High dielectric constant supercooled liquids, tools in energetic problems

Journal of Molecular Liquids, 54 (1992) 103-113 Elsevier Science Publishers B.V., Amsterdam

103

HIGH DIELECTRIC CONSTANT SUPERCOOLED LIQUIDS, TOOLS IN ENERGETIC PROBLEMS GIANFRANCESCO BERCHIESI, FARHAT FARHAT and MARCO DE ANGELIS Dipartimento di Scienze Chimiche dell 'UniversitA, Via S .Agostino 1, 62032 Camerino, Italy and STEFANO BAROCCI European Patent Office, La Haigue, Holland . (Received 2 January 1992)

ABSTRACT The utilization and the model of the systems showing high dielectric constant are emphasized . INTRODUCTION Three aspects are present in any energy planning problem : a) the energy production b) the energy storage c) the energy distribution as outlined in the figure 1 . If the energy flux between the production A and the storage B is different from that between B and the utilization C, the energy will be stored if J AB > J BC or the stored energy will be used if

1

JAB < J BC 2 It is clear that the system B has the same importance as the system A because the energy need of C changes periodically in the time . 0107-7322!92/$0&.00

41992 - Elsevier Science Publishers B_V. AB rights reserved



104 STORAGE SYSTEMS The energy storage may be obtained in a thermal, mechanical or electric way, but all these points may be treated in an unique way : an extensive quantity L (enthalpy change, or electriccharge . . .) and an intensive one 1 (temperature change, or electric potential . . . .) are connected according to : L = p 1 3 where p is a phenomenological coefficient (i .e ., thermal capacity, electric capacity . . .) ; the attention of the technological research must be turned to the p coefficients, because the formula 3 implies that if p is very high it is possible to obtain= large values of L under low change of potential . HIGH DIELECTRIC CONSTANT LIQUIDS : SUPERCOOLED MIXTURES COMPOSED OF ACETAMIDE AND ELECTROLYTE A research on this subject has been carried out (1-21) and the following informations have been collected : 1) Acetamide (and other low molecular weight amides) and alkali or alkali earth salts (particularly Na+ ions) derived from polyatomic strong acids give mixtures which easily supercool in a concentration range around the eutectic composition . 2) Supercooled mixtures exhibit high viscosity and viscoelastic behaviour (15-21) . 3) Ultrasonic and viscoelastic spectrum support a microheterogeneous model for these systems (20) . 4) In the supercooled region, the dielectrir constant reaches very high values (17,20) . The last point is the most interesting according to the equation 3 and to the problems connected with the electric accumulators . Three systems have been studied : 1) Acetamide+NaSCN, XNaSCtr 0 .225, (17) ; 2) Acetamide+CF3000Na, msalt 8 .06, 19 .20, 29 .00 mole kg1 (20) ; 3) Acetamide+Ca(N03)2, msalt =5 .215 mole kg 1 (20) .

105 All these systems show a megavalue of the dielectric constant and, from this point of view, are materials with possible application in the field of the energy storage . Acetamide-i-NaSCN eutectic mixture shows dielectric constant values in the range : 4 10 - 40 10 6 when the temperature varies between -7 .6 and 38 .1 °C, and at the same time, a relaxation frequency changing from 0 .28 Hz to 18 .4 Hz in the same temperature range . Trifluoroacetate+acetamide mixtures present a more interesting dielectric behaviour, table 1 . In fact in some cases the relaxation Frequency, F r, is higher or of the same order of the distribution grid . This parameter is very important because the dielectric constant decreases at normal values for f >f r In figure 2 a three-dimension plot of the dielectric constant c as a function of T and f is shown . TABLE 1 Dielectric constant and relaxation Frequency of some liquids Acetamide+

m/mole kg 1

E/106

fr/Hz

T/°C

CF 3000Na

8 .0604

6 .0

204 40 2 20 1 2 .5 0 .03 0 .25

40 20 0 40 20 40 20 10

19 .20 29 .00 Ca(NO, ; 2

5 .215

4 .5 3 .0 4 .0 2 .0 5 .0 3 .0 1 .6

THE MODEL The low value of the dielectric relaxation frequency implies that the dielectric process is viscosity dependent and it may be

10 6

I-* A

J

JAB B

BC C

Fig . 1 . Schematic drawing concerning the connection between the production, the storage and the utilization of energy . outlined in the following way . The low conductivity (20) shows that the salt is undissociated, whereas the viscoelastic properties suggest the presence of salt regions and amide regions (15,16,18-20) . We suppose that the salt micelles (CF 3COONa) n lose some Na+ ions, which solvate in the acetamide : (CF3000Na) n - [(CF3000) n(Na) + m Na4n.-m3 m m Na+ + p CH 3CONH 2 [Nam (CH 3CONH2 ) 7 +m P So we have two types of polymeric structures, the anionic and the cationic one . We suppose the form of the polymeric structures is spherical and the surface tension maintains this form in the dispersing medium . One sphere, i .e . the cationic one, which is close to the negative electrode, is affected by the electrostatic pressure of the electric field and it is "squashed" on the electrode . The shape changes and the charge is transferred from the body of the



107 sphere to the surface of the "bowl" .

