Light Scattering of Aqueous Solutions of DNA, Poly(acry1ic Acid), and Tobacco Mosaic Virus Under Alternating Electric Field TAKASHI FUJIKADO, REINOSUKE HAYAKAWA, and YASAKU WADA, Department of Applied Physics, Faculty of Engineering, University of Tokyo, Bunkyo-ku, Tokyo, J a p a n
Synopsis Two new techniques, amplitude modulation (AM) and frequency modulation (FM) of an electric field, are developed for the light-scattering study of polymer solutions under ac electric fields. The AM technique makes it possible to observe accurately the frequency dependence of the intensity change of scattered light due to the electric field. The F M one allows us to obtain directly the frequency derivative of the intensity change. The techniques are applied to DNA, poly(acry1ic acid), and tobacco mosaic virus in the frequency range from 10 Hz to 100 kHz. A low-frequency relaxation is found for both DNA and poly(acry1ic acid). The observed relaxation time of DNA agrees with that in the dielectric relaxation of DNA, which has been attributed to the rotation of the molecule with a quasipermanent dipole. In the case of poly(acry1icacid), the relaxation strength increases with increasing degree of neutralization. TMV a t a concentration of 0.1% exhibits a negative relaxation a t low frequencies, which indicates the rotation of TMV aggregate with a permanent dipole along its minor axis.
INTRODUCTION When a particle suspended in a liquid is comparable in size or larger than the wavelength of incident light and possesses an anisotropy in shape, the particle is oriented under an electric field and the scattered light intensity changes thereby. Conceptual and practical aspects of this phenomenon, electric field light scattering, have been reviewed by Jennings' with numerous illustrative applications. When the particle possesses a permanent dipole and the electric field is sinusoidal with an angular frequency w , the orientation distribution of particles is in equilibrium a t w7 > 1,the orientation due to the dipole-field interaction does not occur. The relative change of scattered light intensity, r = AZ/Io (I0 being the scattered light intensity without an electric field and AI the intensity change under the field), therefore depends on w , and from the frequency dispersion curve of r , we can estimate the rotational relaxation time 7. Electric field light scattering has hitherto been applied rather rarely to Biopolymers, Vol. 18,2303-2314 (1979) 0 1979 John Wiley & Sons, Inc.
00oS-3525/79/0018-2303$01.00
2304
FUJIKADO, HAYAKAWA, AND WADA
the relaxation spectrometry of polymers. This is mainly because the intensity change of scattered light is relatively weak. By way of greatly improving the sensitivity of this method, we introduce two new techniques: amplitude modulation (AM) and frequency modulation (FM) of the electric field. The AM technique enables us to avoid the effect of any fluctuation in 10,because AZ alone is modulated, and thus the fluctuation in 10is rejected by the lock-in detection. The frequency dependence of r (dispersion curve) for chain polymers such as DNA and poly(acry1ic acid) [(Acryl),] is rather moderate owing to a wide distribution of relaxation times. In such a case, low- and high-frequency limits of r are not well identified at the same time, and consequently, it is in general difficult to locate the relaxation frequency corresponding to the inflection point of the dispersion curve. In this paper we employ the FM technique, wherein we apply an FM ac field to the sample and directly obtain the derivative of the dispersion curve with respect to log w. The peak of this FM curve gives the relaxation frequency. This paper describes the applications of our new techniques to dilute aqueous solutions of three kinds of polyelectrolytes: DNA, (Acryl),, and tobacco mosaic virus (TMV). Dielectric relaxation spectrometry of aqueous DNA has r e ~ e a l e d that ~-~ the low-frequency dielectric relaxation of DNA arises from rotation of the molecule with a quasipermanent dipole, the dipole with a lifetime longer than the rotational relaxation time. The dipole is parallel to the major axis of the polymer, which possesses an elongated form due to electrostatic interaction among charges along the chain. The magnitude of the dipole is well explained by the counterion fluctuation mechanism. Light scattering of DNA within an ac field making use of widely varied frequencies might give a further support to this conclusion. (Acryl), is studied here by the same approach. The dielectric relaxation of aqueous tetra-n-butyl ammonium polyacrylate was measured by Minakata and Imai.6 They eliminated the electrode polarization effect below 10 kHz, and the data were limited to above 200 Hz. Van der Touw and Mande17 observed the dielectric constant of aqueous (Acryl), partially neutralized with NaOH. The low-frequency limit of their data was 5 kHz. The low optical anisotropy of this polymer makes it difficult to study the low-frequency relaxation from birefringence study in an ac electric field. Our light-scattering method in an ac electric field seems most suitable to revealing the low-frequency relaxation of (Acryl), . TMV, which is a rather rigid particle when compared with DNA and (Acryl),, has been reported to have a small dipole along its minor axis,8 though the dipole characteristics of TMV depend on the strain. The ac field light scattering is expected to give information on the dipole moment of TMV of the ordinary Japanese strain.
LIGHT SCATTERING IN AN AC FIELD
2305
SAMPLES Two samples of DNA were used: DNA-A was calf thymus NaDNA (P-L Biochemical Inc., Lot 4562X) with a molecular weight of 5 X lo6, and DNA-B was obtained by sonication of DNA-A and had a molecular weight of 8 X lo5. The sonication procedures and molecular weight determinations were the same as reported previou~ly.~.~ Both samples were dissolved in lop4M NaCl a t a DNA concentration C, = 0.05%. The sample of (NaAcryl), supplied by Toa Gosei Chemical Industry Co. was transformed into (Acryl), by passing its solution through an ion-exchange column. The stated average degree of polymerization was 2700. The polymer concentration was determined by titrating the solution with aqueous NaOH after the method previously d e ~ c r i b e d . The ~ solution was neutralized with NaOH. No salt was added in the present experiment. The sample of TMV was the ordinary Japanese strain, which was kindly supplied by the Central Research Institute, the Japan Tobacco and Salt Public Corporation. The stock solution (10p2Mphosphoric acid) was diluted to a concentration of 0.1% and subsequently dialyzed for 2 days a t pH 7.4. A sample of lower concentration was obtained by further dilution to 0.01% (pH 7.1). Measurements were made a t 25°C for all the samples.
