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Dielectric study of a ferrofluid Fe2CoO4 in dibutyl phthalate or diethylene glycol in the frequency range 1 mHz–10 MHz
Journal of Magnetism and Magnetic Materials 122 (1993) 182 186 North-Holland
MJ.
Dielectric study of a ferrofluid Fe2CoO 4 in dibutyl phthalate or diethylene glycol in the frequency range 1 m H z - 1 0 MHz A. Siblini, L. J o r a t and G. Noyel L.R. (', C.L, Laboratoire de Recherche sur les (Tapteurs h ('olloides el l'ln,~'trumentation. Unirersitd ,h'an Monm't, 23 rue du Docteur Paul Michelon, 42023 Saint-Etienne Ct:dex 2, France We present a dielectric study on ferrofluid solutions of FeeCoO 4 in diethylene glycol or dibutyl phthalale, from 50 mt Iz to 10 Mltz, in the temperature range - 1 6 0 +40°C. When a transversal magnetic field is applied, a magnetodielectric anisotropy is in evidence. Above a concentration limit the colloidal suspensions do not remain well dispersed at low temperature. Moreover it seems that the melting point of a solution could be affected.
1. Introduction To use the magnetic properties of ferrofluids in a wide temperature range for applications in sensors [1], one must know if the solution, which is a normal colloidal suspension at room temperature, remains homogeneous. A dielectric study in large intervals of frequency and temperature, seems to be a well-adapted means of investigating the homogeneity of the ionic dispersion and its behavior under a continuous magnetic field. In this paper we present a dielectric study of a ferrofluid F % C o O 4 in diethylene glycol (DEG) or dibutyl phthalate (DBP) at different volume concentrations x, from 40°C down to temperatures less than - 100°C, without and with a continuous magnetic field (100 Oe) applied perpendicularly to the electric field. The results obtained in the frequency range 1 m H z - 1 0 MHz on static permittivity E~ and relaxation frequency £~, (corresponding to maximum losses e~,) may give indications of the homogeneity of the ferrofluids, or the existence and growth of possible aggregates.
2. Experimental The ionic ferrofluid solutions prepared in the laboratory of Professor Massart [2] are colloidal Correspondence to: G. Noyel, Universit6 Jean Monnet, 23 rue du Docteur Paul Michelon, 42(123 Saint-Etienne C6dex 2, France. Tel (33) 77.42.15.00, Fax (33)77.42.18.22. (1304-8853/93/$(16.00
dispersions of particles Fe2CoO 4 (diameter 10 nm) in a polar carrier liquid, dibutyl phthalatc (DBP) or diethylenc glycol (DEG). The maximum obtainable volume concentration x of particles without loss of homogeneity at room temperature is 13% for DBP and 6.5% for DEG. All the other mixtures are made by dilution in DBP or DEG for synthesis (purity better than 99%). Measurements were performed using a dielectric spectrometer built up in our laboratory, and described in ref. [3]. The total influence cell has a 24 pF geometric capacitance with thermal variations smaller than (I.5C/( between 100 and 200°C. A continuous transversal magnetic field of 100 Oe is obtained from a coil placed around the cell. The temperature is controlled by a PID regulator which allows to stabilize the sample temperature within +_(I.I°C and provides linear temperature variations at slow rates (0.5, I°C/min), to avoid undesirable gradients. Two types of recording measurements can be done: firstly an isothermal mode where the temperature is constanl and the frequency varies, secondly an isofrcquency mode (fig. 11 where one or several frequencies arc selected and the tcmperalure is varying so slowly that measurements are done in a quasi static state. Figs. 1 and 2 give respectively the temperature dependence of complex permittivity •* for a low volume concentration x 0.01 of FeeCoO 4 in DBP or in DEG. Thcse isofrequency recordings have been obtained at a slow cooling rate
~ 1993 - Elsevier Science Publishers B.V. All rights resm~ed
A. Siblini et al. / Dielectric study of ferrofluid F#2Co0 4
~'* 10 50 mHz ~-.~(e~)
183
e X
Electrode
60
~
somHz F//%~E
lOkHz
-----~rt
4o
:1 MHz
ikHz
4 */ ~lll~',~iliiii : "
Relaxation peak
\
f i ' , ~
\
;/ ii [.! , ~' I~
(E~)
effects
OX',,
J" I
,,, / ! i ~MH= ~
i~ ~
J
Re
axat
on
peak
1/ •
,
(~H ~
O .... 100
-50
O
150
~)°C
Fig. I. Isofrequency recording of complex permittivity E* (e', (") versus temperature (at 50 mHz, 10, 20, 40, 100, 200, 400 kHz, 1 M H z ) for an x = 0.01 ferrofluid solution of FezCoO 4 in DBP, w i t h o u t m a g n e t i c field (at d e c r e a s i n g t e m p e r a t u r e ) .
