6064
J. Phys. Chem. 1991,95,6064-6066
Dlelectrlc Relaxation Tlme of Bound Water In Biological Materials Bo Gestblom Department of Physics, Uppsala University, Box 530, S-751 21 Uppsala, Sweden (Received: April 23, 1991: In Final Form: June 24, 1991)
The permittivity spectrum of a number of biological materials has been studied in the frequency range 107-109Hz by using the dielectric time domain spectroscopy method. Evidence of the reported absorption peak from bound water around 100 MHz was not found. The premature truncation of time domain line shapes was found to introduce a seeming dispersion, the position of which depends on the time window used.
Introduction The properties of water in biological solutions have been investigated with different spectroscopic techniques. Dielectric spectroscopy here offers an attractive alternative; the dielectric relaxation time gives direct information on the reorientational mobility of the water dipoles. In order to probe possible different states of water and resolve the relaxation times of bound and free water, respectively, a wide frequency range has to be covered in the permittivity spectrum. The development of the dielectric time domain spectroscopy (TDS) method here has provided a useful experimental technique; a range of three decades can be covered in a single measurements.'-' In a recent paper, the TDS method was applied to the study of a large number of biological materiak8 The biomaterials showed a wide variation in composition and ranged from living tissue, like human skin, to solutions like milk and DNA solutions. The work on DNA solutions has been further e~tended.~JO Permittivity data were reported in the frequency range 107-109 Hz. It was found that for all these biomaterials the dielectric spectrum was characterized by two dispersion regions around 100 MHz and 10 GHz respectively. The high-frequency dispersion was attributed to free water while the low-frequency dispersion was interpreted as due to bound water. The bound water relaxation should thus be reduced by a factor of order 100 compared to that of free water. The permittivity at lo7 Hz reported for several of the biomaterials was considerably larger than for bulk water; e.g., in potato the water contribution to the static permittivity is about 100 compared to 80 for bulk water. Since the biomaterials have a reduced water content this should also lead to the conclusion that the partially immobilized bound water has a higher static permittivity than free water. This is in contrast to what should be expected, the lowered water content and partial immobilization of the bound water should lead to a lowered static permittivity. The dielectric properties of biological tissue have been studied by Grant et al.1i-i3 Besides the high-frequency water dispersion large dielectric dispersions in the frequency range < lo8 Hz were found, dispersions which cannot be completely encompassed and (1) Cole, R. H. Annu. Reo. fhys. Chcm. 1977, 28, 283. (2) Cole, R. H.; Mashimo, S.;Winsor, P. J . fhys. Chem. 1980,84, 786. (3) Cole, R.H.; Bcrberian, J. 0.;Mashimo. S.;Chryssikos, G.; Burns, A.; Tombari, E. J . Appl. fhys. 1989, 66, 793. (4) Gestblom, B.; Noreland, E. J . fhys. Chem. 1977, 81, 782. (5) Gestblom, B.; Elmgren, H. Chem. fhys. Lett. 1982, 90, 412. (6) Dawkins, A. W. J.; Grant, E. H.; Sheppard, R. J. J . fhys. E Sci. Instrum. 1981, 14, 1429. (7) Chahine, R.; Bose, T. K. J. Chrm. Phys. 1980, 72, 808. (8) Mashimo, S.;Kuwabara, S.;Yagihara, S.; Higasi, K. J . fhys. Chem. 1987, 91, 6331. (9) Kuwabara, S.;Umehara, T.; Mashimo, S.;Yagihara, S.J. fhys. Chem. 1988, 92, 4839. (10) Mashimo, S.; Umehara, T.; Kuwabara, S.;Yagihara, S.J . fhys. Chem. 1988, 93,4963. (1 I ) Dawkins, A. W. J.; Gabriel, C.; Sheppard, R. J.; Grant, E. H. Phys. Med. Btol. 1981. 26. 1. (la Rogers, j 8A.; Sheppard, R.J.; Grant, E. H.; Blecken, N. M.; Honeas, D. J. Br. J . Radiol. 1983, 356, 335. (13) Thurai, M.; Steel, M. C.; Sheppard, R. J.; Grant, E. H. Bioelccvomagnetics 1985, 6, 235.
