A Review on the Adsorption Isotherms and Design Calculations for the Optimization of Adsorbent Mass and Contact Time.

Adsorption is a widely used chemical engineering unit operation for the separation and purification of fluid streams. Typical uses of adsorption include the removal of targeted pollutants like antibiotics, dyes, heavy metals, and other small to large molecules from aqueous solutions or wastewater. To date several adsorbents that vary in terms of their physicochemical properties and costs have been tested for their efficacy to remove these pollutants from wastewater. Irrespective of the type of adsorbent, nature of the pollutant, or experimental conditions, the overall cost of adsorption depends directly on the adsorption contact time and the cost of the adsorbent materials. Thus, it is essential to minimize the amount of adsorbent and the contact time required. We carefully reviewed the attempts made by several researchers to minimize these two parameters using theoretical adsorption kinetics and isotherms. We also clearly explained the theoretical methods and the calculation procedures involved during the optimization of the adsorbent mass and the contact time. To complement the theoretical calculation procedures, we also made a detailed review on the theoretical adsorption isotherms that are commonly used to model experimental equilibrium data that can be used to optimize the adsorbent mass.

Pure Curcumin Spherulites from Impure Solutions via Nonclassical Crystallization.

Crystallization experiments performed with highly supercooled solutions produced highly pure (>99 wt %) and highly crystalline mesocrystals of curcumin from impure solutions (∼22% of two structurally similar impurities) in one step. These mesocrystals exhibited a crystallographic hierarchy and were composed of perfectly or imperfectly aligned nanometer-thick crystallites. X-ray diffraction and spectroscopic analysis confirmed that the spherulites are a new solid form of curcumin. A theoretical hypothesis based on particle aggregation, double nucleation, and repeated secondary nucleation is proposed to explain the spherulite formation mechanism. The experimental results provide, for the first time, evidence for an organic molecule to naturally form spherulites without the presence of any stabilizing agents. Control experiments performed with highly supercooled pure solutions produced spherulites, confirming that the formation of spherulites is attributed to the high degree of supercooling and not due to the presence of impurities. Likewise, control experiments performed with a lower degree of supercooling produced impure crystals of curcumin via classical molecular addition mechanisms. Collectively, these experimental observations provide, for the first time, evidence for particle-mediated crystallization as an alternate and efficient method to purify organic compounds.

Nanoporous Materials for the Onboard Storage of Natural Gas.

Climate change, global warming, urban air pollution, energy supply uncertainty and depletion, and rising costs of conventional energy sources are, among others, potential socioeconomic threats that our community faces today. Transportation is one of the primary sectors contributing to oil consumption and global warming, and natural gas (NG) is considered to be a relatively clean transportation fuel that can significantly improve local air quality, reduce greenhouse-gas emissions, and decrease the energy dependency on oil sources. Internal combustion engines (ignited or compression) require only slight modifications for use with natural gas; rather, the main problem is the relatively short driving distance of natural-gas-powered vehicles due to the lack of an appropriate storage method for the gas, which has a low energy density. The U.S. Department of Energy (DOE) has set some targets for NG storage capacity to obtain a reasonable driving range in automotive applications, ruling out the option of storing methane at cryogenic temperatures. In recent years, both academia and industry have foreseen the storage of natural gas by adsorption (ANG) in porous materials, at relatively low pressures and ambient temperatures, as a solution to this difficult problem. This review presents recent developments in the search for novel porous materials with high methane storage capacities. Within this scenario, both carbon-based materials and metal-organic frameworks are considered to be the most promising materials for natural gas storage, as they exhibit properties such as large surface areas and micropore volumes, that favor a high adsorption capacity for natural gas. Recent advancements, technological issues, advantages, and drawbacks involved in natural gas storage in these two classes of materials are also summarized. Further, an overview of the recent developments and technical challenges in storing natural gas as hydrates in wetted porous carbon materials is also included. Finally, an analysis of design factors and technical issues that need to be considered before adapting vehicles to ANG technology is also presented.

Salt Templating with Pore Padding: Hierarchical Pore Tailoring towards Functionalised Porous Carbons.

