Kinetic study and real-time monitoring strategy for TEMPO-mediated oxidation of bleached eucalyptus fibers

The present work aims at glimpsing the rate-determinant process parameters of TEMPO-mediated oxidation of bleached kraft cellulose for developing kinetic models and real-time monitoring tools. This may contribute to the scaling up of this reaction, frequently used as precursor of the production of cellulose nanofibers. For this, the effect of temperature, TEMPO and NaBr contents, and surface area of the fibers was assessed by means of a total experimental batch of 18 combinations, monitoring the carboxyl content (CC) of the samples and the NaOH consumption during oxidation. The obtained data was used to calculate the kinetic constant as a function of the conditions, as well as correlating the CC with the NaOH consumption, obtaining a strong linear correlation between these parameters. It was found that similar correlations could be used regardless process conditions, except for the case of TEMPO, which was found to protect the fibers from depolymerization and, thus, having different behavior at increasing TEMPO contents. Overall, the obtained results in the present study reveal the suitability of upscaling TEMPO-mediated oxidation, as well as having a deeper understanding on how the key parameters involved in the reaction affect the reaction path and, thus, contributing to the industrial deployment of oxidized cellulose and nanofibers.


Introduction
At the present time, the most popular pathway for the regioselective oxidation of the primary hydroxyl groups of cellulose involves a stable aminoxyl radical, (2,2,6,6-tetramethylpiperidin-1-yl)oxyl (TEMPO). Its key advantages comprise the use of aqueous media and its ease of regeneration in proper systems, allowing for catalytic amounts to be employed (Balea et al. 2019;Turk et al. 2020;Fedorov et al. 2020;Serra-Parareda et al. 2021b). When activated 1 3 Vol:. (1234567890) to its N-oxoammonium form, herein referred to as TEMPO+, it selectively oxidizes primary alcohols to aldehydes, remaining unreactive towards secondary or tertiary alcohols.
The activation of TEMPO can be attained electrochemically on an anode, supplying a certain current (Zeng et al. 2022), but it is more typically carried out in oxidative media at pH 9-11.5, comprising bromide and hypochlorite ions (Tarrés et al. 2022). It involves the loss of one electron from the radical form (aminoxyl), or two electrons from the hydroxylamine form (TEMPOH) (Nutting et al. 2018). It should be noted that the Br -|BrO -||ClO -|Clsystem causes both the generation of TEMPO + and the conversion of carbonyl groups to carboxylate groups (de Nooy et al. 1995). Furthermore, these BrOand ClOions, not TEMPO, are responsible for the depolymerizing side reaction (Spier et al. 2017). Among these ions, ClO -, whose standard reduction potential (0.81 V) is higher than that of BrO -(0.76 V), is the spent oxidant (Kucera 2019). The other oxidants, TEMPO + and BrO -, are regenerated along the process, and thus regarded as catalyst and co-catalyst, respectively (Saito and Isogai 2004;Filipova et al. 2020;Serra-Parareda et al. 2021a).
Back in 1996, one of the earliest reports (if not the earliest) of the TEMPO-mediated oxidation of cellulosic fibers concluded that, unlike for water-soluble polysaccharides, the conversion was not quantitative even in excess of hypochlorite (Besemer et al. 1998). Some years later and up to date, research groups focused on nanocellulose have taken huge advantage of this apparent limitation, since the purpose is generally isolating, hydrating and/or or unbundling fibrils, not dissolving them or completely disrupting their crystalline structure (Tarrés et al. 2016;Isogai et al. 2018;Beaumont et al. 2021). Nonetheless, it may be worth clarifying that the claim only holds true for cellulose I, as a quantitative conversion of OH(6) has been reported for cellulose II, cellulose III, and amorphous cellulose (Isogai et al. 2011).
Many applications require a partial oxidation of cellulose, not even (or not necessarily) reaching the highest conversion. To attain a desirable content of carboxylate groups (CC), it is common practice to select a proper ratio of ClOto cellulose, and then to perform the reaction until all hypochlorite has been spent (Tarrés et al. 2017). Along the reaction, NaOH is added to keep the pH within a certain interval, usually around 10 pH units. Then, the endpoint of the reaction is marked by the attainment of constant pH without further addition of alkali. This signals the complete consumption of hypochlorite, but carrying out the reaction until total conversion of the limiting reagent presents drawbacks. The most evident one is the time spent, which is one of the reasons why the upscalability of the process remains a challenge (Sanchez-Salvador et al. 2021). Moreover, it should be pointed out that ClOis not only consumed in oxidizing hydroxyl groups, but also in the oxidative cleavage of β-1,4 glycosidic bonds. In this context, evaluating the effects of the so-called catalyst and co-catalyst on the reaction rate is key to ease optimization and monitoring on a large scale. Finally, fibers are complex structures that cannot be reduced to cellulose I crystallites, and the possibility of mechanical refining to display higher surface area, and thus higher surface charge (Serra-Parareda et al. 2021b), should be explored.
