**3. Data analysis**

## **3.1. Starting material properties**

The compositional, morphological and structural data for the starting EMD sample are shown in the first row of Table 1. While the details of these initial properties and the resulting changes to the measured parameters as a result of heat treatment will be discussed in detail later, we note here that the EMD chosen for this work is a typical EMD sample. The composition of samples prepared via electrolysis can vary considerably depending on the experimental deposition conditions. We find that the compositional data collected for our starting EMD fit comfortably within the typical range for samples termed EMD [12]. The structure of the starting EMD, as measured by XRD, is shown in Figure 1. The Miller indicies for the peaks in the starting EMD pattern are labelled assuming an orthorhombic unit cell.



Monitoring the Effects of Thermal

Treatment on Properties and Performance During Battery Material Synthesis 277

10

**Figure 2.** TGA data for the EMD sample used in this work recorded at rates of 0.25, 0.5, 1.0, 2.5, 5.0 and

0.25<sup>o</sup> C/min

0.5<sup>o</sup> C/min

0 100 200 300 400 500 600 **Temperature / <sup>o</sup>**

10

**C**

0.25

**Figure 3.** Differential thermogram (DTG) for the EMD sample heated at different heating rates.

0 100 200 300 400 500 600 **Temperature / o**

10.0o C/min

5.0o C/min

2.5 <sup>o</sup> C/min

1.0<sup>o</sup> C/min

**C**

10.0°C/min.

84

**d%/dT**

86

88

90

92

**Mass Percent**

94

96

0.25

98

100

**Table 1.** Composition, morphology and structure of the starting and heat treated EMD samples

**Figure 1.** XRD pattern of the starting EMD showing the γ-MnO2 structure, with the corresponding Miller indices indexed using an orthorhombic unit cell, and XRD patterns for the heat treated EMD.

### **3.2. Thermogravimetric analysis**

The thermogravimetric (TG) and differential thermogravimetric (DTG) data for the thermal decomposition of the EMD sample at the various heating rates are shown in Figures 2 and 3, respectively. The initial loss in mass up to ~120°C is due to the removal of physisorbed water from the EMD surface. Manganese oxides are well known for their ability to adsorb water [13],

276 Heat Treatment – Conventional and Novel Applications

**Micropore Volume (cm3/g)** 

**Meso-pore Volume (cm3/g)** 

**BET SA (m2/g)** 

**3.2. Thermogravimetric analysis** 

**Temp (oC)** 

**Morphology Structure**

**Temp** 

25 37.22 0.0074 0.0293 25 0.34 4.47 9.55 2.83 200 36.68 0.0071 0.0358 200 0.50 4.41 9.35 2.85 250 32.46 0.0047 0.0327 250 0.52 4.43 9.33 2.85 300 30.67 0.0038 0.0348 300 0.73 4.42 9.22 2.86 350 24.90 0.0021 0.0401 350 0.83 4.42 9.11 2.87 400 27.49 0.0034 0.0392 400 0.84 4.42 9.20 2.87

**Table 1.** Composition, morphology and structure of the starting and heat treated EMD samples

**Figure 1.** XRD pattern of the starting EMD showing the γ-MnO2 structure, with the corresponding Miller indices indexed using an orthorhombic unit cell, and XRD patterns for the heat treated EMD.

200

111 040

021

130

110

**Normalised Intensity**

The thermogravimetric (TG) and differential thermogravimetric (DTG) data for the thermal decomposition of the EMD sample at the various heating rates are shown in Figures 2 and 3, respectively. The initial loss in mass up to ~120°C is due to the removal of physisorbed water from the EMD surface. Manganese oxides are well known for their ability to adsorb water [13],

**(oC) Pr**

400o C / 0.27 h

350o C / 1.52 h

300o C / 5.07 h

250o C / 11.12 h

200o C / 31.65 h

<sup>061</sup> <sup>002</sup> <sup>151</sup>

221 240

131 140 121

10 20 30 40 50 60 70 80 **2**θ

Standard EMD

**a0 (Å)** 

**b0 (Å)** 

**c0 (Å)** 

**Figure 2.** TGA data for the EMD sample used in this work recorded at rates of 0.25, 0.5, 1.0, 2.5, 5.0 and 10.0°C/min.

**Figure 3.** Differential thermogram (DTG) for the EMD sample heated at different heating rates.

so it is not surprising that 2-3% of the initial sample mass is physisorbed water. The broad peak at ~200°C in the DTG relates to the removal of structural water; i.e., protons associated with cation vacancies and Mn(III) ions within the manganese dioxide structure. The sharper peak at ~500°C relates to the thermal reduction of the MnO2 to form Mn2O3. The use of faster heating rates has shifted the decomposition temperature to higher values, possibly as a result of slow reaction kinetics and/or since less time is allowed for the equivalent reaction. It is also possible that the thermal conductivity of the EMD contributed to this effect, although with the use of a relatively small sample size (~10 mg) its contribution is expected to be minor.

