Interdependent factors influencing the carbon yield, structure, and CO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{2}$$\end{document} adsorption capacity of lignocellulose-derived carbon fibers using multiple linear regression

Cellulose has experienced a renaissance as a precursor for carbon fibers (CFs). However, cellulose possesses intrinsic challenges as precursor substrate such as typically low carbon yield. This study examines the interplay of strategies to increase the carbonization yield of (ligno-) cellulosic fibers manufactured via a coagulation process. Using Design of Experiments, this article assesses the individual and combined effects of diammonium hydrogen phosphate (DAP), lignin, and CO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{2}$$\end{document} activation on the carbonization yield and properties of cellulose-based carbon fibers. Synergistic effects are identified using the response surface methodology. This paper evidences that DAP and lignin could affect cellulose pyrolysis positively in terms of carbonization yield. Nevertheless, DAP and lignin do not have an additive effect on increasing the yield. In fact, combined DAP and lignin can affect negatively the carbonization yield within a certain composition range. Further, the thermogravimetric CO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{2}$$\end{document} adsorption of the respective CFs was measured, showing relatively high values (ca. 2 mmol/g) at unsaturated pressure conditions. The CFs were microporous materials with potential applications in gas separation membranes and CO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{2}$$\end{document} storage systems.


Introduction
The ongoing transition toward a widespread bioeconomy in Europe has made cellulose one of the key local raw materials [17,60,64].Demonstrated by the current European single-use plastics directive [18], today cellulose is used for foams [35,38,55], textiles [45,48,67], packaging [23,25,69], and electronics [36,53,56].The wide use of cellulose derives from its local abundance, renewability, and biodegradability.Cellulose has been gaining attention as a potential precursor for carbon material production, especially considering the non-renewable nature of fossil fuels and graphite.Recent research has delved into this topic [14, Extended author information available on the last page of the article 27,33].Significant attention has been devoted to utilizing the thermal decomposition of manufactured cellulose fibers (MCFs), such as viscose and Lyocell fibers, to produce activated carbon fibers (ACFs) for a variety of uses, both structural and non-structural [9,10].However, the scalability of cellulose-based carbon fibers (CFs) is hindered by the low carbonization yield of cellulose [70].
In the literature, multiple research papers have addressed the carbonization yield of MCFs [9,10,58,70,76,79].Among the approaches to increase the yield, impregnating fibers with dehydration catalysts, e.g., diammonium hydrogen phosphate (DAP) or diammonium sulfate, before carbonization is a common strategy [9,32,76].Catalysts of this nature promote the dehydration of cellulose and suppress the formation of flammable volatiles such as CO 2 , CO, methane, or levoglucosan [58,76].Furthermore, at higher temperatures, the heteroatoms present in the catalyst can create covalent bonds and crosslink with the intermediate pyrolysis products, hampering the cleavage of the carbon chains [58,76].The carbonization yield of impregnated MCFs has been reported to increase up to 25% compared to the typical 10% yield observed in practice [6,7,9,31,76].
In a recent study, we increased the carbonization yield of Ioncell MCFs by blending the cellulose substrate with lignin [70].The effect of lignin on the carbonization yield of CF precursors was first assessed by Oroumei et al. [50].The authors described having increased the carbonization yield of PAN after blending the polymer with (sulfur-free) organosolv lignin.For the cellulose/lignin blend, we previously reported that respective mixtures showed a carbonization yield of 25% attributed to an additive effect of the carbonization yield of lignin, which is superior to the practical carbonization yield of cellulose [44,70].
The two aforementioned methods, using either dehydration catalysts or lignin, can compromise the mechanical performance of the resulting CFs.In the first case, DAP promotes micropores in the carbon material [9].Lignin reduces the long-range crystallinity of cellulose, increasing the disorder in the precursor fiber [33].A typical procedure to improve the carbonization yield and structural defects of the CFs entails activating the carbon material.Through the development of microporosity and functional sites, ACFs have shown interesting properties in energy storage systems (ESS) and the adsorption of toxic substances [8,9,14].For instance, Breitenbach et al. [9] made an ACF electrode from carbonizing impregnated viscose fibers.
This work assessed the influence of lignin, DAP, and physical activation on the carbonization yield and CF properties.Following the individual effects of dehydration catalysts and lignin on the carbonization yield of cellulose, we address investigating whether these two substances have a cooperative effect when combined.Additionally, we measured the performance of the manufactured CFs and ACFs regarding CO 2 adsorption to elucidate a potential non-structural application for these fibers and other potential applications typical of carbon materials [71,74,75].

