Article pubs.acs.org/JPCA
Reaction-Diffusion Framework: The Mechanism of the Polymorphic Transition of α- to β‑Cobalt Hydroxide Janane Rahbani,† Manal Ammar,† and Mazen Al-Ghoul†,* †
Department of Chemistry, American University of Beirut, P.O.Box 11-0236, Riad El-Solh 1107 2020, Beirut, Lebanon S Supporting Information *
ABSTRACT: A new and simple method is proposed to explore the mechanism of the intercalation/deintercalation of a variety of anions throughout the formation of α-Co(OH)2 crystals and their polymorphic conversion to β-Co(OH)2. This method is based on the reaction-diffusion of hydroxide ions in a gel matrix containing the cobalt salt. The spatiotemporal evolution of each polymorph and their interaction is revealed by tracking the location of the two sharp interfaces between the two polymorphs (conversion zone) and between the gel and α-Co(OH)2 (formation zone) and by measuring the weight composition of each zone. We thereby find that the dynamics of the transformation reaction are correctly described by the two-dimensional Avrami-Erofe’ev equation at different temperatures. The data suggest that the structural redistribution of the atoms inside the α-Co(OH)2 particles plays the fundamental role in establishing the overall rate of the reaction. On the other hand, we notice that other factors such as the nature of the intercalated anions and the concentration of the polymer matrix alter considerably the final rate of the transition reaction through increasing the stability of the α phase.
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INTRODUCTION Layered cobalt hydroxide materials have been extensively studied in recent years due to their applications in various areas of materials science and engineering. For example, they are widely employed in biology to control the release of macromolecules such as DNA,1 in manufacturing of photovoltaic devices,2 and in the fabrication of other electronic materials.3 Their interesting properties are mainly due to the exchange of ions and molecules between the crystal’s interlayers and its surroundings. Cobalt hydroxide possesses two polymorphs: the brucite-like β-Co(OH)2 wherein cobalt(II) cations are octahedrally surrounded by hydroxide ions and the hydrotalcite-like α-Co(OH)2 which is found to be more complex in the presence of tetrahedral cobalt(II) cations capable to interact with a variety of anions and molecules in solution.4−6 Though α-Co(OH)2 is the more interesting of the two polymorphs of cobalt hydroxide, it undergoes a polymorphic transition to β-Co(OH)2 concomitant to a significant decrease of the interlayer spacing.7,8 However, the mechanism of the polymorphic conversion of α to β-Co(OH)2 still lacks full understanding. We have reported in previous papers the cosynthesis of both polymorphs using a reaction-diffusion framework.9,10 This method is based on carrying the reaction of interest using initially separated components in a gel matrix whose internal structure causes the slowdown of the dynamics, the removal of convection currents and the elimination of sedimentation. Therefore, the formation and conversion of cobalt hydroxide crystals are studied by diffusing the hydroxide ions into a gel matrix (agar gel) containing various dissolved cobalt salts. The α polymorph, which exhibits a blue/green color because of the © 2013 American Chemical Society
presence of tetrahedral Co(II), is instantaneously produced upon addition of OH−. Nonetheless, a pale pink color, which is due to the exclusive existence of octahedral Co(II), appears a few seconds later concomitant with the deintercalation of the anions from the interlayer cavities of α-Co(OH)2. Therefore, the system is macroscopically constituted by two propagating and interacting fronts: a leading blue front and a trailing pink front that delineates the interface of the conversion of the blue α-Co(OH)2 to the pink β-Co(OH)2. The SEM imaging of the solids of the two polymorphs reveals a change in the shape and size of α-Co(OH)2 from folded platelets (∼600 nm) to welldefined hexagonal platelets of β-Co(OH)2 (∼1−2 μm). This additional spatial dimension provided by diffusion along the tube allows us to monitor the formation of α particles and their transition to β-Co(OH)2 through fluorescence spectroscopy with rhodamine 6G as a probe.11 We have found that the fluorescence intensity and lifetime increase considerably during the intercalation process indicating that the excited state of rhodamine molecules is stabilized inside the interlayer gallery of α-Co(OH)2. On the other hand, throughout the polymorphic transition, the fluorescence intensity and lifetime drop exponentially signifying that the new formed crystals hold a small interlayer spacing that cannot accommodate the probe molecules. After calculating the activation energy of each process, we are able to deduce that the nucleation is deceleratory (the rate of the reaction decreases concurrently with the reduction of the available sites on α-Co(OH)2 surface) Received: August 22, 2012 Revised: January 28, 2013 Published: January 29, 2013 1685
