BET理论BET theory

BET 理论假设：第一层吸附靠固体表面作用力，吸附热为 E₁；第二层及以上靠吸附质分子之间的作用，吸附热等于液化热 E_L；每一层都满足朗缪尔式的动态平衡，且层数可无限多。由此得到 BET 方程：p/[V(p₀ − p)] = 1/(V_m·C) + (C − 1)/(V_m·C)·(p/p₀)，其中 p₀ 为饱和蒸气压，C 与 E₁ − E_L 有关。在相对压力 p/p₀ ≈ 0.05–0.30 范围内作图得直线，由斜率和截距求出 V_m。

BET theory assumes the first layer is held by the solid surface with heat E₁, higher layers by adsorbate–adsorbate interactions with heat equal to the heat of liquefaction E_L, each layer in Langmuir-type dynamic equilibrium, and an unlimited number of layers. This gives the BET equation p/[V(p₀ − p)] = 1/(V_m·C) + (C − 1)/(V_m·C)·(p/p₀), where p₀ is the saturation vapour pressure and C depends on E₁ − E_L. A plot over relative pressures of about 0.05–0.30 is linear, and V_m follows from slope and intercept.

比表面积 S = V_m·N_A·σ / (22 414·m)，σ 为一个吸附质分子的截面积，77 K 液氮温度下 N₂ 取 0.162 nm²。对于微孔材料（孔径 < 2 nm）BET 模型假设不完全成立，得到的是“表观”比表面积，需谨慎解释。氪气吸附可用于测定比表面积很小的样品。

Specific surface area S = V_m·N_A·σ / (22,414·m), where σ is the cross-section of one adsorbate molecule, 0.162 nm² for N₂ at 77 K. For microporous materials (pores below 2 nm) the BET assumptions do not fully hold, and the result is an 'apparent' area to be interpreted with care. Krypton adsorption is used for samples with very small surface areas.

该理论以三位作者的姓氏首字母命名：斯蒂芬·布鲁诺尔、保罗·埃米特（美国农业部固氮研究实验室）和爱德华·特勒（后以氢弹研究闻名）。BET 比表面积广泛用于表征催化剂、活性炭、二氧化硅、药物粉体、电池材料、水泥和金属有机框架等。

The theory is named for its authors: Stephen Brunauer, Paul Emmett, both at the US Department of Agriculture's Fixed Nitrogen Research Laboratory, and Edward Teller, later known for the hydrogen bomb. BET surface area is used to characterise catalysts, activated carbon, silica, pharmaceutical powders, battery materials, cement and metal–organic frameworks.