Abstract
In a traditional water-based dyeing system, large amounts of salts and water are consumed. However, a non-aqueous media dyeing system achieves salt-free and less-water dyeing. In a non-aqueous media dyeing system, a small amount of water is used, which may affect the aggregation morphology of the dyes. The molecular dynamics of reactive dyes on the surface of cotton fibers were investigated. The results showed that the color depth of dyed cotton fabric did not change much when the dosage of salt was below 5.2% o.w.f. However, continuing to increase the amount of salt could influence the dyeing level of dyed fabric. The diffusion coefficient of dye was 0.3044 × 10−5 cm−2/s when there was no salt in dyeing system. But it was decreased by 14.03% and 16.62% when the salt concentration was increased from zero to 5.2% and 13% o.w.f., respectively. When the concentration of sodium sulfate was zero, the dye molecules in the solution displayed in the form of unimolecular molecules and dimers. However, reactive dyes mainly existed in the form of trimers and polymers when the concentration of sodium sulfate was above 5.2%. When there was no salt in the less-water dyeing system, the van der Waal energy between fiber and dye was 131.29 kJ/mol, but it was increased to 382.92 kJ/mol when the dosage of sodium sulfate was 5.2%. Therefore, with the increase of sodium sulfate dosage, the color depth of the dyed fabric changed little, but the level of dyeing property became poorer.
Cellulose fibers are usually dyed with reactive dyes because reactive dyes have the advantages of bright color, good color fastness, and convenient application.1–3 However, due to the presence of the sulphonate (SO32−) group in reactive dye molecular structure, 4 large amounts of water and chemicals are consumed during dyeing.5–6 Moreover, the fixation of reactive dye is poor in a water base, resulting in a requirement for a large amount of water to wash the loose color on the fiber surface.7–9 Therefore, reactive dyeing in a traditional water bath discharges a lot of wastewater and and consumes a high level of energy.10–13 The wastewater contains high amount of electrolytes and hydrolyzed dyes and causes serious ecological problems.14,15 Therefore, the focus of emission reduction in textile dyeing industry is wastewater treatment, and it is urgent to reduce or even eliminate wastewater discharge at the beginning of dyeing.
In the past 20 years, there has been considerable research and development of clean dyeing and processing technologies to save water, energy, and environmental protection.16–20 Taking supercritical carbon dioxide dyeing as an example,21,22 waterless dyeing of polyester fiber with disperse dyes is achieved in this dyeing system, but it is difficult to establish a universal mainstream dyeing method in the textile dyeing industry because this dyeing technology is not suitable for dyeing hydrophilic fibers (such as cotton, viscose, wool, silk, etc.), and it has some disadvantages such as high cost and operational risk (high pressure equipment). 23 Cationic modification technology of cotton fiber uses cationic chemicals to turn negatively charged cotton fibers into positively charged fibers, which is a method of realizing salt-free dyeing.1,24,25 However, cationic modification increases the fiber pretreatment process, and the pretreatment residue contains a certain amount of cationic chemicals, which increases the difficulty of water treatment.26,27 Moreover, the fixation of dye is still low (50–70%), and it still needs more washing times after dyeing.28,29 Therefore, it can be seen that the existing so-called ‘ecological dyeing’ cannot be employed in textile dyeing industry due to being contrary to human health and environmental protection.
Based on the analysis of the development of the textile dyeing industry, a non-aqueous medium (for example liquid paraffin, siloxane, vegetable oil, etc.) dyeing technology, as an environment-friendly dyeing method instead of water base dyeing,30,31 has achieved salt-free, dyeing of hydrophilic fibers such as cotton fibers without discharging wastewater. 32 The main reason for salt-free dyeing is that reactive dyes have no interaction with the dyeing medium, but have good affinity with cotton fibers. After dyeing, the non-aqueous medium can easily be washed off from the dyed fabric. Since the dyeing medium is insoluble in water, it is conducive to the reuse of water resources. Due to the incompatibility between non-aqueous media and water, the dyeing medium and water can be naturally separated after 2–3 h. The wastewater in the lower layer may contain a small amount of non-aqueous medium. After the oil-water separation membrane treatment, the producing water does not contain silicone oil medium. 8 Moreover, the results of X-ray energy dispersive analysis show that the content of non-aqueous in the dyed cotton fiber is zero, indicating that there is no silicone residue on the dyed cotton fiber.
