Equivalent internal field model

Based on the fundamental dipole moment concepts of mesomeric moment and interaction moment, models to explain the enhanced optical nonlinearities of polarized conjugated molecules have been devised. The equivalent internal field (EIF) model of Oudar and Chemla relates the j8 of a molecule to an equivalent electric field ER due to substituent R which biases the hyperpolarizabilities (28). In the case of donor-acceptor systems anomalously large nonlinearities result as a consequence of contributions from intramolecular charge-transfer interaction (related to /xjnt) and expressions to quantify this contribution have been obtained (29). Related treatments dealing with this problem have appeared one due to Levine and Bethea bearing directly on the EIF model (30), another due to Levine using spectroscopically derived substituent perturbations rather than dipole moment based data (31.) and yet another more empirical treatment by Dulcic and Sauteret involving reinforcement of substituent effects (32). 

A simple model, known as the Internal equivalent field model (9) (see "Figure 1") accounts for the different p values of mono-substltuted benzene derivatives R-X, and relates them to the respective donor or acceptor strength of X. It Is assumed In this model that the substituent action on the it electrons of the ring Is equivalent to that of a D-C field EQ with direction and Intensity related to the substituent electronegativity. Identifying dipole expansions of R-X In presence of E and of R In presence of E0 + E yields ... 

As soon as we consider the molecular nature of a material, we realise that the internal electric field will vary from point to point as a consequence of the interaction of fields from the dipoles which are induced on each molecule by the applied field, although the space-average electric field over a volume large in comparison with molecular size (this is equivalent to the classical electric field based on a continuum model) may still be uniform. The field acting on an individual polarisable entity like an atom or molecule is called the local field Eh, and it is an important concept in linking observable bulk behaviour of a material with the properties of its constituent atoms or molecules. 

The periodic unit cell results are directly comparable to the IMT predictions, because both approaches represent the same matrix/inclusion type microstructure. However, such comparisons have to be done carefully since some assumptions regarding the finite element calculations are not equivalent for the extended unit cell approaches and the present mean-field method. The plane stress analysis of the unit cell models does not take into account the constraints in the out-of-plane direction. In contrast, within the present IMT formulation the inclusions are enclosed three-dimensionally by the matrix material. In contrast to the plane stress unit cell models, the constraint in the out-of plane direction is accounted for. Accordingly, these predictions are denoted as full internal constraint. To overcome this internal constraint in order to simulate the plane stress model assump-... 

It should be pointed out that the present model is based on the space averaging method which is commonly utilized in classic pressure-driven transport phenomena in porous media. This averaging method focuses on the equivalent macroscopic physics without considering the local complexity in the microscale. However, the EOF in porous media originates from the interaction of the external electric field and the EDL at internal surfaces of the porous structure. In reality... 

The Marcelja mean field is applicable to simulations of lipids by using continuous torsion angles. A Brownian dynamics simulation (see Brownian Dynamics) was performed for a simple lipid chain to model a dipalmitoylphosphatidylcholine bilayer. The 44 million-step calculation in this continuous Marcelja model simulation was equivalent to approximately 0.66 ps. The internal dynamics of the hydrocarbon chain were very similar to those of a neat alkane. The magnitude and frequency dependence of the NMR data were explained as fast axial rotation superimposed with slow noncollective diffusive director fluctuations (wobble). 

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