(l°C/min). Measurements above 10 kHz up to 1 MHz, in the present case, are performed by a LCR meter HP4275A. At lower frequencies (below 10 kHz) a temperature scan is necessary to obtain only one (at very low frequency) or two recordings (for example, 1 and 10 Hz or 100 Hz and 1 kHz) because it is necessary that, for a given temperature, the measurement can be done using the same electrometer range. In fig. 1, electrode effects appear only at 50 mHz and the static permittivity e s is well defined by the upper envelope of the dispersion curves e' (e~ being defined by the lower one). On the other hand for DEG, even at the same low volume concentration of Fe2CoO 4, notable electrode ef-
~}.,:~
:
--1gO
,~-zZ::gz;~/ :,:, -b~e, 50
@
0 °C
Fig. 2. I s o f r e q u e n c y r e c o r d i n g of c o m p l e x permittivity E* (E', e " ) v e r s u s t e m p e r a t u r e (at 50 m H z , 1, 10, 100 Hz, 1, 10, 20, 40, 100, 200, 400 kHz, 1 M H z ) for an x = 0.01 solution of F e 2 C o O 4 in D E G ,
w i t h o u t m a g n e t i c field (at d e c r e a s i n g temperature).
fects are clearly perceptible and so e s is not so easily defined versus temperature (fig. 2). At higher volume concentrations, electrode effects increase also faster for D E G as liquid carrier and in this case e s is known with a great imprecision. Moreover, these parasitic effects generate an important increase in conductivity which puts the LCR meter nearly out of range, shifting then the relaxation peak at 1 MHz (fig. 2). However, a comprehensive study, in the largest intervals of frequency and temperature, allows to estimate the dielectric parameters of ferrofluids particularly when the experimental data are very dispersed.
Table 1 Static p e r m i t t i v i t y p a r a m e t e r s (e s = A + B T * + C T . 2 ) for solutions of F % C o O 4 in D E G , with or w i t h o u t a c o n t i n u o u s t r a n s v e r s a l m a g n e t i c field, in the t e m p e r a t u r e r a n g e - 9 2 + 25°C x
0 0.005 0.010 0.020 0.030 0.040 0.065
Without H
With H = 100 O e
A
B
- 13.90 - 36.29 - 37.39 36.14 - 1.934 24.49 14.36
11.59 22.66 23.95 24.59 7.908 19.90 2.873
C
-
0.6731 0.7955 1.0610 1.2625 0.6469 0.9854 0.8076
A
B
C
- 35.36 - 37.16 - 34.85 - 4.178 - 27.61 7.443
21.88 23.40 23.51 8.586 20.61 5.392
- 0.7243 - 1.0157 - 1.1671 11.5131 - 1.0505 0.5439
184
A. Siblini et al. / Dielectric study <~f.l~'rrqfluid Fe eCoO 4 t'sll
3. Results
[]
~;s % ,'-'s
3.1. S t a t i c p e r m i t t i z , i t y
I
T h e static permittivity of each solution: l, 5, 13% of F e z C o O 4 in D B P a n d 0.5, 1, 2, 3, 4, 6.5% of F e 2 C o O 4 in D E G , may be fitted by the relation (with T * = 1 0 0 0 / T ) . Es = A
+BT*
+ C T .2.
