Introduction

Textiles are an extremely diverse group of materials, and some of them are composed of several different classes of fibres blended in a great variety of structures treated with various finishes and dyes. This tendency to blend fibres in textiles allows to combine their properties, producing textiles with the strength of the polyester, the elasticity of elastane, the softness of the cotton or the characteristic crimp of the wool. However, this strategy has some disadvantages. For example, regarding textile recycling, an additional step of fibre separation has to be added, which is not always easy to perform [1]. Moreover, when manufacturing textiles, it has to be considered that each class of fibre has different nature, and so the physical and chemical treatments applied to the textiles have to be adapted to all constituents [2]. For example, the dye of cotton is usually performed at 100 °C, at water boiling temperature to promote the swelling of the fibre [3], but polyester needs at least 130 °C to capture the colour [4], for which the cotton will be dyed at different temperature whether it is processed alone or blended with PET.

One of the properties that can be modified by blending fibres in textiles is the fibre release. This is produced during the use and maintenance of the garments, through mechanical abrasion and deformations that induce fibres to leave the textiles [5]. When different fibres are mixed to form a yarn, it is reasonable to presume that they can interact with each other for example by friction [6], thus affecting the susceptibility of each one to leave the structure when external stress is applied.

One of the great challenges regarding fibre release is the understanding of the interactions between different fibres when blended in the same fabric. For this purpose, an essential measure is the quantification of the fibres that are released compared to their proportion in the original fabric. The classical methods for fibre quantification are divided in manual separation and chemical separation, and in recent years the known as enzymatic and biological separations gained importance as well [7]. Of all methods, the manual is usually recommended even in standards, as it provides the most accurate results [8]. However, for very intricate mixtures, the manual separation becomes a big challenge, sometimes impossible. In the case of chemical analysis, the strategy consists of the selective dissolution of one of the constituents, followed by filtration and drying of the remaining one, comparing the initial and final masses to determine the percentage of each constituent in the initial mixture. As this method is so selective, it requires different procedures and reagents depending on the fibres present in the mixture. Just to give an idea of that complexity, the ISO 1833 standard, about chemical quantitative analysis of textiles, [8] includes 29 different parts, which are devoted to different mixtures of fibres. This becomes more difficult when the blend has more than two constituents, and it gets worse as the number of different fibres in the blend increases. These classical methods are quite time consuming, as they require an operator to manually separate the fibres or perform the experiments in laboratory to selectively dissolve a constituent the mixtures. Moreover, chemical, enzymatic and biological separations require the use of different reagents and solvents, which at its last produces wastes which must be processed [9].

Other methods have been recently introduced to substitute these methods in order to save time, avoid the waste generation and reduce or eliminate the sample preparation. One of the proposed alternatives was made by Haap et al. [10], making use of dynamic image analysis applied to wastewater from laundry. Near-infrared spectroscopy, NIR, has been also studied to determine the PET/cotton proportion on fabrics, based on the spectral differences of both fibres. The spectra of solid-state NMR have been also studied for this purpose, making use of the deconvolutions of pre-defined peak areas [11].

The present study proposes an alternative method based on thermogravimetric analysis (TGA) to estimate the content of different fibres in textiles, and the comparison of this composition with the released fibres in pilling experiments. This method makes use of the deconvolutions of the derivatives of the mass signal (DTG) in order to identify the processes of degradation of different fibres. TGA has been used before to analyse the composition of the fibres released from PET/cotton blends, both in wet [12] and dry conditions [13]. However, that approach presented difficulties to estimate the percentage of fibres in the mixture as the curves of most used fibres in textiles appear in similar ranges of temperature [14]. Cotton and polyester are the most produced textile fibres worldwide, which is probably the reason why most of the studies of classical and new methods are focused on PET/cotton blends. The current work analyses fabrics made of PET fibres blended with one or more of these: cotton, acrylic and wool.

