(700a) Calculation of Chemical Potential of Free and Adsorbed Polymers
The calculation of chemical potentials of chain molecules in the bulk and confined systems is a long-standing problem. The ?modified Widom method,? introduced by Kumar et al, and later verified by Spyriouni et al, suggests that the chemical potential of a long homopolymer chain can be extrapolated by the incremental chemical potential that corresponds to the addition of one monomer to the end of the chain. This is contingent on the independence of the incremental chemical potential on chain length for sufficiently long (> 10 monomer units) chains. From MC simulations performed with long (up to 500 monomer units) chains, we found that this ansatz is valid only for the case for self-avoiding chains (good solvent condition, or above the theta temperature). For temperatures below the theta temperature (poor solvent conditions), we find a logarithmic dependence of the incremental chemical potential on the chain length. We also have extended the Gauge Cell method to the calculation of the incremental chemical potential. The Gauge Cell method overcomes the shortfalls of Widom insertions, namely the improbable insertions in dense fluids, and the poor sampling of inhomogeneous fluids. This method is employed for calculations of adsorption equilibrium of polymer chains confined to nanoscale spheroidal pores. The critical conditions of adsorption are determined from the equality of chemical potentials in the bulk and confinement by varying the pore size and the adsorption potential.