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The binding strength of dispersants to the surface of carbon nanotubes is of crucial importance for the efficiency of the dispersion process and for potential applications, yet data are scarce on this subject. Here we present the results of diffusion NMR experiments in dispersions of single-walled carbon nanotubes (SWNTs) prepared by either the polymer Pluronics F127 or the protein bovine serum albumin (BSA). The experiments detect the amount of F127 molecules adsorbed onto the SWNT surface. This quantity is recorded (i) in F127-SWNT dispersions to which BSA molecules are added and (ii) in BSA-SWNT dispersions to which F127 molecules are added. The data clearly show that F127 replaces BSA adsorbed at the SWNT surface, while BSA leaves the adsorbed F127 coverage intact. Consequently, F127 binds to the nanotube surface more strongly than BSA. Hence, we provide a way to categorize dispersants by adsorption strength. We also provide evidence showing that the nanotubes dispersed by BSA form loose aggregates wh...