(1)
F o r D B P solutions, the C coefficient may be negligible at any c o n c e n t r a t i o n . T h e coefficients of e s ( T * ) are given in tables 1 and 2 for all the solutions, with and w i t h o u t m a g n e t i c field. T h e m a g n e t o d i e l e c t r i c a n i s o t r o p y of ferrofluid solutions leads to a d e c r e a s e in Es (E s b e i n g the u p p e r e n v e l o p e o f d i s p e r s i o n curves e ' ( 0 ) from 50 m H z up to 1 M H z ) when a c o n t i n u o u s magnetic field (100 O e ) is a p p l i e d p e r p e n d i c u l a r l y to the electric field. This d e c r e a s e is o b s e r v e d over the whole t e m p e r a t u r e r a n g e ( - 100 to 40°C) as it has b e e n a l r e a d y shown by t h e o r e t i c a l a n d experimental studies in n a r r o w e r intervals o f frequency a n d t e m p e r a t u r e [4-6]. It is possible to c h a r a c t e r i z e this p e r s i s t e n t a n i s o t r o p y by the relative variation (eSH -- ES)/e s o f static permittivity with a n d w i t h o u t the continuous m a g n e t i c field H (fig. 3). W e can see (fig. 3) for the lowest v o l u m e c o n c e n t r a t i o n s x of F e z C o O 4 in D E G (0.5, 1, 2, 3 % ) that this relative deviation increases with x. F o r each of these c o n c e n t r a t i o n s (ESH -- ES)/e s is nearly c o n s t a n t versus t e m p e r a t u r e , which is consistent with the hypothesis of the h o m o g e n e i t y of these colloidal solutions in the whole t e m p e r a ture range. But above 3% and u n d e r o u r experim e n t a l c o n d i t i o n s this deviation varies on the
Table 2 Static perminivity parameters (E s = A + B T * ) for solutions of Fe2CoO 4 in DBP, with or without a continuous transversal magnetic field, in the temperature range - 8 9 + 35°C x 0 0.01 0.05 0.13
Without t t
With H = 100 Oe
A
B
A
B
(I.366 1.60 2.73 4.56
1.854 1.555 1.251 0.479
1.62 2.49 4.58
1.529 1.287 0.465
-4 -6 -8 10o
-5o
o
o "c
Fig. 3. Relative deviation (ESH -- CS)/e s of static permittivity versus temperature when an H = 100 Oe continuous perpendicular magnetic field is applied, for different volume concentrations x of Fe2CoO 4 in DEG. (a) x = 0.005, (b) x = 0.Ill, (c) x (I.[)2,(d) x = 0.03, (e) x 0.04,(f) x = 0.065,
o p p o s i t e side, which w o u l d s e e m to indicate the a p p e a r a n c e of a g g r e g a t e s or m u l t i l a y e r s which would be m o r e i m p o r t a n t for 6.5%, when a continuous m a g n e t i c field is applied. This b e h a v i o r is similar to that of the ferrofluid F e 2 C o O 4 in D B P previously s t u d i e d [7]. So it s e e m s that the h o m o g e n e i t y of these ionic ferrofluids d i s a p p e a r s a b o v e a v o l u m e c o n c e n t r a tion limit, which w o u l d d e p e n d on e x p e r i m e n t a l conditions. 3.2. R e l a x a t i o n f r e q u e n c y
T h e c a r r i e r liquid D B P or D E G is a p o l a r m a t e r i a l which exhibits a single a b s o r p t i o n p e a k in the i s o t h e r m a l m o d e (at a given t e m p e r a t u r e ) as well as in the isofrequency m o d e (at a given frequency). T h e s a m e b e h a v i o r is o b s e r v e d for ferrofluid solutions at low v o l u m e c o n c e n t r a t i o n s . As we saw in the case of the static permittivity of F e 2 C o O 4 in D E G ( a n d in our e x p e r i m e n t a l conditions), at h i g h e r c o n c e n t r a t i o n s and low temp e r a t u r e , r e c o r d i n g s are d i s t o r t e d p r o b a b l y by a p p e a r a n c e a n d growth of a g g r e g a t e s and multilayers, which affect also the s h a p e and the position of a b s o r p t i o n peaks. W h e n the c o n t i n u o u s transversal m a g n e t i c field is a p p l i e d on a well d i s p e r s e d solution, we note a
A. Siblini et al. / Dielectric stud>' of ferrojquid Fe 2CoO 4
185
Table 3 V o g e l - F u l c h e r - T a m m a n coefficients of r e l a x a t i o n f r e q u e n c y fm for F e 2 C o O 4 in D E G solutions (at low v o l u m e c o n c e n t r a t i o n x), with or w i t h o u t a transversal m a g n e t i c field b e t w e e n - 4 5 and - 100°C x
Without H
0 0.005 0.010 0,020 0.03(I
W i t h H = 100 O e
A
B
~)(K)
A
B
~)(K)
13.26 11.47 12.04 12.07 12.18
- 684.0 - 452.5 519.7 - 520.0 -559.2
127.7 140.4 138.8 138.4 136.8
11,99 11,85 11,83 12,15
- 476.6 - 485.0 - 484.1 -509.2
139.2 139.7 139.2 137.7
shift of the relaxation peak towards lower temperatures in D E G or in DBP [7] as carrier liquid. As the dielectric relaxation time is strongly correlated to the macroscopic viscosity of the medium [8] it seems possible to explain this shift by a local decrease of viscosity when the magnetic field is applied [7]. Variations of fm versus T at each concentration, with and without H, may be fitted by the V o g e l - F u l c h e r - T a m m a n (VFT) relation: log fm
=/4_, +
Bi T - T,~'
(2)
The V F T coefficients are displayed in table 3 in the case of D E G (for DBP see in [7]).
