Bangham Model Research Articles

Equilibrium and kinetics study on hexavalent chromium adsorption onto diethylene triamine grafted glycidyl methacrylate based copolymers

Two porous and one non-porous crosslinked poly(glycidyl methacrylate-co-ethylene glycol dimethacrylate) [abbreviated PGME] were prepared by suspension copolymerization and functionalized with diethylene triamine [abbreviated PGME-deta]. Samples were characterized by elemental analysis, mercury porosimetry, scanning electron microscopy with energy-dispersive X-ray spectroscopy, and transmission electron microscopy. Kinetics of Cr(VI) sorption by PGME-deta were investigated in batch static experiments, in the temperature range 25–70°C. Sorption was rapid, with the uptake capacity higher than 80% after 30min. Sorption behavior and rate-controlling mechanisms were analyzed using five kinetic models (pseudo-first order, pseudo-second order, Elovich, intraparticle diffusion and Bangham model). Kinetic studies showed that Cr(VI) adsorption adhered to the pseudo-second-order model, with definite influence of pore diffusion. Equilibrium data was tested with Langmuir, Freundlich and Tempkin adsorption isotherm models. Langmuir model was the most suitable indicating homogeneous distribution of active sites on PGME-deta and monolayer sorption. The maximum adsorption capacity from the Langmuir model, Qmax, at pH 1.8 and 25°C was 143mgg−1 for PGME2-deta (sample with the highest amino group concentration) while at 70°C Qmax reached the high value of 198mgg−1. Thermodynamic parameters revealed spontaneous and endothermic nature of Cr(VI) adsorption onto PGME-deta.

Adsorption studies of arsenic on nano aluminium doped manganese copper ferrite polymer (MA, VA, AA) composite: Kinetics and mechanism

Aluminium doped nano manganese copper ferrite (average size of 13nm) was synthesized by the chemical co-precipitation method and nanocomposite was prepared by doping this ferrite in methacrylate, vinyl acetate and acrylic acid polymer through slow heating process. This nanocomposite was used as an adsorbent for the removal of arsenic from aqueous solution. The equilibrium data was fitted to Freundlich, Langmuir, Dubinin Rudushkevish and Flory Huggins models. The maximum adsorption capacity (qm) of arsenic on the nanocomposite was found to be 0.053mgg−1 which is higher than that of many other adsorbents reported in literature. Mean sorption energy obtained from DR isotherm was 40.98kJmol−1 indicating chemical nature of the adsorbate–adsorbent interactions. The pseudo-second order kinetic model gave a better fit to the experimental data indicating involvement of both the external as well as internal mass transfer. Bangham's model and intraparticle diffusion model were applied to investigate mechanism of the adsorption process. Non linear Bangham plot and significant value of intercept obtained from intraparticle diffusion model showed the film diffusion as well as pore diffusion to be the rate limiting steps.

Adsorptive separation of Ginsenoside from aqueous solution by polymeric resins: Equilibrium, kinetic and thermodynamic studies

The adsorption behaviour of Ginsenoside from aqueous solution onto polymeric resins such as XAD-4, XAD-7, XAD-16 and XAD-1180 was studied. Adsorption isotherms were interpreted from various isotherm models like Langmuir, Freundlich, Redlich–Peterson, Dubinin–Radushkevich and Temkin and their parameters were evaluated and compared. The adsorption kinetics was analyzed using series of rate equations like first-order rate equation, second-order rate equation, Bangham's model, Intra-particle diffusion model, Boyd's diffusivity model and Elovich kinetic equation. The adsorption performance was investigated thermodynamically under batch equilibrium conditions at 293, 298, 303 and 308 K. The optimum temperature of adsorption was observed to be 298 K. Studies of external mass transfer and pore diffusion effects revealed that both film and pore diffusion play significant role in different extent and stages of contact in the sorption process. The adsorption efficiency and uptake rates of Ginsenoside were compared and the highest adsorption efficiency was observed with XAD-7 (>90%). The removal effectiveness is in order of XAD-7 > XAD-16 > XAD-1180 > XAD-4. The rate of Ginsenoside removal better follows pseudo-second-order rate kinetic model, corroborating high correlation coefficients for calculated parameters with the experimental data.

ZnCl2-Modified Activated Carbon from Biomass Coir Pith for the Removal of 2-Chlorophenol by Adsorption Process

ABSTRACT Coir pith, a waste biomass, from coconut coir industry was used to prepare activated carbon with ZnCl2 and employed for the removal of 2-chlorophenol (2-CP) from aqueous solution and wastewater. Zinc chloride–activated coir pith carbon (ZnCPC) was prepared by mixing coir pith with ZnCl2 in the ratio 2:1 and carbonized at 700°C for 1 h. ZnCPC was characterized using standard physicochemical methods, Brunaver, Emmett, and Teller (BET) surface area, and scanning electron microscopy (SEM) studies. Batch mode adsorption studies were carried out to evaluate the effect of contact time, initial concentration, adsorbent dose, pH, and temperature. The Langmuir adsorption capacity Q 0 was found to be 149.3 mg g−1. Kinetic studies showed that the adsorption obeyed second-order and Bangham's model. Equilibrium adsorption data fit better into Langmuir, Freundlich, and D-R isotherms. pH effect and desorption studies showed that ion-exchange mechanism was involved in the adsorption process. Effect of temperature was not significant. Quantitative removal of 2-CP from synthetic wastewater was also achieved. ZnCPC is economically effective compared to commercial activated carbon, because the raw material is abundantly and freely available and it can be used effectively in the treatment of water contaminated with 2-CP.

