We present molecular dynamics simulation results based on a semi-empirical potential model in analogy to the tight binding theory in the second moment approximation, concerning the structural and dynamical properties of, Various concentrations Pb adlayers on the Cu(111) surface. We found that the adlayer's character changes from lattice gas to solid as, the Pb concentration passes the characteristic value theta(c)=37.5%. Specifically, At concentration less than theta(c) the deposited Pb atoms exhibit lattice gas behaviour while Above theta(c) 2D liquid like character appears, to recover typical solid behaviour above the saturation concentration that is dictated by the lattice mismatch at theta(s) = 56.3%. These conclusions are deduced from the calculated structural and dynamical properties of the overlayer, namely the Pb two-dimensional radial distribution function and the velocity autocorrelation functions as well as the atomic diffusion coefficient. It is found that for concentrations up to theta(c) the adlayer exhibits important expansion with Pb atoms flowing over the substrate and diffusing very fast, while at Os the Pb adlayer is compressed by as much as -2.65% with respect to the lattice spacing of the bulk Pb. Our findings are in agreement with available experimental results. (c) 2005 Elsevier B.V. All rights reserved.