3.3. Crystallization and melt&g Using a not too slow cooling rate ( l ° C / m i n ) the pure dipolar liquid carrier or a well dispersed 80
C*
0/
colloidal solution (x <0.065) is obtained in a supercooled state and then in a glassy state. On heating the material at the same rate (fig. 4), the beginning of relaxation is observed in the supercooled state but crystallization appears and is nearly achieved after about ten minutes. All relaxations disappear, the loss factor E" becomes negligible and ~' falls down to 3.4; these values remain almost constant till the melting region, where E' rises sharply up to its static value %. At all volume concentrations below 6.5% of F e 2 C o O 4 in D E G the melting point temperature is about - 8 . 5 ° C (which is that of pure DEG). When a continuous magnetic field is applied at room temperature, and with the same thermal process (temperature decreasing at l ° C / m i n down to - 140°C and then increasing at the same rate), we note that the melting point is nearly - 11.5°C. The ferrofluid particles oriented by the continuous magnetic field could reduce the number of crystalline bonds and so melting would be obtained at a lower temperature. 4. Conclusion
E n
60
] ,i Crystallization
40
eo
Beginning
//.I/
Relaxation_ - -
,~.....
'~ i; ! :
".~ ";,i M e t ~g
/Y'!'
i.'::S
47:"~ b', ;.q::,t~:.: : ~ ' . , ~ _ _ _ - ~
....................
-]50
-100
50
0
O°C
Fig. 4. I s o f r e q u e n c y r e c o r d i n g for an x = 0.02 solution of F e 2 C o O 4 in D E G w h e n the t e m p e r a t u r e is i n c r e a s i n g at 1° C / m i n .
This experimental study shows the existence of a magnetodielectric anisotropy in ferrofluids containing particles of Fe2CoO 4 in diethylene glycol or dibutyl phthalate. The analysis of data on static permittivity shows that, under given experimental conditions, and under a continuous tranversal magnetic field, these ionic colloidal suspensions do not remain well dispersed at low temperature above a volume concentration limit. Furthermore, a thermal process may generate crystallization of the fluids, and it seems that a continuous magnetic field affects the melting point of the solution.
186
A. Siblini et al. / Dielectric" stu~(v o f ferrofluid Fe 2CoO 4
Dielectric measurements in large intervals of frequency and temperature can be used to test the thermal stability of colloidal solutions which could be selected for applications in sensors. References [1] J. Monin, O. Brevet-Philibert and L. Delaunay, in: C.R. 1()am~ J. Europ6ennes Opto61ectronique (Paris, 1990) p. 367.
[2] R. Massart, IEEE Trans. Magn. MAG-17 (1981) 1247. [3] O. Derriche, L. Jorat and G. Noyel, in: C.R. 11v''" Coll. O[ID (Hammamet, 1991) p. 254. [4] A.J. Mailfert and B. Nahounou, IEEE Trans. Magn. MAG-16 (1980) 254. [5] C. Cotae, J. Magn. Magn. Mater. 39 (1983) 85. [6] A. Espurz, J.M. Alameda and A. Espurz-Nieto. J. Phys. D: Appl. Phys. 22 (1989) 1174. [7] O. Derriche, L. Jorat, G. Noyel and J. Monm, J. Magn. Magn. Mater. 11)2 (1991) 255. [8] L. Jorat, G. Noyel and J. Huck, in: C.R. 1(//:n'~"Coll. OHD (Rennes, 1989) p. 251.
