Indian Journal of Chemi stry Vol. 43A, September 2004, P ). 1876-1 88 1

Excess volume and vi scosity of ethoxy ethanol with n-butyl amine, sec-butylamine,

tert-butylamine, n-hexylamine, n-octylamine and cyclohexylamine

Me S Subha*, G Narayana Swamy, M Eswari Bai & K S V Kri shna Rao

Department of Chemistry, Sri Kri shnadevaraya Uni versity, An<1ntapur 5 I 5 003, Ind ia

Email : mcssubha@rediffmail .com

Recei ved 6 Jal/uC/I}' 2003; revised 28 JUI/e 2004

Densiti es and viscosities o f ethoxy ethanol (E EL) with 1/ ­

butylam ine (N BA), sec-butylamine (SBA), lert-butylami ne (TBA ), I/ -hexy lamine (N HA), I/ -octylam ine (NOA) and cyclohexy lami ne (C HA) have been measured at 308.15 K. From the ex peri me ntal data the excess volu me (0'), deviati on in viscosity ( llE) and the excess molar Gibb' s free energy of the activati on of viscous fl ow (C*E) have been computed and presented as function of composition. The parameter d l of the Grunberg and Nissan has been ca lcul ated . The observed vari ati ons of the properties for the above mi xtures conclude that the in teractions betwecn - unlike molecules predominate over the dissociati on effects in the individual components. It is al so evident that the presence of strong interac ti ons between unli ke molecu les is predominant and characteri zed by the negati ve vE and positi ve ll E, C *E and d l values. The excess volume, deviation in viscosity

and excess molar Gibb's free energy of the ac tivation of viscous fl ow have been fitted to Red lich-Ki ster equation to deri ve the coe ffi cient s and standard dev iati ons.

IPC Code: lilt C17. GOIN 9/04; GOI N 11 /02

In chemi cal industry there exi sts a continuing need fo r reliable thermodynamic data of binary systems. A survey of the literature shows that very few attempts t·3 have been made to study excess properties for mixtures containing alkoxy alcohols. Amines and alkoxy alcohols4

.5 in their pure state exhibit self­

association through hydrogen bonding. Amincs are better electron donors , which allow them to have specific interactions. Further, amines fo rm water insoluble compounds of medicinal importance. The molecular interaction study of alkoxy alcohols is of interest because of investi gating the effect of simultaneous presence of ether and alcoholic function al groups in the same molecule. The presence of etheri al oxygen enhances the ability of the -OH group of the same molecule to form hydrogen bonds with other organic molecules6

.7

. These characteri stics

of amines and alkoxy alcohols make them intcresting fo r our study. A survey of the literature has shown that no attempts have been made to study excess volumes and viscosity of binary mi xtures of ethoxy ethanol (EEL) with a series of amines whi ch include Il-butylamine (NBA ), sec-butylamine (SB A), terl-butylamine (TBA), n-hexy lamine (N HA), Il-octylamine (NOA) and cyclohexylamine (CH A) at 308.15 K aiming for a wider understanding of the molecular interacti ons involved.

Experimental Density measurements were made using bicapill ary

pycnometer hav ing a capill ary di ameter of 0.85 mm. The pycnometer was calibrated using doubly di still ed water and the necessary buoyancy correcti ons were applied. The density values were reproducible within ± 0.2 Kgm·3. A thermostatically contro lled water bath capable of maintai ning the temperature constant to ± 0.02 K was used for the studies.

Vi scosi ty measurements were made using Ubbelhocle viscometer. The time of efflux of a constant volume of liquid through the capill ary was measured with the help of a pre-calibrated ROCA R stop watch capable of recording ± 0.1 s. The viscometer was kept vertical in a thermostat at 308 .1 5 K and the efflu x time for water at 308. 15 K was fo und to be about 302 s. The flow time of pure liquids and liquid mixtures was measured a number of times and the average of the readi ngs was taken.

The vi scos ity was calculated from the average of effl ux time and density p accord ing to:

TJ/p = at-bit ... (1)

where a and b are the characteri sti c constants of the viscometer. These were determined by taking water, benzene, carbontetrachloride and acetonitrile as calibrating liquids. The kineti c energy correc ti ons were calculated from these values and they were found to be negli gible. The viscosity measurements were accurate to ± 0 .5x I 0-4 kg m·t s·t .