However, non-aqueous medium/less-water dyeing system contains only a small amount of water, and there is a strong repulsive force between water and the non-aqueous medium, which would influence the level dyeing property. Previous studies have suggested that the dye adsorption rate is too fast, resulting in a poor level of dyeing property. 25 However, in these investigations, only some traditional adsorption models were employed to describe the adsorption of reactive dyes to cotton fibers, and the mechanism of dyeing leveling difference for reactive dyes was not systematically studied.
Previously, some reports have described studies of the diffusion of dye to fiber using various methods, such as 2D IR spectroscopy, 33 Laser Raman imaging, 34 fiber slices, 35 scanning tunnelling microscopy, 36 etc. Although the dyeing properties of dyes have been investigated through experiments with different methods, it has been difficult to clarify the diffusion process of reactive dyes in the non-aqueous medium/less-water dyeing system. Molecular dynamics (MD) simulation, a type of microscopic computational approach, has been widely used in the study of some substances under the conditions of diffusion, adsorption, emulsification, etc.37,38 Moreover, the water evaporation during the padding-steaming process, and the distribution of dyes in a water base have been studied to improve the dyeing property of reactive dyes. However, there has been no investigation based on the dye aggregation behaviors, and the dye diffusion to cotton fiber in a non-aqueous medium/less-water dyeing system.
In this investigation, the MD method was employed to simulate the aggregation of reactive dyes, diffusion process, and interactions between reactive dyes, dyeing medium, and cotton fibers. From the aggregation of reactive dyes in the dye liquor under different concentrations of inorganic salts, the diffusion process of reactive dyes to the fiber surface, the interaction potential energy, and the influence of inorganic salts on the electrostatic potentials between reactive dyes and cotton fibers were further explained from the molecular level. Some dyeing experiments, such as studies of the phenomenon of uneven dyeing of reactive dyes and color depth of dyed fabric were performed to evaluate the simulation results. These successful studies of the aggregation of reactive dyes, and the influence of inorganic salts on the electrostatic potentials between reactive dyes and cotton fibers can significantly aid development of reactive dye formulations for D5 dyeing technology.
Materials and methods
Materials
Materials used were 100% cotton fabrics (ram weight: 127 g/m2 , yarn count: 15 tex ×15 tex, warp and weft density: 573 × 128) and were purchased from Shandong Mengyin Cotton Textile Co., Ltd. Non-aqueous media (D5, decamethylcyclopentasiloxane, purity >98%) was obtained from GE Toshiba Silicone Ltd. Reactive dye (C.I. reactive black 5) and soaping flakes were supplied by Zhejiang Green Universe Textile Technology Co., Ltd. Sodium sulfate and sodium carbonate were purchased from Sinopharm Inc.
Molecular dynamics simulations of reactive dye aggregation in D5 dyeing system
As shown in Figure 1, the chemical structure of reactive black 5 was constructed and optimized by Material Studio-Dmol3 at B3LYP/DND3.5 level. Molecular dynamics simulations and analysis were performed in the GROMACS 2019.6 package. The solvent model was the SPC model with the OPLS-AA force field.39,40 Periodic boundary conditions were employed during the simulation, and the cutoff radius was 1.05 nm. Ten of the reactive dye molecules and 5510 of H2O molecules were placed in periodic boxes of 5*5*5 nm randomly. Three different sodium sulfate concentrations (0, 40 g/l, 100 g/l) were pre-equilibrated and then simulated at 298.15 K under standard atmospheric pressure. To minimize the energy, the steepest descent method was used to eliminate unreasonable contacts in the simulated system. Then pre-equilibration under canonical ensemble conditions was performed. Electrostatic interactions were calculated using the Partical-Mesh Ewald (PME) method, and the cut-off value of non-bonded interactions was set as 1.0 nm. Finally, MD simulations were performed with a simulation time of 10 ns.

Optimized chemical structure of C.I. reactive black 5.
