Effect of the aramid pulp on the physicochemical, viscoelastic properties and rheokinetics of polyurethanes

This publication highlights the effect of aramid pulp (1 wt.%) on equilibrium swelling, enthalpy reaction, solid viscoelastic properties, and rheokinetics of castor oil (CO) and polyether (PE) polyol blend (50/50 CO/PE) with polymeric isocyanate (pMDI). The CO-pMDI system showed a lower solubility parameter difference (Δδi) than the PE-pMDI and CO/PE-pMDI. Crosslink density values ve\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${v}_{e}$$\end{document} are higher for CO-pMDI, and when added to aramid pulp, there is a slight increase due to the possible restriction of swollen volume. Regarding the pseudo-solid behavior, AP restricts the macromolecular movement and confers reinforcing characteristics to PU systems. The Prout–Tompkins autocatalytic model satisfactorily described the reactions, resulting in activation energy values Ea within 45 − 54 kJ/mol. However, for the CO/PE blend, the difference between the reactivity of the polyols and the solubility parameter with pMDI results in a two-step reaction kinetics. Aramid pulp practically does not change the reaction mechanism, only the viscosity of the medium. Furthermore, the thermodynamic parameters (ΔS* and ΔH*) indicated that the PU with AP resulted in more ordered complexes. The adequate description of the polymerization reaction and the effect of the aramid pulp allowed for obtaining PU formulations with tunable characteristics for strict composite processing composites.


Introduction
Polyurethane (PU) based systems are highly versatile materials used in various applications, varying from linear thermoplastics to thermosetting polymers [1]. PUs are commonly produced by the reaction of petroleum-based molecules containing hydroxyl (-OH) groups with isocyanates (-NCO) [2]. However, from abundant biological sources, vegetable oils can also be used as raw material to produce bio-based PUs, with advantages such as low toxicity, inherent biodegradability, and high purity. In addition, polyols from renewable and petroleum-based sources may be blended to tune specific properties such as reactivity or macromolecular characteristics.
Polyurethane applications can be improved by using new fillers, additives, and reinforcing materials [3,4]. For instance, aramid (poly-p-phenylene-terephthalamide) pulp (AP), a common waste from fabric production facilities, has been used to reinforce PUs and improve mechanical properties [5], thermal stability [1], among other advantages, tackling significant issues of this polymer [1,6,7]. Nonetheless, a filler or reinforcement into a thermoset PU can affect its curing; therefore, the knowledge of reaction kinetics is essential [8]. For instance, when processing PU composites, it is essential to monitor the viscosity increase during polymerization [9]. This increase in viscosity during the pre-gel stage due to the increase in molecular weight indicates the magnitude of chain extension and branching and provides information on reaction rate and profile before and after gelation [10]. In addition, viscosity monitoring and knowledge of the kinetic parameters of a reactive system allow optimization of the composite processing conditions. Many methods are employed to the PU polymerization kinetics, broadly classified into two groups: (i) indirect methods, which measure a physical property functionally related to the extent of the reaction, such as differential scanning calorimetry (DSC), rheometry and viscometry; (ii) direct methods, which measure the concentration of a reactant or product species, such as Fourier transform infrared spectroscopy (FTIR), titration, nuclear magnetic resonance (NMR) and gel permeation chromatography (GPC) [11][12][13][14]. Nevertheless, the very high viscosity and fast gel formation observed when the urethane conversion reaches a significant level brings analytical problems to direct methods, limiting their use [15]. In this context, indirect methods are receiving increasing attention [12].
The rheological measurements approach [12,15,16] has produced similar results to DSC to determine kinetics [13,17]. However, the former allows for lower characteristics of the change in free volume from the macromolecular growth [10]. Furthermore, it can help simulate properties better correlate with actual processing conditions [13]. Rheometry is essential since different rheological parameters, such as viscosity, may increase by as much as 6 − 7 orders of magnitude during polymerization, affecting processability characteristics of great relevance for many PU applications [15,17,18]. In addition, this technique has recently shown great versatility in characterizing the different stages during PU formation and liquid-solid transition [9].
