Non-isothermal DSC and rheological curing of ferrocene-functionalized, hydroxyl-terminated polybutadiene polyurethane

Reactive and Functional Polymers 107 (2016) 60–68

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Non-isothermal DSC and rheological curing of ferrocene-functionalized, hydroxyl-terminated polybutadiene polyurethane Beatriz Lucio and, José Luis de la Fuente ⁎ Instituto Nacional de Técnica Aeroespacial “Esteban Terradas”, INTA. Ctra. de Ajalvir, Km 4, 28850-Torrejón de Ardoz, Madrid, Spain

a r t i c l e

i n f o

Article history: Received 3 May 2016 Received in revised form 2 August 2016 Accepted 3 August 2016 Available online 5 August 2016 Keywords: Kinetic Polyurethane Metallo-polyol DSC Chemorheology Non-isothermal

a b s t r a c t The curing reaction of a novel linear segmented polyurethane (PU) based on a functional metallo-polyol derivative of hydroxyl-terminated polybutadiene (HTPB), (ferrocenylbutyl)dimethylsilane-grafted HTPB, and isophorone diisocyanate (IPDI) is studied under non-isothermal conditions. This reaction is of particular interest in advanced composite energetic materials for the aeronautic technology. Differential scanning calorimetry (DSC) indicates that the curing mechanism involves multiple reactions, which was further substantiated by a rheological analysis. Rheometry was used to analyse the chemorheological behaviour through the evolution of both complex viscosity (η⁎) and storage modulus (Gʹ) at four different heating rates. The profiles obtained for the viscosity were applied to four- and six-parameter Arrhenius models. The curves of rheological conversion degree were also obtained from the elastic modulus data, and values for the activation energy of this polyaddition reaction were estimated by the application of Kissinger's method. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Polyurethanes (PUs) are a versatile class of polymers in which the urethane group imparts most of the important physical properties. Because of the presence of hydrogen bonds, PUs are often the best choice for high-performance applications [1,2]. They are typically prepared through the polyaddition of low- and/or high-molecular-weight diols and diisocyanates. The high reactivity and poor selectivity of diisocyanates have limited the introduction of functional groups onto PU backbones. Much attention has recently been devoted to the development of functional PUs because of anticipated applications outside of the classical PU market [3,4]. Hydroxyl-terminated polybutadiene (HTPB) liquid prepolymers find extensive applications as binders in solid composite propellants used in the aerospace industry [5]. The binder imparts dimensional stability and structural integrity to the propellant grain and acts as a fuel during combustion. The hydroxyl functional groups of HTPB undergo stoichiometric urethane reactions with a variety of isocyanates, with isophorone diisocyanate (IPDI) being the most commonly used in this application, to form a PU network that provides a matrix for the inorganic oxidiser and metallic fuel ingredients and imparts excellent mechanical properties to the composite propellants. For more specific applications, many of these PUs are limited in utility, but their potential applications can be greatly broadened by incorporating pendant functional groups onto the polymer backbone, as has been recently reported ⁎ Corresponding author. E-mail address: [email protected] (J.L. de la Fuente).

http://dx.doi.org/10.1016/j.reactfunctpolym.2016.08.002 1381-5148/© 2016 Elsevier B.V. All rights reserved.

in the literature [6,7]. One clear example of this is the prepolymer Butacene, (ferrocenylbutyl)dimethylsilane-grafted HTPB, which is obtained by a side chain functionalization strategy. The chemical modification reaction grafts a silico-ferrocene derivative across the pendant vinyl group of HTPB to produce a new prepolymer with novel properties [8]. The incorporation of ferrocenyl units onto the polybutadiene main chain of this metallocene PU increases the combustion kinetics when it acts as a binder in composite propellants. PU networks based on Butacene have attracted much attention as advanced propellant binder systems for rocket technology, as they do not have the same drawbacks as classical ferrocene derivatives when used as burning rate catalysts [9]. Besides this particular use, other ferrocene-containing polymers find applications as functional materials in different areas such as electronic and photonics [10–12]. The physical and mechanical properties of composite propellants are largely determined by the extent of PU formation. Hence, knowledge of the kinetic parameters of a reactive resin is essential for the design and processing of polymer and composite technologies. The reactive system of HTPB and IPDI has been investigated by different characterization methods to monitor the kinetics of the polymerization reaction. Some of these methods measure a physical property that can be functionally related to the extent of the reaction, such as rheometry and differential scanning calorimetry (DSC) [13–22]. On the contrary, direct methods measure the concentration of reactant or product species, with Fourier transform infrared spectroscopy (FTIR) and nuclear magnetic resonance (NMR) being the most commonly used [23,24]. Thermoanalytical techniques, DSC in particular, are very popular for monitoring curing processes, but it is well known that these methods

