Adsorbed layer, equilibrium properties

AB diblock copolymers in the presence of a selective surface can form an adsorbed layer, which is a planar form of aggregation or self-assembly. This is very useful in the manipulation of the surface properties of solid surfaces, especially those that are employed in liquid media. Several situations have been studied both theoretically and experimentally, among them the case of a selective surface but a nonselective solvent [75] which results in swelling of both the anchor and the buoy layers. However, we concentrate on the situation most closely related to the micelle conditions just discussed, namely, adsorption from a selective solvent. Our theoretical discussion is adapted and abbreviated from that of Marques et al. [76], who considered many features not discussed here. They began their analysis from the grand canonical free energy of a block copolymer layer in equilibrium with a reservoir containing soluble block copolymer at chemical potential peK. They also considered the possible effects of micellization in solution on the adsorption process [61]. We assume in this presentation that the anchor layer is in a solvent-free, melt state above Tg. The anchor layer is assumed to be thin and smooth, with a sharp interface between it and the solvent swollen buoy layer. 

An entirely different approach to equilibrium adsorption is to assume that adsorbed layers behave like liquid films, and that the adsorbed molecules are free to move over the surface. It is then possible to apply the equations of classical thermodynamics. The properties which determine the free energy of the film are pressure and temperature, the number of molecules contained and the area available to the film. The Gibbs free energy G may be written as ... 

The observed equilibrium thickness represents the film dimensions where the attractive and repulsive forces within the film are balanced. This parameter is very dependent upon the ionic composition of the solution as a major stabilizing force arizes from the ionic double layer interactions between any charged adsorbed layers confining the film. Increasing the ionic strength can reduce the repulsion between layers and at a critical concentration can induce a transition from the primary or common black film to a secondary or Newton black film. These latter films are very thin and contain little or no free interlamellar liquid. Such a transition is observed with SDS films in 0.5 M NaCl and results in a film that is only 5 nm thick. The drainage properties of these films follows that described above but the first black spot spreads instantly and almost explosively to occupy the whole film. This latter process occurs in the millisecond timescale. 

One more interesting fact noted was the time evolution of PDADMAC structure and rheological properties, namely, there were the change of deformation value (here, the change of the value of Af = f p=2 5 atm - ap=45 atm) of PDADMAC adsorbed layer with time. The dependence of the f potential on the pressure was measured immediately after the reaching of equilibrium values off potential (so-called freshly formed layer), in one day and in some cases in 6 days. For example, in Fig. 8 the dependence of f potential on the pressure for the PDADMAC solution with concentration of C = 10—4 g/1 is represented. Here, f changed from +113 to +36 mV for freshly formed layer (AP = 3-45 atm) (curve 1), for the adsorbed layer in one day f changed from +74 to +51 mV (curve 2) and in 6 days there were no f potential dependence on the pressure (f = 64 mV) (curve 3). 

The thickness of the interphase depends on the reactivity of the filler surface with the matrix material. It also depends on their physical affinity.Increased acid-base interaction between chlorinated polyethylene and titanium dioxide increases the thickness of the adsorbed layer. There is a maximum of thickness of interphase which depends on the properties of polymer bulk. The acid-base interaction is more dependent on how the filler is modified than on the matrix properties themselves. Both filler and matrix are responsible for the formation of an equilibrium, although each contributes in a different way. 

The equilibrium properties of an adsorbed layer can be examined based on the chemical or electrochemical potentials of the constituents of this layer and the equilibrium equations derived in the section above. This is the simplest approach, although problems might appear in the description of the adsorbed layer properties during a surface phase transition [18]. Alternatively, the chemical potentials may be used for the determination of the grand ensemble partition function of the adsorbed layer, which in turn is used for the derivation of the equilibrium equations. This approach is mathematically more complex, but it leads to a better description of an adsorbed layer when it undergoes a phase transformation [18]. The present analysis for simplicity is restricted to the first approach. 

The treatment presented above has shown that classical thermodynamics fed with a minimum of modelistic assumptions can be used for the determination of the explicit dependence of the electrochemical potentials of adsorbed species upon the dipole-dipole interactions among these species. The electrochemical potentials can be further used for the derivation of the adsorption isotherm and more general the equilibrium properties of adsorbed layers at uncharged interfaces. 

The proposed thermodynamic treatment has two main advantages. It keeps the modelistic assumptions to a minimum and it is relatively simple. The first advantage increases the applicability and reliability of the treatment, since there is no need for questionable structural assumptions and / or drastical approximations, like those involved in statistical mechanical treatments. The second advantage allows many interesting adsorption phenomena, like co-adsorption and re-orientation processes as well as the effect of the specific adsorption of ions and the heterogeneity of the adsorbing surface on the equilibrium properties of adsorbed layers, to be readily taken into account. 

Some essential discoveries concerning the organization of the adsorbed layer derive from the various spectroscopic measurements [38-46]. Here considerable experimental evidence is consistent with the postulate that ionic surfactants form localized aggregates on the solid surface. Microscopic properties like polarity and viscosity as well as aggregation number of such adsorbate microstructures for different regions in the adsorption isotherm of the sodium dedecyl sulfate/water/alumina system were determined by fluorescence decay (FDS) and electron spin resonance (ESR) spectroscopic methods. Two types of molecular probes incorporated in the solid-liquid interface under in situ equilibrium conditions... 

