Nonisothermal Cure Kinetics of Epoxy/Polyvinylpyrrolidone Functionalized Superparamagnetic Nano-Fe₃O₄ Composites: Effect of Zn and Mn Doping

Abstract

The effects of the bulk and surface modification of nanoparticles on the cure kinetics of low-filled epoxy nanocomposites containing electrochemically synthesized polyvinylpyrrolidone (PVP) functionalized superparamagnetic iron oxide (PVP-SPIO), Zn-doped PVP-SPIO (Zn-PVP-SPIO), and Mn-doped PVP-SPIO (Mn-PVP-SPIO) were studied using differential scanning calorimetry (DSC) and cure kinetics analyses. Integral and differential isoconversional methods were used to calculate the activation energies (Eα) and consequently propose the appropriate reaction model for the curing reaction under nonisothermal conditions. According to the alteration of Eα versus the fractional extent of conversion, the Eα trend was changed through the partial replacement of Fe²⁺ sites by the Zn²⁺ and Mn²⁺ cations in the general formula of M_xFe_3-xO₄, due to smaller amounts of energy being required for curing by the incorporation of Zn-PVP-SPIO and Mn-PVP-SPIO nanoparticles into the epoxy resin. A good agreement was observed between the theoretical calculation and the observed calorimetric data for the model validation.

1. Introduction

The study of the cure reaction of resin composites is key to perceiving the relation between the crosslinking reaction and the ultimate properties of composite materials [1,2,3]. The mysterious nature of the interaction between polymer chains and particles in the thermoset resins makes investigations on cure reactions challenging [4,5,6]. Cure Index (CI) is a new dimensionless criterion that can simply identify the state of cure of thermoset resins in the presence of fillers from a qualitative analysis point of view [7]. Typically, Poor, Good, and Excellent cure are three labels assigned to the thermoset composites in terms of the value of the CI [8,9]. Moreover, the investigation of the kinetics of the curing reaction can be quantitatively analyzed to complete the detailed investigation of the network formation in the thermoset composites [10,11].

The cure behavior and kinetics of epoxy-based nanocomposites containing different types of nanoparticles were investigated in a series of studies. The main consideration of these studies was the investigation of cure reaction in the presence and the absence of surface modifiers and additives with different functional groups in epoxy composites. The effects of the bulk and surface modification of nanoparticles on the cure reaction of the epoxy/amine system were investigated qualitatively with the aid of the CI. The potential of different layered double hydroxides (LDH), such as Mg-Al-LDH [12,13], Zn-Al-LDH [14,15], Mg-Zn-Al-LDH [16], and Ni-Al-LDH [17], with NO₃ and CO₃ intercalating anions on the curability of the epoxy/amine system was investigated, which led to understanding that anions in the structure of LDH are more efficient than the cations in the epoxide ring opening. Analyses on epoxy nanocomposites containing Fe₃O₄ and Mn²⁺-doped Fe₃O₄ demonstrated that Mn²⁺ cations played the role of catalyst in the curing reaction of epoxy/amine, which led to a shift from Poor to Good and Excellent [18]. Nonisothermal differential scanning calorimetry (DSC) demonstrated that the addition of Ni-doped Fe₃O₄ hindered the epoxy curing reaction with amine. The Ni²⁺ dopants tended to be located in the top layer of Fe₃O₄ and increased their tendency to aggregate, which caused a Poor cure state [19]. The Co²⁺-doped Fe₃O₄ significantly increased the amount of heat released by the epoxy system during the curing reaction compared to the epoxy/Fe₃O₄ system [20]. It was found that the incorporation of Fe₃O₄ into the epoxy decreased the curing enthalpy of epoxy, while Gd³⁺-doped Fe₃O₄ facilitated the curing reaction between the epoxy and amine curing agent due to improved dispersion in the epoxy matrix [21]. Moreover, it was found that by substituting Zn²⁺ dopants with Fe²⁺ in the Fe₃O₄ lattice, the curability of the epoxy/amine systems was changed from a Poor to Good state [22]. It was also shown that the surface modification of magnetic nanoparticles with functional organic groups, such as polyvinyl chloride [23], polyethylene glycol [24,25,26], and ethylenediaminetetraacetic acid [27], enhanced the cure reaction of the epoxy resin due to the better dispersibility of nanoparticles and participation of reactive groups on the surface of the functionalized nanoparticles in the epoxide ring opening. The effects of the simultaneous surface modification of the Fe₃O₄ nanoparticles with polyvinylpyrrolidone (PVP) and the bulk modification with Mn [28], Ni [29], and Zn [30] dopants on the cure reaction of epoxy with an amine curing agent were also studied through the lens of CI. A Good cure was the case for epoxy containing 0.1 wt.% Mn-doped PVP-Fe₃O₄, due to the accelerating effect of PVP and Mn²⁺ simultaneously on the crosslinking reaction of epoxy [28]. A shift in the cure state of the epoxy nanocomposites from Poor to Good was also observed by replacing PVP-Fe₃O₄ with PVP-Ni-Fe₃O₄ in the system; this was indicative of the complementary role of superparamagnetic iron oxide nanoparticles’ (SPION’) doping in Ni.

