Introduction

The textile industry is one of the largest water-consuming industries (Rashid et al. 2020). They refuse large amounts of wastewater. Such wastewaters contain toxic dyes and pigments that have a negative influence on human health and the ecosystem (Khan and Malik 2014). The existence of dyes in wastewater creates various hazards for living organisms, such as mutagens and carcinogenic problems, and reduces photosynthesis; by limiting the penetration of oxygen into water (Saini 2017). Multiple methods treat these effluents (Gao et al. 2020). However, in the presence of toxic and non-biodegradable dyes, the biological treatments are ineffective and produce high quantities of sludge; the physicochemical methods do have a high investment cost (Badeenezhad et al. 2019). These limitations mean that new efficient processes are developed. A photocatalytic solution for wastewater polluted by color bleeding from fabric, rubber, natural and artificial fabrics. Bromothymol blue (BTB) is a silk dye product often used as the pH measure (Li et al. 2018). It is a useful probe molecule that is not corrupted by direct oxidation and can only be chemically degraded via free-radical pathways.

The strong oxidizing agent (KMnO4) has some advantages over other oxidizing agents: easier to handle, a readily soluble solid and higher performance in water and soil treatment as seen with some pollutants (Xu et al. 2005). Permanganate ion is an effective oxidant in acid, neutral and basic media that is known to be a leading, environmentally friendly, and active oxidant in kinetic research (Liu et al. 2019). Oxidation by permanganate ion have a various mechanism so, permanganate ion is used as a multi-equivalent oxidant (Hassan 2020). The mechanism of some redox reactions was focused on intermediate complexes (Al-Hossainy and Zoromba 2019) production, whereas free-radical mechanisms (Tittmann 2009; Mollan and Alayash 2013) studied other redox reactions. Methylcellulose kinetics and oxidation mechanism (Shaker et al. 2007; Hassan 1993), alginates (Khairou and Hassan 2000), pectates (Shaker 2001), carboxymethyl cellulose (Hassan et al. 2011), kappa-carrageenan (Zaafarany et al. 2013), and polysaccharides of permanganate ion have been recorded elsewhere in alkaline media. Again, the oxidation of methylcellulose (Hassan et al. 2012), pectates (Abdel-Hamid et al. 2003), carboxymethyl cellulose (Hassan et al. 2009a), carrageenan’s (Hassan et al. 2009b), ADA (Hassan and Ibrahim 2019a), poly (ethylene glycol) (Hassan et al. 2018a) and chondroitin-4-sulfate (Hassan et al. 2020a) by permanganate ion in acidic solutions has been reported earlier. Pseudo-first-order plots were shown to be reversed S-forms in these oxidation reactions and free radical interference carried out the oxidation reactions.

Previous studies have neglected to consider the effects of KMnO4 as an oxidizing agent on the structure characterization, spectroscopic studies, and optical properties of dye [BTB]. In this work, the decoloration of the BTB coloring solutions by KMnO4 was investigated kinetically. Effects of pH, reactant concentration and decoloration temperature have been studied. The application of KMnO4 for the treatment of real textile wastewater was also carried out. The present work seems to merit a study to shed more light on the mechanistic aspects of oxidation and to cover for the lack of information on the existence of both the electron transfer and the transition states in the rate-determining phase. The results obtained will offer important knowledge on the chemistry of BTB dye as one of the sulfones phthalein’s in acidic solutions. Again, this study will boost the elucidation of an appropriate oxidation reaction process in acidic solutions for these alcoholic dyes. Once more, in this work besides the oxidation of BBT we used the unified coverage DMol3 obtained from molecular to solid materials is discussed briefly. So, molecules in the gas state are pertinent for the properties of molecular materials and homogeneous catalysis reactions. In comparison studies between experimental and DFT computations, the structural characterization, and optical properties of [BTB] and [BTB]Keto were examined utilizing characterization techniques comprising Fourier transform infrared (FTIR).

