Kinetics of Hydrolytic Depolymerization of Textile Waste Containing Polyester

Abstract

Textile products comprise approximately 10% of the total global carbon footprint. Standard practice is to discard apparel textile waste after use, which pollutes the environment. There are professional collectors, charity organizations, and municipalities that collect used apparel and either resell or donate them. Non-reusable apparel is partially recycled, mainly through incineration or processed as solid waste during landfilling. More than 60 million tons of textiles are burnt or disposed of in landfills annually. The main aim of this paper is to model the heterogeneous kinetics of hydrolysis of multicomponent textile waste containing polyester (polyethylene terephthalate (PET) fibers), by using water without special catalytic agents or hazardous and costly chemicals. This study aims to contribute to the use of closed-loop technology in this field, which will reduce the associated negative environmental impact. The polyester part of waste is depolymerized into primary materials, namely monomers and intermediates. Reaction kinetic models are developed for two mechanisms: (i) the surface reaction rate controlling the hydrolysis and (ii) the penetrant in terms of the solid phase rate controlling the hydrolysis. A suitable kinetic model for mono- and multicomponent fibrous blends hydrolyzed in neutral and acidic conditions is chosen by using a regression approach. This approach can also be useful for the separation of cotton/polyester or wool/polyester blends in textile waste using the acid hydrolysis reaction, as well as the application of high pressure and the neutral hydrolysis of polyester to recover primary monomeric constituents.

1. Introduction

The textile sector uses a huge quantity of raw materials and produces a substantial amount of different types of waste. This is partly because, to date, only a small number of wearable textiles are reused, regenerated, or recycled. Most of these textiles are still sent to landfill or incinerated, with a high negative environmental impact (mainly relating to the generation of CO₂ and other gaseous pollutants).

Global population growth and improvements in living standards have caused an increase in the consumption of textiles. This has resulted in the growth in textile production during the past few decades [1,2] and, consequently, in the increase in the amount of textile waste. Major components of textile products are natural (bio-organic) fibres (cotton—36% and wool—2%) and man-made fibres (synthetic and cellulosic—62%) [3] (Figure 1). The raw materials of synthetic fibres are based on petroleum, which is a non-renewable resource. Even the production of renewable natural polymers demands non-renewable resources, such as the supply of energy, chemicals for finishing, and synthetic dyestuffs, etc.

Sustainability in the textiles industry is connected with the environmental impact of textiles and the waste products. This has led to increased demand for products manufactured with a minimal negative impact on the world. The demand for “green”, bio-based textiles is therefore steadily growing [4,5].

The main benefits of using recycled raw materials, instead of virgin ones, are the use of natural resources, reduced energy consumption, the suppression of carbon dioxide (CO₂) and other emissions, and the avoidance of the presence of textile waste in landfills. Some of these products, of course, have higher prices than their traditional counterparts. This is partly due to the fact that the cost of waste collection, sorting, pretreatment, and recycling has not been fully passed on to consumers. The supply of waste prepared in a form suitable for recycling (by, for e.g., grinding) is also limited.

This situation is similar for other types of urban and public waste.

For e.g., today, approximately one quarter of drinking bottles made from polyester used in the United States are recycled and this percentage is increasing year by year. These products also tend to be made using bio-based polymers, through more efficient processes. Thus, the higher cost is mitigated by the longer-term benefits gained by protecting the environment.

Today, single-component textile materials are rarely used. The use of two or more component mixtures is much more common. In addition, fiber blends are created in a unique form. Thus, making recycling ever more challenging. Due to the interesting combination of properties including durability, comfort, drape, and elasticity, etc., the delivery of such attributes is the most common use of mixtures of natural and synthetic fibers. However, in the textile industry, combinations of different synthetic fibers, as well as various natural fibers, are also used.

In general, the most widely used textile blend consists of cotton and polyester. These fibers are also global leaders in the production of natural and man-made fibers, respectively. Cotton contributes to properties including comfort, softness, absorption, and breathability, while the presence of polyester delivers ease of care, durability, mildew and abrasion resistance, moisture management, and low-priced clothing. It is common to use this blend in lingerie, shirts, and trousers, etc., and a lot of polyester/viscose blends with similar properties are used in these applications.

Among conventional textile materials, polyester and wool mixtures are used for other end uses, such as men’s jackets and trousers, women’s trousers, and clothing for colder months. Wool used in a mixture with polyester provides insulating value and reduces static pouring and pilling of the material. In contrast, polyester improves dimensional stability and reduces the final price of the product.

