Shirali et al. BMC Chemistry(2024) 18:154
https://doi.org/10.1186/s13065-024-01249-5

BMC Chemistry

RESEARCH

Open Access

Exploring solvatochromism: a comprehensive
analysis of research data of the solvent -soluteinteractions of 4-nitro-2-cyano-azo benzenemeta toluidine
Mahdi Shirali1*, Shohre Rouhani2, Kamaladin Gharanjig2,3 and Fatemeh Mirhashemi4
Abstract
This study investigates the solvatochromic behavior of a new D1 disperse dye, focusing on the 4-nitro-2-cyanoazo-Benzene-metaToluidine type. Using UV-visible spectroscopy, we analyze the dye’s performance in single
solvents and binary mixtures. Our analysis includes the evaluation of solvent polarity parameters and dye structure
parameters, with emphasis on the longest wavelength intramolecular charge transfer absorption band. We identify
nonlinear and linear patterns in the electronic transition energies plots with respect to solvent composition.
Statistical analysis considers correlation coefficients, root mean squared error, mean absolute percentage error,
and other parameters, providing insights into data accuracy and precision. This experimental and statistical study
explores the absorption spectrum, wavelength characteristics, absorption energy, and polarity of a novel azo dye
across various solvent and solute environments. These findings contribute to a comprehensive understanding of
the dye’s photophysical and photochemical properties, potentially enabling applications in optical sensors andadvanced materials.

*Correspondence:
Mahdi Shirali
mehdishirali309@gmail.com
Full list of author information is available at the end of the article© The Author(s) 2024. Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you
give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified thelicensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images orother third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to thematerial. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation
or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://
creativecommons.org/licenses/by-nc-nd/4.0/.

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Graphical abstract

Keywords Solvatochromic behavior, UV-visible spectroscopy, Statistical analysis

Introduction
It is declared that solvents properties including dielectric constant, refractive index values, the dipole moment
and the most pivotal property in this regard, the solvent
polarity have a significant effect on chemical and physical processes. the position of the absorption or emission
spectra band of molecules can be adjusted by the solvent
polarity [1–3].
Solvatochromism is a phenomenon that provides
valuable information about the spectral shift of a soluteinduced by a change in the solvent polarity and describing the interactions that happen in the solvation shell ofsolute [4–7]. Solvatochromism estimates the local field offorces in the interior of liquids, indirectly, by the energyof the intermolecular interactions [8–11]. There are many
several beneficial applications for this phenomenon inindustrial and analytic purposes for instance they can beutilized to develop optical sensor materials to monitor
pollutant levels in the environment [12–15] and also uses
as a Lewis acid-base color indicator [16–21], imaging[22–25] and photo-switching [26, 27]. Conjugated molecules with electron-withdrawing and electron-donatinggroups can be considered an excellent solvatochromic
probe because of the color change of these molecules canbe an indicator for solvent polarity. in these molecules,
electron-withdrawing and electron-donating groups leadto charge transfer within the molecule itself [28]. Amongthe solvatochromic compounds Azo dyes have received
great attention due to their wide application in the printing, plastics, textile, cosmetics and food industries [29,30]. Furthermore, Azo dyes have been utilized as catalyzer exposing to ultraviolet light in photo-catalytic reactions [31]. Some azo dyes could be used as inhibitors fortumour-growth in biological systems [32–34]. The efficacy of azo colorants stems from the straightforwardness of their synthesis through diazotization and azo
coupling processes. The versatility inherent in the myriad
options available for the variation of both the diazo compound and coupling component contributes significantly
to their success. Additionally, their typically high molar
extinction coefficient, coupled with medium to high lightand wet fastness properties, enhances their overall appeal[35].
ET (The electronic transition energy of the solute in
maximum absorption) is a function of all types of interactions between solvent components and solute. theseinteractions are two types including nonspecific interactions such as polarity–polarizability interactions andShirali et al. BMC Chemistry(2024) 18:154

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Fig. 1 Molecular structure of the azo dispersion dye used in the study

Fig. 2 D1 concentrations in various solvents

specific interactions such as hydrogen bonding and electron donor acceptor interactions [36–38]. ET parametersof a solute can be used in order to achieve information
about the preferential solvation phenomena in the mixed
solvent. Also, the change in position of the absorption
maxima and therefore ET values upon changing the solvent composition can reveal the type of the solute-solvent as well as solvent-solvent interactions occurring inthe solvent mixtures [39].
In this current research, an analytical exploration has
been conducted utilizing both inductive and abductive approaches to analyze the structure of azo dye. Our

primary focus is on investigating changes in the absorption energy of a typical azo disperse dye in various polarities of aprotic, protic, and non-polar solvents. Throughthe calculation of statistical parameters such as correlation, standard deviation, standard error, p-value, T-critical, RMSE (root mean squared error), and MAPE (meanabsolute percentage error), as well as the presentation of
formulas in Figs. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21, 22, 23 and 24; Tables 1, 2, 3, 4,
5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21,
22 and 23, a comprehensive evaluation and index of theinteraction effect and changes in the studied componentsof the new azo dye structure have been obtained.
This study encompasses a spectroscopic examinationand experimental as well as theoretical analysis of the statistical behavior of solvatochromism, along with inductive and analogical reasoning, concerning absorptionchanges, absorption energy, and wavelength shifts of theD1 disperse dye. Bathochromic and hypsochromic shifts
are investigated in relation to the influence of intermolecular interactions, molecular polarizability, vibrational
effects, and environmental screening across various solvents. These findings offer a comprehensive understanding of the solvatochromic and absorption characteristics
of azo dyes in diverse solvent environments with distinct
structural features. The primary objective of this researchis to establish a conclusive link between data structure analysis and the combination of electron-donating

Fig. 3 Absorption energy changes of disperse dye D1 with solvent polarity variation (chloroform, methanol, ethanol, acetone)

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Fig. 4 Displays the absorption spectrum graph corresponding to varying concentrations of disperse azo dye D1

Fig. 5 3-D Column analyzing changes in absorption, absorption energy, and wavelength of disperse dye D1 in response to solvent polarity (chloroform,
methanol, ethanol, and acetone)

Fig. 6 Analysis of changes in absorption energy of disperse dye D1 in response to new polarity of chloroform-acetone mixtures with varying ratios

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Fig. 7 3-D column graph analyzing changes in absorption, absorption energy, and wavelength of disperse dye D1 in response to new polarity ofchloroform-acetone mixtures with varying ratios

Fig. 8 Analysis of changes in absorption energy of disperse dye D1 in response to new polarity of acetone-chloroform mixtures with varying ratios

and electron-accepting substitutions within the azo dye
structure. This aims to derive a pertinent and practicalabstract concept that can serve as a model for the development of novel azo dye structures, laying the groundwork for the integration of artificial intelligence into thedesign of these new azo dyes.

Experimental methodology
Materials and reagents

All materials were sourced from Merck with a highdegree of purity. The solvents used were as follows:Shirali et al. BMC Chemistry(2024) 18:154

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Fig. 9 3-D Column graph analyzing changes in absorption, absorption energy, and wavelength of disperse dye D1 in response to new polarity ofacetone-chloroform mixtures with varying ratios

Fig. 10 Analysis of changes in absorption energy of disperse dye D1 in response to new polarity of methanol-chloroform mixtures with varying ratios

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Fig. 11 3-D column graph analyzing changes in absorption, new absorption energy, and wavelength of disperse dye D1 in response to new polarity ofmethanol-chloroform mixtures with varying ratios

Fig. 12 3-D column graph analyzing changes in absorption, new absorption energy, and wavelength of disperse dye D1 in response to new polarity ofchloroform-ethanol mixtures with varying ratios

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Fig. 13 Analysis of changes in absorption energy of disperse dye D1 in response to variations in the polarity of chloroform-ethanol mixtures with different ratios

Fig. 14 Analysis of new absorption energy changes in response to altered polarity within ethanol-chloroform mixtures featuring different ratios fordisperse dye D1

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Fig. 15 Analysis of 3-D changes in absorption, new absorption energy, and wavelength of disperse dye D1 in response to altered polarity in ethanolchloroform mixtures with varied ratios

Fig. 16 Variations in new absorption energy of novel disperse Dye D1 with respect to the polarity of chloroform and methanol solvent mixture at various
ratiosShirali et al. BMC Chemistry(2024) 18:154

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Fig. 17 3-D Column graph depicting changes in absorption, new absorption energy, and wavelength of novel Disperse Dye D1 with varying ratios of achloroform-methanol solvent mixture

Fig. 18 Variations in absorption energy of new disperse dye D1 with polarity changes in benzene, toluene, and xylene solvents

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Fig. 19 Changes in absorption, absorption energy, and wavelength of typical dispersion dye D1 in response to polarity variations in non-polar solvents—benzene, toluene, and xylene

Fig. 20 Depicts the relationship between new polarity of non-polar solvents (benzene, toluene, and xylene) at various ratios and corresponding changes
in new absorption energy for new dispersion dye D1

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Fig. 21 3-D column graph exploring changes in absorption, new absorption energy, and wavelength of new dispersion dye D1. investigation emphasizes variations in polarity within non-polar solvents—benzene, toluene, and xylene—at different ratios

Fig. 22 Graphical analysis of changes in new absorption energy as new dispersion dye D1 is exposed to toluene and xylene solvents at different ratios.
the graph highlights a linear relationship, emphasizing the impact of solvent polarity on the dye’s absorption energy

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Fig. 23 3-D column graph illustrating changes in absorption, new absorption energy, and wavelength of novel dispersion dye D1 in response to varying
polarity of non-polar solvents—toluene and xylene—at different ratios

Polar Aprotic Solvents: Acetone (purity > 99.8%, ɛ:(dielectric constant): 20.7), Formaldehyde (purity > 99.8%,
ɛ: 38.3) and Acetonitrile (purity > 99.8%, ɛ: 35.09).
Non-Polar Solvents: Chloroform (purity > 99.5%,
ɛ: 4.72), Hexane (purity > 99.5%, ɛ: 2.02), Toluene(purity > 99.5%, ɛ: 2.38), Benzene (purity > 99.5%, ɛ: 2.15),
Orthoxylene (purity > 99.5%, ɛ: 2.57) and Diethyl Ether(purity > 99.5%, ɛ: 4.33).
Polar protic solvent: Methanol (purity > 99.8%, ɛ: 32.7),
Propanol (purity > 99.8%, ɛ: 20.1).
Totally, polar protic solvents contain hydrogen atoms
connected directly to highly electronegative atoms likeoxygen or nitrogen, enabling them to participate inhydrogen bonding. Polar aprotic solvents lack hydrogenatoms capable of hydrogen bonding, but still possesspolar bonds. Nonpolar solvents lack significant dipole
moments and do not readily interact with ionic compounds or polar molecules.
Experimental equipment

The following equipment was utilized for the experiments: Multi spec-1501 Shimadzu spectrophotometer(The MultiSpec-1501 can acquire spectra over the entire
wavelength range in just 100 milliseconds, company:
Shimadzu Corporation), EQ-OC1-19 double-beam
UV-Vis Spectrophotometer SP-LUV1910/SP-LUV1920(Wavelength range: 190 nm ~ 1100 nm, company: Infitek China), spectroluminescence device and T80 UV/vis
spectrometer: (Wavelength range: 190 nm ~ 1100 nm,
company: Infitek China).

