In dian Journa l or Pu re & Ap pli ed Ph ysics Vol. 41. December 2003 , pp. 928-935

Volumetric and viscometric studies on N,N-dimethylacatamide + 1-hexanol/1-heptanol binary liquid mixtures at different temperatures

Anwar Ali , Ani ! Kumar Nain , Dine~ h Chand & Bhajan La!

Departmen t or Chemi stry, Jamia Millia Islamia (Centrai University), Jami a Nagar, New Delhi 110 · 25

Received 26 June 2003; revised 26 August 2003 ; accepted 27 August 2003

Dcnsit ies p, and viscos iti es 11, have been measu red for pure N,N-dimethylacetamidc (DMA), 1-hcxanol. 1-heptanol <1nd for the1r 18 bi nary mixtures with DMA as a common component, covering the entire composition range, at 25, 30, 35 , 40 and 45 oc. Using the experi mental values of p and 11 , the excess mol ar vo lume li1\ excess viscosi ty TJ E, excess rheochore IR1\ cxccss partial molm volume v"oE, of alkanol s in DMA at inli nite diluti on and excess free energy or acti va ti on of v J scou~ 1low t:.G c. have been calcu lated. The dependence of these excess functions on composition and temperature has been dJscu,~cd from thc point of view of inter-mol ecular interactions in these mixtures. Furthermore, from the temperature depcndcnce of viscos it y, tile entha lpy 6 H' , and ent ropy t:J.S· , of activati on or viscous !low have also been calcul ated and their dcpcndcncc on composi ti on havc been discussed.

I Keywords: Excess mo lar vol ume. Excess viscosity, Excess rhcochorc, Excess partia l molar vo lu me, Ent ha lpy I

1 lnt•·oduction

The so lut ion properti es o r binary mixtures of amides with a lkano ls have been the subj ect of intensi ve research ow in g to the ir import<mce as super so lvents for chemical reac tions and many indust rial processes. Moreover, am ides are convenient mode l systems for in vestiga ti ng peptide and prote in in teractions in biologica l systems 1

•

A lbno ls serve as simple examp les of bio logica ll y anJ industri a ll y important amph iphilic mater ia ls1

. In view o r the prac ti cal importance of these liquids , acc urate and ex tensive data on the phys ico-chemical properti es o f the ir binaries are often req uired for the ir industrial app lications. As a part of the ongo ing research o f the authors on the the rmodynami c and transport properties of <tmide+alka nol binary mi xtures3.r', results of the study on density . viscos ity and de ri ved parameters o f the bi nary mixtures o f N,N-d imethy lacetam ide with 1-hexanol and 1-heptanol are reported over the e ntire compos iti on range at f ive different temperatures. S imilar studies on inte r-mo lecular interac ti on in binary liquid mixtures have a lso been repo rted by o the rs7·x . The mo lecul es o f DMA are ap rot ic and hig hl y pol ar, but pract ica ll y unassoc iated ; whereas the alkano l mol ecules are

assoc iated through hydrogen bonding~ . To the best of the knowledge of the authors , temperature­dependent study of thermodynamic and viscometric properties have not been made on these systems. The present study is expected to reveal the nature and exten t of interactions between the component molecules in these binary mi xtures.

In the present paper, dens ities p , and viscosities

11 , of binary mixtures of DMA w ith 1-hexanol and !-heptanol , including those of pure liquids, covering the entire composition range (expressed by the mo le

f raction , x 1 of DMA) at 25, 30, 35, 40 and 45 °C are

reported . From the ex perimental va lues of p and 11 , the excess molar vo lume VE, excess viscosity 11 E, excess rheochore [RE], excess free energy of

activation of viscous f low t:J.G' E, and excess parti al

molar volume Vz0E, of alkanols in DMA at infinite

dilution have been calculated. These func tion s offer a conveni ent , mode l-free approach for the study of thermodynamic properties of liquid mixtures. F rom

the tempera ture dependence of viscos ity, e nthalpy

!:J.H' , and entropy !':J.S' , of activation of viscous fl ow have also been calcul ated , us ing the theory of Eyring & John 10

• The dependence o f these

ALI et at.: BINARY LIQUID MIXTURES 929

thermodynamic parameters on composition and te mperature has been di scussed .

