On the scaling of the osmotic pressure of two-dimensional polymers in the transition from the semidilute to the melt regimes

This brief contribution highlights recent results on low-dimensional polymer melts. Numerical simulations demonstrate that the osmotic pressure of polymer solutions under nanoconfinement adheres to expected scaling laws in the semidilute regime. However, as the concentration increases toward the melt state, new scaling regimes emerge. A novel scaling function for the pressure has been developed, one that reveals fractal conformational characteristics unique to the two-dimensional nature of these polymer melts. This newly predicted fractal scaling law for the pressure in two-dimensional melts accounts for previously unexplained molecular simulation results and experimental observations. These observations include the structural features of highly confined or adsorbed long polymers, as detected through scanning tunneling microscopy and atomic force microscopy.