The method proposed here, based on performing deconvolutions of DTG curves using mixtures of generalized logistic derivative functions, has two objectives. The first is to establish an efficient and simple method to estimate the fraction of different fibres in textile blends. The second is to verify the applicability of the method for comparing the susceptibility of different textile fibres to release from a fabric. For this purpose, five blended woven fabrics of known composition are subjected to fibre release experiments in a pilling tester machine, and the lost fibres are collected and tested by TGA. The method was tested by comparing the estimates from the TGA tests with the composition values specified for each fabric.

Materials and methods

Materials

This study considers 5 woven fabrics made of blends of different fibres. All of these fabrics contain PET, being two of them blended with cotton (CO), one blended with wool (WO) and two blended with cotton and acrylic (PA). Table 1 shows the compositions of the fabrics, obtained from the provider.

Table 1 Composition and dimensional features of the woven fabrics to be tested
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Therefore, three systems were studied: PET–cotton (2 fabrics), PET–wool (1 fabric) and PET–cotton–acrylic (2 fabrics).

Samples of raw fibres of the mentioned constituents were tested in the thermogravimetric analysis as well.

Fibre release experiments

The fabrics were subjected to fibre release experiments in a SD Atlas Random Tumble Pilling Tester (RTPT) machine, based on the alternative procedure of the ISO 12945-3:2020 [15]. Squared samples of 10 cm2 of fabric were tested in the machine for a total of 60 min, rotating at 1200 rpm, being tumbled against cork lined drum walls. The experiment was divided into seven time steps at the end of which the fabrics were weighed: 1, 3, 3, 3, 10, 20 and 20 min. The fibres were collected at the end to be analysed by TGA.

Thermogravimetric analysis (TGA)

Three groups of samples were studied in this analysis: fabrics, their released fibres and raw fibres. All were subjected to linear heating ramps at 10 °C min−1 from room temperature to 700 °C in air atmosphere, using 100 mL min−1 of air flow. The tests were run in a simultaneous DSC-TGA instrument (TA Instruments SDT 2960). Fabric samples consisted of two or three 5-mm-diameter discs which were die-cut from the fabric. Fibre samples were directly tested fibres which were directly collected from the RTPT drums. In all cases sample masses ranged between 9 and 11 mg. All samples were tested in triplicate.

Analysis of the data

Deconvolutions of the experimental time-derivative TGA (DTG) curves have been obtained through the Fityk software version 1.3.1 [16]. A number of time derivative generalized logistic (TDGL) functions were used to fit the experimental DTG curves. The Nelder–Mead method from NLopt [17] was used to fit the curves of the model. All experiments were performed and analysed in triplicate.

Results and discussion

Fibre release experiments

The fabrics tested in the RTPT released fibres that were collected after the 60 min of the experiment and saved all together. The mass loss of the fabrics, recorded in the steps of the pilling experiments, is shown in Fig. 1. The results of the final fibre release range from 101 to 102 mg g−1.

Fig. 1
figure 1

Power trends of the fibre loss measured for the fabrics in the RTPT

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Thermogravimetric analysis

Analysis of raw fibres

Figure 2 shows an overlay of the thermal decomposition of the raw fibres. It is seen that they undergo degradation in the same range of temperatures, resulting in an overlap of some processes. That overlapping of processes in the same temperature range may later hinder the identification of single degradation processes on TGA curves obtained from samples composed of a mixture of fibre types. Precisely, the reason for using DTG instead of TGA here is that overlapping processes can be more easily identified in DTG than in TGA curves [18].

