Molecular contribution

There are two molecular contributions to the intrinsic viscosity one from shape, the other from size or volume, as summarized by the relation... 

It must be kept in mind that the Goodrich treatment separates out contributions to intermolecular interactions that arise from film expansion. The differences in film expansion are a reflection of conformation and are accounted for in the pure meso- and ( )-films. However, since ( )- and meso-film components do interact, the intramolecular contribution to film compression may be altered. This effect would arise from conformational perturbations as molecules interact, thereby precluding complete separation of inter- and intra-molecular contributions to the thermodynamics of compression. However, these complicating factors can be mitigated by comparing several molecules with varying structures, as has been carried out in this instance. 

Vb = liquid molar volume at the normal boiling point, can be found fr molecular contributions. 

G. Farrell, T. J. Burkey. How Strong are Metal-Alkane Bonds Separation ofThermal and Molecular Contributions to Photoacoustic Signals Using High Pressure. Abstr. Pap. Am. Chem. Soc. 1994, 208, 523-INOR. 

Electro-osmotic drag phenomena are closely related to the distribution and mobility of protons in pores. The molecular contribution can be obtained by direct molecular d5mamics simulations of protons and water in single iono-mer pores, as reviewed in Section 6.7.2. The hydrod5mamic contribution to n can be studied, at least qualitatively, using continuum approaches. Solution of the Poisson-Boltzmann (PB) equation. 

The total electro-osmotic coefficient = Whydr + mo includes a contribution of hydrodynamic coupling (Whydr) and a molecular contribution related to the diffusion of mobile protonated complexes—namely, H3O. The relative importance, n ydr and depends on the prevailing mode of proton transport in pores. If structural diffusion of protons prevails (see Section 6.7.1), is expected to be small and Whydr- If/ ori the other hand, proton mobility is mainly due to the diffusion of protonated water clusters via the so-called "vehicle mechanism," a significant molecular contribution to n can be expected. The value of is thus closely tied to the relative contributions to proton mobility of structural diffusion and vehicle mechanism. ... 

This expression is given here, without derivation, for the molecular contribution to the total electron scattering intensities (molecular intensities) ... 

A third goal of the research is to measure the distance over which surface effects extend into solution. These experiments face several technical challenges, but if experf-ments are properly designed, results would provide the very distance versus strength of interaction information necessary for incorporating molecular contributions into existing dielectric continuum theories of surface solvation. 

Loveless DM, Abu-Lail NI, Kaholek M, Zauscher S, Craig SL. Molecular contributions to the mechanical properties of reversibly cross-linked surface grafted polymer brushes. Angew Chem Int Ed 2006 45 7812-7814. 

The copolymer approach is interesting, but it does not lead to a direct answer concerning the intra- and inter molecular contributions to the cooperative nature of the /3 transition motions of BPA-PC. This discussion is postponed until later on in this section, after considering the information provided by the whole set of experimental and atomistic modelling investigations. 

The temperature dependence of AH2 for chloral-PC (Fig. 37) shows that the motions of phenyl rings occur above -80°C. Furthermore, the doublet shape observed for the lH spectrum above room temperature presents a splitting constant of 25 d= 0.2 G, which corresponds to the static interaction between the 2,3 phenyl protons, indicating that the phenyl motions do not affect the dipole-dipole interaction parallel to the 1,4 phenyl axis. A quantitative analysis of the intra- and inter molecular contributions to AH2 leads to the conclusion that the phenyl motions correspond to either isolated or concerted rotations around the 1,4 axis, with little (if any) reorientation of this axis. In addition, it excludes other motions as crankshaft motions, or motion of the phenyl-ethylenic unit as a group. The decrease of AH2 above - 40 °C could be intermolecular in nature. 

The frequency variation occurring on going from one molecule to another or to the molecular complex depends on force constants in noncomplexed molecules and reflects, in the final analysis, the ionic nature of the bonds. When no spectra can be obtained in solution or in the gas phase, the inter-molecular contributions should be taken into account, especially in interpreting the Sn—X patterns. It should also be remembered that Sn—X frequencies are markedly dependent on the mass of the halogen involved and increase with atomic number. Nevertheless, the frequencies, which are a function of the nature and the number of halogens and vary over a wide range, are a good reflection of the bond ionicities and of the coordination number. 