Experimental section

Materials

All used products are analytical grade. Water has doubly been distilled from alkaline permanganate and degassed through the atmospheric pressure bubbling, boiling, and cooling (Manhas and Mohammed 2007). Through adding the reagent powder to double distilled water step through process, [BTB] (Aldrich Chemical Co. Ltd) solutions in stock was prepared and the solution rapidly was agitated. A KMnO4 stock solution has been prepared and standardized using traditional methods (Bahar et al. 2020). The stock solution was then placed in a dark container away from light to prevent photoreduction and was spectrophotometrically re-standardized before each use. By dissolving the required sample amounts in double distilled water, all other reagents were prepared. The ionic strength was kept in check by the addition of NaClO4 as non-complexing agent (Hassan et al. 2020b; Tandon et al. 2007). In ± 0.05 °C, the temperature was regulated.

Kinetic measurements

The present oxidation reaction for the available spectrophotometer was relatively quick. All kinetic operations have been made under the scope of pseudo-first-order (Hassan and Ibrahim 2019b; Hicks 1976; Hassan et al. 2018b). The absorption decrease was recorded at 525 nm at permanganate ion, with the maximum absorption depending on time (where [BTB] > 10 \(\left[ {{\text{MnO}}_{4}^{ - } } \right]^{0}\)). During the reaction process, no overlaps were found with other [BTB], \({\text{MnO}}_{4}^{ - }\) and substances at this wavelength. As Fig. 1a indicates, an isosbestic point is found at a wavelength of 274 nm. Once, a new strip at a wavelength of around 380 nm was used to produce the permanganate ion of the same concentration of the mixture being studied (Fig. 1b). These observations may indicate the formation of some intermediate complexes.

Fig. 1
figure 1

Spectral dependence of the absorption in the oxidation of [BTB] by [\({\text{MnO}}_{4}^{ - }\)] in aqueous HClO4 during the reaction progression. a [\({\text{MnO}}_{4}^{ - }\)] = 4.0 × 10−4, [BTB] = 1.0 × 10−3, [HClO4] = 0.5 and I = 1.0 mol dm−3 at 20 °C. Scanning time intervals = 1.0 min. b [\({\text{MnO}}_{4}^{ - }\)] = 4.0 × 10−4, [BTB] = 1 × 10−3, [H+] = 0.5 and I = 1.0 mol dm−3 (Reference cell: [\({\text{MnO}}_{4}^{ - }\)] = 4.0×10−4 mol dm−3 at 20 °C)

Full size image

Absorbance–time plots revealed that the initial component (~ 5–10%) was too quick for the traditional spectrophotometer to be followed. Therefore, the kinetic calculations listed concerned the remaining portion of the completion of the reaction (~ 90–95%). In the presence of a large quantity [\({\text{MnO}}_{4}^{ - }\)] above [BTB] in all kinetic measurements pseudo-first-order conditions were used. Sodium perchlorate, NaClO4, used as an inert electrolyte to maintain ionic strength constant. The absorbance shift measurements on the spectrophotometer Perkin Elmer (Lambada 750) with a thermostat cell partition using a path length of cells of 1 cm in total. The estimation method was the same as elsewhere (Manhas and Mohammed 2007). Figure 1a, b indicates the spectral variations during the redox reaction.

Polymerization test

Ten percent acrylonitrile (v/v) has been used in the reaction mixture during oxidation; to test the possibility of free radical’s formation brown forming after 15 min of warmth indicates the oxidation reaction by free-radical interference process (Ibrahim et al. 2017; Laidler 1965a; Hassan et al. 2013). Again, the same observation occurs when we replaced acrylonitrile by mercuric chloride.

Molecular modeling

The structure molecular, spectral simulation and geometry optimization for [BTB] and [BTB]Keto as isolated molecular have been elucidated in detail by analysis of an Infrared (IR) combined with Gaussian 09 W program (Abdel-Aziz et al. 2020). In IR calculation using the Gaussian 09 W (DFT/B3LYP), the functional exchange–correlation level demonstrates the wavenumber and the location of functional groups in [BTB] and [BTB]Keto as isolated molecular (Pavitha et al. 2017; Bourezgui et al. 2020). Finally, the optical characterization and optical constant have been elucidated in detail by analysis of DMOl3 and CATSTEP computations. Using Gauss View software, the HOMO and LUMO values have been computed in detail by analysis of UV–Vis spectrum using DFT/DMOl3 by typical 6–311G set of bases (Srebro et al. 2011; Zoromba and Al-Hossainy 2020).

