Research Article: Spontaneous Detachment of Colloids from Primary Energy Minima by Brownian Diffusion

Date Published: January 19, 2016

Publisher: Public Library of Science

Author(s): Zhan Wang, Yan Jin, Chongyang Shen, Tiantian Li, Yuanfang Huang, Baoguo Li, Jie Zheng.

http://doi.org/10.1371/journal.pone.0147368

Abstract

The Derjaguin-Landau-Verwey-Overbeek (DLVO) interaction energy profile has been frequently used to interpret the mechanisms controlling colloid attachment/detachment and aggregation/disaggregation behavior. This study highlighted a type of energy profile that is characterized by a shallow primary energy well (i.e., comparable to the average kinetic energy of a colloid) at a small separation distance and a monotonic decrease of interaction energy with separation distance beyond the primary energy well. This energy profile is present due to variations of height, curvature, and density of discrete physical heterogeneities on collector surfaces. The energy profile indicates that colloids can be spontaneously detached from the shallow primary energy well by Brownian diffusion. The spontaneous detachment from primary minima was unambiguously confirmed by conducting laboratory column transport experiments involving flow interruptions for two model colloids (polystyrene latex microspheres) and engineered nanoparticles (fullerene C60 aggregates). Whereas the spontaneous detachment has been frequently attributed to attachment in secondary minima in the literature, our study indicates that the detached colloids could be initially attached at primary minima. Our study further suggests that the spontaneous disaggregation from primary minima is more significant than spontaneous detachment because the primary minimum depth between colloid themselves is lower than that between a colloid and a collector surface.

Partial Text

Investigating attachment and detachment of colloids in porous media is of practical interest for various environmental and engineering applications [1–5]. The Derjaguin-Landau-Verwey-Overbeek (DLVO) theory illustrates that the interaction energies controlling the attachment/detachment of a colloid on/from a collector surface include van der Waals attraction, double layer interaction energy and short-range repulsion [6–8]. Summing the aforementioned interaction energies over the separation distance between the colloid and collector results in the so-called DLVO interaction energy profile, which has been frequently employed to predict the attachment/detachment of colloids on/from collector surfaces [9].

Whereas our theoretical calculations only considered physical heterogeneities on collector surfaces, the presence of physical heterogeneities on colloid surfaces can further decrease depths of primary minima on EPs [62] and accordingly increase spontaneous detachment from primary minima. Our theoretical calculations adopted a low value (i.e., 0.157 nm) for the Born collision parameter to calculate the Born repulsion and a high value (i.e., 1×10−20 J) for the Hamaker constant to calculate the van der Waals energy. The spontaneous detachment from primary minima will be more significant if higher values of Born collision parameter and lower values of Hamaker constant are used. To demonstrate this point for a wider range of possible scenarios, Fig C in S1 File compares calculated values of Upri for the 1156 nm colloid interacting with the planar surface carrying a hemisphere with different radii at 0.0001 M for Born collision parameter of 0.5 nm and 0.157 nm. The range of asperity radii that can cause shallow primary energy well (e.g., < 5 kT) is significantly increased by using 0.5 nm as the Born collision parameter. Similarly, the presence of polymers on latex particle surfaces can cause steric repulsion when the asperities on collector surfaces interact with the polymer coated particle surfaces. By using the method of Kim and Matsen [63] to estimate the steric repulsion energy (see Text B in S1 File), Fig D in S1 File shows that the steric repulsion can significantly decrease the primary minimum depths and accordingly increase spontaneous detachment from primary minima. In contrast, the presence of attractive short-range forces (e.g., hydrophobic and π-π interactions) [64] will decrease the magnitude of spontaneous detachment from primary minima. A distribution of primary energy minimum depths has been obtained in Pazmino et al. [54] by considering power law size-distributed discrete chemical heterogeneities on collector surfaces. Our study, through evaluating the DLVO interaction energies using grid-surface integration technique [31,32], showed that the variation of height, curvature, and density of discrete physical heterogeneities can also result in a distribution of primary minimum depths. Furthermore, we highlighted the EP with a shallow primary minimum comparable to the average kinetic energy of a colloid and a monotonic decrease of interaction energy with separation distance beyond the primary energy well. The EP indicates that colloids attached at the primary energy well can be spontaneously detached to bulk solution by Brownian diffusion. The column transport experiments involving flow interruptions unambiguously verified the presence of spontaneous detachment from primary minima without perturbations in solution chemistry or hydrodynamics under unfavorable conditions for both model colloids (i.e., polystyrene latex microspheres) and engineered nanoparticles (i.e., fullerene C60 aggregates). Whereas the spontaneous detachment is frequently attributed to attachment in secondary minima, our theoretical and experimental results indicate that the detached colloids are not necessarily initially attached at the secondary minima. Our study illustrates the limitation of using a balance of hydrodynamic and adhesive torques as the sole criteria for determining detachment of colloids from primary minima.   Source: http://doi.org/10.1371/journal.pone.0147368