DR是该方程发明者Dubinin,Radushkevich名字的缩写。在细孔直径接近吸附分子直径的微孔中,相对的两个孔壁对吸附分子的作用势场发生重叠,使气体分子的吸附能很大。因此,在低压时吸附量就很大,等温线在低相对压力P/Po时就急剧上升,呈Ⅰ型等温线。Dubinin为了与通常的吸附区分,称之为微孔填充(micropore filling)
微孔充填率θ:在单一吸附质体系,吸附势作用下,吸附剂被吸附质充占的体积分数是吸附体积V与极限吸附体积V0之比,定义为微孔充填率θ.
Dubinin-Radushkevich(D-R)方程:
式中β是亲和系数, (对于苯为1)
n为系数, (活性炭-苯体系的n为2)
k为特征常数
A为固体表面吸附势,![](data:image/png;base64,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)
一、微孔表面积的计算
D-R方程的对数表达式:
Kaganer对D-R方程改进:
作
-
图,得到截距
,可经过Vm计算出微孔表面积,相对压力P/Po一般小于10-2
二、吸附能与平均孔宽的计算
用苯做参比吸附质时:
吸附能:![](data:image/png;base64,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)
平均孔宽:![](data:image/png;base64,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)
式中,
,M和
分别是吸附质和参比吸附质的相对分子量;
和
分别是吸附质和参比吸附质在吸附温度T时的液体密度;K为D-R方程的斜率。