0022-3654/9 1/2095-6064$02.50/0
resolved to give one or several relaxation times. TDS measurements on tissue by Bose et ai. also showed large low-frequency dispersion^.'^ A critical review of the dielectric properties of tissues and biological materials has recently been given by Foster and Schwan.l5 Kaatze,I6 in a recent article on bound water in biological systems, concluded that it appears to be impossible to unambiguously discuss the dielectric spectra of complex biological tissue in which different polarization mechanisms overlap. This is in contrast to the apparently simple spectra presented in ref 8. The dielectric properties of milk have recently been studied by TDS. The quoted permittivities do not show a dispersion region in the 100-MHz range." From frequency domain measurements on mammalian breast milk in the range 0.1-100 MHz, Laogun** fitted permittivity data to a C o l d o l e function with a relaxation time of order 0.1 ps. The influence of solutes on the dielectric properties of water has been extensively studied. Pottel et al.19*20 have investigated solutions of oxygen-containing polymers and amino acids. They found that the water dispersion can be resolved into a contribution from bulk water with its normal relaxation time, and a contribution from the hydration water with a relaxation slowed down by a factor less than ten compared to the free water relaxation. Sugget et aLzi in a pioneering TDS study on polysaccharide solutions similarly found a broadened water dispersion which could be interpreted as due to hydration water and bulk water. This result has also been found by independent TDS measurement on glucose solutions.22 In a recent study, the dielectric properties of water in an L solution phase of trioxyethylene dodecyl ether/water were in~estigated.2~The water concentration was so low that essentially all water molecules could be considered to interact with the oxygen atoms in the ethylene oxide groups in the amphiphile. The relaxation time of the water was found to be slowed down by a factor of 6-8 compared to that of free water. It has recently been shown24that TDS measurements on conducting dielectrics with low-frequency relaxation processes due for instance to counterion diffusion may introduce false dispersions. This may occur if the relaxation processes have not decayed completely within the time window used in the TDS measurement, and the frequency range of the seeming dispersion will depend on this time window. (14) Bose, T. K.; Bottreau, A. M.; Chahine, R. IEEE Trans. Instrum. Meas. 1986, 35, 56. (15) Foster, K. R.; Schwan, H.P. CRC Crir. Reo. Biomcd. Engl. 1989, 17, 1.
(16) Kaatze, U.Phys. Mcd. Biol. 1990,35, 1663. (17) Akyel, C.; Bosisio, R. G.; Bose, T. K.; Merabet, M. IEEE Trans. Electr. Insul. 1990, 25, 493. (18) Laogun, A. A. fhys. Med. Biol. 1986, 31, 555. (19) Kaatze, U.;Gbttmann, 0.;Podbielski, R.;Pottel, R.; Terver, U.J . Phys. Chem. 1978,82, 112. (20) Kaatze, U.;Bieler, H.; Pottel, R. J . Mol. Uq.1985, 30, 101. (21) Suggett, A.; Clark, H. J. Solurion Chem. 1976, 5, 1 . (22) Gestblom, B.; Noreland, E. J . fhys. Chem. 1984, 88. 664. (23) Sjbblom, J.; Gestblom, B. J . Colloid Inreflace Sci. 1989, 127, 141. (24) Gartblom, B.; Gestblom, P. Macromolcculcs,accepted for publication.
Q 1991 American Chemical Society
The Journal of Physical Chemistry, Vol. 95, No. 16, 1991 6065
Letters In view of the above results TDS measurements have been done on a few biomaterials as used in ref 8 to further study the reported relaxation processes with I = 1-2 ns and its possible origin.