Considering that viscosity varies with the length of the polymer chain, it can provide information about its condition [19]. PU polymerization kinetics have been carried out using isoconversional methods based on calorimetry and rheometry [12,15,18]. Activation energy values for the polymerization are in the 45 − 55 kJ/mol range [20,21], considered an autocatalytic reaction mechanism [14], in which the monomer acts as a catalyst for the reaction, increasing the conversion rate. The most used autocatalytic models in these studies were Prout-Tompkins and Kamal-Sourour [16,18]. Lucio and De La Fuente have extensively studied the rheokinetics of functional PUs, HTPB, and (ferrocenylbutyl) dimethylsilane-grafted HTPB and described the reaction kinetics using empirical models (Arrhenius and Kinua) [15,17]. They have found a significant contribution of the autocatalytic effect during the formation of the urethane group, which is noticeable for reactive systems at elevated curing temperatures.
Santhosh et al. [14] evaluated the curing kinetics of a composite propellant based on ammonium perchlorate, hydroxyl-terminated polybutadiene (HTPB), and tolylene diisocyanate system using rheometry under isothermal conditions (60-70 °C). They reported that the reaction follows first-order kinetics with an activation energy value of ~ 48.3 kJ/mol in a single autocatalytic step [14]. However, chemical species with active hydrogens can alter the PU polymerization mechanism [13]. Recently, Echeverria-Altuna and colleagues used the Castro-Macosko model in pre-gel stages in conjunction with DSC data to simulate the processing of PU composites in RTM. They report that using LiCl improves PU processing as the viscosity increases slower, which is essential for processing with liquid resins and fiber impregnation [22]. In the liquid molding of composites, for example, latency in the first stage of the polymerization reaction becomes necessary to guarantee low viscosity (~ 500 Pa.s) values and obtain good impregnation in reinforcements and mold filling [22,23]. Therefore, optimizing PU formulations becomes fundamental to improving their applications. Using physicochemical and rheokinetic parameters can be helpful tools for understanding and improving PU formulations.
The main objective was to evaluate the effect of an aramid pulp and the type of polyol (castor oil or polyeter) on the physicochemical, solid viscoelastic, and kinetic characteristics of the reaction. In addition, the monomers' miscibility and reactivity were used to assume that in the system with the polyols blends (50/50), the polymerization reaction occurs practically in parallel. In this way, it is expected to better understand the effect of fibers and particles during the polymerization reaction of PUs to predict future applications and optimize processing conditions.

PU and composite preparation
In this work, three polyols were used in the formulations, one from castor oil (named CO), one from polyether (named PE), and their 50/50 wt.%/wt.% blend (named CO/PE). In addition, some PU formulations were incorporated with 1 wt.% aramid pulp by weight, as detailed in Table 1.
The content of aramid pulp was defined based on preliminary experiments with 0.5, 1.0, and 1.5 wt.%, evaluating the dispersion using optical microscopy, according to literature recommendations [1]. The dispersion procedure employed by Pearson was used, which consisted in adding the AP amount to the polyol and steering it using a Dispermat N1 high-shear mixer direct disperser [1]. The initial speed was 500 rpm, for 3 min., to break the agglomerates, then it was gradually increased, 500 rpm every 3 min., until 2500 rpm, where it remained until complete dispersion of the pulp in the polyol [1]. The procedure to prepare the composites is illustrated in Fig. 1. The same method, but without AP, was employed to obtain the PU samples.

Characterization
The PU reaction enthalpy (ΔH p ) was monitored via DSC (TA instruments Q20) using ~5 mg sample, N 2 atmosphere (50 ml/min), and heating from 25 to 250 ºC at 10 ºC/min for all samples. The swelling degree was evaluated as a function of time using 5 g of the sample immersed in 200 mL of cyclohexane (based on the solubility parameter) in a container kept at 25 ºC. At pre-determined time intervals, from 1 h until equilibrium (~480 h), the sample was removed from the solvent, the mass was measured, and the sample returned to the solvent. The swelling degree (Q) was obtained according to Eq. 1 [19].
where m t is the mass of the swollen polymer at a particular time; and m o is the mass of the polymer before swelling.
