We investigated the adsorption of a series of hydrophobically modified poly(acrylic acid) sodium salts (HMPAANa) at the air-water interface by dynamic surface tension measurements. We observed a logarithmic decrease of the surface tension with time over several decades, in good agreement with a reptation-diffusion-based model. The kinetics of adsorption in this logarithmic regime depends on the chain molecular weight and is independent of the polymer concentration and amount of hydrophobic moieties. Moreover, we show that no electrostatics takes place during the adsorption process. Finally, existing theoretical models were used to propose an interpretation of the logarithmic dependence of the adsorption with time.