EXPERIMENTAL APPARATUS Figure 1shows the block diagram of our apparatus. The incident light from a He-Ne laser (5-mW output, 6328 A) was focused into the sample cell, which had a rectangular cylinder. The cell was made of Pyrex glass. The temperature of the cell was controlled by circulating water around the cell and was measured with a thermocouple. The ionic strength of the solution was so low that the temperature rise due to Joule's heat was negligible. The separation of a couple of platinum electrodes in the cell was 0.4 cm. The length (optical path length) of the electrodes was 1.8 cm and the width 0.5 cm. The electric field was applied normal to the scattering plane. The scattering angle was taken as 90". The field was applied a t a constant current condition by the V-I con-
Fig. 1. Block diagram of the experimental apparatus for light scattering in an ac electric field.
2306
FUJIKADO, HAYAKAWA, A N D WADA
verter; thus the electrode polarization effect, which becomes appreciable a t low frequencies, was avoided. The resistivity of the sample was measured at l kHz, where both electrode polarization and displacement current are unremarkable. In this case the resistivity is given straightforwardly by the ratio of voltage across the electrodes to current. A t lower frequencies, where the electrode polarization becomes effective, the field strength in the sample was obtained as the product of resistivity and current density. A t high frequencies, on the other hand, where the displacement current becomes appreciable, the field strength was given by dividing the voltage across the electrodes by the electrode separation. The amplitude of the field ranged from 0 to 90 V/cm. The frequency was varied from 10 Hz to 100 kHz. The upper limit of the sample conductivity was determined by the output power capacity of the V-I converter. For measuring the intensity change of scattered light AI with a high accuracy, we employed the chopping of electric field (AM by a square wave) with a chopping frequency QI2a = 1.0 Hz. In this case the square-wave output from the function generator in Fig. 1was used for chopping the electric field. For directly measuring the derivative of r = AIIIo with respect to log w , we used the FM electric field. The frequency of applied field is then given as
G ( t )= w
+ Aw sin Q2t
(1) where w is the variable central frequency and Aw is the modulation amplitude. This frequency modulation was made by use of the sine-wave output of the function generator and the voltage-controlled oscillator (Wavetek, model 113) in Fig. 1. The scattered light was detected by a photomultiplier (Hamamatsu TV, R372). The output current of the photomultiplier was converted to a voltage signal by the I-V converter, and after band-pass filtering and phase adjustment, the 0 component of the signal was supplied to the lock-in amplifier. In the AM operation, the output of the lock-in amplifier is proportional to AI. This AM technique greatly increases the accuracy of measurement of AI, because only AI, and not Io, is modulated at Q , and any fluctuation of 10 might not be detected. In the FM operation, on the other hand, the output of the lock-in amplifier is proportional to A w ( d A I ( w ) / d w )= ( A w / w ) ( d A I ( w ) / dlog w ) if Aw is sufficiently small. The modulation amplitude Aw should, in principle, be as small as possible, but a small amplitude would yield a small output. For detecting the relaxational dispersion curve, however, which varies rather moderately with varying frequency, Aw/w is not required to be so low, and we employed Aw/w = in the present experiment. I0 was measured as the direct output of the I-V converter when no electric field was applied. The relative calibration of AI against 10was made from the total gain of the band-pass filter, phase shifter, and lock-in amplifier.
LIGHT SCATTERING IN AN AC FIELD
2307
The phase shifter might be eliminated if Q was sufficiently smaller than w. Actually, however, a small phase shift occurred between the output of
band-pass filter and the reference wave to lock-in amplifier. The shift was compensated by the phase shifter such that the lock-in amplifier gave a correct output proportional to the steady component of AI or d Alld log w.
METHOD OF DATA ANALYSIS When an ac electric field E sin w t is applied to a dilute solution of rigid rodlike molecules with a permanent dipole p, the steady component of r is given bylo
Here CR is a dimensionless function of the scattering angle and the size of the molecule relative to the wavelength of incident light in solution, T is the rotational relaxation time related to the rotational diffusion constant D by T = 1 / 2 0 , and f? and y are, respectively,
/3 = p E / k T
7 = (a, - ab)E2/2kT
(3)
where a is the electric polarizability, k T has the usual meaning, and the subscripts a and b stand for the major and minor axes, respectively. In Eq. ( 2 ) , the f sign stands for the dipole parallel to major and minor axes of the molecule, respectively. As will be discussed below, DNA was proved to possess a quasipermanent dipole, and the observed dispersion of r arises from the orientational relaxation of the molecule. Even in this case, Eq. (2) is not strictly valid, and the dispersion curve will be broader than that predicted by Eq. ( 2 ) on account of the flexibility of the molecule and distribution in molecular weight. However, the inflection point of the dispersion curve gives an average relaxation frequency, which we call the relaxation frequency for simplicity. If we can observe both high- and low-frequency limits of r and if we knew the numerical value of C R ,we might obtain p and Aa = a, - Cub from the dispersion curve. In the case of DMA and (Acryl),, however, which are not strictly rodlike, calculation of CR is rather difficult. An alternative way of estimating the dipole moment is provided by the saturation effect. At sufficiently low frequencies, we can use the saturation theory derived for dc electric fields." With increasing field strength, r deviates from the linearity against E2. When P2/7is larger than unity, i.e. the contribution of permanent dipole is larger than that of induced one, rlE2 decreases monotonically with increasing E2. The deviation becomes appreciable a t p E 2 k T . DNA and (Acryl),, which possess contour lengths much longer than their
2308
FUJIKADO, HAYAKAWA, A N D WADA
persistence lengths, are not rigid rods in solution. Owing to the electrostatic repulsion between dissociated sites in the molecule, however, they take an expanded form along their major axis, and it may be possible to estimate the length of major axis L from the observed rotational relaxation time by the equation12
where 77, is the solvent viscosity and d is the length of minor axis.