All considered, this works seeks to undertake a comprehensive kinetic study on the TEMPO-mediated oxidation of cellulosic fibers from eucalyptus wood. While softwood-sourced nanocellulose usually displays better properties and usability, hardwood pulps are more effectively oxidized (Tarrés et al. 2019). This reaction has already been found to follow apparent first-order kinetics in different systems (Sun et al. 2005;Dai et al. 2011;Sang et al. 2017). Nonetheless, some knowledge gaps are still to be filled by broadening the interval of temperature values, by observing the effects of refining, and by assessing how the concentrations of TEMPO and Braffect the process. For a wide range of conditions, we plot the NaOH consumption against the CC, thus offering a plausible strategy for real-time monitoring, without the need of sampling for ex situ measurements, which are usually expensive and time-consuming (Balea et al. 2021). Then, the influence of TEMPO dosage, Brdosage, temperature, and surface charge on the reaction rate was assessed. In light of the results, the progressive availability of primary hydroxyl groups in terms that apply to chemical pulp fibers was discussed. Further, the present study can serve as precursor of subsequent studies for continuous production of TEMPO-oxidized cellulose fibers, leaving behind uncertainty in batch processes.

Materials
Bleached eucalyptus kraft pulp (BEKP) was kindly supplied by Torraspapel, S.A. (Zaragoza, Spain). All the chemicals involved in this study, both for TEMPO-mediated oxidation and characterization of the materials, were obtained from Merck (Barcelona, Spain). All reagents were used without further purification.
BEKP fibers preparation and characterization for TEMPO-mediated oxidation BEKP was supplied in the form of dried (10 wt% of water content) laminates. Prior to TEMPO-mediated oxidation, BEKP fibers were disintegrated in a laboratory disintegrator, according to ISO 5263-1:2004. Briefly, 30 g (oven-dried weight) of BEKP were suspended in 1.5 L of deionized water and disintegrated in a laboratory disintegrator for 20 min at 3000 rpm. In the case of mechanically refined pulps, the whole suspension was vacuum-filtered using a 200 mesh filter to be later diluted to 10 wt% consistency. The high-consistency pulps were then refined at 2500, 5000, 7500 and 10,000 revolutions in a PFI mill (Metrotec, model NPFI 02), according to ISO 5264-2:2011. The PFI refiner counts on an energy monitoring and data acquisition system that provides the required energy to mechanically refine the pulps.
Schopper-Riegler degree (°SR) was measured according to ISO 5267-1:1999 in a 95,587 PTI Schopper-Riegler tester, obtaining 16, 19, 24, 32, and 41°SR for 0-10,000 PFI revolutions, respectively. Cationic demand (CD) was also measured in a Mütek Particle Charge Detector PCD-06 from BTG Instruments (Weßling, Germany). Briefly, 0.1 g of dry BEKP were mixed with a known excess of poly(diallyldimethylammonium chloride) (polyDAD-MAC) in a deionized water medium. The suspension was then centrifuged for 30 min at 10,000 rpm and the supernatant, once removed, was titrated with sodium polyethylene sulfonate (PES-Na) until the isoelectric point (0 mV) (Serra-Parareda et al. 2021a). Concretely, cationic demands of 33. 04, 53.62, 71.88, 78.00, and 102.69 µeq/g were obtained for the refined pulps between 0 and 10,000 PFI revolutions, respectively. TEMPO-mediated oxidation: sampling for the kinetic study TEMPO-mediated oxidation was conducted in a stirred batch tank reactor equipped with temperature control under different conditions, aiming at determining the effect of different process parameters to the kinetics of the reaction. In a typical experiment, for the oxidation of 10 g (oven-dried weight) of BEKP, the required amount of TEMPO and NaBr catalysts were previously dispersed in 500 mL of deionized water. After complete dissolution of the catalysts, 10 g of BEKP were incorporated into the stirred batch reactor and additional deionized water was added, until reaching a consistency of 1 wt% with respect to BEKP. Once the fibers were fully dispersed, the reaction was started by means of adding the required amount of NaClO. The starting pH of the reaction was 11.5 dropping to 10.5 in the early stages of the reaction and maintained at 10.5 by means of gradually adding a 0.5 M NaOH solution. The consumed NaOH was constantly monitored as function of time. In order to obtain the correlation between the consumed NaOH and the carboxyl content, one of the determining parameters to monitor the evolution of the oxidation, small batches were prepared in parallel, stopping the reaction at different times. The reactions were stopped after a certain amount of NaOH consumption (0.33, 0.66, 1.00 and 1.17 mmol) per gram of fiber oxidized with 5 mmol/g of NaClO.
