A Diffuse Interface

Suppose that in a system with a film of thickness t deposited on a substrate, the two interfaces are diffuse. The scattering length density profile p(z) is then modified from (7.49) to 

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The most possible reason may be in the higher free energy of the protein adsorption on PolyPROPYL A materials. Chemisorbed neutral poly(succinimide) of molecular weight 13000 apparently forms a diffuse interface as predicted by theory (see Sect. 2.2). Controversially, a short polyethyleneimine exists on a surface in a more flat conformation exhibiting almost no excluded volume and producing... 

Further aspects of the conservative and nonconservative motion of sharp interfaces are presented below. The mechanism for the motion of a diffuse interface is discussed in Section 13.3.4. 

The Allen-Cahn equation applies to the kinetics of a diffuse-interface model for a nonconserved order parameter—for example, the order-disorder parameter r](f,t)... 

On the other hand, a diffuse interface possesses a significantly wider core that extends over a number of atomic distances. A diffuse crystalline/amorphous phase interface is shown in Fig. B.3. Similar structures exist in crystal/liquid interfaces [5]. 

The need for a more flexible model was met by developing the formalism for diffuse interfaces [15,17,18]. First, the electrostatic solvation for a diffuse interface has been... 

A parameter to fix in the calculation at interfaces is the molecular orientation and position with respect to the interface. Different orientations have been tested, among which the most stable one is the one in which both polar heads of the molecule are within the diffuse region (see Fig. 2.1). Such an orientation presents a high sensitivity to different entrance directions due to the vicinity of the propionyl group to the interface Apparently the situation in which PRODAN enters in water with the propionyl group should be more favorable, however, the use of a diffuse interface makes the two directions almost equivalent with respect to the solvation of the propionyl group, while this is not the case for the other polar group which is more efficiently solvated only if we assume that it first enters into water (see Fig 2.1). 

The amplitude of the fringes also yields information about the sharpness of the interfaces in question, since large fringes correspond to a sharp interface, while small fringes are indicative of a diffuse interface. 

All of these drastic modifications observed in the sputtering experiment indicate a strong interaction between A1 and silicone with complexe chemical bonding between Al, O, Si and p atoms and a diffuse interface with intermixing over several tens of A. 

Figure 21.14 TEM of a maleic anhydride-functionalized polymer in polyamide 66. The styrene domains are stained dark with Ru04- The maleic anhydride in the rubber phase reacts with the polyamide producing a diffuse interface and fine dispersion of the block copolymer...

We now briefly consider another important aspect of nonequilibrium thermodynamics, namely phase transformations and how they are modelled. Galenko and Jou198 develop a thermodynamic formalism for rapid phase transformations within a diffuse interface of a binary system in which the system is in a state of local nonequilibrium. The phase-field method, in which the phase- field variable O varies smoothly and continuously between one pure phase (in which O = +1) and another (in which -1), is used to derive... 

Ganesan V, Brenner H (2000) A diffuse interface model of two-phase flow in porous media. Proc R Soc Lond A 456 731-803... 

Torradas [1984]. This contrasts with other reports [Ptaszynski et al., 1975 Hashimoto et al., 1990 Winey et al., 1991] where upon addition of a homopolymer with molecular weight smaller than that of the corresponding block, the average area per junction point was found to increase. SAXS scattering patterns obtained from samples having lamellar morphology followed an idealized model, in which layers of styrene and butadiene (with randomly varying thickness and a diffuse interface) were parallel. 

Oxygen pressures greater than 10 torr induce progressive rounding of the particles. Oxide formation occurs at 10 torr, simultaneously with the appearance of a diffuse interface. 

Immiscible polymers caimot produce molecularly homogeneous mixtures due to finite and often high values of interfadal tension. Consequently, a mixed state in an immiscible polymer system may consist of polymer domains with sharp or diffuse interfaces depending upon how the local properties, such as concentration, viscosity, and density, vary on both sides of the interfaces [138]. A sharp interface results if the properties are discontinuous and there is no mass transport across the interface. In contrast, a diffused interface is obtained when the properties vary gradually and continuously across the interface. A material parameter, the interfadal tension, o, characterizes immiscible polymer systems and is defined as ... 

In this cross-over region, our theory based on the square gradient theory predicts a first order transition from a diffuse interface to a sharp one, which has been supported later by the calculation of Vrij et.al. based on the same model, If it would take place, polymer chains at the interface might collapse at the transition. This situation is similar to that of the adsorption theory by de Gennes. ... 

Our analysis indicates that kinetic retardation of the interphase transport is essential for a well-balanced theory away from the critical point. The available simulations of the motion of a diffuse interface near a three-phase contact line, taking into account viscous retardation only and, in effect, assuming evaporation or condensation to be as easy as plain advection, may grossly overestimate the rate of interphase transport, but the latter remains essential even when its order of magnitude is reduced due to kinetic retardation. 

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