Effect of Mordanting on the Adsorption Thermodynamics and Kinetics

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Effect of Mordanting on the Adsorption Thermodynamics and Kinetics of Cochineal for Wool Aleeza Ajmal, and Polly R. Piergiovanni Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b04915 • Publication Date (Web): 08 Mar 2018 Downloaded from http://pubs.acs.org on March 8, 2018

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Industrial & Engineering Chemistry Research

Effect

of

Mordanting

on

the

Adsorption

Thermodynamics and Kinetics of Cochineal For Wool Aleeza Ajmal and Polly R. Piergiovanni* *Department of Chemical Engineering, Lafayette College, Easton PA, 18042, USA [email protected]

ABSTRACT In this study, wool fabric was mordanted with alum, copper or tin, and then dyed with cochineal.

Adsorption equilibrium and kinetic studies were conducted at several

temperatures to determine mordant effects. The Freundlich isotherm modeled the process, with the mordant affecting both Freundlich constants. The value of the adsorption intensity constant indicated a favorable dyeing process for all mordants. The thermodynamic parameters showed that for all mordants, adsorption is spontaneous and thermodynamically favorable. In addition, the dyeing process is most likely a physisorption process. Finally, the kinetics for mordanted wool are best modeled by a pseudo first order equation. The presence of a mordant has a statistically significant effect on the rate constant.

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1.

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Introduction

Interest in natural dyes is increasing due to their soothing shades and their lack of health and environmental hazards. Cochineal is an ancient natural dye that has been found on fabrics in Peruvian tombs dating between 700 and 1100 AD, before the Inca civilization [1]. The dye is extracted from a scale insect (Dactylopius coccus), which lives as a parasite on prickly pear cacti (Opuntia cacti) in South America, Mexico and Arizona [1]. The insects are pulverized in liquid and the extract contains carminic acid (see Figure 1).

Figure 1. Chemical structure of carminic acid Cochineal dye, the potassium salt of carminic acid, is bright red under acidic conditions, and changes to violet in alkali solutions.

It is widely used as a coloring agent in the food,

pharmaceutical, cosmetic and textile industries. It is an anthraquinone dye, which requires a mordant for permanent attachment [1]. Mordants are polyvalent metal ions that act as electron acceptors to form coordination bonds with dye molecules, making them insoluble in water. The presence of a mordant improves dye uptake and retention, and often alters the color shade [2]. Common mordants used for dyeing include alum, copper, iron, chrome and tin. Fundamental studies are necessary to tackle the problems of mordant and dye fastness properties to allow reproducible fabric dyeing [2, 3]. Studies on the kinetics and thermodynamics of dyeing wool with cochineal dye using different 2 ACS Paragon Plus Environment

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mordants will aid in this understanding. In this study wool was pre-mordanted with alum, tin or copper and then dyed with cochineal to determine the effect of the mordant. A series of kinetic and adsorption equilibrium experiments were undertaken at different temperatures and the experimental data was fitted to model equations to determine the kinetic and thermodynamic parameters. Each experiment was replicated in order to analyze the data statistically.

2. Experimental 2.1. Materials 2.1.1 Wool fabric Natural, 100% pure virgin woven wool fabric was purchased from Pendleton Woolen Mills, Portland, OR, USA. Prior to using it in the dyeing experiments, the wool fabric was cut into 10 cm by 10 cm pieces and soaked in deionized water until completely wet. The soaked wool pieces were mordanted with aluminum, tin and copper ions by placing them into the aqueous mordant salt solutions and heating the solutions at a temperature of 50oC for 30 min with stirring. 2.1.2. Preparation of Cochineal dye The cochineal dye (Carminic acid C.I. 75470) is a red colored, water soluble powder having the molecular formula C22 H20 O13 (molecular weight 492.39 g/mol). It was obtained from Aurora Silk, Portland, OR, USA, which obtains dye cultivated by traditional methods in the Peruvian Andes. Approximately 1.9 g of cochineal dye was dissolved in 1500 mL of deionized water and the aqueous dye solution was filtered to remove any undissolved dye particles. Additional deionized water was added to obtain an absorbance reading of less than 2.5 at the wavelength corresponding to the maximum absorption for the dye solution (λ max = 500 nm). 2.1.3 Mordants



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The three mordants used were potassium aluminum sulfate, copper sulfate and stannous chloride. Finely powdered mordant salts were obtained from Aurora Silk, Portland, OR, USA. Aqueous mordant salt solutions were prepared by dissolving 2.5 g of each mordant salt powder in 1000 mL of deionized water. 2.2. Instruments A Spectronic Genesys 2 UV-Vis Spectrophotometer was employed to determine the concentration of the dye samples through absorbance measurements using cuvettes of path length 1.0 cm. A thermostatic water bath (Fisatom), lab oven (Quincy lab oven model 40 AF) and incubator (Water-jacketed GP Autoflow incubator) were used to study the adsorption kinetics and thermodynamics of cochineal dye onto wool fabric pieces at temperature ranging from 30 85oC.

