Native and US-treated HS, as lignocellulosic material suitable to be used as biosorbent, was previously investigated and characterised14. Briefly, Scanning Electron Microscopy revealed that US determines mechanical ruptures with formation of pores and smother surfaces, while X-ray diffraction showed no modification on cellulose crystalline structure under US treatment. Fourier Transform Infrared spectra emphasised the complex material composition, with many functional groups interacting with metal ions. Thus, the sorption on this vegetal structure was proved as the result of a combination of mechanisms: physical adsorption, ion exchange, electrostatic interactions and formation of complexes14,15,22,23. Furthermore, ultrasounds significantly intensify this process due to acoustic cavitations’ development inside and outside of sorbent particle24–26.
Statistical study of sorption efficiency
The influence of the main studied parameters (\({d}_{p}\), \(pH\), \({m}_{HS}\) and \({c}_{l0}\)) on separation efficiency of Pb(II) and Cd(II) in single and competitive, silent and US assisted adsorption was analysed. Coded experimental design matrices and experimentally obtained sorption efficiencies, are presented in Table 2.
In all cases, for the significance of each coefficient the reproducibility was obtained from four replicated experiments in the centre of experimental plan (see line 17, Table 2).
The following equations (16 – 23) resulted:
$${R}_{1}^{0}=65.57+6.19{x}_{2}-4.21{x}_{4}+3.24\left({{x}_{1}}^{2}-0.8\right)-11.13\left({{x}_{2}}^{2}-0.8\right)+4.41\left({{x}_{4}}^{2}-0.8\right)$$
16
$${R}_{2}^{0}=60.26+6.08{x}_{2}-4.61{x}_{4}+3.312\left({{x}_{1}}^{2}-0.8\right)-11.74\left({{x}_{2}}^{2}-0.8\right)+4.41\left({{x}_{4}}^{2}-0.8\right)$$
17
$${R}_{3}^{0}=53.05+5.06{x}_{2}+3.03{x}_{3}-4.92{x}_{4}-2.3{x}_{2}{x}_{4}-2.99{x}_{2}{x}_{3}{x}_{4}+2.77\left({{x}_{1}}^{2}-0.8\right)-3.63\left({{x}_{2}}^{2}-0.8\right)$$
18
$${R}_{4}^{0}=45.65+5.07{x}_{2}+2.25{x}_{3}-4.94{x}_{4}-1.8{x}_{2}{x}_{4}-3.39{x}_{1}{x}_{2}{x}_{3}{x}_{4}+4.01\left({{x}_{1}}^{2}-0.8\right)-2.29\left({{x}_{2}}^{2}-0.8\right)++6.4\left({{x}_{4}}^{2}-0.8\right)$$
19
$${R}_{1}^{1}=75.51+6.53{x}_{2}+5.58\left({{x}_{1}}^{2}-0.8\right)-13.43\left({{x}_{2}}^{2}-0.8\right)$$
20
$${R}_{2}^{1}=66.54+6.69{x}_{2}-3.67{x}_{4}+6.26\left({{x}_{1}}^{2}-0.8\right)-14.51\left({{x}_{2}}^{2}-0.8\right)$$
21
$${R}_{3}^{1}=58.22+5.98{x}_{2}-2.99{x}_{1}{x}_{3}+6.16\left({{x}_{1}}^{2}-0.8\right)-11.12\left({{x}_{2}}^{2}-0.8\right)$$
22
$${R}_{4}^{1}=50.77+5.74{x}_{2}-2.71{x}_{1}{x}_{3}+6.54\left({{x}_{1}}^{2}-0.8\right)-11.16\left({{x}_{2}}^{2}-0.8\right)+3.46\left({{x}_{3}}^{2}-0.8\right)$$
23
The results of the statistical model described by eq. (16 – 23) show, quantitatively, that US increases the separation efficiency with up to 10 percent (comparison between free term values of \({R}_{1}^{0}\) and \({R}_{1}^{1}\), \({R}_{2}^{0}\) and \({R}_{2}^{1}\), \({R}_{3}^{0}\) and \({R}_{3}^{1}\), and \({R}_{4}^{0}\) and \({R}_{4}^{1}\) respectively). Also, comparing the equations describing single Pb(II) and Cd(II) sorption with the equations obtained for competitive sorption, one can see that the terms expressing the factors interaction are missing in the first cases, while in the competitive sorption they are significant, especially for silent experiments (\({R}_{3}^{0}\), \({R}_{4}^{0}\)).