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is associated to the spot at which the conversion to the pink βCo(OH)2 crystals is taking place (conversion zone). We are capable of monitoring the above-mentioned two phenomena by evaluating the positions of the two fronts manually or via a digital camera that captures and processes the digital photos over a certain period of time. Alternatively, we follow quantitatively the evolution of the bands by measuring the corresponding mass of every front. After a fixed time interval, the outer portion is discarded, the tube is broken and the two adjacent bands (blue and pink) are cut from the gel and separated. Each band is then dissolved in 4 mL of 0.1 M hydrochloric acid. Subsequent to the complete dissolution, the samples are diluted 50 times. Finally, the mass of Co(II) in each sample is measured using a SOLAAR atomic absorption spectrophotometer with ASX-510 autosampler. Effect of anions. Four tubes with four different cobalt salts with the same concentration are prepared: CoBr2, CoCl2, Co(NO3)2, and CoSO4. A typical concentration of the salts is 0.1 M. The same solution of NaOH (2 M) is added to the four tubes. A blue precipitate is instantaneously produced after the addition and the diffusion of NaOH through the gel pores, and the evolution in the four tubes proceeds as previously explained. Effect of the Gel Concentration. Four test tubes each containing 0.2 M of Co(II) chloride solution are prepared at ambient temperature. Then, a certain mass of agar is added into each tube in such a way to obtain the following gel concentrations: 0.5%, 1%, 2%, and 3% w/w. Finally, front distances of both polymorphs are measured after 48 h of the addition of a 2 M solution of NaOH when the rate of the propagation of the pink front has significantly decreased. Similarly, the effect of gelatin concentration is examined by preparing four test tubes containing the following gelatin concentrations: 2%, 4%, 6%, and 8% w/w and with an inner concentration of 0.1 M cobalt chloride and an outer concentration of 0.5 M NaOH. Effect of Temperature. The preparation method is similar to the ones described in previous parts. The agar gel concentration is 1% w/w, and the four sets of tubes (each set contains 10 tubes) are placed in a water bath to achieve the following temperatures: 10, 15, 20, and 25 °C. The inner concentration of the cobalt chloride is 0.1 M, and the outer concentration of NaOH is 2 M. Effect of Inner Concentration. Using the same experimental method, we prepare three sets of tubes (containing each 10 tubes) in a 1% w/w agar gel. To every set, a particular amount of cobalt chloride is added to attain the following concentrations: 0.1, 0.2, and 0.3 M.
throughout the polymorphic transition, and the rate limiting step for the overall reaction is propagation of the reaction boundary. In most solid-state reactions, it is very hard to separate the overlapping stages that underline the production of the final thermodynamically stable crystals. Therefore, one must speculate and analyze all the kinetic parameters that characterize each elementary step (diffusion, nucleation, and growth) as an attempt to describe the mechanism of the overall reaction.12 In recent studies, a variety of analytical, spectroscopic, and microscopic techniques were employed not only to determine such parameters but also to support the selection of the ideal reaction model. Nevertheless, the choice of the most practical model remains difficult in the absence of a complete interpretation of the heterogeneous processes that are taking place.13 Theoretically, a kinetic model is an arithmetical depiction of what is really happening experimentally.14 These models are classified according to particular mechanistic postulations and can take the following graphical shapes: acceleratory, deceleratory, linear, and sigmoidal.15 In fact, when solid-state reaction kinetics are treated, the mobility of the reagents toward the reaction zone, the crystal lattice of the starting phase, which determines the availability and the position of the nucleation potential sites,16 and the distribution of the defects inside the lattice structure17,18 must be taken into account before postulating any model. Consequently, some reactions will be controlled by the permeability of the reactants into the reaction zone (diffusion models) whereas others will depend on the structural rearrangements that take place at the interface (phase boundary models). Although it cannot fit the entire experimental data concurrently, the Avrami-Erofe’ev model is one of the classically used models that describe the nucleation and growth processes.19−21 This model is frequently applied in polymorphic transition reactions in which the transition kinetics is correlated to the nucleation and growth of the newly produced phase.22 In this work, we try via a novel and simple technique to establish a reasonable mechanism for the polymorphic transition reaction and determine some of the external factors that affect it. We are able to follow the spatiotemporal evolution of α-Co(OH)2 and its conversion to β-Co(OH)2 through measuring the locations of the two fronts and analyzing their corresponding compositions in an attempt to associate the macroscopic to the microscopic observations.
