Quantum chemistry calculation and experimental research on the component proportion of black disperse dye

Abstract

Black is a special color that has achromatic characteristics and shows a sought-after sense of mystery. Most of the black disperse dyes are compounded with multiple dyes. In this paper, a quantum chemical calculation method based on density functional theory and time-dependent density functional theory was proposed to predict the components’ proportion of black disperse dye. C.I. disperse blue 291, C.I. disperse red 73, and C.I. disperse orange 61 were selected as components of this black dye. After structure optimization and vertical excitation calculation of many other disperse dyes, and experimental tests of the maximum absorption wavelength of ultraviolet-visible, an equation between the calculated values and the experimental values was obtained by multiple regression analysis. This equation was used to correct the calculated spectrum of each target component. Then the combined spectrum of the three dyes was used to establish the prediction equation set, and the mixing proportion was calculated from this. Through verification of dyeing experiments and related tests, the new method in this study has a good result on the components’ proportion prediction of black disperse dye.

Keywords

Proportion prediction black disperse dye density functional theory/time-dependent density functional theory calculation combined spectrum excited states

Dyestuffs are essential in the textile industry. In industrial production, one purpose of adjusting the printing and dyeing process is to obtain the colors wanted by customers. The reproduction and prediction of dye formulations are effective means to reduce color errors. At present, computer color matching based on the Kubelka–Munk theory,^1,2 which has been widely used in production, usually requires complex work such as making standard dye solutions with different concentrations and multiple corrections. With the development of science and technology, for the color reproduction, formula prediction, or other related issues of dyes, experts have successively studied the application based on new technologies, including support vector machine,^3,4 neural network algorithm,^5,6 ant colony algorithm,⁷ genetic algorithm,^8,9 data mining combined with modular architecture design,¹⁰ as shown in Table 1. These efforts provide an important reference for the deeper development of the global printing and dyeing industry.

Table 1.

Methods about related issues of dyes in recent years

Method	Application	Advantage	Disadvantage	Reference
Particle swarm optimization algorithm of least squares support vector machine	Dye recipe prediction models of reactive dyes on cotton fabrics	Having a small color difference	1. Calibrations between dye concentrations and colorimetric information must be performed2. Models do not apply to other dyes	4
Artificial neural network algorithm	Prediction of cotton fabrics’ shade changes after finishing	Having a high accuracy prediction of shade change	Calibrations among dye concentrations, finish concentrations and colorimetric information must be performed	5
Ant colony algorithm	Color recipe prediction of reactive dyes on cotton fabrics	Minimizing the CMC color difference	Calibrations between dye concentrations and colorimetric information must be performed	7
Genetic algorithm	Color recipe prediction of reactive and direct dyestuffs mixtures	Minimizing the CMC color difference		8
Data mining combined with modular architecture design	Dyeing recipe recommendation of reactive dyes on rayon fabrics	1. Calibrations between dye concentrations and colorimetric information are not needed2. The system can be easily extended for different types of fabric and dyes	Relying on historical dyeing data	10

CMC: colour measurement committee.

In recent decades, also benefiting from modern technology, quantum chemical calculations, especially those based on density functional theory (DFT), have been used increasingly in the research of various materials including dyes. Both color and properties depend on the structure of dyes. So, it has become a trend to apply the powerful DFT method to explore many aspects of dyes, such as dye synthesis and dye optical properties.^11,12 At the same time, keeping an excellent balance between accuracy and efficiency, the time-dependent (TD)-DFT method has become the most common means for investigating the optical properties of organic molecules.¹³ From the research of Jacquemin and his team,¹⁴ we know that after multivariate fitting the results calculated by PBE0 and B3LYP functional, the dye’s estimated value of the maximum absorption wavelength (λ_max) was more accurate, although the vertical excitation calculation results obtained by using B3LYP and PBE0 functional alone are usually relatively precise and reasonable.¹⁵ B3LYP functional with 20% HF exchange and PBE0 functional with 25% HF exchange are both global hybrid functionals.¹⁶ The proportion of HF in this kind is constant in the global, that is, the proportion of HF exchange remains unchanged when the distance between two electrons is arbitrary. Moreover, another commonly used method is the range-separated hybrid functionals,¹⁶ such as CAM-B3LYP. This kind has segmented control of precise HF exchanges between long range and short range, and the proportion of exchanges increases with the increase of the distance between electrons. A statement has been pointed out that the long-range corrected functional CAM-B3LYP, the frequently used one in the study of dyes’ transition,¹⁷ was the most suitable for simulating disperse dyes molecules.¹⁸ In addition to the choice of functional, the influence of solvent on solutes’ spectra needs to be considered in the calculation. A general approach is to combine the TD-DFT method with a solvation model.¹⁹ The most used one among them is the polarizable continuum model (PCM), which regards the environment as a polarizable continuous medium and estimates its effects with limited computational resources and costs.²⁰