The kinetic study was conducted considering four different approaches: (i) effect of temperature (5-35 °C), (ii) effect of TEMPO catalyst concentration (2-32 mg/g), (iii) effect of NaBr amount (25-200 mg/g), and (iv) effect of refining degree of BEKP (0-10,000 revolutions of PFI). The rest of the oxidation conditions are described in Table 1.
All samples were stored in hermetic plastic bags at 4 °C to prevent any degradation. The effect of pH was also assessed, increasing from 10.5 to 11.5 maintaining the rest of the conditions at 20 °C, 16 mg/g of TEMPO, 100 mg/g of NaBr and using unrefined BEKP as substrate.
CC was determined by adapting a methodology introduced by Weber and Husemann (1942), as described in more detail elsewhere (Tarrés et al. 2017). Briefly, 3-5 mg of dry fiber are added in a solution containing 5 mL of methylene blue (300 mg/L) and 5 mL of a borate buffer solution at pH 8.5. After gentle stirring, followed by centrifugation at 10,000 rpm for 20 min, 2 mL of the supernatant were transferred into a 25 mL flask containing 2.5 mL of HCl 0.1 M, the volume was completed with distilled water. The absorbance at 664 nm was then measured. This method allows for simultaneous measurements of several samples per run, speeding up the characterization process in comparison to conventional titrations.

TEMPO-mediated oxidation reaction mechanism and kinetics
The oxidation mechanism of cellulose by the system TEMPO/NaBr/NaClO has been extensively described in the literature since the last century (Farkas et al. 1949;de Nooy et al. 1994;Saito and Isogai 2004;Dai et al. 2011). The oxidation of the primary alcohols of cellulose chains, located in carbon 6 (C6), catalyzed by TEMPO and with NaBr, has been described as a reaction with three main steps, consisting of (i) the formation of HBrO from NaClO, (ii) the generation of TEMPO + , and (iii) the formation of carboxyl groups from primary alcohols in C6. This mechanism previously described in detail in the literature (Saito and Isogai 2004;Sun et al. 2005).
The main reactions occur in the third step, consisting of the oxidation of primary alcohol to an intermediate aldehyde (Eq. 1) and the oxidation of the intermediate aldehyde to carboxyl (Eq. 2).
where R-CHO-H 2 O from Eq. 2 corresponds to the hydrated aldehyde, whose formation is neglected in terms of the rate-controlling stage, as it has been reported significantly more rapid than the oxidation of the alcohol (Friedlander et al. 1966;de Nooy et al. 1995).
The oxidation of alcohol to the intermediate aldehyde (Eq. 1) has been reported to be a ratedetermining step, as k 2 > k 1 , and the oxidation of cellulose can be assumed as a consecutive firstorder reaction system (Jiang et al. 2000;Sun et al. 2005;Dai et al. 2011). Thus, the kinetics of the TEMPO-catalyzed oxidation, in terms of primary alcohols consumption, can be expressed as function of k 1 , which will be assumed as the kinetic constant of the whole reaction (Eq. 3).
where [R-CH 2 OH] 0 and [R-COOH] t are the initial concentration of primary alcohols and the carboxyl content at time t in the BEKP fibers, respectively, and both expressed in µeq/g. k 1 is the kinetic constant, expressed in reciprocal time units. A value of 1500 µeq/g was assumed for R−CH 2 OH 0 , as it has been reported to be the maximum CC that can be achieved through TEMPO-mediated oxidation (Saito et al. 2007). Higher values might be found in the literature but can be attributed to differences on the quantification methods (Fujisawa et al. 2011).
Conversion, expressed as the relationship between the reacted CH 2 O to COO − groups compared to the experimental oxidation limit, this is the maximum carboxyl content achieved, was calculated according to Eq. 4.
where CC t is the carboxyl content at time t, CC 0 is the initial carboxyl content of the neat fiber, and CC max is the maximum carboxyl content experimentally achieved during oxidation. The time required for a complete conversion (t final ) was calculated from the linear regression resulting from Eq. 5, where (1 − X) 1∕2 was expressed as function of time (Sbiai et al. 2011).
The activation energy (Ea) was calculated according to the Arrhenius equation, which is given in Eq. 6.
where k is the kinetic constant, A is the pre-exponential factor, also known as Arrhenius factor, R is the universal gas constant, and T is the temperature.