B.L. and, J.L. de la Fuente / Reactive and Functional Polymers 107 (2016) 60–68

are not useful in monitoring the final stage of the reaction [25,26]. This may be because the chemical changes that occur during the final stage of the process are too small to be detected by standard DSC methods, although they affect other properties that can be easily measured. Another drawback of using dynamic DSC for analysing systems that require excessive reaction times to reach complete conversion, as is the case for the reaction of HTPB with some isocyanates, including IPDI, is the low magnitude of the enthalpy of the curing reaction over a wide range of temperatures [13,14]. Although both isothermal and dynamic DSC curing are often applied to PU resins, non-isothermal conditions are preferred here because the enthalpy change is larger. Another advantage of obtaining kinetic parameters using dynamic DSC experiments at a controlled heating rate is that it reduces the time needed to prepare the samples and run the experiments. However, at very low or very high heating rates, the reaction heat may not be correctly read by the instrument. The complexity of reactive processes and the possibility that physical or chemical effects may overlap as a function of the scanning velocity make the calculation of the reaction heat difficult [26]. Rheological properties are also useful for monitoring the curing of oligomers because of the important changes in these properties that occur during the process [27–29]. In particular, the viscosity and modulus change by many orders of magnitude, and their evolution, which is a consequence of the increase in molecular weight that is associated with chain extension and chain branching, provides information on the reaction rate and curing profile. Therefore, the use of a rheological technique for studying the curing of such systems can overcome the abovementioned disadvantages of the DSC technique. For these reasons, the majority of the studies that have been conducted on the system of HTPB–IPDI are based on rheological measurements using rotational viscometers [15–21]. Through understanding the variables that affect the viscosity build-up, it is possible to improve the pot life and workability of this binder resin. However, it is important to note that this technique only allows the determination of viscosities of the cross-linking polymer below the gel point, which presents a serious limitation to the study of the overall curing process. This drawback can be overcome by conducting the rheological analysis using oscillatory shear flow measurements, which are superior to steady shear measurements in that they can be applied to materials not only in the liquid state but also in the rubbery state, practically throughout the curing process [30]. Another important cure property of a material that can be measured by rheological investigations is gelation. Gelation is a critical time point in reactive systems that describe the formation of an infinite molecular network. In previous studies, the rheological characterization of the reactive curing system of Butacene and IPDI in bulk and under isothermal conditions has been described [15,30]. In this study, DSC measurements and rheological data under non-isothermal conditions are analysed to obtain a deeper insight into the kinetics of this complex polyaddition reaction in PU chemistry. 2. Experimental 2.1. Materials Butacene, which is (ferrocenylbutyl)dimethylsilane grafted to HTPB, was produced and provided by SNPE (Butacene® 800). The Butacene synthesis consists of the addition of an organosilicone ferrocene derivative to a low-molecular-weight HTPB across the pendant vinyl group According to the suppliers, the metallo-prepolymer had an OH value of 0.33 eq/kg and an 8% iron content. The molecular weights of HTPB and Butacene were evaluated by size-exclusion chromatography. The number average molecular weight related to poly(methyl methacrylates) is 4593 and 7555 g/mol and the polydispersity is 2.14 and 2.16 for HTPB and Butacene, respectively [31]. The isocyanate IPDI was supplied by Hülls and used as received. The chemical formula of this prepolymer is illustrated in Fig. 1.

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Fig. 1. DSC curves of the polymerization of Butacene and IPDI in bulk. Inset shows the Tgs of the uncured and fully cured systems.

2.2. Sample preparation Butacene was previously dried and degassed for a minimum of 1 h under continuous vacuum at 60–70 °C using a rotary flash evaporator to remove residual moisture and stored under a nitrogen atmosphere until use. For the preparation of the PU samples, this macroglycol was hand-mixed by vigorous agitation with IPDI for several minutes at room temperature to obtain a homogeneous slurry mass with a stoichiometric ratio of isocyanate to hydroxyl functionalities of unity, r = [NCO]/[OH] = 1. After thoroughly mixing the two reactants, samples were prepared for immediate DSC and rheological analysis.

