Thickness of the Adsorbed Layer

It has been discussed in the previous section of this chapter that the individual isotherms can be calculated by assuming that the adsorption is monolayer. This, however, does not necessarily prove that adsorption from solutions cannot be multilayer. In fact cases have been reported where adsorption from solution phase is certainly multimolecular. 

According to monolayer adsorption, the highest value that n AxIm can have corresponds to complete coverage of the adsorbent surface by any one component and no adsorption of the other component so that the composite isotherm equation is reduced to 

FIGURE 3.26 Composite isotherm showing a linear section. 

The monolayer valne in each case can be obtained by dividing the surface area of the adsorbent by the molecular area of the adsorbate. 

In the case of methanol-n.amyl alcohol on the original charcoal, the thickness of the adsorbed layer is only 1.48. This has been attributed to the fact that methanol and amyl alcohol have the same polar group in their molecules, so they both compete for the active CO2 complex sites present on the charcoal snrface. As the alcohol molecnles lay flat on the carbon snrface, the larger hydrocarbon portion in amyl alcohol occnpies more than one active site, renderingthem inaccessible to interaction with the OH gronp of the alcohols. 

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 represent the correct thicknesses of the adsorbed polymer layers, but it is worth noting that recent theoretical calculations52, have shown that the hydrodynamic thickness is much greater than the average thickness of loops. 

---

The model implies that at any pressure below the saturation vapour pressure, the fractions of the surface covered with 1, 2,. .., i molecules will be 6 02,.., 0i respectively, so that the thickness of the adsorbed layer will not be constant throughout. On the specific surface area A, therefore, the total number Z of molecules adsorbed will be... 

The f-curve and its associated t-plot were originally devised as a means of allowing for the thickness of the adsorbed layer on the walls of the pores when calculating pore size distribution from the (Type IV) isotherm (Chapter 3). For the purpose of testing for conformity to the standard isotherm, however, a knowledge of the numerical thickness is irrelevant since the object is merely to compare the shape of the isotherm under test with that of the standard isotherm, it is not necessary to involve the number of molecular layers n/fi or even the monolayer capacity itself. 

Experimentally, the form of 4>(z) has been recently established for adsorbed homopolymers and terminally anchored tails by the Bristol group (17,20). Knowing 4>(z) one may then calculate the r.m.s. thickness of the adsorbed layer. Previous measurements of the "thickness" (1-4) have usually involved ellipsometry (flat surfaces) or some hydrodynamic technique (particles). In neither case can the calculated thickness be unambiguously related to 4>(z), although recent theoretical work by Cohen Stuart et al. (21), to be discussed at this meeting, has made an attempt to relate the hydro-dynamic thickness, 6, to < >(z). 

The plateau adsorbances at constant molecular weight increased linearly with the square root of NaCl concentration. For the same NaCl concentration the adsorbance was nearly independent of the molecular weight. The thickness of the adsorbed layer was approximately proportional to the square root of the molecular weight for the Theta solvent (4.17 M NaCl). For good solvents of lower NaCl concentrations the exponent of the molecular weight dependence of the thickness was less than 0.5. At the same adsorbance and molecular weight the cube of the expansion factor at, defined by the ratio of the thicknesses for good solvent and for Theta solvent, was proportional to the inverse square root of NaCl concentration. 

Adsorption of polyelectrolyte on interfaces is concerned with various applications such as flocculation and steric-stabilization of colloidal particles in an aqueous phase, oil recovery, and soil conditioning. In these cases, both the adsorbance of polyelectrolytes and the conformation of the adsorbed polymer, which is connected with the thickness of the adsorbed layer, are very important. 

For homopolyelectrolyte, we first studied the ellipsometric measurement of the adsorption of sodium poly(acrylate) onto a platinum plate as a function of added sodium bromide concentration (5). We measured the effect of electrolyte on the thickness of the adsorbed layer and the adsorbances of the polyelectrolyte. It was assumed that the Donnan equilibrium existed between the adsorbed layer and the bulk phase. The thickness was larger and the adsorbance of the polyelectrolyte was lower for the lower salt concentration. However, the data on the molecular weight dependence of both the adsorbance and the thickness of the adsorbed polyelectrolyte have been lacking compared with the studies of adsorption of nonionic polymers onto metal surfaces (6-9). 

The aim of this paper is to offer experimental results for the molecular weight dependence of adsorption of polystyrene-sulfonate) onto a platinum plate from aqueous NaCl solution at 25 °C. Measurements of poly(styrenesulfonate) adsorption were carried out by ellipsometry. The dependences of molecular weight and added salt concentration on the thickness of the adsorbed layer and also the adsorbances of polymer and salt are examined. 

Basic data of the thickness of the adsorbed layer, t, and the refractive index, n, of the adsorbed layer were calculated from the experimental data of the phase difference, A, and the azimuth angle, i >, of the amplitude ratio by computer. The computer program proposed by McCrackin (10) was used. 

Expansion of Thickness of the Adsorbed Layer. In the low salt concentration the large thickness compared with the case of the Theta solvent (4.17 M NaCl) is considered to be due to the electrostatic repulsion, i.e., the excluded volume effect of the adsorbed NaPSS chains. Usually, the expansion factor at, defined by the ratio of the thickness in good solvent and that in the Theta solvent, is used to quantitatively evaluate the excluded volume effect for the adsorbed polymers. 

