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A polymer chain tethered to a surface may be compact or extended, adsorbed ordesorbed, depending on interactions with the surface and the surroundingsolvent. This leads to a rich phase diagram with a variety of transitions. Toinvestigate these transitions we have performed Monte Carlo simulations of abond-fluctuation model with Wang-Landau and umbrella sampling algorithms in atwo-dimensional state space. The simulations' density of states results havebeen evaluated for interaction parameters spanning the range from good to poorsolvent conditions and from repulsive to strongly attractive surfaces. In thiswork, we describe the simulation method and present results for the overallphase behavior and for some of the transitions. For adsorption in good solvent,we compare with Metropolis Monte Carlo data for the same model and find goodagreement between the results. For the collapse transition, which occurs whenthe solvent quality changes from good to poor, we consider two situationscorresponding to three-dimensional (hard surface) and two-dimensional (veryattractive surface) chain conformations, respectively. For the hard surface, wecompare tethered chains with free chains and find very similar behavior forboth types of chains. For the very attractive surface, we find thetwo-dimensional chain collapse to be a two-step transition with the samesequence of transitions that is observed for three-dimensional chains: acoil-globule transition that changes the overall chain size is followed by alocal rearrangement of chain segments.

Transitions of tethered polymer chains: A simulation study with the bond fluctuation lattice model