Polyelectrolytes @ interfaces and in the bulk

To understand how polyelectrolytes behave at interfaces, we first have to get insight in the generic and molecular specific feature of the neutral analogues. Hence we first need to know how polymers behave at interfaces. In turn, for a good understanding of polymers at interfaces, we need to have insight in the solution properties. Hence in my lecture I will briefly review these aspects in reversed order. We will start in the solution and work towards the adsorption problems. The working horse for this is the Edwards diffusion equation.

Key aspects that will be discussed are: (i) the relevant polymer length scale in dilute and semi-dilute solutions. (ii) the appearance of a critical adsorption energy in polymer adsorption and the nature of the adsorption transition; depletion vs adsorption (iii) The de Gennes self-similar adsorption profile for strong adsorption from dilute solutions. (iv) numerical SCF calculations a la Scheutjens and Fleer (v) analytical approximations based on the ground state approximation. (vi) Generic versus molecular specific effects for polymer at interfaces (the role of molecular architecture).

Polyelectrolyte adsorption is a rich topic. On top of the interactions discussed for neutral polymer adsorption we have the electrostatics. We will discuss the Poisson-Boltzmann (PB) equation for the description of ions near electrified interfaces. In this equation the ions are point charges and this is far from the polyelectrolyte case. However we will discuss how to extend the PB approach towards ions with excluded volume and then towards chains that carry charges. In short we will need to solve Edwards diffusion equation in combination with the Poisson equation, which is possible using the Scheutjens-Fleer SCF approach.  

We will argue that in PE systems the nature of the charge on the backbone and the diffuse cloud of ions around it, causes extreme departures from the generic effects discussed above for homopolymer adsorption. Often for PE adsorption the chains are in ‘flat’ train-like conformations. Just next to this thin layer there is a Coulomb hole from which the PEs are strongly depleted. As a consequence, we need to have extremely long PEs before the generic self-similar profile can be  expected and molecular specific features dominate.