2.3. Calorimetric and rheological measurements DSC measurements were performed on a PerkinElmer DSC/TA7DX PC series with an intracooler for low temperatures. The temperature scale was calibrated from the melting points of high-purity chemicals (lauric and stearic acids and indium). Temperature-ramping DSC studies of the cure were performed from −100 to 200 °C at heating rates of 0.5, 1, 2.5 and 5 °C/min in dry nitrogen atmosphere (20 cm3/min), using approximately 20 mg of PU copolymer samples. The heats of reaction were estimated by drawing a straight line connecting the baselines before and after the peak and integrating the area under the peak. The glass transition temperature (Tg) was estimated as the midpoint of the line drawn between the temperature of the intersection of the initial tangent with the tangent drawn through the point of inflection of the trace and the temperature of the intersection of the tangent drawn through the point of inflection with the final tangent. The final value is the average of several measurements taken for each sample. The rheological behaviour of the PU resins was studied by dynamic oscillation using an RDA II rheometric dynamic analyser with parallel plate tools. The polymer samples were heated using a force convection heating oven with a temperature stability of ±0.2 °C. All experiments were performed under a continuous purge of dry nitrogen to prevent oxidative and hydrolytic degradation. The plate diameter and its gap were 25.0 and 0.50 mm, respectively. Measurements were carried out under non-isothermal conditions. The heating rates were varied from 0.5 to 5 °C/min in multifrequency mode (at seven frequencies over the

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range of 0.1–10 Hz). As the cure proceeded, the strain was automatically adjusted to maintain the torque response within the range of the transducer. An initial strain amplitude of 50% in the liquid state at the beginning of the curing was reduced during the reaction to 1% in the solid state to ensure a linear viscoelastic response. The variation in the viscoelastic properties during the cure, such as the shear storage modulus (G′ ), loss modulus (G″) and dynamic viscosity (η⁎), was registered as functions of both the temperature and reaction time. 2.4. Chemorheological models The model most frequently used to describe the viscosity change during the urethane formation is the dual Arrhenius model, which, for non-isothermal conditions, is described by Eq. (1), assuming the Cox– Merz rule [32]:
 ΔEη þ k∞ Lnðη
ðt; T ÞÞ ¼ Ln η
∞ þ RT

Z

  −ΔEk dt; exp RT

ð1Þ

where η⁎ is the complex viscosity at the absolute temperature T. This equation is composed of two terms. The first summands correspond to the Andrade expression, where η⁎∞ is the reference viscosity at ‘infinite temperature’, ΔEη is the Arrhenius activation energy for the resin's viscosity and R is the universal gas constant. The last term represents the resin's curing kinetics and describes the complex viscosity increase due to the increasing molecular weight of the material during its polymerization reaction. The parameter k∞ is a kinetic constant of the process (analogous to η∞) and ΔEk is the activation energy of the viscosity rate constant (analogous to ΔEη). A proportionality factor (ϕ) is suggested to relate the amount of chain entanglement to the rheological behaviour of the resin during its cross-linking and can be introduced into the four-parameter Arrhenius model. This new model was improved to include the reaction order (n) to reduce the limitations that exist in some cases for the fitting of a reactive system's viscosity data to the applied model [33]. The six-parameter Arrhenius chemorheological model is described by the following expression:
 ΔEη Lnðη
ðt; T ÞÞ ¼ Ln η
∞ þ RT   Z ϕ −ΔEk þ dt: ln ð1 þ ðn−1ÞÞk∞ exp RT n−1

G0t −G00 ; G0∞ −G00

  dα Ea ¼ A f ðα Þ exp − RT dt

ð4Þ

  dα A Ea ; ¼ f ðα Þ exp − RT dT β

ð5Þ

where A is the pre-exponential or frequency factor, f(α) is an unknown function of the conversion and β = dT/dt is the heating rate. Kissinger's method is based on the study of the rate equation at the maximum reaction rate [34]. At this point, d2α/d2t is equal to zero, and thus, Eq. (4) can be used to obtain.

ð2Þ

ð3Þ

where G ∞ ′ is the value of G′ at the end of the curing reaction. This value

"

2

d α 2

d t

¼

 #  Ea dα 0 þ Af ð α Þ exp − ¼ 0; m RT m dt m RT 2m Ea β

ð6Þ

where Tm, αm and (dα/dt)m are the temperature, reacted fraction and reaction rate at the maximum, respectively. This equation can be used to obtain Ea β

