## 3 Results and Discussion
### Air-Gap Membrane Distillation--Separation Efficiency of Modified Ceramic Membranes  
Prior to desalination process of NaCl solutions, membranes were tested in contact with pure water as a feed solution to evaluate the nominal value of water permeate flux (Figure 4). The fluxes in contact with pure water were the higher that those for NaCl solutions. Membrane grafted by C8 COEt3 possessed the highest value of permeate flux (Figure 4). On the other hand, the less permeable was the membrane grafted by molecules having the longest alkyl chains. The permeate flux through the grafted ceramic membranes decreased with increasing salt concentration in the feed (Figure 4). This behavior was caused by the fact that, in membrane distillation of NaCl solutions, only vapors of water are transported across the hydrophobic porous structure of the membrane and with higher concentration of non-volatile compounds in the feed (sodium chloride) a decline of the flux is observed. For this reason, with increase of salt concentration a diminution of driving can be noticed, according to the Raoult's law. Figure 3: LEPw evolution with grafting time for alumina and titania ceramic materials grafted with various alkylsilanes. After a shorter grafting (1.5 h), the alumina membrane modified by C8 OEt3 molecules showed the highest value of permeate flux 4.84 kg m\({}^{-2}\)-h\({}^{-1}\) which corresponded to the lowest value of measured LEPw (Figure 4B). On the other hand, a membrane sample hydrophobized by molecules with longer alkyl chain (C18 Cl) showed the poorest transport properties. This can be attributed to the presence of alkyl chain in a tangled environment and/or partially located in pores [56]. The Al-C18 Cl3 membranes produced the lowest value of permeate flux. This observation can be explain by a higher effectiveness of grafting comparing molecules with reactive groups of chlorine atoms and ethoxyl groups. As mentioned above, molecules with chlorine atoms are characterized by the highest ability to generate covalent bonds due to the lower value of energy bonds [60]. The membrane material as well as time of modification process affected the transport properties. Generally, membranes made from alumina possessed a slightly higher value of permeate flux due to slightly bigger pores (100 nm) in comparison with titania ones (\(\approx\)75 nm). The observed reduction of permeate fluxes (Figure 4) as well as LEPw values (Figure 3) with extended grafting time contributed to formation of a smoother surface (Table 1) showing better water-proof character. Summarizing the fabricated hydrophobic membranes possess good transport properties in AGMD compared with literature data [40; 42; 62; 63]. Furthermore, the observed values of permeate fluxes are higher than for ceramic membranes tested in DCMD. This is related to the benefit of AGMD, namely the reduction of conduction heat losses. In AGMD, permeate is condensed on a chilled surface rather than directly in the chilled permeate. Nevertheless, the achieved permeate fluxes for ceramic membranes are smaller than for polymeric one [64]. Retention coefficient of salt (R\({}_{\text{NaCl}}\)) Equation (2) is a very important factor determining efficiency of membrane distillation process. R\({}_{\text{NaCl}}\) corresponds to the separation properties of applied membranes. The salt retention (R\({}_{\text{NaCl}}\)) during the membrane distillation process was calculated according to Equation (2). The obtained values of R\({}_{\text{NaCl}}\) were very high, close to 100% (Table 2). A small effect  
Figure 4: Transport properties of modified ceramic membranes by (**A**) C8 Cl3; (**B**) CSOEt3; and (**C**) C18 Cl3, molecules in AGMD process used for desalination. T\({}_{\text{f}}\) = 90 \({}^{\circ}\)C; T\({}_{\text{p}}\) = 5 \({}^{\circ}\)C, Ap = 688 mbar. of grafting time on the RNaCl values was observed. On the other hand, no influence of membrane materials on their selective properties was noticed.