1. Presented By: Dr. Debashis Das Department of Chemistry
A NEW APPROACH IN THE PHYSICO- CHEMICAL STUDY OF BINARY LIQUID MIXTURES OF N,N-DIMETHYLACETAMIDE WITH FORMAMIDE AND N,N-DIMETHYLFORMAMIDE, AT TEMPERATURES FROM K TO K.
Subject:
Presented By: Dr. Debashis Das
Department of Chemistry
Dinhata College
Dinhata, Cooch Behar,

2. INTRODUCTION
Among the physico-chemical properties of binary liquid mixtures, required for optimizing and designing industrial processes, it should be mentioned that viscosity is one of the most important factors . Recently, the derivation of different thermodynamic parameters from experimental values of various physical properties and their meaningful correlations with one another introduces a new framework of scientific research on binary liquid mixtures. On the other hand, excess thermodynamic functions and deviations of analogous non-thermodynamic functions of binary liquid mixtures are fundamental for understanding different types of intermolecular interactions in these mixtures. In this presentation only viscosity deviations of N,N-DMA with FA and DMF binary liquid mixtures are fitted to the Redlich-Kister, Reduced Redlich-Kister (R-K), Relative reduced R-K, and Herráez equations and are interpreted in terms of molecular interactions and structural effects. These values are also used to study the viscosity and Arrhenius behavior along with a new designated parameter Arrhenius Temperature (TA ) that characterizes each binary system. Comparison between these models at different temperatures and the effect of using different numbers of parameters will be discussed. er

3. D.Das, S.K. Ray & D.K. Hazra, J.Ind.Chem.Soc., 80, 385-390,2003
Table 1 Experimental density (ρ ), absolute viscosity (η), for the binary mixtures of N, N-dimethylacetamide with formamide at , and K.
Fig. 1 Variation of viscosity deviations with the mole fraction of DMA in binary mixtures of N, N-dimethylacetamide with formamide at K(●), K(■) and K(▲).
x1(DMA)
r g cm-3
h mPas
T = K
T = K
T = K
0.0000
1.1254
2.953
1.1118
2.384
1.1072
1.951
0.0350
1.1120
3.217
1.1045
2.532
1.0944
2.077
0.0700
1.0997
3.457
1.0923
2.677
1.0826
2.180
0.1110
1.0866
3.656
1.0791
2.847
1.0700
2.286
0.1500
1.0752
3.822
1.0677
2.950
1.0590
2.357
0.2053
1.0606
3.966
1.0522
3.037
1.0446
2.416
0.2414
1.0518
3.971
1.0442
3.057
1.0361
2.420
0.3009
1.0387
3.932
1.0307
3.027
1.0228
2.389
0.3563
1.0275
3.789
1.0195
2.920
1.0117
2.310
0.4177
1.0162
3.537
1.0080
2.741
1.0001
2.160
0.4580
1.0092
3.338
1.0011
2.594
0.9930
2.076
0.5011
1.0021
3.094
0.9940
2.430
0.9859
1.953
0.5474
0.9948
2.826
0.9867
2.235
0.9785
1.810
0.5972
0.9873
2.530
0.9791
2.028
0.9709
1.650
0.6500
0.9797
2.251
0.9715
1.812
0.9632
1.505
0.7092
0.9717
1.916
1.579
0.9550
1.316
0.7500
0.9663
1.720
0.9578
1.441
0.9495
1.205
0.7948
0.9607
1.540
0.9522
1.289
0.9437
1.096
0.8910
0.9492
1.210
0.9406
1.035
0.9318
0.901
1.0000
0.9371
0.933
0.9283
0.819
0.9193
0.726 X1
The excess viscosity has been calculated using the following equation
η = η – (η1x1 + η 2x2 ) (1)
where η is the respective solution properties and η1 , η2 are the viscosities of the pure components. Graphical representations of  η as functions of mole fraction of DMA(x1) are given in Fig.1
D.Das, S.K. Ray & D.K. Hazra, J.Ind.Chem.Soc., 80, ,2003

