Time domain dielectric spectroscopy. A new effective ... - Springer Link

Colloid & Polymer Science

Colloid Polyrn Sci 270:768-780 (1992)

Time domain dielectric spectroscopy. A new effective tool for physical chemistry investigation Yu. D. Feldman*), Yu. F. Zuev, E. A. Polygalov, and V. D. Fedotov Kazan Institute of Biology of the USSR Academy of Sciences, Kazan, USSR *) School of Applied Science and Technology, Hebrew University of Jerusalem, Israel

Abstract: The general principles of time domain dielectric spectroscopy (TDS) are summarized. The methods of data treatment and presentation, and different TDS methods which enable one to obtain the permanent spectrum of e* (co) in the frequency range of 10s-101~ are given. The examples of TDS application for the investigation of dielectric properties in samples of different nature and structure are considered in this review. Key words: D_ielectric spectroscopy; dielectric r_elaxation; proteins; _biological _materials; s_olutions; microemulsions; polymers

Introduction The dielectric spectroscopy (DS) method occupies a special place among numerous modern methods used for physical and chemical analyses of material, because it can investigate the relaxation processes of objects being tested in an extremely wide range of characteristic times (103--10 - 1 2 S). Although it does not possess the selectivity of NMR and ESR methods, it can offer important and sometimes unique information on the dynamic and structural properties of substances. However, despite its long history of development, this method is not widespread for comprehensive use, because the wide frequency range (10-3--1012 Hz), overlapped by discrete frequency domain methods, had required a great deal of complex and expensive equipment. Also, not all the ranges were equally available for measurement. Investigations of objects with variable properties over time (for example biological materials) were difficult to conduct. All the above-mentioned reasons led to the fact that information on dielectric characteristics of substances could only be obtained over limited frequency ranges. As a result the investigator had only part of the dielectric spectrum at his disposal to determine the relaxation parameters. Hence, many investigations using the DS method were able

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to obtain only a fraction of the dielectric information about the substance. The recent successful development of the time domain dielectric spectroscopy method (generally called time domain spectroscopy - TDS) [1-5] and the appearance of noise-reduction methods [6-7] have radically changed the attitude towards DS, making it an effective tool for substance investigation on both macroscopic and microscopic levels. It should be mentioned that in the last few years vector network analyzer techniques [8] have emerged, both in low- and high-frequency ranges, which can also give one the complete dielectric spectra of the sample system frequency domain, but a comparative analysis of such methods with TDS is not the aim of this article. The basic approaches, the principles of experimental realization, data treatment and presentation, and different TDS methods which enable one to obtain the complete spectrum of e* (co) in frequency range of 10s-101~ are given in the following.

Some principles of dielectric relaxation theory The influence of an applied electric field on a dielectric causes its polarization. By linear approximation the dielectric polarization P (electric dipole

FeIdman et al., Time domain dielectric spectroscopy

769

m o m e n t of the volume unit) is proportional to the electric field tension in the sample [9]: P = zE 9

(1)

Proportionality coefficient )~ is called the dielectric susceptibility and is connected with another macroscopic characteristic of the s a m p l e - dielectric permittivity e - by the following relation: 8--t

Z-

4x

(2)

When an external field is applied the dielectric polarization reaches its equilibrium value, not instantly, but over a period of time. By analogy, when the field is broken suddenly, the polarization decay caused by thermal motion follows the same law as the relaxation or decay function: P(t) a(t) - P(0) "

(3)

The value of the displacement vector D(t) in the field E(t) may be written as follows [9, 10]: t

D(t) = s0oE(t) +

j" E(t')dp(t -- t')dt' ,

(4)

--00

where D ( t ) = E ( t ) + 4~P(t), ~0o is the high frequency limit of complex dielectric permittivity s*(c~), and cp(t)= too + ~(t) is the dielectric response function (4~(t)= (Ss- r ~(t)], where 0~(t) is the relaxation function or the decay function of dielectric polarization). The time derivative in (4) is denoted by the point. The complex dielectric permittivity ~* (co) is the analog of cp(t) in frequency domain: 8" (6o) = icoL[ q)(t) ] 0o

= iCO~oq)(t ) exp( -- io~t)dt,

(5)

where L is the operator of the Fourier-Laplace transform. If o~(t) ~ exp( -- t/z m) , (6) where ~m represents the dielectric relaxation time, then the relation first obtained by Debye, is true for the frequency domain [9, 10]: s*(~o) - s0o ~s - - ~3co

