15


Figure 5: Effect of solids concentration on the mobility of aqueous barium titanate


(called ‘initial contact’) and provides a representation of particles of a material (red circles) within a liquid (white background). The ‘surface chemical nature’ of the material is imagined as a series of blue dots. This could be the fundamental functional groups comprising the material, or something adsorbed on the material’s surface. On the right- hand side is a depiction of that same suspension in which an ‘equilibrium’ has been established between adsorption at the particle surface and the concentration of the same moiety in solution. For a given volume of the suspension, the greater the particle concentration is, the less volume of free liquid/solution is available. This means that the solubility limit for any surface species can be exceeded, thus inhibiting any further desorption, dissolution, or dissociation. So, in concentrated suspensions, the chemical equilibrium is always shifted towards the surface, and the little icon at the bottom right- hand side of Figure 3 represents the surface that will be primarily ‘probed’ (i.e., evaluated/ measured/monitored) in such a situation.


In Figure 4 we have the same sample but after being diluted, as can happen when preparing samples for measurement/analysis for example in light scattering. Now the equilibrium is shifted away from the surface and towards the solution - and, the more dilute the suspension, the greater will be this shift.


This can be demonstrated in the following example using electrophoretic mobility measurements of an aqueous suspension of barium titanate, which is used, for example, in the manufacture of ceramic capacitors. The mobility is related to the surface charge of a material; it is a good index of the magnitude of the electrostatic repulsive interaction between particles and can be used to predict and control dispersion stability. The dispersion characteristics of ceramics and refractories affect green body strength and the degree of shrinkage on sintering. Thus, reliable mobility determinations are of practical concern in ceramics preparation, processing, and application. In these samples, the mobility was measured as a function of pH at a high solids concentration (20% w/w) using an electroacoustic device. The suspension was then extensively diluted using deionised water and the mobility measured, again as a function of pH, using an electrophoretic light scattering device and the results compared (Figure 5).


It is clear that not just the shapes of the mobility vs pH profi le, but also the iso-electric point (IEP), are totally different for the two suspensions. The IEP is the pH at which the material will have no surface potential (charge) and so such a suspension will be inherently unstable, and all the particles will eventually aggregate. This signifi cant difference can


Figure 6: Rate of settling (dispersed area) of an aqueous dispersion barium titanate.


have serious consequences as it impacts, among other things, subsequent formulation - for example, the addition of ionic additives such as surfactants, dispersants and polyelectrolytes - as well as long-term stability.


Figure 6 shows Relaxation experiments on the settling of a concentrated (10% w/w) aqueous dispersion of barium titanate. The relaxation number is directly proportional to the quantity of dispersed area in the sample. The data are highly reproducible and automatic, and allow for a detailed study of the optimum stabiliser concentrations required to control the rate of settling.


The important take-away point is that dilution is never an innocuous process. The consequence is that you will get a value – from whatever characterisation technique used - that is not representative of the original concentrated suspension and so may not translate into a useful performance metric. To avoid this issue, where possible, it is always preferable to make measurements on suspensions or slurries at their use concentration.


This does not mean that you cannot dilute any suspension. There are ways to minimise (but not completely eliminate) the shift in chemical equilibrium that occurs, for example by using the mother liquor from a centrifuged sample of the original suspension but this is often diffi cult to obtain in practice. More discussion of this issue is beyond the subject of this short note.


Formulations, though initially prepared as concentrates, are sometimes subsequently diluted to obtain the commercial product. However, dilution, if not performed correctly, can lead to suspension instability which can affect, for example, long-term shelf storage. Crucially, if it is necessary to dilute a suspension, then it is essential to check the linearity of any metric as a function of the dilution process. NMR relaxation can play a key role in characterising these suspensions


References


1. C. L. Cooper, T. Cosgrove, J. S. van Duijneveldt, M. Murray, and S. W. Prescott. The use of solvent relaxation nmr to study colloidal suspensions. Soft Matter, 9(30):7211–7228, 2013


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