Analytical theory of finite-size effects in mechanical desorptionof a polymer chain

摘要

We discuss a unique system that allows exact analytical investigation of first- and second-ordertransitions with finite-size effects: mechanical desorption of an ideal lattice polymer chain graftedwith one end to a solid substrate with a pulling force applied to the other end. We exploit the analogywith a continuum model and use accurate mapping between the parameters in continuum and latticedescriptions, which leads to a fully analytical partition function as a function of chain length,temperature (or adsorption strength), and pulling force. The adsorption-desorption phase diagram,which gives the critical force as a function of temperature, is nonmonotonic and gives rise tore-entrance. We analyze the chain length dependence of several chain properties (bound fraction,chain extension, and heat capacity) for different cross sections of the phase diagram. Close to thetransition a single parameter (the product of the chain length Nand the deviation from the transitionpoint) describes all thermodynamic properties. We discuss finite-size effects at the second-ordertransition (adsorption without force) and at the first-order transition (mechanical desorption). Thefirst-order transition has some unusual features: The heat capacity in the transition region increasesanomalously with temperature as a power law, metastable states are completely absent, and insteadof a bimodal distribution there is a flat region that becomes more pronounced with increasing chainlength. The reason for this anomaly is the absence of an excess surface energy for the boundarybetween adsorbed and stretched coexisting phases (this boundary is one segment only): The twostates strongly fluctuate in the transition point. The relation between mechanical desorption andmechanical unzipping of DNA is discussed.