The calculation method chosen to apply the four- and six-parameter Arrhenius models to the PU's complex viscosity data to describe the evolution of the viscosity during the curing reaction was as follows. The flow parameters ΔEη and ln(η⁎∞) were calculated by selecting the linearly decreasing stage of the material's complex viscosity data, which corresponds to the thermal softening stage, and fitting them to the Andrade equation by linear regression. The resin-curing parameters provided by the Arrhenius model, −ΔEk and ln(k∞), were obtained by applying the kinetic model to the profile measured up to the gel point for the resin's complex viscosity versus temperature using a least squares sum algorithm and the flow parameters previously calculated. Among the physicochemical methods for studying the curing process, rheokinetics is the closest to calorimetry, yielding the combined characteristics of the chemical dynamics of the process and the morphological changes [27–29]. Rheokinetic models provide the opportunity to follow the entire process of network formation from the evolution of G′, which is generally proportional to the density of the network formed by chemical bonds and physical entanglements. Thus, the rheological degree of conversion α can be defined based on the change in G′ as α¼

is proportional to the maximum cross-linking density of the network reached under the given curing conditions. G0′ is the storage modulus at the beginning of the reaction and G′t is the storage modulus at time t. The profile of the curing degree of the PU resin can be determined from this equation, and thereby, the reaction rate (dα/dt) can be easily obtained. The model-fitting kinetic methods assume that the curing process is consistent with a kinetic model. Using the kinetic parameters, the relationships of the curing rate and degree of cure with time and temperature can be established. Model-free kinetic analysis, also known as isoconversional methods, is superior to the model-fitting methods in that it avoids the error caused by improper models and parameters. These models can obtain more reliable activation energy (Ea) values without specifying a kinetic model. Model-free kinetic approaches have recently demonstrated excellent modelling and prediction abilities for both the degree of cure and the reaction rate during dynamic and isothermal cures. The kinetic expression used for the solid-state transformation is displayed in Eq. (4), and it changes to Eq. (5) when a continuous ramp mode is used:

RT 2m

  Ea 0 : ¼ −A f α m Þ exp − RT m

ð7Þ

Eq. (7) can be rearranged after taking logarithms and, in the case of a first-order reaction for f(α), f′(α) = −1, becomes the final form of the famous Kissinger equation: Ln

β T 2m

!

  AR Ea − ¼ Ln : RT m Ea

ð8Þ

A plot of ln (β/Tm 2) versus 1/Tm, from the data at different heating rates, gives a straight line whose slope provides a means of calculating Ea. However, if the reaction does not follow a first-order kinetic model, the slope of this plot would lead to the activation energy only in the case when αm is independent of the heating rate. As an alternative to the Kissinger equation, a number of so-called isoconversion methods have been developed. In these isoconversion methods, the assumption reflected in the Kissinger equation is further extended to the premise that the degree of conversion is constant in all the characteristic stages of a given process; that is, it is assumed that the reaction mechanism remains strictly unchanged with respect to the changing heating rate. In this way, the activation energy has been determined for a limited number of complex PU systems from both DSC [35–38] and rheometry data [39]. Compared to the original Kissinger equation, the main advantage of isoconversional analysis is that a continuous dependence of Ea on the conversion degree is obtained. Today, the superiority of the isoconversional methods is well

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recognized, and this is indisputably true for simple single processes [40]. However, for complex or multiple overlapping processes, as is the case for many PU systems, the situation may be different. In a recent study, Svoboda and Málek have shown that the original Kissinger equation, at least for certain types of complex processes, provides accurate results, unaffected by the distortion of the data or by overlapping with other processes [40]. The advantageous robustness of the Kissinger evaluation can therefore also be effectively utilized for, for example, the verification of single-process evaluations. In this kinetic study, both the rheological data of η⁎ (from the fourand six-parameter Arrhenius models) and Gʹ (from Kissinger's method and the rheological conversion rate) have been applied for the analysis of non-isothermal curing reactions. To the best of our knowledge, this is the first time to analyse the Kissinger kinetic analysis using rheological data. 3. Results and discussion 3.1. DSC analysis The structures of the components of the functional PU based on Butacene, which is primarily used as a binder in the development of advanced energetic composite materials, are shown in Fig. 1. The uncured reactive system was previously characterized by DSC. The glass transition temperature (Tg0) was determined to be −56 °C, as shown in the inset of Fig. 1. The plot also shows the thermogram for a fully cured sample of this linear segmented PU, in which two transitions can be observed. The first thermal transition corresponds to the soft segments (Tgsoft), and the second one, at a higher temperature, is associated with the hard segment phase glass transition (Tghard). As is well known, one of the distinguishing features of these PUs is the disposition of the hard and soft segments that can be found in their macromolecules. The existence of two Tgs suggests that there is phase segregation of the soft- and hard-segment domains, as has been recently reported in a study of thermal and morphological characterizations analysing the network structure–property relationships in this system [31]. Fig. 1 also shows experimental dynamic DSC curves for curing at four different heating rates. The profile of the thermogram strongly depends on the heating rate, although all the curves exhibit a smooth exothermic characteristic over a wide range of temperature. Thus, a broad and poorly defined peak is observed at approximately 110 °C for the higher heating rates, and other exothermic peaks can be observed down to the lowest heating rate of 0.5 °C/min (Fig. 1). The multimodal shapes of the DSC curves when lower heating rates are applied, with β = 0.5 and 1 °C/min exhibiting trimodal and bimodal characteristics, undoubtedly indicate the reaction mechanism's complexity. The heats of the polymerization reaction were 71, 59, 39 and 35 J/g for the DSC experiments conducted at 0.5, 1, 2.5 and 5 °C/min, respectively. These data show the low magnitude of the enthalpy of the reaction spanning over 120 °C or even higher (Fig. 1). It is also observed that as the heating rate increases, the reaction enthalpy decreases. This decrease in the reaction heat may be caused by the shortened reaction time. At low heating rates, the reaction is more complete, and a larger reaction enthalpy results. This curing behaviour in the PU chemistry has been previously described in the literature, although few studies have used thermoanalytical techniques such as DSC. Dimier et al. studied the mechanism and kinetics of the reaction of an original PU formulation for injection moulding using DSC and rheological experiments based on isoconversional methods. These authors used a three-step kinetic model to fit the experimental DSC data, demonstrating the complex nature of the PU polyaddition reaction [36]. Logically, the situation can be more complicated for those systems that are formed by asymmetric diisocyanates. It is well known that IPDI is an asymmetric cycloaliphatic diisocyanate that contains two nonequivalent isocyanate groups. Hence, two specific reaction rates must be found, one related to each isocyanate

