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Kinetic pathway for thermal exfoliation of pyrophyllite
Applied Clay Science 114 (2015) 40–47
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Research paper
Kinetic pathway for thermal exfoliation of pyrophyllite Mostofa Shamim a, Tapas Kumar Mukhopadhyay b, Kausik Dana a,⁎ a b
Refractory Division, CSIR-Central Glass and Ceramic Research Institute, Kolkata 700032, India Advanced Clay and Traditional Ceramics Division, CSIR-Central Glass and Ceramic Research Institute, Kolkata 700032, India
a r t i c l e
i n f o
Article history: Received 15 December 2014 Received in revised form 6 May 2015 Accepted 7 May 2015 Available online 22 May 2015 Keywords: Pyrophyllite Exfoliation Dehydroxylation Kinetics Activation energy
a b s t r a c t The thermal exfoliation of pyrophyllite on heating above 600 °C was studied to discern its kinetic pathway and correlate it with dehydroxylation. The irreversible thermal expansion data of pyrophyllite was collected from a thermomechanical analyzer at different heating rates (β). Detailed kinetic analysis was performed on the data using model-free and regression analysis (both linear and non-linear) methods. Multivariate non-isothermal kinetic analysis was used to fit the expansion data at all heating rates simultaneously using eighteen kinetic models. It is found that, the exfoliation of pyrophyllite can be successfully fitted with three kinetic models, viz., n-dimensional Avrami (An), two-dimensional diffusion (D2) and three-dimensional diffusion (D3) model with acceptable kinetic parameters. D2 model (Ea, activation energy = 392 kJ·mol−1, regression coefficient = 0.998) provides the most realistic mechanistic pathway by considering the planar geometric constraint of nucleation and growth in the layered structure of pyrophyllite. Electron microscopic images of exfoliated pyrophyllite shows distinct exfoliated layers indicating escape route for heated gas and supports the choice of D2 model. Although this exfoliation process is a consequence of dehydroxylation reaction, its complexity due to diffusional and geometric constraints is reflected by the high energy barrier (Ea) reported consistently by every kinetic model compared to that of dehydroxylation. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Most materials in solid state expand on heating due to asymmetry in the potential energy well of the bonded atoms. This expansion is a characteristic for any material and expressed by its coefficient of thermal expansion (CTE). Solids with strong bonding show lower CTE compared to metals. Apart from this expansion, some solids undergo reactions which may be associated with decomposition, phase change, recrystallisation, etc. leading to abrupt expansion. Heat treatment of clay minerals is practiced industrially to manufacture alumino-silicate based ceramics. Mullite (3Al2O3·2SiO2) is the most important mineralogical phase in terms of bulk ceramic application — which is formed by heating clay mineral at N1000 °C (Mukhopadhyay et al., 2009). Being the most stable phase in Al2O3– SiO2 binary system, its presence is ubiquitous in all aluminosilicatederived ceramics. Clay minerals are most prevalent source of layered alumino-silicates, and mostly consumed in ceramic industry to produce mullite-containing ceramics. Such product ranges from sanitary ware, electrical insulators, dinnerware, and porcelains to refractories (Mukhopadhyay et al., 2006, 2009, 2010). Most clay minerals loose structural hydroxyls by heating at 500–600 °C and this reaction is known as dehydroxylation. Interestingly, rapid heating of vermiculite to temperatures of about 870–900 °C (Justo et al., 1989), or even up to ⁎ Corresponding author. Tel.: +91 33 24733496; fax: +91 33 24730957. E-mail address: [email protected] (K. Dana).
http://dx.doi.org/10.1016/j.clay.2015.05.006 0169-1317/© 2015 Elsevier B.V. All rights reserved.
1500 °C followed by rapid cooling leads to formation of fluffy clay mineral aggregates. This commercially important filler material is known as ‘exfoliated vermiculite’ where exfoliation involves a volume expansion with individual platy particles expanding perpendicular to the cleavage planes, bloating to several times of their original volume. The process of separation of clay mineral layers are commonly expressed by the terms ‘delamination’ and ‘exfoliation’. The term “delamination” is used to describe a layer-separation process between the planar faces of adjacent layers of a particle (Bergaya et al., 2011). Examples include, ion exchange with Na+ for Montmorillonite (Mt) to form thin clay mineral platelets in water, intercalation of Mt with alkylammonium cation to form delaminated clay mineral gels in organic solvent, intercalation of kaolin with urea or DMSO or hydrazine hydrate to separate thin platelets of the clay mineral (Chekin, 1992; Lahav, 1990). Exfoliation (Bergaya et al., 2011) occurs when the orientation between the layers of the original clay mineral structure is lost by overcoming interlayer cohesive forces. In clay polymer nanocomposites (CPN), exfoliation is validated by X-ray diffraction (XRD) and electron microscopy — when the stacking order of clay mineral is lost (RuizHitzky and Van Meerbeek, 2006). In this report the term “exfoliation” would be used hereafter for denoting the process of irreversible thermal expansion due to disarticulation of clay mineral layers. When heated to 600–800 °C, pyrophyllite shows a small (~ 3%) irreversible expansion and as a consequence, the density of pyrophyllite decreases greatly when the specimen is heated at 1000 °C (Mukhopadhyay, 2011). It has been observed that this exfoliation
M. Shamim et al. / Applied Clay Science 114 (2015) 40–47
process depends upon several factors. Many authors (Justo et al., 1989), have pointed out that thermal exfoliation only occurs when the particles are flash-heated; in contrast; slow heating does not result in exfoliation. Secondly, exfoliation is often noted to be a function of particle size (Justo et al., 1989). Smaller particle sizes typically show less exfoliation compared to larger particle sizes. Pyrophyllite [Al2Si4O10(OH)2], consists of an octahedrally coordinated aluminum sheet (O), i.e. gibbsite sheet, which is sandwiched between two corner sharing silica tetrahedron sheets (T) and a low energy basal plane — which act as a cleavage plane (Bucholz et al., 2012). The interlayer electrostatic attraction between these TOT layers is very low (4.1 kcal·mol−1) (Giese, 1975) and gives rise to its softness and perfect cleavage in one direction [001]. Moore and Lockner (2004) reported that the relatively weak interlayer bonds of clay minerals govern their frictional strengths. The coefficient of dry friction increases with increasing interlayer bond strength. The weakest interlayer interaction of pyrophyllite is due to the absence of cation in the interlayer spaces. Low frictional strength in pyrophyllite increases the possibility of frictional sliding along 00l plane, where faults would occur under shear (Collettini et al., 2009). Both these findings lead to the onset of slip or cleavage of pyrophyllite layers due to fault weakening. During rapid production of gas from dehydroxylation reaction during flash-heating, these weakly bonded layers of the referred clay mineral (pyrophyllite/ vermiculite) are forced open to create escape path for the gas from the structure. The kinetic process of removal of lattice hydroxyls (dehydroxylation) has been widely studied for kaolinite utilizing both isothermal and non-isothermal methods (Prodanovic et al., 1997; Saikia et al., 2002; Ortega et al., 2010; Silva et al., 2011; Ptacek et al., 2014). But, the dehydroxylation kinetics is not well reported for other well defined clay minerals, e.g. pyrophyllite — which is a promising mullite-forming clay mineral. As dehydroxylation process in clay mineral precedes mullitisation, the understanding of the former can lead to better control of later (i.e., mullitisation), illuminating on the kinetic process involved with the above phenomena. This thermally activated process of dehydroxylation has two important manifestations in pyrophyllite — viz., mass loss and exfoliation. The mass loss kinetics is directly proportional to the extent of dehydroxylation and follows n-dimensional Avrami model with Ea of 159 kJ·mol−1 (Shamim et al., 2014). But, the thermal exfoliation need not necessarily possess such direct correlation. From both academic and application perspective, it is extremely important to discern this correlation between thermal exfoliation of pyrophyllite and dehydroxylation. Such correlation can reveal the underlying solid state reactions taking place in pyrophyllite (and pyrophyllite-containing ceramic products). In this present study, the kinetics of thermally induced exfoliation of pyrophyllite is investigated using non-isothermal kinetics and a realistic mechanistic pathway with detailed kinetic parameters has been proposed. 1.1. Solid state kinetics Any solid state reaction, e.g., decomposition of carbonates, hydrated calcium oxalate, expansion of clay minerals, may be expressed as
dα ¼ A exp −Ea RT f ðαÞ dt
ð1Þ
A, Ea and f(α) are the ‘kinetic triplet’, assigned as pre-exponential factor, activation energy and reaction model respectively. T = Absolute temperature R = Universal gas constant α = Conversion fraction
41