Materials and methods
Ioncell precursor fibers with and without lignin were prepared as described earlier [70].In short, Enocell dissolvinggrade pulp (cellulose content: 91.7%, hemicellulose: 7.7%) was used as cellulose source and blended with organosolv beech lignin (BL).Three types of fibers were produced: (a) E100, (b) E70, and (c) E50 with the number referring to the weight content of cellulose.For example, E70 is a fiber made up of 70 wt.%cellulose, where the remaining 30 wt.% correspond to the lignin content.Filaments were spun at a draw ratio of 6, resulting in fibers of ca. 15 m diameter.The fibers were cut into 9 cm long pieces.For a detailed description of the Ioncell spinning process, the reader is directed to articles published by Ma et al. [39], Sixta et al. [62], Asaadi et al. [3].The coagulated cellulose in the Ioncell fibers showed a weight average molecular weight (Mw) of 130 kDa and a polydispersity index of 2.7.Protocol and equipment to determine the molar mass distribution of the carbohydrate fraction followed Pitkänen and Sixta [52], who reported using 9.0% LiCl in DMAc rather than 0.9%.DAP (reagent grade ≥ 98%) was obtained from Sigma-Aldrich (India).The solubilized catalyst was prepared using deionized water.

Experimental design
The CF yield ( ŷ ) was modeled as a function of three inde- pendent factors (k): the molar concentration of DAP in the impregnation solution ( x 1 ), CO 2 activation time ( x 2 ), and lignin content in the Ioncell fiber ( x 3 ).Therefore, the experi- mental design was limited to the space limitations of a tridimensional FCCD, calculating the number of sampling points (N) according to Eq. 1.The FCCD provided a framework for analyzing the inter-dependency between the factors and their effects on ŷ at low, medium, and high levels.In addition, a triplicate was chosen at the center point (n) to assess the statistical dispersion of the results.Creating and analyzing the FCCD was assisted by using the Design of Experiments app integrated into OriginPro ® 2021b.Table 1 shows the sampling points of the design matrix.The minimum and maximum of the DAP concentration were fixed based on the concentration ranges suggested in the literature to improve the carbonization yield [8]. CO 2 activation times were chosen based on thermogravimetric analyses on the fibers, see Figure S4.After 40 min, the carbon yield of some fibers was too low for characterization.Finally, the limits for the lignin concentrations were selected based on the results reported by Trogen et al. [70].In other words, 30 and 50 wt.%lignin show a noticeable effect on increasing the carbon yield of the fibers.Equation 1 yields 17 experiments.In other words, eight factorial points, six star points, and three center points.Equation S1 describes the model used to analyze ŷ.

Preparation of the activated carbon fibers
The impregnation protocol followed procedures described in the literature [7,9,24,76,78].First, all the precursor fibers were immersed in aqueous solutions containing the respective molar concentrations of the catalyst (Table 1).To be more precise, the process of impregnation involved the (1) dissolution of DAP in water for 10 min while being stirred magnetically at room temperature.Following this step, 1.2 g of fibers were immersed for 2 h in the freshly prepared solutions (1:200 weight ratio).Then, the soaked fibers were dried overnight at 105 °C in a convection oven, VENTI-Line ® (VWR, Germany), to remove the excess liquid.Once dried, carbonization and CO 2 activation of the fibers took place in a tube furnace Nabertherm RHTH 80-300/16 (Germany).Two samples were heated simultaneously to 800 °C (5 °C/min) in an N 2 gas (flow rate: 120 L/h) atmosphere.Before heating, N 2 gas was purged through the furnace for 15 min.After having reached 800 °C, the temperature was kept for half an hour, and then CO 2 gas (flow rate: 120 L/h) was added to reach the same N 2 gas flow rate.CO 2 gas flowed for the respective activation time of each sample and was then reduced to zero.Then, the fibers were held in the furnace until they reached 100 °C (under N 2 gas atmosphere).The flowchart in Fig. S1 illustrates the sequence to prepare the activated carbon fibers.Lastly, the CF yield was measured after having considered the initial fiber mass put in the furnace and the mass after heat treating them.

