Dispersion component

Let us start with the most investigated molecular or dispersion component of surface forces. Note that in a number of cases, this component is the weakest among all the other components considered in the following section. Surprisingly, this component is used more frequently than others. 

It is well known that at relatively large distances (but stiU in the range of angstroms, that is, 10 cm) aU neutral molecules interact with each other, and the energy of this interaction is proportional to constlr, where r is the distance between molecules. This is apparent by examining two surfaces made of different 

Calculation of the molecular contribution to disjoining pressure, n has been approached in two ways from the approximation of interactions as a pairwise additive, and from a field theory of many-body interactions in condensed matter. The simpler and, historically, earlier approach followed a theory based on summing individual London-van der Waals interactions between molecules pair-bypair, undertaken by Hamaker [1]. 

The more sophisticated, modem theory of was developed (see review [1]) based on the consideration of a fluctuating electromagnetic field. In the following, we give an expression for the molecular component of the disjoining pressure, n , for a film of uniform thickness, h, between two semiinfinite phases in vacuum (for simplicity). The expression is [1]  

In the limiting case of h, large in comparison to X on the other hand, disjoining pressure turns out to be inversely proportional to the fourth power of film thickness [1]  

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A related approach carries out lattice sums using a suitable interatomic potential, much as has been done for rare gas crystals [82]. One may also obtain the dispersion component to E by estimating the Hamaker constant A by means of the Lifshitz theory (Eq. VI-30), but again using lattice sums [83]. Thus for a FCC crystal the dispersion contributions are... 

Aguilar M A and Olivares del Valle F J 1989 A computation procedure for the dispersion component of the interaction energy in continuum solute solvent models Ohem. Rhys. 138 327-36... 

Silica gel, per se, is not so frequently used in LC as the reversed phases or the bonded phases, because silica separates substances largely by polar interactions with the silanol groups on the silica surface. In contrast, the reversed and bonded phases separate material largely by interactions with the dispersive components of the solute. As the dispersive character of substances, in general, vary more subtly than does their polar character, the reversed and bonded phases are usually preferred. In addition, silica has a significant solubility in many solvents, particularly aqueous solvents and, thus, silica columns can be less stable than those packed with bonded phases. The analytical procedure can be a little more complex and costly with silica gel columns as, in general, a wider variety of more expensive solvents are required. Reversed and bonded phases utilize blended solvents such as hexane/ethanol, methanol/water or acetonitrile/water mixtures as the mobile phase and, consequently, are considerably more economical. Nevertheless, silica gel has certain areas of application for which it is particularly useful and is very effective for separating polarizable substances such as the polynuclear aromatic hydrocarbons and substances... 

Fig. 17. A schematic of the alkane line obtained by inverse gas chromatography (IGC) measurements. The relative retention volume of carrier gas required to elute a series of alkane probe gases is plotted against the molar area of the probe times the. square root of its surface tension. The slope of the plot is yielding the dispersion component of the surface energy of...

Amylose (Section 25.15) The water-dispersible component of starch. It is a polymer of a(l,4)-linked glucose units. 

The polar and dispersion components of the surface energy are generally obtained using two liquids, for example water and formamide. To calculate yf and y/, the following values for y/ and yf were taken [3] ... 

Solvents interact with reverse phases in very much the same way as they do with the surface of silica gel. However, in this case it is the more dispersive component of the mobile phase that is adsorbed on the surface as opposed to silica gel, which being a polar stationary phase, adsorbs the more polar solvent onto its surface. 

FIGURE 33.2 Dispersive component of carbon black surface energy as a function of its surface area. 

FIGURE 33.3 Dispersive component of surface energy and dispersion quality in ESBR as a function of heat treatment of N234. 

The phase-twisted peak shapes (or mixed absorption-dispersion peak shape) is shown in Fig. 3.9. Such peak shapes arise by the overlapping of the absorptive and dispersive contributions in the peak. The center of the peak contains mainly the absorptive component, while as we move away from the center there is an increasing dispersive component. Such mixed phases in peaks reduce the signal-to-noise ratio complicated interference effects can arise when such lines lie close to one another. Overlap between positive regions of two different peaks can mutually reinforce the lines (constructive interference), while overlap between positive and negative lobes can mutually cancel the signals in the region of overlap (destructive interference). 

Although this eliminates negative contributions, since the imaginary part of the spectrum is also incorporated in the absolute-value mode, it produces broad dispersive components. This leads to the broadening of the base of the peaks ( tailing ), so lines recorded in the absolute-value mode are usually broader and show more tailing than those recorded in the pure absorption mode. 

The sine-bell, sine-bell squared, phase-shifted sine-bell, and phase-shifted sine-bell squared window functions are generally used in 2D NMR spectroscopy. Each of these has a different effect on the appearance of the peak shape. For all these functions, a certain price may have to be paid in terms of the signal-to-noise ratio, since they remove the dispersive components of the magnitude spectrum. This is illustrated in the following COSY spectra ... 

The pulse sequence for the ID ROESY experiment using purged half-Gaussian pulses is shown in Fig. 7.7. The purging is required to remove the dispersive components, since these are not completely eliminated by the weak spin-lock field employed in the ID ROESY experiment. 

Both the dispersed component and the dispersion medium extend themselves continuously throughout the whole system. 

This dispersion energy is coupled to an exchange-dispersion component ... 

By the geometric-mean method [106] the total surface free energy (y ), the polar (yl") and dispersive component (yf) of both systems were calculated (Fig. 9.10 e,f). 

Experimental data on Op and On for different polymer materials exhibit unique correlations with (hydrogen bonding) and 6(j (dispersion) components respectively of solubility parameter 6gp of polymer (53,60) which can be calculated from data on structural group contributions to and available in the literature (61). The existence of such correlations (Figures 9(a) and 9(b)) indicate that LSC data can be used to characterize the chemical nature of polymeric membrane materials. 

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