2.3. Methods 2.3.1. Kinetic experiments The batch dyeing process was studied at temperatures ranging from 25 to 85oC. The process began by placing 300 mL of the cochineal dye solution in 600 mL beakers. For room temperature experiments, a magnetic stirrer was inserted and the solution was placed on a stir plate. For higher temperature experiments, the 600 mL beakers were placed in the water bath at the respective temperature and the solution was stirred manually. The 10 cm x 10 cm wool fabric pieces were immersed into the beaker containing the dye solution once the temperature was constant. Next, 1000 L of the dye solution was withdrawn from the solution every 30 seconds for 7.5 minutes. Using Beer’s law relationship and the absorbance of the initial dye solution, the concentration of each sample was calculated (mg dye/mL). The mass of dye adsorbed per gram of wool at any time, qt, (mg dye/g wool) was calculated by a mass balance relationship as shown in equation 1: 4 ACS Paragon Plus Environment

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𝑞𝑡 = (𝐶0 − 𝐶𝑡 )

𝑉

(1)

𝑊

In this equation, C0 and Ct (mg dye/mL) represent the initial and dye concentrations after dyeing time t, respectively. V (mL) is the volume of dye solution and W (g wool) is the mass of the wool fabric.

2.3.2. Equilibrium experiments To begin the equilibrium experiments, nine concentrations of cochineal dye were prepared in triplicate by serial dilution and placed in small (40 mL) glass vials with screw tops. The initial concentrations ranged from 0.31 to 1.1 mg dye/mL. After the initial absorbance of the dye solutions was measured, the mordanted 10 cm by 10 cm wool fabric pieces were cut in half, and massed. The wool fabric pieces were gently rolled and placed into the glass vials with the lids, and the glass vials were shaken to ensure that the entire wool fabric was completely suspended in the cochineal dye solution. The vials were then put inside the oven at temperatures of 30, 55, 75 and 85oC. The amount of dye remaining in the solution was measured after 48, 72 and 78 hours. Between 72 and 78 hours, the absorbance values at λmax remained constant, that is, the amount of dye adsorbed was at equilibrium. Beer’s law was used to convert the absorbance values to the initial and equilibrium cochineal dye concentrations, Co and Ce (mg dye/mL) respectively. A material balance was used, as shown in equation 2 to calculate the amount of dye adsorbed at equilibrium, qe, (mg dye/ g wool):

𝑉

𝑞𝑒 = (𝐶0 − 𝐶𝑒 ) 𝑊

(2)



Page 6 of 32

In equation 2, C0 and Ce (mg dye/mL) are the initial and equilibrium cochineal dye concentrations, respectively, V (mL) is the volume of dye solution and W (g wool) is the mass of the wool fabric.

3. Results and discussion 3.1. The effect of temperature and mordants on the adsorption kinetics of cochineal dye onto wool Dyeing is a complex process, and the detailed nature of the dye-fiber interactions is still not fully understood [4]. Complexity arises from the range of chemical and physical interactions possible between the dye molecules, fiber, and mordants when used in the dyeing process [5]. In this investigation, the dye adsorption process was studied at temperatures of 25, 55 and 85 oC at an initial concentration of 1320 mg dye/L, while other parameters were kept constant. The mordant slightly affected the color shade of the fabric, with alum creating a bright pink, tin producing a lighter pink shade, and copper dyeing the fabric a violet shade. The amount of cochineal dye adsorbed per gram of wool (qt) showed different time trends at different temperatures. Figure 2 shows the results for alum. For all mordants, an increase in temperature led to an increase in equilibrium dye adsorption capacity, qe, (mg dye/g wool). At the higher temperatures, the large dye ions are more mobile and are more likely to interact with the mordant molecules active sites, leading to the increased adsorption. In addition, higher temperatures lead to wool fiber swelling which has been shown to increase color strength and dye adsorption capacities [6,7]. This result is consistent with studies using other natural dyes [3, 8].


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45.00 40.00 35.00

qt (mg dye/ g wool)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


30.00

25.00

85ᵒC

20.00

55ᵒC

15.00

25ᵒC

10.00 5.00 0.00 0

1

2

3

4

5

6

7

8

time (min)

Figure 2. Adsorption of cochineal dye onto wool fabric mordanted with alum.

Figure 3 compares the rate of dye adsorption for the different mordants at room temperature. The mordant has an effect. Copper has the greatest absorption capacity at equilibrium, while alum is significantly lower. As the temperature increases the difference among the mordants lessens, as is shown in Figure 4.



