#### 2.1. Physicochemical Characteristics of the Nanofibrous Adsorbents

The V

_{2}O

_{5} nanoparticles were prepared through a sol-gel process. In this regard, the V

_{2}O

_{5} precursor was incorporated into a sacrificial nanofibrous matrix of polyvinylpyrrolidone (PVP), as shown in

Figure 1a. Subsequently, calcination at the high temperature of 500 °C discarded the polymeric matrix and crystallized the nanofiller [

29]. A combination of electrospinning and sol-gel can give rise to the creation of very fine and homogenously dispersed nanoparticles assembled as nanofibers [

30]. In addition, the crystallized nanoparticles possess a higher surface energy and thereby an improved adsorption tendency [

31]. The resulting mat was finally grinded to convert the nanofibers to distinct nanoparticles. As shown in

Figure 1a, the V

_{2}O

_{5}/PES nanofibrous mats were produced by electrospinning of a PES solution (in DMAc) containing V

_{2}O

_{5} nanoparticles (1, 3 and 5 wt %).

The morphology of the PES electrospun nanofibers in terms of bead formation, surface roughness and diameter distribution could affect the available surface area for adsorption. As shown in

Figure 1b, the surface of the nanofibers is smooth, but numerous beads can be seen across the mat. This situation is also the case when the V

_{2}O

_{5} nanoparticles are incorporated into the PES nanofibers (

Figure 1c). Visually, the fiber diameter does not vary significantly between the compositions. At 0 wt % V

_{2}O

_{5} (i.e., PES), the nanofibers’ diameter is 260 ± 110 nm, while at the highest filler concentration (i.e., 5 wt %) it decreases to 200 ± 56 nm. This finding indicates minor changes, i.e., increase of viscosity and viscoelastic property of the solution electrospun by addition of V

_{2}O

_{5} [

32,

33,

34,

35].

The X-ray diffraction (XRD) results, as shown in

Figure 1d, confirm that the V

_{2}O

_{5} nanoparticles after calcination at 500 °C acquire an orthorhombic crystalline structure. The diffraction peaks appeared at 2θ = 16°, 20° and 22° for the V

_{2}O

_{5} nanoparticles, are attributed to (200), (001) and (101) crystallographic planes of V

_{2}O

_{5} crystallites [

36].

The practical amount of the V

_{2}O

_{5} nanoparticles incorporated into PES nanofibers was verified by energy dispersive X-ray spectroscopy (EDX) analysis. As seen in

Figure 2a, other than 3 wt %, the practical value of the nanofillers is in harmony with the theoretical values. This implies that the nanoparticles could be homogenously distributed across and onto the nanofibrous mats. During electrospinning, the viscoelastic jets can possess significant initial longitudinal viscoelastic stresses generated in the preceding flow domain (the transition zone between the Taylor cone and the thin jet zone) [

37]. Such stresses can disrupt the agglomerates of the nanoparticles and make a uniform dispersion of very fine nanoparticles.

Chemical surface analysis via attenuated total reflection Fourier transform infrared (ATR-FTIR) could imply the presence of and probable interaction between the ceramic nanofiller and the polymeric matrix. The ATR-FTIR of the PES electrospun nanofibrous adsorbents (ENAs) are shown in

Figure 2b. The absorption peaks at 1296 and 1146 cm

^{−1} are attributed to the asymmetrical and symmetrical vibrations of the sulfone group, respectively. The absorption peak at 1234 cm

^{−1} is attributed to the stretching vibration of ether C-O-C bond in the PES polymer [

38]. A comparison between ATR-FTIR spectra of the neat and composite ENAs reveal that the position of the peak at 1146 cm

^{−1} for the neat PES ENA shifts to 1153 cm

^{−1} for the V

_{2}O

_{5}/PES ENAs. Another shift is seen for the peak at 1234 cm

^{−1} for the neat PES ENA, which is shifted to 1243 cm

^{−1} for the V

_{2}O

_{5}/PES ENAs. Such shifts primarily indicate the presence of the V

_{2}O

_{5} nanoparticles on/near to the surface of the nanofibers. These shifts are due to the interaction of the V

_{2}O

_{5} nanoparticles with the PES matrix through a hydrogen bonding between the ceramic surface’s OH groups and ether C-O-C bond (or sulfone SO

_{2} group) of PES [

30,

39,

40,

41]. Such a bonding could lead to a more optimal thermal and mechanical stability for the nanocomposite nanofibers, to be proved subsequently via thermogravimetric analysis (TGA) and compaction magnitude during a water permeability test [

30].