RESULTS AND DISCUSSION DNA The low-frequency dielectric relaxation of aqueous DNA has been fully investigated by Sakamoto and coworker^.^-^ According to them, the interaction among DNA molecules becomes almost negligible below a DNA concentration C, of 0.05% (molecular weight, 4.5 X lo5; lOP3MNaC1). For these dilute solutions, the dielectric relaxation time was found to agree with the rotational relaxation time estimated from the reduced viscosity for various molecular weight^,^ added salt species (including monovalent and divalent cations) and concentration^,^ dye concentration^,^ and the alcohol contents mixed in the ~ o l v e n t .The ~ quasipermanent dipole moment estimated from the dielectric increment was found to be well interpreted in terms of counterion fluctuation mechanism for all the above conditions; the mean-square dipole moment ( p 2 )for monovalent counterions is2 ( p 2 ) = N w (1- w)e2
(S2)
(5)
where N is the number of dissociated sites of the molecule, e is the elementary charge, CY is the fraction of free counterions, and ( S 2 )is the squared radius of gyration of the molecule. The fluctuation may have a distribution of relaxation times,13 but modes with relaxation times longer than the rotational relaxation time are effective and the largest part of ( p 2 ) is composed of these modes. Protein contamination of DNA was proved not to be the major origin of the dipole m ~ m e n t . ~ Figure 2 shows the E 2dependence of r = AID0 for DNA-A (C, = 0.05%). Curves a t various frequencies deviate downwards from the linearity a t r > 0.35. The nonlinearity of this type suggests two possibilities: (1)saturation of orientation of permanent dipoles and (2) saturation of orientation or magnitude of induced dipoles with increasing electric field.14 The frequency dependence of these saturation curves may arise, respectively, from (1)orientational relaxation and (2) relaxation of induced polarization. As will be described later, the relaxation frequency agrees well with that of dielectric relaxation, and thus we may conclude that the saturation may be due to mechanism (1). The deviation from the linearity in Fig. 2 occurs a t a higher electric field
LIGHT SCATTERING IN AN AC FIELD
2309
I0 Hz 0.6
0.4
c I
a
0.2
Fig. 2. Relative intensity change of scattered light for DNA-A (C, = 0.05% 25°C) plotted against squared amplitude of electric field a t five frequencies.
for a higher frequency. It is to be noted that the deviation starts at an almost constant value of r , irrespective of frequency. This is reasonable because the degree of orientation of molecules is the same at the same value of r. For DNA-B ( C , = 0.05%)of low molecular weight, the deviation was not observed up to r = 0.28. The dispersion curve for DNA-B a t E = 72 V/cm is illustrated in Fig. 3 with its FM curve. The relaxation frequency is located a t 300 Hz, yielding the relaxation time 0.53 msec. The dielectric relaxation time of calf thymus DNA as a function of molecular weight M , was reported by Sakamoto et al.3 According to their data (Fig. 3 of their paper), the relaxation time a t M , = 8 X lo5 is 1.0 msec at 10°C, which is reduced to 0.68 msec at 25°C. This value is comparable with the present data.
0 2
0.I
Fig. 3. Dispersion curve (open circles) and corresponding FM curve (closed circles) for = 0.05%, 25OC) a t E = 72 V/cm.
DNA-B (C,
2310
FUJIKADO, HAYAKAWA, AND WADA
Sakamoto and coworker^^-^ made a comparison of the dielectric relaxation time with the rotational relaxation time through the Zimm theory on viscoelasticity of a polymer s01ution.l~ The same treatment was made for DNA-B, yielding 7 = 0.56 msec from the observed reduced viscosity. Estimation of the dipole moment from the dispersion curve necessarily involves some ambiguities on account of uncertainties in the low-frequency limit of r and CR in Eq. (2). We estimated the effective length L of DNA from the observed rotational relaxation time along with Eq. (4). We tentatively assumed d = 20 A,but this does not affect seriously the result. The L obtained in this manner was 2800 A for DNA-B, which is more than a half of the contour length, 4000 A. Since r a t 10 Hz in Fig. 2 (DNA-A) starts to deviate from linearity against E 2 a t E = 20 Vlcm, p is estimated to be y N kTIE = 0.6 X 106D. Sakamoto et a1.2 reported y = 1.7 X 106Dfor DNA of M , = 4 X lo6 (lO-*M NaC1) from dielectric measurements. These values agree with each other in order of magnitude. The dispersion curve of DNA shows that the contribution of the permanent dipole to the low-frequency limit of F is larger than that of the induced one a t least by an order of magnitude. The present data afford us further evidence that the low-frequency relaxation of DNA arises from rotation of the molecule, which possesses an elongated form with a permanent dipole along its major axis. The same conclusion was reached by Aoyagi e t a1.16 from a birefringence study of DNA in an ac electric field.
Poly(acry1ic Acid) The concentration employed for (NaAcryl), was much lower than that for DNA because of the high dc conductivity of the former a t the same weight concentration. Nevertheless, the accuracy of the light-scattering measurement for (NaAcryl), was sufficiently high for revealing its lowfrequency relaxation. Figure 4 shows a typical example of the saturation effect a t 30 Hz. rlE2 decreases monotonically with increasing E 2 , in a manner similar to DNA. Figure 5 illustrates dispersion curves for (Acryl), (polymer concentration C, = 0.0072%) for various degrees of neutralization Or. Figure 6 shows the FM curves corresponding to those in Fig. 5. The results clearly indicate that (Acryl), exhibits a low-frequency relaxation similar to DNA. The relaxation time 7 is determined from the peak frequency of FM curves. The increase of 7 with increasing LU is ascribed to extension of molecules due to electrostatic repulsion among ionized sites along the molecule. T o summarize, the present results indicate that (Acryl), possesses, analogously to DNA, a low-frequency relaxation. The origin of the relaxation is probably the same as that of DNA-rotation of molecule with a quasipermanent dipole due to counterion fluctuation with a lifetime longer than the rotational relaxation time. Further work is necessary to reach the conclusion.
