Extended DLVO interactions between spherical particles and rough surfaces

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Abstract

An “extended DLVO” approach that includes Lifshitz–van der Waals, Lewis acid–base, and electrostatic double layer interactions is used to describe interaction energies between spherical particles and rough surfaces. Favorable, unfavorable, and intermediate deposition conditions are simulated using surface properties representing common aquatic colloids and polymeric membranes. The surface element integration (SEI) technique and Derjaguin's integration method are employed to calculate interaction energy. Numerical simulations using SEI demonstrate that nanometer scale surface roughness features can produce a distribution of interaction energy profiles. Local interaction energies are statistically analyzed to define representative interaction energy profiles—minimum, average, and maximum—for various combinations of simulated particles and surfaces. In all cases, the magnitude of the average interaction energy profile is reduced, but the reduction of energy depends on particle size, asperity size, and density of asperities. In some cases, a surface that is on average unfavorable for deposition (repulsive) may possess locally favorable (attractive) sites solely due to nanoscale surface roughness. A weighted average of the analytical sphere–sphere and sphere–plate expressions of Derjaguin reasonably approximates the average interaction energy profiles predicted by the SEI model, where the weighting factor is based on the fraction of interactions involving asperities.

Graphical abstract

Extended DLVO interactions between nanoparticles and surfaces with nanoscale roughness features are modeled.

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Introduction

It is common to describe particle–substrate interfacial interactions in aqueous media via the Derjaguin–Landau–Verwey–Overbeek (DLVO) theory of colloid stability [1], [2], which accounts for attractive van der Waals interactions and repulsive electrostatic double layer interactions. While DLVO theory provides a robust explanation for the stability of lyophobic colloids, there are innumerable reported discrepancies between theoretical predictions and experimental observations of particle stability, deposition, and adhesion in engineered and natural systems. In efforts to overcome such discrepancies, some researchers have additionally considered non-DLVO interactions arising from acid–base [3], steric [4], and hydrodynamic [5], [6], [7] interfacial forces. Addition of non-DLVO interactions (of any type) to van der Waals and electrostatic interactions can be referred to as an “extended DLVO” or “XDLVO” approach [8], [9], [10]. In addition to non-DLVO interactions, physical and chemical heterogeneities have been implicated as the cause of significant discrepancies between DLVO (or XDLVO) theoretical predictions and experimental observations [11], [12], [13].

As a practical example, numerous researchers have studied the governing roles of DLVO and extended DLVO interactions on colloidal fouling in membrane-based water treatment processes [14], [15], [16], [17], [18], [19], [20], [21]. Past research suggests a correlation between membrane surface roughness and the initial rate of colloidal fouling on polymeric reverse osmosis membranes and several studies have shown fouling to be less severe on smooth cellulose acetate (CA) membranes than on rough polyamide (PA) membranes [22], [23], [24], [25]. It is now clear that acid–base interactions play a critical role in the different rates of colloidal fouling on CA and PA membranes [26]. Also, past research has shown that the magnitude of colloid–membrane DLVO interactions tend to be reduced by membrane surface roughness [27].

The objective of this study is to further elucidate the general role of nanoscale surface roughness on particle–substrate interactions via model simulations. Experimentally determined physicochemical properties of aquatic colloids and polymeric membranes define the simulated particle and substrate surface properties [25], [26]. Computed surface tensions and zeta potentials are employed in an extended DLVO approach that includes Lifshitz–van der Waals, Lewis acid–base, and electrostatic double layer interactions. The surface element integration (SEI) technique has been modified to calculate the XDLVO interaction energy between spherical particles and rough surfaces, where the minimum separation distance is defined by the point of closest approach, not the mean plane of the rough surface—as in past studies [27], [28], [29], [30], [31]. Several hundred interaction energy profiles are obtained across representative areas of each substrate (for a given particle). The profiles are statistically analyzed to define minimum, average, and maximum interaction energy profiles. Predictions from the numerical SEI model are compared to analytical model predictions for sphere–sphere and sphere–plate interactions derived using Derjaguin's integration method [32], [33].

Section snippets

Extended DLVO interaction energy

In this study, we compute the total XDLVO interaction energy per unit area between two infinite planar surfaces (separated by a distance h) by adding the unretarded Lifshitz–van der Waals (LW), Lewis acid–base (AB), and the constant potential electrostatic double layer interaction energy (EL) expressions [34], [35]. The total XDLVO interaction energy per unit area between infinite flat plates is given byEPPXDLVO(h)=EPPLW(h)+EPPAB(h)+EPPEL(h). The interaction energies for each individual

Membrane and particle properties

Simulated membrane surface roughness statistics reflect a number of past studies involving characterization of polymeric membranes by atomic force microscopy [22], [23], [24], [25], [27]. Roughness statistics for numerically re-created membrane surfaces are provided in Table 1. Surfaces 1, 2, and 3 were generated with average surface roughness values (asperity radii), R, of 5.29, 10.6, and 35.0 nm, respectively, while maintaining surface area difference (SAD) of 20%. Surface 3 could not be

Conclusion

Simulations were performed to study interfacial interactions between spherical particles and rough substrate surfaces via an extended DLVO potential. Randomly sized, located, and oriented, nanoscale hemispherical roughness features create a distribution of interaction energies, where local particle–substrate interaction potentials may be increased or decreased from that predicted by assuming a smooth surface. We suggest this distribution of interaction energies, engendered by surface roughness

Acknowledgements

This research was performed while Gaurav K. Agarwal was a Master of Science candidate in the Department of Chemical and Environmental Engineering at the University of California, Riverside (UCR). The authors acknowledge financial support received from UCR and from the California Department of Water Resources through the Desalination Research Innovation Partnership (DRIP), which is managed by the Metropolitan Water District of Southern California.

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