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EXPERIMENTAL SECTION Materials. Agar is provided by Bacto and gelatin by Difco. Cobalt(II) sulfate heptahydrate, cobalt(II) chloride hexahydrate, cobalt(II) bromide, and cobalt(II) nitrate are supplied by Fluka. Sodium hydroxide is obtained from Riedel-de Haën. Method. The required masses of cobalt salt and agar are weighed and added to doubly distilled water. The mixture is then heated with continuous stirring to obtain a 1% agar solution containing the required concentration of inner electrolyte Co(II). The solution is poured into thin glass tubes (6 × 200 mm) and left for 4 h at room temperature to rest and polymerize. After gelation the outer electrolyte ([OH−] = 2 M) is added on top of the gel. At the macroscopic scale, following the addition of the hydroxide solution, two reaction interfaces are discerned: the foremost interface is correlated to the formation of the blue αCo(OH)2 particles (formation zone) and the subsequent front
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RESULTS AND DISCUSSION Effect of Anions. The extent of the propagation of the blue and pink bands changes significantly between different αCo(OH)2 species (which differ according to the nature of the intercalated anions). The spatiotemporal evolution of α- and βCo(OH)2 intercalated with bromide, chloride, nitrate, and sulfate anions is displayed in Figure 1. Microscopically, the growth of α and β crystals is directly correlated to the nature of the intercalated anions, which display different sizes and charges. The behavior of the anions in the interlayer cavities is found to have a great impact on the activation energies that range from 32 to 39 kJ/mol for the α to β interconversion reaction and from 29 to 37 kJ/mol for the intercalation reaction.11 Following the propagation of the pink and blue 1686
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Figure 2. Width measurements of the α-Co(OH)2 (blue band) and βCo(OH)2 (pink band) crystals, formed after 3 days of adding 2 M NaOH to 1% agar containing 0.1 M of cobalt salts: chloride, bromide, nitrate, and sulfate.
processes, it is unequivocally involved in the determination of the rate of the reaction. Effect of the Gel Concentration. In an attempt to find out a relation between the concentration of the gel and the kinetics of the formation of α-Co(OH)2 as well as its conversion to βCo(OH)2, we monitor the spatiotemporal evolution of the reactions as a function of the concentration of agar and gelatin matrices. According to Maaloum et al., the size of the pores decreases with increasing agar concentration and the pore radii distribution becomes more homogeneous.23 In the case of agar, SEM micrographs (Supporting Information) show that the average size of β-Co(OH)2 particles (∼1.2 μm) is almost double that of α particles (∼600 nm). To understand the interplay of the gel structure and the dynamics of the system, we perform the experiment in the case of cobalt chloride as the inner electrolyte at different agar gel concentrations. The temporal evolution of the distance traveled by the blue front, dα, and that traveled by the pink front, dβ, is shown in Figure 3. It is obvious that the gel concentration does not affect the evolution of the blue front significantly (Figure 3B); however, there is clear evidence for the dependence of the pink front on the gel concentration (Figure 3A): at higher gel concentrations, the slowdown of the pink front occurs at an earlier time. For example, at gel concentrations of 3%, the slowdown occurs at a time close to 6 h, whereas slowdown at gel concentration of 2% occurs at a time close to 10 h. For gel concentrations below 1%, no slowdown occurs before 36 h. We may then conclude that as the pores become smaller with increasing gel concentration, the ratio of widths of α over β crystals increases, as shown in Figure 4. This corroborates the fact that the gel is stabilizing α versus β polymorph due to a change in its pore diameter distribution. To further prove the impact of such distribution on the whole process, we plot the ratio of the widths versus the gel concentration (Figure 5). We find that the increase is exponential, indicating that significant modifications occur in the distribution of the pore sizes in consequence of changing the polymer concentration. To shed more light on the effect of another polymer matrix (gelatin) on the kinetics of the formation/conversion reactions, we follow the same procedure described in the case of agar gel. Schacht et al. claimed that smaller but higher numbers of pores are produced at large gelatin concentrations due to an increase in the gel nucleation rate.24 Thus, we suspect that increasing the concentration of the gel would stabilize the small α crystals and slow the conversion reaction. The spatiotemporal evolution of
Figure 1. Spatiotemporal evolution of the formation and conversion zones of α-Co(OH)2 (blue band) and β-Co(OH)2 (pink band) after the addition of 2 M NaOH solution to a 1% agar containing 0.1 M CoCl2 (A), CoBr2 (B), Co(NO3)2 (C), and Co(SO4) (D) salts. Pictures are taken after 1, 10, and 24 h of reaction-diffusion.
