scholarly journals Analytical Continuation within the Freundlich Adsorption Model. Comment on Edet, U.A.; Ifelebuegu, A.O. Kinetics, Isotherms, and Thermodynamic Modeling of the Adsorption of Phosphates from Model Wastewater Using Recycled Brick Waste. Processes 2020, 8, 665

Processes ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 1251
Author(s):  
Michael Vigdorowitsch ◽  
Alexander N. Pchelintsev ◽  
Liudmila E. Tsygankova
Keyword(s):  
Experimental Data ◽  
Power Function ◽  
Thermodynamic Modeling ◽  
Mathematical Theory ◽  
Surface Adsorption ◽  
Analytical Continuation ◽  
Adsorption Model ◽  
Saturation Regime

Using experimental data for the adsorption of phosphates out of wastewater on waste recycled bricks, published independently in MDPI Processes before (2020), this message re-visits the mathematical theory of the Freundlich adsorption model. It demonstrates how experimental data are to be deeper treated to model the saturation regime and to bridge a chasm between those areas where the data fit the Freundlich power function and where a saturation of surface adsorption centers occurs.

scholarly journals Freundlich Isotherm: An Adsorption Model Complete Framework

2021 ◽  
Vol 11 (17) ◽  
pp. 8078
Author(s):  
Michael Vigdorowitsch ◽  
Alexander Pchelintsev ◽  
Liudmila Tsygankova ◽  
Elena Tanygina
Keyword(s):  
Experimental Data ◽  
Adsorption Process ◽  
Freundlich Isotherm ◽  
Organic Polymers ◽  
Adsorption Model ◽  
Saturation Regime ◽  
Porous Organic Polymers ◽  
Adsorbate Concentration ◽  
The Absolute ◽  
Complete Framework

The absolute majority of modern studies dealing with the interpretation of experimental data on the basis of the Freundlich isotherm ignore the fact that the data obtained for regions of low and moderate adsorbate concentration/pressure can be analytically continued within the Freundlich adsorption model to the adsorptive saturation area with coverages tending to 100%. Needless to say, this would give valuable extended information about the corresponding adsorption process. This message proposes a framework to comprehensively analyse experimental data first recognised as complying with the Freundlich adsorption model. An algorithm-driven method is presented which enables one to translate the data obtained in the area of small and moderate the coverages of the area of adsorptive saturation regime. As examples, three sets of experimental data for adsorption of mercury (II) on N-rich porous organic polymers and of protein on carrier nano-Mg(OH)2 have been processed and presented according to the framework developed.

scholarly journals Examination of current adsorption models for Pb(II) and Cu(II) adsorption onto Fe3O4@Mg2Al-NO3 Layered Double Hydroxide in aqueous solution

2017 ◽  
Vol 36 (1-2) ◽  
pp. 669-683 ◽  
Author(s):  
Ling-Xi Zhao ◽  
Ming-Chao Jiang ◽  
Ling-Yu Luan ◽  
Qing Li ◽  
Jing Zhang
Keyword(s):  
Experimental Data ◽  
Power Function ◽  
Layered Double Hydroxide ◽  
Equilibrium Adsorption ◽  
Metastable Equilibrium ◽  
Function Model ◽  
Adsorption Models ◽  
Surface Component ◽  
Double Hydroxide ◽  
Activity Equation

The adsorption of Pb(II) and Cu(II) onto Fe3O4@Mg2Al-NO3 Layered Double Hydroxide (LDH) as a function of Fe3O4@Mg2Al-NO3 LDH concentration was studied. An adsorbent concentration effect ( Cs effect), namely adsorption isotherm declines as adsorbent concentration ( Cs) increases, was observed. The experimental data were fitted to the adsorption models including the classic Freundlich model, the metastable-equilibrium adsorption theory, the flocculation model, the power function model, and the surface component activity model. The results show that the Freundlich-type metastable-equilibrium adsorption equation, the power function model, and the Freundlich-surface component activity equation can adequately describe the Cs effect observed in the batch adsorption tests as all the correlation coefficients ( R2) of the nonlinear plots are higher than 0.96. In other words, their intrinsic parameters simulated from the experimental data are independent of Cs value. It is considered that the Freundlich-surface component activity equation is the best model to describe the Cs effect of the studied adsorption systems by Akaike Information Criterion evaluation criterion.