The crosslink density v e (mol/cm 3 ) was calculated based on the degree of swelling at the equilibrium of the samples in cyclohexane, using Eqs. 2-3 as proposed by Flory-Rehner described in ASTM D 6814. where V r gel volume in the swollen sample; V 1 solvent molar volume (cyclohexane -cm 3 /mol); χ is the Flory-Huggins interaction parameter (this parameter can be estimated using group contribution methods [19]). The V As is the volume of the dry sample; and V Sae is the volume of absorbed solvent at equilibrium. Kraus' correction was used to calculate the true crosslink density considering the presence of the aramid pulp for the composites [20,21]. The miscibility of the monomers was evaluated with theoretical solubility parameters based on the Hansen approach using the group contributions method [24]. In addition, Bagley diagrams were built to aid the analysis. In these, the effect of the dispersion (δ d ) and polar (δ p ) components of the solubility parameter was assumed similar, being grouped into δ v , according to Eq. 4: In contrast, the effects of the hydrogen bonding component (δh) are very different [25]. Therefore, in Bagley's approach, the solubility region can be expressed using a δv × δh plot [25], where the distance between two points is calculated using Eq. 5.
The solid linear viscoelastic behavior of the materials was investigated by DMA (TA Instruments, DMA 850), using the dual cantilever geometry. The experiments were carried out in the temperature range of -60 °C to 100 °C, with an oscillation amplitude of 10 μm (linear viscoelastic regime), frequency of 1 Hz, and heating rate of 3 °C/min. Samples with 60.0 mm × 13.0 mm × 3.0 mm were used.
The rheokinetics behavior was carried out by dynamic oscillation employing an Anton Paar MCR 101. The plate diameter and gap were 25.0 and 0.50 mm, respectively. Measurements were performed in 5 isothermal curves (in the 40-80 ºC range) with 1 Hz frequency and 2 Pa (linear viscoelastic regime). The viscoelastic response during the reaction, in terms of complex viscosity (η*) and shear storage and loss moduli (G' and G", respectively), were registered as a function of the reaction time.
In Eq. 6, viscosity is treated as the combination of two exponential expressions, one for the dependence of viscosity and another for the effect of reaction kinetics [8,26]: where K is a constant; E is the flux activation energy; R is the universal gas constant; T is the absolute temperature; is the activation energy; and f(α) is the function that describes the reaction mechanism.
In reactive systems, two effects can be superimposed in rheometric measurements, the dependence of viscosity with temperature and its increase in the degree of reaction [27,28]. These were determined based on the Pahl-Hesekamp approach [26,29] in which it is possible to separate the viscosity and kinetics terms. The viscosity of the reactive system is described with a WLF equation, in which the actual temperature is reduced by the difference between the actual glass transition temperature, T g (x), and the glass transition temperature for the degree of reaction x = 0 (Eq. 7).
where C 1 and C 2 are WLF constants of the non-crosslinked polymer, and B 1 and B 2 are constants of the crosslinked polymer. The model considers that the formation of crosslinks decreases the intrinsic volume because of the reduced ability of the chains to move.
Opfermann described the temperature behavior using an Arrhenius-type equation using two different activation energies, E 0, and E 1 , referring to the beginning and the end of the reaction, that is, the lowest and highest viscosities, respectively [26,30].
where G[T(t)] is a gain function that measures the change in viscosity, described by Eq. 9: Dynamic and/or isothermal measurements allow the calculation of the A 0 , A 1 , A 2, and A 3 parameters by fitting the experimental data. Thus, it is possible to predict the viscosity as a function of time at various temperatures based on the viscosity increase along with the polymerization reaction [27,30]. The data was computed using "Netzsch Thermokinetics: A software modulus for the kinetic analysis of thermal measurements" by non-linear least-squares fitting. The term f(α) was determined by comparing the experimental data with the theoretical mathematical models based on fitting sixteen kinetic models, shown in the supplementary material. The models that best describe the reaction were identified based on statistical tests (f-test) [13,31].
