Band Propagation, Scaling Laws and Phase Transition in a Precipitate

Apr 10, 2012 - Band Propagation, Scaling Laws, and Phase Transition in a Precipitate System. 2. Computational Study. Andrew Abi Mansour and Mazen Al-G...
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Band Propagation, Scaling Laws and Phase Transition in a Precipitate System. I: Experimental Study Mazen Al-Ghoul,*,†,§ Manal Ammar,† and Rabih O. Al-Kaysi‡ †

Department of Chemistry and §Program in Computational Science, American University of Beirut, Beirut, Lebanon ‡ College of Basic Sciences, King Saud bin Abdulaziz University for Health Sciences, National Guard Health Affairs, Riyadh 11426, Kingdom of Saudi Arabia ABSTRACT: In the first part of this work, we present an experimental study of the precipitation/redissolution reaction−diffusion system of initially separated components in two distinct organic gels: agar and gelatin. The system is prepared by diffusing a concentrated ammonia solution into a gel matrix that contains nickel sulfate. In agar, the system exhibits a pulse propagation due to the concomitant precipitation reaction between Ni(II) and hydroxide ions and redissolution due to ammonia. At a later stage of propagation, a transition to Liesegang banding is shown to take place. The dynamics of the distance traveled by the precipitation pulse, its width, and mass are shown to exhibit power laws. Moreover, the mass of the bands is shown to oscillate in time, indicating the emergence of a complex mass enrichment mechanism of the formed Liesegang bands. At the microscopic level, we show evidence that the system undergoes a continuous polymorphic transition concomitant with a morphological change whereby the solid in the pulse, which consists of nanospheres of α-nickel hydroxide transforms to form the bands, which consists of larger platelets of β-nickel hydroxide. This clearly indicates the existence of a dynamic Ostwald ripening mechanism that underlies the dynamics on both scales. On the other hand, in gelatin, although we can still obtain similar power laws as in the case of agar, no transition to bands was observed. It is shown that in this case, the propagating pulse is made of nanoparticles of α-nickel hydroxide with an average diameter ∼50 nm.

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INTRODUCTION The Liesegang banding phenomenon1−6 is a classical example of pattern formation, with many of its theoretical aspects still not very well understood. It emerges from the coupling of the precipitation reactions with diffusion. Experimentally, when a gel solution containing a certain electrolyte (called the inner electrolyte) is placed in a test tube with another electrolyte diffusing from its top (the outer electrolyte), a precipitate pattern appears as a set of alternating precipitation bands that form parallel to the diffusion front and separated by precipitatefree zones. The outwardly simple experimental system can exhibit a multitude of complex spatiotemporal dynamics and morphological changes, depending on many factors, including the chemical reaction itself, initial concentrations of electrolytes, temperature, and the nature of the gel and its concentration.7,11,12 One interesting complexity in Liesegang phenomena arises when the excess diffusing outer electrolyte causes redissolution of preformed bands close to the interface: while band formation continues, this gives rise to a propagating stratum of bands toward the end of the tube. Numerous experimental studies on such periodic precipitation patterns with redissolution exist in the literature and include the Co(OH)2/NH3,13,14 HgI2/ HgI42−,15−18 the Cr(OH)3/Cr(OH)4− 19−21 and the Al(OH)3/Al(OH)4− 22 systems. However, these experimental studies were based on visual observations and macroscopic © 2012 American Chemical Society

measurements of various spacing laws and quantities to infer the dynamic behavior of the observed phenomena. Although most theoretical investigations of these systems5,6,23,24 focus on the relation between microscopic nucleation and growth to the macroscopic resulting patterns, most of the experimental studies did not address such a relationship. Recently, we started investigating the underlying relationship between the microscopic dynamics and the patterns exhibited on the macroscopic level by using spectroscopic and imaging techniques.8−10,14 In this paper, we present a seemingly simple Liesegang system with redissolution and uncover the emerging complexity on the macroscopic and microscopic levels and the interconnection of these scales. The experimental system consists of a vertical tube two-thirds of which contains a gel and the inner Ni(II) salt (here, nickel sulfate). Over the gel matrix, a concentrated solution of ammonia (14 M) is added. The ammonia solution contains mainly ammonia (NH3) and the hydroxide ions (OH−), which is in considerably lower concentration because ammonia is a weak base in water. Nevertheless, a green band of solid nickel hydroxide forms because of its very low solubility product26 (Ksp = 5.48 × Received: January 5, 2012 Revised: April 2, 2012 Published: April 10, 2012 4427

