Response surface methodology approach for dyeing process optimization of Ayous (Triplochiton scleroxylon) wood with acid dye

Dyeing of wood is an important value-adding process. An important indicator in the assessment of the performance of wood dyeing process is the dye penetration. In the present study, the existing method of response surface methodology was extended to study the dyeing process optimization of Ayous (Triplochiton scleroxylon) wood with acid dye using the radial dye penetration percentage as an indicator. The experiments were carried out on the basis of a single factor experiment, and the optimal condition was determined by means of the Box–Behnken Design of response surface methodology. The effects of temperature, dye concentration, dyeing time and accelerant mass fraction on the radial dye penetration percentage of Ayous wood were optimized. The experimental results showed that the maximum radial dye permeability can be achieved under optimum dyeing temperature (86.03 °C), dye concentration (0.31%), dyeing time (8 h), and accelerant mass fraction (2.23%). Under these conditions, the maximum dye-uptake and radial dye penetration percentage were found to be 14.28% and 22.34%, respectively. The results of analysis of variance indicated that the mathematical model proposed in this study can be used to predict the dye-uptake and radial dye penetration percentage of acid dye on Ayous wood by changing the process parameters.


Introduction
As one of the materials that have the closest relationship with human beings and the most harmonious development with the environment, wood and wood-based materials are ubiquitous for a millennium in the development of buildings and furniture of the human living environment, due to their good material properties and environmental characteristics (Hu et al. 2020;Ndukwu et al. 2021). Compared with other commonly used modern engineering materials, such as steel, concrete and plastic, wood has the advantages of high strength-to-weight ratio, good elasticity, easy processing, natural beautiful texture and color, and renewable ability (Bao et al. 2016;Borrega et al. 2015;Knudson and Brunette 2015;López et al. 2018;Yang et al. 2019;Liu et al. 2021a). The uneven color and "dull appearance" of wood are important factors affecting its utilization and commercial value. These visual defects can be eliminated by color modulation techniques such as bleaching, dyeing, etc. to improve the decorative properties of wood (Nguyen et al. 2018a). At the same time, dyeing allows low-quality wood to imitate the color of natural precious wood, so dyeing of wood has always been a vivid field of research and development in wood processing (Jaxel et al. 2020).
Dyeing is an important value-adding process from an industrial perspective. Generally, wood dyeing mainly uses dyes (acid dyes, basic dyes, etc.) to achieve the desired color. The dye molecules enter the wood through the multilevel infiltration channels of wood cells, and are adsorbed, set and fixed into wood fibers or tracheids by intermolecular van der Waals and hydrogen bonding forces (Liu et al. 2015. The quality of dyed wood and dyeing depth depend on the degree of absorption and penetration of dye molecules into the wood structure. However, with the exception of longitudinal tracheids that are naturally quite permeable in the direction in which fluids must flow, there are limited tangential and radial channels available for dye penetration. Comstock (2007) calculated the directional permeability of softwoods based on the available gas permeability data and found that the ratio of longitudinal to tangential permeability 1 3 varies from 520 to 81,600, and the longitudinal to radial ratio varies from 15 to 547,000. The tangential and radial penetration of the wood is related to the dyeing depth, and in general, as the thickness of the wood increases, it becomes more difficult for dyes to penetrate (Rowell 2012).
Atmospheric pressure impregnation is a simple and mature technology, in which expensive high-pressure reactors are not essential, so it is the most commonly used method for wood dyeing at present. The effect of atmospheric dyeing is directly affected by the process parameters, such as dye concentration, temperature, dyeing time, dosage of accelerant and so on. Depending on the dyes and tree species, different dyeing parameters should be adopted (Wang et al. 2017(Wang et al. , 2018b. Hu et al. (2016) studied the influence of dyeing parameters on the dye-uptake and color difference of Acer saccharum veneer, showed that the dye concentration and dyeing temperature had the greatest effect by visual means and analysis of variance, and obtained the optimal process by fuzzy synthetic evaluation. Nguyen et al. (2018b) investigated the types of dye (direct dye and reactive dye) and dyeing parameters (dye concentration, dyeing time, and temperature) in the veneer dyeing process for Eucalyptus globulus, and showed that the reactive dye Procion Brown P2RN at a concentration of 2% resulted in the highest dye penetration.
Ayous (Triplochiton scleroxylon), also known as Obeche, is an important species from the tropical forests in West and central Africa, especially in Equatorial Guinea, Cameroon and Gabon. It is a large deciduous tree growing up to 50 m in height and up to 1.5 m in diameter (Jardine et al. 2016;Nouemsi Soubgui et al. 2021;Togue Kamga 2018). The timber from Ayous possesses unique intrinsic features, such as uniform material properties, high processability, small drying shrinkage and few appearance defects that have led to it being widely used in the production of multilaminar decorative lumber (MDL). In the current MDL research, the dye-uptake is mostly selected as the criteria to evaluate the Ayous wood veneer dyeing process, but little attention has been paid to the dye penetration. Meng et al. (2016b) show that increasing the thickness of veneer can significantly save glue consumption, thereby reducing production costs and environmental pollution (Meng et al. 2016a). To achieve an optimal dyeing process of thicker veneer, the relationship between dyeing parameters and dye penetration must be determined.
The response surface methodology (RSM) is a set of mathematical techniques that investigates the effective parameters on a response. It mainly includes three steps of experimental design, model construction, and data analysis, and then evaluates the interactions between the response factors to determine the optimal conditions (Antony 2014;Hazir and Ozcan 2019;Singh et al. 2016). This technique can be used especially for improving efficiency of the processes. Compared with the traditional univariate method and orthogonal experiment method, RSM can establish a multiple quadratic regression equation containing the factors and the response values, thereby presenting an advantage in clarifying the interaction between variables (Khataee et al. 2011;Witek-Krowiak et al. 2014;Danish et al. 2017). Besides that, this design also has several advantages such as a minimum number of experiments required, and data analysis applied using three-dimensional graphs (Ghaedi et al. 2016;Das and Mishra 2017;Yusop et al. 2021), so it has been widely used as a technique for designing experiments since it was developed by Box and Wilson (1951).
Recent studies have shown that RSM has also been selected as a design of experiment for optimizing process parameters to achieve higher dyeing effect of wood (Deng et al. 2019). However, very few reports are available on using dye penetration to evaluate the effect of Ayous wood staining. Dye penetration is important and realistic for Ayous thicker veneers. Our study has been comprehensively focused on the same to fill this research gap in the field of Ayous staining. This present paper assesses the performance of Ayous wood under different dyeing processes parameters, especially the dye penetration. By using response surface methodology (RSM), the optimum dyeing conditions of temperature, dye concentration, dyeing time and accelerant mass fraction were determined. The aim of the present work is to obtain higher dye-uptake and dye penetration percentage, so as to provide technical guidance and theoretical support for the production of dyed Ayous thick veneers.