LIGHT SCATTERING I N AN AC FIELD
0
2
1
E2
(ld V2 cm2 )
2311
3
Fig. 4. Saturation characteristic of (Acryl), (DP 2700, C, = 0.0072% Z= 1.0).
Tobacco Mosaic Virus Figure 7 shows the dispersion curves at E = 60 Vlcm for TMV solutions of different concentrations. The rotational relaxation frequency of the major axis of TMV is calculated as 105 Hz from its dimension^'^ ( L = 3000 A, d = 150 A) by use of Eq. (4). Therefore, the high-frequency relaxation observed above 1kHz for two curves in Fig. 7 cannot be ascribed to the rotation, but to the relaxation
Fig. 5. Dispersion curves of aqueous (Acryl), (DP 2700) for various degrees of neutralization (C, = 0.0072%, 25OC) at E = 30 V/cm.
FUJIKADO, HAYAKAWA, A N D WADA
2312
- 0.9
4
s0.6
Q
U I
0.3
10
1o2
FREQUENCY
ld ( Hz)
Fig. 6. FM curves of aqueous (Acryl), (DP 2700) for various degrees of neutralization (Cp = 0.0072%,25OC) at E = 30 V/cm.
5 -
v
10
1 o2
1o3
F REQ UE N C Y
1 o4
1o5
( Hz)
Fig. 7. Dispersion curves of electric field light scattering of TMV for two concentrations measured at E = 60 V/cm.
of electric polarizability Aa. The polarizability arises from mobility of counterions around TMV.ls The absence of rotational relaxation with respect to the major axis suggests that the ordinary Japanese strain of TMV does not possess a permanent dipole along its major axis. In contrast to DNA and (Acryl),, TMV at C, = 0.1% shows a distinct negative dispersion below 1 kHz; the sign of the term of p2 in Eq. (2) is negative, and consequently r becomes negative at low frequencies. The negative dispersion is only slight below 1 kHz for TMV at 0.01%. This kind of behavior is similar to that observed by Thurston and Bowlings in their birefringence study in an ac electric field for a solution of TMV.
LIGHT SCATTERING I N AN AC FIELD
2313
0
--
2.5
5 -7.5 -10 I
I
I
2
1
E* (
I
3
1
4
lo3 v 2 c m 2 )
Fig. 8. Relative intensity change of scattered light for TMV (C,, = 0.1%)at three frequencies plotted against squared amplitude of the electric field.
Figure 8 shows the saturation characteristics of TMV. The linearity of r against E 2 holds up to r = 0.2 for C, = 0.01% but only to r = 0.05 for C,
0.1%. As shown in Eq. (2), a negative relaxation arises in general when the particle possesses a permanent dipole along its minor axis. TMV has been reported to have a small permanent dipole along the minor axis.8 If TMV in a concentrated solution aggregates side by side with the moment parallel, the aggregate should exhibit a fairly large permanent dipole moment along the minor axis. When the effect of the resultant moment overcomes that of the induced dipole moment along the major axis, the minor axis of the aggregate is oriented along the electric field, giving rise to the decrease of scattered light intensity. The negative relaxation a t low frequencies may therefore be interpreted in terms of a rotation of the aggregated TMV. In fact, Asai and Watanabe19 reported a negative electric birefringence for TMV a t concentrations higher than 0.03%. =
This work was partly supported by the Grant-in-Aid from the Ministry of Education of Japan.
References 1. Jennings, B. R. (1976) Molecular Electro-Optics, Part 1,O’Konski, C. T., Ed., Dekker, New York, p. 275. 2. Sakamoto, M., Kanda, H., Hayakawa, R. & Wada, Y. (1976) Biopolymers 15, 879892. 3. Sakamoto, M., Hayakawa, R. & Wada, Y. (1978) Biopolymers 17,1507-1521. 4. Sakamoto, M., Hayakawa, R. & Wada, Y. (1978) Rep. Prog. Polym. Phys. Jpn. 21, 615-618. 5. Sakamoto, M. (1979) Doctoral thesis, University of Tokyo. 6. Minakata, A. & Imai, N. (1972) Biopolymers 11,329-346. 7. Van der Touw, F. & Mandel, M. (1974) Biophys. Chem. 2,231-241. 8. Thurston, G. B. & Bowling, D. I. (1969) J. Colloid Interface Sci. 30,3445. 9. Okamoto, H., Nakajima, H. & Wada, Y. (1974) J . Polym. Sci., Polym. Phys. Ed. 12, 1035-1052. 10. Plummer, H. & Jennings, B. R. (1969) J . Chem. Phys. 50,1033-1034.
2314
FUJIKADO, HAYAKAWA, AND WADA
11. O’Konski, C. T., Yoshioka, K. & Orttung, W. H. (1959) J. Phys. Chem. 63, 15581565. 12. Nakajima, H. & Wada, Y. (1977) Biopolyrners 16,875-893. 13. Oosawa, F. (1971) Polyelectrolytes, Dekker, New York, p. 51. 14. Kikuchi, K. & Yoshioka, K. (1976) Biopolyrners 15,583-587. 15. Zimm, B. H. (1956) J . Chern. Phys. 24,269-278. 16. Aoyagi, H., Mori, Y., Hayakawa, R. & Wada, Y. (1978) Rep. Prog. Polym. Phys. J p n . 21,625-628. 17. O’Konski, C. T. & Haltner, A. J. (1957) J. Am. Chem. SOC.79,5634-5649. 18. Van der Touw, F., Briede, J. W. H. & Mandel, M. (1973) Biopolymers 15,583-587. 19. Asai, H. & Watanabe, N. (1976) Biopolyrners 15,383-392.
