NON-EQUILIBRIUM THERMODYNAMIC STUDIES OF ELECTRO-KINETIC EFFECTS-XI. STUDIES WITH

AQUEOUS DIOXANE

R. L. BLDKHRA and M. L. PARMAR

Chemistry Department, Himachal Pradesh University, Simla 171005 and

V. P. Sti~Rm

Chemistry Department, Panjab University, Chandigarh 160014, India

Abstract - Experimental results for the measurements of electro-osmosis, electro-osmotic pressure difference, streaming potential for dioxane-water (DH,O) mixtures (3@!,, WA, 50% and 60% by mass of dioxane) using Pyrex sintered disc (G,) at 25” and at voltages of 40 V to 300 V are reported. The data are aaalysed in the light of the theory of non-equilibrium thermodynamics. It has been found that the validity of the phenomenological relations describing electro-kinetic effects increases with the decrease in the dielectric constant of the mixture. Second-order coefficients estimated from the clcctro-osmosis and electro-osmotic pressure difference are reported. Onsager’s reciprocity relations have been found to hold good for all the mixture& It has been found that the concentration dependence of Lz2 and L,, do not conform to the Spiegler’s frictional model. Efficiency of electro-kinetic enwgy conversion (q,) for electro-osmotic flows has been calculated and it is found that for different composition ofclioxane-water mixtures q_ was obtained at half the value of the electro-osmotic pressure difference.

INTRODUCTION

Electra-kinetic effects involve interactions between the flow of matter and the flow of electricity through membranes, porous media, capillaries, etc, and ther- modynamicsof irreversible processes[l] has been used successfully to treat these phenomena. For systems close to equilibrium, the following linear phenome- nological relations hold:

I=L,,AQ,+L,,AP

J = LzI A@ + L,, AP (1)

Here I and J denote the electric current and the volume flow, respectively,. while A@ and AP are the electric potential difference and the pressure difference. The phenomenological coefficients L,,, L,,, L,,, and L,, relate to electric conduction, streaming con- duction, electro-osmosis, and permeation, respec- tively. It was found earlier[Zd] that the relation (1) has a limited domain ofvalidity, and that it ceases to be applicable when the ‘force’ (A4, in this case) exceeds a certain limit. Further Blokhra et a/[71 showed that the range of validity of the phenomenological relations also depends on the bulk dielectric constant of the liquid phase. One of the objects of the present in- vestigation has been to study the phenomenon with a liquid mixture whose dielectric constant can be varied considerably. Water-dioxane mixtures at different compositions have been selected for the present in- vestigation. Other objects of the investigation are: (i) to estimate the range of validity ofthe equations(l), (ii) to report the phenomenological coefficients, (iii) to verify Onsager’s reciprocity relations (L,, = L,,), (iv) to determine concentration dependence of phenome nological coefficients to check Spiegler’s frictional model, (v) to estimate the efficiency of energy con- version for electro-osmosis.

The present treatment only holds if the system is a discontinuous one[l]. Wechecked the discontinuity of the system by determining the electric conductivity of each of the two subsystems (D-H20 mixture) and that of the diaphragm (disc). It was found that the electric conductivity of the liquid sub-system is ten times greater than that of the diaphragm in the present study, which suggests that there is bound to be a jump of electric potential at the diaphragm and the system fulfills the condition of discontinuity.

EXPERIMENTAL

Dioxane (G.R.) was purified by refluxing over sodium metal 6 h followed by distillation. Triple- distilled water over alkaline KMnO, was used for preparing the different compositions of the mixtures of dioxane and water. All mixtures were prepared by weight. All the experiments were carried out at 25” in an air thermostat, using the apparatus described elsewhere[S].

In investigations with liquid mixtures, there is the danger of development of concentration gradients and this was checked by determining the refractive index of the liquid subsystems before and after the application of the electric potential difference. The electric poten- tial across the disc was applied through bright plati- num electrodes.

RESULTS AND DISCUSSION

The estimation of the phenomenological coefficients L2,, and L,, has been done as described earlier[3-81. The data are given in Table 1.

