TABLE2 - ACTIVATIONENERGIES(kJ/mol) OF CONDUCTANCfSAND FLUJDITIES*AS A FUNCTIONOF TEMPERATURECOMPUTEDUSII"oGDIFFERENTMODELSl'OR (a) Ca(N03) •.4.06H20+(69.68mol %) Co(N03)2.6.18H.O, (b) Ca(N03) • .4.03H.O+(7.02mol %) MnCI. AND(c) Cd(N03)..4.18H20+(12.49 mol %)

MnCI. MOLTENSALT SYSTEMS

T/K VTF CEM ERM EXPTL

SYSTEM(a)313.0 29.79 30.40 31.53 31.20

(35.88) (35.45) (35.95) (35.82)318.0 28.31 28.83 29.54 30.04

(34.lJ) (33.61) (34.14) (34.66)323.0 26.98 27.42 27.48 27.48

(32.50) (3\.96) (32.18) (32.48)328.0 25.76 26.13 25.44 25.19

(31.05) (30.46) (30.14) (29.98)333.0 24.66 24.97 23.46 22.90

(29.72) (29.1 0) (28.11) (27.48)338.0 23.65 23.90 21.60

(28.51) (27.84) (26.13)343.0 22.72 22.92 19.81

(27.39) (26.71) (24.25)

SYSTEM(b)313.0 44.18 46.03 41.64 41.60

(52.16) (54.04) (46.44) (46.20)318.0 41.33 42.93 41.20 41.13

(48.77) (50.41) (46.49) (45.76)323.0 38.81 40.21 40.22 40.21

(45.79) (47.20) (45.95) (45.29)328.0 36.57 37.79 38.77 38.82

(43.14) (44.31) (44.87) (44.83)333.0 34.57 35.64 36.97 36.97

(40.77) (41.84) (43.34) (43.90)338.0 32.77 33.72 34.91 35.12

(38.65) (39.58) (41.46) (41.60)343.0 31.J 5 31.98 32.71

(36.13) (37.54) (39.32)348.0 29.68 30.41 30.46

353.0(35.00) (35.69) (37.04)28.34 28.99 28.22

(33.42) (34.02) (34.69)

313.0SYSTEM(c)

32.17 33.55 30.Li 31.69

318.0(37.14) (38.96) (35.21) (36.97)30.48 31.10 29.54 29.58

(35.20) (36.82) (34.84) (34.66)323.0 28.95 30.05 28.67 28.44

328.0(33.46) (34.89) (34.14) (33.61)27.58 28.55 27.51 27.73

333.0(31.88) (33.16) (33.15) (32.62)26.33 27.19 26.30 26.10

338.0(30.44) (31.59) (31.92) (31.69)25.18 25.96 24.92

343.0(29.14) (30.16) (30.51)24.14 24.84 23.47

(27.94) (28.85) (28.98)348.0 23.18 23.80 21.99

(26.84) (27.66) (27.38).1<. "Activation energies for fluidity are given in parentheses.

For the purpose of comparison the values of theexperimental Ey and those computed from the deri-vatives of VTF, CEM and ERM equations, respec-tively, are listed together in Table 2. Such a com-parison- (Table 2) reveals a relatively better appli-cability of the ERM than those of the VTF andCEM equations to these systems. At this stage itmay be recalled that the superiority of the ERMequation over those of the VTF and CEM stems fromthe fact that only the ERM equation is meant to

NOTES

69· 68moLX or Ca+Co

,_ 30-0oE")

-:.... 2()'()LLo"",- 10-0

200 '·0n/<T-To)l2

8-0

Fig. I - Plots of EY(corr) versus [T/(T - To)]" for moltenCa(N03)2.4 .06H20-Co(N03) s-6.18H20 saltsystem

account for the overall transport behaviour, i.e. non-Arrhenius-Arrhenius regions of each plot.

One of the authors (K.D.) is grateful to the CSIR,New Delhi for awarding fellowship.

