Chitosan Hydrogels Based on the Diels–Alder Click Reaction: Rheological and Kinetic Study

The Diels–Alder reaction is recognized to generate highly selective and regiospecific cycloadducts. In this study, we carried out a rheological and kinetic study of N-furfuryl chitosan hydrogels based on the Diels–Alder click reaction with different poly(ethylene)glycol-maleimide derivatives in dilute aqueous acidic solutions. It was possible to prepare clear and transparent hydrogels with excellent mechanical properties. Applying the Winter and Chambon criterion the gel times were estimated at different temperatures, and the activation energy was calculated. The higher the temperature of gelation, the higher the reaction rate. The crosslinking density and the elastic properties seem to be controlled by the diffusion of the polymer segments, rather than by the kinetics of the reaction. An increase in the concentration of any of the two functional groups is accompanied by a higher crosslinking density regardless maleimide:furan molar ratio. The hydrogel showed an improvement in their mechanical properties as the temperature increases up to 70 °C. Above that, there is a drop in G’ values indicating that there is a process opposing to the Diels–Alder reaction, most likely the retro-Diels–Alder.


Introduction
Chitosan is one of the most abundant polysaccharides in nature. It exhibits biological properties such as low toxicity, mucoadhesivity, biocompatibility, and biodegradability, which make it attractive for use as a drug delivery vehicle [1,2]. Due to the presence of abundant amino (-NH 2 ) and hydroxyl (-OH) groups, chitosan can be chemically crosslinked giving rise to hydrogels with interesting properties for a wide variety of applications [3][4][5]. Chitosan hydrogels can also be prepared by the Diels-Alder reaction [6][7][8][9]. Many chitosan derivatives have been developed to improve the encapsulation efficiency of hydrophilic drugs, including chitosan-g-poly(ethylene) glycol [10,11]. A wide range of poly(ethylene)glycol (PEGs) with functionalized end groups (e.g., azides, thiols, maleimides, carboxylic acids, hydroxyls, and epoxides) are currently available, increasing the attractiveness of their use in biomedical and biomaterial applications [12]. PEG-based hydrogels have shown interesting properties for their implementation in biological applications such as low toxicity and rapid elimination after oral administration.
An alternative and relatively novel approach to classical derivatization methods is the use of click chemistry reactions. The term click chemistry was first coined by K. B. Sharpless in 2001 to describe the rapid formation of crosslinked networks from modular units [13]. Click chemistry reactions are characterized by high yields and proceed without the formation of by-products. These reactions are stereospecific and thermodynamically favorable. Currently, the use of click chemistry in polymer research is an interesting strategy to design polymer-based hydrogels, drug and gene delivery systems, scaffolds for tissue tissue engineering, among other materials [14,15]. This is due to the adva by these reactions to control the properties of hydrogels, their degree of cro in some cases, thermal reversibility.
Among click chemistry reactions, the Diels-Alder (DA) coupling reac highly selective [4 + 2] cycloaddition between a conjugated diene and a dien a stable cycloadduct. The Diels-Alder reaction must be considered as a che rium, where the direct reaction proceeds at low temperatures (normally be the reverse reaction that takes place at higher temperatures as a consequen activation energy [16]. The structural characteristics of furan and its derivat with its natural and renewable origin-make it the ideal dienic reagent for th reaction [17]. Today, the most studied diene/dienophile system is furan/ma can react through the Diels-Alder cycloaddition and is, in many cases, rev peratures above 100 °C [18,19]. It is well known that the cycloadduct formed during the Diels-Alde two stereoisomers, endo and exo. Furans participate in Diels-Alder reactio philes, producing exo-cycloadducts-which are thermodynamically more less steric hindrance-than their counterpart, endo-adducts, which are kine (Scheme 1).

Scheme 1. Diels-Alder cycloaddition reaction between furan and maleimide deriva
In this article, the rheological behavior, and aspects of the kinetics of th crosslinking reaction between N-furfuryl chitosan and PEG-maleimide which takes place in an aqueous medium-are studied. The influence of tem degree of polymerization, and functionality of PEG-maleimide derivative tion, as well as the influence of temperature on the mechanical properties hydrogel, is investigated.

Materials
Chitosan with a degree of acetylation of 18% and weight-average mo of 200 kDa was provided by Primex ehf (Siglufjordur, Iceland). Low polyd ethylene glycol 2-and 4-arm maleimide derivatives were acquired from Jen ogy, TX, USA. The characteristics of these PEG-maleimide derivatives are s Table 1. All other reagents were purchased from Sigma-Aldrich, Merck KGa Germany. Deionized Type I ultrapure water with a conductivity lower th was used in all experiments. Scheme 1. Diels-Alder cycloaddition reaction between furan and maleimide derivatives.
In this article, the rheological behavior, and aspects of the kinetics of the Diels-Alder crosslinking reaction between N-furfuryl chitosan and PEG-maleimide derivatives-which takes place in an aqueous medium-are studied. The influence of temperature, the degree of polymerization, and functionality of PEG-maleimide derivatives on the reaction, as well as the influence of temperature on the mechanical properties of the formed hydrogel, is investigated.