For the expansion of pyrophyllite under thermal activation α may be defined as— l f −l0 l0
α¼
ð2Þ
l0 = Initial length lf = Length at time ‘t’ during the reaction α = Fractional change in length during a solid state expansion reaction The understanding of ‘α’ becomes convoluted for non-isothermal solid state transformation—where multiple heating rates come into play and expressed as dα
. dT
¼
dα dt dt dT
ð3Þ
where the heating rate β ¼ dT dt , and dα dT is the isothermal reaction rate. Substitution between Eqs. (1) and (3) furnishes differential form of the non-isothermal rate law— dα
. dT
¼
A −ðEa = Þ RT f ðαÞ e β
ð4Þ
The integral form is— gðαÞ ¼
A β
Z
T
Ea e−ð =RT Þ dT
0
ð5Þ
where Z gðαÞ ¼
α 0
dα
. f ðαÞ
ð6Þ
Variation of ‘α’ as function of temperature (T) and/or time (t) is the most important parameter to decipher the kinetics of a solid state reaction. Depending on the different shapes of the α vs. T or α vs. t plot at ‘β’, kinetic models (Table 1) can be classified into nucleation, geometrical, diffusion or reaction order model (Gotor et al., 2000). The thermal expansion associated with heating of pyrophyllite at different β was collected from a thermomechanical analyzer and converted to α vs. T and α vs. t data. Detailed kinetic analyses were performed on that data using both model-free and regression analysis methods to discern the kinetic pathway of thermal exfoliation of pyrophyllite. 2. Experimental 2.1. Material and method The pyrophyllite rock specimen used in this study was mined from Maharashtra, India and was used as a component of triaxial porcelain by the authors (Mukhopadhyay et al., 2006, 2011). In this work, a bulk rock sample was used in as-received condition without any purification and its purity was ascertained by XRD and energy-dispersive X-ray spectroscopy (EDS). The expansion of the pyrophyllite was studied by a thermomechanical analyzer (Netzsch, TMA 402 F3) from 30 to 1000 °C under controlled atmosphere (75% N2 and 25% O2), at three different β of 2.5, 5 and 10 °C·min−1. The bulk rock clay mineral was cut into cylindrical samples (6 mm dia × 10 mm length) for the study of thermal expansion. The sample was held in vertical position in the instrument with nominal force of 100 mN, so that this external force does not perturb the exfoliation process under thermal treatment. Secondary electron image images (scanning electron microscope of ZEISS, model-SIGMA 02-88,) were taken on the fractured surface of both raw and exfoliated (at 10 °C·min− 1) pyrophyllite block after
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Table 1 Different solid state reaction models. Model Nucleation models
Power law (P2)
Contracting area (R2) Contracting volume (R3)
Diffusion models
1-D diffusion (D1) 2-D diffusion (D2) 3-D diffusion-Jander (D3) Ginstling–Brounsthtein (D4)
Reaction-order models
1 α =2
α3
3
α4
4α4
–Prout-Tompkins (B1)
Zero order (F0/R1) First-order (F1) Second-order (F2) Third-order (F3)
carbon coating. Since EDS analysis is performed on smooth surface, a polished pyrophyllite rock sample was prepared and taken for EDS analysis during electron microscopy to ascertain the elemental composition (purity) of the experimental clay mineral.
Integral form g(α) = kt
2 3
3α
Avrami–Erofeyev (A4)
dα k dt
2α
Power law (P4) Avrami–Erofeyev (A3)
1 2
Power law (P3) Avrami–Erofeyev (A2)
Geometrical contraction models
Differential form f ðαÞ ¼ 1
1 1
1 2
½− ; ln ð1−αÞ2
2 3
½− ; ln ð1−αÞ3
3 4
½− ; ln ð1−αÞ4 ; ln α =1−α þ ca 1 = 1−ð1−αÞ 2
2ð1−αÞ ½− ln ð1−αÞ 3ð1−αÞ ½− ln ð1−αÞ 4ð1−αÞ ½− ln ð1−αÞ α(1 − α) 1 2ð1−αÞ =2 2 3ð1−αÞ =2
1/(2α) − [1/ln(1 − α)] h i h n oi 2 1 3ð1−αÞ3 = 2 1−ð1−αÞ3 hn oi −1 3= ð1−αÞ =3 −1 1 (1 − α) (1 − α)2 (1 − α)3
1 1 1
1−ð1−αÞ =3 α2 [(1 − α)ln(1 − α)] + α n o 1 2 1−ð1−αÞ3 2 1− 2α 3 −ð1−αÞ =3 1
αZ − ln(1 − α) [1/(1 − α)] − 1 i 1 h ð1−αÞ−2 −1 2
A clear trend of greater expansion with higher heating rate is evident which is supported by previous observations of exfoliation of pyrophyllite. The highest expansion (~ 3%) is recorded for highest heating rate β = 10 °C·min− 1. This expansion occurs when the dehydroxylation product as gas is expelled from the solid matrix by expanding the clay
3. Result and discussion 3.1. Characterization of pyrophyllite The powder diffraction pattern (XRD) of the clay mineral shows several sharp reflections (Fig. 1a), all of which matched that of pyrophyllite-2M1 (PDF #12-0203) as the only crystallographic phase. No other reflections were found, indicating the absence of crystalline impurity. Although XRD established the purity of crystalline phase as pyrophyllite, it cannot detect non-crystalline components (if any) present in the system. To ascertain the presence of all elements in the sample (both crystalline and non-crystalline) EDS analysis was done. The elemental constituents were found to be Al, Si and O only by EDS analysis (Fig. 1b) during SEM investigation. This confirms that the experimental material was a well crystalline, pure phase pyrophyllite and the thermal expansion values can be solely attributed to it. 3.2. Thermal expansion of pyrophyllite The thermal expansion data collected from TMA showed moderate expansion up to 600 °C followed by rapid expansion. The initial expansion takes place due to the characteristic expansion — which is a material constant. The following large expansion is attributed to the exfoliation process. The raw expansion data was subjected to baseline correction to remove the contribution of characteristic thermal expansion. This was done by fitting a linear curve to the moderate expansion region (up to 600 °C) and then subtracting it from the raw data (Fig. 2a). The baseline-corrected thermal expansion (dL/Lo) curves of pyrophyllite at three different β are given in Fig. 2b and represent the expansion due to exfoliation process only. This amount of expansion has contribution both from lowering of density of pyrophyllite during the reaction and progressive separation of clay mineral layers. During exfoliation, a rapid, high rate of expansion takes place (Fig. 2b) with a slow rate during initial and final stages. This is also evident from the differential plot (rate plot) where only a single peak emerges around 850 °C (Fig. 2c) indicating that the expansion reaction probably takes place in single stage.
Fig. 1. a. X-ray powder diffraction pattern of pyrophyllite. b. EDS spectrum of experimental pyrophyllite.
M. Shamim et al. / Applied Clay Science 114 (2015) 40–47
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4. Kinetic analysis 4.1. Model free analysis There are some useful mathematical methods to predict the Ea of a reaction without assuming any kinetic model. Few such models utilize the dependence of the peak temperature (Tp) on the β for a particular reaction to determine the Ea of a reaction using linear relationship between different form of ln β and 1/Tp. Determination of kinetic parameters by the peak temperature method requires very precise measurement of reaction peak temperature as a function of linear programmed β (Simon, 2004, 2005). Here, Kissinger method (Kissinger, 1956), Augis & Bennett method (Augis and Bennett, 1978) and Ozawa method (Ozawa, 1965) was adopted to calculate the effective energy barrier for thermal exfoliation of pyrophyllite. Iso-conversional methods, viz., Friedman (Friedman, 1964) and Ozawa–Flynn–Wall method (Flynn and Wall, 1966) (OFW) adopted separately to study the change in Ea with the progress of the reaction to explore the nature of the reaction (simple or complex). The Kissinger equation (Kissinger, 1956) (Eq. 7) uses a linear relationship between ln (βT−2 p ) and 1000/Tp to determine the Ea of a reaction (Kissinger model). Using the peak temperature data from Fig. 2c, the best fitted straight-line (r2 = 0.996) of ln (βT−2 p ) vs. 1000/Tp plot (Fig. 3a) resulted Ea = 465 kJ·mol−1. ln β
T2P
¼ −Ea
RTP
þ const
ð7Þ
Augis and Bennett (1978) proposed (Augis & Bennett model) a different Eq. (8) by assuming a linear relationship between ln (βT−1 p ) and 1000/Tp, which is different from that of Kissinger Eq. (7). ln β
TP
¼ −Ea
RTP
þ ln K0
ð8Þ
where K0 is the frequency factor. Using the slope of the best fitted straight line (r2 = 0.996) of the ln −1 (βT−1 is determined. p ) vs. 1000/Tp plot (Fig. 3b) an Ea of 475 kJ·mol Assuming a linear relationship between ln (β) and 1000/Tp, unlike the Kissinger and Augis & Bennett model, Ozawa proposed (Ozawa, 1965) (Ozawa model) an Eq. (9) to determine the Ea. Similarly, the best fitted straight line (r2 = 0.996) of the ln (β) vs. 1000/Tp plot (Fig. 3c) was used and Ea is determined to be 486 kJ·mol−1. ln β ¼ −Ea
Fig. 2. a. Base line correction of raw expansion data for β = 5 °C·min−1. b. Thermal expansion of pyrophyllite after base line correction. c. Differential plot (rate plot) of thermal expansion of pyrophyllite.
mineral matrix at the cleavage planes and should correlate with the gas pressure inside the clay mineral matrix. For higher β, evolution of gas is higher than its removal rate — leading to greater pressure build up and greater exfoliation. From this baseline corrected dilation values (Fig. 2b), using Eq. (2) the fractional conversion was calculated. The α vs. t data at different β data were analyzed through model-free (Kissinger, Augis & Bennett, Ozawa, Friedman and Ozawa–Flynn–Wall model) and both linear and non-linear regression analyses using thermokinetics software (Netzsch) to evaluate the kinetic pathway for expansion.