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10−16). The upper gel portion (close to the interface between the two electrolytes) is more influenced by ammonia, which redissolves the green solid forming the blue Ni(NH3)n2+ complex26 (Kf = 5.00 × 104 for n = 6). The chemistry that is expected to describe this process is given by Ni 2 +(aq) + 2OH−(aq) → Ni(OH)2 (s)

on a Jasco V-570 UV/vis/NIR spectrophotometer. the Bragg− Brentano reflection geometry is used for focusing. The atomic absorption measurements are done on a Solaar atomic absorption spectrophotometer with an ASX-510 autosampler. The photographs are taken using a Canon EOS 450D digital camera. SEM measurements are performed using a JEOL JSM6510LV scanning electron microscope. Crystalline samples of the agar-free Ni(OH)2 pulse and bands are obtained and used without further treatment. Tiny crystals from each sample are stuck on a double adhesive carbon tape and attached to an SEM stub. The samples are coated with a fine layer of Pt (5 nm) to enhance sample conductivity and reduce surface charging. The samples are imaged at 20 KV. Several images of each sample are taken with gradual increase in magnification. Transmission electron microscopy (TEM) is performed on particles deposited on a carbon-coated grid with a Philips CM12 microscope operating at 120 kV accelerating voltage.

(1)

Ni(OH)2 (s) + n NH3(l) → Ni(NH3)n 2 + (aq) + 2OH−(aq)

(2)

The index n will be determined by spectroscopy later on. The solid pulse moves down the tube for a relatively long time until bands start appearing in the region above it. In this paper, we study this transition from pulse to bands regimes and show that there are scaling laws that characterize such a transition. On the microscopic level, such a transition is accompanied by a polymorphic transition between the two forms of nickel hydroxide, α-Ni(OH)2 and β-Ni(OH)2. This transition is accompanied by morphological transformation that we describe as a dynamic Ostwald ripening. This paper is organized as follows. In the next section, we discuss the experimental techniques. The Results and Discussion section follows and is divided into three parts: the first part deals with the macroscopic analysis, the deduced power laws during the transition from the pulse regime to the bands regime, the effect of inner and outer concentrations, and the effect of the nature of the gel. The second part consists of the microscopic analysis, which includes the spectroscopic and the imaging results. The third part embraces a proposed mechanism of the transition. In the final section, we conclude the study.

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RESULTS AND DISCUSSION Macroscopic Dynamics. The precipitation takes place seconds after the addition of ammonia over the gel matrix containing the nickel ions. We will assume that, on the basis of our chemical knowledge expressed in eqs 1 and 2, the green solid is nickel hydroxide and the dissolved blue species is the nickel ammine complex. The exact nature of the solids and the dissolved species will be uncovered in the section dealing with the microscopic dynamics. In this section, we shall describe and characterize the macroscopic evolution of the chemical system consisting of the solid nickel hydroxide displayed as a pulse and as bands and their interaction with each other as well as with the subsequent excess ammonia front. Spatiotemporal Evolution. In agar gel, the evolution of the system is characterized by a transition between two regimes: the propagating pulse regime that is followed by a transition to a static Liesegang bands regime after a relatively long time. These are shown in Figure 1, where the transition occurs after 48 h of propagation of the pulse. The three different tubes correspond to three different concentrations of the inner electrolyte (Ni2+) (0.2, 0.3, and 0.4 M) but with the same concentration of ammonia (14 M). A few minutes after the addition of the outer electrolyte, a light green band forms near