The kinetic and thermodynamic parameters of the polymerization process were computed using Wynne-Jones-Eyring-Evans theory [32,33] which relates the temperature-dependent pre-exponential factor with the kinetic constant resulting in: where k B and h are the Boltzmann and Planck constants, N is a parameter related to molecularity. ΔS * is the activation entropy and E a = ΔH * + NRT , is a function of activation enthalpy. Considering the classical Arrhenius constants have N = 0, whereas when the reaction is in a liquid medium N assumes a value of 1 [32] Considering the PU polymerization occurs in the liquid state, N = , the Eq. (10) can be solved using a linear relationship by plotting ln (k/T) vs. 1/T, ΔH * and ΔS * are obtained from the slope and linear coefficients. The values of k can be obtained by using the Arrhenius equation ( k = Ae − E a RT ).

Results and discussion
The miscibility of the polyol blends was computed using the solubility parameters estimated based on group contribution theories [34]. Table 2 shows the solubility parameters of the monomers, that is, the dispersive ( d ), polar ( p ), hydrogen bonding ( h ), volumetric ( v ) and total ( T ) components. These results were relatively close to those of similar studies [25]. Note that CO has a more significant similarity to pMDI regarding dispersive and total components than PE; therefore, less phase separation is expected for the former. A simple analysis can be done by building phase diagrams using the Flory-Huggins mixing theory, according to the work of Ruzette and Mayes, shown here as supplementary material [35]. The ΔG m values at 25 ºC for the CO-pMDI pair (0.177 J) are lower than for PE-pMDI (0.870 J) (for mixtures with equal weight fraction). When evaluating the effect of temperature, an increase in miscibility is observed for the CO-pMDI system based on the ΔG m < 0 values. Increased miscibility between segments reduces phase segregation between rigid and flexible segments, and therefore a single glass transition is observed [2,36]. The Bagley graph is shown in Fig. 2. The van der Waals forces the miscibility is delimited by a relatively welldefined circular miscibility region, with an "interacting radius" of about 2.5 MPa 1/2 , being expanded to the regions 5.5 and 7.0 MPa 1/2 for systems with hydrogen bonding. This figure shows that the polyols used in this study (CO and PE) have a low tendency to phase separation between them at a distance of 1.87 MPa 1/2 . In addition, as observed for ΔG m , CO is closer to pMDI than PE. Figure 3 shows the DSC curves of PU and PU composite samples. PU(CO) has greater reactivity than PE, and the reaction starts at lower temperatures. The PE reactivity is lower due to many secondary hydroxyls due to this polyol's type of synthesis reaction [37]. Also, as the polyether polyol is added to the formulations, the curing peak shifts to higher temperatures and the reaction takes longer to finish.
The onset, endset, peak temperatures, and reaction enthalpy for PU and PU composites were obtained from the DSC curves and compiled in Table 3. The incorporation of 1 wt.% of aramid pulp shows little effect on all samples' enthalpy of reaction ΔH p , with slight differences attributed to experimental deviations. It is important to remember that the aramid pulp has terminal groups (− NH 2 and − COOH) that could react with − NCO, however these side reactions (allophanates, urea biuret, etc. [6,38]) were not able to cause significant changes in ΔH p when compared with pure polyurethane due to its small. This fact is related to the small amount of chain ends in a high molecular weight polymer such as fiber (aramid pulp).
Concerning reactivity, primary hydroxyls are much more reactive than secondary ones [39]. Ismail et al. studied the reaction kinetics of palm oil PUs and showed that it is reduced by about three times when comparing MDI reactions with secondary and primary hydroxyls. Polyester-type polyols react much faster than polyethers due to the observed difference in reactivity. Furthermore, polyesters such as castor oil can stabilize the hydrogen bonds of the produced intermediates and thus react more quickly [40]. Figure 4 shows the swelling curves of the samples in cyclohexane until equilibrium, after approximately 20 days. After this period, the PU(CO), PU(CO/PE), and PU(PE) samples showed 18.1, 20.4%, and 27.9 wt.% swellings, respectively. Samples with PE present more significant swelling than those with CO, attributed to the higher molecular weight between crosslink points of PE (f = 2) compared to CO (f = 2.7), affecting the swelling reticulum volume and the polymer-solvent interaction [2].