In the last few decades, several studies have been carried out that deal with the separation of textile mixtures, especially mixtures of cellulose and polyester, which are commonly used in practice [6]. Serad [7] and colleagues patented the process of separating textile products from a mixture of polyester and cotton using a sulfone solvent. The polyester was dissolved, and filtration yielded pure, relatively undamaged cotton. Optimal separation conditions were achieved when the mixture was treated in a solvent (tetramethylene sulfone) for 90 min at 150 °C; then, the temperature was increased to 190 °C for a period of 35 min.

Ouchi [8] and colleagues have developed a successful two-phase process for separating the mixture from a fabric. It consists of a short-lived process involving the irrigation of the fabric in H₂SO₄ (10 M) at an elevated temperature, followed by a process involving strong mechanical treatment of the sample in water at room temperature. Treatment of the fabric in acid at 95 °C for one minute is effective, but after the mechanical step, cellulose fibers in the form of fine powder are removed from the fabric.

PET is used as a high-molecular-weight polymer (intrinsic viscosity, 0.82 dL/g) in bottles for packaging potable liquids [9]. It is also used as a moderate-molecular-weight polymer (intrinsic viscosity, 0.6 dL/g) for the production of textile fibers, with the highest overall consumption. There are plenty of different ways to carry out the chemical recycling of PET via depolymerization, such as hydrolysis using alkalis and acid, methanolysis, glycolysis, the use of ionic liquid, and combinations of techniques, such as glycolysis–methanolysis, glycolysis–hydrolysis, and methanolysis–hydrolysis [5]. The present paper deals with the description of more environmentally friendly (without catalysts or hazardous chemicals) recycling, involving heterogeneous reaction kinetics using neutral hydrolysis of PET fibers and acid hydrolysis of cotton or wool and PET/cotton textile waste.

2. Theory

The bulk of the global textiles market consists of a multicomponent mixture of PET, cotton, and wool. The neutral hydrolytic degradation kinetics of PET made from pure components has been extensively described in the literature [10,11,12,13], while acid [14,15,16,17] and basic [18,19,20,21] hydrolysis of PET has also been studied. The pure components of cellulose and wool [22,23] degradation have also been investigated.

The hydrolysis of PET, cotton, and wool fibers involves a heterogeneous reaction, taking place primarily at the fiber surface. The reaction rates measured from the concentrations in the fluid surrounding the particle reflect the relative resistance of each reaction step in the hydrolytic depolymerization process. There are three fundamental rate controlling steps [24,25,26] consisting of: (i) the diffusion (external) of the penetrant (water) across the film of the product (ethylene glycol) to the surface of the PET, (ii) the diffusion/transport into the pores/cracks, and (iii) the reaction at the solid surface (Figure 2). Hence, these three resistances can be evaluated to define the controlling mechanism. It is possible to have more than one rate step determining the overall rate, namely the combination of any two or more steps. Figure 2 shows the simultaneous fragmentation and depolymerization of PET during the neutral hydrolysis process. As the temperature is increased, beginning with pure PET in water, cracks/pores are created in the solid surface. This is followed by the penetration of water into the cracks and simultaneous depolymerization, with the formation of the products terephthalic acid (TPA) and ethylene glycol (EG). The water must be transported across the film of the EG to enter the pores and continue to react with the surface [10].

A simplified reaction mechanism, with the derivation of the integral kinetic equation that eventually makes it possible to determine some of the physical, chemical, and thermodynamic parameters, is developed. Assume the circular fiber has a length h [m] that is much greater than its radius R, h >> 2R (see Figure 3). Ideally, this fiber can be divided into very small cubic particles, with an edge size d [m] (see Figure 3).

Using simple geometry, it can be found that the surface of fiber S [m²] is equal to:

$$S=2h\pi R$$

(1a)

The initial number of particles in this ideal fiber n_V is equal to:

$$n_V={\displaystyle \frac{h\pi R^2}{d^3}}$$

(1b)

The initial number of particles on the fiber surface n_S can be simply calculated as:

$$n_S={\displaystyle \frac{S}{d^2}}={\displaystyle \frac{2h\pi R}{d^2}}$$

(1c)

The reaction rate of hydrolysis can be controlled by either the surface reaction or the transport of the active liquid responsible for hydrolysis into the pores/cracks, as is discussed in the next chapter.

