Kinetics of the adsorption of polyDADMAC
Strong ionic interactions were formed between the deprotonated hemiacetal groups (–CH2–O–) of cellulose, as the secondary hydroxyl groups are not expected to become dissociated at the pH of the adsorption process (Bialik et al. 2016), and the quaternary ammonium groups of polyDADMAC. After the washing step and the subsequent reprotonation, the cationic polyelectrolyte was still firmly linking to cellulose via ion-dipole forces, and even to the remaining carboxylate groups of acidic hemicelluloses. This was confirmed by consistently obtaining a positively-charged sample after adsorption during at least 30 min and rinsing.
The evolution of the charge density with time is depicted in Fig. 2a. Originally, all pulps (unrefined and refined) had negative surface charge, due to the polarized hydroxyl groups and the carboxyl groups of the remaining glucuronic acid of hemicellulose units. This negative charge increased with the number of PFI revs., due to the higher number of functional groups exposed per gram of pulp. Likewise, during cationization, these increasingly exposed functional groups were available for adsorption of polyDADMAC. In general, as easily visualized from Fig. 2b and as confirmed by the results of ANOVA analyses, for any given time beyond the first 30 min of cationization, the positive influence of refining on cationicity was deemed significant (p < 10–5 in all cases).
In what pertains to modeling, it is reasonable to assume that cationization happens preferentially at the surface of fibers, at the fibrils protruding from them, and through the most accessible pores. As no covalent bonds are formed or undone during this kind of cationization, the control of the process by any kind of bimolecular substitution kinetics can be discarded. This leaves the modeling of polyDADMAC cationization of cellulose as a case of adsorption kinetics. Eqs. 3, 4, and 5 are adaptations of pseudo-first, pseudo-second and Elovich integrated rate equations (Aniagor and Menkiti 2018; Seema et al. 2018; Aguado et al. 2021), respectively, in such way that the initial surface charge is taken into account:
$$CD={CD}_{0}+\frac{{{CD}_{eq}}^{2} k t}{1+k t {CD}_{eq}}$$
3
$$CD={CD}_{0}+{CD}_{eq}\left(1-{e}^{-kt}\right)$$
4
$$CD={CD}_{0}+\frac{1}{\beta }\text{ln}\alpha t$$
5
Fittings to a pseudo-first order equation (Lagengren kinetics, Eq. 3) resulted in correlation coefficients in the range 0.950–0.972 and, more importantly, a non-random distribution of errors. The goodness of the fitting to Elovich kinetics (logarithmic function, Eq. 5) was intermediate, with correlation coefficients between 0.978 and 0.988, and with random distribution of errors only after 2 h of reaction time.
In contrast, as shown in Table 1, correlation to Eq. 4 was excellent. Moreover, Fig. 2 shows, along with the fitting lines, an inset figure representing the regular residuals for the case of 2500 revs., as an example. The absolute value of the average regular residuals was lower than 2 µeq/g for each of the time values. Therefore, it can be concluded that the non-covalent cationization of cellulose with polyDADMAC follows pseudo-second order kinetics. This is not proof of chemisorption, as commonly misunderstood, but rather an indication of diffusion as the rate-controlling stage. This was discussed in depth in an impressive review from Hubbe et al. (Hubbe et al. 2019). Indeed, due to the high molecular weight of polyDADMAC, its diffusion through each of the fibers is severely hampered (Zhang et al. 2016; Serra-Parareda et al. 2021a), making it the slowest stage of the sorption process. Still, while the diffusion of non-ionic compounds through cellulose may take more than one day to attain the equilibrium (Aguado et al. 2021), cationic polyelectrolytes quickly reach the saturation point.
Zhang et al. (2016) compared the time required for the charge to level off with polyDADMAC of different molecular weight: quick if the MW was 200–350 kDa, much slower if its MW was 7.5–15 kDa. With an intermediate MW, we found the corresponding time to be intermediate as well, although the different source of fibers compels us to take this comparison with due caution.
Table 1
Fitting parameters of the pseudo-second order rate equation (Eq. 4), for each number of revolutions (revs.) undertaken during PFI refining.
PFI revs. | CD0 (µeq/g) | CDeq (µeq/g) | k (g µeq− 1 h− 1) | R2 |
0 | –45 ± 3 | 227 ± 4 | 0.015 ± 0.001 | 0.998 |
2500 | –50 ± 4 | 241 ± 5 | 0.018 ± 0.002 | 0.997 |
5000 | –68 ± 3 | 271 ± 3 | 0.016 | 0.999 |
7500 | –69 ± 4 | 282 ± 5 | 0.013 ± 0.001 | 0.998 |
10000 | –85 ± 4 | 299 ± 5 | 0.016 ± 0.001 | 0.998 |
Influence of the non-covalent cationization on pulp properties
As it is well-known, refining increases the relative amount of water that fibers can hold, both during fast drainage (freeness tests) or when forcing non-bound water out by centrifugation (Zhao et al. 2016). In other words, the proportions of both unbound and bound water were expected to increase, as confirmed in Fig. 3. Moreover, these graphs for WRV (Fig. 3a) and Schopper-Riegler number (Fig. 3b) also show that non-covalent cationization with polyDADMAC resulted, likewise, in more water holding. Indeed, the surface of the fibers became covered by ionic, and thus hydrophilic, functional groups.
