, Vol. 9, No. 3, pp. 123-134, Sep. 2008 Physical Properties of Foods and the Effect of Water on Them II Electrical Properties and Dielectric Relaxation Hitoshi KUMAGAI Department of Food Science and Nutrition, Kyoritsu Women s University, 2-6-1 Hitotsubashi, chiyoda-ku 101-0003, Tokyo Dielectric spectroscopy has been widely used to study molecular dynamics in dispersed systems. With an increase in frequency, the dielectric constant,, often decreases, the electric conductivity increases, and the dielectric loss,, shows a peak, due to the delay in dipole moments, this phenomenon being the so-called dielectric relaxation. By fitting dielectric relaxation data to semiempirical equations, for example, the Cole-Cole equation, one can obtain a parameter reflecting the mobility of molecules, polymer chains and so forth, such as the relaxation time,, which corresponds to the time needed for electric dipoles to orient in the direction of an electric field. The application of the dielectric relaxation to food hydrocolloids such as BSA solution, gelatin solution, alginate solution, and so forth was reviewed. Each dielectric relaxation observed is considered to be ascribable to a different fluctuation or movement of components in the electric field among different hydrocolloid systems, thus giving information on the inner structure of the hydrocolloids. Keywords: electrical properties, dielectric relaxation, relaxation time, solution, viscosity 1 [1] physical properties [2] 2008 8 19 2008 8 26 101-0003 2-6-1 Fax: 03-3237-2787, E-mail: kumagai@s1.kyoritsu-wu.ac.jp [1] 2
124 2 [3] [3] 2.1 charge electrical properties Fig. 1 S [m 2 ] L [m] V [V] I [A] Fig. 1 I I G I c capacitance C [F] F Q [C] Q CV 1 Q V Q V I c I c dq/dt C (dv/dt) 2 t [s] C 1 S L [1] permittivity C (S/L) 3 e o ( 8.854 10-12 [Fm -1 ]) relative permittivity 20 1.000536 25.09 80.10 Fig. 1 I G [A] I G GV 4 G G 1/G R [ ] G 4 S Fig. 1 Measurement of electrical properties and the concept of an equivalent circuit.
125 L C electric conductivity [ -1 m -1 ] G (S/L) 5 1/ [ m] 6 dielectric loss /(2 fe 0) 6 f [Hz] complex permittivity i 7 i 2.2 2.2.1 f electric dipole Fig. 2 dielectric relaxation s s f m 1/(2 f m) 8 relaxation time [s] f 2 f 2.2.2 r r [4] Fig. 1 [3] Fig. 1 C C G f s Fig. 2 Dielectric relaxation phenomena.
126 0 1 1/f [s] 2.4. 2.3 Cole-Cole Cole-Cole Debye Cole-Cole 2.3.1 Cole-Cole 1 Debye Cole-Cole Debye [3] ( s ) 1 i 9 1 i 9 7 s 1 ( ) 2 10-a ( s ) 1 ( ) 2 10-b 10-a 10-bFig. 3 a 0 f Cole-Cole Debye 10-a 10-b 2 1 ( s ) ( ) 2 } 2 2 1 ( s ) 2 } 11 } } Fig. 3 Examples of fitting equations and fitted curves for dielectric relaxation.
127 11 Fig.4 a 2 Cole-Cole Cole-Cole Cole-Cole [5] ( s ) 1 (i ) 1-1 (i ) 1-12 ( s )[1 ( ) 1- sin( /2) ] 1 2( ) 1- sin( /2) ( ) 2(1- ) 13-a ( s )[( ) 1- cos( /2) ] 1 2( ) 1- sin( /2) ( ) 2(1- ) 13-b 13-a 13-b Fig. 3 a Cole- Cole Fig. 4 b Cole- Cole (0 1) Cole-Cole /2 Cole-Cole 0 0 12 Debye 9 3 Cole-Davidson Cole-Cole Cole-Davidson [6] s (1 i CD ) 14 ( s )(cos ) cos( ) 15-a ( s )(cos ) sin( ) 15-b arctan ( ) 0 1 0 14 Debye 9 15-a 15-b Fig. 3 b Cole-Cole Fig. 4 c Havriliak Negami [7] Fig. 4 Complex plane plots of i.
128 s 1 (i HN ) 1- } } 16 2.3.2 Debye Cole-Cole Cole-Davidson Havriliak- Negami 16 Debye Cole-Cole f m 8 Cole- Davidson Havriliak-Negami f m CD HN 2.4 Cole-Cole 0 Cole-Cole NaCl 10 3 10 7 Hz f 10 3 10 7 Hz Cole-Cole 13-a [8] 17 1 2 1 sinh( x) cosh( x) cos ( ) 2 17 x ln (2 f ), ColeCole 0 1 1 Debye 9 0 BSA 0.7 0.8 Debye 17 Fig. 5 a 100MHz R Debye 3 3.1 [8] 7.5 nm 2.0 nm BSA Fig. 5 (a) vs. plot of BSA (a globular protein) solution and (b) the Debye theory on dielectric relaxation.