To investigate the influence of sodium sulfate concentration on the adsorption of reactive dyes at the fiber interface in a non-aqueous medium/less-water dyeing system, the thickness of the cotton fiber layer was set to 3 nm, and a 5.0 nm-thick aqueous solution was placed on the surface of cotton fiber layer. Ten of the reactive dye molecules and 5510 of H2O were placed in periodic boxes. Other simulation methods were carried out as the above conditions.
Mean squared displacement (MSD) analysis
It is well known that the dye molecules cannot be fixed in the same position in the aqueous solution, but they are constantly moving during the MD simulation process. The MSD curve of dye molecules can be achieved by MD to simulate the movement path of dye molecules in the process of movement.41,42 The MSD curve relationship can be expressed as
where, < > is the average value of the squared displacements for all atoms in the group.
When the system is in a liquid state, there is linear relationship between the simulated time and MSD, and its slope and diffusion coefficient have the relationship of equation (2). From this the diffusion coefficient (D) of the reactive dye can be calculated.
Radial distribution function (RDF) analysis
The RDF describes the distribution of molecules in MD, which is the ratio of the local density to the average density of the molecule.
43
From RDF analysis, the bonding, the interaction, the spatial arrangement, and the properties of molecules can be analyzed. Basically, the stacking state of atoms and the distance between each bond are also be also be characterized with RDF. It can be calculated as
where, dN represents the number of molecules that are r+dr away from a given molecule, and ρ is the average number density of the molecule.
Solvent accessible surface area (SASA) analysis
The SASA is actually an “imaginary surface,” which refers to the surface area of the molecule exposed to the solution. SASA is defined as the trajectory of the solvent probe molecular sphere rolling on the surface of the measured molecule.
44
SASA is calculated by Lee and Richards with a probe size of 1.4 Å and a z slice value of 0.05 Å.
45
The SASA A of a given molecule is calculated according to equations (4) and (5).
Molecular electrostatic potential (MEP) calculation
To investigate the influence of inorganic salts on the aggregation of reactive dyes in the non-aqueous medium/less-water dyeing system, the MEP was employed to identify and rank the hydrogen bond donating in dye compounds.46,47 The MEP was performed using Dmol 3 code. 47 The geometry optimization was calculated using BLYP correlation functional with a double numeric plus polarization (DNP) basis set. The energy convergence criterion was 2e−5 Ha, and the convergence standard of SCF was 10−5 Ha.
Reactive dyeing in non-aqueous medium/less-water dyeing system
Reactive dyeing for cotton fabric in D5 dyeing system is described in the Supporting Information.
Color depth and leveling properties of dyed fabric
The K/S value of dyed fabrics is described in the Supporting Information.
To evaluate the leveling properties of the dyed fabric, 12 different positions on the dyed cotton fabrics were randomly selected and the K/S values were measured with Datacolor 800 spectrophotometer (Datacolor, USA). The level dyeing property (Sγ(λ)) was represented with the standard deviation of K/S values at 12 points.
Color fastness
To evaluate the durability of the dyed fabric, the colorfastness to wash and crocking of the dyed samples was measured according to ISO 105-C06 and ISO 105-E04:2013 testing standards respectively. Colorfastness to washing was assessed in respect of color change in sample and staining on the multifiber fabric. Rubbing fastness was evaluated in dry and wet conditions. According to ISO 105-B02, the perspiration fastness of the dyed fabric was also measured.
Results and discussion
MSD
The MSD curve of the dye molecule at equilibrium was simulated and the results are shown in Figure 2. It can be clearly seen that the slope of the MSD curve of reactive black 5 was the highest when there was no salt in the aqueous solution. However, when different concentrations of salt were employed in the aqueous solution, the slope of the MSD curve was decreased to varying degrees. The diffusion coefficient of the reactive black 5 molecule is listed in Table 1. From Table 1, the diffusion coefficient of the reactive black 5 molecule was 0.3044 × 10−5 cm−2/s when there was no salt in the aqueous solution. However it decreased to 0.2617 × 10−5 cm−2/s and 0.2538 × 10−5 cm−2/s respectively when the salt concentration was 5.2% o.w.f. and 13% o.w.f. Therefore, the diffusion coefficient of reactive black 5 molecule was decreased by 14.03% and 16.62% when the salt concentration was increased from zero to 5.2% o.w.f. and 13% o.w.f., respectively.

