Determination of interface layer thickness of a pseudo two-phase system by extension of the Debye equation

Abstract

The Debye equation with slit-smeared small angle x-ray scattering (SAXS) data is extended from an ideal two-phase system to a pseudo two-phase system with the presence of the interface layer, and a simple accurate solution is proposed to determine the average thickness of the interface layer in porous materials. This method is tested by experimental SAXS data, which were measured at 25 °C, of organo-modified mesoporous silica prepared by condensation of tetraethoxysilane (TEOS) and methyltriethoxysilane (MTES) using non-ionic neutral surfactant as template under neutral condition.

A program for SAXS data processing and analysis

“…an interface layer) with average thickness E between two phases, there is a negative deviation from the Debye's theory (see figure 2) [17]. In this case:…”

Investigations of thermal conductivity and viscosity of nanofluids

“…By extending the Debye equation, Li et al [22] also introduced the same model for the determination of interfacial layer thickness of a solid-liquid system. For σ = 0.4 nm, Eq.…”

A thermodynamic model of nanofluid viscosity based on a generalized Maxwell-type constitutive equation

“…Argon is found in the literature, we have assumed that h=0.2 nm, which is of the order of magnitude of the Van der Waals radius of Ar, which, by the way, lies within the range of values proposed for other fluids [44][45][46][47][48][49].…”