Using bar infrared spectra and coincidence indexes to study the diversity of solid cyanuric acid structures

Article abstract of DOI:10.21577/0103-5053.20180023

A general method was developed for studying the diversity of individuals in a population based on the diversity of infrared spectra of solid cyanuric acid analytes obtained from various reactions of trichlorocyanuric acid. This method first generates infrared bar spectra for the analytes and then measures the coincidence and continence among pairs of the spectral peaks via confrontation matrices. Class markers are established to characterize analyte classes. Possible correlations among the employed reaction conditions and the nature of the produced solids, which are based on their infrared bar spectra, are discussed. The method of coincidence may be useful for characterizing polymorphs, particularly those of active pharmaceutical ingredients (APIs). The method may also be extended to define the homogeneity of solid analytes. The ANALIN module of the ANALOR software suite running on a dBase platform is used to generate the bar infrared spectra and to handle all calculations.

Full text of DOI:10.21577/0103-5053.20180023

http://dx.doi.org/10.21577/0103-5053.20180023
J. Braz. Chem. Soc., Vol. 29, No. 7, 1499-1515, 2018
Article
Printed in Brazil - ©2018 Sociedade Brasileira de Química
Using Bar Infrared Spectra and Coincidence Indexes to Study the Diversity of Solid
Cyanuric Acid Structures
a
a
,b
Marcela C. B. G. Nilo, Thais G. Simões and Claudio Costa Neto*
a
Fundação Ataulpho de Paiva (FAP), Av. Pedro II, 260, São Cristóvão, 20941-000 Rio de Janeiro-RJ, Brazil
b
Polo de Xistoquímica, Instituto de Química, Universidade Federal do Rio de Janeiro (UFRJ),
Rua Hélio de Almeida, 40, Cidade Universitária, 21941-614 Rio de Janeiro-RJ, Brazil
A general method was developed for studying the diversity of individuals in a population based
on the diversity of infrared spectra of solid cyanuric acid analytes obtained from various reactions
of trichlorocyanuric acid. This method first generates infrared bar spectra for the analytes and then
measures the coincidence and continence among pairs of the spectral peaks via confrontation
matrices. Class markers are established to characterize analyte classes. Possible correlations among
the employed reaction conditions and the nature of the produced solids, which are based on their
infrared bar spectra, are discussed. The method of coincidence may be useful for characterizing
polymorphs, particularly those of active pharmaceutical ingredients (APIs). The method may also
be extended to define the homogeneity of solid analytes. The ANALIN module of the ANALOR
software suite running on a dBase platform is used to generate the bar infrared spectra and to
handle all calculations.
Keywords: infrared bar spectra, coincidence indexes, cyanuric acid, trichloroisocyanuric
acid, polymorphism
Introduction
characterized by groups of frequencies, the 5-frequency
markers; and (ii) measuring the differences among the
spectra based on the coincidence and continence of
frequencies among the analytes, as calculated from their
infrared bar spectra, and exploring the results obtained. The
method developed aims to represent the differences among
the spectra by numbers (indexes), with these differences
being large or (very) small.
This study began with the authors’ observation of
ca. 30 infrared printed (common) spectra generated directly
from a spectrometer of the white precipitate resulting
from a group of reactions with trichloroisocyanuric acid.
Although all these products are believed to be cyanuric acid,
a diversity of infrared spectra was observed. Notably, some
of these spectra were similar, but not identical, whereas
others were more diverse. Initially, simply defining the
existing differences (were all of the products the same?)
was deemed necessary. Later, the quantification of these
differences was preferred in order to determine a rationale
that could correlate them. The objective of this paper is
to present results on the study of the diversity of infrared
spectra of cyanuric acid obtained from various reactions
using trichloroisocyanuric acid while adhering to two main
directions: (i) generating the bar spectra of the various
products and mapping the frequencies in order to group the
analytes into classes, as well as concurrently determining
the correlations between the reaction conditions and the
structure (the class) of the solids produced. Classes were
Cyanuric acid has been known since a paper from
1
the nineteenth century (1829) by Friedrich Wöhler.
Wöhler produced cyanuric acid by heating urea or uric
acid. The so-called cyanuric acid exists in a tautomeric
equilibrium with isocyanuric acid. The three “phenolic”
hydroxyl groups in cyanuric acid are responsible for its
(weakly) acidic character (the pH of a saturated solution
2
is 4.5-5.0); consequently, it is the preferred tautomer in
basic solution. The literature indicates that isocyanuric
acid is the predominant isomer in the solid phase but is
3
also present in solution.
In the current literature, both cyanuric and isocyanuric
acids are referred to as cyanuric acid. Chemical Abstracts/
SciFinder define one Chemical Abstracts Service (CAS)
registry number (08-80-5) for the isomers cyanuric acid
(2,4,6-trihydroxy-1,3-5-triazine) and isocyanuric acid
*e-mail: ccostaneto@terra.com.br

1
500
Using Bar Infrared Spectra and Coincidence Indexes to Study the Diversity of Solid Cyanuric Acid Structures
J. Braz. Chem. Soc.
21
(
1,3,5-triazine-2,4,6-trione). However, another CAS
Yang et al., who address the effects of cyanuric acid on
registry number, 135581-61-2, is given to the former
species under the name of 1,3,5-triazine-2,4,6-triol, despite
isocyanuric acid also being given as a synonym for this
molecule. Cyanuric/isocyanuric acid will be represented
in this paper by the three letter abbreviation ACN and
trichloroisocyanuric acid by TCI (other abbreviations for
trichloroisocyanuric acid can be found in the literature,
the polymorphism of poly(butylene adipate).
Experimental
This paper addresses a study on the white precipitate
produced in the halogenation of the double bond of methyl
acrylate with TCI and a halogen salt, following a similar
4
5
22
such as TCCA and TICA ).
rationale used by Tozetti et al. for the bromination of
A very complete account on cyanuric acid is presented
by Wojtowicz.
alkenes.
2
,6
With the stoichiometric coefficients added, the complete
equation for the bromination of methyl acrylate with TCI
and potassium bromide may be written as
From cyanuric acid, trichloroisocyanuric acid
(
CAS 87-90-1) can be prepared by direct chlorination
7
with chlorine gas. This compound is extensively used
as a disinfectant agent for swimming pools (algicide and
3CH =CHC(O)OCH + 2 trichloroisocyanuric acid +
2
3
8
bactericide). Presently, TCI is also widely employed as an
6KBr → 3CH Br–CHBrC(=O)OCH + 6KCl +
2
3
effective chlorinating reagent for various chemical reactions,
2 isocyanuric acid
(1)
9
such as the α-chlorination of carbonyl derivatives, the
10
production of nitriles from amines, the halogenation and
A group of 35 reactions of trichloroisocyanuric acid
with methyl acrylate or acrylonitrile and a bromide or
chloride salt of potassium or ammonium using acetone
and water or ammonia as solvents at different temperatures
were selected to study the effect of these reagents
and conditions on the yield and purity of the methyl
11
epoxidation of alkenes, and the chlorination of aromatic
5,12
systems, among others; extensive reviews on the reactions
4
of TCI have been offered by Tilstan and Weinmann, Cunha
13
14
and Ferreira and Mendonça and Mattos. Figure 1 shows
the chemical structures of these molecules.
2
,3-dibromopropionate product. The reaction conditions
used are shown in Table 1.
As a complementary study, the infrared spectra of
the white precipitates produced in all the reactions were
recorded and became the focus of the present work. The
reactions conducted at different conditions produced, in all
cases, a white precipitate.
In a general procedure, a solution of 0.050 mol of the
acrylate derivative dissolved in 25 mL of acetone was added
to an initial solution of 0.116 mol of the salt dissolved
in 20 mL of water. The two solutions were mixed to
generate a final homogeneous solution and subjected to a
defined temperature. Next, a solution of 0.017 mol of TCI
dissolved in 25 mL of acetone was added dropwise with
agitation to the previous solution over 1 h. The mixture was
continually agitated for an additional hour and then filtered.
The precipitate can be easily solubilized in hot water and
reprecipitated by cooling (the solubility of cyanuric acid
Figure 1. Chemical structures of trichloroisocyanuric acid, isocyanuric
acid and cyanuric acid.
Contributions to the assignment of infrared absorption
frequencies to chemical moieties of cyanuric acid can be
found in the literature. These assignments, particularly
those related to hydrogen bonds, are important for
establishing the structures of the solid, as well as for build
correlation maps of frequencies among analytes. In this
15
context, Newman and Badger presented in 1952 a very
complete analysis of a set of 16 peak frequencies for a
sample of sublimed cyanuric acid and then assigned them
to their corresponding chemical moieties.
4
in water is 0.2% at 25 °C and 2.6% at 90 °C). The filtrate
was concentrated and left to cool, leading to the production
of a second crop.
Other, albeit less informative, assignments can be
1
6
found in the literature, such as Padgett and Hamner,
Loughran et al., Chen et al., and Surinwong et al.
The above procedure differs for the one proposed by
1
7
18
19
22
Tozetti et al., mainly in the way TCI is introduced: in
22
References can also be found in the literature regarding
polymorphs of cyanuric acid derivatives, such as
the Tozetti et al. procedure, TCI is added as a powdered
solid directly into the reaction media, whereas in most
of the reaction discussed in this text, TCI was added in
a solution of acetone. Reactions 17.00 to 24.00, 26.00 to
20
Barnett et al., who discuss the polymorphism in hydrogen
bonded adducts of cyanuric acid-bis(4-pyridyl)ethane, and