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group. Scheme 3 in ref. [15] clearly depicts these two reactions between the NCO groups in IPDI (primary and secondary) and the OH groups from a macrodiol. This has been verified by Sultan and Busnel, who studied the kinetics of PU formation by DSC using isocyanates with non-equivalent groups [41], such as IPDI and 2,4-toluene diisocyanate (TDI) (see Figs. 4 and 5 in ref. [41]). Similar conclusions were reached by Papadopoulos et al., who monitored the curing reaction of an oligomeric diisocyanate resin by calorimetric and rheological methods [35]. However, this multimodal characteristic of the thermograms was not observed by Ninan and coworkers in a DSC study of the curing kinetics of HTPB with different isocyanates, among them IPDI and TDI, likely because of the use of higher heating rates (from β = 4 to 15 °C/min) [13, 14]; the same explanation holds for the results reported in a recent paper by Lee et al. [22] and those of the kinetic study of Rodrigues et al. on the reaction between castor oil and IPDI [38]. Salla et al. established that the kinetic parameters obtained by a non-isothermal procedure from the set of heating rates are not unique and depend on the set of rates chosen [26]. These results demonstrate that low heating rates are more suitable when asymmetric diisocyanates are used, and at least two different reaction rates can be observed as a result of the different reactivities of the isocyanate groups. At low heating rates, more time is available for the network to develop, but when higher heating rates are used, only one reaction rate is observed. In other words, the difference in the reaction rate constants of the functional groups narrows with the increase in the heating rate. It could be concluded that the set of rates chosen, the shape of the DSC curves, the lack of definition of the limits of integration and the lack of correct heat detection at the beginning and end of the reaction can have a marked effect on the kinetic parameters that are obtained by non-isothermal DSC measurements for our reactive system. 3.2. Rheological analysis The formation of the PU network structure from Butacene and IPDI can also be evaluated using different dynamic rheological parameters, such as the storage modulus (G′), loss modulus (G″) and complex viscosity (η⁎). The rheological properties were determined during non-isothermal curing using a parallel-plate geometry operating in multifrequency mode. The rheological data were reproducible, which confirmed that the sample homogeneity was good and there was no unwanted cross-linking reaction during the sample loading and gap adjustment. One typical example is illustrated in Fig. 2, showing the evolution of G′ and G″ with the temperature during dynamic curing at the lowest heating rate of 0.5 °C/min. The variation in the loss angle δ (tan δ) at

Fig. 2. Non-isothermal dynamic shear analysis of the Butacene–IPDI system at the heating rate of 0.5 °C/min for various angular frequencies (from 0.1 to 10 Hz).