2.1. Hydrolysis Controlled by the Surface Reaction Rate

Here, the rate-controlling step is the surface reaction rate, which is significantly faster than the transportation of the active penetrant inside the solid material (fiber). Hence, the concentration gradient and the concentration of the hydrolysis products may be neglected. Then, the reaction rate expressed as the time change in terms of the actual number of particles in the fiber n(t), expressed in [mol], is proportional to the reaction surface, and after rearrangements it has the form:

$${\displaystyle \frac{dn\left(t\right)}{dt}}=-2k\sqrt{{\displaystyle \frac{\pi h}{d}}}\sqrt{n\left(t\right)}$$

(2)

where k [1/s] is the reaction rate constant. The solution to this differential equation has the form:

$$n\left(t\right)={\displaystyle \frac{k^2\pi h}{d}}{t}^2-2Ck\sqrt{{\displaystyle \frac{\pi h}{d}}}t+C^2$$

(3)

where C is the constant of integration. Using these boundary conditions:

(a)

initially is $n\left(t=0\right)=n_V$,

(b)

at the end of the reaction time t_E is $n\left(t=t_E\right)=0$ and it can be found that $C=\sqrt{n_V}$. The end of the reaction time can be calculated as $t_E={\displaystyle \frac{\sqrt{n_V}}{k}}\sqrt{{\displaystyle \frac{d}{\pi h}}}$.

The final integral form of the kinetics of the surface reaction equation is then equal to:

$$n\left(t\right)={\displaystyle \frac{k^2\pi h}{d}}{t}^2-2k\sqrt{{\displaystyle \frac{\pi h{n}_V}{d}}}t+n_V$$

(4)

A typical reaction kinetics curve is displayed in Figure 4. There is no equilibrium and the reaction ends in finite time t_E. The unknown parameter $k^2\pi h/d$ can be calculated from the experimental reaction data (dependence of the fiber mass on time $0\le t\le t_E$) at a constant temperature T. Since quantities h and d are not dependent on the temperature, it is possible to calculate the activation energy E_A from experimental data measured at different temperatures using, for e.g., the simple Arrhenius relationship $k=A\exp \left(-{\displaystyle \frac{E_A}{RT}}\right)$.

The mean molecular weight of the soluble particles M_p [g/mol] is equal to $M_p=d^3{\rho }_c{N}_A$, where ${\rho }_c$ [kg/m³] is the density of the fiber. Equation (4) can then be rewritten for the mass. Also, for a given fiber mass and certain critical properties of fibers, such as the molecular weight (MW) and density ${\rho }_c$, etc., the logarithm of the reaction time is proportional to the reciprocal absolute temperature (Kelvin) $t_E\propto 1/T$.

The reaction order with respect to the monomer product is 0.5, based on Equation (2). The order with respect to the solid phase is considered to be zero, as the reaction only takes place on the surface, with a constant surface concentration per unit area. The concentration of water (as the active penetrant) is considered constant at a given temperature.

2.2. Penetrant Diffusion into the Cracks

In the case of penetrant diffusion into the cracks as the rate-controlling step, the initial reaction rate is low, caused by surface penetration of the solvent (water) into the fiber volume. The effect of this behavior can be considered by an additional factor $bt\sqrt[3]{n(t)}$ in Equation (2), which represents the resistance term for water transportation. Quantity b [1/s] represents the solvent penetration rate constant.

Quantity $\sqrt[3]{n(t)}$ is proportional to the size of a particle, with the increase in bt indicating an increasing number of particles in contact with the water. The corresponding differential equation has the form:

$${\displaystyle \frac{dn\left(t\right)}{dt}}=-2kb\sqrt{\frac{\pi h}{d}}{\left[n\left(t\right)\right]}^{\frac{5}{6}}t$$

(5)

The solution to this differential equation leads to the following equation:

$$n\left(t\right)={\left(-{\displaystyle \frac{1}{6}}kb\sqrt{{\displaystyle \frac{\pi h}{d}}}{t}^2+C\right)}^6$$

(6)

The corresponding kinetic plot is shown in Figure 5. The integration constant is $C=\sqrt[6]{n_V}$ and for the end-of-reaction time t_E is valid.

$$t_E={\displaystyle \frac{\sqrt{6}\sqrt{kb{\left(\frac{\pi h}{d}\right)}^{\frac{1}{2}}C}}{kb{\left(\frac{\pi h}{d}\right)}^{\frac{1}{2}}}}$$

(7)