Vol. 29, No. 7, 2018
Nilo et al.
1501
Table 1. Trichloroisocyanuric acid reaction conditions
Halogen acceptor
Reaction
Halogen salt
Salt No. of moles
TCI / mol
Temperature / °C
Medium/solvent
Acceptor
AcrMet
AcrMet
AcrMet
AcrMet
AcrMet
AcrMet
–
No. of moles
0.056
0.050
0.050
0.050
0.050
0.050
0.000
0.050
0.000
0.050
0.050
0.050
0.050
0.111
0.050
1.110
0.050
0.050
0.050
0.050
0.000
0.000
0.000
0.000
0.000
0.050
0.111
2
3
2
2
2
1
1
5
9
2
2
2
1
2
1
3
1
2
1
1
1
4
2
2
3
2
2
.00
0.020
0.017
0.017
0.017
0.017
0.017
0.017
0.017
0.017
0.017
0.017
0.017
0.017
0.371
0.017
0.372
0.017
0.017
0.017
0.017
0.017
0.372
0.017
0.017
0.017
0.017
0.371
KBr
KBr
KBr
KBr
KBr
KBr
KBr
KCl
KCl
KCl
KCl
KCl
0.116
0.100
0.116
0.116
0.116
0.116
0.116
0.100
0.100
0.100
0.100
0.100
0.100
0.222
0.100
2.222
0.100
0.100
0.100
0.100
0.000
0.000
0.000
0.000
0.000
0.000
0.222
r.t./ca. 28+
r.t./ca. 28+
25
H O/acetone
2
.00/4.00/205.00
6.00
H O/acetone
2
H O/acetone
2
0.00
0
H O/acetone
2
1.00
0
NH OH /acetone
4
aq
0.00
r.t./ca. 28+
r.t./ca. 28+
r.t./ca. 28+
r.t./ca. 28+
25
NH OH/acetone
4
1.00
NH OH/acetone
4
.00/6.00/7.00/8.00
.00
AcrMet
–
NH OH/acetone
4
NH OH/acetone
4
7.00
AcrMet
AcrMet
AcrNit
AcrMet
AcrMet
AcrMet
AcrMet
AcrMet
AcrMet
AcrMet
AcrMet
–
H O/acetone
2
14.00
12.00/215.00
4.00
r.t./ca. 28+
r.t./ca. 28+
r.t./ca. 28+
25
H O/acetone
2
H O/acetone
2
NH Br
H O/acetone
4
2
8.00
NH Br
H O/acetone
4
2
7.00/22.00
3.00
NH Br
0
H O/acetone
4
2
NH Br
25
H O/acetone
4
2
5.00
NH Br
r.t./ca. 28+
0
NH OH /acetone
4
4
aq
3.00/18.00
9.00
NH Br
NH OH /acetone
4 aq
4
NH Br
0
NH OH/acetone
4
4
6.00
NH Br
r.t./ca. 28+
r.t./ca. 28+
25
NH OH/acetone
4
4
2.00
–
–
–
–
–
–
NH OH/acetone
4
7.00
–
NH OH/acetone
4
4.00
–
–10
NH OH /acetone
4
aq
5.00
–
r.t./ca. 28+
–15
NH OH /acetone
4
aq
1.00
AcrMet
AcrMet
AcrMet
NH OH
4
10.00
9.00
r.t./ca. 28+
25
HCl/H O/acetone
2
NH Cl
H O/acetone
4
2
TCI: trichloroisocyanuric acid; AcrMet: methyl acrylate; AcrNit: acrylonitrile; r.t.: room temperature.
-
1
2
9.00 and 31.00 were conducted in 100 mL Easy-Max
within the A region (4000-2500 cm ). This region is
chosen because the peaks in the bar spectra in the region of
Mettler-Toledo equipment, and reactions 33.00 and 47.00
were part of a study on reaction calorimetry that used the
Mettler-Toledo RC1 equipment. Both Easy-Max and RC1
provide very strict control of temperature (the reaction
is quite exothermic), which differs from reactions 3.00
and 205.00, for which the TCI was added as a lump (as
-1
4000-3600 cm are always very noisy and, for the purposes
of this paper, do not add any significant information (see
Figure 2).
The false intensity plots (FI-plots or φ-plots) were
drawn with Microcal-Origin 6.0 software from data
2
3
22
recommend in the procedure of Tozetti et al.) to a normal
reaction flask at room temperature.
generated by ANALIN.
1
3
The C nuclear magnetic resonance (NMR) spectra
of the samples were obtained on a Bruker 300 NMR
Equipment and instruments
spectrometer using dimethylsulfoxide-d (DMSO) as the
6
solvent.
All infrared analysis was performed using standard KBr
disks. The instrument used was a Nicolet 6700-Fourier
transform infrared (FTIR) spectrometer operating under
default conditions. The infrared region used in this paper
Chemicals
Methyl acrylate, cyanuric acid, and dimethylsulfoxide-d6
were acquired from Sigma-Aldrich; potassium chloride,
-1
extends from 3600 to 2500 cm (region A’), a subregion

