Abstract
The dyeing mechanism of bio-based polyamide 11 fibers with acid dyes was explored in order to provide a theoretical foundation for the dyeing properties of polyamide 11 fibers. The surface morphology and diameters of polyamide 11 fibers and polyamide 6 fibers were compared. Both polyamide 11 fibers and polyamide 6 fibers were dyed with acid dye Isolan blue NHF-S, and the effects of the initial dye concentration, pH values, dyeing temperature and time on the dyeing properties were investigated. The effects of the dyeing kinetics and thermodynamic model of Isolan blue NHF-S on polyamide 11 fibers were analyzed, and the corresponding parameters were calculated. It was found that the dyeing properties of polyamide 11 fibers were not comparable to those of polyamide 6 fibers, while the washing and rubbing fastness were more or less the same. The dyeing mechanism of Isolan blue NHF-S on polyamide 11 was a combination of localized and non-localized adsorption, which conformed to the pseudo-second-order kinetic model and the Redlich–Peterson thermodynamic model. Increasing dyeing temperature could shorten the half-dyeing time and improve the average diffusion coefficient and affinity between the dye and polyamide 11 fibers.
Nowadays, plastic pollution and rising oil prices have brought great attention to renewable resources and biodegradable polymers, and thus replacing fossil-derived polymers with natural polymers is considered an effective solution to the environmental pollution caused by plastic waste. At present, the bio-based polyamide used in the field of chemical fiber is mainly bio-based nylon 5,6 fiber, which is a semi-bio-based polyamide fiber. 1 Nylon 11 (polyamide 11; PA 11) is a 100% biomaterial prepared by monomeric polymerization of ω-undecanoic acid, which is the terminal derivative of castor oil. 2 The repeating unit of PA 11 is composed of 10 methylene long chains and an amide sequence. Consequently, the mechanical properties of PA 11 are similar to those of polyamide 6,6 (PA 6,6) and the flexibility is like of polyolefins. In addition, PA 11 has a lower melting point, good weather resistance, ultraviolet (UV) radiation resistance, chemical resistance and biocompatibility, 3 and has been widely used in areas such as the automotive industry, oil pipelines, electrical and electronic components, injection molding, coating materials and medical treatments.4–6
Currently, the researches of PA 11 mainly focus on the modification of PA 11 composites by copolymerization, such as mechanical property improvement,7–9 flame retardancy,10,11 electrical conductivity,12,13 energy capture and collection, etc.14,15 PA 11 filament fibers can be prepared by polymerization spinning, while there has been little research about the dyeing of PA 11 textile fibers. Considering the great differences between PA 11 and the other commonly used polyamide fibers, polyamide 6 (PA 6) and PA 6,6, in terms of crystallinity, long-chain structure, the number of hydrophilic groups and dye bases, it is necessary to explore the dyeing mechanism of PA 11 fibers.
In order to analyze the adsorption and diffusion behavior of acid dyes on PA 11 fibers, we selected a special kind of 1:2 acid mordant dye, which is a special acid dye for nylon in industry. The dye has a large molecular structure, which can be combined with nylon by ionic bonds, but also can be combined with van der Waals force, hydrogen bonds, etc. It has better instant dyeing speed, a good levelling property, high fastness and good compatibility of the three primary colors on different polyamide fibers. Isolan blue NHF-S will be used as a representative dye to dye PA 11 fibers, and its dyeing kinetic and thermodynamic adsorption model are investigated.
Materials and methods
Materials and reagents
PA 11 filament fibers, FDY 150d/48f, were spun in our laboratory with chips from the Arkema Company (France), and the conditions were spinning temperature of 220°C, drafting temperature of 100°C and drafting ratio of four times. PA 6 filament fibers (FDY 140d/48f) were provided by Zhejiang Taihua New Materials Co., Ltd. Isolan blue NHF-S (1:2 acid mordant dye) was provided by DyStar Trading Co., Ltd (Shanghai). Sodium hydroxide (analytical purity) and sodium acetate trihydrate (analytical purity) were provided by Xilong Science Co., Ltd. Glacial acetic acid (analytical purity) was provided by Shanghai Lianshi Chemical Reagent Co., Ltd. The multi-functional scouring agent MCH-125CC (industrial product) was provided by Wuxi Yicheng Chemical Co., Ltd.
Pretreatment of PA 11 fibers
PA 11 fibers were added to deionized water containing scouring agent of 2 g/L and sodium hydroxide of 2 g/L at a liquor ratio of 1:20, and treated at 90°C for 40 min. Afterwards, PA 11 fibers were taken out and washed with water of 60°C followed by cold water. Then the fibers were washed with acetic acid solution of pH 5 followed by cold water until neutral, and finally dried in an oven at 60°C.
Diameter determination of PA 11 fibers
Images of PA 11 fibers and PA 6 fibers were collected by an Apreo S scanning electron microscope (Thermo Fisher Co., USA), and the fiber diameters were calculated by ImageJ, which is image processing and calculation software. The average value of 30 fibers was calculated.
Dyeing process of PA 11 fibers
The dyeing of PA 11 fibers was carried out with 1:2 acid mordant dye Isolan blue NHF-S, and the effects of dyeing temperature, time, pH and dye dosage on the dyeing properties were carefully investigated. The dyed fibers were carefully washed and dried at 70°C. All dyeing was carried out in a water bath thermostatic oscillator (Model THZ-82, Shanghai Lichen Bangxi Instrument Technology Co., Ltd, China), and the container has a stopper. The dyeing temperature was verified by thermometer measurements. The dyeing process is shown in Figure 1. PA 6 fibers were dyed with a similar approach as the control.

