Colloidal stability and the role of screened electrostatics.
The measurement of particle size by dynamic light scattering (DLS) is heavily dependent on the stability of materials being investigated. Interactions between simple, spherical, colloidal particles are most frequently described by a balance between attractive and repulsive interactions. For freely diffusing particles, it is these repulsive interactions that minimize the frequency of collisions between particles, as well as reduce the probability that a given collision will result in two surfaces sticking, and thus result in colloidal stability.
If we consider these interactions in terms of sums of pairwise interactions between two like-charged particles both of radius ro , we can define a distance, h, that refers to the surface-to-surface separation of colloidal particles.
The balance between these attractive and repulsive forces form a complex interaction potential, but perhaps the most direct way to augment this potential is by addition of salt. The most immediate effect of salt, or ionic strength (I) is to screen these long-range electrostatic repulsions. Since the most direct impact of adding screening electrolyte is to suppress the Debye length, κ-1, or screening constant. This parameter, sometimes called the double-layer thickness, directly controls the distance over which electrostatic effects falloff, or decay, due to the presence of mobile charge carriers or small ions. For a 1:1 electrolyte, where I = cs, this can be calculated according to the following expression:
κ-1 = [ϵoϵ kBT/ (2NAe2 cs )] 1/2
Where κ-1 is the Debye screening length. In this expression ϵo and ϵ are the vacuum- and relative- permittivity respectively, kBT is thermal energy expressed in terms of the Boltzmann constant, e is the electronic charge, NA is Avogadro’s number, and cs is the molar concentration of salt. This can be simplified at room temperature and expressed directly in terms of salt concentration:
κ-1 (nm) = 0.301/cs1/2
This allows us to calculate screened electrostatics as a function of surface separation, h. For a given ionic strength, the decay of electrostatic potentials is approximated by the following, where Ψo is the surface potential and κ is the reciprocal of the Debye length (κ-1):
Ψ(h) = Ψo exp(-κh)
Ionic strength directly controls the distance over which electrostatics can contribute to particle stability.
At the lowest salt concentrations electrostatic repulsions persist for tens of nanometers as is apparent for salt concentrations < 1 mM. At salt concentrations above 50 mM electrostatics become extremely short range, falling off almost completely at separations greater than several nm. This picture begins to explain the impact of ionic strength on colloidal stability, but so far only addresses the repulsive portion of this interaction. In order to understand this in its entirety we need to also consider attractive interactions.
The most common theoretical framework for understanding the stability of colloidal particles is Derjaguin-Landau-Verwey-Overbeek theory (DLVO). DLVO treats colloidal stability as the sum of van der Waals forces, and screened electrostatics (sometimes referred to as double-layer forces). The form of the interaction potential is complex, but at low ionic strength long-range repulsion dominates. In contrast, at high ionic strength nearly all long-range electrostatics are screened, and thus the attractive portion of the potential dominates. When attractive interactions dominate particles can approach more closely and have a greater likelihood of sticking.
Role of salt in screening interparticle interactions
A small amount of salt can have a major effect on the distances over which repulsive particle-particle interactions can be felt. It is therefore very important when preparing samples for DLS or for Zeta Potential Measurements to keep ionic strength constant. It is rare for samples to have an effective ionic strength << 0.1 mM, even when prepared in the absence of added salt. Commercially produced powders often contain residual salt and buffer. Neutralization of acid or base during pH adjustment can add to the background ionic strength as well. In practice, it is very difficult to precisely control the total concentration of dissolved ions when working at low-salt.
For DLS measurements, it is crucial to be able to control ionic strength, especially when performing a serial dilution, where variable ionic strength can often produce an apparent concentration dependence to particle size. Unfortunately, terms such as high- and low- salt, while ubiquitous, are often subjective; their definitions vary from discipline-to-discipline.
What are typical salt concentrations?
In biological systems, ionic strength is most commonly established by dilution in phosphate buffered saline (PBS) which is meant to approximate biological salt and pH, resulting in an ionic strength of between 120-155 mM depending on the exact composition of the buffer. Nanoparticles tend to be resuspended in pure distilled water, which as discussed earlier is not equivalent to zero ionic strength, and is easily changed by trace salt, as well as adsorption of atmospheric CO2 to form carbonic acid. Another extreme is oil recovery, where it is common to study interactions between surfactant micelles in near brine (> 1 M), or brine-like conditions, nearing the solubility limit of simple salts.
The salt effect is now considered in terms the highly-charged, semi-flexible polyelectrolyte Sodium Polystyrene Sulfonate (NaPSS). NaPSS is an anionic, or negatively charged, synthetic polymer with high, but invariant linear charge density. The sample examined below was a commercial polymer, with a molecular weight on the order of 1 MDa.
Size distributions from DLS for very high molecular weight NaPSS prepared at three different ionic strengths. In the absence of added salt (red), repulsions between monomers are no longer screened, and the normally condensed coil-like polymer (black & purple) extends into a rigid elongated structure, approaching the physical length of the polymer chain. At higher salt this effect becomes suppressed.
Intra-particle interactions and polyelectrolytes
There are numerous methods to introduce charge to a molecular surface, all of which become less energetically favorable as you approach very high charge densities due to charge-charge repulsion. Thermodynamically, this becomes easier to accomplish in the presence of electrolyte or other mobile charge carriers, since these ions minimize the energetic penalty of adding an additional charge to an already highly charged surface. Colloidal particles can minimize these direct repulsive interactions by spontaneously maximizing surface-to-surface separation, and flexible polymers such as polyelectrolytes can rearrange themselves structurally to minimize internal repulsions. At the lowest salt concentrations these long-chain polyelectrolytes lose their semi-compact coil-like structure, forming rod-like extended structures instead.
Measurements made at constant Cp = 2 g/L NaPSS as a function of ionic strength as set by addition of 1:1 electrolyte NaCl. The apparent dimensions of polymer chain become large rapidly at low-salt as NaPSS becomes less flexible, and more rod-like. Note that this data becomes linear when replotted in terms of Debye length, κ-1.
Polyelectrolytes, especially those with permanent, non-titratable, charges become rod-like in the limit of low-, or no-, salt, due to internal repulsion between sidechains. This loss of flexibility at low-salt is most directly observed in the apparent size of the molecule. At low ionic strength, a normally compact, flexible polymer beings to rigidify, and so size measurements reflect its lengthwise dimension, more so than its ensemble average size. Thus, the effect of salt on polyelectrolyte dimensions is easily demonstrated through DLS measurements. The degree of rigidity of a polyelectrolyte is strongly proportional to the length-scale over which charged monomers can experience electrostatic repulsion.
Colloidal stability is a balance between long-range repulsion and short-range attraction.
- Long-range repulsions are attributed to electrostatics, sometimes called double-layer forces.
- These electrostatic interactions can be directly modulated by addition of salt.
- Short-range attraction is derived from van der Waals forces.
- DLVO provides a good theoretical basis for estimating colloidal stability from first principles.
Ionic strength is directly related to the concentration of small ions in solution.
- This is straightforward for simple monovalent salts, and can be more involved for complex salts or other types of small ions, buffers, and charged small molecules.
- High-salt effectively screens out long-range repulsive electrostatics.
- There are many definitions of high-salt, the meaning of which is industry dependent.
DLS measurements of flexible charged molecules demonstrate this principle.
- Flexible polyelectrolytes become rod-like at low-salt.
Ionic strength effects are dramatic for flexible charged molecules such as polyelectrolytes but are of no less importance for other types of charged surfaces, including those of more conventional colloidal particles. Thus, this property is of major importance for colloidal stability and needs to be considered when preparing samples for light scattering.
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