1
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Using Bar Infrared Spectra and Coincidence Indexes to Study the Diversity of Solid Cyanuric Acid Structures
J. Braz. Chem. Soc.
Figure 2. Infrared bar spectra of cyanuric acid analyte 4.04, representing a typical infrared bar spectra produced by ANALIN using the three consecutive
-
1
points algorithm. Note the noise above 3600 cm ; for the discussions in this paper, this region is discarded.
potassium bromide, ammonium chloride, ammonium
bromide and acetone of pure grades, from Vetec Química
Fina; and ammonia, aqueous solution containing 24% NH3,
from Isofar Indústria e Comércio de Produtos Químicos.
Trichloroisocyanuric acid was supplied by HTH (a
swimming pool supplier) and was said to be > 99% pure.
A great advantage of using bar spectra is the ease
with which they work with software. The bar infrared
spectra were generated directly from the output of an
FTIR spectrometer. This process can be achieved quickly
2
4
using version 2 of the ANALIN module of the ANALOR
software suite running on a dBase platform.
Most of the commercial FTIR instruments designed to
produce infrared spectra for routine operations may show a
variation up to ± 2 cm in a frequency value.A comparison
between spectra must always account for this “error”. A
graphic example of a bar infrared spectrum generated by
ANALIN can be seen in Figure 2.
Methodology
-1
The infrared bar spectra
The infrared bar spectrum is a graphic representation
of a subset of the array of frequency-intensity values
generated by an infrared spectrometer. It contains only bars
corresponding to the peaks of the spectrum. Similar to the
conventional way of representing an infrared spectrum,
wavenumbers are shown on the abscissa and intensities
on the ordinate (as transmittances); however, different
from most conventional representation, intensities are
normalized to 100% (the highest value of intensity), and
the peaks are shown extending upwards. The bar spectrum
is a discrete form of spectral representation rather than the
continuous conventional display of spectra, in which all of
the points next to each other are linked.
False intensity plots
A false intensity plot is defined as a frequency-intensity
(transmittance) plot with a proper format in which the
different peak intensities of the spectrum provided by the
spectrometer are substituted by a constant intensity value.
False intensities can be assigned to all the analytes of the
same class or to each analyte of a given class. In the first
case, the various classes can be represented simultaneously
in the same graph, whereas in the second, observing and
comparing the distribution of the analytes of each class is
possible. Examples can be seen later in the Results and
Discussion section under the heading “Maps of analyte
frequency distribution”.
The output of an infrared instrument is a table that
contains ca. 4500 points provided in “.csv” format (Excel).
The intensity values can be set as a simple one-dimensional
array of data from which the subset of peaks can be
extracted by software using proper algorithms.
The coincidence and continence indexes between two
infrared bar spectra
Simple algorithms can be used to extract peaks from the
one-dimensional array of intensity values generated by an
infrared spectrometer, such as the three consecutive points
algorithm, in which the intensity of the middle point of three
consecutive points of a linear array is compared with that
of the other two points: if it is greater than the other two,
then this constitutes a peak (maximum) that is registered
for the bar spectrum as an intensity with the corresponding
frequency. The three consecutive points algorithm is simple
to implement, can almost instantly screen the whole set of
peaks generated by an infrared spectrometer and extract the
subset of peaks and is robust in use; thus, it was chosen to
generate the bar spectra in this paper.
The comparison between two infrared bar spectra may
be accomplished numerically as graphs or indexes and
displayed in two ways:
First, two bar spectra may be initially displayed
graphically. This procedure uses both absorption
frequencies and intensities to display the two spectra
on a computer. In the graphic display mode, many
operations can be further performed on the two spectra,
for instance, eliminating all of the peaks of the analyte that
are not consistent with the reference (intensities are not
considered). This process leaves a residue spectrum (as a

Vol. 29, No. 7, 2018
Nilo et al.
1503
new analyte spectrum) with only the peaks in consonance
with the reference.
to the number of peaks of the analyte; and (ii) the number of
peaks of the reference coincident with peaks of the analyte
relative to the number of peaks of the reference. The index
related to the reference seems to be more appropriate for
the analysis of the results: if the index has a value of 1 (or
100%), then all of the peaks of the reference are contained
in the spectrum of the analyte; by contrast, if the index is 0
(or 0%), even at a large error interval, no coincidence exists
between the analyte and reference, and they are probably
different species. For any value between 0 (0%) and 1
(100%), some resemblance may exist between the analyte
and reference, and the higher the indexes, the more similar
the analytes should be. A similar analysis can be made for
the single coincidence index related to the analyte. Indexes
should always indicate the error used to calculate them.
A double coincidence index (DCI) can be determined by
taking into account the coincident plus the non-coincident
(NDCI) peaks of both the analyte and the reference, referred
to the total number of peaks (peaks of analyte plus peaks
of reference). The DCI and NDCI can be calculated using
the following relations:
A second mode is to calculate the coincidence
between the peaks of the spectrum of an analyte and
those of a reference. The greater the coincidence, the
greater the similarity between the two. As a particular
case of coincidence, the continence of peaks in the
reference spectrum within the analyte spectrum can also
be calculated. These comparisons are based on frequency
values only (intensities have not been considered in the
present version of the software).
The analysis of the coincidence of peaks of two spectra
can be performed in many ways, and depending on how
they are considered, different indexes can be established.
The following indexes are defined in this paper:
The single coincidence index (SCI) relates the ratio of
the number of coincident peaks between the analyte and the
reference to the number of peaks of the reference.An index
relating the same number of coincident peaks between the
analyte and the reference to the number of peaks of the
analyte could also be practical. Here, a group of indexes
relating these types of coincidence can now be expressed
based on the following parameters: the total number of
peaks of the analyte (a); the total number of peaks of the
reference (b); the number of peaks of the analyte coinciding
with those of the reference (c); the number of peaks of
the reference coinciding with those of the analyte (d);
and the error interval for the peak values allowed for the
calculations (this error interval is added to the calculations
to handle the imprecision of the spectrometer when
assigning frequency values to the peaks).
DCI = [(c + d) / (a + b)] × 100
NDCI = 100 – DCI
(2)
(3)
The DCI index gives a better idea (when compared with
the SCI) of how similar two spectra are.
To facilitate the understanding of the coincidence/
continence concept, a pictorial representation of the indexes
is shown in Figure 3.
A single coincidence index relative to the analyte (%):
SCIana = (c / a) × 100
Results and Discussion
A single coincidence index relative to the reference (%):
SCIref = (d / b) × 100
These two indexes indicate (i) the number of peaks of
the analyte coincident with peaks of the reference relative
From an initial observation of a set of 30 (printed)
infrared spectra of the white precipitates (later extended
to 151), grouping the spectra visually (empirically
and roughly) into four classes (called VA-classes)
Figure 3. Pictorial representation of the indexes of the coincidence and continence between two infrared bar spectra.