45 40

qt (mg dye/ g wool)

35 30

25

Alum

20

Copper

15

Tin

10 5 0 0

1

2

3

4

5

6

7

8

time (min)

Figure 3. Adsorption of cochineal dye onto wool fabric mordanted with three different ions at 25oC.

45

40 35

qt (mg dye/ g wool)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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30

25

Alum

20

Copper

15

Tin

10 5 0 0

1

2

3

4

5

6

7

8

time (min)

Figure 4. Adsorption of cochineal dye onto wool fabric at 85oC.

3.2. Adsorption Isotherm


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Further information on the dyeing process can be obtained from equilibrium studies. The adsorption isotherm describes the relationship between the amount of cochineal dye adsorbed on the fabric surface and its concentration in the equilibrium solution at constant temperature. Thus, it represents the amount of cochineal dye bound to the fabric as a function of dye present in the solution. Several models have been published to describe the adsorption isotherm, but for the purposes of this research the two most frequently used models, the Langmuir and Freundlich isotherms, were employed to describe the relationship between the amount of cochineal dye adsorbed and its equilibrium concentration. Figures 5 and 6 show the equilibrium data for nine dye concentrations analyzed in triplicate. Replicate samples yielded equilibrium values within 4% of each other. Figure 5 shows the results for the three mordants at 75 C. Each mordant shows different behavior at equilibrium. At all initial dye concentrations, nearly all of the dye adsorbed onto the tin mordant – the equilibrium dye concentration in solution remained low compared to samples mordanted with copper and especially alum. Figure 6 compares the results for alum at different temperatures. At 85 C, the equilibrium data is significantly different from the data at lower temperatures and more of the dye is adsorbed onto the fabric.



35.00

qe (mg dye/g wool)

30.00 25.00 20.00 Alum

15.00

Copper Tin

10.00 5.00 0.00 0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Ce (mg dye/mL)

Figure 5. Isotherm data for all mordants at 75 C.

Alum 35.00 30.00

qe (mg dye/g wool)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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25.00 20.00

30 C

15.00

75 C

10.00

85 C

5.00 0.00 0.00

0.10

0.20

0.30

0.40

Ce (mg dye/mL)

Figure 6. Isotherm data for alum mordant.

3.2.1. The Langmuir isotherm The Langmuir adsorption model is based on the assumption that adsorption takes place at specific homogeneous sites, only one dye molecule may occupy a site, and the dye molecules do


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not interact. Once a complete monolayer has formed, no further adsorption can occur [3]. The saturated monolayer curve is represented by the expression:

𝐾 𝐶𝑒

𝑞𝑒 = 𝑞𝑚 1+𝐾𝐿

(3)

𝐿 𝐶𝑒

In equation 3, qe (mg dye/ g wool) is the adsorption capacity at equilibrium, qm (mg dye/ g wool) is the maximum monolayer adsorption capacity, Ce (mg dye/mL) is the equilibrium concentration of dye in the solution and KL (mL/mg) is the Langmuir equilibrium constant related to the affinity of binding sites. Equation 3 can be linearized, and the values of qm and KL are obtained from the slope and intercept of a plot of

𝐶𝑒 𝑞𝑒

versus Ce.

The data obtained from the Langmuir isotherm is summarized in Table 1. The values for the correlation coefficient (R2) obtained for all the mordants at all the temperatures ranged from 0.25-0.97, indicating that Langmuir model was not always a good fit. For each mordant, the fit was best at lower temperatures, but was seldom good. The lack of fit of the Langmuir isotherm indicates a heterogeneous distribution of active sites on the absorbent. Mordanting the wool produced binding sites that were not equivalent, which violates one of the key assumptions for the Langmuir isotherm. While the model did not fit all the data, the K L values indicated that the wool fabric had a maximum affinity for cochineal dye at lower temperature. Similar results have been obtained for other dyes [3].

Table 1. Langmuir isotherm constants for the adsorption of cochineal dye onto wool for all mordants at different temperatures



Mordant

Temperature (oC)

qm (mg dye/ g wool)

KL

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R2

(L/ mg dye)

Alum

65

1.4 x 10-3

0.47

Copper

24

23 x 10-3

0.93

Tin

30

Alum

550

Copper Tin

99 75

Alum Copper Tin

37

85

92

x 10-3

130

120

x 10-3

2.0 x 10-3 4.9 x 10-3

280

1.2 x 10-3

99

1.2 x 10-3

53

2.3 x 10-3

0.97

0.012 0.64 0.57

0.25 0.50 0.32

To determine whether the mordants showed statistically significantly different Langmuir isotherm constants, a comparison of the 95% confidence interval of KL and qm values was conducted using Minitab Statistical Software. A comparison of all the mordants at T=30oC (where the Langmuir model fit the data) indicated the maximum adsorption capacity, qm, for all of the mordants was not statistically significantly different at 95% CI. However, the Langmuir equilibrium constants, KL, for alum and tin were statistically significantly different from one another.

