# New Biosorbent Materials: Selectivity and Bioengineering Insights

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Selectivity

^{2+}> Cu

^{2+}> Zn

^{2+}was found [20]. Although biosorption for reclaiming single precious metal was frequently reported, the actual subsistent adsorptive competition among different metal ions sometimes shows diverging reinforcement or prohibition for different species. Another study tried to screen bacteria that are able to absorb certain precious metals with high selectivity under competitive conditions. For binary metal system, the adsorption parameters of extended-Langmuir model were modified by introducing a selectivity factor of the solute [21].

^{+}/H

^{+}/Cd

^{2+}or Na

^{+}/H

^{+}/Pb

^{2+}[22]. The selectivity coefficients of the Na-loaded algae increases in the following order: Na

^{+}< H

^{+}< Cd

^{2+}< Pb

^{2+}, which indicates that carboxylic and sulfonic groups have a higher preference (affinity) to Pb

^{2+}, followed by Cd

^{2+}, H

^{+}and Na

^{+}. The higher affinity of lead ion to sulfonic groups was attributed to the hard and soft acid and base theory. A mass transfer model, considering that the ion exchange limiting step is the intraparticle ion diffusion, was then able to fit the concentration profile of all ionic species at the liquid and solid phases.

#### 2.1. MIPs as Alternative Biosorbent Candidates

**Figure 1.**Example for the synthesis of Molecular Imprinted Polymers (MIPs) for capturing/binding dye molecules.

#### 2.2. Limitations

**Figure 2.**SEM micrographs of dye-MIPs using (

**a**) aqueous and (

**b**) organic solvent. Reproduced with permission from George Z. Kyzas [44], published by Elsevier, 2009.

**Figure 3.**Example for the synthesis of MIP for capturing/binding dye molecules. Reproduced with permission from Rosa A. Lorenzo [50], published by MDPI AG, 2011.

## 3. Isotherm Models

^{m}

_{t}) and the average affinity(K

_{0})); m is the Freundlich constant which represents the heterogeneity index and varies from zero to one (values approaching to zero indicate increasingly heterogeneity and one being homogeneous); C is the equilibrium concentration of template. The term B in Equation (2) was calculated from the simple mass balance equation as follows:

_{0}is the initial pollutant concentration, C is the pollutant concentration at equilibrium, V is the volume of and M is the mass of biosorbent. The linearized form of Equation (2) was obtained by taking log on both sides:

_{t}), using the general expression:

_{t}is the total number of accessible adsorption sites; C is the equilibrium concentration of template; K is the Langmuir isotherm equilibrium constant.

_{1}, N

_{1}and K

_{2}, N

_{2}) for the two classes of binding sites within the imprinted polymer can be obtained. The steeper line corresponds to the high-affinity sites while the flatter line measured the low-affinity ones.

_{t}is the total number of binding sites and K

_{0}is the median binding affinity):

_{0}via K

_{0}= a

^{1/}

^{m}. The fitting parameter “m” is identical to the heterogeneity index of site energies from the Freundlich isotherm. The difference between the L-F model and the Freundlich one is evident at high adsorbate concentrations, for which the L-F model is able to represent the saturation behavior. At low adsorbate concentrations, the L-F equation reduces to the classical Freundlich equation. On the other hand, as m approaches unity, indicative of a completely homogeneous adsorbent surface (i.e., energetic equivalence of all binding sites) the L-F equation reduces to the classical Langmuir equation. Thus, the hybridised L-F isotherm is able to model adsorption of solutes at high and low concentrations onto homogeneous and heterogeneous biosorbents. Although a linear analysis is not possible for a three-parameter isotherm, the L-F isotherm can be fitted to the experimental data following the method of Shimizu et al. [4,5] in which a solver function may be used to maximize the coefficient of determination (R

^{2}) by iteratively varying the three fitting parameters N

_{t}, a and m. R

^{2}is calculated from the sum of residuals (i.e., the difference between the experimental model and model-predicted bound concentrations).

#### 3.1. Examples

## 4. Affinity Distribution Analysis

_{min}− K

_{max}), the sum of all sites N

_{i}multiplied by the corresponding affinity constant, K

_{i}, is divided by the sum of N

_{i}, which is the total number of sites N Equation (9):

_{i}K

_{i}/∑N

_{i}= ∑N

_{i}K

_{i}/N

_{i}K

_{i}of the Equation (8) can be shifted using the integration of the number of binding sites with its corresponding association constant each time. When this is divided by the number of binding sites N from Equation (10), the number average association constant (K

_{av}) is obtained.