Materials
The Ayous (Triplochiton scleroxylon) wood used in this study was purchased from Shenghua Yunfeng New Materials Co., Ltd. in Deqing, Zhejiang Province. The raw material consisted of sapwood with a low density (ρ = 0.33-0.48 g/ cm 3 ) and an initial dry moisture content of 10-12%. The initial color parameters of Ayous in the CIE 1976 L * a * b * homochromatic space were as follows: lightness (L * ) 76.71 ± 1.12, red-green chromaticity index (a * ) 6.02 ± 0.36, and yellow-blue chromaticity index (b * ) 27.26 ± 0.62. Each sample with a size of 10 × 10 × 50 mm (radial (R) × tangential (T) × longitudinal (L)) was sawn from the defect-free parts of the Ayous log for dyeing tests of different processes. Triarylmethane Acid Blue V (C. I. Acid Blue 1) (ABV) dye which is commonly used in the wood dyeing industry was provided by Hengsheng Chemical Co., Ltd., in Hangzhou. The molecular formula is illustrated in Fig. 1. Anhydrous sodium chloride was acquired from Tianjin Kemeiou Chemical Reagent Co., Ltd. The concentrated sulfuric acid and sodium hydroxide were obtained from Sinopharm Chemical Reagent Beijing Co., Ltd. and were reagent grade.