However, the water-holding enhancement effect of cationization was more accentuated on unrefined pulps. We ran a two-way ANOVA factor analysis to check whether the combined effect of refining and polyDADMAC adsorption was significant, resulting in F = 18.7 and p = 1.8 × 10–5. Therefore, the null hypothesis for binary interactions can be safely discarded.
The same cannot be said on the combined effect of refining and cationization of fiber dimensions and on the percentage of fines. These properties are displayed in Table 2, where average values are weighted in weight. As expected, refining shortened fibers (p = 0.04) and generated fines from them (p = 0.02). However, the influence of polyDADMAC adsorption was inconclusive (p > 0.05 in both cases). Regarding fiber width, refining does have well-known effects, but the sum of forces eroding the fiber wall and an increase in fibers’ ability to swell makes the outcome difficult to predict.
Table 2
Evolution of average fiber dimensions and fines content with refining and with the concentration of cationic polyelectrolyte in the medium
PFI revs. | wt.% poly-DADMAC | Fiber length (µm) | Fiber diameter (µm) | Fines (%) |
0 | 0 | 1007 ± 28 | 16 | 41 ± 2 |
20 | 575 ± 47 | 17 | 38 ± 2 |
30 | 717 ± 6 | 17 | 39.4 ± 0.6 |
2500 | 0 | 768 ± 24 | 20 | 40.8 ± 2.7 |
20 | 781 ± 21 | 17 | 41.3 ± 0.6 |
5000 | 0 | 743 ± 71 | 17 ± 1 | 49 ± 3 |
20 | 633 ± 25 | 18 | 50.2 ± 1.0 |
7500 | 0 | 640 ± 16 | 19 | 52.9 ± 0.5 |
20 | 681 ± 19 | 19 | 52.7 ± 1.1 |
10000 | 0 | 614 ± 33 | 19 | 53.7 ± 0.8 |
20 | 617 ± 26 | 20 | 54.1 ± 1.0 |
How polyDADMAC adsorption impacts the nanocellulose suspension
After fibrillation by means of HPH, the presence of cationic polyelectrolyte exerted some evident effects on the suspension of cellulosic micro-/nanofibers. Figure 4a shows the effects of polyDADMAC adsorption to different levels on the nanofibrillation of fibers that had been refined to 10000 PFI revs. CNF suspensions became more easily precipitable, which was not easily predictable considering the opposing effects of electrostatic repulsion between polyDADMAC-coated nanofibers and polyDADMAC-induced aggregation. The latter outweighed the former, as shown by the diminishment of nanofibrillation yield and transmittance. In other words, the weight ratio of fibrils that sedimented by centrifugation increased with the amount of polyDADMAC.
Being a well-known coagulating and flocculating agent, polyDADMAC chains can act as bridges between nanofibers, thus increasing their effective size. Not only was phase separation promoted, but also, within the stably dispersed phase (supernatant), the increase in size resulted in higher opacity due to light scattering. This can be a drawback in applications that require stable and transparent dispersions of nanoscale cellulose, but it should not be a problem if microscale (rather than nanoscale) particles are tolerated or desired.
Figure 4b shows that, regardless of the sign of the surface charge, its absolute value became greater after homogenization. Two conclusions can be drawn from this: i) the adsorption of polyDADMAC on cellulosic fibers was strong enough not to be disrupted by the HPH; ii) fibrillation exposed surfaces that were not accessible to the polyelectrolyte of opposite charge for potentiometric titrations (PES-Na), but where polyDADMAC, at least its shortest chains, had diffused through.
The use of non-covalent cationic nanocellulose for paper strengthening
It is known that nanocellulose, when added to pulps in sheet forming, offers much more surface area for hydrogen bonding and attains a more compact, less porous structure (Li et al. 2021). Overall, this is key to understand why paper is toughened. Therefore, before dealing with the effects on paper strength themselves, it is worth observing Fig. 5, which shows that the least air-permeable paper was not attained with polyDADMAC-containing nanofibers, but with mechanical CNFs without a cationization pretreatment of any kind. Most likely, the cause is the same as that of the lower transmittance, as polyDADMAC-induced aggregation hampered the homogeneous distribution of CNFs across the sheet and their diffusion through interfiber spaces. Even when c-CNFs obtained with polyDADMAC 30% complemented mechanical nanocellulose (+ 3% mechanical CNFs + 3% c-CNFs), in what we could call a dual system given the latter’s slightly negative charge, the sheet was not sealed to a greater degree than when adding + 6% mechanical CNFs. Within non-covalent cationic nanocellulose samples, there is no consistent and significant difference between the different polyDADMAC concentrations, 20% and 30% (p = 0.75).
