Rodrigues Nathann Teixeira, Alves Aarão Reis Fábio David
Instituto de Física, Universidade Federal Fluminense, Avenida Litorânea s/n, 24210-340 Niterói, RJ, Brazil.
Langmuir. 2024 Jun 4;40(22):11371-11380. doi: 10.1021/acs.langmuir.3c03855. Epub 2024 May 17.
The apparent tortuosity due to adsorption of diffusing tracers in a porous material is determined by a scaling approach and is used to analyze recent data on LiCl and alkane diffusion in mesoporous silica. The slope of the adsorption isotherm at small loadings is written as β = /, where is the adsorption-desorption ratio and = ϵ/() - 1 is a geometrical factor depending on the range of the tracer-wall interaction, the porosity ϵ, and the specific surface area . The adsorption leads to a decrease of effective diffusion coefficient, which is quantified by multiplying the geometrical tortuosity factor τ by an apparent tortuosity factor τ. In wide pores or when the adsorption barrier is high, τ = β + 1, as obtained in previous works, but in narrow pores there is an additional contribution from frequent adsorption-desorption transitions. These results are obtained in media with parallel pores of constant cross sections, where the ratio between the effective pore width ϵ/ and the actual width is ≈0.25. Applications to mesoporous silica samples are justified by the small deviations from this ideal ratio. In the analysis of alkane self-diffusion data, the fractions of adsorbed molecules predicted in a recent theoretical work are used to estimate τ of the silica samples, which is ≫1 only in the sample with the narrowest pores (nominal 3 nm). The application of the model to Li ion diffusion leads to similar values of τ and to a difference of energy barriers of desorption and adsorption for those ions of ∼0.06 eV. Comparatively, alkane self-diffusion provides the correct order of magnitude of τ, with adsorption playing a less important role, whereas adsorption effects on Li diffusion are much more important.
通过标度方法确定了由于扩散示踪剂在多孔材料中的吸附而导致的表观曲折度，并将其用于分析最近关于LiCl和烷烃在介孔二氧化硅中扩散的数据。小负载量下吸附等温线的斜率写为β = / ，其中 是吸附 - 解吸比，且 = ϵ/() - 1是一个几何因子，它取决于示踪剂与壁相互作用的范围 、孔隙率ϵ和比表面积 。吸附导致有效扩散系数降低，这通过将几何曲折度因子τ乘以表观曲折度因子τ来量化。在宽孔或吸附势垒高时，如先前工作中所得到的，τ = β + 1，但在窄孔中，频繁的吸附 - 解吸转变会有额外贡献。这些结果是在具有恒定横截面平行孔的介质中获得的，其中有效孔宽度ϵ/ 与实际宽度之间的比率约为0.25。由于与该理想比率的偏差较小，因此将其应用于介孔二氧化硅样品是合理的。在分析烷烃自扩散数据时，最近一项理论工作中预测的吸附分子分数用于估计二氧化硅样品的τ，只有在孔径最窄（标称3 nm）的样品中τ才远大于1。该模型应用于锂离子扩散时会得到相似的τ值，并且这些离子的解吸和吸附能垒之差约为0.06 eV。相比之下，烷烃自扩散给出了正确的τ量级顺序，吸附起的作用较小，而吸附对锂扩散的影响则重要得多。