Dyeing methods
An atmospheric pressure dip-dyeing method was used for wood dyeing. The dye-uptake of the dye liquor and dyeing depth of the dyed samples were examined. The effect of temperature, concentration of dye liquor, dyeing time, and dosage of accelerant on the properties of dyed wood was investigated afterwards.
Acid Blue V dye liquor 0.1%, 0.2%, 0.3%, 0.4%, 0.5% (w/w) was prepared and 0, 1.0%, 2.0%, 3.0%, 4.0% (w/w) anhydrous NaCl was added as an accelerant. The dyeing process was carried out at 65, 75, 85 and 95 °C with ordinary pressure for 2, 4, 6, 8 or 10 h, respectively. The pH value of the dye liquor was adjusted to 4.0 by 10% H 2 SO 4 (w/w) or 10% NaOH (w/w). For each condition, four wood specimens were placed in a beaker, leaving gaps between the wood so as to ensure adequate contact between the samples and the dye solution. The bath ratio was 1:20 (V wood : V dye liquor ). After dyeing, the raffinate of all the samples was washed away by tap water, and air-dried to constant weight with a moisture content of 10-12% in a cool place without light. The dyeuptake and dye penetration percentage of the dye liquor and chromatic value of the dyed samples was measured before and after the experiment.

Color parameters
The chromaticity value is the simplest and most direct parameter to indicate the significant effect of dyed wood on the process method. The difference of color parameters directly determines the visual effect and commercial value of the wood. Color parameters including L * , a * , and b * were measured by Benchtop CR-400 colorimeter (Konica Minolta, Japan) under the operation conditions, i.e. D65 standard illuminant and 0/d vertical illumination/diffuse reflection. The sample was measured three times at different positions. For each group, four samples were measured and the averages of the four were reported. The total color difference ΔE (expressing the distance between two points in the CIE 1976 L * a * b * homochromatic space) was calculated from Eqs. (1-4) (Machová et al. 2019;Liu et al. 2021b;Zhu et al. 2021): where ΔE indicates the degree of total color change after dyeing, L * axis represents the lightness/darkness of the dyed wood ranging from 0 (black) to 100 (white); a * axis stands for redness/greenness of the dyed wood, with positive (+) indicating red and negative (−) representing green; and the b * axis specifies the ratio of yellow (positive) to blue (negative). L 0 * , a 0 * , and b 0 * are the parameters measured for the control; L 1 * , a 1 * , and b 1 * are the parameters measured after dyeing, respectively.
According to the relationship between ∆E and the ability of human visual perception to colour difference: if ∆E is 0-0.5 NBS, human cannot differentiate colour differences; if ∆E is 1.5-3.0 NBS, human eyes will be able to perceive colour differences; and if ∆E is 6.0-12.0 NBS, humans can distinctly perceive colours differences. When the value of ∆E was more than 12.0 NBS, the colour totally changed to the other colour (Tang 1990;Wu et al. 2018).

Measurement of dye-uptake
Dye-uptake is one of the most important parameters for the wood dyeing process because it affects the quality of dyed wood and dye absorption. Measurement of dye-uptake was carried out by different methods in various studies on different materials (Deng and Liu 2010;Zhang et al. 2015). In this study, the dye-uptake was calculated according to the Beer-Lambert law to determine the relationship between the dye concentration and absorption. The S54 spectrophotometer (Lengguang, China) was used for evaluating the absorption of dyes, where the maximum wavelength (λ max ) was at 638 nm. The dye-uptake (U, %) can be obtained based on Eq. (5). (1) where, A 0 is the absorbance of the initial dye solution at λ max , and A 1 is the absorbance of the residual solution at λ max after dyeing.

Radial dye penetration percentage test
To achieve an optimal wood dyeing process, dye penetration was established as an important criteria for selection of suitable dyeing parameters. The dyed wood samples were evenly separated along the transverse and cut into three pieces. The radial minimum depth of the dye penetration on the left and right sides of the second piece were measured, and the average value was the radial dyeing depth of the sample (Fig. 2). The radial dye penetration percentage (W, %) was calculated by Eq. (6).
where H 1 -H 8 represent the depth of the dye solution penetration, mm; H is the radial length of the sample, mm.

