The porosity of a dry resin is typically expressed on a dry volume or dry weight basis. We wish to compare the porosity of a hydrated resin with that of a dry resin. To make this comparison, it is necessary to express the results from the dry resin on the basis of a hydrated resin. The porosity of the dry resin must be expressed in cc of pores/cc of hydrated resin assuming no swelling occurs; therefore, the volume of pores does not increase upon hydration. This assumption is dearly not valid but is made to allow the above comparison. Assuming no swelling occurs, the porosities of the hydrated macroreticular resins are 0.052 and 0.075 cc pores/cc hydrated
resin for the hydrogen and sodium ionic form. The correct hydrated porosities are summarized in Table I. The correct hydrated porosities are approximately four times that of the dry porosities. ACKNOWLEDGMENT
The author wishes to acknowledge Mr. K. TregeI and Dr. J. Barrett for the synthesis of the ion exchange resins. RECEIVED for review April 6, 1971. Accepted June 7, 1971.
Ultraviolet Refractive Indices of Aqueous Solutions of Urea and Guanidine Hydrochloride J. R. Krivacic and D. W. Urry Dioision of Molecular BiophysicslLaboratory of Molecular Biology, Unicersity of Alabama Medical Center, 1919 Secenth Acenue South, Birmingham, Ala. 35233
INSTUDYING PROTEINS AND POLYPEPTIDES, it is often necessary to use denaturants such as urea and guanidine hydrochloride. In evaluating the nature of the unfolding or dissociation of these macromolecules, optical rotatory dispersion (ORD) is often the tool of choice for following such phenomena. To evaluate the results in a meaningful manner, a parameter is required which is independent of the solvent system used. Since the ORD of molecules depends on the background contributions and the field in which the molecule resides, it becomes necessary to adjust the ORD spectra for these variables. The Lorentz field correction, applied to such spectra, yields a solvent independent molar rotation. Applying such a correction requires knowledge of the refractive index, as a function of wavelength, of the solvent. Furthermore, knowledge of refractive index dispersion is necessary for a wider understanding of light scattering phenomena. In our laboratory, distortions in circular dichroism spectra due to light scattering and self absorption of particulate systems can be corrected by using Mie or Rayleigh-Gans approximations for estimating the scattered light and by employing the absorption flattening considerations of Duysens. To apply such corrections, refractive index dispersion of the solvent system and of the particulate system are necessary (1-3). The construction of particle refractive indices has been demonstrated by Urry et al. (1,2). The refractive indices herein reported have been determined by variable angle single reflection spectrometry. The general principles have been elaborated on by Harrick ( 4 ) and Hansen (5). Specific details are presented in our previous works (6,7). Previously, refractive index data in the ultraviolet have (1) D. W. Urry and J. Krivacic, Proc. Nar. Acad. Sci. U. S . , 65, 845 (1970). (2) D. W. Urry, T. A. Hinners, and J. Krivacic, Anal. Biochern., 37, 85 (1970). (3) D. W. Urry, L. Masotti. and J. R. Krivacic. Arch. Biochem. ‘Biophys., in -press. (4) N. J. Harrick, “Internal Reflection Spectroscopy,” Interscience Publishers, New York, N. Y . , 1967, pp 32, 182-188. ( 5 ) W. N. Hansen, Spectrochim. Acta, 21, 815 (1965). (6) J. R. Krivacic and D. W. Urry, ANAL. CHEM., 42, 596 (1970). (7) J. R. Krivacic and D. W. Urry, Aiial. Biochem., i n press. 1508
been limited with little or no data available at wavelengths shorter than 265 mF. This is particularly true of highly absorbing solutions. It is, in fact, shorter wavelengths that are of the most direct interest to studies on proteins and polypeptides-studies which often employ urea and guanidine hydrochloride solutions. To our knowledge, the method used herein provides the first direct measurements of refractive indices for urea and, guanidine hydrochloride solutions to wavelengths of 2000 A. These direct measurements are compared to fitting the long wavelength data to a Sellmeier-type equation which is commonly extrapolated to shorter wavelengths. Also, the direct measurements are least squares fitted by a general dispersion expression. EXPERIMENTAL
Reagents. Urea was supplied by J. T. Baker Chemical Co. as a “Baker Analyzed” reagent and was recrystallized from aqueous ethanol. Guanidine monohydrochloride was also supplied by J. T. Baker as a “Baker Grade” reagent and was twice recrystallized from aqueous ethanol. Both reagents were stored in the cold and solutions were freshly prepared. Final concentrations were determined by refractive index on a Bausch & Lomb Model 3L AbbC Refractometer and compared to the data of Warren and Gordon (8) for urea and of Kielley and Harrington ( 9 ) for guanidine hydrochloride. Apparatus. Reflection spectra were run on the Cary Model 14 Spectrophotometer using the Harrick Scientific Model RMVA-1 variable angle reflectance attachment with a sapphire hemicylinder (IO). We have previously described the use and calibration of this particular device (7). Procedure. The optical constants are determined from two spectral scans at different angles of incidence. The first angle is above the sapphire-sample critical angle and the second is below the critical angle. Both angles must be above the sapphire-air critical angle. Optical constants are calculated for the samples at 50-A intervals using the equations (8) J. R. Warren and J. A. Gordon, J . Phys. Chem., 70, 297 (1966). (9) W. W. Kielley and W. F. Harrington, Biochim. Biophys. Acra, 41, 414 (1960). (10) N. J. Harrick, ANAL. CHEM., 37, 1445 (1965).