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B.L. and, J.L. de la Fuente / Reactive and Functional Polymers 107 (2016) 60–68

seven frequencies is also shown in this figure. As the temperature increases, the moduli initially slowly decreased because of thermal effects (stage I), as is shown in the next figure, in which the different stages can more clearly be observed. After this initial region, there is a curing stage that controls the kinetics of the overall process until the highest operating temperature of approximately 180 °C is attained. At this third stage, there are gradual increases in both moduli. The elastic modulus, which is lower in magnitude than the loss modulus, increases more sharply than the latter. In the liquid state, the viscous properties are dominant, and more energy is dissipated than stored, so that G″ N G′. In the solid state, when the reaction approaches completion, the elastic properties dominate and more energy is stored than dissipated, so that G′ N G″. During this stage, the gelation process occurs, and by monitoring these rheological properties, the gel time (tgel) can be determined. Various methods have been used to determine the gel point in rheological experiments using different definitions [35]. One such criterion is the crossover point of the dynamic moduli. However, the G′ – G″ crossover point is often frequency dependent, and consequently, tan δ, which is independent of the frequency, should be a better criterion for the determination of the gelation. Therefore, the point at which the loss tangent becomes independent of the testing frequency was chosen to determine the tgel values, which are listed in Table 1. In general, the gelation time decreases with increasing heating rate, while the gelation temperature (Tgel) and other relevant temperatures increase, as has been observed in other systems [42]. Tgel is also displayed in this table, along with the temperature of the intersection of G′ and G″ for the frequency of 1 Hz. It is evident that depending on the criterion chosen to determine the gel point, different values are observed. This result was also observed in our previous work analysing the curing reaction under isothermal conditions [30]. The dynamic viscosity measurements η⁎of the curing system are shown in Fig. 3 from rheological runs at different programmed heating rates at the standard frequency of 1 Hz. In stage I, where the moduli decrease, the η⁎ of the PU resin also drops, as was previously noted. The decreasing range depends on the flow activation energy of the resin during this initial stage. The temperature range for this first stage, as well as those of stages II and III, strongly depends on the heating rate. As the operating temperature increases, the resin-curing process starts, and the decrease in viscosity is compensated by the viscosity increase due to the molecular weight increment. Then, a second stage, where the thermal softening and curing phenomena overlap, was found. The temperatures at which the minimum value of the resin's complex viscosity is reached are listed in Table 1 together with other rheological data for our reactive system. These temperatures depend on the heating ramp, and their displacement to higher values as the heating rate increases has been widely reported for thermal analysis techniques [43]. When higher heating ramps are used, the minimum temperatures become a plateau region, for example, from 80 to 120 °C for the heating rate of 5 °C/min. In the higher temperature region, the viscosity build-up shows similar behaviour for all four dynamic curing curves in stage III, in contrast to that observed in stage II. The overall viscosity evolution rate, dη⁎/dT (figure not shown), remains the same regardless of the heating rate, although the temperature at which dη⁎/dT presents a maximum value is Table 1 Non-isothermal rheology data obtained at different heating rates for the curing. reaction between the functional macroglycol Butacene and IPDI. β Tgel (°C/min) (°C)

T at T at tgel TG' = G''a (dη*/dT)max.a η*min.a (min) (°C) (°C) (°C)

T at η*max.a (°C)

ΔTa (°C)

Δta (min)

0.5 1 2.5 5

134 84 38 21

163 165 173 186

103 97 85 90

206 97 34 18

a

97 114 136 146

103 121 145 155

120 136 150 165

For the standard frequency of 1 Hz.

60 68 88 96

Fig. 3. Complex viscosity as a function of temperature for the Butacene–IPDI system at various heating rates in dynamic curing for an angular frequency of 1 Hz.

shifted to a higher temperature (see Table 1). In the same way, as the heating rate increases, the final plateau viscosity is reached at higher temperatures, with a viscosity level of approximately 2500 Pa·s for the lower heating rates and well below this value, ~ 600 Pa·s, for 2.5 and 5.0 °C/min. The four-parameter Arrhenius chemorheological model, Eq. (1), was applied to our PU's complex viscosity data for all heating rates tested. The experimental values and those predicted by the rheokinetic model are compared in Fig. 4, and the kinetic parameters calculated for the reactive system under study are exhibited in Table 2. Good fits were found in accordance with the methodology proposed (R2 N 0.96). It is important to note that this proposed calculation procedure was chosen because there is no compensation effect between the viscous flow and the curing reaction of a reactive system [33]. The average flow activation energy was 34.7 kJ/mol, and the average curing activation energy was 40.1 kJ/mol, although this latter parameter increases slightly with the heating rate. Both values are slightly lower than those obtained for the same material using steady shear rheological analysis under isothermal conditions [15]. This result confirms the similitude between the kinetic data obtained from dynamic conditions with those calculated in isothermal curing. Consequently, the applicability of the non-isothermal regime measurements for the determination of rheokinetic parameters in PUs curing complex processes is illustrated, whose advantages from an experimental point of view are known as it has been mentioned in Introduction. In view of the calculated values and following the model suggested by Dominguez et al. and their results for a resol resin [33], the six-parameter Arrhenius model was used, according to Eq. (2). In this case, the viscous flow parameters were those obtained previously, and the other kinetic parameters calculated are shown in the same table. The accuracy of the fit was not better than that found when the four-parameter Arrhenius model was applied, and the values obtained for the curing activation energy were the same. The estimated chain entanglement parameter (ϕ = 1.15) was in the range found for other systems such as epoxy [43] and resol resin [33], and the reaction order was equal to the most common value (unity) found for resin-curing processes [33]. Therefore, the application of a six-parameter Arrhenius model is not capable of improving the quality of the fit achieved for the data of this functional PU's complex viscosity during its curing. On the contrary, by treating these rheological experimental data using Eq. (3), it is possible to obtain corresponding plots of the rheological conversion as a function of temperature. The change in the curve G′ versus temperature for the different heating rates at the standard frequency of 1 Hz is shown in Fig. 5. The variation in the modulus curve

