not important for condensed phases. If the solute is not crystalline, we can still use a spatial lattice, as good an approximation for an amorphous solid as it is for a liquid. The Flory–Huggins solution theory provides the entropy of mixing for polymer solutions, in which the macromolecules are huge compared to the solvent molecules. In this case, the assumption is made that each monomer subunit in the polymer chain occupies a lattice site. Note that solids in contact with each other also slowly interdiffuse, and solid mixtures of two or more components may be made at will (alloys, semiconductors, etc.). Again, the same equations for the entropy of mixing apply, but only for homogeneous, uniform phases. Mixing under other constraints Mixing with and without change of available volume In the established customary usage, expressed in the lead section of this article, the entropy of mixing comes from two mechanisms, the intermingling and possible interactions of the distinct molecular species, and the change in the volume available for each molecular species, or the change in concentration of each molecular species. For ideal gases, the entropy of mixing at prescribed common temperature and pressure has nothing to do with mixing in the sense of intermingling and interactions of molecular species, but is only to do with expansion into the common volume. According to Fowler and Guggenheim (1939/1965), the conflating of the just-mentioned two mechanisms for the entropy of mixing is well established in customary terminology, but can be confusing unless it is borne in mind that the independent variables are the common initial and final temperature and total pressure; if the respective partial pressures or the total volume are chosen as independent variables instead of the total pressure, the description is different. Mixing with each gas kept at constant partial volume, with changing total volume In contrast to the established customary usage, "mixing" might be conducted reversibly at constant volume for each of two fixed masses of gases of equal volume, being mixed by gradually merging their initially separate volumes by use of two ideal semipermeable membranes, each permeable only to one of the respective gases, so that the respective volumes available to each gas remain constant during the merge. Either one of the common temperature or the common pressure is chosen to be independently controlled by the experimenter, the other being allowed to vary so as to maintain constant volume