2 Experimental Details

DMA was the same as that used in the previous study of the au th ors' . 1-Hexanol and 1-heptanol (both s.d. fin e c he mica ls, AR grade) were purified usin a the standard methods described in the . 0

I ite rature 11• Be fore use, a ll the liquids were stored

over 0.4 nm molecul ar s ieves to reduce water content, if any, and were degassed . The mixtures were prepared by mass and were kept in special a irti ght bott les . The we ighing was done on Afcoset

ER- 120A e lec tronic bal ance with a precis ion of ± 0 . 1 mg.

The dens ities of pure liquids and their binary mi xtures were measured us ing a s ingle-capillary pycnometer (made of Boros il g lass) having a bulb

capac ity of 8x lo-~> m' . The capillary, with graduated marks, had a uniform bore and could be c losed by a well-fitting glass cap. The marks on the capillary were ca li brated by us ing triple-di stilled water. The viscosities of pure liquids and the ir binary mixtures were measured using Ubbelohde type suspended­leve l viscometer calibrated with triple-di stilled water. T he viscometer conta ining the test liquid was a ll owed to stand for about 30 min in thermostatic water bath so that, the thermal fluctuati on in visco meter was minimi zed . Reliability of the ex pe rime nta l data may be ascertained by comparing the dens iti es and viscosities of the pure components with the literature va lues . For instance, the. experimental va lues of densities of pure 1-hexanol

at 30 °C, 1-heptano l and DMA at 25 oc are 8 11.9, 8 19.2 and 936.6 kg m-', respec tive ly (l iterature va lues: 8 11.86

, 8 19.5 12, and 936.7 1.1 kg m-.1); the

experimental va lues of viscosit ies of pure 1-hexanol at 30 °C, and 1-heptanol and DMA both at 35 oc are 3.904, 4.285 and 0 .803 cP, respective ly, (literature val ues: 3.807", 4 .263 1 ~ and 0.826 15 cP) . The te mperature of the tes t liquids and their binary mixtures, duri ng the measurements, was maintained to an accuracy of ±0.02 oc in an e lectronica lly contro lled thermostat ic water bath .

3 Results and Discussion

The experimental va lues of density p, and

viscos ity 11 , of pure DMA, 1-hex anol , 1-heptano l and those of 18 binary mixtures of DMA with

1-hexanol and 1-heptano l over the whole compos ition range, expressed in the mole fraction ,

x, of DMA, at 25 , 30, 35, 40 and 45 °C are li sted in Table I. The excess functions, a measure of deviation from the ideal behaviour of the mixture, are found to be highly sensiti ve towards molecular interactions between the component molecules of the liquid mixtures . The sign and magnitude of these excess functions from ideality depend on the strength of interactions between unlike mo lecules. The excess functions such as, excess molar volume

\fo, excess viscosi ty 11 E, and excess rheochore [RE], were calculated by using the fo llowing relation :

... ( I)

where Y is the mol ar volume V, or viscosi ty 11 , or rheochore [R] ; x is the mole fracti on; subscripts I and 2 refer to DMA and 1-hexanol/1-heptanol , respectively. The va lues of V and [R] were calculated using the re lati o~s:

V = (x 1M1 + x2M2)/p

[R] = V11 ''x

... (2)

. . . (3)

where M is the molar mass. The values of \fo, 11 E and [RE] were fitted to a Redlich-Ki s te r '~> type po lynomial equation :

5 yE = x 1x2 I Ai ( l-2x, Y- ' ... (4)

i= l

T he va lues of the coefficients A, of Eq . (4) were evaluated by the method of least squares. The variations of smoothed values of v'[, 11 E and [RE], us ing Eq. (4), wi th mole frac tion x, of DMA are shown graphically in Figs 1-3.