Materials
Chitosan with a degree of acetylation of 18% and weight-average molecular weight of 200 kDa was provided by Primex ehf (Siglufjordur, Iceland). Low polydispersity polyethylene glycol 2-and 4-arm maleimide derivatives were acquired from JenKem Technology, TX, USA. The characteristics of these PEG-maleimide derivatives are summarized in Table 1. All other reagents were purchased from Sigma-Aldrich, Merck KGaA, Darmstadt, Germany. Deionized Type I ultrapure water with a conductivity lower than 0.05 µS/cm was used in all experiments.

Synthesis of N-Furfuryl-Chitosan (FCs)
The synthesis of N-furfuryl chitosan was carried out as described by Montiel-Herrera et al. with modifications [6]. Briefly, 2.58 g chitosan (12.17 -NH 2 mmol) was dissolved in 1000 mL of 2% aqueous acetic acid overnight. Next, 433 µL of furfural (5.23 mmol) was dropped under stirring into the Cs solution at room temperature and allowed to react for 4 h at pH 5. Then, 16 mL of a freshly prepared aqueous solution containing 0.987 g of NaH 3 BCN was slowly added with the aid of a peristaltic pump (Minipuls 3, Gilson, France), and the reaction was further conducted for 3 h. After the completion of the process, the chitosan derivative was precipitated with 1 M NH 4 OH until a pH~7-8 was attained, and successively washed with water until reaching a 0.5 µS/cm conductivity, water:ethanol mixtures 40:60, 20:80 (v:v) and ethanol. Finally, the purified sample was dried at room temperature under vacuum (yield: 83%).

Fourier Transformed Infrared Spectroscopy (FTIR)
The spectra were recorded with a Nicolet Protege team (System 460 E.S.P) FT-IR spectrometer (Madison WI, USA) by the accumulation of 64 scans with a resolution of 4 cm −1 . The attenuated total reflectance (ATR) module was used.

Nuclear Magnetic Resonance ( 1 H-NMR)
High-resolution 1 H-NMR spectroscopy was carried out on a Bruker Avance 400 spectrometer (Billerica, MA, USA) operating at 400 MHz, and 90 • pulse was 14.0 ms. The spectra were registered at 25 • C. Samples of FCs were solubilized in D 2 O/DCl (polymer concentration ≈ 6 mg/mL).

Rheological Studies
Dynamic viscoelastic measurements were carried out using an AR-G2 rheometer (TA Instruments, New Castle, DE, USA) equipped with a stainless-steel parallel plate geometry (diameter: 40 mm; gap: 1000 µm) and a Peltier system for temperature control.
A fresh FCs solution prepared the day before in acetic acid (2%) was mixed with the appropriate amount of the maleimide compound and stirred for a few minutes. The mole ratio of maleimide to furan groups, R, was chosen to be 0.25 or 0.5. Before loading the sample into the rheometer, it was centrifuged for 6 min at 15,000× g, to remove bubbles. A thin layer of low viscosity silicone oil was added around the periphery of the geometry plate to prevent the evaporation of the sample.
All experiments were performed isothermally, according to the following program: initially, a mechanical spectrum was recorded at 25 • C within a frequency range of ω = 0.1-100 rad·s −1 , followed by rapid heating of the sample up to the gelation temperature, typically in 30-45 s. The Diels-Alder reaction was then monitored isothermally by the variation of G and G at three frequencies between 1 and 10 rad·s −1 . In all cases, a 2.5% strain was used, thus ensuring that measurements were performed within the linear viscoelastic region and avoiding damages to the gel that is forming. Unless otherwise stated, at the end of the crosslinking process a mechanical spectrum was accomplished at the gelation temperature, followed by another one at 25 • C under the same conditions as described above.

Diels-Alder Click Reaction for Chemical Crosslinking of Chitosan
Diels-Alder cycloaddition is one of the click chemistry reactions, allowing a high process control and valuable versatility. In macromolecular chemistry, it can be used for polymerization, polymer modification, gelation, and thanks to its dynamic character, advanced applications have also been proposed. There are studies in which this reaction is applied for the formation of chemical gels of polysaccharides in particular chitosan, rendering networks with interesting properties.
A synthetic pathway for grafting furan groups into the chitosan backbone under mild conditions with adequate regioselectivity has been proposed (Scheme S1) [6]. The derivative obtained was characterized by FTIR and 1 H-NMR spectroscopies ( Figures S1 and S2, respectively). In the FTIR spectra there are three bands at 746, 821, and 901 cm −1 due to the presence of the furan ring on the N-furfuryl chitosan. Meanwhile, the NMR spectrum of the derivative shows the characteristic signals of the furan ring between 6.25 and 7.5 ppm. From the latter, a degree of N-furfuryl substitution of 21% was estimated.
In the present study, polyethylene glycol maleimide-terminated derivatives with different degrees of polymerization and functionalities were chosen ( Table 1). The Diels-Alder reaction between N-furfuryl chitosan and these PEG-maleimide derivatives gives clear and transparent hydrogels, with excellent mechanical properties, as can be appreciated in Scheme 2.
Polymers 2022, 14, x 4 of 17 gelation temperature, followed by another one at 25 °C under the same conditions as described above.

