Intermolecular interactions in ordered (lyotropic liquid crystalline) assemblies formed by hydrated poly(ethylene oxide)-poly(propylene oxide) (PEO-PPO) block copolymers (Pluronics or Poloxamers) have been probed using the osmotic stress method. This method involves the equilibration, following the removal or the addition of an appropriate amount of water, of hydrated block copolymer samples with a system (aqueous polymer solution or water vapor) of known osmotic pressure (in the range 0.05-3000 atm). The primary result from such an experiment is a relationship between osmotic pressure (and consequently the corresponding chemical potential and activity of the solvent water) and block copolymer volume fraction. The osmotic pressure of the two PEO-PPO block copolymer-water systems examined here increased exponentially from 5 x 10(3) to 3 x 10(8) Pa over the 6-99.9 wt % block copolymer concentration range. The osmotic pressure of the PEO-PPO block copolymer-water systems in the block copolymer concentration range 6-50 wt % can be well represented by an empirical scaling law for semidilute polymer solutions. A change in the scaling exponent occurs at concentrations close to the disorder-order transition. The activity of water obtained from PEO-PPO block copolymer solutions and gels was fitted well by the Flory-Huggins equation up to 70 wt % block copolymer using an interaction parameter that represents the interactions between the PEO segments and water. The work of dehydration was estimated within each ordered phase and for phase transitions between different ordered structures. Finally, the combination of osmotic force data with data on the distance (spacing) between assemblies in the ordered block copolymer samples (determined via small-angle X-ray scattering), allowed us to construct a force vs distance curve, which reveals that interactions occur at two levels, that of the PEO coil and that of the PEO segment.