Fig. 2
figure 2

Overlay of the TGA curves of the standard fibres

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The deconvolutions are based on peak shape functions for fitting the DTG experimental data using the Fityk software with Nelder–Mead fitting method from NLopt. The chosen peak shape function is the time derivative of a generalized logistic function, which is assumed to represent a single reaction in the decomposition process.

$$y\left(t\right)= \frac{c\cdot b\cdot {e}^{-(b/(m-t))}}{{\left[1+\tau \cdot {e}^{-(b/(m-t))}\right]}^{(1+\tau )/\tau }}$$
(1)

In this equation, \(m\) represents the time at which the maximum degradation rate is observed or, in other words, the time at the maximum of the DTG peak. The \(b\) parameter is related to the reaction rate, hence inversely proportional to the peak width with respect to the height. \(c\) is the peak area, which represents the mass loss corresponding to that single process, and \(\tau\) represents the symmetry of the peak. This model has been used before in works related to degradation models of similar materials, such as cellulose powder [19].

The experimental curves were fitted by a number of TDGL functions, never greater than the number of single degradation processes that can be inferred from visual observation of the experimental DTG curves. The parameter values of all functions were optimized to obtain the best possible fit. The weighted sum of squared residuals (WSSR) was used as the goodness-of-fit criterion. As some of the fibres presented a mass loss below 100 °C due to the water evaporation, the deconvolutions were restricted to the peaks at higher temperatures, using the dry mass as reference. Figure 3 illustrates how the deconvolution method is applied on a two-component degradation process.

Fig. 3
figure 3

Deconvolution of a polyester standard DTG curve using two time-derivative generalized logistic function components. The experimental data are represented in green and the fitting red. The fit corresponds to the sum of the two degradation processes, DL1 and DL2

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Figure 4 collects the deconvolution curves of the DTG signals of the raw fibres. The first one, in Fig. 4A, corresponds to the degradation of polyester, which is composed of polyethylene terephthalate molecular chains. Two deconvolution curves can be seen, the first one with its maximum at 432 °C and the second one at 516 °C, which correspond to a pyrolysis followed by a combustion reaction [20].

Fig. 4
figure 4

Deconvolutions of the DTG curves of A polyester, B acrylic, C cotton and D wool fibres, based on mixtures of time-derivative generalized logistic functions

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In Fig. 4B, the acrylic decomposition is reproduced by three TDGL functions, each representing a different process. The first mass loss is observed at 313 °C. It is relatively fast, and it is followed by a slower reaction at 395 °C. Both processes have been reported in air [21] and N2 atmospheres [22] and were related to polyacrylonitrile and polyvinyl acetate decomposition [23, 24]. The peak at 638 °C is related to a combustion of the remaining char as it has been only observed in air experiments [21].

Figure 4D represents the deconvolutions of cotton. The plot shows the degradation of cellulose in two sharp peaks, at 333 and 455 °C, which correspond to a non-oxidative reaction followed by a combustion process [25]. The other processes correspond to the degradation of non-cellulosic constituents, such as pectin and hemicellulose, which appear as a small peak at 327 °C [26], followed by the decomposition of the remaining non-cellulosic matter produced in a wide range of temperature, with its maximum at 404 °C [27].

Finally, the decomposition of wool, in Fig. 4D, is described by four overlapping processes. The first step, at 271 °C, has been previously associated with the release of H2S and CO2, together with disulphide bond cleavage [28]. The second step, observed at 322 °C, corresponds to the loss of some side chain residues of high thermal stability. The third process, at 512 °C, is related to a pyrolytic transformation of the chain backbone [29]. Finally, the minor peak observed at 592 °C can be related to a deep oxidation of pyrocarbon, due to oxygen remnants into the furnace, as that process has been reported in air conditions at similar temperatures [30].