1

(7)

relation only. This causes the necessity of using empiric relations which formally take into account the distribution of relaxation times with the help of various parameters (~, fl, 7) [11]. The main complication is that the equipment used by the investigator usually does not cover the whole dielectric spectra of interest. In this case, data analysis in frequency domain when the number of experimental points is limited may give ambiguous results and the physical interpretation of semi-empiric parameters 0~,/3, 7 is not always clear. In this case, the TDS method offers a great advantage as its frequency range is wider and measurement precision more improved. An alternative approach is to obtain information on the dynamic molecular properties of the substance directly in time domain. Relation (5) shows that the equivalent information on dielectric relaxation properties of the sample being tested can be obtained both in frequency and time domain. Indeed, polarization fluctuations caused by thermal motion in the linear response case are the same as for macroscopic reconstructions induced by the electric field [12, 13]. This means that one can equate the relaxation function 0~(t) and the macroscopic dipole correlation function F(t): (~I(0) Kl(t)) ~(t) = F(t) - (M(0)~I(0)) ' (8) where ~I(t) is the macroscopic fluctuation dipole m o m e n t of the sample volume unit which is equal to the vectorial sum of all the molecular dipoles; symbol ( ) denotes averaging of the ensemble. The velocity and laws governing the decay function F(t) are directly related to the structural and kinetic properties of the sample and characterize the macroscopic properties of the system studied. The question of a relationship between the macroscopic and molecular dipole correlation functions is still open and the subject of thorough investigation [13].

Thus, the experimental function (p(t) and, hence, ~(t) or F(t) can be used to obtain information on dynamic properties of dielectric in terms of the dipole correlation function. The basic principles of TDS

1 + io)'E m '

where Cs is the static dielectric permittivity. For most of the investigated systems the experimental results cannot, as a rule, be described by such a

The TDS method is based on the reflectometry principle in time domain in order to study heterogeneities in the coaxial lines according to the

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Colloid and Polymer Science, Vol. 270 9 No. 8 (1992)

change of the test signal shape [14, 15]. Until the line is homogeneous this pulse is not changed. But, when there is heterogeneity in the line and in the presence of a dielectric, for example, the signal is partly reflected from the air-dielectric interface, while the remainder of the signal passes through it. The simplified block diagram of the setup common to all TDS methods is presented in Fig. 1. The only differences are those regarding the construction of the sample cell and its position on the coaxial line, which leads to different relationships between the values that are registered during measurement and the dielectric characteristics of the objects under study. For the configuration represented in Fig. 1 a rapidly increasing voltage step Vo(t ) comes to the sampling head where the signal R(t) reflected from the dielectric sample is also registered. The R(t) signal goes to a sampler with a time delay corresponding to double length of coaxial line from the sampler to the air-dielectric interface (Fig. 2). Further analysis of TDS data is based on the consideration of the relations between the incident and the reflected signals [4, 5, 16]. There are several ways to associate the dielectric characteristics of the sample with the signals observed in the experiment, namely: a) by means of the reflection coefficient or the scattering and transmission coefficients [2-5]; b) by complex admittance of the system [4, 16-19]; c) via the electric charge of the capacitor containing the dielectric [5, 17, 21-23].

R(t) f

~ ,

.

(9)

where Vo(t ) and R(t) are the incident and the reflected signals respectively (Fig. 2). Here, the expression for the current flow through the sample is [16, 21]: PULSE gENERATOR

$nMPLING HE~9

8RHPLING 8COPE

I

DnTn PBOCESSING

>

.

.

.

.

.

. .

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

(10)

where Z 0 is the characteristic impedance of the empty line. The conducting dielectric's total current is composed of the displacement current IQ(t) and the low-frequency conductivity current IR (t). Since the active resistance of the cell containing the sample is [16, 21]: Vo(oO ) I(oo~-

r-

~. Vo(oO ) + R(oo) L~ ) - R(oo) '

(11)

the low-frequency conductivity current can be expressed as: v(t) I R (t)

T

1 V o ( o O ) - R((~)[Vo(t)

= Z-~ Vo ( oo ) + R , _ _ )

+ R (t)] . (12)

Thus, relation (10) can be written as:

I(t) = Io(t ) + IR(t ) - Zo

[Vo(t) - R(t)]

Vo(~ ) - R(~) [Vo(t ) + R(t)]}. (13) V 0 ( ~ ) + R(oo) Relations (9) and (13) present the basic equations that relate I(t), V(t) to the signals recorded during the experiment. In addition, relation (13) shows that TDS permits one to determine the low-frequency conductivity of the sample: Vo ( oo ) - R ( o o )

~o

(14) ZoCo Vo(oO) + R(oo) ' where eo = 8.85.10 -12 f/m, and C o is the electric capacity of the coaxial line partially filled by the sample. Using I (t), V (t) and their Fourier - images: ~-

-

-

oo

v(ico) = J'oV(t)exp( - loot)dr, 00

Fig. 1. Schematic drawing of the TDS arrangement

.