Statistical analysis of solvatochromism effects on
new disperse dye D1 in single-solvent and dualsolvent systems
In this section, we delve into the statistical analysis of thesolvatochromism behavior of new disperse dye D1 withinboth single-solvent and dual-solvent systems. Single-solvent and dual-solvent systems, comprising solvents withdiverse structural and functional properties, encompass
non-polar, polar aprotic, and polar protic solvents. Solutions containing electrolytes and more than one solvent
are commonly referred to as mixed solvent systems.
Also, Single solvent systems refer to a solvent system thatconsists of only one solvent, while dual solvent systems

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Fig. 24 Presents a comprehensive analysis of statistical data pertaining to various solvent structures and their influence on solvent polarity. This 3-Dcolumn graph visually depicts the intricate interaction between solvent polarity and crucial components, encompassing absorption energy, extinction
coefficient, maximum wavelength, and molecular weight. The graph serves as a visual representation, illustrating how shifts in solvent polarity impact
these essential parameters

Fig. 25 Analysis of absorption test results measurement for new disperse dye D1 in various solvents (Fig. 25; Table 11)

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Table 1 The measurement of variations in polarity, absorptionenergy, wavelength, and absorption of new disperse dye D1 in
different solvents

Table 4 The measurement of variations in new polarity, newabsorption energy, wavelength, and absorption of disperse dye
D1 in methanol-chloroform mixtures with varying ratios

The blending of diverse
solvents with novel
disperse dye D1
The chloroform and novel
disperse dye D1 blend
The methanol and novel
disperse dye D1 blend
The ethanol and novel
disperse dye D1 blend
The acetone and novel
disperse dye D1 blend

The mixture of methanoland chloroform with novel
disperse dye D1 in different proportions
The mixture of methanoland chloroform with novel
disperse dye in a ratio of 1:1
The mixture of methanoland chloroform with novel
disperse dye with a ratioof 2:1
The mixture of methanoland chloroform with novel
disperse dye with a ratioof 3:1
The mixture of methanoland chloroform with novel
disperse dye in a ratio of 4:1

Abs

Wave
Length(nm)

Et

0.831

556

51.4235

Polarity*
0.259

0.23

548

52.1742

0.762

0.239

552

51.796

0.654

0.4

548

52.17420.355*

The polarity of a solvent is determined by its solvation behavior, which inturn depends on the action of intermolecular forces (Coulomb, directional,
inductive, dispersion, and charge transfer forces as well as hydrogen bonding
forces) between the solvent and the solute

Table 2 The measurement of variations in polarity, absorptionenergy, wavelength, and absorption of disperse dye D1 inchloroform-acetone mixtures with varying ratios
The solvent-dye D1 mixture with varying ratios

Abs

Et mix

0.311

Wave
Length(nm)
552

The 1:1 ratio mixture ofchloroform and acetone
The 2:1 ratio mixture ofchloroform and acetone
The 3:1 ratio mixture ofchloroform and acetone
The 4:1 ratio mixture ofchloroform and acetone

Polarity

51.7988

0.614

0.23

548

51.6736

0.29

0.232

552

51.6111

0.282

0.215

554

51.5736

0.278

mix

Table 3 The measurement of variations in polarity, absorptionenergy, wavelength, and absorption of disperse dye D1 in
acetone-chloroform mixtures with varying ratios
Mixture of solvents with
Abs
novel dispersion dye D1 in
different proportions

Wave
Length(nm)

Et mixPolarity

A mixture of acetone andchloroform with a ratio of
2:1
A mixture of acetone andchloroform with a ratio of
3:1
A mixture of acetone andchloroform with a ratio of
4:1

0.286

552

51.9239

0.322

0.31

552

51.9864

0.33

0.312

552

52.024

0.335

mix

involve the use of two different solvents in a system.
These systems are commonly used in various fields suchas chemistry, pharmaceuticals, and material science fordifferent purposes, including extraction, purification, andsynthesis processes, this analysis aims to provide a comprehensive understanding of the dye’s behavior in different solvent environments.

Abs

Wave
Length(nm)

Et mixPolarity

0.138

557

51.7988

1.021

0.136

556

51.6736

0.426

0.129

556

51.6111

0.384

0.128

558

51.5736

0.359

mix

Table 5 The measurement of variations in new polarity, newabsorption energy, wavelength, and absorption of disperse dye
D1 in chloroform-ethanol mixtures with varying ratios
The mixture of chloroform
and ethanol solvents withnew disperse dye D1 in
different ratios
The mixture of chloroform
and ethanol solvents witha new disperse dye with aratio of 1:1
The mixture of chloroform
and ethanol solvents witha new disperse dye with aratio of 2:1
The mixture of chloroform
and ethanol solvents witha new disperse dye with aratio of 3:1
The mixture of chloroform
and ethanol solvents witha new disperse dye with aratio of 4:1

Abs

Wave
Length(nm)

Et mixPolarity

0.206

556

51.4235

0.913

0.234

559

51.1475

0.39

0.207

558

51.2392

0.357

0.195

558

51.2392

0.337

mix

Investigation of solvatochromism’s influence on solutesolvent interactions

In this study, we explored the impact of solvatochromism on solute-solvent interactions by employing spectroscopic statistical data analysis. Our focus was on the
behavior of the well-established disperse dye, D1, whenintroduced to solvents with diverse structural and functional properties, encompassing non-polar, polar aprotic,
and polar protic solvents.
By scrutinizing the alterations in absorption position, intensity, and spectral shape, and by examining the
wavelength characteristics of the spectrophotometricdevice, we analyzed how the color attributes of the newShirali et al. BMC Chemistry(2024) 18:154

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Table 6 Analysis of measurement variations in new polarity, newabsorption energy, wavelength, and absorption of disperse dye
D1 in ethanol-chloroform mixtures with varying ratios
The mixture of ethanoland chloroform with newdisperse dye D1 in different proportions
The mixture of ethanol andchloroform with a new disperse dye at a ratio of 2:1
The mixture of ethanol andchloroform with a new disperse dye at a ratio of 3:1
The mixture of ethanol andchloroform with a new disperse dye at a ratio of 4:1

Abs

Wave
Length(nm)

Et mix556

51.4235

Polarity
mix

0.267

0.522

0.273

555

51.5162

0.554

0.302

555

51.5162

0.575

Table 7 Analysis of measurement changes in new polarity, newabsorption energy, wavelength, and absorption of novel disperse
dye D1 in chloroform and methanol mixtures with varying ratios
The mixture of chloroform
and methanol solventswith a novel disperse dye
D1 in different proportions
The mixture of chloroform
and methanol solvents witha novel disperse dye with aratio of 2:1
The mixture of chloroform
and methanol solvents witha novel disperse dye with aratio of 3:1
The mixture of chloroform
and methanol solvents witha novel disperse dye with aratio of 4:1

Abs

Wave
Length(nm)

Et mix0.151

553

51.7025

Polarity
mix

0.149

0.146

552

553

51.7961

51.7025

0.426

0.384

0.359

Table 8 Investigation of measurement changes in new polarity,
new absorption energy, wavelength, and absorption disperse
dye D1 in non-polar solvents (benzene, toluene, and xylene)
Mixture of non-polar solventsin novel disperse paint

Abs

Et

0.677

Wave
Length(nm)
541

52.8493

Polarity
0.111

Non-polar solvent mixture ofbenzene in novel disperse dye
Non-polar solvent mixture oftoluene in novel disperse dye
Non-polar solvent mixture of
xylene in novel disperse dye

0.516

539

53.0454

0.099

0.492

537.2153.22220.072

azo dispersion D1 evolved within solvents characterized
by different polarities and distinct intermolecular interactions, including ion-dipole, dipole-dipole, induced
dipole-dipole, and hydrogen bonding. Furthermore, we
conducted both experimental and theoretical assessments of alterations in adsorption and desorption energies and other pertinent parameters associated with thenovel structure of azo dye D1.

Table 9 Investigation of measurement changes in new polarity,
new absorption energy, wavelength, and absorption of nonpolar solvents (benzene and xylene) when mixed with typicaldispersion dye D1 at various ratios
The mixture of benzene
and xylene solvents withnovel disperse dye D1 in
different proportions
The mixture of benzene andxylene solvents with a novel
dispersion color at a ratioof 1:1
The mixture of benzene andxylene solvents with a novel
dispersion color at a ratioof 2:1
The mixture of benzene andxylene solvents with a novel
dispersion color at a ratioof 3:1

Abs

Wave
Length(nm)

Et mixPolarity

0.782

539

53.0454

0.183

0.904

540

52.9472

0.098

0.872

540

52.9472

0.101

mix

Table 10 Comprehensive analysis of measurement changes
in new polarity, new absorption energy, wavelength, andabsorption characteristics in non-polar solvents (toluene andxylene) interacting with new dispersion dye D1 at different ratios
The non-polar solvent
mixture of toluene and xylene with a new disperse
dye D1 in different ratios
The non-polar solvent mixture of toluene and xylene
with a new dispersion dyewith a ratio of 1:1
The non-polar solvent mixture of toluene and xylene
with a new dispersion color
with a ratio of 2:1
The non-polar solvent mixture of toluene and xylene
with a new dispersion color
with a ratio of 3:1
The non-polar solvent mixture of toluene and xylene
with a new dispersion color
with a ratio of 4:1

Abs

Wave
Length(nm)

