4176
S. TAKASHIMA AND H. P. SCHWAN
In proton-donor solvents, the formation of hydrogeneffect,22electric field effect due to the presence of posibonded complexes is consistently interpreted in terms tive charges on the nitrogens in the cations, etc.) have of a perpendicular orientation (cp = SO-l0O0) of the two not been taken into account; it is very likely, however, pyridine rings. For the iron complex [FeIT(C~~N&I8>,]-that their contributions to the chemical shifts are small Clz the cis-planar conformation of the pyridyl groups and do not invalidate the internally consistent interhas been found perfectly in line with the measured pretation of the results presented in this paper. values of the chemical shifts: From the latter data a metal-nitrogen distance of 2 A. has been derived. Acknowledgments. We are profoundly indebted to Finally, we want to point out that, although only Dr. A. A. Bothner-By for many helpful and construcstatic molecular models have been used in the calculative suggestions given to us during the course of the tions, the dihedral angles proposed must be interpreted present work as well as for reading this manuscript. as averaged positions of equilibrium over all the posComputations were performed at the University of sible vibrational and torsional states present in the Pittsburgh Computer Center with the partial support molecule. Several secondary effects (reaction field of the National Science Foundation.
Dielectric Dispersion of Crystalline Powders of Amino Acids, Peptides, and Proteins'
by S. Takashima and H. P. Schwan Electromedical Division, Moore School of Electrical Enoineering, University of Pennsylvania, Philadelphia, Pennsylvania (Receiced June 17,1066)
The dielectric constants of crystalline powders of glycine, tyrosine, glycylglycine, and ovalbumin were measured in the frequency range of 20 C.P.S. t o 200 kc.p.s. It was found that dry crystals did not have an appreciable dielectric constant but that adsorbed water increased the dielectric constant markedly. The static dielectric constants, their dispersions, and the dielectric losses were measured with varied amounts of adsorbed water. The increase of the dielectric constant is proportional to the increase of water of adsorption until the first water layer is completed. The second and third layers are formed if the vapor pressure is increased. The dielectric constant, however, does not increase any more and practically levels off. The formation of multilayers does not seem to affect the dielectric constant of crystals. Apparently, only the first layer of water of adsorption makes the major contribution to the dielectric constant of wet crystals.
Introduction The dielectric constants of crystalline powders of amino acids, peptides, and proteins were measured by Bailey2 in the dry and wet state. His results indicate that these materials have very small dielectric constants when they are carefully dried. He observed, I
however, that the adsorption of water was accompanied by considerable increases in the dielectric constant and the dielectric loss. Unfortunately, Bailey
-
The JOUTTd of Physical Chemistry
(1) This study was supported by National Institutes of Health Grant N ~ 1253. . (2) 8. T. Bailey, Trans. Faraday Soe., 47, 609 (1951).
4177
DISPERSIONOF CRYSTALLINE POWDERS OF AMINOACIDS
did not establish complete dispersion curves, probably because of the frequency limitation of his instrument. The dielectric constant of sodium bicarbonate crystalline powder was studied by O ’ K ~ n s k i . ~He observed that bicarbonate crystals did not have an appreciable dielectric constant when they were thoroughly dried but that a small amount of adsorbed water increased the dielectric constant markedly. The crystals of fcrroelectric potassium dihydrogen phosphate, however, showed a considerably larger dielectric constant than those of sodium bicarbonate, even in the dry state. On the other hand, the dielectric constants of microscopic particles of synthetic polymers, clay, and living cells have been extensively investigated by Friclie, Cole, and S ~ h w a n . The ~ enormously large dielectric polarization in the low-frequency region is evidently not due to particle orientation but is considered to be due to the time-dependent surface conductance of these particles. The frequency-dependent character of this surfacc conductance is explained by Schwarz5to be the result of counterion movement. The purpose of this experiment is to establish the static dielectric constant and dispersion of crystalline materials and to analyze the mechanism of the dielectric polarization in terms of the electrical double layer formed between the crystal surface and the water of adsorption.
Technique and Materials Impedance Bridge. The bridge has been designed and constructed to meet a wide range of requirements of conductivity and capacity within a frequency range from 20 C.P.S. to 200 kc.p.s. The details of this bridge are given in review articles by S c h ~ a n . ~ ~ ~ Electrode Polarization and Sample Cell. Since the dielectric constant of these materials exhibits an anomalous dispersion in the audiofrequency range, correction for electrode polarization errors is crucial in order to obtain significant dispersion curves. Noting that the electrode admittance is in series with the admittance of the sample, the following derived equation is pertinent7I8 C = C.