The swelling curves of PUs and PU composites have a similar shape, but the latter reached lower swelling values than the respective polymers, being 16.1, 17.5, and 25.0 wt.% for PU(CO) + AP, PU(CO/PE) + AP, and PU(PE) + AP samples, respectively. The lower swelling may be related to the reduction in the swollen volume after AP addition. Indeed, the AP swells very little compared to the PU matrix and could reduce the overall swelling. Also, the -NCO group can react with groups containing reactive hydrogen, yielding different products [31].
It is known that more crosslink points, i.e., higher crosslink density, reduce the polymeric network's mobility and hinder solvent permeation [41,42]. In Fig. 5, the calculated crosslink density is consistent with the previous swelling results. Also, PE tends to produce a structure of higher molecular weight between crosslink points than CO.
The V e values for the composites, also shown in Fig. 5, considered the Kraus correction to account for the fiber incorporation. A slight increase in V e values is noticed compared to the respective PU samples, which may be related to the swelling restraint that the pulp exerts on the PU [20].   Figure 6 shows the storage module (E´) and Tan delta vs. temperature (-50 to 100 ºC) for PU and composite samples with AP. The moduli values at -50, 100 ºC, T g from Tan delta peak, full width at half maximum (FWHM) in T g region, and E'' peak are summarized in Table 4. All samples showed elastic pseudo-solid behavior in the investigated temperature range. The AP increased the rigidity of all samples, mainly above the T g . The displacement of the modulus values in the glass transition region is related to the restriction to the movement that the fibers result.
For all samples, only one glass transition temperature was observed. For PU (CO) a Tg of ~ 28 ºC was observed [4,43], while for the composite with AP a small change to ~ 32 ºC was noted. However, a broadening in the transition peak (FWHM) was noticed, which is related to the heterogeneity of the T g of the composites. PU (PE) showed a T g at -7.2 ºC, while PU(PE) + AP changed to 12.7 ºC. Two glass transitions were not observed concerning PU(CO/PE). According to the solubility and thermodynamic parameters, there may be immiscibility between the polyols. However, the DMA investigation Furthermore, it is noted that the values of Tan delta increase in magnitude in the AP samples, which is a reflection of the higher elastic component (E') compared to the viscous (E''), which reflects lower energy dissipation capacity per sinusoidal deformation cycle. On the other hand, the lower T g values observed for PU(PE) reflect the higher molecular weight between crosslink points and the oxygen in the polyol main backbone chain, which results in greater mobility [2].
Note that the modulus values in the elastic plateau region (E`r 100ºC ) are higher for all composite systems with AP. It is also noted that E`r 100ºC presents a practically linear behavior concerning pure polyols and the 50/50 blend. Based on the theory of rubber elasticity [4] ( E � = 3 e RT) it is noted that a similar trend to the swelling results, that is, as PE is used, there is a greater distance between the crosslink points. Still, movement restriction caused by the AP increases the modulus values as well as ve according to the swelling data. According to Flory [44] any cross-linkable polymer system has a sharply defined gel point at a particular critical conversion (extent) of the p c reaction, which must be independent of temperature, type, and amount of catalyst, among others [45] When polymers gel, a sudden and dramatic increase in viscosity is observed until the molecular weight becomes infinite (degree of polymerization, DP → ∞). Thus, the second term of the Carother's equation ( DP = 2∕(2 − pf m ) disappears, and the critical extent of the reaction becomes p c = 2∕f m . This occurs at a lower reaction degree (0.75) for the castor oil system than for the polyether (0.85). The gel time at each temperature was estimated according to ASTM D7750 as the point at which the storage modulus abruptly increased, shown as Supplementary Material (Table S2). As expected, as the temperature increases, the time for crossover (G' = G'') to occur decreases, suggesting that molecular mobility increases in the early stages at higher temperatures, allowing the reaction to proceed at a faster rate. This time reduction in relation to temperature can be described with an Arrhenian relation (Fig. S2). Note that there are a reduction in gel time and lower activation energy values (E gel : 30 − 52 kJ.mol −1 ) for PUs with pulp. Because it is highly fibrillated, even with a low degree of reaction in pulp systems, the material formed already reaches a pseudosolid state long before pure PU. The values found are in agreement with the literature [14].