## 5. Kinetics

_{1}is the reaction rate constant [L × (mg

^{−1}of metal) × min

^{−1}]; C is the metal bulk concentration (mg·L

^{−1}). Subscripts 0 and t denote conditions at the beginning and any other instant (time, t) of the process, respectively; and the subscript e denotes equilibrium conditions.

_{2}is the reaction rate constant (min

^{−1}). When in the above treatment it is not necessarily q

_{e}to dictate the sorbate uptake then a pseudo 2nd order rate expression is more appropriate:

_{m}is the reaction rate constant [g of sorbent × (mg

^{−1}of metal) × min

^{−1}] and q

_{m}is a numerically determined parameter which under ideal 2nd order rate control corresponds to q

_{e}. It is noted that in the literature [92] various other kinetic equations have been attempted: zero, first (forward or reversible) order, Langmuir-Hinshelwood, Elovich-type, etc.

**Figure 4.**Comparison of experimental removal curves against theoretical predictions based: (

**a**) on the Ritchie 2nd order equation (at initial cadmium concentration of 5 mg·L

^{−1}) and (

**b**) on the pseudo 2nd order equation (at initial cadmium concentration of 50 mg·L

^{−1}). Reprinted with permission from reference [94]; copyright (2005) Taylor & Francis.

_{n}is given by the non-zero roots of

_{0}− C

_{∞})/C

_{0}is the fraction of metal ultimately adsorbed by the sorbent.

_{c}/ R

_{c}

^{2}, D

_{c}and R

_{c}being the intraparticle diffusion coefficient (m

^{2}·s

^{−1}) and mean particle radius (m), respectively. The same expression is the solution of the diffusion equation for a (macro) pore diffusion control but only in cases where the equilibrium isotherm is linear for the concentration range under investigation.

_{m}is the external mass transfer coefficient (m·s

^{−1}), S is the specific surface area of the sorbent particles per unit volume of the reactor (m

^{2}·m

^{−3}) and X is the sorbent feeding per unit volume of solution (g·L

^{−1}); dimensionless variables could be also used. The conversion a system of two first-order ordinary differential equations that must be solved simultaneously [99]. The values of Λ, ξ and the computed values of D

_{c}(being the intraparticle diffusion coefficient, m

^{2}·s

^{−1}) were displayed in the form of a table.

_{m}S, respectively. The non-linear numerical regression to fit experimental data to those equations is performed by the Levenberg-Marquardt method, which gradually shifts the search for the minimum of the sum of the errors squared, from steepest descent to quadratic minimization—i.e., Gauss-Newton [100]. Figure 5a presents the results of fitting Equation (15) to biosorption data obtained with different initial concentrations, solids loads and temperatures. It is apparent that despite some scatter in measurements the finite volume diffusion model can describe fairly well the entire range of data, including also the steep concentration gradient at short times. Such behavior has been customary met as a consequence of the decreasing slope of a non-linear equilibrium curve, e.g., Langmuir isotherm, which causes the diffusivity to increase rapidly with increasing concentration [93].

**Figure 5.**Experimental degree of conversion, α, against predictions based on the solution of the: (

**a**) diffusion equation, for various adsorbent loads and (

**b**) mass transfer equation, for various temperatures (both at initial chromium concentration of 5 mg·L

^{−1}). Reprinted with permission from Ref. [99]; copyright (2004) American Chemical Society.

## 6. Conclusions

## Conflicts of Interest

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**MDPI and ACS Style**

Kyzas, G.Z.; Fu, J.; Matis, K.A.
New Biosorbent Materials: Selectivity and Bioengineering Insights. *Processes* **2014**, *2*, 419-440.
https://doi.org/10.3390/pr2020419

**AMA Style**

Kyzas GZ, Fu J, Matis KA.
New Biosorbent Materials: Selectivity and Bioengineering Insights. *Processes*. 2014; 2(2):419-440.
https://doi.org/10.3390/pr2020419

**Chicago/Turabian Style**

Kyzas, George Z., Jie Fu, and Kostas A. Matis.
2014. "New Biosorbent Materials: Selectivity and Bioengineering Insights" *Processes* 2, no. 2: 419-440.
https://doi.org/10.3390/pr2020419