In order to further explore the adsorption isotherms of lac red on wool and silk fiber, two parameter equations including Nernst and Freundlich equation were used to analyze the experiment data.

The Nernst [20] Equation (1) is an important model for the analyzing of the adsorption process of dyes:

C f = K N C s (1)

where C_f (mg/g) and C_s (g/L) are the adsorption amount of dyes on fiber and the concentrations of dyes in final solutions, respectively; K_N is the distribution coefficient. The line could be obtained through the plotting C_f against C_s (Figure 3 & Figure 4). The index (R²) was used to evaluate the fitness of experiment data and thermodynamic models.

In addition, the Freundlich [21] [22] Equation (2) is another important model about the adsorption process of dyes.

lg C f = lg K F + n lg C s (2)

where K_F and n are the adsorption constant and the adsorption intensity, respectively. The line of ln C_f versus ln C_s is shown in Figure 5 & Figure 6.

It is worthy noticing that the correlation coefficients R² are in the range of 0.9337 to 0.9859 obtained by linear fitting, indicating the adsorption process of lac red on silk and wool fiber showed better agreement with the Nernst model and the Freundlich model. The fixation and the adsorption of the dye molecules at the surface or the interior of the fiber are governed by affinity between natural dyestuff of lac red and protein fiber. So, the inference natural dyestuff of lac red

dyes silk and wool fiber probably mainly by van der Waals force and hydrogen bonds.

The adsorption property of luteolin on wool fiber is similar to the adsorption of disperse dyes on polyester fiber and the nature of luteolin adsorption pertains to distribution mechanism [23]. The thermodynamic parameters such as standard affinity (−Δµ⁰), dyeing enthalpy (ΔH) and dyeing entropy (ΔS) were computed

as shown in Equations (3)-(5) [11] [24].

− Δ μ 0 = R T ln [ D f ] / [ D s ] (3)

Δ H = ( T 2 Δ μ 1 − T 1 Δ μ 2 ) / ( T 2 − T 1 ) (4)

− Δ μ 0 = T Δ S − Δ H (5)

where, D_fand D_s are the concentration of dye on the fiber and in the dyebath respectively, T is the temperature and R is a constant standing for 8.314 J·(mol·K)⁻¹. The thermodynamic parameters obtained at different temperatures are presented in Table 1.

Table 1 shows the negative values of Δμ and ΔH that lac dye adsorption is a spontaneous and an exothermic process. Within certain temperature range, the affinity of lac red on silk fiber increased in the wake of the increase of temperature, and the affinity of lac red on wool fiber decreased with the increase of temperature. The affinity indicates the trend of the sorption behavior of dyes onto fibers and the higher value reflects more energetically favorable sorption [25], which is consistent with the previous conclusion that the optimal dyeing temperatures for silk and wool are 60˚C and 90˚C, respectively. The ΔS represents the degree of randomness of dye molecule and the negative value of the ΔS manifests the decreased randomness after the adsorption of lac dye on wool [26].

Geometries of Laccaic acid A and glycine optimized with B3LYP/6-31G(d) basis set were shown in Figure 7.

ESP on molecular surface is critical for understanding and predicting intermolecular interaction [27] [28] [29] [30] [31]. In-depth investigation of ESP of Laccaic acid A must be very helpful for deeper understanding of the important interaction between Laccaic acid A and glycine molecular. The ESP mapped vdW surface of Laccaic acid A is shown in Figure 8(A). The surface area in each ESP range is plotted as Figure 8(B). The two sections of Fig. 8 show that most part of vdW surface of Laccaic acid A have positive value of ESP and low ESP value (i.e. within −10 to +10 kcal/mol), but there is also a large portion vdW surface has large negative value of ESP (i.e. <−30 kcal/mol); they attribute to the surface close to the carbonyl group and the oxygens of the carboxyl group and hydroxyl group which have the obvious negative charge. Only tiny part of the vdW surface has ESP value larger than +40 kcal/mol, and they stem from the hydrogens in hydroxy and carboxyl group. The global minima and maxima of ESP on the surface are −48.14 and +69.89 kcal/mol, and correspond to the oxygen in carbonyl group and the hydrogen in carboxyl group, respectively. It has lower negative extrema at the 9-quinone carbonyl oxygen group compared with the potential at the other quinone group because of the delocalization of the lone pairs of electrons from the phenolic groups at positions 3 and 6 [32].

The charge of each atom was obtained by Mulliken charge analysis method. Atomic charge distribution of Laccaic acid A was −0.682e to 0.572e, C53 in amide group showed highest positive charge of +0.572e. O17, O18, O21 and O22 in carboxyl group, O32 and O33 in quinone group and O24, O26, O28, O30 and O42 in hydroxyl group showed negative charges of O17 (−0.458), O18 (−0.554), O21 (−0.437), O22 (−0. 559), O32 (−0.477), O33 (−0.464), O24 (−0.620), O26

(−0.610), O28 (−0.682), O30 (−0.616), O42 (−0.624), respectively. Atomic charge distribution of Laccaic acid A will play important role on hydrogen bond interaction or electrostatic attraction toward glycine.