Against this background, the purpose of this paper was to try to use a quantum chemical calculation method based on DFT/TD-DFT to predict the components’ proportion of black disperse dye. Most commercial black disperse dyes are a mixture of various dye components in proportion. The study of Kato et al. showed the number of disperse dyes detected in black polyester products ranged from two to eight, with an average of about five.²¹ We selected C.I. disperse blue 291, C.I. disperse orange 61, and C.I. disperse red 73 from the dye varieties detected in the research of Kato et al. as the target components of black disperse dye for the proportional prediction experiment. Their chemical structures are shown in Figure 1. With limited computational resources, we used B3LYP, PBE0, and CAM-B3LYP functional to calculate the dyes’ vertical excitation to increase the applicability of the disperse dye system in this paper. And N, N-dimethylformamide (DMF) was used as a solvent in both experiments and calculations.

Figure 1.

Chemical structures of the three target components.

Experiments and calculations

Dyes and materials

The dyes and other materials used in this experiment are listed in Table 2 and Table 3.

Table 2.

Experimental dyes

Dyes	Strength	Manufacturer	Dyes	Strength	Manufacturer
C.I. disperse red 167 (DR167)	100%	Shaoxing County Fine Chemical Co. Ltd., China	C.I. disperse red 60 (DR60)	200%	Zhejiang Changzheng Chemical Co. Ltd., China
Disperse black HPS (DBK-HPS)	200%	Wuxi Jiatai Textile Raw Material Co. Ltd., China	C.I. disperse blue 56 (DB56)	100%	Zhejiang Jihua Group Co. Ltd., China
C.I. disperse violet 26 (DV26)	100%	Changshu Jinyushan Dyestuff Co. Ltd., China	C.I. disperse blue 79 (DB79)	200%	Zhejiang Runtu Co. Ltd., China
C.I. disperse red 73 (DR73)	200%	Hangzhou Flariant Co. Ltd., China	C.I. disperse orange 73 (DO73)	200%
C.I. disperse blue 291 (DB291)	300%		C.I. disperse orange 30 (DO30)	100%
C.I. disperse orange 31 (DO31)	300%		C.I. disperse orange 44 (DO44)	200%
C.I. disperse yellow 42 (DY42)	100%		C.I. disperse orange 61 (DO61)	200%
C.I. disperse yellow 211 (DY211)	200%		C.I. disperse blue 60 (DB60)	200%
C.I. disperse blue 183 (DB183)	200%	Zhejiang Lonsen Dyestuff Chemical Co. Ltd., China	C.I. disperse yellow 23 (DY23)	100%
C.I. disperse blue 291-1 (DB291-1)	300%	Zhejiang Lonsen Dyestuff Chemical Co. Ltd., China	C.I. disperse yellow 114 (DY114)	200%

Table 3.

Experimental materials

Material	Type	Manufacturer	Material	Type	Manufacturer
N, N-dimethylformamide (DMF)	Analytical pure	Xilong Science Co. Ltd., China	Toluene	Analytical pure	Hangzhou Chemical Reagent Co. Ltd., China
Sodium hydroxide		Xilong Science Co. Ltd., China	Acetone		Hangzhou Chemical Reagent Co. Ltd., China
Acetic acid		Jiangsu Qiangsheng Functional Chemical Co. Ltd., China	Sodium dithionite		Jiangsu Yonghua Chemical Technology Co. Ltd., China
Thin-layer chromatography (TLC) silica gel 60 f254 aluminum sheets	20 × 20 cm	Germany Merck KGaA Group	Lignin dispersant DS10	Industrial grade	Sweden Domsjö Fabriker AB Company
Woven polyester fabric	128 g/m²	Zhejiang RGB Textile Printing and Dyeing Co. Ltd., China	Dispersant MF	Industrial grade	Hangzhou Flariant Co. Ltd., China