Bifurcation analysis of the Nowak–Bangham model in CTL dynamics

This paper investigates the local bifurcations of a CTL response model published by Nowak and Bangham [M.A. Nowak, C.R.M. Bangham, Population dynamics of immune responses to persistent viruses, Science 272 (1996) 74]. The Nowak–Bangham model can have three equilibria depending on the basic reproduction number, and generates a Hopf bifurcation through two bifurcations of equilibria. The main result shows a sufficient condition for the interior equilibrium to have a unique bifurcation point at which a simple Hopf bifurcation occurs. For this proof, some new techniques are developed in order to apply the method established by Liu [W.M. Liu, Criterion of Hopf bifurcations without using eigenvalues, J. Math. Anal. Appl. 182 (1) (1994) 250]. In addition, to demonstrate the result obtained theoretically, some bifurcation diagrams are presented with numerical examples.

Liquid‐phase separation of reactive dye by wood‐rotting fungus: A biotechnological approach

The live and pretreated mycelial pellets/biomass of Trametes versicolor was used for the biosorption of a textile dye, reactive blue MR (RBMR) from aqueous solution. The parameters that affect the biosorption of RBMR, such as contact time, concentration of dye and pH, on the extent of RBMR adsorption were investigated. To develop an effective and accurate design model for removal of dye, adsorption kinetics and equilibrium data are essential basic requirements. Lagergren first-order, second-order and Bangham's model were used to fit the experimental data. Results of the kinetic studies showed that the second order kinetic model fitted well for the present experimental data. The Langmuir, Freundlich and Temkin adsorption models were used for the mathematical description of the biosorption equilibrium. The biosorption equilibrium data obeyed well for Langmuir isotherm and the maximum adsorption capacities were found to be 49.8, 51.6, 47.4 and 46.7 mg/g for live, autoclaved, acid- and alkali-pretreated biomass. The dye uptake capacity order of the fungal biomass was found as autoclaved > live > acid-treated > alkali-pretreated. The Freundlich and Temkin models were also able to describe the biosorption equilibrium on RBMR on live and pretreated fungal biomass. Acidic pH was favorable for the adsorption of dye. Studies on pH effect and desorption show that chemisorption seems to play a major role in the adsorption process. On comparison with fixed bed adsorption, batch mode adsorption was more efficient in adsorption of RBMR.

Experimental and Isothermal Studies on Sorption of Congo Red by Modified Mycelial Biomass of Wood‐rotting Fungus

AbstractBatch biosorption experiments were carried out for the removal of Congo red from aqueous solution using native and pretreated mycelial pellets/biomass of Trametes versicolor. The effect of process parameters such as contact time, dye concentration, and pH on the extent of Congo red biosorption has been investigated. Higher dye concentrations resulted in lower biosorption. Increases in biomass dosage led to increases in the levels of biosorption. Biosorption kinetics and equilibrium data are essential basic requirements to develop an effective and accurate design model for the removal of the dye. A kinetic study showed that the biosorption of the dye on fungal biomass was a gradual process. Pseudo‐first‐order, pseudo‐second‐order, and Bangham's model were used to fit the experimental data. The results of the kinetic studies showed that the second‐order kinetic model fitted well for the present experimental data. Equilibrium isotherms were analyzed by Langmuir, Freundlich, Dubnin‐Radushkevich, and Temkin isotherms. The biosorption equilibrium data obeyed the Langmuir and Temkin isotherms well. Acidic pH was favorable for the biosorption of the dye. Studies on the pH effect and desorption show that chemisorption seems to play a major role in the biosorption process. Among the native and pretreated biomass studied, autoclaved biomass showed a better biosorption capacity.

Analysis of adsorption characteristics of 2,4-dichlorophenol from aqueous solutions by activated carbon fiber

In this study experiments were conducted to investigate the adsorption of 2,4-dichlorophenol (2,4-DCP) by activated carbon fiber (ACF) activated by static air. With the results of batch experiments at various temperatures, the adsorption isotherms, kinetics and thermodynamics of this adsorption process were evaluated. Four adsorption isotherm models, Langmuir, Freundlich, Redlich-Peterson and Toth equations, were used to fit the experimental data and the results reveal that the adsorption isotherm models fitted the data in the order of: Langmuir > Redlich-Peterson > Toth > Freundlich isotherms. A pseudo second-order adsorption model was better to describe the adsorption data than the pseudo first-order model and the Bangham model at the temperatures tested. The activation energy was calculated to be 40.90 kJ/mol, while the thermodynamic parameters Δ H and Δ S were estimated to be −5.82 kJ/mol and 0.07 kJ/(mol K), respectively.