W.F. Maddams

III. The effect of band width and band shape on resolution enhancement by derivative spectroscopy

Abstract The effect of band width on the resolution of pairs of overlapping peaks, using second and fourth derivative spectra, and hence on the specificity of such derivative functions for peak finding, has been examined. Calculations for doublets generated from Lorentzian peaks of varying half width ratio and intensity show that the specificity for the broader component decreases rapidly as the half width ratio increases. The effect is more marked in the case of the fourth derivative and this factor, rather than the signal to noise ratio in experimental spectra, determines what can be achieved. The practical limitations are considered in terms of the second and fourth derivative spectra of the nine overlapping configurational and conformational bands in the carbon-chlorine stretching region of the vibrational spectrum of poly(vinyl chloride). Explicit algebraic expressions have been derived for the second derivatives of peaks with asymmetry and partial Gaussian character by the use of inverse polynomials. Calculated derivatives of overlapping doublets of this type show that there is a loss of resolution; this may lead to a failure to detect if one component is broad or is relatively weak.

The measurement of derivative i.r. spectra—I. Background studies

Abstract The performances of the Butler and Hopkins and the Savitzky and Golay methods for obtaining derivative spectra have been examined by calculating second and fourth derivatives of the synthetic peak consisting of the sum of two Lorentzian profiles of equal height and half width separated by their semi half width. The resolution achieved and the amplitude of the derivative as a function of the derivatization interval, α, have been determined. With the Butler and Hopkins method the signal amplitude increases with α but the resolution decreases and the best compromise is at about 20% of the semi half width for the second derivative and 30% for the fourth derivative. The amplitude and resolution are not markedly dependent on α for values up to 50% in the case of the Savitzky and Golay method. The loss of resolution for varying degrees of Trott and Beynon three point multipass smoothing has also been determined. Calculations using the doublet with added random noise show that the Butler and Hopkins method, with Trott and Beynon smoothing, gives a better signal to noise ratio than the Savitzky and Golay method with equal smoothing. However, when the loss of resolution is also considered the overall performances of the two methods are similar. Satisfactory results are obtained with noise levels of 0.2% and 1.0%, indicating that it should be possible to obtain useful experimental second and fourth derivative i.r. spectra, particularly for peak finding purposes.

The measurement of derivative i.r. spectra—II. Experimental measurements

Abstract The performances of the Butler and Hopkins, and Savitzky and Golay methods, used in conjunction with the Trott and Beynon smoothing technique, for generating derivative i.r. spectra have been assessed experimentally, primarily in the context of peak finding. The test bands used were tert.-butyl benzene (761 cm- −1 ), 1,2,3-trimethylbenzene (764.5 cm −1 ) and m -xylene (766.5 cm −1 ), together with doublets from two component mixtures of these hydrocarbons and a computer-generated doublet from the 1,2,3-trimethylbenzene band. Measurements were made on Perkin-Elmer 577 and 580 spectrometers, with off-line data processing; very satisfactory second and fourth derivative spectra were obtained. Conditions for the optimum compromise between signal to noise ratio and resolution, in terms of the derivatization and smoothing parameters, were established and prove to be similar to those previously deduced from a study of synthetic Lorentzian peak systems. Of the two derivatization techniques the Butler and Hopkins method gives the somewhat superior performance.

The characterization of infrared absorption band shapes. II. Experimental studies

Abstract The profiles of twenty-five well defined i.r. absorption bands have been measured, to test various methods for characterizing their shapes in the context of a realistic approach to the mathematical separation of overlapping peaks. Inverse polynomials of the type y = a (1 + bx 2 + cx 3 + dx 4 ) −1 prove to be very convenient and, unlike truncated moments and log/log plots of band shapes, do not require the location of an accurate experimental baseline. The second derivative approach could not be tested as it proved impossible to make measurements without incurring noise or some distortion of the profiles. Most of the bands examined are a close approximation to the Lorentzian shape, with slight asymmetry. Curve fitting of synthetic spectra consisting of Lorentzian peaks distorted by the use of an inverse polynomial with a term in x 4 , and of mixtures of three of the compounds used for the profile study was undertaken in terms of the commonly assumed Lorentzian shape. The results show that modest differences between the assumed and the actual shapes, which are manifest in a worsening of the overall fit, can be tolerated. Problems posed by lack of knowledge of the number of component bands and their half widths are more serious. A few of the profiles studied deviate appreciably from Lorentzian; these are explicable in terms of association effects and solvent/solute interactions.