Parameter b is specific to the heterogeneous reaction, with the transportation of the penetrant. It is defined as the solvent penetration rate in the solid phase. The penetration rate constant D [1/s²] (with respect to surface geometry) is expressed as $D=-{\displaystyle \frac{1}{6}}kb\sqrt{{\displaystyle \frac{\pi h}{d}}}$. It is composed of a kinetic term $kb$ (reaction rate constant) and a geometric term $-{\displaystyle \frac{1}{6}}\sqrt{{\displaystyle \frac{\pi h}{d}}}$. It can be thought of as the penetration reaction rate controlling constant with respect to surface geometry. The kinetic term depends on the temperature, while the geometric term is constant. From the reaction kinetic data, it is only possible to estimate the value of D, which is proportional to the reaction rate constant and, therefore, can be used to find the activation energy of the reaction using the Arrhenius equation. If the reaction, for some reason, is not measured from the beginning or is measured in different units (grams, %, etc.), i.e., n(t = 0) ≠ 1, an estimable scale parameter Q_S [−] may be introduced without a loss of generality, so Equation (6) becomes:

$$n\left(t\right)=Q_S{\left(-{\displaystyle \frac{1}{6}}kb\sqrt{{\displaystyle \frac{\pi h}{d}}}{t}^2+C\right)}^6$$

(8)

Parameter C corresponds to the initial amount of the polymer at time t = 0.

The parameters of the suggested models can then be estimated from the experimental data using nonlinear regression, with the criterion of least squares in terms of the deviation of the experimental points from the model course. The reaction order with respect to the monomer product is roughly 5/6, according to Equation (5). As stated previously, the order with respect to the solid phase is considered to be zero, as the reaction only takes place on the surface, with a constant surface concentration per unit area. The concentration of water is considered constant at a given temperature.

2.3. Multicomponent Degradation Analysis

The theory developed for a single solid component can be extended to the case of surface reaction control for the multicomponent blend composed of p components with relative molar ratios r_i, where ${\displaystyle \sum _{i=1}^p{r}_i=1}$.

Consider the case of the molar reaction rate of an i-th component expressed as:

$${\displaystyle \frac{d{n}_i\left(t\right)}{dt}}=-2k_i\sqrt{{\displaystyle \frac{\pi h_i}{d_i}}}\sqrt{n_i\left(t\right)}$$

(9)

The total molar amount is $n(t)={\displaystyle \sum _{i=1}^p{n}_i(t)}$.

The solution to this differential equation has the form:

$$n(t)={\displaystyle \sum _{i=1}^p{n}_i(t)}={\displaystyle \sum _{i=1}^p{r}_{i}n(t)}={\displaystyle \sum _{i=1}^p{r}_i\left(\frac{k_i^2\pi h_i}{d_i}{t}^2-2k_i\sqrt{\frac{\pi h_i{n}_{Vi}}{d_i}}\mathrm{t}+n_{Vi}\right)}$$

(10)

Here, indexed quantities correspond to components with known molar ratios r_i. The kinetics plot for the component blend is shown in Figure 6. The degradation curve indicates two distinct regions (the plots are for a two-component blend) consisting of a region with a rapid decline (steep slope), followed by a region of slow decay. The region of rapid decline appears first, followed by the region with a more gradual slope.

In the case of water transportation (diffusion) in the solid phase as the rate-controlling step for a multicomponent blend, the molar reaction rate of the i-th component is expressed as:

$$\frac{d{n}_i(t)}{dt}=-2k_i{b}_i\sqrt{\frac{\pi h_i}{d_i}}{\left[n_i(t)\right]}^{\frac{5}{6}}t$$

(11)

The solution to this differential equation has the form:

$$n(t)=Q_S{\displaystyle \sum _{i=1}^p{r}_i}{\left(-{\displaystyle \frac{1}{6}}{k}_i{b}_i\sqrt{{\displaystyle \frac{\pi h_i}{d_i}}}{t}^2+C\right)}^6$$

(12)

The fibrous blend hydrolysis kinetics at different temperatures are shown in Figure 7.

For our models, we consider the total number of particles available, n_V, in terms of the cylindrical fiber geometry for the degradation reaction. In the case of pure component hydrolytic kinetics and surface reaction rate control, the decline in the active site is instantaneous in terms of time. The nature of the decline is concave in shape towards the ordinate. With increasing temperature, the slope of the decline is steeper than at a reduced temperature. The magnitude of the decline is governed by the activation energy of the reaction. The order with respect to the solid phase is considered to be zero, as the reaction only takes place on the surface, with a constant surface concentration per unit area.

In the case of multicomponent blend kinetics, we present conversion curves for two components only. The conversion curves have two distinct zones, due to the presence of two components in the reaction that is occurring.