• i''/s ue•i~

L/I V//I- !//IIIi!I//IA : -` 'I///I~WIII//~ //~'/%~~ ~`

•/

/~~

7~

'o_o Fig . 2-a . Three dimension plot : dielectric Constant/frequency/ temperature, concerning the acetamide-sodium trifluoroacetate mixture (8 .06 mole lcg l ) . The sphere will be strained till the force originated by the surface tension and the electric Field force become equal : 4Wra° S z- 8'K 'Y r 4 where a° is the charge density (without dielectric) in the electrodes, z the number of charges on the sphere and 5 the value of the electronic charge, -y the surface tension and r the curve radius of the strained surface . The equation 4 may be written 47r a° a 4 y 2 7r rh/z S h 5 where h is the height of the bowl and 2-rrh the surface of the bowl . supposing that the height h is very low and that consequently the charge z S is on the surf ace, we have 6 411a° = 2 y /a h where a is the density charge on the bowl surface . the equation 6 gives :



1 08 aa° =y/2rh

7

4

4A

A

4°

;O

Fig . 2-b . Three dimension plot concerning the dependence of the dielectric constant on temperature and frequency For the 19 .30 mole kgI sodium triFluoroacetate-acetamide supercooled liquid . 4

. 0

59

4 5,0 Q4 4_9

9A 4A 4A ggg39

4,4 as

y9

7A 4, . 0

`to

40

Fig . 2-c . Dependence of the dielectric constant on temperature and frequency for the 29 .00 mole kg1 sodium trifluoroacetateacetamide supercooled liquid .



109 Being a

a ° . 47r a ° =E and E=V/d, we have = 82r7 d2/V2 h 8 where d stands for the electrode distance and V the potential difference . In a heterogeneous system, like those we are treating, the electrode surface is not completely covered by "squashed bowls" but only a Fraction 9 . If a and a' stand for the surface density in the region covered by the bowls and in the region which is in contact with the amorphous amide respectively, we have atrue ' a o - a' (1- B) 9 which easily gives 10 aura =LB Es ; E (1- e) a° where (:stands for the dielectric constant of the amorphous amide . = E

s

log E, 7

5

3

O I -2

0

2

4

log f/ H z

Fig . 3 . Comparison between the experimental (o) values of £' and the curve calculated according to the equations 22 and 25, and using a viscosity value of 10O P in the equation 25 . Experimental values refer to the 8 .o6 mole kg 1 mixture .



1 10 The previous equation gives =B 8W-1 d2/hV2 + E (1-g) 11 Etrue The First term contains 871- 'yd2/5l2 which For d-0 .1 cm, V=1/300 stat volt (the experimental conditions),-y=1 dyne cm-1 is 2 .3 1o 6 ; the second term may be neglected in comparison to the first owing to the fact that normal liquids exhibit a dielectric constant in the range 1-10 . By comparison of the Formula 11 with the experimental value of E true, it is possible to adjust the term 9 y /h, which varies in the range 0 .71 1 .99 dyne cnC 2 for the different solutions at 20°C . From a kinetic point of view the model gives the following equation : a charge transfer from the bulk to the surface of the bowl and viceversa (charge) surface + A (charge) bulk + A (A being one of the molecules surrounding the ion and which behaves as a catalyst) is controlled by the relaxation equation, when an alternating field is applied 12 +iw T) = n exp (i Wt)/(1+iw r) ion = ne ion l n is the number /(1whern of ions which relax at the frequency w , whereas neion is the number of ions in equilibrium conditions,T is the relaxation time . The equation 12 easily gives P* = B' exp(i wt)/(1+iwT) 13 where P* is the polarization . B', being the limit of Pt when co tends to zero, it is possible to write PA=P°exp(i w t)/(1+i w T) =(P°/E°) E+/(1+iw T) 14 4 wP*=(e s1 )E*/(1+iWT) 15 4r (P,*) + P.* )/E* _ ( e s-1 )/(1+iwr) 16 Em)/(1+iwT) D/E* - (c s 4WP* 17 Being the relaxation equation dP"D/dt = Ps - P** 18 According to the equation 17, the equation 18 gives pt = S exp(-t/T)+ [(ES Em )/47F (1+iw T) ]E°expiwt 19 Neglecting the first term in comparison to the second, the follonW

o



1 11 wing equation is obtained 4 wPJJ/E* _ ( e 5 4Q/(1+icT) E- -4E .- (ES E m )/(1 +itoT)

