TGA and DTG analyses were performed in the ambient condition for operating temperatures ranging from 30 to 750°C to comprehend the changes that occur during the heat treatment of prepared Ni(OH)2 NPs, as shown in Fig. 3. In chemical precipitation, the two-stage gravimetric differences appear, revealing that weight loss occurred twice during the thermal processing. The primary weight changes that occurs in the temperature ranging from 30 to 110°C can be ascribed to the dehydration of lattice H2O from the synthesised NPs [34]. Lattice water refers to water molecules that are constrained in the crystalline lattice by weak H-bond to the anion or weak ionic bonds to the metal, or both [35, 36].
The occurrence of the subsequent gravimetric discrepancy at temperatures between 250 and 300°C refers to a further weight loss brought on by the thermal degradation of Ni(OH)2 to NiO NPs [37]. There is a modest weight increase in the temperature range of 110 to 250°C, which may be caused by the endothermic reaction-assisted oxidation of the nanoparticles [38, 39]. The same results were already reported by Changyu Li et al., for the synthesis of Ni(OH)2 NPs [40]. The TGA curve shows that there is an almost 17% weight loss from Ni(OH)2 to NiO. The theoretical loss value of 19.4% is similar to the observed weight loss of 17%. The half decomposition temperature of the prepared NPs is 289.62°C (562.62 K). Since it records mass losses as endothermic reactions occur, the TGA result is consistent with the DTA result.
In Sol-gel, the slight weight changes may well be initiated by the desorption of water on the Ni(OH)2 surface in the first step, which is from 40 to 250°C [17]. The second weight loss happens when the temperature is between 250 and 291°C. Ni(OH)2 will be converted to NiO in this stage. Furthermore, the potential weight loss of Ni(OH)2 to NiO is 19.4%, but the experimental result is 16%. As stated by the report, a minor amount of Ni2+ has been oxidized to a higher oxidation state [41]. There are no noticeable endothermic or exothermic peaks in the DTG curve when the Ni(OH)2 sample is heated to above 300°C. The little mass changes above 300°C are due to oxygen desorption from bulk NiO [40]. The same result is already reported in the case of preparation of nickel hydroxide using sodium hydroxide [42]. The half decomposition temperature is 277.91°C (550.91 K). As a result of TGA and DTG analysis, 300°C is considered to become the threshold suitable temperature for both methods in subsequent calcination procedures.
3.3.1. Kinetic parameters analysis
The TGA/DTG is an effective quantitative method of evaluating the kinetic characteristics of various materials, which gives fundamental information about the material's stability [43]. Several approaches for estimating the kinetic parameters of thermal decomposition have been developed. These are based on two main assumptions: (a) there is no difference between the thermal and diffusion processes and (b) the Arrhenius equation holds across the entire temperature range. Because tiny materials are used in TGA/DTG analysis, the barriers between the heat and diffusion processes are low, making the Arrhenius equation acceptable to presume validity [44].
The Hexagonal β-Ni(OH)2 decomposes thermally to face-centered cubic NiO as follows:
$${\text{N}\text{i}\left(\text{O}\text{H}\right)}_{2} \left(\text{s}\right) \to \text{N}\text{i}\text{O} \left(\text{s}\right)+ {\text{H}}_{2}\text{O} \left(\text{g}\right) \left(1\right)$$
Because the reaction described above is a solid-state decomposition methodology, the reaction rate is commonly demonstrated as
$$\frac{d\alpha }{dt}={Ze}^{-\left({E}_{a}/RT\right)}F\left(\alpha \right) \left(2\right)$$
where α (mass fractional conversion), Z (pre-exponential factor), Ea (activation energy), R (universal gas constant), and F(α) is the kinetic model function chosen to represent the decomposition [17].
For a gravimetric measurement, α is defined by,
$$\alpha =\frac{{m}_{i}-{m}_{t}}{{m}_{i}-{m}_{\infty }} \left(3\right)$$
Where mi is initial weight, mt is weight at time t, and m∞ is final weight [17]. The following approaches were used to determine the kinetic parameters and identify a suitable mechanism of thermal decomposition using the TGA/DTG data.
3.3.1.1 Sharp–Wentworth (SW) method
Using the equation derived by Sharp and Wentworth [18],
$$\text{log}\left(\frac{dC/dT}{1-C}\right)= \text{log}\left(\frac{Z}{\beta }\right)- \frac{{E}_{a}}{2.303}\times \frac{1}{T} \left(4\right)$$
Where dC/dT is the rate of change of fraction of weight with change in temperature, β is the linear heating rate, 'Z' is the pre-exponential factor of frequency and 'C' is a concentration of mole fraction or amount of reactant. The graph of log ((dc/dT)/(1-C)) versus 1000/T gives a slope of -Ea/2.303R with an intercept on the y axis where x = 0. The SW plot for prepared NPs is presented in Fig. 4 (a & d). From the graph, the activation energy Ea (10.23 ± 0.19 kJ mol− 1) is same for both the methods.