Since, wastewater streams to be purified are mostly in a hot condition, the adsorbent material must be sufficiently thermally resistant. The chemical affinity of V

_{2}O

_{5} nanoparticles towards the PES molecules, as verified by ATR-FTIR, could enhance thermal properties of the adsorbent. This hypothesis was probed by TGA. As shown in

Table 1, such thermal characterization implies a meaningful increment in the thermal decomposition temperature (

T_{d}) for the nanocomposite ENAs versus the neat one. As mentioned earlier, the reason is most probably the interactions between the V

_{2}O

_{5} nanoparticles and the polymer [

42,

43,

44]. The hydrogen bond between the V

_{2}O

_{5} nanoparticles and PES increases the rigidity of the polymer chain and thereby the energy of breaking it down [

42]. On the other hand, some of the heat is absorbed by the V

_{2}O

_{5} phase during heating-up, delaying the decomposition of PES and raising the decomposition temperature [

45]. In this regard, the higher residual mass of the nanocomposite ENAs is a supportive finding. The same behavior was seen in our previous study [

30]. Among the nanocomposite nanofibers,

T_{d} has a descending trend with mass fraction of the filler. The reason could be a slight agglomeration of the nanoparticles, especially at the highest amount of the nanofiller, and thereby less uniform dispersion of them across the mat.

#### 2.2. Structural Characteristics of the Nanofibrous Adsorbents

The PES nanofibrous adsorbent was designed to encompass the maximum possible amount of water. Such ultrahigh surface area can facilitate a reaction of the adsorbent material and the pollutant. The water permeability of the structure represents the available surface area and porosity of the adsorbent. As shown in

Figure 2c, the PES ENA demonstrates a high water permeability of 2× 10

^{4}–6 × 10

^{4} L/h·m

^{2}, which is quite larger than that of commercial microfiltration membranes [

46]. This means a hydrodynamic adsorption-based separation could be done with a low energy consumption. As seen in

Figure 2c, the permeability is enhanced via the nanocomposite strategy. The reasons for this behavior could be attributed to optimized physicochemical characteristics of the membranes and/or their porosity.

Of the physicochemical properties, mechanical stability and hydrophilicity are the most influential ones on water permeability. As proved through the water contact angle measurements, hydrophillicity of the ENAs does not vary by incorporation of the nanoparticles. The water contact angle remains in the range of 135°–140°. This effect can imply particles are partly buried under the surface and the rest are exposed on the surface. The exposed particles are not enough to induce a notable hydrophilicity effect. While incorporation of the nanoparticles does not confer a superior wettability to the ENAs, it can promote mechanical stability and lower the compaction tendency, thus optimizing water permeability [

32]. The descending trend of water flux from 50 to 200 mL for each sample is attributed to compaction of the ENAs during the water flux measurement. The relevant magnitude is less notable for the nanocomposite ENAs, i.e., they are mechanically more resistant against disintegration induced by water flow stresses.

Based on porosity characteristics, the permeance behavior of the ENAs can be described according to Hagen–Poisseuille’s equation (Equation (1)) [

47,

48]:

where

J is the water flux (m

^{3}/s), ε the porosity,

r the pore radius (m), τ the tortuosity, Δ

P the pressure difference across the membrane (Pa) (1 Pa = 10

^{−5} bar), µ the dynamic viscosity (Pa·s) and Δ

x the membrane thickness (m). Among the involved parameters in this equation, only porosity and pore size could be variable and directly influential on the water flux of the membranes. As measured by us, the porosity for all the samples varies in the range of 45%–60%. In addition, as shown in

Figure 2d, the difference in pore size of all the samples, whether bubble point—i.e., the largest pore size—or mean flow pore diameter—the mean flow pore diameter is such that 50% of flow is through pores larger than the mean flow pore diameter and 50% of flow is through pores smaller than the mean flow pore diameter [

15]—is not that significant. Therefore, the higher water permeability of the nanocomposite ENAs could be solely attributed to their more optimal mechanical stability induced by the presence of the nanoparticles.

#### 2.4. Adsorption Thermodynamics

To comprehend the effect of temperature on the adsorption, the thermodynamic parameters such as standard Gibbs free energy ΔG^{0}, standard enthalpy ΔH^{0}, and standard entropy ΔS^{0} should be studied.

Δ

G^{0} is determined from the following equation [

4,

52]:

where

K_{c} is the adsorption equilibrium constant and correlated to Δ

H^{0} and Δ

S^{0} of adsorption by the van’t Hoff equation:

where

R is the gas constant and

T the temperature. The

K_{c} value is calculated from Equation (7):

where

C_{Ae} and

C_{Se} are the equilibrium concentration (mg/L) of the dye ions on the adsorbent and in the solution, respectively. The van’t Hoff plots (

lnK_{c} vs. 1/

T (kelvin)) for the adsorption of MB onto PES ENAs (not shown here) were used for calculation of Δ

H^{0} and Δ

S^{0}. The slope is equal to −Δ

H^{0}/R and its intercept to Δ

S^{0}/R. All the thermodynamic parameters obtained are presented in

Table 2. As shown in the table, the negative values of Δ

G^{0} at basic pHs at both temperatures indicate the spontaneous nature of the adsorption process. The degree of spontaneity also increases with temperature. A similar behavior was observed in other researches [

55,

56].

