Studies in generalized hydrodynamics for chemical reactions and shock waves

This thesis is made of two parts. In the first part, we study pattern formations and dissipation of energy and matter by using hyperbolic reaction-diffusion equations for reacting systems. Two-dimensional hyperbolic reaction-diffusion equations are numerically solved for the Selkov model and the Brusselator. It is shown that the evolution equations used can give rise to various kinds of patterns such as hexagonal structures, stripes, maze structures, chaotic structures, etc., depending on the values of the reaction-diffusion number and the initial and boundary conditions. The values of the entropy production computed indicate that the system maintains the particular organized local structures at the expense of energy and matter. However, when the system produces a chaotic pattern, the entropy production is lower than the locally organized structures. The phase speed of travelling oscillating chemical waves can be obtained from the linearized hyperbolic reaction-diffusion equations. The Luther-type speed formula is obtained in the lowest order approximation in the case of the Brusselator. The two-dimensional power spectra computed for chaotic patterns still preserve some kind of symmetry.In the second part of this thesis, the generalized hydrodynamics is applied to calculate the shock profiles, shock widths, and calortropy production for a Maxwell gas. Shock solutions are shown to exist for all Mach numbers. This is in contrast to the Grad moment equation method which does not admit shock solution for $N sb{M} ge 1.65$ and to the method of Anile and Majorana which breaks down for $N sb{M} ge 2.09.$ The energy dissipation in the shock is shown to increase with the Mach number as a power law of the form $(N sb{M} - a) sp{ alpha}$ where a and $alpha$ are real constants

Superdiffusive Cusp-Like Waves in the Mercuric Iodide Precipitate System and Their Transition to Regular Reaction Bands

We report a two-dimensional (2D) reaction–diffusion system that exhibits a superdiffusive propagating wave with anomalous cusp-like contours. This wave results from a leading precipitation reaction (wavefront) and a trailing redissolution (waveback) between initially separated mercuric chloride and potassium iodide to produce mercuric iodide precipitate (HgI₂) in a thin sheet of a solid hydrogel (agar) medium. The propagation dynamics is accompanied by continuous polymorphic transformations between the metastable yellow crystals and the stable red crystals of HgI₂. We study the dynamics of wavefront and waveback propagation that reveals interesting anomalous superdiffusive behavior without the influence of external enhancement. We find that a transition from superdiffusive to subdiffusive dynamics occurs as a function of outer iodide concentration. Inner mercuric concentrations lead to the transition from the anomalous cusp-like to cusp-free regular bands. While gel concentration affects the speed of propagation of the wave, it has no effect on its shape or on its superdiffusive dynamics. Microscopically, we show that the macroscopic wave propagation and polymorphic transformations are accompanied by an Ostwald ripening mechanism in which larger red HgI₂ crystals are formed at the expense of smaller yellow HgI₂ crystals

Superdiffusive Cusp-Like Waves in the Mercuric Iodide Precipitate System and Their Transition to Regular Reaction Bands

We report a two-dimensional (2D) reaction–diffusion system that exhibits a superdiffusive propagating wave with anomalous cusp-like contours. This wave results from a leading precipitation reaction (wavefront) and a trailing redissolution (waveback) between initially separated mercuric chloride and potassium iodide to produce mercuric iodide precipitate (HgI₂) in a thin sheet of a solid hydrogel (agar) medium. The propagation dynamics is accompanied by continuous polymorphic transformations between the metastable yellow crystals and the stable red crystals of HgI₂. We study the dynamics of wavefront and waveback propagation that reveals interesting anomalous superdiffusive behavior without the influence of external enhancement. We find that a transition from superdiffusive to subdiffusive dynamics occurs as a function of outer iodide concentration. Inner mercuric concentrations lead to the transition from the anomalous cusp-like to cusp-free regular bands. While gel concentration affects the speed of propagation of the wave, it has no effect on its shape or on its superdiffusive dynamics. Microscopically, we show that the macroscopic wave propagation and polymorphic transformations are accompanied by an Ostwald ripening mechanism in which larger red HgI₂ crystals are formed at the expense of smaller yellow HgI₂ crystals

Crystal Growth of ZIF-8, ZIF-67, and Their Mixed-Metal Derivatives

A facile method to produce zeolitic imidazolate frameworks (ZIF-8, ZIF-67, and solid–solution ZIFs (mixed Co and Zn)) is reported. ZIF crystals are produced via a reaction–diffusion framework (RDF) by diffusing an outer solution at a relatively high concentration of the 2-methyl imidazole linker (HmIm) into an agar gel matrix containing the metal ions (zinc­(II) and/or cobalt­(II)) at room temperature. Accordingly, a propagating supersaturation wave, initiated at the interface between the outer solution and the gel matrix, leads to a precipitation front with a gradient of crystal sizes ranging between 100 nm and 55 μm along the reaction tube. While the precipitation fronts of ZIF-8 and ZIF-67 travel the same distance for the same initial conditions, ZIF-8 crystals therein are consistently smaller than the ZIF-67 crystals due to the disparity of their rate of nucleation and growth. The effects of the temperature, the concentration of the reagents, and the thickness of the gel matrix on the growth of the ZIF crystals are investigated. We also show that by using RDF we can envisage the formation mechanism of the ZIF crystals, which consists of the aggregation of ZIF nanospheres to form the ZIF-8 dodecahedrons. Moreover, using RDF, the formation of a solid–solution ZIF via the incorporation of Co­(II) and Zn­(II) cations within the same framework is achieved in a controlled manner. Finally, we demonstrate that doping ZIF-8 by Co­(II) enhances the photodegradation of methylene blue dye under visible light irradiation in the absence of hydrogen peroxide