Dyeing profile of polyamide 11 fibers with Isolan blue NHF-S.
Determination of dye uptake
The dye liquor and residual liquor were diluted in a volumetric flask to a certain volume, respectively, and a P3 ultraviolet-visible (UV-vis) spectrophotometer (Mapada Co., China) was used to measure the absorbance of the dye liquor before dyeing (A0) and the absorbance of the dyeing residue (A1) at the maximum absorption wavelength. The dye uptake can be calculated from
Dyeing rate curve of dye on PA 11 fibers
PA 6 and PA 11 fibers were dyed with Isolan blue NHF-S of 2% (on the weight of, o.w.f.) in a 250 mL stoppered conical flask with a liquor ratio of 1:100, where the pH value was adjusted to 4 by an acetic acid/sodium acetate buffer and the dyeing temperature was set at 80°C, 90°C and 98°C, respectively. After dyeing for 3, 5, 7, 10, 15, 20, 30, 45, 60, 90, 120, 150, 180, 240 and 300 min, the residual liquor was separated to obtain the dye uptake for each dyeing time, where three parallel values were averaged. Finally, the dye uptake versus dyeing time for each fiber at each temperature was plotted to produce the dyeing rate curve.
Dyeing adsorption isotherm of dye on PA 11 fibers
PA 6 and PA 11 fibers were dyed with Isolan blue NHF-S of 0.2%, 0.4%, 0.8%, 1.2%, 1.6%, 2%, 3%, 4%, 5%, 6%, 7% and 8% (o.w.f.) in a 250 mL stoppered conical flask with a liquor ratio of 1:200, where the pH value was adjusted to 4 by an acetic acid/sodium acetate buffer and the dyeing temperature was set at 80°C, 90°C and 98°C, respectively. After dyeing for 300 min, the residual liquor was separated to obtain the dye uptake for each dye concentration, where three parallel values were averaged. The dye concentration on fibers Cf and the dye concentration in the residual bath at equilibrium Cs were calculated
16
according to
Determination of the K/S value
The K/S value of the dyed PA 11 fibers at the maximum absorption wavelength was obtained using an SF-800 spectrophotometer (Datacolor International, USA) under illuminant D65 and 10° standard observer. Each sample was tested five times and the average value was calculated.
Color fastness tests
Color fastness to washing and rubbing were determined in accordance with the textiles test standards ISO 105-C06 (2010) and ISO 105-X12 (2016). The changes in color of the dyed fibers were evaluated using a standard five-point visual gray scale. The five grades in color fastness rating are as follows: 5 denotes no color change; 4 denotes a slight color change; 3 denotes a noticeable color change; 2 denotes a considerable color change; and 1 denotes an excessive color change.
Results and discussion
Morphology of PA 11 fibers
It is known that the fiber diameter has a certain influence on dye uptake. The smaller the fiber diameter, the larger the surface area of the fiber. 17 Therefore, a larger contact area between fibers and dyes is achieved, resulting in better dye adsorption performance on the fibers. It can be seen from Figure 2 that little obvious difference in the surface morphology between PA 11 fibers and PA 6 fibers is observed. In addition, the diameter of PA 11 fibers is 19.42 µm, slightly thicker than PA 6 fibers of 18.71 µm.