Received September 25,1978 Returned for Revision February 17,1979 Accepted March 16,1979
Synopsis Two new techniques, amplitude modulation (AM) and frequency modulation (FM) of an electric field, are developed for the light-scattering study of polymer solutions under ac electric fields. The AM technique makes it possible to observe accurately the frequency dependence of the intensity change of scattered light due to the electric field. The F M one allows us to obtain directly the frequency derivative of the intensity change. The techniques are applied to DNA, poly(acry1ic acid), and tobacco mosaic virus in the frequency range from 10 Hz to 100 kHz. A low-frequency relaxation is found for both DNA and poly(acry1ic acid). The observed relaxation time of DNA agrees with that in the dielectric relaxation of DNA, which has been attributed to the rotation of the molecule with a quasipermanent dipole. In the case of poly(acry1icacid), the relaxation strength increases with increasing degree of neutralization. TMV a t a concentration of 0.1% exhibits a negative relaxation a t low frequencies, which indicates the rotation of TMV aggregate with a permanent dipole along its minor axis.
INTRODUCTION When a particle suspended in a liquid is comparable in size or larger than the wavelength of incident light and possesses an anisotropy in shape, the particle is oriented under an electric field and the scattered light intensity changes thereby. Conceptual and practical aspects of this phenomenon, electric field light scattering, have been reviewed by Jennings' with numerous illustrative applications. When the particle possesses a permanent dipole and the electric field is sinusoidal with an angular frequency w , the orientation distribution of particles is in equilibrium a t w7 > 1,the orientation due to the dipole-field interaction does not occur. The relative change of scattered light intensity, r = AZ/Io (I0 being the scattered light intensity without an electric field and AI the intensity change under the field), therefore depends on w , and from the frequency dispersion curve of r , we can estimate the rotational relaxation time 7. Electric field light scattering has hitherto been applied rather rarely to Biopolymers, Vol. 18,2303-2314 (1979) 0 1979 John Wiley & Sons, Inc.
00oS-3525/79/0018-2303$01.00
2304
FUJIKADO, HAYAKAWA, AND WADA
the relaxation spectrometry of polymers. This is mainly because the intensity change of scattered light is relatively weak. By way of greatly improving the sensitivity of this method, we introduce two new techniques: amplitude modulation (AM) and frequency modulation (FM) of the electric field. The AM technique enables us to avoid the effect of any fluctuation in 10,because AZ alone is modulated, and thus the fluctuation in 10is rejected by the lock-in detection. The frequency dependence of r (dispersion curve) for chain polymers such as DNA and poly(acry1ic acid) [(Acryl),] is rather moderate owing to a wide distribution of relaxation times. In such a case, low- and high-frequency limits of r are not well identified at the same time, and consequently, it is in general difficult to locate the relaxation frequency corresponding to the inflection point of the dispersion curve. In this paper we employ the FM technique, wherein we apply an FM ac field to the sample and directly obtain the derivative of the dispersion curve with respect to log w. The peak of this FM curve gives the relaxation frequency. This paper describes the applications of our new techniques to dilute aqueous solutions of three kinds of polyelectrolytes: DNA, (Acryl),, and tobacco mosaic virus (TMV). Dielectric relaxation spectrometry of aqueous DNA has r e ~ e a l e d that ~-~ the low-frequency dielectric relaxation of DNA arises from rotation of the molecule with a quasipermanent dipole, the dipole with a lifetime longer than the rotational relaxation time. The dipole is parallel to the major axis of the polymer, which possesses an elongated form due to electrostatic interaction among charges along the chain. The magnitude of the dipole is well explained by the counterion fluctuation mechanism. Light scattering of DNA within an ac field making use of widely varied frequencies might give a further support to this conclusion. (Acryl), is studied here by the same approach. The dielectric relaxation of aqueous tetra-n-butyl ammonium polyacrylate was measured by Minakata and Imai.6 They eliminated the electrode polarization effect below 10 kHz, and the data were limited to above 200 Hz. Van der Touw and Mande17 observed the dielectric constant of aqueous (Acryl), partially neutralized with NaOH. The low-frequency limit of their data was 5 kHz. The low optical anisotropy of this polymer makes it difficult to study the low-frequency relaxation from birefringence study in an ac electric field. Our light-scattering method in an ac electric field seems most suitable to revealing the low-frequency relaxation of (Acryl), . TMV, which is a rather rigid particle when compared with DNA and (Acryl),, has been reported to have a small dipole along its minor axis,8 though the dipole characteristics of TMV depend on the strain. The ac field light scattering is expected to give information on the dipole moment of TMV of the ordinary Japanese strain.
LIGHT SCATTERING IN AN AC FIELD
2305
SAMPLES Two samples of DNA were used: DNA-A was calf thymus NaDNA (P-L Biochemical Inc., Lot 4562X) with a molecular weight of 5 X lo6, and DNA-B was obtained by sonication of DNA-A and had a molecular weight of 8 X lo5. The sonication procedures and molecular weight determinations were the same as reported previou~ly.~.~ Both samples were dissolved in lop4M NaCl a t a DNA concentration C, = 0.05%. The sample of (NaAcryl), supplied by Toa Gosei Chemical Industry Co. was transformed into (Acryl), by passing its solution through an ion-exchange column. The stated average degree of polymerization was 2700. The polymer concentration was determined by titrating the solution with aqueous NaOH after the method previously d e ~ c r i b e d . The ~ solution was neutralized with NaOH. No salt was added in the present experiment. The sample of TMV was the ordinary Japanese strain, which was kindly supplied by the Central Research Institute, the Japan Tobacco and Salt Public Corporation. The stock solution (10p2Mphosphoric acid) was diluted to a concentration of 0.1% and subsequently dialyzed for 2 days a t pH 7.4. A sample of lower concentration was obtained by further dilution to 0.01% (pH 7.1). Measurements were made a t 25°C for all the samples.