1
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Using Bar Infrared Spectra and Coincidence Indexes to Study the Diversity of Solid Cyanuric Acid Structures
J. Braz. Chem. Soc.
Figure 4. Infrared spectra of the cyanuric acid VA-classes derived from trichloroisocyanuric acid reactions.
1
3
based on the visual pattern presented by the peaks in
region 3600-2500 cm was possible. Figure 4 shows a
representative infrared spectrum of each class.
Table 2. C NMR results for the analytes produced in the reactions
-
1
listed in Table 1
1
3
C NMR
These spectra are clearly different, and the spectra
within each class are similar but not equal. The comparison
between two spectra could be established by examining the
coincidence between the peaks of both spectra. However,
obtaining (good) quantitative data by comparing two printed
spectra (as the ones above) using either method is difficult
if not impossible. Conversely, a quantitative measurement
of the coincidence or continence between two spectra may
be easily and quickly accomplished using bar spectra and
appropriate algorithms. In both cases, a relation between two
quantities of the same species is measured, with the ratio
between the two being represented by a number (indexes).
Other methods for comparatively quantifying infrared
spectra are described in the literature. For instance,
Analyte
VA-class
Solvent
peaks / ppm
insoluble
insoluble
insoluble
149.01
0
2
0
1
1
4.10
05.10
9.04
4.06
7.05
1
1
–
–
1
–
2
DMSO
2
149.11
DMSO
17.06
33.09
15.06
2,3
2
149.07
DMSO
149.13
DMSO
3
149.04
DMSO
1
2
1
2
2
4
8.04
3.04
9.06
1.04
6.06
7.18
3
149.08
DMSO
3
149.07
DMSO
4
150.35
DMSO/difficult to dissolve
4
insoluble (plates)
insoluble (plates)
149.17
–
2
5
Luo et al. used three-dimensional Hirshfeld surfaces and
two-dimensional fingerprint plots to quantitatively compare
the polymorphs of pyrazinamide.
4
–
2,3
2
DMSO
DMSO
ACN
TCI
150.09
1
3
C NMR of the white precipitates
–
145.33
acetone-d
6
VA-Class: four classes based on the visual pattern presented by the peaks
-1
in region 3600-2500 cm ; NMR: nuclear magnetic resonance; DMSO:
Although all these precipitates are expected to be
dimethylsulfoxide-d ;ACN: cyanuric acid; TCI: trichloroisocyanuric acid.
6
cyanuric acid, because the infrared spectra are quite
dissimilar, the first question to be answered was whether or
not they are all really the same chemical species.A prompt
except analyte 19.06, which had a single peak at
150.35 ppm. Analytes 4.10, 205.10, 9.04, 21.04 and 26.06
were insoluble in DMSO (macroscopically, they appeared
to be plates, in contrast to the others). Therefore, it can be
established that the analyzed samples in solution presented
13
answer was provided by obtaining C NMR spectra of the
analytes dissolved in DMSO. The chemical shifts recorded
for these analytes are presented in Table 2.
Table 2 shows that the spectra of the analytes soluble
in DMSO exhibited only one peak at 149.07 ± 0.06 ppm,
13
only one peak at 148.58 ± 0.57 ppm. The C NMR spectra

Vol. 29, No. 7, 2018
Nilo et al.
1505
in solution provide a clear indication that the precipitates
are symmetric single carbon-type products.
of recrystallization on the class of the product formed is
pertinent.
2
7
The simulated spectra for cyanuric and isocyanuric
In the literature, crystallization is considered a
critical operation regarding polymorphs, where sensitive
parameters such as solvent and cooling rate of the
solution should be carefully controlled to obtain a given
“monomorph”. Many references on how to conduct
well-monitored crystallization operations, particularly
those concerning active pharmaceutical ingredients (APIs),
26
acids showed a peak at 163.87 ppm for the former species
and one at 149.90 ppm for the latter species, indicating
that isocyanuric acid is the species present in solution
and is most likely predominant in the solid product. The
value of 150.3 ± 0.25 ppm is appropriate for the carbon
atom of an imide group. The slight displacement of the
delta values of most analytes from the central value may
indicate a (small) difference in the carbon environment
of these analytes.
28
can be found in the literature.
In general, we observed (very small) changes in the
number of peaks when the analytes were recrystallized from
water but no changes inVA-classes (no strict protocols were
used in these recrystallizations). These results lead to a few
persistent questions: why does recrystallization of a cyanuric
acid analyte of a given VA-class from water tend to produce
an analyte of the same class (albeit occasionally adding or
subtracting peaks from the spectrum of the original analyte)?
Why does the analyte not move toward a more stable
configuration? If the solubilization of the analyte would result
in the complete disruption of the original solid in isolated
molecules (as observed with the dissolution of the analytes
in DMSO), then the new solid formed by recrystallization
of the dissolved individual molecules would be expected
to crystallize into a more stable structure. However, it was
observed that even when the crystallizations were conducted
under no special conditions, the VA-class of the original
analyte was conserved. The retention of the VA-classes
after recrystallization of the analytes of differentVA-classes
suggests that during the process of recrystallization, a
“memory” of the original solid form remains in the solution
with the entire polymorph or parts of it (oligomorphs)
acting as seeds. This proposal also indicates that the solid
does not decompose completely in solution to form isolated
cyanuric/isocyanuric acid molecules (at least, not under the
recrystallization conditions used in this study); otherwise,
the migration of at least one of the analytes from a given
class to another class would be expected.
Despite these observations, the behavior of some of
the analytes causes doubt about the “class conservation”
mentioned above. Infrared spectra I001504S and
I001504A of analyte 15.04, for instance, are two spectra
from the same sample prepared on two different dates,
05/07/2012 and 05/25/2016, respectively (the only
difference between these two spectra seems to be that
the analyst picked up different parts of the same sample
from the same vial at different times). Table 3 reveals that
each spectrum belongs to a different VA-class. According
to this Table, the same observation could be made with
analytes 17.06 and 47.18. A question could be raised
regarding whether these two VA-classes were present
13
The spectra of solid C NMR for the complete set of
analytes in this paper are more complex, and the discussion
of these spectra will be presented in another publication
jointly with other data.
Furthermore, these measurements allowed the
establishment of a clear distinction between VA-classes 1
and 4 and VA-classes 2 and 3 because of their solubility
in DMSO: VA-classes 1 and 4 are insoluble (with the
exception of analyte 19.06, which was, however, difficult
to dissolve), whereas VA-classes 2 and 3 are soluble.
1
3
The list is completed with the C NMR peaks of
Sigma-Aldrich cyanuric acid (150.09 ppm in DMSO) and
trichloroisocyanuric acid (145.33 ppm in acetone-d6).
Additional information can be added here: energy
dispersive X-ray spectroscopy (EDS) measurements of
analytes of VA-classes 1 and 4 that did not dissolve in
DMSO showed the presence of potassium in their structure
(
analyte 21.04, VA-class 4, 21.6% K; analyte 26.06,
VA-class 4, 11.9% K; and analyte 205.10, VA-class 1,
5.3% K). Despite being categorized in VA-class 4,
1
analyte 19.06 was different from the other analytes of
this class: it did not crystallize into plates (unlike all the
others) and presented a very low value of potassium: 0.1%.
The presence of chlorine, an indication of possible residue
from trichloroisocyanuric acid, was detected only in trace
amounts in some of the analytes and should not interfere
with the spectra of the analytes (the presence of chlorine
2
3
was verified using very sensitive Feigl tests).
13
On the one hand, the results from the C NMR spectra
of a group of analytes in solution described in this paper
showed that they had only one peak with practically equal
chemical shifts. On the other hand, the bar infrared data
of the respective solid analytes differ quite massively. The
combination of these two pieces of information suggests
the existence of different arrangements of the isocyanuric
acid in the solid analytes (polymorphism).
Since all analytes resulting from these reactions were
recrystallized from water, presenting a short discussion
regarding the observations made of the possible effect