4. D.Das, S.K. Ray & D.K. Hazra, J.Ind.Chem.Soc., 80, 385-390,2003
Table 2 Experimental density (ρ), absolute viscosity (η),
for the binary mixtures of N, N-dimethylacetamide with
N,N-dimethylformamide at , and K.
Fig. 2 Variation of viscosity deviations with the mole fraction of DMA in binary mixtures of N, N-dimethylacetamide with N,N-dimethylformamide at K(●), K(■) and K(▲).
x1(DMA)
r g cm-3
h mPas
T = K
T = K
T = K
0.0000
0.9436
0.802
0.9348
0.713
0.9256
0.638
0.0500
0.9433
0.809
0.9345
0.718
0.9253
0.642
0.1062
0.9429
0.816
0.9341
0.724
0.9249
0.647
0.1500
0.9426
0.822
0.9338
0.729
0.9246
0.652
0.2171
0.9421
0.831
0.9332
0.737
0.9242
0.658
0.2600
0.9418
0.837
0.9330
0.742
0.9239
0.662
0.3094
0.9414
0.843
0.9326
0.747
0.9235
0.666
0.3500
0.9411
0.849
0.9323
0.752
0.9233
0.670
0.4050
0.9407
0.856
0.9319
0.758
0.9229
0.675
0.4550
0.9404
0.863
0.9316
0.763
0.9226
0.679
0.5042
0.9400
0.870
0.9313
0.769
0.9223
0.684
0.5500
0.9397
0.876
0.9309
0.774
0.9219
0.688
0.6071
0.9393
0.883
0.9305
0.781
0.9216
0.694
0.6550
0.9389
0.890
0.9302
0.786
0.9213
0.698
0.7140
0.9385
0.898
0.9298
0.793
0.9209
0.704
0.7500
0.9383
0.903
0.9295
0.797
0.9206
0.707
0.7968
0.9379
0.909
0.9292
0.803
0.9203
0.712
0.8500
0.9375
0.916
0.9288
0.9199
0.717
0.9112
0.9370
0.925
0.9284
0.9196
0.723
0.9500
0.9368
0.930
0.9281
0.820
0.9193
0.727 ∆η
mPas
The excess viscosity has been calculated using the following equation
η = η – (η1x1 + η 2x2 ) (1)
where η is the respective solution properties and η1 , η2 are the viscosities of the pure components. Graphical representations of  η as functions of mole fraction of DMA(x1) are given in Fig. 2.
D.Das, S.K. Ray & D.K. Hazra, J.Ind.Chem.Soc., 80, ,2003

5. REDLICH-KISTER EQUATIONS
The excess viscosity η were fitted to the Redlich- Kister equations [1].
YE = x1(1 – x1)  A j (1 – 2x1)j (2)
Where A0, A1, A2 are adjustable parameters.
The values of these parameters along with the standard deviation σ(YE) of YE as defined by the equation.
σ (YE) = [  (YEobs - YEcal )2 / (N – M) ] (3)
In equation 3, N is the total no. of points and M is the number of parameters. 5
1.O. Redlich, A. T. Kister, Ind. Eng. Chem. 40, 345–348 (1948)

6. D.Das, S.K. Ray & D.K. Hazra, J.Ind.Chem.Soc., 80, 385-390,2003
Co-efficients of redlich-kister equations along with standard deviations of n,n-dimethylacetamide with formamide and n,n dimethylformamide mixtures
D.Das, S.K. Ray & D.K. Hazra, J.Ind.Chem.Soc., 80, ,2003

7. 2. J.E. Desnoyers, G. Perron, J. Solution Chem. 26, 749–755 (1997).
Reduced Redlich-Kister Equations
In this context, Desnoyers et al. [2] stated that:
“While there is a general consensus among chemists on the use of the Redlich-Kister equation to analyze thermodynamic data on mixtures of liquids, we would like to suggest, in agreement with the original statements of Redlich and Kister, (Eq. 3) that it is better to plot YEx/x2(1 - x2) for this purpose. This function is directly related to the apparent molar quantities of both components and therefore has a thermodynamic significance. A rapid examination of the trends of the YEx dependence on x2 suggests that many of these systems are similar but that the differences in interactions are mostly significant in the solution rich in component 2.”.
2. J.E. Desnoyers, G. Perron, J. Solution Chem. 26, 749–755 (1997).

8. Reduced Redlich-Kister Equations
This ratio is so called the experimental reduced Redlich-Kister excess properties QY,exp,T(x1) which is expressed by Eq. 3,
QY,exp,T(x1)= YjE/(x1(1- x1) (4)
where YjE denotes Dh.
The reduced Redlich-Kister excess property is more sensitive than the direct excess property YE or ∆η to interactions that occurs at low concentrations [3].
Redlich and Kister treated the data with a power series, putting all the weight on data near 0.5 mole fraction [2]. As Desnoyers et al. have shown, this is not always the best approach for mixtures having specific interactions such as association at low concentration.
3. R. Besbes, N. Ouerfelli, H. Latrous, J. Mol. Liq. 145, 1–4 (2009)

