Interfadal region

A schematic of the interfadal region is provided in Figure 18.9, which shows three main states (i) adsorption when the surface concentration F is lower than the equilibrium value F (ii) the equilibrium state when F = F and (iii) desorption when F > F. ... 

The first unequivocal demonstration of this important, well-known constraint appears in O. Stern, Zur Theorie der elektrolytischen Doppelschicht, Z. Elektrochem. 30 508 (1924). The Stem model of the interfadal region was the first chemical model in the spirit of the present chapter. 

Based on earher work, Weber and Newman [27] postulate the formation of approximately spherical clusters in regions with a high density of sulfonate heads, and an interfadal region that under vapour-equilibrated conditions consists of collapsed chaimels (Figure 4.1a) that can fill with water to form a liquid channel when the membrane is equilibrated with liquid water (Figure 4.1b). In their collapsed form, the channels allow for conductivity, since sorbed waters can dissociate from the sulfonate heads, but the amount of water sorbed is not sufficient to form a continuous liquid pathway [27],... 

In the discussions to follow, the concept of the interfadal region will be presented from a molecular (or atomic) perspective and from the viewpoint of the thermodynamics involved. In this way one can obtain an idea of the situations and events occurring at interfaces and have at hand a set of basic mathematical tools for understanding the processes involved and to aid in manipulating the events to best advantage. The concepts presented are intended to be primarily qualitative in nature and do not necessarily represent reality in every detail. Similarly, the mathematical tools will be, for the most part, the basic elements necessary for accomplishing the purpose, with little or no derivation presented. More elaborate and sophisticated treatments of the subjects will be referenced but left for the more adventurous reader to pursue as needed. 

Mathematically, an interface is a two-dimensional region. In reality, it will be three-dimensional, although the third dimension may have the thickness of only one or two molecules. Because it is three-dimensional, the interfadal region may be treated in the context of hydrostatics, or in terms of molecular forces and distribution functions. Alternatively, a thermodynamic approach may be taken to arrive at the same conclusions. 

In the present chapter, different uses of nanocomposites in structural composites are presented. They can be used in the polymer matrix as nano-reinforcements or in the interfadal region in conventional composites in order to mainly improve interlaminar strength, and hence to avoid delamination. They can also exist in the form of nanocomposite fibers as reinforcement in all-polymer composites or directly as self-reiifforced nanocomposites. 

As we have seen, the interfadal region is, in fact, three dimensional (i.e., it has a finite thickness). It is very convenient, however, to represent an interface as a mathematical surface of zero thickness because such properties as area and curvature are well defined and because the differential geometry of surfaces is well understood. How can a thermodynamic analysis be developed that reconciles the use of mathematical surfaces with die actual three-dimensional character of the interface ... 

Mote than a century ago, Gibbs (1878) introduced surface excess quantities as a first step toward resolving this problem. The basic idea is to choose a reference surface S somewhere in the interfadal region. This surface is everywhere perpendicular to the local density or concentration gradient. Consider a property such as internal energy in the region between surfaces and of Figure 1.2 whieh are parallel to S but are located in the respective bulk phases. Because the... 

With the interfadal region still maintained at a constant shape, we can write Equation 1.3 and subtract from it the analogous equations that would apply for its two parts if they were occupied by bulk fluids A and B, respectively. The result is... 

Our next step is to analyze the interfadal region at static equilibrium from a mechanical point of view. It is necessary to specify the latraal boundary of the region, which will be taken to be a surface everywhere normal to S, 5, and Sg of Figure 1.2, and to all other surfaces parallel to these three which could be constructed within the region. The result is a closed interfacial region boimded by 5a, 5g, and (Figure 1.3). 

General mass and momentum balances for an interfadal region were derived in Chapter 5 and used in the analyses of interfadal stability presented there. In dealing with heat and mass transport near interfaces we require additional balances for energy and individual spedes. 

FIGURE 1.54 Capacitance for bulk and interfadal regions for stressed and unstressed PAni/Yellow/Ba device as a function of current [121],... 

Because charge transfer is involved, the presence of an electric field at the interface affects the energies of the various species differently as they approach the interfadal region. In other words, the activation energy barrier for the reaction depends on the potential difference across the interface. It is convenient to express the potential dependence of the rate constants in the following manner ... 

A key factor in the NIA theory is the constant value of the interfadal layer thickness at the domain-matrix boundary. There has been mudt discusaon on the existence and magnitude of an interfadal region where partial mixing of the two components takes place. Its existence has been established by positron annihalation studies whilst its magnitude is still a source of interest. Williams has proposed that this interface is unsymmetric and of considerable extent, in terms of volume fraction, whilst Krause concludes that the interphase volume fraction is very small. Mechanical and dynamical mechanical properties have been discussed , in greater or lesser detail, in terms of the interphase volume fraction and Williams has successfully... 

The minimum in y can be explained in terms of the change in curvature H of the interfadal region, as the system changes from O/W to W/O. 

Much of what has been done on the theory of the near-critical interface has been within the framework of the van der Waals theory of Chapter 3, so much of our present understanding of the properties of those interfaces comes from that theory or from some suitably modified or extended version of it. As we shall see, an interface thickens as Hs critical point is approached, and the gradients of denaty and composition in the interface are then small. Thus, the view that the interfadal region may be treated as matter in bulk, with a local free-energy density that is that of a hypothetically uniform fluid of composition equal to the local composition, with an additional term arising from the non-uniformity, and that the latter may be approximated by a gradient expansion, typically truncated in second order, is then most likely to be successful and perhaps even quantitatively accurate. In this section we shall see what the simplest theory of that kind— that which comes from treating simple models in mean-field approximation, as in Chapter 5— yields for the structure and tension of an interface near a critical point. 

In solution-crystallized polyethylene fractions, Raman spectra have demonstrated that crystalline structure is invariant with molecular mass and that crystallinity is far from complete. The interfadal region is relatively small, as expected from theoretical considerations. Densities of solution-grown crystals of linear polyethylene show that the crystals are 8(C90% crystalline [145 147]. This conclusion is supported by measurements of the enthalpy of fusion, infrared and Raman spectroscopy, and other physical properties [148]. Consequently there is a small but appreciable... 

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