Results

Stoichiometry

The oxidation reaction with varying initial [BTB] and \(\left[ {{\text{MnO}}_{4}^{ - } } \right]\) concentrations was combined at room temperature at [H+] = 0.5 and I = 1.0 mol dm−3. The unreacted permanganate ion is expected to reach a constant value regularly. There has been a stoichiometric average of 1.0 mol ([\({\text{MnO}}_{4}^{ - }\)] unreacted \(/\left[ { {\text{BTB}}} \right]^{0}\)). The corresponding stoichiometric equation is agreed with

$${\text{C}}_{27} {\text{H}}_{28} {\text{Br}}_{2} {\text{O}}_{5} {\text{S}} + {\text{MnO}}_{4}^{ - } + 4{\text{H}}^{ + } \overset { } \rightleftharpoons {\text{C}}_{27} {\text{H}}_{24} {\text{Br}}_{2} {\text{O}}_{5} {\text{S}} + {\text{Mn}}^{2 + } + 4{\text{H}}_{2} {\text{O}}$$
(1)

where C27H28Br2O5S and C27H24Br2O5S represent the [BTB] and [BTB]Keto, respectively. The [BTB]Keto had been isolated by another approach (Hassan et al. 2019).

The product was also recognized by the FTIR spectral bands detected at frequency 3448 cm−1 and 3443 cm−1 that characterize the two –OH groups in [BTB] and these two bands converted to one band at 3443 cm−1 so, this confirms the oxidation occurs at one –OH group (Abd-Elmageed et al. 2020; Xu et al. 2020; Surowka et al. 2020; Al-Hossainy et al. 2019a). Moreover, band observed at 1720 cm−1 that characterize the carbonyl group of α-ketones; strong band appear at 2962 cm−1 which characterize CH2 group in case of [BTB] but appear weak band at 2962 cm−1 in case of [BTB]Keto which characterize –CH group (Zoromba et al. 2018). Enhancing the OH group absorption band at a wavelength of 1720 cm−1 in the product’s IR spectra can show oxidation of the OH group present in [BTB] dye to its corresponding keto-forms as display in Fig. 2a (Rauf et al. 2015).

Fig. 2
figure 2

a FTIR spectrum experimental of [BTB] and [BTB]Keto. b IR spectrum of [BTB] using DFT simulation. c IR spectrum of [BTB]Keto using Gaussian 09 W (DFT/B3LYP) simulation

Full size image

In the simulated IR spectrum of [BTB] (Fig. 2b), the band at 3600 cm−1 bands disappeared in the [BTB]Keto in Fig. 2c spectrum. This is attributed to stretching hydroxyl group ν(O–H) present in benzene oxidized to ketone group and formation [BTB]Keto dye. It is essential to note that the experimental curve shows great conformity with Gaussian 09 W (DFT/B3LYP) simulation (Thabet et al. 2020; Farzaneh et al. 2020; Ibrahim et al. 2020; Abbasi and Sardroodi 2016). Especially, 3750 cm−1.

Influence of reaction rate on [\({\text{MnO}}_{4}^{ - }\)] and [BTB]

ln (absorbance) against time, plots showed that the redox reaction in \({\text{MnO}}_{4}^{ - }\) is first in a sequence, with well straight lines for more than two half-lives of end reaction. Not only pseudo plotting but also an independently of the oxidation rates at different initial permanganate concentrations ranging from 1 × 10−4 to 5 × 10−4 mol dm−3 have confirmed this effect. The influence of [BTB] on the oxidation rates has been investigated. The values of oxidation rate were found to increase with increasing the [BTB]. So, these values at [BTB] = (1.0 and 3.0) × 10−3 mol dm−3 were found to be (0.58 and 1.47) × 10−3 s−1, respectively. A fractional-first-order in [BTB] was obtained from the plots of ln kobs and ln[BTB] and is confirmed by (ln kobs = n ln [BTB] equation). Once more, straight lines were achieved by drawings of 1/kobs in the HClO4 positive intercept axis on an X-axis against 1/[BTB]. The present redox system shows the creation of 1:1 intermediate complex shown by Michaelis–Menten kinetics (Fig. 3). The naked eye examination of the mixture revealed that the purple color of the permanganate ion in the mixture was modified to the orange color which changes rapidly to the rose color as shown in inset Fig. 3.