Once the degradation of each raw fibre is described by a mixture of logistic derivative functions, binary blends of PET and cotton were prepared to evaluate the interactions between them, without interference from additional dyes or finishes. The PET–cotton ratios in the mixtures were 25:75, 50:50 and 75:25. The samples were labelled according to their cotton content, except that one of only PET, which was marked as PET 100. Figure 5 shows the sum of the TDGL components associated with PET, in Fig. 5A, and cotton, in Fig. 5B, obtained from the DTG curve fits of the binary blends, in addition to the pure constituents, PET and cotton. Plots of all fittings are displayed in Appendix. The single component curves obtained from each blend TGA experiment were associated with those of the material constituents, PET or cotton. This association was made taking into account the shape, size and location of the curve on the temperature axis. Each graph is divided into two parts: one shows the sum of PET-related curves (Fig. 5A) and the other the cotton-related components (Fig. 5B). In Fig. 5A, it is noticeable that the second degradation process is shifted towards lower temperatures as the percentage of PET decreases in the mixture. In Fig. 5B, it can be seen that the last decomposition reaction of cotton appears as a sharp peak, the area of which decreases, moving towards higher temperatures, as the percentage of cotton in the mixture decreases. This peak, as commented before, corresponds to the combustion of cellulose in its second step of degradation. This cotton degradation process is clearly affected by the presence of PET, and the effect is proportional to the amount of PET present in the mixture. It is observed that the incorporation of PET clearly delays that the onset of combustion of the pyrolyzed cotton char remains. For every 25% of PET that enters the sample, combustion is delayed by about 10 °C. This retarding effect may be due to the fact that the PET has formed a layer on the cotton char fibres that prevents their contact with the atmosphere. However, once combustion begins, oxidation proceeds at a faster rate than when it occurred at lower temperatures in the absence of PET.

Fig. 5
figure 5

PET (A) and cotton (B) curves estimated from the deconvolutions of the DTG curves of the blends. For comparison, the curves of neat fibres are included

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Figure 6 shows the binary system PET–wool, on which the mixtures were prepared in the same percentages as the system of PET–cotton. The deconvoluted peaks associated with each constituent were separated as well in Fig. 6A and B. Notice that the scale of the wool has a different scale in order to properly appreciate the shape of the signals. The decrease in temperature of the second PET degradation is less defined than in Fig. 5A, but the endset of the first reaction appears to decrease with the PET content in the mixture. Regarding wool, the most noticeable change in presence of PET is the increase in rate of the two last degradation processes. In wool curves, these processes appear strongly overlapping. However, when wool is mixed with PET, the processes become separated from each other and proceed at a faster rate. It is also worth noting that the two first stages of wool degradation, although largely overlapping, can be better identified as distinct processes as the fraction of wool in the mixture decreases.

Fig. 6
figure 6

PET (A) and wool (B) curves estimated from the deconvolutions of the DTG curves of the blends. For comparison, the curves of neat fibres are included

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Figure 7 corresponds to a ternary system of mixtures with PET, cotton and acrylic. A blend of PET and cotton in a ratio 1:1 was mixed with acrylic, obtaining PA-CO-PET systems of 75–12.5–12.5, 50–25–25 and 25–37.5–37.5, labelled PA_75, PA_50 and PA_25, respectively. It can be seen that, in presence of PET and cotton, the second peak of acrylic becomes sharp, and an additional reaction, smaller as the acrylic content decreases, appears at the final stage of its decomposition. The combination with PET and cotton also produces that the degradation of acrylic finishes at lower temperatures.

Fig. 7
figure 7

PET (A), cotton (B) and acrylic (C) curves estimated from the deconvolutions of the DTG curves of the blends. For comparison, the curves of neat fibres are included

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Considering the signals of PET for the three systems, it can be seen that the first peak presents similar shape in all cases. The second one follows similar behaviour, as well. In the case of cotton, the first reaction is the one that conserves the most the original shape of the pure fibre. In presence of PET, the last peak of cotton is quite significant, due to its high rate and its peak height. The curves of wool can be detected because of their significant width, and small height. As the wool percentage decreases in favour of PET, sharp peaks appear at the higher temperatures. In the case of PA, when mixed with PET and cotton, the most significant feature of the peaks to identify them is the temperature at which they appear, many of them out of the range of PET and cotton peaks. It is also observed in Fig. 7B that the aforementioned retardant effect of PET on combustion of the pyrolyzed cotton char remains.

Once the proposed method has been verified with mixtures of known composition, the study of its possible application to fabrics and their released fibres, which normally have dyes and finishes that can increase the complexity of the behaviour making the identification of the constituents more difficult, is addressed.