MJ.
Dielectric study of a ferrofluid Fe2CoO 4 in dibutyl phthalate or diethylene glycol in the frequency range 1 m H z - 1 0 MHz A. Siblini, L. J o r a t and G. Noyel L.R. (', C.L, Laboratoire de Recherche sur les (Tapteurs h ('olloides el l'ln,~'trumentation. Unirersitd ,h'an Monm't, 23 rue du Docteur Paul Michelon, 42023 Saint-Etienne Ct:dex 2, France We present a dielectric study on ferrofluid solutions of FeeCoO 4 in diethylene glycol or dibutyl phthalale, from 50 mt Iz to 10 Mltz, in the temperature range - 1 6 0 +40°C. When a transversal magnetic field is applied, a magnetodielectric anisotropy is in evidence. Above a concentration limit the colloidal suspensions do not remain well dispersed at low temperature. Moreover it seems that the melting point of a solution could be affected.
1. Introduction To use the magnetic properties of ferrofluids in a wide temperature range for applications in sensors [1], one must know if the solution, which is a normal colloidal suspension at room temperature, remains homogeneous. A dielectric study in large intervals of frequency and temperature, seems to be a well-adapted means of investigating the homogeneity of the ionic dispersion and its behavior under a continuous magnetic field. In this paper we present a dielectric study of a ferrofluid F % C o O 4 in diethylene glycol (DEG) or dibutyl phthalate (DBP) at different volume concentrations x, from 40°C down to temperatures less than - 100°C, without and with a continuous magnetic field (100 Oe) applied perpendicularly to the electric field. The results obtained in the frequency range 1 m H z - 1 0 MHz on static permittivity E~ and relaxation frequency £~, (corresponding to maximum losses e~,) may give indications of the homogeneity of the ferrofluids, or the existence and growth of possible aggregates.
2. Experimental The ionic ferrofluid solutions prepared in the laboratory of Professor Massart [2] are colloidal Correspondence to: G. Noyel, Universit6 Jean Monnet, 23 rue du Docteur Paul Michelon, 42(123 Saint-Etienne C6dex 2, France. Tel (33) 77.42.15.00, Fax (33)77.42.18.22. (1304-8853/93/$(16.00
dispersions of particles Fe2CoO 4 (diameter 10 nm) in a polar carrier liquid, dibutyl phthalatc (DBP) or diethylenc glycol (DEG). The maximum obtainable volume concentration x of particles without loss of homogeneity at room temperature is 13% for DBP and 6.5% for DEG. All the other mixtures are made by dilution in DBP or DEG for synthesis (purity better than 99%). Measurements were performed using a dielectric spectrometer built up in our laboratory, and described in ref. [3]. The total influence cell has a 24 pF geometric capacitance with thermal variations smaller than (I.5C/( between 100 and 200°C. A continuous transversal magnetic field of 100 Oe is obtained from a coil placed around the cell. The temperature is controlled by a PID regulator which allows to stabilize the sample temperature within +_(I.I°C and provides linear temperature variations at slow rates (0.5, I°C/min), to avoid undesirable gradients. Two types of recording measurements can be done: firstly an isothermal mode where the temperature is constanl and the frequency varies, secondly an isofrcquency mode (fig. 11 where one or several frequencies arc selected and the tcmperalure is varying so slowly that measurements are done in a quasi static state. Figs. 1 and 2 give respectively the temperature dependence of complex permittivity •* for a low volume concentration x 0.01 of FeeCoO 4 in DBP or in DEG. Thcse isofrequency recordings have been obtained at a slow cooling rate
~ 1993 - Elsevier Science Publishers B.V. All rights resm~ed
A. Siblini et al. / Dielectric study of ferrofluid F#2Co0 4
~'* 10 50 mHz ~-.~(e~)
183
e X
Electrode
60
~
somHz F//%~E
lOkHz
-----~rt
4o
:1 MHz
ikHz
4 */ ~lll~',~iliiii : "
Relaxation peak
\
f i ' , ~
\
;/ ii [.! , ~' I~
(E~)
effects
OX',,
J" I
,,, / ! i ~MH= ~
i~ ~
J
Re
axat
on
peak
1/ •
,
(~H ~
O .... 100
-50
O
150
~)°C
Fig. I. Isofrequency recording of complex permittivity E* (e', (") versus temperature (at 50 mHz, 10, 20, 40, 100, 200, 400 kHz, 1 M H z ) for an x = 0.01 ferrofluid solution of FezCoO 4 in DBP, w i t h o u t m a g n e t i c field (at d e c r e a s i n g t e m p e r a t u r e ) .
