ARTICLE pubs.acs.org/JPCA
Thermal Dehydration of Monohydrocalcite: Overall Kinetics and Physico-geometrical Mechanisms Tomoyasu Kimura and Nobuyoshi Koga* Chemistry Laboratory, Department of Science Education, Graduate School of Education, Hiroshima University, 1-1-1 Kagamiyama, Higashi-Hiroshima 739-8524, Japan ABSTRACT:
Monohydrocalcite (CaCO3 3 H2O: MHC) is similar in composition and synthetic conditions to hydrated amorphous calcium carbonate (ACC), which is focused recently as a key intermediate compound of biomineralization and biomimetic mineralization of calcium carbonate polymorphs. Detailed comparisons of the physicochemical property and reactivity of those hydrated calcium carbonates are required for obtaining fundamental information on the relevancy of those compounds in the mineralization processes. In the present study, kinetics of the thermal dehydration of spherical particles of crystalline MHC was investigated in view of physico-geometrical mechanism. The reaction process was traced systematically by means of thermogravimetry under three different modes of temperature program. A distinguished induction period for the thermal dehydration and cracking of the surface product layer on the way of the established reaction were identified as the characteristic events of the reaction. By interpreting the kinetic results in association with the morphological changes of the reactant particles during the course of reaction, it was revealed that nucleation and crystal growth of calcite regulate the overall kinetics of the thermal dehydration of MHC. In comparison with the thermal dehydration of hydrated ACC, which produces anhydrous ACC as the solid product, the kinetic characteristics of the thermal dehydration of MHC were discussed from the viewpoint of physico-geometry of the component processes.
1. INTRODUCTION Monohydrocalcite (CaCO3 3 H2O: MHC) is known as a rare mineral in geological setting found in the environments of saline lakes,15 seawater,68 and limestone-dolomite caves.911 Biogenetic MHC has also been found in some animals,1218 such as in the otoliths of a tiger shark12 and in the gall bladder of guinea pig.13 In laboratory, MHC has been synthesized by the reaction of Ca2+ and CO32 in artificial seawater1924 or in a mixed aqueous solution of Ca2+ and Mg2+,25 where a high Mg2+/Ca2+ ratio in the mother solution is the requirement of the selective precipitation of MHC. MHC deserves attention in the compositional similarity with hydrated amorphous calcium carbonate (ACC), because hydrated ACC is recently focused as a key intermediate compound in biomineralization and biomimetic mineralization of calcium carbonate polymorphs (CCPs).26 Comparative studies on the fundamental physicochemical properties of MHC and hydrated ACC are required for discussing possible participation of MHC in biomineralization of CCPs and r 2011 American Chemical Society
possible utilization of MHC for biomimetic mineralization of CCPs as a substitute for hydrated ACC. Although it has been shown that the local structures of MHC and hydrated ACC are different,27,28 both of the compounds, which are metastable thermodynamically with respect to CCPs,2932 transform to different CCPs with various morphological and functional characteristics depending on the transformation conditions applied. We recently reported that the precipitation conditions of MHC single phase in a mixed aqueous solution of Ca2+ and Mg2+ by the reaction with CO32 are very restricted, which is just adjacent to those of hydrated ACC.33 In addition, two different MHC particles in views of crystallinity and morphology are precipitated within the limited region of the precipitation conditions. These MHCs, one is well-crystalline spherical particles of 12 μm and another is Received: July 13, 2011 Revised: August 15, 2011 Published: August 18, 2011 10491
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Figure 1. Typical SEM image of the sample particles of MHC.
poorly crystalline aggregates in the shape of twisted spindle of 15 μm, indicate different thermal stabilities and reaction behaviors of the thermal dehydration. The former exhibits the higher thermal stability and dehydrates in a well-distinguished single mass-loss step by producing calcite. The thermal dehydration of the latter initiates from room temperature at a slower reaction rate and completes at the temperature higher than that of the well-crystalline MHC, where anhydrous ACC is produced as the dehydration product. After thermal dehydration was completed, as-produced anhydrous ACC crystallizes to calcite with an exothermic effect. The reaction behavior of the latter is comparable to that of hydrated ACC.30,3335 Further detailed comparisons of the physicochemical properties and reaction behaviors of these MHC with hydrated ACC can be one of the probable routes to obtain fundamental information for discussing the relevancy of these compounds in the mineralization process of CCPs. In the present study, we approached the kinetics and mechanisms of the thermal dehydration of MHC, where the wellcrystalline spherical particles were subjected to a systematic thermoanalytical study. It is expected form the existence of a remarkable induction period that the thermal dehydration of the well-crystalline spherical MHC is regulated by the nucleation and crystal growth of calcite.33 The mechanisms of the thermal dehydration are verified in view of physico-geometry through examining the kinetics of the induction period and effects of the preannealing treatments and of partial pressure of water vapor on the overall rate behavior of the thermal dehydration. The overall kinetics of the thermal dehydration is analyzed by the measurements of kinetic rate data under three different types of temperature program, that is, isothermal, linear nonisothermal, and constant transformation rate modes. A possible physico-geometrical model of the thermal dehydration is proposed on the basis of the kinetic results interpreted in association with the observations of the morphological changes of the reactant particles during the course of the reaction.