+ 1/w2R2C,
(1)
where C is the total observed capacity, CBis the capacity of the sample, w is the angular frequency, R is the resistance, and C, is the electrode capacity. The following technique was chosen to facilitate the use of eq. 1.8 It is known that the electrode polarization capacity varies as a power function of frequency, and the power factor is usually between 0.3 and 0.5. Hence, in a plot of log C against log f, a straight line results with a slope of about -1.6 if C, is small compared
104
r-
I
I
I -I_------
II
i\
100 c.
10 kc. Frequency.
1 kc.
$n
100 kc.
Figure 1. Logarithmic plot of the electric sample capacity C of glycine crystals against frequency: curve 1, the total capacity before correction; curve 2, the capacity after correction. Curve 2 is obtained by taking the difference between curve 1 and the limit slope of 1.5. The dashed curves pertain to a slope value of 1.6. They are shown to demonstrate the effect of the chosen slope value on the dispersion curve and the insensitivity of the characteristic frequency fo (arrow) from the limiting slope.
to the second term of the equation, ie., at sufficiently low frequencies. If C, is appreciable, a curve will result which will deviate from this straight line. Thus, by taking the difference between the experimental curve and the limiting slope, approached at very low frequencies, we can obtain the true capacity of the sample. The validity of this procedure is illustrated by the example in Figure 1, using a dilute KC1 solution. This correction procedure also permits evaluation of the electrode polarization capacitance C,. C, data, presented in Table I, increase rapidly with increasing water content according to an approximate relationship, C, = awm, where w is water content. The data in Table I indicate m to be between 3 and 4. Extrapolation to 100% water content gives quite reasonable C, values near 100,OOO pf. Note that the strong dependence of C, on the water content w readily can be rationalized. The Polarization capacitance is determined by the amount of electrode area in contact with the water of adsorption. If C, were in direct proportion to this contact area, C, would change in proportion to w. However, each particle near the electrodes exerts a restriction on the current (3) C. T. O’Konski, J . Am. Chem. SOC., 73, 5093 (1951). (4) (a) See the review article by H. P. Schwan, Aduan. Bwl. Med. Phys., 5, 148 (1957); (b) H. P. Schwan, G. Schwars, J. Maczuk, and H. Pauly, J. Phus. Chem., 66,2626 (1962). (5) G.Schwarz, ibid., 66, 2636 (1962). (6) H.P.Schwan and K. Sittel, Trans. AIEE, 114 (1953). (7) H. P. Schwan, “Physical Techniques in Biological Research,’’ Vol. 6,Academic Press Inc., New York, N. Y., 1963,p. 323. (8) H.P.Schwan, 2. Naturforsch., 6b, 121 (1951).
Volume 69, Number 12 December 1966
4178
S. TAKASHIMA AND H. P. SCHWAN
strength a t the electrode surface. This restriction effectively causes C, to decrease as w decreases.s Thus, C, should change more rapidly than linearly with t o . In the case of pronounced electrode polarization, the accuracy with which the low-frequency limit of the dielectric constant eo can be stated is poorest and is about 20% as indicated in Figure 1. This figure demonstrates a case in which electrode polarization is particularly prominent. Even here it is possible readily to establish the limiting slope of about 1.6. This slope of about 1.6 is, of course, characteristic of the second term of eq. 1 even in cases where polarization at the electrodes does not contribute strongly. I n such cases, the ordinate level a t which the limiting slope curve must be placed in order reasonably to explain the observed data is usually rather well defined. Usually eo and the characteristic frequency can be estimated with an accuracy of about 10%. 'In cases of still lesser contribution of the electrodes to the total polarization, correction techniques can be omitted altogether. More detailed discussions of the limitations of this technique are in ref. 8.
).mho
\
\ \
100
.c 1
\ \
4 a
2.0 50
1.0
100 0 .
1 kc. Frequency.
____ & 10 kc. 100
Figure 2. Dielectric dispersion and loss tangent of glycine crystals: curve 1, dry crystal; curve 2, dielectric constant with 0.67% water; curves 3 and 4, the specific conductivity and the loss tangent of the same sample. The dashed branch of curve 2 holds before electrode polarization is corrected for.