RSM approach of experimental design
The Box-Behnken design (BBD) was chosen as the experimental design. This method is suitable for fitting a quadratic surface (Ryan 2007). The BBD is effective in optimizing parameters with a minimum number of experiments, and also useful in analyzing the interaction between the parameters (Azargohar and Dalai 2005). The independent variables selected for this experiment were temperature (X 1 ), dye concentration (X 2 ), dyeing time (X 3 ) and accelerant mass fraction (X 4 ). These four variables and their ranges were chosen based on a single-factor analysis before designing this experiment. The factor codes and levels are shown in Table 1. The dye-uptake and radial dye penetration percentage were measured. With five replicates at the center point, the BBD for four independent variables was a total number of 29 experiments as calculated in Eq. (7).
where N is the total number of experiments, k is the number of independent variables and n c is the number of central points.
In this research, the Design Expert 12.0.3 software (Stat-Ease, USA) was utilized. The quadratic polynomial model was used to investigate the effects of factors. Analysis of variance (ANOVA) was used to make the developed models adequate through the observed data.

Effect of temperature on wood dyeing
Under the conditions of dye concentration of 0.2%, dyeing time of 4 h, and accelerant mass fraction of 1%, the relationship between increased temperature and dye-uptake, radial dye penetration percentage and color parameters of the dyed wood is demonstrated in Fig. 3. It can be found from Fig. 3a that the dyeing temperature has a certain positive effect on the dyeing of Ayous wood. When the temperature was 65 °C, the dye-uptake was 5.66%, and it increased slightly with the increase in temperature. At 85 °C, the dye-uptake reached a maximum of 7.80%. Increasing temperature made the dye molecules get more energy, and the movement of the dye molecules was accelerated, which increased the probability of the collision between the dye and the wood to form van der Waals forces and hydrogen bonds (Liu et al. 2015). Moreover, the amorphous area within wood fibers increased along with temperature, thus allowing more dye molecules to be adsorbed, diffused and fixed in wood fibers (Wang et al. 2017;Song and Shen 2009). When the temperature continued to rise to 95 °C, the dye-uptake decreased slightly, which was mainly due to the desorption of the adsorbed  dye molecules with the excessively high temperature (Wang et al. 2018a). At the same time, high temperature created a strong affinity between dyes and wood surface, which may cause dyes to be adsorbed on the orifice of capillary, forming triangular adsorption and hindering further diffusion of dyes (Zhao et al. 1993).
As can be seen from Fig. 3a, the increase in dyeing temperature has obviously positive effects on the improvement of dye penetration percentage. When the temperature was 65 °C, the dye penetration percentage was 8.77%, and the value increased significantly with the increase in temperature. When the temperature rose to 95 °C, the dye penetration percentage reached 14.87%, which is 1.70 times that of 65 °C. This was because the increase in temperature improved the activation energy of the dye molecules, which is the ability of dye molecules to penetrate from surface to interior of the wood fibers (Vakhitova and Safonov 2003). When dye anions were transferred to fibers, they must move with their own sodium ions to maintain electrical neutralization. However, the concentration of sodium ions near the fiber interface was much higher than that in the dye liquor, so it would take energy to transfer sodium ions from the area with low concentration to high concentration. In addition, increasing the temperature could significantly reduce the aggregation degree of dyes, thereby improving the diffusion properties of dye molecules (Lv et al. 1994;Li et al. 2011).
The effect of dyeing temperature on the surface color of Ayous wood is shown in Fig. 3b. In the CIE 1976 L * a * b * homochromatic space, the L * value of untreated wood is about 76.71, and both a * and b * are greater than 0. After dyeing, L * decreased obviously, meanwhile a * and b * changed from positive to negative. The results showed that the lightness of dyed wood surface became dark, the red-green index changed from near red to near green, and the yellow-blue index changed from near yellow to near blue. The changes of lightness, red-green index and yellow-blue index of dyed wood had a certain correlation with the changes of dye-uptake. Generally speaking, as the dye-uptake rose, the adsorption of ABV dye on the wood surface increased, the L * became lower, while the a * and b * were higher. Wood dyed at 85 °C had the highest dye-uptake, the lowest L * (30.57), and the highest a * (− 14.08) and b * (− 20.32). However, in the range of 65-95 °C, the difference between the maximum and minimum of dye-uptake was only 2.14%, so the surface total color difference ΔE only changed by 2.53 NBS (from 66.73 NBS to 69.26 NBS). According to the relationship between color difference and people visual recognition, when ΔE is in the range of 1.5-3.0 NBS, the color difference was only perceptible but not obvious (Duan 2002). Dyeing temperature had no significant effect on surface color difference. Figure 4 shows the trends of dye-uptake, dye penetration percentage and color parameters as a function of dye liquor concentration. Different dye concentrations had different results of dye-uptake. When the concentration of dye solution was 0.1%, the dye-uptake was 7.16%. The dye-uptake increased rapidly as the concentration grew, and the highest value was 10.79% at 0.3% concentration. Then, continuing to expand the concentration would result in decreased uptake, and the dye-uptake was 6.48% when the concentration reached 0.5%. This was mainly due to the increase in dye concentration, which can cause a larger concentration difference between wood cells and dye solution. This concentration difference was beneficial for dye liquor to penetrate into wood interior, thus improving the dye-uptake (Li et al. 2013). At the same time, the enlargement of the concentration means that the number of dye molecules in the dye liquor increases, Fig. 3 Effect of temperature on the dyeing properties of Ayous wood. a Dye-uptake and radial dye penetration percentage; b wood surface color parameters and dye contacts and collides with the wood fiber surface more frequently. When the concentration reached a certain degree, the adsorption of dyes on wood arrived at saturation state. After the absolute adsorption amount was stable, the increase in concentration would naturally reduce the dyeuptake (Liu et al. 2015;Wang et al. 2018a).