Viscosity vs. time curves for the PU and PU composites at 40, 50, 60, 70, and 80 °C isotherms are shown in Fig. 7A-F. The given viscosity data is required up to the gel time for each temperature above that time. The red solid reference lines represent the model proposed. The Prout-Tompkins model ( f ( ) = m (1 − ) n Bna mechanism) was found the most adequate to describe the polymerization mechanism, with all determination coefficients higher than 0.970. Initially, 16 mechanisms were tested (supplementary files). However, in this reaction, what he wrote best was based on the Bna model. This model is an expression derived from the model of Šesták-Berggren [46].
The increase in temperature Fig. 7A-F contributes to the increase in reaction rate, decreasing the time to reach the same viscosity value. In addition, according to several studies [47,48] the aramid pulp is highly fibrillated, with a large surface area and free amine groups, increasing the viscosity of the reaction.
Viscosity at the start and end of the reaction is lower for polyether than for castor oil PU. Still, the increase in the rate of viscosity is less pronounced due to the lower reactivity of the PE polyol [49]. Concerning the polyol blend, an intermediate behavior is noted, with two regions of viscosity increase related to the reaction rate of each polyol, as indicated in the DSC results. Since both polyols have close solubility parameters, there is poor phase separation and apparent homogeneity. However, the difference in reaction kinetics can induce phase separation, yielding the two observed reaction stages in Fig. 7C, D [2,24]. Therefore, these observations considered a parallel reaction approach for the CO/PE blend.
The values of the kinetic parameters of the six samples of the best model (B na mechanism) are presented in Table 5. The single-step (when only one polyol is used) and autocatalytic mechanism have been used in several curing kinetics studies of PU systems, with or without reinforcement/ filler [15,50]. Regarding the pre-exponential factor (log A 1 ), one can notice a decrease with aramid pulp incorporation. Considering that this parameter reflects the frequency of collisions between groups, decreased reactivity of the system occurs after AP addition. This term also contains information about mobility reduction due to the increase in system viscosity from the pulp addition [51]. Although the fibers have reactive -NH 2 and -COOH terminal groups, their importance is reduced since the fiber has limited mobility. It can also be noted that the pre-exponential factor values are lower for PU(PE) and PU(PE) + AP, justified by the lower PPO reactivity due to the synthesis method used in the production of this polyol type [37]. The values of Eα increase in the systems with AP which results in the increase of the energy barrier for the formation of activated species. The increase in Eα is related to the increase in system viscosity in the pre-gel period. The higher initial viscosity causes the system to pass from the pseudoliquid state to a pseudo-solid in shorter reaction times, as observed in the gel time values. Although it is evident that the pulp practically does not participate in the polymerization reaction, the effect of increasing viscosity significantly alters the viscous response of the system. Regarding the polyol blend, it is noted that the two activation energy values found are of the same order of magnitude in both steps. However, the reaction occurs more slowly in PE due to its structural characteristic. The Eα values are consistent with those reported in the literature for PU systems (45 − 60 kJ/mol) [15,17,52].
In general, the parameters of the reaction order "m" and "n" are only slightly different, indicating that the same reaction mechanisms prevail. In general, values of m lower than 1 indicate that an autocatalytic reaction dramatically contributes to the overall reaction rate. These values also agree with previous studies on PU curing kinetics [15,22,42].
Os valores de n encontrados variam de 1.8 − 1.98 e m de 0.10 − 0.46. Taking the works of Fernandez d'Arlas et al. [52] and Lucio and de la Fuente [12] as a comparison, the parameters estimated by the methodology used are not so far from the literature. Both authors used the Kamal-Sourour autocatalytic model and obtained m and n parameters of the same magnitude. In the case of the work by Lucio and de la Fuente, the main difference between the models applied in this work is in the form of obtaining the degree of conversion. Thus, it is evident that the method applied in this work can produce very similar results concerning other methodologies for obtaining kinetic data using viscosity.