I(t) = 1 / Z o IV0 (t) - R(t)] ,

G"

$RHPLE SECTIO~

.

Fig. 2. Characteristic shape of signal recorded during TDS experiment; Vo (t): incident pulse, R(t): reflected signal

Generally, the voltage applied to the sample is:

V(t) = Vo(t) + R(t) ,

.

................

i(im) = [I(t) e x p ( - i~ot)dt, "o

(15)

Feldman et al., Time domain dielectric spectroscopy

771

one can deduce the relations that will describe the dielectric characteristics of a sample under study b o t h in frequency and time domain. T h e concrete f o r m of these relations depends on the geometric configuration of the cell and its equivalent presentation [5, 16, 17, 24]. For the sample cell, for example, whose equivalent circuit can be represented as a lumped capacitance terminating the coaxial line (the sample is located at the end of the line), the electric charge Q(t) is connected to dielectric response function 4~ (t) and the applied voltage V(t) by the relation:

Q(t) = Co[eooV(t) + So~P(t -- t ' ) V ( t ' ) d t ' ,

(16)

where ~(t) = L-l{[e*(ico) - eo~ ]/ico}, L -x is the o p e r a t o r of the inverse F o u r i e r - L a p l a c e transt

form,

Q(t)=

S I(t')dt',

and

C o is the empty

sample cell capacitance. Relation (16) is also true w h e n the sample in the line is considered as a section with distributive parameters, in which case C O is the geometric capacitance per unit length of line [17, 18, 24]. T h e n , if one applies the Laplace t r a n s f o r m to both sides of Eq. (16), we obtain the spectrum of the c o m p l e x dielectric permittivity of the sample: e.=

1 L[I(t)] icnZ o C o L[ V (t) ] '

(17)

where I(t) and V(t) are determined by relations (9) and (13). If one takes into account the definite physical length of the sample and n u m e r o u s reflections f r o m the air-dielectric or dielectric-air interfaces this relation has the form:

C

L[I(t)],

e* (co) = ico(?d) ~ - ] - A

spectrum e*(co). T h e essential advantage of TDS methods in c o m p a r i s o n with frequency ones is the ability to obtain a point at almost any given frequency to obtain practically continuous spectrum. Another i m p o r t a n t feature of the T D S m e t h o d is the ability to obtain the relaxation characteristics of the sample being tested directly in time domain. Thus, by solving the integral equation, one can obtain the results in terms of the dielectric response function @(t) for the lumped capacitance m e t h o d [ 5 , 1 7 , 2 1 ] . It is then possible to associate cp (t) = @ (t) + e00 with the macroscopic dipole correlation function F(t) [12, 13] in the f r a m e w o r k of linear response theory.

Ctg(X)

(18)

where X = c o d ~ / C , d is the effective length of inner c o n d u c t o r , ? is the ratio of the vaccum capacitance per unit length of the cell to that of the m a t c h e d coaxial cable [16, 19]. Expression (18), in contrast to relation (17), is the transcendental equation, and its exact solution is very difficult to determine. Relations (17) and (18) enable one to obtain the dielectric characteristics of samples under investigation in the form of the c o m p l e x permittivity