Effect of dye concentration on wood dyeing
The change of dye penetration percentage showed a similar trend to dye-uptake. When the dye concentration was 0.1%, the dye penetration percentage was 11.13%. An increased permeability occurred before the concentration reaches 0.4%. Subsequently, improving the dye concentration resulted in a diminution of dye penetration. At low concentrations, more dye molecules represent more opportunities for exposure of dyes to wood. Because of the difference of dye concentration inside and outside the wood, it was beneficial for dye molecules to penetrate into the wood (Liu et al. 2015). However, at higher concentrations, the dye molecules were seriously aggregated. It was difficult for the aggregates to flow and diffuse in the wood. The movement resistance of dye molecules increased, and the diffusion speed was slowing down even causing color degradation. Excessive concentrations could even cause insoluble dye deposits on the surface of the wood (Chen and Wu 2015).
As shown in Fig. 4b, with the increase in dye concentration, the lightness value and the yellow-blue index of dyed wood surface gradually decreased, while the red-green index gradually increased. The results showed that the color of wood surface was deepened, and shifted towards red and blue when the dyeing concentration got larger. When the mass fraction of dye spread from 0.1% to 0.5%, the total color difference on the wood surface gradually increased, and the maximum value was 73.25 NBS. Due to the enlarged number of dye molecules adsorbed and aggregated on the wood surface, the promotion of dye concentration results in more pronounced color difference. The ΔE of dyed sample at 0.5% concentration changed by 4.83 NBS compared with that dyed at 0.1% concentration. When ΔE is in the range of 3.0-6.0 NBS, the color difference can be recognized by the human visual system. This result shows that the dye concentration had a significant effect on the surface color difference. Figure 5 shows the influence of dyeing time on dye-uptake, dye penetration percentage and color parameters. As shown in Fig. 5a, the dye-uptake gradually increased until the dyeing time exceeded 8 h. The dye-uptake value of 10 h dyed wood was 9.57%, which was less than the value of 10.48% at 8 h. Dyeing is a slow process in which dye molecules adsorb to the wood surface, diffuse and penetrate into the wood, and finally precipitate on the wood fiber (Convert et al. 2000;Mikhailovskaya et al. 2001). In the process, adsorption and desorption existed simultaneously. At the initial stage of dyeing, the degree of adsorption was greater than that of desorption, so the whole action was dominated by adsorption, and the dye-uptake increased with time (Yu et al. 2002;Nguyen et al. 2018b). When the dye-uptake reached the maximum, desorption became the main action. With the extension of dyeing time, some dye molecules adsorbed on wood fiber might be desorbed, causing a decrease in dyeuptake (Wang et al. 2017).