Results and discussion
Validation of NaOH consumption as real-time monitoring parameter The relationship between NaOH consumption during TEMPO-mediated oxidation and the oxidation degree of fibers has been already reported (Sun et al. 2005). However, this correlation may depend on the availability of -CH 2 OH groups at the fiber surface and their concentration. An appropriate study correlating the NaOH consumption with the CC of the TEMPOoxidized fibers at different reaction conditions (i.e. temperature, TEMPO/NaBr concentration, surface area of the fibers) is required for suitably monitoring the evolution of the reaction in real time. This would underpin the hypothesis of using the NaOH consumption for the real-time monitoring of the TEMPOmediated oxidation kinetics and, thus, minimizing the use of time-consuming techniques such as the determination of the CC during an industrial batch production of TEMPO-oxidized fibers. Figure 1 shows the correlation between the NaOH consumption, in mmol/g, and CC, in µeq/g, at different temperatures (Fig. 1A), different TEMPO concentrations (Fig. 1B), different NaBr concentrations (Fig. 1C), and different cationic demand of the fibers (Fig. 1D).
The CC of the samples evolved linearly with the NaOH consumption during TEMPO-mediated oxidation in all cases. However, while the variation of the temperature (Fig. 1A), the NaBr concentration ( Fig. 1C) and the initial cationic demand of the fibers (Fig. 1D) did not affect the tendency, leading to similar slopes and y-intercepts (Tables S1, S3 and S4 from the Supplementary Material), the case of TEMPO catalyst (Fig. 1B) differed from the rest (Table S2). In this case, as the amount of TEMPO increased from 2 to 16 mg/g in the reaction media, the consumption of NaOH decreased for a certain CC. However, a similar slope was found between 16 and 32 mg/g indicating no effect of increasing the dosage of TEMPO catalyst from 16 mg/g. As revealed in Tables S1 to S4, the correlation factors (R 2 ) were around 0.99 in all cases, indicating an excellent fitting of the linear regression for all the reaction conditions and, thus, the suitability of NaOH consumption as an indicator of the CC during TEMPO-mediated oxidation. Albeit it is not shown in Fig. 1, additional NaOH was added to the fibers, and no change was observed on the CC, finding its maximum at 800 µeq/g. This is in accordance with previously published studies, where this maximum was already reported at 5 mmol/g of NaClO addition (Serra et al. 2017).
The linear regressions from Fig. 1A, C, D exhibited similar average slopes and y-intercepts (corresponding to the theoretical initial CC of the fibers), and low standard deviation. Except for the case represented in Fig. 1B, corresponding to variable amounts of TEMPO, the correlation between the CC and the NaOH consumption was the same regardless the reaction conditions, which is of interest for the industrialization of the reaction. This clearly confirms that NaOH consumption could be easily used as realtime monitoring parameter of the TEMPO-mediated oxidation at large scale, and reveals a new opportunity for this reaction not only in batch processing, but also for continuous production. Focusing on the exception, the lowest CC at low TEMPO addition (2 to 4 mg/g) for a certain NaClO addition (i.e. 5 mmol/g) was previously observed by Serra et al. (2017). Lin et al. (2018) also found a strong influence of TEMPO during the formation of carboxyl groups at the fibers. However, the authors worked only in two conditions regarding TEMPO, in absence and containing 16 mg/g. Considering the reaction mechanism, widely described in the literature, limiting the presence of TEMPO has a direct influence over the reaction from Eq. 1, corresponding to the formation of the aldehyde group, which is the most determinant in the process of TEMPO-mediated oxidation of cellulose. Further, the lower generation of aldehyde groups also limits the formation of carboxyl groups, which is the selected parameter to monitor the oxidative reaction (Saito and Isogai 2004;Sun et al. 2005;Dai et al. 2011;Isogai et al. 2011). The slope between the CC and NaOH consumption reveals that the reaction maximum conversion from -CH 2 OH to -COO − groups is satisfactorily achieved for dosages between 8 and 32 mg/g of TEMPO, to be significantly decreased below 8 mg/g. This can be clearly observed in Table S2, where the slopes at different TEMPO dosages are provided and similar values from 8 to 32 mg/g are reported, indicating the achievement of lower CC for a certain amount of NaOH.