Diels-Alder Click Reaction for Chemical Crosslinking of Chitosan
Diels-Alder cycloaddition is one of the click chemistry reactions, allowing a high process control and valuable versatility. In macromolecular chemistry, it can be used for polymerization, polymer modification, gelation, and thanks to its dynamic character, advanced applications have also been proposed. There are studies in which this reaction is applied for the formation of chemical gels of polysaccharides in particular chitosan, rendering networks with interesting properties.
A synthetic pathway for grafting furan groups into the chitosan backbone under mild conditions with adequate regioselectivity has been proposed (Scheme S1) [6]. The derivative obtained was characterized by FTIR and 1 H-NMR spectroscopies ( Figures S1 and S2, respectively). In the FTIR spectra there are three bands at 746, 821, and 901 cm −1 due to the presence of the furan ring on the N-furfuryl chitosan. Meanwhile, the NMR spectrum of the derivative shows the characteristic signals of the furan ring between 6.25 and 7.5 ppm. From the latter, a degree of N-furfuryl substitution of 21% was estimated.
In the present study, polyethylene glycol maleimide-terminated derivatives with different degrees of polymerization and functionalities were chosen ( Table 1). The Diels-Alder reaction between N-furfuryl chitosan and these PEG-maleimide derivatives gives clear and transparent hydrogels, with excellent mechanical properties, as can be appreciated in Scheme 2. Scheme 2. Diels-Alder reaction between N-furfuryl chitosan and PEG-maleimide compounds.
The FTIR spectra of the N-furfuryl chitosan, PEG-bismaleimide, and the Diels-Alder adduct hydrogel are presented in Figure S3. The bismaleimide compound exhibits the characteristic bands of poly(ethylene glycol)s and maleimide groups, particularly the bands at 1707 cm −1 (C=O stretching), 1466 cm −1 (C=C stretching), 1341 cm −1 (C-N stretching), 1150 cm −1 (C-N-C bending), 840 cm −1 (C-H wagging vibration), and 695 cm −1 (=C-H out-of-plane bending) [20][21][22]. The chitosan derivative, among others, displays the signals corresponding to the furan ring: 1374 cm −1 (C=C furan ring stretching vibration), 895 cm −1 (out-of-plane deformation vibration), and 660 cm −1 (furan ring deformation). After the crosslinking Diels-Alder reaction, it is evident that maleimide and furan characteristic bands are all diminished in the adduct spectrum, confirming the consumption of the maleimide and furan groups. Moreover, there are new peaks at 1454 cm −1 (C=C stretching), 1258 cm −1 (C-O symmetric stretching), 947 cm −1 (C-H in-plane deformation), and 799 cm −1 (C-H out-of-plane deformation) [8,23,24]. These results confirm the crosslinking Diels-Alder reaction between N-furfuryl chitosan and PEG-bismaleimide, and the formation of the cycloadduct. The hydrogel system formed by N-furfuryl chitosan (1%-w/w), PEG(mal) 2 -7500, and a mole ratio of maleimide to furan groups of 0.25 was first selected. The dynamic mechanical spectra at 25 • C of the precursor solution, and that of the corresponding hydrogel prepared at 50 • C, are displayed in Figure S4. The viscoelastic behavior of the reaction mixture matches that of a concentrated polymer solution, with both G and G showing frequency dependence ( Figure S4a). Moreover, the frequency sweep of the resulting hydrogel is the typical mechanical spectrum of a crosslinked polymer system ( Figure S4b): the storage modulus has no dependence on the frequency and is almost two orders of magnitude higher than G . This corroborates that the Diels-Alder reaction gives rise to a hydrogel with good mechanical properties, as it will be confirmed later.

Rheological Analysis of the Influence of Temperature on Diels-Alder Cycloaddition for Chemical Crosslinking
Among the different experimental parameters having a major effect on the Diels-Alder click reaction, temperature is of the utmost importance. Indeed, the Diels-Alder cycloaddition is, in fact, an equilibrium chemical process. The relationship between Diels-Alder and retro-Diels-Alder reactions determines many of their applications, as well as the mechanical properties of the resulting hydrogels.
The kinetics of the gelation process and the viscoelastic properties of the hydrogels prepared via the DA reaction between N-furfuryl chitosan and PEG-maleimide derivatives were then investigated by low deformation dynamic rheology, under isothermal conditions at temperatures between 50 and 90 • C.
In Figure 1, the evolution of the storage and loss moduli during the gelation at 50, 70, and 90 • C is presented. It is evident that, as the temperature increases, the time necessary to reach equilibrium decreases from 12 to around 2 h, while the equilibrium values of the storage modulus also diminish.
The hydrogel system formed by N-furfuryl chitosan (1 %-w/w), PEG(mal)2-7500, and a mole ratio of maleimide to furan groups of 0.25 was first selected. The dynamic mechanical spectra at 25 °C of the precursor solution, and that of the corresponding hydrogel prepared at 50 °C , are displayed in Figure S4. The viscoelastic behavior of the reaction mixture matches that of a concentrated polymer solution, with both G' and G'' showing frequency dependence ( Figure S4a). Moreover, the frequency sweep of the resulting hydrogel is the typical mechanical spectrum of a crosslinked polymer system ( Figure S4b): the storage modulus has no dependence on the frequency and is almost two orders of magnitude higher than G''. This corroborates that the Diels-Alder reaction gives rise to a hydrogel with good mechanical properties, as it will be confirmed later.

