Depolarisation ratio

Resonance Raman spectroscopy Intensity profiles, depolarisation ratios Allows study of chromophoric active sites in biological molecules at low concentration can provide information on metal—ligand bonding... 

In the usual experimental set up, the scattered radiation is collected in some small solid angle around an observation direction at 90° to that of the incident radiation. A schematic diagram of a typical laser Raman set-up involving 90° collection optics is shown in Fig. I, together with the definition of the depolarisation ratio... 

Fig. 1. Experimental set up (90° collection optics) for the measurement of laser Raman scattering, illustrating the definition of the depolarisation ratio. ly and Ij are the intensities of light scattered, respectively, parallel and perpendicular to the polarisation of the incident exciting beam...

Pi Ii/I for linearly polarised incident radiation. In this case, Eq. (1) must be multiplied by the factor (3/8 rr) (1 + pj)/(l + 2pi). (5a). If only the parallel component of scattered radiation is measured the factor is (3/8 tt) (1 + 2 px) . (I = Pi I ). For naturally polarised (unpolarised) or circularly polarised incident light the relevant factors are given in terms of the depolarisation ratio, p , for natural polarisation, where... 

In the normal vibrational Raman effect it has been traditionally assumed that the scattering tensor is symmetric ( p = ffap). However, even in 92 Placzek (5) considered the consequences of antisymmetric contributions, which he termed magnetic-dipole scattering because of the agreement between the selection rules for an antisymmetric Raman process and for a magnetic-dipole transition. Placzek gave the expected value of the depolarisation ratio, p i = Ij /I = > for purely antisymmetric scat-... 

So, in this case a y = Uy owing only to the difference in the energy denominators. The tensor is therefore asymmetric. In resonance with the 0-0 transition, scattering is dominated by the element tty and, for the 0-1 resonance, by the element a y. The behaviour of the depolarisation ratio in this case (anomalous polarisation) is discussed in Section 2.11.2. 

The definition of the depolarisation ratio, pi, is illustrated in Fig. 1 for linearly-polarised incident radiation and a 90° scattering geometry. In the normal Raman effect it is well known that the measurement of p may identify the symmetry of the vibrational mode responsible for a given Raman band pi < 3/4 (pi = 0 in cubic or higher symmetries) for totally symmetric modes and Pi= 3/4 for non-totally symmetric modes. In the resonance Raman effect, the value of P, and its dependence on the exciting frequency, may be more informative. This is because the symmetries of... 

The definitions of the invariants used here follow those of Placzek (5d) and are prefened because of their simple relation. to the irreducible tensors. Many authors use the invariants a, y, 72 where =-50 , y and y =- G . Values of the depolarisation ratio are unaffected but the constant of proportionality in intensity expressions will be different. The quantities 0, 0 and y of Ref. (54) correspond exactly with G , G and G respectively. 

Further important technical advances include the development of devices for the automatic scanning of the depolarisation ratio, for measuring Raman CID (circular intensity differentials), for measuring difference Raman spectra (i.e. the difference between the Raman signals from solutions and solvents), for studying optical-fibre Raman spectroscopy, for rapid (i.e. picosecond) Raman spectroscopy and Raman micrography 64). 

The depolarisation ratio of the Vi (A 1) band of the FeBr4 ion at resonance is 0.15 rather than zero. Although the reason for this is not entirely certain, it is undoubtedly relevant that the ground state is not totally symmetric ( Ai) 29). 

The resonance Raman spectra of the [IrClg] and [IrBr J ions are important in that several bands of each are anomalously polarised. Although this discovery was initially made early in 1972 (75), its significance was not appreciated at the time. Independently,i/awqgMc/i/ and Shimanouchi (61,62) reported the results in detail and interpreted them as being a consequence of the degenerate ground state in each case moreover, they related the specific values of the depolarisation ratio to the symmetry of the excited electronic states. 

The depolarisation ratio, p, of a feature in the Raman spectrum is defined as... 

In the usual Raman experiment, the observations are made perpendicular to the direction of the incident beam, which is plane polarised. The depolarisation ratio is defined as the intensity ratio of the two polarised components of the scattered light which are parallel and perpendicular to the direction of the propagation of the (polarised) incident light. The polarisation of the incident beam is perpendicular to the plane of propagation and observation. For this geometry, the depolarisation ratio is defined as the intensity ratio ... 

Consequently, the Raman scattered light emanating from even a random sample is polarised to a greater or lesser extent. For randomly oriented systems, the polarisation properties are determined by the two tensor invariants of the polarisation tensor, i.e., the trace and the anisotropy. The depolarisation ratio is always less than or equal to 3/4. For a specific scattering geometry, this polarisation is dependent upon the symmetry of the molecular vibration giving rise to the line. 

With increasing sensitivity of detectors, the detection of unenhanced surface Raman scattering becomes a possibility, and if this is achieved a wide range of effects can be investigated. In particular the determination of adsorbate orientation from depolarisation ratios and the angular dependence of the Raman signal will be possible. Currently, such measurements only serve as a means of investigating the enhancement mechanism. 

Bartoli and Litovitz [6] found values of C of about 0.2% for some typical polarised (A) bands - by making measurements on the 459 cm" band of CCl which has a well-known [18] depolarisation ratio. Calculation of I ((1d) is then straightforward. Polarisation scrambling behind the main entrance slit ensures that the monochromator is equally sensitive to transmission of and lyy scattered light. There have been reports of local heating effects caused by a relatively high powered laser beam. However, we have never found this to be a problem although, of course, it is not possible to physically monitor the microscopic temperature. Stokes/Antistokes intensity ratios which measure the Boltzman population factors (and hence the microscopic temperature) have always corresponded well to the laboratory (bath) temperature even for input powers up to 2w. 

The assignment of bands given in Fig. 1 are confirmed by the laser Raman spectra [4]. The vibrations assigned to Ai species appear as the polarized Raman lines and those assigned to Bi and B2 species appear as the depolarized Raman lines. The results are just expected from the above assignments except some weak lines, for which the depolarisation ratio cannot be measured definitely. 

Deformation vibrations 2 Depolarisation ratio 3 Depolarised 3 Diacyl peroxides 105. 130 Diacylamines 145 Diamides 146 Diamines 108 Diamond 327 Diazirines 80 Diazo compounds 24, 90 Diazoketones 80, 90 Diazonium salts 12,24,86,92 Diboranes 247 Dicarbonyl compounds 116 Dicarboxylic acids 125 Dichromate ions 284, 287 Dienes 68,71 Diesters 132... 

In Raman spectroscopy, the direction of observation of the radiation scattered by the sample is perpendicular to the direction of the incident beam. Polarised Raman spectra may be obtained by using a plane polarised source of electromagnetic radiation (e.g. a polarised laser beam) and placing a polariser between the sample and the detector. The polariser may be orientated so that the electric vector of the incident electromagnetic radiation is either parallel or perpendicular to that of the electric vector of the radiation falling on the detector. The most commonly used approach is to fix the polarisation of the incident beam and observe the polarisation of the Raman radiation in two different planes. The Raman band intensity ratio, given by the perpendicular polarisation intensity, /j., divided by the parallel polarisation intensity, 7, is known as the depolarisation ratio, p. 

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