## 3 Results and Discussion
### Batch Tests
#### 3.2.3 Thermodynamic Analysis  
Based on [PERSON] free energy theory, the thermodynamic behavior of adsorption processes can be determined using Equations (S8) and (S9) [38]. Thus, TNT adsorption on the loess was investigated at a given TNT concentration with different temperatures (278-318 K), and these data were analyzed and the results were obtained (Table S3). \(\Delta\text{G}^{0}\) was negative with a range from \(-8.93\) to \(-3.91\) kJ\(\cdot\)mol\({}^{-1}\) for TNT adsorption on the loess, demonstrating the spontaneity of adsorption. It is also evident that the adsorption process was not only a physical process but also driven by a chemical synergistic effect. \(\Delta\text{G}^{0}\) increases with decreasing temperature, and the increase range doubled, approximately, implying that the potential for spontaneity becomes stronger, and therefore TNT adsorption on the loess is sensitive to temperature and favorable with high temperatures. The positive values of \(\Delta\text{H}^{0}\) were obtained for TNT at all tested temperatures, i.e., 408.24, 278.02, 200.68, 158.19, 143.18 and 130.18 kJ\(\cdot\)mol\({}^{-1}\), indicating that the adsorption process is endothermic and driven by the synergistic forces of physics and chemistry, and that the binding between soil particles and TNT has physical and chemical effects [39]. Similar phenomena have also been found in the studies on NH\({}_{4}\)+ [33] and the adsorption of heavy metals like Pb and Cd on loess [13]. The positive value of \(\Delta\text{S}^{0}\) implies that TNT is less hydrated in the loess layer than in the aqueous solution, and the orderliness is increased between TNT molecules and loess in the studied system [40]. Moreover, [PERSON] et al. (2008) [33] noted that the positive value of \(\Delta\text{S}^{0}\) appeared due to the redistribution of energy between adsorbate and adsorbent. The distribution of rotational and translational energy among some molecules will enhance adsorption by producing positive \(\Delta\text{S}^{0}\), and simultaneously the randomness will increase at the solid-solution interface during the process of adsorption. Thus, the absolute values of \(\Delta\text{S}^{0}\) are small, at 1.0 and even 0.48, suggesting that there is a weak binding force for TNT adsorption on the loess. All this understanding is consistent with the results obtained in the previous adsorption kinetics and isotherms above. The analysis of \(\Delta\text{G}^{0}\) showed that aniline adsorption on the loess was also feasible and spontaneous thermodynamically (Table S4). However, the increase in \(\Delta\text{G}^{0}\) values with temperature decrease was not like that for the results from TNT adsorption, implying that the potential for spontaneity becomes weaker, and the adsorption process is exothermic and favored by low temperatures [41]. In particular, the absolute value of \(\Delta\text{G}^{0}\) for aniline is much higher than that for TNT, showing that the loess tends to adsorb aniline rather than TNT, and this is on account of their different chemical properties, as aniline has a stronger polarity and higher ratio of chemical adsorption compared to TNT. Negative values of \(\Delta\)H\({}^{0}\) were obtained for aniline adsorption at all studied temperatures, further confirming that the process is exothermic, unlike that for TNT. The \(\Delta\)H\({}^{0}\) values increase with temperature increase, and their absolute values are much smaller than those of TNT, showing that aniline adsorption on the loess is far less sensitive to its concentration than that of TNT, which is consistent with the analysis obtained from isothermal experiments. This is also supported by the negative values of \(\Delta\)S\({}^{0}\), which are \(-47.27\), \(-37.77\), \(-34.52\), \(-29.25\), \(-27.92\) and \(-22.28\) kJ/(mol\(\cdot\)K), respectively.