Thus, for a given biosorbent structure (porous HS particles in our case), the equations clearly indicate that process equilibrium, and consequently the maximum effectiveness of the separation, is mainly influenced by 3 factors in the following order: \(pH\) \(\left({x}_{2}\right)\) > \({c}_{l0}\) \(\left({x}_{4}\right)\) > \({m}_{HS}\) \(\left({x}_{3}\right)\), with an average variability, depending on specific case, from \({R}_{1}^{0}\) to \({R}_{4}^{1}\) (for pH, for instance, the variability is ranging from -4.5 % to +11.3 %). Howeer, in allabove equations a quadratic dependence can be noticed \(\left({{x}_{1}}^{2}-0.8\right)\). Its contribution is between -2.45 % and +0.65 % for silent srption, andbetween -5.2 % and +1.7 % in the case o US-assistd sorption. This could be explained, as described before, by mechanical structure modification under US field.
The effect of pH (\(pH\)) and initial concentration of transferable species (metal ion/s) (\({c}_{l0})\) on separation efficiency (\(R\)) is presented in Fig. 1. Here the other two factors, namely sorbent particle size (\({d}_{p}\)) and sorbent dosage (\({m}_{HS}\)) were maintained in the centre of the experimental plane. In addition to the statistical model representation of \(pH\) and \({c}_{l0}\) influence on separation efficiency, in Fig. 1 experimental data are added. The experimental data (represented as white stars) were also obtained for pH and the initial ion metal concentration as manipulated variables while the other variables were maintained in the centre of the experimental plane. The white line in Fig. 1 allows us to compare theoretical data (resulted from statistical model) with the experimental obtained ones.
As example, with reference to the Fig. 1a, for an initial metal ion concentration of 50 mg/L, and pH=3, Pb(II) theoretical (from model) and experimental separation efficiency is 51% and 53% respectively. Overall, we can notice a satisfactory agreement between experimental and model data. An important finding however refers to US-assisted single and competitive adsorption, where, as can be seen in Fig. 1e, and Fig. 1g, the separation efficiency depends only on solution pH.
Concerning adsorbent particle size and solid liquid ratio, the two parameters could be connected to specific area of porous particles27. Thus, the internal area, directly related to the total weight of used adsorbent (here HS) determines metal removal, while the external area becomes important only for very large particles. This limited contribution of external surface area was in fact generalized for natural biomaterials, as mentioned in previous studies, even in the absence of ultrasounds28. While, clearly, the highest removal efficiency of Pb(II) and Cd(II) was obtained for single sorption experiments, the above observation is applicable for competitive adsorption experiments also. At the same time, the high percent removal obtained in a very short time, gives a good indication that ultrasounds penetrate the pores, enhancing convective mass transport due to acoustic cavitations29,30.
Modelling of experimental sorption dynamic
Another direction of present research refers to identification of a quantitative expression characterizing the interphases equilibrium for Pb(II) and Cd(II) sorption, in single and competitive systems, using grinded HS particles. The main objective was to determine biosorption process equilibrium constant, \({K}_{e}\) expressed as ratio of desorption and sorption rate constants. As previously shown, this rate constants ratio (equilibrium constant) is important in identifying the characteristic parameters of sorption dynamic model at particle level. It must be said that all the above presented data, concentrated in eq. system (16 – 23), are in fact an indirect expression of the interphase sorption equilibrium. Using these equations, the interphase equilibrium can be expressed as equation (4) or as the equations (14 – 15) or as equivalents, depending on the characteristics of the adsorption system.
The results of the sorption dynamic evaluation presented in Table 3, were obtained for pH 5.5, considered as optimum value. Specifically, equilibrium ion metal concentration in the liquid phase, \({c}_{le}\) and the equilibrium/maximum sorption efficiency, \(R\), were determined experimentally while the equilibrium ion metal concentration in the solid phase, \({c}_{se}\), was determined using eq. (3). All fixed and manipulated parameters are described in Table 3.
Table 3
Experimental parameters and equilibrium data for Pb(II) and Cd(II) sorption on HS at 25 ºC
Fixed factors, m.u.
|
Manipulated factors, m.u.