Experimental realization of TDS methods The standard time-domain reflectometers used to measure the nonhomogeneities of coaxial lines [14, 15] are the basis of the majority of modern TDS-set-ups. The reflectometer consists of a high-speed voltage step generator and a wide-band registering system with a single or double-channel sampling head. But to meet the high requirements of TDS measurements such commercial equipment must be considerably improved. The main problem is due to the fact that the registration of incident Vo(t) and reflected R(t) signals is accomplished by several measurements. In order to enhance the signal-noise ratio, one must accumulate all the registered signals. The high level of drift and instabilities during generation of the signal and its detection in the sampler are usually inherent to the serial reflectometry equipment. Therefore, special modifications are necessary to improve the measurement system of analogous and digital modules. Some methodological approaches are also required to compensate for the technical shortcomings and, essentially, to increase the measurement precision within the wide frequency range. Figure 3 is a typical block-diagram of a TDS setup [25, 26]. Besides purely technical modernizations which improve the amplitude and time stability of the measuring system, it is of great importance to be able to flexibly change the experimental conditions. This is achieved by means of various modifications of differential methods and by varying of sample cell configuration [19, 24-32]. The essence of the differential method is in recording of standard sample signals with the known dielectric characteristics and signals of the object being tested. This approach allows compensation of undesirable reflections within the coaxial line and the increase in sensitivity while measuring weak signals (e.g., the measurement of dilute solutions of some samples with respect to a solvent [25, 26,29,31]). A further development of the differential method is the creation of the bridge circuit which allows direct recording of the difference signal in analogous form. It has made possible the high-precision measurements of e* (co) in a frequency range even up to 10 GHz [20, 24]. The choice of an optimum sample cell is another condition for precise TDS measurements. Figure 4 presents some possible sample cell configurations which are used to study a wide

Colloid and Polymer Science, Vol. 270 9 No. 8 (1992)

772 SaMpte

,~ fl

The existing experimental set-ups are precision measuring systems which provide coverage of the 100 KHz-10 GHz frequency range. Most of them are now highly accurate. If pure water is measured to prove accuracy, one can see that, at frequencies lower than 6 GHz, the real part z' could be obtained within an error of • 2%. The imaginary part ~" could be obtained within an error of + 5% below 6 GHz and within + 10% at 10 GHz [24, 25]. This is approximately the same precision that can be obtained by the modern frequency domain methods based on a network analyzer in the same frequency range [8]. However, one of the characteristic drawbacks of all these systems is the limited frequency range that can be overlapped by a single measurement with the uniform time discretization signal. Since the number of N samples is no more than 103 for the majority of experimental settings, the overlapped frequency range is no more than 2.5 decades. In this case, in order to extend the frequency range of interest, it is necessary to carry out at least two measurements in the corresponding time windows [16, 25-27]. This, in turn, inevitably leads to the complicated problem of matching the results obtained in several separate experiments, and it considerably increases the duration of the measurements. One of the possible ways for solving this problem is the registration of primary signals in nonuniform time scale, i.e., with variable time-step sampling [38]. In this case the highest frequency fh detectable in the spectrum of the signal is determined according to the wellknown Shannon-Kotelnikov theorem as:

Sampling8c0pe

vider

HoStel,

Fig. 3. Circuit diagram of a TDS set up [25]

fh -a Te:fl

b on

Sampl

2~rain

,

(19)

and the lowest frequency f1 is defined by the whole length of the registered signal T m

C ~

1

e

T....

=

~ cSiNi = ~ Ti, i=l

Fig. 4. Simplified drawings of sample cells, a) Open coaxial line cell; b) lumped capacitance cell; c) end capacitance cell class of objects [16, 19, 24-26, 29, 31, 32]. The cell of type (a) is a cylindrical capacitor filled with sample [28]. Such a cell can also be regarded as a coaxial line segment, with the sample having an effective Fd length [16, 24-26, 29, 31] characterized in this case by the corresponding spread parameters. This makes it possible to use practically identical cells for various TDS method modifications. The choice of cell shape is, to a great extent, determined by the aggregate condition of the object studied. Thus, while cell (a) is convenient to measure liquids, configuration (b) is more suitable for the study of solid disks and films. Both cell types can be used to measure powder samples. While studying anisotropic systems (liquid crystals, for instance) the investigator may replace a coaxial line by a strip line or construct the cell with a configuration which provides measurements in various directions of applied electric field [34]. The (c)-type cell is used only when it is impossible to put the sample into the (a) or (b) cell types [35-37]. The fringing capacity of the coaxial line end is the working capacity for such a cell. This kind of cell will probably be widely used in the future while developing methods for dielectric parameter investigations of plant and animal tissues [35, 37].

(20)

i=l

where J i and N i are the step of discretization and the number of points in i-th time interval, respectively. The number of n intervals may be chosen quite arbitrarily and signal length Tmeas will be determined by the number of points with the maximum step of discretization CSmax,on the condition that c$1~ cSi+l- The set-up built according to this principle permits the overlap of a frequency range of five orders by a single measurement while the number of the samples within the measured signal is limited [38]. The existing theoretical approach and the experimental realization of the TDS method give an opportunity to quickly and precisely measure the dielectric characteristics of a wide class of objects and provide data treatment, both in frequency and time domains. The different applications of the TDS method in fundamental and applied investigations is discussed below.