Mean squared displacement (MSD) curves of reactive dye with different sodium sulfate concentrations in water base.
Diffusion coefficient of reactive black 5 with different salt concentration
Generally, a higher slope of the MSD curve indicates that the diffusion of molecules is faster, 48 indicating that the dye molecules are not aggregated or the aggregates formed are small, resulting in a faster diffusion of dye. Therefore, when the sodium sulfate concentration was lower, the aggregates of dye molecules were smaller. Moreover, the greater the slope of the MSD curve, the greater the diffusion coefficient. Therefore, the reactive dye has a low degree of aggregation in the non-aqueous medium/less-water dyeing system because this dyeing system does not contain salt.
Aggregation morphology of reactive dye in non-aqueous medium/less-water dyeing system
In order to investigate the aggregation morphologies of reactive dyes with a different concentration of inorganic salts in the non-aqueous medium/less-water dyeing system, the aggregation morphologies of reactive dyes in the equilibrium stage were simulated by MD 2. Figure 3 shows one side of the morphology maps of the dye molecule. In salt-free or salt environments, the aggregation morphology of reactive dyes showed an evident difference at the equilibrium time of 10 ns in the periodic boxes. When the concentration of sodium sulfate was zero, the dye molecules in the solution displayed in the form of unimolecular molecules and dimers. However, the dye molecules mainly existed in the form of unimolecular molecules and polymers when the concentration of sodium sulfate was 5.2% o.w.f. If the concentration of sodium sulfate was increased to 13% o.w.f., there was obvious aggregation phenomenon between dye molecules, and the dye molecules mainly existed in the form of trimers and polymers.

Aggregation morphology of reactive black 5 with different salt concentration (a) 0; (b) 5.2% o.w.f. and (c) 13% o.w.f.
It is well known that reactive dyes are negatively charged in aqueous solution because the dye molecules contain some anionic groups. 49 There was no salt in the non-aqueous medium/less-water dyeing system, and the agglomeration of dye was very small which could be attributed to the repulsive force between dye molecules. 50 The interaction between sodium ions and negatively charged dyes could reduce the repulsive interaction between anionic dyes.
RDF
For a molecule system, RDF can represent the density of other atoms around a central atom. 51 As shown in Figure 4(a), it can be observed the RDF between dye molecules had a peak at 0.52 ∼ 0.62 nm, where 0.52 nm was the distance between the center of mass of the dye molecule and the dye molecule when the dye was agglomerated. When the dye existed in the form of a unimolecular molecule, 0.62 nm was the distance between the center of mass of the dye and the dye molecule. When the sodium sulfate concentration was 5.2% o.w.f. in the simulated system, the peak at 0.62 nm gradually disappeared (Figure 4(b)), and when the sodium sulfate concentration was 13% o.w.f., the peak near 0.62 nm completely disappeared (Figure 4(c)). Therefore, it can be considered that the dye molecules existing in the form of unimolecular molecules gradually disappeared and changed to the form of aggregates with the increase of sodium sulfate concentration. On the other hand, the peak near 0.52 nm gradually moved forward to 0.42∼0.36 nm, and the peak height was also increased, indicating that the agglomeration of dye molecules can be reinforced when the concentration of sodium sulfate is increased in the dyeing system.

Radial distribution function of dye molecules with different salt concentrations.
SASA
The SASA of the dye molecule in the water bath is described as the surface area of the dye molecule which is exposed to water surface. 52 From 0–10,000 ps, the SASA data of dye molecules was simulated by MD. As shown in Figure 5, after 5000 ps, the SASA of reactive dye 5 basically reached equilibrium. Compared with no salts in non-aqueous medium/less-water dyeing system, the SASA of the dye molecules was decreased with the increase of the sodium sulfate concentration. It is well known that the larger the SASA of the dye in the solvent, the greater the degree of aggregation between dye molecules. 53 Conversely, the smaller the SASA of the dye in the solvent, the smaller the degree of aggregation among dye molecules. Therefore, the degree of aggregation of dye molecules was more severe with the increase of the sodium sulfate concentration.