In the present study, the effect of PVP-functionalized superparamagnetic iron oxide with different dopants of Mn and Zn on the cure kinetics of the epoxy/amine system was examined and compared with the neat epoxy as a reference sample [31,32]. Isoconversional model free methods were applied to the nonisothermal scanning calorimetry data for obtaining the kinetics parameters, including the activation energy and order of reaction rate.

2. Experimental Section

See Appendix A for materials and methods. Nonisothermal DSC was used in our study for the qualitative analysis of the curing reactions of the epoxy/amine system and its nanocomposites containing polyvinylpyrrolidone functionalized superparamagnetic iron oxide (PVP-SPIO), Zn-doped PVP-SPIO (Zn-PVP-SPIO), and Mn-doped PVP-SPIO (Mn-PVP-SPIO) nanoparticles. Details about the materials and their physical properties are proposed in Section Appendix A.1 of Appendix A. Section Appendix A.2 of Appendix A describes the preparation of epoxy nanocomposites containing PVP-SPIO, Zn-PVP-SPIO, and Mn-PVP-SPIO. Briefly, 0.1 wt.% of each nanofiller was employed in the nanocomposite preparation, and nonisothermal DSC at the heating rates (β) of 5, 10, 15, and 20 °C/min was used for the curing reaction analysis. The cure behavior and cure kinetics are represented by the quantitative cure analysis; this was performed based on the protocol suggested for the cure analysis of thermoset composites [33].

3. Results

3.1. Cure Behavior Analysis

Figure 1 shows DSC thermograms of the neat epoxy and its nanocomposites containing 0.1 wt.% of PVP-SPIO, Zn-PVP-SPIO, and Mn-PVP-SPIO at four heating rates of 5, 10, 15, and 20 °C/min. Single-step kinetics reaction was confirmed by the observation of a unimodal peak in the DSC curves [34]. Obviously, for all samples, by increasing the heating rate from 5 to 20 °C/min, the peak temperature of thermograms (T_p) shifted to higher values due to the intensified kinetic energy of the system per molecule at higher temperatures [35].

The enthalpy of the curing reaction and the conversion, α, is assumed to be proportional, and this relevance is calculated by following equation:

$$\alpha =\frac{\Delta H_T}{\Delta H_{\infty }},$$

(1)

where ΔH_∞ and ΔH_T are defined as the total heat release of the reaction over the whole temperature range and the amount of total heat release of the reaction at a given temperature T, respectively. Figure 2 shows the variation of α versus temperature at different heating rates for all the studied samples (neat epoxy as reference sample [31,32] and epoxy systems including PVP-SPIO, Zn-PVP-SPIO, and Mn-PVP-SPIO nanoparticles). The sigmoidal shape of conversion charts is indicative of the autocatalytic mechanism of curing reaction [36]. The considerable point is that with the presence of PVP-SPIO and Zn-PVP-SPIO nanoparticles in the epoxy matrix, the conversion profiles kept their shape as a symptom of the dominance of autocatalytic reactions.