We propose a new synthetic route towards nanoporous functional carbon materials based on salt templating with pore-padding approach (STPP). STPP relies on the use of a pore-padding agent that undergoes an initial polymerisation/ condensation process prior to the formation of a solid carbon framework. The pore-padding agent allows tailoring hierarchically the pore-size distribution and controlling the amount of heteroatom (nitrogen in this case) functionalities as well as the type of nitrogen (graphitic, pyridinic, oxides of nitrogen) incorporated within the carbon framework in a single-step-process. Our newly developed STPP method offers a unique pathway and new design principle to create simultaneously high surface area, microporosity, functionality and pore hierarchy. The functional carbon materials produced by STPP showed a remarkable CO2 /N2 selectivity. At 273 K, a carbon with only micropores offered an exceptionally high CO2 adsorption capacity whereas a carbon with only mesopores showed promising CO2 -philicity with high CO2 /N2 selectivity in the range of 46-60 %, making them excellent candidates for CO2 capture from flue gas or for CO2 storage.

Co-adsorption of N2 in the presence of CH4 within carbon nanospaces: evidence from molecular simulations.

Molecular simulations were performed to study the separation of CH(4) and N(2) from mixtures of composition x(CH(4))/x(N(2)) = 5/95 and x(CH(4))/x(N(2)) = 10/90 at 50 bar and 298 K on prototype carbon materials with different pore structures. The studied carbon structures include a slit and a tubular pore, that represent the simplest form of activated carbon and carbon nanotubes, respectively, in addition to a realistic porous carbon model with disordered pore structure and a recently introduced carbon foam model, which has a three-dimensional pore structure. The results indicate that, depending on the pressure and composition, the pore structure influences both the CH(4)/N(2) selectivity and the adsorption behaviour of the fluid molecules. The selectivity was decided by the interactions between CH(4) and N(2) molecules within the pore structure, in addition to the solid-fluid interactions. The simulation results indicate that, at least for the case of activated carbons (slit and random pores), it would not be appropriate to predict the binary adsorption behaviour of methane and nitrogen by means of pure component information. Regardless of the pore structure, the simulation results indicate that carbon materials show a CH(4)/N(2) (thermodynamic) selectivity of only 2-3 up to 2 bar at 298 K, and above this pressure, at equilibrium, none of the carbon materials is adequate for the efficient separation of this mixture.

A site energy distribution function from Toth isotherm for adsorption of gases on heterogeneous surfaces.

A site energy distribution function based on a condensation approximation method is proposed for gas-phase adsorption systems following the Toth isotherm. The proposed model is successfully applied to estimate the site energy distribution of three pitch-based activated carbons (PA, PFeA and PBA) developed in our laboratory and also for other common adsorbent materials for different gas molecules. According to the proposed model the site energy distribution curves of the activated carbons are found to be exponential for hydrogen at 77 K. The site energy distribution of some of the activated carbon fibers, ambersorb, Dowex optipore, 13X Zeolite for different adsorbate molecules represents a quasi-Gaussian curve with a widened left hand side, indicating that most sites have adsorption energies lower than a statistical mean value.

On the effect of a non-ionic surfactant on the surface of sucrose crystals and on the crystal growth process by inverse gas chromatography.

The effect of Hodag CB6, a widely used non-ionic surfactant in sugar crystallization process, on the surface properties of sucrose was studied in detail by inverse gas chromatography (IGC) experiments. IGC experiments were performed with pure sucrose crystals, surfactant coated sucrose crystals, and crystals grown in the presence of surfactant at 313.05 and 323.05 K. The surfactant promotes the specific interactions with the polar probes. The sorption of basic, acidic and amphoteric probes onto pure and surfactant coated sucrose was found to be endothermic and in the case of neutral probes was found to be exothermic. The surfactant increases both the acidity and basicity of the sucrose surface with the latter effect being significant. The role of interfacial tension on the growth kinetics of sucrose crystals was studied using IGC for different surfactant concentrations. IGC results with the surfactant coated sucrose were used to interpret the thermodynamic effect of surfactants during the crystal growth process. The dispersive component of the surface energy, gamma(s)(D), of surfactant coated sucrose crystals was found to be lower than that of pure sucrose crystals and was found to be in the range of 33.49-35.27 mJ/m(2).