Fig. 3
figure 3

Chart 1/kobs against 1/[BTB] in perchlorate solutions to oxidize [BTB] through permanganate ion. [MnO4−] = 4.0 × 10−4, [H+] = 0.5 and I = 1.0 mol dm−3 at 35 °C. Inset figure, Naked eye examination for color shift a: BTB in 0.5 M HClO4; b: MnO4− in 0.5 M HClO4; c: during progression, d: after reaction of the of completion

Full size image

Influence of reaction rate on hydrogen ion concentrations

To explain the reaction rate and evaluate the successful reaction mechanism, [H+] controlled the constant ionic strength of 1.0 mol dm−3 and the constant concentrations of all other reagents. There was a rise in the acid amount to speed up the rates of oxidation and then the values of the rate constants at [H+] = 0.5 and 1.0 mol dm−3 were found to be 0.58 × 10−3, 1.51 × 10−3 s−1, respectively. The oxidation reaction is therefore catalyzed acidically. Dependence from [H+] was fractional first order (\(\ln k_{\text{Obs}} - \ln \left[ {{\text{H}}^{ + } } \right]\) plots).

Influence of reaction rate on ionic strength

The effect of the ionic strength was studied in constant [H+] reaction levels with the rise of NaClO4 concentration to 1.5 mol dm−3. This result was found to fit the extended Debye–Huckel equation (\(\ln k_{\text{Obs}} {\text{vs}} . \frac{\sqrt I }{1 + \sqrt I } {\text{plot}}\)) with a positive slope as shown in Fig. 4. The dependence of ionic strength is as expected in consideration of the charges, despite the ionic strength used, far from the Debye–Huckel range (Laidler 1965b). The oxidation reaction between a neutral and cation molecule can therefore occur.

Fig. 4
figure 4

The relationship between \(t\) \(\sqrt I / \left( {1 + \sqrt I } \right)\) versus \(\ln k_{\text{Obs}}\) of [BTB] by [MnO4−] in HClO4 solutions. [MnO4−] = 4.0 × 10−4, [BTB] = 1.0 × 10−3, [H+] = 0.5 mol dm−3 at 35 °C

Full size image

Reaction rate impact on salts added

The oxidation rate effect of Mn2+ must be studied as it is one of the oxidation materials is indicated that Mn2+ is reduced to MnIII and MnIV as a transient species (Radhakrishnamurti and Rao 1977; Gunter et al. 2010).

Where reactive oxidizing species are intermediates of \({\text{Mn}}^{\text{III}}\) and/or \({\text{Mn}}^{\text{IV}}\), the addition of \({\text{Mn}}^{\text{II}}\) will lead in the oxidation rate accelerations. While, fluoride ions should slow down the reaction if manganese ions are primarily the oxidation responsible species, but if permanganate ions are the primary oxidizing entities, they should not be significantly altered (Knežević et al. 2020). In addition to the redox reaction, either [\({\text{Mn}}^{\text{II}}\)] or [F−] ions were found to have no significant changes in the reaction rates under our experimental conditions. This negative outcome can be perceived as suggesting the absence of \({\text{Mn}}^{\text{III}}\) or \({\text{Mn}}^{\text{IV}}\) formation as transient material intermediates in the oxidation reaction.

Discussion

Although there has been substantial research on the kinetics of oxidation by permanganate ion of organic, inorganic substrates and alcoholic macromolecules in acidic solutions as multi-equivalent oxidants, several unanswered questions concerning the mechanisms of oxidation in terms of electron transfer and the intermediate states in the rate-determining processes have been recorded (Wasserman et al. 2016). Therefore, there may be a problem of fundamental importance, whether the transition, in a series or the simultaneous two-electron transitions, of electrons, takes place through a sequential one-electron transfer procedure: \({\text{Mn}}^{\text{VII}} \;{\text{to}}\;{\text{Mn}}^{\text{VI}} \;{\text{to}}\;{\text{Mn}}^{\text{V}}\) in a sequence or \({\text{Mn}}^{\text{VII}} \;{\text{to}}\;{\text{Mn}}^{\text{V}} \;{\text{to}}\;{\text{Mn}}^{\text{III}}\) in a single step.