Dye purification and ultraviolet-visible absorption experiment

Dyes were purified by the DMF recrystallization method and the thin-layer chromatography (TLC) method.²² We dissolved commercial dyes in DMF at a 1:4 ratio of dye mass to DMF volume, heated and stirred it for 0.5 h, then poured it into a beaker filled with distilled water and stirred it evenly. The volume ratio of distilled water and DMF was 2:1. After 4 h of standing, the solution was completely cooled and dye crystals were precipitated, the steps of suction filtration, cleaning and drying were carried out.

For dyes that were not targeted components, after being purified by the DMF recrystallization, a few of them were dissolved in DMF and developed on a thin-layer chromatography silica gel aluminum sheet with a mixture of toluene and acetone as a developing agent. The volume ratio of toluene and acetone was 5:3. After the parts of the dye were separated on the sheet, the main part, the darkest part with the largest spot area, was cut out and re-dissolved in DMF to obtain a purer dye solution. Then the dye solution’s ultraviolet-visible (UV-vis) absorption spectrum was measured with a UV2450 UV-vis spectrophotometer (Shimadzu Co. Ltd., Japan) to confirm the maximum absorption position and spectral shape. For the solution’s dilution, it was necessary to ensure the maximum absorbance value was in the range of 0.2–0.8.

Structure optimization and excited-state calculation

A preliminary conformation search was performed on the dyes, and their conformations with relative energy within 3 kcal/mol or 5 kcal/mol were selected for structure optimization according to our calculation condition and the number of conformations. The structure optimization calculation adopted the B3LYP-D3(BJ)/6-31G* level with the PCM solvent model (DMF solvent).^23–31 Then the Boltzmann distribution proportion of conformations was calculated, and conformations with a proportion of at least 5% were selected for excited-state calculation. The TD-DFT method was used to calculate the six lowest excited states of dyes, and the functionals combined with D3(BJ) dispersion correction were B3LYP, PBE0, and CAM-B3LYP. The basis set was TZVP,^32,33 and the solvent model was also PCM (DMF solvent). According to the Boltzmann distribution proportions of the conformations and their corresponding excited-state data, the conformational weighted spectrum of the dye was drawn, and then the simulation value of λ_max was obtained by this spectrum. The full width at half maximum (FWHM) was set as 0.45 eV. Used in the calculation, software programs included Gaussian 16 C01,³⁴ Molclus 1.9.9.1,³⁵ Orca 4.2.1,³⁶ Crest 2.10.2,³⁷ Xtb 6.3.3,³⁸ Shermo 2.0.5,³⁹ OpenBabel 2.4.1,⁴⁰ and Multiwfn 3.7.⁴¹

Proportion prediction

The λ_max values of dyes, obtained by measurement and each functional calculation, were analyzed by multiple regression. Then the equation among these four was used for spectral data correction of three target dye components. A combined spectrum of these three dyes was plotted by using the corrected data. A system of equations was built according to this spectrum, the absorbance additivity of dyes, and the corresponding restrictive conditions, making the absorbance value at the maximum absorption position of each dye consistent. The solutions of this group’s equations were the proportions of three dyes’ molar concentrations.

Dyeing

Comparison

After unit conversion, the obtained molar ratios were used in dyeing experiments, and the dyeing experiments in this paper both used the method of high temperature and high pressure. Each component dye was purified by the DMF recrystallization mentioned above and re-ground to make a single-color dyeing mother liquor with a certain concentration. The mass ratio of dye and dispersant was 1:1, and the dispersant was a mixture of DS10 and MF at a mass ratio of 1:1. The concentrations of the mixed pure dyes were set to 1% and 2% on weight of fabric (owf). According to these concentrations and the different proportions of the three dyes, the corresponding dyeing mother liquor was transferred and mixed for dyeing experiments. The dye concentrations of the commercial dye DBK-HPS were set to 1%, 2%, 3%, and 4% (owf), assuming the additives’ content was 50%. The polyester cloth was 1 g/piece, and the cloth to dye liquor ratio was 1:50. After reduction cleaning of dyed polyester cloth, chromatic parameters were measured by Datacolor 600 spectrophotometers (Datacolor Co., USA) using artificial daylight 6500 K at 10° observer. Four different positions of each dyed sample were selected for testing and the mean value was taken.

