Lecture 11 Colloidal interactions I

In the last lecture… h Capillary pressure due to a curved liquid interface Capillary pressure is responsible for phenomenon of capillary rise Capillary action can be used to manufacture novel nanoscale structures

In this lecture… 1)What are Colloids and why are they important? 2) Colloidal stability 3) Interactions between charged surfaces in solutions 4) Osmotic pressure between two surfaces Further reading Intermolecular and Surface Forces J. Israelachvili, Chapter 12 p Colloidal Dispersions: suspensions, emulsions and foams, I. D. Morrison and S. Ross, Wiley p

Colloids and nanoparticles Colloids are mixtures where small particles (<1  m in diameter) of one substance are suspended in a second medium or continous phase They are not solutions! The material is not completely dispersed, but exists as discrete particles Continuous phase (e.g. water) Colloidal particle

Why are colloids important? Colloidal interactions govern the properties of nanoscale systems in liquid environments Gold colloids FerrofluidsQuantum dots (CdSe) Food Science Biomolecules

Key challenge in manufacturing colloidal dispersions When materials are dispersed in particulate form they have a very large surface area. Their natural tendency is to stick together or flocculate to form an aggregate (more on aggregation in a later lecture) We have already seen that dispersion forces result in a mutual attraction between particles which can drive the flocculation of even very dilute systems

How do we stop things sticking together? We need to introduce a short range repulsion force to keep particles apart. In water, this is often done by decorating the surface of the particles with charged groups and adding a small amount of salt But the reason why the particles repel is not purely electrostatic … add water add salt

Charged surfaces in electrolytes The added salt is often referred to as an electrolyte In practice the electrolyte concentration is much higher than the concentration of ions due to dissociated groups Some of the charged ions from the salt form layers at the particle surfaces, ensuring that charge neutrality is maintained So if everything is charge neutral, how do the particles repel one another?

Repulsive forces between charged surfaces in an electrolyte When two charged surfaces are brought close together the counter-ion concentration between the surfaces is larger than outside this region. This results in an osmotic pressure, , which pushes the surfaces apart and tries to restore a uniform concentration (see OHP) Where n+ and n- are number densities of positive and negative ions in gap

How do we calculate n + and n - ? The number of counter ions of each charge is determined by Boltzmann statistics Where n o is the number density in bulk solution The energies of the charged counter ions with valence z are given by Where V(x) is the electrostatic potential at a position x in the solution

Osmotic pressure between charged surfaces Inserting the previous result into our expression for the osmotic pressure gives (see OHP) In the limit of small surface potentials this reduces to So if we know V(x) we can calculate the osmotic pressure!

What form of V(x) should we use? The true form of the electrical potential between colloids is complicated. A good approximation to V(x) is the form for the potential for an isolated charged surface in an electrolyte. To obtain this we must first solve the Poisson equation Note: This equation is a differential form of Gauss’s law! (see F31CO1 + F32ON1 notes). Derivation not examinable where  is the charge density (Cm -3 ) and  o is the permittivity of free space

Potential near a planar charged surface I The total charge density in the gap between the two surfaces is the sum of densities due to positive and negative counterions If counterions have a valence of ± z then assuming that n+ and n- obey Boltzmann statistics, as before we have (see OHP)

Potential near a planar charged surface II Combining the above results gives a modified version of the Poisson equation In the limit of small potentialsthis reduces to

The Debye screening length Assuming that the potential decays to zero for infinite x, this equation has a solution which is a simple exponential decay Where 1/  is the Debye screening length 1/  is the distance over which electrostatic interactions are screened in an electrolyte and V o is the potential at the surface

Problem 1 Two surfaces are charged to a surface potential of 10mV and are suspended in water (  =80) which also has a monovalent salt dissolved in it. Calculate the Debye screening length between the surfaces at room temperature if the salt concentration is a)1mM b)100mM

Osmotic pressure between surfaces (revisited) Recall from a previous slide that the osmotic pressure due to counterions has the form If we insert our exponential form for the decay of the potential this gives where D=2x is the separation between the surfaces

Total pressure between surfaces The total pressure between two charged surfaces in an electrolyte is where P dispersion is the pressure due to attractive dispersion interactions This is a simplified form of the Derjaguin, Landau, Verwey, Overbeek (DLVO) theory of colloidal stability

Pressure (Force) vs separation Long range attractive dispersion forces (negative) Short range double layer repulsion forces (positive)

The effects of adding electrolyte As more salt is added, electrostatic effects are more strongly screened → eventually attractive dispersion forces dominate and surfaces will stick together

Summary of key concepts Colloidal stability is important in many areas of nanotechnology It can be achieved by charging surfaces The pressure exerted on charged surfaces in an electrolyte is determined by a balance between the osmotic pressure due to counter-ions and the dispersion pressure