For adsorption of nonionic polymer, Hoeve (15) and Jones-Richmond (16) attempted to incorporate the excluded-volume effect into the expansion factor, respectively. They suggested that the thickness of the adsorbed layer in good and 0 solvents should be taken at the same adsorbance and molecular weight3 respectively. We may calculate the expansion factor at the bulk NaPSS concentration of 0.02 g/lOOml, since the adsorbances are almost the same for the respective NaCl concentrations, as seen from Figure 5. 

The thickness of the adsorbed layer, t, is approximately proportional to at the Theta point but in good solvent the... 

PVA and TaM -for the 88%-hydrolyzed PVA. The same dependence was found for the adsorbed layer thickness measured by viscosity and photon correlation spectroscopy. Extension of the adsorption isotherms to higher concentrations gave a second rise in surface concentration, which was attributed to multilayer adsorption and incipient phase separation at the interface. The latex particle size had no effect on the adsorption density however, the thickness of the adsorbed layer increased with increasing particle size, which was attributed to changes in the configuration of the adsorbed polymer molecules. The electrolyte stability of the bare and PVA-covered particles showed that the bare particles coagulated in the primary minimum and the PVA-covered particles flocculated in the secondary minimum and the larger particles were less stable than the smaller particles. 

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... 

The final proof of the physical reality of our model of macromolecular adsorption was provided by simultaneous independent work, by an entirely different method, at the National Bureau of Standards (27). Stromberg et al., allowed polystyrene fractions, besides other polymers, to become adsorbed on ferrochrome plates and determined the thicknesses of the adsorbed layers... 

Fmpirical methods can be applied in order to determine the validity of the BFT surface area. The derived standard isotherms can be obtained by normalization of the y-axis (volume adsorbed) of adsorption isotherms. It is strongly recommended that data should always be derived from standard isotherms related to a nonpor-ous sample of the same type of material. Various methods have been established like the as-method where the quantity of gas adsorbed V], is related to the value at a relative pressure of 0.4. In the t-plot, the vertical axis is normalized in relation to the average thickness of the adsorbed layer. The shape of the constructed reduced isotherms reveal the presence or absence of micropores and allows the determination of their volume [79, 80]. 

A reliable way of identifying the existence of micro- and mesoporosity and of estimating pore volume is the t-plot analysis of de Boer et al. (1966). The amount of gas adsorbed by the test material is related to the amount adsorbed by a non porous reference material. For the latter, there is a linear relationship between the amount adsorbed, V, and the average thickness of the adsorbed layer, t, i. e. 

The other major casein monomer in bovine milk is asi-casein. The SCF theory suggests that a loop-like protein conformation is favoured for adsorbed asi-casein (see Figure 8.1a) (Dickinson et al., 1997 Home, 1998). This implies a reduced hydrodynamic thickness of the adsorbed layer for as]-casein as compared with p-casein. 

FIG. 9.12 Five models for capillary condensation. The radius of the pore equals r, the radius of curvature of the spherical meniscus is Rs, and t is the thickness of the adsorbed layer. The subscripts a and d refer to adsorption and desorption. 

Figures 9.12d and 12e illustrate another model for adsorption hysteresis that considers multilayer adsorption explicitly. During adsorption the capillary is viewed as a cylinder of radius (r - t), with t the thickness of the adsorbed layer at that pressure. This is represented by Figure 9.12d. For such a surface the Kelvin equation becomes...

Attachment of a single segment of the polymer chain is sufficient to confine the molecule to the layer of solution adjacent to the adsorbing surface. The solid exerts very little influence on the polymer molecule as a whole in such a case. In fact, the overall spatial extension of the polymer chain is expected to be about the same as that of an isolated molecule in this situation. The polymer-solvent interaction plays a more important role than the polymer-surface interaction in determining the thickness of the adsorbed layer in this case. This is only one of the relative interaction combinations possible, but it is the one that we consider in the greatest detail. As the number of polymer segments actually attached to the surface increases, the influence of the surface causes the spatial extension of the adsorbed chains to decrease. 

EXAMPLE 13.5 Determination of the Thickness of Adsorbed Polymer Layer from the Intrinsic Viscosity of the Dispersion. An adsorbed layer of thickness 8RS on the surface of spherical particles of radius R increases the volume fraction occupied by the spheres and therefore makes the intrinsic viscosity of the dispersion greater than predicted by the Einstein theory. Derive an expression that allows the thickness of the adsorbed layer to be calculated from experimental values of intrinsic viscosity. 

Concerning the experimental side of polymer adsorption studies the quantity A was only measurable at the early stage of the study, but in 19SS the thickness of the adsorbed layer became accessible to measurement by a hydrodynamic method and in 1961 the quantity p was first determined by infrared spectroscopy. Ellipsometry came up in 1963, which enabled both the adsorbance and the thickness of the adsorbed layer to be measured simultaneously. 

Scheutjens and Fleer further calculated50 the concentration distributions of loop and tail segments, the root-mean-square thickness of the adsorbed layer, and the average numbers and lengths of trains, loops, and tails. They also computed the distributions of trains, loops, and tails from the free segment probability Pj, which may be represented by... 

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. 

---