The simulation of hydrogen bonds in supramolecular structure elucidates lac red dyes silk fiber by combining the amino acid with two to five hydrogen bonds. Figures 9(A)-(H) shows 8 stable compounds without imaginary frequency obtained by structure optimization and frequency calculation of complex space configuration of Laccaic acid A and glycine at B3LYP/6-31G(d) level. The

superposition of the ESP colored vdW surface maps of glycine monomer and Laccaic acid A monomer in the complexes A~H can be seen in Figures 9(a)-(h). Typical hydrogen bonds and bond length of the complexes were summarized in Table 2.

As shown in Figure 9 and Table 2, four type hydrogen bonds (N-H…O, O-H…O, C-H…O, O-H…N) were found in in these compounds. Oxygen atoms in hydroxyl group or carboxyl group of Laccaic acid A formed hydrogen bonds with glycine in three ways: 1:1, 1:2, and 2:1. 1:1 type, an oxygen atom in hydroxyl group or carboxyl group forms hydrogen bond with a hydrogen atom in glycine;

1:2 type, an oxygen atom in hydroxyl group or carboxyl group forms hydrogen bond with two hydrogen atoms in glycine; 2:1, two oxygen atoms in hydroxyl group or carboxyl group form hydrogen bond with a hydrogen atom in glycine. Oxygen atom in quinone group of Laccaic acid A formed hydrogen bonds with glycine in one way: 1:1, such as N66-H67…O33 (2.492Å).

The bond lengths of O42-H43, O24-H25, O28-H29, O22-H23, O30-H31, O18-H19 increased after the formation of complex between l Laccaic acid A and glycine because of the electron withdrawing effect of oxygen atoms and hydrogen atom in glycine, for example, O42-H43 bond length increased from 0.970Å to 0.987Å, whereas the bond lengths of 2C-H15 and C39-H41 decreased.

Binding energy (D₀) means the difference between total energy of Laccaic acid A-glycine complexes and corresponding single molecules (Laccaic acid A and glycine). The total energy of single molecule (Laccaic acid A and glycine) and different complexes was originated from Gaussian simulation according to the following Equation (6).

D 0 = − Δ E = E L + E G − E C (6)

where E_L, E_G, E_C show the total energy of corresponding single molecules (Laccaic acid A and glycine) or different complexes, respectively. Total energy (E), binding energy (D₀), and dipole moment were summarized in Table 3.

As shown in Table 3, the binding energy of 8 complexes range from 25.455 - 71.835 kJ/mol and the complexes containing four or five hydrogen bonds are generally more stable than those with two or three hydrogen bonds because the binding energy of the former is higher than the latter. It is worthy noticing that A and H binding energy which have five hydrogen bonds are lower than B binding energy in that the shorter average bond length of B. These phenomena demonstrate hydrogen bond possesses additivity and the stability of complex of lac red and glycine is closely associated with the number and length of hydrogen bonds.

From Figures 9(a)-(h), the inter-penetration between the vdW surfaces of the

glycine and Laccaic acid A monomer due to formation of hydrogen bonds can be clearly seen. In addition, the mapped colors show that the complexes were formed in ESP positive-negative complementary way, revealing the electrostatic nature of the hydrogen bonds. It is well known that molecules always tend to approach each other in a complementary manner of ESP to maximize electrostatic interaction energy. Therefore, we can also intuitively the structural stability sequence of glycine-Laccaic acid A complexes by simply observing the way and extent of superposition of ESP mapped vdW surfaces.

Dipole moment elucidates the polarity of the complex. The higher dipole moment of the complex clarified a higher polarity of the complex. It was apparent that B which has the highest dipole moment possesses good water solubility.

To sum up, the complex space configuration of Laccaic acid A and glycine was mainly as shown in B when lac red dyed on silk.

The noncovalent interaction (NCI) method, which is also known as reduced density gradient (RDG) method, is a popular method in graphically displaying occurrence region and nature of inter-molecular non-covalent interactions. In order to provide a clear insight into the inter-molecular interactions between the Laccaic acid A and glycine monomer of the complex B, we utilized this analysis method see Figure 10. In Figure 10, the regions enclosed by the RDG isosurfaces are where weak interactions present; the mapped color indicates the type of interaction (see the color bar). From this figure, we can very clearly view the H-bonds between the polar groups in Laccia acid A and glycine (blue isosurfaces) as well as the strong steric effect in the aromatic rings (red or orange isosurfaces). According to the color of isosurfaces, it can be seen that 1-hydroxy hydrogen group in Laccaic acid A formed strong H-bonds with and amino group

in glycine (blue isosurfaces). The hydroxyl group on the side chain of Laccaic acid A formed two H-bonds with the amino and hydroxyl groups in glycine, the color in the corresponding RDG isosurfaces is blue-green, manifesting that these two hydrogen bonds are weaker than the first one. It is worth noting that the RDG maps also reveal very weak C39-H41...O62 type of H-bond (green isosurfaces), the strength of H-bond is no different than van der Waals.