9. D. Das & N. Ouerfelli., J. Solution Chem., 41(8), 1334-1351, 2012
Reduced R-K viscosity deviation Qη,T(x1) ), Eq. 4, vs x1 of DMA is plotted in Figs. 3 and 4. at temperatures: (●): K ; (○): K; (▲): K.
Fig. 3: DMA (1) + FA (2)
Fig. 4: DMA (1) + DMF (2)
N,N-dimethylacetamide is a dipolar aprotic solvent having dielectric constant (ε = at K). Formamide is a protic solvent with a high dielectric constant (ε = at K) and are strongly self-associated through extensive networks of hydrogen bonds. N,N-dimethylformamide is an aprotic, protophylic solvent with a moderate dielectric constant (ε = 37.5 at K) and a weak hydrogen bonded interaction existed between DMF molecules. The changes in curvature found in Fig.3 indicates more hydrogen bonded interactions existed between DMA+FA than DMF. As the temperature increases, the magnitude of the viscosity deviation sharply decreases due to the breaking up of the hydrogen bonds in both the systems. Large separation of curves near x1 ≈ 0 and their closeness near
x1 ≈ 1 (Fig. 3)suggests that the solute-solvent interaction parameter is much larger for N,N-DMA in FA than for the reverse case but it is same for DMA in DMF and for the reverse case (Fig. 4).
D. Das & N. Ouerfelli., J. Solution Chem., 41(8), , 2012

10. relative reduced Redlich-Kister function, QY,rel,T(x1) = QY,T(x1)/Y
relative reduced Redlich-Kister function, QY,rel,T(x1) = QY,T(x1)/Y. at temperatures: (●): K ; (○): K; (▲): K.
Like the relative deviation ∆η /η, the Qη,rel,T(x1) versus mole fraction x1 of DMA is shown below:
Fig. 6: DMA (1) + DMF (2)
Fig. 5: DMA (1) + FA (2)
Comparing with earlier figure it seems that Qη,rel,T(x1) depend very slightly on temperature. Fig. 5 shows that the nearness and then the larger separation of curves in Fig. 3 at the two limits of infinite dilution do not depend only on the value of the solute-solvent interaction parameter but are also affected by temperature and further it affects the FA rich-region more than the DMA one. Comparing Figs. 4 and 6 it is noticed that temperature has no significant effect in the viscosity of binary mixtures of the DMA + DMF system. We remark that the differences between their Arrhenius activation energy of viscosity Ea can play an important role in this effect.
D. Das, Z. Barhoumi, N.Dhouibi, M. Sanhouri & N Ouerfelli, Physics and Chemistry of Liq.,
50(6), , 2012

11. Viscosity temperature-dependence Arrhenius equation
ln h = lnAs + Ea/RT (5)
The plot of ln η against (1/T) is practically linear (Fig. 7 & 8) and the Arrhenius parameters Ea and As are thus independent of temperature over the studied temperature range ( to ) K. Using both graphical and least-squares fitting methods, the slope of the straight line is equal to Ea/R and the intercept is equal to ln(As).
Fig. 7: DMA (1) + FA (2)
Fig. 8: DMA (1) + DMF (2)
at some fixed mole fractions. (●): x1 = 0.0 ;
(○): x1 = ; (▲): x1 = ; (∆): x1 = ; (■): x1 = ; (□): x1 = (♦): x1 =
and (◊): x1 = 1.0.
at some fixed mole fractions x1. (●): x1 = ;
(○): x1 = ; (▲): x1 = ; (∆): x1 = ;
(■): x1 = ; (□): x1 = ; (♦): x1 = ;
(◊): x1 = and (▼): x1 =

