Typically, most adsorption processes follow the second-order kinetic model, and this is determined by the correlation coefficient (R2) and adsorption capacity. But in some cases, the correlation coefficient difference is minimal. In such cases, by using the error function, we can find out which model is the best fit. Therefore, with the help of the calculated adsorption capacity and theoretical adsorption capacity, compute the error function.

Thank you

You can use Bayesian Information Criteria to distinguish if these 2 kinetic models are different. Please write to [email protected]

Hi Rosa Soria ,

without having seen your data the reason for the minimal difference observed could also be due to the (inappropriate) sampling interval and frequency used. Have you carried out the adsorption kinetics at different concentrations? Bear in mind also that adsorption can be a multistage process where rapid adsorption onto outer surface is followed by diffusion-controlled sorption onto inner pore surfaces.

To me, theoretically, it is not possible that adsorption follows both 1st and 2nd order.

Check out following discussion in Researchgate: https://www.researchgate.net/post/What_is_the_difference_between_pseudo_first_and_second_order_reaction

Kind regards Rob.

PS: Send my regards to Joby Boxall.

Dear Rosa,

What kind of heavy metal did you work on? If it is As or rare earth metal, i suggest you repeat your experiment in replicates with the appropriate adsorbent dose and apply the non-linear form of the kinetics equation on the average experimental data. If the heavy metal is none of the above, my best bet will be to increase the adsorbate concentration and perform the kinetics experiment again. The adsorbate concentration you choose must give a reasonable removal efficiency. Biochars as a metal adsorbent conveniently correspond to the appropriate kinetic mode if the experimental conditions are right. Good luck.

Hello Rosa Soria,@

Even though they might look similar when fitted to your data,, they represents different perspectives of the mechanisms that is ruling the process. I suggests, you look into the process not just to the kinetics models, you should also look closely to some intra particle diffusion, thermodynamic and FTIR in order to better understand the interaction between the absorbent and the metals. Therefore, you may assure whether it is a chemisorption or physisorption process, which are directly related to 1st and 2nd order, respectively.

Although they might look similar but they represent two different approaches and the model with higher correlation coefficient, minimal standard error of estimation and similar Qe calculated and experimental is governing the adsorption phenomenon. Please check this paper Article Ultrasonic-assisted synthesis of polyacrylamide/bentonite hy...

Dear Rosa Soria,

The adsorption kinetic models, namely, the pseudo-first-order, pseudo-second-order, are useful for determining whether physical or chemical adsorption process. If the pseudo-first-order model provided better fit result, then the adsorption is a physical process; while the pseudo-second-order model fits better, then it is chemical adsorption. The validity of these models are evaluated by the coefficient of regression, R2, which varies between 0 to 1, and by the normalized standard deviation Δq (%).

You can refer to the following article for non-linear fiting of kinetic models:

https://www.sciencedirect.com/science/article/abs/pii/S2213343719300703

Hope it helps.

There is no correlation of pseudo-first-order, pseudo-second-order kinetic models with physical adsorption and chemical adsorption. This is an error committed throught the literature. The order of a kinetics just indicates if the process present dq/dt with n=1 or n=2. The physical and chemical adsorption will depends on the chemical nature of adsorbent and sorbing specie.

@

First order and second order kinetic models are actually an exponential function and a hyperbolic function. These are two mathematically different functions, but their course (for the same parameter values) is similar. For this reason and due to measurement errors, discrimination between these functions is usually not possible. It is worth asking, however, if it is needed?

Sinan Kutluay You wrote that "The adsorption kinetic models, namely, the pseudo-first-order, pseudo-second-order, are useful for determining whether physical or chemical adsorption process." Can you prove it? I would like to know such proof.

Eder Lima You are absolutely right that "There is no correlation of pseudo-first-order, pseudo-second-order kinetic model ........". However, you confuse the order of the process (kinetics) with the order (degree) of the right side of the differential equations: dq/dt=k1(qe-q) and dq/dt=k2(qe-q)2. In addition, the so-called PFO and PSO is a flight of imagination of Ho and McKay. It is good to stop spreading this nonsense.