|
\({c}_{l0}\), mg/L
|
10
|
25
|
50
|
75
|
100
|
dp = 0.87 mm
mHS = 10 g/L
pH= 5.5
|
Silent sorption
|
Single system
|
Pb(II)
|
\({c}_{le}\), mg/L
|
0.96
|
4.42
|
12.15
|
40.05
|
60.71
|
\(R\), %
|
90.4
|
82.3
|
75.7
|
46.6
|
39.3
|
\({c}_{se}\), g/g
|
0.904
|
2.058
|
3.785
|
3.495
|
3.931
|
Cd(II)
|
\({c}_{le}\), mg/L
|
1.14
|
6.36
|
14.95
|
47.85
|
72.5
|
\(R\), %
|
87.6
|
74.5
|
70.1
|
36.2
|
27.5
|
\({c}_{se}\), g/g
|
0.886
|
1.865
|
3.505
|
2.715
|
2.75
|
Competitive system
|
Pb(II)
|
\({c}_{le}\), mg/L
|
0.73
|
3.21
|
10.82
|
21.77
|
33.11
|
\(R\), %
|
84.4
|
73.9
|
56.7
|
44.6
|
33.8
|
\({c}_{se}\), g/g
|
0.427
|
0.929
|
1.418
|
1.672
|
1.69
|
Cd(II)
|
\({c}_{le}\), mg/L
|
1.57
|
5.32
|
13.97
|
26.17
|
38.25
|
\(R\), %
|
68.6
|
57.7
|
44.1
|
30.2
|
23.5
|
\({c}_{se}\), g/g
|
0.313
|
0.721
|
1.106
|
1.131
|
1.171
|
US-assisted sorption
|
Single system
|
Pb(II)
|
\({c}_{le}\), mg/L
|
0.26
|
0.69
|
6.65
|
31.82
|
54.7
|
\(R\), %
|
98.4
|
97.1
|
86.7
|
57.6
|
45.3
|
\({c}_{se}\), g/g
|
0.984
|
2.435
|
4.335
|
4.329
|
4.53
|
Cd(II)
|
\({c}_{le}\), mg/L
|
1.04
|
2.85
|
11.45
|
33.61
|
62.5
|
\(R\), %
|
89.6
|
87.6
|
77.1
|
53.2
|
37.5
|
\({c}_{se}\), g/g
|
0.896
|
2.215
|
3.855
|
4.145
|
3.751
|
Competitive system
|
Pb(II)
|
\({c}_{le}\), mg/L
|
1.08
|
3.09
|
7.83
|
20.41
|
32.63
|
\(R\), %
|
78.4
|
75.3
|
68.6
|
45.6
|
34.8
|
\({c}_{se}\), g/g
|
0.392
|
0.941
|
1.718
|
1.715
|
1.739
|
Cd(II)
|
\({c}_{le}\), mg/L
|
1.77
|
4.93
|
11.72
|
25.42
|
39.25
|
\(R\), %
|
64.6
|
60.5
|
50.1
|
33.2
|
24.5
|
\({c}_{se}\), g/g
|
0.323
|
0.758
|
1.208
|
1.218
|
1.225
|
Using the parameters presented in Table 3, Langmuir isotherms for single silent and US-assisted sorption of Pb(II) and Cd(II) were plotted (Fig. 2). The sorption characterizing parameters are presented in Table 4. The results, as expected, confirm the difference between silent and US-assisted sorption performance. Thus, higher values for \(Q\) were obtained in US-assisted experiments. Comparing the results of Table 4, it should also be noted that values of total sorption capacity obtained for competitive systems (Q) exceeds any of the individual sorption capacities, whether ultrasonic field is applied or not, so it can be assumed that Pb(II) and Cd(II) are not oriented towards the same sorption sites. Also, higher values of equilibrium constants (\({K}_{e}\)), correlated with lower sorption capacities obtained for Cd(II) could be explained by its lower tendency to form hydrolysis products31,32. Similar findings regarding factors influence on separation efficiency and solid-liquid equilibrium for Pb(II) and Cd(II) adsorption in single and competitive systems could be found in many other published reports33–35.
Table 4
Sorption isotherm parameters (\(Q\), \({\alpha }_{1}\), \({\alpha }_{2}\), \({K}_{e}\)) and dynamic model parameters (\({D}_{ef}\) and \({k}_{a}\)) at 25 ºC, pH=5.5 and \({m}_{HS}\) = 10 g/l
Langmuir constants, m.u.
|
Silent adsorption
|
US-assisted adsorption
|
single
|
competitive
|
single
|
competitive
|
Pb(II)
|
Cd(II)
|
Pb(II)
|
Cd(II)
|
Pb(II)
|
Cd(II)
|
Pb(II)
|
Cd(II)
|
Q, mg/g
|
4.096
|
3.051
|
5.013
|
4.555
|
3.626
|
5.492
|
α1, α2, -
|
-
|
-
|
α1 = α2 = 0.5
|
-
|
-
|
α1 = α2 = 0.5
|
Ke, -
|
5.95 10−4
|
6.58 10−4
|
6.02 10−3
|
8.11 10−3
|
8.94 10−4
|
7.62 10−4
|
5.51 10−3
|
7.61 10−3
|
\({k}_{a}\), s−1
|
2.91 10−4
|
4.35 10−4
|
9.05 10−5
|
4.13 10−5
|
4.05 10−3
|
6.43 10−3
|
3.01 10−4
|
2.25 10−4
|
\({D}_{ef}\), cm2/s
|
2.9 10−8
|
3.5 10−8
|
1.5 10−8
|
1.6 10−8
|
6.4 10−7
|
6.1 10−7
|
6.3 10−7
|
6.1 10−7
|
The isotherm plots for competitive sorption presented in Fig. 3 were obtained using \(Q\), \({K}_{e1}\) (as \({k}_{d1}/{k}_{a1}\)) and \({K}_{e2}\), (as \({k}_{d2}/{k}_{a2}\)) identified from eq. (14 – 15). They show the differences between sorption equilibrium in silent and US-assisted approach; specifically, for \({c}_{le}>5\) mg/L, \({c}_{se}\) is 8-10 % higher in US-assisted adorption.