Ethoxy ethanol and all the amines were purchased from Merck KGOA, Germany. The chemicals were distilled and kept tightly sealed and protected fro m atmospheric moisture and carbondioxide as far as possible. Prior to measurements, all liq uids were kept

NOTES ]877

over 0.4 nm molecular sieves to reduce water content and were partially degassed under vacuum. The purities of these chemicals were checked by measuring their densities and comparing with those reported in literatures.9. Mi xtures were prepared by mixing weighed amounts of the pure liquids adopting the method of closed system. The measurements were made with proper care in an AC room to avoid evaporation losses.

Results and discussion The excess functions 1{ and 0, Grunberg and

Nissan lo interaction parameter i and the Gibb's free energy of activation of viscous flow C*E were calculated respecti vely from Eqs 2 to 5.

11 E = 11 - [x 11 1 + (I-x) 112] ... (2)

0 = V - [XVI + ( l-x)V2 ] . . . (3)

In 11= x ln 111 + (1-x) In 112 + x(1-x)i ... (4)

The molar volume V of a mi xture is calculated usi ng Eq.6.

V=M/p .. . (6)

where M = xM I + (I-X)M2' X is a mole fraction of component 1, MI and M2 are molecul ar weights of compounds I and 2 respectively.

The measured density (p) and viscosity (11) at 308.15 K for the mixtures of 2-ethoxyethanol (EEL) + II-butylamine (NBA), + sec-butylamine (SBA), + terl­butylamine (TBA), + II-hexylamine (NHA), + /l­

octy lamine (NOA) and + cyclohexy lamine (CHA) are used to calculate the excess molar volume (0), deviation in viscosity ( 11 E), excess Gibb 's free energy of activation of viscous fl ow (C*E) and Grunberg­Nissan interaction parameter (d l

) and the results are presented in Table I.

The vari ation of the parameters 0 and 11 E with the mole fraction of EEL (XEEL) for the systems under study are graphically shown in Figs 1 and 2 respectively.

The mixing quantit ies, yE (0, 11 E and C*E) were fitted to Redlich and Ki sterll type equation by least­square fitting.

5

yE = x( l-x) LA . (1- 2x)j-1 .1 = 1 J

... (7)

In each case, the optimum number of coefficients, Aj ,

was determined from an examination of the variati on of standard devi at ion, cr( yE) as calculated by

... (8)

where m is the number of ex perimental data and II is the number of coefficients in Eq. 8. Aj coefficients considered (n = 5 in the present case), have been presented in Table 2.

From Table ] , it is observed that the vi scosity of binary liquid mixtures under study varied non-linearly with the mole fraction of EEL (XEEL) . This suggests the presence of intermolecul ar interactions between unlike molecul es of these mixtures. A simil ar observation was made by Narayana Swamy et al. s

from the viscosity studies of binary liquid mixtures of acetonitrile + amines.

From Fig. ] , it is observed that 0 is negati ve over the whole range of composi tion and increases in the order of increase with size of the normal amine molecu le. But in the case of EEL + NBA, + SBA and + TBA positi ve 0 values are observed only at hi gher mole fractions of EEL. An interpretation to th is behaviour can be given using the experience made with the quantitative evaluation of alcohol + amine mixtures by the ERAS model proposed by the earl ier workers 12-16. The observed negative excess volu mes may be explained in terms of two opposing effects. Mixing of EEL with different amines will induce the mutual dissociation of component molecul es and the fo rmation of hydrogen bonds between unli ke molecules. The former effect leads to positive excess volume and the latter effect leads to negative excess volume. The actual volume change wou ld depend upon the relative strengths of the two effects. The observed negative values of 0 show that the main contribution to 0 is due to hydrogen bond formati on (OH ...... N) between unlike molecules. Moreover, the negative values of VI:: may also be partly due to the specific acid-base interactions between EEL and amine molecules by considering EEL as Lewis acid and amines as Lewis bases . Very recently Nam­Tram l7 emphasized the importance of acid-base interactions between tert-butyl alcohol and N,N­dimethy lformamide/N ,N-dimethyl acetamide in order to evaluate the interacti on energy of alcohol-amine systems.