12. For system DMA (1) + DMF (2)
ARRHENIUS ACTIVATION ENERGY EA / (kJ·mol-1), ENTROPIC FACTOR OF ARRHENIUS As / (10-6 Pa·s) AS A FUNCTION OF THE MOLE FRACTION OF N,N-DMA (x1) OVER THE TEMPERATURE RANGE ( to ) K.
For system DMA (1) + FA (2)
For system DMA (1) + DMF (2) x1
Ea/ kJ·mol−1
As /10−6 Pa·s
0.0000
16.41
3.95
0.0350
17.25
3.05
0.0700
17.97
2.44
0.1110
18.57
2.04
0.1500
19.07
1.74
0.2053
19.47
1.53
0.2414
19.62
1.45
0.3009
19.65
1.42
0.3563
19.52
1.44
0.4177
19.09
1.60
0.4580
18.73
0.5011
18.15
2.05
0.5474
17.57
2.35
0.5972
16.81
2.87
0.6500
15.85
3.73
0.7092
14.81
4.87
0.7500
14.03
6.00
0.7948
13.26
7.29
0.8910
11.70
10.82
1.0000
9.884
17.30 x1 Ea As
kJ·mol-1
10-6 Pa·s
0.0000
9.053
20.815
9.097
20.614
9.147
20.392
9.183
20.240
9.237
20.020
9.272
19.872
9.309
19.736
9.339
19.627
9.379
19.475
9.413
19.363
9.445
19.266
9.475
19.167
9.512
19.049
9.543
18.948
9.579
18.850
9.600
18.786
9.624
18.739
9.653
18.669
9.685
18.599
9.704
18.565
1.0000
9.726
18.538
Since, the As-values are closely related to the viscosity of the system in vapor-phase [4], we
observe that for DMA+FA system, high values of viscosity in the DMA-rich region indicates that the DMA molecules bounding are more correlated and ordered in vapor state and for another
system it happens in the DMF-rich region. We can predict that in vapor-liquid equilibrium study, the values of the mixing enthalpy must be high positives values in this region.
4. N. Ouerfelli, Z. Barhoumi, and O. Iulian, J. Solution Chem. 41, 458 (2012)

13. absolute reaction rate theory
In case of liquid phase Eyring et al. [5] and Ali et al. [6] relates viscosity with the free energy (DG*) of activation of viscous flow:
(6)
where h, h, R, NA, r and M are the viscosity of binary mixture, Plank’s constant, universal gas constant, Avogadro’s number, density and molar mass of mixture (Eq. 6), respectively, and:
DG* = DH* - T DS* (7)
M = x1(M1 – M2) + M (8)
where M1 and M2 are the molar mass of the pure component 1 (DMA )and component 2 ( FA or DMF) respectively.
By assuming that the activation parameters ∆H* and ∆S* [6,7] are independent of temperature, we obtained the value of these parameters for each composition of mixture (x1,x2), when ln(η·V/(h·NA)) is plotted against 1/T. In fact, the plot of ln(η·V/(h·NA)) against the reciprocal of absolute temperature (1/T) is practically linear and the enthalpy ∆H* of activation of viscous flow are presented in Table
5. H. Eyring and M.S. John, Significant liquid structure. (Wiley, New York 1969).
6. A. Ali, A.K. Nain and S. Hyder, J. Indian Chem. Soc. 75, 501 (1998).
7. D.G. Leaist, K. MacEwan, A. Stefan and M. Zamari, J. Chem. Eng. Data 45 (5), 815, (2000).

14. D. Das & N. Ouerfelli., J. Solution Chem., 41(8), 1334-1351, 2012
ENTHALPY OF ACTIVATION OF VISCOUS FLOW ∆H* / (kJ·mol-1) FOR THE TWO STUDIED MIXTURES AS A FUNCTION OF THE MOLE FRACTION OF N,N-DIMETHYLACETAMIDE (x1) OVER THE TEMPERATURE RANGE ( TO ) K.
For system DMA (1) + FA (2)
For system DMA (1) + DMF (2) x1
Ea/ kJ·mol−1
As /10−6 Pa·s
DH*/ kJ·mol−1
0.0000
16.41
3.95
15.769
0.0350
17.25
3.05
16.622
0.0700
17.97
2.44
17.349
0.1110
18.57
2.04
17.958
0.1500
19.07
1.74
18.470
0.2053
19.47
1.53
18.870
0.2414
19.62
1.45
19.027
0.3009
19.65
1.42
19.044
0.3563
19.52
1.44
18.906
0.4177
19.09
1.60
18.458
0.4580
18.73
18.095
0.5011
18.15
2.05
17.504
0.5474
17.57
2.35
16.921
0.5972
16.81
2.87
16.148
0.6500
15.85
3.73
15.182
0.7092
14.81
4.87
14.129
0.7500
14.03
6.00
13.334
0.7948
13.26
7.29
12.554
0.8910
11.70
10.82
10.974
1.0000
9.884
17.30
9.1447 x1 Ea As
DH*
kJ·mol-1
10-6 Pa·s
0.0000
9.053
20.815
8.292
9.097
20.614
8.336
9.147
20.392
8.386
9.183
20.240
8.423
9.237
20.020
8.478
9.272
19.872
8.515
9.309
19.736
8.552
9.339
19.627
8.583
9.379
19.475
8.625
9.413
19.363
8.659
9.445
19.266
8.692
9.475
19.167
8.722
9.512
19.049
8.761
9.543
18.948
8.793
9.579
18.850
8.829
9.600
18.786
8.851
9.624
18.739
8.876
9.653
18.669
8.906
9.685
18.599
8.939
9.704
18.565
8.959
1.0000
9.726
18.538
8.982
D. Das & N. Ouerfelli., J. Solution Chem., 41(8), , 2012
D. Das, Z. Barhoumi, N.Dhouibi, M. Sanhouri & N Ouerfelli, Physics and Chemistry of Liq.,50(6), , 2012