Thermogravimetry
The thermal decomposition of Ioncell fibers with DAP and lignin was studied using a thermogravimetric analyzer from Netzsch STA 449 F3 Jupiter in Germany.The purpose was to evaluate the impact of temperature and CO 2 activation on CF yield under carbonization conditions in a tube furnace.The experiment involved heating the samples from 40 to 800 °C (5 °C/min) with a constant flow of N 2 gas (60 ml/min).Then, at 800 °C, the samples were held at that temperature for 30 min; then, CO 2 gas flow (60 ml/min) was injected to match the conditions of the protective atmosphere.The oxidizing atmosphere was maintained for two hours, and the mass loss was recorded throughout the entire procedure.

Textural characterization
At a temperature of − 196 °C, the N 2 physisorption capacity was measured.The CF samples were cut into short threads that were less than 5 mm in length for analysis.To degas the samples, N 2 gas was used at a temperature of 150 °C for a period of 12 h.An analyzer called the Micromeritics TriStar II 3020 (United States) was then employed to gradually increase the relative pressure ( p∕p 0 ) and register the loaded adsorbate, thereby creating the adsorption isotherms.Using a Python TM -based framework named "pyGAPS" [26], the BET surface area ( a s ) and microporosity volume of each sample were esti- mated.It is worth noting that Osterrieth et al. [51] recently highlighted the wide statistical dispersion associated with treating N 2 adsorption data.This dispersion arises due to different procedures used to calculate textural properties like the For the design matrix, the minimum and maximum levels for each factor were manually inputted, as well as the medium level for the lignin content.The factorial points in the design matrix are experiments N1 to N8, while N9 to N14 represent star points.BET surface area a s .To standardize the procedure for calculat- ing a s and microporosity volume ( V ), the Rouquerol [57] and t-plot (non-porous carbon as reference) methods were used, respectively, by pyGAPS for this study.

Raman spectroscopy
The CF samples were analyzed using an inVia TM Raman microscope Renishaw ® Qontor (United Kingdom) using a green laser ( = 532 nm and 10% intensity) and a 20× objective within a Raman shift wavenumber ( ) range from 850 to 1930 cm −1 .The interval was scanned 30 times.Each spectrum was the average of three measurements at different spots.The background was subtracted from all the spectra using the intelligent baseline subtraction tool of WiRE TM 5.1 (first-degree function as baseline).
As proposed in the literature [40,41,46], we analyzed the CF spectra by applying a three-peak decomposition of the D and G bands.The D band was fitted with two Gaussian functions centered at the same spectral position, and a Breit-Wigner-Fano (BWF) was used to fit the G band.One of the most widely accepted approaches for fitting the Raman spectra of disordered carbons involves the use of three peaks [40,41,46].The former stems from the meaningful parameters, which compose the cumulative fitting function presented in Eq. 2 [40,41,46].In Eq. 2, I is the intensity as a function of .There, D and G represent the D and G band phonons.D 1 and D 2 are the bandwidths of the two D sub-bands, while G represents the width of the G band. q represents a coupling factor of the BWF function.To determine the average crystallite diameter in the basal plane ( L a ) using the I D /I G ratios, we employed Ferrari's and Robertson's law (Eq.3) [19].Being the D band decomposed into two sub-bands with the same phonon, the sum I D 1 + I D 2 yields the parameter I D .In Eq. 3, E L is the laser energy in eV (2.33 eV), and is the exponent to be calculated.For graphene, is 4 [12].