EXPERIMENTAL APPARATUS Figure 1shows the block diagram of our apparatus. The incident light from a He-Ne laser (5-mW output, 6328 A) was focused into the sample cell, which had a rectangular cylinder. The cell was made of Pyrex glass. The temperature of the cell was controlled by circulating water around the cell and was measured with a thermocouple. The ionic strength of the solution was so low that the temperature rise due to Joule's heat was negligible. The separation of a couple of platinum electrodes in the cell was 0.4 cm. The length (optical path length) of the electrodes was 1.8 cm and the width 0.5 cm. The electric field was applied normal to the scattering plane. The scattering angle was taken as 90". The field was applied a t a constant current condition by the V-I con-
Fig. 1. Block diagram of the experimental apparatus for light scattering in an ac electric field.
2306
FUJIKADO, HAYAKAWA, A N D WADA
verter; thus the electrode polarization effect, which becomes appreciable a t low frequencies, was avoided. The resistivity of the sample was measured at l kHz, where both electrode polarization and displacement current are unremarkable. In this case the resistivity is given straightforwardly by the ratio of voltage across the electrodes to current. A t lower frequencies, where the electrode polarization becomes effective, the field strength in the sample was obtained as the product of resistivity and current density. A t high frequencies, on the other hand, where the displacement current becomes appreciable, the field strength was given by dividing the voltage across the electrodes by the electrode separation. The amplitude of the field ranged from 0 to 90 V/cm. The frequency was varied from 10 Hz to 100 kHz. The upper limit of the sample conductivity was determined by the output power capacity of the V-I converter. For measuring the intensity change of scattered light AI with a high accuracy, we employed the chopping of electric field (AM by a square wave) with a chopping frequency QI2a = 1.0 Hz. In this case the square-wave output from the function generator in Fig. 1was used for chopping the electric field. For directly measuring the derivative of r = AIIIo with respect to log w , we used the FM electric field. The frequency of applied field is then given as
G ( t )= w
+ Aw sin Q2t
(1) where w is the variable central frequency and Aw is the modulation amplitude. This frequency modulation was made by use of the sine-wave output of the function generator and the voltage-controlled oscillator (Wavetek, model 113) in Fig. 1. The scattered light was detected by a photomultiplier (Hamamatsu TV, R372). The output current of the photomultiplier was converted to a voltage signal by the I-V converter, and after band-pass filtering and phase adjustment, the 0 component of the signal was supplied to the lock-in amplifier. In the AM operation, the output of the lock-in amplifier is proportional to AI. This AM technique greatly increases the accuracy of measurement of AI, because only AI, and not Io, is modulated at Q , and any fluctuation of 10 might not be detected. In the FM operation, on the other hand, the output of the lock-in amplifier is proportional to A w ( d A I ( w ) / d w )= ( A w / w ) ( d A I ( w ) / dlog w ) if Aw is sufficiently small. The modulation amplitude Aw should, in principle, be as small as possible, but a small amplitude would yield a small output. For detecting the relaxational dispersion curve, however, which varies rather moderately with varying frequency, Aw/w is not required to be so low, and we employed Aw/w = in the present experiment. I0 was measured as the direct output of the I-V converter when no electric field was applied. The relative calibration of AI against 10was made from the total gain of the band-pass filter, phase shifter, and lock-in amplifier.
LIGHT SCATTERING IN AN AC FIELD
2307
The phase shifter might be eliminated if Q was sufficiently smaller than w. Actually, however, a small phase shift occurred between the output of
band-pass filter and the reference wave to lock-in amplifier. The shift was compensated by the phase shifter such that the lock-in amplifier gave a correct output proportional to the steady component of AI or d Alld log w.
METHOD OF DATA ANALYSIS When an ac electric field E sin w t is applied to a dilute solution of rigid rodlike molecules with a permanent dipole p, the steady component of r is given bylo
Here CR is a dimensionless function of the scattering angle and the size of the molecule relative to the wavelength of incident light in solution, T is the rotational relaxation time related to the rotational diffusion constant D by T = 1 / 2 0 , and f? and y are, respectively,
/3 = p E / k T
7 = (a, - ab)E2/2kT
(3)
where a is the electric polarizability, k T has the usual meaning, and the subscripts a and b stand for the major and minor axes, respectively. In Eq. ( 2 ) , the f sign stands for the dipole parallel to major and minor axes of the molecule, respectively. As will be discussed below, DNA was proved to possess a quasipermanent dipole, and the observed dispersion of r arises from the orientational relaxation of the molecule. Even in this case, Eq. (2) is not strictly valid, and the dispersion curve will be broader than that predicted by Eq. ( 2 ) on account of the flexibility of the molecule and distribution in molecular weight. However, the inflection point of the dispersion curve gives an average relaxation frequency, which we call the relaxation frequency for simplicity. If we can observe both high- and low-frequency limits of r and if we knew the numerical value of C R ,we might obtain p and Aa = a, - Cub from the dispersion curve. In the case of DMA and (Acryl),, however, which are not strictly rodlike, calculation of CR is rather difficult. An alternative way of estimating the dipole moment is provided by the saturation effect. At sufficiently low frequencies, we can use the saturation theory derived for dc electric fields." With increasing field strength, r deviates from the linearity against E2. When P2/7is larger than unity, i.e. the contribution of permanent dipole is larger than that of induced one, rlE2 decreases monotonically with increasing E2. The deviation becomes appreciable a t p E 2 k T . DNA and (Acryl),, which possess contour lengths much longer than their
2308
FUJIKADO, HAYAKAWA, A N D WADA
persistence lengths, are not rigid rods in solution. Owing to the electrostatic repulsion between dissociated sites in the molecule, however, they take an expanded form along their major axis, and it may be possible to estimate the length of major axis L from the observed rotational relaxation time by the equation12
where 77, is the solvent viscosity and d is the length of minor axis.