It was found that, in the case of dioxane-water mixtures, the linear phenomenological relations (1)do not describe the phenomena beyond a certain value of, A@ and that these equations cease to hold beyond A@

533

534 R. L. BLOKHRA, M. L. PARMAR AND V. P. SHARM

Table 1. Electra-osmotic data for different dioxane-water mixtures at 25” (The percentages are mass fractions of dioxane multiplied by 100)

- A@ AP x IO’ Lo,,=, 41 x IO& 42 x 105 (V) dyn.cm12 (cm”s-‘) (cm3sm’V-‘) (cm”dyn-‘s-l)

40 0.60 60 1.00 80 1.41

100 1.81 120 2.01 140 2.41 160 2.81 200 3.41 220 3.61 240 4.02 260 4.41 280 4.82 300 5.22

40 0.59 60 0.99 SO 1.19

loo 1.39 120 1.78 140 2.18 180 2.17 200 2.97 220 3.17 240 3.56 260 4.16 280 4.35 3ocl 4.95

40 0.59 60 0.99 80 1.38

100 1.78 120 2.17 140 2.37 160 2.57 180 2.96 200 3.36 220 3.75 240 3.95 260 4.15 280 4.54 300 4.74

40 0.39 60 0.59 80 0.79

100 1.18 120 1.38 140 1.77 160 1.97 180 2.17 200 2.36 220 2.56 240 2.95 260 3.15 280 3.55 300 3.94

30% Dioxane-Water

0.015 0.023 0.030 0.038 0.041 0.045 0.052 0.064 0.070 0.078 0.084 0.107 0.129

40”/, Dioxane-Water

0.021 0.032 0.042 0.052 0.063 0.066 0.067 0.072

3.75 3.83 3.75 3.80 3.41 3.21 3.25 3.20 3.18 3.25 3.23 3.82 4.30

5.25 5.33 5.25 5.20 5.25 4.71 3.12 3.60

1.68 2.36 2.87 3.09 2.51 2.20 2.20 2.09 2.01 2.06 2.06 2.30 2.58

3.53 3.96 4.53 4.95 5.39 3.85 3.18 2.70

0.077 3.50 2.60 0.084 3.50 2.47 0.090 3.46 2.21 0.099 3.53 2.12 0.110 3.66 1.95

50% Dioxane-Water

0.012 3.00 1.97 0.018 3.00 1.65 0.024 3.00 1.74 0.031 3.10 1.73 0.037 3.08 1.74 0.042 3.00 1.73 0.045 2.81 2.24 0.052 2.88 2.24 0.058 2.90 1.86 0.065 2.95 1.74 0.071 2.95 1.77 0.077 2.96 1.69 0.083 2.96 1.86 0.089 2.96 1.74

60% Dioxane-Water

0.10 2.50 2.29 0.015 2.50 2.37 0.020 0.025 0.030 0.036 0.039 0.041 0.045

2.50 2.24 2.50 2.30 2.50 2.26 2.57 2.34 2.43 2.26 2.27 2.30 2.25 1.89

0.049 2.04 1.85 0.053 2.01 1.70 0.056 2.cil 1.64 0.058 1.93 1.48

Non-equilibrium thermodynamic studies 535

Table 2. Values of first-order and second-order coefficients of (2)

Composition of dioxane

(% by mass)

30 40 50 60

b, x IO’ (cm3AJ-‘)

3.80 5.25 3.00 250

+ 0.20 -3.40 +2.30 - 2.70

L2 x lo8 L x 10’0 (cmsdyn-ls-‘V-L) (cm’dyn-*s-l)

4.00 12.00 3.10 0.10 5.30 0.26

= 100 V, 120 V, 140 V, 160 V for 30x, 40x, 50”/,, and 60% dioxane mixtures, respectively, These values of A@ suggest that the range of validity of the phenome- nological relations increases with increasing dioxane content and it is in accordance with our earlier analysis[5-81 that, the lesser the value ofthe dielectric constant, the greater the domain of the validity of the linear relations.

It is found, on analysing the data as described earlier[3-81, that the following types of the phenome- nological relations describe the phenomena in the non- linear range :

I= L,lA@ + L,,AP +&,,(A@)*

+ &,,(A@AP) + L&AP)* + . . . (2)

I=L,,A~+L,,AP+L2,1(A~)2 + I&A@AP) + .!&AP)* + . .

where L,(i, k,j = 1,2) are known as second-order phenomenological coefficients. The second-order coefficients Lzllr L,,, and L,,, have been determined as described earlier[6,8] and these, along with the first order coefficients (L2,), for different mixtures, are given in Table 2.

The streaming potential A@ was measured with the help of the apparatus as described earlie@]. The data on the streaming potential is given in Table 3.