Scanning electron microscopy
A Field Emission Scanning Electron Microscope (FE-SEM) Zeiss Sigma VP from Germany was used for inspecting the CF surface.The samples were cut into small segments and coated with a gold-palladium 80/20 alloy before imaging the CF.The coated CF was mounted on carbon adhesive tape and placed under high vacuum.To observe their longitudinal sections, the fibers were laid horizontally on the sample holder.An electric potential ranging from 5 to 9 keV was required for imaging the CFs.In some selected cases, the analyses were accompanied by Energy-Dispersive Spectroscopy (EDS) using Ultim Max from Oxford Instruments.

Carbon fibers performance in CO 2 adsorption
This paper evaluated the ability of CF to adsorb CO 2 without affecting the structure.The experiments were conducted using the methodology described by Ojwang et al. [49].Thermogravimetric CO 2 gas adsorption tests were selected, and 13-15 mg of CF was mounted in a thermogravimetric analyzer STA 449 F3 Jupiter, Netzsch (Germany).The experimental procedure involved degassing the CF at 150 °C for an hour under He gas flow (200 ml/min).Then, the temperature was reduced to 40 °C, and the samples remained under the same gas flow for two hours to stabilize the temperature.The adsorption and desorption process was carried out gradually and step-wise by replacing the atmosphere from He to CO 2 .Figure S2 shows the gas exchanging process and CO 2 loading recorded during the experiment.Finally, CO 2 adsorption and desorption isotherms were plotted from the experimental data after weight-averaging the loaded adsorbate at each step indicated in Fig. S2.

X-ray photoelectron spectroscopy
To analyze the effect of oxygen-containing functional groups on CO 2 adsorption, five CF samples were chosen for examination.These samples, named N4, N7, N8, N11, and N16, underwent X-ray photoelectron spectroscopy (XPS).The XPS analysis was performed with a Kratos AXIS Ultra DLD X-ray photoelectron spectrometer utilizing a monochromated Al k X-ray source (1486.7 eV) at 100 W. The XPS spectra were obtained with a pass energy of 80 eV and a step size of 1.0 eV.In contrast, collecting high-resolution spectra necessitated a pass energy of 20 eV and a step size of 0.1 eV.High vacuum conditions were used to acquire photoelectron signals at a takeoff angle of 90 °C.The X-ray beam had a diameter of 1 mm, and the analysis area was 300×700 μm .The XPS spectra were collected at three different spots in the samples, and all of them were charge-corrected based on the position of the graphitic bonding of carbon at 284.2 eV.

