Engineering topics
Publications and source records attributed to Frisch, H. L..
The exact Mayer series is derived for the pressure, density, and equation of state of a hard-sphere fluid in the limit of infinite space dimensions D. The Mayer series can be analytically continued into the full (cut) activity plane, and there is no sign of a phase transition. The quantum-mechanical system is also treated. For D = infinity, the fluid behaves like an ideal Bose gas and undergoes a Bose-Einstein condensation.
The equation of state of the fluid phase of the classical hard-sphere system in infinitely many dimensions has been obtained exactly. Only the first two virial coefficients are nonvanishing. The upper bound for the coefficients of the Mayer series for nonnegative interaction potentials is reached by this system.
A phenomenological theory is formulated for chemically quenched binary interpenetrating polymer networks (IPNs), considering both simultaneously crosslinked networks and sequentially crosslinked networks, as well as pseudointerpenetrating networks (where only one component is crosslinked and the other is a linear polymer). The construction of free energy functionals for homogeneous weakly crosslinked IPNs and pseudo-IPNs and their spinodal curves and critical points of unmixing is described. These free energy functionals are augmented with gradient energy terms in order to consider effects due to spatially varying small inhomogeneities in the network chain concentration. The dynamic response and the initial spinodal decomposition of IPNs are discussed.