Experimental and theoretical study of the dielectric properties of 1-cyanoadamantane; spectrum of the compact crystal from measurements on powder

Size: px

Start display at page:

Download "Experimental and theoretical study of the dielectric properties of 1-cyanoadamantane; spectrum of the compact crystal from measurements on powder"

Silas Nichols
5 years ago
Views:

Journal of Physics D: Applied Physics Experimental and theoretical study of the dielectric properties of 1-cyanoadamantane; spectrum of the compact crystal from measurements on powder To cite this

1 Journal of Physics D: Applied Physics Experimental and theoretical study of the dielectric properties of 1-cyanoadamantane; spectrum of the compact crystal from measurements on powder To cite this article: M D Benadda et al 1982 J. Phys. D: Appl. Phys View the article online for updates and enhancements. Related content - Estimation of permittivity of a compact crystal by dielectric measurements on its powder: A stochastic mixture model for the powder-dielectric P S Neelakantaswamy, B V R Chowdari and A Rajaratnam - A measuring device for the determination of the electric permittivity of materials in the frequency range MHz M D Benadda, J C Carru and C Druon - Different aspects of an interesting glassy crystal: 1-cyanoadamantane M Foulon, J P Amoureux, J L Sauvajol et al. Recent citations - Geometrical Description in Binary Composites and Spectral Density Representation Enis Tuncer - Dielectric properties of 1- fluoroadamantane C 10 H 15 F J.P. Amoureux et al - Low frequency dielectric properties of 1- cyanoadamantane C 10 H 15 CN J.P. Amoureux et al This content was downloaded from IP address on 23/08/2018 at 06:16

2 J. Phys. D: Appl. Phys., 15 (1982) Printed in Great Britain Experimental and theoretical study of the dielectric properties of l-cyanoadamantane; spectrum of the compact crystal from measurements on powder M D Benaddat, J C Carrut, J P AmoureuxS, M Castelainf and A Chapotoni t Equipe 'Nouveaux MatCriaux', Centre HyperfrCquences et Semiconducteurs LA CNRS No 287, BLtiment P3-32 Etage, UER IEEA, Universite de Lille 1,59655-Villeneuve d'ascq Cedex, France $ Laboratoire de Physique des Solides, Equipe de Dynamique des Cristaux Moleculaires, associce au CNRS No 465, UniversitC de Lille Villeneuve d'ascq Cedex, France Received 16 December 1981 Abstract. In this paper, the dielectric properties of l-cyanoadamantane powder, studied in a wide frequency band (1 khz-l GHz), are presented. We calculated the dielectric spectra from various equations for mixtures given in the literature. The spectra were established in the static state and extended here to the dynamic state. A comparative study between the experimental and calculated spectra confirms the validity of two equations: that of Bijttcher for high volume fractions and that of Looyenga for small volume fractions. This study allows us to deduce the dielectric spectrum of l-cyanoadamantane compact crystal in the frequency band considered. 1. Introduction Numerous dielectric studies of mixtures have been performed to measure the static permittivity (van Beek 1967) or the quasi-static permittivity (Iwauchi et a1 1971, Srivastava et a1 1971, Iwauchi 1971, Mansingh and Bawa 1974a, b, Mansingh and Rai 1976) using the following parameters, particle size (Dube eta1 1971, Mansingh and Bawa 1974, Paletto et a1 1974, Srivastava et a1 1974, Bawa and Khanna 1975, Sambasiva and Bhanumathi 1978), temperature (Mansingh and Bawa 1973, Rossiter and Scaife 1973, Mansingh and Bawa 1974a, b, Emoto et a1 1979), etc... In this paper, a study of dielectric properties as a function of concentration is made in a wide frequency band (1 khz-l GHz) on a molecular polar compound, l-cyanoadamantane. From many experimental measurements performed on this compound, we obtain results for the general complex dielectric constant using equations established for the static state. We compare the experimental spectra with the spectra calculated from the most used equations for mixtures. This comparison allows us to determine the validity of these equations extended to the dynamic state. Thus we can obtain the dielectric spectrum of l-cyanoadamantane ccmpact crystal from measurements on powder The Institute of Physics 1477