From the examination of the results in Table J and Fig. J, it is observed that the negative values of 0 fall

1878 INDIAN J CHEM, SEC A, SEPTEMBER 2004

Table I-Values of density (p), viscosi ty (11), deviation in viscosity ( llE), excess molar volume (\/'\ excess Gibbs free energy of activation of viscous now (C' E) and Grunberg-Ni ssan interaction parameter (d') for the binary mi xtures of 2-ethoxyethanol (EEL) + ami nes at 308. 15 K

Mole fraction px l0') 11 x I 03 1{x103 V'x 106 C*Ex103 (/'

of EEL, XEEL Kg m') Kg m" s-' Kg m" s" m3 mol" N mar'

2-Ethoxyethanol + II-butylamine 0.0000 0.7239 0.4249 0.0000 0.0000 0.00 0.0802 0.7445 0.5335 0.0261 -0.7426 74.48 1.7487 0.2044 0.7654 0.6473 0.0122 -0.373 1 101.62 1.0430 0.3059 0.7857 0.7671 0.0276 -0.4824 128.51 1.0 I 07 0.4065 0.8055 0.8896 0.0466 -0.5316 143.17 0.9908 0.5068 0.8248 1.0066 0.0605 -0.5120 143.41 0.9572 0.6065 0.8426 1.l148 0.066 1 -0.3183 132.04 0.9 165 0.7058 0.8599 1.2089 0.0581 -0.0726 108.38 0.8555 0.8434 0.8779 1.2947 0.0024 0.9432 52.99 0.5828 0.9024 0.8978 1.3757 0.0227 0.0155 39.98 0.7391 1.0000 0.9173 1.4534 0.0000 0.0000 0.00

2-Ethoxyethanol + sec-butylamine 0.0000 0.7083 0.3996 0.0000 0.0000 0.00 0.1045 0.7325 0.5211 0.0114 -0.4649 77.25 1.3953 0.2080 0.7553 0.64 19 0.0231 -0.706 1 12 1.68 1.2471 0.3105 0.7778 0.7668 0.0400 -0.8908 148.4 1 1.1719 0.4120 0.7985 0.8957 0.0619 -0.8367 163.63 1.1361 0.5124 0.8184 1.0158 0.0762 -0.6902 162. 17 1.0863 0.6 188 0.8394 1.1303 0.0786 -0.5059 144.55 1.0209 0.7103 0.8567 1.2171 0.0690 -0.2457 119.07 0,9557 0.8078 0.8762 1.3045 0.0536 -0.0805 85.42 0.9024 0.9043 0.8954 1.3845 0.0319 0.1080 46.67 0.8668 1.0000 0.9173 1.4534 0.0000 0,0000 0.00

2-Ethoxyethanol + tert-butylamine 0.0000 0.6812 0.4126 0.0000 0.0000 0.00 0.1082 0,7121 0,5474 0.0222 -1.0918 83 ,61 1.5181 0.2 145 0,7389 0,6798 0,0439 -1.4979 132.03 1,3607 0.3189 0,7644 0.8102 0.0657 -1.6928 157.87 1.2583 0.4214 0.7897 0.9309 0.0797 -1.8460 162.93 1. 1611 0.5221 0,8 136 1.0461 0,0901 - 1.8 124 156.85 1.0940 0.6211 0,8361 1.1494 0.0904 -1.6109 139.28 1.0304 0.7182 0,8547 1.245 1 0.0850 -0.9740 117.13 0.9891 0.8138 0.8732 1.327 1 0.0675 -0.3580 86.09 0.9475 0.9077 0,8934 1.3994 0.0421 0.03 18 48.40 0.9355 1.0000 0,9173 1.4534 0.0000 0.0000 0.00

2-Ethoxyethanol + II-hexy lamine 0,0000 0.7522 0.6 0.0000 0.0000 0.00 0.1321 0.7732 0.7283 0.0156 -0.7523 46.75 0.6710 0.2550 0.7921 0.8766 0,0590 -1.0886 94.12 0,8082 0.3698 0.8099 1.0256 0.1100 -1.2221 128.59 0.8967 0.4772 0.8274 1.1724 0.1652 -1.2981 152.36 0.9930 0.5779 0.8432 1.3048 0,2116 -1.1387 163.96 1.0890 0,6726 0.8589 1.4256 0.2516 -0.9785 167.00 1.2279 0.7616 0.8736 1.4689 0.2 190 -0.7139 137.36 1.2203 0.8456 0.8886 1.4569 0, 1353 -0.5051 86.39 1.0649 0.9249 0.9038 1.4449 0,0556 -0.3373 37.35 0.8723 1.0000 0.9173 1.4534 0.0000 0.0000 0.00