Rheological Analysis of the Influence of Temperature on Diels-Alder Cycloaddition for Chemical Crosslinking
Among the different experimental parameters having a major effect on the Diels-Alder click reaction, temperature is of the utmost importance. Indeed, the Diels-Alder cycloaddition is, in fact, an equilibrium chemical process. The relationship between Diels-Alder and retro-Diels-Alder reactions determines many of their applications, as well as the mechanical properties of the resulting hydrogels.
The kinetics of the gelation process and the viscoelastic properties of the hydrogels prepared via the DA reaction between N-furfuryl chitosan and PEG-maleimide derivatives were then investigated by low deformation dynamic rheology, under isothermal conditions at temperatures between 50 and 90 °C.
In Figure 1, the evolution of the storage and loss moduli during the gelation at 50, 70, and 90 °C is presented. It is evident that, as the temperature increases, the time necessary to reach equilibrium decreases from 12 to around 2 h, while the equilibrium values of the storage modulus also diminish.  Polymeric materials are characterized by broad relaxation spectra, reflecting the variety of polymeric species present. Before the gel point, a crosslinking system exhibits increasingly slower movements as the polymeric crosslinked clusters increase in size, which is accompanied by an increase in their viscosity values. Near the critical point, the relaxation time grows sharply, the relaxation modes are no longer independent, and a characteristic relaxation time cannot be identified anymore. The gel point is reached when the largest molecular group diverges to a theoretical infinite size, limited by the volume of the reactor.
At the critical gelation point, the shear flow properties under steady flow conditions are a sensitive indicator of the proximity of the gel point. The viscosity of the sol fraction increases due to the size of the divergent cluster. The equilibrium modulus gradually increases as an increasing fraction of the molecules binds and thus the sample spanning the entire permanent lattice is strengthened.
A common condition used to determine the isothermal gel time by rheology was suggested by Tung and Dynes as the G -G crossover point, tan(δ) = G /G = 1 [25]. However, in multi-frequency tests, this crossover point is frequency dependent, and it is obvious that the gel point cannot depend on the frequency, as in our system (e.g., Figure S5).
Instead, Winter and Chambon have proposed another criterion, considering that at the critical gel point the system is neither in a viscous liquid state nor an elastic network [26]. Before the gel point, the medium can be considered as a liquid for which G ~ω 2 and G ~ω. As the crosslinking reaction progresses, there is an instant-the critical gel point-at which G and G exhibit a power-law dependence with frequency, ω, of the type G (ω)~G (ω)~ω n .
In this case, "n" is the critical relaxation exponent [27]. After the gel point, the reaction medium is considered equivalent to an elastic solid.
That means that at the critical gel point the tan(δ) is independent of frequency, so in a multi-frequency experiment, the tan(δ) curves pass through a single point. Thus, during a dynamic viscoelastic experiment, simultaneous measurement of tan(δ) at several frequencies provides a convenient method of interpolation for determining the gel point, which is known as the Winter-Chambon criterion. This is under the condition that the deformation remains within the limits of linear viscoelasticity, and the stress is so low, as to avoid any chance of breaking the delicate network in its incipient stages [28].
Applying this approach, it was possible to assess the critical gel times for this hydrogel at temperatures between 50 and 90 • C. The estimation of the gel time at 50 • C is exemplified in Figure 2. According to the Winter and Chambon criterion, n, the critical relaxation exponent, equals 0.552. Values of n larger than 0.5 have been evaluated for stoichiometrically imbalanced gels, characterized with a crosslinker deficiency as in this case [29]. The critical relaxation exponent is known to be independent of temperature [30].
The values of the critical gel time for all temperatures, as well as those of the gel strength, S, are summarized in Table 2. The latter is a parameter depending on the material structure at the transition state and affects the linear constitutive viscoelastic equation. It could be estimated from G at the intersection with G , and it is accepted that it varies with temperature [26,30,31]. As it can be appreciated, the reaction proceeds faster as the temperature increases up to 90 • C, while the strength of the gel decreases under the same conditions.
According to the theory of Winter and Chambon, the gel time should be interpreted as the time at which the critical sol-to-gel conversion occurs during chemical crosslinking under isothermal conditions. Gel times are an intrinsic property of the material at the critical gel point, in the sense that they do not depend on the method, but on the specific characteristics of the polymeric system, under the experimental conditions in which the process takes place. It is reasonable, therefore, to assume that-under the condition that there is only one reaction mechanism involved-the gel time can be considered a quantitative measure of the rate of the overall reaction [32].  Table 2. The latter is a parameter depending on the material structure at the transition state and affects the linear constitutive viscoelastic equation. It could be estimated from G' at the intersection with G'', and it is accepted that it varies with temperature [26,30,31]. As it can be appreciated, the reaction proceeds faster as the temperature increases up to 90 °C, while the strength of the gel decreases under the same conditions. According to the theory of Winter and Chambon, the gel time should be interpreted as the time at which the critical sol-to-gel conversion occurs during chemical crosslinking under isothermal conditions. Gel times are an intrinsic property of the material at the critical gel point, in the sense that they do not depend on the method, but on the specific characteristics of the polymeric system, under the experimental conditions in which the process takes place. It is reasonable, therefore, to assume that-under the condition that there is only one reaction mechanism involved-the gel time can be considered a quantitative measure of the rate of the overall reaction [32].
From the previous discussion, it could be understood that the gel time adequately reflects the kinetics of a chemical crosslinking process, such as the one that concerns us in this study. It is then possible to develop the following mathematical considerations on the kinetics of chemical gelation [32][33][34]. Given the concentration of each type of functional From the previous discussion, it could be understood that the gel time adequately reflects the kinetics of a chemical crosslinking process, such as the one that concerns us in this study. It is then possible to develop the following mathematical considerations on the kinetics of chemical gelation [32][33][34]. Given the concentration of each type of functional groups, C, the rate constant, k, and the kinetic order, n, the general equation for the reaction rate is expressed as: Since we are interested in the kinetic expression at the gel point, Equation (2) should be integrated. The concentration of functional groups at the beginning of the reaction, t 0 , and at the gel point, t gel , will be labeled as C 0 and C gel , respectively. The term on the right is a constant, and will be set equal to B, which makes the rate constant equivalent to k = B/t gel . Being an expression of the kinetics of the reaction, its dependence on temperature obeys the Arrhenius equation with a dependence of this type: where A is the pre-exponential factor, and R and T have their usual significance. Applying logarithms and rearranging, the following expression is attained: which allows for a straightforward evaluation of the activation energy from the values of the gel time on isothermal experiments at different reaction temperatures. This kinetic analysis should be valid under initial conditions in which the direct Diels-Alder reaction is the predominant one. The experimental conditions that must prevail before the critical gel point-particularly in aqueous media and low temperatures, compared to those of other systems-are not logical to be affected by the retro-Diels-Alder reaction since it would be denying the very fact of gelation. Beyond the gel point, when the mobility of the reacting species is severely restricted, it can be speculated that the probabilities of the reverse reaction will increase, affecting the mechanical properties of the final hydrogel. Figure 3 depicts the dependence of gel time on temperature. It is evident that good correlation is attained within the temperature range under study. This result could be indicating that, at least under these experimental conditions, the retro-Diels-Alder reaction does not appear to be affecting the kinetics of the chemical crosslinking process as evidenced by rheological means. From this plot, the activation energy was calculated to be 76 kJ·mol −1 . This value is slightly higher than those found for similar systems by other authors. Normally, values between 30 and 55 kJ·mol −1 have been reported [22,[35][36][37][38][39][40]. This wide range of values in the activation energy could be explained by the specific differences between the chosen diene/dienophile, as well as by other important experimental conditions, such as the solvent or the bulk reaction. To our knowledge, the highest value that has been obtained is 67 kJ·mol −1 , for the bulk maleimide-furan DA reaction assuming second-order kinetics [41].
The present investigation was carried out in a dilute aqueous solution of acetic acid. It is known that the Diels-Alder reaction is considerably faster in water than in organic solvents [42][43][44]. Although there is still no single explanation, it is considered that this effect is a consequence of the polarity of the medium, and the "enforced hydrophobic interactions", generating a packing of the diene and dienophilic groups. Hydrogen bond interactions also contribute to this acceleration. What is more significant in this case, however, is the role of solvent and temperature in the resulting ratio of the two stereoisomers, although here are some conflicting data as well [43].
In 1952 Kwart reported that, in the reaction of maleimide with furan, regardless of the solvent used (water or ether), at 25 • C the endo-isomer is favored, but at 90 • C the exo-adduct is formed [45]. The use of high temperatures allows dissociation and recombination of the adduct, leading to the formation of the thermodynamically stable (exo) adduct, at the expense of the kinetically favored isomer (Scheme 1) [46]. At the same time, reports are indicating that water and other strongly polar solvents cause a loss in the aromaticity of furan, causing the reaction to be thermodynamically controlled (exo-adduct formation) [47]. In the specific case of the reaction of furfural with maleimide derivatives in water (60 • C), exo-adducts are preferably formed in all cases [48]. Polymers 2022, 14, x 9 of 17 The present investigation was carried out in a dilute aqueous solution of acetic acid. It is known that the Diels-Alder reaction is considerably faster in water than in organic solvents [42][43][44]. Although there is still no single explanation, it is considered that this effect is a consequence of the polarity of the medium, and the "enforced hydrophobic interactions", generating a packing of the diene and dienophilic groups. Hydrogen bond interactions also contribute to this acceleration. What is more significant in this case, however, is the role of solvent and temperature in the resulting ratio of the two stereoisomers, although here are some conflicting data as well [43].
In 1952 Kwart reported that, in the reaction of maleimide with furan, regardless of the solvent used (water or ether), at 25 °C the endo-isomer is favored, but at 90 °C the exoadduct is formed [45]. The use of high temperatures allows dissociation and recombination of the adduct, leading to the formation of the thermodynamically stable (exo) adduct, at the expense of the kinetically favored isomer (Scheme 1) [46]. At the same time, reports are indicating that water and other strongly polar solvents cause a loss in the aromaticity of furan, causing the reaction to be thermodynamically controlled (exo-adduct formation) [47]. In the specific case of the reaction of furfural with maleimide derivatives in water (60 °C), exo-adducts are preferably formed in all cases [48].
At the same time, recent kinetic studies on the stereochemistry of the furan/maleimide DA reaction reveal that the endo-isomer has a lower activation energy value than the exo-isomer [49][50][51].
On the one hand, a higher value of activation energy would suggest that, under our experimental conditions, the exo-adduct is being formed preferentially. Nevertheless, the effect of diffusion constraints on the mobility of the polymer chains during the progressive crosslinking, cannot be ruled out either [52]. The former suggests the formation of exoisomers, while the latter would explain why a reaction with higher activation energyrequiring more thermal activation-is favored if it is kinetically disfavored [53,54]. At the same time, recent kinetic studies on the stereochemistry of the furan/maleimide DA reaction reveal that the endo-isomer has a lower activation energy value than the exo-isomer [49][50][51].
On the one hand, a higher value of activation energy would suggest that, under our experimental conditions, the exo-adduct is being formed preferentially. Nevertheless, the effect of diffusion constraints on the mobility of the polymer chains during the progressive crosslinking, cannot be ruled out either [52]. The former suggests the formation of exo-isomers, while the latter would explain why a reaction with higher activation energy-requiring more thermal activation-is favored if it is kinetically disfavored [53,54].