Monitoring the Effects of Thermal

Treatment on Properties and Performance During Battery Material Synthesis 279

**Figure 5.** Extent of conversion versus temperature for the different heating rates.

0 50 100 150 200 250 300 350 **Temperature / <sup>o</sup>**

**C**

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

50

100

150

**Temperature / o**

**C**

200

250

300

350

**Extent of Conversion,** α

0.25<sup>o</sup> C/min 0.5<sup>o</sup> C/min 1.0<sup>o</sup> C/min 2.5<sup>o</sup> C/min 5.0<sup>o</sup> C/min 10.0<sup>o</sup> C/min

**Figure 6.** Variation of temperature with heating rate for given extent of conversion.

α

β <sup>d</sup><sup>α</sup>

=0 to all

α

we will apply the method used for

Kinetic analysis using this method is conventionally applied to the data corresponding to

=0 for the different heating rates. However, since we have access here to the temperature corresponding to various extents of conversion for different heating rates, and the fact that

0 2 4 6 8 10 12 **Heating Rate / <sup>o</sup>**

**C/min**

α

EA

how the resultant kinetic parameters change. Kinetic analysis is based on the rate equation:

dT =Afሺαሻ ቀ-

values, then it will be interesting to observe

0.0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

RTቁ (10)

## **3.3. Multiple curve isoconversional analysis**

In this analysis, we will be considering the first step in the EMD thermal decomposition; i.e., the process of removing water from the structure beginning at ~175°C, since this is most important when the material is to be used in a non-aqueous battery system.

The first step in the analysis was background correction of the DTG data. To do this an exponential background curve was fitted to the data surrounding the peak for each heating rate used. The resulting curve after background correction describes the processes occurring in this region, as shown in Figure 4 for a heating rate of 10°C/min. The normalized extent of conversion (α) was then found by numerical integration of the background-corrected DTG data, with the normalization being carried out by expressing each point relative to the maximum area determined. A plot of α as a function of temperature for the range of heating rates considered is shown in Figure 5. From this data the temperatures corresponding to a pre-defined set of *α* values can be found for each heating rate, as shown in Figure 6.

**Figure 4.** Fitting of DTG data for heating rate 10°C/min with background curve and resulting process.

**Figure 5.** Extent of conversion versus temperature for the different heating rates.

278 Heat Treatment – Conventional and Novel Applications

**3.3. Multiple curve isoconversional analysis** 

to be minor.

conversion (

α

maximum area determined. A plot of

so it is not surprising that 2-3% of the initial sample mass is physisorbed water. The broad peak at ~200°C in the DTG relates to the removal of structural water; i.e., protons associated with cation vacancies and Mn(III) ions within the manganese dioxide structure. The sharper peak at ~500°C relates to the thermal reduction of the MnO2 to form Mn2O3. The use of faster heating rates has shifted the decomposition temperature to higher values, possibly as a result of slow reaction kinetics and/or since less time is allowed for the equivalent reaction. It is also possible that the thermal conductivity of the EMD contributed to this effect, although with the use of a relatively small sample size (~10 mg) its contribution is expected

In this analysis, we will be considering the first step in the EMD thermal decomposition; i.e., the process of removing water from the structure beginning at ~175°C, since this is most

The first step in the analysis was background correction of the DTG data. To do this an exponential background curve was fitted to the data surrounding the peak for each heating rate used. The resulting curve after background correction describes the processes occurring in this region, as shown in Figure 4 for a heating rate of 10°C/min. The normalized extent of

data, with the normalization being carried out by expressing each point relative to the

rates considered is shown in Figure 5. From this data the temperatures corresponding to a

**Figure 4.** Fitting of DTG data for heating rate 10°C/min with background curve and resulting process.

) was then found by numerical integration of the background-corrected DTG

as a function of temperature for the range of heating

important when the material is to be used in a non-aqueous battery system.

α

pre-defined set of *α* values can be found for each heating rate, as shown in Figure 6.

**Figure 6.** Variation of temperature with heating rate for given extent of conversion.

Kinetic analysis using this method is conventionally applied to the data corresponding to α=0 for the different heating rates. However, since we have access here to the temperature corresponding to various extents of conversion for different heating rates, and the fact that we will apply the method used for α=0 to all α values, then it will be interesting to observe how the resultant kinetic parameters change. Kinetic analysis is based on the rate equation:

$$\beta \frac{d\alpha}{d\Gamma} \text{=} \text{Af}(\alpha) \exp\left(-\frac{\text{E}\_{\text{A}}}{\text{RT}}\right) \tag{10}$$

where *A* is the pre-exponential factor (min-1), *β* is the heating rate (°C/min), *EA* is the activation energy (J/mol), the term *f(*α*)* represents the model chosen to represent the mechanism of thermal decomposition, and all other symbols have their usual significance. In this case we will use *f(α)*=1-*α* as our decomposition model [14]. Separation of variables leads to:

$$\frac{\text{d}\alpha}{\text{s}} = \frac{\text{A}}{\beta} \exp\left(\text{-}\frac{\text{E}\_{\text{A}}}{\text{RT}}\right) \text{dT} \tag{11}$$