Dyeing build-up performance and colorfastness

A set of predicted proportions were selected as examples to test for build-up performance and colorfastness. The mixed pure dyes’ concentration gradients in the build-up performance experiment were 0.5%, 1%, 1.5%, 2.5%, 3.5% and 4.5% (owf). Other operations of dyeing are referred to in the Comparison section. Dyed cloth with a pure dye concentration of 2% (owf) was tested for its colorfastness of rubbing, soaping, and sunlight, according to relevant standards.^42–44 All dyed cloths were measured after reduction cleaning.

Results and discussions

Experiment and calculation of dyes’ λ_max

Before calculating vertical excitation, conformation searches were performed on dyes in this experiment, and the weighted spectrum of conformations with a proportion of at least 5% was drawn to obtain the λ_max in Table 4. The purpose of the conformation search is to find a batch of relative stable molecular conformations,³⁵ and then the proportions of different conformations can be calculated after structure optimization of this batch.³⁹ Generally speaking, molecules with rotatable bonds usually have several or many conformations, and the conformation with lower energy is more stable. In actual situations, the different conformations of molecules exist in different proportions in a solvent. Surely, different conformations have different spectra. In the example of Figure 2, it could be seen from the molecular structure that DV26 had tiny flexibility and rotatable bonds. After conformation search and structure optimization, two stable conformations accounting for a large proportion were found, and the weighted average spectrum of DV26 was quite like the spectrum with a conformation proportion of nine-tenths.

Table 4.

Maximum absorption wavelength of dyes

Method		Dyes
Method		DB183	DB60	DB291-1	DB79	DB56	DY23	DY42	DY114
λ_exp (nm)		592	672	598	583	621	389	419	417
λ_cal (nm)	B3LYP	566.5	673.4	607.7	622.2	565.1	462.6	450.2	394.9
	PBE0	548.6	654.6	587.9	591.0	548.5	444.4	426.8	383.3
	CAM-B3LYP	519.4	600.5	544.1	512.7	496.4	399.7	379.1	354.9
		DY211	DV26	DR167	DR60	DO73	DO30	DO44	DO31
λ_exp (nm)		436	549	521	520	466	423	425	438
λ_cal (nm)	B3LYP	427.7	534.2	533.0	487.9	533.3	537.1	532.5	528.0
	PBE0	399.7	520.7	509.2	473.6	504.0	502.2	505.0	499.6
	CAM-B3LYP	351.2	480.3	457.9	430.4	428.9	399.1	439.6	431.9

Figure 2.

Experimental and calculated spectra of anthraquinone dye DV26 (B3LYP/TZVP).

Besides, the dyes collected in this experiment mostly belong to azo and anthraquinone. For anthraquinone dyes, their experimental spectrum had multiple absorption peaks in the UV-vis region, as shown in Figure 2. Ordinary vertical excitation energy calculations cannot provide this shape information, but it does not hinder getting the λ_max value of the main absorption peak.¹⁵ For azo dyes, the shape of calculated and experimental absorption spectra could match well.

Table 4 lists the experimental and calculated values of dyes’ λ_max, and Figure 3 corresponds to the data in Table 4.

Figure 3.

Maximum absorption wavelength of dyes.

It could be seen from Table 4 and Figure 3, for the disperse dyes used in this experiment, λ_max of orange dyes calculated by CAM-B3LYP functional were closer to experimental values, while PBE0 and B3LYP functional were suitable for excited-state calculation of other color dyes. We chose DO31 and DR167 as examples. Their experimental values were closer to the calculated values of CAM-B3LYP and PBE0, respectively. In the conformation with the largest proportion of Boltzmann distribution, a transition with maximum oscillator strength was selected to conduct hole-electron analysis to investigate its electron excitation characteristics.⁴⁵ For the selection of this transition, a result could be seen from Figure 4, DR167 and DO31 should choose the transition from the ground state to the first excited state (S0 → S1) and the transition from the ground state to the second excited state (S0 → S2), respectively. In addition, we knew from this figure the total spectra of DR167 calculated by PBE0 functional and DO31 calculated by CAM-B3LYP functional, respectively, coincided with the spectrum of corresponding excited states, indicating the dye spectrum was near 100% contributed by this transition.