The usual way of treating the optical properties of systems containing organic molecules is in terms of the oriented gas model, that is, the macroscopic property is treated as the sum of molecular contributions, allowing... 

Sheppard, J N. F., Senturia, S. D. Molecular contributions to the dielectric permittivity of unreacted epoxy/amine mixtures, p. 22 a, Technical Program Summary, Adhesion Society Annual Meeting, Savannah, GA, 1985... 

In a careful study of thiourea, Smith and Cotts 42> not only determined the principal directions of the electric field gradient tensor, they also detected a small deviation in the orientation of these directions from the symmetry axes of the corresponding chemical bonds. They suggested this deviation was due to intra- and extra-molecular contributions to the electric field gradients. 

Now we study in detail how the macroscopic susceptibilities are related to the molecular properties. A thorough understanding of these relations is essential for both the rational design of molecular NLO materials as well as the experimental determination of the molecular electric properties. Models for the interpretation of macroscopic susceptibilities in terms of molecular dipole moments and polarizabilities usually assume additive molecular contributions (Liptay et al., 1982a,c). Thus, an nth-order susceptibility can be represented by (99) as a sum of terms that are proportional to concentrations Cj (moles per cubic metre, mol m ) of the different constituents J of the medium. 

Since the EFG vanishes at cubic symmetry and the symmetry around the ions can be high, the negative amplitude of the cross EFG-TCE represents the static quenching of the individual contributions to the EFG. The cross correlation in the molecular contributions to the EFG does not necessarily results in a quenching, in a very inhomogeneous media the individual contributions could add on to enhance the self EFG-TCF. However, the cross correlation can never have a more positive amplitude than the self EFG-TCF, since when they are equal the total EFG-TCF cancels. There is both a static quenching of the amplitude of the... 

Figure 12 The molecular contributions to the electric field gradient (EFG) can be correlated. Hence the EFG-TCF can be divided into molecular self-EFG-TCF and cross-EFG-TCF terms (See equation (25)). The static quenching of the EFG is due to the momentary symmetry in the solvation shell. The cross EFG-TCF has a different decay that the self-EFG-TCF which results in a dynamic quenching of the molecular contributions.

There a been a number of interesting applications of the framework developed in the studies of the simple ions were MD simulations of the quadrupolar relaxation has been performed on counterions in heterogeneous systems. Studies of a droplet of aqueous Na embedded in a membrane of carboxyl groups [54], showed that the EFG was strongly effected by the local solvent structure and that continuum models are not sufficient to describe the quadrupolar relaxation. The Stemheimer approximation was employed, which had been shown to be a good approximation for the Na ion. Again, the division into molecular contributions could be employed to rationalize the complex behavior in the EFG tensor. Similar conclusions has been drawn from MD simulation studies of ions solvating DNA... 

According to this equation, the solubility of the polymer molecules in a liquid will increase with increasing positive values of AC n. as the polymer molecules will increasingly repel each other and thereby tend to disperse. If AG n < 0. solubility decreases due to molecular attraction. In most pharmaceutical systems, molecular contributions to AG2T2 will be from apolar Lifshitz-van der Waals (AG212) forces and from Lewis acid/base (AGm) forces. Hence, AG2T2 is represented by... 

Additionally, molecular weight at the maximum of the differential form of distribution of mass fractions is often designated the peak molecular weight (Mp), and fraction percentages may indicate critical fractions of low- or high-molecular contributions. 

A turbulent core from to where the contribution of turbulent eddy transport is much larger than the molecular contribution... 

Now consider the A molecules case. For simplicity we assume that the spatial extent of this N molecule system is much smaller than the radiation wavelength. In this case all molecules are subject to the same incident beam and respond coherently. Following the short pulse of duration r = jiti/(2 o/ ) the density matrix of each molecule j evolves as before. The density matrix of the whole system is a direct product of these molecular contributions. The expectation value of the total system dipole operator Ajv = Az is... 

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