The longitudinal section of (a) polyamide 11 (PA 11) and (b) polyamide 6 (PA 6) and cross-sections of (c) PA 11 and (d) PA 6 fibers.
Dyeing property of PA 11 fibers
An increase in the initial dye concentration leads to a stronger dyeing driving force, and thus the adsorption capacity of the dye on fibers is enhanced. 18 Figure 3 shows the effect of different initial dye concentrations on the equilibrium adsorption capacity of dyes on PA 11 fibers. With the initial dye concentration rising from 0.2% to 8%, the Isolan blue NHF-S concentration on PA 11 fibers at dyeing equilibrium gradually increases. The dye adsorption on fibers is close to saturation with o.w.f. of more than 7%. Therefore, In order to obtained darkness of the color for PA 11 fibers, the dye concentration is advised to be more than 2%.

The effect of initial dye concentrations on adsorption capacity. Conditions: bath ratio: 1:200; contact time: 300 min; dye solution pH: 4; temperature: 98°C.
In acid dyeing, the pH value is of great importance to the dyeing process. It is necessary to explore the effect of pH on the dyeing property of PA 11 fibers. In Figure 4, the K/S value and dye uptake on PA 11 decreases with the increasing pH value from 4 to 7. The reason might be that the amine group in PA 11 fibers is protonated when the pH is lower than the isoelectric point of PA 11 fibers, which are positively charged to interact with sulfonyl anions of acid dye. The stronger the electrostatic attraction between acid dyes and fibers, the greater the dye uptake. When the pH is higher than the isoelectric point of PA 11 fibers, electrostatic repulsion between negatively charged PA 11 fibers and anionic Isolan blue NHF-S results in a decrease of the dye uptake and K/S value.

Effect of pH on K/S values and dye uptake on polyamide 11 fibers. Conditions: liquor ratio: 1:100; dyeing time: 300 min; dye concentration: 2% (o.w.f.); dyeing temperature: 98°C.
The dyeing rate curves of PA 6 and PA 11 fibers at temperatures of 80°C, 90°C and 98°C were measured and are shown in Figure 5. The initial dyeing rates of both PA 6 and PA 11 fibers are high due to the high initial dye concentrations. As the dyeing goes on, the driving force of dyeing gradually decreases with lowering dye concentrations until dyeing equilibrium. In addition, with the generally lower dye uptake of PA 11 fibers than PA 6, it takes 20 min for PA 6 fibers to reach dyeing equilibrium, but more than 90 min for PA 11 fibers. There are several reasons for this. Firstly, with longer hydrophobic chains and poorer hydrophilicity of PA 11 fibers than PA 6, there are fewer amino groups of PA 11 with which ionic bonds are created with dye molecules, as shown in Figures 6 and 7. Secondly, the diameter of PA 11 fibers is larger than that of PA 6 fibers, leading to a smaller specific surface area and thus difficulty of dyeing. In addition, it has been reported that different from other polyamides, such as PA 6, PA 11 cannot reflect the process of glass transition and cold crystallization from differential scanning calorimetry (DSC) after rapid cooling by melt.19,20 This may also be the reason for the slower dyeing rate of PA 11. On the other hand, increasing the dyeing temperature obviously enhances the dye uptake of PA 11 fibers because of the relatively low crystallinity of PA 11 fibers,8,21 since heating was beneficial to the pore enlargement of PA 11 fibers and thus it was easier for dye molecules to diffuse into the interior of the fibers.

Dyeing rate curves of polyamide 11 (PA 11) fibers and polyamide 6 (PA 6) fibers at temperatures of 80°C, 90°C and 98°C. Conditions: liquor ratio: 1:100; dye solution pH: 4; dye concentration: 2% (o.w.f.).

Chemical structure of polyamide 11.