ANALYTICAL CHEMISTRY, VOL. 43, NO. 11, SEPTEMBER 1971
Table I-a. Wavelength, A 5900 NaP2D" 4500 3500 2900 2650 2500 2400 2300 2200 2100 2000
Refractive Indices of Aqueous Urea Solutions Concentration (molarity) 2.136 4.218 1.078 1.3565 1 ,3684 1.3460 1,3676 1 ,3504 1.3418 1.3744 1.3620 1,3513 1.3692 1.3834 1.3594 1 ,4220 1 ,3922 1.3870 1 ,4349 1.4053 1 ,3966 1,4324 1.4028 1,3931 1.4381 1.4070 1.3969 1.4471 1.4137 1.4028 1.4549 1.4192 1.4080 1.4692 1.4287 1.4148 1.4934 1.4497 1.4352
0.678 1,3401 1.3385 1.3445 1.3522 1.3814 1.3927 1.3855 1.3925 1.3986' 1.4030 1.4113 1.4296
Table I-b. Refractive Indices of Aqueous GuHCl Solutions Concentration (molarity) 4.131 1.052 2.090 Wavelength, A 0.532 1.4015 1.3715 1.3562 5900 1.3481 1,3681 1.4015 1.3511 NaZ2Da 1.3426 1.3801 1.4095 1.3636 4500 1.3542 1.4234 1 ,3905 1.3732 3500 1.3625 1,4794 1.4260 1.4063 2900 1.3994 1.4951 1.4396 1.4178 2650 1.4111 1.4903 1.4338 1.4104 2500 1.4038 1.4978 1.4400 1.4142 1.4077 2400 1.4485 1.5084 1.4214 1.4126 2 m 1.4573 1.5185 1.4272 2200 1.4202 1.4715 1.5367 1.4380 1.4299 2100 1.5792 1.5035 1.4603 2000 1.4528 Determined on Bausch & Lomb Model 3L Ab& Refractometer.
6.242 1.3815 1.3843 1.3877 1.3980 ,4340 ,4473 ,4467 ,4534 ,4630 ,4717 ,4892 ,5179
6.143 1.4310 1,4344 1.4398 1,4544 1.5061 1,5266 1.5244 1.5353 1,5495 1.5649 1,5871
Table II. Analysis of Dispersion Equation Coefficients of dispersion eq.' Wavelength range A c x 10" of greatest error 0.33086 9.09221 4000-2650 0.33676 9.05982 4000-2100 0.34786 8.32994 4M)0-2650 2W1950 0.35622 10.9292 4000-2650 2000-1950 0.36900 IO. 8252 4000-2650 2050-1950 0.38548 11.2257 4000-2650 2150-2000
Urea 0.678M 1.078M 2.136M
4.218M 6.242M 8.163M GuHCl 0.532M
0.33747
10.5029
1.052M
0.34589
10.2561
2.090M
0.35977
11 0754
4.131M 6.143M
0.38513 0.41406
13.6032 13.0376
I
4000-2650 2450-1950 4000-2650 2450-1950 4000-2050 2000-1950 4000-2ooo
4000-2650
8.163 1.3986 1.4000 1.4060 1.4197 1 ,4546 1.4701 1.4716 1.4785 1 ,4884 1 ,4979 1.5133 1.5446
Maximum error of fit, Zb 3Z0.9 3Z0.6 =t0.7 +0.9 10.9 +0.4 +0.9 +0.9 +0.9 +0.6 +1.1 -0.9
$1.0 -0.9 f0.9 +0.7 11.4 f1.2
At 23 "C.
+ Experimental value above equation.
If greater accuracy is required, use experimental values directly listed in Table I.
of Hansen (5, 11). The refractive indices are least squares fitted to a general dispersion equation,
nx
=
1
+ AX*/X2 - C
(1)
where X is the wavelength in centimeters. All spectra were run at 23 "C. RESULTS AND DISCUSSION
The refractive index data are presented in Table I. For comparison, sodium D line data are also included. Coeffi(11) W. N. Hansen, Spectrochim.Acta, 21, 209 (1965).
cients A and C of Equation 1 are given in Table I1 along with the regions of maximum error of fit. A more detailed explanation for the errors in the least squares fitted equation in the region of 4000 to 2650 A has been presented elsewhere (7). The maximum error is usually in the 3500 to 3000 region where the rising absorption of the sapphire-UV mirrors unit makes reflectivity measurements of sample unit us. air unit less accurate. The errors in this region tend to make the dispersion equation fit well in high absorption regions where anomalous dispersion occurs. While the present method is the first to give far UV data for highly absorbing samples, the increasing absorption of the unit does decrease the signal to
ANALYTICAL CHEMISTRY, VOL. 43, NO. 11, SEPTEMBER 1971
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Table III. 8M Urea at 20 "0 A 0,38835 0.38818 0.38794
3b 5c
6d
cx
10" 10,2636 10.3604 10.4943
3500 1.4239 1.4240 1.4243
c
See reference 12. Points fitted 5461 A - 1.4022; 4358 A - 1.4105; 3131 A Plus 3650 A - 1.4208 and 2894 A - 1.4433.