3.2. Cure Kinetics Analysis

The primary assumption of isoconversional methods is the dependency of reaction rate on the temperature in a specific α [37,38,39]. The model-free methods appeared successful in description of variation of activation energy (Eα) versus α [10]. Kissinger–Akahira–Sunose (KAS) integral models and the Friedman differential model are two popular isoconversional methods available for the calculation of Eα [10]. Using two different views, integral and differential cases enable a deeper explanation of the reaction mechanism. The Freidman model is more accurate in comparison with KAS. However, there are some other available accurate models, especially for the late stages of the reaction where diffusion plays the key role in the curing phenomenon [40].

As mentioned above, KAS and Freidman seem to be the most readily available methods for the description of cure reaction. Furthermore, they are trustworthy in the range of 0.1 < α < 0.9. Details on the calculation of Eα derived from both models with mathematical and graphical explanations are available in Appendix B.

Variation patterns of Eα versus α based on differential Friedman and integral KAS models are represented in Figure 3 for EP, EP/PVP-SPIO, EP/Zn-PVP-SPIO, and EP/Mn-PVP-SPIO systems. Figure 3 also indicates that presented data extracted from Freidman and KAS methods are almost identical. The value of Eα is reduced mildly by increasing the degree of conversion, particularly for α > 0.3, which is a signature of the autocatalytic nature of the reaction of epoxy with amine curing agent.

On the other hand, before the gelation point, crosslinking reactions are progressed through chemical reactions, while after passing the gelation area, a diffusion-controlled mechanism is responsible for the improvement of the reaction [41]. The decrease of activation energy for α > 0.3 could be due to the inaccuracy of the used isoconversional models or facilitated autocatalytic ring openings fueled by the hydroxyl functional groups generated in the early stage of reaction, but activated in the middle stage [42].

The average value of the activation energy dropped with the incorporation of PVP-SPIO nanoparticles into the epoxy matrix. This descending order is not only due to the facilitating effect of nanoparticles, but also because of agglomeration arising from nanofillers with detrimental effects on crosslinking. On the other hand, the hindered cure can be traded off through the introduction of Zn and Mn into the bulk structure of Fe₃O₄. Zn and Mn dopants play an effective role in changing the dispersion state of nanoparticles. The contribution of OH to epoxy ring opening with the Lewis acid effect of Zn²⁺ and Mn²⁺ should be considered in this regard. Therefore, one would assume that the presence of Zn-PVP-SPIO and Mn-PVP-SPIO nanofillers facilitated the cure reaction of epoxy, and hence, Eα was decreased [43]. Figure 4 illustrates the structure of Zn-PVP-SPIO and Mn-PVP-SPIO nanofillers and the possible reaction between the cure components and ring-opening reaction. Zn dopant prefers to be placed on the Fe₃O₄ surface, while the third Fe layer changes the efficiency of Fe₃O₄ [22]. By contrast, Mn dopant prefers to be located in the bulk layers of Fe₃O₄ to form Mn²⁺ ions. The effects of dopants on the surface or, in the interior layers of Fe, on the reactivity of Fe₃O₄ toward epoxy should be checked in this context. Since Zn-SPIO and Mn-SPIO nanofillers have different surface reactivity, they may be dispersed in a different manner in the epoxy resin. In our previous works, it was found that vibrational sample magnetometer (VSM) parameters including the saturation magnetization, remanence, and coercivity for Zn-PVP-SPIO are lower than those of Mn-PVP-SPIO [30]. The lower values of VSM parameters indicate single-domain centers for Zn-PVP-SPIO. Hence, it is expected that Zn-PVP-SPIO is dispersed more appropriately than the Mn-PVP-SPIO in the epoxy matrix, resulting in its contribution to the epoxide ring opening, as reflected in lower values of activation energy.

