A Capillary Break-up Extensional Rheometer (CaBER) was modified to enable measurements of the axial force in combination with the related displacement. This makes it possible to determine the separation energy, the tackiness, of a polymer solution between two parallel plates with the CaBER. Separation energies of solutions of linear polystyrene, comb polystyrene and linear poly(methyl methacrylate) in dimethylformamide were measured as model systems. For linear polymers at a critical polymer concentration, there was a drastic change in slope of the separation energy. This critical concentration was shown to be the minimum concentration at which continuous bead-free fibers could be electrospun.