# Metachrylate-Based Polymeric Sorbents for Recovery of Metals from Aqueous Solutions
## 9 Overview of Characterization Methods
### Porosity Determination  
Macroporous polymeric sorbents were synthesized in the shape of spherical particles by suspension copolymerization in the presence of a pore-forming agent (inert component, porogen), having a permanent well-developed porous structure even in the dry state [123]. The particles consist of smaller microspheres (10-20 nm), which are often fused. As a result of the mechanism of porous structure formation, a pore size distribution is obtained, i.e., micropores with diameters smaller than 2 nm, mesopores with diameters in the range 2-50 nm and macropores with diameters over 50 nm. Porosity can be determined by two complementary methods-mercury porosimetry, and N\({}_{2}\) adsorption/desorption isotherms determination at 77 K. For the sake of illustration, pore size distribution (PSD) plots and nitrogen adsorption/desorption isotherm measured at 77 K for sample PGME-data is presented in Figure 6a and 6b, respectively. Mercury porosimetry is based on the penetration of mercury into the pores as a function of the applied pressure and cover pores ranging from 7.5 nm (at the high pressure of 200 MPa) to 15 \(\upmu\)m (at atmospheric pressure) [150]. Nitrogen sorption experiments were carried out at 77 K, in the relative pressure region of \(p/p_{0}=0.05\) to \(p/p_{0}=1.00\) and cover pores smaller than 7.5 nm. The mesopore distribution curve can be obtained from the adsorption branch of the N\({}_{2}\) isotherm by the Barrett-Joyner-Halenda (BJH) method. Specific surface area was then calculated from the well-known Brunauer-Emmett-Teller (BET) equation for multilayer adsorption, given in the inset of Figure 6b, where: \(p^{0}\) is the adsorbate saturated vapor pressure, \(C\) is a constant related to the heat of adsorption. At the same time, \(\alpha_{m}\) is the amount of adsorbate adsorbed in a monolayer. In the linear range of the adsorption isotherms (\(0.05\leq p/p_{0}\leq 0.3\)), \(\alpha_{m}\) and \(C\) were estimated from the slope and the intercept of the straight line. The total pore volume was calculated as the volume of liquid adsorbate at a relative pressure of 0.99. Figure 6: (a) Integral (cumulative) and differential pore size distribution curves and (b) adsorption/desorption isotherm measured at 77 K for sample PGME-data. The porous structure of the macroporous polymeric sorbents can be described by porosity parameters: specific surface, \(S_{Hg}\), specific pore volume, \(V_{p}\), average pore diameter, \(d_{p}\), and pore diameter that corresponds to half of the pore volume, \(d_{V/2}\). The values of \(V_{p}\), and \(d_{V/2}\), of the copolymer samples, can be read from pore size distribution curves determined by mercury porosimetry. The specific surface area, \(S_{Hg}\), can be calculated as the sum of incremental specific surface area from the pore size distribution curves, as described elsewhere [150]. Inverse gas chromatography under finite surface coverage, IGC-FC, can be used as an additional method, which enables the calculation of specific surface area by determining the adsorption isotherms of organic compounds [151]. The IGC method has been used for the investigation of polymer structure, the interactions of various liquids and gases with polymeric materials, and polymer-polymer miscibility [152; 153; 154; 155]. The technique is especially advantageous for the investigation of macroporous crosslinked copolymers that conventional methods cannot characterize. A variety of polymer surface characteristics (dispersive component of surface free energies, enthalpy, and entropy of adsorption, acid/base constants), as well as interaction parameters and thermal transitions of polymers, can be calculated from the peak positions [156]. In the IGC-FC mode, measurable amounts of solutes were injected. From the peak shapes, adsorption isotherms, isosteric heat of adsorption, and adsorption energy distributions can be calculated. [PERSON] et al.