The curves in Fig. I show that, the values of V' are positi ve, for both the binary syste ms (DMA + 1-hexano l/1 -heptanol ) under study, over the whole composition range. A plaus ible qualitati ve explanation on the behaviour of these mi xtures has been suggested. Mixing of DMA wi th 1-alkanols causes dissoc iation of hyd rogen bonded structure of 1-alkanol s ( 1-hexanol and 1-heptanol) and subsequent formation of (new) H-bond (C=O---­

H- 0) between proton acceptor oxygen atom (with lone pair of e lec tron s) of C=O group of DMA and proton of OH group of 1-alkanols. The first effect (di ssociation) leads to an inc rease in vo lume, resulting in positive \fo va lues, whereas the second

930 INDIAN J PURE & APPL PHYS, VOL 4 1, DECEMB ER 2003

1 (

Table I - Density p, and viscosity 11 of binary mi xtu res of DMA wit h 1- hexano l and 1-heptanol as a fu ncti on of mole fract ion. x 1 of DMA at differelll temperatures

0.0000 0.1302 0.25 ISJ 0.3660 0.473 1 0.5739 0.6689 0.7586 0.8435 0.9238 1.0000

0.0000 0. 1449 0.2760 0.3952 0 504 1 0.6040 06958 0.7X06 0.8592 0.932 1 1.0000

0.0000 0. 1302 0.25 19 0.3660 0.473 1 0.5739 0 6689 0.7586 0.8435 0.9238 1.0000

0.0000 0. 1449 0.2760 0.3952 0.5041 0.6040 0.6958 0.7iW6 O. X592 ()()321 I . 0000

25

X 15 .5 X27.2 l·m.9 X50.7 862.5 X74.4 8!.\6.4 !i9X.6 9 11.0 923.7 936.6

8 19.2 !.\29.9 X40.6 85 1.4 X62.5 873 .9 X85.7 !.\97.9 'J I 0.4 'J23.3 93(l.6

5.042 3.7'J3 2.% 1 2.402 2.029 1.765 1.560 1.384 1.234 1. 11 5 0 'J'J4

6.422 4.653 3.525 2.773 2.254 l.XS5 1.602 1.403 1.238 1.103 O.'J'J4

30 35

p (kg 111- 3)

DM A + 1-hexanol

!i i i.'J SOS.3 823.5 X I 'J.ll !.\35.1 ll3 1.3 X46.!i !i42.ll ll58.5 !.\54.5 870.4 X66 .3 882.3 87ll.2 894.4 X90.2 906.7 'J02.4 9 19.3 9 15.0 'J32.4 'J28.2

DM A + 1-heptanol

ll l 5.7 8 12.2 826.5 823.0 837 . 1 833.6 847.9 844.4 85ll.9 855.3 870.2 866.5 882.0 878.2 8'J4. 1 ll90.4 906.6 902.8 'J I'J.4 'J I5.5 932.4 'J2lU

11 ( 10-J N m- 2 s)

DM A + 1-hcxanul

3.904 3.3S2 2.'JS5 2.676 2.392 2. 135 1.968 1.760 1.673 1.523 1.485 1.349 1.330 1. 2 18 1.1 92 1.097 1.073 0.996 0.97 1 0.903 O.S5'J 0.803

DM A + 1-heptanol

5.027 4.2S5 3.65 1 3.206 2.7RO 2.506 2.26 1 2.05 8 1. 898 1.754 1.607 1.4SO 1.383 1.266 1.22 1 1.1 28 1.067 O.'J99 O.'J77 O.S96 O.S5Sl O.lW3

