Distribution interface

Let s suppose now that the piece of a two-phase material (grains of A within matrix of B) is assembled from these isotropic domains, where domain boundaries are some arbitrary distributed interfaces. For domains outside the A-phase grain and with conditions (3-5), it follows div u = 0. 

Brown, G., Keegan, J., Vigus, B. and Wood, K. 2001. The Kellogg Company optimizes production, inventory, and distribution. Interfaces, 31, 1-15. 

Fig. 8.3 Schematic of a bulk heterojunction oiganic photovoltaic consisting of a thin film of an electron-accepting material A blended with an electron-donating material D, sandwiched between two dissimilar electrodes. Photoinduced exdtons are dissociated at the distributed interface. Electrons and holes require a continuous pathway through the A and D material respectively to reach their respective electrodes. The light is incident through the substrate and lower electrode...

In 1972 the photovoltaic effect was first demonstrated in devices with nematic liquid crystals by means of ionic conduction [36]. Although electronic charge transport was widely researched in these materials [37, 38], it was not until 2006 that electronic conduction was first applied to photovoltaics in nematics [39]. A novel approach based on reactive mesogens was used to create a D-A bilayer with a distributed interface. Reactive mesogens are polymerisable equivalents of small molecule LCs, but with two additional polymerisable groups, one at each end of a flexible aliphatic spacer attached to the aromatic core. Chapters 2 and 5 discusses charge transport in these materials. Figure 8.8 illustrates the photopolymerisation of such molecules. 

Fig. 8.9 Schematic of ideal organic photovoltaic with a distributed interface between a diffuse D...

A liquid crystal composite approach was used to provide a distributed interface to vertically separate D and A films in an OPV device [39, 47]. The concept is illustrated in Fig. 8.9. A nematic polymer network with a porous surface with sub-micron scaled grooves and electron-donating properties was prepared by pho-topolymerising a thin film containing a blend of the reactive mesogen, FTl, which has a fiuorene-thiophene structure, and a non-polymerisable analogue, compound FT2. Photopolymerisation leads to phase separation of the polymerised and the non-polymerised materials, the latter of which is removed by washing in a suitable solvent [39]. The chemical structures of the nematic materials discussed here are... 

FigureBl.5.16 Rotational relaxation of Coumarin 314 molecules at the air/water interface. The change in the SFI signal is recorded as a fimction of the time delay between the pump and probe pulses. Anisotropy in the orientational distribution is created by linearly polarized pump radiation in two orthogonal directions in the surface. (After [90].)...

Lamellar morphology variables in semicrystalline polymers can be estimated from the correlation and interface distribution fiinctions using a two-phase model. The analysis of a correlation function by the two-phase model has been demonstrated in detail before [30,11] The thicknesses of the two constituent phases (crystal and amorphous) can be extracted by several approaches described by Strobl and Schneider [32]. For example, one approach is based on the following relationship ... 

Figure Bl.9.12. The schematic diagram of the relationships between the one-dimensional electron density profile, p(r), correlation fiinction y (r) and interface distribution fiinction gj(r).

This intensity can be used to calculate the correlation fiinction (Bl.9.101) and the interface distribution fiinction (B 1.9.102) and to yield the lamellar crystal and amorphous layer thicknesses along the fibre. 

Figure Bl.14.13. Derivation of the droplet size distribution in a cream layer of a decane/water emulsion from PGSE data. The inset shows the signal attenuation as a fiinction of the gradient strength for diflfiision weighting recorded at each position (top trace = bottom of cream). A Stokes-based velocity model (solid lines) was fitted to the experimental data (solid circles). The curious horizontal trace in the centre of the plot is due to partial volume filling at the water/cream interface. The droplet size distribution of the emulsion was calculated as a fiinction of height from these NMR data. The most intense narrowest distribution occurs at the base of the cream and the curves proceed logically up tlirough the cream in steps of 0.041 cm. It is concluded from these data that the biggest droplets are found at the top and the smallest at the bottom of tlie cream.

Toney M F, Floward J N, Richter J, Borges G L, Gordon J G, Meiroy O R, Wiesier D G, Yee D and Sorensen L B 1995 Distribution of water moiecuies at Ag(111 )/eiectroiyte interface studied with surface x-ray scattering Surf. Sc/. 335 326-32... 

A very important aspect of both these methods is the means to obtain radial distribution functions. Radial distribution functions are the best description of liquid structure at the molecular level. This is because they reflect the statistical nature of liquids. Radial distribution functions also provide the interface between these simulations and statistical mechanics. 

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