fronts, we notice that α-Co(OH)2 intercalated with relatively small anions such as chloride and bromide are more stable than those intercalated with nitrate and sulfate anions because the interconversion slows down at distances close to each other (Figure 1A,B) after 12 to 18 h. The ionic radii of the anions in this study are 181, 196, 219, and 230 pm for the chloride, bromide, nitrate, and sulfate, respectively. We define the width of the pink band as the distance between the gel−liquid interface and the trailing pink front and the width of the blue band as the distance between the trailing pink front and the leading blue front. Width measurements, depicted in Figure 2 confirm the fact that bigger anions are expelled faster from the interlayer spacing than smaller ones. For instance, sulfate anions display a shorter blue band, a larger pink band and smaller activation energies. Thus, as the size of the intercalated anion increases, the stability of α polymorph decreases. If we compare the activation energy of the conversion of α-Co(OH)2 crystals intercalated with bromide (39 kJ/mol) to the ones intercalated with sulfate (32 kJ/mol), we realize that in the latter case the transition is faster. Therefore, the growth of the pink band stops after 1 day in the case of nitrate (Figure 1C), and after 2 days in the case of sulfate (Figure 1D). Although the nature of anions does not alter the whole mechanism of the intercalation/deintercalation 1687
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Figure 3. Distances traveled by α-Co(OH)2 (blue front), dα, and by β-Co(OH)2 (pink front), dβ, as a function of time at different gel concentrations. The outer base concentration is 2 M NaOH and inner salt concentration is 0.2 M of cobalt chloride in 0.5% (circles), 1% (squares), 2% (diamonds), and 3% (stars) of agar.
Figure 4. Width measurements of the α-Co(OH)2 (blue band) and βCo(OH)2 (pink band) crystals, formed after 48 h of adding 2 M NaOH to 0.2 M of cobalt chloride in 0.5%, 1%, 2%, and 3% of agar.
Figure 6. Width measurements of the α-Co(OH)2 (blue band) and βCo(OH)2 (pink band) crystals, formed after 48 h of adding 0.5 M NaOH to 0.1 M of cobalt chloride in 2%, 4%, 6%, and 8% gelatin.
Figure 5. Width ratio (blue width/pink width) variation as a function of agar gel concentration, after 48 h of adding 2 M NaOH to 0.2 M of cobalt chloride in 0.5%, 1%, 2%, and 3% agar.
Figure 7. Width ratio (blue width/pink width) variation as a function of gelatin concentration, after 48 h of adding 0.5 M NaOH to 0.1 M of cobalt chloride in 2%, 4%, 6%, and 8% gelatin.
the pink and blue bands as a function of the polymer concentration is displayed in Figure 6 and its resultant plot is revealed in Figure 7. Nevertheless, the increase of the width ratios is found to be linear, proving that gelatin pores are more homogeneous than those of agar. Effect of Temperature. One of the main parameters that influences the kinetics of the formation of layered cobalt hydroxide materials is temperature. Hence, it is essential to follow the evolution of the reactions macroscopically through a novel method to gain insight into the accurate amount of each
polymorph. Front distance measurements are important because they qualitatively reflect this progression, yet they cannot give us the complete picture of the mechanism of the reactions. On the other hand, we are able to extract, separate, and measure the corresponding weights of each band via atomic absorption spectroscopy (AAS) to verify whether the intercalation/deintercalation processes are diffusion or surface controlled. Figure 8 shows the variation of the conversion fractions mα (mass fractions of the blue polymorph) and mβ (mass fraction 1688
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Table 2. Kinetic Data Summary of the Formation Reaction at Different Temperatures n
temp (°C) 25 20 15 10
2.3 1.7 1.3 1.2
± ± ± ±
t (h) 0.4 0.4 0.4 0.1
10 12 13 14
k 0.059 0.052 0.044 0.038