Therefore, it is important to know whether the pathways for the process of electron transfer outer-sphere or inner-sphere type. The complexity of the reactions concerning the formation of unstable intermediates by the transfer of manganese ions from heptavalent to divalent in acidic solutions will cause these difficulties. Consequently, this oxidant has proposed different reaction pathways for the oxidation of various substrates. Many redox reactions tend to take place by free-radical (Zhou 2020) or free-radical interventions through creating ion-pairs, and inner-sphere nature intermediate complexes (Glebov et al. 2011). Absent free-radical intervention certain reactions of oxidation were carried out via outer-sphere mechanisms (Matyjaszewski 1998).

Considering the above discrepancies between the kinetic outcome and those for other polysaccharides oxidized by this oxidant, all reactants with a more aggressive permanganic acid (HMnO4) and alkoxinium ion (BTBH+) are protonated in the most possible reaction pathway that may be proposed to oxidize BTB by permanganate ion [H+], [substrate], and ionic strength depending on the reaction specimen indicate that the most suitable reaction mechanism for oxidation triggered by both [BTB] and MnO4−.

$${\text{BTB}} + {\text{H}}^{ + } \overset {K_{1} } \rightleftharpoons {\text{BTBH}}^{ + }$$
(2)
$${\text{MnO}}_{4}^{ - } + {\text{H}}^{ + } \overset {K_{2} } \rightleftharpoons {\text{HMnO}}_{4}$$
(3)

The \(\left[ {\text{BTBH}} \right]^{ + }\) a substrate, with proton release before the speed determinant stage, was followed by an HMnO4 attack at the centre of a 1:1 intermediate complex (C1).

$${\text{HMnO}}_{4} + {\text{BTBH}}^{ + } \overset {K_{3} } \rightleftharpoons {\text{C}}_{1} + {\text{H}}^{ + } .$$
(4)

Instead, in a rate-determining stage, the slow decomposition of the formed intermediate complex to give radical (C1.) substrate and reduced (Red) shape (as MnIII/MnIV) of the permanganate ion, throughout the slow stage first oxidation products as follows.

$$C_{1} \mathop{\longrightarrow}\limits{\text{k}}C_{1}^{.} + {\text{Red}} .$$
(5)

Under pseudo first-order conditions used, the change of the rate constants with changing the [H+] and [BTB] and rearrangement, the following relationship is obtained,

$$\frac{{\left[ {\text{BTB}} \right]}}{{k_{\text{obs}} }} = \frac{1}{{k_{n} }} = \left( {\frac{{[{\text{H}}^{ + } ]^{ - 1} }}{{k^{\prime}}} + \frac{1}{{k^{\prime\prime}}}} \right)$$
(6)

where \(k _{n}\) is the second-order rate constant, k` \(= kK_{1} K_{2} K_{3}\) and \(k^{\prime\prime} = kK_{2} K_{3}\), respectively. In compliance with Eq. (6) \(\left[ {\text{BTB}} \right]/k_{\text{Obs}}\) versus [H+]−1 has given good straight lines with a positive intercept on [BTB]/kobs axes, as shown in Fig. 5; the values of the apparent rate constants k′, k″ and the protonation constant \(K_{1}\) can be determined on their slopes and intercepts. These values were determined to utilize the least square method and found at 20, 30, 40 and 50 °C, respectively, to be 0.91, 0.79, 0.57 and 0.55. It was observed that, the measured values of the protonation constants (\(K_{1}\)) are in strong agreement.

Fig. 5
figure 5

Plots of [BTB]/kobs vs 1/[H+] in the oxidation of bromothymol blue by permanganate ion in aqueous perchlorate solutions. [MnO4−] = 4.0 × 10−4, [BTB] = 1.0 × 10−3, I = 1.0 mol dm−3 at various temperatures

Full size image

The negative entropies of activation (∆S≠) values in Table 1 show the density of the intermediates rather than the reactants. Again, the values of positive for \(\Delta G^{ \ne }\) indicated that the intermediate complexes produced were non-spontaneity as suggested by the proposed mechanism. As shown by the ionic strength dependency of the rate constant, the strong reaction propensity between the neutral molecule and the positive ion will support the low energy activation value of E≠ (Table 1) observed in this step. It implies that the reactants need little energy to interact and create the intermediate states of the complexes developed.