Monitoring the Effects of Thermal

*)*) used, the measured activation

α

*<sup>n</sup>*, *Tn*) to

). Again, this suggests the presence of multiple

Treatment on Properties and Performance During Battery Material Synthesis 281

reference [14] were examined here using this approach. Firstly, despite the broad range of

to the experimental data – hence the use of the incremental approach in our analysis. As we will discuss later, this provides strong supporting evidence for multiple weight loss processes occurring. Additionally, with the application of the incremental approach, it was

energy was similar to that reported in Figure 7, with similar variation in the activation

weight loss processes, as well as providing us with some confidence for using the first order *f(α)*=1-*α* expression over the range used. Finally, the use of this model enables us to quite easily calculate the required isothermal time necessary to achieve a specified extent of

Another approach to solving the rate expression in Eqn. 10 is the incremental integral method [14,15]. This method can also be used to take into account the dependence of the kinetic parameters on the extent of conversion, focussing instead on an individual TG experiment rather than a range of different heating rate experiments. In this case, the Runge-Kutta method, an iterative technique for the approximation of ordinary differential

equations, was used to solve Eqn. 10. This method uses the previous point (

an estimated average of the slopes. To begin we have the initial condition:

αn+1=αn+

where *h* is the size of the interval (1°C was used in this analysis), and:

α

1

Tn+1=Tn+h (16)

k1=f�Tn,αn� (17)

h <sup>2</sup> ,αn+ hk1

h <sup>2</sup> ,αn+ hk2

k4=f�Tn+h,αn+hk3� (20)

extent of conversion against temperature, which can be fitted to the experimental curve using linear least squares regression in a restricted range of *α* (hence employing the incremental integral method), by varying values for the activation energy, *EA*, and the pre-

α

vs. *T*) that these models generate, no single one was able to fit satisfactorily

α

*n+1*, *Tn+1*), by using the size of the interval between the points (*h*) and

*)* is implied by Eqn. 10. This gives rise to a theoretical curve for the

*n+1* and *Tn+1* are given by:

α�T0�=a0=0 (14)

<sup>6</sup> <sup>h</sup>�k1+2k2+2k3+k4� (15)

<sup>2</sup> � (18)

<sup>2</sup> � (19)

curve shapes (

conversion.

approximate the next (

where the function *f(T,*

α

noted that for each thermal decomposition function (*f(*

**3.4. Single curve incremental isoconversional analysis** 

energy across the extent of conversion (

α

k2=f �Tn+

k3=f �Tn+

α

Then, using the Runge-Kutta method,

and then integration of the left-hand side from 0 to *αi* in Eqn. 11, gives:

$$\mathbf{F}(\alpha\_{\rm i})\mathbf{-}\mathbf{F}(0) = \int\_{0}^{\mathbf{T}\_{\rm I}} \frac{\mathbf{A}}{\beta} \exp\left(-\frac{\mathbf{E}\_{\rm A}}{\mathbf{RT}}\right) \mathbf{dT} \tag{12}$$

where *F* represents the integrated form of *f(*α*)*, and *Ti* corresponds to the temperature at α*i*. Upon rearrangement we can write:

$$\beta = \int\_0^{T\_l} \frac{A}{\text{F}(\alpha\_l) \cdot \text{F}(0)} \exp\left(-\frac{E\_A}{RT}\right) \text{ dT} \tag{13}$$

This integration was performed numerically using the trapezium method and optimised to fit the experimental data using a linear least squares regression. Consequently, the dependence of activation energy on the extent of conversion and the pre-exponential factor was found, as shown in Figure 7. With the exception of the first point at α=0 (which was likely due to the noisy data for these conditions, cf. Figure 6), the activation energy clearly increases with extent of conversion, ranging from 109-250 kJ/mol.

**Figure 7.** Activation energy and pre-exponential factor for process occurring against extent of conversion calculated using the first order kinetic analysis.

Before going further, an additional comment needs to be made regarding the choice of thermal decomposition model (*f(*α*)*) used in the analysis. Each of the models listed in reference [14] were examined here using this approach. Firstly, despite the broad range of curve shapes (α vs. *T*) that these models generate, no single one was able to fit satisfactorily to the experimental data – hence the use of the incremental approach in our analysis. As we will discuss later, this provides strong supporting evidence for multiple weight loss processes occurring. Additionally, with the application of the incremental approach, it was noted that for each thermal decomposition function (*f(*α*)*) used, the measured activation energy was similar to that reported in Figure 7, with similar variation in the activation energy across the extent of conversion (α). Again, this suggests the presence of multiple weight loss processes, as well as providing us with some confidence for using the first order *f(α)*=1-*α* expression over the range used. Finally, the use of this model enables us to quite easily calculate the required isothermal time necessary to achieve a specified extent of conversion.