B.L. and, J.L. de la Fuente / Reactive and Functional Polymers 107 (2016) 60–68

65

Fig. 4. Experimental values of the complex viscosity as a function of temperature for the Butacene–IPDI system at various heating rates in dynamic curing for the angular frequency of 1 Hz and those predicted by applying the four-parameter Arrhenius model.

for the lower heating rates is of an asymptotic nature, and G′ tends to approach a constant G ∞ ′ value. The conversion at G ∞ ′ has been experimentally found by FTIR to be 100%. This has been done by following the evolution of the peak corresponding to the NCO group at 2260 cm−1 (see Fig. 1 in ref. [15]). However, incomplete curing is observed when the heating rate is higher, β = 2.5 or 5 °C/min, and in this case, the limiting value of the elastic modulus is different, because it relates to a different degree of transformation. This can be seen clearly when α values are plotted against the curing temperature (plot inset). The forms of all curves are analogous to those shown for G′, but the ordinate axis is limited to 1.

Fig. 6 shows the plot of the reaction rate (dα/dt) versus temperature for non-isothermal scans at different heating rates. The curves displayed in this figure indicate that the rate conversion typically increases rapidly at the start of the reaction to a maximum and then decreases

Table 2 Viscous flow and kinetic parameters for the curing reaction between the functional macroglycol Butacene and IPDI obtained by the four- and six-parameter Arrhenius chemorheological models. Six-parameter model

Four-parameter model β (°C/min)

ΔEη (kJ/mol)

ln η ∞

ΔEk (kJ/mol)

ln k ∞

R2

ln k ∞

ϕ

n

0.5 1 2.5 5 Average

32.2 32.4 39.7 34.5 34.7

−9.40 −9.63 −12.41 −10.60 −10.51

34.0 38.5 42.0 46.1 40.1

7.14 8.67 9.86 11.29 9.24

0.963 0.975 0.968 0.982 0.972

6.89 8.35 9.69 11.63 9.14

1.25 1.57 1.08 0.69 1.15

0.96 1.30 0.84 0.94 1.01

Fig. 5. Curves of G′ versus reaction temperature of the Butacene–IPDI system for nonisothermal curing at four heating rates at a frequency of 1 Hz. Inset shows degree of rheological conversion α plotted against the temperature.

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Fig. 6. Curing rate dα/dt versus reaction temperature of the Butacene–IPDI system at different heating rates.

exponentially. However, the profiles of these curves show a clear evolution when the heating rate increases. Thus, for the lowest heating rate of 0.5 °C/min (Fig. 6a), the profile presents a first intense maximum rate centred at 117 °C for α = 38% and a second peak at approximately 150 °C. However, for higher heating rates, a unique peak is observed with an asymmetric form, and a clear shift of the maximum to a higher temperature is found. The peak value of the rate and the temperature at which it is achieved vary with the heating rate. It should be noted that an increase in the heating rate results in a proportional shift of the peak to a higher temperature and an increase in the rate. These results suggest again that the cure of our system follows multistep kinetics. Several independent and/or competing reactions can occur, and one reaction may dominate at one temperature, while others may dominate at another temperature [36]. Hence, the contributions of individual reactions cannot be resolved. As a result, the complex curing reaction is often approximated by a single global reaction. However, to determine the possible reactions, these curves were deconvoluted by varying the temperature, width at half height and intensity of Gaussian peaks. A good fit is found for all curves, resulting in two individual peaks, as displayed in the figure. The peak deconvolution qualitatively illustrates the complexity of the mechanism of the reactions, with at least two individual reactions. The apparent activation energy for the curing reaction was also determined for other criteria, using the temperature where the reaction rate takes a maximum value and by applying Kissinger's kinetic analysis. Generally, it is assumed that the degree of conversion at this point can