3.2.2. Freundlich isotherm The Freundlich isotherm assumes multisite adsorption on a heterogeneous surface, which differs from the Langmuir isotherm assumption of monolayer adsorption on a homogeneous surface. While the Langmuir isotherm assumes that the enthalpy of adsorption is independent of 12 ACS Paragon Plus Environment

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the amount adsorbed, the Freundlich isotherm equation can be derived assuming a logarithmic decrease in the enthalpy of adsorption with the increase in the fraction of occupied sites [9]. Hence the Freundlich isotherm model describes the equilibrium on heterogeneous surfaces and does not assume a monolayer capacity. This is possible especially with the multivalent metal mordants, where different sites with different adsorption energies may be involved.

The

Freundlich equation is: 1 𝑛

𝑞𝑒 = 𝐾𝐹 𝐶𝑒

(4)

In equation 4, KF and n are the Freundlich constants, and are representative of the adsorption capacity and adsorption intensity (or surface heterogeneity), respectively. Values of n greater than 1.0 represent favorable adsorption conditions [10]. Equation 4 can be linearized and the slope and intercept can be used to find n and KF, respectively. Table 2 summarizes the results.

Table 2. Freundlich constants for the adsorption of cochineal on wool for all mordants at different temperatures. Mordant

Temperature

n

(oC) Alum

R2

KF (mg dye/ g wool)

1.1

61

0.94

2.2

38

0.94

Tin

1.5

202

0.95

Alum

0.93

Copper

Copper Tin

30

75

74

0.97

1.2

110

0.94

1.4

160

0.95



Alum Copper Tin

85

Page 14 of 32

0.92

320

0.97

1.2

76

0.97

0.70

430

0.95

For the range of concentrations tested, the Freundlich isotherm fits the data, with all R2 greater than 0.94. The adsorption process is favorable with most values of n greater than 1.0 at 30 and 75 C. At temperatures above 80 C, wool fibers start to swell, tightly cling together and begin to entangle and “felt” [6,7,11]. This process may leave less space for the dye molecules, leading to a less favorable process. The adsorption capacity increases with temperature, with the tinmordanted wool exhibiting the highest value at all temperatures. This may be due to the presence of tin(IV) ions which can adsorb more dye molecules. Figures 7 and 8 show the 95% confidence intervals for the Freundlich constants along the xaxis, with the mordant and temperature on the y axis. While the replicates showed little error among them, for some experimental conditions, the 95% CI were large. Figure 7 shows that the values of the adsorption intensity constant, n, are not unique for each mordant.

At each

temperature, however, the adsorption intensity for two mordants is statistically significantly different from each other, while the third overlaps.


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12.0

10.0

Alum 30 8.0

Copper 30 Tin 30 Alum 75

6.0

Copper 75 Tin 75

4.0

Alum 85 Copper 85

2.0

Tin 85

0.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

Adsorption intensity constant, n [-]

Figure 7. 95% confidence intervals for the adsorption intensity constant, n.

At 30 and 75 C, the value of the adsorption capacity constant, Kf, for tin is statistically significantly different from that for copper and alum but the 95% confidence interval is large (see Figure 8). The results for tin were less reproducible than those for alum or copper. Perhaps this is due to the different ionic charges possible (Al3+, Cu+ and Cu2+, Sn2+ and Sn4+). Perhaps the presence of tin(IV) affected the reproducibility. At 85 C, where the wool is felted, the constant for copper is different from that for tin and alum. Thus the mordant affects the adsorption isotherm constants, perhaps through the different ionic charges.



Page 16 of 32

12.0

10.0

Alum 30 8.0

Copper 30 Tin 30 Alum 75

6.0

Copper 75 Tin 75

4.0

Alum 85 Copper 85

2.0

Tin 85

0.0 0.0

100.0

200.0

300.0

400.0

500.0

600.0

700.0

800.0

Adsorption capacity constant, Kf [mL/g wool]

Figure 8. 95% confidence intervals for the adsorption capacity constant. The

3.2.3. Effect of temperature on the thermodynamic parameters Thermodynamic parameters for the equilibrium adsorption process were calculated to further understand the effect of temperature on cochineal dye adsorption equilibrium. The change in the Gibbs free energy (∆Go), enthalpy (∆Ho) and entropy (∆So) are used to determine whether the adsorption is physical or chemical in nature. Kc, the equilibrium constant, was first calculated according to equation 5: 𝐾𝑐 =

𝐶𝑎𝑑,𝑒

(5)

𝐶𝑒

where Cad,e (mg dye/mL) is the equilibrium dye concentration adsorbed onto the fabric calculated as the difference between the initial dye concentration, Co, and the dye remaining in the vial at