Results and discussion
Carbon fibers were produced from Ioncell cellulose fibers and the experimentally observed CF yields ( ŷ ) were fitted to the model described by Eq.S1 using multiple linear regression (MLR) in OriginPro 2021b.In the first trial, the factor CO 2 activation time showed a negligible effect on ŷ .How- ever, knowing that the activation process should contribute to the increase in sample burn-off [5], we reviewed the effect of the oxidizing atmosphere on ŷ before continuing with further experimentation.Therefore, it was found that during CO 2 activation, the initial Ioncell fibers shape (ca. 9 cm long fiber bundles) hindered CO 2 diffusion from the gas atmosphere into the bulk matrix.The described phenomenon led to an ineffective activation via the Boudouard reaction [65].
To circumvent this experimental impediment, the CFs were cut into fragments smaller than 5 mm, and samples with activation times were reactivated by following the procedure in Fig. S1.
After reactivating the fibers, Eq.S1 successfully fitted the experimental ŷ and gave the coefficients in Table 2.In addition, Fig. S3 compares the observed and predicted ŷ ; the regression model that fitted the experimental results led to a coefficient of determination ( R 2 ) of ∼0.993.From the model, the quadratic term ( b 22 ) for the CO 2 activation time was removed due to it was indistinguishable from noise.Analyzing the effects of each factor on ŷ revealed a positive influence of both DAP and lignin on the average yield ŷ .However, this increase was more noticeable when the precursor fibers contained only one of them.The negative coefficient b 13 implies that the combination of DAP and lignin had a minor synergistic effect on increasing ŷ .The independ- ent effects of DAP and lignin, respectively, were anticipated.Breitenbach et al. [9] have recently reported a yield of 34.6% by impregnating viscose fibers with a solution of 56 mmol/L DAP.Similarly, Bai et al. [6] reported that the carbonization yield of DAP-impregnated Lyocell fibers increased from 19 to 23%.The effect of lignin on ŷ was already addressed ear- lier in this discussion [70].
The enhanced yield promoted by adding DAP to Ioncell fibers was to be expected.DAP is known to promote the dehydration of cellulose, reducing the amount of volatile and flammable carbonaceous compounds [76].Zeng and Pan [76] pointed out that remaining traces of DAP or condensation products thereof with cellulose can lead to an apparent increase in the CF yield.To assess this effect, we performed an EDS analysis on sample N10.The EDS results in Fig. 1 showed a residual DAP content in a few CF segments.Therefore, the remaining products of DAP should be considered when using DAP as a carbonization catalyst.Concerning the effect of lignin on ŷ , Ioncell fiber blends (E70 and E50) decomposed slowly over a broad temperature range [70].Above 200 °C, lignin pyrolysis promotes a melt phase radical process, consisting of initiation, propagation, and termination reactions [70].These reactions have a similar effect as observed for DAP; lignin and DAP can have an oxidative effect on the precursor fiber [70,76].Oxidation of the precursor fibers at low temperature (not to be confused with activation) creates cross-links and olefinic moieties, reducing the probability of forming volatile compounds during the heat treatment [42].
In contrast, CO 2 activation time impacted negatively on ŷ .The negative sign of b 2 is in agreement with the lit- erature; the sample burn-off (gasified carbon) increases by increasing the CO 2 activation time [5,9].Nonetheless, the interactions between CO 2 gas, DAP, and lignin had mixed effects on ŷ .First, when the precursor fibers contain DAP, a positive coefficient b 12 denotes a low reactivity between CF and CO 2 .Similar trends were observed by Breitenbach et al. [9] and Zeng and Pan [76].For example, a concentration interval in which DAP and CO 2 activation increase carbonization yield was reported.Another aspect to consider is the presence of inorganic elements, such as phosphorous, which may have hindered the gasification kinetics [16].The former statements may also explain the extended area in the contour plot in Fig. 2, where the CO 2 activation does not drop the yield below 22% when increasing the activation time and fixing the DAP concentration to 40 mmol/L.
The interaction between lignin and CO 2 activation time, represented by b 23 , shows that CO 2 gas tends to react with should not be overinterpreted as its standard error is high.After evaluating the physical meaning of the model, we made the contour plot in Fig. 2. In Fig. 2, the highest ŷ stems from mixing DAP and lignin in their maxima.Nonetheless, this yield is 2% higher than predicted and observed from the individual effects of adding DAP or lignin at their highest levels.As mentioned before, the negative coefficient b 13 means that the combination of DAP and lignin does not grant an increase of ŷ .The pyrolysis of lignin and DAP are melt-phase processes [70].Thus, the interactions of DAP and lignin in the liquid transition state may affect the interaction between DAP and cellulose.
In order to gain a better understanding of the mass loss that occurs during carbonization, we analyzed selected thermogravimetric results as shown in Fig. S4.Our observations for samples E100, E70, and E50 were similar to those reported by Trogen et al. [70].When cellulose is combined with lignin, the yield of Ioncell fibers during carbonization is increased.Similarly, the inclusion of a dehydration catalyst in the precursor fibers has a comparable effect to tube furnace carbonizations.A lower carbonization yield was discovered in sample E70/DAP in comparison to samples E100/ DAP, indicating that the combination of lignin and DAP does not enhance carbonization yield.However, the addition of lignin and DAP in higher concentrations (E50/DAP) resulted in an increased yield, which was also observed during tube furnace carbonizations.Finally, Fig. S4 illustrates the mass loss behavior during CO 2 activation.The CO 2 activation segment for all samples containing DAP exhibited a slight mass loss of approximately 1.5%, consistent with our earlier interpretation that residual catalyst on the CF surface may hinder solid carbon gasification due to lower reactivity when precursor fibers contain DAP.