Measurements of the streaming potential, AD*,, for diierent mixtures show that AmS varies linearly with the applied pressure difference, BP, across the disc. The vaIues of the cross-coefficient L,, has been estimated

Table 3. Streaming-potential data for different dioxane- water mixture at 25”

- hP x lo3

(dyn.cm-‘) $1

30% Dioxane-Water

10.04 6.38 20.08 14.52 30.12 21.50 40.16 29.10 50.20 35.95 60.24 42.98

40% Dioxane-Water

9.90 13.50 19.80 20.52 29.49 39.48 39.59 52.97 49.49 65.91 59.38 79.46

BP x lo3 (dyn cm-‘) (2,

50”/, Dioxane-Water

9.87 11.48 19.75 24.12 29.62 36.46 39.50 49.10 49.37 60.98 59.24 72.53

60% Dioxane-Water

9.85 9.02 19.70 17.95 29.55 27.16 39.40 36.55 49.25 45.9 1 59.10 55.17

as described earlier[8,9]. The values of L,, for different mixtures (composition shown in parenthesis) came out as: 4.05 x 10M4 (30x), 5.17 x 10m4 (40”/,), 2.91 x lo-’ (50x), 2.50 x 1O-4 (cm’AJ_‘) (60%). These values are in fairly good agreement with the values of L,, obtained from electro-osmotic data (given in Table l), showing that Onsager’s reciprocity relations hold for the dioxane-water/Pyrex-sintered- glass system.

The phenomena of electro-osmotic flow and streaming potential can be used with advantage in the design of energy-conversion devices. In the former case, electric energy is converted into mechanical work whilein the latter the reverse conversion of mechanical work into electric energy takes place.

In general, the equation for the conversion efficiency, ‘I, in terms of thermodynamic conjugate fluxes and forces J and X have been deduced by Osterle[lO, 111 as:

J,X, 9 = - JiXi

where the subscripts ‘0’ and ‘< represent the output and input quantities respectively. The negative sign in (3) indicates that output forces and fluxes are in the direction opposite to that of input forces and fluxes. In the case of electro-osmosis, the applied electric poten- tial difference A# is the input force and the consequent pressure difference Af is the output force. Therefore, the expression for the energy conversion efficiency, qo, for electro-osmosis, in the range of the linear pheno- menological laws, is given by :

JAP

% = - (A@)‘/R (4)

where R is the electric resistance of the total system (sub-systems plus the diaphragm)[l2-141 and the assumption L,, A0 >> L,, AP has been made (see equation (1)). The values of qe at A@ = 100 V, ob- tained from (4), are given in Table 4.

In the case of electro-osmosis, the volume flow I vanishes when the steady-state is reached so that AP equals the electro-osmotic pressure. This means that tie will be zero if either AP equals the electro-osmotic pressure or if AP = 0. Therefore, the plot of ve us AP, for a fired value of the electric potential difference A@, must pass through a maximum in all the mixtures of dioxane and water. This is shown in Fig. 1. This figure shows that the conversion efficiency is a maximum in case of 50% dioxane.

It is, further, revealed that qmar appear appro- ximately at AP equal to half the value of electro-osmotic pressure. This observation can be

536 R. L. BLOKHRA, M. L. PARMAR AND v. p. %.4RMA

Table 4. Values of the energy conversion efliciency, ‘I~, for different dioxane-water mixtures at Aa = lOOV, and at 25”

J(cm3s-‘) AP x 103(dyn.cm-2) ‘le X 10s

0.038 0.035 0.032 0.030 0.027 0.022 0.017 0.012 0.007 0.004 O.@Xl

0.052 0.046 0.042 0.036 0.033 0.030 0.025 0.020 0.017 0.014 0.010 0.x)4 0.tXX-J

0.031 0.029 0.027 0.025 0.022 0.018 0.015 0.012 0.008 0.006 0.004 O.ooO

0.025 0.024 0.020 0.018 0.015 0.013 0.009 0.008 0.005 0.004 O.tKKl

30% Dioxane-Water 0.000 0.100 0.200 0.261 0.361 0.522 0.682 0.843 1.003 1.104 1.204

40% Dioxane-Water 0.000 0.098 0.178 0.296 0.356 0.415 0.514 0.613 0.673 0.732 0.811 0.930 0.989

50% Dioxane-Water 0.000 0.118 0.217 0.335 0.513 0.730 0.908 1.086 1.303 1.421 1.540 1.658

