## 3 Results
### Adsorption of Pluronic-F-127-Decorated Silica Nanoparticles at the Water-Vapor Interface
#### 3.3.2 Dilational Elasticity of Particle-Laden Interfaces  
The interfacial dilational elastic modulus, \(\varepsilon^{\prime}\), of the particle-laden interfaces was determined upon the equilibration of the adsorption process, i.e., when the interfacial tension reaches its equilibrium value. The frequency dependence of the interfacial dilational elastic modulus for Pluronic F-127 and copolymer-decorated silica nanoparticles with different concentrations of Pluronic F-127 is shown in Figure 5.  
As expected, in almost all of the experiments, as the deformation frequency increased, the value of the interfacial dilational elastic modulus also increased. However, for the lowest Pluronic F-127 concentrations and the highest particle concentrations, the interfacial dilational elastic modulus appeared to be weakly dependent on the frequency, which may indicate the formation of a solid-like particle-laden interface, in agreement with the discussion by [PERSON] et al. [49]. On the other hand, the copolymer concentration dependence of the interfacial dilational elastic modulus is not the same for all of the particle concentrations. At low particle concentrations, i.e., for layers formed only by Pluronic F-127 and layers formed when the particle concentration is 0.1% \(w/w\), the interfacial dilational elastic modulus decreases with increasing concentration. This situation changes as the particle concentration increases (1% \(w/w\)), where \(\epsilon^{\prime}\) initially increases with the Pluronic F-127 concentration and then, after reaching a threshold, the interfacial dilational elastic modulus begins to decrease with increasing concentration. The above behavior can easily be seen in the plot of the interfacial dilational modulus versus Pluronic F-127 concentration for experiments performed at a fixed frequency of 10\({}^{-1}\) Hz (see Figure 6). It should be noted that the existence of a peak for the adsorption of colloids from dispersions where the particle concentration is 1% \(w/w\) has a real physical origin. In fact, considering the state of the monolayer at the lowest concentration range, an increase in the dilational elasticity with Pluronic F-127 concentration is consistent with the sharp decrease in surface tension observed in the isotherm shown in Figure 4. It is expected that a similar dependence may  
Figure 5: Dependence of the interfacial dilational elastic modulus on the frequency of the sinusoidal deformation (the amplitude of deformation was maintained at 10% for all of the experiments) for equilibrated layers of Pluronic F-127 and copolymer-decorated silica nanoparticles: (**a**) \(c_{\text{NP}}=0\%\)\(w/w\) (Pluronic F-127 solutions), (**b**) \(c_{\text{NP}}=0.1\%\)\(w/w\), and (**c**) \(c_{\text{NP}}=1\%\)\(w/w\). The use of symbols with different colors indicates the different concentrations of Pluronic F-127 in the studied samples: (**b**) 0.1 mg/mL, (**c**) 0.2 mg/mL, (**d**) 0.5 mg/mL, (**e**) 1 mg/mL, (**e**) 2 mg/mL, (**f**) 5 mg/mL, and (**p**) 10 mg/mL. The lines are guides for the eyes, and the error bars were obtained as the standard deviation of three replicates for each experiment. appear for Pluronic F-127 solutions and dispersions with a particle concentration of 0.1% \(w/w\) by decreasing the Pluronic F-127 concentration below the range studied here. The analysis of the frequency dependence of the interfacial dilational elastic modulus shows the presence of a relaxation mechanism in the investigated frequency range, as evidenced by the inflection point in the curves. Considering the analyzed frequency range and its shift to higher values of frequency with the copolymer concentration, it can be assumed that the observed relaxation may correspond to the diffusion transfer of the copolymer (or copolymer-decorated particles) to the interface [10; 42]. The results do not rule out the presence of additional relaxation processes occurring at the interface [10; 50].