Etmix

Polarity

0.541

538

53.1444

0.171

0.601

538

53.1444

0.081

0.582

536

53.3423

0.078

0.571

538

53.1440.234

mix

Significance of absorption spectrum, absorption energy,
solute-solvent interactions, and solvent-solvent behavior

The absorption spectrum and absorption energy of a dye
are critical parameters that yield valuable insights into its
structure and properties. In the case of a novel azo dye
within a disperse dye, the absorption spectrum helps
identify the wavelengths at which the dye absorbs light,
revealing its color characteristics. Additionally, analyzing absorption energy provides a deeper understandingof the electronic transitions occurring within the dyemolecule. When examining the dye’s behavior in mixed
solvents, it is essential to consider solute-solvent interactions. The interaction between the dye molecule andShirali et al. BMC Chemistry(2024) 18:154

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Table 11 Comprehensive analysis of measurement changes and statistical summary of investigated components in conventional
disperse dye D1 and corresponding solvent structures
Et
εPolarprotic solvent
52.3653
1728.75
52.94724987.5
Polaraprotic solvent
51.056212256.25
52.7518
12,825
Non-polar solvent
56.06171018.375
53.9462
11,88553.342311828.75
55.8427
2893.75
53.342311942.5
53.3423
12213.75

Abs

λmax

Solvent polarity

Solvent

Mw

0.1383
0.399

546
540

0.617
0.762

1- Propanol
Methanol

60.1
32.04

0.9805
1.026

560
542

0.386
0.46

DMF
Acetonitrile

73.09
41.05

0.081470.95080.94630.23150.9554
0.9771

510
530
536
512
536
536

0.009
0.111
0.099
NO
0.073
0.074

HexaneBenzeneTolueneDiethyl ether
Mixture of xylene
Ortho xylene

86.18
78.11
92.138174.12
106.16106.17

Table 12 Statistical analysis of adsorption energy data forvarious solvents interacting with representative dispersive dye
D1

Table 13 Statistical description of quenching absorption
coefficient data from various solvents interacting with newdisperse dye D1

Disperse dye D1
MeanStandard Error
MedianModeStandard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
Largest (1)Smallest (1)Confidence Level (95.0%)

Disperse dye D1
MeanStandard Error
MedianModeStandard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
Largest (1)Smallest (1)Confidence Level (95.0%)

53.4998
0.476670696
53.342353.34231.507365093
2.272149522
0.351932208
0.531790578
5.005551.056256.0617534.99810
56.061751.0562
1.078304029

solvent molecules can significantly influence its solubility, stability, and optical attributes. Depending on thenature of the solvents, variations in the absorption spectrum and absorption energy may occur, resulting in solvatochromism behavior, which signifies changes in thedye’s color or absorption properties in distinct solvent
environments. Moreover, comprehending solvent-solvent
interactions within dual-solvent systems is paramountfor dye dissolution and application. The interactions
between the two solvents, encompassing factors such as
miscibility and preferential solvation, can directly impact
the dye’s solubility and stability. These aspects have farreaching implications for the dye’s utilization across various industries, including textile dyeing, ink formulation,and colorant production.
In summary, the investigation of the absorption spectrum, absorption energy, solute-solvent interactions, and8357.9625
1586.005023
11856.875
5015.388253
25154119.33-1.866458189-0.606275062
11806.625
1018.375
12,82583579.625
10
12,8251018.375
3587.792623

solvent-solvent behavior plays a pivotal role in understanding solvatochromism behavior and the dissolutionof a novel azo dye structure. This knowledge serves asa foundation for optimizing the dye’s performance andapplication in diverse solvent environments and industrial applications.

Experimental procedure
Experimental design

A concentrated stock solution of a new disperse dye D1,
featuring an azo structure, was prepared with a concentration of 0.001 M in chloroform solvent. Subsequently,
solutions with lower concentrations were derived fromthis stock solution for spectrophotometric analysis. To
achieve this, the initial concentration of 0.001 M in various solvents was used as a starting point. For instance,
0.1 cc of the concentrated 0.001 M solution in chloroform

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Table 14 Statistical overview of absorption rate data for new
disperse dye D1 across various solvents

Table 16 Statistical analysis of polarity data for polar protic,
polar aprotic, and non-polar solvents

Disperse dye D1
MeanStandard Error
MedianModeStandard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
Largest (1)Smallest (1)Confidence Level (95.0%)

Disperse dye D1
MeanStandard Error
MedianModeStandard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
Largest (1)Smallest (1)Confidence Level (95.0%)

0.668637
0.126880402
0.948550.40123106
0.160986364-1.866458189-0.606275062
0.944530.08147
1.026
6.6863710
1.026
0.081470.28702341

0.287888889
0.091970473
0.111
0.275911419
0.076127111-1.07004814
0.723734372
0.753
0.009
0.762
2.591
9
0.762
0.009
0.212084291

Table 15 Statistical analysis of maximum wavelength data for asolvent mixture in combination with novel disperse dye D1Table 17 Statistical analysis of molecular weight for various
solvents and the new disperse dye D1

Disperse dye D1
MeanStandard Error
MedianModeStandard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
Largest (1)Smallest (1)Confidence Level (95.0%)

Disperse dye D1
MeanStandard Error
MedianModeStandard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
Largest (1)Smallest (1)Confidence Level (95.0%)

534.8
4.715930449
536
536
14.91308151
222.4
0.388680833-0.388984613
50
510
560
5348
10
560
510
10.66817584

was employed to create 10 cc solution with 0.001 M concentration in acetonitrile. The procedure involved transferring 0.1 cc of the stock solution to 10 cc volumetricflask, allowing complete evaporation of chloroform, andthen adding acetonitrile to the flask to reach the desired
volume. This methodology facilitated the generation ofsolutions with different solvents, eliminating the need toprepare separate solutions for each measurement. Consequently, we obtained solutions representing a rangeof solvents and the new azo dispersion dye D1. Furthermore, using the stock solution, a blend of polar aprotic,
polar protic, and non-polar solvents was prepared invarying ratios, creating a spectrum of polarities for theD1 dye structure, as illustrated in Fig. 1.

98.74164545
24.87042184
78.11
82.48585761
6803.916705
8.730363075
2.817314674
304.9632.04
337
1086.1581
11
337
32.04
55.41475316

In this experiment, we employed three distinct classesof solvents characterized by varying structures andfunctionalities: polar protic, polar aprotic, and nonpolar solvents. Additionally, a new azo dispersion dye, D1(depicted in Fig. 1), was utilized. The use of statistical
data allowed us to integrate empirical and theoretical
approaches comprehensively. Our objective was to analyze, predict, explain, and draw generalizations from thestatistical data. This encompassed a thorough examination of the interaction between the diverse solventsand the D1 dye, offering insights into its behavior andperformance.
The Fig. 1 illustrates the molecular structure and nameof the new dispersive dye utilized in this study: 4-nitro2-cyanoazobenzene-meta-toluidine, designated as D1.

Shirali et al. BMC Chemistry(2024) 18:154

Page 19 of 31

Table 18 Results of two-sample t-test (assuming equalvariances) for two sets of statistical data on absorption energy
Mean
Variance
Observations
Pooled Variance

Hypothesized Mean
Differencedft StatP(T < = t) one-tailt Critical one-tailP(T < = t) two-tailt Critical two-tailVariable 1
53.4998
2.272149522
10
2.311011744

Variable 2
54.0898
2.349873967
10
Pooled standard deviation
1.520201218

0

Statistical Errors
n
MAD
MSE
RMSE
MAPE

Table 19 Results of two-sample t-test (assuming equalvariances) for two sets of statistical data on absorption
Variable 1
0.668637
0.160986
100.197047

Hypothesized Mean Differencedft StatP(T < = t) one-tailt Critical one-tailP(T < = t) two-tailt Critical two-tail018-0.36435
0.359921
1.734064
0.719842
2.100922

Variable 2
0.740967
0.233107019
10
Pooled standard deviation
0.443899416

Table 20 Results of two-sample t-Test (assuming equalvariances) for two statistical data series related to maximum
wavelength
Mean
Variance
Observations
Pooled Variance

Hypothesized Mean
Differencedft StatP(T < = t) one-tailt Critical one-tailP(T < = t) two-tailt Critical two-tailVariable 1
534.8
222.4
10
225.6944444

018-0.937702593
0.18040492
1.734063607
0.36080984
2.10092204

Statistical Errors
n
MAD
MSE
RMSE
MAPE

10
0.59
0.443
0.6655825
1.1040355

Table 22 Statistical errors for 10 data related to absorption invarious solvent mixtures with novel dispersed dye D1

18-0.867832555
0.198454422
1.734063607
0.396908844
2.10092204

Mean
Variance
Observations
Pooled Variance

Table 21 Statistical errors for 10 data related to absorptionenergy in a solvent mixture with novel disperse dye D1

Variable 2541.1
228.9888889
10
Pooled standard deviation
15.02313031

100.07233
0.028632299
0.169210812
10.19100671

Table 23 Statistical errors for 10 data related to maximum
wavelength in a solvent mixture with novel disperse dye D1
Statistical Errors
n
MAD
MSE
RMSE
MAPE

10
6.3
47.3
6.877499546
1.179161087

The compound is a new azo purple disperse pigmentwith a molecular weight of 337 g/mol. It contains electron donor groups (CH3, N(C2H5)2) and electron acceptor groups (N2, NO2, CN). The critical pressure (PC) is4328.25 KPa, the normal boiling point temperature (Tboil)
is 620.57 K, the normal melting point temperature (Tfus)
is 446.98 K, and the critical volume (VC) is 0.430 m3/
kmol.
The Fig. 2 illustrates the concentrations of new disperse
dye D1 in solvents, including benzene, toluene, orthoxylene, acetonitrile, methanol, 1-propanol, and DMF.

