The heating or cooling of a solid sphere in a well-stirred fluid

Frequency controlled agglomeration of pt-nanoparticles in sonochemical synthesis

Optimizing the surface area of nanoparticles is key to achieving high catalytic activities for electrochemical energy conversion devices. In this work, the frequency range (200 kHz-500 kHz) for maximum sonochemical radical formation was investigated for the sonochemical synthesis of Pt-nanoparticles to assess whether an optimum frequency exists or if the entire range provides reproducible particle properties. Through physical and electrochemical characterization, it was found that the frequency dependent mechanical effects of ultrasound resulted in smaller, more open agglomerates at lower frequencies with agglomerate sizes of (238 ± 4) nm at 210 kHz compared to (274 ± 2) nm at 326 kHz, and electrochemical surface areas of (12.4 ± 0.9) m2g-1 at 210 kHz compared to (3.4 ± 0.5) m2g-1 at 326 kHz. However, the primary particle size (2.1 nm) and the catalytic activity towards hydrogen evolution, (19 ± 2) mV at 10mA cm2,remained unchanged over the entire frequency range. Highly reproducible Pt-nanoparticles are therefore easily attainable within a broad range of ultrasonic frequencies for the sonochemical synthesis route.

A Fractal-Based Correlation for Time-Dependent Surface Diffusivity in Porous Adsorbents

Fluid–solid adsorption processes are mostly governed by the adsorbate transport in the solid phase and surface diffusion is often the limiting step of the overall process in microporous materials such as zeolites. This work starts from a concise review of concepts and models for surface transport and variable surface diffusivity. It emerges that the phenomenon of hindered surface diffusion for monolayer adsorption, which is common in zeolites, and models able to fit a non-monotonic trend of surface diffusivity against adsorbate solid phase concentration, have received limited attention. This work contributes to the literature of hindered diffusion by formulating a time-dependent equation for surface diffusivity based on fractal dynamics concepts. The proposed equation takes into account the contributions of both fractal-like diffusion (a time-decreasing term) and hopping diffusion (a time-increasing term). The equation is discussed and numerically analyzed to testify its ability to reproduce the possible different patterns of surface diffusivity vs. time.

Experimental study of zeolitic diffusion by use of a concentration-dependent surface diffusion model

Surface diffusivity in adsorption and ion exchange processes is probably the most important property studied expensively in the literature but some aspects, especially its dependence on solid phase concentration, is still an open subject to discussion. In this study a new concentration-dependent surface diffusion model, equipped with a flexible double selectivity equilibrium relationship is applied on the removal of Pb²⁺, Cr³⁺, Fe³⁺ and Cu²⁺ from aqueous solutions using a natural zeolite. The model incorporates the Chen-Yang surface diffusivity correlation able to deal with positive and negative dependence with surface coverage. The double selectivity equilibrium relationship successfully represents the experimental equilibrium data, which follow Langmurian isotherm type for Pb²⁺, sigmoidal for Cr³⁺ and Fe³⁺ and linear for Cu²⁺. The concentration-dependent surface diffusion model was compared with the constant diffusivity surface diffusion model and found to be moderately more accurate but considerably more useful as it provides more insights into the diffusion mechanism. The application of the model resulted in an average deviation of 8.56 ± 6.74% from the experimental data and an average solid phase diffusion coefficients between 10⁻⁹ and 10⁻¹⁰ cm²/s. The results showed that the diffusion of metal ions in the zeolite structure is unhindered following the surface diffusion mass transfer mechanism.

Variable diffusivity homogeneous surface diffusion model and analysis of merits and fallacies of simplified adsorption kinetics equations

Adsorption and ion exchange phenomena are encountered in several separation processes, which in turn, are of vital importance across various industries. Although the literature on adsorption kinetics modeling is rich, the majority of the models employed are empirical, based on chemical reaction kinetics or oversimplified versions of diffusion models. In this paper, the fifteen most popular simplified adsorption kinetics equations are presented and discussed. A new versatile variable-diffusivity two-phase homogeneous diffusion model is presented and used to evaluate the analytical adsorption models. Aspects of ion exchange kinetics are also addressed.

Liquid/Solid Interfaces: Studies of Kinetics of Isotope Exchange

Many radiotracer methods based on the phenomenon of isotope exchange are used in the studies of interfaces. These methods enable an investigation of heterogeneous systems at equilibrium. Studies of the kinetics of isotope exchange also give valuable information about systems in which ions appearing in the solution are at the equilibrium state with the same ions adsorbed on the solid particles or built into their crystalline lattice. Such systems, in which the solids are either ionic crystals or ion-exchanger beads, are taken into account in the present paper. In spite of wide applications, the phenomenon of heterogeneous isotope exchange is rather poorly understood and the fragmentary results reported in the literature do not lead to unambigous conclusions concerning the mechanism of this phenomenon. In the present review, the theoretical models of isotope exchange are discussed and compared with experimental results. The results are also discussed with respect to enlargement of applications of isotope exchange to investigation of heterogeneous systems, e.g. containing porous solid particles.

A comparison of basic dye adsorption onto zeolitic materials synthesized from fly ash

This investigation reveals the adsorption characteristics of two basic dyes, thionine (TH) and safranine T (ST), onto fly ash (FA) and its three zeolitized products prepared at different hydrothermal conditions. Typical two-step isotherms were observed for TH adsorption onto four adsorbents, whereas the isotherms of the larger ST molecules were S-shaped. The adsorption capacities of the zeolitized fly ash (ZFA) estimated from the first plateau region of the TH isotherms was nearly twice the FA capacity. The capacities increased by up to five times in the second plateau region. The adsorption capacity of FA for ST is equivalent that of TH, whereas the capacities of ZFA are lower than those found for TH. The equilibrium results were well-described by the Freundlich isotherm model. The kinetic data obtained in the temperature range of 298-318 K was analyzed using Paterson's and Nernst Plank's approximations based on the homogeneous surface diffusion model (HSDM). The thermodynamic functions for the transition state were evaluated from the temperature-dependence of the surface diffusion coefficients by applying the Eyring model.