40

R04.7 S l6.0 827.4 838.'J 850.5 862.2 874.0 S86.0 898.2 9 10.7 'J24.0

808.7 8 19.5 830. 1 840.9 85 1.7 S62.9 874.4 886.5 8'J8 .9 9 11.5 924.0

2.869 2.302 1.908 1.585 1.37 1 1.237 1. 114 1.002 0.9 12 0.829 0.747

3.737 2.869 2.247 1. 867 1.595 1.367 1. 175 1.042 0.930 0.846 0.747

45

80 1. 1 8 12.3 823.6 835.0 846.5 S58. 1 869.9 88 1.8 893.9 906.4 9 19.S

805 .2 8 16.0 S26.6 837.4 848.1 859.2 870.7 882.7 895.0 907.5 9 19.S

2.544 2.056 !.70S 1.440 1.259 1. 143 1.035 0.937 0.859 0.790 0.70S

3.220 2.5 16 2 0 14 1.70 1 1.452 1.249 1.08 1 0.969 0.867 0.796 0.708

effec t tends to reduce the vo lu me, leading to negative VI' values. The observed posit ive VI' va lues fo r both the systems over whole compositi on range (Fig. I ) suggest that, the effect due to rupture of H­bonded assoc iates of a lkanols dominate over that of H-bonding between unlike molecules, 1.e., the DMA-alkanol inte racti on ts weaker than DMA­DM A or alkanol-alkanol inte rac ti ons In both the systems. Further, the VI' va lues (F ig. I ) are more pos iti ve fo r DMA+ 1-heptanol syste m than those fo r DMA+ 1-hexanol, suggesting that, stre ngth of hydrogen bond formed between DMA and a lkanol mo lecules should fo ll ow the order: 1-hexanol > 1-heptanol.

Table 2 - Enthalpy of activn tion o f viscous fl ow L'l. H* (kJ mol- 1

) for binary mixtures of DM A with 1-hexanol and 1-heptnnol as a fu nction of mule fractio n, x 1 o f DM A at different temperatures

0.0000 0.1302 0.25 19 0.3660 0.473 1 0.5739 0.6689 0.7586 O.S435 0.9238 1.0000

0.0000 0. 1449 0.2760 0.3952 0.504 1 0.6040 0.6958 0.7806 0.8592 0.932 1 1.0000

25 30 35

DMA + 1-hexanol

35.7 19 30.409 3 1.234 26 .68 1 28.644 24. 134 27 .6 16 22.928 25.925 2 1.4 13 24.0 14 19.657 2 1.962 I S.253 20.65 1 17.262 19.2 14 16.040 19.493 15.838 19.783 15.745

25 .397 22.397 19.!)96 18.5 14 17. 167 15.555 14.76 1 14.069 13.048 12.39 1 11 .944

DMA + 1-heptanol

34. 156 32.510 30.886 26.937 2 1.568 20.6 15 20.039 18.774 18.960 IS.094 19.783

29.692 27 . 182 25 .273 22.06 1 18.572 17.548 16.970 15.963 15.634 14.790 15.745

25.49 1 22 . 175 19.998 17.477 15.76 1 14 .66S 14.0S4 13.3 19 12.5 10 11.677 11.944

40 45

20.663 16. 1 S7 18.365 14.565 15.9 12 12. 163 14.356 I 0.435 13. 167 9.397 I 1.690 8.046 I 1.469 X.3 66 I 1.057 X.2 14 10.226 7.562 9. 136 6.063 8.362 4.985

21. 537 17.467 15.038 13. 163 13.1 2 1 11.963 11 .368 10.828 9.573 8.740 8.362

17. S II 13.038 10.370 9. 103 10.64 1 9.42 1 8.8 10 8.48 1 6.8 10 5.969 4.985

T his may be convinc ing ly expla ined by cons idering DMA as a proton acceptor, fo rms hydrogen bond more favo urably with 1-hexanol (a good proton donor) as compared to 1-heptanol, re lati ve ly poor proton donor due to bi gger a lkyl

ALI eta/.: BINARY LIQUID MIXTURES 93 1

group~- 17 • The finding of the authors is also supported by the views proposed by Fort & Moore 1x, according to which , yE becomes increas ingly positive with decreas ing strength of inte raction between component molecules . Similar result s have a lso been reported for N ,N­dimethy lformamide + n-alkanol s (C7- Cill) 19 and tolue ne+ n-alkano ls (C,- Cxro binary mixtures .

Table 3- Entro py or act ivation of viscous llow ~:;.s* (J mol- 1)

for binary mixtures of DMA with 1-hcxanol and 1-heptanol as a function or mole frac ti on, X I of DMA at different temperatu res

..I"J

0 .0000 0. 1302 0.251~

0.3660 0.473 1 0.573~

0.6689 0.75!\6 0.8435 0.9238 1.0000

25

5!\ .62 46 .25 3~ . 8!\

38.41 34.41 29.40 23.77 20.60 16.96 18.96 2 1.1 3

0.0000 50.35 0.1449 47 .~4

0.2760 45.21 0.3952 34.3 I 0.504 1 0.6040 0 . 6~58

0.7806 0.!\592 0.~321

1.0000

18.38 17.01 16.76 1 3 . ~4

15.95 14.27 21 . 13

T (°C)

