 
XMAX=YR/12. SSD01720 
DO 47 I=2,13 SSD01730 
47 YS(I)=YS(I-1)-XMAX SSD01740 
WRITE(6,71) (XS(I),I=1,11) SSD01750 
WRITE(3,71) (XS(I),I=1,11) SSD01760 
II=1 SSD01770 
KK=0 SSD01780 
DO 146 LINE=1,49 SSD01790 
DO 104 J=1,61 SSD01800 
104 IGRID(J)=ICHAR(7) SSD01810 
IF(YT.GT.0.0) GO TO 109 SSD01820 
IF(LINE.NE.IXAX) GO TO 109 SSD01830 
DO 105 J=1,61 SSD01840 
105 IGRID(J)=ICHAR(6) SSD01850 
109 IF(XT.LT.0.0) IGRID(IYAX)=ICHAR(6) SSD01860 
J2=0 SSD01870 
DO 125 J=1,NCUR SSD01880 
J2=J2+2 SSD01890 
JIX=(JXY(J2-1)-1)*NDIM SSD01900 
JIY=(JXY(J2)-1)*NDIM SSD01910 
JC=MOD(J,5) SSD01920 
DO 125 I=1,N SSD01930 
IJX=JIX+I SSD01940 
IJY=JIY+I SSD01950 
IPTY=48.0*(YS(1)-XY(IJY))/YR+1.5 SSD01960 
IF(IPTY.GT.49)IPTY=49 SSD01970 
IF(IPTY.LT.1)IPTY=1 SSD01980 
IF(IPTY.NE.LINE) GO TO 125 SSD01990 
IPTX=60.0*(XY(IJX)-XS(1))/XR+1.5 SSD02000 
IF(IPTX.LT.1)IPTX=1 SSD02010 
IF(IPTX.GT.61)IPTX=61 SSD02020 
IF(JC.NE.0) GO TO 119 SSD02030 
IGRID(IPTX)=ICHAR(5) SSD02040 
GO TO 125 SSD02050 
119 IGRID(IPTX)= ICHAR(JC) SSD02060 
125 CONTINUE SSD02070 
IF(KK.GT.0)GO TO 134 SSD02080 
WRITE(6,72) YS(II),(IGRID(I), I=1,61),YS(II) SSD02090 
WRITE(3,72) YS(II),(IGRID(I), I=1,61),YS(II) SSD02100 
II=II+1 SSD02110 
GO TO 135 SSD02120 
134 WRITE(6,73) (IGRID(I), I=1,61) SSD02130 
WRITE(3,73) (IGRID(I), I=1,61) SSD02140 
135 KK=KK+1 SSD02150 
IF(KK.NE.4) GO TO 146 SSD02160 
KK=0 SSD02170 
146 CONTINUE SSD02180 
WRITE(6,74) (XS(I), I=1,11) SSD02190 
WRITE(3,74) (XS(I), I=1,11) SSD02200 
FILE: 
SSDECONV FORTRAN A UCONN CMS REL3 SL302 4/86 
71 FORMAT(F9.0,10F6.0/6X,1H*,20(3H+**),2H+*) SSD02210 
72 FORMAT(F5.0,1X,1H+,61A1,1H+,1X,F5.0) SSD02220 
73 FORMAT(6X,1H*,61A1,1H*) SSD02230 
74 FORMAT(6X,1H*,20(3H+**),2H+*/F9.0,10F6.0) SSD02240 
RETURN SSD02250 
END SSD02260 
__________________________________________________________________________ 
The present invention may be embodied in other specific forms without 
departing from the spirit and scope thereof. These and other modifications 
of the invention will occur to those skilled in the art and are intended 
to fall within the scope of the appended claims.