ACOUSTICAL INVESTIGATION OF CLASSICAL KNESER LIQUIDS

Transcription

1 Molecular and Quantum Acoustics vol. 8 (007) 187 ACOUSTICAL INVESTIGATION OF CLASSICAL KNESER LIQUIDS Bogumił B.J. LINDE*, Nikołaj B. LEZHNEV** * Instiute of Experimental Physics, University of Gdańsk, Gdańsk, POLAND, ** Academy of Sciences of Turkmenistan, Ashgabat, TURKMENISTAN. In this paper the experimental values of acoustical parameters determined from ultrasonic spectroscopy for eleven Kneser liquids are presented. The experimental data give the possibility to calculate several values describing acoustical relaxation. From these results it was possible to conclude that in the relaxation process with one relaxation time all vibrational degrees of freedom take part. 1. INTRODUCTION The Kneser relaxation is present in polyatomic gases as well as in unassociated polyatomic liquids where the basic fluid particles are simple molecules. When ultrasound waves travel through such a fluid, the energy is taken by the molecules as kinetic energy in the direction of the wave propagation at first ( due to compression mechanism), and than it flows into other degrees through the collision mechanism. In an analogous way, energy is taken at first from the translational degrees of freedom in the direction of the wave during expansion. While few collisions are sufficient to set up energy equipartition among translational degrees and, in general, the rotational degrees of freedom, many collision are needed to change the energy distribution in the vibrational degrees: a relaxation time of appreciable value is therefore associated with the establishment of equilibrium between the degrees which rapidly adjust to pressure changes (translational + rotational) and the vibrational degrees [1]. From acoustical measurements in wide frequency range it is possible to determine relaxation time τ (eq.1.), specific thermal heat C i (eq..) and active vibrational degrees of freedom [].

2 188 Linde B.B.J, Lezhniv N.B. α f A + B 1+ ω τ = (1) Ac CpCV C i(acoust) = π ( Cp - CV ) () τ where: A and B represents the absorption for where: C p, C V, C i specific thermal heats at low and high frequency range, τ - relaxation constant pressure, volume and for vibrational time, ω = πf c, f frequency degrees of freedom, c ultrasound velocity.. EXPERIMENTAL PART The ultrasonic absorption spectra α/f (f) were measured by the ultrasonic pulse method in the frequency range from 10 MHz to 3 GHz [3] and ultrasonic velocity were obtained using an ultrasonic pulse-phase interferometer [4,5]. The temperature was stabilized with accuracy of 0.01K. The measuring errors ranging from 7-4 % for attenuation in the frequency range MHz, and from % in the frequency range GHz. The liquids used were of analytical purity and were used after additional distillation and they were made by Fluka AG and Buchs IG. In this paper the results of acoustical investigation in the following chemical substances: Br, CS, CCl4, CHCl3, CHBr3, CH3 I, CH Cl, CH Br, (CH Br), C4H4 S are presented. 3. RESULTS AND DISCUSSION Acoustical spectroscopy in the frequency range from 0.3 to 3 GHz [19] gives a possibility to investigate of liquid substances, where exists acoustic absorption, higher than classical one, caused by vibrational relaxation. Observed dispersion was used for estimation of relaxation parameters to prove the interpretation of obtained results. Mathematical formalism [6] of experimental data handling allow as to take an advantage of computer calculation what make the description of a great number of measured data easier. The procedure of obtaining the information about the irreversible process from acoustical experiments were following: 1. From the experimental results of dependence α/f against f the characteristic frequencies fc of relaxation processes were estimated [3].. Asymptotes: low frequency range A and high frequency range B, the branches of relaxation curve α/f (f) were calculated from the fitting procedure []. 3. From the experimental values of ultrasound velocity c0 for the low frequency range:

3 Molecular and Quantum Acoustics vol. 8 (007) 189 f << fc, (ωt << 1), A and fc the dispersion quantities D were calculated (eq.3), c D = c0 ( 1 ε) 1/ μ max π ε π 4 (3) α/f = (η v η s ) ρ 3 o c 3 + π 4 (4) ( α/f ) class. = η 3 s (5) 3 o ρ o c o where: c 0, - ultrasound velocity for f above the relaxation process, c o ultrasound velocity for f below the relaxation process, η v i η s - volume & shear viscosities. 4. The relationships (6) was used for calculation of acoustical force ε, Afcc0 1 B Afcc Mv ε = (6) 0 α T T κ π 4 A τ 0 = 1+ C 0 p (7) In Table 1. the results of computed acoustical data are presented. As a basic information ultrasonic velocity and absorption of investigated organic liquids were taken. The values of classical absorption were calculated from eq. 5, without taking into account the thermal conductivity (it is negligible for these liquids [7,8,9]. The continuation of the analysis would not be possible without the other data measured or found in the literature: coefficient of thermal expansion αt, and specific thermal heat - Cp 0. It was also necessary to measure shear viscosity - η, density - ρ, and molecular weight M for all investigated compounds. The values of these parameters are presented in Table. They were found in the literature [13,17,18] or calculated with a help of known methods for estimation of viscosity and thermal coefficient of expansion at different temperatures. 5. All these physical data of the investigated compounds allow us to calculate the values of relaxing volume viscosity η v, from the equation (4); the ratios of viscosities η S /η v, nearly in all investigated liquids were smaller than 1 and it indicated the possibility of existence of relaxation in high frequency range.

4 190 Linde B.B.J, Lezhniv N.B. Table 1. Acoustical values of measured liquids with vibrational relaxation Substance Br CS CCl 4 CHCl 3 CHBr 3 CH 3 I CH Cl CH Cr (CH Br) C 4H 4 S Parameters T [K] A[10-15 s /m] B[10-15 s /m] α/f ) class [10-15 s /m] f c [10 6 /s] c 0 [m/s] D μ m τ C i [Jmol -1 K -1 ] τ [10-9 s] In equation () the values of C v were calculated from κ = Cp/Cv values, which were estimated using the values of ultrasound velocities from relation (7). All these results as well as those taken from the literature as determined from acoustical measurements of Kenser liquids are presented in the Table 1 &. In the Figs. 1 examples of ( f ) and c (f) for some examined compounds are shown. f α Fig. 1. Absorption in liquid Br at T=01K. Fig.. Dispersion of acoustic waves in liquid Br at T = 301K. In the Fig. 3-4 the influence of solved bromine, in benzene, for value of the relaxation time in the mixture of Br + C6H6 and the relaxation process in Br is shown. The value of specific heat Cv is calculated in agreement with theory, it refers to gas state. The investigation in the liquids from the group so called Kneser liquids showed that it is possible to use it successfully to liquid state as well.

5 Molecular and Quantum Acoustics vol. 8 (007) 191 It is necessary to notice that for kinetic and thermodynamic characteristic of observed relaxation in non-associated liquids with high volume viscosity some kind of impurities has a great influence[10-15]. It is main reason of discrepancies of the ultrasonic waves absorption data of these kind of compounds (benzene, CO, CCl 4 etc). It is possible to notice it from the example presented in fig. 5 for the mixture of water and pyridine. Fig. 3. Illustration of chemical reaction influence of Br and benzene on the kinetic of vibrational relaxation. Fig. 4. Relaxation (μ =αλ) process in gaseous bromine in a function of (f/p). From Fig.6 it is also clear that the influence of added methanol caused the change of relaxation time in bromine. Fig. 5. Molar (mol) and mass (m) concentration dependence of ultrasonic absorption (ωτ<<1) in the mixtures of pyridine and water. Fig. 6. Influence of little quantities of methanol in bromine for characteristic relaxation frequency.