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EXPERIMENTAL SECTION The preparation of the tubes consists of the following simple experimental procedures: The required masses of NiSO4·6H2O (Mallinckrodt) and Agar (0.5%) (Bacto) are weighed to the nearest 0.0001 g. These masses are then transferred to a beaker containing 5.00 mL of doubly distilled water. After dissolution of the solid, 0.0250 g of agar powder are added to make a 0.5% agar solution. The solution is then heated with continuous stirring until the entire agar is dissolved. The resulting gel is immediately transferred using a Pasteur pipet into clean test tubes (25 cm long with 0.4 cm diameter) in such a way that each tube is two-thirds full. The tubes are then covered with Parafilm paper and stored in a thermostatic chamber at 18 °C. Before adding the outer electrolyte (NH3 solution), the upper edge of the gel is marked to indicate the interface. Then 14 M (mol/L) of ammonia solution is added to the remaining onethird empty portion of each tube above the solidified Ni2+−gel interface. Once the outer electrolyte solution is added over the interface, a homogeneous green precipitate starts to form. The same procedure is carried out when gelatin is used instead of agar. The chemical structures of the products are characterized using different spectroscopic and imaging techniques. For FTIR measurements, a Thermo Nicolet 4700 Fourier transform infrared spectrometer equipped with a class 1 laser is used. The KBr pellet technique is applied to perform the transmission experiments in the range between 4000 and 400 cm−1. The XRD data are recorded by a Bruker d8 discover X-ray diffractometer equipped with Cu Kα radiation (λ = 1.5405 Å). The UV−vis diffuse reflectance experiments are performed

Figure 1. Transition after 48 h from a propagating pulse regime (left panel) to a banding regime (right panel) in 0.5% agar for the same outer concentration of ammonia ([NH3] = 14 M) and different inner concentrations of Ni(II), as indicated on the bottom of each tube. The photos in the first panel were taken after 12 h. 4428

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the interface. This band starts moving downward due to the concomitant precipitation of nickel hydroxide and its redissolution due to excess ammonia. After 1 h, as the band reaches a few millimeters away from the interface, it splits, giving rise to new closely separated bands (Figure 2) which last

Figure 2. Band-splitting at the ealy stages of evolution.

for a few minutes until they recombine again in one band. This splitting behavior was observed for different concentrations of the inner and outer electrolytes as well as for different gel concentrations. It is clear from Figure 1 that the speed of the pulse increases when the difference between the inner and outer concentrations, which we denote as δ, increases. The pulse continues to move down the tube with increasing width, leaving behind a blue gel region due to the formation of the ammonia complex Ni(NH3)n2+ (eq 2). As the pulse reaches about half the tube, a hazy solid region above it starts forming. The haze region is separated from the pulse region by a clear gel region a few millimeters wide, which means that the transition occurs away from the pulse. As time progresses, the haze region develops into multiple bands. Different experiments are carried out in which we fix the inner concentration (0.2 M) and vary the outer concentrations (1.75, 3.5, 7, and 14 M), as shown in Figure 3. It is also clear that the speed of the pulse increases with an increasing δ; however, the width of the pulse looks similar for the four tubes. This indicates that although the precipitation rate is increasing when δ increases, the rate of dissolution due to excess ammonia is also increasing, leading to a similar width of the pulse. The number of bands depends on the concentration difference of inner and outer electrolyte, as clearly seen in the tubes in Figure 3 where multiple bands appear in the region above the pulse after 72 h. Fully developed bands might take a few days to be achieved. The transition to bands occurs faster when δ is larger. Although the leading pulse continues its path down the tube, those newly formed bands appear to be static and do not change location once they are formed. Power Laws. To characterize the dynamics of the observed pulse and bands, three different initial concentrations of Ni2+ (0.2, 0.3, and 0.4 M) were used, and the outer ammonia concentration was fixed at 14 M. The distance traveled by the propagating pulse, its width, and the mass content were measured directly after the addition of the outer electrolyte until after the formation of the static bands, when we also start measuring the mass of the solid in those bands. All distances are

Figure 3. Pulse propagation and band formation for different outer concentrations of ammonia as shown on the top of each tube in 0.5% agar with fixed inner concentration of Ni(II) ([Ni(II)] = 0.2 M). The snapshot is taken at time t = 72 h.