Figure 4.

Main conformation’s calculated ultraviolet-visible (UV-vis) absorption spectra of DR167 and DO31 and transitions with oscillator strength greater than 0.1 (left PBE0, right CAM-B3LYP).

Characteristic data for the hole-electron spatial distribution of DR167 and DO31 are listed in Table 5. The corresponding distribution graph and the Chole–Cele graph with a highly smoothed description of this distribution are shown in Figure 5, where blue and green, respectively, represent holes and electrons. The D indices of the two dyes calculated by PBE0 were both large, indicating that there were long charge transfer distances. Therefore, the excitation type of the two should belong to charge transfer (CT) excitation. However, this result was questionable. In the TD-DFT calculation of excited states, PBE0 and B3LYP are suitable for molecules with local excitation (LE) and singlet excited state, while CAM-B3LYP is more suitable for molecules with CT.^46,47 We analyzed the calculation results of CAM-B3LYP functional which can describe CT well. For DR167, the D value calculated by CAM-B3LYP was a little small, about 1.9, indicating a little CT characteristic. At the same time, it could also be seen from Figure 5(b) that although the dye carried some CT features when excited, it still mainly showed signs of LE. Moreover, its t index was very small, which meant there was no significant separation between holes and distribution. This also proved that the first excited state of DR167 was characterized by LE mainly. For DO31, the D index calculated by CAM-B3LYP was larger, showing the second excited state belongs to CT. From the relevant hole-electron graph, there was an obvious charge transfer tendency during excitation, and the electrons flowed from the azo group’s right side to the left side. These also determined that S0 → S2 of DO31 had more CT features.

Table 5.

Hole-electron spatial distribution data of DR167 and DO31

Dyes	Functional	Index
Dyes	Functional	D (Å)	Sr (a.u.)	H (Å)	T (Å)
DR167(S0 → S1)	PBE0	4.033	0.647	4.027	0.255
DR167(S0 → S1)	CAM-B3LYP	1.917	0.727	3.783	−1.590
DO31(S0 → S2)	PBE0	3.309	0.646	3.583	−0.044
DO31(S0 → S2)	CAM-B3LYP	2.797	0.702	3.694	−0.671

Figure 5.

Hole-electron distribution graph (left) and Chole–Cele graph (right) of DR167 and DO31.

According to the above analysis, here is a suggestion for reference. When we need to perform excited-state studies on an unfamiliar dye with a known structure, the range separation functional (CAM-B3LYP, ωB97XD, M06-2X, etc.) and the traditional low HF functional (PBE0, B3LYP, etc.) could be selected to calculate the excited states separately if there are sufficient computational resources. Then use the Multiwfn software to do the corresponding hole-electron analysis and comparison to investigate the electronic excitation characteristics. After finding out the dye’s electronic excitation type, select the appropriate functional to do the follow-up work. The functionals used to calculate have a lot, and some of them need to be learned before starting a calculation.

Prediction of components proportion

Relationship model between experimental and calculated values

Except for DB291, DR73, and DO61, other dyes’ data in Table 3 were all used for multiple regression analysis, and the fitting equation, equation (1), was obtained as a predictive model of the dye’s λ_max:

λ_{\exp} = \sin ({(λ_{b 3 l y p} + 0.5388)}^{0.6863}) \times ({λ_{b 3 l y p}}^{0.5467}) - (1.1878 \times (λ_{b 3 l y p} - λ_{cam} - λ_{pbe 0}))

(1)

where λ_exp, λ_cam, λ_b3lyp, λ_pbe0 represents the λ_max of the experimental value, and that of the calculated value under CAM-B3LYP, B3LYP, and PBE0 functional, respectively. The determination coefficient R² of the equation was 0.93, and the mean absolute error was 19.4 nm, signaling a good fitting degree. This regression equation is for a single disperse dye, and its wider applicability needs more follow-up work on dyes’ data calculation and collection.