15. D. Das & N. Ouerfelli., J. Solution Chem., 41(8), 1334-1351, 2012
VARIATION OF Ea AND ∆H* FOR THE TWO MIXTURES VERSUS x1 OF DMA IN THE TEMPERATURE RANGE ( to K). (●): Ea / kJ·mol-1; (○): ∆H* / kJ·mol-1.
Fig.9 DMA (1) + FA (2)
Fig. 10 DMA (1) + DMF (2)
Both the curves show that the Ea and ∆H* values are very closely related. Variation of the Ea versus (x1) can give evidence of eventual change in the complex structure or cluster formed in binary liquid mixtures under temperature effect and/or mixture composition. Fig. 9 indicates strong interactions between the FA and N,N-DMA molecules in the vicinity of x1 = There is no observable change of curvature found in Fig. 10. Monotonous variation of the activation energy Ea, suggests that there is a progressively change of solvent’s structure when one component is introduced into other in the mixture.
D. Das & N. Ouerfelli., J. Solution Chem., 41(8), , 2012
D. Das, Z. Barhoumi, N.Dhouibi, M. Sanhouri & N Ouerfelli, Physics and Chemistry of Liq.,50(6), , 2012

16. Fig.12 does not give such type of indication.
Correlation between the Arrhenius activation energy Ea (kJ·mol-1) of viscosity and the logarithm of the Arrhenius entropic factor (lnAs) for N,N-dimethylacetamide with formamide and dimethylformamide mixtures in the temperature range ( to K).
Fig.11 DMA (1) + FA (2)
Fig.12 DMA (1) + DMF (2)
Fig. 11 also indicates the formation of association type structures by a composition around mole fraction x1 ≈ 0.3 of N,N-DMA, but
Fig.12 does not give such type of indication.
M. Dallel, D. Das, E.S.Hmida, N. Al-Omair, A. Al-Arfaj, N. Ouerfelli. Phys. & Chem. of Liquids, 52, (3), 2014, 442–451.

17. From the two curves it is observed that the Arrhenius activation energy Ea(x1 ) of viscosity increases against the logarithm of the Arrhenius entropic factor, – R·ln(As). Likewise, the pre-exponential entropic factor (As) equivalent to the viscosity at infinite temperature (As = η∞) is very closely related to the viscosity of the same system in vapour phase at the normal boiling temperature and at the same pressure. We can add that for both the studied mixture, even in the case of the existing of different domains with distinct behaviors, we note that all different branches exhibit approximately the same slope of their quasi-straight line. This inspires us to deduce the following standardized empirical equation and apply it to the present system:
Ea/R = TA·ln(As) + B
where B is a constant related to the viscosity of the liquid system at boiling temperature and which is the intercept on the ordinate when lnAs is mathematically null; while the slope TA characterises each binary system and it is equivalent to an absolute temperature for which we suggest the viscosity Arrhenius temperature TA as a name for the corresponding binary system.
In the case of the DMA+FA mixtures, the TA value is equal to K with correlation factor of , while the boiling temperature of DMA and FA are K and K, respectively. For DMA-DMF mixtures, the TA value is equal to 687.3K with correlation factor of , while the boiling temperature of DMA and DMF are K and K, respectively.
N. Dhouibi, M. Dallel, D. Das, M. Bouaziz, N. Ouerfelli, A.H. Hamzaoui. Phys. & Chem. of Liquids, Accepted, 2014,