30 35

DMA + 1-hexanol

40.96 3 I. I I 24.88 22 .82 19.40 14.90 I I .44 9.33 6.40 6.80 7.70

24.56 17.09 I 1.0 I 8.38 5.50 1.48 0.0 1 - 1.12 -3.39 -4.48 -4.74

DMA + 1-heptanol

35.49 30.22 26.54 18.09 8.42 6.!\1 6.55 4.59 4 .89 3.2!\ 7 .70

2 1.75 13.84 9.28 3.09 -0.78 -2.6 I -2.90 -4 .07 -5 .33 -6.9 I -4.74

40

9.32 4. i I - I .82 -5.0 I -7.37 - 10.96 - 10.59 - 10.82 -12.48 -14.95 - I 6.27

9.02 - I .32 -6.69 -10.80 -9 .28 - I 1.32 - I I .64 - 12.09 - 14.79 - I 6.36 -16.27

45

-4.86 -7.93 - 13.69 -17.43 -1 9.32 -22.51 -20.42 -19.82 -20.92 -24.69 -26.97

-2.78 - 15.35 -21.48 -23.66 - 17.14 - 19.37 - 19.74 -19.52 -23.54 -25. 14 -26.97

It is inte res ting to note that, at a ll the mole fract ions , the va lues of yE (Fig . I ) become more pos iti ve for DMA+ I -hexano l, show a decreas ing trend for DMA+ 1-heptano l, as the temperature of the sys te ms increases. It seems that for DMA+ 1-hexano l, rise in temperature induces the rupture of H-bonds be tween unlike molecules, leading to an ex pansion in vo lume, which is not compensated by the mutu al fitting of component molecul es into each other's struc ture . Consequently, an increase in yE

with te mpe rature is quite obvi o us. However, for

DMA+ 1-heptanol , the expansion in vol ume due to increase in te mperature of the syste m seems to be dominated by favourable fitting of smalle r DMA (molar volume = 9.30x lo-> m3 mol- 1 at 25 °C) molecules into the vo ids created by the bigger 1-

heptanol (molar volume= 14.19x I o--1 m3 mol- 1 at 25 0 C) molecules, resu lti ng in decrease in yE values .

0.3

> 0.1

0.0

0.6

(b)

, ....... 0.4 0 E

ME "i' -+- 25°C 0 -- 30 "C "'> 0.2 --.-- 35 °C

--x- 40 "C

-liE- 4s •c

0.0 0.2 0.4 0.6 0.8 1.0

Xi

Fig. I - Variation of excess molar volume 0 , wi th mole fraction x 1 of DMA for (a) DMA + 1-hcxanol and (b) DMA T

I -heptanol binary mixtures at different temperatures

T he excess viscos ity r{, are negative (Fig . 2) for both the syste ms (DMA+ 1-hexanol/ 1-heptanol ) under study over the whol e compos iti on range at al l

investigated temperatures . The negative 11 E va lues indicate that, the di spers ion forces (o r weak forces) are dominant in these systems6

·2 1

• It has been

932 INDIAN J PURE & APPL PHYS, VOL 4 1, DECEMBER 2003

reported rdl that , di spers ion forces are dominant in the systems, where the compo nent molecul es have d ifferent mo lecular size, as in the present cases. It may be noted that , DMA+ 1-heptanol mi xtures

ex hibit more pronounced negati ve llE va lues than DMA+ 1-hexanol. T hi s sugges ts that, the strength of

interaction is in the order: DMA-1-hexanol > DMA-1-heptanol. Also, the re la tive diffe rence in molar volumes between DMA and 1-hexanol/ 1-heptanol supports the above view22

. Similar trends

in 11E values have also been reported for ACN+ 1-alkanols (C5-C 111f 1 and aniline + 1-alkanol s (Cr,­C 111)""1 binary mixtures.