Viscoelastic Characterization of the Hydrogels Obtained at Different Temperatures
A general outlook of the viscoelastic properties of the hydrogels prepared at temperatures between 50 and 90 • C appears in Figure 4 (regardless of the gelation temperature, all mechanical spectra were recorded at 25 • C for comparison purposes). At first glance, it should be noted that, by varying the temperature of the Diels-Alder reaction, hydrogels with good mechanical properties are obtained. The storage modulus is independent of the frequency and shows values between 200 and 500 Pa. The loss modulus, on the other hand, exhibits values two orders of magnitude lower than G', except for the material formed at 90 • C, which is the weakest of the series.
As was already outlined in Figure 1 and Table 2, the elastic modulus follows a tendency to diminish as the gelation temperature increases. This effect does not seem to be an experimental artifact, nor a consequence of the retro-Diels-Alder reaction. The latter should be ruled out as the kinetics of the process does not shed light on the existence of this reaction under the employed experimental conditions. This behavior seems to be a consequence of the reaction kinetics itself because as the crosslinking between the polymer chains takes place faster, the mobility of the polymer segments freezes earlier, and the possibilities of reaction between complementary functional groups become scarcer. This phenomenon is also evident from the very rapid evolution of the storage modulus at 90 • C, compared to that observed at 50 • C (Figure 1). Therefore, the lower the crosslinking density, the weaker the elastic response of the material should be.
atures between 50 and 90 °C appears in Figure 4 (regardless of the gelation temperature, all mechanical spectra were recorded at 25 °C for comparison purposes). At first glance, it should be noted that, by varying the temperature of the Diels-Alder reaction, hydrogels with good mechanical properties are obtained. The storage modulus is independent of the frequency and shows values between 200 and 500 Pa. The loss modulus, on the other hand, exhibits values two orders of magnitude lower than G', except for the material formed at 90 °C, which is the weakest of the series. As was already outlined in Figure 1 and Table 2, the elastic modulus follows a tendency to diminish as the gelation temperature increases. This effect does not seem to be an experimental artifact, nor a consequence of the retro-Diels-Alder reaction. The latter should be ruled out as the kinetics of the process does not shed light on the existence of this reaction under the employed experimental conditions. This behavior seems to be a consequence of the reaction kinetics itself because as the crosslinking between the polymer chains takes place faster, the mobility of the polymer segments freezes earlier, and the possibilities of reaction between complementary functional groups become scarcer. This phenomenon is also evident from the very rapid evolution of the storage modulus at 90 °C, compared to that observed at 50 °C ( Figure 1). Therefore, the lower the crosslinking density, the weaker the elastic response of the material should be.
To validate this hypothesis, the crosslinking density and the network mesh-size of these hydrogels were calculated. For this purpose, if we assume that the frequency sweeps were carried out under linear viscoelastic conditions-and it is reasonable given the experimental conditions used-then it is possible to estimate the crosslinking density from the basic concepts of Flory's theory of elasticity. Then, the crosslinking density, , was evaluated by the following equations [55]: while the network average mesh-size, , becomes: To validate this hypothesis, the crosslinking density and the network mesh-size of these hydrogels were calculated. For this purpose, if we assume that the frequency sweeps were carried out under linear viscoelastic conditions-and it is reasonable given the experimental conditions used-then it is possible to estimate the crosslinking density from the basic concepts of Flory's theory of elasticity. Then, the crosslinking density, ρ x , was evaluated by the following equations [55]: while the network average mesh-size, ξ a , becomes: where R, T, and N a are the universal gas constant, the absolute temperature, and the Avogadro Number, respectively. From the average values of the equilibrium storage moduli shown in Figure 4, the crosslinking density and network mesh-sizes values were estimated and presented in Table 3. Table 3. Values of crosslinking density, ρ x , and network mesh-size values, ξ a , of the hydrogels, calculated from Equations (6) and (7), respectively. All experimental parameters as specified in Figure 4. Indeed, the values of the crosslinking density from Table 3 confirm that this parameter decreases as the reaction temperature increases. At high temperatures, crosslinking is rapid, which "freezes" the segmental motions of the chains, thus preventing a closer approach between functional groups. Consequently, a lower reaction completion and slightly weaker mechanical properties were observed. In other words, the crosslinking density and the elastic properties of the hydrogel seem to be controlled by the diffusion of the polymer segments, rather than by the kinetics of the Diels-Alder reaction. The possible influence of the reverse reaction at higher temperatures once the gel is maintained at these temperatures after the gel point cannot be ruled out either.