TEMPO has been reported to prevent polysaccharide depolymerization. Indeed, Spier et al. (2017) demonstrated that TEMPO acts as a "sacrificial molecule" in polysaccharide TEMPO-mediated oxidation, reporting that TEMPO protects the polysaccharides during oxidation from depolymerization and non-selective oxidations. This is of particular interest for the present study, as the oxidation, expressed in terms of CC, decreased with the amount of TEMPO. The oxidant was consumed during the process, as the reaction was stopped once no changes were observed on the pH. However, the obtained results indicate that a higher amount of the spent oxidant (i.e. NaClO) was consumed by non-selective oxidations, also described in the literature as side-reactions, and for fiber degradation. In this sense, the concentration of TEMPO not only affects the kinetics of the main reaction, but also the selectivity and, thus, the resulting fiber properties and characteristics.
TEMPO-mediated oxidation kinetics: effect of processing conditions While the correlation between CC and NaOH consumption remained constant for all process conditions, except for the case of modifying TEMPO dosages, the evolution of the CC with time, this is the reaction rate, was significantly influenced by temperature, TEMPO and NaBr dosages, and the CD of the suspension, this is the surface area (Serra-Parareda et al. 2021b). Figure 2 provides the evolution of CC as function of time for the tested temperatures (A), TEMPO and NaBr dosages (B and C, respectively) and the CD (D). Figure 2A clearly indicates an effect of temperature over the kinetic constant of the reactions, particularly in k 1 , which was taken as rate-determinant. The differences on the slope correspond to the increasing temperatures. In addition, those reactions carried out between 5 and 20 °C exhibited a slight temporal shift compared to those occurring at higher temperatures, which may be attributed to their lower activation energy or frequency factor. This delay on the increase of the CC was not considered to determine the reaction rate, as it may interfere on the slope and increase the fitting error of the data. Table 2 shows the obtained reaction rates (slope of Eq. 3), the logarithm of the initial CH 2 OH concentration (y-intercept) and the experimental data fitting (R 2 ) for each temperature. In addition, the evolution of the reaction rate (k 1 ) as function of temperature is provided in Fig. 3A for further clarification, as well as its fitting to the Arrhenius equation (Fig. 3B).
The obtained reaction rates are in agreement with some previously reported for other raw materials, such as cotton (Dai et al. 2011) or regenerated cellulose (Sun et al. 2005). In addition, the reaction rate evolved linearly with temperature from 5 to 25 °C (R 2 = 0.9877), where an important change on the slope was observed to be stabilized at 35 °C. This indicates that temperature imparts a positive effect on reaction kinetics until certain point, where selectivity starts to decrease, affecting the conversion of the alcohol groups into carboxyl. Oxidative reactions, but also exothermic reactions in general, tend to decrease their selectivity with the increase of temperature, mainly because it becomes harder to maintain locally optimal concentrations of feed, oxidant, and product (Towler and Sinnott 2021). The average y-intercept accounted for 7.24 ± 0.06, which results in an average initial concentration of CH 2 O of 1400 µeq/g. The evolution of the kinetic constants as function of temperature allowed the determination of activation energy (Ea) using the Arrhenius equation (Eq. 6), as reflected in Fig. 3B, where a good linear relationship between the different temperatures and the reaction rate can be observed. The slope accounted for − 8864.37, which resulted in an Ea of 73.70 kJ/mol for the selected conditions of catalyst concentration and oxidizer amount. This value of Ea is of the same order of magnitude than those reported for cotton or regenerated cellulose, which validates the kinetic study with a commercial bleached kraft pulp (Sun et al. 2005;Dai et al. 2011).
In the case of the effect of TEMPO concentration, Fig. 2B shows the evolution of the CC, in µeq/g, as function of time for the tested catalyst concentrations. As expected, not only the kinetic constant decreased with lower TEMPO catalyst concentration, but the oxidation was considerably lower for the cases using 2 and 4 mg/g of TEMPO, particularly in the case of the former. These results are in accordance with the ones reported by Sun et al (2005) and Lin et al (2018), where it was demonstrated the possibility of reaching between 800 and 850 µeq/g of CC, which is the maximum value found in previous works for an NaClO amount of 5 mmol/g. The lag time at the beginning of each kinetic curve is related to the availability of TEMPO and Br -. Although the rate equations considered here are empirical and not mechanistic, this lag is due to the activation of the catalyst (TEMPO+). This stage is faster than the regioselective oxidation of primary -OH groups (Pääkkönen et al. 2015), especially in the case of high Brdoses, but it is of utmost relevance. In fact, we have observed that both lag and total reaction times decrease with TEMPO concentration for a given dose of NaBr ( Figure S1), and that those times are roughly but significantly intercorrelated (Pearson's r = 0.914).