2. EXPERIMENTAL SECTION 2.1. Sample Preparation. The sample of MHC was synthesized according to the previously reported method25 after reviewing the detailed preparation condition of crystalline precipitate.33 The same batch of sample utilized in our previous study33 was subjected to the present kinetics study of the thermal dehydration process. The preparation condition of the sample is
Figure 2. Change of XRD pattern during the isothermal dehydration of MHC. (a) Reactant MHC, (b) change of XRD pattern during heating at 443 K under flowing N2 (100 cm3 min1), and (c) after heating at 443 K for 250 min.
as follows. Every 0.06 mol dm3 of CaCl2 aq and MgCl2 aq was mixed in a fixed volume ratio of 4:1 to give the mother solution of 200 cm3. The mother solution in 200 cm3 beaker stood for 5 min in a stirrer with temperature controlled by keeping at 288 K. Anhydrous Na2CO3 of 1.7 g was dispersed in the mother solution. The resultant solution was stirred mechanically for 48 h at 288 K. Precipitates obtained were filtered and washed with deionizeddistilled water. The precipitates filtered were dried in a vacuum desiccator for 24 h and stored in a refrigerator at 278 K. The sample has been characterized by the measurements of powder X-ray diffraction (XRD), Fourier transfer infrared spectroscopy (FT-IR), and simultaneous thermogravimetry/differential thermal analysis and mass spectrometry (TG/DTA-MS) as MHC single phase.33 From scanning electron microscopic (SEM) observations, the texture of the sample particles was confirmed as spherical and/or spherical polygons of 12 μm in diameter as is shown in Figure 1. Substitution of about 5 mol % of Ca2+ by Mg2+ was estimated by the atomic absorption spectroscopy for the sample dissolved in a hydrochloric acid, which is in agreement with that reported for MHC precipitated in the comparable conditions.25 2.2. Measurements of Kinetic Rate Data. Using a hangingtype TG (TGA-50, Shimadzu Co.), the kinetic rate data of the thermal dehydration were recorded for the sample of 10.0 mg, weighed into a platinum cell (6 mm ϕ and 2.5 mm in height), in flowing N2 (80 cm3 min1), where three different modes of temperature program, that is, isothermal, linear nonisothermal, 10492
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Figure 4. SEM images of the sample during the thermal dehydration process. (a) The sample just before the dehydration reaction at 450 K, (b and c) the sample just after the abrupt noise of DTG single at 480 K, and (d) the sample just after completing the mass-loss due to thermal dehydration.
Figure 3. Typical records of mass-loss data for the thermal dehydration of MHC under three different modes of temperature program: (a) isothermal at T = 448 K, (b) linear nonisothermal at β = 3.0 K min1, and (c) constant mass-loss rate at C = 10 μg min1.
and constant transformation rate modes, were applied. After the sample was heated at a heating rate β = 10 K min1 to the programmed temperatures, isothermal mass-change traces were recorded at different constant temperatures in the range from 432 to 468 K. The linear nonisothermal measurements were carried out at different β, 1 e β e 10 K min1. The temperature profiles to maintain the different constant mass-loss rate during the course of thermal dehydration were recorded by equipping a self-constructed Sample Controlled Thermal Analysis (SCTA)36 controller to the above TG instrument.3742 The sample was heated at β = 2 K min1, while during the thermal dehydration reaction the mass-loss rate was regulated at different constant transformation rates C, 7.5 e C e 20 μg min1. For evaluating the influence of the preannealing treatment on the thermal dehydration behavior, the sample of 10.0 mg, weighed into a platinum cell (6 mm ϕ and 2.5 mm in height), was annealed at 433 K for different duration times from 0 to 160 min in flowing N2 (80 cm3 min1) using the above TGA-50 instrument and subsequently heated linearly at β = 10 K min1 for measuring TG curves. Similarly, several TG curves were recorded at different β, 1 e β e 10 K min1, for the sample preannealed at 443 K for 30 min. 2.3. Other Supplemental Measurements. Phase changes of the sample during isothermal heating at 443 K were followed by powder XRD measurements using a diffractometer (RINT2200 V, Rigaku Co.) with monochrome Cu Kα radiation (40 kV, 20 mA) by equipping with a programmable heating chamber (PTC-20A, Rigaku Co.). By heating the sample press-fitted on a platinum plate at 443 K in flowing N2 (100 cm3 min1), the
diffraction measurements were started repeatedly in a fixed time interval of 15 min. Influence of the atmospheric water vapor on the rate behavior of the thermal dehydration was evaluated using a TG (TG8120, Rigaku Co.) connected with a programmable humidity controller (HUM-1, Rigaku Co.). By keeping the sample of 10.0 mg weighed into a platinum cell (5 mm ϕ and 2.5 mm in height) at 350 K, the mixed gases of N2H2O with a controlled partial pressure of H2O, p(H2O), were introduced into the reaction tube of the TG instrument (ca. 450 cm3 min1). After the reaction system was stabilized for 30 min, the sample was heated at β = 5 K min1. Textural change of the sample during the thermal dehydration was examined by SEM observations. The sample was dehydrated to different fractional reactions in the above TG under the same reaction conditions with the measurements of kinetic rate data. After the samples were cooled to room temperature, SEM images of the partially dehydrated samples were examined using a scanning electron microscope (JSM-6510, Jeol) after coating the samples with Pt by sputtering.