± ± ± ±
0.005 0.003 0.004 0.01
where k is the rate constant, t is the time of the reaction, and n is the Avrami exponent. On the basis of the values of n in Table 1, we can claim that the importance of the reaction itself in determining the overall rate of the reaction increases with temperature. Indeed, because the rate of diffusion increases as a function of temperature, the reconstruction of the layers through breaking the bonds between the tetrahedral Co(II) and the intercalated anions and forming new Co−OH bonds turns out to be the rate determining step. The high value of n (2.3) at 25 °C validates our assumption. On the other hand, during the formation of α-Co(OH)2, the data are fitted with the Avrami-Erofe’ev equation within a specific time interval (depending on the temperature). The time at which the mechanism switches is displayed in Table 2. The calculated values of n are close to those found for the conversion reaction. This further proves that the transformation process in layered cobalt materials is boundary controlled at high temperatures. Nevertheless, when the conversion reaction is slow compared to the precipitation reaction, the amount of α-Co(OH)2 produced augments exponentially with a rate constant k displayed in Table 2 (Note that k is defined by k = e−mt). In conclusion, we suspect that the variation of the composition of the bands at different temperatures is related not only to the diffusion of hydroxide anions but also to the chemical structure of the crystals. The findings are in agreement with those demonstrated microscopically in our previous work11 and with those established by O’Hare.26 To verify the mechanism of the reactions, distances are measured with respect to the marked gel−hydroxide interface. The temporal evolution of the width of the pink band (wβ) is displayed by the log−log plot of w as a function of time (Figure 9). The graphs indicate that while the width scales as w(t) ∼ tn,
Figure 8. Spatiotemporal pink/blue bands composition variation at different temperatures. The data are fitted with Avrami−Erofe’ev equation at 25 °C (circles), 20 °C (squares), 15 °C (diamonds), and 10 °C (triangles), respectively. The red line represents the exponential fit of the data when the conversion reaction becomes extremely slow.
of the pink polymorph) at different temperatures. mβ is defined by m mβ = t m∞ where mt is the mass at time t and m∞ is the final mass. The curves demonstrate that the formation and conversion reactions are faster at higher temperatures because larger amounts of both polymorphs are produced. Note that the composition of the blue band depends on two different chemical processes: the precipitation reaction (CoX + OH−) and the transformation reaction, whereas the composition of the pink band relies solely on the extent of the conversion reaction. Therefore, we can distinguish in the formation reaction of α-Co(OH)2 between two kinetic behaviors: the first one depends on both reactions (before the deceleration of the conversion reaction), and the second one relies only on the precipitation reaction (when the conversion becomes very slow). The chemistry that expresses the process is given by Co2 +(aq) + 2NaOH(aq) → 2Na +(aq) + α − Co(OH)2 (s) α ‐Co(OH)2 (s) → β ‐Co(OH)2 (s)
Moreover, during the intercalation of the guest anions into the interlayer spacing, the edge of each layer is considered a potential nucleation site, whereas throughout the conversion reaction, the defect locations on these layers play the major role in the structural rearrangement of the crystals.25 The values of n, which are summarized in Tables 1 and 2, are obtained after fitting the curves with the Avrami-Erofe’ev equation that takes the form mβ (t ) = 1 − exp( −kt n)
Figure 9. Log−Log plots exhibiting scaling laws for α- and βCo(OH)2 at different temperatures as shown in the legends. The dashed line represents a typical diffusion process with a slope n = 0.5.
