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Investigation of H-bonded Investigation of H-bonded media by means of Raman media by means of Raman scattering in terms of the scattering in terms of the

fractal formalismfractal formalism

Maksymov A.O., Yakunov A.V., Bily Maksymov A.O., Yakunov A.V., Bily M.M.M.M.

National Taras Shevchenko Univ. of National Taras Shevchenko Univ. of Kyiv, Physics Department, UkraineKyiv, Physics Department, Ukraine

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IntroductionIntroductionThe purpose of the work is to determine the limits of The purpose of the work is to determine the limits of applicability for the conception and it’s practical applicability for the conception and it’s practical application. The low-frequency Raman scattering application. The low-frequency Raman scattering spectra of H-bonded liquids and their solutions are spectra of H-bonded liquids and their solutions are discussed in terms of supramolecular fractality. The discussed in terms of supramolecular fractality. The peculiarities of structural dynamics and the origin of peculiarities of structural dynamics and the origin of numerous anomalies in the liquids under numerous anomalies in the liquids under consideration need to be studied since they remain consideration need to be studied since they remain still far from understanding.still far from understanding.

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Comparison with Comparison with amorphous mediaamorphous media

The most similar state is amorphous one. It The most similar state is amorphous one. It shares condensed and irregular features of shares condensed and irregular features of liquid. In every moment of time liquid can be liquid. In every moment of time liquid can be represented as amorphous medium. It seems to represented as amorphous medium. It seems to be dynamically blurred amorphous network.be dynamically blurred amorphous network.

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However the molecular arrangement is compact the However the molecular arrangement is compact the topology of hydrogen network is tracery.topology of hydrogen network is tracery.

Percolation modelPercolation modelOwing to specific symmetry of each molecule and thermal Owing to specific symmetry of each molecule and thermal molecular motions some of H-bonds are broken. molecular motions some of H-bonds are broken.

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Fractal dimensionalityFractal dimensionality

d=2 – Euclidian dimensionalityMedium behaves like homogeneous.

d<2 – Hausdorf dimensionalityMedium behaves like a fractal.

The total area covered by cluster scales like ξ powered:

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Scattering intensityScattering intensity In amorphous and liquid states over the lack of In amorphous and liquid states over the lack of translational symmetry and violation of the wave-translational symmetry and violation of the wave-vector selection rule the observed scattering vector selection rule the observed scattering intensity for the Stokes component is given by intensity for the Stokes component is given by expression,expression, proposed by Gammon and Shuker proposed by Gammon and Shuker

,, wherewhere - - light to vibration coupling light to vibration coupling coefficientcoefficient; ; - - density of states functiondensity of states function andand - - the Bose-Einstein’s factor the Bose-Einstein’s factor ..

/1 ngCI

C

g n

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Density of vibrational Density of vibrational statesstates

The density of vibrational states for the excitations of The density of vibrational states for the excitations of transition type istransition type is:: ,,where is Hausdorf (fractal) space dimensionalitywhere is Hausdorf (fractal) space dimensionality..For vibrational excitations in such medium the dispersion For vibrational excitations in such medium the dispersion relation is the following:relation is the following: ,,wherewhere is an exponent of anomalous diffusion is an exponent of anomalous diffusion..Substitution gives DOVS for vibrational excitations on fractal Substitution gives DOVS for vibrational excitations on fractal structuresstructures::

,,wherewhere is called spectral (fracton) dimensionality andis called spectral (fracton) dimensionality and appropriate vibrational excitations are called fractonsappropriate vibrational excitations are called fractons. .

fd

wd wdk 2

1 dg wf ddd 2

dkkdg fd 1

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CrossoverCrossover

ξ0,1 1 10 100

sizerestriction

crossoverfrequency

phonon range fracton range

ln(I re

d)

, cm-1

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.

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Light to vibration coupling Light to vibration coupling functionfunction

The light-vibration coupling functionThe light-vibration coupling function is a weighting function is a weighting function from frequency. It indicates a contribution into the scatteringfrom frequency. It indicates a contribution into the scattering whichwhich is produced by fractons with this current frequencyis produced by fractons with this current frequency. . The The contribution depends on fracton wave functioncontribution depends on fracton wave function::

wherewhere is ais a superlocalization exponentsuperlocalization exponent..

A number of fracton wave functions for different values of frequency

C

,exp~ 2/

lrlr fd

f

The light-vibration coupling function behaves like power-law The light-vibration coupling function behaves like power-law dependence from frequencydependence from frequency::

./2 ddd fC

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Effective density of Effective density of vibrational statesvibrational states

The effective DOVS function can be obtained from the The effective DOVS function can be obtained from the scattering intensity spectrum immediately. It equals to the scattering intensity spectrum immediately. It equals to the reduced intensityreduced intensity::

Since the effective DOVS is a product of functions with Since the effective DOVS is a product of functions with power-law dependence, it could be expressed as wellpower-law dependence, it could be expressed as well::

Structural parameter is a superposition of structural and Structural parameter is a superposition of structural and vibrational properties of the mediumvibrational properties of the medium::

.121

effd

x

ggC

./22 fdddx

.

1

effred ggC

nII

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Scheme of equipmentScheme of equipment

1. Argon laser with output power ~100 mW excited at 514 1. Argon laser with output power ~100 mW excited at 514 nmnm

2. Sample, contained in glass medicine ampoule2. Sample, contained in glass medicine ampoule3. Cylindrical lens3. Cylindrical lens4. Automated spectrometer DFS-244. Automated spectrometer DFS-24

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Initial spectraInitial spectra

20 40 60 80

I, a.

u.

cm-1

Glycerol

Ethanol

Water

Acetone

The obtained Raman spectra of pure H-bonded substances are presented left. This spectra are reduced and presented right in log-log scale.

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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-Including of the molecule of another sort into the hydrogen-bond network leads to the structural rearrangement of bond network leads to the structural rearrangement of medium and changes it’s features.medium and changes it’s features.

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Behavior of structural Behavior of structural parameterparameter

The concentration dependences for water-glycerol, water ethanol The concentration dependences for water-glycerol, water ethanol and water- acetone solutions reflects the structure competition and water- acetone solutions reflects the structure competition between the H-bond networks of their components.between the H-bond networks of their components.

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DiscussionDiscussionThe 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.

cSNNNtd ff 1221 ,,

1N 2N

cS12

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ConclusionsConclusions The employment of low-frequency Raman scattering with The employment of low-frequency Raman scattering with

the fractal conception involved allows us to investigate the fractal conception involved allows us to investigate macroscopic parameters of a media caused by its macroscopic parameters of a media caused by its microscopic features: peculiarities of instantaneous microscopic features: peculiarities of instantaneous short-range structure of intermolecular arrangement and short-range structure of intermolecular arrangement and the propagation of vibrational excitations.the propagation of vibrational excitations.

The fractal conception provides useful mathematical The fractal conception provides useful mathematical methods for describing complex-ordered dynamic media, methods for describing complex-ordered dynamic media, thus conserving the general form of relations which thus conserving the general form of relations which describe collective effects. describe collective effects.

It is apparent for the solutions under investigation that It is apparent for the solutions under investigation that the low-frequency range of the Raman scattering the low-frequency range of the Raman scattering spectrum is sensitive to the changes in concentration of spectrum is sensitive to the changes in concentration of the measured solution. This could be used as the optical the measured solution. This could be used as the optical method for concentration identification in transparent method for concentration identification in transparent solutions of associated liquids. solutions of associated liquids.