Surface Element Integration Technique Research Articles

Colloidal interactions for a polystyrene particle and a smooth silicon surface: Atomic force microscopy, XDLVO theory, and Surface Element Integration

In this study Liftshitz van der Waals, electrostatic and acid base interaction forces of a 4 µm polystyrene particle with flat silicon surfaces were experimentally determined using interfacial interaction energy measurements and atomic force microscopy (AFM). Interfacial forces computed using analytical expressions based on the Surface Element Integration (SEI) technique were compared with the standard Derjaguin Approximation (DA) and Continuum Mechanics Adhesion approaches, namely: Derjaguin, Muller and Toporov (DMT), Johnson, Kendall and Roberts (JKR) and Maugis and Pollock (MP) theories in order to assess the effect of curvature on a sphere-plate geometry. For acid base interactions, the SEI was found to deviate from the DA at small particles radii (less than 100 nm) and over a wide ratio of decay length, λ, to particle size, R. Accounting for curvature for acid base interaction requires geometric factors that are functions of λ/R. For van der Waals force of interaction, the SEI and DA showed large variation at large ratios of interparticle separation, D, to particle radius, R. For Double layer interaction force large variation between SEI and DA was observed for small κa values, and good agreement observed at large κa values. The AFM forces of adhesion of polystyrene in 0.01 mM and 100 mM KCl electrolyte solutions were found to be 2.38 ± 2.15 nN and 9.29 ± 6.89 nN, respectively. These results were found to be consistent with the SEI technique that gave adhesion forces of 4.8 and 10.2 nN at the low and high electrolyte concentrations, respectively. These data are also aligned with Maugis and Pollock (MP) theory that accounts for elasto-plastic deformation, Pe.

Interactions between nanoparticles and fractal surfaces

This study evaluated attachment of a 30-nm nanoparticle to and detachment from fractal surfaces by calculating Derjaguin-Landau-Verwey-Overbeek (DLVO) interaction energies in three-dimensional space using the surface element integration technique. The fractal surfaces were generated using the Weierstass-Mandelbrot function with varying values of fractal dimension D (2.3 ≤ D ≤ 2.7) and fractal roughness G (0.000136 ≤ G ≤ 0.136). Results show that maximum energy barrier is reduced at peak areas of a fractal surface, and hence attachment in primary minima is favored. Some nanoparticles attached in primary minima at the peak areas can be detached by decreasing ionic strength (IS) due to monotonic decrease of interaction energy with increasing separation distance at low ISs. While the attachment in primary minima at valley areas is irreversible to IS reduction, the attachment is inhibited due to enhanced maximum energy barrier at these areas. A nonmonotonic variation of attachment efficiency in primary minimum (AEPM) with IS is present at high fractal dimension (D ≥ 2.4) or low fractal roughness (G < 0.00136), whereas the AEPM decreases monotonically with decreasing IS at low fractal dimension (D < 2.4) or high fractal roughness (G ≥ 0.00136). The AEPM decreases monotonically with increasing D or decreasing G at ISs from 1 mM to 200 mM. The decrease of AEPM with D or G is much slower at 10 mM compared to other ISs. These theoretical findings can explain various experimental observations in the literature, and can have important utility to development of water filtration techniques in engineered systems and to assessment of environmental risks of nanoparticles.

Can nanoscale surface charge heterogeneity really explain colloid detachment from primary minima upon reduction of solution ionic strength?

This study theoretically examined colloid detachment from primary minima with ionic strength (IS) reduction on heterogeneous collector surfaces. The chemically and physically heterogeneous collector surfaces were modeled as a planar surface carrying nanoscale patches of different zeta potentials and nanoscale pillars/hemispheroids, respectively. The surface element integration technique was used to calculate interaction energies between colloid and collector surfaces. Two boundary conditions for the double-layer interaction energy were considered, namely constant surface potential (CSP), and linear superposition approximation (LSA). In contrast to prevailing opinions in the literature, our results show that colloids attached on the chemically heterogeneous surface cannot be detached by IS reduction under CSP condition due to an increase of the adhesive force/torque with decreasing IS. Detachment from chemically heterogeneous surfaces by IS reduction can occur under LSA condition only when the flow velocity is very high. In contrast, the presence of nanoscale physical heterogeneity can cause colloid detachment from primary minima by IS reduction under both CSP and LSA conditions at flow velocities commonly used in experimental studies because of a significant reduction in the adhesive forces/torques.