Influence of Other Eexperimental Parameters: Concentration of Chitosan, Maleimide to Furan Molar Ratio, and Characteristics of the Maleimide Crosslinker
After analyzing the influence of reaction temperature, some other important experimental parameters were considered as well. Figure 5 summarizes the mechanical spectra registered at 25 • C, of hydrogels prepared at 70 • C, varying the following parameters: (i) polymer concentration: 1.0 and 1.8 wt.%; (ii) maleimide to furan molar ratio: 0.25 and 0.5; and (iii) characteristics of the maleimide crosslinker: degree of polymerization and functionality (as specified in Table 1). From a first general analysis of their mechanical spectra, it is evident that in all cases (except for the hydrogels prepared with a concentration of FCh 1% and PEG(mal) 2 -2000), the storage modulus presents values greater than 200 Pa, reaching a limit of 2000 Pa. Following the same calculation procedure as for the hydrogels prepared at different temperatures, the crosslinking density was also calculated using Equation (6), and the results obtained are summarized in Table 4. Table 4. Values of crosslinking density, , calculated from Equation (6) for hydrogels based on the Diels-Alder click reaction at different degrees of polymerization and functionalities of the PEGmaleimide compound. To keep the visual association with the curves in Figure 5, the black and red Following the same calculation procedure as for the hydrogels prepared at different temperatures, the crosslinking density was also calculated using Equation (6), and the results obtained are summarized in Table 4. Table 4. Values of crosslinking density, ρ x , calculated from Equation (6) for hydrogels based on the Diels-Alder click reaction at different degrees of polymerization and functionalities of the PEGmaleimide compound. To keep the visual association with the curves in Figure 5, the black and red colors are maintained. * All experimental parameters as specified in Figure 5.
As expected, by increasing the concentration of chitosan there is a reinforcement of the mechanical properties, regardless of the value of R employed. The same happens when comparing the maleimide:furan molar ratio, at equal chitosan concentrations. In both cases, an increase in the concentration of any of the two functional groups is accompanied by a higher crosslinking density (Table 4). A similar effect has been reported during the chemical crosslinking of furan/maleimide system with hyaluronic acid, and semidiluted solutions of poly(vinyl alcohol) [8,56].
The role played by the degree of polymerization of polyethylene glycol on the hydrogel characteristics is interesting. For bifunctional maleimide derivatives, it is evident that an increase in chain length (DP: 45 vs. 170) has a noticeable effect on the gel. It can be speculated that due to their remarkable hydrophilicity and chain flexibility, PEGs have a significant impact on reaction completion by allowing better diffusion of maleimide groups in the reaction medium. This effect is more important at low concentrations of chitosan, whose chains are notably more rigid.
The effect of the functionality of the maleimide crosslinker deserves separate mention. As expected, the introduction of a tetrafunctional PEG-maleimide derivative leads to an increase in the storage modulus, accompanied by a higher crosslinking density.