#### **3.4. Single curve incremental isoconversional analysis**

280 Heat Treatment – Conventional and Novel Applications

F(α<sup>i</sup>

Upon rearrangement we can write:

where *F* represents the integrated form of *f(*

α

energy (J/mol), the term *f(*

where *A* is the pre-exponential factor (min-1), *β* is the heating rate (°C/min), *EA* is the activation

thermal decomposition, and all other symbols have their usual significance. In this case we

EA

<sup>β</sup> exp <sup>ቀ</sup>-

EA RTቁ Ti

EA

will use *f(α)*=1-*α* as our decomposition model [14]. Separation of variables leads to:

)-F(0)= <sup>A</sup>

α

<sup>F</sup>ሺαiሻ-F(0) exp <sup>ቀ</sup>-

RT<sup>ቁ</sup> Ti

This integration was performed numerically using the trapezium method and optimised to fit the experimental data using a linear least squares regression. Consequently, the dependence of activation energy on the extent of conversion and the pre-exponential factor

likely due to the noisy data for these conditions, cf. Figure 6), the activation energy clearly

dα f(α) = A <sup>β</sup> exp <sup>ቀ</sup>-

<sup>β</sup><sup>=</sup> <sup>A</sup>

was found, as shown in Figure 7. With the exception of the first point at

**Figure 7.** Activation energy and pre-exponential factor for process occurring against extent of

α

Before going further, an additional comment needs to be made regarding the choice of

0 0.2 0.4 0.6 0.8 1 1.2 **Extent of Conversion,** α

conversion calculated using the first order kinetic analysis.

0

50

100

150

**Activation Energy, EA / kJ/mol**

200

250

300

thermal decomposition model (*f(*

increases with extent of conversion, ranging from 109-250 kJ/mol.

and then integration of the left-hand side from 0 to *αi* in Eqn. 11, gives:

*)* represents the model chosen to represent the mechanism of

RT<sup>ቁ</sup> dT (11)

<sup>0</sup> (12)

*)*, and *Ti* corresponds to the temperature at

α

=0 (which was

<sup>0</sup> dT (13)

*)*) used in the analysis. Each of the models listed in


0

4

8

**log(A / min-1)**

12

16

α*i*.

> Another approach to solving the rate expression in Eqn. 10 is the incremental integral method [14,15]. This method can also be used to take into account the dependence of the kinetic parameters on the extent of conversion, focussing instead on an individual TG experiment rather than a range of different heating rate experiments. In this case, the Runge-Kutta method, an iterative technique for the approximation of ordinary differential equations, was used to solve Eqn. 10. This method uses the previous point (α*<sup>n</sup>*, *Tn*) to approximate the next (α*n+1*, *Tn+1*), by using the size of the interval between the points (*h*) and an estimated average of the slopes. To begin we have the initial condition:

$$\mathbf{a}(\mathbf{T}\_0) \mathbf{=} \mathbf{a}\_0 = \mathbf{0} \tag{14}$$

Then, using the Runge-Kutta method, α*n+1* and *Tn+1* are given by:

$$\alpha\_{\mathbf{n}+1} = \alpha\_{\mathbf{n}} + \frac{1}{6} \mathbf{h} (\mathbf{k}\_1 + 2\mathbf{k}\_2 + 2\mathbf{k}\_3 + \mathbf{k}\_4) \tag{15}$$

$$\mathbf{T}\_{n+1} = \mathbf{T}\_n + \mathbf{h} \tag{16}$$

where *h* is the size of the interval (1°C was used in this analysis), and:

$$\mathbf{k}\_1 \mathbf{=f}(\mathbf{T}\_\nu, \mathbf{a}\_\mathbf{n}) \tag{17}$$

$$\mathbf{k}\_2 \mathbf{=f}\left(\mathbf{T}\_\mathrm{n} + \frac{\mathrm{h}}{2}, \alpha\_\mathrm{n} + \frac{\mathrm{hk}\_1}{2}\right) \tag{18}$$

$$\mathbf{k}\_3 \text{=f}\left(\mathbf{T}\_\mathbf{n} + \frac{\mathbf{h}}{2}, \alpha\_\mathbf{n} + \frac{\mathbf{hk}\_2}{2}\right) \tag{19}$$

$$\mathbf{k}\_4 = \mathbf{f}\{\mathbf{T}\_\mathrm{n} + \mathrm{h}\_\mathrm{\prime}\mathrm{a}\_\mathrm{n} + \mathrm{hk}\_3\} \tag{20}$$

where the function *f(T,*α*)* is implied by Eqn. 10. This gives rise to a theoretical curve for the extent of conversion against temperature, which can be fitted to the experimental curve using linear least squares regression in a restricted range of *α* (hence employing the incremental integral method), by varying values for the activation energy, *EA*, and the pre-

#### 282 Heat Treatment – Conventional and Novel Applications

exponential factor, *A*. Figure 8 demonstrates how the activation energy changes as a function of extent of conversion and heating rate for this analysis method. Because the focus here is on just one data set, particular attention was paid to the fitting procedure to ensure that a global minimum was determined. This was achieved by repeating the fitting multiple times, from different starting points. In each case, across the complete α range and for each heating rate used, the same result was achieved.