measured with respect to the marked gel−ammonia interface. The distance traveled by the pulse is defined as the distance between the tip of the pulse and this interface and is denoted by d. The log−log plot of d as a function of time, t, is shown in Figure 4a and reveals that the distance scales as d(t) ∼ tα with α close to 1/2 for all three inner concentrations. The distance traveled increases as δ increases, as expected. The width of the pulse, denoted by w, also exhibits a similar scaling law, w(t) ∼ tβ with β close to 1/2, as shown in Figure 4b. It is, however, worth noting that width of the propagating pulse is almost independent of the initial inner concentration of Ni2+, as seen in the overlapping parallel lines, indicating an excellent correlation between the formation of the precipitate and its dissolution. To see how the weight of the solid in the pulse and in the bands varies with time, the precipitates in the pulse and in the bands are collected over time and weighed. To do this, a set of identical tubes were prepared (all possess the same inner and outer concentrations). The gel containing the solid is periodically extracted from each tube. The regions containing the pulse and bands are cut, washed to remove the gel matrix, filtered, and dried. The solids are then dissolved in acid, and atomic absorption is used to determine the initial weight. Using this technique, we notice that the pulse gets enriched with the solid as it propagates in time and exhibits a power law of the form m(t) ∼ tγ, where m is the weight of the precipitate and γ is an exponent that depends on the difference, δ, as shown in Figure 4c. The rate of the precipitation reaction 9 , which is the time derivative of the m(t), thus scales like 9 (t) ∼ tγ−1. The exponent γ varies from 1/3 to 1/2 and is shown to increase toward 1/2 as δ is decreased. The evolution of the total mass of 4429

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Figure 4. Log−Log plots exhibiting scaling laws for pulse propagation of α-nickel hydroxide in agar for different inner concentrations of Ni(II) as shown in the legends. (a) Logarithm of distance traveled (d) vs logarithm of time (t). Slopes of the linear fits are 0.50 (0.2 M), 0.50 (0.3 M), and 0.53 (0.4 M). (b) Logarithm of the width of the pulse (w) vs logarithm of time (t). Slopes of the linear fits are 0.49 (0.2 M), 0.51 (0.3 M), and 0.49 (0.4 M). (c) Logarithm of the mass of the pulse (m) vs logarithm of time (t). Slopes of the linear fits are 0.48 (0.4 M), 0.44 (0.3 M), and 0.31 (0.2 M).

the bands is shown in Figure 5. It is interesting to see that the total mass exhibits oscillations in time indicating that, although the location of the bands is static, the bands are subject to a complicated continuous precipitation and redissolution processes. The mass oscillations in the bands that accompany the

pulse−bands transition can be understood using further spectroscopic and imaging experiments. Effect of the Gel. The same experiments were performed in gelatin instead of agar. In Figure 6, we observe similar propagation of a single green precipitate pulse; however, no transition to multiple static bands is observed for all the different inner, outer, and gel concentrations that we tried. This can be understood on the basis of the recent report by Lagzi and Ueyama,25 who proposed that in gelatin, due to its internal branching structure, a higher nucleation rate than that in agar leads to a large number of small crystals dispersed in the polymer matrix. Such a fast rate of nucleation favors a faster redissolution of the nuclei in ammonia due to their small size, hence inhibiting the transition to bands. In contrast, in agar, fewer nuclei are formed, and crystals are grown by successive aggregation, leading to a more continuous and homogeneous precipitation. Scaling laws are also obtained in this case and reveal a different type of dynamics, as shown in Figure 7. Although d scales in time with an exponent close to 1/2 as in the case of agar (Figure 7a), the scaling of the width, w, in this case is different, with an exponent β close to 0.6 (Figure 7b). In addition, w is shown to increase with δ, unlike the case of agar, for which it was independent of δ. The mass of the pulse also exhibits a power law, as shown in Figure 7c. The

Figure 5. Mass of the bands (excluding the mass of the pulse), m, as a function of time (t) for different inner concentrations. Fewer oscillations are obtained when the δ is decreased. 4430

