Structural and dynamic characterisation of charged microemulsions grafted with telechelic polymers at high dilution

Microemulsions are widely studied model colloidal systems due to their well-defined structure and tunable interactions. In this work, we investigate the structural and dynamic properties of a mixed system composed of microemulsion droplets grafted with a steric telechelic polymer, polyethylene oxide-C $_{12}^{}$ H $_{25}^{}$ (PEO-m), at a low volume fraction ( $\varphi =2\%$ ). The microemulsions studied are direct (oil-in-water) microemulsions, stabilised by cetylpyridinium chloride (CpCl) as the surfactant and octanol as the co-surfactant. The interaction potential of this system is modelled using the Derjaguin-Landau-Verwey-Overbeek (DLVO) framework, which combines a hard sphere potential, a van der Waals potential, and a Coulomb potential. Three complementary approaches are employed: small-angle neutron scattering (SANS) experiments, Ornstein-Zernike integral equations with the hypernetted chain (HNC) closure, and molecular dynamics (MD) simulations. SANS results show that the microemulsion droplets exhibit a spherical shape with an average radius $R_{\text{m}}=61\text{Å}$ and a polydispersity $\Delta R=8\text{Å}$ and that this morphology remains unchanged as long as the number of grafted polymers does not exceed $N_{\text{p}}\le 20$ . However, for $N_{\text{p}}>20$ , both the average radius and the polydispersity decrease to $R_{\text{m}}=49.5\text{Å}$ and $\Delta R=7.1\text{Å}$ . These results also indicate that the addition of PEO-m strengthens the repulsive interactions between droplets, thereby confirming that this polymer effectively stabilises the microemulsions. The Ornstein-Zernike integral equation with the HNC closure is used to determine the parameters of the potential describing the interactions between droplets. These parameters are subsequently introduced into MD simulations to assess the dynamic properties of the system. The results show that the addition of PEO-m reduces droplet mobility, while the diffusion behaviour remains normal.