Physical Pharmacy 2 Electrokinetic properties of colloid: Electrical Double Layer Kausar Ahmad Kulliyyah of Pharmacy Physical Pharmacy 2 KBA

Contents Electrical double layer theories Physical Pharmacy 2 Contents Electrical double layer theories Repulsive effect of electrical double layer Potential energy of interaction Physical Pharmacy 2 KBA

Helmholtz double layer Physical Pharmacy 2 Helmholtz double layer Helmholtz in 1879 introduced the concept of the electrical double layer. The charge on the particles of a lyophobic colloid was due to an unequal distribution of ions at the particle-water interface. If ions of one charge were closely bound to the particle, ions of opposite charge would line up parallel to them, forming a double layer of charges Physical Pharmacy 2 KBA 3

Gouy diffuse double layer Physical Pharmacy 2 Gouy diffuse double layer Gouy proposed that the double layer is diffused, with the outer ionic layer having an electric density falling off according to an exponential law. Physical Pharmacy 2 KBA 4

Stern diffuse double layer Physical Pharmacy 2 Stern diffuse double layer Stern compromised Helmholtz and Gouy. The double layer is in two parts: 1. Helmholtz layer - one layer approximately a single ion in thickness, remains essentially fixed to the interfacial surface. In this layer, there is a sharp drop of potential. 2. Gouy layer – this layer extends some distance into the liquid dispersing phase and is diffuse, with a gradual fall in potential into the bulk of the liquid. Physical Pharmacy 2 KBA 5

Physical Pharmacy 2 Electric double layer is a region of molecular dimension at the boundary of two substances across which an electrical field exists. The substances must each contain electrically charged particles, such as electrons, ions, or molecules with a separation of electrical charges (polar molecules). In the electrical double layer, oppositely charged particles attract each other and tend to collect at the surface of each substance but remain separated from one another by the finite size of each particle or by neutral molecules that surround the charged particles. The electrostatic attraction between the two opposite and separated charges causes an electrical field to be established across the interface. Physical Pharmacy 2 KBA 6

Electrical double layer Physical Pharmacy 2 Electrical double layer The double layer is formed in order to neutralize the charged surface and, in turn, causes an electrokinetic potential between the surface and any point in the mass of the suspending liquid. This voltage difference is on the order of millivolts and is referred to as the surface potential. The magnitude of the surface potential is related to the surface charge and the thickness of the double layer. As we leave the surface, the potential drops off roughly linearly in the Stern layer and then exponentially through the diffuse layer, approaching zero at the imaginary boundary of the double layer. The potential curve is useful because it indicates the strength of the electrical force between particles and the distance at which this force comes into play. A charged particle will move with a fixed velocity in a voltage field. This phenomenon is called electrophoresis. The particle’s mobility is related to the dielectric constant and viscosity of the suspending liquid and to the electrical potential at the boundary between the moving particle and the liquid. This boundary is called the slip plane and is usually defined as the point where the Stern layer and the diffuse layer meet. The relationship between zeta potential and surface potential depends on the level of ions in the solution.The figure above represents the change in charge density through the diffuse layer. One shows considered to be rigidly attached to the colloid, while the diffuse layer is not. As a result, the electrical potential at this junction is related to the mobility of the particle and is called the zeta potential. Although zeta potential is an intermediate value, it is sometimes considered to be more significant than surface potential as far as electrostatic repusion is concerned. Physical Pharmacy 2 KBA 7

Repulsive effect of double layer Physical Pharmacy 2 Repulsive effect of double layer The repulsive effect from the double layer is responsible for stability. Verwey and Overbeek proposed that the repulsive energy is a function of: Distance between droplets The reciprocal of the effective radius of the double layer Physical Pharmacy 2 KBA 8

From Verwey and Overbeek Physical Pharmacy 2 From Verwey and Overbeek VR = 4.62 x 10-6 (r/2) e-kHo VR Repulsive energy r Particle radius  Valence of counter ions Ho distance between two particles  = (ez/2 – 1) / (ez/2 + 1); Z = ueo/kT, o is the double layer potential  Boltzmann constant Exercise: Predict VR in the presence of high valency counter ions Exercise: Predict VR when distance between particles is small Physical Pharmacy 2 KBA 9

Physical Pharmacy 2 Attractive force A small attractive Van der Waals force operating between the droplets, can be given by: VA = -Ar/12H0 A is a constant depending on the polarisability of the molecules of which the droplet is composed and is known as the Hamaker constant; A ca. 10-19 J to 10-20 J. Exercise: what happen if you have big ‘r’? Physical Pharmacy 2 KBA 10

DLVO Theory From Deryagin, Landau, Verwey and Overbeek Physical Pharmacy 2 DLVO Theory From Deryagin, Landau, Verwey and Overbeek Describes the stability of hydrophobic suspension Combination of electrostatic repulsive energy, VR, and the attractive potential energy, VA, gives the total potential energy of interaction: Vtotal = VA + VR The forces on colloidal particles in a dispersion are due to electrostatic repulsion and London-type Van der Waals forces Physical Pharmacy 2 KBA 11

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Interaction potentials Physical Pharmacy 2 Interaction potentials http://griergroup.uchicago.edu/~grier/leshouches2/leshouches2.html polystyrene sulfate spheres in deionized water at 25oC. Curves are labelled by the spheres' radii. Exercise: Compare the interaction potentials of big particles to small particles when the distance that separates them is the same. Physical Pharmacy 2 KBA 13

Physical Pharmacy 2 Reference RJ Hunter, Foundations of Colloid Science Volume 2, Clarendon Press Oxford (1989)‏ Physical Pharmacy 2 KBA