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propagating pulse reveals the formation of the other polymorph of nickel hydroxide, α-Ni(OH)2 (JCPDS 22-444), as put forward by the presence of the peaks at 11.14 (003), 22.02 (006), 34.27 (101), 40.43 (015), and 60.14 (110). This polymorph is hydrotalcite-like27,28 with lattice parameters a = b = 3.10 Å and c = 23.81 Å. Due to the increase in interlayer spacing, this polymorph possesses an interesting interlayer and ion exchange dynamics, in which the counterion of the nickel ion initially present in the gel, which is regarded as spectator, now plays an important role and can alter the chemistry of the system, hence affecting the resulting band−pulse structure. The low crystallinity as well as the small crystallite sizes of the αpolymorph is expected to be the result of some disorder of the layers oriented along the c-axis, leading to a small number of parallel planes available for the diffraction, meaning that the αpolymorph is turbostratically crystallized. FTIR and UV−Vis Spectroscopy. The collected solids from the pulse and bands regions were also subject to FTIR measurements as described in the Experimental section. The FTIR spectra of the solids in the two regions are shown in Figure 9 and also confirm the XRD results regarding the existence of two different solid structures in the pulse and bands regions. Both spectra exhibit bands centered around 3240 cm−1, corresponding to the O−H stretching vibrations of the interlayer water molecules and hydrogen atoms bound to OH groups, but the sharp peak appearing at 3644 cm−1 which is attributed to the O−H stretching mode of the free Ni−OH groups is a clear indication of the existence of β-Ni(OH)2 in the bands.9,29 The bands appearing around 1624 cm−1 correspond to the water molecule deformation vibration. Peaks around 1094, 1145, and 1471 cm−1 are assigned to carbonate ions, whose existence could be due to the dissolution of dissolved carbon dioxide molecules in water. The spectra showed clearly that the charatcteristic peak at 3644 cm−1 is more intense in the β-Ni(OH)2 than in the α-Ni(OH)2. This difference in the peaks intensities could be due to the existence of a larger number of free OH in the charge-neutral nickel hydroxide layers than in the layers in the α-polymorph, where the OH group vibrations are expected to be lowered due to the existence of hydrogen bonding between the hydrogen atoms and the intercalated anions within the layers. The peaks appearing at low frequency (496 and 641 cm−1) are assigned to the bending vibration mode of the free Ni−OH groups in the brucite-like structure.9 The UV−vis spectra of all the species involved were also measured as shown in Figure 10. The spectrum of Ni2+ in agar gel exhibits maximum absorbance at wavelength 394 nm (not shown), and three weak peaks32 at 652, 688, and 722 nm. For the blue region where redissolution takes place, the UV−vis spectrum exhibits a maximum absorbance at 574 nm and a weak absorbance peak at 689 nm, which is consistent with the spectrum of the complex ion Ni(NH3)62+.32 On the other hand, the diffused reflectance spectra of the two solid compounds in the pulse and bands region were measured, and then the spectrum was converted to absorbance using the Kubelka− Munk equation. For the solids in the pulse, two bands were observed at 391 (not shown) and 668 nm, which is a characteristic absorption of tetrahedral nickel(II).30−32 For the solids in the bands region, similar peaks in the visible, albeit with smaller intensity, are obtained, which is indicative of the existence of octahedral nickel(II). SEM and TEM Imaging. SEM images of the solid material in the bands and pulse regions are taken. At first glance, both phases of Ni(OH)2, pulse and bands, have similar surface

Figure 6. Pulse propagation for different inner concentrations of Ni(II) as shown on the bottom of each tube in 5% gelatin at fixed outer ammonia concentration ([NH3] = 14 M). The snapshot is taken at time t = 48 h.

scaling exponent γ is shown to increase toward the value 1/2 as δ is decreased, similar to the case of agar. Microscopic Dynamics. After we characterized the macroscopic evolution of the system, which reveals complex spatiotemporal dynamics and transition from pulse to bands, we explored the microscopic transformations of the precipitate concomitant to the aforementioned alteration in an attempt to relate the two distinct scales. Therefore, we resorted to different spectroscopic and imaging techniques, which divulge an even greater complexity at the microscopic level, as shown in the following subsections. XRD Spectroscopy. The collected solids from the pulse and bands regions were subject to powder XRD measurements. The XRD data were measured in a 2θ range from 5 to 80° in steps of 0.100°. The powdered sample was mounted on the sample holder using double-sided celophane tape and a plastic slide. By coupling the chemical nature of the expected products to the positions and intensities of the diffraction peaks, we deduce by clear evidence the existence of nickel hydroxide crystals in two distinctive crystal structures for the powder in the pulse and the band regions, as shown in Figure 8. The powder in the band region corresponds to the polymorph β-Ni(OH)2, where the main peaks (and their corresponding plane assignments) are observed at 18.86 (001), 33.05 (100), 38.35 (101), 51.85 (102), 59.05 (110), 62.66 (111), 69.46 (103), and 72.65 (112). This polymorph is a brucite-like crystalline solid possessing hexagonal symmetry27,28 with calculated lattice parameters a = b = 3.13 Å and c = 4.70 Å. The XRD spectrum for the 4431

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Figure 7. Log−Log plots exhibiting scaling laws for pulse propagation of α-nickel hydroxide in gelatin for different inner concentrations of Ni(II), as shown in the legends. (a) Logarithm of distance traveled (d) vs logarithm of time (t). Slopes of the linear fits are 0.51 (0.2 M), 0.51 (0.3 M), and 0.50 (0.4 M). (b) Logarithm of the width of the pulse (w) vs logarithm of time (t). Slopes of the linear fits are 0.58 (0.2 M), 0.60 (0.3 M), and 0.60 (0.4 M). (c) Logarithm of the mass of the pulse (m) vs logarithm of time (t). Slopes of the linear fits are 0.44 (0.2 M), 0.46 (0.3 M), and 0.53 (0.4 M).