129 4 R 3 18 k BT Fig. 5 b k B 1.380 10-23 J/K T BSA [8] Fig. 5 a 18 R T 298.15 K 25 313.15 K 40 R 4.7 nm R 4.5 nm BSA BSA 7.5 nm 2.0 nm 3.2 [8] 40 25 10 3 10 7 Hz Cole-Cole 17 17 Cole-Cole 40 0.5 25 0.4 BSA BSA Fig. 6 40 40 25 1 mpa s 40 25 C [1] 3.3. C junction zone 3 Fig. 6 Dependence of the relaxation time, on the viscosity, for a gelatin solution.
130 C junction zone Fig. 6 Cole-Cole. 3.3 [9-12] 3.3.1 MHz counter ion [9-12] - f 10 3 10 7 Hz Cole-Cole 17 3.3.2 scaling law [1] Fig. 7 Fig. 7 C 1/3 C 1/2 [9] [10] s ( ( 0)/ 0 :. ; 0. rel / 0 0 s C 19-a 0 C 1/3 C -2/3 19-b 19-c rel C 1/2 20-a 0 Fig. 7 The scaling law of viscosity and dielectric parameters in the dilute and semi-dilute region of a polyelectrolyte solution.
131 C 0 20-b C -1 20-c [1] 19-a 20-c 6 C 3.3.3 [9-11] Figs. 8 a b 19-a 1 20-a 1/2 C Figs. 8 a b 0.2 mm Figs. 8 c d 19-b 19-c 20-b 20-c C C 0.2 Fig. 8 Analysis of viscosity and dielectric parameters by using the scaling concept. (a), s of sodium alginate solution; (b), rel of sodium alginate solution; (c), of sodium and calcium alginate solutions; (d), of sodium and calcium alginate solutions
132 mm Figs. 8 a b C Figs. 8 c d C 1 [11] [9, 12] 3.4 W/O [3] water in oil emulsion; W/O emulsion Fig. 9 a W/O oil in water emulsion; O/W emulsion Fig. 9 b O/W W/O Fig. 9 Electrical properties of W/O and O/W emulsions.
133 Ohnishi [13] Cole-Cole Impedance 3.5 GHz 4 [1] 9 79-89 2008 [2] ; 2005 [3] 2000 [4] ; 2007, pp. 54-56 [5] K. S. Cole, R. H. Cole; Dispersion and Absorption in Aielectrics, I. Alternating Current Characteristics, J. Chem. Phys., 9, 341-351 (1941), [6] D. W. Davidson, R. H. Cole; Dielectric Relaxation in Glycerol, Propylene Glycol, and n-propanol, J. Chem. Phys., 19, 1484-1490 (1951). [7] S. Havriliak, S. Negami; A Complex Plane Analysis of -Dispersions in Some Polymer Systems, J. Polymer. Sci. Part C, 14, 99-117 (1996). [8] S. Iwamoto, H. Kumagai; Analysis of Dielectric Relaxation of a Gelatin Solution, Biosci. Biotech. Biochem., 62, 1381-1387 (1998). [9] H. Kumagai, S. Ikeda; Dielectric Analysis of the Inner Structure of Food Polyelectrolyte Solutions and Gels, Recent Res. Dev. in Agric. & Biol. Chem., 2, 133-141 (1998). [10] S. Ikeda, H. Kumagai; Scaling Behavior of Physical Properties of Food Polysaccharide Solutions: Dielectric Properties and Viscosity of Sodium Alginate Aqueous Solutions, J. Agric. Food Chem., 45, 3452-3458 (1997). [11] S. Ikeda, H. Kumagai, K. Nakamura; Dielectric Analysis of Food Polysaccharides in Aqueous Solution, Carbohydrate Research, 301, 51-59 (1997). [12] S. Ikeda, H. Kumagai, K. Nakamura; Dielectric Analysis of Interaction between Polyelectrolytes and Metal Ions within Food Gels, Food Hydrocolloids, 11, 303-310 (1997). [13] S. Ohnishi, Y. Shimiya, H. Kumagai, O. Miyawaki; Effect of Freezing on Electrical and Rheological Properties of Food Materials, Food Sci. Technol. Res., 10, 453-459 (2004). ( / (2 fe 0) : e 0 ; f f Cole-Cole Cole-Davidson
134 10 3 10 7 Hz BSA W/O