## 3 Results  
### Permeability  
The liner structure used in landfills is an important factor affecting permeability [32]. The permeability of an effective liner must be low to prevent groundwater contamination by minimizing the leakage of leachate from waste in landfills [32; 33; 34].  
Figure 2 shows the permeability results of kaolin containing different amounts of iron oxide, aluminum oxide, and Oltu clay over 90 days. The initial permeability of kaolin was determined to be 2.87 \(\times\) 10\({}^{-8}\) cm/s. The permeability of kaolin samples with all nanomaterials added was lower than that of kaolin without nanomaterials. The addition of 1% iron oxide, 1% aluminum oxide, and 1% Oltu clay to kaolin decreased the initial permeability of kaolin to 2.15 \(\times\) 10\({}^{-8}\) cm/s, 1.78 \(\times\) 10\({}^{-8}\) cm/s, and 3.66 \(\times\) 10\({}^{-9}\) cm/s, respectively. The addition of 5% iron oxide, 5% aluminum oxide, and 5% Oltu clay to kaolin decreased the initial permeability of kaolin to 1.93 \(\times\) 10\({}^{-8}\) cm/s, 6.74 \(\times\) 10\({}^{-9}\) cm/s, and 9.8 \(\times\) 10\({}^{-10}\) cm/s, respectively. This reduction in permeability can be attributed to the nanomaterials reducing the large voids of kaolin [21; 22; 25].  
The permeability decreased gradually with increasing ratio of nanomaterials added to kaolin. The addition of 1% iron oxide, 1% aluminum oxide, and 1% Oltu clay to kaolin reduced permeability by 25.11%, 38.09%, and 87.25%, respectively; 5% iron oxide, 5% aluminum oxide, and 5% Oltu clay reduced the permeability by 32.99%, 76.54%, and 96.59%, respectively. The permeability decreased with increasing nanomaterial ratios, as increased ratio of all nanomaterials caused more clogging of the porous structure of kaolin.  
The permeability of all kaolin and kaolin/nanomaterial samples decreased until day 60, but increased on day 90. The decrease in permeability until the 60 th day can be attributed the adsorption of contaminants such as heavy metals, suspended solids, and microorganisms in the leachate to the kaolin and nanomaterial surfaces or clogging of the voids in the soil structure by these pollutants [9; 32; 35]. On the other hand, permeability increased in all kaolin samples due to desorption on the 90 th day. In addition, the results of the increase or decrease in the permeability as a function of the number of days were found to be in harmony with the heavy metal removal efficiency described in Section 3.2.  
The maximum reduction in permeability was achieved in the case of the combination of kaolin + 5% Oltu clay on the first day, day 30, day 60, and day 90. For both 1% nanomaterial  
Figure 2: Permeability of kaolin and kaolin/nanomaterial samples.  
addition and 5% nanomaterial addition, the performance of the nanomaterials in terms of reducing permeability was determined to follow the following order from high to low on all days: Oltu clay > aluminum oxide > iron oxide. The order of the size of the nanomaterials included in kaolin, from largest to smallest, was Oltu clay > aluminum oxide > iron oxide. Oltu clay (5-10 nm), which has a smaller size than the other nanomaterials, clogged the pores of the kaolin more, causing a further decrease in the permeability of the leachate. The permeability results showed that the permeability decreased with decreasing size of the nanomaterial added to the kaolin.  
Figure 3 shows the results for the average permeability of kaolin with the addition of 1% and 5% nanomaterials over 90 days. With the addition of 5% iron oxide, 5% aluminum oxide and 5% Oltu clay to kaolin, the average permeability decreased by 63.36%, 81.26%, and 96.89%, respectively. The improved performance of Oltu clay, aluminum oxide, and iron oxide in reducing permeability can be explained by the increased packing density due to their smaller size, as well as their structural properties. Results similar to those suggesting that smaller-diameter nanomaterials reduce the permeability more reported in this study can be found in [PERSON] et al. [36] and [PERSON] [37].