~
Table I : Increase of Electrode Polarization with Increasing Water of Adsorption" ~~
Water content, %
8
80-
0
Resistance, ohma
0
.4
CP
-4
-
0
a
0
0.15 0.20 0.67 1.50 2.50 O
108 108 107 5 x 106 3 x 106
5
x
33.3 ppf. 60.6 ppf. 44,000 ppf. (0.044 pf.) 0.13 pf. 0.58 pf.
Frequency 20 c.P.s., electrode area 4.4 em.*.
A dielectric cell, the details of which are described in a previous p~blication,~ was used. It consists of two parallel platinum electrodes whose diameter is 2.54 em. Stray field errors cancel out since the sample thickness is small compared with its diameter, and the results obtained with the filled and the empty sample cell are subtracted from each other. Capacitance and conductance values as measured by the bridge are converted into dielectric constants and conductivities by using cell constants which are calculated from the geometry of the sample. Materials and Procedure. Dried crystalline powders of amino acids, peptides, and proteins, spread in petri dishes as thin layers, were placed in a desiccator over a small amount of water. After some time, an The Journal of Physical Chemistry
40
-
100 c.
1 kc. 10 kc. Frequency.
100 kc.
Figure 3. Dependence of the dielectric dispersion of solid glycine on the crystal size: curve 1, average diameter 0.3-0.5 mm.; curve 2, 0.02-0.08 mm. Curves are not corrected for a small electrode polarization contribution a t low frequencies. Water content is 2.5%.
aliquot of the powder was examined for its water content. The rest of the powder was placed in the cylindrical test cell and pressed moderately between the electrodes, which were usually heavily platinized with platinum black. The polarization capacity as determined with ~b 0.1 N NaCl solution was about 200,000 pf. a t 20 C.P.S. for the total area of the electrode.
Results Glycine. The dielectric constant of a dry crystalline powder of glycine is shown by curve 1 in Figure 2.
DISPERSION OF CRYSTALLINE POWDERS OF AMINOACIDS
A
t
4u
4179
Glvcine
3
I
I
0
80
00
6
I
60
I
40
1
01
20
0
Cly-Glycine
20
B"
I
I 6
10
10 % water.
I
I
15
20
Figure 5. Plot of the static dielectric constant e against the amount of water of adsorption: curve 1, glycine; curve 2, glycylglycine; curve 3, tyrosine.
C E"
Ovalbumin
0 -
100
9
g 0
'e .c1 a
1 10
Figure 4. Cole-Cole plot of (A) glycine with 1.5% water, (B) glycylglycine with 1.0% water, and (C) albumin with 11% water.
a
I
100 c.
The dielectric constant is very small even at 20 c.P.B., and the dielectric loss of the sample is negligible over the whole frequency range. However, as the water content is increased, the dielectric constant and the dielectric loss increase rapidly, as shown by curves 2 and 3 in the same figure. The effect of crystal size was studied with coarse crystals whose average diameter was about 0.3-0.5 mm. and a fine powder of particles whose average diameter was 0.02-0.08 mm. As illustrated in Figure 3, the size of the crystals does not have a marked effect on the magnitude of the dielectric constant, but it greatly influences the relaxation times. The dispersion curve shifts considerably towards higher frequencies with smaller particle size, indicating that the relaxation time decreases as the particle size decreases. The dielectric loss of the glycine crystals was calculated according to the equation e'' = [ ( K - ~ o ) / w ] r ~ , where e" is the dielectric loss, KO is the conductivity approached at low frequency, o is the angular frequency,
I
1 kc.
I 10 kc.
I
,
-
100 kc.
Frequency.
Figure 6. The dielectric dispersion of (1) glycylglycine with 2.5% water and (2) tyrosine with 2.5% water. The figure in the upper corner shows a Cole-Cole plot for tyrosine crystals.
and er = 8.85 X 10-14. The real and imaginary parts of the dielectric constant were plotted on a complex plane. The resultant Cole-Cole plot is shown in Figure 4. The Cole-Cole parameter which indicates the distribution of relaxation times is found t o be 0.25. The loss tangent was calculated by tan 6 = eft/,'.
The low-frequency dielectric constant eo for the crystalline powder of glycine changes with its water content as shown in Figure 5 (curve 1). The curve consists of two parts: (1) below 5%) the dielectric constant increases very rapidly; (2) above 5%) the dielectric constant tends t o level off and reaches a constant value. Volume 69, Number 18 December 1966
4180
8. TAKASHIMA AND H. P. SCHWAN
4
4 60 2
8
e"
.3
40
w
f 20
100 0.