Textural characterization
The assessment of activated carbon texture using the BET specific surface area ( a s ) parameter has been a topic of debate in previous years, according to sources such as Shi [61], Marsh and Rodríguez-Reinoso [42].However, the focus of this research is on the unclear approach to calculating a s , as highlighted by Osterrieth et al. [51].To address this problem, the N 2 adsorption isotherms in this study were analyzed using "pyGAPS", a framework based on Python which processes adsorption isotherms, as developed by Iacomi and Llewellyn [26].The goal of pyGAPS is to standardize the mathematical processes involved in analyzing adsorption isotherms.To compare the results of pyGAPS with another Python-based framework, "betsi-gui," which uses the Rouquerol criteria to calculate BET surface areas, this research processed adsorption isotherms with both tools [54].The conclusion of this study was that pyGAPS and betsi-gui produced the same results, demonstrating the usefulness of both tools in standardizing the process.
For our analyses, we opted to use pyGAPS since it offers a variety of algorithms that can calculate different textural properties, such as V .The outcomes of our isotherm pro- cessing are outlined in Table 2. Any CF samples lacking an activation protocol, as depicted in Fig. 3, did not show any detectable N 2 physisorption.This resulted in some missing data for a s and V in Table 2.The isotherms (Fig. 3) showed substantial gas adsorption at low relative pressures ( p∕p 0 < 0.1), followed by a sharp knee, ultimately leading to asymptotic gas adsorption at its highest point.This type of adsorption behavior corresponds to the IUPAC classification type I(a), which is generally found in microporous materials [68].The lack of adsorption data observed in the unactivated samples can be explained by the microporous nature of the CF studied.The diffusion kinetics of N 2 molecules into the solid carbon faces limitations due to the narrow pore size (< 2 nm) at the experimental temperature (− 196 °C) [22].To overcome this diffusion constraint, a few authors have proposed supplementing N 2 adsorption with CO 2 adsorption isotherms at room temperature [1,2,22].
To evaluate the relation between a s and V , Fig. S6 illus- trates a comparison between these textural properties.We observed in the literature that the criticism toward a s comes from its deficiency to include the effect of microporosity on the surface area of activated carbons [42,61].Particularly, this controversy considers that micropores and mesopores have different adsorption capacities [61].Nevertheless, for the studied CF, Fig. S6 demonstrates that a s comes mainly from the formation of microporosity since the scatter points align linearly.Therefore, a s is a sensible property for the studied microporous CF to characterize the material texture.

Raman spectroscopy
When non-graphitizable precursors like cellulose and lignin are carbonized, they result in disordered carbon structures that are made up of graphene layers.These structures lack higher-order orientation [46,47].According to Oberlin [47], at low pyrolysis temperatures (< 600 °C), cross-linking reactions take place in cellulose and lignin, which can impede the formation of graphene stacks.This can result in a relatively small average crystal size L a [46].The Ioncell CF under study is expected to have turbostratic structures due to its non-graphitizable nature and the inclusion of DAP in Fig. 3 Nitrogen adsorption and desorption isotherms measured for the samples in the Face-centered Central Composite Design.The x-axis on each plot shows the relative pressure ( p∕p 0 ) and the y-axis indicates the N 2 load in mmol/g the precursor fibers.DAP is known to introduce cross-linked functionalities that prevent the release of small volatile carbon compounds [76].Figure 4 illustrates the experimental and fitted Raman spectra of all the studied CF specimens.The maxima of the sp 2 C bonding excitation known as G band were at ≈ 1590-1594 cm −1 .Alternatively, the D band (formation of six-fold aromatic rings and point defects) had their maxima at ≈ 1337-1346 cm −1 [19, 46].According to Ferrari and Robertson [19], the D band intensity ( I D ) could be directly proportional to the probability of finding long-range polyaromatic structures in the CF.Therefore I D ∕I G ratio is one procedure which estimates the crystallite size L a [19,40,41,46].
We utilized the methodology proposed by various researchers, including Mallet-Ladeira et al. [40,41] and Mubari et al. [46], to calculate the parameter L a for each CF sample.This approach involves deriving the I D ∕I G ratio from a three-peak decomposition of the Raman spectra.To accomplish this, we fit the D band using two Gaussian functions with the peak maximum at the same wave number, while the G band was fitted using a BWF function.While Mallet-Ladeira et al. [40,41] initially proposed using two Lorentzian functions to deconvolve the D band, we found that in biobased carbons, the presence of a shoulder at 1100-1200 cm −1 alters the shape of the D band and makes it more Gaussian-like [63].Additionally, the low carbonization temperature of 800 °C contributes to observing broad D and G bands, which is attributed to a confinement effect in nanomaterials [73].The BWF function was used to fit the asymmetric G band typical of disordered carbons, which deviates from a perfect Lorentzian as a result of the density of vibrational states [19,40,43].The results of the decomposition process are shown in Fig. 4 and Fig. S7, demonstrating an excellent fit to the experimental data for all spectra with R 2 values ranging between 0.996 − 0.997.
The crystallite sizes L a and characteristics of the fitted bands are summarized in Table 2 and Table S2, respectively.Ferrari's and Robertson's law (Eq.3) was adequate for calculating L a since the crystal parameter was smaller than 2 nm in all the cases [19].However, as observed in Table 2, the samples displayed similar L a values (ca.1.2 nm) despite their initial compositions.To illustrate these similarities, L a is plotted against the intensity ratios of the D and G bands in Fig. S8.A reason for the similar L a sizes could be the maxi- mum carbonization temperature and heating rate effects, which remained the same (800 °C and 5 °C/min) for all sample carbonization (Fig. S1).Modifying the thermal parameters significantly affects the crystal size as the Gibbs free energy and pyrolysis kinetics change.For example, Mubari et al. [46] and Breitenbach et al. [10] reported the effect of the carbonization temperature and heating rate on the crystal size of biobased carbons, respectively.At a higher carbonization temperature and a slower heating rate could increase L a .The former would explain why the response surface analysis designed herein to analyze would not be suitable for studying L a .Furthermore, the replicates (N15- N17) showed a significant scatter of the L a values (Fig. S8).