Effect of dyeing time on wood dyeing
It can be seen from the figure that dyeing time had a positive effect on dye permeability. The dyeing time ranged from 2 to 10 h, the radial dye penetration percentage of Ayous wood increased from 9.53% to 17.90%. During the dyeing process, the dye quickly penetrated into the interior of wood, and the dye penetration percentage rose significantly in the first 6 h. Over 8 h, this trend gradually slowed down. Since the structure and chemical Fig. 4 Effect of dye concentration on the dyeing properties of Ayous wood. a Dye-uptake and radial dye penetration percentage; b wood surface color parameters composition of wood are different from cotton and linen textiles, the dyeing of wood with dyes is a gradual and slow process (Chen and Wu 2015). Due to the thickness of the sample, the resistance of the dye to diffuse into the wood would become greater and greater, and the penetration of the dye would become more and more difficult. Therefore, the longer the dyeing time, the smaller the increase in dye penetration.
As shown in Fig. 5b, dyeing time had little effect on wood surface color parameters. In the dyeing time range of 2-10 h, the change range of L * value was from 27.05 to 31.51, the change range of a * value was from −12.70 to −15.83, the change range of b * value was from −18.86 to −23.60, and the change range of total color difference ΔE was from 68.75 NBS to 71.91 NBS. Except for the 8 h dyed sample, there was no obvious color difference between the remaining wood. The dyeing time had little influence on color difference, which was consistent with previous research results (Chen et al. 2000). Figure 6 shows the influence of accelerant mass fraction on dyeing performance. As can be seen from Fig. 6a, the dyeuptake increased obviously after adding accelerant, and the addition of NaCl had a significant promotion effect on the adsorption of dyes. When the mass fraction was 1%, the dyeuptake was 7.80%, which was 2.19 times that without NaCl. Compared with 0% concentration, adding 2% NaCl could improve the dye-uptake by 2.74 times. NaCl in dye liquor is ionized into sodium ions and chloride ions. Studies have shown that wood has negative charge in dye liquor. Therefore, sodium ions are attracted by the negative charge of wood, while chloride ions are repelled. Under the shielding effect of sodium ions, the repulsive force of dye anions on wood surface was greatly weakened, thus improving the dyeuptake (Chen et al. 2000). However, excessive accelerant concentration would cause the aggregation of dye molecules and even dye precipitation, decreasing the dye-uptake. The dye penetration percentage showed similar trends to dye-uptake. When the concentration of NaCl was 2%, the dye penetration percentage reaches the maximum value of 16.83%. The results showed that the increase in NaCl could enlarge the diffusion boundary layer on the wood surface and promote dye diffusion into wood at lower accelerant concentration (Chen and Wu 2015). Increasing the concentration of NaCl led to the aggregation and precipitation of dye molecules. The movement resistance of dye molecules got bigger after aggregation, and it was difficult for the aggregates to flow and diffuse in wood. Therefore, excessive NaCl was not conducive to dye penetration (Wang et al. 2018a;Yuan 2019).

Effect of accelerant mass fraction on wood dyeing
The effects of different mass fractions of NaCl on the surface color parameters of Ayous wood are shown in Fig. 6b. Compared with the dyed wood without NaCl, the values of L * and b * were lower, and the a * was higher of the samples with NaCl addition, and the ΔE was also higher. With the change in NaCl content, the total color difference increased at first and then decreased. When the concentration of NaCl was 3%, the ΔE was 73.26 NBS. The reason for the above changes was that NaCl as an accelerant weakened the Coulomb force between the wood fiber and dye anions. It was beneficial to the adhesion and combination between wood and dyes, thereby increasing the dye-uptake and color difference. If the amount of accelerant continued to increase, the dye molecules would self-polymerize, which was not conducive to dyeing, so the color difference value would be reduced. Table 2 shows the results of BBD experiments in studying the combined effect of four independent variables with different combinations along with the experimentally observed and predicted values of dye-uptake and dye penetration percentage of Ayous wood. According to Table 2, the highest dye-uptake (14.48%) was achieved for actual data in standard order 18 and the highest dye penetration percentage (22.43%) was achieved in standard order 6. Coincidentally, both results were achieved under the same conditions, that is, temperature 85 °C, dye concentration 0.3%, dyeing time 8 h, and accelerant mass fraction 3%.

