Particle size measurement through the means of dynamic light scattering (DLS) is largely dependent on the stability of materials that are being examined. Interactions between simple, spherical and colloidal particles are commonly defined as a balance between attractive and repulsive interactions. For freely diffusing particles, it is these repulsive interactions that minimize the particle collision incidence, in addition to reducing the likelihood that a given collision will lead to two surfaces sticking, and thus colloidal stability being the result.
These interactions can be considered in terms of sums of pairwise interactions between two similarly charged particles both of radius ro, and then distance, h, can be defined, which refers to the surface-to-surface separation of colloidal particles. An attractive and repulsive force balance forms a complex interaction potential, but research has shown that the addition of salt is possibly the most direct way to augment this potential.
Salt, or ionic strength (I) creates an immediate effect to screen these long-range electrostatic repulsions. The most direct effect of a screening electrolyte addition is to suppress the Debye length, κ-1, or screening constant. This parameter is sometimes referred to as the double-layer thickness, and because of the existence of mobile charge carriers or small ions, it has direct control over the distance over which electrostatic effects fall off or decay. For an electrolyte that is 1:1, where I = cs, calculations can be done according to the expression:
κ-1 = [ɛoɛ kBT/ (2NA e2 cs )] 1/2
κ-1 is the Debye screening length and in this expression ɛo and ɛ are the vacuum- and relative- permittivity respectively, kBT refers to the thermal energy expressed in reference to the Boltzmann constant, e is the electronic charge, NA is Avogadro’s number, and cs is the salt molar concentration. It is possible for this to be simplified at room temperature and expressed directly in terms of salt concentration:
κ-1 (nm) = 0.301/cs1/2
Screened electrostatics as a function of surface separation, h, can then be calculated. For a specific ionic strength, the electrostatic potential decay is approximated by the following, where Ψo refers to the surface potential and κ refers to the reciprocal of the Debye length (K-1):
Ψ(h) = Ψo exp(-Kh)
Ionic strength directly controls the distance over which electrostatics can contribute to particle stability.
At the lowest salt concentrations, electrostatic repulsions continue for tens of nanometers, as is seen for salt concentrations < 1 mM. At salt concentrations higher than 50 mM, electrostatics become very short range, falling off virtually completely at separations higher than several nm. This can begin to describe the impact of ionic strength on colloidal stability, however, thus far, it only takes the repulsive portion of this interaction into consideration. Attractive interactions also need to be considered to understand it in its entirety.
Derjaguin-Landau-Verwey-Overbeek theory (DLVO) is the commonly used theoretical framework used for understanding the stability of colloidal particles. DLVO treats colloidal stability as the sum of van der Waals forces and screened electrostatics (often known as double-layer forces). The form of the interaction potential is complex, but repulsion dominates at low ionic strength long-range. Conversely, at high ionic strength, the attractive portion of the potential dominates because nearly all long-range electrostatics are screened. When there is a domination of attractive interactions, particles have a higher probability of sticking because they can approach more closely.
Screening Interparticle Interactions: The Role of Salt
Even a small quantity of salt can have a significant effect on the distances over which repulsive particle-particle interactions can be felt. Therefore, it is extremely important to keep ionic strength constant during sample preparation for DLS or for Zeta Potential Measurements. Even when prepared with no added salt, it isn’t common for samples to have an effective ionic strength << 0.1 mM.
Commercially produced powders frequently consist of residual salt and buffer. An addition to the background ionic strength can also come from the neutralization of acid or base during pH adjustment. In practice, it is very hard to control the total concentration of dissolved ions with precision when working at low-salt.
It is vital to be able to control ionic strength for DLS measurements, particularly when carrying out a serial dilution, where inconstant ionic strength can frequently create an apparent concentration dependence on particle size. Unfortunately, terms like high- and low- salt, while ubiquitous, are frequently subjective; their definitions differ from discipline-to-discipline.
Typical Salt Concentrations
In biological systems, ionic strength is usually recognized by dilution in phosphate-buffered saline (PBS). The aim of this is to approximate biological salt and pH, leading to an ionic strength of between 120-155 mM depending on the buffer’s specific composition.
In pure distilled water, nanoparticles have a tendency to be resuspended which, as mentioned earlier, is not equal to zero ionic strength, and can be altered easily by trace salt, in addition to the adsorption of atmospheric CO2 to form carbonic acid. An additional extreme is oil recovery, where the study of interactions between surfactant micelles in near brine (> 1 M), or brine-like conditions are common, approaching simple salt solubility limits.