1
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Using Bar Infrared Spectra and Coincidence Indexes to Study the Diversity of Solid Cyanuric Acid Structures
J. Braz. Chem. Soc.
from the very beginning, i.e., whether they were formed
simultaneously during the reaction with TCI, or whether
one class moved to the other (albeit only slightly) during
the recrystallization process (this possibility could be
feasible if some individual molecules of cyanuric acid
were formed in the dissolution process, and when cooled,
these individual molecules crystallized into another class).
Another, more provocative hypothesis is the occurrence
of a natural and spontaneous transformation of one class
into the other with time and prevalent conditions.
Table 4. Different analytes of a same reaction showing differentVA-classes
Reaction
Analyte
9.04
Spectra
I000904A/B/C/S
I000906S
VA-class
1
2
4
3
3
2
3
2
3
2
2
2
3
3
4
3
3
3
9
1
.00
9.06
10.04
I001004A/B/C
I001006A/B/S
I001504A
0.00
1
1
0.06
5.04
1
1
5.00
7.00
15.04
I001504B/S
1
1
5.06
7.05
I001506A/B/C/S
I001705A/B/C/S
I001706A/B
I001706C/S
Table 3. The same analytes presenting spectra of different VA-classes
1
7.06
Reaction
Analyte
15.04
Spectra
5.04B/S
5.04A
7.06S/C
7.06A/B
7.18S
7.18A/B/C
VA-class
1
1
1
7.10
7.18
8.04
I001710
1
3
2
2
3
3
2
1
1
4
5.00
7.00
7.00
I001718A/S
1
I001804A/B/C/S
I001806S
1
17.06
47.18
1
3
8.00
3.00
18.06
1
1
3
8.09
3.04
I001809S
4
I003304S
4
33.09
3.11
I003309S/A/B/C/D/E
I003311S/A/B/C
VA-Class: four classes based on the visual pattern presented by the peaks
-
1
in region 3600-2500 cm ; spectra ending in S were made in the period
of 2012 and 2013; spectra ending in A, B or C were made in the period
of 2015 and 2016.
3
VA-Class: four classes based on the visual pattern presented by the peaks
-1
in region 3600-2500 cm ; spectra ending in S were made in the period
of 2012 and 2013; spectra ending in A, B or C were made in the period
of 2015 and 2016.
Another question addresses the crystallization from the
mother liquor that resulted from the first crop. Table 4 shows
that, in many cases, the second crop belonged to another
VA-class, as indicated by its infrared spectra.Analyte 10.04,
for instance, presents all three spectra (I001004A, B and C)
inVA-class 4, whereas analyte 10.06 exhibited three spectra
procedures able to reproduce a given class for further
studies would also be useful.
An overall view of the reaction conditions and the
VA-classes produced is presented in Supplementary
Information Table S1, which shows that 135 analytes
belong to VA-class 1, 53 to VA-class 2, 29 to VA-class 3
and 27 to VA-class 4. Sixteen analytes were derived from
Sigma-Aldrich cyanuric acid (VA-class Y), bringing the
total to 27 different reaction conditions and 151 analytes
and the corresponding infrared bar spectra. These analytes
include the different crystallization fractions of the product
of a reaction and the repetitive infrared spectra obtained
for each of the analytes.
Four variables were studied in these reactions: (i) the
nature of the salt (potassium bromide and chloride,
ammonium chloride and bromide and no salt); (ii) the
temperature of the reaction. As the reaction is quite
exothermic, particularly when ammonia is used, the
temperature was carefully controlled by performing some
reactions an Easy-Max reactor (Mettler-Toledo), and
these reactions were compared with reactions performed
in normal laboratory flasks with little attention paid to
temperature changes. As TCI was added via the slow and
dropwise introduction of a solution of the compound in
(I001006A, B and S) inVA-class 3. Reaction 15.00 displays
very bizarre behavior: analyte 15.04 exhibits two different
VA-classes (I001504A of VA-class 3 and I001504B and S
ofVA-class 2), whereas all four 15.06 spectra of I001504A
have the same VA-class of 3. A hypothesis may also be
raised for these facts: a fractionation of the original material
when proceeding from one crystallization to the other or a
change in class due to the heating and time to which this
sample was subjected (less probable). Further research is
needed to clarify these occurrences.
Correlation among reaction conditions and VA‑class of
cyanuric acid formed
Different observed VA-classes resulting from different
reaction conditions raises the question of whether the
reaction conditions induce the formation of a certain
form of solid cyanuric acid (VA-class). In addition to the
theoretical interest in understanding how the conditions
may induce the structure of the solid formed, having

Vol. 29, No. 7, 2018
Nilo et al.
1507
acetone (with the exception of reaction 31.00, in which
small lumps of solid TCI were added directly to the
ammonia solution), the temperature of the reaction flask
did not change much; (iii) the nature of the medium, which
was varied from water/acetone, ammonia/acetone, dilute
ammonia/acetone and pure ammonia; and (iv) the presence
or absence of methyl acrylate or the use of acrylonitrile as a
substitute for the acrylate as the chlorine/bromine acceptor.
The data in Table S1 were used to produce Table 5,
which lists 19 different reaction conditions that lead to
analytes of only one VA-class.
A more detailed analysis of the influence of the reaction
parameters used to define which reactions lead to a certain
VA-class will now be presented:
Table 5 shows that the formation of VA-class 1 is
strongly dependent on the presence of potassium salts and
that no VA-class 1 analytes are formed when ammonium
salts or no salt are used. Conversely, VA-class 2 and
VA-class 3 analytes occur mainly when ammonium salts are
used. VA-classes 1 and 4 occurs mainly when KBr is used.
The 21 reactions performed with KCl are distributed among
VA-classes 1 (10), 2 (8) and 3 (3), whereas no VA-class 4
analytes were produced.
Regarding the influence of temperature, Table 5 shows
that lower temperatures (0 °C) favor the formation of
VA-classes 3 and 4 over VA-classes 1 and 2. The reaction
is highly exothermic, and the number of reactions that lead
to VA-class 2 analytes is greater when the temperature is
increased from 0 to 25 °C and even when the reactions are
conducted without strict temperature control (r.t./ca. 28+).
These findings indicate that the formation of VA-class 2
products could be favored by an increase in temperature.
The products of the reactions performed in
H O/acetone and NH OH/acetone are not neatly distributed
2
4
Table 5. Reactions leading to analytes of a single VA-class
Halogen acceptor
Acceptor
TCI
Salt
Temperature /
Medium/solvent
Reaction
2.00
°
C
No. of moles
No. of moles
Salt
VA-class 1
KBr
No. of moles
AcrMet
AcrMet
–
0.056
0.050
0.000
0.020
0.017
0.017
0.116
0.100
0.116
r.t./ca. 28+
r.t./ca. 28+
r.t./ca. 28+
H O/acetone
2
3
.00
KBr
KBr
H O/acetone
4.00
2
2
05.00
NH OH/acetone
11.00
4
VA-class 2
–
0.000
0.050
0.111
0.050
0.050
0.050
0.050
0.017
0.017
0.371
0.017
0.017
0.017
0.017
–
0.000
0.100
0.222
0.000
0.100
0.100
0.100
r.t./ca. 28+
r.t./ca. 28+
25
NH OH/acetone
12.00
14.00
4
AcrMet
AcrMet
AcrMet
AcrNit
AcrMet
AcrNit
NH Br
H O/acetone
4
2
NH Cl
H O/acetone
29.00
4
2
–
r.t./ca. 28+
r.t./ca. 28+
r.t./ca. 28+
r.t./ca. 28+
HCl/H O/acetone
210.00
212.00
214.00
215.00
2
KCl
KCl
KCl
H O/acetone
2
H O/acetone
2
H O/acetone
2
VA-class 3
–
0
0
0.017
0.017
0.017
–
–
0.000
0.000
0.100
–10
r.t./ca. 28+
25
NH OH /acetone
24.00
25.00
27.00
4
aq
–
NH OH /acetone
4 aq
AcrMet
0.05
KCl
H O/acetone
2
VA-class 4
AcrMet
AcrMet
AcrMet
AcrMet
AcrMet
–
0.050
0.050
0.050
0.050
0.050
0.000
0.017
0.017
0.017
0.017
0.017
0.017
KBr
0.012
0.100
0.100
0.116
0.116
0.000
0
H O/acetone
20.00
16.00
19.00
21.00
26.00
31.00
2
NH Br
r.t./ca. 28+
NH OH/acetone
4
4
NH Br
0
0
NH OH /acetone
4
4
aq
KBr
KBr
–
NH OH /acetone
4 aq
25
–15
H O/acetone
2
NH OH
4
-1
TCI: trichloroisocyanuric acid;VA-class: four classes based on the visual pattern presented by the peaks in region 3600-2500 cm ;AcrMet: methyl acrylate;
AcrNit: acrylonitrile; r.t.: room temperature.

