(a) DLVO and XDLVO interaction energy profiles for the SG membrane and polystyrene colloid; I 5 10 mM NaCl, pH 5 5.4. (b) Normalized force vs. piezo scanner position for the SG membrane and a polystyrene colloid-tipped cantilever; I 5 10 mM NaCl, pH 5 5.4.  

(a) DLVO and XDLVO interaction energy profiles for the SG membrane and polystyrene colloid; I 5 10 mM NaCl, pH 5 5.4. (b) Normalized force vs. piezo scanner position for the SG membrane and a polystyrene colloid-tipped cantilever; I 5 10 mM NaCl, pH 5 5.4.  

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Theoretical predictions of interaction energies for several membrane–colloid pairs were made using the classical DLVO theory and an extended DLVO (XDLVO) approach. The XDLVO approach accounts for acid-base (polar) interactions that are not considered in the classical DLVO theory. For all membrane-colloid pairs studied, DLVO interactions were simila...

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... XDLVO theory was used to explain the GQD transport in the porous media, through describing the interaction energy profile between nanoparticles and sand media and explain the stability through the energy profile between nanoparticles. The total interaction energy could be described as the sum of van der Waals attraction (VDW), electrostatic repulsion (EL) and Lewis acid-base interaction (AB) (Brant & Childress, 2002), which could be written as: ...
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... However, in the case of the aggregation and the flotat hydrophobic particles, in order to harmonize the theory and the experiment, necessary to apply new mechanisms of long-range surface forces. They are collec called "non-DLVO" forces in the literature [53][54][55] and are taken into account b extended DLVO theory (XDLVO [56][57][58]). The relationship between the particle adh to the bubble during flotation and the interaction forces caused by the altered struct the liquid present in the wetting film, i.e., hydrophobic attractive forces, is show [41,59], including during gold flotation with xanthogenate [44,60,61]. ...
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... In addition, according to the Eqs in Table S4, Lewis acid-base interaction energy absolute value is commonly greater than LW and EL energies. It plays a decisive role in the negative or positive characteristics of the total energy [44]. There is hydrophobic attraction energy between two completely non-polar particles (ΔE s-Water-s = − 102 mJ/m 2 ) [45]. ...
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... According to the work in [50], the XDLVO theory does not take into account biological-specific interactions and takes into account only the Lifshitz-van der Waals and acid-base components responsible of first steps of adhesion. Other authors reported that the cause of these significant discrepancies is due to the non-DLVO interactions and physical and chemical heterogeneities [51][52][53]. So, microbial adhesion is a multifactorial phenomenon in which other factors could contribute other than the Lifshitz-van der Waals and acid-base interactions. ...
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