TDS Measurements In a dielectric time domain spectroscopy measurement the permittivity spectrum is determined by the study of the influence of the dielectric sample on the shape of a pulse propagating in a transmission line. The sample may be arranged for the observation of the transmitted or reflected line shapes. In the total transmission method, a Fourier transformation F(w) = .flhf(t)e-'u' dt of the pulse v ( t ) transmitted through the empty cell and of the pulse r(t), transmitted through the sample, gives the transmission coefficient at a chosen frequency T(w) = R( w ) / V(w). The complex permittivity e* = e' - id' of the sample is then obtained from T(w) by numerical solution of the transmission line equation (1 - pz) exp[-(iwl/c)(e*1/2
T(w) =
- I)] (1)
1 - p2 e~p[-(2iwl/c)e*~/z]
Here p = (1 - ~ * ' / ~ ) /+ ( le*II2), c is the speed of light in free space, and 1 is the sample cell length. The influence of deviations from the ideal transmission line, eq 1, due to connector mismatches etc. can be reduced by measuring relative to a standard dielectric with known permittivity spectrum not too different from that of the unknown. The transmission coefficient for the reference liquid can then be calculated from eq 1 and the unknown spectrum obtained from solution of the equation
Rb) -=-
T(w)
RredU)
Tredw)
(2)
Analogously the reflection coefficient for an open-ended cell of effective length I is given by the reflection coefficient S(w) ~ ( w ) (p
S(w) =
= V(W)
+ e~p[-2iwle*'/~/c])exp(2iwl/c) 1 + p exp[-2i~le*'/~/c]
(3)
where the symbols have the same meaning as in eq 1. For a measurement relative to a reference dielectric, eq 2 is again applicable with a replacement of the transmission coefficient T(w) by the reflection coefficient S(w). For a dielectric wit!. a dc conductivity u the transmitted pulse will not reach the final level of the incident step pulse. If a sufficiently long time window is used to allow the complete decay of all dielectric processes the conductivity can be calculated from the final pulse levels 1
- -01 Coc
for the two methods respectively. Here eo is the permittivity of vacuum. The biomaterials show a high conductivity. As reference liquids, aqueous potassium chloride solutions were used. The electrolyte concentration was adjusted to give conductivities close to those of the biomaterials as judged from the pulse levels. At low concentrations the dielectric parameters of water are not significantly influencedzs*%and the reference spectrum was calculated from f*,f
= em
- e-w - icr +1 + iwr, 0% CSW
(5)
The water parameters at 20 OC are e,, = 80.2, em, = 5.6, and I, = 9.4 psSz7 To test the applicability of the TDS method to the (25) Winsor, P.; Cole, R. H. J . Phys. Chem. 1985, 89, 3775. (26) Kaatze, U. J . Phys. Chcm. 1987. 91, 3113.
s°F
1
I
b'
I
I
I
I I l l
I
I 1 1 1 1 1 1
I
lo8 lo9 HZ Figure 1. (a) Permittivity spectrum e' of milk (X) and an ATP solution (0)of the same conductivity. The full line shows the theoretical spectrum using a two relaxation time model function. (b) Permittivity spectrum c' of egg albumen. 10'
high-conductivity samples, solutions of the sodium salt of adenosine triphosphate (ATP) were prepared to the same conductivity as the biomaterials. ATP shows a dispersion in the 108-109-Hz region, and the resolution of such a dispersion may serve as a critical test of the experimental method.
Results Figure l a shows the permittivity spectrum e' of one of the biomaterials reported in ref 8, milk, and of an ATP solution of the same conductivity cr = 0.5 S/m. The total transmission method was used with a cell length of 10 mm. This can be compared with the "zero" cell length used in the measurements in ref 8. The time window T, used to obtain the milk spectrum was 100 ns, and the lower limit in the evaluation of this spectrum has been set to T;', Le., 10 MHz. The ATP spectrum was similarly obtained with a time window of 50 ns and evaluated from 20 MHz. In the ATP spectrum a dispersion centered at 400 MHz is well resolved and the full line shows the fit to a model function with two relaxation times, due to water with T~ = 9.4 pr and ATP with 72 = 0.51 ns. In contrast, the milk spectrum in this frequency range shows a trailing permittivity, indicating the presence of a strong dispersion at lower frequencies than the available range. The presence of such long relaxation time processes can be observed already from the time domain line shapes, the pulse difference r(t) - rr(t) not having reached a final steady level within the time window used. Figure 1b shows the e' spectrum from egg albumen obtained by a measurement using the total reflection method. The effective sample length 1 was 2.25 mm and the time window was 50 ns. Also in this case a trailing end of strong low-frequency dispersions can be observed at frequencies above 20 MHz. The spectra in Figure 1 do not show the reported6 dispersion around 100 MHz attributed to bound water in biomaterials. However, as previously demonstratedz4J6for polyelectrolyte solutions with strong low-frequency dispersions, the evaluation of (27) Kaatze, U.; Uhlendorf, V. Z . Phys. Chcm. (Frankfurr am Maln) 1981, 126, 151. (28) Gestblom, B.; Elmgren, H. J . Collofd Interface Scl. 1983, 95. 183.