3 1478 M D Benadda, J C Carru, J P Amoureux, M Castelain and A Chapoton 2. Experimental details 2.1. Choice of substance For the experimental study, the powder should have properties relevanto the mixture problem. We have chosen l-cyanoadamantane for the following five reasons: (i) it is commercially available in very fine powder form (Janssen Pharmaceutica) (ii) it is not hygroscopic and has very a low vapour pressure (i.e. it does not sublime) (iii) its conductivity is practically negligible (iv) it has a narrow dielectric relaxation spectrum (v) it has a significant dipolar moment (3.94D) related to the -C = N cyano group (Amoureux and Bee 1979). The chemical formula of l-cyanoadamantane (also known as adamantane carbonitrile) is 1-CloHI5CN. It is obtained from adamantane CI0Hl6 by substituting a cyano radical -C = N for one methyl hydrogen (see figure 1). The molecule thus obtained is very strong and is not distorted by this hydrogen substitution (Chadwick et a1 1972, Maciel et a1 1974). The physical properties of this compound have been studied by other authors (Amoureux 1980, Amoureux et a1 1980, Amoureux et a1 1981a, b). t' Figure 1. Molecule of l"& HI5 CN Dielectric results We give the dielectric results, taking as a parameter the concentration 8 (or volume fraction), which is the ratio of the solid volume to the total volume. The sample is put in an electrically open coaxial cell (Ravalitera 1975, Ravalitera et a1 1977, Benadda et a1 1982). The real and imaginary parts E' and Ell of the complex permittivity E* are taken at T = 25? 0.1 "C in the frequency band 1 khz-l GHz. For all the measurements the filling was done in the same way: the sample was homogeneously distributed in the cell. The dielectric measurements are reproducible within l%, which justifies the filling method.

4 measurements Dielectric on mixtures High concenfration: In this case, air embeds l-cyanoadamantane polycrystals. we have produced samples with 8 values ranging from 0.47 to It is not possible to produce mixtures with concentration 6 less than 0.47, because the volume fraction taken up by polycrystals is too small. Thus, the sample becomes a two-layer system; the first is air, the second is the mixture 'polycrystals-air'. This is not the object of our study. We give the d' spectra as a function of frequency in figure 2 and the corresponding E' spectra in figure 3. Note that (Benadda ef a1 1981): (i) the maximum value of d' (&',Aax) increases with 8; (ii) the frequency which corresponds to &,, (critical frequency F,) is constant in the first approximation; (iii) the distribution of the region is the same whatever the value of Low concentration: 8 < In this case, we produced a ternary homogeneous mixture with air, Teflon and l-cyanoadamantane polycrystals. The latter forms the component A, Teflon and air form the embedding mixture B. B is made up of two nonpolar components which are chemically inert. Its permittivity, studied in earlier work (van Beek 1967), is known. This ternary mixture permits us to have 8 varying from 0.1 to 0.47 while keeping the permittivity of B constant and equal to The d' spectra as a function of frequency are shown in figure 4 and the corresponding E' spectra in figure 5. We can make the same remarks in the as case of high concentrations. Note that for 6 = 0.47, the measurements have been made with air (E; = 1) and also with the mixture (E; B = 1.87). G,, increases with the surrounding medium permittivity: it varies from to (see figures 2 and 4). t L.e W, -m W 0.47 \ 0.02 l 1 I l (g F lg F Figure 2. d' spectra versus frequency for various 0 Figure 3. E' spectra versus frequency for various e values, at T = 25 "C. Embedding medium :air. values, at T = 25 "C. Embedding medium: air.

5 1480 M D Benadda, J C Carru, J P Amoureux, M Castelain and A Chapoton t 0.50 "O l Figure 4. d' spectra versus frequency for various 6 values at T = 25 "C. Embedding medium : air-teflon. 3. Theory Among the numerous equations for mixtures, given in the literature, we have chosen some from the critical study recently made by Grosse and Greffe (1979). They are applicable either to small concentrations or high concentrations (van Beek 1967, Grosse and Greffe 1979). On the other hand, the equation of Polder and van Santen (1946) is applicable to every 8 value. It gives the static permittivity for spheres embedded in a continuous medium 51 e= 24 l l I I 1 - L lg F Figure 5. E' spectra versus frequency for various 6' values at T = 25 "C. Embedding medium : air-teflon.