Results and discussion
Results from tables and figures
The analogy reasoning of polarity changes correlates withvariations in absorption energy, wavelength, and absorptionof new azo dyes within single solvent environments

The table provides information on the highest and lowest absorption rates, wavelength, absorption energy andpolarity for various solvent mixtures with novel disperse
dye D1. The chloroform-D1 mixture exhibited the highest absorption rate, reaching 0.831, while the methanolD1 mixture displayed the lowest absorption rate at 0.23.
Additionally, the maximum wavelength (λ) recorded was
556 nm in the chloroform-D1 mixture, whereas the lowest wavelength, 548 nm, was observed in the methanolD1 mixture. The data suggests that altering the polarity

Shirali et al. BMC Chemistry(2024) 18:154

of the solvent significantly influences both the absorption level and absorption energy. Notably, the absorption energy (ΔEt) for individual mixtures was calculated,yielding a value of 0.7507. The maximum absorptionenergy (E) can be determined using the Eq. (1):E(kcal/mol) = 28591.5/λ max (1)The Eq. 1 allows the calculation of E based on the maximum wavelength (λ max).
Figure 3 illustrates the variations in absorption energyof disperse dye D1 as a function of solvent polarity, specifically in chloroform, methanol, ethanol, and acetone
solutions. In Fig. 3; Table 1, the highest absorptionenergy of 52.1742 was recorded for both the methanolD1 and acetone-D1 mixtures, corresponding to the highest observed polarity of 0.762. Conversely, the lowest
polarity value, 0.259, was observed in the chloroformD1 mixture. Figure 3 presents the relationship between
energy and solvent polarity, showed by the equation
Y = 0.1874X + 51.424, with a correlation coefficient (R²)
value of 0.4526, a statistic is the standard deviation ofits sampling distribution standard error (SE) has been
calculated. The data analysis and processing were conducted through laboratory experimentation, yielding a
low R2 value and a high SE value, indicating increased
uncertainty in the experimental and laboratory data.
However, employing these statistical and theoretical calculations has enabled the analysis of experimental data
and the inferential estimation of the dispersed dye Azo
D1’s interaction effects across various solvent and soluteenvironments. Therefore, the absorption energy of a dye
disperse solution is significantly influenced by the polarity of the system. In polar solvents, interactions between
novel dye and solvent molecules can modify the electronic environment around the novel dye, causing shifts
in absorption energy. This effect is due to changes in solvation energy and charge transfer interactions, impacting
the absorption spectra of the novel dye disperse system.
Overall, the absorption of energy in the solution can altermolecular interactions, affecting charge distribution andsystem polarity [40, 41].
The absorption spectrum graph in Fig. 4 has been computed and plotted based on different concentrations of
new disperse azo dye D1. The formula Y = 19640x-1.048
with an R2 value of 0.8101 and a calculated standard
error.
Figure 5 depicts a 3-D column graph that explores thevariations in absorption, absorption energy, and wavelength of disperse dye D1 in relation to the polarity of thesolvents: chloroform, methanol, ethanol, and acetone.
An important observation from the absorption energy
data is that the mixtures of methanol-D1 and acetoneD1 exhibit a hypsochromic shift, leading to shorter

Page 20 of 31

wavelengths. In contrast, the mixtures of ethanol-D1
and chloroform-D1 display a bathochromic shift, resulting in longer wavelengths. The visualization and observability of the results from experimental tests, statistical
data structuring, and inductive reasoning, along with thefindings presented in Table 1; Figs. 3 and 5, collectively
constitute an inferential model. This model suggeststhat the primary cause of the hypsochromic change isthe solvent effect. Increasing solvent polarity facilitateselectron transfer from the π* molecular orbital to nonbonding pairs of electrons in n and π* molecular orbitals,
thus shifting absorption towards higher frequencies. The
bathochromic shift is also attributed to solvent-induced
structural changes. Increased solvent polarity facilitateselectron transfer from the π and π* molecular orbitals,causing a shift towards lower frequencies (longer wavelengths). This phenomenon arises from the polarizing
forces between the solvent and the absorber, resulting in
the lowering of energy levels of the π* and π molecularorbitals, consequently amplifying the influence on π*.
The objectification of experimental and statistical data
into a 3-D Column representation has facilitated thedevelopment of a computational, descriptive, and inferential model for the new disperse dye D1. This approach
has led to a reduction in cognitive errors and uncertainty
in the experimental results. Therefore, the polarity ofthe solution in a novel dye disperse system can significantly affect absorbance and wavelength characteristics.
In such systems, changes in the polarity of the solvent
can influence the solubility and dispersion of the noveldye molecules, leading to variations in absorbance levels
and absorption wavelengths. The polarity of the solution
can impact the electronic transitions within the new dye
molecules, affecting their spectral properties and overall
performance in the disperse system. This information is
crucial for understanding the dye’s behavior in various
applications, such as in dye-sensitized solar cells, fluorescence imaging, or coloration processes.
The analogy reasoning explores how changes in polarity
correlate with shifts in absorption energy and wavelengthsof new azo dyes in dual solvent systems with different
chloroform-acetone ratios

The adsorption energy in binary mixtures can be calculated using the following Eq. 2:

E 12 (id) = x1 ET 1 = x2 ET 2(2)The calculation of the new polarity in solvent mixtures isperformed using Eq. 3:

P 12 (id)x1 p1 + x2p2 (3)Shirali et al. BMC Chemistry(2024) 18:154

Table 2 presents the findings from the analysis of chloroform and acetone mixtures with varying ratios. Notably,
the mixture of chloroform and acetone with a 1:1 ratio
exhibited the highest absorption rate, recording a valueof 0.311, while the mixture with a 2:1 ratio displayed thelowest absorption rate at 0.23. In terms of wavelength,
the mixture of chloroform and acetone with a 4:1 ratio
showed the highest wavelength, measuring 554 nm, while
the mixture with a 2:1 ratio had the lowest wavelength,
at 548 nm. Additionally, the absorption energy (ΔEt) for
these binary mixtures was calculated, resulting in a valueof 0.225.
The results further indicate that the mixture of chloroform and acetone with a 1:1 ratio exhibited the highest
absorption energy at 51.7988. This resulted in a hypsochromic shift (shorter wavelength). Conversely, themixture with a 4:1 ratio displayed the lowest absorptionenergy and a bathochromic shift (longer wavelength).
It seems that the highest absorption levels and absorption energies are observed in solvents with the highest
polarity.
This observation and the inductive reasoning fromexperimental data suggest that the increasing ratio of
chloroform to acetone, along with the interactive effectsof these solvents, contribute to the observed phenomenon. The interaction between chloroform (a non-polar
solvent) and acetone (a polar aprotic solvent) gives riseto new molecular dipoles, consequently increasing thepolarity of the solvent. This enhanced polarity facilitateselectron transfer from the π* molecular orbital to the πmolecular orbital.
The test results and statistical inference presented inTable 2 support the assumption that the polarizing forces
between the solvent and the absorber significantly influence the alignment of molecular orbitals, particularly
impacting the π* (unexcited) and π (excited) orbitals.
This effect is more pronounced on the π* orbital.
In Table 2; Fig. 6, the highest absorption energy value,
52.7988, was observed in the mixture of chloroform andacetone with a 1:1 ratio and disperse dye D1, while thelowest absorption energy value, 51.5736, was found in the
mixture of chloroform and acetone with a 4:1 ratio anddisperse dye D1.Furthermore, the highest new polarity
value, 0.614, was recorded for the 1:1 mixture of chloroform and acetone with disperse dye D1, while the lowest
new polarity value, 0.278, was observed in the 4:1 mixture of chloroform and acetone with disperse dye D1.
Figure 6 demonstrates a linear relationship inthese changes, characterized by the equation
Y = 0.5495x + 51.463, along with R² value of 0.8477.
Additionally, a statistic is the standard deviation of its
sampling distribution SE has been calculated to assess
the model’s reliability. The data analysis and processing
were conducted through laboratory experimentation,

Page 21 of 31

resulting in an increase in the R2 value and a decrease in
the SE value. Consequently, a decrease in uncertainty wasobserved in the experimental and statistical data.
Figure 7 presents a 3-D column graph that investigates
the alterations in absorption, absorption energy, andwavelength of disperse dye D1 in response to the changing polarity of chloroform and acetone mixtures withdifferent ratios. Within Fig. 7, the analysis encompasseschanges in absorption, new absorption energy, and wavelength for disperse dye D1 based on the new polarity ofchloroform and acetone solutions with varying ratios.
These changes are characterized by linear relationships.
Remarkably, the investigation revealed that the mixtureof chloroform and acetone with a 1:1 ratio displayed thehighest new polarity and new absorption energy. Additionally, the effects of increasing the molecular weight ofchloroform and acetone solvents on polarity and absorption energy are supposition within this concept. Furthermore, increasing the proportion of chloroform relative
to acetone in the mixed solvents leads to a decrease inpolarity, absorption, and absorption energy.
The analogy-based reasoning examines how changes inpolarity correlate with variations in absorption energy andwavelengths of new azo dyes in dual solvent systems withvarying acetone-chloroform ratios

Table 3 presents the findings obtained from the experiment. Notably, the mixture of acetone and chloroform
with a 1:4 ratio exhibited the highest absorption energy
at 52.024, resulting in a hypsochromic shift (shorter
wavelength). Conversely, the mixture with a 2:1 ratio displayed the lowest absorption energy, measuring 51.9239,
leading to a bathochromic shift (longer wavelength). The
observed effects are attributed to the increasing ratio of
acetone to chloroform and the interactive influence of
acetone (a polar aprotic solvent) with chloroform (a nonpolar solvent). This interaction results in the emergenceof a new polarity marked by new molecular dipoles.
Increasing the new polarity of the solvent induces abathochromic shift and facilitates electron transfer fromthe π * molecular orbital. This shift is assumed by thepolarizing forces between the solvent and the absorber,
which impact the molecular orbital levels of π (unexcited) and π * (excited), with a greater effect on π *.
Additionally, the highest absorption rate, 0.312, was associated with the 4:1 mixture of acetone and chloroform
with disperse dye D1, while the lowest absorption rate,
0.286, was related to the 2:1 mixture of acetone and chloroform with disperse dye D1. Minor changes in wavelength were also observed for the acetone-chloroform
mixtures with different ratios. The calculated absorptionenergy (ΔEt) for these binary mixtures yielded a valueof 0.1001. These findings offer valuable theoretical andexperimental insights into the impact of solvent-to-soluteShirali et al. BMC Chemistry(2024) 18:154