1 kc. 10 kc. Frequency.
100 kc.
I ,No.
Figure 7. The dielectric dispersion of ovalbumin a t lorn (curve 1) and 11% water content (curve 2 ) .
200 4
9 :: 8
2
0
r
m
8 100 4
io
20
30
% water.
Figure 8. The static dielectric constant of albumin crystals as function of water content. The data in Figures 7 and 8 were obtained by Takashima at the Institute for Protein Research, Osaka University.
Tyrosine. I n spite of the much smaller solubility of tyrosine in water, the dielectric behavior of the tyrosine crystals is qualitatively the same as that of glycine (Figure 6, curve 2). However, the shape of the dispersion curves is very flat, indicating a wide distribution of relaxation times. The Cole-Cole plot, also shown in Figure 6, indicates perhaps two circular portions, suggesting that the dielectric behavior of tyrosine crystals involves two separate relaxation processes, The relationship between the dielectric increment and the water content is shown in Figure 5 (curve 3). Glycylglycine. The dielectric dispersion of crystalline glycylglycine is shown in Figure 6. Apparently, it exhibits two dispersion curves, but the magnitude of The Journal of Phgsical Chemistrg
the one a t the higher frequency region is not clearly established. The Cole-Cole plot, which is shown in Figure 4 (B) does not strongly indicate a dual circle, and the distribution parameter obtained from this plot corresponds to a fairly well-defined spectrum of relaxation times. The dielectric increment of glycylglycine crystals is plotted against the water content in Figure 5 (curve 2). Obviously, the saturation level of EO is considerably smaller than for glycine and tyrosine. Ovalbumin. The dielectric dispersion of freezedried powder is shown in Figure 7 (curve 2). This specimen, however, was found to contain approximately 10 to 11% water. Although we were not able to remove with certainty all of the water molecules from the proteins, we assumed that another specimen which was dried over phosphorus pentoxide under vacuum was a dry protein. The dielectric constant of this dry powder is shown in Figure 7 (curve 1). As shown, the dielectric constant of the dry ovalbumin powder is as small as 2-3 in the frequency range between 60 C.P.S. and 200 kc. p.s. It, therefore, is obvious that the electric polarization of the freeze-dried powder is due to water of hydration or adsorption. The dispersion curves are very flat which indicates a wide distribution of the rehxation times. The ColeCole plot is shown in Figure 4. I n contrast to those of glycine and glycylglycine, the distribution parameter is much larger, and a value 0.41 was obtained. The relationship between the dielectric constant EO and the water content is shown in Figure 8. It is worth noting that the curve consists of three portions. Up to a water content of lo%, the dielectric constant is independent of the water content, and the value is close to 3 or 4. The dielectric constant increases rapidly between 10 and 20% and then slows down above 20%, FuossKirkwood Plot. Since the Cole-Cole distribution parameters of some crystals such as ovalbumin were observed to be large, the Cole-Cole plot was not suitable for an accurate determination of a. A different method was introduced by Fuoss and Kirkwooda which often gives better results. Their equation states
where em" is the imaginary dielectric constant at the maximum of the dielectric loss, f m is the frequency a t maximum loss, and p is a distribution parameter which is numerically different from the Cole-Cole parameter. (9) R. M. Fuoss and J. G. Kirkwood, J. Am. Chem. (1941).
Soc., 63, 385
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DISPERSION OF CRYSTALLINE POWDERS OF AMINO ACIDS
-1
0 Log V/fm).
1
2
Figure 9. Fuoss-Kirkwood plot. Solid lines are theoretical curves for various values of p. The low-frequency side of the plot is omitted because of symmetry: open circles, ovalbumin; closed circles, glycine.
The relationship between this parameter and the ColeCole parameter is given by the following good approximation
Plots of the Fuoss-Kirkwood equation are given in Figure 9. The curves are fairly close to each other when @ is small. They separate more as ,8 becomes larger. The dielectric losses of glycine fit the curve P = 0.2. This value converts to the Cole-Cole parameter (= 0.27) which is in excellent agreement with the value obtained from the Cole-Cole plot. The Fuoss-Kirkwood plots of two samples of albumin also are shown in Figure 9. Obviously these data do not fit the Fuoss-Kirkwood plot. Hence, the dielectric dispersion of albumin involves a different distribution function of relaxation times than that in the underlying equation (2).