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J. Braz. Chem. Soc.
among VA-classes 1, 3 and 4, although it seems that
classes were defined, calledVA-classes 1 to 4, as presented
in the beginning of this session.
H O/acetone favorsVA-class 1 slightly more. However, this
2
latter medium seems to very strongly induce the formation
of VA-class 2 analytes.
FI-plots very conveniently allow the recognition of
similarities among the analytes (after all, they are all
cyanuric acid), as well as differences among the classes or
among analytes of a given class. Moreover, these plots very
clearly show the great diversity of the infrared absorption
frequencies of the analytes.
Figure 5 displays the FI-plot for the cyanuric acid
VA-classes, showing the distribution of the frequencies for
the various classes. The most notable feature of this plot
is that the distribution of the frequencies is different for
each VA-class and that no two classes are superimposable.
Although they show common frequencies, these classes
concurrently present characteristic frequencies not present
in the others. This latter feature was the criterion used to
define aVA-class. The FI-plot makes the differences among
the classes very clear and precise.
To determine the role of the acrylate moiety in
VA-class formation, reactions were performed with no
methyl acrylate or acrylonitrile and compared with those
conducted with these chlorine/bromine acceptors. The
reactions of TCI dissolved in acetone with ammonia/
acetone and with or without salt at different temperatures
produced all types ofVA-classes. However, onlyVA-class 4
was produced when the reaction was performed with
solid TCI on pure ammonia (no acetone), no acrylate
moiety and no salt at –15 °C. The reaction of solid TCI
with ammonia is very exothermic. At room temperature,
it produces plenty of fumes of ammonium chloride and,
after a few minutes, starts producing a strong green color
29
upon reacting with the Berthelot reagent. This observation
can be explained by the formation of chloramine (NH Cl)
2
and its involvement as an intermediate in the process of
30
color production because, as stated by Patton and Crouch,
when sodium aquopentacyanoferrate was substituted for
“
sodium nitroprusside the reaction mixture turned green”.
No green color being produced when the reaction is
conducted with TCI dissolved in acetone and further treated
with the Berthelot reagent (only a brown product is formed)
may be a good indication of chloramine formation since, in
acetone, it would be captured to form a Schiff base. Studies
are in progress to clarify these observations.
We may conclude this section by stating that
analytes of a single VA-class may be produced when the
reaction conditions presented in Table 5 are followed.
Nevertheless, although no strict controlled conditions
for the reactions were used, it should be stressed that
if there is an objective to obtain a certain VA-class, it
is advisable to conduct the reactions under stringently
controlled conditions, particularly those involved in the
Figure 5. FI-plot for cyanuric acid VA-classes.
Figures 6-10 show FI-plots for the analytes of
VA-classes 1 to 4 and for the Sigma-Aldrich cyanuric acid.
Because a class defines a proper pattern for the structure
of the solids, the members of a class would be expected
to exhibit very similar spectra. However, although they
present many common peaks at a first glance, the analytes
of a single class are observed to not all absorb exactly at the
same frequencies, with the differences mainly being due to
the diversity of the structures of each solid analyte (it should
also be considered the error of the infrared instrument).
Figures 6-10 show that they actually present similarities, i.e.,
many frequencies are common to all analytes of the class, but
they also present many differences, i.e., many frequencies
do not have similarities among all the analytes. The Sigma-
Aldrich cyanuric acid spectra (VA-class Y) are remarkably
similar, but not equal. Through the bar representation of
the spectra, these graphs very clearly stress once more the
2
7
crystallization processes.
The bar infrared spectra of solid cyanuric acid analytes:
maps of analyte frequency distribution and classes of
cyanuric acid analytes
The diversity of frequencies presented by the infrared
spectra of the analytes obtained from the reactions with
trichloroisocyanuric is, indeed, overwhelming. This section
is a tentative attempt to find some order in the chaos of
frequencies encountered.
The first step to achieve this goal was to confine analytes
into classes based on similar patterns presented (visually) in
-1
region A’ (3600-2500 cm ) of the infrared spectrum. Four

Vol. 29, No. 7, 2018
Nilo et al.
1509
Figure 6. FI-plot for VA-class 1 analytes.
Figure 9. FI-plot for VA-class 4 analytes.
Figure 10. FI-plot for VA-class Y analytes.
Figure 7. FI-plot for VA-class 2 analytes.
characteristic set of frequencies of a VA-class that will
not collect analytes from another class when applied to
a mixture.
To find frequencies that could be used to define a
class, a group of frequencies must be used. A group of five
frequencies was then chosen to define, for each of the five
classes, arrays of five characteristic frequencies of each
VA-class that, at the same time, do not collect analytes of
any other class.
To determine the class markers, arrays of 5 frequencies
must be computed for each VA-class by combining the
(different) frequencies of the analytes of that class with
size 5 and then searching for which analytes absorb in all
and each of the generated 5 frequencies (plus or minus
the error considered). However, using all the different
frequency values of aVA-class would require the handling
of a number of possible arrays that may be too high for
the software/computer presently in use (for instance,
combiningVA-class 1 containing 146 different frequencies
with size 5 leads to 15,853,624 combinations).
Figure 8. FI-plot for VA-class 3 analytes.
great diversity of infrared absorption frequencies for solid
cyanuric acid and, consequently, the great diversity of spatial
arrangements that solid cyanuric acid may assume.
The class marker concept
Table 6 presents 5-frequency markers for VA-classes 1
to 4 and for the Sigma-Aldrich cyanuric acid class, covering
the region A’ of the infrared spectrum. The total number
The next step in the analysis of these spectra raises
the concept of class markers, which are defined as a

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Table 6. 5-Frequency markers for cyanuric acid VA-classes
-
1
5
-Frequency marker / cm
No. of analytes in the No. of analytes in the
Class/region
δ
class
5-frequencies marker
Frequency 1 Frequency 2 Frequency 3 Frequency 4 Frequency 5
2
2
4
3
2
1
1
2
2
6
6
3
8
2
4
4
a
b
a
b
a
b
a
b
a
b
3144
3456
2885
3213
3446
3446
3035
3564
3413
3213
3055
3143
2832
3084
3413
3149
3032
3167
3213
3084
2968
3055
2780
2885
2881
3028
2981
3043
2885
2885
2829
2829
2700
2831
2779
2882
2978
2978
2829
2781
2704
2704
2633
2780
2631
2779
2827
2827
2779
2700
a
VA1
VA2
VA3
VA4
26
7
53
29
27
16
17
6
11
15
19
1
8
1
1
5
3
b
VAY
3
a
b
VA1 stands for visual spectrum of class 1 for the region A’of the infrared spectrum, and so on; the letter “Y” in VAY refers to the class/group of cyanuric
acid samples derived from the Sigma-Aldrich product. δ: difference between analytes in the class and analytes in the 5-frequencies marker; a: the marker
that contains the maximum number of analytes among all 5-frequency markers; b: the marker that contains all important/reference peaks of the printed
-
1
-1
spectra. Region A’: 3600-2500 cm (error = ± 2 cm ).
of peaks of the class and the number of peaks of the
corresponding marker are also shown.
Two types of markers are shown in Table 6: one
(
frequencies present in lines marked “a”) that collects
the largest number of analytes, sometimes close to the
total number of analytes of the VA-class, and the other
(
shown in lines “b”) that contains all important/reference
peaks of the printed spectra. Markers of line “a” may not
collect some of the peaks that were used visually to define
the VA-class because only a limited number of groups of
5
frequencies derived from the total number of frequencies
of the class were computed. Therefore, a question arises:
which marker should be preferred for representing the
VA-classes when needed? The markers with the largest
number of analytes, or the others encompassing fewer
analytes but containing the frequencies responsible for
the visual classification of the VA-classes? It seems more
reasonable to adopt the marker that collects the largest
number of analytes as the one to use as theVA-class marker
when needed. In this way, theVA-class of any cyanuric acid
analyte may be determined by determining the continence
Figure 11. FI-plot of 5-frequency markers with the largest number of
analytes (lines marked “a” in Table 6).
(
instead of the coincidence) of the respective spectra
with the V-class markers. This tool may be of particular
importance when applied to the characterization of API
polymorphs.
Figures 11 and 12 show FI-plots for these two types of
5
-frequency markers in order to emphasize that diversity
is always present.
Coincident frequencies among the VA-classes indicate
that the corresponding analytes should contain similar
structural moieties in the same way that non-coincident
frequencies should correspond to different structural
Figure 12. FI-plot of 5-frequency markers containing the most significant
peaks shown in the “printed” spectra (lines marked “b” in Table 6).