Influence of the Temperature on the Mechanical Properties of a Diels-Alder Hydrogel
The effect of the temperature on the mechanical properties of a Diels-Alder crosslinked hydrogel was also investigated. For this purpose, a hydrogel was prepared with N-furfuryl chitosan 1.0 wt.% and PEG(mal) 2 -7500, R = 0.5 at 70 • C. Once the hydrogel was formed, after 5 h of reaction, the temperature was lowered to 25 • C, and a frequency sweep was recorded after 15 min of equilibration. Then, the temperature was successively raised to 37, 50, 60, 70, 80, and 90 • C, and a mechanical spectrum registered after equilibration at the corresponding temperature for 15 min. The results of the thermorheological behavior of the hydrogel are displayed in Figure 6 (the dependence of the storage modulus with angular frequency is magnified inside the figure).
In the inset of Figure 6, a slight variation in the G values is observed as the temperature of the hydrogel increases. To obtain a clear view about the dependence of this parameter on temperature, the average values of the equilibrium storage modulus were plotted on an Arrhenius-type plot, which are shown in Figure 7.
In Figure 7 it is interesting to note a strengthening of the elastic characteristics of the hydrogel as it is heated from 25 to 70 • C, resulting in a strong linear Arrhenius-type dependence. The origin of this behavior is not clear, but it could be due to an increase in the completeness of the Diels-Alder reaction. It should be noted that an Arrhenius-like behavior is the overall result of interactions between macromolecules and conformational changes, which inevitably leads to the dissociation and reformation of the crosslinks. The latter reflects the behavior of a system with dynamic crosslinking bonds, as in the case of the Diels-Alder and retro-Diels-Alder reactions [57]. In other words, the hydrogel crosslinked by Diels-Alder cycloadducts is capable of self-completion, increasing the storage modulus (from 330 to 470 Pa) and the crosslinking density (from 1.3 to 1.5 × 10 −7 mol/cm 3 ).

