Ultraviolet and Visible Refractive Indices of Spectro-Quality Solvents J. R. Krivacic and D. W. Urry Institute for Biomedical Research, Education and Research Foundation, American Medical Association, Chicago, Ill. 60610 The single reflectance method was used to determine the ultraviolet refractive indices of several spectroscopic solvents. The solvents-trifluoroethanol, trimethylphosphate, acetic acid, acetonitrile, methanol, and ethanol-are commonly used in studies of polypeptides and proteins. The data are presented in terms of constants for the dispersion equation. WITHTHE EVER-INCREASING utility of ultraviolet spectroscopy, it is significant to directly determine the ultraviolet refractive indices of spectroscopic solvents. Optical rotatory dispersion data require solvent refractive indices for the Lorentz field corrections before adequate comparative studies can be made, and corrections for light scattering effects described in terms of solvent and solute refractive indices become particularly important as attempts are made to study larger macromolecular systems. This paper presents the refractive indices of trimethylphosphate, trifluoroethanol, acetonitrile, methanol, ethanol, acetic acid, cyclohexan!, and, for comparative purposes, water from 6500 to 1900 A. Data were also obtained for dimethylformamide and N-methyl acetamide to 4250 and 4000 A, respectively. All of these solvents are commonly used in studying proteins and polypeptides. Our interest in the refractive indices is in utilizing the values to correct circular dichroism spectra on particulate systems and films. The circular dichroism spectra of films and optically active aggregates contain two types of light scattering distortions: one is an obscuring of chromophores and the other is a differential scatter of the left and right circularly polarized beams (I, 2 ) . The method employed here, single reflectance spectroscopy, has been described by several authors (3-8). One uses the Fresnel reflection equations, as outlined by Fahrenfort and Visser (7), to solve for the optical constants-n, the relative refractive index and K, the attenuation index. In the approach two scans are required at different angles of incidence with known beam polarization or, alternatively, at two different polarizations of the light source (6, 7). The rather lengthy mathematical analysis of the data is outlined in the appendix using the formalism and nomenclature of Hansen (9). The data, fitted by a least squares procedure, are reported in terms of the constants A and C of the dispersion equation n=1+-
AX 2 X2
-
c
where X is in centimeters. (1) D. W. Urry and T. H. Ji, Arch. Biochem. Biophys., 128, 802 (1968). (2) D.W. Urry and J. R. Krivacic, Proc. Nut/. Acad. Sci., U.S., in press, 65 (1970). (3) W. N. Hansen, ANAL.CHEM., 37, 1142 (1965). (4) . , A. C . Gilbv. J. Burr., Jr... and B. Crawford.. Jr.., J. Phvs. Chern., 70, 1520 (1966). (5) A. C. Gilby, J. Burr, Jr., W. Kruger, and B. Crawford, Jr., ibid., p 1525. (6) J. Fahrenfort, Spectrochim. Acta, 17,698 (1961). (7) J. Fahrenfort and W. M. Visser, ibid., 18, 1103 (1962). (8) W. N. Hansen and J. A. Horton, ANAL.CHEM.,36, 783 (1964). (9) W. N. Hansen, Spectrochim. Acta, 21, 815 (1965). 596
ANALYTICAL CHEMISTRY, VOL. 42, NO. 6, MAY 1970
EXPERIMENTAL
The single reflectance device, designed and described by Hansen (3), was obtained from Wilkes Scientific Corp., South Norwalk, Conn., as the Model 20 Variable Angle Reflectance Attachment for the Cary Model 14 Spectrophotometer. The internal reflecting element is a fused quartz (suprasil) prism. In order to properly use the single reflectance method to obtain refractive index, polarization and collimation characteristics of the monochromator must be determined. The reflectivity R, of a partially polarized beam is given by the weighted average of the perpendicular and parallel components (4, 5, 9), i.e.,
(2) ., where y = I11/1~ and l i s the effective light intensity. The parameter y, was determined by the use of the Polaroid Corporation’s HNP’B neutral density polarizers oriented perpendicular and, subsequently, parallel to the plane of incidence of the prism. With the Wilkes apparatus and one poolarizer in the beam path, the absorption risesfo 2.0 at 1950 A. The scans were made from 6500 to 1900 A with the Wilkes unit in and out of the beam path with the purpose of assessing possible depolarization by the prism. No depolarization occurred. Although the Cary 14 has a double monochromator of a 30” fused silica prism in series with a 600 line/mm echellette grating, which one would expect to give wavelength dependent pol;rization, y was found to be 1.38 + 0.22 from 6500 to 2300 A (which is the effective range of the polarizer). Assuming a constant y gives an error of 2% or less in the reflectivity (5). Other errors resulting from uncertainties in angle of incidence and accuracy of obtaining optical density are the limiting considerations for determining refractive index. Beam collimation data for the Cary 14 was obtained for the free beam from the Cary 14 Instruction manual. The half angle spread in the beam was correSted for the refractive index of the prism at intervals of 50 A throughout the spectrum studied. The beam spread (parallel to plane of incidence) and the spectrophotometer accuracy of 0.006 optical density unit were used in a computer program called TABLE supplied by H. C. Gilby of Wilkes Scientific Corp. The function of this program is to optimize the angle of incidence for specific wavelength ranges (see below). The refractive index of the prism from 6500 to 2000 A was determined by the critical angle method and then compared to known data available on the refractive index of fused quartz (10). The experimental data coincided with the handbook within 0.5 or better. Errors here are due to the fact that the angle of incidence on the prism-air interface could be measured to within 10.15”. As a consequence, the handbook data were least squares fitted to a dispersion equation which was then used to generate the refractive index of the prism when required by the optical constant program REFRAC (see appendix). Preliminary reflection spectra were made in the following manner: (10) “Handbook of Chemistry and Physics,” Chemical Rubber Co., Cleveland, Ohio, 39th ed., 1957-58, p 2734.