References1. ISLAM,N. & DHAWAN, K., Indian J. Chem., 20A(I981),

911.2. ISLAM,N. & KHAN, M. M., Indian J. Chem., 20A(l981), 13. ISLAM, N., KUMAR, S. & SINGH, K. P., J. chem, Soc.,

Faraday Transi Y, 75 (1979), 1830.

Controlling Factors of Transport Behaviour & TheirVariations with Concentration

N. ISLAM*& (Mrs.) K. DHAWANDepartment of Chemistry, AIigarh Muslim University,

Aligarh 202 001

Received 24 October 1980; revised 13 February 1981; accepted13 March 1981

The energy of activation of flow behaviour and the ideal glasstransition temperature seem to be the controlling factors indetermining the trend and the magnitude of flow behaviour. Atthe same time, they are independent of the models employed toexplain them. The concentration dependence of flow propertiesof several melts has been explained by an isoenergic equationbased on the constant T/To values in which T is the correspon-ding temperature while To is an ideal glass transition tempe-rature.

IN view of the fact that the flow properties areindependent of the model employed, an attempt

is made here to investigate the dependence of suchproperties on some physically meaningful para-meters irrespective of the model employed to ex-plain them. For this purpose, our reported- resultshave been examined in terms of Eq. (1)

A'y = IIG 00 't'o •.. (1)which envisages the dependence of pre-exponentialterm of Adam and Gibbs2 equation, A' y on themodulus of rigidity '(G00) of the system. With theincrease of concentration the system becomes

915

INDIAN J. CHEM., VOL. 20A, SEPTEMBER 1981

increasingly more rigid and therefore, a decreasein the average cooperative transition probability isexpected. In other words, the relaxing species willhav~ .greater period of vibration in their equilibriumposition as compared to those in dilute solutions.

This consideration has made it possible to under-stand the dependence of viscosity on the rigidity ofsupercooled liquids and glasses. The average rela-xation time is defined as," = "fJ/G = IG cp, whereGoo is the shear modulus and 00cp rep~sents thefluidity.

In the case of molten systems Ca(N03)2.4.03H20-MnC12 and Cd(N03)2.4.18HIP-MnC12, To shows alinear increase with increasing solute concentration,while a linear decrease with increasing solute con-centration is observed in those of Ca(N03)2.4.06H20-Co(N03t 6.18H20 and Ni(N03)2.6.0IH20-Mg(N03)2'6.13H20 systems. This discrepancy in the varia-tion of To with solute concentration can neither beexplained by invoking the concept of cationic poten-tial nor by that of the inverse dependence of To onthe square root of the solute concentration. Similardifficulties also arise in explaining a linear decreasein Ay with [solute] in the cases of Ca(NOa)2.4.03H20-MnC12 and Cd(N03)2.4.18H_O-MnCI2 systems,and a corresponding increase in the cases ofCa(NOa) .4.06H20-Co(N03)2·6.18H20 and Ni(N03h.6.0IH20-Mg(NOa)2.6.13H20 systems. Such a dis-crepancy has been viewed" as the outcome of thedifference in the lability of water of the hydrated ions.Thus, in an attempt to account for both the trendsencountered in the behaviour of Ay with [solute],Ay or A'y has been correlated- to To,

Ay = IX + ~To ... (2)which successfully demonstrates a similar trend inthe plots of Ay; versus To, i.e. Ayalways increaseswith an increase in the To values in all the systemsinvestigated. This may throw some light on theirbeing some sort of controlling factor in determiningthe flow behaviour. This is, however, not the casewith the behaviour of A" y of Doolittle equation withmolar intrinsic volume (Vo),

A"y = IX' + ~'Vo ... (3)

Such a difficulty is understood in terms of the rela-tion,

To = «" + ~"Vo ... (4)as shown in Fig. 1. In fact Vo should have beenreplaced by the free-volume, VI = V-Vo, whichshows an inverse dependence on To. In view ofthe fact that To is a measure of the potential strengthand so also the energy of activation, they have beencorrelated to yield,