2-Ethoxyethanol + II-octy lam ine 0.0000 0.7702 0.9267 0.0000 0.0000 0.00 0.1595 0.7898 1.1 361 0,1254 -0.9703 87.4 1 0.9844 0.2992 0.7989 1,2384 0.1541 -0.1319 112.66 0.7408

COlltd.-

NOTES 1879

Table I-Values of density (p), viscosity (11), deviation in viscos ity (l1E), excess molar volume (vE), excess Gibbs free energy of acti vation of viscolls flow (C'E) and Grunberg-Nissan interaction parameter (dl) for the binary mi xtures of 2-ethoxyethanol (EEL) + amines at 308. 15 K-Colltd

Mole fraction px 10·3

of EEL , XEEL Kg m·3

0.4226 0.8254 0.5324 0.8421 0.6307 0.8579 0.7193 0.8726 0.7994 0.8862 0.8723 0.8975 0.9389 0.9083 1.0000 0.9173

0.0000 0.8527 0.1163 0.863 0.2284 0.8713 0.3366 0.8779 0.4411 0.8842 0.542 1 0.8856 0.6398 0.8957 0.7342 0.9008 0.8257 0.9056 0.9142 0.911 1.0000 0.9173

11x I 03 11 EX 103 vEx I 06

Kg m·1 S· I Kg m·1 S· I m3 mor l

1.51 24 0.363 1 -1.8569 1.6548 0.4477 -2.0284 1.7500 0.4911 -2.0446 1.7254 0.4198 -1.9074 1.6542 0.3065 -1.6499 1.5684 0. 1823 -1.1487 1.4968 0.0756 -0.6448 1.4534 0.0000 0.0000

2-Ethoxyethanol + cyclohexylamine 1.3249 0.0000 0.0000 1.3451 0.0053 -0.132 1 1.3662 0.0120 -0.3272 1.3912 0.0230 -0.4575 1.41 85 0.0369 -0.4810 1.4366 0.0420 -0.401 3 1.4572 0.0501 -0.2024 1.4594 0.0402 -0.0511 1.455 1 0.024 1 -0.0115 1.4501 0.0077 -0.0 175 1.4534 0.0000 0.0000

C'Ex 103

N mor l

195.85 220.63 226.52 191.43 141.04 86.38 36.90 0.00

0.00 0.80 3.34 8.66 15.00 20.0 1 21.16 17.38 11.08 4.08 0.00

1.2282 1.3668 1.5111 1.4756 1.3702 1.1997 0.9924

0.0425 0.0542 0.0792 0.1113 1.0744 0.1560 0.1472 0.1203 0.0723

Table 2-Coefficients AJ of Eq. (7) and standard deviations a( yE) of binary mi xtures of 2-ethoxyethanol + amines at 308.15 K

yE AI A2 A3 A4 A, a(yE)

2-Ethoxycthanol + Il -butylamine vEx I06(m3 mor l) -2.210 0.485 10.359 7.214 -20.782 0.511 ll ExlO\Kg m· 1 S· I) 0.280 0.178 -1.055 -0.355 1.536 0.081

C'Ex IO'{N mor l) 595.316 -37.670 -508.932 -403.974 1002.489 26.972

2-Ethoxyethanol + sec-butylamine vEx l06(m'mOr l) -2.899 3.027 0.715 1.147 1.304 0.206 11 EX IO\Kg n,- I S-I) 0.299 0.205 -0.279 -0.083 0.305 0.004 c*Ex I03(N mor l) 65 1.817 -1 3 1.994 - 102.927 -78.443 242.451 2.669

2-Ethoxyethanol + tert-butylamine vEx lO6(m3 mor l) -7.480 2.005 6.433 8.465 -5 .830 0.22 1 11 EX IO\Kg m·1 S· I) 0.354 0.139 -0.036 0.045 0.075 0.005 C'Ex l0\ N mor l) 635.858 -1 96.8 13 121.104 18.619 26.747 3.866

2-Ethoxyethanol + Il-hexylamine vEx I 06(m3 mor I) -5.087 1.684 2.6 11 -0.029 -5.770 0.151 11Ex lO\Kg m·1 S· I) 0.725 1.11 9 0.300 -0.945 -1 .026 0.046 C 'Ex IO\N mor l) 632.077 343.734 59.898 -329.378 -454.088 18.855

