Maxwell effect

The ability of anisotropic and anisometric particles to assume some co-orientation in external force fields is not only responsible for significant changes in scattering properties but also causes birefringence (double refraction), i.e., the average refractive indexes of two beams polarized in perpendicular planes happen to be different. The specific orientation of particles and birefringecne may be caused by the action of electric field (Kerr effect), magnetic field (Cotton-Mouton effect), or in the case of anisotropic particles by flow of medium (Maxwell effect) [25]. 

In polymer 1, the Kerr effect coincides in sign with the Maxwell effect, which means that the orientation of the side chains in an electric field correlates with the direction of the main chain. However, both the small values of K and [ig / Ql] and the absence of dispersion of the Kerr effect show that the chains of polymers 1 and 6 exhibit no high orientational axial and orientational polar orders characteristic of polymers with mesogenic side groups. In these polymers (1 and 6), the Kerr effect is due to small scale chain motion the kinetic elements are much smaller in size and their mobility is much higher than, for example, for polymer 7. 

Polymer solutions are isotropic at equilibrium. If there is a velocity gradient, the statistical distribution of the polymer is deformed from the isotropic state, and the optical property of the solution becomes anisotropic. This phenomena is called flow birefringence (or the Maxwell effect). Other external fields such as electric or magnetic fields also cause birefringence, which is called electric bire ingence (or Kerr effect) and magnetic birefiingence (Cotton-Mouton effect), respectively. 

For an isotropic polymer, the thickness ( 3) and traverse (xi) strain responses due to the Maxwell effect are ... 

Based on Equations (16.9) and (16.15), the Maxwell effect and electrostrictive effect result in the same relationship between the strain and electric field and they therefore share some common features. For instance, an apparent piezoelectric effect can be observed when a DC bias is applied the strain response can be enhanced by the nonuniformity of the electric field, which can be created either by employing nonuniform materials or by the presence of the space (trapping) charge. Due to the electrostrictive effect and the appearance of the space charge, an insulation material can exhibit piezoelectricity and is known as an electret [9, 10]. The piezoelectric constant of an electret depends on the space charge and its distribution as well as the nonuniformity in the elastic properties and electrostrictive coefficient of the materials. 

This point was taken up by Reynolds in a letter addressed to G. G. Stokes, in the latter s capacity as Secretary of the Royal Society [83]. Reynolds pointed out that Maxwell s theory evaluated the effects of thermal transpiration only in circumstances where they were too small to be measured, and complained that Maxwell had misrepresented his own theoretical treat ment of the phenomenon. However, this incipient controversy never developed... 

In addition to the set of Voigt elements, a Maxwell element could also be included in the model. The effect is to include a contribution given by Eq. (3.69) to the calculated compliance. This long time flow contribution to the compliance is exactly what we observe for non-cross-linked polymers in Fig. 3.12. 

The purpose of this problem is to consider numerically the effect of including more than two Maxwell elements in the model for a relaxation experiment. Prepare a table analogous to Table 3.2 for a set of four Maxwell elements having the following properties ... 

Pinto-Graham Pinto and Graham studied multicomponent diffusion in electrolyte solutions. They focused on the Stefan-Maxwell equations and corrected for solvation effects. They achieved excellent results for 1-1 electrolytes in water at 25°C up to concentrations of 4M. 

We studied the effect of the mechanical stretching field on the conformations of the macromolecules in the melt. It is known that for a freely jointed chain the Maxwell distribution of end-to-end distances holds50). 

Because of the assumption that linear relations exist between shear stress and shear rate (equation 3.4) and between distortion and stress (equation 3.128), both of these models, namely the Maxwell and Voigt models, and all other such models involving combinations of springs and dashpots, are restricted to small strains and small strain rates. Accordingly, the equations describing these models are known as line viscoelastic equations. Several theoretical and semi-theoretical approaches are available to account for non-linear viscoelastic effects, and reference should be made to specialist works 14-16 for further details. 

According to Maxwell s law, the partial pressure gradient in a gas which is diffusing in a two-component mixture is proportional to the product of the molar concentrations of the two components multiplied by its mass transfer velocity relative to that of the second component. Show how this relationship can be adapted to apply to the absorption of a soluble gas from a multicomponent mixture in which the other gases are insoluble and obtain an effective diffusivity for the multicomponent system in terms of the binary diffusion coefficients. 

J I I Describe the effect of molar mass and temperature on the Maxwell distribution of molecular speeds (Section 4.11). 

The Ether is not useful to teach MT. The EM field is most effectively viewed as an irreducible entity completely defined by Maxwell s equations. (If one wants to make the interaction with point charges in N.M or QM explicit, one can add the Lorentz force or the minimal coupling.) All physical properties of th EM field and its interaction with matter follow from Maxwell s equations and the matter equations. 

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