3.2.1. Determining the Reaction Model and Order of Reaction

The reaction model detection is the prime essential step to study the effect of PVP-SPIO, Zn-PVP-SPIO, and Mn-PVP-SPIO nanoparticles on the curing mechanism of the epoxy/amine system. The Friedman and Malek methods were chosen to recognize the autocatalytic reaction; the nature of the cure depends on a deep understanding of the details of these methods, as explained in the Appendix C. The curing mechanism can be calculated through Equation (A3), from the shape of the plot of ln[Af(α)] against ln(1 − α).

The network formation of neat epoxy and its nanocomposites show autocatalytic behavior, where the maximum points are placed in the range of 0.2 < α < 0.4, derived from Figure A3.

Furthermore, Appendix C gives information about the calculation of the kinetic model based on the Malek method using the maximum points of y(α) = (α_m), z(α) = (α_p^∞) and the maximum point of conversion in DSC curves (α_p). Further information on the Malek method is reported in Appendix C. The values of α_m, α_p and α_p^∞ for epoxy samples at different heating rates are listed in

Table 1. The values of α_p, α_m and α_p^∞ obtained from the Malek model at various heating rates.

Designation	Heating Rate (°C/min)	αp∞	αm	αp
EP as reference sample [31,32]	5	0.487	0.144	0.512
	10	0.555	0.073	0.510
	15	0.418	0.236	0.498
	20	0.383	0.251	0.483
EP/PVP-SPIO	5	0.476	0.058	0.499
	10	0.393	0.095	0.483
	15	0.453	0.107	0.491
	20	0.495	0.219	0.475
EP/Zn-PVP-SPIO	5	0.513	0.142	0.530
	10	0.567	0.145	0.500
	15	0.545	0.152	0.492
	20	0.452	0.252	0.481
EP/Mn-PVP-SPIO	5	0.500	0.011	0.514
	10	0.366	0.086	0.480
	15	0.426	0.125	0.473
	20	0.467	0.175	0.475

.

The two-parameter autocatalytic kinetic model was confirmed via data from Table 1, α_m < α_p and at the same time α_p^∞ < 0.632, for EP, EP/PVP-SPIO, EP/Zn-PVP-SPIO, and EP/Zn-PVP-SPIO systems.

As mentioned above, the cure mechanism of the EP, EP/PVP-SPIO, and EP/Zn-PVP-SPIO nanocomposites is autocatalytic according to the Friedman and Malek models, which is calculated by the below equation:

$$\frac{d\alpha }{dt}=A\mathit{exp}(-\frac{E_{\alpha }}{RT}){\alpha }^m{(1-\alpha )}^n,$$

(2)

where m and n are introduced as the degrees of autocatalytic and noncatalytic reactions, and A is the pre-exponential factor. The values of m, n, and lnA were determined from Equations (A11) and (A12) in Appendix D. Moreover, the Eα value in this table is the average amount over the whole range of α, based on the Friedman and KAS methods (

Table 2. The kinetic parameters evaluated for the curing of the prepared samples based on the Friedman and KAS models at different heating rates.