2-Ethoxyethanol + II-octylamine vEx IO\ m3 mor l) -7 .628 -1 3.652 14.882 25.265 -34.761 1.655 l{ x lO'{Kg m·1 S·I) 1.737 2.175 -2. 146 -3.386 2.749 0.0827 C'Ex lO\ N mol·l) 868.494 692.324 -773.922 - 1228.673 1017.518 36.326

2-Ethoxyethanol + cyclohexylamine vEx IO\m'mor l) -1.748 2.310 3.334 -2.587 -2.602 0.071 11 EX I O,{Kg m·1 S· I) 0.168 0. 187 -0. 106 -0.233 -0.044 0.009 C' Ex 103(N mor I) 73.332 90.1 82 -77.970 -93.337 22.004 1.012

1880 INDI AN J C HEM. SEC A, SEPTEM BER 2004

0.5

0.0

r--. -0.5 (3 E

M

E -1.0 '-' 'D

3 ><

til

> -1.5

-2.0

-2.5

Fig. I- Plo ts of excess vo lume (V' ) vs mole frac ti on o f 2-e thoxyethano l CrEEL) at 308.15 K for the binary mix tures of EEL with NBA (_ ), SBA (D), TBA ( .A ), NHA ( - ), NOA (0 ) and C HA (t-)

0.60

0.50 ,-.,

en -: E 0.40 bO ~

M

3 0.30 til ~

0.20

0.10

0.00

0.0 0.2 0.4 0.6 0.8 1.0

Fig. 2-Plots of dev iation in viscosity l1 E vs mo le frac tion of 2-ethoxyethanol (XEEtJ at 308. 15 K for the binary mi xtures of EEL with NBA (_ ), SBA (D), T BA ( .A ), NHA (_ ), NO A (0 ) and CHA

(M

in the sequence: EEL + CHA < + NB A < + SBA < + NHA < + TBA < + NOA.

From Fig. I , it is observed that the negati ve excess volumes of normal amines with EEL increase with increase in chain length of amines. This can be explained by considering amines as proton acceptors and EEL as proton donor. As the chain length of th e normal amines increases, proton-accepting ability of these amines increases and electron density wi ll be more and more on nit rogen atom of NH2 group due to inductive effect. So, as the chain length of the amines increases, the interacti on abili ty (hydrogen bond ing abili ty) of amines with EEL increases.

In the case of branched amines, negative yE va lues increases with increase in branching. Th is is very clear that as the amines become more and more branched, the proton accepting ability increases due to the increase in -CH.1 groups on the carbon atom attached to amine group. However, sl ight positi ve \I" val ues are observed at higher EEL mole fraction in case of NBA, SBA and TBA indicati ng lesser speci fi c interacti ons at these mole fractions. A similar observation was made by Haraschta el al. 18 from the yE studies of y-picoline + sec-butano l and + l ert -

butanol. In the case of cyclohexylamine, '0' values are less

negati ve than the corresponding normal hexy lamine, which may be due to steri c and other effects because of cyclic nature of cyclohexy lamine.

Figure 2 shows that 11E va lues are positi ve over the whole composition range fo r all the systems under study. A correlation between the si",ns of ll E and ,;E has been observed for a number of binary systems, t9.2U ll E being pos iti ve, where yE is negati ve and vice­versa. In general , for systems where di spersion and dipolar interac tions are operating llE values are fo und to be negati ve whereas charge transfer and hydrogen bonding interactions lead to the formation of complex species between unlike molecules thereby resulting in positive llE values9. The positi ve values of ll E fo r the mixtures of EEL + amines fall in the order: EEL + CHA < + NBA < + SBA < + TBA < + NHA < + NOA.

It can be predicted that in View of the strong proton donating ability of EEL and strong; proton accepting ability of amines, the overall negati ve yE va lues and overall positi ve l1 E values in all these systems may be regarded as an evidence for the formati on of 2 sets of hydrogen bonds between EEL and ami nes . Among them, the first set of hydrogen bond formati on is between N atom of amino group of am ine and H atom

NOT ES 188 1

of - OH group of ethoxy ethanol and the second set of hydrogen bond

H I

R-~--- -----H-O-C2H5-0-C2H5

H

fo rmatio n is between H ato m of amino group of amines and oxygen atom of e theric group of EEL. Among the two, the first set of hydrogen bond fo rmati on predominates.

