Polymer adsorption theory : universal aspects and intricacies

The work presented in this thesis is based on the theory for polymer adsorption by Scheutjens and Fleer (SF). Roughly, the thesis can be divided into two parts: the first two chapters consider the original theory from a new viewpoint, attempting to find universal laws and to establish connections with analytical theories. The last three chapters are devoted to extensions of the theory to more intricate systems.In chapter 1 polymer adsorption from dilute solution is studied. We try to find the universal behaviour in the volume fraction profile as predicted by De Gennes from scaling arguments. In this analysis, three regimes are distinguished: close to the surface a proximal regime , which is dominated by the numerous contacts between polymer and surface, next to that a central regime , where the volume fraction profile decays as a power law which is independent of solution concentration and polymer chain length, and finally a distal regime with an exponential decay towards the bulk volume fraction. With the SF theory these regimes can indeed be found provided the polymer chains are sufficiently long (more than, say, 5000 segments). However, the exponent in the power law regime does depend on solution concentration and polymer chain length. Extrapolation to infinite chain length yields the proper mean-field exponent. Although in general mean-field theories (like the SF theory) can yield incorrect exponents, they tend to predict the proper trends, so that it can be expected that a chain length dependence is actually present. In *-solvents, where the mean-field treatment is thought to be exact because the second virial coefficient vanishes, an additional regime is found in between the central and distal regime. Its origin is, as yet, unclear.The volume fraction profile is also the main topic in chapter 2, which discusses polymers adsorbing from a semi-dilute solution in a good solvent. In a semi- dilute solution the correlation length is independent of chain length, and it is found that this correlation length and the adsorption energy are the only parameters determining the volume fraction profile. Thus, in contrast to the case of dilute solutions in chapter 1, the profile for adsorption from semi-dilute solutions is independent of the polymer chain length. The free energy equation derived by SF is shown to be equivalent to that obtained in analytical mean-field theories if it is assumed that all segments of a polymer chain are distributed within the system in a similar way. Such an assumption is called a ground-state approximation. This ground-state approximation can also be used to extract the adsorbed volume fraction profile (comprising only the polymer chains touching the surface) from the overall profile. This has been done by Johner et al . Their results compare well with SF calculations when the bulk concentration is high and the adsorption energy low, but the agreement is much less when this is not the case, possibly due to the larger influence of tails under these conditions. When a bidisperse polymer mixture adsorbs from a semi-dilute solution the overall profile is not affected, even though the individual components may show a very different profile.In chapter 3 we leave the case of simple flexible homopolymers and consider the influence of partial rigidity within the chain. Rigid polymers possess less conformational entropy, and hence adsorb more easily than flexible polymers. Chain stiffness is modelled by excluding direct backfolding and defining an energy difference between a straight and a bent conformation of two consecutive bonds, where the straight conformation is more favourable. When all parts of the polymer are equally stiff, a persistence length can be defined, which increases with the energy difference. Using this persistence length, the radius of gyration of a stiff polymer in solution can be rescaled to a flexible one with a smaller number of segments. However, it turns out that this procedure does not work out well for adsorption from dilute solution: the scaling laws in the central regime as found in chapter 1 are altered. The critical adsorption energy decreases with increasing persistence length, in full agreement with an equation formulated by Birshtein, Zhulina and Skvortsov. The situation gets complicated when only part of the polymer is stiff. As the stiffer par's lose less entropy upon adsorption, they adsorb preferentially. This effect leads to copolymer adsorption behaviour, even when there is no difference in interaction energy between the stiff and the flexible moieties.Entropic effects play a major role also in chapter 4, where the adsorption of comb polymers is considered. Comb polymers consist of a backbone and a (large) number of teeth, hence they have a large number of chain ends per molecule. These ends prefer to protrude into the solution to form dangling tails. As a result, combs tend to adsorb in a conformation where the backbone is preferentially on the surface and the teeth stick out. This leads to relatively thin adsorbed layers, and if the distance between the branch points of the comb is small compared to the tooth length a depletion zone develops adjacent to the adsorbed layer. For comb copolymers it is found that if the teeth adsorb preferentially over the backbone segments the critical adsorption energy is lower than in the case where the backbone adsorbs, even though both types of molecules have the same number of adsorbing segments. At the point of desorption only a few segments are on the surface, and a polymer in which only the tooth segments adsorb loses less entropy than a polymer adsorbing with its backbone.Finally, in chapter 5 we consider chemical surface heterogeneity by incorporating in the chain statistics a probability that a surface site has a particular adsorption energy. The surface can be constructed such that, on average, no energetic interaction between the polymer and the surface is present. Nevertheless, adsorption can take place on such a surface, provided "adsorbing sites" (sites with a favourable adsorption energy) are grouped together. The distribution of adsorbing sites determines largely the adsorption behaviour. If the driving force for adsorption is high, more polymer adsorbs on a surface with an equal distribution of adsorbing sites, as more of the available surface can be used. On the other hand, at low adsorption energy, it is more favourable to have the adsorbing sites group together, so that little of the non-adsorbing sites are in contact with the polymer.In conclusion, universal behaviour is found only in the case of flexible, linear homopolymers adsorbing from a semi-dilute solution in a good solvent. In all other cases studied (dilute solutions, chain rigidity, chain branching and surface heterogeneity) the structure is more intricate. Although the meanfield character of the Scheutjens-Fleer theory is definitely a serious approximation, it does enable the modelling of a large variety of equilibrium systems, even at high concentrations, providing an abundance of detailed information. It is worthwhile to continue to check its assumptions and predictions with other theories and obviously with experiment. The volume fraction profile determines the properties of the system and is also very sensitive to the approximations used in the model. Therefore, precise and unambiguous measurements of the density profile remain of the utmost importance