The viscoelastic properties of the surface layer are important parameters. The most useful technique for studying the viscoelastic properties of surfactant monolayers is surface scattering. When transversal ripples occur, a periodic dilation and compression of the monolayer occurs, and this can be accurately measured, enabling the viscoelastic behaviour of monolayers under equilibrium and nonequilibrium conditions, to be obtained, without disturbing the original sate of the adsorbed layer. Some correlations have been found between surface viscosity and elasticity and foam stability an example of this is the addition of lauryl alcohol to sodium lauryl sulphate, which tends to increase the surface viscosity and elasticity [10]. 

The surface rheological properties of adsorbed layers of MeC at equilibrium... 

In the present case, at time t = t, the adsorption layer has reached an intermediate coverage and consists of almost only molecules of type A. After a time t = tj, equilibrium has not yet been reached, but component B occupies already a remarkable part of the interfacial area. The final equilibrium state of the adsorbed layer is established at time t > tj, and the interfacial properties are mainly controlled by the contaminant B. The evolution of the adsorbed layer composition with time is on a logarithmic scale. The absolute time ranges are a function of the absolute concentration, the time differences and concentration ratios at the interface and the surface activities of the two components. In practical cases, surfactants are not only contaminated by one but often by several components of different surface activity. This complicates the analysis of purification procedures and the grade of purity of prepared surfactant solutions. 

The macroscopic description of the adsorption on electrodes is characterised by the development of models based on classical thermodynamics and the electrostatic theory. Within the frames of these theories we can distinguish two approaches. The first approach, originated from Frumkin s work on the parallel condensers (PC) model,attempts to determine the dependence of upon the applied potential E based on the Gibbs adsorption equation. From the relationship = g( ), the surface tension y and the differential capacity C can be obtained as a function of E by simple mathematical transformations and they can be further compared with experimental data. The second approach denoted as STE (simple thermodynamic-electrostatic approach) has been developed in our laboratory, and it is based on the determination of analytical expressions for the chemical potentials of the constituents of the adsorbed layer. If these expressions are known, the equilibrium properties of the adsorbed layer are derived from the equilibrium equations among the chemical potentials. Note that the relationship = g( ), between and , is also needed for this approach to express the equilibrium properties in terms of either or E. Flere, this relationship is determined by means of the Gauss theorem of electrostatics. 

It is seen that the calculation of the chemical potentials of the adsorbed species and consequently the study of the equilibrium properties of the adsorbed layer by means of the STE approach necessarily require knowledge of the dependence of upon the adsorbed layer composition and the potential drop AGauss theorem of electrostatics, which readily yields ... 

The great flexibility of the present model as well as of the STE model lies in the simple expression of the chemical potentials, Eqs. (8) and (13). In order to investigate the equilibrium properties of an adsorbed layer, we may write down the equilibrium equations in terms of chemical potentials and apply Eqs. (13) and (14). Thus, for the single adsorption of a solute A that is described by Eq. (2), the equilibrium equations in terms of chemical potentials may be expressed as... 

Note that in the inset we may observe that the capacity in the region between the two peaks is not symmetrical indicating transformations of the surface aggregates. Models for transformations of the surface aggregates have been developed and certain experimental features have been explained. However, we should keep in mind that the surface aggregation is usually governed by slow kinetics and this makes it difficult to determine precisely the equilibrium properties of the adsorbed layer and compare them with model predictions. 

In the remainder of this chapter, we discuss theoretically the properties of grafted polymer layers in Section II and of adsorbed polymer layers in Section III. In each case, we first consider the equilibrium properties of a single layer and then discuss briefly the interactions between two surfaces. 

It may be concluded that the adsorptive properties of the investigated compounds are to be attributed to the quinone containing moiety of the molecule, not to the presence of the side chain. The structure of this quinonic moiety is of particular importance since the an-thracycline is strongly adsorbed without any equilibrium while adsorption of naphthoquinonic compounds is an equilibrium process between the adsorbed and solved species when the deposition step is performed under stirring. The side chain of vitamin Ki may however play a role in the rearrangement of the molecules because it increases the area occupied by each molecule. This favours a rapid modification of their position, and can be seen in the immediate decrease of the current within ten seconds after the deposition step, due to stabilization of the structure of the adsorbed layer. 

This paper proposes a phenomenological analysis, based on laboratory experimental work, of the effects of adsorption properties on pol3nner slug propagation. The adsorption properties studied include kinetic aspects, i.e. instantaneous adsorption, reorganization of macromolecules inside adsorbed layer, exchanges between free and adsorbed polymer, desorption as well as properties at thermodynamic equilibrium which can be described by a partially reversible adsorption isotherm. The conditions for hydro-dynamic retention are also discussed. In addition, an analysis of the effects of polymer polydispersity on each of these adsorption phenomena shows that these effects cannot be neglected in a predictive simulator. 

The diffuse layer is the region between the bulk and the Outer Helmholtz Plane (OHP) which is recognised as the plane of closest approach of non-specifi-cally adsorbed species. The properties of this layer can be explained in terms of an equilibrium between thermal motion and the long range coulombic interaction of the ions with the charge on the electrode. It can be regarded as the ionic atmosphere of the metal electrode, and is independent of the chemical nature of the ion. 

Figure 9 Characterization of the equilibrium properties of the adsorption layer by ellipsometry and Surface second harmonic generation, SHG. The SHG-signal I (P = 45, d = 90) (circles) is proportional to the surface coverage and increases monotonously with the bulk concentration. The ellipsometric quantity dA = A - Ao (triangles) shows an extremum at an intermediate concentration far below the cmc. The inset clearly shows the nonmonotonic dependency of dA on the adsorbed amount, (redrawn from (20 )...

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