Carbon fibers performance in CO 2 adsorption
The CO 2 adsorption and desorption capacity of the CF was estimated via thermogravimetry.Figure 5a depicts the adsorption and desorption isotherms of all the CF samples, and Table 2 the CO 2 adsorption capacities at p∕p atm = 0.75, respectively.Overall, the isotherms depict almost negligible hysteresis, a characteristic typically observed in ultramicroporous materials [15,59,72].At the experiment temperature (40 °C), hysteresis lacks since there are no kinetic restrictions for CO 2 molecules to move through the narrow micropores [72].This feature may also indicate that the studied CF physically adsorb CO 2 molecules (physisorption).To assess the physisorption mechanism, we attempted to correlate the CF textural properties with their CO 2 adsorption capacity.Thus, the adsorption isotherms were fitted using Freundlich's equation (Eq.4), which represents a basic adsorption model [21].Freundlich's empirical equation describes adsorption as a phenomenon Fig. 4 Raman spectrum of samples N3 (0 mmol/L DAP, 40 min CO 2 activation, and 0 wt.% lignin) and its decomposition using the three bands method.The x-axis in each plot represents the Raman shift wavenumber in cm −1 , and the y-axis is the G band normalized Raman intensity in arbitrary units.The solid line depicts the cumulative fit in each spectrum after decomposing the experimental spectrum in three bands: two Gaussian functions at the same wavenumber for the D band and one Breit-Wigner-Fano function for the G band following a power law-like behavior.In Eq. 4, is the adsorbate mass divided by the adsorbent mass while C and r are adsorption constants for the pair adsorbate-adsorbent at the experimental temperature.Jaroniec [28] demonstrated that C could be related to heterogeneities present in the adsorbent, which, in this case, could translate to the CF textural properties.Canevesi et al. [13] have used a modified version of Eq. 4 to assess the effect of texture and surface chemistry of activated carbons on their CO 2 uptake.Hence, Fig. 5b plots the calculated C values as a function of the BET surface areas.Although Fig. 5b shows that the parameter C tends to increase as a function a s , there is no relationship visible between the empirical parameter C and a s .Therefore, we conclude that the observed CO 2 adsorption capacity does not depend exclusively on the CF surface area but can also be connected to other factors, as Canevesi et al. [13] have reported.Especially in biobased activated carbons, Ashourirad et al. [4] underlined that CO 2 adsorption capacity depends on both the surface area and oxygen-containing functionalities.To investigate the potential impact of oxygen content on CO 2 adsorption performance, five samples (N4, N7, N8, N11, and N16) of CF were analyzed using XPS.Table 3 displays the relative concentrations of elements in the samples.All samples exhibited signals for C, N, O, and P, as well as traces of Ca, which is characteristic of biomass products.Based on the results presented in Table 3, it can be concluded that the CO 2 adsorption performance is influenced by the oxygen-containing functionalities present.Specifically, the samples with higher oxygen concentrations exhibited greater CO 2 adsorption.Although the relationship between oxygen functionalities and CO 2 adsorption is commonly overlooked, it is possible that oxygen sites in the CF may increase CO 2 uptake by polarizing and trapping CO 2 adsorbate molecules in the micropores through dipole-dipole and quadrupole van der Waals interactions [4,29,34,37].Consequently, the observed differences in CF chemistry may explain why CF with a larger surface area did not always exhibit higher CO 2 uptake in some instances.For example, sample N4 had the largest surface area but adsorbed less CO 2 than N7.By examining the precursor chemistry of N7 (Table 2), it is evident that N7 contained lignin, which may have generated more oxygen functionalities in the final CF.Therefore, N7 had a higher CO 2 adsorption capacity than N4.However, this is not a definitive conclusion since  3 Quantitative relative surface chemistry in wt.% estimated from X-ray photoelectron spectroscopy.The BET surface area ( a s ) in m 2 /g and CO 2 uptake ( ) in mmol/g are presented to remark both texture and surface chemistry effects on the CO 2 adsorption performance a Adsorption at p∕p atm = 0. other samples containing lignin (e.g., N8 and N9) showed lower CO 2 adsorption than N4.In summary, all the samples exhibited high CO 2 adsorption at unsaturated conditions ( ∼ 2 mmol/g) that could be utilized in the future to create gas separation membranes and CO 2 storage systems.Additionally, it is important to consider both textural and chemical heterogeneities in the CF when modeling CO 2 uptake.