Figure 9. IR spectrum of the solid in the pulse (dashed line) region and in the bands region (solid line).

Figure 8. Powder XRD spectrum of the solid in the pulse region (below) and in the bands region (above). The peaks are assigned with the Miller indices as shown above.

complexing reagent34 or simply using a solution of nickel sulfate and NaOH.35 On the other hand, the pulse phase has an overall wavelike morphology, but the surface is budded with tiny spherical crystals with a narrow size distribution around 100 nm in diameter (Figure 12a, b, c). Upon closer inspection, these tiny spheres appear to be sputtered with tiny protrusions on the order of 10 nm or less (Figure 12d). Similar spherical shapes of nickel hydroxide were recently obtained by electrodeposition in Ni(NO3)2 aqueous solution.33 When looking at a sample from

morphology with intersecting platelets showing a smooth wavelike pattern. The bands phase shows smooth hexagonal platelets that are approximately 20 nm thick (Figure 11a, b). This phase has a porous structure with randomly sized pores that can be as small as 10 nm (Figure 11c). It is interesting to note that powders of single-crystalline β-Ni(OH)2 nanosheets with the hexagonal structure have been synthesized by the hydrothermal method at 200 °C using nickel acetate as the nickel source and aqueous ammonia as both an alkaline and 4432

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The spacing of these planes is measured and found to be ∼3 Å, in good agreement with the XRD results. The hexagonal crystals exhibit a perfectly ordered structure in which the measured interlayer spacing was 4.8 Å. This interplanar spacing is in excellent agreement with the results found in XRD. The pulse phase revealed the presence of spheres with a narrow size distribution and an average diameter of 100 nm (Figure 15a). A high-resolution scan of the pulse phase revealed that these spheres are composed of aggregated crystalline nanorods with an average diameter of 20 nm and an unknown length (Figure 15b). These nanorods seem to propagate from a central core outward until they reach a growth limit. A TEM scan of the phase in gelatin did show the presence of tiny spheres with uniform size distribution (Figure 16). The spheres are similar to those produced in the pulse phase. Nonetheless, structural information of these spheres was blurred and lost in the background due to the presence of gelatin. Mechanism. In this section, we attempt to propose a mechanism that describes the complex dynamics exhibited by the seemingly simple nickel hydroxide/ammonia Liesegang system. The detailed chemical processes as unveiled in the preceding sections in agar can now be recast as

Figure 10. UV−vis spectra of Ni(II) in agar gel (solid curve) and of the blue region containing the ammonium complex salts (dashed curve). The diffused reflectance spectra (dotted curve) of the two solids in the pulse and bands regions exhibit two transmittance peaks at 391 (not shown) and 668 nm.

the interface between the pulse and the bands, we can clearly see the coexistence of the two phases. In Figure 13, we can distinguish the smooth texture of the haze compared to the rough surface of the pulse as well as the difference in size between the particles of the two phases. This presents direct proof that one phase is being reconstructed out of another phase. A SEM scan of the Ni(OH)2 propagated in gelatin did not yield any useful information since we were not able to digest the gelatin and separate it from the phases. TEM images of the pulse and the bands phases that were propagated in Agar gel were clearly visible and distinguishable from one another. A high-resolution TEM of the bands phase shows the presence of parallel crystalline planes (Figure 14).