This equation was used to calculate the predicted experimental value (λ_p-exp) of three dye components’ λ_max, and the results are shown in Table 6. From these data comparisons, the predicted values of DB291, DO61, and DR73 were, respectively, closest to the calculated values of B3LYP, CAM-B3LYP, and PBE0. Conformational weighted spectrum data of individual dyes corresponding to the calculation of their optimal functional were exported and corrected by spectral shift, and this shift was a difference between the λ_cal value of optimal functional and the corresponding λ_p-exp value. Through that method, a similarity between the calculated spectrum and the experimental spectrum of the dye’s UV-vis absorption was improved.

Table 6.

The target dyes’ prediction results of λ_max

Method	Dyes
Method	DB291	DO61	DR73
λcal
B3LYP	609.3	547.9	546.6
PBE0	584.2	511.5	521.9
CAM-B3LYP	529.1	410.7	464.8
λp-exp	594.7	457.9	532.4

For black disperse dyes, the main coverage wavelength range and absorbance of its absorption spectrum are important. Its spectrum is a combination of each dye component’s spectrum, and the spectrum of different dyes will be weighted and superimposed according to the proportions of dye components. After the spectra of different shapes are superimposed, the spectral band characteristics of the spectrum will be weakened due to the coverage and superposition of the spectrum. At this time, the spectral peak of each compound dye can be used as a prominent feature to obtain relevant information. For the excited state calculations of vertical absorption, the resulting dyes’ UV-vis absorption spectra already have an acceptable and fairly good simulation. The TD-DFT method can also calculate the vibrationally resolved electronic spectrum with fine spectral bands,⁴⁸ but it takes more time and requires more computational resources, so we chose the former calculation method according to limited conditions. There are two important data at the spectral peak, absorption wavelength and absorption coefficient. In this paper, we made a model to predict the maximum absorption wavelength of a single dye, which was used to adjust the position of the calculated spectrum of component dyes on the horizontal axis to reduce the calculation error, and the correction of the calculated spectrum on the vertical axis needs to be further researched in the future.

Calculation of compound proportion

DB291, DR73, and DO61 (B-R-O) were used as black disperse dye components in this experiment. As shown in Figure 6, we drew a combined spectrum with the corrected spectral data of dye components. Obviously, this figure confirmed that after the correction steps in the previous section, the simulated spectrum of this compound black disperse dye was close to the measured one.

Figure 6.

Simulated and measured spectra of B-R-O at an equimolar ratio.

At a given wavelength, the absorbance of a multicomponent dilute solution is equal to the sum of each part’s absorbance. This is the well-known absorbance additivity based on Lambert Beer’s law. For example, the absorbance of a two-component dilute solution system at wavelengths of λ₁ and λ₂ conforms to equation (2), where A is absorbance, ε is the molar absorption coefficient, C is the molar concentration, and L is the optical path.

A (λ_{1}) = A_{1} (λ_{1}) + A_{2} (λ_{1}) = ε_{1} (λ_{1}) C_{1} L + ε_{2} (λ_{1}) C_{2} L

A (λ_{2}) = A_{1} (λ_{2}) + A_{2} (λ_{2}) = ε_{1} (λ_{2}) C_{1} L + ε_{2} (λ_{2}) C_{2} L

(2)

Therefore, according to this theory, calculation formulas suitable for the three-component black disperse dye solution of this paper can be obtained. At the same time, for black dye, its UV-vis absorption spectrum has a characteristic of wide absorption, with an absorption range of about 400 nm to 700 nm. In this experiment, we assumed an equal absorption of each dye at its spectrum peak in this range. In other words, the absorbance of these three components at their respective λ_max was equal. Besides, there was a restrictive condition that must be stated. As could be seen from Figure 6, due to the characteristic of absorbance additivity, the dye concentration of DR73, whose absorption position was in the middle of the combined spectrum, should be less than that of other dyes to avoid its excessive UV-vis absorption during compounding. Equations (3) and (4) were built according to these analyses. Among them, the optical path L in this experiment was 1 cm not listed here:

A (λ_{B}) = A (λ_{R}) = A (λ_{O})

A (λ_{B}) = ε_{B} (λ_{B}) C_{B} + ε_{R} (λ_{B}) C_{R} + ε_{O} (λ_{B}) C_{O}

A (λ_{R}) = ε_{B} (λ_{R}) C_{B} + ε_{R} (λ_{R}) C_{R} + ε_{O} (λ_{R}) C_{O}

A (λ_{O}) = ε_{B} (λ_{O}) C_{B} + ε_{R} (λ_{O}) C_{R} + ε_{O} (λ_{O}) C_{O}

C_{B} + C_{R} + C_{O} = 1

(3)

C_{R} < C_{B}

C_{R} < C_{O}

(4)

After exporting and processing the corrected spectral data of each dye component, some data needed by the above equations were selected to substitute into and sort out. Solutions of these equations were the prediction results of B-R-O proportions, which could be compounded as black disperse dye. The seven equation solutions, whose approximate solutions had been merged, are listed in Table 7. That is, these were the seven predicted mixed molar proportions of three dye components.

Table 7.

Predicted molar proportion of B-R-O

Component	Serial number of proportions
Component	1	2	3	4	5	6	7
DB291	0.4710	0.4075	0.4287	0.4327	0.4462	0.4654	0.4757
DR73	0.2145	0.2386	0.2062	0.2000	0.1794	0.2065	0.2213
DO61	0.3145	0.3539	0.3651	0.3673	0.3744	0.3281	0.3030

Dyeing

Comparison

After unit conversion, the seven predicted proportions were used for high-temperature and high-pressure dyeing of polyester cloths. Listed in Table 8 and Table 9 are the test results of different dyed cloths’ chromatic parameters. From the data in these two tables, the dyeing chromatic parameters L, a*, b*, C*, and h of different B-R-O proportions were close to those of DBK-HPS. In addition, these parameters of B-R-O dyeing with 1% and 2% concentration were near the parameter range of DBK-HPS dyeing with 1–2% and 3–4% dye concentration, respectively. This showed that all predicted compound proportions could be dyed black with good effects. The ideal black color is without brightness and chroma, and its theoretical chromatic parameters L, a*, b*, and C* are zero. Overall, according to the experimental data in Table 8, as the dye concentration increased from 1% to 2%, parameters with different B-R-O proportions changed as follows: the brightness value L decreased to varying degrees with a range of about 7; the red-green value a*, the yellow-blue value b*, and the chromatic value C* all approached zero or fluctuated around zero. These trends were consistent with those of DBK-HPS. In short, through these data, we knew the calculations and experiments in this paper were quite effective for the compound proportional prediction of black disperse dye’s components.

Table 8.

Chromaticity parameters of B-R-O dyeing with different dye concentrations and proportions

Serial number of proportions	Dye concentrations (owf) and chromaticity parameters
	1%					2%
	L	a*	b*	C*	h	L	a*	b*	C*	h
1	23.48	–0.04	–2.99	2.99	269.17	16.38	0.54	–1.61	1.70	288.48
2	23.65	1.36	–0.76	1.55	330.81	16.56	0.86	–0.81	1.18	316.77
3	23.88	0.33	–0.70	0.77	295.00	16.66	0.51	–0.79	0.93	302.73
4	24.07	0.08	–0.75	0.75	275.98	16.57	0.42	–0.78	0.89	298.23
5	24.05	–0.67	–0.53	0.85	218.00	16.81	0.23	–0.75	0.79	287.32
6	23.46	–0.23	–2.53	2.54	264.74	17.13	0.47	–1.31	1.39	289.78
7	23.14	0.18	–3.70	3.70	272.79	16.59	0.62	–1.73	1.84	289.71

Table 9.