The solvent accessible surface area (SASA) cures of dye molecules with different salt concentration.
Adsorption of reactive dye with different concentration salts in the non-aqueous medium/less-water dyeing system
To investigate the adsorption of reactive dyes on the interface of cotton fibers in the non-aqueous medium/less-water dyeing system, the thickness of the cotton fiber layer was set to 3 nm, and a 5.0 nm-thick aqueous solution was placed on the cotton fiber surface layer. As shown in Figure 6, the adsorption process of the reactive dye molecules on the surface of cotton fibers was different under different simulation times in different sodium sulfate concentration dyeing systems. At the beginning of adsorption (2.5 ns), due to the water layer on the cotton fiber surface (Figure 6(a)), the dye molecules were mainly distributed in the water phase. As the adsorption time increased (5 ns, 7.5 ns, 10 ns), the dye molecules gradually migrated from the aqueous phase to the solid phase (fiber). However, due to the ionization of dye molecules in the aqueous phase into dye anions and sodium ions, sodium ions and water molecules could form hydrates to form energy barriers on the fiber surface, resulting in difficulty for the dye molecules to adsorb on the cotton fibers.54,55 Therefore, reactive dyes can aggregate in the water phase to form dye aggregates, which make it difficult for the dye molecules to transfer from the aggregated structures and migrate to the cotton fiber surface. When the sodium sulfate concentration was 5.2% o.w.f. (Figure 6(b)) and 13% o.w.f. (Figure 6(c)), as the simulation time increased, the diffusion of reactive black 5 shifted to the direction which benefited the cotton fibers, and the number of reactive dyes migrated on to the cotton fiber surface was increased. The reason maybe that the sodium sulfate in the system was ionized to increase the sodium ions. As the concentration of sodium ions increased, the energy barrier between the fiber and the dye was neutralized, resulting in more of the reactive dye molecules diffusing into the cotton fiber.56,57

Adsorption of reactive dye with different salt concentration on cotton fiber surface: (a) 0; (b) 5.2% o.w.f.; (c) 13% o.w.f.
Molecular surface electrostatic potential (ESP) distribution
The ESPs of reactive dyes and cotton fibers with or without salts were calculated. As shown in Figure 7, the ESP surfaces have been mapped with a color scheme with blue representing the highest negative potential region while the red represents the highest positive potential region. For reactive dye (Figure 7(a)), most regions of dye showed a strong electronegativity. However, the positive ESP area of reactive dyes was increased significantly after adding some sodium ions. For cotton fiber molecules (Figure 7(b)), after adding some sodium ions, the positive ESP area of fiber molecules was increased significantly too.

Surface electrostatic potential of (a) reactive dye and (b) cotton molecules.
The interaction energy between cotton fibers and dye molecules
The interaction force mainly refers to the non-bonding forces such as van der Waals force and Coulomb force, which become interaction energy when substances interact with each other. 58 The interaction between dye molecules and fiber molecules is one of the main factors which influence the adsorption of dyes on fibers. The simulation calculation results of the interaction energy between fibers and dyes, dyes and dyes in different sodium sulfate concentration systems are shown in Table 2. The fiber-dye and dye-dye interaction values under different sodium sulfate systems were negative, indicating the mutual attraction between fibers and dyes, and dyes and dyes. Compared with no salt in the non-aqueous medium/less-water dyeing system, the coulomb energy (Coul-SR) and van der Waal energy (LJ-SR) between fiber and fiber were increased with the increase of salt concentration. For example, the LJ-SR energy was improved from 131.29 kJ/mol to 382.92 kJ/mol when 5.2% o.w.f. sodium sulfate was employed during dyeing. As is known, the interaction energy calculation is that a negative value indicates a binding effect, a positive value indicates a repulsive effect, and the larger the absolute value is, the greater the interaction strength. Therefore, the mutual attraction between cotton fibers and reactive dyes was enhanced after adding sodium sulfate.