Paper mechanical properties are displayed in Table 3. The burst index, the internal cohesion (Scott bond) and the tensile index were consistently and significantly improved by all kinds of nanocellulose. However, although partially overlapped tolerance intervals do not necessarily imply non-significant differences (MacGregor-Fors and Payton 2013), most of the differences between mechanical and cationic CNFs, or between c-CNFs obtained with different polyelectrolyte concentrations, were non-significant (p > 0.05).
Here follows a list of valuable statements drawn after neglecting those non-significant differences. First, a 3% addition of c-CNFs attained a higher tensile index than a 3% addition of mechanical CNFs. Second, combining a 3% addition of c-CNFs (polyDADMAC 30%) with a 3% addition of mechanical CNFs (dual system) attained a lower improvement in the tear index than a direct 6% addition of mechanical CNFs. Third, a 6% addition of c-CNFs attained a higher internal cohesion than a 6% addition of mechanical CNFs.
In any case, and regardless of the deviation, Fig. 6 highlights the trends followed by the mean values for the sake of direct visualization. All in all, the differences between the polyDADMAC-pretreated nanocellulose and the mechanical one were inconsistently positive, negative, or simply non-significant. It may be suggested that the negative effects from polyelectrolyte-induced agglutination were somehow compensated by the favored nanofiber-fiber interaction.
Table 3
Mechanical properties of recycled board sheets, without and with nanocellulose of different kinds. The amplitude of the tolerance intervals equals twice the standard deviation
| Tensile index (N m g− 1) | Tear index (N m2 kg− 1) | Burst index (kPa m2 g− 1) | Scott bond (J m− 2) |
Control recycled board | 28 ± 1 | 7.1 ± 0.8 | 1.2 ± 0.1 | 197 ± 8 |
+ 3% mechanical CNFs | 38 ± 4 | 7.6 ± 0.4 | 1.55 ± 0.08 | 256 ± 8 |
+ 3% c-CNFs 20% polyDADMAC | 43 ± 2 | 7.5 ± 0.5 | 1.44 ± 0.07 | 237 ± 11 |
+ 3% c-CNFs 30% polyDADMAC | 44 ± 2 | 7.1 ± 0.5 | 1.54 ± 0.08 | 261 ± 14 |
+ 6% mechanical CNFs | 40 ± 3 | 8.6 ± 0.3 | 1.74 ± 0.01 | 256 ± 16 |
+ 6% c-CNFs 20% polyDADMAC | 36 ± 2 | 8.1 ± 0.8 | 1.6 ± 0.2 | 289 ± 9 |
+ 6% c-CNFs 30% polyDADMAC | 38 ± 5 | 7.6 ± 0.4 | 1.7 ± 0.2 | 285 ± 15 |
+ 3% mechanical CNFs + 3% c-CNFs | 37 ± 5 | 7.6 ± 0.7 | 1.6 ± 0.1 | 289 ± 15 |
Pulp, polyelectrolyte and nanocellulose: schematizing the interactions
In light of all the results, we can draw some conclusions about the hypotheses tested and, not less importantly, new hypothesis to be considered in future research. The former include the aggregation of micro-/nanofibers that was evidenced by lower transparency and greater proportion of sediment after centrifugation. The latter involve the double-edge effect of c-CNFs in paper strengthening, as we presumed that the loss of surface area due to aggregation accounted for a negative influence, while the favored adsorption on the pulp exerted a positive contribution.
All of this discussion should be combined with our previous elucidations on the relationship concerning polyDADMAC adsorption, the specific surface area and the influence of the pH and the ionic strength (Serra-Parareda et al. 2021a). As estimated therein, the area of the DADMAC monomer is 1.55 × 1017 nm2 µeq− 1 and the weight-average end-to-end chain length of the polymer is not greater than 321 nm, corresponding to a rod-like model. Under conditions of low ionic strength and slightly alkaline pH, polyDADMAC can behave as a semi-flexible polymer (Zhang et al. 2019). While the charged ring is planar and stiff, rotation around CH2–CH2 bonds is allowed, at least in small angles.
Figure 7 represents a plausible and simplified model for the adsorption of polyDADMAC onto CNFs and the subsequent interactions with the recycled pulp. Here follows a discussion from bottom to top. The pulp, which has not been submitted to any treatment that could have caused conversion to cellulose II or amorphous cellulose, has its chains arranged in a parallel fashion, at least along the crystalline domains. From the moment that the pH held during adsorption decreases, the reprotonated hemiacetal groups and even some secondary hydroxyl groups are capable of remain attached to polyDADMAC by ion-dipole interactions, while free monomers grant a positive surface charge. At a higher scale, the same free monomers or even large chain segments promote the coagulation-flocculation of nanofibers. Finally, although aggregated to a certain extent and thus heterogeneously distributed, c-CNFs diffuse through spaces between fibers, between fines, and between fines and fibers, while the adsorbed polyDADMAC chains provide some bridging and anchor points between nanoscale cellulose and fibers/fines.