3. RESULTS AND DISCUSSION 3.1. Characteristics of the Kinetic Behavior. In our previous study,33 it has been confirmed that the present sample dehydrates quantitatively to CaCO3 of poorly crystalline calcite according to: CaCO3 3 H2O f CaCO3 + H2O. Figure 2 shows the change of XRD pattern of the sample during isothermal heating at 443 K in flowing N2. Intensities of the diffraction peaks attributed to MHC (CaCO3 3 H2O, P31, a = b = 10.5547, c = 7.5644),5,43 Figure 2a, remain unchanged for 60 min at 443 K, from which a remarkable induction period can be confirmed as one of the characteristics of the present reaction. After the induction period, the diffraction peaks of MHC start to attenuate accompanied by compensative growth of the diffraction peaks of calcite (CaCO3, R-3c, a = b = 4.9910, c = 17.0620),44 Figure 2b and c. 10493
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Figure 5. Influence of the partial pressure of atmospheric water vapor on Te.o. and Tp of the DTG curves recorded at β = 10 K min1.
Figure 3 shows typical records of mass-loss data for the thermal dehydration of the present sample under three different modes of temperature program, that is, (a) isothermal, (b) linear nonisothermal, and (c) constant mass-loss rate. Two characteristics of the thermal dehydration process are observed from the mass-loss records. One is the distinguished induction period for the thermal dehydration observed in the isothermal mass-change trace, Figure 3a, as has also been confirmed by the above XRD measurements. In general, such induction period can be taken as the kinetic process of nucleation and/or formation of nucleus forming sites for the subsequent thermal dehydration process, which is supported by various experimental evidences of the nucleation for the thermal dehydration of crystalline hydrates.4550 The existence of the induction period indicates the possibility of the significant influence of the thermal history of the sample on the kinetic rate behavior of the subsequent thermal dehydration process. Another is the abrupt noise observed for the derivative TG (DTG) curves irrespective of the temperature program modes applied. Figure 4 shows SEM images of the samples heated nonisothermally to different degrees of thermal dehydration. The sample particles just before the dehydration reaction tend to couple by forming necks, Figure 4a. On the way of the thermal decomposition, cracking of the surface layer of the sample particle is taking place accompanied by the abrupt noise of the DTG signal, Figure 4b and c. The crack formations on the surface product layer on the way of the thermal dehydration and/or decomposition of inorganic solids have sometimes been observed.5154 The cracks may be produced by the strain caused by the crystal growth of the product solid in the surface product layer. In the case that the surface product layer impedes the diffusion of the product gases produced at the internal reaction interface, stress by the increased internal pressure of gaseous product may also be one of the possible causes of the cracking. Such cracking of the surface product layer triggers the immediate escape of the product gases retained in the internal of the reactant particle, resulting in the abrupt noise on the DTG signal. Drastic change of the morphology of the sample particle during the thermal dehydration process from spherical and/or spherical polygons to rhombohedra should also be noted from Figure 4d. This indicates a high mobility of the ionic species in the matrix of the dehydrating particle to recrystallize the calcite particle,
Figure 6. Influence of the annealing treatments at 433 K on the TGDTG curves for the thermal dehydration of MHC. (a) Selected TGDTG curves recorded after the annealing treatments for different times and (b) dependences of Te.o. and Tp of the DTG curves on the annealing time.
which is also supported by the coupling of the reactant particles during the course of reaction. Figure 5 shows the influence of the partial pressure of atmospheric water vapor, p(H2O), on the extrapolated onset temperature, Te.o., and the peak top temperature, Tp, of the DTG curves recorded at β = 10 K min1, where no practical changes of Te.o. and Tp can be observed. The kinetic behavior of the thermal dehydration invariant with the variation of atmospheric p(H2O) can be explained by assuming two different cases. One is the case that the dehydration reaction is taking place at temperatures far from the equilibrium temperature. The other is that, even in the lower atmospheric p(H2O), the dehydration reaction is taking place under the high enough partial pressure of water vapor or the presence of the liquid water at the reaction sites. Self-induced gelation during the course of thermal dehydration is very probable for the latter case, as has been observed during the thermal dehydration of crystalline hydrates of alkaline borates.5557 Because the composition of present sample is similar to that of hydrated ACC, the self-induced gelation at the reaction interface during the thermal dehydration process can be proposed as a possible mechanism. This is also supported by the empirical fact that the sample particles removed from the TG instrument on the way of the thermal dehydration under flowing dry N2 are very sticky. In such a condition, the higher mobility of the ionic species to couple the reactant particles and to crystallize calcite particle with drastic change of the morphology and size of the crystallites is also explained. 3.2. Apparent Kinetics for the Induction Period. To infer the possible chemical event taking place during the induction 10494
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Figure 7. Kinetic analysis for the induction period of the thermal dehydration of MHC. (a) Change in the time intervals of the induction period with temperature and (b) the Arrhenius plot.
