DIELECTRIC BEHAVIOR OF AQUEOUS SOLUTIONS OF BOVINESERUM ALBUMIN site is vacant, all six O(3) oxygens have shifted 0.50 A toward Ni(1) and the center of the double six ring-a striking demonstration of the ability of the aluminosilicate framework to adjust to change: in cation position. The Ni(l)-0(3) distance, 2.29 A, is an average value that includes O(3) oxygen positions for SI sites containing no nickel ions. This fact is illustrated by the O(3) thermal ellipsoids, which are elongated in the Ni-0 direction. Finding the nickel ion on both sides of the supercage six ring may be due to the presence of the residual water, O(w2), and the resultant Ni(3)O(w2) bond formation. Although the nickel ions prefer SI sites, they are distributed among four, and possibly five, different sites, with no site completely filled. This distribution agrees with conclusions drawn by Barry and Lay.a From esr studies of manganese in mixed cation X zeo-
4373
lites, these authors found manganese(I1) distributed in a number of sites and concluded that Mn2+ does not have very strong site preference. Also, from ir studies of CO adsorbed on various cationic forms of zeolite Y, Angel1 and Schaffer4 found that Ni2+ and Go2+ ions have no overwhelming preference for site I. Although site I has the highest occupancy in nickel faujasite (66%), it is not fully occupied. I n this respect, ie., a lack of high site preference, transition metal zeolites differ from calcium in zeolite Y, which prefers site SI,24and rare earth ions in zeolites X and Y, which prefer SI' sites.l1Vz6J6 (24) R. P. Dodge, unpublished research. (See ref 1.) (25) J. V. Smith, J. M. Bennett, and E. M. Flanigen, Nature, 215, 241 (1967). (26) D. H. Olson, G. T. Kokotailo, and J. F. Charnell, ibid., 215, 270 (1967).
The Dielectric Behavior of Aqueous Solutions of Bovine Serum Albumin1 from Radiowave to Microwave Frequencies by Edward H. Grant, Department of Physics, Queen Elizabeth College, London, England
Susan E. Keefe, Physics Department, Guy's Hospital Medical School, London, England
and Shiro Takashima Electromedical Division, Moore School of Electrical Engineering, University of Pennsylvania, Philadelphia, Pennsylvania (Received February 6,1088)
The purpose of the work described in this paper was to investigate the dielectric behavior of the protein bovine serum albumin. The investigation was made to try and solve some of the problems that had arisen from measurements obtained by other workers in the radiowave and microwave frequency range. To do this, measurements were made over as wide a concentration, temperature, and pH range as possible. It was confirmed that there was a subsidiary dispersion in the frequency range 200-2000 MHz, and the possible molecular interpretation of the dispersion is discussed. It can be concluded that this dispersion is probably due to water bound to the protein. By assuming a dielectric mixture theory the variation of the amount of bound water with concentration and pH is estimated.
Introduction From dielectric measurements made by Oncley2 and Buchanan, Haggis, Hasted, and Robinsona on egg albumin at megacycle and microwave frequencies, respectively, it has been suggested that a further dielectric dispersion may occur between the two principal dispersion regions (Figure 1). This extra dispersion (6 region) for egg albumin was observed by Grant4
and was followed by similar work on BSA.6 Prior to these studies the first direct observation of this sub(1) In this paper, bovine Berum albumin will be abbreviated as BSA. (2) J. L. Oncley, Chem. Rev., 30, 433 (1942). (3) T. J. Buchanan, G. H. Haggis, J. B. Hasted, and B. G . Robinson,
Proc. Roy. SOC.,A213, 379 (1952). (4) E. H. Grant, Nature, 196, 1194 (1962). (5) E. H. Grant, J . Mol. Biol., 19, 133 (1966). Volume 79,Number 13 December 1868
4374
E. H. GRANT,S. E. KEEFE,AND S. TAKASHIMA
90
80 70 60 50
40
30 20
10 u 10-8
10-2
10-1
1.0
io
io*
io*
104
108
108
f, MHz.