Ni 2 +(aq) + 2OH−(aq) → α ‐Ni(OH)2 (s) [pulse, spheres] (3)

(α , β)‐Ni(OH)2 (s) + 6NH3(l) → Ni(NH3)6 2 + (aq) + 2OH−(aq)

(4)

α ‐Ni(OH)2 (s) [pulse, sphere] → β ‐Ni(OH)2 (s) [bands, platelets]

(5)

On the other hand, in gelatin, we have the following chemical processes:

Figure 11. SEM image of the Ni(OH)2 haze phase. (a) A (×2000) magnification of the haze phase (scale bar, 10 μm). (b) A close-up (scale bar, 2 μm) of the haze revealing the presence of interlocking platelets. (c) A semiporous surface with pores as small as 10 nm (scale bar, 0.5 μm). 4433

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Figure 12. SEM of the pulse phase. (a) A (×2000) magnification view has a similar overall morphology when compared with the haze phase (scale bar, 10 μm). (b) A close-up (scale bar, 2 μm) of the surface reveals the presence of tiny spheres. (c) Zoom in (scale bar, 0.5 μm) on the spheres reveals their rough texture and an average size of 100 nm. (d) Further zoom in (scale bar, 0.2 μm) on the spheres reveals their rough texture and an average size of 100 nm.

Figure 13. A mixed phase of bands and pulse (scale bar, 2 μm).

Ni 2 +(aq) + 2OH−(aq) → α ‐Ni(OH)2 (s) [pulse, spheres] (6)

α‐Ni(OH)2 (s) + 6NH3(l) → Ni(NH3)6 2 + (aq) + 2OH−(aq)

Figure 14. High-resolution TEM of the bands phase (scale bar, 20 μm).

(7)

In a recent paper, Abi Mansour and Al-Ghoul37 investigated the initial and intermediate temporal dynamics of front propagation in the family of reactions (nA + mB →kC) with initially segregated reactants. Using perturbation techniques, they confirmed the previously obtained results that the center (d), width (w), and global reaction rate (9 ) of the front scale in the short time regime as t1/2 and that those scaling laws are independent of the stoichiometric coefficients n and m. In the

asymptotic regime,37 however, the following scaling, which depends on the stoichiometric coefficients, is found for n, m ≥ 1: for the center (d), d ∼ t1/2; for the width (w), w ∼ tβ, β = (n + m − 1)/2(n + m + 1); and for the global reaction rate (9 ), R ∼ t‑γ, γ = 2/(n + m + 1). The transition from early time scaling to asymptotic scaling depends on many parameters and might actually take a long time to be reached. In this work, it seems 4434

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Figure 15. TEM of the pulse phase. (a) The spheres are almost uniform in diameter. (b) A zoomed-in view of the spheres shows that they are formed of nanorods with 10 nm diameter aggregating to form a spherical structure that is almost 100 nm in diameter.

Figure 16. TEM of a pulse phase in gelatin gel. (a) The spheres are almost 50 nm in diameter (scale bar, 0.2 μm). (b) Zoom in with a scale bar of 50 nm.

that the subsequent ammonia front following the precipitation of the hydroxide is keeping the system in the early time regime and away from the asymptotic regime. This is deduced from the fact that both the center and width exponents (1/2) are the same as the theoretical prediction for the early time regime. On the other hand, the global rate scaling, which was found to range between 2/3 and 1/2, depending on δ (the exponent 1/2 is approached as δ increases), is also not far from the theoretical early time prediction of 1/2. Therefore, the dynamics of the leading pulse of an α-nickel hydroxide front in agar is simply described by the precipitation reaction Ni(aq) + 2OH−(aq) → α-Ni(OH)2(s). However, the dynamics of the transition to bands cannot be deduced using the previous analysis and will require further theoretical modeling of the system by incorporating nucleation, growth, and redissolution and by coupling these processes to the reaction-diffusion equations involving the initially separated reactants. This will be studied in the sequel to this work. In gelatin, on the other hand, the center of the front and the global reaction rate exhibit scaling exponents very close to the aforementioned theoretical value of 1/2. The global reaction rate exponent 1/2 is approached as δ decreases, a trend opposite to that of the agar case. However, the scaling exponent

for the width is consistently close to 0.6 and greater from the theoretical value of 1/2, which might indicate a more complex transformation in the reaction zone than a simple (m = 1, n = 2) type of reaction. Apparently, the dynamics of the system at the macroscopic level has an interesting underlying microscopic connection. The pulse region is made of small particles of α-nickel hydroxide (eq 3), with well-defined crystallinity as revealed by XRD, whose rate of formation depends on the supersaturation wave that is propagating down the tube. Microscopic imaging also reveals that those particles have a spherical morphology, which is also affected by the fast nucleation rate and also by the structure of the gel matrix. Close to the interface, the pulse redissolves by ammonia, leaving a blue region due to the formation of the ammonia nickel complex (eq 4), as revealed by UV−vis spectroscopy in Figure 10. As the pulse propagates farther, a polymorphic transition takes place, as confirmed by XRD and FTIR, whereby the αnickel hydroxide transforms to give rise to β-nickel hydroxide (eq 5), which appears first as a haze that later divides into bands that focus in space as time passes. This is also revealed in the mass oscillations in Figure 5, indicating a dissolution− reformation mechanism giving rise to the bands. There is not 4435

