## 1 Introduction  
Recently, nanotechnological applications have attracted great attention in the context of oil reservoirs with small pores and pore throats [1; 2; 3; 4; 5; 6; 7; 8]. Nanoparticle (NP) dispersions change the wettability of porous media. Wettability controls the fluid flow, thus affecting oil recovery during water flooding. Many studies have shown that NPs render rock surfaces more hydrophillically wettable [9; 10; 11; 12]. In addition, NPs reduce interfacial tension (IFT) when they adsorb to oil-water interfaces [13; 14; 15]. This greatly improves displacement efficiency, and thus, oil recovery. However, in many studies regarding enhanced oil recovery using NPs, NP stability remained problematic [16; 17]. The low stability of individual particles in a high-saline environment triggers aggregation, which may obstruct pores and possibly damage the rock formation [17; 18]. Initially, small clusters form, followed by larger clusters, reflecting the balance of forces according to the Derjaguin-Landau-Verwey-Overbeek theory. The gradual increase in cluster size causes undesirable NP sedimentation in a porous medium, separating the NPs from the nanofluid [19]. High temperature enhances Brownian motion and the consequent probability of particle collision; oppositely charged ions in solution limit the electrostatic repulsion between particles, and thus, promote flocculation [17]. Therefore, particle surface modification is essential when preparing thermally and kinetically stable NP dispersions. To this end, NPs are blended with surfactants (stabilizers) [20; 21]. The synergistic effects of surfactants and NPs have been widely researched; these lower the IFT and change the surface wettability of reservoir rock [22; 23]. Surfactant-NP systems have attracted attention because of their increased particle stability, reduced NP dosage, decreased surfactant adsorption loss, and enhanced efficiency [17; 24]. As well as the surfactant-NP system, NP surface modifications using a polymer chain improve particle stability. [PERSON] et al. [25] found that PAA (polyacrylamide acid)-modified nanoparticles were more dispersible in aqueous solutions compared with unmodified particles. They concluded that PAA-modified particles flowed approximately 10-fold longer through a silica sand column compared with unmodified particles. [PERSON] et al. [26] also modified NP surfaces by copolymerization with PSS (polystyrene sulfonate); the modified particles formed stable colloids in high-concentration brine. In our previous study, silica NP stability was enhanced after absorption of a zwitterionic surfactant and PSS-\(co\)-MA [27]. We found that the adsorption of PSS-\(co\)-MA on silica NPs was possibly generated by van der Waals attraction. Furthermore, adsorption of zwitterionic surfactant onto NPs is mediated by dipole-charge interaction between the trimethylammonium groups of zwitterionic surfactant and negatively charged particles with PSS-\(co\)-MA under brine. Previous study showed that our surface-modified could reduce the IFT and enhance oil recovery. For further research, this study focused on the effect of nanoparticle size on interfacial tension and rock wettability. Size variation of NPs strongly affects their physical properties. For example, NP size can affect wettability. [PERSON] and [PERSON] [28; 29] showed that the pressure caused by NP deposition at oil-water-solid contact regions (i.e., disjoining pressure) is the primary mechanism of oil displacement in sandstone. They concluded that disjoining pressure is related to the size of the NP because the energy at oil--water-solid contact regions is a function of the particle diameter. However, in contrast, [PERSON] et al. [30] found that the NP size (5 and 25 nm) did not influence the wettability alteration of the oil-wet calcite rocks, indicating that there was no difference in particle adsorption on the rock surface. These previous studies have shown different results. Further experimental studies are needed to determine the effect of the size of NP on rock wettability.