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Investigation of H-bonded media by means of Raman scattering in terms of the fractal formalism Maksymov A.O., Yakunov A.V., Bily M.M. National Taras Shevchenko Univ. of Kyiv, Physics Department, Ukraine
Introduction <ul><li>The purpose of the work is to determine the limits of applicability for the conception and it’s practical application. The low-frequency Raman scattering spectra of H-bonded liquids and their solutions are discussed in terms of supramolecular fractality. The peculiarities of structural dynamics and the origin of numerous anomalies in the liquids under consideration need to be studied since they remain still far from understanding. </li></ul>
Comparison with amorphous media The most similar state is amorphous one. It shares condensed and irregular features of liquid. In every moment of time liquid can be represented as amorphous medium. It seems to be dynamically blurred amorphous network.
Percolation model However the molecular arrangement is compact the topology of hydrogen network is tracery. Owing to specific symmetry of each molecule and thermal molecular motions some of H-bonds are broken.
Fractal dimensionality d=2 – Euclidian dimensionality Medium behaves like homogeneous . d<2 – Hausdorf dimensionality Medium behaves like a fractal . The total area covered by cluster scales like ξ powered :
Scattering intensity <ul><li>In amorphous and liquid states over the lack of translational symmetry and violation of the wave-vector selection rule the observed scattering intensity for the Stokes component is given by expression, proposed by Gammon and Shuker , </li></ul><ul><li>where - light to vibration coupling coefficient ; </li></ul><ul><li> - density of states function </li></ul><ul><li>and - the Bose-Einstein’s factor . </li></ul>
Density of vibrational states <ul><li>The density of vibrational states for the excitations of transition type is : </li></ul><ul><li>, </li></ul><ul><li>where is Hausdorf (fractal) space dimensionality . </li></ul><ul><li>For vibrational excitations in such medium the dispersion relation is the following: </li></ul><ul><li>, </li></ul><ul><li>where is an exponent of anomalous diffusion . </li></ul><ul><li>Substitution gives DOVS for vibrational excitations on fractal structures : </li></ul><ul><li>, </li></ul><ul><li>where is called spectral (fracton) dimensionality and appropriate vibrational excitations are called fractons . </li></ul>
Crossover ξ The right sketch illustrates typical reduced Raman scattering spectrum that consists of the phonon and the fracton regions. The structure inhomogeneity size which is designated as correlation length ξ shown left is inversely proportional to the crossover frequency which separates fracton region from the phonon one.
Light to vibration coupling function <ul><li>The light-vibration coupling function is a weighting function from frequency. It indicates a contribution into the scattering which is produced by fractons with this current frequency . The contribution depends on fracton wave function : </li></ul><ul><li>where is a superlocalization exponent . </li></ul>A number of fracton wave functions for different values of frequency The light-vibration coupling function behaves like power-law dependence from frequency :
Effective density of vibrational states <ul><li> The effective DOVS function can be obtained from the scattering intensity spectrum immediately. It equals to the reduced intensity : </li></ul><ul><li> Since the effective DOVS is a product of functions with power-law dependence, it could be expressed as well : </li></ul><ul><li> Structural parameter is a superposition of structural and vibrational properties of the medium : </li></ul>
Scheme of equipment <ul><li>1. Argon laser with output power ~100 mW excited at 514 nm </li></ul><ul><li>2. Sample, contained in glass medicine ampoule </li></ul><ul><li>3. Cylindrical lens </li></ul><ul><li>4. Automated spectrometer DFS-24 </li></ul>1 2 3 4
Initial spectra The obtained Raman spectra of pure H-bonded substances are presented left. This spectra are reduced and presented right in log-log scale.
The information about the σ -exponent by itself is not useful since we have too many unknown parameters to make any conclusions about the structural dynamics of the investigated media. But the comparison may result in something more informative. Including of the molecule of another sort into the hydrogen-bond network leads to the structural rearrangement of medium and changes it’s features.
Behavior of structural parameter <ul><li>The concentration dependences for water-glycerol, water ethanol and water- acetone solutions reflects the structure competition between the H-bond networks of their components. </li></ul>
Discussion The fractal dimensionality in the most general form could be expressed as the function of the binary solution concentration: Here and are the numbers of potential H-bonds per molecule for the molecules of the first and the second sort accordingly; is the binary packing parameter for a given concentration of the molecules of two sorts. This parameter reflects the result of different molecule mixing.
Conclusions <ul><li>The employment of low-frequency Raman scattering with the fractal conception involved allows us to investigate macroscopic parameters of a media caused by its microscopic features: peculiarities of instantaneous short-range structure of intermolecular arrangement and the propagation of vibrational excitations. </li></ul><ul><li>The fractal conception provides useful mathematical methods for describing complex-ordered dynamic media, thus conserving the general form of relations which describe collective effects. </li></ul><ul><li>It is apparent for the solutions under investigation that the low-frequency range of the Raman scattering spectrum is sensitive to the changes in concentration of the measured solution. This could be used as the optical method for concentration identification in transparent solutions of associated liquids. </li></ul>
Investigation of H-bonded media by means of Raman scattering in terms of the fractal formalism