Monitoring the Effects of Thermal

α=0.5

Treatment on Properties and Performance During Battery Material Synthesis 283

limiting factor in chemical reactions. What is also interesting about the data in Figure 8 is the general decrease in calculated activation energy as the heating rate was increased. This is quite clearly demonstrated in Figure 9, which shows how the activation energy at

changes with heating rate. The data in this figure indicates that there are two heating rate regions for which there is an exponential decrease in calculated activation energy with heating rate. The cause of this may lie in the apparently less than ideal thermal transfer of heat from the furnace to the sample during the TG experiment. Whether there is a thermal gradient within the powdered sample in the TG pan, or within individual sample particles, it does mean that the thermal decomposition reaction will be occurring at different rates within the sample and/or individual particles. Certainly at higher heating rates this thermal gradient will be much more pronounced, meaning that there is expected to be a greater error in the estimated activation energy when determined at faster heating rates. While the thermal conductivity of manganese dioxide is, to the best of our knowledge, not available in the literature, other similar metal oxides have relatively high thermal conductivities, as shown in Table 2 [16]. Typical thermal conductivity values lie within the range 2-30 W m-1 K-1. Of these, the value for titanium dioxide (3.8 W m-1 K-1) is most likely very similar to manganese dioxide given the proximity of the metals to each other in the periodic table, and the iso-structural nature of the corresponding oxides. This relatively low value does imply that there will be a reasonable thermal gradient across each particle. To eliminate the effect of thermal conductivity, the exponential relationship between heating rate and calculated activation energy was extrapolated to predict the activation energy under the hypothetical condition of a 0°C/min heating rate. This extrapolated data is also shown in Figure 8, and is expected to more closely represent the true activation energy for this thermal decomposition

process.

**Figure 9.** Activation energy (for *α*=0.5) as a function of heating rate.

0.1 1 10

**Heating Rate / oC/min**

66

67

68

69

70

**EA, (**α**=0.5) / kJ/mol**

71

72

73

**Figure 8.** Activation energy with respect to extent of conversion for the different heating rates.

The pre-exponential factor for all analyses remained essentially constant at a value of (5.3±0.8)×106 min-1, where the error analysis here takes into account the variation in the calculated *A* value.

Overall, the calculated activation energy for the mass loss associated with the thermal decomposition of γ-MnO2 fell within the rather narrow range 66-77 kJ/mol. Nevertheless, within this range there were some systematic changes observed. For all heating rates there was a minimum, or for lower heating rates, a plateau in the activation energy within the extent of conversion range 0.1<α<0.7. At both higher and lower α values the activation energy increased. This increase is interesting in that it tells us something about the availability of energy or heat, as well as reactants, to affect the thermal transformation. At low α values, corresponding to lower temperatures, there is insufficient heat to activate the reaction, so for all intents and purposes, the activation energy is much larger than normal because very little reaction is occurring. Conversely, at higher α values there is a relatively low concentration of unreacted species available to actually undergo the thermal transformation, and as such the rate of the thermal transformation here is also inhibited (manifested as an increase in activation energy) since reactant concentration is also a limiting factor in chemical reactions. What is also interesting about the data in Figure 8 is the general decrease in calculated activation energy as the heating rate was increased. This is quite clearly demonstrated in Figure 9, which shows how the activation energy at α=0.5 changes with heating rate. The data in this figure indicates that there are two heating rate regions for which there is an exponential decrease in calculated activation energy with heating rate. The cause of this may lie in the apparently less than ideal thermal transfer of heat from the furnace to the sample during the TG experiment. Whether there is a thermal gradient within the powdered sample in the TG pan, or within individual sample particles, it does mean that the thermal decomposition reaction will be occurring at different rates within the sample and/or individual particles. Certainly at higher heating rates this thermal gradient will be much more pronounced, meaning that there is expected to be a greater error in the estimated activation energy when determined at faster heating rates. While the thermal conductivity of manganese dioxide is, to the best of our knowledge, not available in the literature, other similar metal oxides have relatively high thermal conductivities, as shown in Table 2 [16]. Typical thermal conductivity values lie within the range 2-30 W m-1 K-1. Of these, the value for titanium dioxide (3.8 W m-1 K-1) is most likely very similar to manganese dioxide given the proximity of the metals to each other in the periodic table, and the iso-structural nature of the corresponding oxides. This relatively low value does imply that there will be a reasonable thermal gradient across each particle. To eliminate the effect of thermal conductivity, the exponential relationship between heating rate and calculated activation energy was extrapolated to predict the activation energy under the hypothetical condition of a 0°C/min heating rate. This extrapolated data is also shown in Figure 8, and is expected to more closely represent the true activation energy for this thermal decomposition process.