18. Comparision between thermodynamic parameters study and spectroscopic observation for dma+dmf mixtures
Correlation between the rel. red. R–K function Qrel,Ea and Qrel,lnAs Of DMA +DMF system in the temperature range to K
NMR study of DMA+DMF mixture
Chemical shifts δ (in ppm) as a function of the mole fraction of DMA (x1) at the temperature K. x1
δ (–CHO)
δ (CH3–N-CH3)}1
δ (–CH3CO)
{δ (CH3–N-CH3)}2
δ (CH3---N)
0.0000
8.1 -
3.0
2.9
0.3005
7.35
2.3
2.05
1.55
2.2
0.5009
7.45
2.5
2.39
1.5
2.45
2.35
3.05
0.6002
7.00
2.1
1.8
1.1
2.0
1.9
0.7000
7.4
2.4
1.4
2.29
0.7500
7.9
2.91
2.85
2.00
2.8
0.8001
7.5
2.6
0.9000
7.3
1.45
2.19
1.0000
3.1
Probable molecular structure of the complex in the cluster of [6(DMA):4(DMF)].
D. Das, Z. Barhoumi, N.Dhouibi, M. Sanhouri & N Ouerfelli, Physics and Chemistry of Liq.,50(6), , 2012

19. THE PROPOSED HERRÁEZ EQUATION
In recent paper [8], Herráez et al propose a new empirical correlation equation (Eqs. H12-a and H21-b) which introduces a correcting polynomial (Eq. H12-c) as an exponential-acting upon the molar fraction of one of mixture components. It is observed that, the viscosity deviations calculated with this model generally yield satisfactory results for many studied mixtures showing monotonous variation in viscosity values with molar fraction, but records inferior performance when distribution exhibits a maximum or minimum [8].
η(x1) = η 2 + (η 1 – η2)·x1P12,T(x1) (H12-a)
where P12,T(x1) is a power polynomial with order (n) and (n+1) adjustable parameters Bp,T:
(H12-b)
P12,T(x1) =
Hence, the Herráez Pn,T(x1) polynomials of Eq. H12-b can be inspected experimentally by using Eq. H12-c.
(H12-c)
P12,exp,T(x1) =
where η1 and η2 are the dynamic viscosity of pure components (1) and (2)
respectively and ηexp,T(x1) the dynamic viscosity of mixture at molar fraction x1 and temperature T for [x1 =0,1].
8. V. Herráez, R. Belda, O. Diez and M. Herráez, J. Sol. Chem. 37, 233 (2008).

20. D. Das & N. Ouerfelli., J. Solution Chem., 41(8), 1334-1351, 2012
VARIATION OF THE EXPERIMENTAL HERRÁEZ EXPONENT P12,EXP,T (x1) (Eq. H12-c) FOR DMA (1) WITH FA AND DMF (2) MIXTURES AGAINST MOLE FRACTION x1 OF DMA AT THE TEMPERATURES, (●): K; (○): K; (▲): K.
Fig.13 DMA (1) + FA (2)
Fig.14 DMA (1) + DMF (2)
D. Das & N. Ouerfelli., J. Solution Chem., 41(8), , 2012
D. Das, Z. Barhoumi, N.Dhouibi, M. Sanhouri & N Ouerfelli, Physics and Chemistry of Liq.,50(6), , 2012

21. η(x2) = η1 + (η2 – η1)·x2P21,T(x1) (H21-a)
On the other face of the model and when it mathematically possible we can write:
η(x2) = η1 + (η2 – η1)·x2P21,T(x1) (H21-a)
where P21,T(x2) is a power polynomial with order (n) and (n+1) adjustable parameters Bp,T:
P21,T(x1) =
(H21-b)
Hence, the Herráez Pn,T(x2) polynomials of Eq. H21-b can be inspected experimentally by using Eq. H21-c.
(H21-c)
P21,exp,T(x2) =
where η1 and η2 are the dynamic viscosity of pure components (1) and (2) respectively and ηexp,T(x2) the dynamic viscosity of mixture at molar
fraction x2 and temperature T for [x2 =0,1].

22. Fig.15 DMA (1) + FA (2) Fig.16 DMA (1) + DMF (2)
VARIATION OF THE EXPERIMENTAL HERRÁEZ EXPONENT P21,EXP,T (X2) (Eq. H21-c) FOR DMA (1) WITH FA AND DMF (2) MIXTURES AGAINST MOLE FRACTION X2 IN FA AND DMF RESPECTIVELY AT THE TEMPERATURES, (●): K; (○): K; (▲): K.
Fig.15 DMA (1) + FA (2)
Fig.16 DMA (1) + DMF (2)
However, at infinite dilution (xi → 0+), the Pexp,T(xi) values converge to a surprising single point (Pexp,T(0) = 1.0) independent of temperature (Figs ) indicates that the solute-solute interaction is absent at very high dilution of DMA in the two regions.
Note that the same remark is observed in the previous works investigating viscosity in isobutyric acid + water and 1,4-dioxanne + water mixtures [9,10].
9. N. Ouerfelli, T. Kouissi, N. Zrelli and M. Bouanz, J. Sol. Chem. 38, 983 (2009).
10. N. Ouerfelli, T. Kouissi and O. Iulian, J. Sol. Chem. 39 (1), 57 (2010).