Comparison of various error functions in predicting the optimum isotherm by linear and non-linear regression analysis for the sorption of basic red 9 by activated carbon.

A comparison of linear and non-linear regression method in selecting the optimum isotherm was made to the experimental equilibrium data of basic red 9 sorption by activated carbon. The r(2) was used to select the best fit linear theoretical isotherm. In the case of non-linear regression method, six error functions namely coefficient of determination (r(2)), hybrid fractional error function (HYBRID), Marquardt's percent standard deviation (MPSD), the average relative error (ARE), sum of the errors squared (ERRSQ) and sum of the absolute errors (EABS) were used to predict the parameters involved in the two and three parameter isotherms and also to predict the optimum isotherm. Non-linear regression was found to be a better way to obtain the parameters involved in the isotherms and also the optimum isotherm. For two parameter isotherm, MPSD was found to be the best error function in minimizing the error distribution between the experimental equilibrium data and predicted isotherms. In the case of three parameter isotherm, r(2) was found to be the best error function to minimize the error distribution structure between experimental equilibrium data and theoretical isotherms. The present study showed that the size of the error function alone is not a deciding factor to choose the optimum isotherm. In addition to the size of error function, the theory behind the predicted isotherm should be verified with the help of experimental data while selecting the optimum isotherm. A coefficient of non-determination, K(2) was explained and was found to be very useful in identifying the best error function while selecting the optimum isotherm.

Isotherms and thermodynamics by linear and non-linear regression analysis for the sorption of methylene blue onto activated carbon: comparison of various error functions.

A comparison of linear and non-linear regression method in selecting the optimum isotherm was made to the experimental equilibrium data of methylene blue sorption by activated carbon. The r2 was used to select the best fit linear theoretical isotherm. In the case of non-linear regression method, six error functions, namely coefficient of determination (r2), hybrid fractional error function (HYBRID), Marquardt's percent standard deviation (MPSD), average relative error (ARE), sum of the errors squared (ERRSQ) and sum of the absolute errors (EABS) were used to predict the parameters involved in the two and three parameter isotherms and also to predict the optimum isotherm. For two parameter isotherm, MPSD was found to be the best error function in minimizing the error distribution between the experimental equilibrium data and predicted isotherms. In the case of three parameter isotherm, r2 was found to be the best error function to minimize the error distribution structure between experimental equilibrium data and theoretical isotherms. The present study showed that the size of the error function alone is not a deciding factor to choose the optimum isotherm. In addition to the size of error function, the theory behind the predicted isotherm should be verified with the help of experimental data while selecting the optimum isotherm. A coefficient of non-determination, K2 was explained and was found to be very useful in identifying the best error function while selecting the optimum isotherm.

Comments on "Biosorption of nickel from protonated rice bran".

This letter explains the appropriate way to calculate the parameters in pseudo first and second order kinetics, Langmuir and Freundlich isotherm.

Comments on "Removal of lead from aqueous solution using Syzygium cumini L.: equilibrium and kinetic studies".

This letter reports the importance and advantages of the constraints in the Redlich-Peterson isotherm exponent.

Comments on "Adsorption of 4-chlorophenol from aqueous solutions by xad-4 resin: isotherm, kinetic, and thermodynamic analysis".

This letter reports the importance and advantages of the constraints in the Redlich Peterson isotherm exponent.

Mass transfer, kinetics and equilibrium studies for the biosorption of methylene blue using Paspalum notatum.

Batch experiments were carried out for the sorption of methylene blue onto Paspalum notatum. The operating variables studied were initial dye concentration, initial solution pH, adsorbent dosage and contact time. Experimental equilibrium data were fitted to Freundlich, Langmuir and Redlich-Peterson isotherms by non-linear regression method. Six error functions was used to determine the optimum isotherm by non-linear regression method. The present study shows r2 as the best error function to determine the parameters involved in both two- and three-parameter isotherms. Langmuir isotherm was found to be the optimum isotherm for methylene blue onto P. notatum. The monolayer methylene blue sorption capacity of P. notatum was found to be 31 mg/g. The kinetics of methylene blue onto P. notatum was found to follow a pseudo second order kinetics. A Boyd plot confirms the external mass transfer as the rate-limiting step in the dye sorption process. The influence of initial dye concentration on the dye sorption process was represented in the form of dimensionless mass transfer numbers (Sh/Sc0.33) and was found to vary as C(0)-5x10(-6).

