For the conformation of adsorbed polymer chains, the loop-train model and/or the loop- train-tail model are now widely accepted. In formulating the theory, segment-segment, segment-surface, and segment-solvent interactions are taken into consideration. Regard- less of the model, all the existing theories predict that at high adsorption energy, the conformation of adsorbed polymer chains is flat and the fraction of adsorbed segments is large. The conformation of adsorbed polymer chains is controlled by the segment dis- tribution in the adsorbed layer. The root-mean-square thickness of this layer may be used to interpret the experimental data obtained, for examble, by ellipsometry (cf. Sect.
C.2.2). Theories based on the loop-train model indicate that this average thickness at the theta point is proportional to the square root of the polymer molecular weight. However, the same molecular weight dependence is also derived from the loop-train-tail model.
Furthermore, this average thickness is predominantly determined by tails rather than by loops. Existing theories allow other important quantities such as the adsorbed amount, the fraction of adsorbed segments, and the surface coverage to be calculated, but the results from different theories are not very different from one another. The diffusion equation approach and the scaling theory lead to very simple results.
Existing theories of the adsorption of polyelectrolyte allow effects of the polymer charge density, the surface charge density, and the ionic strength on the adsorption behavior to be predicted. The predicted adsorption behavior resembles that of nonionic polymers if the ionic strength is high or the polymer charge density is very low.
The Structure of Macromolecules Adsorbed on Interfaces 35
C. Experimental Techniques
As has been depicted in Fig. 1, various conformations are possible for adsorbed poly- mers, depending on polymer-polymer, polymer-solvent, and polymer-interface interac- tions and the flexibility of polymers. To determine experimentally the conformation of adsorbed polymers only adsorption isotherm data are insufficient. The average thickness of the adsorbed polymer layer, the segment density distribution in this layer, the fraction of adsorbed segments, and the fraction of surface sites occupied by adsorbed segments must be measured. Recently, several unique techniques have become available to mea- sure these quantities.
C.l Adsorption Isotherms
Adsorption isotherms are readily determined by measuring polymer concentrations in the bulk solutions before and after adsorption equilibrium has been attained. However, the time required to reach equilibrium is often considerable.
Measured isotherms are usually of the high-affinity type for which reliable and accu- rate data can be obtained only in the plateau region of the isotherm. The initial rising part of the isotherm is often difficult to measure accurately, because we have to determine trace amounts of polymer
Cohen-Stuart et al.58) demonstrated that the molecular weight distribution affects the shape of adsorption isotherms. In fact, often observed round-shaped isotherms are attri- buted to a broad molecular weight distribution.
C.2 Thickness of the Adsorbed Layer C.2.1 Hydrodynamic Methods
The most convenient of these methods is viscosity measurement of a liquid in which particles coated with a polymer are dispersed, or measurement of the flow rate of a liquid through a capillary coated with a polymer. Measurement of diffusion coefficients by photon correlation spectroscopy as well as measurement of sedimentation velocity have also been used. Hydrodynamically estimated thicknesses are usually considered to repre- sent the correct thicknesses of the adsorbed polymer layers, but it is worth noting that recent theoretical calculations52'59) have shown that the hydrodynamic thickness is much greater than the average thickness of loops.
C.2.2 Ellipsometry
Ellipsometry2 7'6 0 _ 6 2 ) is based on the principle that light undergoes a change in polarizabil- ity when it is reflected at a surface. The refractive index of the surface and the reflection coefficient of a system can be calculated from the change in the phase retardation A and the change in the amplitude ratio tan V- Adsorption of a polymer on a surface gives rise
36 A. Takahashi and M. Kawaguchi to additional changes in A and tan ψ, which allow the thickness and refractive index of the adsorbed layer to be determined. However, since the thickness so determined con
cerns the thickness of a hypothetical homogeneous layer, the root-mean-square thickness must be estimated therefrom by making appropriate assumptions for the distribution of segments in the adsorbed layer. This root-mean-square thickness may be compared with the root-mean-square thickness for loops or tails predicted by theory. However, the segment distribution itself cannot be measured directly. The refractive index gives the average segment density in the adsorbed layer, and its product with the average thickness of the adsorbed layer gives the adsorbance. The advantage of ellipsometry allows in situ measurements of the refractive index and the thickness of the adsorbed layer to be made, although its applicability is limited to the adsorption onto a flat, smooth, reflective surface, i.e. a metallic or mirror surface.
C.2.3 The ATR Method
The attenuated total reflection (ATR) method measures the reflection coefficients of vertically and horizontally polarized light reflected from a polymer layer adsorbed on a transparent surface63). These coefficients allow the thickness of the adsorbed layer and the polymer concentration in it to be determined.
In principle, the ATR method would provide information about the segment distribu
tion in the adsorbed layer if light could penetrate in different depths into the layer, but this possibility still remains untested.
C.3 Fraction of Adsorbed Segments and Fraction of Occupied Surface Sites
The infrared band of a particular group in a polymer shifts when some groups of the polymer are adsorbed onto active sites, e.g. silanol groups on a silica surface25. This phenomenon has been used to measure the fraction of adsorbed polymer segments. The fraction of the surface sites occupied by adsorbed polymer segments can also be deter
mined from the frequency shift of IR band caused by the interaction between functional groups and an active site.
When spin-labeled species are chemically attached to a polymer at random, the difference in mobility between the labeled segments adsorbed (trains) and unadsorbed (loops or tails) gives rise to a variation in the magnetic relaxation time. This difference allows an estimation of the fraction of adsorbed segments if the signals from the adsorbed and unadsorbed labeled segments can be separated. However, the applicability of this electron paramagnetic resonance (EPR) method64) to polymer adsorption has two limila- tions. One is that the introduction of the spin-labeled species sometimes affects the adsorption behavior. The other is that the mobility of unadsorbed segments is often disturbed by adjacent adsorbed segments. The latter is notable for short loops, leading to mistaking such loops as trains. Thus, the EPR method may estimate the fraction of adsorbed segments over the values obtained by the IR method.
The Structure of Macromolecules Adsorbed on Interfaces 37 C.4 Heat of Adsorption
Calorimetry65) is the only direct method concerning the energetics of adsorption proces
ses. The heat of adsorption should be generated from the difference between surface- segment and surface-solvent interactions, i.e. the χs parameter, and from the difference among segment-segment, segment-solvent, and solvent-solvent interactions. No relation
ship between the heat of adsorption and these parameters has as yet been established.