RESULTS AND DISCUSSION DNA The low-frequency dielectric relaxation of aqueous DNA has been fully investigated by Sakamoto and coworker^.^-^ According to them, the interaction among DNA molecules becomes almost negligible below a DNA concentration C, of 0.05% (molecular weight, 4.5 X lo5; lOP3MNaC1). For these dilute solutions, the dielectric relaxation time was found to agree with the rotational relaxation time estimated from the reduced viscosity for various molecular weight^,^ added salt species (including monovalent and divalent cations) and concentration^,^ dye concentration^,^ and the alcohol contents mixed in the ~ o l v e n t .The ~ quasipermanent dipole moment estimated from the dielectric increment was found to be well interpreted in terms of counterion fluctuation mechanism for all the above conditions; the mean-square dipole moment ( p 2 )for monovalent counterions is2 ( p 2 ) = N w (1- w)e2
(S2)
(5)
where N is the number of dissociated sites of the molecule, e is the elementary charge, CY is the fraction of free counterions, and ( S 2 )is the squared radius of gyration of the molecule. The fluctuation may have a distribution of relaxation times,13 but modes with relaxation times longer than the rotational relaxation time are effective and the largest part of ( p 2 ) is composed of these modes. Protein contamination of DNA was proved not to be the major origin of the dipole m ~ m e n t . ~ Figure 2 shows the E 2dependence of r = AID0 for DNA-A (C, = 0.05%). Curves a t various frequencies deviate downwards from the linearity a t r > 0.35. The nonlinearity of this type suggests two possibilities: (1)saturation of orientation of permanent dipoles and (2) saturation of orientation or magnitude of induced dipoles with increasing electric field.14 The frequency dependence of these saturation curves may arise, respectively, from (1)orientational relaxation and (2) relaxation of induced polarization. As will be described later, the relaxation frequency agrees well with that of dielectric relaxation, and thus we may conclude that the saturation may be due to mechanism (1). The deviation from the linearity in Fig. 2 occurs a t a higher electric field
LIGHT SCATTERING IN AN AC FIELD
2309
I0 Hz 0.6
0.4
c I
a
0.2
Fig. 2. Relative intensity change of scattered light for DNA-A (C, = 0.05% 25°C) plotted against squared amplitude of electric field a t five frequencies.
for a higher frequency. It is to be noted that the deviation starts at an almost constant value of r , irrespective of frequency. This is reasonable because the degree of orientation of molecules is the same at the same value of r. For DNA-B ( C , = 0.05%)of low molecular weight, the deviation was not observed up to r = 0.28. The dispersion curve for DNA-B a t E = 72 V/cm is illustrated in Fig. 3 with its FM curve. The relaxation frequency is located a t 300 Hz, yielding the relaxation time 0.53 msec. The dielectric relaxation time of calf thymus DNA as a function of molecular weight M , was reported by Sakamoto et al.3 According to their data (Fig. 3 of their paper), the relaxation time a t M , = 8 X lo5 is 1.0 msec at 10°C, which is reduced to 0.68 msec at 25°C. This value is comparable with the present data.
0 2
0.I
Fig. 3. Dispersion curve (open circles) and corresponding FM curve (closed circles) for = 0.05%, 25OC) a t E = 72 V/cm.
DNA-B (C,
2310
FUJIKADO, HAYAKAWA, AND WADA
Sakamoto and coworker^^-^ made a comparison of the dielectric relaxation time with the rotational relaxation time through the Zimm theory on viscoelasticity of a polymer s01ution.l~ The same treatment was made for DNA-B, yielding 7 = 0.56 msec from the observed reduced viscosity. Estimation of the dipole moment from the dispersion curve necessarily involves some ambiguities on account of uncertainties in the low-frequency limit of r and CR in Eq. (2). We estimated the effective length L of DNA from the observed rotational relaxation time along with Eq. (4). We tentatively assumed d = 20 A,but this does not affect seriously the result. The L obtained in this manner was 2800 A for DNA-B, which is more than a half of the contour length, 4000 A. Since r a t 10 Hz in Fig. 2 (DNA-A) starts to deviate from linearity against E 2 a t E = 20 Vlcm, p is estimated to be y N kTIE = 0.6 X 106D. Sakamoto et a1.2 reported y = 1.7 X 106Dfor DNA of M , = 4 X lo6 (lO-*M NaC1) from dielectric measurements. These values agree with each other in order of magnitude. The dispersion curve of DNA shows that the contribution of the permanent dipole to the low-frequency limit of F is larger than that of the induced one a t least by an order of magnitude. The present data afford us further evidence that the low-frequency relaxation of DNA arises from rotation of the molecule, which possesses an elongated form with a permanent dipole along its major axis. The same conclusion was reached by Aoyagi e t a1.16 from a birefringence study of DNA in an ac electric field.
Poly(acry1ic Acid) The concentration employed for (NaAcryl), was much lower than that for DNA because of the high dc conductivity of the former a t the same weight concentration. Nevertheless, the accuracy of the light-scattering measurement for (NaAcryl), was sufficiently high for revealing its lowfrequency relaxation. Figure 4 shows a typical example of the saturation effect a t 30 Hz. rlE2 decreases monotonically with increasing E 2 , in a manner similar to DNA. Figure 5 illustrates dispersion curves for (Acryl), (polymer concentration C, = 0.0072%) for various degrees of neutralization Or. Figure 6 shows the FM curves corresponding to those in Fig. 5. The results clearly indicate that (Acryl), exhibits a low-frequency relaxation similar to DNA. The relaxation time 7 is determined from the peak frequency of FM curves. The increase of 7 with increasing LU is ascribed to extension of molecules due to electrostatic repulsion among ionized sites along the molecule. T o summarize, the present results indicate that (Acryl), possesses, analogously to DNA, a low-frequency relaxation. The origin of the relaxation is probably the same as that of DNA-rotation of molecule with a quasipermanent dipole due to counterion fluctuation with a lifetime longer than the rotational relaxation time. Further work is necessary to reach the conclusion.
