Amount of polymer adsorbed per unit area

The importance of adsorbed polymer conformation at interfaces was first recognized by Jenkel and Rumbach in 1951. A model of adsorbed polymer conformation was proposed based on the observation that amount of polymer adsorbed per unit area of the surface corresponds to a layer more than ten molecules thick. In that model, not all the segments of a polymer are in contact with the surface. As schematically shown in Figure 7.27, those segments that are in direct contact with the surface are termed trains, those between and extending into solution are termed loops, the free ends of the polymer extending into solution are termed tails. Sato and Ruch classified the possible conformations for most situations into the six types shown in Figure 7.28. 

It is clear from the above theories that for full characterization of polymer adsorption and configuration at the interface, one needs to measure the following values, i.e. the amount of polymer adsorbed per unit area of the surface, r(mol m ), the fraction of segments in direct contact with the surface (in trains), p, and the segment density distribution p(z). Measurement of F and p as a function of polymer concentration is fairly straightforward. The parameter F can be directly determined by equilibrating a known amount of disperse phase (particles or droplets) of known surface area with polymer solutions with various concentrations, starting... 

For full characterization of the process of adsorption, it is necessary to know the amount of polymer adsorbed per unit area of the snrface, the fraction of segments in close contact with the surface, and the distribution of polymer segments. 

As discussed in Chapter 6, complete information on polymer adsorption may be obtained if the segment density distribution can be determined - that is, the segment concentration in all layers parallel to the surface. However, such information is generally unavailable, and therefore three main parameters must be determined, namely the amount of adsorption F per unit area, the fraction p of segments in direct contact with the surface (i.e., in trains), and the adsorbed layer thickness 5. 

We have previously shown by means of SEM micrographs 1, that our polyethylene has an uneven surface and that during oxidation etching of polymer (mainly amorphous regions) takes place. This would mean that the roughness factor of pitted surfaces may be considerably high and that the amount of protein adsorbed per unit of true area for PE samples would in reality be less by an unknown factor than those shown in Fig. 3 and Fig. 4. 

The simplest example is a mixture of two homodisperse polymer samples differing only in molecular weight. The adsorption of such a mixture is conveniently discussed In terms of the total poljmer mass (free and adsorbed) per unit area in the system (T ), which is subdivided into the amount adsorbed on the surface (f) and the free molecules in the bulk solution (T ). The parameter r is either r or r in dilute solutions, to which we shall restrict ourselves, there is no difference between r, r and r , as discussed in sec. 5.3b. The quantity may be defined as c t, where Cp is the pol rmer concentration and t the thickness of the solution layer available to the adsorbent surface. The latter parameter may also be taken as the ratio between the total solution volume and the total surface area in the system. The quantities F, F and r are expressed in the same units, e.g., mg/m. ... 

The amount of polymer adsorbed F (in mg or mol) per unit area of the particles. It is essential to know the surface area of the particles in the suspension. N itrogen adsorption on the powder surface may provide such information, by application of the Bmnauer-Emmett-Teller (BET) equation, provided that no change will occur in area when the particles are dispersed in the medium Eor many practical systems, a change in surface area may occur on dispersing the powder, in which case it would be necessary to use dye adsorption to measure the surface area (some assumptions must be made in this case). 

A simple way for the determination of the polymer mass per unit area is through gravimetric analysis. Usually the porous membranes that are used for the preparation of concave brushes have a very large surface area, so the formation of a polymer brush inside the pores produces an easily measurable change of the sample s weight. Precise knowledge of the membrane porosity and pore size permits the straightforward calculation of the polymer mass per unit area, which for the case of self-assembled brushes is the adsorbed amount P. 

To determine the conformation of adsorbed polymers the fraction of adsorbed polymer segments (p) and the fraction of the occupied surface sites (6) are often measured. Fontana and Thomas2 were the first to measure p and 6 by IR spectroscopy. At present, the application of IR spectroscopy is limited to finely divided substrates, e.g. nonporous silica, and requires that the surface area and the number of surface sites (e.g. the silanol groups) per unit area are accurately known in advance. The adsorbed amount T of polymer per surface site can be determined from adsorbance A(g/cm2) and the total area of the adsorbent. However, it can also be evaluated from the ratio 6/p. 

Figure 5.29. Adsorption isotherms for a binary mixture of dextran samples (9 K and 500 K in equal mass fractions) adsorbed on Agl from aqueous solution, for three values of (indicated). In the top figure (a) the Isotherms are plotted In the conventional way (r versus 0 ). in the lower diagram (b) they are plotted as r(r ). where amount of polymer (per unit area) in the bulk solution. In (b) the adsorption Isotherms of the individual fractions are given as the dashed curves.

As our first case study, dealing with pol)miers, we consider Langmuir mono-layers of poly(methacrylic ester), PMA, at the water-air interface. Data for these layers can be used to illustrate some trends and principles, laid down in sec. 3.41. In that section we discussed how the surface pressure of physisorbed polymers depends on surface concentration. In a dilute monolayer of pancakes, the surface pressure was found to be given by the ideal term plus an excluded-area contribution. We rewrite [3.4.56] in terms of the adsorbed amount r = n°/A = N°/ N A) in moles of chains per unit area... 

Related to the surface excess F is the amount of charges (in units of e) carried by the adsorbing PE chains, /F. In some cases the polymer carries a higher charge (per unit area) than the charged surface itself, /F > a, and the surface charge is overcompensated by the PE, as we will see later. This does not violate charge neutrality in the system because of the presence of counterions in solution. 

In many experiments the total amount of adsorbed polymer per unit area T is measured as function of the physical characteristics of the system such as the charge fraction /, the pH of the solution, or the salt concentration Cgait [103-110]. 

Adsorption equilibria for polymers out of concentrated solutions as function of concentration frequently exhibit very pronounced maxima (Fig. 12). These unusual curves can be accounted for if one assumes that the adsorbed species are in aggregation equilibrium in the solution, depending upon the amount of surface area per unit volume of solution. Hence one expects that the adsorption equilibrium out of concentrated polymer solution may not only be approached with "infinite slowness but is also a function of the system characteristics, and the definition of reproducible conditions contains many more variables than one is used to from the more common work with dilute solution. This complexity is particularly awkward when one deals with the important case of competitive adsorption of polymers out of concentrated multicomponent solutions, a common phenomenon in many industrial processes, such as paint adhesion, corrosion prevention, lubrication, especially wear prevention, etc. 

---