Anomalous Attachment Behavior of Nanoparticles inside Narrow Channels

Core Ideas We examined interaction energy for a nanoparticle inside a cylindrical nanochannel. A non‐monotonic variation of energy barrier with ionic strength exists. The energy barrier can disappear at all ionic strengths. A critical ratio of inner channel radius to particle radius exists where transport is most favored. Attachment of nanoparticles is inhibited inside channels with small thicknesses. Understanding nanoparticle (NP) attachment inside narrow passages such as the pore throats of porous media and plant and animal tissues is critically important to assess the potential ecological and toxicological impact of NPs. This study investigated the attachment of a NP inside a cylindrical nano‐sized channel with finite wall thickness at various ionic strengths (ISs) by calculating the Derjaguin–Landau–Verwey–Overbeek (DLVO) interaction energy using a modified surface element integration technique. Results show that there is a critical value of the ratio of the inner channel diameter to NP diameter (RCN) at which the repulsive energy barrier reaches a maximum at a given IS and NP transport is most favored. A non‐monotonic variation of the energy barrier with IS was observed for RCNs smaller than the critical value. The repulsive energy barrier disappears at all ISs when the NP diameter is close to the inner channel diameter, resulting in favorable attachment at primary minima. The attached NP cannot be detached in these cases by a disturbance of system conditions because of increased primary‐minimum depths and accordingly enhanced adhesive forces. For a given RCN, decreasing the channel thickness can increase and decrease the interaction energy barrier and primary‐minimum depth for a NP inside the channel, respectively. Accordingly, NP attachment in primary minima is inhibited whereas transport is favored in channels with thin walls. These theoretical results provide plausible explanations of experimental observations that the retention of colloids in pore throats of porous media via straining is chemically favorable (i.e., no repulsive energy barrier exists) even at very low ISs and irreversible to reduction of the solution IS, and that NPs are favorably attached in narrow passages such as plant tissues and membrane pores.

Impact of Flow Velocity on Transport of Graphene Oxide Nanoparticles in Saturated Porous Media

Core Ideas We examined the influence of flow velocity on transport of graphene oxide nanoparticles (GONPs). Attachment efficiency (α) increased with increasing flow velocity for GONPs. Hydrodynamic shear cannot release the attached GONPs, even from nanoscale asperities. Increasing flow velocity increased attachment of GONPs at concave surfaces. Saturated column experiments were conducted to systematically examine transport of graphene oxide nanoparticles (GONPs) in sand porous media at different solution ionic strengths (ISs) with different flow velocities. Results show that deposition of GONPs increase with decreasing IS. However, the Derjaguin–Landau–Verwey–Overbeek (DLVO) interaction energy calculations using a surface element integration technique show that the energy barrier increases with increasing IS for the sheet‐shaped colloids interacting with a planar sand surface. In contrast, the presence of nanoscale protruding asperities (NPAs) can cause a decrease in the energy barrier with increasing IS, which facilitates the attachment in primary minima at higher IS. At a given IS, increasing flow velocity increases attachment efficiency on the rough sand surfaces. Torque analysis shows that the maximum hydrodynamic torques are smaller than the adhesive torques, even for GONPs located on the NPAs where the adhesions are the lowest. Consequently, the attachment efficiency cannot be reduced by increasing flow velocity. Additional column experiments confirm that deposited GONPs cannot be detached by increasing flow velocity. Conversely, increase of flow velocity may enhance approaching of GONPs in low‐flow regions such as concave areas of sand surfaces and subsequent attachment. Although it has been recognized in the literature that the presence of NPAs can cause decrease of attachment efficiency with increasing flow velocity for spherical colloids under both unfavorable and favorable chemical conditions, our results highlight a different role of surface roughness in attachment and detachment of sheet‐shaped colloids under unfavorable conditions.

DLVO Interaction Energies between Hollow Spherical Particles and Collector Surfaces.