The characterization of Raman band shapes

Abstract The profiles of eight well defined Raman bands have been measured and the results have been expressed in terms of inverse polynomials of the type y = (1 + x 2 + cx 3 + dx 4 + fx 6 ) −1 . They are very similar to those previously reported for a wider range of i.r. bands; the coefficients c and d which are a measure, respectively, of asymmetry and deviation from the Lorentzian shape are, with one exception, small.

The vibrational spectrum and conformations of allyl chloride

Abstract Infrared and Raman spectra are reported for allyl chloride in vapour and liquid phases and also by matrix isolation in argon and nitrogen. Assignments are made in terms of a predominant low energy gauche form with a smaller amount of high energy cis form in all phases.

The vibrational spectra, conformational and thermodynamic properties of 2-chlorobuta-1,3-diene (chloroprene) and propenoyl chloride

Abstract The vibrational spectrum of 2-chlorobuta-1,3-diene has been recorded in the gaseous, liquid, solid and solution phases, and also in an argon matrix. Several weak bands present in the i.r. spectrum of the fluid phases and unannealed matrix were observed to be absent after careful annealing. Thermodynamic functions for the ideal gas have been estimated from those of other compounds, and their values, taken together with the spectral changes on annealing, are concluded to be evidence of a conformational equilibrium. The most probable molecular structure has been calculated using previous microwave data, and the asymmetric potential function to internal rotation has also been calculated using a value of Δ H θ of 8.2 kJ mol −1 , as derived by statistical methods. The i.r. spectrum of gaseous propenoyl chloride has been recorded to aid in assignment of the spectral features of the isoelectronic compound 2-chlorobuta-1,3-diene, and improved vibrational assignments of both compounds are presented. New values for the thermodynamic functions of propenoyl chloride are presented to take into account the significant changes made to the vibrational assigmnent.

Solvent effects in u.v. absorption spectra. III. Phenol in various solvent mixtures

Abstract The loss of fine structure in the u.v. absorption spectrum of phenol in solution in mixtures of cyclohexane and any one of a range of solvents has been examined. These latter, chloroform, octene-1, acetic acid, acetonitrile, tetrahydrofuran, dimethyl sulphoxide and hexamethyl phosphoramide, are either potential proton donors or acceptors, covering a wide range of anticipated association strengths. The results confirm this expectation. Although the effect is weak in the case of chloroform and octene-1 it is possible to distinguish it from the general type of bulk solvent effects which occur with polar media. The relatively weak bonding found with acetic acid is tentatively assigned to the presence of some open chain dimer. The loss of fine structure occurs with very low concentrations of dimethyl sulphoxide and hexamethyl phosphoramide, in agreement with the known strong proton accepting ability of these solvents.

Conformations of chlorinated hydrocarbons. A vibrational spectroscopic study of 2-chlorobutane, 2,4-dichloropentane and 2,4,6-trichloroheptane

Abstract The i.r. (solution and matrix isolation) spectra and Raman spectra of 2-chlorobutane are presented and Δ H ° values are reported by both methods which are in good agreement. Infrared spectra in solution and matrix isolation are also reported for d,l - and meso -2,4-dichloropentane, the syndiotactic, and (together with Raman spectra) isotactic, and heterotactic forms of 2,4,6-trichloroheptane. The results are discussed in terms of those vibrational assignments which add further information concerning the structure of poly(vinyl chloride).

Solvent effects in u.v. absorption spectra. II. The use of matrix rank analysis.

Abstract The principles of matrix rank analysis are outlined with particular reference to its use in determining the number of species present in unknown mixtures giving characteristic u.v. absorption spectra. The method is applied to the spectra of phenol in solution in mixtures of cyclohexane and di- n -butyl ether, cyclohexane and ethanol, and phenol at various concentrations in cyclohexane. With the first system only two species are present and the detailed interpretation of the spectra show that they are the unbonded phenol and phenol, acting as proton donor, bonded with the ether. In the case of the phenol—ethanol and phenol—phenol systems three species are present over the concentration range in which the u.v. spectra change markedly. They are unbonded phenol and two hydrogen bonded species with open chain and cyclic structures. The u.v. spectra have been interpreted semi-quantitatively on the basis of some reasonable assumptions. The results show that in the case of phenol-ethanol bonding the open chain species is favoured, particularly at higher ethanol concentrations, but the cyclic species is likely to predominate in the self bonding of phenol.