282 Heat Treatment – Conventional and Novel Applications

heating rate used, the same result was achieved.

66

68

70

72

**Activation Energy, EA (kJ/mol)**

74

76

78

calculated *A* value.

low α

extent of conversion range 0.1<

exponential factor, *A*. Figure 8 demonstrates how the activation energy changes as a function of extent of conversion and heating rate for this analysis method. Because the focus here is on just one data set, particular attention was paid to the fitting procedure to ensure that a global minimum was determined. This was achieved by repeating the fitting multiple

α

range and for each

times, from different starting points. In each case, across the complete

0.25<sup>o</sup> C/min 0.5<sup>o</sup> C/min 1.0<sup>o</sup> C/min 2.5<sup>o</sup> C/min 5.0<sup>o</sup> C/min 10<sup>o</sup> C/min 0o C/min

**Figure 8.** Activation energy with respect to extent of conversion for the different heating rates.

α

because very little reaction is occurring. Conversely, at higher

The pre-exponential factor for all analyses remained essentially constant at a value of (5.3±0.8)×106 min-1, where the error analysis here takes into account the variation in the

0 0.2 0.4 0.6 0.8 1 **Extent of Conversion,** α

Overall, the calculated activation energy for the mass loss associated with the thermal decomposition of γ-MnO2 fell within the rather narrow range 66-77 kJ/mol. Nevertheless, within this range there were some systematic changes observed. For all heating rates there was a minimum, or for lower heating rates, a plateau in the activation energy within the

energy increased. This increase is interesting in that it tells us something about the availability of energy or heat, as well as reactants, to affect the thermal transformation. At

low concentration of unreacted species available to actually undergo the thermal transformation, and as such the rate of the thermal transformation here is also inhibited (manifested as an increase in activation energy) since reactant concentration is also a

<0.7. At both higher and lower

 values, corresponding to lower temperatures, there is insufficient heat to activate the reaction, so for all intents and purposes, the activation energy is much larger than normal

α

α

values the activation

values there is a relatively

**Figure 9.** Activation energy (for *α*=0.5) as a function of heating rate.


Monitoring the Effects of Thermal

=1.0. On the other hand the

Treatment on Properties and Performance During Battery Material Synthesis 285

α

conversion, varying from ~109 kJ/mol at

addressed.

between the two methods.

the preferred method.

α

incremental integral method led to an activation energy of '66—76 kJ/mol throughout the majority of the thermal transformation, with slightly higher values at both lower and higher extents of the conversion. Clearly there are significant differences in the results obtained from the application of the two kinetic analysis methods, and these differences need to be

From a purely statistical perspective, the use of multiple experiments to produce data for analysis is bound to contain more variation than just using a single experiment. Under these circumstances, therefore, we might expect that the incremental integral approach should inherently be more reliable than the first order analysis method. Nevertheless, the contribution to the total variation in the analysis made by the individual TG experiments is expected to be quite small, certainly not enough to account for the significant difference

As part of the analysis, a background correction of the DTG data was employed to focus specifically on the mass loss process of interest; i.e., the loss of structural water from the manganese dioxide. While this background correction was applied to all of the data reported here, it was in no way constant between experiments. Furthermore, the shape of the background correction curve was arbitrarily chosen to be exponential. The point being made is that the background correction being made could have easily over- or undercompensated its contribution to the total response, thus inducing some variability between experiments. This would certainly suggest that the incremental integral approach should be

Another likely contributor to variability in the analysis is the thermal conductivity of the manganese dioxide in relation to the heating rate used. Despite the fact that only a small quantity of material (~10 mg) was used in each experiment, the rate with which heat is transferred through the sample is very critical in determining the validity of the resultant information, particularly so since the kinetic analysis model assumes that the sample temperature is uniform throughout. As has already been mentioned, the thermal conductivity of manganese dioxide is not available in the literature; however, the thermal conductivity of similar materials (e.g., titanium dioxide) does suggest that there may be thermal gradients within the manganese dioxide, particularly with the use of fast heating rates. Therefore, those experiments that make use of the higher heating rates could be judged as having a higher relative error compared to those using slower heating rates. Therefore, the incremental integral approach, particularly for those experiments employing

As a final comment, the first order kinetic analysis involved the use of separation of variables to solve Eqn. 10. An inherent assumption made with this approach is that the extent of conversion is independent of temperature, when in fact this is not the case given the thermal gradients within the manganese dioxide sample and the fact that the conversion process we are examining covers a very broad temperature range. Under these

a slower heating rate, is most likely to be the preferred method.