TGA of fabrics and released fibres

Fabrics and their released fibres were tested by TGA in the same way than the raw fibres. Since compositional data of the fabrics were provided by the supplier, it was possible to use these data to validate our estimations obtained from TGA experiments of the fabrics and of the raw fibres. This validation of the estimations is crucial to then identify the different constituents in the TGA plots obtained from the released fibres in the RTPT experiments at different times. The DTG curves obtained from the TGA tests of the fabrics were deconvoluted in the same way than those obtained from the raw fibres. The TDGL functions were associated with the constituents into the samples in order to determine of the origin of each TDGL function, based on the previous study of the mixtures of raw fibres. The parameters obtained for the different mixtures of raw fibres were used as a guide to generate the deconvolution of fabrics and their released fibres. Then, the maximum rate temperature was considered as the main characteristic to determine the associated constituent, being in second place supported by the shape of the curves. Tables 3–7 of Appendix contain the data of temperatures at peak maxima for all TDGL functions. Figure 8 shows the deconvolution of the DTG curves of one fabric per system.

Fig. 8
figure 8

Fitted curve and its single TDGL components obtained from the optimal fitting of DTG curves corresponding to A PC1, B PW and C PCA2 fabrics

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Thus, for example, Fig. 8A shows the deconvolution curves of the PC1 fabric sample, theoretically composed of 40% PET and 60% cotton. For this fabric, 6 TDGL functions of thermal decomposition are found. Of these steps, the one at 419 °C and the small peak at 497 °C are associated with the polyester degradation. The other curves are associated with cotton: the ones at 341 and 483 °C can be related to the cellulose degradation, and the curve at 321 °C is likely to be produced by the decomposition of hemicellulose. Finally, the peak at 458 could be a retarded degradation of non-cellulosic constituents.

Figure 8B and C represents the deconvolution curves of the PW and PCA2 fabrics obtaining 7 and 5 TDGL functions, respectively.

After that, each TDGL function was assigned to one material constituent of its corresponding sample (fabric or its released fibres). For example, in the case of the PC1 fabric two TDGL functions were associated with PET and three were associated with cotton, as explained above.

Figure 9 shows the deconvolution curves corresponding to the DTG of the PC1 fabric and the DTG of its released fibres. Figure 9A shows an overlay of the PC1 TDGL components associated with PET that were obtained from the fabric and the TDGL components obtained from neat PET fibres. Similarly, Fig. 9B shows the cotton-related TDGL components for fabric and neat fibres. In the same way, Fig. 9C and D displays overlays of the components obtained from released and neat fibres. Using the sum of the areas of the components corresponding to the same constituent, the percentage of each constituent in the different samples was calculated. A 44% of PET and 56% of cotton was obtained in the case of the PC1 fabric, which agrees with the compositional data provided by the supplier, 35–45% and 55–65%, respectively. In the case of the released fibres, the cotton percentage rises up to 80%, with a PET content of 20%. This result suggests a greater susceptibility of the cotton to be released from this fabric compared to PET.

Fig. 9
figure 9

PET and cotton TDGL components estimated from the deconvolutions of the DTG curves of the PC1 fabric (A and B) and its released fibres (C and D)

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It is important to note that even the polyester is produced as a continuous fibre, when blended into yarns with natural fibres it is cut at similar length, so this difference on shedding behaviour does not only arise from the fibre length, but also from other properties that are different in PET and cotton.

As the proportion of one constituent decreases, it becomes more difficult to correctly identify the curves of each decomposition process. This can be clearly seen in Fig. 9 when comparing the components obtained from the fabric with those obtained from the released fibres. This is understandable if we consider that the contribution of the minority components to the overall fit is relatively small.

Other noticeable effect in the deconvolutions of the PC1 is shown in Fig. 9D where the increase in the height of the last peak is related to the increase in the ratio cotton/PET as previously described in the section Analysis of raw fibres (Fig. 5). Similar behaviour has been found for the fabric PC2, represented in Fig. 11 of Appendix, in which the 71% of PET measured in the fabric decreased until 12% in its released fibres.