23. CONCLUSION:
Correlation between the two Arrhenius parameters for N,N-DMA+FA mixtures can give evidence of the existence of distinct composition regions with different behaviors. Therefore, there will be a significant degree of H-bonding leading to strong correlation between the molecules.
Correlation between the two Arrhenius parameters for DMA+DMF mixtures can give no observable change in curvature. Therefore, there will be a weak dipole-dipole interaction and a slight structure breaking effect observed in the DMA+DMF mixture when we introduce one component into other in the mixture.
The reduced R-K function and calculation of the Arrhenius activation energy is also required along with the direct excess property to get information about the different interactions played in the binary systems.
In addition, the relative reduced R-K equation has been introduced to reduce the temperature effect and can also be good tools, like the reduced R-K function for interpreting different types of interactions.

24. In the case of viscosity data having a maximum or minimum as a function of mole fraction, this divergence is more pronounced in the Redlich–Kister model than in the Herráez model.
Corelation between the two Arrhenius parametes for binary mixtures permits us to reveal the viscosity Arrhenius temperature that characterises the studied binary liquid mixture and can provide information on the vaporisation temperature of the isobaric liquid-vapour equilibrium.
The Redlich–Kister polynomial is more sensitive to the number of experimental points whereas the Herráez model offers a good smoothed interpolation without any oscillation between data points, even in the case with few experimental measurements.
In the case of some nonelectrolyte mixtures, the net absence of solute-solute interactions leads to a fixed value of the Herráez constant of 1.0 or more.

25. REFERENCES
1 D. Das, S. K. Ray and D. K. Hazra, J. Indian Chem. Soc., 80, , (2003).
2. J.V. Herráez, R. Belda, O. Diez, M. Herráez, J. Solution Chem. 37, 233–248 (2008)
3. O. Redlich, A. T. Kister, Ind. Eng. Chem. 40, 345–348 (1948)
4. J.E. Desnoyers, G. Perron, J. Solution Chem. 26, 749–755 (1997).
5. R. Besbes, N. Ouerfelli, H. Latrous, J. Mol. Liq. 145, 1–4 (2009)
6. A.K. Covington and T. Dickinson, Physical Chemistry of Organic Solvent Systems, (Plenum Press, New York 1973).
7. N. Ouerfelli, Z. Barhoumi, O. Iulian, : J. Sol. Chem. (Manuscript ID: JOSL1581R2 ; Accepted for publication ).
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10. D.G. Leaist, K. MacEwan, A. Stefan and M. Zamari, J. Chem. Eng. Data 45 (5), 815 (2000).
11. N. Ouerfelli, O. Iulian, R. Besbes, Z. Barhoumi and N. Amdouni, Phys. Chem. Liq. 50 (1), 54 (2012).
12. N. Ouerfelli, Z. Barhoumi, R. Besbes and N. Amdouni, Phys. Chem. Liq. 49 (6), 777 (2011).
13. O. Iulian and O. Ciocîrlan, Rev. Roum. Chim. 55 (1), 45 (2010).
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15.V. Herráez, R. Belda, O. Diez and M. Herráez, J. Sol. Chem. 37, 233 (2008).
16. N. Ouerfelli, T. Kouissi, N. Zrelli and M. Bouanz, J. Sol. Chem. 38, 983 (2009).
17. E. Cherif, N. Ouerfelli and M. Bouaziz, Phys. Chem. Liq. 49 (2), 155 (2011).
18. N. Ouerfelli, T. Kouissi and O. Iulian, J. Sol. Chem. 39 (1), 57 (2010).
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26. ACKNOWLEDGEMENT:
The author is grateful to Prof. N. Ouerfelli (Laboratoire de Chimie Analytique et Electrochimie, Département de Chimie, Faculté des Sciences de Tunis, Campus Universitaire, 2092 El Manar Tunisia) and his research scholars for some calculations made by their computer programmes and helpful suggestions.