Figure 1. A typical dielectric dispersion curve for a protein solution.
sidiary dispersion region for any protein had been made by Schwane for haemoglobin. However, the egg albumin and BSA work suffered by being restricted to one or two concentrations only, and the haemoglobin studies were carried out at one temperature only. Therefore, it was decided to investigate the 6 region further. The present paper shows results taken over wider frequency and temperature ranges for five different concentrations of BSA and also indicates the effect of a variation in the pH of the solution. I n order to extend the frequency range for the purpose of obtaining a full analysis, the present results were used in conjunction with those taken by Buchanan, et al., at microwave frequencies. This means that results of the dielectric constant (e') are available for the 7 g/dl solution over the frequency range 50 kHz to 24 GHz and 50 kHz to 2000 MHz for the remainder. In this paper it will be shown that the results confirm the general propositions of a previous paper5 but that modifications have been made to the detailed conclusions drawn.
Experimental Section Apparatus. The measurements were made between 50 and 200 kHz on a low-frequency bridge which was designed by Schwanr and between 500 kHz and 200 MHz with a Boonton RX meter, Type 250 A. At 100 kHz and 1 MHz checks were made with 7 g/dl BSA solution using a Wayne Kerr B201 transformer ratio arm bridge, and in both cases agreement was obtained to within 1%. At these frequencies it was not possible to measure the dipolar contribution to e" with any accuracy, owing to the high ionic conductivity. I n the frequency range 190-2000 MHz, measurements were carried out using coaxial line apparatus similar to that described by Buchanan and Grant.8 From the observations made on the standing wave pattern set up in a short-circuited coaxial line cell containing the BSA solution, values of the dielectric constant (e') and dielectric loss (E' ') were calculated. A description The Journal of Physical Chemistry
of the modified apparatus will form the basis of a future paper.O iiaterials. The protein used was supplied by the Armour Pharmaceutical+3ompany, Eastbourne, England (Lot No. KB0472), and the figure quoted for the dimer content was 1-5%. This figure is comparatively low for a commercial product but values as low as 1%have been reportedlo for the Armour product. Conductivity water was used as the solvent, and the concentration of the solution was found from the ultraviolet absorption spectrum at 215 and 225 mp. The pH of the solution was varied by dialyzing the BSA solution with a buffer solution of tris(hydroxymethy1aminomethane) in hydrochloric acid or sodium carbonate and sodium bicarbonate until the required pH was obtained. The pH of the solution was measured on a direct-reading pH meter.
Results The dielectric decrement (6e') and the absorption increment (6e") for a protein solution at each temperature and frequency were defined by the equations Ae' = die' =
E'W
- e'
(1)
and Ae" = d e " =
E"D
- (E''~),,~~
(2)
where e', is the dielectric constant of pure water at the appropriate wavelength and c is the concentration in grams of protein per 100 ml of solution. The parameter (e''rv)co, is the dielectric loss of water, corrected for the volume of the protein molecules, and is given by (3) where E"D is the total dipolar contribution to the dielectric loss and fl is the partial specific volume. I n these experiments 0 was taken to be 0.73 cm8/g a t 250.11 Owing to the high errors in 6e" (discussed previously12), all the quantitative deductions about the 6 dispersion parameters have been made from values of E'. Values of e' were obtained for five different concentrations of BSA solution from 7 to 34 g/dl in the temperature range from 2.5 to 25", and the variation of e' with log frequency df> in the two extreme cases is shown in Figures 2 and 3,13respectively. The variation (6) H. P. Schwan, Advan. Biol. Med. Phye., 5 , 191 (1957). (7) H.P.Schwan and K. Sittel, Tram. A w . Imt. Elec. Engrs., 72,
114 (1963). (8) T. J. Buchanan and E. H. Grant, BrQ. J . A& Phye., 6, 65 (1966). (9) S. E.Keefe and E. H. Grant, to be submitted for publication. (10) H. A. Peterson and J. F. Foster, J . Bid. Chem., 240, 2503 (1966). (11) M.J. Hunter, J . Phys. Chem., 70, 3285 (1966). (12) E.H.Grant, Ann. N . Y . Acad. Sci., 125, 478 (1966). (13)Individual results will be supplied on request.