LIGHT SCATTERING I N AN AC FIELD
0
2
1
E2
(ld V2 cm2 )
2311
3
Fig. 4. Saturation characteristic of (Acryl), (DP 2700, C, = 0.0072% Z= 1.0).
Tobacco Mosaic Virus Figure 7 shows the dispersion curves at E = 60 Vlcm for TMV solutions of different concentrations. The rotational relaxation frequency of the major axis of TMV is calculated as 105 Hz from its dimension^'^ ( L = 3000 A, d = 150 A) by use of Eq. (4). Therefore, the high-frequency relaxation observed above 1kHz for two curves in Fig. 7 cannot be ascribed to the rotation, but to the relaxation
Fig. 5. Dispersion curves of aqueous (Acryl), (DP 2700) for various degrees of neutralization (C, = 0.0072%, 25OC) at E = 30 V/cm.
FUJIKADO, HAYAKAWA, A N D WADA
2312
- 0.9
4
s0.6
Q
U I
0.3
10
1o2
FREQUENCY
ld ( Hz)
Fig. 6. FM curves of aqueous (Acryl), (DP 2700) for various degrees of neutralization (Cp = 0.0072%,25OC) at E = 30 V/cm.
5 -
v
10
1 o2
1o3
F REQ UE N C Y
1 o4
1o5
( Hz)
Fig. 7. Dispersion curves of electric field light scattering of TMV for two concentrations measured at E = 60 V/cm.
of electric polarizability Aa. The polarizability arises from mobility of counterions around TMV.ls The absence of rotational relaxation with respect to the major axis suggests that the ordinary Japanese strain of TMV does not possess a permanent dipole along its major axis. In contrast to DNA and (Acryl),, TMV at C, = 0.1% shows a distinct negative dispersion below 1 kHz; the sign of the term of p2 in Eq. (2) is negative, and consequently r becomes negative at low frequencies. The negative dispersion is only slight below 1 kHz for TMV at 0.01%. This kind of behavior is similar to that observed by Thurston and Bowlings in their birefringence study in an ac electric field for a solution of TMV.
LIGHT SCATTERING I N AN AC FIELD
2313
0
--
2.5
5 -7.5 -10 I
I
I
2
1
E* (
I
3
1
4
lo3 v 2 c m 2 )
Fig. 8. Relative intensity change of scattered light for TMV (C,, = 0.1%)at three frequencies plotted against squared amplitude of the electric field.
Figure 8 shows the saturation characteristics of TMV. The linearity of r against E 2 holds up to r = 0.2 for C, = 0.01% but only to r = 0.05 for C,
0.1%. As shown in Eq. (2), a negative relaxation arises in general when the particle possesses a permanent dipole along its minor axis. TMV has been reported to have a small permanent dipole along the minor axis.8 If TMV in a concentrated solution aggregates side by side with the moment parallel, the aggregate should exhibit a fairly large permanent dipole moment along the minor axis. When the effect of the resultant moment overcomes that of the induced dipole moment along the major axis, the minor axis of the aggregate is oriented along the electric field, giving rise to the decrease of scattered light intensity. The negative relaxation a t low frequencies may therefore be interpreted in terms of a rotation of the aggregated TMV. In fact, Asai and Watanabe19 reported a negative electric birefringence for TMV a t concentrations higher than 0.03%. =
This work was partly supported by the Grant-in-Aid from the Ministry of Education of Japan.
References 1. Jennings, B. R. (1976) Molecular Electro-Optics, Part 1,O’Konski, C. T., Ed., Dekker, New York, p. 275. 2. Sakamoto, M., Kanda, H., Hayakawa, R. & Wada, Y. (1976) Biopolymers 15, 879892. 3. Sakamoto, M., Hayakawa, R. & Wada, Y. (1978) Biopolymers 17,1507-1521. 4. Sakamoto, M., Hayakawa, R. & Wada, Y. (1978) Rep. Prog. Polym. Phys. Jpn. 21, 615-618. 5. Sakamoto, M. (1979) Doctoral thesis, University of Tokyo. 6. Minakata, A. & Imai, N. (1972) Biopolymers 11,329-346. 7. Van der Touw, F. & Mandel, M. (1974) Biophys. Chem. 2,231-241. 8. Thurston, G. B. & Bowling, D. I. (1969) J. Colloid Interface Sci. 30,3445. 9. Okamoto, H., Nakajima, H. & Wada, Y. (1974) J . Polym. Sci., Polym. Phys. Ed. 12, 1035-1052. 10. Plummer, H. & Jennings, B. R. (1969) J . Chem. Phys. 50,1033-1034.
2314
FUJIKADO, HAYAKAWA, AND WADA
11. O’Konski, C. T., Yoshioka, K. & Orttung, W. H. (1959) J. Phys. Chem. 63, 15581565. 12. Nakajima, H. & Wada, Y. (1977) Biopolyrners 16,875-893. 13. Oosawa, F. (1971) Polyelectrolytes, Dekker, New York, p. 51. 14. Kikuchi, K. & Yoshioka, K. (1976) Biopolyrners 15,583-587. 15. Zimm, B. H. (1956) J . Chern. Phys. 24,269-278. 16. Aoyagi, H., Mori, Y., Hayakawa, R. & Wada, Y. (1978) Rep. Prog. Polym. Phys. J p n . 21,625-628. 17. O’Konski, C. T. & Haltner, A. J. (1957) J. Am. Chem. SOC.79,5634-5649. 18. Van der Touw, F., Briede, J. W. H. & Mandel, M. (1973) Biopolymers 15,583-587. 19. Asai, H. & Watanabe, N. (1976) Biopolyrners 15,383-392.
Received September 25,1978 Returned for Revision February 17,1979 Accepted March 16,1979