Conclusion
The model successfully assessed the impact of DAP impregnation, CO 2 activation time, and lignin content on the carbonization yield of Ioncell fibers.DAP and lignin could affect cellulose pyrolysis positively in terms of carbonization yield.DAP increased the carbonization yield of the fibers as it is known to promote the dehydration temperature of cellulose and thereby induce cross-links in the emerging carbon structure, reducing the formation of volatile carbonaceous products.Similarly, lignin can alter cellulose pyrolysis when in intimate contact with the fiber matrix and shifts the onset of degradation to temperatures.Interpreting the regression coefficients of the carbonization yield model showed that combining DAP and lignin does not have an additive effect on increasing the yield.DAP and lignin can even affect the carbonization yield negatively within a certain composition range, while the CO 2 activation time showed a reduced effect on the carbonization yield.The low reactivity was attributed to mass diffusion constraints at the carbonization conditions and to the presence of cross-linked carbon atoms, which may arise in the CFs upon adding DAP to the precursor fibers.However, a more detailed study of the pyrolysis phases would be necessary to confirm the phenomena.This study also provided answers to existing controversies in the literature.For example, the results showed that, especially in biochars, the precursor chemistry generates oxygen-containing functionalities, which may significantly contribute to the CO 2 uptake capacity of CF.Based on all our findings, we foresee gas separation membranes and CO 2 capture systems as future applications for the studied CF.

Fig. 5 a
Fig. 5 a Thermogravimetric CO 2 isotherms (40 °C) of the samples in the Face-centered Central Composite Design.The x-axis in each plot represents the relative pressure p∕p atm and the y-axis the CO 2 load in mmol/g.The dotted line represents Freundlich's empirical equation for gas adsorption.b Freundlich's empirical parameter C as a function of the BET surface areas a s of the samples composing the Face-centered Central Composite Design

Table 1
Sampling points of the Face-centered Central Composite Design The last three experiments are replicates located at the center point

Table 2
Carbonization yields and properties of the CF samples composing the Face-centered Central Composite Design a Adsorption at p∕p atm = 0.75 the carbon produced after lignin pyrolysis.However, b 23