TDS-method

application

The investigation of dielectric relaxation processes in s a m p l e s o f v a r i o u s n a t u r e a n d s t r u c t u r e b y TDS methods provides much new information on

773

Feldman et al., Time domain dielectric spectroscopy

structural-dynamic properties of these objects. But because of the lack of the commercial TDS set-ups the present use of these methods is limited. Not comparing the TDS method with the frequency ones, we should note that the former has great advantages in the 105-101~ frequency range in cases when the complete ~* (co) spectrum within the possibly wide frequency range is necessary. Such a problem very often arises when investigating multi-component systems, polymers, biopolymers, associated liquids, and many other objects when both the position of the absorption peak and its shape, which reflect the molecular nature of the registered relaxation processes, are to be determined. Even if the modern frequency domain methods [8, 37] can give the complete dielectric spectrum, the TDS methods allow one to obtain all information directly in time domain in terms of dipole correction function and are cooperatively cheaper than wide-band network analyzers.

the investigation of dielectric properties of these materials. Naturally, to create the correct physical model it is necessary to have as much comprehensive dielectric information within the broad frequency range as possible. The simplicity and reliability of such test systems that are used to examine the capacity for work of the set-ups built under laboratory conditions have prompted a large number of studies on pure liquids and their solutions by the TDS method. These studies provided new, interesting results about mechanisms of molecular motion in normal aliphatic alcohols [3, 5, 12, 17-19, 25, 26, 38-44], about features of the hydrogen connections redistribution in water-alcohol systems [45, 46] and diols [47, 48], about the peculiarities of liquids during phase transition [49], and more.

Polymers

There has been renewed interest to study dielectric properties of polymers in order to investigate their phase transitions, molecular mobility in soluPure liquids and solutions tions and in solid state, and to control the chemical The DS method is widely used to study the reaction of polymerization, polycondensation, and structure of pure liquids and their solutions [10, 11, degradation [49, 50]. Of great importance are the 13]. These investigations are of great interest be- studies of polymers at frequencies higher than cause of the important and often unique informa- 100 KHz. This range has rarely been used before tion about liquid-state physics and solvent-solute for such purposes. The possibilities of the TDS substance interaction that can be obtained during method to study the rapid relaxation processes in polymer chains is shown below. Figure 5 represents some data obtained by TDS while studying poly(methyl vinyl ketone) solution in dioxane [51]. g g 2.50 The frequency range from 1 MHz to several GHz was overlapped only by two measurements. 0.09 The differential method was applied with the solvent being used as a dielectric standard. Two 2.40 relaxation processes were recorded, each having a shape characteristic of the Havrilijk-Negate re0.07 laxation time distribution. The low-frequency process was identified as the display of the local conformational displacements of the polymer chain 2.30 0.05 backbone, while the high-frequency one was related to the internal rotation of the lateral acetyl groups. The components of the dipole moment corresponding to both slow and rapid processes 2.20 0.03 were determined. The results of the investigations 10 100 1000 Frequency MHz have been correlated with NMR and ESR data. Interesting results were obtained when investigFig. 5. e* (co) spectrum of 4.2% solution of poly(methylvinyl ketone) in dioxane at 20 ~ [5l] ating dilute solutions of methyl methacrylatei

.

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Colloid and Polymer Science, Vol. 270 9 No. 8 (1992)

774

methyl acrylate copolymers in benzene [52]. Two dielectric processes discovered in the diluted solutions of these compounds were caused by the motion of two types of chain bonds along the same chain moving independently of each other with different velocities. Data on the correlation of dynamic properties of a separate monomeric link with the motion of neighboring links were also obtained. New information was also obtained by this method on poly(e-amino acids) [53]. Two relaxation processes with relaxation times in the ranges of 100 nanoseconds and deserts picoseconds were observed for three polymers in dioxane solutions. The authors suppose that lower frequency relaxation process can be attributed to restricted rotations of C - C bonds in the side chain, neighboring the e-helical backbone. The short-time relaxation process is caused by free rotations of C - O bonds in the side chain. Such results are very significant for understanding the intramolecular fast motion nature in biopolymers. The use of dipole correlation functions obtained in a TDS experiment is even more promising. They present the opportunity to simulate flexible relaxation processes by dynamic molecular methods and to compare the results obtained at this level with the data of other dynamic and mechanical methods [49].