Table 1. Kinetic Data Summary of the Phase Transition Reaction at Different Temperatures
25 20 15 10
the magnitude of n increases with temperature. The values of n for the conversion reaction are displayed in Table 3. It is noteworthy that in a typical diffusion process, the front distance (the width of the blue and pink bands) scales as d(t) ∼ t0.5. Thus, the width (w) of the pink band must also exhibit a comparable scaling law with an exponent near 0.5 if the
n
temp (°C) 2.3 1.7 1.5 1.4
± ± ± ±
0.1 0.2 0.2 0.1 1689
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concentration does not have a great effect on the mechanism of the phase conversion reaction because the value of n remains approximately constant (Table 5). Nonetheless, it is obvious
Table 3. Slopes of the Linear Fits of the Log−Log Plots for the Conversion Reaction n
temp (°C) 25 20 15 10
0.44 0.44 0.38 0.33
± ± ± ±
0.03 0.03 0.03 0.01
Table 5. Kinetic Data Summary of the Phase Transition Reaction for Different Inner Concentrations of Co(II)
conversion reaction is diffusion-limited. However, in our system, the exponent n is less than 0.5 at all temperatures, which indicates evidently that the diffusion of OH− is not the rate-determining step. Indeed, there is a high probability for an anomalous diffusion to take place, especially in porous media in which random trapping decreases the propensity of the particles to diffuse.27 Hence, the chemistry of the matrix and the reagents themselves contribute significantly to the final rate of the reaction. According to the second graph of Figure 9, we can clearly distinguish between two kinetic regimes as previously explained. In the early stages of the formation reaction, the slopes of the linear fits are much greater than 0.5. Nevertheless, the exponent n diminishes simultaneously with the slowing of the conversion reaction. Table 4 shows that the formation of α-
n
m
25 20 15 10
1.0 ± 0.2 1.1 ± 0.1 0.83 ± 0.03 0.93 ± 0.1
0.53 ± 0.03 0.51 ± 0.02 0.7 ± 0.3 0.59 ± 0.08
n
0.1 0.2 0.3
1.8 ± 0.1 1.9 ± 0.4 1.9 ± 0.4
that a higher amount of α particles is produced at larger inner concentrations because the cobalt salt is the limiting reagent in the initial precipitation reaction. On the other hand, we can still discern between two kinetic regimes while examining the dynamics of the blue band even at different inner concentrations. The Avrami-Erofe’ev fits validate the reliability of the proposed mechanism wherein the reaction itself is the rate limiting step in the early phase of the reaction (Table 6). However, the formation of α particles increases Table 6. Kinetic Data Summary of the Formation Reaction for Different Inner Concentrations of Co(II)
Table 4. Slopes of the Linear Fits of the Log−Log Plots for α-Co(OH)2 Formation before (n) and after (m) the Slowing of the Transition Reaction temp (°C)
concn (M)
concn (M)
n
k
0.1 0.2 0.3
1.5 ± 0.4 1.6 ± 0.2 1.4 ± 0.3
0.046 ± 0.005 0.044 ± 0.005 0.040 ± 0.005
exponentially (with a rate constant k) as soon as the composition of the band becomes dependent on the precipitation reaction only.
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Co(OH)2 tends to be diffusion limited (exponent m) in the later period of the reaction. This corroborates the fact that the precipitation reaction is the only factor affecting the dynamics of the blue band at that time. Effect of Inner Concentration. In this section we try to investigate the sensitivity of the reactions to the initial concentration of Co(II). Figure 10 reveals the variation of the conversion fractions (mβ and mα) of the pink and blue bands for different inner concentrations of Co(II). In the first graph, the magnitudes of n are extrapolated after fitting the data with the Avrami-Erofe’ev equation. We find that the inner
CONCLUSION The kinetics and mechanism of the formation of α-Co(OH)2 and its conversion to β-Co(OH)2 are studied macroscopically for the first time in this work. The size of the intercalated anions is found to have a great impact on the stability of αCo(OH)2 particles. The outcomes suggest that the incorporation of relatively large anions accelerates the transformation reaction by destabilizing the α polymorph. Moreover, we find that the concentration of the polymer influences significantly the reconstruction of the octahedral planes in α-Co(OH)2 samples. Because the size of the pores is reduced at higher concentrations, the carrier molecules cannot accommodate the big β crystals inside their voids. Furthermore, the width traveled by the pink and blue fronts is measured and its corresponding composition is revealed at different temperatures. The data, which are fitted with the Avrami-Erofe’ev equation, complement the speculation that the phase conversion is boundary controlled, especially at higher temperatures. Finally, we find that the mechanism of the deintercalation process does not depend on the concentration of the inner solution (CoX solution) because the exponent n remains constant in all cases.
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Figure 10. Spatiotemporal pink/blue bands composition variation for different inner concentrations of Co(II). The data are fitted with Avrami−Erofe’ev equation at 0.1 M (circles), 0.2 M (squares), and 0.3 M (diamonds), respectively. The red line represents the exponential fit of the data when the conversion reaction becomes extremely slow.
ASSOCIATED CONTENT
S Supporting Information *
SEM of the solids of the two polymorphs of cobalt hydroxide. This information is available free of charge via the Internet at http://pubs.acs.org 1690
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AUTHOR INFORMATION
Corresponding Author
*AUTHOR EMAIL ADDRESS
[email protected] Phone: +961 1 350000 (ext. 3970); Fax: +961 1 365217. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS
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REFERENCES
The authors gratefully acknowledge the funding provided by the American University of Beirut Research Board and by the Lebanese National Council for Scientific Research (LCNSR).
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dx.doi.org/10.1021/jp308354f | J. Phys. Chem. A 2013, 117, 1685−1691