Designation	Heating Rate (°C/min)	Ēα (kJ/mol)	ln(A) (1/s)	Mean (1/s)	m	Mean	n	Mean
Friedman
EP as reference sample [31,32]	5	59.23	18.80	18.87	0.410	0.39	1.54	1.596
	10		18.56		0.139		1.44
	15		18.98		0.445		1.68
	20		19.12		0.551		1.73
EP/PVP-SPIO	5	59.36	18.55	18.60	0.151	0.22	1.67	1.685
	10		18.56		0.183		1.71
	15		18.57		0.199		1.62
	20		18.74		0.340		1.73
EP/Zn-PVP-SPIO	5	47.48	14.99	14.99	0.441	0.46	1.47	1.483
	10		14.81		0.396		1.40
	15		14.83		0.409		1.41
	20		15.31		0.582		1.64
EP/Mn-PVP-SPO	5	58.35	18.35	18.47	0.309	0.38	1.72	1.778
	10		18.50		0.390		1.80
	15		18.46		0.386		1.77
	20		18.56		0.452		1.82
KAS
EP as reference sample [31,32]	5	57.35	18.18	18.27	0.430	0.406	1.52	1.579
	10		17.96		0.163		1.42
	15		18.39		0.464		1.66
	20		18.54		0.569		1.71
EP/PVP-SPIO	5	54.73	17.02	17.13	0.209	0.272	1.62	1.633
	10		17.08		0.238		1.66
	15		17.12		0.253		1.57
	20		17.31		0.389		1.68
EP/Zn-PVP-SPIO	5	47.42	14.97	14.97	0.442	0.458	1.47	1.483
	10		14.79		0.397		1.40
	15		14.81		0.409		1.41
	20		15.29		0.583		1.64
EP/Mn-PVP-SPO	5	54.59	17.12	17.28	0.355	0.424	1.68	1.736
	10		17.30		0.429		1.754
	15		17.29		0.424		1.73
	20		17.41		0.489		1.78

).

By comparing the data in Table 2 for the differential Friedman and integral KAS methods, it can be speculated that both models show almost the same results. Taking (m + n) as the overall order of crosslinking reaction, the values higher than one for EP, EP/PVP-SPIO, EP/Zn-PVP-SPIO, as well as EP/Mn-PVP-SPIO nanocomposites are evidence of the complexity of the curing reaction [44].

As can be observed in Table 2, the presence of PVP-SPIO nanoparticles in the system changed the mechanism of cure of nanocomposites from autocatalytic to noncatalytic reactions, as clearly evidenced by the reduction in the values of m. By contrast, adding Zn-PVP-SPIO and Zn-PVP-SPIO nanoparticles into the epoxy matrix can revive the autocatalytic reaction, which is verified by a rise in the m value. Moreover, incorporation of PVP-SPIO, Zn-PVP-SPIO, and Mn-PVP-SPIO nanoparticles led to a decline in the collision between curing moieties, evidenced in the decline in ln(A). The above proves the role of Zn and Mn in facilitating epoxy ring-opening reaction.

3.2.2. Model Validation

Figure 5 compares the kinetics parameters derived from the experiments and those calculated theoretically. The rate of cure reaction (dα/dt) was calculated by determining f(α). It can be confirmed that both calculated values (Freidman and KAS) are in good agreement with experimental data, except at the primary and last stages, which are insignificant.

4. Conclusions

In conclusion, the general mechanism explaining the curing reaction of epoxy and its nanocomposites remained unchanged by adding PVP-SPIO, Zn-PVP-SPIO, and Mn-PVP-SPIO nanofillers. Moreover, the presence of PVP-SPIO nanoparticles influenced the activation energy and led to lower amounts due to the hindrance effect of PVP-SPIO nanoparticles. However, the presentation of Zn dopant could subsequently improve the surface activity and the curing process of the system through a facilitated cure trend. Based on the KAS method, the average values of activation energy for neat epoxy and epoxy containing 0.1 wt.% Zn-PVP-SPIO and Mn-PVP-SPIO were found to be 57.35, 47.42, and 54.59 kJ/mol, respectively. The lower value of activation energy for the Zn-PVP-SPIO incorporated epoxy system compared to the epoxy containing Mn-PVP-SPIO can be attributed to its appropriate dispersion, which allowed for a higher surface area such that PVP groups available for reacting with epoxy played the key role.