6066 The Journal of Physical Chemistry, Vol. 95, No. 16, 1991
701
I
Figure 2. Permittivity of milk on truncation of time domain pulse sham after 10 ns. A conductivity contribution has been subtracted from e”.
permittivity spectra from TDS pulse shapes may introduce seeming dispersions. This occurs if the frequency range is extended far below what is allowed by the time window used. Figure 2 shows the permittivity spectrum obtained from the same pulse shapes for milk as underlie Figure l a but truncated after 10 ns. The spectrum was also in this case calculated from 10 MHz. A seeming dispersion is introduced falling in the frequency range near T$. This is further brought out by subtracting a conductivity contribution from the e” spectrum: a clear loss peak is observed. The correlation between the truncating time window and the position of this seeming dispersion was also checked by extending the spectrum calculated in Figure 1 with T, = 100 ns down to 1 MHz. The seeming dispersion and the apparent loss peak then become stronger and are shifted a decade to lower frequency. The total reflection method was also applied to potato and natural cheese, two of the biomaterials listed in ref 8. Also here low-frequency relaxation processes are present, and it was similarly found that the premature truncation of line shapes introduced strong seeming dispersions the position of which was dependent on the truncating time window. The appearance of a seeming dispersion on the premature truncation of line shapes has recently been shown from a mathematical modeL2‘ On the assumption of a thin sample, the transmission/reflection coefficients can be expanded and solved for the permittivity. Assuming a dielectric characterized by two Debye dispersion and a dc conductivity, the true total permittivity is given by t’
= e.
ia ACl At2 - ++1+ 1+ we0 IWT~
~
W
T
~
(6)
Here Ae, is the dielectric increment of the dispersion and T , the corresponding relaxation time. For an aqueous solution with T~ of order 10 p and a long relaxation time T ~the , apparent spectrum on truncation of line shapes at time T, is given by c’app
= At1
1
Letters
+ iWT1
+-1 +Le2
i(a +e,--
- d)
weo
jOT2
Ae2e-(Tw/Tde-hTw
+ iw2(1 + i w 2 )
(7) Here the conductivity contribution -id/oc has been subtracted. The truncation of line shapes leads to an overestimation of the conductivity d , in the thin sample approximation given by Ae2e&Tw/Td d=a+ (8) ‘2
1 10’
1
I
I I I I I I
10’
1
I 1 1 1 1 1 1
lo9
I
Hz
Figure 3. Model permittivity spectra calculated from q 20 with parameters c, = 5 , Pel = 75, T~ = 10 p,Ac2 = 400, T~ = 50 ns, and u = 0.5 S/m. The time window is T, = 10 ns.
The consequences of eq 7 can now be illustrated by calculation of a model spectrum. What actual values should be used for Ac2 and 72 depends on the system and would for a real dielectric require a measurement of the permittivity spectrum to frequencies below T F I in order to be determined. Figure 3 shows a model spectrum calculated with parameters Acl = 7 5 , = 10 ps, and e, = 5 for water, Atz = 400 and r2 = 50 ns as parameters for the low-frequency dispersion and a conductivity Q = 0.5 S/m. The time window T, was set to 10 ns. The model spectrum clearly demonstrates the introduction of a seeming dispersion, the corresponding relaxation time of which would be estimated to -3 ns.
Conclusions TDS offers a fast method of measuring permittivity spectra over a wide frequency range. For nonconducting dielectrics the completion of relaxation processes within the observation time window can be directly checked from the pulse levels. This becomes more difficult for a conducting dielectric with a long relaxation time, the conductivity contribution may then be misjudged if a too short observation time is used. The pulse response r ( t ) - u ( t ) becomes larger with a longer cell length, and the observation of an incomplete decay of slow dielectric relaxation processes is then facilitated. The premature truncation of low-frequency relaxation processes will introduce a seeming dispersion the position of which depends on the truncating time window. At the same time the subtraction of an overestimated conductivity contribution will introduce a loss peak in what would be interpreted as the dipolar contribution to the e” spectrum. The biomaterials studied show trailing ends of low-frequency dispersions above 10 MHz. No distinct dispersion around 100 MHz could be resolved. However, the premature truncation of time domain line shapes introduced such a dispersion, which could easily be mistaken as due to dipolar processes. This may be the background to the reported dispersions in ref 8 and suggested there to be due to the relaxation of bound water. The truncation of a strong low-frequency dispersion may also explain the high permittivity values quoted for several of the biomaterials. It would appear that, in order to resolve any possible dipolar features above 10 MHz, the permittivity spectrum has to be accurately determined also to much lower frequencies. The contributions from low-frequency dispersions into the discussed frequency region may then be properly accounted for.