4375
DIELECTRIC BEHAVIOR OF AQUEOUS SOLUTIONS OF BOVINESERUM ALBUMIN
90
Y
80
0.06
I
I
I
I
0.1
1.0
10
10'
I
108
ft MHz
Figure 2. The variation of e' with frequency for a 7 g/dl BSA solution (pH 5.07): €3, measured on a B201 bridge a t 25 or 10'; X, 2.5'; 0,10'; 0 , 20'; A, 25". (Errors in e' (fl%)have been omitted for clarity.)
100
90
80 .*
70
60
60 0.1
109
10'
Figure 3. The variation of e' with frequency for a 34 g/dl BSA solution (pH 5.07): X, 2.5'; 0,loo; 0 , 200; A, 250, ( e' (&I%) have been omitted for clarity.)
of Le' with concentration was found to be similar a t all frequencies; Figure 4 shows the shape of the curve at 700 MHz:. The dielectric element decreases with temperature a t all concentrations, the curves for the 7 g/ dl solution being shown in Figure 5. I n order t o obtain information on the behavior of solutes in water, it is necessary 'to calculate from the known values of e' and 'E the following parameters for each dispersion. These are the relaxation wavelength, A, (or relaxation frequency, fs) ; the dielectric constant a t the low-frequency end of each dispersion, e,; the dielectric constant at the high-frequency end
E in ~
of each dispersion, em; and a,which is a measure of the spread of relaxation times. It is convenient to use the wavelength notation (A,) in the microwave region and the frequency notation (fa) in the radiofrequency range. With a protein solution there are three dispersions and consequently there will be three sets of values of e8, e,, X, (or fa), and a, so each parameter will be allotted a further subscript p, 6, or y when referring to an actual dispersion. These dispersions will now be considered individually, starting with the y dispersion. The y dispersion has been studied by Buchanan, et al.,awho made measureVolume r.& Number 13 December 1068
~
~
4376
E. H. GRANT,S. E. KEEFE, AND S. TAKASHIMA
10
1
+ 2 sin *"()'-u 2
+
6)
2 -
and 0
10
20 Temp, O C .
30
40
Figure 5 . The variation of dielectric decrement with temperature for a 7 g/dl BSA solution: A, 2000 MHz; 0 , 700 MHz; 0, 25; MHz; x) Ig0 MHz* (Errors in (18%) have been omitted for clarity.)
ments of e' and e'' at 1.264, 3.175, and 9.22 em. To obtain all the dielectric parameters a range of values of A, and a was initially calculated for the y dispersion by using their values of e ' and e'' in the equation
A€' ' = ") - e,
l-u
€'
[1
- (?)l-
y]
(4)
and hence obtaining the most probable value of a and This equation was derived by Grant, et al.,14 assuming the Cole-Cole dielectric theory.16 It was assumed that e, for free water is 4.5,14which when corrected for the volume occupied by the protein molecules gave a value of 4.4 for emy. Buchanan, et al., concluded that their results were consistent with a dispersion having a single relaxation time and e, = 5.5, but subsequently Grantle suggested a distribution of relaxation times in conjunction with a lower value of e,. A,.
The Journal of Physical Chemistry
The relatively large experimental errors in e' and the range of frequency over which the measurements have been taken make it difficult to extrapolate the p dispersion curve to give an accurate value of ess. Therefore, the parameters for the p dispersion were found by substituting the experimental values of e' and X into eq 6 and finding the best fit with the use of eq 7 and 8. By this means em@,esp as,and fsa were determined. This approach should be compared with the previous work of Moser, et aZ.,19and Oncley,2who analyzed their dispersion curves in terms of a superposition of two single relaxation times rather than a distribution of relaxation times. I n the case of Oncley's work, very dilute solutions were employed (thereby minimizing (14) E.H.Grant, T. J. Buchanan, and H. F. Cook, J . Chem. Phys., 25, 156 (1957). (15) K.S. Cole and R. H. Cole, ibid., 9, 341 (1941). (16) E.H.Grant, Phys. Med. Biol., 2, 17 (1957). (17) E. H. Grant and R. Shack, Brit. J . A p p l . Phys., 18, 1807 (1967). (18) M. W.Aaron and E. H. Grant, ibid., 18, 967 (1967). (19) P.Moser, P.Q. Squire, and C. T. O'Konshi, J . Phys. Chem., 70, 744 (1966).