From the rheological kinetic model, it is possible to predict the behavior of viscosity as a function of time or temperature. Figure S3 (supplementary files) shows the studied systems' time-temperature-transformation diagram curves. These diagrams are essential because they can be used directly to predict the behavior of the polymerization reaction. These diagrams constructed curves to predict viscosity, as shown in Fig. S4. In these curves, the viscosity at 25 ºC and the conversion curve are estimated as a function of what was obtained from the TTT diagrams generated by the rheokinetic model. As can be seen, in systems with AP, the viscosity starts at higher values but has slight variation concerning the reaction conversion, as also shown in the DSC measurements. However, the increase in viscosity caused by AP can often hinder processes that demand a fast flow of resin inside a mold or cavity.
The thermodynamic reaction parameters, such as enthalpy and entropy change, have been calculated using the Wynne-Jones-Eyring-Evans theory and summarized in Table 6. These parameters help understand the reaction mechanism based on the Prout-Tompkins model of urethane reaction. The activation entropy variation (ΔS*) indicates the degree of randomness of the constituent throughout the reaction, while ΔH* indicates the nature of the reaction heat in the activated complex [16,53]. The negative values for activation entropies (ΔS*) ratify the importance of the association of reagents prior to the polymerization, thus ratifying that the assumed model shows coherence for the PU systems. Also, the reaction process resulted in positive ΔH* values regardless of the temperature, suggesting an endothermic process for forming a complex. Fernandez d'Arlas et al. determined the thermodynamic parameters for catalyzed and uncatalyzed PU (1,6-hexamethylene diisocyanate/poly(carbonate-co-ester) diol) polymerization reactions from DSC analyses. They used the Wynne-Jones-Eyring-Evans approach equation and reported ΔS* of -173.5 J/K.mol and ΔH* of 40.2 kJ/ mol for uncatalyzed reactions [52].
Taking into account that ΔS* reflects the variation between a final and an initial state and that PU(CO), PU(CO/PE), and PU(PE) are in similar initial states (i.e. when molecules are very separated one to each other) a lower value for the entropy of the activation state would suggest a final state of the PU(CO/PE) formation reaction is more ordered and thermodynamically unfavorable. The addition of AP increased the values of ΔS* in all compositions, while ΔH* was noted for a reduction when comparing the systems with AP with castor oil and polyether polyol. The greater heterogeneity of the reaction medium caused by the presence of fiber seems to cause the ΔS* values concerning the respective pure resins.
Due to the nature of the complexes formed, the polymerization reaction of PUs with AP becomes more complex and tends to be less favorable in thermodynamic terms. Therefore, an optimal balance of viscosity increase and reactivity must be devised when PU resins are used in different processes, such as liquid composite molding, where viscosity and gel time are crucial parameters.

Conclusions
The effect of aramid pulp addition on the physicochemical properties and rheokinetics of polyurethanes based on CO, PE, and a CO/PE blend as a polyol and isocyanate (pMDI) was investigated. Using solubility parameters (δ) together with ΔG m contributed to elucidating the miscibility behavior of polyols. Furthermore, the number of steps in the PU polymerization reaction can be determined with the help of physicochemical parameters and the reactivity of the polyols. AP restricts the macromolecular movement of the solid material and confers reinforcing characteristics to PU systems. The Prout-Tompkins autocatalytic model, with one reaction stage for PU(CO) or PU(PE) and two stages for the polyol blend, best described their polymerization reaction. The aramid pulp did not affect the reaction's enthalpy, but the consequent increase in viscosity reduced the reaction rate and increased the activation energy. Besides, the reaction complexes formed in a blend CO/PE tend to be more ordered than those in PU(CO) and PU (PE). Furthermore, the greater heterogeneity of the reaction medium caused by AP makes the reaction thermodynamically unfavorable. Finally, the approach described in this work allows direct parameters for the liquid molding of composites in general since viscosity and gel time are crucial processing parameters.