The electrical double layer

A major source of kinetic nonlability of colloids is the existence of an electric charge on the surfaces of the particles. On account of this charge, ions of opposite charge tend to cluster nearby, and an ionic atmosphere is formed, just as for ions (Section 5.9). We need to distinguish two regions of charge. First, there is a fairly immobile layer of ions that adhere tightly to the surface of the colloidal particle, and which may include water molecules (if that is the support medium). The radius of the sphere that captures this rigid layer is called the radius of shear and is the major factor determining the mobility of the particles. The electric potential at the radius of shear relative to its value in the distant, bulk medium is called the zeta potential, ζ, or the electro kinetic potential. Second, the charged unit attracts an oppositely charged atmosphere of mobile ions. The inner shell of charge and the outer ionic atmosphere is called the electrical double layer. The theory of the stability of lyophobic dispersions was developed by B. Derjaguin and L. Landau and independently by E. Verwey and J.T.G. Overbeek, and is known as the DLVO theory. It assumes that there is a balance between the repulsive interaction between the charges of the electric double layers on neighbouring particles and the attractive interactions arising from van der Waals interactions between the molecules in the particles. The potential energy arising from the repulsion of double layers on particles of radius a has the form

where A is a constant, ζ is the zeta potential,1 R is the separation of centres, s is the separation of the surfaces of the two particles (s = R − 2a for spherical particles of radius a), and r_D is the thickness of the double layer. This expression is valid for small particles with a thick double layer (a << r_D). When the double layer is thin (rD << a), the expression is replaced by

V_repulsion = Aaζ² ln (1 + e^−s/rD)

In each case, the thickness of the double layer can be estimated from an expression like that derived for the thickness of the ionic atmosphere in the Debye–Hückel theory (eqn 5.80):

Where I is the ionic strength of the solution, ρ its mass density, and b7 = 1 mol kg⁻¹. The potential energy arising from the attractive interaction has the form

Where I is the ionic strength of the solution, ρ its mass density, and b7 = 1 mol kg⁻¹. The potential energy arising from the attractive interaction has the form

V_attraction =−

where B is another constant. The variation of the total potential energy with separation is shown in Fig. 19.38.

At high ionic strengths, the ionic atmosphere is dense and the potential shows a secondary minimum at large separation. Aggregation of the particles arising from the stabilizing effect of this secondary minimum is called flocculation. The flocculated material can often be redispersed by agitation because the well is so shallow. Coagulation, the irreversible aggregation of distinct particles into large particles, occurs when the separation of the particles is so small that they enter the primary minimum of the potential energy curve and van der Waals forces are dominant. The ionic strength is increased by the addition of ions, particularly those of high charge type, so such ions act as flocculating agents. This increase is the basis of the empirical Schulze–Hardy rule, that hydrophobic colloids are flocculated most efficiently by ions of opposite charge type and high charge number. The Al3+ ions in alum are very effective, and are used to induce the congealing of blood. When river water containing colloidal clay flows into the sea, the salt water induces flocculation and coagula tion, and is a major cause of silting in estuaries. Metal oxide sols tend to be positively charged whereas sulfur and the noble metals tend to be negatively charged. The primary role of the electric double layer is to confer kinetic non-lability. Colliding colloidal particles break through the double layer and coalesce only if the collision is sufficiently energetic to disrupt the layers of ions and solvating molecules, or if thermal motion has stirred away the surface accumulation of charge. This disruption may occur at high temperatures, which is one reason why sols precipitate when they are heated. The protective role of the double layer is the reason why it is important not to remove all the ions when a colloid is being purified by dialysis, and why proteins coagulate most readily at their isoelectric point.

Fig. 19.38 The potential energy of interaction as a function of the separation of the centres of the two particles and its variation with the ratio of the particle size to the thickness a of the electric double layer r_D. The regions labelled coagulation and flocculation show the dips in the potential energy curves where these processes occur.

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Surface pressure

Membrane formation

Micelle formation

Classification and preparation

The stability of proteins and nucleic acids

The structure of nucleic acids

Helices and sheets

Conformational energy

The Corey–Pauling rules

The different levels of structure

Viscosity