Discussion Carefully dried crystalline powders of glycine, glycylglycine, and protein have low and nearly frequency-independent dielectric constants even at very low frequencies. This fact suggests that the individual molecule in the crystals has no freedom of rotation and that the contribution of ion transfer to the polarization in a dry crystal is negligible for the frequencies employed. It was already found by Bailey that the dielectric constant of crystalline powders of dipolar ions increased with an increasing admount of water of adsorption.
He did not, however, establish the static, low-frequency dielectric constant of these crystals, probably owing to a limitation of his instrumentation. By using highresolution, low-frequency techniques, we succeeded in determining the low-frequency, static dielectric constants of various crystals with various amounts of water of adsorption. The wet crystals exhibit an anomalous dispersion even below 1 kc., and static dielectric constant values are first approached below 100 C.P.S. The increased dielectric constant of wet crystals may be caused by a conductivity on the surface between the adsorbed water and the crystal s ~ r f a c e . ~ ~ ~ The rapid increase of the dielectric constant at the early stage of adsorption is proportional to the increase of the surface area which is covered by the adsorbed water. Thus, the linear increase of the dielectric constant with the initial increase in adsorbed water could be easily understood. The dielectric constant levels off sharply near a 2.5% water content. This may indicate some change in the properties of the crystal surfaces. It is interesting to note that the actual adsorption isotherms of dipolar ion crystals show an obvious break at a water content level near 2_5’%,10-12 and additional adsorption, if any, proceeds with a smaller slope. According to the theory of Brunauer, Emmet, and Teller,13 the change of the slope is due to the completion of the first layer of adsorbed water, and the further rise of the adsorption curve is due to the formation of additional layers. The fact that both dielectric constant and adsorption curve change slope at nearly the same water content value may indicate that the leveling off of the dielectric constant is due to the completion of the first layer of adsorbed water. It is not understood why the water in excess of 2-3% which probably forms additional layers does not contribute to the polarizability of the wet crystals. The mean thickness of the water layer at 2.5% water content can be calculated to check the above hypothesis. If we assume that all water molecules are adsorbed on the surface of the crystals and do not penetrate into the crystals, we can estimate the thickness of the water layer by the formula
AR
=
R
R
(4)
(10) H.Bull, J. Am. Chem. Soc., 66, 1499 (1944). (11) W.S. Hnojewyj and L. H. Reyerson, J. Phys. Chem., 65,1694 (1961). (12) R. L.Altman and S. W. Benson, ibid., 64, 851 (1960). (13) S. Brunauer, P. H. Emmet, and E. Teller, J . Am. Chem. Soc., 60, 309 (1938).
Volume 69,Number 1.9 December 1966
S. TAKASHIMA AND H. P. SCHWAN
4182
where AR is the thickness of the water layer, R is the mean radius of the crystals assuming spherical shape, and w is the weight fraction of water.14 For example, assuming 2.5% adsorbed water, the water layer thickness AR on a crystal for which R = 0.002 cm. is about 1600 B., which is far more than the thickness of a single water layer. Clearly, either the assumption that the water of adsorption does not penetrate into crystals is wrong or the concept that leveling off of the curves occurs upon completion of a monolayer of water is erroneous. An alternative explanation is to assume that leveling off of the curves of the dielectric constant takes place when the water layer is sufficiently thick so that the electrical double layer can be completed. The thickness of electrical double layers ranges from 3 to 30 8. for moderate ionic strength values. These values are still much smaller than 1600 8. In any case, the assumption that the water of adsorption does not penetrate into the crystals is an oversimplification, and it is
The J o u d of Physical Chemistry
reasonable to assume that water molecules go into the crystals and occupy interstitial spaces. As shown in Figure 8, the relationship between the water of adsorption and the static dielectric constant of protein crystals is much more complicated than in the case of amino acid crystals. The dielectric constant of protein crystals is not affected by the adsorption of water until the water content is about 10-12%. A similar phenomenon was observed also by Rosen,16 with various proteins, and it seems to be a general characteristic of the water of adsorption on protein crystals. No detailed explanation may be given of this observation at present. (14) This equation was derived on the assumption that crystals are spherical with a radius of R and that the thickness of the water layer is AR. Then, the volume fraction of adsorbed water will be =
+
‘/dR ‘/dR
- ‘//snR8
+ a)’
from which eq. 4 is obtained. (15) D. Rosen, Trans. Faraday Soc., 59, 489, 2178 (1963).
