Manikiam, B

Narasimham, A V

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NOTEIndian J. Phys. 68B (6), 549-555 (1994)U P  B- an international journalUltrasonic relaxation in some organic liquids and their activation energiesA V Narasimham and B Manikiam *Department of Physics, Indian Institute of Technology, Madras 600 036, India Received I! March 1994, accepted 19 July 1994Abstract : The concept of the complex and frequency dependent bulk vis^ cosity coefficient of a liquid is used to obtain expressions for the ultrasonic relaxation time in terms of absorption and dispersion of the wave in the liquid. Available experimental data on ultrasonic absorption and dispersion are used to calculate the ultrasonic relaxation times in nine liquids at various temperatures Variation of relaxation time with temperature is used to calculate activation energies for these liquids. It is found that the orders of magnitude of relaxation times and values of activation energies are fairly reasonableKeywords : Ultrasonic relaxation, activation energies, organic liquids .PACS Nos. : 43.35 B f, 43.35. Fj, 62.60 vPropagation of low intensity ultrasonic waves and measurement of their absorption and dispersion in liquids form an important method for the evaluation of various thermodynamic and inter and intra-molecular processes in liquids. Absorption and dispersion can be connected to the inter [1,2] and intra [3,4] molecular relaxation times. The response of the medium, under the action of an ultrasonic wave, is not exactly in phase with the applied pressure wave, due to inertia of the molecules (or atoms) and various intermolecular (or atomic) forces operating in the medium, leading to a phase shift between cause and effect. This phase shift leads to an intermolecular ( compressional) relaxation in the liquid, leading to absorption and dispersion of the wave in the liquid. A part of the energy o t e wave is utilised to excite internal modes (rotational, vibrational etc.) leading to intramo ecu ar relaxation. This paper discusses evaluation of intermolecular ultrasonic relaxation times using the concept of the bulk viscosity [1] coefficient of a liquid. The tem r^ature variations of relaxation times are used to evaluate the molecular activation energies (U).•now in India Meteorological Department. New Delhi-110 003. India © 19941ACS68B-(11)550 A V Narasimham and B M anikiamThe complex (*) and frequency (co) dependent bulk viscosity coefficient [1] of a liquid is closely connected [2] with ultrasonic absorption [5], dispersion and relaxation [1] by the following equations :andIh = T]i(co) -i7i2(coXn i ( 0>)-Tii(oo) = [ r j ,(0 ) -  rj,(oo)] [ 1 / (I  +  T )^,rj2(<o)= [T}t(0) -r7i(~)] [o)t/(1  +(1)(la)(lb)7Ji(0) and Tji(oo) are the values of the in-phase component rji(fi>), at very low and very high frequencies, mis the angular frequency of the ultrasonic wave, propagated through the liquid; Tis the bulk viscous relaxation time, associated with dilatational processes in the liquid, r is connected witii the transition of the molecules from one equilibrium position to another, due to compressional viscosity of the medium. We also have the following equations(a/co^) = [77l(^ o) + (4/3)^7,)/2pVo^2 p  K ( V - V o )  =  corj2(co),and(2a)(2b)where a  is the amplitude absorption coefficient of the wave, is the shear viscosity coefficient of the liquid, p is the density of undisturbed liquid, Vq is the wave velocity at very low frequencies, V is the velocity at any frequency co, and rf2(co) is the imaginary component of rj^(m). For liquids that are considered in the present context, T]i(m) ))rj .