period, annealing treatments were performed isothermally at 433 K for different times on the way of heating the sample at β = 10 K min1. Figure 6a shows several selected TG-DTG curves for the thermal dehydration of the samples preannealed at 433 K for different times. Systematical shift of the TG-DTG curves to the lower temperatures with increasing the annealing time can be observed. Change in the shape of the DTG curves is also apparent, especially at the initial part of the reaction. The behavior can be clearly seen by comparing the Te.o. and Tp of the DTG curves as is shown in Figure 6b. The observed shift of Te.o. to the lower temperatures depending on the annealing time is larger than that of Tp, indicating the change in the shape of the DTG curves. From the apparent influence of the annealing treatment on the onset temperature of the thermal dehydration and the shape of the initial part of the DTG curve, it is deduced that the nucleation and/or formation of nucleus forming sites at the surface of the sample particles are very probable events taking place during the induction period. It is also expected that the selfinduced gelation of the particle surface layer is largely contributing to the nucleation and/or the formation of nucleus forming sites. From the series of isothermal mass-change traces at different constant temperatures ranging from 432 to 458 K, the induction periods of the thermal dehydration at the respective temperatures were determined operationally as the time interval between the initial time of isothermal heating and the extrapolated onset of the DTG peak. Figure 7a shows the change in induction period, tip, with reaction temperature. When the kinetic phenomenon in the induction period is the constant rate nucleation and/or formation of nucleus forming sites on the surfaces, the rate behavior is expressed by the following kinetic equation composed of a kinetic model function f(αip) and the
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Figure 8. Kinetic rate data for the thermal dehydration of MHC at different constant temperatures. (a) The isothermal mass-change traces and those derivative curves and (b) the kinetic rate data represented as the plots of dα/dt against α.
Arrhenius-type temperature dependence:53 dαip Eip ¼ kip f ðαip Þ with kip ¼ Aip exp dt RT
ð1Þ
where αip and kip are the degree of nucleus saturation on the overall surfaces and the rate constant of surface nucleation, respectively. The values of Aip and Eip are the apparent Arrhenius parameters for the chemical events taking place in the induction period. Because the reciprocal value of the induction period, (1/tip), corresponds to the averaged value of nucleation rate, (dαip/dt)avr, and the nucleation rate attains to (dαip/dt)avr at a constant αip irrespective of reaction temperature applied, the apparent activation energy, Eip, can be evaluated through a kind of isoconversional plot according to the following equation:53 ! Eip 1 ð2Þ ln ¼ ln½Aip f ðαip Þ tip RT As shown in Figure 7b, the plot of ln(1/tip) against T1 indicates fairly good linearity with the correlation coefficient γ = 0.9965, from which the value of Eip = 228.1 ( 8.6 kJ mol1 was evaluated as the apparent value for characterizing the physicochemical events taking place in the induction period. 3.3. Kinetic Rate Data for the Thermal Dehydration. Figure 8a shows the isothermal mass-change traces and those derivative curves for the thermal dehydration of MHC at different temperatures. The shape of the mass-loss traces is sigmoidal irrespective of the reaction temperatures. In Figure 8b, the kinetic rate data under isothermal conditions are represented as the plot of dα/dt against fractional reaction α. The rate data 10495
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Figure 9. Kinetic rate data for the thermal dehydration of MHC at different β. (a) TG-DTG curves and (b) the kinetic rate data represented as the plots of dα/dt against α.
Figure 10. Kinetic rate data for the thermal dehydration of preannealed MHC at different β. (a) TG-DTG curves and (b) the kinetic rate data represented as the plots of dα/dt against α.