In a previous work, the authors already observed that reaction time increased at decreasing TEMPO concentration, but no further discussion was provided except for a significant reduction on production costs (Serra et al. 2017). The catalyst concentration that can be most commonly found in the literature is 16 mg/g, as it corresponds to 1 mol of TEMPO per mol of cellulose (Tarrés et al. 2017;Levanič et al. 2020). Indeed, the stoichiometric relationship corresponds to 1:1 and, as revealed in Fig. 2B, doubling up the TEMPO:cellulose ratio (32 mg/g) had no effect on reaction time. Table 3 shows the evolution of the obtained reaction rates as function of the catalyst concentration, as well as the value of the y-intercept and the experimental fitting (R 2 ) of Eq. 3.
The effect of TEMPO concentration was significant, as k 1 was decreased to 0.47 s −1 , from the maximum of 3.63 s −1 for 16 mg/g at 20 °C. In this case, the average y-intercept was found at 7.30 ± 0.07, corresponding to an initial CH 2 O concentration of 1477 µeq/g. Differently from the TEMPO concentration, reducing the amount of Br − available (Fig. 2C) was not found to affect the oxidation degree of the resulting fibers, as all the batches resulted in fibers with a CC near to 800 µeq/g. This might indicate that the concentration of TEMPO holds a higher interference than NaBr when considering side reactions than the Br − concentrations (Spier et al. 2017). However, due to the reaction scheme provided in the previous section, the availability of Br − influences the reaction rate, particularly to k 1 and, thus, the evolution of the primary alcohol conversion into carboxyl as function of time. Table 4 shows the evolution of the reaction rate as function of the co-catalyst concentration, along with the value of the y-intercept and the experimental fitting (R 2 ) of Eq. 3. Again, no significant changes were found between 100 and 200 mg/g, while the reduction of the NaBr dosage from 100 to 50 and 25 mg/g dramatically affected the reaction kinetics, clearly indicating that operating below 100 mg/g would be detrimental in terms of production.
The decrease on k 1 with the reduction of NaBr concentration can be explained by the fact that the availability of Br − dictates the pace of radical formation, which is a fundamental step of the oxidative reaction. In addition, a decrease in the oxidation degree with higher concentrations of NaBr has been previously reported, hypothesizing that higher presence of Br − would suppress the formation of the secondary oxidant (HBrO) and, therefore, hindering the consecution of the reactions (Lin et al. 2018). Thus, doubling the amount of NaBr would be detrimental for the reaction rate, clearly indicating that it should remain at 100 mg/g. Finally, Fig. 2D reveals an increase on the reaction rate with the refining degree of the BEKP. The mechanical action of mechanical refining has been reported to increase the surface area of fibers, as well as the accessibility of water into the fiber structure, leading to higher swelling at increasing refining degrees. Indeed, this is supported by the higher ability of refined pulps to retain water, represented by the °SR, but also for the increasing CD, indicating that a higher number of electron-rich sites are exposed per mass unit. Considering that TEMPO-mediated oxidation consists of an oxidation in a heterogeneous system, increasing the surface area of fibers may promote the interactions between the reagents and catalysts. Indeed, this becomes to the light in Fig. 2D, where it can be observed that oxidation occurs faster. The correlation between the CC and time, properly evaluated by means of Eq. 3, lead to different k 1 for each refining degree (Table 5), but similar y-intercept, corresponding to the logarithm of the initial CC, and excellent correlation factors (R 2 ), as in the previous cases.
The evolution of k 1 with the refining degree in revolutions, equivalent to applied energy, evolved linearly with an R 2 of 0.9877. This indicates a clear effect of surface area over the kinetics of TEMPOmediated oxidation, which can be quantified in a 13% for 10,000 rev of PFI. This is of particular interest, as 4.12 × 10 -4 s −1 is the highest k 1 obtained in the present study but requires the application of additional energy. This energy was quantified in 4.44 kWh/ kg. Concretely, Carrasco et al. (1996) determined the surface area of the same pulp used in the present study. For equivalent drainability (°SR), the surface area of fibers accounted for 0.98, 1.34, 2.24, 3.50, and 4.92 m 2 /g for 0 to 10,000 PFI revolutions, respectively.
Out of the different parameters, temperature was found to have the most significant effect over the kinetics of the reaction. Indeed, the increase of the temperature from 20 to 30 °C enhanced k 1 in a 51.52%, while increasing the TEMPO dosage from 16 to 32 mg/g had a negative effect and increasing the NaBr content from 100 to 200 mg/g resulted in a 4.68% increase. Only in the case of mechanical refining the constant was increased by 13%, being still far from the improvement derived from a change on the temperature.