^ Hence, rj^ can be neglected in eq. (2a) without much error. Also, Tjj(m) decreases with m, according to eqs. (la) and (2a). Hence, 7]^  (oo) ))r]i {co)< rf] (0). Making these approximations, we get from eqs. ( 1) and (2)lV2X r: (I/O)) [{t7,(0) -  77,(o>)}/r7,(ft))] Combining eqs. (2a) and (3a), we also set(3a)(3b)where /./and « ./ refer to low and ultrasonic frequencies. We also have, according to eqs. (lb) and (2b)[<ot]2((o)] = [ { t?i(0) -or [o)rj2(‘B)l«»-*- = [J?i(0) -  r7i(«>)]/T =Oh (0)/t,and also [fit) rj2(<»)] <b-»~ = 2pV o(V „- V©).But according to eq. (2a), we also have Tj,(0) ~ 2  pVb^  ia/(0^\f Combining eqs. (4), (5) and (6), we get for r,T = [VoV(V»-Vo)](o/fiJ?)v(4a)(4b)(5)(6) (7)Ultrasonic relaxation in some organic liquids etc From eqs. (1) and (2), using the aforesaid approximations,we get CUT ~  T72(ct^/ni(cu) =(V-V'o)/[V'o2(a/cu)], or T =  ( V  -  V o) /  [ ft? ( aUsing eqs. (lb), (2b), (4) and (5), we also get r^ (\/c o )  [ (V -V o) / (V ^-V )F .(8)(9)( 10)551Eqs. (3b), (7), (9) and (10) give various expressions for ultrasonic relaxation time ( r) due to bulk viscosity of the medium. We also haveT= Toexp(U/kT)y ( 1 1 )where tb is a constant (independent of temperature, 7), U is the molecular activation energy, associated with transition of molecules from one equilibrium position to the next, k is Boltzman’s constant and T is in degrees Kelvin. A plot of log t v s  1 /7^ A gives ib and U.Experimental data required for these calculations are obtained from literature |6-17]. All the data required for the aforesaid eqs. (3b), (7), (9) and (10) are not available neatly in all the references. For example eq. (3b) requires co, (oJco^)if and (alco^)uf at the same frequency, but at various temperatures for evaluation of r at these temperatures and hence U.F igu re 1. Variation o f  log rw ith 1/T® A for 1,2-dibromopropane.D ifferent workers [6-17] have presented their experimental data at slightly different frequencies, at various temperatures. Thus, the values of (a/(B?),./and (a/ai^)^/ at vanous temperatures used in the present calculations, refer to slightly different frequencies, and not (stricUy) at a single frequency. This may result in a very negligible error in the values of rand552 A V N arasim h am  a n d  B  M an ikiamF ig u r e  2 . V a ria tio n  o f  lo g  r w ith  \fT°  A  for 1,2 -d ich lorop rop an eF igu re  3 . Variation o f  log rw ith 1/7*® A for 1 J,2-trichloroethane.practically no error in U. Experimental data required for these calculations are chosen from the data, reported by various [6—17] authors. Hence, these data are not reproduced here. Likewise, Vq, and (a/to^),/required for evaluation of Tat various temperatures, are obtained by suitable extrapolation of the existing data [6-17] on the frequency scale. TheseUltrasonic relaxation in some organic liquids etc 553F igu re 4 . Variation o f  log rwith 1/7 ° A for l-bromopropanc.extrapolations are not shown here. Values of (0, (a/tb^^and V, for the various calculations refer to ultrasonic frequencies, between 5 to 15 MHz (even more in some cases), at various temperatures. Thus, the relaxation times are calculated for nine liquids, using one (or other) of the four eqs. (3b), (7), (9) and (10), making a suitable choice of the equation, according to available data, at various temperatures. These values are given in Figures 1 to 4 (and hence, no table is presented for the variation of T with T), for four liquids. The circled dots (0 )  are the experimental points, in Figures 1 to 4. In addition, simijar calculations are made, and similar plots between logtand l/T^A are drawn, in the case of five more liquids, shown in Table 1, which gives