Presently, the salt effect is thought of in terms of 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 investigated in the graph seen below was a commercial polymer, with a molecular weight on the order of 1 MDa.
It displays size distributions from DLS for very high molecular weight NaPSS. Preparations for these were done at three different ionic strengths. Due to the absence of added salt (as seen in red), monomer repulsions were not screened, and the normally condensed coil-like polymer (as seen in black and purple) extended into a rigid elongated structure, approaching the physical length of the polymer chain. This effect becomes suppressed at higher salt.
Intra-Particle Interactions and Polyelectrolytes
Several methods can be used to introduce a charge to a molecular surface. All of these methods become decreasingly energetically favorable as very high charge densities are approached due to charge-charge repulsion. Thermodynamically, accomplishing this becomes easier in the presence of electrolyte or other mobile charge carriers. This is because these ions lessen the energetic penalty of adding an extra charge to an already highly charged surface.
These direct repulsive interactions can be minimized by colloidal particles by impulsively maximizing surface-to-surface separation, and flexible polymers like polyelectrolytes can structurally reorganize themselves to lessen internal repulsions. These long-chain polyelectrolytes lose their semi-compact coil-like structure at the lowest salt concentrations, creating rod-like extended structures as an alternative.
These measurements are made at constant Cp = 2 g/L NaPSS as a function of ionic strength as set by the addition of 1:1 electrolyte NaCl. The seeming dimensions of the polymer chain at low-salt quickly become large as NaPSS becomes less flexible and increasingly rod-like. A noteworthy point is that this data becomes linear when replotted in terms of Debye length, κ -1.
Polyelectrolytes, particularly those with permanent, non-titratable, charges become rod-like in the limit of low-, or no-, salt. This is due to the sidechains internal repulsion. This flexibility loss at low-salt is most directly seen in the apparent size of the molecule.
At low ionic strength, a usually compact, flexible polymer slowly becomes rigid, and so size measurements are reflected in its lengthwise dimension, more so than its ensemble average size. Therefore, DLS measurements easily demonstrate the effect of salt on polyelectrolyte dimensions. The polyelectrolyte’s degree of rigidity is largely proportional to the length-scale over which charged monomers can experience electrostatic repulsion.
Colloidal stability is described as the balance between long-range repulsion and short-range attraction.
- Long-range repulsions are credited to electrostatics, which is often referred to as double-layer forces
- The addition of salt can directly modulate these electrostatic interactions
- Short-range attraction is a resultant of van der Waals forces
- DLVO offers a successful theoretical basis for approximating colloidal stability from first principles
There is a direct relation between ionic strength and the concentration of small ions in solution.
- This is easy for simple, monovalent salts, and has the ability to be more involved for complex salts or further types of small ions, buffers, and charged small molecules.
- High-salt ultimately screens out long-range repulsive electrostatics
- There are several definitions of high-salt, the meaning of which is industry dependent
DLS measurements of flexible charged molecules prove this principle.
- At low-salt, flexible polyelectrolytes become rod-like.
For flexible charged molecules like polyelectrolytes, ionic strength effects are dramatic but are no less important for other types of charged surfaces, inclusive of those of more traditional colloidal particles. Consequently, for colloidal stability, this property is of high importance and it is vital that it is considered when preparing samples for light scattering.
References and Further Reading
- Stevens, M.J. and Plimpton, S.J., 1998. The effect of added salt on polyelectrolyte structure. The European Physical Journal B-Condensed Matter and Complex Systems, 2(3), pp.341-345.
- Tadmor, R., Hernandez-Zapata, E., Chen, N., Pincus, P. and Israelachvili, J.N., 2002. Debye length and doublelayer forces in polyelectrolyte solutions. Macromolecules, 35(6), pp.2380-2388.
- Lin, M.Y., Lindsay, H., Weitz, D.A., Ball, R.C., Klein, R. and Meakin, P., 1989. Universality in colloid aggregation. Nature, 339(6223), p.360.
- Derjaguin, B.V., Rabinovich, Y.I. and Churaev, N.V., 1978. Direct measurement of molecular forces. Nature, 272(5651), p.313.
- Verwey, E.J.W., Overbeek, J.T.G. and Van Nes, K., 1948. Theory of the stability of lyophobic colloids: the interaction of sol particles having an electric double layer. Elsevier Publishing Company
This information has been sourced, reviewed and adapted from materials provided by TESTA Analytical Solutions.
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