Identification of parameters characterizing biosorption dynamics
Two parameters are considered to characterize biosorption dynamics: the diffusion coefficient (\({D}_{ef}\)) and the adsorption rate constant (\({k}_{a}\)). To determine their values, experimental obtained data according to procedure detailed in subchapter 2.2.4 and the dynamic model equations (5-11) were used.
In the case of single sorption systems, the identification algorithm consisted in: i) numerical transposition of dynamic model equations as a function showing species dynamic concentration in liquid \({c}_{l}\left({D}_{ef}, {k}_{a}\right)\), ii) building the objective function (eq. 12) for parameters identification based on experimental values \({c}_{lexp}\), iii) minimization of the objective function.
A similar procedure was used for competitive sorption. In this case however, instead of a numeric function with two parameters, \({c}_{l}\left({D}_{ef}, {k}_{a}\right)\), an equivalent function with four parameters, \({c}_{l}\left({D}_{ef1}, {k}_{a1}, {D}_{ef2}, {k}_{a2}\right)\) was used. Since it’s not recommended to identify more than two parameters based on a single data set16, it was considered that the values of \({D}_{ef1}\), \({D}_{ef2}\), \({k}_{a1}\), and \({k}_{a2}\) are close to those characterizing single component sorption.
Table 4 shows the identified values of dynamic model parameters, for all experimentally investigated cases. Fig. 4 show the variation of ion metal liquid concentration in time, both experimentally obtained and by means of mathematically modelling (Fig. 4a, c), and the sensitivity of mean square deviation of concentration as a function of \({D}_{ef}\) for single silent and US-assisted adsorption (Fig. 4b, d). The results indicate an accurate and valid identification of model parameters. Experimental and model based predicted ion metal concentration dynamic in time, for liquid phase, is presented in Fig. 4e,f.
The above presented allow highlighting several aspects of general and particular interest: i) the dynamic of US-assisted adsorption is almost 30 times faster than the dynamic in classic, silent contacting (Fig. 4a vs. Fig. 4c, Fig. 4e vs. Fig. 4f); ii) Fig. 4 show very similar concentration profiles so we can assume, that disregarding the contacting approach, the adsorption process can be characterized by the same mathematical model; iii) the diffusion coefficients for Pb (II) and Cd (II) in single sorption are, on average, 20 times higher in US field (6.4 10-7 cm2/s, respectively 6.1 10-7 cm2/s) than in US absence (2.9 10-8 cm2/s, respectively 3.5 10-8 cm2/s); iv) in competitive systems, the diffusion coefficients of Pb(II) and Cd(II) in HS, disregarding the sorption procedure, are very close, as shown in Table 4; v) the diffusion coefficients of Pb(II) and Cd(II) in competitive single sorption are almost 2.5 times lower than in single competitive systems (Table 4); vi) in US-contacting the effect of species interaction on competitive sorption does not appear to be significant (close values of diffusion coefficients in silent and competitive adsorption); vii) overall, the obtained values of diffusion coefficients for Pb(II) and Cd(II) in HS, a porous vegetal structure, correspond with some other reported36–39; viii) besides the diffusion coefficients, the major difference between adsorption in silent and US-assisted approach is also indicated by the obtained constant rates, \({k}_{a}\); thus, as can be seen in Table 4, for single sorption the ratios ka_USPb/ ka_silentPb and ka_USCd/ ka_silentCd are both around 14, while in competitive systems ka_USPb/ ka_silentPb = 3.3 and ka_USCd/ ka_silent Cd = 5.44; ix) comparing the values of the adsorption rate constants (Table 4) as well as these ratios of constants, it can be concluded that species competition determines a lower frequency of active sorption sites loading.
The obtained results, confirm that the model of sorption dynamics of Pb(II) and Cd(II) on HS is adequate. It was thus possible to identify the diffusion coefficients of Pb(II) and Cd(II), as well as the values of sorption and desorption rates of these species, in their interaction with the HS porous structure, in the absence or presence of the US field.