3. Experimental Part

The model described by Equation (7) was used for the description of polyester yarns in terms of neutral hydrolysis kinetics. Polyester multifilament yarn (Julon Co), with a count of 78 dtex/36 filaments, was cut into portions with a length of 1–2 cm. The experiment was carried out in a special high-pressure reactor (see Figure 8) at 250 °C and 35–38 bars and with a PET/water ratio of 1:8. The hydrolysis products were dissolved in sodium hydroxide, with subsequent precipitation in hydrochloric acid, and analyzed using a Perkin Elmer FT-IR Spectrum GX spectrometer.

The experimental results are summarized in

Table 1. Experimental results for polyester neutral hydrolysis.

Run No.	Reaction Time (min)	Mass of the Solid Phase (g)	Mass of Remnants Insoluble in NaOH Solution (g)	Mass of Obtained and Purified TPA (g)	Yield of TPA from the Purification Process (According to the Mass of the Solid Phase) (%)	Produced Solid Material, According to Theoretical Values of Max. Produced TPA (%)	Yield of Purified TPA, According to the Theoretical Value, Final Yield of the Reaction (%)
011713/1	0	11.94	1.05	11.03	101.29	92.13	85.11
011713/2	0	12.12	0.81	11.24	99.38	93.52	86.73
011413/2	0	11.82	0.65	11.42	102.24	91.20	88.12
011513/1	30	12.10	0.12	12.03	100.42	93.36	92.82
011613/1	30	12.22	1.06	11.35	101.70	94.29	87.58
011813/1	30	12.00	0.17	11.76	99.41	92.59	90.74
011413/1	60	12.38	0.06	12.28	99.68	95.52	94.75
012213/2	60	11.98	0.22	11.82	100.51	92.44	91.20
012213/3	60	12.43	0.33	12.05	99.59	95.91	92.98

.

4. Results and Discussion

The hydrolysis of PET involves the chemical scission of an ester linkage by a water molecule, i.e., the mechanism of ester bonds is cleaved through the attack of nucleophilic agents is shown in Figure 9.

Each chain succession uses one water molecule and creates one carboxyl end group. Initially, virgin PET contains two moles of ester linkages per mole of repeat unit (whose molar mass is 192 g/mol) or 0.0104 mol/g PET. Terephthalic acid monomers contain two mol of carboxyl groups per mole of acid (whose molar mass is 166 g/mol) or 0.01205 mol/g acid. During the degradation reaction, the succession of chains with ester linkages results in a decrease in the molecular weight, either through random scission at the ester linkages or through chain ends with an increase in the carboxyl end group concentration. Furthermore, an increase in the carboxyl end group concentration will increase the rate of hydrolysis of the polymer.

The estimated kinetic parameter $D=-\left(kb\sqrt{\pi h/d}\right)/6$ and the integration constant C obtained using nonlinear least squares are D = 2.69 × 10^–5 and C = 1.04. The hydrolytic PET kinetics are shown in Figure 10. The 95% confidence interval band for the estimated curve is shown as well (red curves). It is visible that the model of penetrant transportation (water) during the solid phase (Equation (7)) shows good agreement with the experimental data. The reaction theoretically reaches completion in 197 min at 523 K. The rapid decline is due to the availability of a large number of active sites needed for the reaction to proceed. The reduced rate is due to the reduced number of reaction sites for the hydrolytic reactions towards the end of the reaction.

5. Conclusions

In the case of penetrant diffusion into the cracks as the rate-controlling step, the initial reaction rate is low, caused by the surface penetration of water during the solid phase. The reaction path follows a sigmoidal curve, with a slow reaction rate in the beginning and at the end. In the beginning, there are very few active sites due to the small number of pores, while at the end of the reaction, there are no new pores created due to the complete fragmentation of PET into TA and EG. Hence, the region of rapid degradation is between 10 to 90 percent of active site availability. Furthermore, the conversion curves are closer together with respect to time at a given temperature for the surface reaction rate control versus penetrant diffusion into the pores. The reaction order with respect to the monomer product is roughly 5/6. The theory developed can be readily extended to situations involving the presence of more components. The conversion curves have distinct zones due to the presence of the components in the reaction that is occurring. The steep zone reflects the rapidly degrading components, while the shallow slope reflects the slowly degrading components.

In future studies, this model can also be used for the description of catalytic activation involving hydrolysis processes. The form of the model will be the same, but the model parameters will be different. The proposed model is useful for modelling different forms of fibrous waste (woven, knitted, nonwoven) and their different morphologies.