Electrolyte solutions One of the most important aims of physical chemistry and electrochemistry of solutions is the study of polarization and the nature of dielectric relaxation in electrolyte solutions. It is rather difficult to study complex ion-ion, ion-dipole, and dipole-dipole interactions superposition in the presence of an external electric field when there exists a high level of low-frequency conductivity and electrode effects when using the dielectric method. The numerous frequency experiments conducted were mainly limited to the SHF range and to lowfrequency measurements [54, 55]. This is not enough to build adequate models of dielectric relaxation in these systems. It should be noted that the difficulties arising while measuring the dielectric parameters of high conducting systems by frequency methods are also inherent in the TDS method. But they can be overcome and there are

several examples of successful application of the TDS method to study the electrolyte solution [56-61]. Figure 6 represents the results of sulfuric acid and its aqueous solution [56]. The fact that the dielectric relaxation characterization of these objects, can be made by no less than two and probably three or more Debye functions, was quite unexpected even to the authors of the work. The TDS method offers an opportunity to solve the general problem of dielectric characteristics measurement of high conducting liquids [19, 21, 25, 60] to obtain new data on mechanisms of solvation [57, 58] and on the influence of Hubbard-Onsager kinetic depolarization on the relaxation of the molecules of a solvent [56, 59].

Microemulsions Dielectric spectroscopy is widely used to study microemulsions of various composition. These thermodynamically stable solutions of water, hydrocarbons, and surface-active substances are used to aid in understanding the principles of their compatibility with biological membranes and in many other spheres of science and techniques. It was shown with the help of TDS methods that a 10s-101~ frequency range is quite useful to study these systems [62-67]. Static permittivity is sensitive to geometrical changes of the aggregates and the dielectric relaxation is an indicator of interfacial polarization, counterion movements in the aggregates, and special changes inthe domain sizes of microdroplets. The conductivity, which is also obtained from TDS, gives additional information about the mobility of the ions in the system [65]. For water-in-oil microemutsions (for example), a

8"

80 ~_

20 Z

40

84

0

,

0

,i

20

40

60

80

1 O0

Fig. 6. Cole-Cole diagram for 100% sulphur acid (A) and after water dilution ([2) at 25 ~ [56]

775

Feldman et al., Time domain dielectric spectroscopy

step-increase in the conductivity with increasing water concentration gives hints of a percolation phenomenon of water droplets [66, 67]. The explanation of dielectric behavior of these systems within the framework of percolation theory leads one to understand why a maximum of static permittivity and a minimum of the characteristic frequency of the dielectric relaxation are associated with the percolation threshold [67]. The investigation of structure and dynamics in w / o and o / w microemulsion droplets by TDS can provide information about the difference between the spherical geometry of discrete droplets and bicontinuous structures, and may help resolve difficult questions related to the size and shape of the droplets, aggregation phenomena, and interchanges between droplet interfaces and the continuous phase.

Biological systems Among the variety of investigations of biological components by dielectric spectroscopy methods, we shatl discuss some works from the many that have already shown interesting results. They are: aqueous protein solutions [31, 68-72], hydrate water in biopolymers [36, 73-76], and animal tissue investigations [77, 78]. In addition, there have been investigations of dielectric properties of DNA solutions [79, 74-76], lipids [80], plant matter [81], and more, by the TDS method. While studying the dielectric properties of aqueous protein solutions, one can obtain important information o 7 the structure and dynamic characteristics of both macromolecules and solvent molecules. These data, while interesting, are quite useful when interpreting the experimental results regarding dynamic protein structure obtained by other methods [68, 69]. Before TDS methods appeared these investigations were restricted by the lack of techniques which allowed the quick determination of the ~*(co) spectrum within the 105-10 i~ frequency range. It was quite difficult to guarantee the stability of biological material because of the long duration of the experiment. These problems, together with the high conductivity of protein solutions, made a detailed investigation impossible. As a rule, the globular proteins have been studied at pH values close to their isoelectric point within a narrow temperature range, i.e., under conditions

