Dissymmetry

Circular dicliroism has been a useful servant to tire biophysical chemist since it allows tire non-invasive detennination of secondary stmcture (a-helices and P-sheets) in dissolved biopolymers. Due to tire dissymmetry of tliese stmctures (containing chiral centres) tliey are biaxial and show circular birefringence. Circular dicliroism is tlie Kramers-Kronig transfonnation of tlie resulting optical rotatory dispersion. The spectral window useful for distinguishing between a-helices and so on lies in tlie region 200-250 nm and hence is masked by certain salts. The metliod as usually applied is only semi-quantitative, since tlie measured optical rotations also depend on tlie exact amino acid sequence. 

In Example 10.5 we extracted both the molecular weight and the radius of gyration from Ught-scattering data. There may be circumstances, however, when nothing more than the dimensions of the molecule are sought. In this case a simple alternative to the analysis discussed above can be followed. This technique is called the dissymmetry method and involves measuring the ratio of intensities scattered at 45° and 135°. The ratio of these intensities is called the dissymmetry ratio z ... 

Figure 10.13 Variation of the dissymmetry ratio z with a characteristic dimension D (relative to X) for spheres, random coils, and rods. (Data from Ref. 4.)...

The helix can be approximated as a rod therefore values of L/X which are consistent with the observed dissymmetries can be read from Fig. 10.13 or equivalent sources. Also, X = Xo/n = 436/1.446 = 302 nm in each of these systems. In view of these considerations, the following results are obtained ... 

Draw a plot in polar coordinates of the scattering envelope in the xy plane. How would the envelope of a Rayleigh scatterer compare with this plot By interpolation, evaluate 145, iiss, and z. Use Fig. 10.13 to estimate the value of rrms to which this dissymmetry ratio corresponds if X (in toluene) is 364 nm. What are some practical and theoretical objections to this procedure for estimating rrms ... 

The UV spectrum of a complex conjugated molecule is usually observed to consist of a few broad band systems, often with fine structure, which may be sharpened up in non-polar solvents. Such a spectrum can often be shown to be more complex than it superficially appears, by investigation of the magnetic circular dichroism (MCD) spectrum, or by introduction of dissymmetry and running the optical rotatory dispersion (ORD) or circular dichroism (CD) spectrum. These techniques will frequently separate and distinguish overlapping bands of different symmetry properties <71PMH(3)397). 

The term aromatic will be used in a strict non-historical sense to mean possessing a cyclic 7r-electron system (6 and 10 electrons for the mono- and bi-cyclic rings discussed in this review). Heteroaromatic compounds, like carboaromatics, have widely different degrees and types of electronic dissymmetry and polarizabihty. Consequently, their reactivity varies tremendously with any one reagent and their relative reactivity changes drastically with the type of reagent. In this sense, aromatic compounds show differences in reactivity but not in aromaticity. The virtues of this qiuilitative concept of aromaticity and the pitfalls of trying to use it as a quantitative concept in modern context have been ably presented by Peters and by Balaban and Simon. ... 

A more serious limit to this implementation is due to the volume of the recycling pump and associated equipment such as flowmeters and pressure sensors. As the pump moves with respect to the zones, its volume leads to a dead volume dissymmetry, which can lead to a decrease extract and raffinate purities. This decrease can be significant for SMB with short columns and/or compounds with low retention. However, it can be easily overcome by using a shorter column or asynchronous shift of the inlets/outlets [54, 55]. This last solution is extremely efficient and does not induce extra costs because it is a purely software solution. 

The ability to disperse the calcium soap formed from a given amount of sodium oleate has been studied for a number of a-sulfo fatty acid esters with 14-22 carbon atoms [28,30]. In principle, the lime soap dispersion property increases with the number of C atoms and the dissymmetry of the molecule. Esters with 14 C atoms have no dispersion power and in the case of esters with 15-17 carbon atoms the least symmetrical are the better lime soap-dispersing agents. However this property does not only depend on the symmetry but on the chain length of the fatty acid group. For example, methyl and ethyl a-sulfomyristate have better dispersing power than dodecyl propionate and butyrate. The esters with 18 and more carbon atoms are about equal in lime soap dispersion power. Isobutyl a-sulfopalmitate is the most effective agent under the test conditions. 

Obviously, the analysis of the correlation between the two fields emerging from the telescope and related devices makes necessary to avoid dissymmetry between the interferometric arms. Otherwise, it may result in confusion between a low correlation due to a low spatial coherence of the source and a degradation of the fringe contrast due to defects of the interferometer. The following paragraphs summarize the parameters to be controlled in order to get calibrated data. 

The fringes contrasts are subject to degradation resulting from dissymmetry in the interferometer. The optical fields to be mixed are characterized by a broadband spectrum so that differential dispersion may induce a variation of the differential phase over the spectrum. Detectors are sensitive to the superposition of the different spectral contributions. If differential dispersion shifts the fringes patterns for the different frequency, the global interferogramme is blurred and the contrast decreases. Fig. 5 shows corresponding experimental results. 

