Segments, bound fraction

The polymer concentration profile has been measured by small-angle neutron scattering from polymers adsorbed onto colloidal particles [70,71] or porous media [72] and from flat surfaces with neutron reflectivity [73] and optical reflectometry [74]. The fraction of segments bound to the solid surface is nicely revealed in NMR studies [75], infrared spectroscopy [76], and electron spin resonance [77]. An example of the concentration profile obtained by inverting neutron scattering measurements appears in Fig. XI-7, showing a typical surface volume fraction of 0.25 and layer thickness of 10-15 nm. The profile decays rapidly and monotonically but does not exhibit power-law scaling [70]. 

Several experimental parameters have been used to describe the conformation of a polymer adsorbed at the solid-solution interface these include the thickness of the adsorbed layer (photon correlation spectroscopy(J ) (p.c.s.), small angle neutron scattering (2) (s.a.n.s.), ellipsometry (3) and force-distance measurements between adsorbed layers (A), and the surface bound fraction (e.s.r. (5), n.m.r. ( 6), calorimetry (7) and i.r. (8)). However, it is very difficult to describe the adsorbed layer with a single parameter and ideally the segment density profile of the adsorbed chain is required. Recently s.a.n.s. (9) has been used to obtain segment density profiles for polyethylene oxide (PEO) and partially hydrolysed polyvinyl alcohol adsorbed on polystyrene latex. For PEO, two types of system were examined one where the chains were terminally-anchored and the other where the polymer was physically adsorbed from solution. The profiles for these two... 

Figure 2. The bound fraction, , as a function of mean segment concentration, < >j, in an interfacial region of width equal to 5d (6 lattice planes).

It is not always possible to measure c(z) in full detail so that introduction of some average properties remains useful. One such parameter is the train fraction or bound fraction p. In terms of fig. 5.6 it is the amount of polymer within the thickness f of a segment on the surface, divided by the total adsorbed amount. Spectroscopic and other techniques can often be successfully applied to determine p. The general trends found support the picture sketched above, i.e., p Is close to unity when the adsorbed amount is low, and it decreases as the pseudo-plateau of the adsorption Isotherm (see fig. 5.7) is approached. Reported bound fractions vary widely, depending on the system and method chosen. It should be said that bound fraction measurements leave much room for differences in Interpretation some results are still not well understood. We will briefly discuss the methods in sec. 5.6, and give some exjjerimental data in secs. 5.7 and 5.8. 

For the determination of the fraction of segments in trains or, equivalently, the bound fraction p, one relies on features which allow differentiation between free (non-adsorbed) segments and segments in contact with the surface. In some cases, it is also possible to discriminate between parts of the solid substrate covered with polymer segments, and bare surface parts. One can then also determine the train density. 

The polymer bound fraction, p, can be directly determined using spectroscopic methods such as NMR. The method depends on the reduction in the mobility of the segments that are in close contact with the surface. By using a pulsed NMR technique, one can estimatep. An indirect method for estimation of p is to use microcalorimetry. Basically one compares the enthalpy of adsorption per molecule with that per segment [9]. The latter may be obtained by using small molecules of similar structure to a polymer segment. 

Several methods can be used to determine the fraction of segments, (p), of the polymer chain actually in contact with the surface. Small-angle neutron scattering (SANS) and neutron reflectivity (NR) ellipsometry, electron paramagnetic resonance (EPR), IR, and NMR spectroscopy have all been used. Most suffer from the drawback that the distinction between bound and free segments close to the interface is often difficult to define. This distinction is important as the bound fraction effectively determines how well anchored the polymer is to the surface. 

The bound fraction is defined as the fraction of segments physically in contact with the surface ... 

EPR is comparable to solid-state NMR but has the same principal limitation in that the distinction between the segments bound in trains and short loops close to the interface is not easily made. These limitations lead to an overestimation of the bound fraction. Nevertheless, EPR and NMR results generally show rather good agreement. Any perturbing effects due to the presence of the spin-active group are ignored. 

Average bound fraction of segments of polymer chain... 

The fraction of segments attached to the surface (bound fraction) increases monotonically for all molecular weights as the surface interaction energy increases. For energies above the transition point, the average number of surface contacts is proportional to N and the bound fraction approaches a constant, large value. The constant bound fraction results in adsorbed polymer dimensions which are independent of N, with the molecule lying close to the surface. 

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