Phase behavior of tethered polymers with lateral mobility in poor solvents

We present a scaling theory (ST) for the phase behavior of tethered polymers with lateral mobility in poor solvents. The coupling between inter- and intrachain interactions is included to describe the crossover between the "mushroom" and the layer regimes. The macroscopic phase separation and the associated changes in the chain configurations along the coexistence curve are obtained. The coupling between the thermodynamic state and the configurational behavior is described in detail. Good agreement between the ST and a molecular approach (single-chain mean-field theory) is obtained for the thermodynamic behavior and most of the conformational properties of the chains. Based on the ST, the renormalization group (RG) analysis is employed to derive the degree of polymerization, N, exponents in the critical amplitudes of the phase separation. It is found that some of the critical amplitudes have no N dependence, as expected in the semidilute regime, while others do show a dependence. These findings are in line with the fact that the critical region is in the crossover between the dilute and the semidilute regimes. The N exponents also differ from those for 2D polymer solutions, due to the fact that the thickness of the tethered chain layer has a power law dependence on N.