Universality Classes and Unusual Thermodynamics of Unbinding Transitions of Semi-flexible Polymers Confined to a Surface

We theoretically address unbinding of semi-flexible polymers from long line-like attractive potential wells of various forms. These transition phenomena are seen in recent experiments with DNA adsorbed on microstructured supported cationic lipid membranes, and they provide a new way to stretch single DNA molecules [Hochrein, Leierseder, Golubovic, and Raedler, 2005]. For simple attractive potential wells (``rectangular wells'') the transition is of the second order. Heat capacity divergence however has a non-standard from, C$\sim $1/[$\vert $Tc - T$\vert $ log($\vert $Tc - T$\vert )$], marked by a logarithmic correction related to the fact that the probability to find the polymer within the well region vanishes as $\sim $1/ log($\vert $Tc-T$\vert )$ at the transition point. On the other hand, for attractive potential wells having a hard wall potential added on one side, the transition becomes a non-standard hybrid between the first and second order phase transitions: the probability to find the polymer within the well approaches a non-zero value as the transition is approached and then it discontinuously drops to zero (producing a latent heat consumption). However, interestingly, in addition to the latent heat consumption, an unusual heat capacity divergence (of the form C$\sim $1/$\vert $Tc - T$\vert$$^{1/2}$) also occurs as the polymer unbinding point is approached.