Adsorption scaling theory for investigation of distance between clay-layers with adsorbed polymer and adsorption-isotherm versus polymer-concentration: Comparison to experiment

The purpose of this paper is to introduce an adsorption scaling theory for explaining the experimental results dealt with the clay-polymer hybrids. The main problem to apprehend is the evolution of two interesting physical quantities which are the equilibrium adsorbed quantity (adsorption-isotherm), Q_eq, and the clay-layer-spacing, d₀₀₁ upon the initial bulk-polymer-density, C_d. In the present investigation, we are concerned with the case where the polymers are highly attracted by the clay-layers (strong adsorption). For such an attractive case, the adsorption-isotherm shape and scenario of the interlaminar-space are explained using an elaborated adsorption scaling theory, and we show the existence of distinct regimes depending on the value of the initial bulk-polymer-density with water as host liquid. Within each density-regime, we give explicit expressions for the quantities Q_eqC_d and d₀₀₁C_d. On the other hand, the present adsorption scaling theory was tested and compared with two practical cases concerning bentonite-polygycols (PEGs) and montmorillonite-polycarboxylate ethers (PCEs) hybrids. For the two systems, the interlayer-distance was measured as a function of the polymer-amount based on X-ray Diffraction (XRD) analysis. We find that, quantitatively, these experiments are in good agreement with the adsorption scaling theory. Also, it is noted that such a theory is more general and powerful than the classical Langmuir adsorption theory. Finally, we state that the present theory can be applied to any polymer–clay hybrid, independently on its chemical and physical details.