ratios and intermolecular interactions, molecular polarizability, vibrational effects, and environmental screening
on the absorption spectral properties. They enhance predictability regarding the behavior and performance of theD1 disperse dye [42].
Figure 8 explores the variations in absorption energy
exhibited by disperse dye D1 in response to the dynamic
polarity changes in acetone-chloroform mixtures withvarying ratios. As detailed in Table 3 and illustrated inFig. 8, the investigation identified the highest absorptionenergy value, 52.024, occurring in the 4:1 ratio mixtureof acetone and chloroform with disperse dye D1. In contrast, the lowest absorption energy value, 51.9239, wasobserved in the 2:1 ratio mixture of acetone and chloroform with disperse dye D1.
Moreover, the analysis revealed the highest recorded
new polarity value, 0.335, for the 4:1 mixture of acetone and chloroform with disperse dye D1, while thelowest new polarity value, 0.322, was observed in the
2:1 mixture of acetone and chloroform with the samedye. Figure 8 effectively depicts a linear relationshipamong these changes, represented by the equation
Y = 7.7105x + 49.441, with R² value of 0.9999. Additionally,
to ensure the model’s reliability, a statistic is the standard
deviation of its sampling distribution SE has been calculated and considered in the analysis. This rigorous examination contributes valuable insights to the understandingof absorption energy variations in disperse dye D1 withincomplex solvent mixtures. The data analysis and inductive reasoning processing were conducted through laboratory experience, resulting in an increase in the R2 value
and a decrease in the SE value. Consequently, a decreasein uncertainty was observed in the experimental and laboratory data.
Figure 9 introduces a 3-D column graph designed toassess the fluctuations in absorption, absorption energy,
and wavelength of disperse dye D1 in response to thechanging polarity of acetone-chloroform mixtures withvarying ratios. The graphical representation within Fig. 9
accents a linear relationship in the alterations of absorption, new absorption energy, and wavelength. Remarkably, the 4:1 ratio mixture of acetone and chloroform
solvents emerged with the highest new polarity and newabsorption energy values.
Furthermore, this diagram not only illustrates linearchanges but also offers valuable theoretical and experimental insights into the impact of molecular weight andnew structures of acetone and chloroform solvent mixtures on polarity, absorption energy, absorption, wavelength, vibrational effects, and environmental screening.
The structured presentation in Fig. 9 enhances the clarity
and coherence of the data and findings, contributing toa more comprehensive understanding of the interaction
between solvent composition and key color properties.

Page 22 of 31

Through analogy reasoning, we explore the relationshipbetween changes in polarity and shifts in absorption energy
and wavelengths of new azo dyes in dual solvent systems
with varying methanol and chloroform ratios

Table 4 summarizes the outcomes derived from an indepth analysis of methanol and chloroform mixtures atvarying ratios in conjunction with disperse dye D1. The
findings reveal that the highest absorption energy was
discerned in two instances: first, in the 1:1 ratio mixtureof methanol (a polar protic solvent) and chloroform (anon-polar solvent), and second, in the mixture of methanol and chloroform with a 1:2 ratio. This observation
assumed a hypsochromic shift, attributed to the escalating solvent polarity and the ensuing electron transferfrom π* to n molecular orbitals. This electron transfer
prompts interaction between the solvent and non-bonding electron pairs in molecular orbitals, inducing a shift
towards higher frequencies.
Conversely, elevating the ratio of chloroform (a nonpolar solvent) in methanol (also a non-polar solvent)results in the emergence of new solvent structureswith varying polarities. This precipitates a reduction inabsorption energy, leading to a bathochromic shift. This
shift is propelled by the polarizing forces between thesolvent and the absorber, influencing the energy levelsof the π (unexcited) and π* (excited) molecular orbitals,
with a supposed impact on the π* molecular orbital. The
observed phenomenon appears to stem from the intermolecular interactions within the novel solvent mixture
structure, coupled with the altered polarizability andvibrational effects.
Additionally, the highest absorption rate, 0.138, corresponds to the 1:1 mixture of methanol and chloroform
with disperse dye D1, while the lowest absorption rate,
0.128, is associated with the 4:1 mixture of methanol andchloroform with disperse dye D1. Minor fluctuations inwavelength were also noted for the methanol-chloroform
mixtures at different ratios. The calculated absorptionenergy (ΔEt) for these binary mixtures resulted in a valueof 0.225. These findings offer nuanced insights into theintricate interaction of solvent ratios and interactions,delineating their profound impact on the absorption
characteristics and behavior of disperse dye D1.
Figure 10 delves into the nuanced variations in absorption energy exhibited by disperse dye D1 in responseto the changing polarity of methanol-chloroform mixtures with diverse ratios. The corresponding findings inTable 4; Fig. 10 reveal noteworthy insights. The highest
absorption energy value, 51.7988, surfaced in the 1:1
mixture of methanol and chloroform with disperse dye
D1, while the lowest absorption energy value, 51.5736,
was identified in the 4:1 mixture of methanol and chloroform with the same dye.

Shirali et al. BMC Chemistry(2024) 18:154

Furthermore, the investigation unveiled the highest
recorded new polarity value, 1.021, associated with the
1:1 mixture of methanol and chloroform with disperse
dye D1, compared against the lowest new polarity value,
0.359, observed in the 4:1 mixture of methanol and chloroform with the same dye. Illustrating these changes,
Fig. 10 summarizes the relationship between new absorption energy and new polarity, showed by the equation
Y = 0.2933X + 51.504, showcasing a strong R² value of
0.8864. In the pursuit of model reliability, a statistic is
the standard deviation of its sampling distribution SE
has been meticulously calculated, fortifying the robustness of the findings. The data analysis and processing,conducted through laboratory experimentation, resulted
in an increase in the R2 value and a decrease in the SE
value. This led to a reduction in uncertainty observed in
the experimental and laboratory data.
Figure 11 introduces a 3-D column graph meticulously
designed to assess the dynamic variations in absorption,
new absorption energy, and wavelength of disperse dye
D1 in response to the changing polarity of methanolchloroform mixtures across various ratios. The analysis
within Fig. 11 distinctly reveals a linear trend showing
the alterations in absorption, new absorption energy, andwavelength.
Remarkably, the 1:1 ratio mixture of methanol andchloroform solvents emerges as a focal point, exhibiting
the highest new polarity and new absorption energy values. This graphical representation not only elucidates thelinear changes but also offers valuable insights into theimpact of the molecular weight of methanol and chloroform solvents on new polarity, new absorption energy,
absorption, wavelength and optimization of experimental design. By systematically exploring these interactions,Fig. 11 enhances our understanding of the interaction
between solvent composition and key characteristics ofthe disperse dye D1, contributing to a more comprehensive interpretation of the experimental data and inductive
reasoning.
By employing analogy reasoning, we explore how changes inpolarity correlate with variations in absorption energy andwavelengths of new azo dyes in dual solvents with varying
chloroform-ethanol ratios

Table 5 presents the findings obtained from the analysisof chloroform and ethanol mixtures with varying ratios
in conjunction with new disperse dye D1. The results
indicate that the highest absorption energy was observedin the 1:1 mixture of chloroform (a non-polar solvent)and ethanol (a polar protic solvent) with disperse dye
D1, yielding an absorption energy of 51.4235. In contrast, the lowest absorption energy, 51.1475, was found in
the 2:1 mixture of chloroform and ethanol with disperse
dye D1. This trend is indicative of the impact of varying

Page 23 of 31

solvent ratios on absorption energy. Furthermore, thenew polarity of the solvent mixtures showed the highest
value, 0.913, in the 1:1 mixture of chloroform and ethanol with disperse dye D1, while the lowest new polarity
value, 0.337, was observed in the 4:1 mixture of chloroform and ethanol with disperse dye D1. These variations
in new polarity are a consequence of changing solvent
ratios. Additionally, the highest absorption rate, 0.234,
was associated with the 2:1 mixture of chloroform andethanol with disperse dye D1, while the lowest absorption rate, 0.195, was linked to the 4:1 mixture of chloroform and ethanol with disperse dye D1. Tiny changes
in wavelength were observed for the different ratios ofchloroform and ethanol solvents with disperse dye D1.
The calculated absorption energy (ΔEt) for these binary
mixtures yielded a value of 0.276. These findings offer
valuable insights into the influence of different ratios ofchloroform and ethanol solvents on absorption properties, intermolecular interactions, polarizability in highsolvent dielectric constants, and solvation behavior of thedispersed dye D1.
Figure 12 introduces a 3-D column graph designed tocomprehensively and inductive reasoning assess variations in absorption, new absorption energy, and wavelength of disperse dye D1 in response to alterations in thepolarity of chloroform-ethanol mixtures across diverse
ratios. The analysis within Fig. 12 distinctly reveals alinear trend characterizing changes in absorption, newabsorption energy, and wavelength.
Significantly, the 1:1 ratio mixture of chloroform andethanol solvents stands out, exhibiting the highest newpolarity and new absorption energy values. This graphical representation not only elucidates the linear changes
but also provides valuable insights into the impact of themolecular weight of chloroform and ethanol solvents on
new polarity, new absorption energy, absorption, andwavelength. This visualization enhances the presentation of the data structure and findings depicted in Fig. 12,
thereby augmenting the interpretability and depth of thetheoretical and experimental results.
Using analogy reasoning to examine how changes in polarity
relate to shifts in absorption energy and wavelengths of new
azo dyes in dual solvents with different ethanol-chloroform
ratiosTable 6 succinctly summarizes significant findings
derived from the comprehensive analysis of ethanol andchloroform mixtures across varying ratios in conjunction
with disperse dye D1. The results highlight the highest
observed new absorption energy, 51.4235, in the 2:1 mixture of ethanol (a polar protic solvent) and chloroform (anon-polar solvent) with disperse dye D1. In contrast, thelowest new absorption energy, 51.5162, was identified in
the 4:1 and 3:1 mixture of ethanol and chloroform with