20 21

which gives the real and imaginary part of the dielectric constant : -1 22 { E'- E m )/( E s- Em ) _ (1+W2 T2 )

23 =wr/(1+CJ2 T.2 ) The relaxation time in this type of dielectric relaxation is concerning the equilibrium between surface and bulk ions and is given by T = (k d+k i )/C A 24 Under the reasonable supposition that this kinetic is diffusion controlled and using the Stokes-Einstein equation for k d and ki , we can write T - (3/16)7)/(RICA ) 25 .) E"/(E 5 E

which correlates the relaxation time and the ratio viscosity/temperature (7lstands for the viscosity) . A logy versus log ()7/T) plot cuts the vertical axis at -2 (20) (using the cgs system), that is CA =2 .3 10-4 mole/liter . In figure 3 the trend of E • and E", calculated according to the equations 22, 23 and 25 is shown together with the experimental curve . The viscosity value employed in the equation 25 is 100 P, which is close to the experimental value (20) . It is possible to deduce that the agreement is satisfactory around the relaxation frequency . At higher frequency a second relaxation is present (17) . At lower frequency a distribution of relaxation times is also present (20) and in this sense the model must be improved . We can conclude that owing to the fact that the dielectric mechanism is viscosity dependent, it is slow and the aim of the future research in this Field is to Find the best conditions to increase as much as possible the relaxation frequency .

1 12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

F .Castellani, G .Berchiesi, F .Pucciarelli, V .Bartoccl, J .Chem . Eng .Data , 27 (1982) 45 ; ibid . 26 (1981) 150 G .Berchiesi, F .Castellani, F .Pucciarelli, J .Pure Appl . Ultrason ., 5 (1983) 66 G .Berchiesi, G .Gioia Lobbia, V .Bartocci . G .Vitali, Thermochim . Acta, 70 (1983) 317 G .Gioia Lobbia, G .Berchiesi, Thermochim .Acta, 74 (1984) 251 G .Gioia Lobbia, G .Berchiesi, Thermochim .Acta, 72 (1984) 391 G .Gioia Lobbia, G .Berchiesi, G .Poeti, Thermochim .Acta, 74 (1984) 247 G .Berchiesi, G .Gioia Lobbia, M .A .Berchiesi, G .Vitali, J . Thermal Analysis, 29 (1984) 729 G .Gioia Lobbia, A .Amico, Thermochim .Acta, 87 (1985) 257 G .Gioia Lobbia, G .Berchiesi, G .Poeti, Thermochim .Acta, 78 (1984) 297 G .Gioia Lobbia, G .Berchiesi, Thermochim .Acta, 118 (1987) 223 G .Gioia Lobbia, G .Berchiesi, J .Chem .Eng .Data, 109 (1987) 52 G .Vitali, G .Berchiesi, Thermochim .Acta, 143 (1989) 205 ; ibid. 142 (1989) 13 F .Castellani, G .Berchiesi, V .Bartocci, J .Thermal Analysis, 36 (1990) 1071 G .Vitali, G.Berchiesi, F .Castellani, Thermochim .Acta, 179 (1991) 231 G.Berchiesi, G .Vitali, P .Passamonti, R .Plowiec, J .Chem .Soc . Faraday Trans .2, 83 (1987) 619 R .Plowiec, A .Amico, G .Berchiesi, J .Chem .Soc .Faraday Trans .2, 81 (1985) 217 A .Amico, G .Berchiesi, C .Cametti, A .W. Biasio, J .Chem .Soc„ Faraday Trans .2, 83 (1987) 619 G .Berchiesi, g .Vitali, A .Amico, J .Mol .Liquids, 32 (1986 99 G .Berchiesi, G .Vitali, R .Plowiec, S .Barocci, J .Chem .SUPw Faraday Trans .2, 85 (1989) 635 G.Berchiesi, M .De Angelis, G .Rafaiani, G .Vitali, J .Mol . Liquids, in press (1991)

113 21

G .Berchiesi, "Amide-Electrolyte molten systems : mixtures showing megavalue of the dielectric constant", in "Molten fait chemistry and technology", M.Chemla and D .Devilliers Ed ., Materials Science Forum 1991, vol-73-75, p .653-662