6 Dielectric measurements on mixtures 1481 where: E = heterogeneous mixture permittivity el = embedding medium permittivity ~2 = dispersed material permittivity in the embedding medium E1 = permittivity of the medium surrounding a particle with el < El < E ~. From this expression, we consider two boundary cases. When the concentration is high (6 > 0.70), we consider in the first approximation that every particle is surrounded by mixture (van Beek 1967). So, we have El = &and expression (1) becomes Expression (2) is known as Bottcher's mixture equation (Bottcher 1945). When the concentration is small (Polder and van Santen 1946) (8 < 0.20), we consider in the first approximation that every particle is surrounded by the embedding medium (van Beek 1967). So, we have E, = and expression (1) becomes Expression (3) is known as Fricke's mixture equation (Fricke 1953). For small concentrations the results obtained (D ) necessitate the use of other equations than that of Fricke. They are: Rayleigh (1892) E = E1 Bruggeman (1935) ~2 + 2 ~1 + 28(~2 E2 + 2E ~ 1 ) Looyenga (1965) These equations have been established for the static state. To our knowledge, only Hanai proposed a new theory to explain the dielectric dispersion due to complex interfacial polarisation (Hanai 1960, Hanai er a1 1959). We propose now to extend all the equations previously cited to the dynamic state. Quantities E, EZ and are then written for W = 2nF E = &*(W) = &'(W)- j&"(o) = &$(W) = &$(W)- j&(w) E = E; (nonpolar substance)

7 1482 M D Benadda, J C Carru, J P Amoureux, M Castelain and A Chapoton 4. Comparison between theoretical and experimental results 4.1, AE Theoretical curve 4.1.l. High concentration: 8 > 0.50, ~1 = Ei = 1 (embedding medium : air). The dynamic behaviour of this system is obtained by substituting E, and in equation (2) by F*, 1 and E; respectively. Then, equation (2) is written: & (U) - j& (w) - 1 &$(U) - je ;(o) - 1 = e( ~[E (w) - jd (o)] ~[E (u) - je (w)] + &;(U) - jdi(w) ). (7) The spectrum of the complex permittivity &$(W) shows a dielectric absorption region with a critical frequency F, with: E:, = real permittivity when F G F,: the zero-frequency dielectric constant &L2 = real permittivity when F 9 F,: the infinite-frequency dielectric constant AE; = E;, - &L2. For F e F,, E~(U) =&S2 and &*(W) =E:, &l &li- 1 e- 3 &: 2&; + &f2 equation (7) is written &: - 1 EL, - 1 -e 3 E:: 2E:: + ELz. In equations (8) and (9), &L2 and &S2 values have been established from measurements performed for the closest value of 8 to 1, i.e. 8 = In these conditions, it is possible to calculate from equations (8) and (9), E; and EL values of the mixture for various 8 l I // 0 0: 5 1 e Figure 6. Calculated (A) and experimental (B) A& versus Ofor high concentration.

8 measurements Dielectric on mixtures 1483 values. This allows us to calculate the curve AE = (4- EL) versus 8. This curve is given in figure 6 with the corresponding experimental curve. We notice that both curves vary nonlinearly versus 8. Deviations between calculated and measured values are given in table 1. The deviation is very small for 8 > On the other hand for 8 < 0.75, deviation becomes important. This due to Bottcher s equation a for mixture which overestimates interactions between particles (Grosse 1979, Grosse and Greffe 1979). Table 1. Deviations between calculated and measured values for high concentrations E: measured E: calculated EL measured EL calculated Ad measured A& calculated JAE&, -AE&~/AE~~~~I (76) e Low concentration. Recall that E: =E; = 1.87 (embedding medium: air-teflon). This value was measured in the frequency range 1 Hz-l GHz. The curve AE versus 8 is deduced from Fricke s formula. Calculations were developed in the same way as for high concentrations. We notice that the theoretical curve is a straight line whereas the experimental curve varies nonlinearly. Deviations between calculated and measured values are given in table 2. We observe an important deviation between the calculated and the measured Ad for every 8. This is due to Fricke s equation for mixtures which underestimates interactions between particles (Grosse 1979, Grosse and Greffe 1979). From figure 7, we see that a nonlinear equation is needed to explain the results. For that, we tried the three equations given in 03 (expressions (4), (5) and (6)). Figure 8 shows AE versus 8 calculated from these equations. We can see that only the results obtained with Looyenga s equation agree well with the experimental values. We notice that deviations increase with 8. For 8 > 0.35, they become important (see table 3). This is because this equation is only valid for small 8. Table 2. Deviations between calculated and measured values for low concentrations AE measured AE calculated IA&eas -AddA&eas/ % e

9 1484 M D Benadda, J C Carru, J P Amoureux, M Castelain and A Chapoton 31 l 2- Af e Figure 7. Calculated (A) and experimental (B) As versus 0 for small concentration using Fricke s equation. I 3-2- BE 1- e Figure 8. Calculated and experimental As versus efor small concentration (using Rayleigh s (1892), Bruggeman s (1935) and Looyenga s (1965) equations) (A) Rayleigh, (B) Bruggeman, (C) Looyenga, (D) experimental.