RTP
þ const:
ð9Þ
The above three analyses predict almost comparable Ea (465, 475 and 486 kJ·mol−1) for the thermal exfoliation of pyrophyllite. So it is expected that a high Ea is required for pyrophyllite exfoliation. Friedman (1964) and OFW (Flynn and Wall, 1966; Ozawa, 1970) methods predict the Ea by using iso-conversional points at each α and results for Ea for every α = 0.05 to 0.95 is shown in an energy plot which gives idea about the progress of the reaction with time or temperature. The results of Friedman and OFW analysis are presented in Fig. 4. Both plots show that Ea increases monotonously with progress of reaction and varies between 350 and 450 kJ·mol−1. There is almost a linear change in Ea throughout the course of the reaction. The absence of any sharp step in the results of these iso-conversional methods signifies the absence of multiple stages. So, the model free methods conclude that the exfoliation of pyrophyllite under heating is a single stage process is involved with 350 b Ea b 450 kJ·mol−1. Model free analyses have several advantages. Apart from suggesting a probable Ea for the entire reaction, they provide reasonable indication about the nature of the reaction: single stage or multistage or autocatalytic. But the model free analyses do not predict any model to interpret the nature of the reaction. The two-principal objective of any kinetic analysis is to determine the model f(α) which can satisfactorily describe
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M. Shamim et al. / Applied Clay Science 114 (2015) 40–47
Fig. 4. Evolution of activation energy during progress of exfoliation process of pyrophyllite.
model based on statistical fit. In this method, 18 different reaction types (Table 1) were fitted to the expansion data set (all β concurrently). During each iteration, apart from kinetic triplet (i.e., model, Ea and A), % reaction was also varied in order to achieve best fit with experimental α vs. t data at different β. It was found that, different reaction models fit to the expansion data. The comparative quality of fit can be tested though an F-test (Richard and Hahs-Vaughn, 2007). An F-test is a statistical test in which the test statistic has an F-distribution under the null hypothesis. It is most often used when comparing statistical models that have been fitted to a data set, in order to identify the model that best fits the population from which the data were sampled (Richard and HahsVaughn, 2007). The F-test value (Table 2) ranks the different kinetic models for fitting of expansion data of pyrophyllite. From the F-test value table (Table 2) it is evident that three models, viz., D3F (three-dimensional diffusion according to Fick's law), D2 (2dimensional diffusion) and An (n-dimensional Avrami type nucleation model) have high success of fitting into the whole expansion process. For others, the F-test value is much higher and hence less probable to fit into the α vs. t data at different β, so excluded from further analysis. 4.2.2. Fit of individual models using non-Linear regression analysis A non-linear multivariate regression analysis was performed with all the three models (D3F, D2 and An) to ascertain the best model in terms of both excellent regression coefficient (r2) and realistic kinetic parameters. It was found that all the models can achieve reasonable good fit with r2 N 0.996. 4.2.2.1. Kinetic fitting with D3F model. Fitting with D3F model results in excellent r2 value (0.997) with acceptable kinetic parameters (Table 3). Except the initial deviation of the fitting curves from the expansion data points in integral form, the calculated data matched
Fig. 3. Plots of (a) ln (βT−2) vs. 1000/T (b) ln (βT−1) vs. 1000/T and (c) ln (β) vs. 1000/T for pyrophyllite exfoliation.
the degree of conversion with time and the effect of temperature on f(α) to evaluate Ea and A. With the help of linear and non-liner regression analysis an attempt has been made to find a model which can satisfactorily explain the exfoliation of pyrophyllite under heating. 4.2. 2-kinetic model: prediction and justification 4.2.1. Success of fitting by F-test A linear regression analysis on the dynamic thermal expansion data at different β was performed to determine the most probable kinetic
Table 2 F-test table of linear regression analysis. Model
D3F
D2
An
Fn
F2
F1
F-test value
1.00
1.02
1.06
1.78
1.80
2.32
Table 3 Kinetic triplets for exfoliation of Pyrophyllite. Model
Ea (kJ·mol−1)
log A (s−1)
r2
D2 An (n = 0.34) D3F
392 715 429
15.12 30.29 16.21
0.998 0.996 0.997
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45
Fig. 5. Fitting of expansion data in integral form for D3F model. Inset shows the initial deviation of fitting curves.
Fig. 7. Fitting of expansion data in integral form for An model. Inset shows the initial deviation of fitting curves.
experimental data well (Fig. 5). In the differential plot of fitting (Fig. 6), although the fitting curves comparatively match the peak temperatures, a marked deviation is observed (up to 25% of reaction) with the width of the peaks. Here the reaction rate has a little acceleratory nature (compared to D2 model). According to D3F model, the rate of growth of the nuclei is equal in all the three direction, generating hemispheres of product and an increasing area of active reactant/product surface (Dominey et al., 1965). Such unrestricted growth of nuclei is unfeasible in pyrophyllite, keeping in mind the restrictions arising out of layered silicate crystal structure, material morphology and imperfection in crystal packing. So, in spite of reporting an acceptable Ea and r2 value, the D3F model is less physically meaningful to justify the generation and growth pattern of nuclei for a two dimensional layered material in spite of successfully explain the progress of the reaction.
b) The Avrami dimension (n) is indicative of ease of nucleation and growth (Avrami, 1939; Galwey et al., 1974). For dehydroxylation, a higher value is reported (n = 0.454) compared to 0.34 for expansion. This data reveals the physical circumstance during reaction, since the propensity of formation of surface nucleus was far greater in the powdered sample (with more surface area) used in dehydroxylation kinetics than that of a monolithic block used for expansion study. Again, the nuclei growth process is severely hindered for a bulk sample as it impedes the removal of gaseous reaction product. c) The probability of coalescence of growth nuclei is significantly more in the case of a compact bulk solid structure compared to powder form used in dehydroxylation kinetics — which also contributes in lower value of effective nuclei population and Avrami dimension (n) for expansion kinetics (Galwey and Brown, 1999). Due to the unavailability of effective nuclei the expansion process becomes hindered and automatically increases the Ea value.
4.2.2.2. Kinetic fitting with An model. Like D3F model, the fitting with the Avrami model is also quite satisfactory. Apart form predicting a slightly different nucleation regime for the expansion process, Avrami model successfully explains the remaining course of the reaction (Figs. 7 and 8). In a previous study (Shamim et al., 2014) using thermogravimetry (TG) data Avrami dimension n = 0.454 (An) model with an Ea of 159 kJ·mol− 1 was reported for the dehydroxylation of pyrophyllite. But here, for expansion, the same Avrami model (with n = 0.34) predicts Ea of 715 kJ·mol−1. Probable explanations for this divergence in kinetic parameters are given below. a) Dehydroxylation kinetics was studied with mass loss data — which are directly correlated, whereas, thermal expansion is a complex consequence of dehydroxylation.
Fig. 6. Fitting of expansion data in differential form for D3F model.
4.2.2.3. Kinetic fitting with D2 model. The fitting curves of D2 model almost overlap with the α vs. t data at different β data points in integral form (Fig. 9) of fitting which automatically generates an excellent (highest) r2 value of 0.998 with acceptable kinetic parameters (Table 3). In the differential form the fitting (Fig. 10) curves exactly match the peak temperature and width of the expansion curves. So a good agreement between the selected model and the experimental data has been established. The fitting curves deviate a little in the initial
Fig. 8. Fitting of expansion data in differential form for An model.