=0.1 to ~250 kJ/mol at

**Table 2.** Thermal conductivity of selected metal oxides [16].

As was mentioned previously, the systematic variation in the activation energy, as shown in Figure 8 and highlighted specifically in Figure 9, quite nicely validates the use of this method for the thermal analysis of kinetic parameters. The International Confederation for Thermal Analysis and Calorimetry (ICTAC) has recommended that single scan methods of analysis be avoided where possible (see for example reference [17]). However, in this work the activation energies obtained were not just based on one analysis. In fact, what we have shown here is that the systematic variation within the activation energy over two orders of magnitude change in heating rate (Figure 9) not only provide us with considerable confidence in the resultant data, but also allows us to extrapolate to what the theoretical activation energy would be at a 0°C/min heating rate. This latter outcome has not been reported previously, at least for this system, and in actual fact represents a novel approach to determining an activation energy that is free of experimental artefacts, such as thermal transfer of heat to the sample.

Finally, the kinetic parameters determined for the water loss process can be used to calculate the required isothermal time to achieve complete conversion of the material (α=1), i.e., completely remove water from the material, at a range of temperatures. This value can be found by employing the Arrhenius equation to calculate the rate constant (k) and subsequently, assuming first order kinetics, the heating time can be determined. This was performed for the heating rate 1°C/min, and is shown in Table 3.


**Table 3.** Isothermal heating regimes to achieve complete conversion of the water loss process.

## **3.5. Comparison of methods**

The first order analysis of the kinetics has shown that the activation energy for the loss of water from the manganese dioxide structure increased relatively linearly with extent of conversion, varying from ~109 kJ/mol at α=0.1 to ~250 kJ/mol at α=1.0. On the other hand the incremental integral method led to an activation energy of '66—76 kJ/mol throughout the majority of the thermal transformation, with slightly higher values at both lower and higher extents of the conversion. Clearly there are significant differences in the results obtained from the application of the two kinetic analysis methods, and these differences need to be addressed.

284 Heat Treatment – Conventional and Novel Applications

**Table 2.** Thermal conductivity of selected metal oxides [16].

transfer of heat to the sample.

**3.5. Comparison of methods** 

**Metal Oxide Thermal Conductivity (W m-1 K-1)** 

Al2O3 (sintered) 26 (373 K) BaTiO3 6.2 (300 K) Fe3O4 (magnetite) 7.0 (304 K) MnO 3.5 (573 K) SiO2 (fused silica) 1.6 (373 K) SrTiO3 11.2 (300 K) TiO2 3.8 (400 K)

As was mentioned previously, the systematic variation in the activation energy, as shown in Figure 8 and highlighted specifically in Figure 9, quite nicely validates the use of this method for the thermal analysis of kinetic parameters. The International Confederation for Thermal Analysis and Calorimetry (ICTAC) has recommended that single scan methods of analysis be avoided where possible (see for example reference [17]). However, in this work the activation energies obtained were not just based on one analysis. In fact, what we have shown here is that the systematic variation within the activation energy over two orders of magnitude change in heating rate (Figure 9) not only provide us with considerable confidence in the resultant data, but also allows us to extrapolate to what the theoretical activation energy would be at a 0°C/min heating rate. This latter outcome has not been reported previously, at least for this system, and in actual fact represents a novel approach to determining an activation energy that is free of experimental artefacts, such as thermal

Finally, the kinetic parameters determined for the water loss process can be used to calculate the required isothermal time to achieve complete conversion of the material (α=1), i.e., completely remove water from the material, at a range of temperatures. This value can be found by employing the Arrhenius equation to calculate the rate constant (k) and subsequently, assuming first order kinetics, the heating time can be determined. This was

> **Temperature (°C) Heating time (h)** 200 31.65 250 11.12 300 5.07 350 1.52 400 0.27

**Table 3.** Isothermal heating regimes to achieve complete conversion of the water loss process.

The first order analysis of the kinetics has shown that the activation energy for the loss of water from the manganese dioxide structure increased relatively linearly with extent of

performed for the heating rate 1°C/min, and is shown in Table 3.

From a purely statistical perspective, the use of multiple experiments to produce data for analysis is bound to contain more variation than just using a single experiment. Under these circumstances, therefore, we might expect that the incremental integral approach should inherently be more reliable than the first order analysis method. Nevertheless, the contribution to the total variation in the analysis made by the individual TG experiments is expected to be quite small, certainly not enough to account for the significant difference between the two methods.