Ecorr = [E'corr- Toco)(Qy/Q'y)]+(Qy/Q'y)To ... (5)

where E' con is the value of corrected energy ofactivation for the pure solvent at its glass transitiontemperature, T 0(0) while other parameters havetheir usual significance. In order to obtain thevalue of E' COTT, the corrected activation. energiesfor the pure solvent were plotted against the tempe-rature and extrapolated to To(o). Such an extra-polation is possible only if the variation of Ecorr withconcentration is linear. A linear increase of Ecorrwith To (Fig. 2) in the present cases provides anexperimental support to Eq. (5).

Thus the opposing trends encountered in thevariations of Ey values with increase in solute con-centration appear to be guided by the correspondingTo values which either increase with concentrationas a result of increase in the compactness, inter-molecular forces, and rigidity of the system or showa downward trend in order to achieve the lower To

To, A

194·0 19!1<l 202·0

Co+Co

1«1·0

~ 135·0

,,~ 1300

130·0 '--_-'--_--'-_--'--~'---""--....J'190·0· 194·0 196·0 202·0

To, </l

Fig, 1 - Variation of Vo with To for molten salt system,Ca(N03)2.4.06HcO-Co(N03)2.6.18H20 [Similar linear plotshave been obtained for other systems investigated]

135·0

TABU! I - COMPUTEDPARAMETERSOF ISOENERGICEQUATION

Molten salt system c Ao3Y QIY k.y To(o) Q2Y Std. dev. inIn Y

Ca(N03)2.4.06H20 +i.

1.6 2945.0 13.2 580.0 204.5 0.21 0,052

tCo(NO')2·6,18H2O (9050.0) (112.7) (679.5) (205.0) (0.58) (0.066)Cd(NO.) s-4.18H2O+ 1.8 4165.0 16.4 577.9 189.5 0.42 0.015MnCI. 0222.0) (95.3) (666.7) (189.3) (0.44) (0.027)Ca(N03).·4.03H20 + 1.7 2817,0 44.7 579,9 204,8 0.91 0.009MnCI. (8005.0) (77.7) (670.7) (205.3) (u.9:") (0.051)Ni(N03)2.6.01 H20 + 1.7Mg(N03)2·6.13H20 (7380.0) (10.5) (695.0) (194.5) (0.11) (0.043)

Fluidity data are given in parentheses.

916

NOTES

"7·0I~"0E38'0 ...,..:,(c1....

36·0 :;u

ILl

Ca + Mn

206-0 201-0 210-0 212·0To,~,1\

Fig. 2 - Variation of Ey(corr~ w.ith To. for molten salt system,Ca(NOs)sA.03H.O-MnCI. [SImilar linear ' plots have' been

obtained for other systems investigated.]i

values of the solute as anticipated on- the basis of theadditive nature of To. . .

Similarly, Ecorr has been correlated to the inverseof free volume in order to yield meaningful results.These correlations seem to provide bases for' under-standing the concentration dependence of the flowproperties satisfactorily.

In view of the linear dependence of the para-meters Ay, A'y, and To on concentration, thefluidity and conductance data were least squaresfitted (Table 1) to the isoenergic equation+s forseveral values of constant T/To (=c). The corres-ponding temperature T lying in the experimentalrange and the values of c which gave reasonably goodfits were selected. The linear plots of J/ln [Y{c(TO(Ol± Q_yX)}]l/2/(AoY± Q...yx) against x mol % sup-port such an analysis.

K. Dhawan is grateful to the CSIR, New Delhifor the award of a fellowship.

References1. ISLAM, N. & DHAWAN, K., Indian J, Chem., (in press).2. ADAM, G. & GIBBS,J. H., J. chem. Phys., 43 (1965), 139.3. MOYNIHAN, C. T., SMALLEY,C. R., ANGELL, C. A. &

SARB, E. J., J. phys, Chem., 73 (1969), 2287.4. ISLAM, N. & Au, A., Bull. chern. Soc., Japan, 53 (1980),

2371.5. IsLAM, N., KUMAR, S. & SINGH, K. P., Bull. chem. Soc.,

Japan, 51 (J 978), 2712.6. ISLAM, N., SINGH, K. P. & KUMAR, S., J. chem, Soc.,

Faraday Trans. I, 75 (1979), 1312.

