Structureless liquid

For a structureless liquid the relation between (i) and (vi) is quite simple. Approximately it is given by ... 

From the adduced above values and the Eq. (7) the condition follows. At Tjj the polymer melt transition from liquid with fixed structure (where residual structural ordering is observed [27]) to truly liquid state or structureless liquid is observed [28], Nevertheless, structure absence of melt at is related to supramolecular structure absence, but macro-molecular coil structure in melt remains an important structural factor (as a matter of fact, the only one at T>T ). Thus, a polymer melt structure can be considered as a set of separate clusters (macromolecular coils) large number and an oxidant (for example, oxygen) molecule (atom) trajectory in thermooxidative degradation process on such structure is simulated by... 

This effective medium or mean field assumption is easy to understand if there is a very large size difference between the newly added particles and any there previously, for example if we think of adding particles to a molecular liquid, we merely treat the liquid as a structureless continuum. However when the dimensions become comparable, the finite volume of the particles present prior to each addition must be considered, i.e. new particles can only replace medium and not particles. The consequence of this crowding is that the concentration change is greater than expressed in Equation (3.52) and it must be corrected to the volume available ... 

Because the solvent molecules are usually of a similar size to the reactants, the assumption that reactants diffuse in a structureless and isotropic continuum is not very satisfactory. Liquids possess short-range order. Solvent molecules are several times more likely to be separated by a distance equal to their diameter than separated by about one and a half diameters. More details are revealed by the radial distribution function [see Figs. 38 (p. 216) and 44 (p. 235)]. This implies that there is an... 

In this section, we shall focus on the use of CMs to study molecules at the interface between a solid and a fluid (gas or liquid). In particular, we reserve the term continuum models to approaches that consider both the solid and the fluid as structureless continuum bodies characterized by their dielectric response, and treat the molecule at some microscopic level. 

The most advanced theories of relaxation phenomena in a system of entangled macromolecules is based on the dynamics of a single macromolecule. Dynamics of the tagged macromolecule is simplified by the assumption that the neighbouring macromolecules can be described as a uniform structureless medium and all important interactions can be reduced to intramolecular interactions. The dynamic equation for a macromolecule can be written as a modification of equation (2.1) for dynamics of macromolecule in viscous liquid... 

The dominant interaction in molecules is covalent. The geometrical arrangement of atomic nuclei in molecules is mainly known from diffraction experiments in the solid state, and the persistence of such structures in the liquid, solution and gas phases is inferred from magnetic resonance and other spectroscopic studies. Apart from exceptional, nominally structureless, molecules to be discussed later on, most of these molecules may be considered as clusters of touching spheres, which represent atomic cores, and overlapping valence densities. 

Here 4iir/>incl is the structure-independent scattering, while Pstr(r) is the structure-dependent part. For a disordered liquid or solid, as r increases—say, beyond 10 or 15 A—the peaks in R(r) fade into the structureless scattering from electrons Ircr2p[nd, as the short-range order is exceeded. The area under the first few peaks of R(r) will yield the coordination number of the atoms in the peak. 

To go further than Eq. (4.108), one has to examine the factors that govern the mean jump distance / and the jump frequency k. For this, the picture of a liquid (in which diffusion is occurring) as a structureless continuum is inadequate. In reality, the liquid has a structure—ions and molecules in definite arrangements at any one instant... 

Experimental techniques usually only measure certain aspects of the structure, either static (density, number of certain molecular contacts, etc.) or dynamic (local diffusion coefficients, residence times of molecules, etc.). It must be kept in mind that with these techniques only part of the overall structure is recovered. The simplest models are based on primitive liquids, defined as those where the liquid is a homogeneous, structureless medium. 

In principle all kind of interactions are contained In (3.6.11. In the present section we shall consider a solid-liquid interface although the treatment is also valid for liquid-liquid Interfaces. Solid and liquid su e taken as primittve, l.e. as structureless continuums with dielectric permittivities and = , respectively. In this model the surface is hard, planar and uniformly charged. Considering the surface charge a° as discrete would mean a further improvement. The... 

Figure 5 shows the absorption spectrum of irradiated SAA and the emission spectrum of irradiated SAT. As can be seen, the spectra are red-shifted compared to the corresponding spectra of the cis-quinoid tautomers by about 2000 cm . The transient observed after flashing a liquid solution shows a spectrum similar, although structureless, to the photoproduct in solid solution (Fig. 6). 

The most significant indication for the existence of excimers is a broad and structureless fluorescence band shifted 5000 to 6000 cm"l to lower frequencies relative to the monomer fluorescence. This fluorescence has been observed as well in solutions as in the liquid and in the crystalline state. The typical emission may however be absent, because of rapid dissociation or efficient radiationless deactivation (7). 

The model we are usually speaking about is shown in the lower left corner - a structureless solid behaving in an environment of liquid, or gas, more rarely an imperfect, impure vacuum. The latter environment has the spatial extent. 

The earliest theory of nuclear structure was the liquid drop theory, developed around 1940. It pictured the nucleus as a structureless drop of liquid in which repulsions between positive charges are opposed by a kind... 

For a structureless particle or liquid drop on a support, the contact angle 0 that it makes at equilibrium depends upon the surface energies at the three interfaces (see Figure 2.8) according to the equation ... 

Correlation between liquid behavior at thermodynamic equilibrium and that during flow follows from the mean-field approach, which assumes that liquids are structureless and that the dynamic behavior can be considered a semiequilibrium state. Evidently, this approach is unable to explain kinetic phenomena. The S-S lattice-hole mean-field theory does not consider polymeric chain structure, but its effects are reflected in the values of the characteristic reducing parameters, P, T, V, and tlie L-J interaction parameters. Characteristically, the PVT data rarely show secondary transformation temperatures at about 0.8r and 1.2r, which are evident in derivative properties (see Figures 6.1 and 6.2). By contrast, all flow models (e.g., reptation, cell structures, hole jumping) implicitly postulate that such configurational or conformational changes affect liquid dynamic behavior. 

Due to Anderson s compensation theorem (Anderson 1961), which holds for sufficiently structureless bands, may be identified with the number of electrons residing in the partially filled shell of the impurity. The phase shift 8 in Fermi-liquid theory is given by... 

In phase I, there is rotational and translational disorder of H2O and species, i.e. a quasi-liquid state of the water layer, with considerable orientational disorder of phosphate tetrahedra. The spectroscopic manifestation of such a state is the presence of a structureless broad absorption in the OH stretching and HjO and HsO librational region, i.e. individual contributions of protonic species are smeared out while the distinction between HjO and is observed only in the OH bending region. In... 

The S/L interfaces, in general, have much in common with the surfaces from the structural point of view, in that both the vapor and liquid in contact with a crystal surface are a structureless fluid. However, the presence of a short-range structural order clearly distinguishes a liquid from a vapor. Bernal [72] noted that the short-... 

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