indicate the maximum reaction rate at α = 0.41 ( 0.02. Apparently, the sigmoidal shape of the integral rate data and the derivative rate data with a maximum on the way of the reaction are corresponding to one of the nucleation and growthtype reactions.58 The abrupt noises in the rate data appear first at α = 0.60 ( 0.02 and are repeating several times in the range 0.60 e α e 0.76. The kinetic rate data recorded under linearly increasing temperatures at different β are shown in Figure 9. As can be seen in Figure 9a, the shift of TG and DTG curves to the higher temperatures with increasing β is accompanied by the prolongation of the reaction tail, resulting in the increase in the temperature width of the reaction. In Figure 9b, the kinetic rate data under nonisothermal conditions are represented as the plots of dα/dt against α. The abrupt noise in the derivative rate data appears just after reaching the maximum reaction rate. The α value at the abrupt noise due to the crack formation is α = 0.58 at β = 1.0 K min1 and decreases systematically to α = 0.53 at β = 10 K min1. It is indicated by the relationship between the maximum reaction rate and the crack formation that the maximum reaction rate is observed apparently by the impedance effect of surface product layer on the diffusion of product water vapor, where the continuous increase in the internal pressure by the water vapor produced at the reaction interfaces is the trigger of the cracking of the surface product layer. Because in the above nonisothermal measurements the sample is passing through the temperature region of the surface nucleation, observed as the induction period in the isothermal measurements, at a constant β, it is probable that the number of surface nuclei for the subsequent growth by the thermal dehydration is not saturated and changes depending on β applied. Figure 10 shows the kinetic rate data recorded at different β for
the thermal dehydration of the sample preannealed at 443 K for 30 min on the way of the measurements of TG-DTG. In comparison with the TG-DTG curves for the nonannealed sample shown in Figure 9a, the kinetic rate data shift to the lower temperature region irrespective of β applied. The initial acceleration process proceeds gradually in a temperature region wider than that in the nonannealed sample. The change in the shape of the kinetic rate data by the preannealing treatment is more clearly seen by plotting dα/dt against α; see Figure 10b. The major difference in the shape of the kinetic rate data from that for the nonannealed sample is observed for the initial acceleration part. The reaction rate is accelerating linearly to ca. α = 0.2 in the preannealed sample, while the linear acceleration is completed at around α = 0.1 in the nonannealed sample. The relationship between the maximum reaction rate and crack formation is practically identical to that of the nonannealed sample, as well as the final deceleration process in the range α > 0.8. Figure 11 shows the kinetic rate data recorded by controlling the reaction rate to be constant during the course of thermal dehydration. The mass-loss rate during the course of reaction was controlled successfully, except the part of the crack formation, see Figure 11a. The temperature profile during the constant rate thermal dehydration is shown in Figure 11b. Because the sample is heated at the constant β until the initiation of the mass-loss process, the nucleation at the surface of the reactant particles is expected not to be completed at the beginning of the thermal dehydration as is in the measurements of the kinetic rate data under linear nonisothermal condition without preannealing treatment. Immediately after the initiation of the mass-loss process, the sample temperature drops rapidly to maintain the mass-loss rate to be constant at a programmed value C. At this 10496
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The Journal of Physical Chemistry A stage, the surface nucleation proceeds simultaneously with the dehydration reaction from the primary nuclei, resulting in the saturation of the surface nuclei at the early stage of the dehydration reaction. The subsequent established reaction thus advances from the saturated surface nuclei as in the reaction under isothermal conditions. The temperature profile during the course of reaction indicates the minimum temperature at a nearly constant value of α irrespective of C applied, that is, at α = 0.39 ( 0.01, which is very close to the α value of the maximum reaction rate observed for the kinetic rate data recorded under isothermal conditions. Appearance of the minimum temperature on the way of the reaction under constant reaction rate conditions is also indicating the apparent kinetic agreement with a
Figure 11. Kinetic rate data for the thermal dehydration of MHC at different C. (a) Mass-change traces and (b) temperature profiles during the course of reaction.
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nucleation and growth-type reaction.59,60 The abrupt noises in the mass-change trace, derivative mass-change trace, and sample temperature due to the crack formation appeared in the range α > 0.6, in agreement with those observed for the isothermal rate data. 3.4. Overall Kinetics of the Thermal Dehydration. The following kinetic equation was assumed for analyzing the kinetic rate data recorded in the three different modes of temperature programs universally.6164 dα Ea ¼ A exp f ðαÞ ð3Þ dt RT where A and Ea are the apparent Arrhenius pre-exponential factor and apparent activation energy, respectively, for describing the apparent temperature dependence of the overall reaction rate of the thermal dehydration reaction. Taking logarithms of eq 3, an isoconversional relationship among the kinetic rate data at a restricted α can be expected. dα Ea ð4Þ ¼ ln½Af ðαÞ ln dt RT According to eq 4, the plot of ln(dα/dt) against T1 for the data points at a restricted α, known as the Friedman plot,65 should be a straight line irrespective of the temperature program modes of the kinetic rate data, if the rate process were approximated as the single mechanistic step described by a certain kinetic model function and by the constant values of the Arrhenius parameters. In Figure 12, the kinetic rate data at three different α were plotted on the ln(dα/dt) versus T1 coordinates. The data points of constant transformation rate and isothermal measurements line up on a straight line irrespective of α. Even at the early stage of the reaction, that is, α = 0.1 in Figure 12a, the data points of linear nonisothermal measurements deviate from the regression line for those of constant transformation rate and isothermal measurements. The deviation increases as reaction advances. It should be noted in Figure 12a that, at α = 0.1, the data points of the linear nonisothermal measurements with the preannealing treatment fit to the regression line for those of constant transformation rate and isothermal measurements. This indicates that by the preannealing treatments the early stage of the reaction advances from the saturated surface nuclei as in the cases of the reactions under constant transformation rate and isothermal conditions. As reaction advances, the data points of linear nonisothermal measurements with the preannealing treatment deviate gradually from the regression line for those
Figure 12. The Friedman plots for the thermal dehydration of MHC at selected α. 10497
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Figure 13. The values of Ea at different α for the thermal dehydration of MHC.