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M. Shamim et al. / Applied Clay Science 114 (2015) 40–47
Fig. 9. Fitting of expansion data in integral form for D2 model. Inset shows the initial deviation of fitting curves.
phase of the reaction but they maintained the nature of the experimental data points. The model predicts that ‘the initial establishment of a new and discrete product particle within the solid reactant’ (Galwey and Laverty, 1990) i.e. nucleation required a certain induction period. Once the growth nuclei has been established it follows a twodimensional growth pattern (Avrami, 1939). After achieving a well established growth pattern the reaction rate accelerated and maintains almost a constant speed till the end of the reaction.
cristobalite by a topotactic reaction. The dehydroxylation of pyrophyllite to pyrophyllite dehydroxylate involves the reaction of two OH groups (adjacent to each other on an Al octahedron) with the liberation of water (Fitzgerald et al., 1996). Usually, the dehydroxylation of pyrophyllite is studied with powder samples, so the removal of reaction product (i.e. water as gas) is not hindered and large amount of surface of power provided ample source of surface nuclei for the reaction to progress. But, in the present study, a monolithic block of pyrophyllite was used for studying the exfoliation — which has limited the number of such surface nuclei, and added enormous difficulty in escape of the reaction product and thereby increasing the Ea barrier. While explaining the exfoliation of vermiculite, Hillier et al. (2013) found that mosaic structures found in phyllosilicate layers slow down the removal of those gases and thereby decrease the rate of the reaction. This type of mosaic structure acts as the maze to the escaping gas and some dead ends of the mosaic plate become the pressure points. When the force applied by the gas pressure exceeds the bonding forces between these phyllosilicate layers, the build-up pressure pushes the layers apart, i.e. exfoliate the layer, to relieve the pressure build up similar geometric constraint may be attributed here too which can contribute to the increase in the Ea for the process. 6. Geometric constraint on the exfoliation process
All the models report significantly higher value of Ea of exfoliation (392–715 kJ·mol− 1) compared to dehydroxylation of pyrophyllite (Shamim et al., 2014) (An, 159 kJ·mol−1) indicating that the exfoliation process needs to overcome greater Ea barrier (higher Ea) compared to dehydroxylation reaction. This can be explained with the mechanism of dehydroxylation. Pyrophyllite dehydroxylation reaction was studied by Wardle and Brindley (1972), who indicated that pyrophyllite dehydroxylate is produced after total dehydroxylation and this phase retains a well organized structure similar to hydroxylate and is stable over a wide range of temperature. Although extensive breakup of the structure occurs in the 00l planes (perpendicular to the sheets), but order is preserved along hk0 planes and only relatively minor rearrangements take place, as envisaged by Wardle and Brindley (1972). On further heating, the dehydroxylate structure is destroyed, forming mullite and
At this point, all three models selected by the linear regression analysis, can mathematically explain the kinetic model for the expansion of pyrophyllite under heating. To decide the most feasible model, the outline of mechanism of expansion of pyrophyllite is reviewed here to sort out most physically meaningful geometric constraint which may be operating in the kinetic pathway. The structure of pyrophyllite may be imagined as stacked TOT (Tetrahedral Si+ 4–Octahedral Al+3) layer (Bucholz et al., 2012). The bonding between these sandwiches is weak van der Waals type and gives rise to its softness and perfect cleavage along 001 plane. During dehydroxylation, the reaction product in gaseous form is liberated from the interactions between hydroxyls in the octahedral gibbsite layer. This high pressure gas finds weakest bonding links in the crystal structure to escape. As the cleavage plane of pyrophyllite is the weakest link, micro cracks are nucleated by the gas, so it is highly probable that the planer growth of nuclei may be effectively confined to two dimensions. The scanning electron microscopy (SEM) images of the fracture surface of unheated raw pyrophyllite (Fig. 11 inset) comprise of tightly stacked clay mineral layers, while that of 10 °C heated sample (Fig. 11) shows that the stacked layers have variable separation perpendicular to the layers, revealing exfoliation. This variable separation along 00l axis is reminiscent of the effect of escape of the high pressure gas. Thus these
Fig. 10. Fitting of expansion data in differential form for D2 model.
Fig 11. SEM image of the fracture surface of exfoliated pyrophyllite, (inset) pristine pyrophyllite.
5. Correlation between thermal exfoliation and dehydroxylation of pyrophyllite
M. Shamim et al. / Applied Clay Science 114 (2015) 40–47
lamellar structures with variable separation validate the microstructural basis and geometric constraint for exfoliation. Such obvious geometric constraint in the kinetics of pyrophyllite exfoliation cannot be accommodated with D3F model which assume hemispherical interface of the reaction front (Dominey et al., 1965) and An model. This justifies the choice and success of D2 model over other models in explaining thermal exfoliation of pyrophyllite. 7. Conclusion i) The exfoliation of pyrophyllite is a single stage reaction and can be successfully fitted with three kinetic models (An, D2 and D3F) with Ea range 392–715 (kJ·mol−1). ii) The energy barrier (Ea) reported by every model for expansion is greater than of dehydroxylation indicating the complexity of the exfoliation process. iii) D2 model with Ea = 392 (kJ·mol−1) provides the best physically significant fit by justifying the planar geometric constraint of nucleation and growth revealed with SEM image in the layered structure of pyrophyllite.
Acknowledgment The research work was funded by CSIR (Grant number ESC 0202) under GLASSFIB project and one of the author (MS) acknowledges the “JRF-GATE” research fellowship granted to him by CSIR, New Delhi, India to carry out this work. References Augis, J.A., Bennett, J.E., 1978. Calculation of Avrami parameters for heterogeneous solid state reactions using a modification of Kissinger method. J. Therm. Anal. 13, 283–292. Avrami, M., 1939. Kinetics of phase change. I. General theory. J. Phys. Chem. A 7, 1103–1112. Bergaya, F., Jaber, M., Lambert, J.F., 2011. Clays and clay minerals. In: Galimberti, M. (Ed.), Rubber Clay Nanocomposites: Science, Technology and Applications. Wiley, New York. Bucholz, E.W., Zhao, X., Sinnott, S.B., Perry, S.S., 2012. Friction and wear of pyrophyllite on the atomic scale. Tribol. Lett. 46, 159–165. Chekin, S.S., 1992. Swelling of kaolinite crystals in polar organic liquids. Clay Clay Miner. 40, 740–741. Collettini, C., Niemeijer, A., Viti, C., Marone, C., 2009. Fault zone fabric and fault weakness. Nature 462, 907–910. Dominey, D.A., Morley, H., Young, D.A., 1965. Kinetics of the decomposition of nickel oxalate. Trans. Faraday Soc. 61, 1246–1255. Fitzgerald, J.J., Hamza, A.I., Dec, S.F., Bronnimann, C.E., 1996. Solid-state Al-27 and Si-29 NMR and H-1 CRAMPS studies of the thermal transformations of the 2:1 phyllosilicate pyrophyllite. J. Phys. Chem. 100, 17351–17360. Flynn, J., Wall, L., 1966. General treatment of the thermogravimetry of polymers. J. Res. Natl. Bur. Stand. 70A, 487–523. Friedman, H.L., 1964. Kinetics of thermal degradation of char-forming plastics from thermogravimetry — application to a phenolic plastics. J. Polym. Sci. C Polym. Lett. 06, 183–195.