Table 1 The constant of protonation (K1) and the values of the apparent rate constants (k` and k”) in the oxidation of [BTB] by \(\left[ {{\text{MnO}}_{4}^{ - } } \right]\) in aqueous HClO4 solutions
Full size table

However, the entropy of activation has been previously reported (Hassan 1992, 2011) as being more negative for inner reactions, with reactions with negative values of the ∆S≠ being conducted through an inner-sphere of one- and two-electron transfer mechanism. Considering the values found for the entropy of activities (Table 1), it is better to use permanganate ion to oxidize BTB by means of two-electron shifts within the sphere rather than by the outside-sphere method. It should be remembered in this context that the mechanism of outer-sphere two-electron transition does not seem to be experimentally confirmed.

The disturbance of the alteration in spectra (Fig. 1) can suggest that the original quick portion of the reaction to oxidation is not the true phase of electron transfer. Therefore, the quick development of an intermediate between the reactants can be due to the first strong portion of the oxidation. Once again, several trials were conducted to detect the formation of intermediate hypomanganate (V) as transient species. Unfortunately, all attempts were unsuccessful. Under our experimental conditions of lower concentrations of reactants or the rapid reaction between the formulated Mn(V) and Cr, this failure may be due to the lower absorptivity of formed Mn(V). Equation 5 defining the final products for oxidation. In view of the above-mentioned kinetic definitions and study results, as outlined in Scheme 1, a tentative reaction process can be proposed for oxidation of bromothymol blue by acidic permanganate.

Scheme 1
scheme 1

Mechanism of oxidation of bromothymol blue by permanganate ion in aqueous perchlorate solutions

Full size image

Energy gap

From Fig. 1, Spectral changes of wavelength 200 nm < λ < 900 nm in the oxidation of [BTB] by permanganate ion in aqueous HClO4 during the reaction progression to obtained [BTB]Keto. The optical transitions occur by direct transitions in semiconductor materials (Cong et al. 2020). At incident photons energy (hυ), the \(\left( {\alpha h\upsilon } \right)^{m} = B\left( {h\upsilon - E_{\text{g}} } \right)\) the equation may be used to obtain optical band gap \(\left( {E_{\text{g}}^{\text{Opt}} } \right)\) and transition bandgap (\(E_{\text{g}}^{\text{trans}}\)) values according to Tauc’s equation from the optical transition spectrum, where m = 2 for direct transitions allowed spectrum, respectively. They allow direct transitions of [BTB] and [BTB]Keto are shown in Fig. 6. Extrapolating the right part of the plot (αhν)2 to the energy axis at α = 0 in addition to (hν) obtains the optical gap values. Figure 6 displays the (αhν)2 × 1012 (eVm−1)2 versus hν (eV) (Al-Hossainy et al. 2017; Rammah et al. 2019). The meaning \(\left( {E_{\text{g}}^{\text{Opt}} } \right)\) is described as the lower part of the energy, or a pair of bound electron–hole generators assigned to Frankel’s exciton. The meaning \(\left( {E_{\text{g}}^{\text{Opt}} } \right)\) applies to the disparity between LUMO and HOMO in the energy value (Awad et al. 2004).

Fig. 6
figure 6

Experimental plot of (αhν)2 versus photon energy (hν) for [BTB] and [BTB]Keto. Inset this figure HOMO and LUMO for the [BTB] and [BTB]Keto using DFT/CASTEP program

Full size image

Application of Tauc’s equation, the results clearly display that the values of the optical energy bandgap \(\left( {E_{\text{g}}^{\text{Opt}} } \right)\) direct transition decreases from 2.849 eV for [BTB] to 2.35 eV for [BTB]Keto. The various between the \(\left( {E_{\text{g}}^{\text{Opt}} } \right)\) of [BTB] to [BTB]Keto thin film is 0.499 eV. This indicates that [BTB]Keto (result from oxidation process) integrates the energy levels into the bandgap, which reduces the energy gap value. In DFTs simulation section by utilizing DMol3, the \(\left( {E_{\text{g}}^{\text{Opt}} } \right)\) values for [BTB] and [BTB]Keto are 3.047 eV and 2.869 eV, respectively (Nayeri et al. 2014; Al-Hossainy et al. 2019b). It can also be noted that the HOMO and LUMO simulation is shown in inset Fig. 6 indicates the average similarity of the energy gap values calculated by Tauc’s equation with a small difference in values.