6 19 Linde B.B.J, Lezhniv N.B. From these investigations it was concluded, that absorption in the low frequency range in pyridine was lowering with a time with no change of the conditions. This abnormal behaviour was the result of high hygroscopic properties of the compound and it was connected with shortening of the relaxation time with water absorption. Growth quantity of water in pyridine about 1% decreases absorption twice. A mutual solubility of some compounds is sometimes limited e.g. water and benzene. However, it is known that benzene absorbs this small amount of water very quickly from the surrounding if there is a close contact with atmosphere. Thus, the reason of lowering of ultrasonic absorption data in benzene for low frequencies ωt<<1 is mainly a contamination of benzene by water. As a consequence experimental values of A, μm, ε, Ci and τ are also considerably changed. Interpretation of the results in this case leads to false conclusions. Table. Physical parameters of the liquids Substance Br CS CCl 4 CHCl 3 CHBr 3 CH 3 I CH Cl CH Br (CH Br) C 4H 4 S Parameters M [10-3 kg mol -1 ] ρ [10 3 kg/m 3 ] α t [10-3 K -1 ] n 0 d T melt. [K] T boil. [T] T exp. [T] C p [Jmol -1 K -1 ] Κ[C p /C v ] η S [10-3 Puaz s] η v [10-3 Puaz s] η v/η S CONCLUSIONS Now it is clear that characteristic features connected with dependences of absorption in the frequency range ωτ << 1 are resulted in small amount of impurities of liquids with short relaxation time in the liquids with the longer relaxation time, as well as existing intermolecular energy exchange VV' between the vibrational level of different molecules [16]. Majority of liquids are characterized by short relaxation time and practically their addition to other liquid causes non-linear shortening of the relaxation time [0]. Thus, it is necessary, to be very careful when the objects are prepared for investigation. processes. All eleven compounds chosen for investigation demonstrate the acoustical relaxation

7 Molecular and Quantum Acoustics vol. 8 (007) 193 All possible methods of purification should be applied to liquids before final measurements of their acoustic parameters. (pollution). The acoustic absorption could be used for quantitative controlling of some admixtures ACKNOWLEDGEMENT The work was supported by the National Research Committee (KBN grant dec 17/E 335/S/ 005) for international cooperation. REFERENCES 1. A.J. Matheson, Molecular Acoustics, Wiley-Interscience a division of John Wiley & Sons Ltd, London, New York, Sydney, Toronto B.B.J. Linde, Acoustical spectroscopy of cyclic & heterocyclic compounds, ketones and polluted water surface, Wydawnictwo Uniwersytetu Gdańskiego, ISBN N.B. Lezhnev, Issledovanie kolebatelnoy relaksaci v zhidkostyakh metodami akustitcheskoy spektroskopi na sverkhvysokikh chastotakh, Doctor Thesis, Ashgabat J. Wehr, Pomiary prędkości i tłumienia fal ultradźwiękowych, PWN, Warszawa W. Ilgunas, Yaronis, W. Sukackhas W., Ultrazvukovyye interferometry, Wilnius "Mokslas" (1983). 6. N.B Lezhne, Ch. Orazdurdyev, G.P. Stanev, Izvestya Akademi Nauk Turkmenistana 3, 80-8 (1984). 7. I.G. Mikhaylov, V.A. Soloviev, Q.P. Syrnikov, Osnovy molekularnoy akustiki, Nauka, Moscow V.F. Nozdrev, N.V. Fedorishtchenko, Molekularnaya akustika, Izdateląstvo "Wysshaya Shkola" W. Schaaffs, Molekularakustik, Springer Verlag, Berlin - Göttingen - Heidelberg T. Hornowski, A. Skumiel, M. Labowski, Molecular and Quantum Acouostics 5, (004). 11. B. Linde, Molecular and Quantum Acoustics 7, (006). 1. E. Zorebski, Molecular and Quantum Acoustics 6, (005). 13. Landoldt-Börnstein, Zahlwerte unf Functionen aus Physik-Chemie-Astronomie- Geophysik und Technik, 5 Teil, Bandtei a, Springer Verlag, Heidelberg-New York P.A. Bazhulin, Doklady Academy of Sciences of Soviet Union 14, 5, 73-4 (1937). 15. W.P. Mason, Physical Acoustics, Vol. II Part A, Properties of gases, liquids, and Solutions, Academic press, New York and London B.B.J. Linde, N.B. Lezhnev, J Mol. Structure 754, 1-3, (005). 17. J. Timmermans, Physico-chemical constants of pure compounds, Elsevier Publishing Company, New York J. Timmermans, Physico-chemical constants of pure organic compounds, Amsterdam- London-New York 1965.

8 194 Linde B.B.J, Lezhniv N.B. 19. B.B.J. Linde, N.B. Lezhnev, Ultrasonics 38, (000). 0. B.B.J. Linde, N.B. Lezhnev, accepted for publication in Ultrasonics, 006.