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Galwey, A.K., Brown, M.E., 1999. Thermal Decomposition of Ionic Solids: Chemical Properties and Reactivities of Ionic Crystalline Phases. Elsevier, Amsterdam (Chapter 3). Galwey, A.K., Laverty, G.M., 1990. The nucleus in solid state reactions: towards a definition. Solid State Ionics 38, 155–162. Galwey, A.K., Jamieson, D., Brown, M.E., 1974. Thermal decomposition of three crystalline modifications of anhydrous copper(II) formate. J. Phys. Chem. A 78, 2664–2670. Giese, R.F., 1975. Interlayer bonding in talc and pyrophyllite. Clay and Clay Miner. 23, 165–166. Gotor, F.J., Criado, J.M., Malek, J., Koga, N., 2000. Kinetic analysis of solid-state reactions: the universality of master plots for analyzing isothermal and nonisothermal experiments. J. Phys. Chem. A 104, 10782. Hillier, S., Marwa, E.M.M., Rice, C.M., 2013. On the mechanism of exfoliation of vermiculite. Clay Miner. 48, 563–582. Justo, A., Maqueda, C., Perez-Rodriguez, J.L., Morillo, E., 1989. Expansibility of some vermiculites. Appl. Clay Sci. 4, 509–519. Kissinger, H.E., 1956. Variation of peak temperature with heating rate in differential thermal analysis. J. Res. Natl. Bur. Stand. 56, 217–221. Lahav, N., 1990. Preparation of stable suspensions of delaminated kaolinite by combined dimethylsulfoxide–ammonium fluoride treatment. Clay Clay Miner. 38, 219–222. Moore, D.E., Lockner, D.A., 2004. Crystallographic controls on the frictional behavior of dry and water saturated sheet structure minerals. J. Geophys. Res. 109, 1978–2012. Mukhopadhyay, T.K., 2011. Effect of incorporation of pyrophyllite in triaxial composition to mullitization. University of Calcutta Doctoral thesis. Mukhopadhyay, T.K., Ghosh, S., Ghatak, S., Maiti, H.S., 2006. Effect of pyrophyllite on vitrification and on physical properties of triaxial porcelain. Ceram. Int. 32, 871–876. Mukhopadhyay, T.K., Ghatak, S., Maiti, H.S., 2009. Effect of pyrophyllite on the mullitization in triaxial porcelain system. Ceram. Int. 35, 1493–1500. Mukhopadhyay, T.K., Ghatak, S., Maiti, H.S., 2010. Pyrophyllite as raw material for ceramic applications in the perspective of its pyro-chemical properties. Ceram. Int. 36, 909–916. Mukhopadhyay, T.K., Dana, K., Ghatak, S., 2011. Pyrophyllite — a potential material for application in tri-axial porcelain systems. Ind. Ceram. 31, 165–173. Ortega, A., Macias, M., Gotor, F.J., 2010. The multistep nature of the kaolinite dehydroxylation: kinetics and mechanism. J. Am. Ceram. Soc. 93, 197–203. Ozawa, T., 1965. A new method of analyzing thermogravimetric data. Bull. Chem. Soc. Jpn. 35, 1881–1886. Ozawa, T., 1970. Kinetic analysis of derivative curves in thermal analysis. J. Therm. Anal. 2, 301–324. Prodanovic, D., Zivkovic, Z.B., Radosavljevic, S., 1997. Kinetics of the dehydroxylation and mullitization processes of the halloysite from the Farbani Potok locality, Serbia. Appl. Clay Sci. 12, 267–274. Ptacek, P., Opravil, T., Soukal, F., Brandstetr, J., Havlica, J., Masilko, J., 2014. HT-XRD nonisothermal kinetics study of delamination of kaolinite from termite mound. Appl. Clay Sci. 95, 146–149. Richard, G.L., Hahs-Vaughn, D.L., 2007. Statistical Concepts: A Second Course. Fourth ed. Taylor and Francis Group, New York. Ruiz-Hitzky, E., Van Meerbeek, A., 2006. Clay mineral- and organoclay-polymer nanocomposite. In: Bergaya, F., Theng, B.K.G., Lagaly, G. (Eds.), Handbook of Clay Science: Developments in Clay Science Vol. 1. Elsevier Ltd., Amsterdam. Saikia, N., Sengupta, P., Gogoi, P.K., Borthakur, P.C., 2002. Kinetics of dehydroxylation of kaolin in presence of oil field effluent treatment plant sludge. Appl. Clay Sci. 22, 93–102. Shamim, M., Molla, A.R., Mukhopadhyay, T.K., Dana, K., 2014. Non-isothermal kinetic evaluation of pyrophyllite dehydroxylation. Trans. Ind. Ceram. Soc. 73, 181–186. Silva, R.A., Teixeira, S.R., Souza, A.E., Santos, D.I., Romero, M., Rincon, J.M., 2011. Nucleation kinetics of crystalline phases from a kaolinitic body used in the processing of red ceramics. Appl. Clay Sci. 52, 165–170. Simon, P., 2004. Isoconversional methods — fundamentals, meaning and application. J. Therm. Anal. Calorim. 76, 123–132. Simon, P., 2005. Single-step kinetics approximation employing non-Arrhenius temperature functions. J. Therm. Anal. Calorim. 79, 703–708. Wardle, R., Brindley, G.W., 1972. The crystal structure of pyrophyllite, 1Tc, and of its dehydroxylate. Am. Mineral. 732–750.
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Research paper
Kinetic pathway for thermal exfoliation of pyrophyllite Mostofa Shamim a, Tapas Kumar Mukhopadhyay b, Kausik Dana a,⁎ a b
Refractory Division, CSIR-Central Glass and Ceramic Research Institute, Kolkata 700032, India Advanced Clay and Traditional Ceramics Division, CSIR-Central Glass and Ceramic Research Institute, Kolkata 700032, India
a r t i c l e
i n f o
Article history: Received 15 December 2014 Received in revised form 6 May 2015 Accepted 7 May 2015 Available online 22 May 2015 Keywords: Pyrophyllite Exfoliation Dehydroxylation Kinetics Activation energy
a b s t r a c t The thermal exfoliation of pyrophyllite on heating above 600 °C was studied to discern its kinetic pathway and correlate it with dehydroxylation. The irreversible thermal expansion data of pyrophyllite was collected from a thermomechanical analyzer at different heating rates (β). Detailed kinetic analysis was performed on the data using model-free and regression analysis (both linear and non-linear) methods. Multivariate non-isothermal kinetic analysis was used to fit the expansion data at all heating rates simultaneously using eighteen kinetic models. It is found that, the exfoliation of pyrophyllite can be successfully fitted with three kinetic models, viz., n-dimensional Avrami (An), two-dimensional diffusion (D2) and three-dimensional diffusion (D3) model with acceptable kinetic parameters. D2 model (Ea, activation energy = 392 kJ·mol−1, regression coefficient = 0.998) provides the most realistic mechanistic pathway by considering the planar geometric constraint of nucleation and growth in the layered structure of pyrophyllite. Electron microscopic images of exfoliated pyrophyllite shows distinct exfoliated layers indicating escape route for heated gas and supports the choice of D2 model. Although this exfoliation process is a consequence of dehydroxylation reaction, its complexity due to diffusional and geometric constraints is reflected by the high energy barrier (Ea) reported consistently by every kinetic model compared to that of dehydroxylation. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Most materials in solid state expand on heating due to asymmetry in the potential energy well of the bonded atoms. This expansion is a characteristic for any material and expressed by its coefficient of thermal expansion (CTE). Solids with strong bonding show lower CTE compared to metals. Apart from this expansion, some solids undergo reactions which may be associated with decomposition, phase change, recrystallisation, etc. leading to abrupt expansion. Heat treatment of clay minerals is practiced industrially to manufacture alumino-silicate based ceramics. Mullite (3Al2O3·2SiO2) is the most important mineralogical phase in terms of bulk ceramic application — which is formed by heating clay mineral at N1000 °C (Mukhopadhyay et al., 2009). Being the most stable phase in Al2O3– SiO2 binary system, its presence is ubiquitous in all aluminosilicatederived ceramics. Clay minerals are most prevalent source of layered alumino-silicates, and mostly consumed in ceramic industry to produce mullite-containing ceramics. Such product ranges from sanitary ware, electrical insulators, dinnerware, and porcelains to refractories (Mukhopadhyay et al., 2006, 2009, 2010). Most clay minerals loose structural hydroxyls by heating at 500–600 °C and this reaction is known as dehydroxylation. Interestingly, rapid heating of vermiculite to temperatures of about 870–900 °C (Justo et al., 1989), or even up to ⁎ Corresponding author. Tel.: +91 33 24733496; fax: +91 33 24730957. E-mail address: [email protected] (K. Dana).
http://dx.doi.org/10.1016/j.clay.2015.05.006 0169-1317/© 2015 Elsevier B.V. All rights reserved.