corresponding to their native state [82]. Implementation of TDS methods extended the sphere of problems solved by dielectric spectroscopy. The method can be used to study temperature-induced phase transitions [68-70], as well as to examine the influence of pH on dynamic protein structure [71, 72] or intramolecular motion in globular proteins [70-72]. A 4% lysozyme solution in potassium-phosphate buffer, tested at pH = 7.0, was investigated by the differential method with nonuniform signal discretization [38]. The results are shown in Fig. 7. The data analysis was done using the "lumped capacitance" method directly in time domain in terms of DCF F (t), which was calculated from the dielectric response function cp (t) (Fig. 7a). Figure 7b represents the same results as the e*(c0) spectrum obtained with the help of the FourierLaplace transformation of the dielectric response function. Three dispersion regions of e* (co) are fixed: the so-called fl, c~l, and ~2 dispersions. The first one is stipulated by rotational diffusion of the solute macromolecules [68, 69] (dielectric relaxation time ~t~ = 58.6 ns). The natures of the second (%~ = 7.5 ns) and the third ones (%2 = 690 ps) are now the object of thorough investigation. While the existence of fl-dispersion and 7-dispersion (the latter is due to solvent molecule relaxation and does not enter the "time window" of the TDS setup used to obtain the results shown in Fig. 7) has been known for quite a while [68, 82], but only

848280

/.

78 767472 ~ 70-

.......................................................................................

27

54

81

108

135

162

189

216

t(ns)

24,3 270

Fig. 7a. The dielectric response function cp(t)for 4% lysozyme solution at 25~ (pH = 7.0) obtained by TDS with nonuniform signal discretization with the following parameters: T l = 3 0 n s , T 2=60ns,andT 3 = 1 8 0 n s ( T = T l + T 2 + T 3 = 270 ns). Signal A i discretization steps in these time intervals were 0.1 ns, 0.3 ns, 0.9 ns, respectively [38]

776

Colloid and Polymer Science, Vol. 270 9 No. 8 (1992)

9ot

of fast motion which may be nonexponential in general [72, 83]. One must keep in mind that q2 and f(t/~ 1 ) may reflect the fast local motion of different fragments of the protein globule in the case of both magnetic and dielectric relaxation. In the case of TDS the parameter q2 is obtained from the equation

3

85

H

d

i

=

-

,

(22)

where #0 is the whole electrical dipole moment of the macromolecule, (calculated from the experimental data using the Onsager-Oncly formula); /.q - t h e unaveraged (by local motion) part of dipole moment. The functions of rla, ZlN, and q2 7O 1 10 1 O0 1000 parameters obtained by TDS and by N M R for frequency MHz aqueous lysozyme solution are shown in Fig. 8. Fig. 7b. The dielectricspectrum obtained for the same sample This approach has provided new information on by Fourier transform of the dielectric response function protein dynamics in the process of pH-dependent transition [72]. It is well known that a wide dielectric relaxation recently has detailed information on 6-dispersions domain of small amplitude, called cS-dispersion, is been successfully obtained, thanks to the TDS observed in aqueous biopolymer solutions within the frequency range of hundreds MHz [73, 77, 82, method. The dielectric relaxation data (DCF analysis) of 84]. The nature of this dispersion is not completely the globular protein solutions used as examples clear. Although it was shown above that at least have helped identify the processes by a general part of this dispersion (81) for lysozyme solution approach towards interpretation of the results ob- can be explained by intramolecular rotation, the tained by various dynamic methods. A "model- investigations within this frequency range leave free" approach [83] toward N M R data analysis is many questions unanswered. The relaxation of quite widespread. It has been used in the study of fixed or hydrate water may be one possible reason molecular motion of protein globules within the for the 8-dispersion effect, as polar water molecules solvent, assuming that all macromolecular atoms in bulk at room temperature reveal dielectric reparticipate in two types of motion - the slow rota- laxation at a frequency 17-18 GHz. tional diffusion of the globule as a whole, and the more localized fast intramolecular motion. The 2 correlation function in this case can be written as 0.45 7-~oco,N,ms 5.0 q di~ [69-72]: 75

F(t) = A e x p ( - t/zR) [(1 -- q2) + q a f ( _ t / r l )],

4.0

0.40

(21) where A in the case of N M R is the second moment, and in the case of dielectric relaxation it is the square of the dipole moment; rR is the correlation time of macromolecular rotation as a whole (rRa = 3rRN , where TDS and N M R are denoted by (d) and (N), respectively); q2 is the anisotropic parameter, characterizing that part of the interaction which has been averaged by the fast local motion (when q2 = 1 the motion is isotropic and the parameter q2 decreases with the increase of anisotropy), and f ( t / z l ) is the correlation function

3:0

o.35

Z ~ A / A A A A Z~Z~Az~

7A

s % AA,,

0,30

0.25

~

2.0

*"

~

1.0

............................................ 2 3 4 5 6 7 8 9

pH

0

0.0

Fig. 8. The pH-dependence of parameter q~ -- A, q~ -- *, via -- + and zlN - [] for 4% lysozymesolution in D20 at 20 ~ The best fitting by spline is shown by solid line [72].