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equilibrium, Ce (mg dye/mL). Knowing the equilibrium constant for a process, the Gibbs free energy can be calculated according to equation 6: ∆𝐺 𝑜 = −𝑅𝑇𝑙𝑛𝐾𝑐

(6)

where R is the gas constant (8.314 J/mol K), and T is the absolute temperature in Kelvin. The enthalpy and entropy of adsorption were calculated from the slope and intercept of a Van’t Hoff plot of equation 7: ln 𝐾𝑐 =

∆𝑆 𝑜 𝑅

−

∆𝐻 𝑜

(7)

𝑅𝑇

Plotting ln(Kc) as a function of 1/T yields a slope of -(∆Ho/R) and an intercept of (∆So/R). Nine initial of cochineal dye concentrations (each in triplicate) were used for the equilibrium experiments. The Gibbs free energy, enthalpy and entropy values were determined from the equilibrium data for each dilution used to dye wool mordanted with alum, copper and tin mordants. All values of the Gibbs free energy, enthalpy and entropy for each dilution and mordant combination were negative.

The negative Gibbs free energy indicates the adsorption of

cochineal onto mordanted wool is spontaneous and thermodynamically favorable. Generally, the Gibbs free energy change for physical adsorption is in the range of 0 – 20 kJ/mol, and for chemical adsorption is in the range of 80 – 400 kJ/mol [12]. The values obtained in this study were all less than 10 kJ/mol, confirming that the adsorption of cochineal dye on wool is a physical adsorptive process. The negative values of the change in enthalpy show that adsorption is exothermic as has been found in other studies [10]. The negative values of ∆So indicate the dye adsorption process decreases randomness, as expected [13].



The Gibbs free energy change can be calculated at each temperature, and is shown in Figures 9 to 11. At 30 C, ∆Go is affected by the initial dye concentration only for the copper mordant. At the higher temperatures, concentration had no significant effect for any mordant. ∆Go values were not affected by temperature for tin, but alum showed a more negative value at 85 C. At a higher temperature, the dye adsorption was more favorable; again, this is to be expected.

Temp= 30oC 10 9 8

|Δ Go| (kJ/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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7 6 5

Alum

4

Copper

3

Tin

2 1 0 0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

Initial Concentration (mg dye/mL)

Figure 9. Absolute values of ∆Go for 9 different tin, copper and alum dilutions at 30oC


Page 19 of 32

Temp= 75oC 10 9

|Δ Go| (kJ/mol)

8 7 6

5

Alum

4

Copper

3

Tin

2 1

0 0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

Concentration (mg dye/mL)

Figure 10. Absolute values of ∆Go for 9 different tin, copper and alum dilutions at 75oC

Temp= 85oC

|Δ Go| (kJ/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


10 9 8 7 6 5 4 3 2 1 0

Alum Copper

Tin

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1


Figure 11. Absolute values of ∆Go for 9 different dilutions of tin, copper and alum at 85oC

The bar charts in figures 12 and 13 show the absolute value of enthalpy and entropy changes as a function of dye concentration. The change in enthalpy and entropy for alum and tin was not



significantly affected by the dye concentration. However, the enthalpy and entropy of coppermordanted wool was affected by the dye concentration.

As the concentration of the dye

increased, both enthalpy and entropy values decreased.

45 40

|Δ Ho| (kJ/mol)

35 30 25

Alum

20

Copper

15

Tin

10 5 0 0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1


Figure 12. Average values of |∆H|o obtained for 9 different dilutions for alum, copper and tin at 30, 75 and 85oC.

120 100

|Δ So | (J/ mol K)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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80 Alum

60

Copper

40

Tin

20 0 0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1



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Figure 13. Average values of |∆S|o obtained for 9 different dilutions for alum, copper and tin at 30, 75 and 85oC.

3.3. Kinetics of adsorption Adsorption kinetics establishes the dye uptake rate, which determines the residence time required for the dyeing process and helps to evaluate dye-mordant-adsorbent combinations and applications [14]. In this study, the effect of temperature on adsorption kinetics was studied using a batch technique for all mordants. The data was fit to pseudo first order and second order kinetic models to examine the controlling mechanism of adsorption and potential rate controlling steps. 3.3.1. Pseudo-first order kinetics model In 1898, Lagergren presented a first order rate equation for the adsorption of ocalic acid and malonic acid onto charcoal [15]. Since that time, nearly 200 papers have used this model to describe solid adsorption kinetics, and it is applicable to a wide range of systems including dye adsorption [16]. It is called a pseudo-first order rate equation to indicate the kinetics are between a liquid and a solid, instead of two liquids. The model describes only the sorption sites, and not the entire adsorption process. Since the concentration of dye is present in excess, it can be adsorbed at a constant rate. The rate depends only on the access to adsorption sites. The ratelimiting step is diffusion – independent of concentration – and thus the process is called physisorption [17]. Lagergren’s differential equation is: 𝑑𝑞𝑡 𝑑𝑡

