Model samples of polyethylene (PE) with different degrees of branching (up to seven side groups, mostly of butyl type, at 100 C) are melt-crystallized at two undercoolings, 10 and 68 degrees C, in order to obtain samples with various crystalline structures. The last is verified by the observation that the commonly reported equilibrium melting point T-m(infinity) of PE is again obtained via extrapolation to infinitely large crystals from both small-angle X-ray scattering and wide-angle X-ray scattering measurements. The samples are also characterized with respect to their density and microhardness (H). The very strong effect of crystallinity and crystal sizes on H is clearly demonstrated. It is emphasized that the crystal size effect reflects rather the effect of crystal perfection, i.e. packing density. Via extrapolation of H the equilibrium microhardness of PE crystals H-c(infinity) = 160 MPa is determined. It is also shown that H vanishes when the crystal size approaches 27 Angstrom. Using the recently derived analytical expression for T-g and H, the T-g of completely amorphous samples of PE is calculated and a value of -25 degrees C is obtained which agrees with the reported highest values for T-g of PE. In addition, a simple equation for the calculation of H from the paracrystalline lattice distortions g((hk0)) is Proposed (H = H-c(id) - kg((hk0))), provided the structure of the crystallites can be described by the one-phase paracrystalline concept. Finally, in addition to previous results on other systems, it is demonstrated that the application of the additivity law to multicomponent and/or multiphase systems is justified only in the case when all components (phases) have a melting or glass transition temperature (T-m,T-g) above the temperature at which the H-measurements are carried out. In the case where the system contains a liquid-like component (phase), its contribution to the overall His by changing the deformation mechanism and in order to apply the additivity law, H must be expressed as H = 1.97T(g) - 571. (C) 2000 Elsevier Science Ltd. All rights reserved.