Interaction energy of reactive dyes and cotton fibers
Coul-SR: coulomb energy; LJ-SR: van der Waal energy.
Compared with the interaction energy between cotton fibers and reactive dyes, the interaction energy between reactive dyes was decreased with the increase of sodium sulfate dosage. For example, the LJ-SR energy between reactive dyes was decreased from 630.08 kJ/mol to 531.48 kJ/mol when the dosage of sodium sulfate increased from zero to 5.2% o.w.f. Therefore, the repulsive force between reactive dyes and cotton fibers was getting smaller and smaller, which might have increased the adsorption rate of reactive dyes.
Level dyeing property of reactive dye in the non-aqueous medium/less-water dyeing system
The level dyeing property is the basic requirement of dyeing products, otherwise it would be difficult to appear in the market. As shown in Figure 8, three different levels of salt dosage showed behavior differences in the levelness of dyed fabric (Figure 8(a)), due to the aggregation of reactive dyes and the interaction energy between cotton fibers and reactive dyes being different. When there was no salt in the non-aqueous medium/less-water dyeing system, the color depth of the dyed fabric was 23.46, and its maximum variation of Sγ(λ) value was +0.02. When the amount of salt was 5.2% o.w.f., the K/S value of the dyed fabric was 23.21, and the Sγ(λ) value was +0.033. However, the maximum Sγ(λ) value was increased to +0.045, which might have resulted in poor levelness and uneven dyeing when the concentration of salt was 13% o.w.f. Therefore, with the increase of sodium sulfate dosage, there was little change in the color depth of the dyed fabric, but the level dyeing property was reduced.

Dyed fabric in (a) non-aqueous medium/less-water dyeing system and (b) level dyeing property of dyed fabrics.
As shown in Table 3, in acidic and alkaline conditions, the perspiration fastness of the dyed fabrics was level 4 or 4–5. The dry crocking fastness of the dyed fabric was level 5, and the wet crocking fastness was level 3–4. Moreover, after washing 25 times, the color change of the dyed fabric was level 4, and the staining of the dyed fabric to cotton, acrylic, wool, and acetate was level 3–4 or 4. Therefore, the perspiration, crocking, and washing fastness of the dyed fabrics can meet industry requirements.
The dyed cotton fabrics dyed color fastness in the D5 dyeing system
Conclusion
In summary, the MD method was employed to investigate the adsorption of reactive dyes on the surface of cotton fibers in the non-aqueous medium/less-water dyeing system. The influence of sodium sulfate on dye aggregation behavior, diffusion property, and the interaction energy between fibers and dyes, dyes and dyes were studied to investigate the reason for the poor dyeing properties. The results showed that the dye molecules in the solution displayed in the form of unimolecular molecules and dimers when there was no sodium sulfate in the non-aqueous medium/less-water dyeing system. If sodium sulfate was employed during dyeing, there was an obvious aggregation phenomenon between dye molecules, and the dye molecules mainly existed in the form of trimers and polymers. From the MSD curve, the SASA and RDF, the unimolecular dye molecules gradually dispersed and changed to the form of aggregates with the increase of sodium sulfate dosage. The increasing positive ESP area between reactive dyes and cotton fibers contributed to the increasing adsorption rate of reactive dye in the non-aqueous medium/less-water dyeing system. More trimers and polymers would adsorb on the cotton fiber surface, resulting in less desorb to the dyeing bath. Compared with sodium sulfate environment, the level dyeing property of the dyed fabric was better. This can be attributed to the weak interaction forces between fiber and dye which would make the dye diffuse slowly onto the fiber, and more single-molecule dyes were adsorbed to the fiber surface. Therefore, this investigation explains how salt-free reactive dyeing of cotton fabrics is feasible in the non-aqueous medium dyeing bath, which can reduce the the difficulty of wastewater treatment.
Footnotes
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) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China (22072089), the Key Technology Research and Development Project of Anhui Province (2023t07020001), the Industrial and Agricultural Project of Haining Science and Technology (2021003), and the Opening Project of Key Laboratory of Clean Dyeing and Finishing Technology of Zhejiang Province (QJRZ2301).