Feldman et al., Time domain dielectric spectroscopy

777

While coupling with a biomacromolecule the rotational motion of a water molecule becomes slower, causing the relaxation time to increase. With the appearance of TDS methods several attempts have been made to thoroughly investigate dielectric relaxation processes within the c%dispersion frequency range, which is rather complicated using the usual frequency methods [36, 74-76, 84]. The ~* (co) spectra of the intestinal bacillus DNA E. Coil [74] are shown as an example in Fig. 9. The authors have shown the dielectric dispersion with its center near 100 MHz to be stipulated by the motion of hydrated water molecules. The most probable type of motion here is the anisotropic rotational diffusion of H 2 0 molecules about the hydrogen bond attached to the DNA surface. The application of the TDS method can offer great insight into the properties of bound water in biopolymer powders [85-87]. The fact that there are no macromolecular or solvent signals greatly exceeding the amplitude of the bound water signal makes these investigations particularly useful. TDS has also been used successfully to study bound water in biological systems which are more complicated than simple solutions and powders of biopolymers. The parameters of dielectric relaxation of bound and bulk water in some biopolymers obtained by differential methods [88] are shown in Table 1. It is stressed that there has appeared the real possibility of obtaining a range of 107-10 l~ Hz dielectric spectra very quickly (approximately one spectrum per minute) with high precision (error within percent unit limits).

:tO ~o-

log f(Hz) 9' Fig. 9. 'Dielectric D N A

A -70~

spectrum

[ ] - - 9 0 ~ [74]

10 of E. coli ( , -

50~

Table 1. Dielectric relaxation parameters of bulk and hydrate water in biomaterials at 20 ~ [88] Sample

As1

"c1 (ns) A s 2

~2 (ps) so0

Human skin (36~ Carp (muscle) Radish Apple Mutton (muscle) Aqueous solution of lysozyme (6.01%)

17.9 38.6 8.88 6.05 34.4

1.18 1.67 1.62 1.37 1.34

15.0 53.5 65.7 51.7 52.7

7.1 10.0 11.2 13.2 14.5

3.97 4.11 3.93 4.15 3.34

2.46

1.22

73.3

10.0

4.14

Investigation of the electrical properties of tissues is of special interest in solving medical-biological problems. Although there are few examples of the use of TDS methods to study such material, this method could be very useful for diagnostics and express analysis of certain trends, namely, the aging and physiological change in tissues due to the variation of water quantity within them [35, 78, 89-92]. Investigations of the tissues may further the development and application of the method of local hyperthermy of cancerous tumors by application of high-frequency electromagnetic fields

[93-95]. Conclusions During the 20 years of its development, TDS has gone through the traditional stages of every experimental method: The numerous methodological approaches at the first stage, the first successes and enthusiasm concerning the opening possibilities, the discovery of mistakes and deadlocks and, finally, the appearance of a serious method of investigation. Naturally, it is very difficult to overcome the desire to implement a new instrument of investigation in studying various objects. We have not discussed separate works in this review containing the results of metal surface polymer covers [33], of water absorbed by silica gels [96] and synthetic absorbents [97], of liquid crystals [34, 98], conducting glasses [99], and other substances investigated. The results obtained stand as proof of the existence of an informative, convenient, and precise instrument of measurement whose widespread use is restricted simply due to the lack of serial devices. The commercial-type TDS spectrometer (compact and comparatively inexpensive) which will

778 a p p e a r o n the m a r k e t m a y s t i m u l a t e its a p p l i c a t i o n in o t h e r fields besides t h o s e t h a t h a v e been discussed as a c o n v e n i e n t , fast, a n d sensitive m e t h o d o f testing m a t e r i a l d u r i n g r e a c t i o n s u n d e r v a r i a b l e c o n d i t i o n s ; the c r e a t i o n o f e x p r e s s - d i a g n o s t i c s in m e d i c i n e ; the s t u d y o f dielectric p r o p e r t i e s o f f o o d , a g r i c u l t u r e m a t e r i a l s a n d so o n [14, 15, 84, 100,

101]. Acknowledgement

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Received October 29, 1990; accepted September 17, 1991 Authors' address: Dr. Yu. D. Feldman School of Applied Science and Technology Hebrew University of Jerusalem Givat Ram Jerusalem 91904 Israel