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only a polymorphic transformation between α- and β-nickel hydroxide, but also accompanying morphological transformations in which the aforementioned spheres in the pulse reappear as larger hexagonal platelets in the bands, as revealed by SEM. Such a behavior confirms the fact that Ostwald ripening38,39 is taking place in the gel during the transition between pulse and bands whereby larger crystalline β-Ni(OH)2 is formed at the expense of the smaller α-Ni(OH)2. The Ostwald ripening mechanism involves the reconstruction of octahedral Ni(II) in the layers from the tetrahedral ones existing in the hydrotalcite-like α-Ni(OH)2, as revealed in the UV−vis reflectance spectrum, which, in fact, involves the breaking and forming of bonds, proceeded by a dissolution− reformation process. All this also involves a morphological change of the crystals in the two phases, where smaller spheres are preferred in the α polymorph, whereas hexagonal plates are preferred in the β polymorph. Striking similarities are noticed between our mechanism and a recent and interesting study by Du et al.36 wherein the phase conversion in the presence of a NaOH solution of the hydrotalcite-like Co(OH)1.6Cl0.4·4H2O to β-Co(OH)2 has been studied using time-resolved, in situ, energy-dispersive X-ray diffraction (EDXRD), which allows monitoring largely spaced Bragg reflections. This compound is in principle similar to the α-Ni(OH)2 in the pulse. Using this technique, they found that there is a considerable activation energy for this conversion process (28.4 kJ mol−1) that is due to the reconstruction of octahedrally coordinated Co(II) in the brucite-like from the tetrahedrally coordinated Co(II) in the hydrotalcite-like αCo(OH)2. Furthermore, the in situ simultaneous small/wideangle X-ray scattering (SAXS/WAXS) showed that during this conversion, the number of particles during the reaction drops to a steady state, indicative of an Ostwald ripening phenomenon.36 In addition, the dependence of the rate of conversion on the concentration of NaOH was determined to be proportional to [NaOH]0.9 at 60 °C, with a rate constant k = 1.78 ± 0.14 × 103 s−1 and t1/2 = 990 s for [NaOH] = 1 M.36 A reaction order of 0.9 can be indicative of a complex chemical mechanism that might be responsible for the aforementioned deviations of the width exponent β from its theoretical value in the case of gelatin.

The dynamics of formation of the two phases is also worth investigating theoretically from the point of view of reaction− diffusion coupled to nucleation, growth, and competitive particle size formulation. This study is presented in the second manuscript of this series.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +961 1 350 000, ext 3970. Fax: +961 1 365 217. Email: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

This work is supported by the Lebanese National Council for Scientific Research and by the American University of Beirut Research Board. R. O. Al-Kaysi acknowledges the support of KSAU-HS/KAIMRC through Grants RC08/093 and RC10/ 104 and King Abdulaziz City for Science and Technology (KACST) through Grant AT-435-30.

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CONCLUSION We report a polymorphic transformation between α- and βNi(OH)2 during the transition from a propagating pulse to a static Liesegang band regime in the precipitation of nickel hydroxide in agar with redissolution in excess ammonia. This polymorphic transition is also accompanied by a change of morphology, as revealed by SEM and TEM. The system is shown to proceed through a continuous Ostwald ripening process that transforms one polymorph to the other, giving rise to an interesting propagating chemical pulse. The Ostwald ripening mechanism was confirmed using various microscopy techniques. The method sheds some light into the not very well understood phase conversion of the different polymorphs of nickel hydroxide. It will also help in understanding Ostwald ripening in these types of systems and how one can tailor the system to obtain certain crystal sizes and shapes. This gave us impetus to study the formation of nickel hydroxide in gelatin because this system might allow us to synthesize nanoparticles of α-Ni(OH)2. We are in this regard focusing on the control of the size of the nanoparticles and the evolution of its distribution. 4436

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