DIELECTRIC BEHAVIOR OF AQUEOUS SOLUTIONS OF BOVINESERUM ALBUMIN the effect of intermolecular attractions), and with Moser, et ul., the dielectric measurements were all extrapolated to infinite dilutions and the analyses were carried out with the extrapolated values. Since in the present case the concentration of macromolecules is high enough to permit molecular interaction, it is not surprising that a satisfactory explanation of the results can be obtained by assuming a distribution of relaxation times, although for small to moderate distribution the Cole-Cole function and the superposition of two Debye functions approximate to any given situation equally well. Therefore, there is no variance between the present and previous methods of analysis, and, of course, in all cases the reliability of the extrapolated values depends upon the correctness of the assumed theory. I n Table I the errors quoted in connection with the listed parameters are of experimental origin only and take no cognizance of the fact that it may be possible to fit the parts better by some other (as yet unknown) form of dispersion curve. Since the parameters for the 0 and y dispersions were calculated, this fixes the parameters for the 6 dispersion, since E , @ = cas and esy = E,~, and therefore ffg and fss can be calculated from eq 7 and 8. The suggested parameters for a 7 g/dl BSA solution a t 25" are shown below in Table I. ~
Table I : Dispersion Parameters for 7 g/dl BSA at 25' Diepersion region
p 8 y
e%
em
(fsh
(-1O.a)
(-10.5)
MHz
a
88.2 75.9 71.0
75.9 71.0 4.4
0.3 250 20,000
0.3 9 ~ 0 . 1 0.7 &0.1 0.02 f 0.01
So far the results given here have all been for solutions having a pH of approximately 5, which is near the isoelectric point. Measurements were also made on solutions of BSA of concentration approximately 7 g/dl at frequencies of 250, 700, and 2000 MHz in the temperature range of 2.5-40" for three other pH values. The decrement values referred to unit concentration for these solutions are shown in Table 11. The dielectric behavior of the buffer solution was measured to see if the addition of the salt had any effect on the value of e l as compared with pure water. The change was found to be negligible in the case of E', but the dielectric loss was found to be higher due to the increase in conductivity. Discussion The 6 dispersion region lies between the fl and y regions, which therefore suggests that its molecular origin is connected with the relaxation of molecules having an activation free energy of rotation between that of
4377
Table I1 : Variation of 8 ~ 'with pH
-
Frequency, MH5
Temp, "C
5.07
6s' (f0.07)-PH 7.85 8.8
250
2.5 10 20 30 40
0.93 0.83 0.70 0.57 0.44
0.75 0.87 0.7 0.64 0.52
0.73 0.74 0.7 0.71 0.48
0.75 0.72 0.58 1.22 1.58
700
2.5 10 20 30 40
1.05 0.94 0.87 0.77 0.70
0.97 0.85 0.85 0.72 0.58
0.81 0.88 0.87 0.7 0.52
0.94 0.86 0.77 0.7 0.38
2000
2.5 10 20 30 40
1.2 1.12 1.0 0.78 0.67
0.76 0.52 1.04 0.85 0.59
0.88 0.93 0.68 0.79 0.65
0.03 0.31 0.99 0.68 0.76
I
9.8
the protein and free water. It had been suggested previously by Schwan6 for haemoglobin and by GrantI2 for egg albumin that the origin of this dispersion was the relaxation of bound water, and this proposal will now be further examined. The term bound.water is taken to mean water bound to the protein molecules by bonds of greater strength than the water-water bond existing in pure water. If the bound-water hypothesis is correct, the quantity of bound water (or water of hydration, w) present must accord with a reasonable molecular picture, and, subject to the stated assumptions, this will now be shown to be so by the following analysis. The estimation of hydration from dielectric results has the disadvantage that a dielectric mixture formula must be chosen, and the uncertainty in the choice of this can lead to some error. I n the initial studies of Buchanan, et dla the following equation was used
where p is the volume concentration of the solute and K is a constant depending upon the shape of the solute particle. This expression was based on the equation originally derived by Fricke20
- €1
€'
+
XEI
=P-
€2
€2
-
+
€1 xe1
(10)
where el and €2 refer to the solvent and solute, respectively, and x is another constant depending upon particle shape. The value of x is 2 for a spheroid and decreases for both prolate and oblate ellipoids. When B Z / E ~ is small compared with unity, eq 10 reduces to eq 9 and K = (l/x) (1 2); otherwise
+
(20) H. Frioke, Phys. REV.,24, 575 (1924).