(l°C/min). Measurements above 10 kHz up to 1 MHz, in the present case, are performed by a LCR meter HP4275A. At lower frequencies (below 10 kHz) a temperature scan is necessary to obtain only one (at very low frequency) or two recordings (for example, 1 and 10 Hz or 100 Hz and 1 kHz) because it is necessary that, for a given temperature, the measurement can be done using the same electrometer range. In fig. 1, electrode effects appear only at 50 mHz and the static permittivity e s is well defined by the upper envelope of the dispersion curves e' (e~ being defined by the lower one). On the other hand for DEG, even at the same low volume concentration of Fe2CoO 4, notable electrode ef-
~}.,:~
:
--1gO
,~-zZ::gz;~/ :,:, -b~e, 50
@
0 °C
Fig. 2. I s o f r e q u e n c y r e c o r d i n g of c o m p l e x permittivity E* (E', e " ) v e r s u s t e m p e r a t u r e (at 50 m H z , 1, 10, 100 Hz, 1, 10, 20, 40, 100, 200, 400 kHz, 1 M H z ) for an x = 0.01 solution of F e 2 C o O 4 in D E G ,
w i t h o u t m a g n e t i c field (at d e c r e a s i n g temperature).
fects are clearly perceptible and so e s is not so easily defined versus temperature (fig. 2). At higher volume concentrations, electrode effects increase also faster for D E G as liquid carrier and in this case e s is known with a great imprecision. Moreover, these parasitic effects generate an important increase in conductivity which puts the LCR meter nearly out of range, shifting then the relaxation peak at 1 MHz (fig. 2). However, a comprehensive study, in the largest intervals of frequency and temperature, allows to estimate the dielectric parameters of ferrofluids particularly when the experimental data are very dispersed.
Table 1 Static p e r m i t t i v i t y p a r a m e t e r s (e s = A + B T * + C T . 2 ) for solutions of F % C o O 4 in D E G , with or w i t h o u t a c o n t i n u o u s t r a n s v e r s a l m a g n e t i c field, in the t e m p e r a t u r e r a n g e - 9 2 + 25°C x
0 0.005 0.010 0.020 0.030 0.040 0.065
Without H
With H = 100 O e
A
B
- 13.90 - 36.29 - 37.39 36.14 - 1.934 24.49 14.36
11.59 22.66 23.95 24.59 7.908 19.90 2.873
C
-
0.6731 0.7955 1.0610 1.2625 0.6469 0.9854 0.8076
A
B
C
- 35.36 - 37.16 - 34.85 - 4.178 - 27.61 7.443
21.88 23.40 23.51 8.586 20.61 5.392
- 0.7243 - 1.0157 - 1.1671 11.5131 - 1.0505 0.5439
184
A. Siblini et al. / Dielectric study <~f.l~'rrqfluid Fe eCoO 4 t'sll
3. Results
[]
~;s % ,'-'s
3.1. S t a t i c p e r m i t t i z , i t y
I
T h e static permittivity of each solution: l, 5, 13% of F e z C o O 4 in D B P a n d 0.5, 1, 2, 3, 4, 6.5% of F e 2 C o O 4 in D E G , may be fitted by the relation (with T * = 1 0 0 0 / T ) . Es = A
+BT*
+ C T .2.