In all conditions in terms of composition, pH and temperature, Δ

H^{0} is positive, indicating an endothermic adsorption [

55]. This fact has been reported by other researchers as well [

55,

57,

58]. The positive values of Δ

S^{0} in all the conditions suggest the increased randomness at the solid/solution interface during the adsorption due to redistribution of energy between MB and the PES nanofibers, i.e., the affinity of the adsorbent for MB [

55,

56,

59]. A similar trend has been reported for the adsorption of Congo red onto activated carbon and also some reactive dyes onto aluminium hydroxide sludge adsorbents [

55,

57].

#### 2.5. Adsorption Kinetics

The efficiency of adsorption and applicability of scale-up operation is determined by kinetic study of the adsorption process [

3]. In this regard, pseudo-first-order and second-order kinetic models were used to gain a better understanding of the adsorption process. First, the kinetic data were fitted to the first-order kinetic model of Lagergen [

57]:

where

q_{e} and

q are the amounts of dye adsorbed (mg/g) at equilibrium and at time

t (min), respectively, and

K_{1} is the rate constant of adsorption (1/min). Values of

K_{1} were calculated from the plots of

log(q_{e} −

q) vs.

t (e.g.,

Figure 4a,b related to 5 wt % V

_{2}O

_{5}/PES that shows the most optimal adsorption capacity at all pH levels) for different samples. An

r^{2} value approaching 1 as well as a good agreement between the experimental

q_{e} values with the ones calculated from the linear plots (

Table 3) are indications of a proper harmony with the Lageregen model and first-order interaction of MB and the adsorbents. Accordingly, mostly at the high temperature of 50 °C and mostly at higher pH values, the adsorption of MB onto the V

_{2}O

_{5}/PES nanofibers is a first-order reaction [

57]. For the other conditions in terms of pH and temperature, the kinetic data were further modeled with the pseudo second-order kinetic equation.

The second-order kinetic model is expressed as [

57,

60,

61]:

where

k_{2} (min g/mg) is the rate constant of second-order adsorption. In the case of a linear plot of

t/q versus

t, the kinetic is of a second order. The second-order constants

k_{2} and

q_{e} were calculated from the intercept and slope of the plots. At the lower temperature of 25 °C regardless of pH as well as at the high temperature of 50 °C at pH10 and in some cases pH7, the linear plots of

t/q vs.

t show a good agreement of experimental data with the second-order kinetic model for different samples (e.g.,

Figure 4c,d). The

r^{2} values for the second-order kinetic model are mostly greater than 0.98 (

Table 3). In addition, the calculated

q_{e} values comply very well with the experimental ones. Thus, the adsorption system at such conditions behaves as the second-order kinetic model. Accordingly, it is assumed that the rate limiting step may be chemisorption, involving valency forces through sharing or exchange of electrons between sorbent and sorbate [

61]. A similar behavior is observed in the biosorption of dye Remazol Black B on biomass [

62,

63] and adsorption of Congo red on activated carbon prepared from coir pith [

57].

#### 2.6. Adsorption Isotherms

The equilibrium isotherm is of significant importance to understand the behavior of adsorption process and the affinity of dye molecules [

3]. The analysis of equilibrium data for the adsorption of MB onto the PES ENAs was performed considering the Freundlich isotherm model [

52,

57]. Assuming that the adsorbent surface is heterogeneous, the Freundlich adsorption isotherm is expressed as [

4,

52]:

where

q is the amount of dye adsorbed (mg) per gram of the adsorbent,

C_{e} and

C_{i} are the equilibrium and initial concentrations (mg/L),

m is the adsorbent mass used (g),

V_{sol} is the solution volume (L) and

K_{f} and

n are isotherm constants indicating the capacity and intensity of the adsorption, respectively.

The plots of log

q versus log

C_{e} at different pHs and two temperatures of 25 and 50 °C (not shown here) were used for calculation of

K_{f} (slope) and

n (intercept) isotherm constants (as shown in

Table 4). According to the values of the correlation coefficient (adjusted

r^{2}) of the plots (

Table 4), unlike in basic condition (wherein the adsorbent surface is homogenous due to saturation of –OH groups), the plots at acidic and especially neutral pHs are in a good harmony with the Freundlich adsorption model. The dye adsorption capacity of the adsorbent is directly proportional to the

K_{f} values [

57]. Increase of the value of

K_{f} with temperature indicates that the adsorption process is endothermic [

55]. On the other hand, when 0 < (1/

n) < 1, the adsorption is suitable [

55] which was applicable only in basic condition.