In addition, although the mechanical refining increased the reaction rate, the yield of the reaction, in terms of mass loss during the process, experienced a reduction with refining intensity. Concretely, the obtained yields accounted for 98. 68, 94.32, 91.86, 85.16, and 78.59% for 0 to 10,000 PFI revolutions, respectively, while no differences on yield were observed when modifying the rest of the parameters (temperature and/or TEMPO and NaBr dosages). The negative impact of refining on mass yield is mainly due to two phenomena. First, refining causes external fibrillation, and the protruding fibrils are more prone to degradation towards solubilized by-products than the fiber core. Second, the remaining xylans (which lack primary hydroxyl groups) can only undergo oxidative cleavage during TEMPO-mediated oxidation, not contributing positively to CC values (Syverud et al. 2011). It is known that the surface of hardwood fibers is richer in xylans than that of softwood fibers (Syverud et al. 2011;Pääkkönen et al. 2016).
Conversion as function of time was also determined, aiming at glimpsing the most appropriate conditions in terms of reaction kinetics (Sbiai et al. 2011). For this, conversion was calculated according to Eq. 4 and plotted according to Eq. 5. Figure 4 shows the correlation between the t final and k 1 , indicating that as k 1 is increased, the required time for total conversion is decreased.
Starting from the most widely reported conditions for TEMPO-mediated oxidation, indicated in Fig. 4 with the yellow vertical line, it is clear that few improvements in terms of time can be achieved modifying process conditions. Only temperature showed a significant effect on the kinetic constant, as well as on the required time to achieve the complete conversion of CH 2 OH to COOgroups. It becomes apparent that increasing the temperature from 20 °C to 25 or 30 °C would significantly decrease the t final , while the required extra energy is residual compared to other strategies such as mechanical refining. Furthermore, increasing the amount of TEMPO or NaBr would be detrimental in terms of production costs. In this context, TEMPO prices have been regarded as a key barrier for the industrial-scale production of nanoscale oxycellulose (Clauser et al. 2022). The improvement in terms of reaction time due to the increase of the initial surface area of the fibers, this is PFI refining, is not justified because of the lower yield (waste generation) and additional energy consumption (4.44 kWh/kg for 10,000 PFI revolutions). According to the literature, pH of roughly 10-11 should be maintained to ensure optimal conditions of reaction. As seen from Fig. 5, the difference in pH from 10.5 to 11.5 shows, at the beginning of the process, higher reaction rates (inset figure) and a higher conversion for the same consumption of NaOH (Lin et al. 2018). Differences beyond 0.5-0.6 mmol COO -/g are non-significant, and thus the final oxidation degree does not depend on pH over this narrow range. Differing from previous results, reactions conducted with pH values above 11 did not result in fibers with lower oxidation degree.
Taking into account the pK a values of hypobromous and hypoclorous acids, respectively 8.6 and 7.5 (Kim et al. 2021), their ionization under the pH range studied is quantitative, with little difference at pH 10.5 or pH 11.5. Therefore, all possible effects of OHconcentration are related to cellulose itself. With a pK a value between 12 and 13 for the primary hydroxyl groups (Bialik et al. 2016), an increase in pH from 10.5 to 11.5 is enough to explain why the polymer is more accessible during the first stages of the reaction in the latter case.
Insights into the progressive accessibility of primary hydroxyl groups through OH(6) oxidation and depolymerization Reservations to reality compel us to justify why homogeneous models satisfactorily describe the TEMPO-mediated oxidation of cellulosic fibers, while etherification of cellulose, for instance, tend to be better fitted by chemisorption models (Aguado et al. 2018). It is possible to observe from Fig. 2 that for lower temperature and concentration of catalysts and co-catalysts, there is an increase in the latency time until the reaction assumes an apparent firstorder pattern. That could be explained by lower energetic availability from a thermodynamic perspective. In addition, we hypothesize that kinetic control is favored by the initial effect of surface oxidation, rapidly disrupting the supramolecular structure of the fiber. In cases of optimal conditions, this latency time is absent. Hence, the presence or lack of mass transfer limitations depends on proper TEMPO activation and on the initial rates of reaction, affected by catalyst concentration. Figure 5 schematizes the different processes undergone by a cellulosic fiber through TEMPO-mediated oxidation, from its supramolecular structure to a molecular scale. We claim that there is synergy involving regioselective oxidation, depolymerization, and subsequent processes of hydration, spacing, peeling, and unbundling. First, carboxylate groups grant the presence of more water molecules while hindering cellulose-cellulose intermolecular interactions. Hence, a higher hydration degree results in more effective mass transfer phenomena, therefore exposing the β-1,4 acetal bonds to oxidative cleavage by BrO -/ClO -. This effect is also highlighted by how mechanical refinement improves the reaction rate, as it increases the availability of groups susceptible to oxidation (Fig. 2D).
