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Surface heterogeneity is ubiquitous in both natural and man-made materials, and can significantly influences material properties. However, it is very challenging to noninvasively probe the variation of surface properties in porous materials. Recently, we have proposed a method, i.e., the generalized Porod's scattering law method (GPSLM), to obtain the surface heterogeneity information in bulk porous materials by extending the classic Porod's scattering method. However, it was not clear if the GPSLM can be applied to other more complex materials, such as porous materials with dead pores, i.e., pores that guest fluid molecules cannot access or porous materials whose solid matrix can adsorb small guest molecules. In this paper, we theoretically extend the GPSLM to study those more complex situations. For all five cases with different levels of complexity discussed in this work, the scattering intensity at the Porod's law region always follows a parabolic function of scattering length density (SLD) of the guest fluid. Moreover, the minimum value of the scattering intensity is all related to the surface heterogeneity of the porous materials. The SLD of the guest fluid at which the minimum intensity is reached is always related to the surface-averaged SLD of materials. We also discuss the potential limitations and possible future applications of the GPSLM. As the GPSLM is based on the contrast variation method commonly used for a wide range of materials, such as geological materials, biomaterials, and colloidal suspensions, the theoretical development here is potentially useful for researchers who would like to apply the GPSLM to more complicated materials besides porous materials.

Investigation of porous materials with large surface heterogeneity using the generalized Porod's scattering law method