1500 °C followed by rapid cooling leads to formation of fluffy clay mineral aggregates. This commercially important filler material is known as ‘exfoliated vermiculite’ where exfoliation involves a volume expansion with individual platy particles expanding perpendicular to the cleavage planes, bloating to several times of their original volume. The process of separation of clay mineral layers are commonly expressed by the terms ‘delamination’ and ‘exfoliation’. The term “delamination” is used to describe a layer-separation process between the planar faces of adjacent layers of a particle (Bergaya et al., 2011). Examples include, ion exchange with Na+ for Montmorillonite (Mt) to form thin clay mineral platelets in water, intercalation of Mt with alkylammonium cation to form delaminated clay mineral gels in organic solvent, intercalation of kaolin with urea or DMSO or hydrazine hydrate to separate thin platelets of the clay mineral (Chekin, 1992; Lahav, 1990). Exfoliation (Bergaya et al., 2011) occurs when the orientation between the layers of the original clay mineral structure is lost by overcoming interlayer cohesive forces. In clay polymer nanocomposites (CPN), exfoliation is validated by X-ray diffraction (XRD) and electron microscopy — when the stacking order of clay mineral is lost (RuizHitzky and Van Meerbeek, 2006). In this report the term “exfoliation” would be used hereafter for denoting the process of irreversible thermal expansion due to disarticulation of clay mineral layers. When heated to 600–800 °C, pyrophyllite shows a small (~ 3%) irreversible expansion and as a consequence, the density of pyrophyllite decreases greatly when the specimen is heated at 1000 °C (Mukhopadhyay, 2011). It has been observed that this exfoliation
M. Shamim et al. / Applied Clay Science 114 (2015) 40–47
process depends upon several factors. Many authors (Justo et al., 1989), have pointed out that thermal exfoliation only occurs when the particles are flash-heated; in contrast; slow heating does not result in exfoliation. Secondly, exfoliation is often noted to be a function of particle size (Justo et al., 1989). Smaller particle sizes typically show less exfoliation compared to larger particle sizes. Pyrophyllite [Al2Si4O10(OH)2], consists of an octahedrally coordinated aluminum sheet (O), i.e. gibbsite sheet, which is sandwiched between two corner sharing silica tetrahedron sheets (T) and a low energy basal plane — which act as a cleavage plane (Bucholz et al., 2012). The interlayer electrostatic attraction between these TOT layers is very low (4.1 kcal·mol−1) (Giese, 1975) and gives rise to its softness and perfect cleavage in one direction [001]. Moore and Lockner (2004) reported that the relatively weak interlayer bonds of clay minerals govern their frictional strengths. The coefficient of dry friction increases with increasing interlayer bond strength. The weakest interlayer interaction of pyrophyllite is due to the absence of cation in the interlayer spaces. Low frictional strength in pyrophyllite increases the possibility of frictional sliding along 00l plane, where faults would occur under shear (Collettini et al., 2009). Both these findings lead to the onset of slip or cleavage of pyrophyllite layers due to fault weakening. During rapid production of gas from dehydroxylation reaction during flash-heating, these weakly bonded layers of the referred clay mineral (pyrophyllite/ vermiculite) are forced open to create escape path for the gas from the structure. The kinetic process of removal of lattice hydroxyls (dehydroxylation) has been widely studied for kaolinite utilizing both isothermal and non-isothermal methods (Prodanovic et al., 1997; Saikia et al., 2002; Ortega et al., 2010; Silva et al., 2011; Ptacek et al., 2014). But, the dehydroxylation kinetics is not well reported for other well defined clay minerals, e.g. pyrophyllite — which is a promising mullite-forming clay mineral. As dehydroxylation process in clay mineral precedes mullitisation, the understanding of the former can lead to better control of later (i.e., mullitisation), illuminating on the kinetic process involved with the above phenomena. This thermally activated process of dehydroxylation has two important manifestations in pyrophyllite — viz., mass loss and exfoliation. The mass loss kinetics is directly proportional to the extent of dehydroxylation and follows n-dimensional Avrami model with Ea of 159 kJ·mol−1 (Shamim et al., 2014). But, the thermal exfoliation need not necessarily possess such direct correlation. From both academic and application perspective, it is extremely important to discern this correlation between thermal exfoliation of pyrophyllite and dehydroxylation. Such correlation can reveal the underlying solid state reactions taking place in pyrophyllite (and pyrophyllite-containing ceramic products). In this present study, the kinetics of thermally induced exfoliation of pyrophyllite is investigated using non-isothermal kinetics and a realistic mechanistic pathway with detailed kinetic parameters has been proposed. 1.1. Solid state kinetics Any solid state reaction, e.g., decomposition of carbonates, hydrated calcium oxalate, expansion of clay minerals, may be expressed as
dα ¼ A exp −Ea RT f ðαÞ dt
ð1Þ
A, Ea and f(α) are the ‘kinetic triplet’, assigned as pre-exponential factor, activation energy and reaction model respectively. T = Absolute temperature R = Universal gas constant α = Conversion fraction
41
For the expansion of pyrophyllite under thermal activation α may be defined as— l f −l0 l0
α¼
ð2Þ
l0 = Initial length lf = Length at time ‘t’ during the reaction α = Fractional change in length during a solid state expansion reaction The understanding of ‘α’ becomes convoluted for non-isothermal solid state transformation—where multiple heating rates come into play and expressed as dα
. dT
¼
dα dt dt dT
ð3Þ
where the heating rate β ¼ dT dt , and dα dT is the isothermal reaction rate. Substitution between Eqs. (1) and (3) furnishes differential form of the non-isothermal rate law— dα
. dT
¼
A −ðEa = Þ RT f ðαÞ e β
ð4Þ
The integral form is— gðαÞ ¼
A β
Z
T
Ea e−ð =RT Þ dT
0
ð5Þ
where Z gðαÞ ¼
α 0
dα
. f ðαÞ
ð6Þ
Variation of ‘α’ as function of temperature (T) and/or time (t) is the most important parameter to decipher the kinetics of a solid state reaction. Depending on the different shapes of the α vs. T or α vs. t plot at ‘β’, kinetic models (Table 1) can be classified into nucleation, geometrical, diffusion or reaction order model (Gotor et al., 2000). The thermal expansion associated with heating of pyrophyllite at different β was collected from a thermomechanical analyzer and converted to α vs. T and α vs. t data. Detailed kinetic analyses were performed on that data using both model-free and regression analysis methods to discern the kinetic pathway of thermal exfoliation of pyrophyllite. 2. Experimental 2.1. Material and method The pyrophyllite rock specimen used in this study was mined from Maharashtra, India and was used as a component of triaxial porcelain by the authors (Mukhopadhyay et al., 2006, 2011). In this work, a bulk rock sample was used in as-received condition without any purification and its purity was ascertained by XRD and energy-dispersive X-ray spectroscopy (EDS). The expansion of the pyrophyllite was studied by a thermomechanical analyzer (Netzsch, TMA 402 F3) from 30 to 1000 °C under controlled atmosphere (75% N2 and 25% O2), at three different β of 2.5, 5 and 10 °C·min−1. The bulk rock clay mineral was cut into cylindrical samples (6 mm dia × 10 mm length) for the study of thermal expansion. The sample was held in vertical position in the instrument with nominal force of 100 mN, so that this external force does not perturb the exfoliation process under thermal treatment. Secondary electron image images (scanning electron microscope of ZEISS, model-SIGMA 02-88,) were taken on the fractured surface of both raw and exfoliated (at 10 °C·min− 1) pyrophyllite block after
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M. Shamim et al. / Applied Clay Science 114 (2015) 40–47
Table 1 Different solid state reaction models. Model Nucleation models
Power law (P2)
Contracting area (R2) Contracting volume (R3)
Diffusion models
1-D diffusion (D1) 2-D diffusion (D2) 3-D diffusion-Jander (D3) Ginstling–Brounsthtein (D4)
Reaction-order models
1 α =2
α3
3
α4
4α4
–Prout-Tompkins (B1)
Zero order (F0/R1) First-order (F1) Second-order (F2) Third-order (F3)
carbon coating. Since EDS analysis is performed on smooth surface, a polished pyrophyllite rock sample was prepared and taken for EDS analysis during electron microscopy to ascertain the elemental composition (purity) of the experimental clay mineral.
Integral form g(α) = kt
2 3
3α
Avrami–Erofeyev (A4)
dα k dt
2α
Power law (P4) Avrami–Erofeyev (A3)
1 2
Power law (P3) Avrami–Erofeyev (A2)
Geometrical contraction models
Differential form f ðαÞ ¼ 1
1 1
1 2
½− ; ln ð1−αÞ2
2 3
½− ; ln ð1−αÞ3
3 4
½− ; ln ð1−αÞ4 ; ln α =1−α þ ca 1 = 1−ð1−αÞ 2
2ð1−αÞ ½− ln ð1−αÞ 3ð1−αÞ ½− ln ð1−αÞ 4ð1−αÞ ½− ln ð1−αÞ α(1 − α) 1 2ð1−αÞ =2 2 3ð1−αÞ =2
1/(2α) − [1/ln(1 − α)] h i h n oi 2 1 3ð1−αÞ3 = 2 1−ð1−αÞ3 hn oi −1 3= ð1−αÞ =3 −1 1 (1 − α) (1 − α)2 (1 − α)3
1 1 1
1−ð1−αÞ =3 α2 [(1 − α)ln(1 − α)] + α n o 1 2 1−ð1−αÞ3 2 1− 2α 3 −ð1−αÞ =3 1
αZ − ln(1 − α) [1/(1 − α)] − 1 i 1 h ð1−αÞ−2 −1 2
A clear trend of greater expansion with higher heating rate is evident which is supported by previous observations of exfoliation of pyrophyllite. The highest expansion (~ 3%) is recorded for highest heating rate β = 10 °C·min− 1. This expansion occurs when the dehydroxylation product as gas is expelled from the solid matrix by expanding the clay
3. Result and discussion 3.1. Characterization of pyrophyllite The powder diffraction pattern (XRD) of the clay mineral shows several sharp reflections (Fig. 1a), all of which matched that of pyrophyllite-2M1 (PDF #12-0203) as the only crystallographic phase. No other reflections were found, indicating the absence of crystalline impurity. Although XRD established the purity of crystalline phase as pyrophyllite, it cannot detect non-crystalline components (if any) present in the system. To ascertain the presence of all elements in the sample (both crystalline and non-crystalline) EDS analysis was done. The elemental constituents were found to be Al, Si and O only by EDS analysis (Fig. 1b) during SEM investigation. This confirms that the experimental material was a well crystalline, pure phase pyrophyllite and the thermal expansion values can be solely attributed to it. 3.2. Thermal expansion of pyrophyllite The thermal expansion data collected from TMA showed moderate expansion up to 600 °C followed by rapid expansion. The initial expansion takes place due to the characteristic expansion — which is a material constant. The following large expansion is attributed to the exfoliation process. The raw expansion data was subjected to baseline correction to remove the contribution of characteristic thermal expansion. This was done by fitting a linear curve to the moderate expansion region (up to 600 °C) and then subtracting it from the raw data (Fig. 2a). The baseline-corrected thermal expansion (dL/Lo) curves of pyrophyllite at three different β are given in Fig. 2b and represent the expansion due to exfoliation process only. This amount of expansion has contribution both from lowering of density of pyrophyllite during the reaction and progressive separation of clay mineral layers. During exfoliation, a rapid, high rate of expansion takes place (Fig. 2b) with a slow rate during initial and final stages. This is also evident from the differential plot (rate plot) where only a single peak emerges around 850 °C (Fig. 2c) indicating that the expansion reaction probably takes place in single stage.