d
Plus 2655
a
b
A
2900 1.4423 1.4427 I ,4433
-
2650 1 ,4548 1 I4554 1.4561
2200 1.4929 1.4939 1 ,4954
2000 1.5224 1 5239 1.5259 I
1.4340.
- 1.4572.
noise ratio which decreases accuracy in reflectivity measurements. The attenuation index, K, in the 2300 to 1950 A region varies from 0.01 to 0.05 for both guanidine monohydrochloride (6M) and urea (8M). While these indices appear small in magnitude when compared to typical indices obtained by reflection studies in the infrared regions, one must recall that, in general, the penetration depth varies directly with wavelength which results in a much shorter penetration depth in the ultraviolet regions. The penetration depth also increases as the relative refractive index approaches one (4). The sapphire hemicylinder has a refractive index of approximately 1.9 in the far UV region and thus is sufficiently different from that of bulk solutions. (A suprasil hemicylinder, on the other hand, has a refractive index of approximately 1.6, such that the relative refractive index with the solutions of interest is very nearly one.) Thus, the attenuation indices obtained are reasonable in these wavelength regions. Even with such values of the attenuation index, well defined critical angles are not observed. Thus the two angle method for obtaining the optical constants becomes an important procedure in slightly to highly absorbing regions. One of the reasons for providing the data in Tables I and I1 has been alluded to in the introduction. This reason, the Lorentz field correction, can be clarified by the following example. Frequently refractive indices are obtained at three or four wavelengths in a non-absorbing region by refractometric means and then fitted to a dispersion equation. The dispersion equation is then used to compute the refractive indices into absorbing regions where the anomalous rotatory dispersion occurs, but this is, of course, a region where anomalous ordinary dispersion also occurs, It is in this region that the dispersion equation underestimates the true refractive index. For 8M urea (12) fitted to Equation 1 using three, five, and six points, we present in Table 111 the coefficients and refractive indices in the far UV region for comparison with our data in Tables I and 11. Clearly, the fitting of long wavelength dispersion data can underestimate the true refractive index, in this case by approximately 2 %. The dips i n n observed in Table I, a and b, between 2650 and
2400 A are due to changes in the angle of incidence for continuing the spectra into the far UV region where net absorption due to the reflecting mirrors and sample are higher. The purpose is to optimize the angles of incidence (13). Several changes of angles of incidence are required throughout the spectral region studied (6500-1950 A). Agreement of our data with those of Warren and Gordon (8) has also led us to conclude that the birefringence of the sapphire hemicylinder has a negligible effect. Harrick Scientific supplies a sapphire hemicylinder which has an optical axis coinciding with the hemicylinder axis. The accuracy of the method has been discussed by many authors. Analysis of the equations described elsewhere (6) yields maximum errors in the refractive index of the sample of 0.5 to 0.6%. These errors are based on reading the absorption to *0.006; the angle of incidence to *0.1" of arc; and assuming a constant polarization of the beam, i.e., y = 1 1 1 / 1 ~ , to within =k 10 %. There are inherent systematic errors also in the technique, such as supplying reflectivities to only three decimal places, thus introducing an error of 1.3% in n (13), and determining y to *lo% yields a maximum error in the reflectivity of 2 % (14). The refractive index data are presented with a maximum possible error of *2 to 3 %. However, comparison of the sodium f line data, presented in Table I, a and b, with our 5900 A results gives a standard deviation of 0.0082 and 0.0099, respectively. Comparison at 2650 A gives a deviation of 0.012. On this basis the expected error is 0.6 to 0.8 %. This note presents the refractive indices of aqueous solutions of urea and guanidine monohydrochloride as a function of concentration and wavelength for the 6500 to 2000 A region. Coefficients of a least squares fitted dispersion equation using 90 to 92 points are presented for generating the refractive indices. Experimental values of the refractive index were determined from variable angle single reflection spectrometry.
(12) J. Foss, Y. Kang, and J. Schellman, in G . D. Fasman,
(13) J. Fahrenfort and W. M. Visser, Spectrochim. Acta, 18, 1103 (1962). (14) A. C. Gilby, J. Barr, Jr., W. Krueger, and B. Crawford, Jr., J . Phys Chem., 70, 1525 (1966).
"Methods of Enzymology," S. P. Colowick and N. 0. Kaplan, Ed., Academic Press, New York, N. Y.,1963, Volume 6, Chapter 126.
1510
RECEIVED for review April 14, 1971. Accepted May 19, 1971.
ANALYTICAL CHEMISTRY, VOL. 43, NO. 11, SEPTEMBER 1971