3.3.1.2 Freeman-Carroll (FC) method
The below Freeman-Carroll (FC) equation is utilized to assess different dynamic parameters [15].
$$\frac{\varDelta \text{log}\left(dW/dt\right)}{\varDelta \text{log}{W}_{r}}=n-\frac{{E}_{a}}{2.303R}\times \frac{\varDelta \left(1/T\right)}{\varDelta \text{log}{W}_{r}} \left(5\right)$$
Where dW/dt is a rate of change of weight with time. Wr = Wc- W; Wc is weight loss at the completion of reaction; W is total weight loss up to time. Ea is activation energy; n is the order of the reaction. Consequently, draw a graph between Δlog(dW/dt)/ΔlogWr and Δ(1/T)/ΔlogWr gives a slope of –Ea/2.303R with an intercept equal to n. The FC plot is shown in Fig. 4 (b & e). The activation energy Ea are 13.60 ± 3.13 and 15.98 ± 0.38 kJ mol− 1 for chemical and sol-gel respectively.
3.3.1.3 Horowitz–Metzger (HM) method
For a first-order kinetic process the Horowitz-Metzger equation may be written in the form [21]:
$$\text{log}\left(\text{log}\frac{{W}_{\alpha }}{{W}_{r}}\right)=\frac{{E}_{a}\times \theta }{2.303R{T}_{s}^{2}}-\text{log}2.303 \left(6\right)$$
Where Wr=Wα – W, Wα is mass loss at the completion of reaction, W is mass loss upto time t, θ = Ti-Ts, Ti is the temperature at time t, and Ts is half decomposition temperature of the curve. The slope is obtained from a plot of log(log(Wα/Wr)) Vs. θ yield the energy of activation. The HM plot for prepared NPs is presented in Fig. 4(c & f). From the graph, the activation energy Ea are 12.70 ± 1.26 and 5.15 ± 0.34 kJ mol− 1.
3.3.1.4 MacCallum-Tanner (MT) method
The MacCallum-Tanner (MT) equation is used for regression analysis [19].
$$\text{log}\left(\frac{1-{\left(1-{\alpha }\right)}^{1-\text{n}}}{1-\text{n}}\right)=\text{log}\frac{Z{E}_{a}}{\beta R}-0.485{E}_{a}^{0.435}-\frac{\left(0.449+0.217{E}_{a}\right)\times {10}^{3}}{T}$$
7
The following is the technique for analyzing thermogravimetric data. (a) The corrected expressions must be used to establish the reaction order, n. The order, n, can then be found by trial-and-error. (b) Having evaluated n, the appropriate log ((1-(1-α)1−n)/(1-n)) is then plotted against 1/T according to Eq. (7). The activation energy, Ea, and the pre-exponential factor, Z, for the reaction may then be calculated. Figure 5 shows the plot of MT method for various n values. The activation energy Ea values are 03.79 ± 1.34, 04.71 ± 1.31, 09.93 ± 0.89, and 14.22 ± 0.32 kJ mol− 1 for the order of reaction n values of 0, 0.5, 1.5, and 2 respectively for chemical precipitation. The activation energy Ea values are 0.80 ± 0.17, 1.52 ± 0.19, 4.41 ± 0.58, and 6.58 ± 1.00 kJ mol− 1 for the order of reaction n values of 0, 0.5, 1.5, and 2 respectively for sol-gel. According to the correlation coefficient, the activation energy Ea are 09.93 ± 0.89 and 01.52 ± 0.19 kJ mol− 1 for chemical precipitation and sol-gel respectively.
3.3.1.5 Coats-Redfern (CR) method
The following expression is employed to analysis the kinetic parameter using Coats-Redfern (CR) method as [20],
$${log}\left(\frac{1-{\left(1-\alpha \right)}^{1-n}}{{T}^{2}\left(1-n\right)}\right)=\text{log}\frac{ZR}{\beta {E}_{a}}\left[1-\frac{2RT}{{E}_{a}}\right]-\frac{{E}_{a}}{2.303RT}$$
$$for n=0, 0.5, 1.5, 2,\dots \left(8\right)$$
$$\text{log}\left(\text{log}\left(\frac{1-{\alpha }}{{\text{T}}^{2}}\right)\right)=\text{log}\frac{ZR}{\beta {E}_{a}}\left[1-\frac{2RT}{{E}_{a}}\right]-\frac{{E}_{a}}{2.303RT} for n=1 \left(9\right)$$
Thus draw a plot of either log((1-(1-α)^(1-n))/(T^2 (1-n) )) against 1/T or, where n = 1 log(log((1-α)/T^2 ) ) against 1/T should results in a straight line. Ea and Z can be calculated from the slope of the graph and intercept respectively. According to the literature, the trial and error method for identifying function that is the value of 'n' is determined by trial and error. For various order of reaction n values, the CR plot is presented in Fig. 6. The activation energy Ea values are 16.19 ± 3.07, 20.01 ± 3.17, 41.69 ± 4.79, 59.55 ± 7.12, and 27.72 ± 3.51 kJ mol− 1 for the order of reaction n values of 0, 0.5, 1.5, 2, and 1 respectively for chemical precipitation. The activation energy Ea values are 03.79 ± 0.79, 06.78 ± 0.80, 18.79 ± 2.23, 27.81 ± 4.02, and 11.55 ± 1.07 kJ mol− 1 for the order of reaction n values of 0, 0.5, 1.5, 2, and 1 respectively for sol-gel. From the trial and error methods, the activation energy Ea are 41.69 ± 4.79 and 11.55 ± 1.07 kJ mol− 1 for chemical precipitation and sol-gel respectively.