Fig. 1. a. X-ray powder diffraction pattern of pyrophyllite. b. EDS spectrum of experimental pyrophyllite.
M. Shamim et al. / Applied Clay Science 114 (2015) 40–47
43
4. Kinetic analysis 4.1. Model free analysis There are some useful mathematical methods to predict the Ea of a reaction without assuming any kinetic model. Few such models utilize the dependence of the peak temperature (Tp) on the β for a particular reaction to determine the Ea of a reaction using linear relationship between different form of ln β and 1/Tp. Determination of kinetic parameters by the peak temperature method requires very precise measurement of reaction peak temperature as a function of linear programmed β (Simon, 2004, 2005). Here, Kissinger method (Kissinger, 1956), Augis & Bennett method (Augis and Bennett, 1978) and Ozawa method (Ozawa, 1965) was adopted to calculate the effective energy barrier for thermal exfoliation of pyrophyllite. Iso-conversional methods, viz., Friedman (Friedman, 1964) and Ozawa–Flynn–Wall method (Flynn and Wall, 1966) (OFW) adopted separately to study the change in Ea with the progress of the reaction to explore the nature of the reaction (simple or complex). The Kissinger equation (Kissinger, 1956) (Eq. 7) uses a linear relationship between ln (βT−2 p ) and 1000/Tp to determine the Ea of a reaction (Kissinger model). Using the peak temperature data from Fig. 2c, the best fitted straight-line (r2 = 0.996) of ln (βT−2 p ) vs. 1000/Tp plot (Fig. 3a) resulted Ea = 465 kJ·mol−1. ln β
T2P
¼ −Ea
RTP
þ const
ð7Þ
Augis and Bennett (1978) proposed (Augis & Bennett model) a different Eq. (8) by assuming a linear relationship between ln (βT−1 p ) and 1000/Tp, which is different from that of Kissinger Eq. (7). ln β
TP
¼ −Ea
RTP
þ ln K0
ð8Þ
where K0 is the frequency factor. Using the slope of the best fitted straight line (r2 = 0.996) of the ln −1 (βT−1 is determined. p ) vs. 1000/Tp plot (Fig. 3b) an Ea of 475 kJ·mol Assuming a linear relationship between ln (β) and 1000/Tp, unlike the Kissinger and Augis & Bennett model, Ozawa proposed (Ozawa, 1965) (Ozawa model) an Eq. (9) to determine the Ea. Similarly, the best fitted straight line (r2 = 0.996) of the ln (β) vs. 1000/Tp plot (Fig. 3c) was used and Ea is determined to be 486 kJ·mol−1. ln β ¼ −Ea
Fig. 2. a. Base line correction of raw expansion data for β = 5 °C·min−1. b. Thermal expansion of pyrophyllite after base line correction. c. Differential plot (rate plot) of thermal expansion of pyrophyllite.
mineral matrix at the cleavage planes and should correlate with the gas pressure inside the clay mineral matrix. For higher β, evolution of gas is higher than its removal rate — leading to greater pressure build up and greater exfoliation. From this baseline corrected dilation values (Fig. 2b), using Eq. (2) the fractional conversion was calculated. The α vs. t data at different β data were analyzed through model-free (Kissinger, Augis & Bennett, Ozawa, Friedman and Ozawa–Flynn–Wall model) and both linear and non-linear regression analyses using thermokinetics software (Netzsch) to evaluate the kinetic pathway for expansion.
RTP
þ const:
ð9Þ
The above three analyses predict almost comparable Ea (465, 475 and 486 kJ·mol−1) for the thermal exfoliation of pyrophyllite. So it is expected that a high Ea is required for pyrophyllite exfoliation. Friedman (1964) and OFW (Flynn and Wall, 1966; Ozawa, 1970) methods predict the Ea by using iso-conversional points at each α and results for Ea for every α = 0.05 to 0.95 is shown in an energy plot which gives idea about the progress of the reaction with time or temperature. The results of Friedman and OFW analysis are presented in Fig. 4. Both plots show that Ea increases monotonously with progress of reaction and varies between 350 and 450 kJ·mol−1. There is almost a linear change in Ea throughout the course of the reaction. The absence of any sharp step in the results of these iso-conversional methods signifies the absence of multiple stages. So, the model free methods conclude that the exfoliation of pyrophyllite under heating is a single stage process is involved with 350 b Ea b 450 kJ·mol−1. Model free analyses have several advantages. Apart from suggesting a probable Ea for the entire reaction, they provide reasonable indication about the nature of the reaction: single stage or multistage or autocatalytic. But the model free analyses do not predict any model to interpret the nature of the reaction. The two-principal objective of any kinetic analysis is to determine the model f(α) which can satisfactorily describe
44
M. Shamim et al. / Applied Clay Science 114 (2015) 40–47
Fig. 4. Evolution of activation energy during progress of exfoliation process of pyrophyllite.
model based on statistical fit. In this method, 18 different reaction types (Table 1) were fitted to the expansion data set (all β concurrently). During each iteration, apart from kinetic triplet (i.e., model, Ea and A), % reaction was also varied in order to achieve best fit with experimental α vs. t data at different β. It was found that, different reaction models fit to the expansion data. The comparative quality of fit can be tested though an F-test (Richard and Hahs-Vaughn, 2007). An F-test is a statistical test in which the test statistic has an F-distribution under the null hypothesis. It is most often used when comparing statistical models that have been fitted to a data set, in order to identify the model that best fits the population from which the data were sampled (Richard and HahsVaughn, 2007). The F-test value (Table 2) ranks the different kinetic models for fitting of expansion data of pyrophyllite. From the F-test value table (Table 2) it is evident that three models, viz., D3F (three-dimensional diffusion according to Fick's law), D2 (2dimensional diffusion) and An (n-dimensional Avrami type nucleation model) have high success of fitting into the whole expansion process. For others, the F-test value is much higher and hence less probable to fit into the α vs. t data at different β, so excluded from further analysis. 4.2.2. Fit of individual models using non-Linear regression analysis A non-linear multivariate regression analysis was performed with all the three models (D3F, D2 and An) to ascertain the best model in terms of both excellent regression coefficient (r2) and realistic kinetic parameters. It was found that all the models can achieve reasonable good fit with r2 N 0.996. 4.2.2.1. Kinetic fitting with D3F model. Fitting with D3F model results in excellent r2 value (0.997) with acceptable kinetic parameters (Table 3). Except the initial deviation of the fitting curves from the expansion data points in integral form, the calculated data matched
Fig. 3. Plots of (a) ln (βT−2) vs. 1000/T (b) ln (βT−1) vs. 1000/T and (c) ln (β) vs. 1000/T for pyrophyllite exfoliation.
the degree of conversion with time and the effect of temperature on f(α) to evaluate Ea and A. With the help of linear and non-liner regression analysis an attempt has been made to find a model which can satisfactorily explain the exfoliation of pyrophyllite under heating. 4.2. 2-kinetic model: prediction and justification 4.2.1. Success of fitting by F-test A linear regression analysis on the dynamic thermal expansion data at different β was performed to determine the most probable kinetic
Table 2 F-test table of linear regression analysis. Model
D3F
D2
An
Fn
F2
F1
F-test value
1.00
1.02
1.06
1.78
1.80
2.32
Table 3 Kinetic triplets for exfoliation of Pyrophyllite. Model
Ea (kJ·mol−1)
log A (s−1)
r2
D2 An (n = 0.34) D3F
392 715 429
15.12 30.29 16.21
0.998 0.996 0.997
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Fig. 5. Fitting of expansion data in integral form for D3F model. Inset shows the initial deviation of fitting curves.