(1)
F o r D B P solutions, the C coefficient may be negligible at any c o n c e n t r a t i o n . T h e coefficients of e s ( T * ) are given in tables 1 and 2 for all the solutions, with and w i t h o u t m a g n e t i c field. T h e m a g n e t o d i e l e c t r i c a n i s o t r o p y of ferrofluid solutions leads to a d e c r e a s e in Es (E s b e i n g the u p p e r e n v e l o p e o f d i s p e r s i o n curves e ' ( 0 ) from 50 m H z up to 1 M H z ) when a c o n t i n u o u s magnetic field (100 O e ) is a p p l i e d p e r p e n d i c u l a r l y to the electric field. This d e c r e a s e is o b s e r v e d over the whole t e m p e r a t u r e r a n g e ( - 100 to 40°C) as it has b e e n a l r e a d y shown by t h e o r e t i c a l a n d experimental studies in n a r r o w e r intervals o f frequency a n d t e m p e r a t u r e [4-6]. It is possible to c h a r a c t e r i z e this p e r s i s t e n t a n i s o t r o p y by the relative variation (eSH -- ES)/e s o f static permittivity with a n d w i t h o u t the continuous m a g n e t i c field H (fig. 3). W e can see (fig. 3) for the lowest v o l u m e c o n c e n t r a t i o n s x of F e z C o O 4 in D E G (0.5, 1, 2, 3 % ) that this relative deviation increases with x. F o r each of these c o n c e n t r a t i o n s (ESH -- ES)/e s is nearly c o n s t a n t versus t e m p e r a t u r e , which is consistent with the hypothesis of the h o m o g e n e i t y of these colloidal solutions in the whole t e m p e r a ture range. But above 3% and u n d e r o u r experim e n t a l c o n d i t i o n s this deviation varies on the
Table 2 Static perminivity parameters (E s = A + B T * ) for solutions of Fe2CoO 4 in DBP, with or without a continuous transversal magnetic field, in the temperature range - 8 9 + 35°C x 0 0.01 0.05 0.13
Without t t
With H = 100 Oe
A
B
A
B
(I.366 1.60 2.73 4.56
1.854 1.555 1.251 0.479
1.62 2.49 4.58
1.529 1.287 0.465
-4 -6 -8 10o
-5o
o
o "c
Fig. 3. Relative deviation (ESH -- CS)/e s of static permittivity versus temperature when an H = 100 Oe continuous perpendicular magnetic field is applied, for different volume concentrations x of Fe2CoO 4 in DEG. (a) x = 0.005, (b) x = 0.Ill, (c) x (I.[)2,(d) x = 0.03, (e) x 0.04,(f) x = 0.065,
o p p o s i t e side, which w o u l d s e e m to indicate the a p p e a r a n c e of a g g r e g a t e s or m u l t i l a y e r s which would be m o r e i m p o r t a n t for 6.5%, when a continuous m a g n e t i c field is applied. This b e h a v i o r is similar to that of the ferrofluid F e 2 C o O 4 in D B P previously s t u d i e d [7]. So it s e e m s that the h o m o g e n e i t y of these ionic ferrofluids d i s a p p e a r s a b o v e a v o l u m e c o n c e n t r a tion limit, which w o u l d d e p e n d on e x p e r i m e n t a l conditions. 3.2. R e l a x a t i o n f r e q u e n c y
T h e c a r r i e r liquid D B P or D E G is a p o l a r m a t e r i a l which exhibits a single a b s o r p t i o n p e a k in the i s o t h e r m a l m o d e (at a given t e m p e r a t u r e ) as well as in the isofrequency m o d e (at a given frequency). T h e s a m e b e h a v i o r is o b s e r v e d for ferrofluid solutions at low v o l u m e c o n c e n t r a t i o n s . As we saw in the case of the static permittivity of F e 2 C o O 4 in D E G ( a n d in our e x p e r i m e n t a l conditions), at h i g h e r c o n c e n t r a t i o n s and low temp e r a t u r e , r e c o r d i n g s are d i s t o r t e d p r o b a b l y by a p p e a r a n c e a n d growth of a g g r e g a t e s and multilayers, which affect also the s h a p e and the position of a b s o r p t i o n peaks. W h e n the c o n t i n u o u s transversal m a g n e t i c field is a p p l i e d on a well d i s p e r s e d solution, we note a
A. Siblini et al. / Dielectric stud>' of ferrojquid Fe 2CoO 4
185
Table 3 V o g e l - F u l c h e r - T a m m a n coefficients of r e l a x a t i o n f r e q u e n c y fm for F e 2 C o O 4 in D E G solutions (at low v o l u m e c o n c e n t r a t i o n x), with or w i t h o u t a transversal m a g n e t i c field b e t w e e n - 4 5 and - 100°C x
Without H
0 0.005 0.010 0,020 0.03(I
W i t h H = 100 O e
A
B
~)(K)
A
B
~)(K)
13.26 11.47 12.04 12.07 12.18
- 684.0 - 452.5 519.7 - 520.0 -559.2
127.7 140.4 138.8 138.4 136.8
11,99 11,85 11,83 12,15
- 476.6 - 485.0 - 484.1 -509.2
139.2 139.7 139.2 137.7
shift of the relaxation peak towards lower temperatures in D E G or in DBP [7] as carrier liquid. As the dielectric relaxation time is strongly correlated to the macroscopic viscosity of the medium [8] it seems possible to explain this shift by a local decrease of viscosity when the magnetic field is applied [7]. Variations of fm versus T at each concentration, with and without H, may be fitted by the V o g e l - F u l c h e r - T a m m a n (VFT) relation: log fm
=/4_, +
Bi T - T,~'
(2)
The V F T coefficients are displayed in table 3 in the case of D E G (for DBP see in [7]).