Pseudo-second order models for the adsorption of safranin onto activated carbon: comparison of linear and non-linear regression methods.

Kinetic experiments were carried out for the sorption of safranin onto activated carbon particles. The kinetic data were fitted to pseudo-second order model of Ho, Sobkowsk and Czerwinski, Blanchard et al. and Ritchie by linear and non-linear regression methods. Non-linear method was found to be a better way of obtaining the parameters involved in the second order rate kinetic expressions. Both linear and non-linear regression showed that the Sobkowsk and Czerwinski and Ritchie's pseudo-second order models were the same. Non-linear regression analysis showed that both Blanchard et al. and Ho have similar ideas on the pseudo-second order model but with different assumptions. The best fit of experimental data in Ho's pseudo-second order expression by linear and non-linear regression method showed that Ho pseudo-second order model was a better kinetic expression when compared to other pseudo-second order kinetic expressions.

Relation between some two- and three-parameter isotherm models for the sorption of methylene blue onto lemon peel.

Equilibrium uptake of methylne blue onto lemon peel was fitted to the 2 two-parameter isotherm models namely Freundlich and Langmuir and 3 six-parameter isotherm models namely Redlich-Peterson, Toth, Radke-Prausnitz, Fritz-Schluender, Vieth-Sladek and Sips isotherms by non-linear method. A comparison between two-parameter and three-parameter isotherms was reported. The best fitting isotherm was the Sips isotherm followed by Langmuir isotherm and Redlich-Peterson isotherm equation. Redlich-Peterson isotherm is a special case of Langmuir isotherm when the Redlich-Peterson isotherm constant g was unity. Radke-Prausnitz, Toth, Vieth-Sladek isotherm were the same when the Toth isotherm constant, n(T) and the Radke-Prausnitz isotherm, m(RP) are equal to unity and when the Vieth-Sladek isotherm constant, K(VS) equals zero. The sorption capacity of lemon peel for methylene blue uptake was found to be 29 mg/g.

Linear and non-linear regression analysis for the sorption kinetics of methylene blue onto activated carbon.

Batch kinetic experiments were carried out for the sorption of methylene blue onto activated carbon. The experimental kinetics were fitted to the pseudo first-order and pseudo second-order kinetics by linear and a non-linear method. The five different types of Ho pseudo second-order expression have been discussed. A comparison of linear least-squares method and a trial and error non-linear method of estimating the pseudo second-order rate kinetic parameters were examined. The sorption process was found to follow a both pseudo first-order kinetic and pseudo second-order kinetic model. Present investigation showed that it is inappropriate to use a type 1 and type pseudo second-order expressions as proposed by Ho and Blanachard et al. respectively for predicting the kinetic rate constants and the initial sorption rate for the studied system. Three correct possible alternate linear expressions (type 2 to type 4) to better predict the initial sorption rate and kinetic rate constants for the studied system (methylene blue/activated carbon) was proposed. Linear method was found to check only the hypothesis instead of verifying the kinetic model. Non-linear regression method was found to be the more appropriate method to determine the rate kinetic parameters.

Comments on "Equilibrium studies for the adsorption of acid dye onto modified hectorite".

The present letter discusses the significance of the dimensionless separation factor of solid/liquid adsorption systems. The present letter also explain citing the original paper for using the term separation factor 'R'.

Comparative analysis of linear and non-linear method of estimating the sorption isotherm parameters for malachite green onto activated carbon.

The experimental equilibrium data of malachite green onto activated carbon were fitted to the Freundlich, Langmuir and Redlich-Peterson isotherms by linear and non-linear method. A comparison between linear and non-linear of estimating the isotherm parameters was discussed. The four different linearized form of Langmuir isotherm were also discussed. The results confirmed that the non-linear method as a better way to obtain isotherm parameters. The best fitting isotherm was Langmuir and Redlich-Peterson isotherm. Redlich-Peterson is a special case of Langmuir when the Redlich-Peterson isotherm constant g was unity.