= 𝑘1 (𝑞𝑒 − 𝑞𝑡 )

(8)



Page 22 of 32

where k1 (min-1) is the rate constant for the pseudo first order adsorption, and qe and qt (mg dye/ g wool) are the adsorption density at equilibrium and at time t, respectively. Using the boundary conditions that qt= 0 at time = 0 and qt= qt at time = t, and integrating, yields ln(𝑞𝑒 − 𝑞 𝑡 ) = 𝑙𝑛𝑞𝑒 − 𝑘1 𝑡

(9)

Thus, a plot of ln(qe-qt) as a function of time should be linear with the slope being the rate constant. In addition, a calculated value of the adsorption density at equilibrium, qe, can be obtained from the y-intercept. In order to investigate the pseudo-first order kinetics model, qe,exp values were determined from the experimental data.

The first order rate constant k1 and

equilibrium adsorption density (qe,cal) were then calculated from the slope and the intercept of the plot of equation 9. A nonlinear least squares method was also applied to the data to determine the parameters to avoid the high weight placed on initial data values and the estimate of the equilibrium adsorption density. No significant difference was found. 3.3.2. Pseudo-second order kinetics model Experimental data was also tested with pseudo second-order kinetic model which is based on adsorption equilibrium capacity [3,8,18]. The adsorption mechanism is the rate-controlling step in the chemisorption process [19]. The model can be expressed as: 𝑑𝑞𝑡 𝑑𝑡

= 𝑘2 (𝑞𝑒 − 𝑞𝑡 )2

(10)

where k2 (g wool/ mg dye min) is the rate constant for pseudo second-order process. The driving force (qe-qt), is proportional to the available fraction of active sites. Integrating equation 10 and applying the same boundary conditions as before yields 1

1

(𝑞𝑒−𝑞𝑡 )

= 𝑞 + 𝑘2 𝑡

(11)

𝑒

which can be linearized to: 𝑡 𝑞𝑡

=𝑘

1 2 2 𝑞𝑒

1

+𝑞 𝑡

(12)

𝑒


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The second-order rate constant (k2) and the adsorption capacity at equilibrium (qe), were calculated from the intercept and slope of equation 12.

Table 3 summarizes the data from the first and second order kinetic models. Comparing the correlation coefficients for the two models shows that the R2 values for the first-order models were all above 0.98, while for the second order model they ranged from 0.63 – 0.99, with a median value of 0.95. In addition, the difference between the experimental and calculated values of the equilibrium dye adsorption, qe,cal, showed less than 2% difference for the first order model, but showed significant deviation for the second order model.

Finally, the first order rate

constant, k1, constantly increases with temperature for all mordants. The second order rate constant shows some variation. Thus, it was determined that the first order model is a better representation for the adsorption of cochineal dye onto mordanted wool, and the process is likely controlled by physisorption. While some dyeing processes have been better represented by chemisorption, the presence of the mordant in this investigation likely has an effect.


Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

Page 24 of 32

Table 3. Parameters from kinetic experiments for the first and second order dye adsorption models.

Pseudo first-order model

Pseudo second-order model

% error Mordant

Temperature

(oC)

qe,exp

(mg dye/

k1

(min-1)

qe,cal

(mg dye/ g wool)

g wool)

Alum

between

% error R2

qe,exp and

k2

(g silk/ mg dye min)

qe,cal

qe,cal

(mg dye/ g wool)

between

R2

qe,exp and qe,cal

52.4

0.192

52.1

0.6

0.99

0.00250

69.4

25

0.94

78.2

0.0965

78.2

0

0.99

0.000408

137

43

0.95

Tin

54.4

0.138

54.2

0.4

0.99

0.00114

84

35

0.95

Alum

30.1

0.370

30.4

1.0

0.99

0.0090

39.1

23

0.99

32.3

0.167

32.4

0.3

0.99

0.0023

36

0.97

Copper

Copper

25

75

50.5


Page 25 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47


Tin

20.2

0.269

20.3

0.5

0.99

0.00213

45

55

0.63

Alum

30.3

0.375

30.7

1.3

0.99

0.00815

40.5

25

0.99

37.5

0.226

37.3

0.5

0.99

0.00219

62.1

40

0.95

18.3

0.362

18.0

1.7

0.98

0.0155

23.5

22

0.98

Copper

Tin

85



To determine whether the three mordants used showed statistically significantly different kinetics at each temperature, 95% confidence intervals of the pseudo first-order rate constants were determined. Figure 14 is a graphical representation of the values. The results indicate that all three mordants had statistically significantly different rate constants at 25 and 75oC. However, at 85oC, only copper had a significantly different rate constant. The rate constant for alum and tin overlapped. Furthermore, the pseudo first order rate constants obtained for copper and tin were statistically significantly different at all temperatures, but the rate constant for alum overlapped at 75 and 85 C. This may be due to wool fiber swelling and felting.