the values of T,to and U for all the nine liquids.It may be noted from Table 1, that the order of magnitude of the relaxation times m these associated liquids is fairly large. Acetic acid has the largest relaxation time. It may be reasonable to have relatively large values for T. in associated liquids which exhibit relaUve y high ultrasonic absorption (and hence large relaxation time). The acuvation energies ( U) are small (about 0.1 to 0.3 eV). consistent with known activation energies for many liquids. Itmay be noted that f/depends upon the rate of change of rwith T and does not depend much554 A  VNam sim ham  and B  Manikiamon the absolute value of T . Xq gives the relaxation time at very high temperatures (7* —» or(l/lT ) -^0). Examination of Figures 1 to 4 shows some non-linearity in the variation of log r 1/r, at higher values of 1/r, or lower temperatures. This may be, partly, due to the factT a b le  1. V alues o f  activation energies and relaxation tim es using existing data  and equations (3b), (7). (9) and (10).liquid r  in sec at 303®Ax 10* secActivation energy (eV)1. 1,2-cUbfoniopropane 2.985 5.577 X lOr'^ 0.17442. 1,2-dicliloropfopane 2.113 1.97) X 1(T‘2 0.18203. 1 , 1,2-lrichloroethane 4.677 7.584 X IC r'* 0.23154. 1-bfOfnopropane 0.3715 4.563 X 10r>* 0.27785. n-propyl alcohol 0.3278 6.673 X 10-'^ 0.0898(at243°A )6. Pentachlorobiphenyl 9.797 5.136 X 10” '^ 0.23817. 2-methyl pentanediol [2,4] 1.126 3.814 X 10"'^ 0.19858. H exanetrial [1,2,6] 4.624 4.890 X 10-'^ 0.24479. Acetic A d d 54.12 1.325 X 10-'” 0.154that shear viscosity ( 77J  has been neglected in the above equations, and usually, 77^  increases as temperature decreases. Thus, these equations may not be valid well at low temperatures. Possible error (slight) in experimental data may also lead to some experimental points away from the linear plot. However, more experimental points may be needed, to confirm the deviation from linear behaviour of the log Tvs I/T  plots.In conclusion, it may be added that measurement of ultrasonic absorption and dispersion in liquids provides a very convenient way to study their molecular properties.AcknowledgmentOne of the authors (BM) wishes to thank the Council of Scientific and Industrial Research^ India, for the award of a research scholarship to carry out this work.R e fe re n c e s[1] A  V  N arasim ham , IEEE Transactions on Sonics and Ultrasonics SU  16 p 182 (1969)[2] L  H all Phys. Rev. 7 3  775 (1948)[3] L  T isza  Phys. Rev. 61 331 (1942)[4] J  M  M  P inkefton  Proc. Phy. Soc. (London) B 62 129 (1949)[5] K F  H erzfe ld  and T  A  L itovitz  Absorption and Dispersion of Ultrasonic Waves (N ew  Y ork : A cadem ic) Ch. 1 (1959)J K aipovich  J: Chem. Phys. 22 1767 (1954)[7] P  V igoureux Ultrasonics (New Y o rk : W iley) p  129 (1951)[8] A  B B h ^  Ultrasonic Absorption (London : O xford Univ. Press) p  171 (1967)Ultrasonic relaxation in some organic liquids etc 555[9] D Sette Phys. Rev. 78 476 (1950)[10] C Eckart Phys. Rev.73 6S (1948)[11] L N Liebeimann Phys. Rev. 75 1415 (1949)[12] J Lamb and J M M Pinkerton Proc. Roy. Soc. (London) A199114 (I949)[13] RM eisterrta/ J. Appl. Phys. 31 854(1960)[14] T Lyon and T A Litovitz J. Appl. Phys. 27 179 (1956)[15] T A Litovitz, T Lyon and L Peselnick J. Acoust. Soc. America 26 566 (1954)[16] J LambZ Electrochem. 64 136 (1960)[17] R A Padmanabhan J. Sci. Indus. Res. (India) 19 336 (1959)

Ultrasonic Relaxation in Some Organic Liquids and Their Activation Energies

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Ultrasonic Relaxation in Some Organic Liquids and Their Activation Energies

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