of constant transformation rate and isothermal measurements, see Figure 12b, and finally fit to the regression line for those of linear nonisothermal measurements for the nonannealed MHC, see Figure 12c. The discrepancy between the rate data under constant transformation rate and isothermal conditions and those under linear nonisothermal conditions in view of the isoconversional relationship is resulting not only by the differences in surface nucleation but also by the deviation of the reaction mechanisms under linear nonisothermal conditions from those under constant transformation rate and isothermal conditions. The applicability of the idealized rate equation of eq 3 for analyzing the kinetic rate data is also examined by the constancy of the apparent value of Ea during the course of reaction. Figure 13 shows the values of Ea calculated from the slopes of the Friedman plots at various α from 0.01 to 0.99 in steps of 0.01, where the data points of constant transformation rate and isothermal measurements, those of nonisothermal measurements, and those of nonisothermal measurements with preannealing treatment were subjected separately to the Friedman plots. The apparent values of Ea calculated for the reaction under constant transformation rate and isothermal measurements are satisfactorily constant in a wide region of α, that is, Ea = 210.3 ( 5.1 kJ mol1 averaged over 0.1 e α e 0.9, indicating the practical applicability of eq 3 to describe the whole course of the reaction. The value is slightly lower than that for the physicochemical events during the induction period. The Ea values evaluated for the reaction under linear nonisothermal condition decrease systematically from 200 to 105 kJ mol1 as the reaction advances, where a nearly constant value of Ea = 107.5 ( 3.2 kJ mol1 (0.5 e α e 0.9) is observed during the second half of the reaction. Although, in the early stage of the reaction (α e 0.1), the reaction of the preannealed MHC under linear nonisothermal condition indicates the value of Ea comparable with that evaluated for the reaction under constant transformation rate and isothermal conditions, the values decrease in a similar manner with the reaction of nonannealed MHC under linear nonisothermal condition, attaining the nearly constant value of Ea = 138.2 ( 4.7 kJ mol1 (0.5 e α e 0.9). In these cases of the reactions under linear nonisothermal conditions, the direct application of eq 3 is limited to the second half of the reactions. The kinetic rate data in the restricted range of α, which satisfy the prerequisite of the ideal kinetic equation in view of the establishment of the isoconversional relationship and the
Figure 14. The experimental master plots of dα/dθ versus α for the thermal dehydration of MHC and fitting curves drawn by assuming f(α) evaluated by nonlinear least-squares fittings.
constant Ea value, were extrapolated to infinite temperature, using the averaged values of Ea, by the following equation:6164 dα dα Ea ¼ exp dθ α dt α RT Z t Ea exp with θ ¼ dt ð5Þ RT 0 where θ, known as Ozawa’s generalized time,66,67 is the hypothetical reaction time evaluated by extrapolating the kinetic rate data to infinite temperature according to eq 4. In Figure 14, the values of dα/dθ were plotted against α as the experimental master plot, where error bars indicate the standard deviation of dα/dθ values calculated from the respective experimental rate data at the fixed α. The experimental master plot drawn for the reaction under constant transformation rate and isothermal conditions, see Figure 14a, shows the maximum at α = 0.40, which corresponds to the α value at the maximum reaction rate under isothermal condition and the minimum temperature under constant transformation rate condition. For the nonisothermal dehydration of nonannealed and preannealed MHC, the α range of the approximately constant Ea is the decelerate part of the reaction after the crack formation, see Figure 14b. These experimental master plots can be correlated to f(α) and A according to:6164 dα ¼ Af ðαÞ dθ
ð6Þ
Because the experimental master plot with the maximum on the way of the reaction at α < 0.642 is categorized superficially into the nucleationgrowth-type reaction, the experimental master plot for the reaction under constant transformation rate and isothermal conditions was fitted by the typical 10498
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Table 1. Results of Kinetic Analyses for the Thermal Dehydration of MHC measuring condition
Ea/kJ mol1 (range of α)
kinetic model (range of α)
constant transformation rate and isothermal 210.3 ( 5.1 (0.10 e α e 0.90) JMA(m) (0.10 e α e 0.90)
kinetic exponents m = 2.12 ( 0.03
A/s1
γ2a
(1.29 ( 0.02) 1021 0.9752
SB(m, n, p) (0.10 e α e 0.90) m = 1.70 ( 0.76 (2.72 ( 0.15) 1021 0.9838 n = 1.75 ( 0.29 p = 2.24 ( 0.74
a
R(n) (0.56 e α e 0.90)
n = 3.37 ( 0.31
(6.19 ( 0.37) 1020 0.9638
nonisothermal
107.5 ( 3.2 (0.50 e α e 0.90) R(n) (0.61 e α e 0.90)
n = 2.92 ( 0.07
(1.62 ( 0.02) 109
nonisothemal with preannealing treatment
138.2 ( 4.7 (0.50 e α e 0.90) R(n) (0.61 e α e 0.90)
n = 3.31 ( 0.13
(3.82 ( 0.10) 1012 0.9920
0.9966
Square of correlation coefficient of the nonlinear regression analysis.