0.45 0.40 0.35

ln(k) [k in minutes]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 32

0.30 0.25

Alum

0.20

Copper

0.15

Tin

0.10 0.05 0.00 0.0025

0.0027

0.0029

0.0031

0.0033

0.0035

1/T [1/K]

Figure 14. Comparison of the first order rate constant with 95% confidence intervals for different mordants at different temperatures.

3.3.3 Activation parameters

ACS Paragon Plus Environment

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Since the pseudo first-order kinetic model was identified as the best suitable kinetic model for the adsorption of cochineal dye onto wool fabric, the pseudo first-order rate constants at different temperatures were used to calculate the activation energy of the adsorption process using the Arrhenius equation as shown in equation 13: ln𝑘 = ln 𝐴 −

𝐸𝑎

(13)

𝑅𝑇

In this equation, Ea, is the activation energy (kJ/mol), R is the gas constant (8.314 J/mol K) and A is the Arrhenius pre-exponential factor. The activation energy was determined from a plot of the data. Table 4 lists the values of Ea for the three mordants. Typical values of activation energy range from 11 – 40 kJ/mol [3, 10, 17]. The Ea values in this study fall in that range. Further, ranges of 8 – 25 kJ/mol are typical for physisorption processes, again indicating that is the mechanism for this process [20]. The lower activation energy shows that weak intermolecular forces are involved rather than stronger chemical bonds. The positive value of activation energy for all mordants indicated that the process is exothermic with a positive forward activation barrier. Alum required the lowest activation energy for the adsorption of cochineal whereas tin required the highest activation energy, but the differences are small.

Table 4. Activation energy and thermodynamic parameters for adsorption kinetics. Mordant

Temperature

Ea

R2

∆H#

∆S#

∆G#

R2

(oC)

(kJ/mol)

(eqn 17)

(kJ/mol)

(J/mol K)

(kJ/mol)

(eqn 18)

25 Alum

75

77.1 10.4

0.99

7.72

-233

88.5

85

91.1

25

78.8

0.97


27


Copper

75

Tin

11.5

0.95

8.79

-235

Page 28 of 32

90.4

85

92.9

25

77.9

75

0.97

13.3

10.6

-226

85

0.92

0.95

89.0 91.5

The changes in enthalpy (∆H#), entropy (∆S#), and free energy (∆G#) of activation were also calculated using the Eyring equation: 𝑘

𝑘

ln (𝑇) = ln ( ℎ𝑏) +

∆𝑆 # 𝑅

−

∆𝐻 #

(14)

𝑅𝑇

In this equation kb and h represent the Boltzmann and Planck constants, respectively. The changes in enthalpy of activation (∆H# ) and entropy of activation (∆S#) were calculated from the slope and intercept of a plot of ln(k/T) versus 1/T using the first order rate constants from Table 3. Finally, the change Gibbs free energy of activation (∆G#) values were calculated in terms of enthalpy and entropy using the following equation: ∆𝐺 # = ∆𝐻# − 𝑇∆𝑆 #

(15)

at each temperature. Table 4 summarizes the data. The positive values obtained for ∆H# for all mordants confirms that the process is exothermic with a positive forward activation barrier and the negative value for ∆S# obtained for all mordants reflects the interaction between cochineal dye and wool fabric. The values of ∆G# increased with temperature and were positive, suggesting that the adsorption reaction requires energy. The 95% confidence interval for the values of activation energy, and changes in enthalpy and entropy of activation were also determined. With data from only three temperatures, the 95% CI for the values of ∆H#, ∆S# and Ea overlapped for all mordants (data not shown).


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Conclusions The choice of mordant is important when developing a natural dyeing process. The mordant not only affects the color shade, but also affects the kinetics and thermodynamics. The adsorption of cochineal dye onto mordanted wool can be modeled by the Freundlich equation, which is in agreement with previous results [21]. This model assumes a physisorption process with a multilayer of adsorbate possible, which is likely with multivalent mordants. The value of the adsorption intensity constant, n, is greater than 1.0 indicating a favorable process as long as the temperature is below the felting temperature of wool (about 80 C). The choice of mordant affects both the adsorption intensity constant and the adsorption capacity constant. The thermodynamic parameters thermodynamically favorable.

indicate that the adsorption is spontaneous and

The range of Gibbs free energy values again indicate a

physisorption process. The kinetics are best modeled by a pseudo-first order equation when a mordant is included in the process. The choice of mordant has a statistically significant effect on the rate constant. In addition, the activation energy values fall into the physisorption range.