Vol. 29, No. 7, 2018
Nilo et al.
1511
moieties. Both sets of information are important for
establishing the 3D structures for the solids.
to be included in this text; thus, only the relevant results will
be shown and discussed here. For more details about these
Tables/databases, the authors should be contacted.
These results show that although the initial choice
of the VA-classes was made empirically (visually), it is
possible to recognize sets of characteristic frequencies
of analytes of each VA-class that are absent in the others,
thereby providing evidence for the initial hypothesis of the
existence of these classes. The common peaks among the
classes define cyanuric acid as a chemical species, whereas
the characteristic group of peaks of a class establishes that
the analyte belongs to a particular set of structures of solid
cyanuric acid.
Table S1 (Supplementary Information section) also
allows a discussion regarding the issue of the analytes
that have a 100% coincidence index (equal analytes) or
a 0% coincidence index (completely different analytes).
Figure 13 shows these cases. A case of 100% coincidence
may be expected for analytes from the same reaction (as
occurs with analytes 3.10.A and 3.10.C of VA-class 1);
however, pairs of spectra of analytes from different
reactions with 100% coincidence were also observed:
2
804C and 3311C, both of VA-class 2.
The coincidence and continence indexes for the cyanuric
acid analytes
In contrast to the cases with 100% coincidence, in
the pairs with 0% coincidence, each analyte belongs to a
differentVA-class, but no pairs with analytes ofVA-class 4
were formed.
A very general analysis of the infrared spectra of
cyanuric acid involves the calculation of the respective
coincidence and continence indexes among all the analytes
of the groups. This calculation is accomplished using
confrontation matrices. In the present case, a 159 × 159
confrontation matrix was set to calculate both the SCI
relative to the reference (which indicates how much of the
reference is contained in the analyte) and the DCI (which
provides some more information about the coincidence
between the spectra) for the 159 spectra of the analytes of
cyanuric acid analyzed in this paper. The resulting 2D matrix
has 25077 slots filled with the respective indexes. For the
purpose of analysis, it is better to have the results presented
in a list sorted in descending order of the double and single
coincidence indexes. However, in any case, the list is too long
In the cases where the single coincidence index is
higher than that of double coincidence index, the number
of peaks of the analyte is generally much higher than
the number of peaks of the reference, indicating that the
reference is completely contained within the analyte and
that the analyte has some peaks “left over”. For instance,
the single continence index between analytes 2904S
(VA-class 2, 36 peaks) and 1204S (VA-class 2, 11 peaks)
is 100%, whereas the double coincidence index is 48.94%.
However, there are some cases where the single continence
index is lower than the double coincident index, as observed
with the pair 4718B (VA-class 2, 13 peaks) and 3309A
(VA-class 2, 14 peaks) having a double coincidence index
of 62.96% and single continence index of 57.14%. In this
Figure 13. Graphic comparison of analytes according to their coverage indexes: Left: two analytes with a 0% double coincidence index (no coincidence
exists among any of the peaks of analytes I021509S and I000904A). Middle: two analytes with a 100% double coincidence index (all peaks of analytes
I003311C and I002804C coincide). Right: two analytes with 57.15% double coincidence index and 100% single continence index of the reference
(I001705B) relative to the analyte (I001415S). Notice that the reference is completely contained within the analyte. Notice also that in an enlarged view
of the spectra, not all the peaks of the reference coincide perfectly with those of the analyte, but the software takes them as coincident due to the error of
-
1
±
2 cm given to the frequency values.

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Using Bar Infrared Spectra and Coincidence Indexes to Study the Diversity of Solid Cyanuric Acid Structures
J. Braz. Chem. Soc.
Figure 14. Graphic comparison of analytes 2904S and 20919S presenting a single coincidence index of 100% and a double continence index of 42.22%
and of analytes 4718B and 3309A presenting a double coincidence index of 62.96% and a single coincidence index of 57.14%.
case, only ca. half of the peaks of the reference coincide
with peaks of the analyte. Thus, there is a reasonable “left
over” from both analytes. The spectra relative to these two
cases are shown in Figure 14.
Analytes selected from a 5-frequency marker generally
have high double coincidence and single continence
indexes, as expected. For example, the pair 1706S and
peaks that are common to the various spectra of the group. It
is used primarily to “average” (to some extent) the slightly
different spectra of an analyte into one spectrum.
Table 7 clearly shows the differences between
these spectra based on their coverage indexes: a double
coincidence index of only 26.19%, and the continence of the
SDBS spectra into the Sigma-Aldrich spectra of 22.73%.
The bar graph representations of these two spectra are
also compared (Figure 15), again showing very clearly the
difference between these spectra.
3
309S exhibits a double coincidence index of 96.30% and
a single coincidence index of 92.86%. However, this does
not occur in all cases. For instance, with the pair 21218B
and 3309A, the double coincidence index is 61.54%, and
the single coincidence index is 57.14%. Therefore, although
some patterns could be established for the solid cyanuric
acid analytes, the diversity of structures is high, and a
spreading of all the parameters can be observed over the
whole range of frequencies.
Use of coincidence indexes to measure the homogeneity
of an analyte
Coincidence and continence indexes are good
qualitative and quantitative criteria for defining the
similarity and difference among bar spectra. In this way,
the use of these indexes can be extended further to measure
the homogeneity of an analyte. Previously, the set of spectra
of a solid analyte taken from a same vial at different times
was shown to often be different from one another (some are
only slightly different, but very rarely they are all equal),
with the difference arising from heterogeneities in the
The results of a small study of the coincidence and
continence of the Spectral Database for Organic Compounds
3
1
(
SDBS) spectrum for cyanuric acid (No. 2043) and the
common spectra for the Sigma-Aldrich cyanuric acid are
particularly interesting. A common spectrum is, as the
name indicates, a spectrum that results from a comparison
operation of different spectra of a group, leaving only the
-1
Table 7. Comparison of the coverage indexes between the Sigma-Aldrich and SDBS cyanuric acid infrared spectra. Region: 3500-500 cm ; intensity:
-
1
0
-100; error = ± 2 cm
Sigma-Aldrich ACN (analyte)
No. of
SDBS (reference)
No. of
Coverage index / %
No. of
coincident peaks
No. of peaks
non-coincidence
non-coincidence
peaks
No. of peaks
Double
26.19
Single (reference) Single (analyte)
peaks
2
2
17
5/6
14
20
30.00
22.73
ACN: cyanuric acid; SDBS: Spectral Database for Organic Compounds.

