= Solution
The <Flory interaction parameter> measures the energetic preference for unlike rather than like contacts in <Flory–Huggins solution theory>. For polymer volume fraction $\phi$ and $N$ lattice sites per chain, the dimensionless mixing <Helmholtz free energy> per site is
$$
\frac{f_{\rm mix}}{k_BT}=\frac\phi N\log\phi+(1-\phi)\log(1-\phi)+\chi\phi(1-\phi).
$$
The logarithmic terms represent combinatorial <entropy>; polymer connectivity reduces the chain's translational mixing entropy by the factor $N$. In a simple contact model $\chi=z[\epsilon_{ps}-(\epsilon_{pp}+\epsilon_{ss})/2]/(k_BT)$, where $z$ is the coordination number. Positive $\chi$ penalizes polymer-solvent contacts. Increasing it can overcome mixing <entropy> and cause <phase separation>; a negative second derivative of the mixing <free energy> marks the <spinodal> region. For a long dilute chain, $\chi<1/2$ corresponds to a <good solvent>, $\chi=1/2$ to the idealized theta condition, and $\chi>1/2$ to a <poor solvent>. Real effective parameters can depend on <temperature> and <concentration>, rather than being universal chemical constants.
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