RSM model establishment and significance test
The experimental data were analyzed using analysis of variance (ANOVA); the results indicated that the established model was significant. The dye-uptake and dye penetration percentage were quadratic polynomial functions of four parameters studied in Table 2. The R 2 value of the developed model of dye-uptake and dye penetration percentage was found to be 0.985 and 0.982, respectively, and the adjusted R 2 was 0.970 and 0.963, respectively. These values of the correlation coefficients were close to the ideal and statistically acceptable to establish the relationship between the experimental and predicted values (Ahmad and Hameed 2010). The predicted R 2 (Pred. R 2 ) of dye-uptake and dye penetration percentage was 0.936 and 0.909, respectively, which was in reasonable agreement with R 2 and adjusted R 2 . Measuring the adequate precision can estimate the signalto-noise ratio, and an adequate precision greater than 4.0 is acceptable (Danish et al. 2014a). The values of adequate precision (Adeq. Precision) of dye-uptake and dye penetration were 26.74 and 27.68, respectively, and were high enough to guarantee the accuracy of the experiment. Therefore, the proposed model can be used to predict experimental results.
The statistical significance of the proposed quadratic model for both the responses was evaluated by ANOVA and corresponding F-values and the values of "Probability > F" (P-value). For statistically significant model terms, the P-value less than 0.05 indicates that the model is significant, and the P-value less than 0.01 indicates that the model is extremely significant (Amini and Younesi 2009). For both responses of dye-uptake and dye penetration percentage, the quadratic model was selected, as suggested by the software. By using multiple regression analysis, the responses (dye-uptake and dye penetration percentage) were correlated with the four variables studied using the second-order polynomial (Danish et al. 2014b). For this model, development of the main effects, square effects and interaction effects of the temperature, dye concentration, dyeing time, and accelerant mass fraction were statistically evaluated and are reported in Table 3.
As shown in Table 3, the model F-value for dye-uptake and dye penetration percentage was 64.90 and 52.92, respectively, and P-value < 0.0001 for both responses. These values indicate that the models were extremely significant and the quadratic polynomial regression models of dye-uptake (Y 1 ) and dye penetration percentage (Y 2 ) proposed as in Eqs. (8) and (9) for the responses were valid for Ayous wood dye.
As can be seen from the P-value, X 2 , X 4 , X 1 X 3 , X 1 2 , X 2 2 , X 3 2 and X 4 2 had extremely significant effects on dye-uptake, X 1 , X 4 , X 1 X 4 , X 3 X 4 , X 1 2 , X 2 2 , X 3 2 , X 4 2 had extremely significant influence on dye penetration percentage, respectively. X 1 X 2 , X 3 X 4 had significant influence on dye-uptake and X 2 X 4 had significant influence on dye penetration percentage, respectively. X 3 , X 2 X 3 had insignificant influence on dye-uptake and dye penetration percentage. According to the results of variance analysis, it was concluded that the order of influence of each factor on dye-uptake within the scope of this experiment was as follows: accelerant mass fraction, dye concentration, dyeing time and temperature, while the order of influence of each factor on dye penetration percentage was as follows: accelerant mass fraction, temperature, dye concentration and dyeing time. From Table 3, it can be seen that X 1 X 3 was the interactive item that had a significant impact on dye-uptake, X 1 X 4 and X 3 X 4 were the interactive items that had a significant impact on dye penetration percentage.

Effect of temperature and dyeing time
The effect of different levels of temperature and dyeing time on the dye-uptake can be evaluated from the response surface plot as shown in Fig. 7. The temperature was raised from 75 to 95 °C, and the dyeing time was raised from 6 to 10 h, the dye concentration remained constant at 0.3% and accelerant mass fraction was 2%. As the temperature increased to nearly 86.24 °C or the dyeing time increased to nearly 7.98 h, the dye-uptake was found to increase. After that, continued increase in temperature and dyeing time would result in a decrease in dye-uptake. The elliptical curve for contour at the bottom surface of the plot signifies that the interaction between the variables had a strong influence on the response factors (Anupam et al. 2011). The contour lines showed more concentric ellipses close to dyeing time, from which it can be inferred that the dyeing time has more influence on the dye-uptake.