Figure 15. Schematic illustration of the physico-geometrical mechanism of the thermal dehydration of MHC.
nucleationgrowth-type model, that is, the Johnson MehlAvrami model JMA(m),4548,68,69 f(α) = m(1 α)[ln(1 α)]11/m, together with the empirical model function of the SestakBerggren model SB(m,n,p),70 f(α) = αm(1 α)n[ln(1 α)]p, which fits to various physicogeometric types of reaction and those deviated cases with very high flexibility.64,71,72 Through the nonlinear regression analysis by applying the LevenbergMarquardt optimization algorithm,72,73 the best values of the kinetic exponents in those model functions and the value of A were evaluated simultaneously. The fitting curves by means of JMA(m) and SB(m, n, p) are compared in Figure 14a. The experimental master plot can be fitted nearly perfectly by JMA(2.12) with A = (1.29 ( 0.02) 1021 s1, which is supported by the similarly good fitting by SB(1.70,1.75,2.24) with A = (2.72 ( 0.15) 1021 s1. Despite the many inconstancies of the present reaction with the physico-geometrical assumptions of the JMA(m) model, the kinetic parameters evaluated by the above formal kinetic analysis have, at least, the practical significance to simulate the rate process under the comparable reaction conditions, because nearly the whole course of the reaction was described empirically by those sets of kinetic parameters including the constant value of Ea. The phase boundary controlled type model R(n),4548,68 f(α) = n(1 α)11/n, was selected as the most appropriate kinetic model function for fitting the decelerate part of the nonisothermal dehydration, where experimental master plots of the limited α range of the nonannealed and preannealed MHC were fitted by R(2.92) with A = (1.62 ( 0.02) 109 s1 and R(3.31) with A = (3.82 ( 0.10) 1012 s1, respectively, see Figure 14b. Theoretically, the R(n) model with n ≈ 3 is interpreted as the three-dimensional shrinkage of the reaction interface in a reactant particle, where the linear advancement rate of the reaction interface is controlled by the chemical reaction, that is, the linear law. The decelerate part of the experimental master plot of the reaction under constant transformation rate and isothermal conditions is similarly fitted by R(3.37) with
A = (6.19 ( 0.37) 1020 s1, see Figure 14a. Table 1 summarized the results of the above formal kinetic analyses for the thermal dehydration of MHC. 3.5. Physico-geometrical Mechanism of the Thermal Dehydration of MHC. On the basis of the above observations, a physico-geometrical mechanism of the thermal dehydration of spherical MHC is proposed as illustrated schematically in Figure 15. Within the induction period, the reaction initiates by the nucleation and/or formation nucleus forming sites accompanied by the self-induced gelation at the surface, where the coupling of the reactant particles is enhanced at the contacts, Figure 15a. The established reaction seems to be proceeding by the advancement of the reaction interfaces, characterized by the reactive zone located at the contact of gelatinized phase and internal reactant, toward the center of the particles, Figure 15b. Within the transient gel phase, random nucleation of calcite is taking place successively, followed by the subsequent growth of calcite crystallites accompanied by the evolution of water vapor. The acceleration part of the rate process is characterized by the increase in the gel phase as the substrate of nucleation and growth of product crystallites. The evolved water vapor is removed from the reactant particles by diffusion through the surface layer of calcite crystallites assemblage. As the reaction advances, the impedance effect of the surface product layer on the diffusion of water vapor is to be remarkable by the prolonged diffusion path and the mass-loss rate turns to be decelerate. By the increases in the internal pressure by the evolved water vapor and in the stress of the surface product layer due to the crystal growth of calcite crystallites, cracking of the surface product layer takes place abruptly accompanied by the rapid release of internal water vapor, Figures 4c and 15c. The surface cracks serve as the possible diffusion channels of water vapor for the decelerate mass-loss process in the second half of the reaction, which is accompanied by the distinguished crystal growth of calcite crystallites, Figures 4d and 15d. The existence of the induction period for the thermal dehydration and the apparent value of Eip for the induction period, 10499
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The Journal of Physical Chemistry A which is larger than Ea for the mass-loss process, indicate that the initiation of the reaction is regulated by the nucleation and/or formation of nucleus forming sites on the surface of the reactant particles. According to the above physico-geometrical model of the reaction, the overall rate of mass-loss due to thermal dehydration is determined by the mutually dependent concurrent and consecutive processes of gelation of the reactant solid, crystal nucleation and growth of calcite, formation of water vapor, diffusion of water vapor through the surface product layer of calcite crystallite assemblage, and so on. The constant values of Ea observed in a wider range of α for the reaction under isothermal and constant transformation rate conditions imply that the influence of the other component processes on the ratelimiting process are negligible or unchanged among the measuring conditions within the α range of constant Ea. When the nucleation and growth of calcite on the gel substrate is the ratelimiting process for the overall dehydration, the nucleation and growth-type model function, JMA(2.12), evaluated by the formal kinetic analysis of the