Shirali et al. BMC Chemistry(2024) 18:154

the same dye, showcasing a nuanced interaction withchanges in solvent ratios.
Additionally, the analysis revealed the highest newpolarity value, 0.575, in the 4:1 mixture of ethanol andchloroform with disperse dye D1, while the lowest newpolarity value, 0.522, was observed in the 2:1 mixture ofethanol and chloroform with the dye. These fluctuations
in new polarity underscore the sensitivity of the system
to varying solvent ratios. Moreover, the highest absorption rate, 0.302, was attributed to the 4:1 mixture, while
the lowest absorption rate, 0.267, was linked to the 2:1
mixture, indicating the distinct influence of different
ratios on absorption characteristics.
Despite tiny changes in wavelength observed for thedifferent ratios of ethanol and chloroform solvents inconjunction with disperse dye D1, it’s crucial to note thatthe alterations in absorption energy, although relatively
slight, result in bathochromic and hypsochromic shifts
in the absorption spectra, as explained in previous sections (Tables 2 and 4, and 3). The calculated absorptionenergy (ΔEt) for these binary mixtures yielded a value of
0.092, providing a quantitative measure of these subtle
variations. These findings offer valuable theoretical andexperimental insights into the intricate impact of varying
ratios of ethanol and chloroform solvents on the absorption characteristics and behavior of the D1 dispersedye. Specifically, they display the changes in absorption,
absorption energy, and the polarities of new mixed solvent structures across different levels (high/medium/
low).
Figure 13 conducts a detailed analysis of the common
relationship between changes in the absorption energyof disperse dye D1 and shifts in the polarity of chloroform-ethanol mixtures across different ratios. The graphserves as a valuable tool for understanding the dynamics
between new absorption energy and the varying polarityof the solvent mixture. These changes are presented distinctly, revealing a clear linear trend within the graph.
The formulated equation, Y = 0.3756X + 51.075, summarizes the calculated alterations in new absorptionenergy corresponding to the changing polarity. The highR²=0.8055 attests to the reliability and strength of theobserved trend, while a statistic is the standard deviationof its sampling distribution SE quantifies the precision of
the results. These clarifying’s contribute to a more structured and clear presentation of the data and findings in
Fig. 13, enhancing the interpretability and robustness ofthe observed trends. The data analysis and processing,conducted through laboratory experiments, resulted in
an increase in the R2 value and a decrease in the SE value,indicating a reduction in uncertainty observed in theexperimental and laboratory data.
Figure 14 meticulously analyzes the impact of shifts inthe polarity of ethanol-chloroform mixtures with varying

Page 24 of 31

ratios on the new absorption energy of disperse dye D1.
The graph distinctly portrays the trend of changes in newabsorption energy in response to alterations in the polarity of the solvent mixture, presenting it as a clear and linear progression.
The formulated equation, Y = 1.8436X + 50.471, succinctly captures the calculated changes in new absorption energy corresponding to shifts in the polarity of thesolvents. The high R²=0.8452 attests to the reliability androbustness of the observed trend, while a statistic is thestandard deviation of its sampling distribution SE quantifies the precision of the results. These clarifications
contribute to a more structured and clear presentationof the data and findings in Fig. 14, facilitating enhanced
interpretation and understanding of the observed trends.
The data analysis and processing, conducted through laboratory experience, revealed an increase in the R2 value
and a decrease in the SE value, resulting in a decrease inuncertainty observed in the experimental and laboratory
data.
Figure 15 undertakes a comprehensive evaluation of theabsorption characteristics, encompassing new absorption energy and wavelength, of a typical diffuse dye (D1)within mixed solvents of ethanol and chloroform featuring diverse ratios. The ensuing graphs reveal a discernible
linear trend, with the solvent mixture at a 4:1 ethanol tochloroform ratio demonstrating the highest new polarity
and absorption energy.
Moreover, the analysis delves into the impact of themolecular weights of ethanol and chloroform on newpolarity, absorption energy, absorption levels, and wavelength, emphasizing on the intricate interaction between
solvent composition and key features of the disperse dye.
These findings, abbreviated in Fig. 15, provide valuable
insights into the nuanced effects of varying solvent ratios
and molecular weights on the absorption properties ofthe disperse dye D1.
Using analogy reasoning, we explore how changes inpolarity correspond to variations in absorption energy andwavelengths of new azo dyes in dual solvents with different
chloroform-methanol ratios

Table 7 offers valuable insights into the nuanced changes
in new polarity, new absorption energy, wavelength, andabsorption of novel disperse dye D1 across various mixtures of chloroform and methanol. The results underscore that, despite variations in these parameters withchanging ratios of chloroform and methanol, the differences in absorption energy remain relatively minor. The
mixture of chloroform and methanol with a ratio of 3:1
exhibits the highest new absorption energy, while thelowest is observed in the 4:1 ratio mixture. This suggeststhat the composition of the solvent mixture, particularly
the ratio of the non-polar solvent (chloroform) to theShirali et al. BMC Chemistry(2024) 18:154

polar protic solvent (methanol), has a subtle impact on
the electronic transitions within the dye molecule.
Similarly, new polarity values vary with the ratios,
peaking in the 2:1 mixture and reaching the lowest pointin the 4:1 mixture. These changes in new polarity reflect
alterations in the solvent environment, influencing theoptical properties of the dye. Notably, despite thesevariations in new polarity and new absorption energy,
the shifts in absorption are minor. These subtle changesalign with bathochromic and hypsochromic shifts, consistent with the explanations provided in previous sections (Tables 2 and 4, and 3). Such shifts are influenced
by alterations in the polarity of the solvent, impacting
electron transitions within the dye molecule.
In summary, the data in Table 7 highlights the subtle
yet discernible changes in the properties of new disperse dye D1 when exposed to different ratios of chloroform and methanol. While the differences in absorptionenergy are minimal, they can still exert influence on thecolor and optical characteristics of the dye. These findings are crucial for comprehending the solvatochromism
behavior that occurs in response to alterations in solvent
composition.
Figure 16 undertakes an examination of the changes
in new absorption energy for novel disperse dye D1regarding the new polarity of the mixture of chloroform and methanol solvents across various ratios. However, the data presented in Fig. 16 reveals a weak ornearly non-existent correlation between new polarity
and new absorption energy. The formulated equation,
Y = -0.2313X + 51.824, succinctly describes the calculated changes in new absorption energy corresponding
to shifts in the polarity of the solvents. However, the low
R² value of 0.021 indicates a minimal linear relationshipbetween these two variables. This lack of a strong correlation suggests that changes in the polarity of the solvent
mixture (chloroform and methanol) within the tested
range have little impact on the absorption energy of new
disperse dye D1. It implies that other factors may exerta more substantial influence on the absorption energy ofthe dye in this particular solvent mixture. Furthermore,considering the SE, which offers a measure of variability in the data, becomes relevant. If the standard error isrelatively high, it indicates significant uncertainty in therelationship between new polarity and new absorptionenergy. In conclusion, Fig. 16 implies that the new polarity of the mixture of chloroform and methanol solvents,
with different ratios, does not strongly correlate withnew absorption energy for normal disperse dye D1. The
observed relationship lacks statistical robustness, indicating that additional factors or interactions may contribute significantly to determining the absorption energy ofthe dye in this specific solvent mixture.

Page 25 of 31

Figure 17 unfolds as a 3-D column graph, offering avisual representation of the changes in absorption, newabsorption energy, and wavelength of a new disperse dye
D1 in response to the new polarity of mixed solvents ofchloroform and methanol across different ratios. The
graph distinctly portrays linear changes in these parameters as a function of the new polarity. Notably, the solvent mixture of chloroform and methanol with ratios of
2:1 and 3:1 exhibits the highest new polarity and newabsorption energy, it seems that increasing the ratioof chloroform to methanol increases the new polarity,
absorption and absorption energy.
The observed linear relationships between new polarity, new absorption energy, and wavelength emphasis on
the significance of changes in solvent composition, particularly the ratio of chloroform to methanol, in influencing the absorption characteristics of disperse dye D1. The
graph supposes further exploration of the effects of themolecular weight of these solvents on new polarity, newabsorption energy, absorption, and wavelength to achieve
a comprehensive understanding of the dye’s behavior inthese solvent mixtures.
Using analogy reasoning, we explore how changes inpolarity correlate with variations in absorption energy andabsorption wavelengths of new azo dyes in single solvent
systems

The notable high absorption energy observed in the mixture of toluene (a non-polar solvent) with disperse dye
D1 has resulted in a hypsochromic shift. This shift isindicative of a transition towards shorter wavelengths in
the absorption spectrum. The underlying mechanism forthis hypsochromic shift lies in the solvent’s interaction
with the non-bonding electron pairs in the n molecularorbitals. By assuming these electron pairs, the solvent
influences the electronic transitions within the dye molecule, causing a shift towards shorter wavelengths.
Conversely, in the case of benzene (also a non-polar
solvent), a typical bathochromic shift is observed withdisperse dye D1. This bathochromic shift signifies a shift
towards longer wavelengths in the absorption spectrum.
The reasons for these bathochromic and hypsochromic
shifts have been elucidated in detail in the corresponding sections of Tables 2 and 4, and 3. Furthermore, these
specific solvent ratios and changes in Gibbs’s formationenergy and enthalpy are hypothesized to have an effecton absorption spectroscopic properties, absorptionenergy, as well as solvent and solute polarity. For thesebinary mixtures, the absorption energy has been calculated, and ΔEt = 0.372 serves as a measure of the energychanges and polarity associated with these spectral shifts.
This value quantifies the extent of energy change related
to the observed shifts in absorption, wave length providing a comprehensive understanding of the spectral

Shirali et al. BMC Chemistry(2024) 18:154

behavior of disperse dye D1 in the presence of toluene
and benzene solvents.
Figure 18 adeptly illustrates the trend of changes inabsorption energy concerning the polarity of non-polar
solvents, namely benzene, toluene, and xylene, whenemployed in conjunction with a novel dispersion dye D1.
The observed changes display a linear nature, suggestinga systematic relationship between the solvents’ polarity
and the absorption energy of the dye.
The absorption energy is accurately modeled basedon the solvents’ polarity, as summarized in the formulaY = -9.0518X + 53.89. This mathematical representation
provides a concise expression of the linear relationship,enabling predictions of absorption energy changes corresponding to alterations in solvent polarity. The model
achieves a high degree of explanatory power, reflected in
the R² value of 0.9396. Additionally, the SE has been calculated and presented, offering insights into the precisionand reliability of the modeled relationship. The data analysis and processing, conducted through laboratory experience, resulted in an increased R2 value and a decreased
SE value, indicating a decrease in uncertainty observed in
the experimental and laboratory data.
In summary, Fig. 18 not only visually portrays the linear trend of changes in absorption energy with respect
to the polarity of non-polar solvents but also provides aquantifiable model that enhances the understanding of
this relationship.
Figure 19 unfolds as a 3-D column graph, offering acomprehensive investigation into the changes in absorption, absorption energy, and wavelength of a novel dispersion dye D1. The analysis is centered around thedegree of polarity in non-polar solvents, specificallybenzene, toluene, and xylene. The graph visually abbreviates the variations in these parameters, providing a clear
and intuitive representation of how they respond to thepolarity of the solvents. The highest absorption energyof 53.2222 and the lowest polarity of 0.072 correspondto the non-polar solvent of xylene, whereas the lowest
absorption energy of 52.8493 and the highest polarity of
0.111 are associated with the non-polar solvent of toluene containing the novel dispersed azo dye D1. Additionally, changes in solvent structure and variations in Gibb’s
energy and enthalpy of formation are assumed to impact
the dye’s absorption properties, particularly absorptionenergy, polarity, and wavelength.
Through analogy reasoning, we examine how changes inpolarity correlate with variations in absorption energy andabsorption wavelengths of new azo dyes in dual solventswith different benzene-xylene ratios