It should be noted that these oxidants are consumed by both reactions, OH(6) oxidation and oxidative cleavage of glycosidic bonds. For lower TEMPO concentrations, a lower carboxyl content is achieved, possible due to a higher consumption of oxidants into oxidative cleavage, since the presence of aldehyde groups formed by the first stage of oxidation remains low during the reaction time. In other words, a higher ratio of TEMPO to ClO -/BrOgrants higher selectivity to OH(6) oxidation, avoiding excessive depolymerization (Spier et al. 2017) (Fig. 6).
The degree of polymerization of polysaccharides and the carboxyl content attained by TEMPO-mediated oxidation are unequivocally correlated, both increasing with the oxidative charge and pH (Shinoda et al. 2012;Serra et al. 2017). While it is known that a pH around 10 is ideal for the stability of TEMPO, it has been as well reported that the higher the pH, the higher the extent of the depolymerization (Spier et al. 2017;Lin et al. 2018). This is due to both the higher Fig. 6 Schematic representation of oxidation, depolymerization, hydration, and partial disruption of fibers and microfibers concentration of hydroxide ions and the availability of deprotonated hyprobromite and hypochlorite ions.
Whilst a high enough concentration of oxidants is required for TEMPO activation, we envisage further research on plausible alternative methodologies that uphold this activated TEMPO without majorly compromising the supramolecular structure of fibrils. These conditions could involve controlled addition of oxidants or use of HBr, which would grant lower values of pH since the early stages of reaction while not affecting the Bravailability; therefore not hindering the catalysis provided by it during TEMPO activation followed by -CHO oxidation into -COO -. These two measures have the potential to achieve high carboxyl content in fibers with higher degree of polymerization than the ones reported elsewhere (Serra et al. 2017;Lin et al. 2018).

Conclusions
The present work provides a deep understanding of the reaction mechanism of cellulose with TEMPO/ NaBr/NaOH system, as well as the effect of process conditions on the reaction kinetics. In a first part of the study, it was found that regardless the process conditions, the NaOH consumption exhibited a linear relationship with the carboxyl content of the fibers, which indicates that the evolution of the reaction could be directly monitored by means of considering the amount of NaOH per gram of fiber. This infers the possibility of using a calibration curve to estimate the oxidation degree based on NaOH addition, potentially skipping a characterization step that could be performed only for validation purposes. In addition, this relationship was found to be the same at varying temperature, NaBr content and surface area of the fibers, while different TEMPO contents were found to have different impact on this correlation. This was attributed to the capacity of TEMPO to protect the fibers and then, preventing their depolymerization. In light of the competing OH(6) oxidation and the oxidative cleavage of β-1,4 bonds, we advise against the common practice of quenching the reaction once the pH remains stable. This way, the last period of the process still shows consumption of ClO -, but particularly directed to depolymerization. Instead, the process should be finished in a predetermined, optimized NaOH consumption.
The obtained results were consistent with those previously reported for cotton or regenerated cellulose, particularly in terms of energy of activation, which validates the study. Modifying the process conditions only resulted in positive impact for temperature, where the required time for complete conversion was found to be significantly decreased at 25 and 30 °C. However, this was not observed at increasing TEMPO and NaBr contents, and only a slight reduction was observed at increasing PFI revolutions. Further, the increase on surface area resulted in lower yield reactions, which implies the generation of higher amount of waste in the form of dissolved substances. Finally, pH was found to have low effect on oxidation, at least between 10.5 and 11.5, where no significant differences were observed at relatively high CC.
The present work was conducted at a NaClO dosage of 5 mmol/g and results are consistent with a pseudo-first order kinetics. However, the need of conducting further studies at different NaClO amounts, as well as further understanding the mechanism of TEMPO, is clear. Moreover, despite the proven usefulness of monitoring NaOH consumption and CC, other characteristics of the oxidized fibers should be taken into account: rheology, transmittance, conductivity. Besides these properties, which can be measured in-line, the effects of TEMPO-mediated oxidation on remaining hemicelluloses can impact the quality and usability of the end product. received funding for his PhD thesis by the University of Girona (PhD grant IFUdG2020).
Data availability Raw data of the present work can be made available upon request.

Declarations
Conflict of interest Authors declare that they have no known competing interests or personal relationships that could have appeared to influence the work reported in this paper.
Ethics approval and consent to participate Authors declare that the manuscript is not submitted to any other journal at the time of submission for simultaneous consideration, that the submitted work is original and has not been published elsewhere in any form, that this work is not part of a single study, that results are presented under the principles of honesty, without fabrication falsification or inappropriate data manipulation and that no data, text or theories by others are presented as our own.

Consent for publication
All authors have revised the last version of the submitted manuscript and we approve its submission.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.