朗缪尔吸附等温式Langmuir adsorption model

吸附速率与气体压力和空位分数成正比 r_a = k_a·p·(1 − θ)，脱附速率与覆盖度成正比 r_d = k_d·θ；平衡时两者相等，得 θ = Kp/(1 + Kp)，K = k_a/k_d 为吸附平衡常数。低压时 θ ≈ Kp（线性，亨利区）；高压时 θ → 1（饱和）。线性化形式 p/V = 1/(K·V_m) + p/V_m 可由实验数据求出单层饱和吸附量 V_m。解离吸附（如 H₂ → 2H）时 θ = (Kp)^½/[1 + (Kp)^½]。

The adsorption rate is proportional to pressure and the fraction of empty sites, r_a = k_a·p·(1 − θ), and the desorption rate to coverage, r_d = k_d·θ; equating them gives θ = Kp/(1 + Kp), with K = k_a/k_d. At low pressure θ ≈ Kp (linear, the Henry region); at high pressure θ → 1 (saturation). The linear form p/V = 1/(K·V_m) + p/V_m yields the monolayer capacity V_m from data. For dissociative adsorption, such as H₂ → 2H, θ = (Kp)^½/[1 + (Kp)^½].

1916–1918 年美国通用电气公司的欧文·朗缪尔在研究钨丝白炽灯中气体与金属表面的相互作用时提出该理论。他还研究了液面单分子膜（朗缪尔-布洛杰特膜），因表面化学的发现和研究获 1932 年诺贝尔化学奖，是第一位获得诺贝尔化学奖的美国工业科学家。

Irving Langmuir at General Electric developed the theory between 1916 and 1918 while studying how gases interact with metal surfaces in tungsten-filament lamps. He also studied monolayers on liquids (Langmuir–Blodgett films) and received the 1932 Nobel Prize in Chemistry for discoveries in surface chemistry, the first industrial scientist in the United States to win it.

朗缪尔方程是多相催化动力学中朗缪尔-欣谢尔伍德机理和埃利-里迪尔机理的基础，也用于描述溶液中染料、重金属在吸附剂上的吸附、以及酶与底物结合（与米氏方程形式相同）。实际表面不均匀、吸附分子间存在相互作用，因此常需用弗罗因德利希、焦姆金或 BET 方程修正。

The Langmuir equation underlies the Langmuir–Hinshelwood and Eley–Rideal mechanisms in heterogeneous catalysis, and describes adsorption of dyes and heavy metals from solution and enzyme–substrate binding, which has the same form as the Michaelis–Menten equation. Real surfaces are heterogeneous and adsorbed molecules interact, so Freundlich, Temkin or BET equations are often needed instead.