The data presented in Table 9 unveils several noteworthy findings regarding the behavior of the novel dispersion dye D1 in mixed solvents of benzene and xylene

Page 26 of 31

at varying ratios. The highest absorption energy value,
reaching 53.0454, is observed in the 1:1 mixture of benzene and xylene, both being non-polar solvents. In contrast, the lowest absorption energy value of 52.9472 isfound in the 2:1 mixture of benzene and xylene with thesame dispersion dye. This variation highlights the significant impact of changing solvent ratios on the absorptionenergy of the dye.
Additionally, the highest polarity value of 0.183 corresponds to a 1:1 mixture of benzene and xylene, while thelowest polarity value of 0.098 is observed in a 2:1 mixture of the same solvents with dispersion dye D1. Thesepolarity values reflect the varying degrees of interaction between the dye and the solvents as the benzene
to xylene ratio increases. They elucidate the complex
dynamics within the solution structure and focuses on
the vibrational and screening effects of the environmenton the properties of the absorption spectrum.
The data also includes information about absorption
rates, with the lowest rate of 0.782 found in the 1:1 mixture of benzene and xylene, and the highest rate of 0.904
observed in the 2:1 mixture of the same solvents withthe dispersion dye D1. These absorption rates provide
insights into the efficiency of the dye-solvent interactions.
The absorption energy for binary mixtures, denoted as
ΔEt, is calculated to be 0.093. This calculated value summarizes the overall energy changes associated with theobserved shifts in the absorption spectrum.
In summary, the findings in Table 9 collectively underscore how alterations in the ratios of benzene and xylene
can significantly influence absorption energy, polarity,
wavelength, and absorption rates of the dispersion dye
D1. These insights contribute to a deeper understanding of the behavior of this dispersion dye in diverse solvent environments. The experimental and statistical data,
along with the analysis and inductive reasoning presented
in the previous tables and figures, have been generalized
to elucidate the effects of changes in the interaction ofvarious solvent and solute environments on the bathochromic and hypsochromic shifts of the new azo dispersedye.
Figure 20 illustrates the trend of changes in newabsorption energy based on the new polarity of nonpolar solvents, specifically benzene, toluene, and xylene,
with the new dispersion dye D1 at varying ratios. The
graph demonstrates a linear relationship between the
new polarity and new absorption energy. The equation
used to represent this relationship is Y=-1.1749x + 52.83,
where Y represents the new absorption energy and x corresponds to the new polarity of the solvents. The high R²
value of 0.999 indicates a strong correlation between newpolarity and new absorption energy, underlining the reliability of the relationship depicted in the graph.

Shirali et al. BMC Chemistry(2024) 18:154

The SE, which measures the accuracy of the calculated
values, has been computed and is also shown. These findings provide valuable insights into how changes in thepolarity of non-polar solvents impact the absorptionenergy of the new dispersion dye D1, show its behavior
in different solvent compositions. The data analysis andprocessing, conducted through laboratory experience,
resulted in an increased R2 value and a decreased SE
value, indicating a decrease in uncertainty observed in
the experimental and laboratory data.
Figure 21 shows a comprehensive analysis of the linear
relationships among key parameters—new polarity, newabsorption energy, absorption, and wavelength—and
their dependency on the degree of new polarity in mixed
solvents of benzene and xylene with the new dispersion
dye D1. The graphs within Fig. 21 reveal a systematic andpredictable connection between these parameters andthe evolving polarity of the solvent mixtures.
The highest recorded new polarity value, standing at
0.183, corresponds to the 1:1 mixture of benzene andxylene with the dispersion dye D1. In contrast, the lowest new polarity value, measured at 0.098, is associatedwith the 2:1 mixture of the same solvents with the samedye. This distinct polarity gradient underscores the dye’s
sensitivity to variations in the proportion of non-polar
solvents and offers valuable theoretical and experimental insights into how changes in polarity influence its
absorption properties.
Examining new absorption energy, the highest value of
53.0454 is identified in the 1:1 mixture of benzene andxylene with the dispersion dye D1. On the other hand, thelowest new absorption energy value, measuring 52.9472,
is observed in the 2:1 and 3:1 mixture of benzene andxylene with the same dye. These findings underscore thesignificant role played by varying ratios of non-polar solvents in influencing the absorption energy of the dispersion dye D1.
The exploration of the potential effects of the molecular weight of non-polar solvents such as benzene, toluene, and xylene on new polarity, new absorption energy,
absorption, and wavelength opens avenues for further
understanding the nuanced interactions within these solvent-dye systems.
Analogical reasoning explores how changes in polarity
correlate with variations in absorption energy andabsorption wavelengths of new azo dyes in dual solventswith different toluene-xylene ratios

The results presented in Table 10 demonstrate significant
insights into the behavior of the novel dispersion dye D1
when exposed to non-polar solvents, specifically toluene and xylene, across varying ratios. Key findings fromthis analysis include: The highest new absorption energy,
recorded at 53.3423, was observed in the 3:1 mixture ofPage 27 of 31

toluene and xylene with new dispersion dye D1, indicating the impact of the solvent composition on the dye’s
absorption energy. Conversely, the lowest new absorption energy was 53.144, occurring in the 4:1 mixture oftoluene (non-polar) and xylene (non-polar) with newdispersion dye D1, showcasing the variation in absorption energy under different conditions. New polarity
values exhibited considerable differences, with the highest value of 0.234 found in the 4:1 mixture of toluene andxylene, while the lowest value of 0.078 was present in the
3:1 mixture, underlining the role of solvent ratios in influencing polarity. The wavelength experienced fluctuations,with the highest wavelength recorded at 538 nm in the
4:1, 2:1 and 1:1 mixture of toluene and xylene with newdispersion dye D1, while the lowest wavelength, 536 nm,
was observed in the 3:1 mixture. The absorption rate also
varied, with the highest rate of 0.601 associated with the
2:1 mixture of toluene and xylene, and the lowest rate of
0.541 found in the 1:1 mixture, emphasizing the role ofsolvent ratios in absorption characteristics. The calculated absorption energy for binary mixtures, ΔEt = 0.198,
further emphasizes the variations in the behavior of new
dispersion dye D1 when exposed to different ratios of toluene and xylene. These findings offer valuable theoreticaland experimental insights for researchers and professionals exploring the interaction between dispersion dyes andnon-polar solvents with novel structures and dielectric
constants. They show new intermolecular interactions,vibrational effects, and molecular screening, emphasizing the significance of solvent composition in influencing
spectrum characteristics and color absorption.
Figure 22 presents a graphical analysis of the changes
in new absorption energy exhibited by novel dispersion
dye D1 when exposed to toluene and xylene solvents at
various ratios. The graph reveals a linear relationship,
showcasing the influence of solvent polarity on the dye’s
absorption energy. The equation derived from the data
is as follows: Y=-0.7305x + 53.297. However, R2 = 0.3106
indicates that the correlation between the new absorption energy and solvent polarity, while linear, is not particularly strong. The standard error is not provided in
the description, but it may offer additional insights into
the accuracy of the model. This graph provides valuable
information for researchers studying the behavior of
new dispersion dyes in non-polar solvents, such as toluene and xylene, and highlights the relationship between
solvent polarity and dye absorption energy. The data
analysis and processing, conducted through laboratory
experience, resulted in a decrease in the R2 value and anincrease in the SE value, indicating an increase in uncertainty observed in the experimental and laboratory data.
The graph reveals that the highest recorded new polarity value is 0.234, corresponding to the mixture of toluene and xylene with novel dispersion dye D1 at a 4:1

Shirali et al. BMC Chemistry(2024) 18:154

ratio. Conversely, the lowest observed new polarity value
is 0.078, associated with the mixture of toluene andxylene with the same dye and a 3:1 ratio. In terms of newabsorption energy, the highest value is 53.3423, obtained
from toluene solvent with xylene and novel dispersion
dye D1 at a 3:1 ratio. The lowest new absorption energy,
53.144, is related to toluene with xylene and novel dispersion dye D1 at a 4:1 ratio. This graph allows researchers
to visualize the relationship between solvent polarity,
new absorption energy, and wavelength changes in nonpolar solvents, toluene and xylene, when exposed to normal dispersion dye D1 at various ratios. It also suggeststhat the molecular weight of these solvents can be a significant factor in influencing polarity, absorption energy,
and other properties.
Analogical reasoning investigates how changes in polarity
correlate with variations in absorption energy andabsorption wavelengths of new azo dyes across polar protic,
polar aprotic, and non-polar solvent environments

MW dye D1:337.
In Table 11; Fig. 24, we meticulously examined theinteraction between the statistical components and thedata structure of new disperse dye D1 across various
types of solvent structures. Our analysis involved careful calculations and the presentation of findings throughvisual aids and abductive reasoning. The components
analyzed for novel disperse dye D1 included absorption energy, extinction absorption coefficient, maximum
wavelength, absorption, and molecular weight. This study
delves into the influence of solvent polarity on thesecomponents, revealing a clear and direct relationshipbetween the quenching absorption coefficient and thelevels of absorption energy, absorption, and molecularweight in the solvents.
In Fig. 25; Table 11, we examine the results of theabsorption test for new disperse dye D1 in various solvents. Acetonitrile, a polar aprotic solvent with a polarity of 0.46, demonstrates the highest absorption at 1.026
and the highest extinction coefficient at 12,825. Similarly,
DMF solvent, another polar aprotic solvent with a polarity of 0.386, exhibits the highest absorption of 0.9805 andthe highest extinction coefficient of 12,256.25. Notably,both acetonitrile and DMF solvents display a noticeable
tendency toward a bathochromic shift. Additionally, they
demonstrate the highest dye aggregation in Fig. 25. In
contrast, hexane and diethyl ether, non-polar solventswith a polarity of 0.009, present the lowest absorption at
0.08147 and the lowest extinction coefficient at 1,018.375.
These solvents also feature the highest absorption energy
at 56.0617. Similarly, diethyl ether, with a dielectric constant of 40.34, demonstrates the lowest absorption at
0.2315, the lowest extinction coefficient at 2,893.75, andthe highest absorption energy at 55.8427. Hexane andPage 28 of 31

diethyl ether solvents exhibit a propensity for a hypsochromic shift, resulting in lower absorption. Additionally,
they show the lowest dye aggregation in Fig. 25. Hence,in theoretical and experimental analysis, the influenceof intermolecular interactions, molecular polarizability, vibrational effects, and molecular screening on theabsorption spectrum properties of various solvents canbe elucidated.
Computation of descriptive statistical indices forexperimental data pertaining to the novel dispersed azo dye