Chemical structure of polyamide 6.
Dyeing kinetic of PA 11 fibers
In order to analyze the dyeing kinetics of PA 11 fibers at temperatures of 80°C, 90°C and 98°C, the pseudo-first-order kinetic equation

Fitting of dyeing rate curves of Isolan blue NHF-S on polyamide 11 fibers with the pseudo-first-order model (a) and pseudo-second-order model (b) at temperatures of 80°C, 90°C and 98°C. Conditions: liquor ratio: 1:100; dye solution pH: 4; dye concentration: 2% (o.w.f.).
Experimental and calculated equilibrium adsorption capacity of Isolan blue NHF-S on polyamide 11 fibers
Notes:
As shown in Figure 8, the fitting coefficients R2 of the pseudo-first-order kinetic model at temperatures of 80°C, 90°C and 98°C are 0.9533, 0.9597 and 0.9627, respectively. If the initial dyeing stage is considered only, this model seems to be more suitable due to the localized adsorption of anionic dyes with amino groups of PA 11 fibers at the initial dyeing stage. When the pseudo-second-order kinetic model is used for fitting, the coefficients R2 at temperatures of 80°C, 90°C and 98°C are 0.9944, 0.9960 and 0.9978, respectively, all of which are greater than 0.99, indicating a better fitting result of the pseudo-second-order kinetic model. Moreover, in Table 1, compared with the fitting result of the pseudo-first-order kinetic model, the experimental dyeing equilibrium adsorption capacity
The half-dyeing time (t1/2), calculated from
Pseudo-second-order kinetic parameters of Isolan blue NHF-S on polyamide 11 (PA 11) fibers
PA 6: polyamide 6.
Dyeing thermodynamics of PA 11 fibers
In Figure 9, we used Origin 2018 software to fit the data obtained. Adsorption isotherms of PA 11 fibers dyed with Isolan blue NHF-S at temperatures of 80°C, 90°C and 98°C are fitted with the nonlinear least square custom functions of Freundlich

Freundlich adsorption model (a), Langmuir adsorption model (b) and Redlich–Peterson adsorption model (c) fitting curves of polyamide 11 fibers dyed with Isolan blue NHF-S. Conditions: liquor ratio: 1:200; dye solution pH: 4; contact time: 300 min.
Langmuir
Normalized deviations (ND) and fitting coefficients (R2) of Isolan blue NHF-S adsorption on polyamide 11 fibers
At dyeing temperatures of 80°C, 90°C and 98°C, the fitting coefficients (R2) of the Freundlich adsorption model and the Redlich–Peterson adsorption model are both above 0.99, indicating their excellent modeling of Isolan blue NHF-S adsorption on PA 11 fibers, while the fitting of the Langmuir adsorption model is poor due to the lower R2 value. In addition, the normal deviation (ND) of Redlich–Peterson fitting (5.40–8.16%) is smaller than that of Freundlich (5.84–14.35%). Therefore, the Redlich–Peterson adsorption model is the best fitting of Isolan blue NHF-S adsorption on PA 11 fibers, which is a combination of the Langmuir adsorption model and the Freundlich adsorption model, indicating that the dyeing process of Isolan blue NHF-S on PA 11 fibers consists of physical adsorption and chemical adsorption.
The calculated adsorption parameters from Redlich–Peterson fitting of Isolan blue NHF-S adsorption PA 11 fibers are listed in Table 4. It is obvious that adsorption quantity constant (KR), adsorption capacity constant (αR) and heterogeneity factor (β) all decrease with increasing dyeing temperature. The smaller the heterogeneity factor, the greater the contribution of physical adsorption in the Redlich–Peterson adsorption model. As the dyeing temperature is elevated, gaps inside the fibers become more numerous and larger, which is favorable for multi-layer non-localized adsorption of Isolan blue NHF-S with a large molecular structure, besides its monolayer localized adsorption associated with a few amino groups.
Calculated adsorption parameters from Redlich–Peterson fitting of Isolan blue NHF-S adsorption on polyamide 11 fibers
The dyeing affinity (–△μ0) of Isolan blue NHF-S on PA 11 fibers is calculated using
At a certain temperature range, the dyeing heat (△H0) is considered to be constant. According to