Vol. 29, No. 7, 2018
Nilo et al.
1513
Figure 15. Comparison between the cyanuric acid spectra from Sigma-Aldrich (upper spectrum) and SDBS (lower spectrum).
sample. The concept of coincidence indexes may thus be
extended to quantify the homogeneity of an analyte via a
homogeneity index (HI) calculated from the coincidences
among the samples. To calculate this index, it is first
necessary to calculate the double coincidence indexes
among the analytes using a confrontation matrix among the
bar spectra of the analytes involved in the determination
of the homogeneity. Second, the calculated values of the
coincidence indexes are averaged, and the mean deviation
is also calculated. The HI is then calculated by means of
the following equation:
calculated from coincidences among their bar infrared
spectra. Homogeneity can be scaled considering that
for a completely homogeneous sample HI = 100 (equal
samples will give a coincidence indexes equal to 100), the
average will also be 100, and the mean deviation is zero
for any value of δ. If the analyte comprises a mixture of
completely different analytes (no coincidences at all among
the spectra), then HI = 0. Mixtures of solid analytes of the
same species will give intermediate values between 0 and
100: the more homogeneous the sample, the closer the HI
will be to 100.
All analytes described in this paper are solids
composed of one species of a molecule: isocyanuric acid
Homogeneity index = average – (δ × mean deviation) (4)
(although some analytes may contain some of its tautomer,
This equation indicates that homogeneity increases
when the average increases (in other words, when the
coincidence among the analytes increases). However, the
average does not account for everything.
cyanuric acid). If the definition of polymorph is derived
directly from what the word says (many forms, from the
Greek poly = many and morph = form), then the special
“macro” shapes that these analytes show (plates, rods,
sometimes not well-defined agglomerates of “particles”, a
fine talc-like powder, etc.) give the observer the impression
that they should be seen as polymorphs, as indicated by their
quite different infrared spectra. We can therefore say that
we have obtained polymorphs of cyanuric acid. However,
due to the great diversity of infrared spectra that these
analytes present, it is difficult to say how proper it would
be to define which are the crystals of cyanuric acid and/or
polymorphs because it is difficult to compare the observed
properties with the ones presently required to characterize
Adding the concept of dispersion to the values around
the average is necessary because homogeneity increases
when the dispersion of values around the average decreases.
Therefore, the mean deviation should also be used to
complement the calculation of homogeneity. δ is an
empirical factor (chosen by the analyst) that may be added
to the calculations to modulate the contribution of the mean
deviation: it may vary from 0 (neglecting the influence of
the deviations) upward. One is considered the default value.
To demonstrate the use of the HI, an example involving
the group of analytes 0310A, 0310B, 0310C and 0310S
follows. Four spectra of these analyte generated 12
coincidence indexes calculated from the respective square
matrix of 4 × 4 (confrontation between equal spectra are
eliminated). The average value of the indexes is 81.93,
and the mean deviation is 6.02. For a value of δ = 1, the
homogeneity indexes will be 75.91 relative to the double
coincidence index. This indicates that the homogeneity
of an analyte can now be associated with a number
27
polymorphs. Notably, none of the cyanuric acid analytes
melt but instead sublime.
Polymorphs are generally characterized more thoroughly
by a group of analytical methods, including infrared
spectra, X-ray diffraction, thermal analysis and optical
27
microscopy. We decided to limit this paper solely to a
discussion of the method that uses the infrared bar spectra,
with its maps of frequencies and coincidence indexes, as
a precondition for develop the models necessary to better

1
514
Using Bar Infrared Spectra and Coincidence Indexes to Study the Diversity of Solid Cyanuric Acid Structures
J. Braz. Chem. Soc.
explain the vibrational behavior of solid cyanuric acid.
The coupling of infrared bar results with X-ray diffraction,
thermal analysis and microscopy of the samples from this
paper will be the subject of another publication, which will
aim to more rigorously define the solid phase arrangements
of cyanuric/isocyanuric acid molecules.
display precise frequencies in a simple discrete display,
facilitating the production of algorithms and design
software to answer posed questions. Calculations of
coincidence indexes and the establishment of class markers
and FI-plots are examples of the ability of bar spectra to
translate spectra into numbers.
The data provided in this paper indicate the need for a
deeper study to correlate frequencies to molecular moieties
in solid cyanuric/isocyanuric acid and for better models
to simulate vibration frequencies in order to describe the
configurations of molecules in space that mimic those of
the bar spectra of real molecules.
Conclusions
This paper showed the great diversity of the infrared
spectra of the analytes produced from various reactions
of trichloroisocyanuric acid (all said to be cyanuric acid).
It also described the characterization of the similarities
and differences among the products through the use of
graphs (FI-plots) or numbers (indexes), both of which were
calculated from the respective bar spectra.
Finally, the use of the bar spectra together with
coincidence indexes may be seen as a step forward for
infrared spectrometry because it opens a large space for
investigating the fine structure of the spectra of single
molecules and mixtures, representing a better way to assign
frequencies to vibration modes through its neater and more
precise numbers and to calculate the relationships between
spectra. Infrared spectroscopy has been an important
The method used in this paper to create an infrared bar
spectra directly from the output of the spectrometer was
successful, and the produced bar spectra could be used to
quantitatively compare infrared spectra via coincidence/
continence indexes. The usefulness of the method was
demonstrated with a set of infrared bar spectra of the white
precipitates resulting from reactions of trichloroisocyanuric
acid, all of which were said to be cyanuric acid. Using this
method enabled the demonstration of the great diversity of
the cyanuric acid analyte spectra, which could be grouped
into (mainly) four classes (VA-classes). The ability to group
these spectra suggests the presence of polymorphs.
The simple three consecutive points algorithm was
effective in creating a bar spectrum directly from the data
generated by the spectrometer. In addition, the common
peaks algorithm can be effectively used to calculate
coincidence and continence indexes in confrontation
matrices. Furthermore, any type of comparison and
calculation is readily accomplished using bar spectra due
to the ease with which they can be handled by software.
Class markers, a set of five bar frequencies common
to the analytes of a VA-class, were established for each
VA-class of cyanuric acid analytes. The concepts of both
class and class markers may be used to characterize classes
of analytes, including polymorphs.
32
tool for studying polymorphism and is widely used by
the pharmaceutical industry as a method to characterize
32,33
polymorphs inAPIs. As bioavailability has been shown to
be dependent on the solid structure of the active molecule, the
characterization of polymorphs inAPIs remains an important
issue in this context. The coincidence indexes calculated from
the bar infrared spectra may contribute to this field through
their capacity to translate spectra into numbers.
Supplementary Information
Supplementary information is available free of charge
at http://jbcs.sbq.org.br as PDF file.
Acknowledgments
The authors thank the Laboratório de Análise,
Departamento de Química Inorgânica, Instituto de Química,
UFRJ. Our particular thanks go to Mrs Leonice B. Coelho
and to Miss Glaucia W. Martins, for running the (many!)
infrared spectra used in this paper. The authors also thank
the Laboratório de Ressonância Magnética Nuclear,
Departamento de Química Orgânica, for the carbon
magnetic resonance spectra of the samples in the solid
phase and in solution.
Many applications can be ascribed to coincidence
and continence indexes based on the bar infrared spectra
of analytes, as it was shown to define, quantitatively,
differences among analytes. The use of coincidence and
continence indexes can be further extended to calculate the
homogeneity of an analyte, to clustering sets of different
analytes (in development), etc.
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