H-------- O-C H -I I 2)

R-N C H --OH I 2 )

H

From Table 1, it is a lso observed that a ll the values of C*E are found to be positi ve whi ch is an indicati on of the presence of stro ng spec ific inte racti ons9 and fa ll in the order: EEL + C HA < + NBA < + SB A < + TB A < + NHA < + NOA.

F d M 1 1 11 1} ort an oore- and Ramamoorthy--'- reported

that for any binary liquid mi xture, the pos iti ve value of i indicates the presence of stro ng· interactio ns and the negati ve value of d l indicates the presence of weak interacti ons between the compo nents. On thi s bas is, the d l values in the present study for all the systems confirm the presence o f strong interac ti o ns between the compo nent molecul es. A simil ar observation was made by Subha et 0 1. 24 fro m the d l

values of the binary liquid mi xtures of propio nic ac id with a lcoho ls.

In conclusion, it may be sa id that the observed variat ion of the properti es of the mi xtures studi ed supports the view that the interactio ns be tween unli ke molecules predo minate over the di ssociati o n effects in the individual components. It is a lso ev ident that the

presence of strong interactions between unli ke mo lecules is predo minant and characteri zed by the negative 0 and positive ll E, C*E and d l values .

References Ramana Reddy K Y, Rambabu K, Devarajulu T & Kri shnaiah A, Phys Chelll Liq. 28 (1994) 16 1.

2 Pal A & Singh W, J Chelll Th erlllodYllalll ics. 29 ( 1997) 639. 3 Pal A, Illdiall J Chelll , 37A (1 998) 109. 4 Row linson J S, Liqllid alld Liqll id Mixtll res, 2nd editi on

(B utterworths: London), (1969) 159. 5 Pri gogine I, De fay R & Everett B H, Chelllical

TherlllodYllalllics Tra lls /ator (Lo ngman G reen & Co, London), ( 1953) 470.

6 Ful vio C, Marcheselli L, Tass i L & Tosi G, Call J Chelll. 70 ( 1992) 2895.

7 Pal A, Sharma H K & Singh W, Illd iall J Chelll . 34A ( 1995) 987.

8 Narayana Swamy G, Subha M C S & Srini vasa Rao P. AClistica, 75 ( 199 1) 86.

9 Ramana Reddy K N, Reddy K S & Krishnaiah A, J Chelll £ lIgg Data , 39 ( 1994) 6 15.

10 G run berg L & Nissan A H, Natllre (Londo n), 164 (19-19) 799.

II Redli ch 0 & Ki ster A T , J Illd £lIgg Gelll , 40 (1948) 345. 12 Bender M, Hauser J & Heintz A, Ber Bllllsel/ -Ges Pin's

G elll . 95 ( 199 1) 80 1. 13 Funke H, Wetzel M & Hei ntz A, J Pll re Appl Chelll, 6 1

(1989) 1429. 14 Hei ntz A, Naicker P K, Yerevkin S P & Pfestorf. Ber

BIII/Sell-Ges Phys Chelll , 102 ( 1998) 953. IS Mohren S & Heintz A, Flu id Phase £qlli/ib. 133 (1997) 247 . 16 Reimann R & I-le intz A, J SO/Il tioll Chelll , 20 ( 199 1) 29. 17 Nam-T ram H, J Phys G elll , 98 (1994) 5362. 18 Harasc hta P, He intz A, Lehmann J K & Peters A, J Chelll

£ lIgg Data , 44 ( 1999) 932. 19 Marcus Y, lOll So /vatioll (W il ey Intersc ience, New York).

( 1985). 20 Prolongo M G, Masegosa R M, Fuentes H I & Horta A. J

Phys Chelll . 85 ( 1984) 2 163. 21 Fort R J & Moore W R, TrailS Faraday Soc. 62 (1966) 11 12. 22 Ramamoorthy K, J Pllre Appl Phys. II ( 1973) 554. 23 Ra mamoorthy K, J Pllre App/ Phys. II ( 1973) 556. 24 Subha M C S, Rao K C, Swamy G N & Rao S B, J Ph),s

Gelll Liq, 18 ( 1988) 185.