Fig. 7. Fitting of expansion data in integral form for An model. Inset shows the initial deviation of fitting curves.
experimental data well (Fig. 5). In the differential plot of fitting (Fig. 6), although the fitting curves comparatively match the peak temperatures, a marked deviation is observed (up to 25% of reaction) with the width of the peaks. Here the reaction rate has a little acceleratory nature (compared to D2 model). According to D3F model, the rate of growth of the nuclei is equal in all the three direction, generating hemispheres of product and an increasing area of active reactant/product surface (Dominey et al., 1965). Such unrestricted growth of nuclei is unfeasible in pyrophyllite, keeping in mind the restrictions arising out of layered silicate crystal structure, material morphology and imperfection in crystal packing. So, in spite of reporting an acceptable Ea and r2 value, the D3F model is less physically meaningful to justify the generation and growth pattern of nuclei for a two dimensional layered material in spite of successfully explain the progress of the reaction.
b) The Avrami dimension (n) is indicative of ease of nucleation and growth (Avrami, 1939; Galwey et al., 1974). For dehydroxylation, a higher value is reported (n = 0.454) compared to 0.34 for expansion. This data reveals the physical circumstance during reaction, since the propensity of formation of surface nucleus was far greater in the powdered sample (with more surface area) used in dehydroxylation kinetics than that of a monolithic block used for expansion study. Again, the nuclei growth process is severely hindered for a bulk sample as it impedes the removal of gaseous reaction product. c) The probability of coalescence of growth nuclei is significantly more in the case of a compact bulk solid structure compared to powder form used in dehydroxylation kinetics — which also contributes in lower value of effective nuclei population and Avrami dimension (n) for expansion kinetics (Galwey and Brown, 1999). Due to the unavailability of effective nuclei the expansion process becomes hindered and automatically increases the Ea value.
4.2.2.2. Kinetic fitting with An model. Like D3F model, the fitting with the Avrami model is also quite satisfactory. Apart form predicting a slightly different nucleation regime for the expansion process, Avrami model successfully explains the remaining course of the reaction (Figs. 7 and 8). In a previous study (Shamim et al., 2014) using thermogravimetry (TG) data Avrami dimension n = 0.454 (An) model with an Ea of 159 kJ·mol− 1 was reported for the dehydroxylation of pyrophyllite. But here, for expansion, the same Avrami model (with n = 0.34) predicts Ea of 715 kJ·mol−1. Probable explanations for this divergence in kinetic parameters are given below. a) Dehydroxylation kinetics was studied with mass loss data — which are directly correlated, whereas, thermal expansion is a complex consequence of dehydroxylation.
Fig. 6. Fitting of expansion data in differential form for D3F model.
4.2.2.3. Kinetic fitting with D2 model. The fitting curves of D2 model almost overlap with the α vs. t data at different β data points in integral form (Fig. 9) of fitting which automatically generates an excellent (highest) r2 value of 0.998 with acceptable kinetic parameters (Table 3). In the differential form the fitting (Fig. 10) curves exactly match the peak temperature and width of the expansion curves. So a good agreement between the selected model and the experimental data has been established. The fitting curves deviate a little in the initial
Fig. 8. Fitting of expansion data in differential form for An model.
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M. Shamim et al. / Applied Clay Science 114 (2015) 40–47
Fig. 9. Fitting of expansion data in integral form for D2 model. Inset shows the initial deviation of fitting curves.
phase of the reaction but they maintained the nature of the experimental data points. The model predicts that ‘the initial establishment of a new and discrete product particle within the solid reactant’ (Galwey and Laverty, 1990) i.e. nucleation required a certain induction period. Once the growth nuclei has been established it follows a twodimensional growth pattern (Avrami, 1939). After achieving a well established growth pattern the reaction rate accelerated and maintains almost a constant speed till the end of the reaction.
cristobalite by a topotactic reaction. The dehydroxylation of pyrophyllite to pyrophyllite dehydroxylate involves the reaction of two OH groups (adjacent to each other on an Al octahedron) with the liberation of water (Fitzgerald et al., 1996). Usually, the dehydroxylation of pyrophyllite is studied with powder samples, so the removal of reaction product (i.e. water as gas) is not hindered and large amount of surface of power provided ample source of surface nuclei for the reaction to progress. But, in the present study, a monolithic block of pyrophyllite was used for studying the exfoliation — which has limited the number of such surface nuclei, and added enormous difficulty in escape of the reaction product and thereby increasing the Ea barrier. While explaining the exfoliation of vermiculite, Hillier et al. (2013) found that mosaic structures found in phyllosilicate layers slow down the removal of those gases and thereby decrease the rate of the reaction. This type of mosaic structure acts as the maze to the escaping gas and some dead ends of the mosaic plate become the pressure points. When the force applied by the gas pressure exceeds the bonding forces between these phyllosilicate layers, the build-up pressure pushes the layers apart, i.e. exfoliate the layer, to relieve the pressure build up similar geometric constraint may be attributed here too which can contribute to the increase in the Ea for the process. 6. Geometric constraint on the exfoliation process
All the models report significantly higher value of Ea of exfoliation (392–715 kJ·mol− 1) compared to dehydroxylation of pyrophyllite (Shamim et al., 2014) (An, 159 kJ·mol−1) indicating that the exfoliation process needs to overcome greater Ea barrier (higher Ea) compared to dehydroxylation reaction. This can be explained with the mechanism of dehydroxylation. Pyrophyllite dehydroxylation reaction was studied by Wardle and Brindley (1972), who indicated that pyrophyllite dehydroxylate is produced after total dehydroxylation and this phase retains a well organized structure similar to hydroxylate and is stable over a wide range of temperature. Although extensive breakup of the structure occurs in the 00l planes (perpendicular to the sheets), but order is preserved along hk0 planes and only relatively minor rearrangements take place, as envisaged by Wardle and Brindley (1972). On further heating, the dehydroxylate structure is destroyed, forming mullite and
At this point, all three models selected by the linear regression analysis, can mathematically explain the kinetic model for the expansion of pyrophyllite under heating. To decide the most feasible model, the outline of mechanism of expansion of pyrophyllite is reviewed here to sort out most physically meaningful geometric constraint which may be operating in the kinetic pathway. The structure of pyrophyllite may be imagined as stacked TOT (Tetrahedral Si+ 4–Octahedral Al+3) layer (Bucholz et al., 2012). The bonding between these sandwiches is weak van der Waals type and gives rise to its softness and perfect cleavage along 001 plane. During dehydroxylation, the reaction product in gaseous form is liberated from the interactions between hydroxyls in the octahedral gibbsite layer. This high pressure gas finds weakest bonding links in the crystal structure to escape. As the cleavage plane of pyrophyllite is the weakest link, micro cracks are nucleated by the gas, so it is highly probable that the planer growth of nuclei may be effectively confined to two dimensions. The scanning electron microscopy (SEM) images of the fracture surface of unheated raw pyrophyllite (Fig. 11 inset) comprise of tightly stacked clay mineral layers, while that of 10 °C heated sample (Fig. 11) shows that the stacked layers have variable separation perpendicular to the layers, revealing exfoliation. This variable separation along 00l axis is reminiscent of the effect of escape of the high pressure gas. Thus these
Fig. 10. Fitting of expansion data in differential form for D2 model.
Fig 11. SEM image of the fracture surface of exfoliated pyrophyllite, (inset) pristine pyrophyllite.
5. Correlation between thermal exfoliation and dehydroxylation of pyrophyllite
M. Shamim et al. / Applied Clay Science 114 (2015) 40–47
lamellar structures with variable separation validate the microstructural basis and geometric constraint for exfoliation. Such obvious geometric constraint in the kinetics of pyrophyllite exfoliation cannot be accommodated with D3F model which assume hemispherical interface of the reaction front (Dominey et al., 1965) and An model. This justifies the choice and success of D2 model over other models in explaining thermal exfoliation of pyrophyllite. 7. Conclusion i) The exfoliation of pyrophyllite is a single stage reaction and can be successfully fitted with three kinetic models (An, D2 and D3F) with Ea range 392–715 (kJ·mol−1). ii) The energy barrier (Ea) reported by every model for expansion is greater than of dehydroxylation indicating the complexity of the exfoliation process. iii) D2 model with Ea = 392 (kJ·mol−1) provides the best physically significant fit by justifying the planar geometric constraint of nucleation and growth revealed with SEM image in the layered structure of pyrophyllite.
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