Volume 78, Number 13 December 1068
4378
E. H. GRANT,S. E. KEEFE,AND S. TAKASHIMA
+
+
K = [(I .>/$I (del) The above approach depends on the assumption that the system under consideration corresponds to a suspension of macroscopic particles in a continuum, and it has been pointed out previously by Grant5that there is no good reason why this a priori assumption should be made for a protein solution. To take the other extreme, if the dielectric constant of the mixture is related to the components in relation to their volume proportions, then €'
- €1 =
p(e2
- €1)
(11)
The interesting point to notice, however, is that provided p is small ( €1, which, in turn, would require existence of strongly hydrated particles, with the bound water taking a dielectric constant too high to be consistent with the present analysis. As is clear from Table I11 a high value for the dielectric constant of the bound water must be coupled with a high value of k.
Table I11: Variation of the Hydration and Static Dielectric Constant of Bound Water with k near the Isoelectric Point (pH 5.07) W,
k
g/g of protein
enB
1.0 1.1 1.2 1.3 1.4 1.5
0.64 0.51 0.41 0.33 0.24 0.18
114 f 15 128 f 20 148 & 25 170 f 35 212 & 50 264 f 75
W(€'w
- 4) + w(elw - esB>]
The Journal of Physical Chemistry
(13)
(14)
where € s is ~ the dielectric constant of bound water at frequencies well below its dispersion. A similar equation can be written for 6e-6; hence when eS6 and emb are both known (as in the case of 7 g/dl BSA solution having a pH of 5.07), a range of values of w and e s a~t 25' can be found as shown in Table 111. In order to calculate the variation of hydration with pH, these values of k and w were then substituted into eq 13, and the value of the dielectric constant of the bound water (e'=) at a given temperature and frequency was calculated at pH 5.07. It was then assumed that t'g and k remained constant as the pH changed, and the quantity of bound water was then calculated by substituting different values of &', corresponding to changes in pH and frequency, into eq 13. In Table IV is shown the variation of e ' at ~ 25" with frequency, and Table V shows the change of w with pH a t this temperature for values of k = 1.1 and 1.3. It is worth remarking that Moser, et aZ.,l9obtained w = 0.64 for BSA by combining measurements made in the p dispersion with birefringence results. Taking this value in conjunction with the present data gives a value of 114 for the static dielectric constant of bound water corresponding to a k factor of 1 (Table 111). I n order to investigate the variation of w with concentration, it would be necessary to have the values of Table IV: Variation of for Two Values of k"
€'B
with Frequency a t 25"
e'B
The purpose of the above discussion is to emphasize the fact that in our view there is no way, a t present, of deciding which is the correct mixture formula appropriate to the case of a protein solution, although there is every expectation that it will take the form of eq 12. I n the subsequent analysis two representative values of k will be chosen and the dielectric parameters will be calculated for each case.
- E'B)]
where w is the weight of the bound water per unit ~ the permitweight of protein and elp, etw, and e ' are tivities of the protein, free water, and bound water, respectively. It is also assumed that the contributions of the bound water and protein to E- a t the high-frequency end of the 6 dispersion are due to their atomic and electronic polarizations only and are assumed to have values of 4.4 and 4.0, respectively, the precise magnitudes being unimportant. At the low-frequency end of the 6 dispersion, eq 13 becomes 1 0 0 6 ~=~h[0(etw ~
(12)
€1)
+
Frequency, MHz fa
(Azo%)
k 1.1
1.3
128 71.6 42.0 29.6 4.4
170 95.2 54.2 38.2 4.4
Relaxation frequency (fa) of -250 parameter (ad)of -0.6.
MHz;
distribution
DIELECTRIC BEHAVIOR OF AQUEOUS SOLUTIONS OF BOVINE SERUM ALBUMIN Table V : Varia,tion of the Hydration (w) with p H at 25’ for Two Values of k (Calculated from Measurements at Three Frequencies) w (f0.2),g/g of protein
7 -
Fre CIquenw, PH MHz 6.07a
250 700 2000 a
PH
PH
PH
7.85
9.8
5.07a
7.85
...