3.3. Crystallization and melt&g Using a not too slow cooling rate ( l ° C / m i n ) the pure dipolar liquid carrier or a well dispersed 80
C*
0/
colloidal solution (x <0.065) is obtained in a supercooled state and then in a glassy state. On heating the material at the same rate (fig. 4), the beginning of relaxation is observed in the supercooled state but crystallization appears and is nearly achieved after about ten minutes. All relaxations disappear, the loss factor E" becomes negligible and ~' falls down to 3.4; these values remain almost constant till the melting region, where E' rises sharply up to its static value %. At all volume concentrations below 6.5% of F e 2 C o O 4 in D E G the melting point temperature is about - 8 . 5 ° C (which is that of pure DEG). When a continuous magnetic field is applied at room temperature, and with the same thermal process (temperature decreasing at l ° C / m i n down to - 140°C and then increasing at the same rate), we note that the melting point is nearly - 11.5°C. The ferrofluid particles oriented by the continuous magnetic field could reduce the number of crystalline bonds and so melting would be obtained at a lower temperature. 4. Conclusion
E n
60
] ,i Crystallization
40
eo
Beginning
//.I/
Relaxation_ - -
,~.....
'~ i; ! :
".~ ";,i M e t ~g
/Y'!'
i.'::S
47:"~ b', ;.q::,t~:.: : ~ ' . , ~ _ _ _ - ~
....................
-]50
-100
50
0
O°C
Fig. 4. I s o f r e q u e n c y r e c o r d i n g for an x = 0.02 solution of F e 2 C o O 4 in D E G w h e n the t e m p e r a t u r e is i n c r e a s i n g at 1° C / m i n .
This experimental study shows the existence of a magnetodielectric anisotropy in ferrofluids containing particles of Fe2CoO 4 in diethylene glycol or dibutyl phthalate. The analysis of data on static permittivity shows that, under given experimental conditions, and under a continuous tranversal magnetic field, these ionic colloidal suspensions do not remain well dispersed at low temperature above a volume concentration limit. Furthermore, a thermal process may generate crystallization of the fluids, and it seems that a continuous magnetic field affects the melting point of the solution.
186
A. Siblini et al. / Dielectric" stu~(v o f ferrofluid Fe 2CoO 4
Dielectric measurements in large intervals of frequency and temperature can be used to test the thermal stability of colloidal solutions which could be selected for applications in sensors. References [1] J. Monin, O. Brevet-Philibert and L. Delaunay, in: C.R. 1()am~ J. Europ6ennes Opto61ectronique (Paris, 1990) p. 367.
[2] R. Massart, IEEE Trans. Magn. MAG-17 (1981) 1247. [3] O. Derriche, L. Jorat and G. Noyel, in: C.R. 11v''" Coll. O[ID (Hammamet, 1991) p. 254. [4] A.J. Mailfert and B. Nahounou, IEEE Trans. Magn. MAG-16 (1980) 254. [5] C. Cotae, J. Magn. Magn. Mater. 39 (1983) 85. [6] A. Espurz, J.M. Alameda and A. Espurz-Nieto. J. Phys. D: Appl. Phys. 22 (1989) 1174. [7] O. Derriche, L. Jorat, G. Noyel and J. Monm, J. Magn. Magn. Mater. 11)2 (1991) 255. [8] L. Jorat, G. Noyel and J. Huck, in: C.R. 1(//:n'~"Coll. OHD (Rennes, 1989) p. 251.