Table 12 provides a thorough analysis of statistical criteria computed for the adsorption of the new structureof azo dye D1. This presentation encompasses vital statistical parameters: Mean: 53.4998, SE: 0.476670696,
Standard Deviation: 1.507365093 and Confidence Level(95.0%): 1.078304029.
Moreover, the table functions as a valuable resource,
given a comprehensive reference point for displaying additional relevant features derived from statisticalexperimental data of the typical azo disperse dye D1.
This statistical information enhances our understanding,facilitating the interpretation and analysis of the intrinsic
characteristics of the experimental data set in relation to
the azo disperse dye D1.
Table 13 provides a full statistical examination of theextinction coefficient associated with the novel structureof azo dye D1. The analysis encompasses essential statistical parameters: Mean: 8357.9625, SE: 1586.005023,
Standard Deviation: 5015.388253 and Confidence Level(95.0%): 3587.792623.
This table functions as a robust and comprehensive
reference, presenting crucial features derived from statistical experimental data pertaining to the extinction
coefficient of the new azo disperse dye D1. Beyond thebasic statistical measures, it serves as a valuable tool for
researchers, enriching our holistic understanding andfacilitating the interpretation and analysis of the inherent
characteristics within the experimental dataset. This statistical information significantly contributes to developing a theoretical perspective on the distinctive structureof azo dye D1.
Table 14 presents a detailed statistical analysis
of absorption rates for the new azo dye D1 structure. This analysis includes key statistical measures:
Mean: 0.668637, SE: 0.126880402, Standard Deviation:
0.40123106 and Confidence Level (95.0%): 0.28702341.
Additionally, Table 14 functions as a practical and comprehensive reference, offering insight into additional relevant features derived from statistical experimental data
pertaining to the new azo disperse dye D1. This statisticalinformation deepens our understanding and facilitates
the interpretation and analysis of the basic aspects of theShirali et al. BMC Chemistry(2024) 18:154

experimental data set, contributing to a theoretical perspective on the new structure of azo dye D1.
Table 15 conducts an in-depth statistical scrutiny of the
maximum wavelength associated with the novel structure of azo dye D1. The statistical metrics encompass
fundamental measures: Mean: 534.8, SE: 4.715930449,
Standard Deviation: 14.91308151 and Confidence Level(95.0%): 10.66817584.
Moreover, Table 15 serves as a pragmatic and comprehensive reference, providing insights into features derived
from statistical experimental data concerning the maximum wavelengths of the prevalent azo scattering dye D1.
This statistical information enriches our comprehension,facilitating the interpretation and analysis of the intrinsic
features within the experimental dataset in connection to
the new structure of azo dye D1. Consequently, it significantly contributes to shaping a theoretical perspective.
Table 16 brings an exhaustive statistical analysis of thepolarity associated with diverse solvent structures. Key
statistical metrics encompass: Mean: 0.287888889, SE:
0.091970473, Standard Deviation: 0.275911419 and Confidence Level (95.0%): 0.212084291.
Additionally, Table 16 serves as a pragmatic and comprehensive reference, providing insights into featuresderived from statistical experimental data related to thepolarity of different types of solvent structures. This statistical information enhances our understanding, facilitating the interpretation and analysis of the intrinsic
characteristics within the experimental datasets concerning various solvent structures. Consequently, it significantly contributes to shaping a theoretical perspective.
Table 17 presents a detailed statistical analysis of themolecular weight of various solvents and the new structure of disperse azo dye D1. Key statistical measures
include: Mean: 98.74164545, SE: 24.87042184, Standard
Deviation: 82.48585761 and Confidence Level (95.0%):
55.41475316.
Furthermore, Table 17 serves as a practical and comprehensive reference, providing insights into properties
derived from the statistical data of the molecular weightof various solvent structures and the molecular weight of
the new azo dye D1 structure. This statistical information
deepens our understanding and aids in the interpretation and analysis of the essential attributes of the experimental data sets, pertaining to the molecular weights ofvarious solvents and the new azo dye D1 structure, contributing to a theoretical perspective.
Conducting t-tests on statistical data concerning absorptionenergy, absorption, and wavelength of the novel dispersed
azo dyeTable 18 presents the results of a two-sample t-test,
assuming equal variances, for two separate sets of statistical data concerning the absorption energy values ofPage 29 of 31

a solvent mixture with the new structure of new azo disperse dye D1. This analysis includes key statistical factors
such as variance, combined standard deviation, degrees
of freedom (df ), t-statistics, and t critical value (one-tail,two-tail). The absence of a significant statistical discrepancy between the two data series is indicated by the low t
Stat value of -0.867832555 when compared to the t critical value of (two-tail) 2.10092204. Therefore, there is no
statistically significant difference between the two data
series.
Table 19 displays the outcomes of a two-sample t-test,
assuming equal variances, for two distinct sets of statistical data related to absorption values in different solvent mixtures featuring the new structure of the novel
dispersed azo dye D1. This comprehensive analysis
incorporates essential statistical parameters, including
variance, combined standard deviation, degrees of freedom (df ), t-statistics, and the t critical (one-tail, two-tail).
The insignificance of statistically discernible differences
between the two data series is evidenced by the low t
Stat of -0.36435 when contrasted with the t critical valueof(two-tail) 2.100922. Consequently, no statistically significant disparities are identified between the two data
series.
In Table 20, the outcomes of a two-sample t-test,
assuming equal variances, are presented for two distinct
sets of statistical data relating to the maximum wavelength values in different solvent mixtures with the newdispersed azo dye D1. This analysis encompasses crucial statistical parameters, including variance, combined
standard deviation, degrees of freedom (df ), t-statistics,
and the t critical (one-tail, two-tail). The insignificance ofstatistically significant differences between the two data
series is evidenced by the low t Stat value of -0.937702593
when compared with the t critical value (two-tail) of
2.10092204. Consequently, there is no statistically significant discrepancy between the two data series.
Calculating the statistical errors in experimental data for
novel dispersed azo dye

Table 21 showcases the computation and presentation of statistical errors, specifically RMSE = 0.6655825
and MAPE = 1.1040355, for 10 statistical data related toabsorption energy in a solvent mixture with the new dispersed dye D1. These error calculations offer a thoroughevaluation of the experimental data, providing valuable
insights into the interaction effects of various solventson the new structure of the dispersed azo dye D1. Consequently, this enhances the analysis, interpretation, andcomprehension of the absorption energy data and theunderlying theoretical patterns inherent in the new D1
dye structure.
In Table 22, statistical errors in the form of
RMSE = 0.169210812 and MAPE = 10.19100671 areShirali et al. BMC Chemistry(2024) 18:154

calculated and presented for ten sets of statistical data
related to the absorption in different solvent mixtureswith the new dispersed dye D1. These error calculations
provide a comprehensive assessment of the experimental data, enhancing the understanding of the interaction
effects of various solvents on the new structure of thedispersed azo dye D1. This, in turn, facilitates the analysis
and interpretation of the experimental adsorption data
and a better grasp of the theoretical adsorption relationships and patterns for the new D1 dye structure.
Table 23 presents the calculation and presentation of
statistical errors, specifically RMSE = 6.877499546 and
MAPE = 1.179161087, for 10 statistical data related tothe maximum wavelength in a solvent mixture with the
new disperse dye D1. These error calculations offer athorough assessment of the experimental data, providing valuable insights into the effects of various solventson the new structure of the disperse dye D1. Consequently, this enhances the analysis and interpretation of
the experimental maximum wavelength data, providing aclearer understanding of the theoretical absorption patterns associated with the new D1 dye structure.

Conclusions
In this paper, we conducted a comprehensive study of a
new D1 disperse dye, 4-nitro-2-cyanoazobenzene-metatoluidine (D1), within various polar aprotic polar, protic,
and nonpolar solvents, each with different solvent ratios.
Our investigation encompassed essential componentsof the D1 dye structure, including absorption energy,
absorption wavelength, polarity, and other characteristics when placed in different solvent environmentswith diverse structures. To evaluate the impact of solvatochromism on the new structure of azo dye D1, In
our analysis, we utilized statistical methods to calculate
various types of errors, including RMSE = 0.6655825 and
MAPE = 1.1040355, as well as R2 = 0.999, t-test= -0.36435,
and other relevant statistical factors. These analyses
facilitated the comparison of experimental data with statistical and theoretical information. By integrating experimental data, statistical calculations, theoretical insights
and inductive reasoning we gained a deeper understanding and predictive capacity regarding the interaction ofdifferent solvent structures on the novel azo disperse dye
D1. This work contributes to a comprehensive framework
for the photophysical and photochemical examination of
the new D1 dye structure, enhancing our knowledge ofits features.
Acknowledgements
The authors thank the National Iranian South Oil Company (NISOC), Iran Color
Research Center, Amirkabir University of Technology and the Research Council of
Yazd University for partial support of this work.

Page 30 of 31

Author contributions
All authors contributed to the study conception, literature, analysis, andwriting. Mahdi Shirali put forward the research ideas and finally approved thewhole content. Shohre Rouhani, Kamaladin Gharanjig, Fatemeh Mirhashemi
and Mahdi Shirali did the experiments and characterizations, analyzed theresults and organized the writing framework.
Funding
Not applicable.
Data availability
No datasets were generated or analysed during the current study.

Declarations
Ethics approval and consent to participate
Not applicable.
Consent for publication
Not applicable.
Competing interests
The authors declare no competing interests.
Author details
1
Department of Chemistry Laboratory of Oilfields in Southern Iran(NISOC), Ahvaz, Iran2
Department of Colorant Manufacture, Iran Color Research Center, P. O.
Box 1665618481, Tehran, Iran
3
Faculty of Textile Engineering, Amirkabir University of Technology, P. O.
Box 15875-4413, Tehran, Iran4
Department of Chemistry, College of Science, Yazd University, P. O. Box
89195-741, Yazd, Iran
Received: 5 March 2024 / Accepted: 15 July 2024

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