0.32 0.23 0.1 ,.. 0.32 0.20 0.22 . . . 0.32 0.44 0.1 0.21
8.8
0.52 0.8b . . . 0.52 0.42 0.45 0.52 0.64 0.25
Values of
20
‘Error of f0.8.
-
= 1.1PH PH
IC
7 ,
0.3 0.4
at pH 5.07 calculated from eS
1.3PH
PH
8.8
9.8
-
,E
values.
e‘ at all concentrations over the complete frequency range 0.05-24,000 MHz. I n the absence of any measurements in the y dispersion region for concentrations other than 7 g/dl, it was only possible to obtain a rough estimate of the variation of w with concentration, and this was done as follows. The variation of Ae’ with concentration was found to be very similar at all frequencies, and Figure 4 shows the general shape of the curve at 700 MHz. The marked change in the slope at a concentration of about 22 g/dl solution indicates a decrease in 66’ at higher concentrations, but as there was no definite variation with frequency of this change it was difficult to predict any change of e, - E, with concentration. From eq 7 it can be seen that if a were to remain constant with concentration, the slope of the e’ against the log f curves at the point f = fs for any Also concentration. would be proportional to es - e,. it can be shown from eq 13 that 6 r , - Bes is proportional to the quantity of bound water (w), assuming that E.B is constant with concentration. Values of slope per unit concentration for five different concentrations are tabulated below in Table VI. It can be seen that an abrupt change in e, - e, occurs at approximately the same concentration as the change in slope in Figure 4, suggesting a sudden increase in the amount of bound water at this concentration (between 21 and 2301,). This should be compared with a similar transition observed by Schwan6 for haemoglobin where the change in slope occurred at around 10%. The variation of w with temperature could not be calculated owing to lack of data, but the corresponding curve for Ae’ with temperature is shown in Figure 5.
Table VI : The Variation of E* - E, with Concentration Assuming a Constant Spread Parameter a . Concn, g/dl
Slope/c
7 14 20.5 23 34
0.063&0.007 0.065 f 0.004 0.061 f 0 . 0 0 3 0.126 & 0.004 0.12 f O . 0 0 3
a (e.
4379
The amount of bound water for BSA in solution near its isoelectric point was found to vary from 0.18 to 0.64 g/g of protein, depending on the mixture formula chosen, and this range is in agreement with other workers. Both Fisher21 and Chatterjee and Chatterjeez2 have summarized the values of w obtained for BSA by 15 different methods and show that w lies in the range 0.1-0.6 g/g of protein. This result, taken in conjunction with the present work, reinforces our proposal that the 6 dispersion is due to the relaxation of bound water. The values of E’B in Tables I11 and IV should be compared with Schwan’s2aproposal for the dielectric behavior of water bound to haemoglobin. Schwan found that e’B falls from about 90 to around 5, but the latter value is approached at frequencies as low as 2000 MHz, In our case t sis~over 100, and at 2000 MHz the value of B’B is still considerably above the infinitefrequency value. Schwan also remarks that a wider distribution of relaxation times exists for bound water, as compared with free water, and this observation is supported by the present work, assuming that BSA and haemoglobin are comparable cases. The magnitude of the values of E’B indicated in Tables I11 and IV may appear high for the ordinary water substance, but it should be remembered that the dielectric constant of an associated liquid depends not only on the molecular dipole moment but also on local molecular interaction as well. These are unknown for water bound to BSA and would be expected to be different from the situation existing in pure liquid water. A closer parallel may exist between bound water and ice when the dielectric constant exceeds 130 at - 66’ . 2 4 It is also interesting to notice that T a k a ~ h i m afound ~ ~ that the dielectric constant of water bound to protein crystals exceeds 200. The variation of bound water with the pH of the solution is shown in Table V when no significant trends are observed. As far as we are aware, no previous measurements on the dielectric behavior of protein solutions at different pH values have been carried out at the high-frequency end of the ,8 dispersion.