Acknowledgment We gratefully acknowledge the Chemical and Biomolecular Engineering department at Lafayette College for its support of our project. Competing Interests The authors have no competing interests to declare. Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.


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References 1. Dutton, L.M. Cochineal: A Bright Red Animal Dye, (Unpublished master’s thesis). Baylor University, Waco, TX, 1992. http://www.cochineal.info/. 2. Samanta, A.K.; Konar, A. Dyeing of Textiles with Natural Dyes, Natural Dyes, edited by Dr. E.A. Kumbasar, IntechOpen, 2011, pp 29-56. DOI: 10.5772/21341. Available from: https://www.intechopen.com/books/natural-dyes/dyeing-of-textiles-with-naturaldyes 3. Chairat, M.; Rattanaphani, S.; Bremner, J.B.; Rattanaphani, V. An Adsorption and Kinetic Study of Lac Dyeing on Silk. Dyes and Pigments. 2005, 64, 231. 4. Septhum, C.; Rattanaphani, S.; Bremner, J.B.; Rattanaphani, V. An Adsorption Study of Alum-morin Dyeing onto Silk Yarn. Fibers and Polymers, 2009, 10, 481. 5. Raisanen, R.; Nousiainen, P.; Hynninen, P.H. Emodin and Dermocybin Natural Anthraquinones as Mordant Dyes for Wool and Polyamide. Textile Research Journal, 2001, 71, 1016. 6. Kamel,M.M.; El-Shishtawy,R.M.; Yussef, B.M.; Mashaly, H. Ultrasonic Assisted Dyeing. II. Dyeing of Wool with Lac as a Natural Dye. Dyes and Pigments. 2005, 65, 103. 7. Nasirizadeh, N.; Dehghanizadeh, H.; Yazdanshenas, M.E.; Moghadam, M.R.; Karimi,A. Optimization of Wool Dyeing with Rutin as Natural Dye by Central Composite Design Method. Industrial Crops and Products. 2012, 40, 361. 8. Chairat, M.; Rattanaphani, S.; Bremner, J.B.; Rattanaphani, V. Adsorption kinetic study of Lac Dyeing on Cotton. Dyes and Pigments 2008, 76, 435. 9. Meroufel, B.; Benali, O.; Benyahia, M.; Benmoussa, Y.; Zenasi, M.A. Adsorptive Removal of Anionic Dye From Aqueous Solutions by Algerian Kaolin: Characteristics, Isotherm, Kinetic and Thermodynamic Studies. J. Mater. Environ. Sci. 2013, 4, 482. 10. Chiou, M. S.; Li H.Y. Equilibrium and Kinetic Modeling of Adsorption of Reactive Dye on Cross-linked Chitosan Beads. Journal of Hazardous Materials 2002, B93, 233. 11. Dobozy, O.K. Cause of Wool Felting. Textile Research Journal 1958, 28, 717. 12. Sawasdee, S.; Watcharabundit, P. Equilibrium, Kinetics and Thermodynamics of Dye Adsorption by Low- Cost Adsorbents. International Journal of Chemical Engineering and Applications 2015, 6, 444. 13. Kumar, U. Thermodynamics of the Adsorption of Cd (II) from Aqueous Solution on NCRH. International Journal of Environmental Science and Development 2011, 2, 334. 14. Qui, H.; Lv, L.; Pan, B.; Zhang, Q.; Zhang, W. Critical Review in Adsorption Kinetic Models. Journal of Zhejiang University 2009, 10, 716. 15. Lagergren, S. Zur Theorie der Sogenannten Adsorption Geloster Stoffe, K. Sven. Vetenskapsakad. Handl. 1898, 24, 1. 16. Ho, Y.S. Citation Review of Lagergren Kinetic Rate Equation on Adsorption Reactions. Scientometrics 2004, 59, 171. 17. Ho, Y.S.; McKay, G. Sorption of Dye from Aqueous Solution by Peat. Chemical Engineering Journal 1998, 70, 115.


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18. Dogan M.; Alkan M. Adsorption Kinetics of Methyl Violet onto Perlite. Chemosphere 2003, 50, 517. 19. Chiou, M.S.; Li, H.Y. Adsorption Behavior of Reactive Dye in Aqueous Solution on Chemical Cross-linked Chitosan Beads. Chemosphere 2003, 50, 1095. 20. Engineering Department, NTPEL, IIT-Bombay Course Coordinator, “Surface Chemistry”, 2009, http://nptel.ac.in/courses/122101001/35#. 21. Tang, R.-C.; Tang, H.; Yang, C. Adsorption Isotherms and Mordant Dyeing Properties of Tea Polyphenols on Wool, Silk and Nylon. Ind. Eng. Chem. Res. 2010, 49, 8894.


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Effect of Mordanting on the Adsorption Thermodynamics and Kinetics

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