Effect of temperature on the affinity of polyamide 11 fibers dyed by Isolan blue NHF-S.
Thermodynamic parameters of polyamide 11 dyed with Isolan blue NHF-S at different temperatures
It is known that increasing the dyeing temperature is beneficial to the transfer of dye from the bath to the fibers, and thus the dyeing affinity –Δμ0 accordingly increases. Meanwhile, the dyeing heat value is positive, indicating that the dyeing process is endothermic, and thus a higher dyeing temperature is beneficial to dye adsorption and the amount of adsorbed dye. In addition, the dyeing entropy is positive as well. This is ascribed to the fact that hydrophobic parts of the molecular structure of Isolan blue NHF-S may promote water molecules forming a special structure, leading to disorder of the dyeing system. In most cases of dye uptake, dyeing is an exothermic reaction, with higher temperature and lower affinity, but the result of this paper is opposite. This is because the molecular structure of PA 11 contains a large amount of methylene and has high hydrophobicity. Although the 1:2 acid mordant dye and PA 11 have ionic bond binding, the combination of the van der Waals force, hydrogen bond and hydrophobic bond is also high. It is similar to direct or disperse dyes with a large molecular weight that dye fibers by the dissolution mechanism, especially when the dye concentration is high.24,25 The molecular weight of Isolan NHF-S is relatively large, and the molecule is relatively complex. So, it is not easy for the dye to enter the amorphous region of the fiber when the temperature is low. When the temperature is increased, the micro-gaps of the fiber become larger, and the dye molecules are easy to diffuse into the fiber and bind with the fiber, which shows that the affinity increases with the increase of temperature.
In summary, Isolan NHF-S exists in the form of negative ions in weakly acidic dye solution, and these dye anions can be bonded with the ionized amino group on PA 11 fiber by ionic bonds. Although the amino content of PA 11 fiber is low, it has a large number of non-polar van der Waals forces that can interact with dyes. At the same time, the fiber also has groups that can form hydrogen bonds with sulfonyl amino groups and other groups on the structure of the dye matrix. Therefore, in addition to ionic bonding, PA 11 fibers can also be dyed by strong van der Waals forces and hydrogen bonding. In addition, the dye molecules of Isolan NHF-S are complex, with a large relative molecular weight, relatively low solubility in water and certain hydrophobicity, while the PA 11 fiber has more hydrophobic methylene. According to the principle of similar phase solubility, the dye molecules can also form non-polar hydrophobic bonds with the PA 11 fiber.
Color fastness of dyed PA 11 fibers
The washing and rubbing fastness of PA 11 fibers and PA 6 fibers dyed at the pH of 4, o.w.f. of 2%, at 80°C, 90°C and 98°C for 300 min are listed in Table 6. Their grades of washing fastness evaluated by staining in adjacent multi-fiber strip fabrics and rubbing fastness are all larger than 4. Compared with PA 6 fibers, PA 11 fibers have almost no difference in multi-fiber color fastness and rubbing fastness.
Fastness and K/S value of polyamide (PA 6) and polyamide (PA 11) fibers dyed with Isolan blue NHF-S
Conclusions
The dyeing property and mechanism of acid dyes Isolan blue NHF-S on bio-based PA 11 fibers has been comprehensively investigated. Scanning electron microscopy images indicate that the surface morphology of PA 11 fibers is similar to that of PA 6 fibers. Under the same dyeing condition, Isolan blue NHF-S shows a better adsorption performance on PA 6 fibers than on PA 11 fibers, mainly because of the lower number of amino groups of PA 11 with which ionic bonds are created with dye molecules. In addition, an increase in adsorption time and initial dye concentration enhances the dye adsorption onto PA 11 fibers, and lower pH values and higher temperature can improve the color strength of PA 11 fibers. The dyeing rate of PA 11 fibers with Isolan blue NHF-S conforms to the pseudo-second-order kinetic model, revealing that the dyeing process is combination of monolayer localized adsorption and multi-molecular non-localized adsorption generated by the anionic groups and the large molecular structure of the dye. The adsorption isotherm of Isolan blue NHF-S on PA 11 fibers is more in line with the Redlich–Peterson thermodynamic adsorption model, indicating that the dyeing process of Isolan blue NHF-S on PA 11 fibers consists of physical adsorption and chemical adsorption. It is hoped that the theoretical study of acid dyes on PA 11 fibers will be of significance in promoting the development of all bio-based PA 11 fibers.
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 the receipt of the following financial support for the research, authorship, and/or publication of this article: This research was supported by Zhejiang Provincial Natural Science Foundation of China (No. LGG20F020019), Jiaxing Industry-Education Integration Project (No. 002072101), Jiaxing Science and Technology Plan Project (No. 2019AY11020) and Research Project of Jiaxing Nanhu University (No. 62216ZL).
