  Using surface-tension measurements, we study the brush-limited adsorption
dynamics of a range of amphiphilic polymers, PAAH-$\alpha$-$\textrm{C}_n$
composed of a poly(acrylic acid) backbone, PAAH, grafted with a fraction
$\alpha$ 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.