The surface element integration technique was used to systematically study Derjaguin-Landau-Verwey-Overbeek (DLVO) interaction energies/forces between hollow spherical particles (HPs) and a planar surface or two intercepting half planes under different ionic strength conditions. The inner and outer spheres of HPs were concentric (CHP) or in point contact (PHP). In comparison to a solid particle, the attractive van der Waals interaction was reduced with increasing inner radius of the CHP, but the reduction effect was less significant for the CHP at smaller separation distance. Increasing the inner radius for CHP therefore reduced the depths of the secondary minima, but had minor influence on the energy barrier heights and depths of the primary minima. Consequently, increasing inner radius reduced the potential for CHP retention in secondary minima, whereas did not influence the retention in primary minima. For PHP these interaction energy parameters and colloid retention depended on the orientation of the inner sphere relative to interacting surface. In particular, the van der Waals attraction was significantly reduced at all separation distances when the inner sphere was closest to the interacting surface, and this diminished retention in both secondary and primary minima. The PHP retention was similar to that of CHP when the inner sphere was farthest from the interaction surface. These orientation dependent interaction energies/forces resulted in directional bonds between PHPs and the formation of aggregates with contact points of the primary PHPs facing outward. The findings in this study have important implications for the design and utilization of HPs in soil remediation and colloid assembly.

Analyzing adhesion in microstructured systems through a robust computational approach

Analyzing surface forces for myriad geometric structures facilitates the design of properties in interacting interfacial systems. Along these lines, we demonstrate a generalized technique that can be utilized to evaluate the orientation dependence of a particle interacting with multiple finite or semi‐infinite objects. Specifically, the surface element integration technique is modified to account for surface elements of a particle not directly adjacent to the object with which it is interacting; this facilitates the analysis of objects with finite shape and with arbitrary orientations. Furthermore, as a technology‐relevant proof‐of‐concept demonstration, the influence of van der Waals (vdW) forces on the performance and reliability of microstructured systems used for the collection of trace particles is reported. The importance of the location of the particle contact with the microstructure and the independence of vdW forces generated by each microstructure is demonstrated using the developed computational approach. Thus, the methodology presented here can ultimately be utilized for a variety of interfacial forces generated by nontrivial systems with heterogeneous properties in order to provide design motifs in a low‐cost, high‐throughput manner.

Heteroaggregation of microparticles with nanoparticles changes the chemical reversibility of the microparticles’ attachment to planar surfaces

This study theoretically investigated detachment of homoaggregates and heteroaggregates attached on the planar surfaces at primary minima during transients in solution chemistry. The homoaggregates were represented as small colloidal clusters with well-defined structures or as clusters generated by randomly packing spheres using Monte Carlo method. The heteroaggregates were modeled as microparticles coated with nanoparticles. Surface element integration technique was adopted to calculate Derjaguin–Landau–Verwey–Overbeek (DLVO) interaction energies for the homoaggregates and heteroaggregates at different ionic strengths. Results show that attached homoaggregates on the planar surface at primary minima are irreversible to reduction in solution ionic strength whether the primary spheres of the homoaggregates are nano- or micro-sized. Heteroaggregation of nanoparticles with a microparticle can cause DLVO interaction energy to decrease monotonically with separation distance at low ionic strengths (e.g., ⩽0.01M), indicating that the heteroaggregates experience repulsive forces at all separation distances. Therefore, attachment of the heteroaggregates at primary minima can be detached upon reduction in ionic strength. Additionally, we showed that the adhesive forces and torques that the aforementioned heteroaggregates experience can be significantly smaller than those experienced by the microspheres without attaching nanoparticles, thus, the heteroaggregates are readily detached via hydrodynamic drag. Results of study provide plausible explanation for the observations in the literature that attached/aggregated particles can be detached/redispersed from primary minima upon reduction in ionic strength, which challenges the common belief that attachment/aggregation of particles in primary minima is chemically irreversible.

Influence of surface chemical heterogeneity on attachment and detachment of microparticles

This study theoretically examined attachment/detachment of negatively charged microparticles onto/from a negative planar surface carrying a positively charged square patch of different sizes. The surface element integration technique was used to calculate Derjaguin–Landau–Verwey–Overbeek (DLVO) interaction energies at different ionic strengths. Results show that a critical patch size is needed to attach a particle at a given ionic strength. The critical size decreases with increasing ionic strength and decreasing particle size. Colloid attachment on the patch via primary-minimum association is irreversible to reduction of ionic strength, in contrast to the experimental observations in the literature. We attributed the discrepancy to the fact that chemical heterogeneity is commonly accompanied with topographical variation. To account for the coupled effects on colloid detachment, the collector surface was modeled as a negative planar surface carrying a square prism. If the size of the prism is ≤5nm×5nm×5nm, whether the prism surface is positively or negatively charged does not have significant influence on the interaction energy curves at ≤0.01M. These tiny asperities mainly play a role in eliminating the primary minima of interaction energy curves at the low ionic strengths, causing detachment of colloids from primary minima. For larger prisms, the primary-minimum depths can be increased significantly if the prism surfaces are positively charged, resulting in more irreversible attachments in primary minima. Findings from this study have implications to understanding particle–surface interactions that involve only one ligand–receptor bond (e.g., cell–biomaterial interactions via a single contact).