Chromaticity parameters of DBK-HPS dyeing with different dye concentrations

Parameters	Dye concentrations (owf)
Parameters	1%	2%	3%	4%
L	25.30	18.89	16.97	16.13
a*	–1.71	–0.11	0.57	0.71
b*	–4.25	–2.71	–1.91	–1.56
C*	4.58	2.71	1.99	1.71
h	248.04	267.77	286.65	294.50

Disperse dyes are nonionic dyes with minimal water solubility and simple structure. They have a good affinity with hydrophobic fibers and diffuse into the molecular chain pores of these fibers in molecular form during dyeing. Due to their characteristics, disperse dyes have different adsorption and diffusion capacities on different types of fibers.^49,50 In this paper, only ordinary woven polyester fabric was selected for dyeing experiments with compound dyes, which had limitations in the diversity of dye-bearing fabrics. Thus the feasibility and applicability of this calculation and prediction method applied to other fibers need to be further explored in the future.

Build-up performance and colorfastness

A group of prediction proportions, no. 4 (0.4327-0.2000-0.3673), was selected for dyeing experiments of build-up performance and colorfastness. As could be seen from the result in Figure 7, when the B-R-O pure dye concentration was bigger than 2%, the color depths of dyeing were close and had a slowly rising trend. That was like the dyeing effect of commercial dye DBK-HPS. It could be said the visual appearances of dyed cloths with these two black dyes were close to the same.

Figure 7.

Build-up performance of black disperse dyes.

The three black dye components used in this experiment are mature dyes on the market. Their individual dyeing effects meet the relevant standards, and there should be no problem with their colorfastness when used as a combination. Of course, we still verified it through a colorfastness experiment. The test results of no. 4 proportions dyed with 2% pure dye concentration are listed in Table 10. These data showed that, including sunlight resistance, rubbing resistance, and soaping resistance, the colorfastness of compound black disperse dye obtained by predicting components’ proportions were all good and could meet the requirements of commercial applications.

Table 10.

Colorfastness of B-R-O

Sunlight (24 h)/level	Rubbing/level				Soaping/level
	Dry		Wet		Staining		Fading
	Fading	Staining	Fading	Staining	Cotton	PET	Fading
7–8	5	4–5	5	4–5	5	5	5

PET: polyester fabric.

Conclusion

With the help of dye DFT/TD-DFT calculations, we carried out a multiple regression analysis on the calculated and experimental values of dyes’ maximum absorption wavelength, and acquired a well-fitting equation. The calculated spectra of three dyes DB291, DO61, and DR73 were corrected by this equation, which was beneficial to the calculation of proportional prediction. Moreover, the system of equations got by dye absorbance additivity and other conditions could well predict the dyes’ proportions that met the requirements. This paper verified these results through dyeing experiments, including each proportion’s dyeing, sampling proportion’s build-up performance and colorfastness. The results of dyeing and comparison showed that our proposed proportion prediction of black disperse dyes’ components could achieve a dyeing effect as commercial dyes do. The advantage of using the DFT calculation method in this paper is that it can be simulated for the dyes’ compounding according to the calculated spectral data of the relevant dyes before purchasing the dyes, to achieve the purpose of buying dye materials in a planned and targeted manner and obtaining the required mixed dyes. From another view, this proportional prediction method of black disperse dye’s components based on the DFT/TD-DFT calculation has some reference value and development potential. Furthermore, future work needs to be carried out from the following points to increase the applicability of this calculation method. The first is to enrich dye varieties and add more dye data to improve the application performance of the prediction model. The second is to model and correct the molar absorption coefficient of dyes’ calculated spectra to reduce simulation errors. The third is to explore the feasibility of this method in other fibers’ dyeing.

Footnotes

Acknowledgements

The authors truly appreciate the equipment support provided by the Key Laboratory of Clean Dyeing and Finishing Technology of Zhejiang Province, China.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Yue Liu

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Quantum chemistry calculation and experimental research on the component proportion of black disperse dye

Abstract

Keywords

Experiments and calculations

Dyes and materials

Dye purification and ultraviolet-visible absorption experiment

Structure optimization and excited-state calculation

Proportion prediction

Dyeing

Comparison

Dyeing build-up performance and colorfastness

Results and discussions

Experiment and calculation of dyes’ λmax

Prediction of components proportion

Relationship model between experimental and calculated values

Calculation of compound proportion

Dyeing

Comparison

Build-up performance and colorfastness

Conclusion

Footnotes

Acknowledgements

Declaration of conflicting interests

Funding

ORCID iD

References

Experiment and calculation of dyes’ λ_max