10 mixtures Dielectric on measurements 1485 Table 3. Differences between measured values and those calculated using Looyenga s equation E! measured E: calculated EL measured EL calculated A& measured AE calculated AEE:~I/AE~~~~I % e 4.2. &;(W) theoretical curves High concentration. & (W) and d ( W) spectra are obtained by inversion ofbottcher s equation which can be written as follows: [& (W) - jd (w) - 1][2s (w) - Zjd (0) + &$(W)- j& i(w)] = ~O[E~(W) - ~&(W)][E$(O) - j& i(w) - l] (10) when separating real and imaginary parts &;(W)[E (W)(I - 3e) ~;(W)Y(~)(I - 3e) + [2ef2(w)- 2d *(0) - ~E (w) + 3ed(~)] = o (11) &;(W),qw)(1-3e) + d;(w)[tqw)(~ - 3e) ~ w)[~e (w) = o (12) From equations (11) and (12), it is possible to determine & (W) and $ (W) spectra for various 8 values. That is possible only if we know &$(W) and & (W). These values were obtained by extrapolation from the measured values for 8 = 0.95, by using Bottcher s equation. For & (W) spectra, the deviation between calculated and measured values is at the maximum equal to that given in table 1. We give in figure 9,.?(W) spectra (full curve) and experimental points for three 8 values. Contrary to the case with & (W) spectra, it is possible to extend comparison with observations to the relaxation region (distribution, critical frequency F,). For e < 0.75, the deviation between calculated the and experimental values is great, thus Bottcher s equation is not applicable for these values. For 8 > 0.75, this deviation is within our measurement errors (2% for E and 4% for d ) (Benadda et a1 1982). In these conditions, we observe for the region drawn from calculated values that (i) the distribution is not changed-the value of (Y according to Cole and Cole (1941) (deduced from the domain slope) is 0.12; (ii) the critical frequency F, is constant in first approximation. Thus, Bottcher s equation can be extended to the dynamic state high for concentrations (8 > 0.75). In these conditions, is possible to calculate the spectrum of l-cyanoadamantane compact crystal. This calculation is justified because l-cyanoadamantane has a cubic lattice. Thus, the compact crystal has an isotropic dielectric constant (Bottcher and Bordewijk 1978). We give the spectrum in figure 10 in the form of a Cole-Cole diagram, i.e. Y(w) =~[E (w)].

11 1486 M D Benadda, J C Carru, J P Amoureux, M Castelain and A Chapoton 1 I l 1 1 L 5 6 l k F e= L Figure9. Calculated and experimental d'(w) spectra for high concentration. 0 experimental points; full curves calculated d'(o). We notice that this spectrum has Cole-Cole a distribution with parameter (Y = 0.10, this value being very close to that obtained for high concentrations Small concentration. &'(m) and $(m) spectra are obtained as for high concentrations, but from Looyenga's equation. For &'(m) spectra, the deviation between calculated and measured values is at the maximum equal to that given in table 3. We give rl(w) spectra (full curve) and experimental points for four 8values in the range (see figure 11). We notice, for the region drawn from calculated values, for the four 8 values, that Figure 10. Calculated l-cijilscn compact crystal Cole-Cole diagram. 0 = 1.

12 Dielectric measurements on mixtures E " L 5 6 i 8 [g F Figure 11. Calculated andexperimental e(w) spectra forlow concentration..experimental points; full curve, calculated ~''(0) for various values of 8. (i) its critical frequency is almost equal to that of the experimental region; (ii) the distribution is maintained. However, for frequencies smaller than F,, the experimental points are generally over the theoretical curve. This can be explained by the existence of a low frequency contribution related to the superficial conductivity. The above remarks and conclusions of D being taken into account, we can consider that the application of Looyenga's equation can be extended to the dynamic state for small concentrations (8 < 0.35). l L10 khz Figure 12. Calculated 1-CloH15CN compact crystal Cole-Cole diagram. + calculated from Looyenga (1965); 0 calculated from Bottcher (1945). 8 = 1, (Y = 0.10.