Conclusions The parameters found for the p dispersion agree fairly well with those found by Moser, et al.,l9 who made measurements on BSA at 25” between 1 KHz and 10 MHz. They obtained values of 0.17 and 350 KHz for the low-frequency increment and relaxation frequency, respectively, compared with the corresponding present value of 0.14 and 250 KHz. The disagreement in the former parameter is likely to be due to the
- rm) (21) H.F. Fisher, Biochim. Biophys. Acta, 109, 544 (1965). (22) A. Chatterjee and S. N. Chatterjee, J. Mol. Biol., 11, 432 (1965). (23) H.P.Sohwan, Ann. N . Y . Acad. Sci., 125,366 (1965). (24) R.P.Auty and R. H. Cole, J. Chem. Phys., 2 0 , 1309 (1962). (25) S. Takashima, J. Polyn. Sci., 62, 233 (1962).
Volume 7.9, Number 19 December 1968
4380
K. MOEDRITZER, L.
fact that lVIoser, et al., used defatted material. In the case of the relaxation frequency, our result refers to a 7 g/dl solution, whereas the previous value was obtained by extrapolating the dielectric parameters to infinite dilution; precise agreement is therefore not to be expected. With regard to the high-frequency decrement, Moser, et al., quote 0.60 as compared with our 0.35, which is probably due to our use of the Cole-Cole function (rather than two Debye functions) as the best representation of the p dispersion. However, there would still appear to be some unresolved difference present which must await further work for explanation; experimentally the region around 10 MHz is one of the most difficult to investigate. For the y dispersion it was found that the results were not consistent with a single relaxation time ( i e . , 01 = 0 ) as has been suggested by Buchanan, et u Z . , ~ but were more compatible with a small distribution with 01 = 0.02. A large degree of overlap between the 6 and y dispersion is also indicated. The results clearly confirm the existence of the 6 dispersion and are compatible with the suggestion that it is due to the rotation of the bound water. However, it has been pointed out previously by Schwana that the polar side chains could also relax in this frequency region, and the present measurements cannot be taken to disprove this. Although at the beginning of this re-
c. D. GROENWEGHE, AND J. R. V A N W A Z E R
search it had been hoped that it would be possible to account unambiguously for the 6 dispersion in molecular terms, this has not been proved to be the case. Measurements on very pure proteins of known structure will have to be carried out to illuminate the situation further, and future progress will also depend on some theoretical advancement being made on the question of the appropriate mixture formula. Acknowledgments. The authors wish to thank Professor C. B. Allsopp of Guy’s Hospital Medical School and Professor H. P. Schwan of the Vniversity of Pennsylvania for providing the facilities which enable the experimental work to be carried out. Acknowledgment is also due to Dr. W. L. G. Gent and Mr. F. A. Huthwaite for valuable discussions and technical assistance, respectively. We are also indebted to Mr. G. Pugh of the Borough Polytechnic for advice in connection with the use of the computer. This work formed part of a research program leading to the Ph.D. degree of the University of London for s.E. K., and it is a pleasure to thank the Science Research Council for a research studentship. We also thank the Central Research Fund of London University and the Science Research Council for equipment grants, and we acknowledge the support by Grants NSFGB-855, NIHHE-01253, and KONR-551-(52).
Multicomponent Equilibria in Exchange of Substituents between the Dimethylsilicon and Dimethylgermanium Moieties by Kurt Moedritzer, Leo C. D. Groenweghe, and John R. Van Wazer Central Research Department, Monsanto Company, St. Louis,Missouri
63166
(Received February 6,1968)
Scrambling equilibria of the substituents C1, Br, and I (system I) and C1, Br, I, and OGH6 (system 11)between the dimethylsilicon and dimethylgermaniummoieties have been studied by quantitative proton nuclear magnetic resonance spectroscopy. The experimental data have been evaluated in terms of sets of the minimum number of equilibrium constants, which in turn have been used to compute theoretical equilibrium distributions. As a result of preferential affinities for silicon us. germanium, certain species do not appear at equilibrium. Although a few studies by various authors deal with redistribution equilibria involving the exchange of more than two different kinds of substituents on a given central moiety, we believe that there has not been a report prior to this one of the situation where more than two kinds of substituents were scrambled between more The Journal of Physical Chemistry
than one kind of polyfunctional moiety. The work reported herein was undertaken as part of a broad study of equilibrium-controlled structural chemistry, and it demonstrates the fact that reactions involving as many as 20 different product species may be treated quantitatively. The goal of the broad study is to be able to