-;;;- -0.4

M I 0

"'!=" -0.8

-!.2

0.0

-0.4

-;;;-'1 E

;z. -0.8 M I 0

w !="

-1.2

-1.6

(b)

-.-3s •c """"*- 40 ·c ~45 "C

0.0 0.2 0.4 0.6 0.8 l.O

Xi

Fig. 2- Variation of excess viscosity r{ , with mole fraction x 1

of DMA for (a) DMA + 1-hexanol and (b) DMA + i -heptanol binary mixtures at different temperatures

It is worthwhi le to consider the rheochore excess funct ion [f?E], which is sens itive to inter­mol ecular interactions . Fig. 3 shows the va ri at ion of

[RE] with composition fo r both the systems under study. The curves in Fig. 3 indicate that, the va lues of [RE] are negat ive over the entire range of mole fraction at a ll in vestigated temperatu res, indicating the presence of weak inte rac ti on between unlike molecules in the mixtures. As expected, [f?E] values are more negati ve for DMA+ 1-heptanol mi xtures than those for DMA+ 1-hexanol mixtures. Thi s again supports the earlie r view of the authors that, the interacti on between DMA and 1-alkano l

molecules is in the order: DMA- 1-hexanol > DMA-1-heptanol. Such trends in the behaviour of [RE] have also been reported for N ,N-dime­thy lformamide + I ,2-ethanedioF5 binary mi xtures.

I

] -0.10 ._,E

"' 0

;:=:: -0.15

"'e:.

-0.20

se~ ~ -0.05

Ill N

IE

;;s -0.10 I 0 E

.-.E -0.15

b

UJ e:.. -0.20

-0.25

-+- 25"C

--- 3o •c ·-...- 35 "C

""""*- 40 •c

-----45"C

(b)

0.0 0.2 0.4 0.6 0.8 1.0

Fig. 3-Variation of excess rheochore [RE], with mole fraction x 1 of DMA for (a) DMA + 1-hexanol and (b) DMA + 1-heptanol binary mixtures at dilTerent temperatures

ALI ct a/.: BINARY LIQUID MIXTURES 933

~

I ~

I

0 E

...... ~

z >E >

:::::-::s e:.

-;.: I 0 E

:::!-

z >E >

:::::-::s fS

62

58

54

50

46

42

65

60

55

50

45

40

3.12 3.19

l-Hcxanol

3.26

l!f(I0-3 K)

3.33

DMA

3.40

Fig. 4- Variation of R In (llV/hN) with liT lor (a) DMA +1 -hexanol and (b) DMA + 1-heptanol binary mi xtures at different compositions

The apparent molar volumes V¢.2, of alkano ls in DMA were e va luated by using the followin g

relation 26:

.. . (5)

where V'2 and x2 are the molar volume and mol e frac ti on of pure alkanol. The partial molar

volumes V02, of a lkanol in DMA at infinite dilution

were obtained by us ing the method described el sewhere2

('·27

. The excess partial molar

volumes V 2°E, of alkanol s in DMA at infinite diluti on, which provide information regardin g inter­mo lecular inte ractions were calculated using the equati on2(',

. . . (6)

The values of v 2 DE for 1-hexanol and 1-

heptanol in DMA are found to be I .682x I o-7 and

3.9 10~ 10-7 m3 mot-•, respectively, at 25 oc. The V2°E values are positive for__?oth the alkanol s

(i.e., the partial molar volumes V02, of alkanols in

DMA are greater than _!heir corresponding molar

volumes V 2)· Further, v 2oE value is greater for 1-heptano l than that for 1-hexanol. This agai n clearl y suggests that, the mixing of DMA with alkanol s ( 1-hexanol/l-heptanol) causes an expansion in volume of the mi xture, indicating that the dissolution o f associated structures of 1-alkanols dominates ove r the effect due to hydrogen bonding between unlike molecules . This further supports the conclusions drawn earlie r.