Influence of the Temperature on the Mechanical Properties of a Diels-Alder Hydrogel
The effect of the temperature on the mechanical properties of a Diels-Alder crosslinked hydrogel was also investigated. For this purpose, a hydrogel was prepared with N-furfuryl chitosan 1.0 wt-% and PEG(mal)2-7500, R = 0.5 at 70 °C. Once the hydrogel was formed, after 5 h of reaction, the temperature was lowered to 25 °C, and a frequency sweep was recorded after 15 min of equilibration. Then, the temperature was successively raised to 37, 50, 60, 70, 80, and 90 °C, and a mechanical spectrum registered after equilibration at the corresponding temperature for 15 min. The results of the thermorheological behavior of the hydrogel are displayed in Figure 6 (the dependence of the storage modulus with angular frequency is magnified inside the figure). In the inset of Figure 6, a slight variation in the G' values is observed as the temperature of the hydrogel increases. To obtain a clear view about the dependence of this parameter on temperature, the average values of the equilibrium storage modulus were plotted on an Arrhenius-type plot, which are shown in Figure 7. In Figure 7 it is interesting to note a strengthening of the elastic characteristics of the hydrogel as it is heated from 25 to 70 °C, resulting in a strong linear Arrhenius-type dependence. The origin of this behavior is not clear, but it could be due to an increase in the completeness of the Diels-Alder reaction. It should be noted that an Arrhenius-like behavior is the overall result of interactions between macromolecules and conformational changes, which inevitably leads to the dissociation and reformation of the crosslinks. The latter reflects the behavior of a system with dynamic crosslinking bonds, as in the case of the Diels-Alder and retro-Diels-Alder reactions [57]. In other words, the hydrogel crosslinked by Diels-Alder cycloadducts is capable of self-completion, increasing the storage modulus (from 330 to 470 Pa) and the crosslinking density (from 1.3 to 1.5 × 10 −7 mol/cm 3 ). At temperatures above 70 °C, there is a drop in G' values. This deviation from the Arrhenius-like behavior unequivocally indicates that there is a process opposing to the Diels-Alder reaction, most likely the retro-Diels-Alder. Both the Diels-Alder and retro-Diels-Alder reactions proceed at different rates and their equilibrium is strongly influ- At temperatures above 70 • C, there is a drop in G values. This deviation from the Arrhenius-like behavior unequivocally indicates that there is a process opposing to the Diels-Alder reaction, most likely the retro-Diels-Alder. Both the Diels-Alder and retro-Diels-Alder reactions proceed at different rates and their equilibrium is strongly influenced by temperature [37]. The hydrogel-which is already crosslinked-can reach an equilibrium between the direct and inverse reactions. That is, the dynamic character of this reaction allows certain rearrangement of the crosslinks within the hydrogel to take place. As a consequence, at temperatures below 80 • C the formation of the cycloadduct is likely to be favored, whereas above 80 • C, the breakdown of the adducts becomes increasingly important.
It should be mentioned that the actual difference in the values of the storage modulus during the heating of the hydrogel from 25 to 90 • C is very small (330-467 Pa), and therefore the variation in the degree of crosslinking is not large, as it would be expected for such a dynamic rearrangement of the polymer network.
These dynamic features of the Diels-Alder equilibrium underlie the self-healing and remendability behavior of these hydrogels. They represent a challenging and rapidly developing scientific frontier in polymeric materials science.

Conclusions
Clear and transparent hydrogels with excellent mechanical properties were prepared between N-furfuryl chitosan and PEG-maleimide derivatives in dilute aqueous acidic conditions. Applying the Winter and Chambon criterion, the gel times were estimated at different temperatures, and the activation energy was calculated to be 76 kJ·mol −1 . This value suggests that, under our experimental conditions, the exo-adduct is being formed preferentially.
The elastic modulus of the hydrogels prepared at temperatures between 50 and 90 • C follows a tendency to diminish as the gelation temperature increases. At high temperatures, crosslinking is rapid, which "freezes" the segmental motions of the chains; thus, preventing a closer approach between functional groups and the possibilities of reaction between complementary functional groups become scarce. The possible influence of the reverse reaction at higher temperatures once the gel is maintained at these temperatures after the gel point cannot be ruled out either.
The role played by the degree of polymerization of the crosslinking PEG-maleimide derivatives on the hydrogel mechanical properties is interesting. For bifunctional maleimide derivatives, it is evident that an increase in chain length of PEG has a noticeable effect on the strength of the gel. It can be hypothesized that, due to their remarkable hydrophilicity and chain flexibility, PEGs chains display an important effect on reaction completion by allowing a better diffusion of the maleimide groups in the reaction medium. This effect is more important at low concentrations of chitosan, whose chains are notably more rigid.
Once obtained, the hydrogel showed an improvement in its mechanical properties as the temperature increases up to 70 • C. Above this temperature, a decrease in the storage modulus is observed, indicating the existence of a process opposite to the Diels-Alder reaction, most likely the retro-Diels-Alder.
Supplementary Materials: The following are available online at https://www.mdpi.com/article/ 10.3390/polym14061202/s1, Scheme S1: Synthesis of FCs; Figure S1: FT-IR spectra of chitosan and FCs; Figure S2: 1 H-NMR spectrum of FCs; Figure S3: FTIR spectra of the N-furfuryl chitosan, PEGbismaleimide, and the Diels-Alder cycloadduct; Figure S4: Dynamic mechanical spectra at 25 • C of the precursor solution, and that of the corresponding hydrogel prepared at 50 • C; Figure S5: Storage and loss moduli as a function of the reaction time of the gelation process.