Order between molecules

The next point of interest has to do with the question of how deep the surface region or region of appreciably unbalanced forces is. This depends primarily on the range of intermolecular forces and, except where ions are involved, the principal force between molecules is of the so-called van der Waals type (see Section VI-1). This type of force decreases with about the seventh power of the intermolecular distance and, consequently, it is only the first shell or two of nearest neighbors whose interaction with a given molecule is of importance. In other words, a molecule experiences essentially symmetrical forces once it is a few molecular diameters away from the surface, and the thickness of the surface region is of this order of magnitude (see Ref. 23, for example). (Certain aspects of this conclusion need modification and are discussed in Sections X-6C and XVII-5.)... 

It has long been known from statistical mechanical theory that a Bose-Einstein ideal gas, which at low temperatures would show condensation of molecules into die ground translational state (a condensation in momentum space rather than in position space), should show a third-order phase transition at the temperature at which this condensation starts. Nonnal helium ( He) is a Bose-Einstein substance, but is far from ideal at low temperatures, and the very real forces between molecules make the >L-transition to He II very different from that predicted for a Bose-Einstein gas. 

Despite these simplifications, a typical or F NMR spectrum will nomially show many couplings. Figure BTl 1.9 is the NMR spectrum of propan-1-ol in a dilute solution where the exchange of OH hydrogens between molecules is slow. The underlymg frequency scale is included with the spectrum, in order to emphasize how the couplings are quantified. Conveniently, the shift order matches the chemical order of die atoms. The resonance frequencies of each of the 18 resolved peaks can be quantitatively explained by the four... 

The most well-known and at the same time the earliest computer model for a molecular structure representation is a wire frame model (Figure 2-123a). This model is also known under other names such as line model or Drciding model [199]. It shows the individual bonds and the angles formed between these bonds. The bonds of a molecule are represented by colored vector lines and the color is derived from the atom type definition. This simple method does not display atoms, but atom positions can be derived from the end and branching points of the wire frame model. In addition, the bond orders between two atoms can be expressed by the number of lines. 

Until surface contact, the force between molecules is always one of attraction, although this attraction has different origins in different systems. London forces, dipole-dipole attractions, acid-base interactions, and hydrogen bonds are some of the types of attraction we have in mind. In the foregoing list, London forces are universal and also the weakest of the attractions listed. The interactions increase in strength and also in specificity in the order listed. 

In condensed phases, the separation between molecules is of the order of the molecular dimensions and the result is that each molecule is polarized not by just the ordinary applied electric field E but by a local field F consisting of E plus the fields of all the other dipoles. Once the local field is known, we can use equation 15.8 to find the polarization, simply by substituting aF for aE. The calculation of F is difficult because the dipoles that contribute to F are themselves determined by F and a self-consistent treatment is necessary. This is achieved by relating F to P, ultimately giving an equation for Xe-... 

The x-ray diffraction pattern from a liquid resembles that from a powdered sample, but the lines are diffuse rather than sharp. This pattern indicates that the molecules of a liquid have a degree of short-range order but that the distances between molecules vary this variation produces the diffuse lines. 

Fig. 37. (continued)—(b) An axial view projected along the r-axis shows the packing arrangement of three welan double helices in the trigonal unit cell. The helix drawn in solid bonds is antiparallel to the remaining helices (open bonds). Note that calcium ions are positioned between the helices and each water molecule (large open circle) shown here is connected to all three surrounding helices. The interstitial space is occupied by several other ordered water molecules (not shown). 

The frictional coefficient varies with concentration, but at infinite dilution it reduces to the coefficient (/o) for an isolated polymer molecule moving through the surrounding fluid unperturbed by movements of other polymer molecules (see Chap. XIV). At finite concentrations, however, the motion of the solvent in the vicinity of a given polymer molecule is affected by others nearby binary encounters (as well as ones of higher order) between polymer molecules contribute also to the observed frictional effects. The influence of these interactions will persist to very low concentrations owing to the relatively large effective volume of a polymer molecule, to which attention has been directed repeatedly in this chapter. Since the sedimentation con-stant depends inversely on the frictional coefficient, s must also depend bn concentration. 

Previously, we have proposed that SFG intensity due to interfacial water at quartz/ water interfaces reflects the number of oriented water molecules within the electric double layer and, in turn, the double layer thickness based on the p H dependence of the SFG intensity [10] and a linear relation between the SFG intensity and (ionic strength) [12]. In the case of the Pt/electrolyte solution interface the drop in the potential profile in the vicinity ofelectrode become precipitous as the electrode becomes more highly charged. Thus, the ordered water layer in the vicinity of the electrode surface becomes thiimer as the electrode is more highly charged. Since the number of ordered water molecules becomes smaller, the SFG intensity should become weaker at potentials away from the pzc. This is contrary to the experimental result. 

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