27. Our contributions:
D. Das 1,N. Ouerfelli , The Relative Reduced Redlich-Kister and Herráez Equations for Correlating Excess Properties of N,N-Dimethylacetamide + Formamide Binary Mixtures atTemperatures from K to K. Journal of Solution Chemistry 41(8), , 2012
D. Das 1,*, A. Messaâdi 2, Z. Barhoumi 2, N. Ouerfelli 2,3 The Relative Reduced Redlich-Kister Equations for Correlating Excess Properties of N,N-Dimethylacetamide + Water Binary Mixtures at Temperatures from K to K. Journal of Solution Chemistry, 41(9), , 2012
D. Das1,*, Z. Barhoumi and N.Ouerfelli, The relative reduced Redlich–Kister equations for correlating excess properties of N,N-dimethylacetamide + 2-methoxyethanol binary mixtures at temperatures from K to K., Physics and Chemistry of Liquids,Vol. 50, No. 3, 346–366, 2012,
D. Das 1,*, Z. Barhoumi, N. Ouerfelli, The reduced Redlich-Kister equations for correlating volumetric and viscometric properties of N,N-dimethylacetamide + dimethylformamide binary mixtures at temperatures from K to K., Physics and Chemistry of Liquids, Vol. 50, No. 6, 712–734, 2012.
D. Das1,*, A. Messaâdi, N. Dhouibi, N. Ouerfelli., Investigations of the Reduced Redlich-Kister Equations for Correlating Excess Properties of N,N-Dimethylacetamide + 2-Ethoxyethanol Binary Mixtures at Temperatures from K to K., Physics and Chemistry of Liquids, Vol. 50, No. 6, 773–797, 2012
A. Messaâdi 1, N. Ouerfelli 2,*, D. Das 3, H. Hamda 4, M.A. Hamzaoui5 , Correspondence between Grunberg-Nissan, Arrhenius and Jouyban-Acree Parameters for Viscosity of Isobutyric Acid + Water Binary Mixtures from K to K., Journal of Solution Chemistry, Vol 41, 2186–2208, 2012.

28. Our contributions
7. D. Das 1,*, A. Messaâdi 2, N. Dhouibi 2, N. Ouerfelli 2,3, A.H.Hamzaoui, Viscosity Arrhenius activation energy and derived partial molar properties in N,NDimethylacetamide + Water Binary Mixtures at Temperatures from K to K., Physics and Chemistry of Liquids, Vol. 51, No. 5, 677–685, 2013.
8. M. Hichri , D. Das ,*, A. Messaâdi, E.S. Bel Hadj Hmida, N. Ouerfelli ,I. Khattech , Viscosity Arrhenius activation energy and derived partial molar properties in of N,N-Dimethylacetamide + 2-Ethoxyethanol Binary Mixtures at Temperatures from K to K. Physics and Chemistry of Liquids, Vol. 51, No. 6, 721– 730, 2013.
9. M.Dallel*, D.Das, E.S. Bel Hadj Hmida, N.A. Al-Omair, A.A. Al-Arfaj & N. Ouerfelli , Derived partial molar properties investigations of viscosity Arrhenius parameters in formamide + N,N-dimethylacetamide systems at different temperatures, . Physics and Chemistry of Liquids, Vol. 52, (3), pp 442–451, 2014.
10. N. Ouerfelli, D. Das*, H. Latrous, M. Ammar, J. Oliver, Transport behaviour of the lanthanide 152Eu(III), Gd(III) and 170Tm(III) and transplutonium element 254Es(III), 244Cm(III), 241Am(III),249Cf(III) and 249Bk(III) ions in aqueous solutions at 298 K , Journal of Radioanalytical and Nuclear Chemistry, Vol 300 issue 1 pp, , 2014.
11. Z. Trabelsi , M. Dallel , H. Salhi , D. Das *, N.A. Al-Omair , N. Ouerfelli , On the viscosity Arrhenius temperature for methanol + N,N-dimethylformamide binary mixtures over the temperature range from K to K. Physics and Chemistry of Liquids, Accepted, 2014
12. N. Dhouibi ,*, M. Dallel , D. Das , M. Bouaziz, N. Ouerfelli , A.H. Hamzaoui, Notion of Viscosity Arrhenius temperature for N,N-dimethylacetamide with N,Ndimethylformamide binary mixtures and its pure components, Physics and Chemistry of Liquids, Accepted, 2014
13. D. Das *, H. Salhi , M. Dallel , Z. Trabelsi , A.A. Al-Arfaj , N. Ouerfelli , Viscosity Arrhenius activation energy and derived partial molar properties in isobutyric acid + water binary mixtures near and far away from critical temperature from K to K., Journal of Solution Chemistry, Accepted, 2014.

29. Perspectives
The study of other physicochemical properties to apply other methods or models for estimating excess functions to highlight the existing interactions along with some more information's inside the mixtures in solution in collaboration with thermodynamics and organic chemists.

30. Thank You all