Molecular electrostatic potential (MEP) and potential (P)

[BTB] and [BTB]Keto chemical and physical comparisons were tested using the electron density and the electrostatic potential. For the [BTB] and [BTB]Keto, the electron density is often discussed as the essential factor in determining the ground state of a significant number of electron systems. Based on the constant electron density, the MEP defines electrostatic potential. A 3D diagram reveals the active position of the MEP in Fig. 7a, c respectively for [BTB] and [BTB]Keto. The color blue is the appropriate zone for nuclear attacks, whereas the appropriate zone for electrophilic attacks is a color red. In the isolated molecule and crystal models the range molecular electrostatic potential of [BTB] and [BTB]Keto is − 5.929 × 10−2 ≥ [MEP] ≥ 5.929 × 10−2, and in the order of increase is − 6.838 ≥ [MEP] ≥ 6.838 in volume, respectively: red < brown < blue (Cruz et al. 2019; Kumar et al. 1996). The largest attraction is the blue color, while the red color one seems to have a strong repudiation. The MEP graph indicates (Abdel-Aziz et al. 2018) that electron-negative nitrogen atoms represent negative potential regions and that positive potential is present in the hydrogen atoms (Al-Hossainy et al. 2019c). The potential possible diagrams (Fig. 7b, d), the potential growth of [BTB] is shown to be lower than that of [BTB]Keto. This shows the electron transfer probabilities (Hassan et al. 2009c; Li et al. 2020; Al-Hossainy et al. 2019d) in [BTB]Keto are increased.

Fig. 7
figure 7

a MEP of [BTB]; b potential of [BTB]; c MEP of [BTB]Keto and d potential of [BTB]Keto by use the material studio and Gaussian program calculation DFT

Full size image

Conclusions

The significant structural characteristics, optical dispersion and dielectric properties of [BTB] and [BTB]Keto are determined using FTIR technique and compared with DFT calculations. The simulated FTIR (Gaussian DFT) of [BTB] and [BTB]Keto in isolated and gas state are in great agreement for the same compounds obtained from experimental analyses. The kinetics and oxidation processes of BTB in acid perchlorate solutions with a constant ionic strength of 1.0 mol dm−3 as sulfonphthaleine dyes by permanganate ion oxidizer have been analyzed spectrophotometrically. The experimental results of the pseudo-first-order plots revealed that oxidation displays a single pathway reaction; \({\text{MnO}}_{4}^{ - }\) first-order, [BTB] fractional-first order and hydrogen ion concentration fractional-first order. Dependence on acidity in reaction levels suggested acid-catalyzed reaction. The addition of MnII to the reaction mixtures confirmed the absence of either MnIII and/or MnIV transient species as involvement species in the oxidation phase. Formation of 1:1 intermediate complex prior to the rate-determining step was revealed, kinetically. A tentative method of the reaction was introduced and discussed with respect to the kinetic observations and measured kinetic parameters. The \(E_{\text{g}}^{\text{Opt}}\) values achieved from Tauc’s equation are 2.849 eV and 2.35 eV for [BTB] and [BTB]Keto respectively. While the \(E_{\text{g}}^{\text{Opt}}\) computed by DFT (DMol3) are 3.047 eV and 2.869 eV for [BTB] and [BTB]Keto as—isolated and gas state, respectively. There is a good agreement between \(E_{\text{g}}^{\text{Opt}}\) values determined by the DFT (DMol3) computations and the Tauc’s equation calculations. Based on the \(E_{\text{g}}^{\text{Opt}}\) values and DFT calculation (\(E_{\text{HOMO}} - E_{\text{LUMO}}\)) of [BTB] and [BTB]Keto can be used as an application to textile industrial wastewater treatment.