Interfacial density

Fig. ni-7. (a) Interfacial density profile for an argonlike liquid-vapor interface (density in reduced units) z is the distance normal to the surface, (b) Variations of P-p of Eq. ni-40 (in reduced units) across the interface. [From the thesis of J. P. R. B. Walton (see Ref. 66).]... 

Fig. 9. Adhesion of P.M.M.A. to P.P.O. Effect on fracture toughness, Fc, of interfacial density, E, of a reinforcing dihlock copolymer (after Creton et al. [80]).

Good agreement between C(- and the dipole moment of the solvent (H20) molecules (i.e., by the hydrophilicity of metals) established by Trasatti25,31 was found and the reasons for this phenomenon were explained 428 The Valette and Hamelin data150 251 387-391 are in agreement with the data from quantum-chemical calculations of water adsorption at metal clusters 436-439 where for fee metals it was found that the electrode-H20 interaction increases as the interfacial density of atoms decreases. 

Comparison of Interfacial Density Differences Resulting from the Deposition of Copper, the Cathodic Reduction of Ferricyanide, and the Anodic Oxidation of Ferrocyanide at the Limiting Current Density (7" = 25°C)... 

Another notion regarding the interfacial viscosity is as a measure of the motion of an interfacial layer. Consider an interfacial layer, a monolayer bound to the surface with interfacial density p2 a mass per unit area, moving at a constant velocity. If the surface stops suddenly, the monolayer velocity will decay exponentially with a relaxation time r. Through a quantum mechanical derivation involving the sliptime, Krim and Widom [39] determined a relationship between the interfacial viscosity, the interfacial density, and the sliptime, of the form... 

The interfacial densities of 1-octadecanol and of dodecylammonium chloride F are evaluated, respectively, by... 

Figure 4. Interfacial density of dodecylammonium chloride vs curves at constant and 298.15 K (1) = 0 mmol kg (2)...

The competitive adsorption of a short symmetric PS-PI diblocks or a long asymmetric PS-PI diblock to the surface of a PS homopolymer was examined by Budkowski etal. (1995).They used nuclear reaction analysis (Section 1.4.18) with labelled diblocks to determine the concentration of deuterium atoms as a function of depth, and hence the volume fraction of labelled chains. It was thus found that the shorter diblock tends to adsorb preferentially to the interface. The surface excess of PS and its interfacial density were compared to a theory for bidisperse brushes, a generalization of the model due to Leibler (1988). Excellent quantitative agreement was found, with no adjustable parameters. 

But we have evaluations of (5 ) and C1 (L ) in terms of the interfacial densities. Thus, substituting eqns. (202) and (206) into eqn. (211) gives us, after some algebraic rearrangement, the final expression for the potential difference across zone 2, viz. 

Figure 1.9 Carbon- and water-oxygen interfacial densities as a function of z. The dashed and solid lines indicate the observed carbon and oxygen densities, respectively, at 300 K determined from molecular simulation. The disks plot the water-oxygen densities reconstmcted from the proximal radial distribution function for carbon-oxygen (see Fig. 1.2), averaged over alkyl chain conformations sampled by the molecular simulation. The interfacial mid-point (z = 0) is set at the point where the alkyl carbon- and water-oxygen densities are equal. See Figs. 1.1 and 1.2, p. 7.

The relationship between (r) for water oxygen atoms (Fig. 1.11) and the oxygen atom interfacial density profile (Fig. 1.9) can be established by superposing these proximal radial distribution functions to model the conditional densities as... 

R-t,R) = interaction potential between an adsorbate molecule at r and the entire sohd surrounding the pore, while (f)FF(r,R) represents the corresponding potential if the bulk fluid was instead present in place of the surrounding sohd. Both these potentials incorporate the interfacial density profile. Using an analysis similar to that described in section 2.1, the equations for estimating the critical thickness are given by... 

The same qualitative conclusions can be drawn from the analysis of curves in Fig.2b. At free pH (pH 6.5 before adsorption), alumina sample represents a moderately-charged hydrophilic substrate because the pH value is close to the pzc. The maximum quantity of adsorption corresponds to the area of 0.52 nm per one adsorbed molecule (cf. 0.35 nm at the water-air interface). For pH 3 surfactant ions achieve a close-packed arrangement in the adsorbed bilayer and the density of bilayer adsorption at the plateau (0.11 nm /molecule) is even less than the air-water interfacial density. At the same time, the cmc is markedly diminished by a decrease in the pH. Both effects can be attributed to the appearance of a non-ionized surfactant species in a solution. The neutral form of the surfactant is less soluble in water and thus exhibits a greater affinity for a hydrophobic surface of alumina modified with grafted aliphatic chains. The decresed repulsion between uncharged heads causes a closer packing of the adsorbate in a mixed surface structure. 

In the third adsorption region, above 2.7 //mol-m (0=0.63), all the plots unequivocally indicate the completion of bilayer on the silica surface. At surface saturation, the average adsorption density corresponds to 0.38 nm per one adsorbed molecule, which is approximately twice less than the air-water interfacial density. 

The ionic conductivity of YSZ can be also enhanced by the introduction of high density of dislocations [17] or interfaces that act as rapid diffusion paths for oxygen vacancies. Such an idea has been discussed for BaF2/CaF2/Bap2 superlattices where a substantial increase of ionic conductivity was observed [18]. In this system a progressive increase in the conductivity was correlated with the increase of interfacial density. 

Before leaving the subject of interfacial behavior in polymers, it is instructive to consider the interfacial tension, and resulting interfacial density profiles. Making effective use of the Flory interaction parameter x, Helfand and Tagami (1972), Gaines (1972), Wu (1974), and others estimated the interfacial surface tension between incompatible polymer pairs (see Table 13.1). Also shown in Table 13.1 are theoretically estimated values of x-(See Section 4.7 and especially Sections 4.7.3 and 9.6 for related discussion.) Helfand and Tagami found that the characteristic thickness of the interface is proportional to x — y for small /. For a polystyrene/poly(methyl methacrylate) system, the value of / leads to an estimated interfacial thickness of 50 A. This value is much less than that estimated by Voyutskii and Vakula... 

The scattering experiment provides the interfacial density 0 (the interfacial area per unit of volume), and thus observes the decay of O with Correspondingly, the linear domain size of the new phase increases as... 

Figure 7. The interfacial density profiles for the system hexane propanol at Xp =0.80 and 298.15 K, computed with the PR equation of state. The solid lines denote the profiles at p 2=0.01, while the dashed lines represent the results at Pi2=0.10.

In Figure 7 two different interfacial density profiles are shown, of which the first is obtained with p 2=0.01 (solid curve), while the second is obtained with Pi2=0.10... 

In addition, the interface disorder can scatter phonons at grain boundaries or interfaces between similar materials [51]. Thus, it may be expected that materials with high interfacial densities should reduce the thermal conductivity of TBCs. For instance, a multilayered W/AI2O3 film could give rise to a thermal conductivity of 0.6 W.m K [51]. For EBPVD coatings, the introduction of interfaces into each column, which are parallel to the ceramic/metal interface, can reduce the thermal conductivity by 37-45% compared to state-of-the art EBPVD TBCs (Fig.8) [9, 52]. 

The presence of different interfacial force characteristics dependent on the structure and interfacial density strongly affects the technical performance, and the increased knowledge about adsorbed layer morphologies can hopefully also facilitate important new methods for the fabrication of nanostructured functional surfaces in fact, synthetic methods already allow the tailoring of specific molecules in order to fulfill new requirements and aims at a wider range of industrial applications such as skincare, antibacterial properties, vesicle formation, high porosity materials, and so on. 

---