Effect of temperature and accelerant mass fraction
According to Table 3, X 1 X 4 and X 3 X 4 have significant influence on dye penetration percentage. The effect of the temperature and accelerant mass fraction on the dye penetration   Figure 8 shows the combined effect of temperature and accelerant mass fraction on the dye penetration percentage. The dye penetration percentage plot shows the peak in the center of the three-dimensional network. This illustrated that at low temperature and accelerant mass fraction, the dye penetration percentage was less; as the temperature and accelerant were increased, the dye penetration showed an increasing trend. At a temperature of 85.85 °C and accelerant mass fraction of 2.24%, the dye penetration percentage reached a maximum value of 22.38%.
The contour lines showed more concentric ellipses close to accelerant mass fraction, from which it can be inferred that the accelerant mass fraction has more influence on the dye penetration percentage.

Effect of dyeing time and accelerant mass fraction
The influence of dyeing time and accelerant mass fraction, in the range of 6-10 h and 1-3%, respectively, on the dye penetration percentage at fixed temperature of 85 °C and dye concentration of 0.3% was observed. Figure 9 shows the combined effect of dyeing time and accelerant mass fraction on dye penetration percentage. The dye penetration percentage plot shows the peak in the center of the three-dimensional network. The maximum dye penetration percentage was observed to be 22.33% for a dyeing time of 8.01 h and an accelerant mass fraction of 2.25%.

Optimization and validation
A multiple response approach was applied for optimization of any combination of the six goals viz. temperature, dye concentration, dyeing time, accelerant mass fraction, dye-uptake and dye penetration percentage. Finally, a set of conclusions was drawn from the optimization results as shown in Table 4. The goal was set for maximum dye-uptake and dye penetration percentage, keeping the temperature in range, dye concentration in range, dyeing time in range, and accelerant mass fraction in range, the desirability function obtained was 0.970. The outcome of the model gives a set of factors as shown in Table 4. The optimum dyeing conditions were temperature of 86.03 °C, dye concentration of 0.31%, dyeing time of 8 h and accelerant mass fraction of 2.23%. The dye-uptake and dye penetration percentage predicted by the model were 14.28% and 22.34%, respectively. Three experiments were carried out under the optimum conditions. The actual dye-uptake was 14.50% and the actual dye penetration percentage was 22.59%. The relative errors with the theoretical values were 1.57% and 1.12%, respectively, which shows that the model was reasonable and effective.
According to the actual production of enterprises, on the basis of meeting the requirements of relevant standards, the production cost should be reduced as much as possible. From the predicted results, the dye-uptake and dye penetration percentage can be effectively increased by optimizing the process conditions. It can significantly reduce the cost of raw materials and time required for actual production by enterprises in the development of dyed thick veneer products, further enhancing the market competitiveness of the products.

Conclusion
In the present work, the effect of temperature, dye concentration, dyeing time and accelerant mass fraction on the dyeuptake and dye penetration percentage of Ayous wood in the dyeing process with acid dye was studied. The following outcomes of the experiment were noticed: (1) With the increase in temperature, dye concentration, dyeing time and accelerant mass fraction, the dyeuptake and dye penetration percentage of Ayous wood rose first and then fell. Appropriate conditions were beneficial to dye uptake and penetration. Excessive dye and accelerant concentration would cause dye aggregation, which is not conducive to dye diffusion and penetration.
(2) The response surface methodology was extended to study the optimization of dyeing process. The results of ANOVA showed that the value of R 2 , adj. R 2 , Pred. R 2 were all close to the ideal, Adeq. precision of models was greater than 4.0, and P-value of models was less than 0.01, so the quadratic models were significant. (3) The optimum dye-uptake and dye penetration percentage were found to be 14.28% and 22.34%, respectively, at temperature of 86.03 °C, dye concentration of 0.31%, dyeing time of 8 h and accelerant mass fraction of 2.23%. The results demonstrated the applicability of the response surface methodology to optimizing Ayous wood dyeing process, and may provide technical guidance and theoretical support for the production of dyed Ayous thick veneers.

Data availability
The authors confirm that the data supporting the findings of this study are available within the article.

Conflict of interest
The authors declare no competing interests.