60% Dioxane-Water 0.000 0.039 0.196 0.295 0.413 0.531 0.650 0.709 0.807

0.866 1.181

0.00 0.63 1.15 1.41 1.75 2.07 2.09 1.82 1.26 0.79 0.00

0.00 1.13 1.87 2.66 2.94 3.11 3.21 3.07 2.86 2.54 2.03 0.93 0.00

0.00 1.37 2.34 3.35 4.51 5.26 5.45 5.21 4.17 3.41 2.44 0.00

0.00 0.34 1.41 1.91 2.23 2.49 2.11 2.04 1.45 1.25 0.00

justified on theoretical considerations. On substituting the value of J from (1) in (4), we get:

q. = -(L, 1 A@ + L,, AP) . AP/(A@)‘/R (5)

Here the term containing 4 i( =4J has not been neglected. Since the input force is kept constant, the quantity (A@)‘/R in (5) is constant. Now applying the condition

(&# AP) = 0

40

“0 2 32 %

24

02 04 05 08 1.0 1.2 Itl 1.6 APxI03Cdyncni2) atA+..lo~v

Fig. 1.

for a maximum we get

&,(AP/AQ) + L2, = 0 (6) But we know from equation (1) that at the steady state where J = 0

(APIA@), _ ,, = - 3 (7) 22

From equations (6) and (7), we get

AP = t(AP),- o

where (AP), = 0 represents the value of electro-osmotic pressure difference at J = 0.

If the total volume flux (J),,=, is identified with the sum of the velocity of dioxane (V,) and velocity of water (V,), then, according to Spiegler’s assumption of addivity of the hictional forces involved in the process, bz can be represented[8] as:

where S stands for the Pyrex-sintered disc, W stands for water and D for dioxane and f stands for the frictional coefficients between the species denoted by the subscripts.

Substituting the bracketed terms in (8) as (I&, and (L&, respectively, the equation (8) can be written as:

L22 = XDG22)D + x,w,,hv

or

L22 = tL22)D + (L22h’ - &,,)fi,” (9) This equation suggests that h2 should vary linearly with the mass fraction X,. The present investigations show that J& does not vary linearly with X,, showing thereby that the frictional model of Spiegler does not apply to the dioxane-water mixtures. This suggests that the frictional forces are not additive in the present case. The above mentioned considerations in case of

Non-equilibrium thermodynamic studies 537

Iet also do not fit in the frictional model and this may 4. be attributed to the associated solvent molecules in these mixtures.

5

6. Acknowledgement - Authors are grateful to Professor M. L. Lakhanpal (Chandigarh) for encouragement, discussion and teen interest in this investigation. One of the authors (M.LP.) is also grateful to C.S.I.R., New Delhi (India) for the award of Post Doctoral Fellowship.

7.

8.

9.

10. REFERENCES 11.

R. L. Itlokhra and T. C. Singhal, J. elecrroauul. Cheat. 57, 19 (1974). R. L. Blokhra and M. L. Parmar, J. Colloid Sci. 51,214 (1975). R. L. Blokhra and M. L. Parmar, J. electroanal. Chem.62, 373 (1975). R. L. Blokhra, C. L. Kaul, B. R. Soni and S. K. Jalota, Elecrrochimica Acra 12. 773 11967). R. L. Blokhra, M. L. Parmar and V: P. Sharma in Colloid and Jnterjhce S&ace (Bdited by Milton Kerker), Vol. IV. Academic Press, New York (1976). R. L. Bloklua and T. C. Singhal, J. phys. Chem. X$2302 (1974). J. F. Osterle, Appl. scient. Res. 12,425 (1964). I. F. Osterle, J. appl. Mach. 31, 161 (1964).

R. Haase. 7hermodvnamics of Irreversible Process. 12. R. C. Srivastava and A. K. Jain, J. P&u. Sci. (Physics Addison-Wesley (19i9). _ Section) 13, 1603 (1975). R. P. Rastogi and K. M. Jha, J. phys. C/tern. 70, 1017 13. R. C. Srivastava and M. G. Abraham, J. them. Sm. (1966). Faraday 7?anraction I, 72,263l (1976). R. L. Blokhra and T. C. Singhal, J. electroaml. Chm. 48, 14. R. C. Srivastava and M. G. Abraham, J. C&id Sci. 57, 353 (1973). 58 (1976).