Stability of Dispersions and Interactions in Nanostructured Fluids

Kimberly Hamad-Schifferli    Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139

Abstract

Stability in solution is a critical fundamental property of nanoparticles (NPs). Understanding NP stability enables their manipulation and processing for a wide variety of applications that exploit the unique material properties of NPs. Here, we invoke descriptions of colloidal stability from DLVO theory and the use of polymeric stabilizers and discuss its extension to NP stability and aggregation. Applications of NP aggregation will be discussed.

Keywords

nanoparticle stability

DLVO theory

colloidal stability

nanoparticle aggregation

nanoparticle passivation

1 Motivation

Nanoparticles (NPs) have been of great interest for many applications due to their unique size and material-dependent properties. In particular, their high surface-to-volume ratios have made them useful for catalysts, incorporation into devices, and solid supports for small molecules or proteins or DNA. One of the most useful properties of NPs is that they are soluble in solution, so they can be processed like chemical reagents. NPs can be dissolved into solution, dispersed into polymers, cast into thin films, and covalently linked to small molecules, biomolecules, polymers, and substrates. In addition, their solubility enables them to be introduced into fluids so that they can travel in the bloodstream and be imaged, target tumors and disease sites, and deliver drugs.

However, the high surface-to-volume ratio of NPs makes them highly prone to aggregation. When NPs aggregate, their utility is often compromised, as it can lead to precipitation out of solution, often dramatically and irreversibly. It is immediately apparent that the precipitated NPs in Figure 2.1 (left tube) cannot be incorporated into biological fluids or readily dispersed into polymers or multilayers. As a precipitate, NPs cannot be manipulated as readily as when they are in solution, and thus this limits their capabilities. In addition, NP aggregation and precipitation can lead to further undesirable side effects, particularly in biological applications. For example, in cellular applications of NPs, their aggregation can give rise to new cytotoxic effects due to the NP sedimentation [1,2]. Precipitation of nanomaterials complicates their consequences in toxicology and in the environment, of which we currently have a poor understanding. Unfortunately, aggregation is often difficult to predict and prevent, given the multitude of forces at play and wide variety of conditions under which we use NPs.

Figure 2.1 Gold nanorods (NRs) stable in solution (right) versus aggregated (left). Photo credit: H. de Puig Guixé and A. Cifuentes Rius.

However, aggregation can be useful, especially if it is reversible. For example, if NPs are temporarily aggregated and put into the solid phase, they can be separated from small molecules or biomolecules also in solution and then later resuspended. This has been an essential way to separate biomolecules conjugated to NPs from free, unconjugated biomolecules and widely used in biology for purification of expressed proteins, DNA, and numerous other species. In addition, NP optical properties can sometimes change upon aggregation, enabling an optical readout of aggregation. If aggregation occurs in the presence of an analyte, then one can detect it colorimetrically or spectroscopically [3,4].

Stability is an essential property of particles. The gold sols made by Michael Faraday in 1857 are still stable in solution today after more than 150 years [5]. For colloids, the larger counterpart of NPs, understanding their stability has been key to understanding their fundamental properties and in their manipulation. Why do colloids aggregate under certain conditions but remain stable in others? Consequently, a theoretical understanding of their stability has been well described. Historically, for colloids, aggregation is called “flocculation,” which is a reversible process, or “aggregation,” which is irreversible. Electrostatic effects are known to be important, and we see demonstrations of this in numerous everyday instances. For example, silt forms at river deltas where the freshwater river meets the sea. The colloids present in the freshwater are stable and do not precipitate, resulting in a clear solution. However, when they encounter the saltwater from the sea at the river deltas, the increase in ionic strength reduces their stability and causes them to precipitate out, giving rise to the silt deposits.

Obviously, the surface properties of colloids are important, as aggregation is very dependent on surface chemistry. Surface passivation has been successfully used to increase their stabilization. For NPs, their surface chemistry is deeply intertwined with their physical and chemical properties, especially for NPs produced by solution-phase methods. Because these NPs are made by solution-phase synthesis, the surface coating chemistries play an important part in the synthesis, capping the molecule and limiting its size, preventing aggregation during synthesis, and kinetically trapping the NP in a particular size or morphology [6]. The chemical nature of the molecule is often designed for manipulating the shape of the NP. Also, the surface coating molecule dictates what solvent into which the NPs can be dissolved. Often, the surface coating molecule cannot be simply removed without drastic consequences on the stability of the particles. Thus, one must treat NP plus its surface molecule as a single chemical entity.

Here, we discuss the stability of NPs, first drawing on the thermodynamic treatment based on colloids. We then extend the discussion to NPs and describe how surface chemistry of NPs plays a role in stability and how surface chemistry is manipulated. We discuss experimental methods for probing NP aggregation and applications that utilize aggregation. This chapter is not intended to be an exhaustive review of colloidal stability; rather, it touches on select topics that are of relevance to NP stability and surface chemistry.

2 Background: Fundamentals from Colloid Chemistry

First, we will briefly discuss the thermodynamic treatment of colloidal stability [7].

2.1 DLVO Theory

Under what conditions do colloids precipitate? What are the forces that are responsible for their aggregation? Answering these questions is essential to understanding fundamental colloidal properties. Deryagin, Landau, Verwey, and Overbeek developed the theory that describes how two particles interact. DLVO theory shows that colloidal stability is due to the balance between the repulsion from the double layer and the attraction due to van der Waals forces, and has been used to predict colloidal stability under different conditions. The total interaction energy function, VT, is the sum of the attractive potential energy, VA, and the repulsive potential energy, VR:

  (2.1)

VA is the interparticle attraction per unit surface area due to van der Waals interactions:

  (2.2)

where H is the Hamaker constant for the attraction between two planes separated by a distance h. VR is due to the repulsion between two charged species due to the overlap of the double layers of the particles. The Gouy-Chapman model for a symmetric electrolyte results in VR per unit area of

  (2.3)

where n0 is the solute concentration and γ0 is

  (2.4)

and the Debye length is

  (2.5)

where Z is the charge of the ions. The total energy can be written as

  (2.6)

VA and VR have different dependences on h. VA is negative and has an inverse-square dependence on h, while VR is positive and decays exponentially with h (Figure 2.2). The attractive term VA dominates at short distances (low h), while the repulsive term VR dominates at very long or very short distances. Thus, the contributions of VA and VR to VT vary with h. Consider the case of low and high screening. For low electrolyte concentrations or low screening, the Debye length κ− 1 is long, resulting in a higher VR. This results in an energy barrier in VT (case 1, shown as curve VT(1) in Figure 2.2), which must be crossed if the particles were to come into contact with one another. The particles cannot approach each other, so they do not get close enough for the VA to dominate, so the particles do not aggregate and thus are stable. For the particles to be reasonably stable, this barrier must be ~ several kBT. For high electrolyte concentration, the Debye screening length is short, eliminating the barrier in VT, so the particles are not prevented from coming in contact with one another, so they can approach one another without having to surmount an energy barrier. Thus, the regime where VA dominates can be reached,...