3.3.1.6 Broido (BR) method
Broido [22] demonstrated that the weight of the NPs (Wt) submitted to thermal analysis at time t is proportional to the fraction of the original molecules that have not yet decomposed. For n = 1,
$$ln\left(ln\left(\frac{1}{\alpha }\right)\right)=-\frac{{E}_{a}}{R}\times \frac{1}{T}+constant \left(10\right)$$
For 2nd order reaction, (n = 2)
$$ln\left(\frac{1-\alpha }{\alpha }\right)=-\frac{{E}_{a}}{R}\times \frac{1}{T}+constant \left(11\right)$$
Thus, the slopes of plots of ln[ln (1/α)] and ln[(l-α)/α] Vs. 1/T for n = l and n = 2 respectively should yield the energy of activation. The BR plot is express as shown in Fig. 7. The activation energy Ea values are 35.87 ± 3.55 and 67.69 ± 7.27 kJ mol− 1 for chemical precipitation with the order of reaction n values of 1 and 2 respectively. The activation energy Ea values are 19.69 ± 1.18 and 35.96 ± 4.19 kJ mol− 1 for sol-gel with the order of reaction n values of 1 and 2 respectively. As stated in the correlation coefficient, the activation energy Ea are 35.87 ± 3.55 and 19.69 ± 1.18 kJ mol− 1 for chemical precipitation and sol-gel respectively.
The calculated activation energy for different models with correlation coefficient is presented in Table 3. From Table 3, when several models are used on the same TGA data, the activation energy should be the same (~ 10 kJ mol− 1). Consequently, different approaches result in varied activation energies. The CR and BR methods frequently result in different activation energies. Some approaches, such as FC and HM, produce closer activation energy values. This is maybe due to the different assumptions for different models. However, one can find the best value of activation energy concerning the best correlation coefficient (R2). From this, the activation energy of prepared NPs is 10.23 ± 0.19 kJ mol− 1 for both methods using the SW method with the best correlation coefficient (R2 = 0.9917) amongst the other models. M. El-Kemary et al. was already reported the same result in the case of nickel hydroxide decomposition to nickel oxide [45]. The main conclusion of the above said work is that one should use different methods to get realistic kinetic parameters.
The thermodynamical parameters of entropy change (ΔS), free energy change (ΔF), apparent entropy (S*), and frequency factor (Z) were determined using the formulas in Table 4, based on the thermal activation energy (Ea) [46]. The kinetic parameters were estimated and shown in Table 5 using SW methods. Due to the low activation energy of the decomposition process, the thermal stabilities of the prepared NPs were projected to be high. The slower decomposition reaction is predicted by the low pre-exponential factor value [17]. The fact that the entropy change (ΔS) is negative contributes to the support of slower decomposition. Additionally, negative values of free energy (ΔF) indicate spontaneous process at the reported temperature [45].
3.3.1.7 Phadnis–Deshpande (PD) method
Phadnis–Deshpande expression is as follows [25],
$${g}^{{\prime }}\left(\alpha \right)=-\frac{{E}_{a}}{RT} \left(12\right)$$
Where g'(α) is the integral function of conversion α. Solid state kinetics plot for as prepared NPs from various growth model is shown in Fig. 8. Table 6 lists the most commonly used g'(α) procedures. Tables 7 & 8 show the activation energies determined for prepared NPs using the Phadnis–Deshpande model for chemical precipitation and sol-gel method.
The value of prepared NPs activation energy (11.95 ± 1.18 and 9.32 ± 0.71 kJ mol− 1) determined using the above calculation closely matches the value of Phadnis–reaction Deshpande's mechanism-6 and mechanism-8 for chemical precipitation and sol-gel respectively. This is similar to activation energy determined using the SW methods. As a result, the nucleation and nuclei growth (Avrami-Erofeev nuclei growth) and (Valensi) 2-dimensional diffusion mechanism is used in the prepared NPs decomposition kinetic model for chemical precipitation and sol-gel respectively.