Effect of pH on the ultrastructure of the conidial wall of Aspergillus niger aggregate conidia and its relationship to zearalenone adsorption

2016 ◽  
Vol 9 (3) ◽  
pp. 389-395
Author(s):  
C.M. Pereyra ◽  
L.R. Cavaglieri ◽  
V. Poloni ◽  
S.M. Chiacchiera ◽  
A. Cristofolini ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Experimental Data ◽  
Aspergillus Niger ◽  
Surface Adsorption ◽  
Theoretical Models ◽  
Dense Layer ◽  
Effect Of Ph ◽  
Transmission Electron ◽  
Conidial Surface ◽  
Chemical Groups

The purpose of the present study was to evaluate the effect of pH on the ultrastructure of the conidial wall of dead conidia harvested from the non-toxicogenic Aspergillus niger aggregate strain RC084 and its relationship to zearalenone (ZEA) adsorption capacity. Moreover, mathematical models were applied to explain the interaction between conidia and ZEA absorbance. A ZEA adsorption test was performed using a concentration of 1×107 dead conidia/ml at pH 2 and 6 at 37 °C for 30 min. Unbound ZEA was quantified by high-pressure liquid chromatography. The ZEA adsorption was strongly dependent on the pH of the medium; the highest values were 2.2×10-6 μg ZEA/conidia at pH 6. Isotherms representing the amount of bound ZEA as a function of ZEA concentration in equilibrium after adsorption have typical S- or L-shapes. The experimental data could be fitted to the Frumkin-Fowler-Guggenheim (FFG) and Hill theoretical models. The ultrastructure of the conidial wall was studied by infrared spectroscopy (IR) and transmission electron microscopy (TEM). The representative IR spectra showed that pH did not produce significant changes in the different chemical groups. However, ultrastructure studies by TEM detected considerable changes in the organisation of the conidial wall. This is the first study showing that the loss of the outermost electron dense layer, responsible for the ornamentations on the conidial surface. Adsorption is favoured at pH 6".

Adsorption of toluene from the mixed water−toluene system on medicinal activated carbon

2014 ◽  
Vol 92 (5) ◽  
pp. 392-396
Author(s):  
Igor Winkler ◽  
Volodymyr Diychuk
Keyword(s):  
Experimental Investigation ◽  
Activated Carbon ◽  
Adsorption Kinetics ◽  
Surface Adsorption ◽  
Equilibrium Concentration ◽  
Coal Surface ◽  
Adsorption Model ◽  
Insufficient Amount ◽  
Mixed Water ◽  
Kinetics Of

An experimental investigation of adsorption of toluene from the aqueous phase on medicinal activated carbon revealed that the process runs by the mechanism of preactivated adsorption. Kinetics of the initial stages of adsorption can be adequately represented by the empirical Elovich adsorption model. An insufficient amount of the adsorbent can cause an unexpected jump in the toluene equilibrium concentration in water caused by transferring this substance from the toluene phase into water through the process of additional adsorption on the coal surface. Adsorption constants and “imaginary” adsorption values have been determined for a series of toluene contents.

scholarly journals III . Mathematical contributions to the theory of evolution.—XII. On a generalised Theory of alternative Inheritance, with special reference to Mendel's laws

1904 ◽  
Vol 203 (359-371) ◽  
pp. 53-86 ◽  
Keyword(s):  
Experimental Data ◽  
General Theory ◽  
Special Reference ◽  
Mathematical Theory ◽  
Individual Case ◽  
Experimental Results ◽  
Theory Of Evolution ◽  
Original Theory ◽  
Growing Mass ◽  
Mendel’S Laws

It seems likely to be of interest at the present time to consider rather at length a fairly full mathematical theory of the pure gamete. We do not venture to call this theory a generalised Mendelian theory of inheritance, partly because it is not even the most general theory of the pure gamete conceivable, partly because Mendel’s original theory of heredity was perfectly clear and perfectly simple, and is not the theory here developed. The pure and simple Mendelian theory seems to have been discarded in the light of recent experimental results by more than one Mendelian, both in this country and abroad. The original Mendelian theory has been replaced by what are termed “ Mendelian Principles.” In this aspect of investigation the fundamental principles propounded by Mendel are given up, and for each individual case a pure gamete formula of one kind or another is suggested as describing the facts, This formula is then emphasised, modified or discarded, according as it fits well, badly, or not at all with the growing mass of experimental data. It is quite clear that it is impossible while this process is going on to term anything whatever Mendelian as far as theory is concerned.

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