Crystal Growth of ZIF-8, ZIF-67, and Their Mixed-Metal Derivatives

A facile method to produce zeolitic imidazolate frameworks (ZIF-8, ZIF-67, and solid–solution ZIFs (mixed Co and Zn)) is reported. ZIF crystals are produced via a reaction–diffusion framework (RDF) by diffusing an outer solution at a relatively high concentration of the 2-methyl imidazole linker (HmIm) into an agar gel matrix containing the metal ions (zinc­(II) and/or cobalt­(II)) at room temperature. Accordingly, a propagating supersaturation wave, initiated at the interface between the outer solution and the gel matrix, leads to a precipitation front with a gradient of crystal sizes ranging between 100 nm and 55 μm along the reaction tube. While the precipitation fronts of ZIF-8 and ZIF-67 travel the same distance for the same initial conditions, ZIF-8 crystals therein are consistently smaller than the ZIF-67 crystals due to the disparity of their rate of nucleation and growth. The effects of the temperature, the concentration of the reagents, and the thickness of the gel matrix on the growth of the ZIF crystals are investigated. We also show that by using RDF we can envisage the formation mechanism of the ZIF crystals, which consists of the aggregation of ZIF nanospheres to form the ZIF-8 dodecahedrons. Moreover, using RDF, the formation of a solid–solution ZIF via the incorporation of Co­(II) and Zn­(II) cations within the same framework is achieved in a controlled manner. Finally, we demonstrate that doping ZIF-8 by Co­(II) enhances the photodegradation of methylene blue dye under visible light irradiation in the absence of hydrogen peroxide

Dynamics and Mechanism of Intercalation/De-Intercalation of Rhodamine B during the Polymorphic Transformation of the CdAl Layered Double Hydroxide to the Brucite-like Cadmium Hydroxide

We studied the kinetics of intercalation of a fluorescent probe (rhodamine B (RhB)) during the formation of hierarchal microspheres of cadmium–aluminum layered double hydroxide (CdAlA LDH) and its de-intercalation upon transformation from the LDH phase into the cadmium hydroxide β phase (Cd­(OH)₂) using a reaction-diffusion framework (RDF) where the hydroxide anions diffuse into an agar gel matrix containing the proper salts–fluorescent probe mixture. In this framework, we achieved the stabilization of the CdAlA LDH, which is known to be thermodynamically unstable and transforms into Cd­(OH)₂ and Al­(OH)₃ in a short period. RDF is advantageous as it allows with ease the extraction of the cosynthesized polymorphs and their characterization using X-ray diffraction (XRD), differential scanning calorimetry (DSC), thermal gravimetric analysis (TGA), solid-state nuclear magnetic resonance (SSNMR), Fourier transform infrared (FT-IR), and energy dispersive X-ray (EDX). The kinetics of inter/de-intercalation is studied using <i>in situ</i> steady-state fluorescence measurements. The existence of RhB between the LDH layers and its expel during the transition into the β phase are examined via fluorescence microscopy, XRD, and SSNMR. The activation energies of intercalation and de-intercalation of RhB are determined and show dependence on the cationic ratio of the corresponding LDH. We find that the energies of de-intercalation are systematically higher than those of intercalation, indicating that the dyes are stabilized due to the probe–brucite sheets interactions. SSNMR is used to shed light on the mechanism of intercalation and stabilization of RhB inside the layers of the LDH

Metal–Organic Framework-74 for Ultratrace Arsenic Removal from Water: Experimental and Density Functional Theory Studies

This study investigates and compares arsenic, As­(V), removal from aqueous media using the water-stable zinc metal–organic frameworks (Zn-MOF-74) prepared via room-temperature precipitation (RT-Zn-MOF-74) and a solvothermal procedure (HT-Zn-MOF-74). The Zn-MOF-74 crystals possess average particle sizes of 66 nm and 144 μm for RT-Zn-MOF-74 and HT-Zn-MOF-74, respectively. Moreover, nanosized RT-Zn-MOF-74 exhibited a superior performance to HT-Zn-MOF-74. While the Brunauer–Emmett–Teller surface area of RT-Zn-MOF-74 was smaller than that of HT-Zn-MOF-74, higher adsorption uptake took place on the room-temperature-synthesized ones because of their small particle size and better dispersion. Adsorption isotherm studies showed that the Langmuir isotherm was effective for the adsorption of As­(V) onto RT-Zn-MOF-74 and HT-Zn-MOF-74 with maximum adsorption uptake (<i>q</i>_max) values of 99.0 and 48.7 mg g^–1, respectively. These values exceed most reported maximum adsorption capacities at neutral pH. The thermodynamics of adsorption revealed a spontaneous endothermic process that is due to the substitution of adsorbed water molecules by arsenate in the pores of the MOF crystal. This was further investigated using plane-wave density functional theory calculations. This study constitutes direct evidence for the importance of tuning the size of the MOF crystals to enhance their properties