13 1488 M D Benadda, J C Carru, JP Amoureux, M Castelain and A Chapoton We give in figure 12 the Cole-Cole diagram for the calculated compact crystal (8 = 1) with that already obtained by Bottcher s equation. Note that (i) the critical frequency is the same, i.e. approximately 400 khz; (ii) the distribution is the same with cuclose to 0.1; (iii) deviation between these spectra is within 10%. 5. Conclusions In this work, we studied dielectric properties of l-cyanoadamantane in a wide frequency band (1 khz-l GHz). From this study, we showed that it is possible to extend to the dynamic state two equations for mixtures established for the static state. We showed the applicability of Looyenga s equation for the low concentrations, and Bottcher s equation for high concentrations. Acknowledgments We thank Dr J M Wacrenier for his interest and much helpful discussion during the progress of this work. References Amoureux J P 1980 These Docteur As-sciences Physiques Universite de Lille Amoureux J P and Bee M 1979 Acta. Cryst. B Amoureux J P, Bee M and Damien J C 1980 Acta. Crysr. B Amoureux J P, Castelain M, Bee M, Arnaud B and Shouteenten M L 1981a Molec. Phys Amoureux J P, Sauvajol J L and Bee M 1981b Acta. Cryst. A Bawa S S and Khanna L K 1975 J. Phys. Soc. Japan van Beek L K H 1967 Prog. Dielectrics Benadda M D, Carru J C, Chapoton A, Amoureux J P and Castelain M ) Colloque de I Optique Hertzienne Dielectrique (Toulouse), Sept. 81 Benadda M D, Carru J C and Druon C 1982 J. Phys. E: Sci. Instrum Bottcher C J F 1945 Rec. Trav. Chim. Pays-Bas Bottcher C J F and Bordewijk P 1978 Theory ofelectric Polarisation Vol. 2 2nd edn (Amsterdam: Elsevier) pp Bruggeman D A G 1935 Ann. Phys Chadwick D, Legon A C and Millen D J 1972 J. Chem. Soc. Faraday Trans. I Cole R H and Cole K S 1941 J. Chem. Phys Dube D C, Yadava R S and Parshad R 1971 Ind. J. Pure Appl. Phys Emoto T, Motegi H and Nakamura E 1979 J. Phys. Soc. Japan Fricke H 1953 J. Phys. Chem Grosse C 1979 These Doctorat 32 cycle UniversitC de Nancy Grosse C and Greffe J L 1979 J. Chim. Phys Hanai T 1960 Kolloid Z Hanai T, Koizumi N and Gotoh H 1959 Kolloid Z Iwauchi K 1971 Japan J. Appl. Phys C-8 Iwauchi K, Yamamoto S, Bando Y, Hanai T, Koizumi N, Takada T and Fukishima S 1971 Japan J. Appl. Phys Looyenga H 1965 Physica Maciel G E, Dorn H C, Greene R L, Kleschick W A, Peterson M R and Wahl G H 1974 Org. Magn. Res Mansingh A and Bawa S S 1973 J. Phys. Soc. Japan a Phys. Status Solidi a

14 Dielectric measurements on mixtures b J. Phys. D: Appl. Phys c Ind. J. Pure. Appl. Phys Mansingh A and Rai G 1976 Can. J. Phys Polder D and van Santen J H 1946 Physica Paletto J, Grange G, Goutte R and Eyraud L 1974 J. Phys. D: Appl. Phys Ravalitera G 1975 Th& Doctorat 32. cycle Universite de Lille Ravalitera G, Carru J C and Chapoton A 1977 J. Chem. Soc. Faraday. Trans. I Rayleigh Lord 1892 Phyl. M ap Rossiter V and Scaife B K P 1973 Collectioe Phenomena Sambasiva Rao K and Bhanu mathi A 1978 Current Sci Srivastava G P, Mathur P C, Krishna (Mrs) and Mehra R M 1971 Ind. J. Pure. Appl. Phys Srivastava G P, Mathur P C, Tripathi K N, Singh B and Dawar A L 1974 Japan J. Appl. Phys

USEFUL RELATIONSHIPS BETWEEN DIELECTRIC PROPERTIES AND BULK DENSITIES OF GRANULAR AND POWDERED MATERIALS

USEFUL RELATIONSHIPS BETWEEN DIELECTRIC PROPERTIES AND BULK DENSITIES OF GRANULAR AND POWDERED MATERIALS Stuart O. Nelson U. S. Department of Agriculture, Agricultural Research Service Richard B. Russell