It deserves mention that the peaks of PET do conserve their shape with all the mixtures studied, which helps to identify them. However, sometimes the second step of the PET degradation cannot be detected by this method probably due to its small size it occurs as well with the wide peak in cotton degradation. In general, when a process is overlapped with a much higher mass loss of other constituents, the small peak is hidden and it is not possible to identify it.

In the case of the PET–wool system, the differences between the maxima of the degradation peaks allow them to be easily assigned to the constituent that corresponds in each case. However, the partial overlap of the peaks resulted in an underestimation of the PET content in the three fabric replicates. Even so, a marked decrease in PET content could be detected in the released fibres as compared to the fabric. The PET measured in the released fibres resulted to be half of the content measured in the fabric, suggesting a higher susceptibility of the wool to be released from the fabric compared to the PET. The deconvolutions are plotted in Fig. 10 of Appendix.

The complexity of the analysis escalates with the three-constituent blends. Two fabrics of PET–cotton–acrylic systems were studied: PCA1 and PCA2, represented in Figs. 12 and 13 of Appendix. Both present similar amount of acrylic, 18 and 20%, in a theoretical context. However, the significantly greater content in cotton of PCA2 led the last peak of acrylic to shift to considerably lower temperatures, maybe due to the energy released in the last step of cotton degradation. When analysing the fibres released by the fabric PCA1, it is clear how PET content is reduced, as the peaks identified as PET are much smaller in the fibres sample (8%) than in the fabric sample (66%). The same occurs with acrylic.

On the other hand, the PET content in PCA2 is very similar in the fabric (10%) and in its released fibres (13%), while the acrylic content in the released fibres decreases to almost half of its content in the fabric, and the cotton content increases from 63 to 74%. In general, for the fabrics the PET % was found higher than in their released fibres as represented in Figs. 10–13 of Appendix. Table 2 compiles the results of the compositions in both fabrics and released fibres. Polyester fibres are the least susceptible to release of all the fibres considered in this work. Cotton, which is present in four fabrics, always shows a greater concentration in the released fibres than in the original fabric.

Table 2 Estimated composition of the woven fabrics and their released fibres along, with the theoretical values for the fabrics
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This difference between polyester and cotton has been reported before, where a higher tendency was found for the cotton to be released from fabrics when compared with polyester garments. Now, this method opens a door to a deeper study of mixtures of fibres, allowing the use of the same instrument and experimental conditions to any blend, independent of the nature of their constituents. The results in Table 2 confirm that it is possible to make realistic estimates quickly and easily from thermogravimetric measurements. The variability observed in the experiments is generally lower than what is legally allowed in fabric labelling. Future work with fabrics of more controlled composition could allow further refinement of the accuracy of the method, and its use could be extended to other fields of application.

Conclusions

A method based on convolution of mixtures of logistic derivative functions has been developed to estimate the composition of textile fibre blends from thermogravimetric data. At first, raw fibres analysed separately determined the curves of degradation for each raw fibre. Then, interactions between the various constituents have been identified that make the DTG curve of a mixture somewhat different from the simple weighted sum of the individual constituent curves. The accuracy of the method was validated using blends of known composition (PET + cotton), (PET + wool) and (PET + cotton + acrylic). Such blends determined the interactions between their constituents in the degradation. Finally, the gathered information was applied to fabrics and their released fabrics in order to determine the peaks corresponding to each constituent.

The sum of the peaks areas of each constituent gave the composition of the fabrics and their released fibres. The method proved to be suitable for rapid and accurate identification of the constituents of the textile structures tested. The method is helpful to assist the study of fibre release from textiles, simplifying the method of analysis. However, a limitation of the method is the difficulty of identifying minority constituents. With further work, the field of application of this methodology can be extended to other different or more complex textile systems.