Applicability of Modified Hildebrand Equation toFlow Behaviour of Molten Salt Systems

NURUL ]SLAM· & M. IBRAHIMDepartment of Chemistry, Aligarh Muslim University,

Aligarh 202 001

Received 30 October 1980; revised 6 February 1981; accepted26 February 1981

The least-squares fits and the relevant plots support the appli-cability of the modified Hildebrand equation to several moltensalt systems : Zn(NO.) •.6.33H.O-Ca(N03h.4.1H20; Ca(NO.),..4.1H.O-Cu(N03) •• 2.9H.O; Zn(NO.) s-6.18H.O-MnCI s-4.43H.O;Ca(NO.) •.4.1H.O-MnCI •.4.43H.O; Zn'NO.) z-6.27H.O-CoCI.;Zn(NO.) •.6.27H.O-NICI. and Cd(NO.) •.4.1H.O-CoCI ••

. ,- IN view @f the superiority- of equation,

tP = B' [(VfV'B)D-I] ... (1)over that or Hildebrand in explaining the behaviourof all sorts of. liquids including ,highly associatedones, an attempt-has been made herein to explain.the flow behaviour of highly viscous molten saltsystems and those supercooling to glassy states interms of Eq. (1). An attempt is made to correlatethe n values with the range of interaction, relaxa-tion or the extent of association in highly viscousglassy melts for the purpose of comparison. The systemschosen include Zn(NOS)2.6.33H:p-Ca(NOs)2' 4.lH20;Ca(NOs)2A.I H20-Cu(NOsh·2.9H20; Zn(NOS)2'6. I 8H20-MnCI2.4.43H20; Ca(NOS)2.4.1 H20-MnCI2.-4.43H,p; Zn(N0a)z.6.27H20-CoCI2; Zn(N0S)2'6:27HP-NiCI2 and Cd(NOshA.lH20-CoClz. .

Presuming the applicability of Eq. (1) to theabovesystems, we may compare Eq. (1) with that of theVogel-Tammann-Fu1cher (VTF) equation,

tP = A;T-l{2 exp[-k; j(T - To)] ... (2)

in order to express temperature, T as follows

lnB'+ln[(Y:B)" -lJ=lnA;-t!nT-'r~~oor

k;T = [ Y n J+ To ... (3)

c' - tin T -In (Y'B) - I

in which c' stands for In (A;/B'). The temperature(in Kelvin) and molar volumes were least-squaresfitted to Eq. (3) for the above listed melts. The k;and To values for all the seven systems have beenreported earlier" a. The values of the parametersn, V'Band c' thus computed from Eq. (3) are givenin Table 1. The fluidity was plotted against (Y/vo)nin order to calculate B' and Y'B from the interceptsand slopes of these plots, respectively. The lattervalues agree with those obtained from Eq. (3) asshown in Table 1. The linear plots of fluidity versus

[ (v: ). - I] have been found to pass through the

origin in all the seven molten salt systems as shownin a representative case (Fig. I). These plots demons-trate the applicability of Eq. (1) to such systems. Itis interesting to note that the values of n increasewith increase in solute concentration (Table I)suggesting a corresponding increase in the inter-molecular interaction except in the case of Zn(N03)2'6.18H20-MnCI2A.43H20 system where such inter-actions seem to be independent of solute concen-tration. The magnitude of n, being large in thepresent cases, reflects a significantly high degree ofassociation. The values of Y'B reinforce the abovedeductions, except in the case cited in which adecrease in the V'B values with solute concentrationdoes not seem to alter the resultant strength ofintermolecular interaction.

917