0. 10

0.00

~

~ -0.10 E

...... c. r, -0.20

<l

-0.30

0.05

0.00

I

0 E -0.05 ...... c.

"J. -0.10 0 <l

-0.15

-0.20

-0.25 L-__ ..__ __ ..__ __ ..__ __ ..__ _ __J

0.0 0.2 0.4 0.6 0.~ 1.0

x ,

Fig. 5 - Variation of excess free energy of activati on of viscous llow t.G*E, with mole rracti on x 1 of DM/\ tor ta) DMA + 1-hcxanol r.nd (b) DMA + 1-hcptano l binary mixtures at di f' f'erent temperatures

914 INDIAN J PURE & APPL PHYS , VOL 4 1, DECEMBER 2003

It is eq ually useful to study the activation parameters of viscous flow of the binary mixtures. Eyring's viscos ity equat ion 111 2x:

11 = (hN/V) exp(!lG'IRT) 0 0 .(7)

when combined with the equati on:

!lG' = !lH' - T!lS' 00 .(8)

yie lds the equat ion:

R ln(llVIhN) = M-1*/T-!lS' 00 .(9)

where h is Planck's constant , N the Avogadro number, R the uni versa! gas constant, T the absolute

te mperature , !lH' and !lS' the en thalpy and entropy of viscous flow , respectively. The suitability of Eq.

(9) to eva luate !lH' and !"JS may be es tab lished by plott ing the term on the left h~nd side of Eq . (9) agai nst l iT at constant compos iti on. The plots are rep resented in Fig. 4 for both the sys tems under study. The non-linearity of these plots indicates that

111-1* is dependent on temperature. Therefore, in

order to obtain the va lues of !::,.H' and 6S*, the authors have fitted left hand side of Eq. (9) into the polynomial equat ion of the type:

R ln (1lVIhN)=a.,+aJT+aiT-+a/r= I a(floo.( IO) j=O

where o; are adjustment coefficients . The AH' and

!lS' values were obtai ned us ing the re lations:

!lH' = u 1 + 2u/T + 3a)T­

!1S' = - a., + a2/T- + 2a,/T1

00 .( II )

00 .( 12)

The calculated va lues of !::,.H' and !lS' are given in Tab les 2 and 3, respec tive ly. It is c lear from Table 2 that, at a ll mol e fracti on and invest igated

temperatures , !1H' va lues are positive for both the systems and tend to decrease as the mole fraction of DMA and temperature of the systems increase. T hi s sugges ts that, the formation of act ivated species necessary for the viscous flow appears quite easy in the DMA-rich reg ion, and becomes difficult as the alka no l content incretises in the mixture. Th is may be due to the fo rmati on of hyd rogen bond be tween DMA and a lkanol molecules. T he !lS' va lues (Tab le 3) a re fo und to be pos itive at lower temperatures and dec rease with increase in DMA mole fraction.

As the temperature increases, /lS* values change sign and become increas ing ly negati ve (Tabl e 3) at a ll the mole fractions of DMA for both the systems

under study. Such a dec rease in !lS' with te mperature may be ascribed to the breaking up of the associated structures in the mixture, wh ich fac ilitates the process of viscous flow . At low temperatures as we ll as for highly structured liquids (a lkanol s in the present study), a considerable degree of order may be expected , so that a large enthalpy of activation assoc iated to a relative ly high va lue of flow entropy is observed. Similar results in the variations of llH' and /lS* with composition and temperature have a lso been reported for N,N-dime­thylformamide+ I ,2-e thanedi oF5 binary mixtures.

The excess free energy of activation of viscous fl ow !::,.G'E was calculated us ing the equatio n:

The values of /lG'E, at each temperature, were fitted to the polynomial Eq. (4), as described for the othe r excess functions. T he variation of the

smoothened va lues of !::,.G'E agai nst mole fraction .. r 1

of DMA for both the systems are presented in

F ig. 5. The !::,.G*E values are found to be negative (Fig . 5) for both the syste ms (DMA+ 1-hexano l/ I·· heptano l) over the whole compos ition range, except a few pos iti ve values in DMA-rich (x 1>0.85) region

at higher temperatures. Like 11E, the negati ve !lG'E values are, genera lly , indicati ve of the presence of di spers ion forces in the mi xtures. Similar conclus ions were a lso arrived at by Meyer et al2~

and Oswa l & Rathnam22, where in negative !lG'E

values were ascribed to the dispersion forces present in the binary liquid mi xtures . It is observed

that, like 11E and [RE], !lG'E values also become less negative with increase in temperatu re, indi ca ting that the systems under study te nd towards idea l behaviour.

Acknowledgement

The authors AA and AKN are, respect ive ly, thankful to Department of Science and Technology, New Delhi and CSIR, New Delh i, for financ ial support in form of a major research project and research associateship.

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