含义Meaning
晶格模型下高分子溶液（或共混物）的混合自由能。由于一条长链只算一个“分子”，混合熵很小，因此高分子之间普遍不相容，微小的正 χ 就会导致相分离。
Lattice-model free energy of mixing for polymer solutions and blends. Because each long chain counts as one molecule, the entropy of mixing is tiny, so polymers are generally immiscible and a small positive χ causes phase separation.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(\phi_i\) | 体积分数volume fraction | 1 |
| \(n_1\) | 溶剂物质的量moles of solvent | mol |
| \(\chi\) | 弗洛里–哈金斯相互作用参数Flory–Huggins interaction parameter | 1 |
| \(N\) | 链段数（聚合度）segments per chain | 1 |
推导Derivation
把溶剂分子和链段放在同一晶格中，每条链占 N 个相邻格点。
Place solvent and chain segments on a lattice; each chain occupies N connected sites.
计算放置方式数得组合熵 \(\Delta S = -R(n_1\ln\phi_1 + n_2\ln\phi_2)\)——与小分子的区别是用体积分数代替摩尔分数。
Counting arrangements gives \(\Delta S = -R(n_1\ln\phi_1 + n_2\ln\phi_2)\), with volume fractions.
平均场的接触能 \(\Delta H = RT\chi n_1\phi_2\)，\(\chi = z\Delta w/k_\mathrm BT\)。
Mean-field contact energy \(\Delta H = RT\chi n_1\phi_2\).
对 φ 求二阶导等于零、三阶导等于零得临界点；N 大时 χ_c → 1/2（θ 条件）。
Spinodal and critical conditions give χ_c → ½ for large N (θ condition).
适用条件与局限Assumptions & limitations
平均场、不可压缩晶格、忽略链段间关联；χ 实际随浓度和温度变化（χ = A + B/T）。
Mean field, incompressible lattice; χ actually depends on composition and T.