Adsorption dynamics of hydrophobically modified polymers at an air-water interface
Using surface-tension measurements, we study the brush-limited adsorption dynamics of a range of amphiphilic polymers, PAAH-$α$-$\textrm{C}_n$ composed of a poly(acrylic acid) backbone, PAAH, grafted with a fraction $α$ of alkyl moieties, containing either $n=8$ or $n=12$ carbon atoms, at pH conditions where the PAAH backbone is not charged. At short times, the surface tension decreases more sharply as the degree of grafting increases while at long times, the adsorption dynamics becomes logarithmic in time and is slower as the degree of grafting increases. This logarithmic behavior at long times indicates the building of a free-energy barrier which grows over time. To account for the observed surface tension evolution with the degree of grafting we propose a scenario, where the free-energy barrier results from both the deformation of the incoming polymer coils and the deformation of the adsorbed brush. Our model involves only two fitting parameters, the monomer size and the area needed for one molecule during adsorption and is in agreement with the experimental data. We obtain a reasonable value for the monomer size and find an area per adsorbed polymer chain of the order of 1nm$^2$, showing that the polymer chains are strongly stretched as they adsorb.