be considered constant for thermosetting systems. However, it is necessary to verify that the values of the reacted fraction at the maxima remain unchanged for all analysed curves, as is suggested in the literature [44]. These conditions are not maintained in our system. Thus, for the lower heating rates, β = 0.5 and 1 °C/min, the rheological conversion for the main peak is approximately 40%, while for higher heating rates, the conversion is only 10%. The plot of Kissinger's equation gives different Ea values from the maximum reaction rate data. On the one hand, the Ea for the curing reaction is 37.1 kJ/mol according to Kissinger's method for lower heating rates, β ≤ 1 °C/min. This value is almost the same as that calculated for the viscosity build-up, 40.1 kJ/ mol. On the other hand, the apparent Ea exhibits a higher value of approximately 70 kJ/mol when the curing process is carried out at a higher heating rate. The variation in Ea for the two sets of rates cannot be attributed to shape effects of the experimental curves. It should be accepted that this is a consequence of how the reactive process (the heating rate, in our case) was carried out, which has different effects on how the reaction develops [26]. A summary of the activation energies obtained using the various thermoanalytical methods is presented in Table 3. The table also lists the values described in the literature survey for the PUs based on HTPB and IPDI in bulk and under non-isothermal conditions. It is evident that reasonable agreement is achieved between DSC and rheometry in measuring the activation energy of these PU systems. This conclusion was also reported by Papadopoulos et al., who monitored the curing reaction of an oligomeric diisocyanate resin by

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67

Table 3 Comparison of the activation energies for the Butacene–IPDI and HTPB–IPDI systems obtained through various methods in bulk and under non-isothermal conditions.

Reactive system

Technique/method

HTPB + IPDI + DBTLa HTPB + IPDI HTPB + IPDI + FeAAb

DSC/Coast-Redfern DSC/Coast-Redfern DSC/Ozawa

HTPB + IPDI + TPBc

DSC/Coast-Redfern DSC/Ozawa

Butacene + IPDI

a b c

Ea (kJ/mol)

DSC/Kissinger Rheometry/Arrhenius Rheometry/Kissinger Rheometry/Kissinger

Reference

35.1 72.97 61.1 71–87

[13,14] [13,14] [13,14]

87.5 79.5

[22]

40.1 37.1 68.9

This study

Dibutyl tin dilaurate. Ferris tris-acetyl acetonate. Triphenyl bismuth.

calorimetric and rheological methods, [35] and later by Lee and his group in the reactive system HTPB-IPDI [22]. Again, the dynamic rheometry capabilities in the curing studies of this functional system are proved.

through the Program FPI fellowship and project ESP2014-51989-P of the Spanish MINECO.

References 4. Conclusions The dynamic curing of a ferrocene-functionalized PU system, which acts as a binder in advanced energetic composite materials for rocket technology of great significance to the development of aerospace industry, was monitored and analysed using two different techniques. DSC measurements demonstrated that the non-isothermal heat flow profile strongly depends on the heating rate and hence the kinetic parameters that can be derived from them. On the contrary, the rheological analysis provided further information about the curing reaction and was used to follow the curing process and calculate different kinetic properties. Three different regions were determined for the rheological behaviour by analysing the η⁎ data under non-isothermal curing conditions: viscous flow, overlapping and curing reaction. The temperature ranges of these regions depend on the heating rate used; thus, for example, for a 0.5 °C/min temperature ramp, the initial viscous flow region was quite narrow. Insignificant differences were found when four- and sixparameter models were used to obtain the curing kinetic data of this binder material through the Arrhenius chemorheological model. The average Ea obtained for this metallocene–PU resin curing was 40.1 kJ/ mol. The results from the isothermal and non-isothermal methods were compared, and they matched closely. Therefore, the kinetic parameters, based on dynamic measurements (at least three adequate heating rates should be used to obtain a good model), may be used to predict the isothermal curing model in further development of this type of functional PU systems. Rheokinetic curves for the G′ dependence are different for various heating rates. For the lower heating rates, the final equivalent state is reached, and this state is characterized by the limiting (or equilibrium) values of G ∞ ′. Then, the rate conversion degree can be determined and analysed to evaluate the activation parameter by the application of Kissinger's method. Dissimilar Ea values were obtained from different sets of heating rates, demonstrating how much the experimental process affects this fundamental kinetic parameter. Understanding the variables that affect the viscosity build-up in the pre-gel region will allow gaining higher control over the pot life and the workability time of this functional resin. In addition, the gelation of the material, an important cure property, can also be analysed through these rheological measurements. Acknowledgments The authors are grateful to the Instituto Nacional de Técnica Aeroespacial, ‘Esteban Terradas’ (INTA) for the financial support

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