mass-loss data can be interpreted as a modified case of the classical nucleation and growth model, accompanied by the volume increase of the gel substrate as the reaction advances. The systematic decrease in the values of Ea depending on α observed in the first half of the reaction under linear nonisothermal conditions implies possible change in the contribution of the process of diffusion of water vapor through the surface product layer with β applied. With increasing β, the rate of water vapor production at the reaction sites increases by the shift of the reaction temperature to higher temperature region, but the overall mass-loss rate does not increase in proportion to the gross increase in the rate of water vapor production at the reaction sites because the removal of water vapor through diffusion is a necessary condition to be detected by the overall mass-loss data. The interpretation is supported by the nearly constant values of Ea observed in the final stage of the reaction after the possible channels of water vapor diffusion have been established by the cracking of the surface product layer. In comparison with the thermal dehydrations of hydrated ACC and poorly crystalline MHC, which produce anhydrous ACC as the dehydration product,3335 the higher thermal stability of spherical particles of crystalline MHC is the major factor to attract the crystallization of calcite during the thermal dehydration process. In the present time scale of tracing the thermal dehydration reaction by means of thermoanalytical measurements and in the temperature range where the destruction of crystal structure of MHC takes place, the surface nucleation of calcite can take part in the overall reaction as one of the component processes. Kinetic behavior of subsequent overall process of the thermal dehydration is regulated by the nucleation and growth of calcite crystals. Because the thermal dehydrations of hydrated ACC and poorly crystalline MHC take place at the lower temperatures, the nucleation of calcite cannot take part in the overall reaction. Accordingly, the differences of the reaction pathways of the thermal dehydration of hydrated calcium carbonates result from the mutual relationship between the kinetics of overall dehydration and crystal nucleation and growth of calcite. This implies the possibility that the thermal dehydration pathway of spherical particles of crystalline MHC can be altered to produce anhydrous ACC as in the cases of hydrated ACC and poorly crystalline MHC if the reaction temperature were lowered successfully by controlling the reaction conditions. The dehydration reaction under reduced pressure may be one of
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the possible routes to produce anhydrous ACC from crystalline MHC, as has been demonstrated by the formation of amorphous Al2O3 during the thermal decomposition of synthetic bayerite, Al(OH)3, at a constant transformation rate under a reduced pressure.74,75
4. CONCLUSIONS The spherical particles of crystalline MHC indicate the higher thermal stability as compared to those of hydrated ACC and poorly crystalline MHC. Thermal dehydration initiates being regulated by the nucleation of calcite on the particle surfaces, characterized by the distinguished induction period with Eip = 228.1 ( 8.6 kJ mol1. At the same time, an indication of selfinduced gelation of the particle surfaces is deduced from the coupling of reactant particles and the kinetic behavior independent of atmospheric water vapor pressure. The established reaction is regulated by the nucleation and crystal growth of calcite on the gel substrate with Ea = 210.3 ( 5.1 kJ mol1. Under the conditions of linearly increasing temperature, a remarkable influence of the diffusion process of evolved water vapor through the surface product layer of calcite crystallites on the overall mass-loss rate can be detected from the systematic decrease in the apparent value of Ea as the reaction advances. On the way of the established reaction, the cracking of surface product layer takes place abruptly, resulting from the crystal growth of calcite in the surface product layer and the possible increase in the internal pressure due to the impedance for the diffusion of evolved water vapor by the surface product layer. After the possible channels for the diffusion of water vapor were secured by the cracking, the final stage of the dehydration reaction advances in a decelerated behavior, accompanied by the remarkable growth of calcite crystals. ’ AUTHOR INFORMATION Corresponding Author
*Tel/Fax: +81-82-424-7092. E-mail:
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’ ACKNOWLEDGMENT The present work was supported partially by a grant-in-aid for scientific research (B) (21360340 and 22300272) from the Japan Society for the Promotion of Science. ’ REFERENCES (1) Sapozhnikov, D. G.; Tsvetkov, A. I. Akad. Nauk SSSR 1959, 124, 131–133. (2) Stoffers, P.; Fischbeck, R. Sedimentology 1974, 21, 163–170. (3) Krumbein, W. E. Sedimentology 1975, 22, 634–635. (4) Taylor, G. F. Am. Mineral. 1975, 60, 690–697. (5) Swainson, I. P. Am. Mineral. 2008, 93, 1014–1018. (6) Krauss, F.; Schriever, W. Z. Anorg. Allg. Chem. 1930, 188, 259–273. (7) Ito, T.; Matsubara, S.; Miyawaki, R. J. Mineral. Petrol. Econ. Geol. 1999, 94, 176–182. (8) Dahl, K.; Buchardt, B. J. Sediment. Res. 2006, 76, 460–471. (9) Fishbeck, R.; Muller, G. Contrib. Mineral. Petrol. 1971, 33, 87–92. (10) Broughton, P. L. Contrib. Mineral. Petrol. 1972, 36, 171–174. (11) Onac, B. P. Theor. Appl. Karstol. 2000, 13, 33–38. (12) Carlstrom, D. Biol. Bull. 1963, 125, 441–463. (13) Skinner, H. C. W.; Osbaldiston, G. W.; Wilner, A. N. Am. Mineral. 1977, 62, 273–277. 10500
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