Evaluation of DLVO interaction between a sphere and a cylinder

Van der Waals (vdW) and electrostatic double layer (EDL) interactions between a sphere and a cylinder are determined using the surface element integration (SEI) technique. Compared with Derjaguin approximation, the SEI technique gives more accurate predictions for the EDL interaction between a sphere and a cylinder. However, the SEI technique slightly overestimates the vdW interaction compared with predictions based on Hamaker's approach. The curvature effect is important at small cylinder-to-sphere size ratios, but when the ratio is greater than 10, both EDL and vdW interactions between a sphere and a cylinder can be approximated adequately by that between a sphere and a flat plate. In addition, as Debye length decreases, the EDL interaction energy between a sphere and a cylinder decays more quickly. At small separation distances, a smaller Debye length leads to a stronger EDL interaction between a sphere and a cylinder, whereas at large separation distances, a larger Debye length results in a stronger EDL interaction. The combination of vdW and EDL interactions, known as the Derjaguin–Landau–Verwey–Overbeek (DLVO) theory, was applied to the problem of colloidal fouling in hollow fiber membrane filtration. At low ionic strength (0.001M), a smaller energy barrier exists between smaller particles and the membrane, hence smaller particles more easily attach to the fiber and subsequently cause more severe colloidal fouling. At high ionic strength (0.1M), the energy barrier is eliminated for all particle sizes, which implies that colloidal fouling is more severe at elevated ionic strength.

Influence of Surface Potential on Aggregation and Transport of Titania Nanoparticles

To investigate the effect of pH on nanoparticle aggregation and transport in porous media, we quantified nanoparticle transport in two-dimensional structures. Titania was used as a model compound to explore the effects of surface potential on particle mobility in the subsurface. Results show that pH, and therefore, surface potential and aggregate size, dominate nanoparticle interactions with each other and surfaces. In each solution, nanoparticle aggregate size distributions were bimodal or trimodal, and aggregate sizes increased as the pH approached the pH of the point of zero charge (pHzpc). Over 80% of suspended particles and aggregates were mobile over the pH range of 1-12, except close to the pHzpc of the surfaces, where the particles are highly aggregated. The effect of pH on transport is not symmetric around the pHzpc of the particles due to charging of the channel surfaces. However, transport speed of nanoparticle aggregates did not vary with pH. The surface element integration technique, which takes into account the effect of curvature of particles on interaction energy, was used to evaluate the ability of theory to predict nanoparticle transport.

Effect of Membrane Surface Roughness on Colloid−Membrane DLVO Interactions

Recent experimental investigations suggest that interaction of colloidal particles with polymeric membrane surfaces is influenced by membrane surface morphology (roughness). To better understand the consequences of surface roughness on colloid deposition and fouling, it is imperative that models for predicting the Derjaguin−Landau−Verwey−Overbeek (DLVO) interaction energy between colloidal particles and rough membrane surfaces be developed. We present a technique of reconstructing the mathematical topology of polymeric membrane surfaces using statistical parameters derived from atomic force microscopy roughness analyses. The surface element integration technique is used to calculate the DLVO interactions between spherical colloidal particles and the simulated (reconstructed) membrane surfaces. Predictions show that the repulsive interaction energy barrier between a colloidal particle and a rough membrane is lower than the corresponding barrier for a smooth membrane. The reduction in the energy barrier is ...

DLVO Interaction between Rough Surfaces

The interaction energy between microscopic bodies is almost exclusively determined assuming perfectly smooth and geometrically regular surfaces. Quite often, such interactions fail to explain several colloidal phenomena. These inexplicable behaviors of colloidal systems are generally ascribed to surface chemical and morphological heterogeneities. Here, we employ the surface element integration technique to determine the interaction energy between surfaces containing morphological heterogeneity. Random asperities are generated to represent surface morphological heterogeneity (roughness), and their influence on the DLVO interaction potential is investigated. Incorporation of surface roughness causes a significant reduction in the repulsive interaction energy, the extent of which depends on the size of the asperities and their densities on the surface. Predictions of interaction energy indicate that the DLVO interaction energy profiles for rough surfaces deviate significantly from those derived assuming perf...