The investigation of chiral molecular phenomena, and associated technique development, thus hnds potentially signihcant practical applications to place alongside the fundamental interest of this topic. This chapter will examine the recently investigated phenomenon of photoelectron circular dichroism (PECD) that arises from a dissymmetry in the angular distribution of photoelectrons... 

It is very obvious from the peaks and troughs displayed in Fig. 1 that the anticipated dissymmetry between forward and backward electron ejection directions (relative to the photon beam direction) is borne out by experiment. Moreover, one sees that the dissymmetry lies in opposite directions for ionization of the two energetically accessible orbitals observed here. 

Quite generally, we will find that the magnitude and direction of these chiral dissymmetries varies greatly with both electron energy and initial orbital. The prediction or interpretation of such characteristics falls beyond the capability of the simple, intuitive analogy presented in II.B.l, so that we must now turn to consider the quanmm interference effects that control the observable distributions in order to enhance our predictive abilities. A reader wishing to pass over these details at first encounter will find a summary of the deductions made at the start of the subsequent Section, IV. 

Implicitly, their data treatment assumes that the photoemission dissymmetry simply reverses direction with the enantiomer switch, equivalently to its... 

The root-mean-square distance Vr separating the ends of the polymer chain is a convenient measure of its linear dimensions. The dissymmetry coefficient will be unity for (VrV 0< l and will increase as this ratio increases. 

It should be noted that relative intensity measurements suffice for the determination of z. The absolute value of ie/Ie required for calculation of the molecular weight usually is determined at 90° and the appropriate correction factor 1/P(90°), obtained from the dissymmetry as described above, is applied to obtain Pgo°. The factor P B) is strictly applicable only at infinite dilution, and it is therefore impor-... 

Fig. 46.—Dissymmetry ratio for light scattered at 45° and 135° as a function of -x/r /X for random coil polymer chains. ...

Apart from their utility in determining the correction factor 1/P( ), light-scattering dissymmetry measurements afford a measure of the dimensions of the randomly coiled polymer molecule in dilute solution. Thus the above analysis of measurements made at different angles yields the important ratio from which the root-mean-square... 

Before scattering intensity measurements can be converted to molecular weights, the two corrections previously discussed—the dissymmetry correction for intraparticle interference and the extrapolation to zero concentration—must be introduced, or established to be negligible. The relationships given in the preceding sections unfortunately account rigorously for either only in the absence of the other. The theory of the concentration dependence of the scattered intensity applies to the turbidity corrected for dissymmetry, and the treatment of dissymmetry is strictly valid only at zero concentration (where interference of radiation scattered by different polymer molecules vanishes). 

The dissymmetry to be expected for the polymer in a given solvent may be estimated with the aid of the following semiempirical formula, provided the intrinsic viscosity [r ] (see Sec. 4b) in the same solvent and the approximate molecular weight of the polymer are known. The... 

The approximate dissymmetry correction may then be computed from Vr /X using Eqs. (31) and (32). Corrections so calculated are not regarded as acceptable substitutes for actual dissymmetry measurements, but they may prove highly useful as preliminary estimates of the correction. 

Typical results of lightscattering measurements are shown in Figs. 47 and 48 for polystyrene fractions of medium and of very high molecular weight, respectively. The small dissymmetry correction for the former was calculated from the measured dissymmetry coefficient 45°( l-2) using Eqs. (31) and (32). 

The similarity between the plots of c/r vs. c shown in Figs. 47 and 48 and those for tc/c vs. c shown in Figs. 38 and 39 is apparent. Deviations from ideality (i.e., the changes in iz/c and in c/r with c) have the same origin for both types of measurements. As with the osmotic pressure-concentration ratio, the change of c/r with c may be reduced by choosing a poor solvent. A further advantage of a poor solvent enters because of the smaller size assumed by the polymer molecule in a poor solvent environment, which reduces the dissymmetry correction. 

Mixed solvents are generally unsatisfactory for use in the determination of polymer molecular weights owing to the likelihood of selective absorption of one of the solvent components by the polymer coil. The excess of polarizabilit f of the polymer particle (polymer plus occluded solvent) is not then equal to the difference between the polarizabilities of the polymer and the solvent mixture. For this reason the refractive increment dn/dc which would be required for calculation of K, or of i7, cannot be assumed to equal the observed change in refractive index of the medium as a whole when polymer is added to it, unless the refractive indexes of the solvent components happen to be the same. The size Vmay, however, be measured in a mixed solvent, since only the dissymmetry ratio is required for this purpose. 

The physical reason for the inherent lack of incentive for mixing in a polymer-polymer system is related to that already cited in explanation of the dissymmetry of the phase diagram for a polymer-solvent binary system. The entropy to be gained by intermixing of the polymer molecules is very small owing to the small numbers of molecules involved. Hence an almost trivial positive free energy of interaction suffices to counteract this small entropy of mixing. 

Value based on light-scattering dissymmetry for a fraction of molecular weight 220,000.22... 

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