As part of the analysis, a background correction of the DTG data was employed to focus specifically on the mass loss process of interest; i.e., the loss of structural water from the manganese dioxide. While this background correction was applied to all of the data reported here, it was in no way constant between experiments. Furthermore, the shape of the background correction curve was arbitrarily chosen to be exponential. The point being made is that the background correction being made could have easily over- or undercompensated its contribution to the total response, thus inducing some variability between experiments. This would certainly suggest that the incremental integral approach should be the preferred method.

Another likely contributor to variability in the analysis is the thermal conductivity of the manganese dioxide in relation to the heating rate used. Despite the fact that only a small quantity of material (~10 mg) was used in each experiment, the rate with which heat is transferred through the sample is very critical in determining the validity of the resultant information, particularly so since the kinetic analysis model assumes that the sample temperature is uniform throughout. As has already been mentioned, the thermal conductivity of manganese dioxide is not available in the literature; however, the thermal conductivity of similar materials (e.g., titanium dioxide) does suggest that there may be thermal gradients within the manganese dioxide, particularly with the use of fast heating rates. Therefore, those experiments that make use of the higher heating rates could be judged as having a higher relative error compared to those using slower heating rates. Therefore, the incremental integral approach, particularly for those experiments employing a slower heating rate, is most likely to be the preferred method.

As a final comment, the first order kinetic analysis involved the use of separation of variables to solve Eqn. 10. An inherent assumption made with this approach is that the extent of conversion is independent of temperature, when in fact this is not the case given the thermal gradients within the manganese dioxide sample and the fact that the conversion process we are examining covers a very broad temperature range. Under these circumstances, while the data we have collected shows a nice asymptotic change with heating rate (Figure 9), the assumptions made in the numerical analysis do not lead to an accurate estimate of the activation energy, again implying that the incremental integral approach is superior.

Monitoring the Effects of Thermal

Treatment on Properties and Performance During Battery Material Synthesis 287

The structural changes can be further elucidated by consideration of the unit cell parameters (determined from the XRD patterns of these materials assuming an orthorhombic unit cell) as a function of heat treatment temperature. The unit cell parameters for the starting EMD were a0 = 4.468 Å, b0 = 9.554 Å and c0 = 2.833 Å, which is an expansion in the *a*-*b* plane, but a slight contraction in the *c* direction, compared with ramsdellite [20]. The unit cell parameters for the heat treated materials are shown in Table 1. The decrease shown for both the a0 and b0 parameters represents a structural contraction in these directions, while the steady increase in the c0 parameter indicates lattice expansion in this direction. By considering the differences in the crystal structures of γ-MnO2 and pyrolusite, it is clear that the main differences are found in the *a*-*b* plane. Since the unit cell is found to contract along both these directions, this suggests that ion (Mn(IV)) movement predominates in these directions during heat treatment. The excess of edge sharing octahedra in a uniform array in the *c* direction, without any vacancies present to compensate or provide a buffer for the close

The changes in BET surface area for the HEMD samples are shown in Table 1. The relatively high surface area for these materials indicates that they are quite porous. Most evident from this data is the general decrease in surface area as temperature increases, barring a slight increase between the 350°C and 400°C samples. Given the structural changes occurring during heat treatment, the decreasing surface area suggests that the pores in EMD are removed as Mn(IV) ions diffuse through the structure, creating a more defect free and crystalline material [18]. The slight increase in surface area for the 400°C material is likely to be caused by slow kinetics for this process (relating to the much shorter heating period applied to this material), thus not allowing for the completion of pore collapse. Noticeably, at the lower temperatures (e.g., 200°C), the surface area has not decreased significantly from the original value. This is likely to be connected to insufficient activation energy at the relatively low temperature to drive Mn(IV) diffusion, a factor responsible for pore closure. Table 1 also lists the changes in micro- (<2 nm) and meso-pore (2-50 nm) structures as a result of heat treatment. Clearly, heat treatment causes the collapse of micro-pores, while an increase in the meso-pore volume was observed. The increase in the micro-pore volume for the 400°C material with respect to the 350°C sample indicates that kinetic limitations in the collapse of these pores is responsible for the increase in BET surface area for this material.

A comparison of how the structural changes relate to morphological changes clearly portrays the key differences in the HEMD materials prepared. Figure 10 compares the changes in the orthorhombic unit cell volume with BET surface area. From this data, it is evident that between the temperatures tested, small changes in BET surface area can relate to large structural changes (e.g., between the standard EMD and 200°C material), or vice versa. Generally, however, the interplay of the thermodynamics and kinetics influencing the variation in these parameters leads to an approximately exponential decrease in unit cell volume with respect to BET surface area. Decreases in the unit cell volume can be attributed to manganese ions within the structure having sufficient thermal energy to move to positions consistent with pyrolusite, thus causing intra-crystallite rearrangement within the material. Conversely, changes in BET surface area relate to either the sintering of crystallites

proximity of the Mn(IV) ions, results in expansion in this direction [18].