(1) The critical angle of the sample-prism was estimated from sodium D line data. The prism unit was inserted into the beam path without a sample. The beam (in the visible region) was aligned with the detector and sample chamber with the use of a dental mirror and a sheet of paper. This method of alignment, though crude, leads to fewer fine adjustments. The fine adjustment consists of moving the prism parallel to the beam until absorption is at a minimum. The angle of incidence is chosen such that there is total reflection (above the prism-air critical angle). The angle should be below the estimated critical angle of the sample-prism interface. The spectrum taken is the base line for that angle of incidence. (2) The sample is then introduced and run at the same angle. (3) Steps 1 and 2 are repeated for an angle of incidence above the critical angle for the prism-sample interface. The preliminary reflection data is used in the program REFRAC to calculate preliminary optical constants, nz and n 2 ~for 2 the sample. This data are then used by the program TABLE to analyze and suggest angles of incidence that should be chosen for the least errors when taking into account spectrophotometric accuracy, half-beam spread, and accuracy in defining angle of incidence. Two additional factors must be taken into account in both the programs REFRAC and TABLE: (i) the beam spread at the prism-sample interface as a function of prism refractive index and (ii) the correction for refraction of internal reflection (11). The program, TABLE, indicates angles of incidence and how the scans are repeated breaking up the wavelength region when different pairs of angles are suggested. A complete discussion of TABLE is found in Reference 5. Solvent refractive indices were determined at the Na D line by thermostatting an Abbe Bausch-Lomb refractometer to temperatures corresponding to those existing for the internal reflection method. The solvents studied were the following: (a) Trifluoroethanol (TFE), Halocarbon Products, 82 Burlews Ct., Hackensack, N. J. Redistilled in glass (b.p. 72 "C, 738 mm Hg) with Duflon Column containing glass beads (lower 3/4) and glass helices (upper l / d ) , 10% take. The first l0-15% of distillate was discarded. A small amount of NaHC03 was added to remove traces of acid which may be present. Pot residue was 20-30Z. Solvent was stored under dry nitrogen in amber glass bottles. Water0.002 % by Karl Fischer method. (b) Trimethylphosphate (TMP), Ethyl Corp., New York. (Ignition Control Compd #4). (b.p. 193 "C, 760 mm Hg) Glass redistilled using same column as for TFE, 10% take. First 10-15% distillate and pot residue 20-30Z were discarded. Distillate was partially frozen (approx. '13) and the remaining liquid was discarded. Freezing was repeated and liquid discarded. Solvent was stored in a sealed flask under dry nitrogen. Water-0.045 by Karl Fischer Method. (c) Acetonitrile, Matheson, Coleman and Bell, Spectroquality. Water (max), 0.03 %; evap. res. (rnax), 0.0003 %; fluores. (rnax), 0.25 ppb as quinine base. (d) Methanol, Matheson, Coleman and Bell, Spectroquality. Water (rnax). 0.05%; evap. res. (max), 0.0003%; fluores. (max), 0.25 ppb as quinine base. (e) Ethanol, U. S. Industrial Chemicals Co., Division of National Distillers & Chemical Corp., New York. U.S.P.N.F., Reagent Quality. Absolute. (f) Glacial acetic acid, Baker Analyzed Reagent, evap. res. 0.0008 %; C1, 0.0001 %; Sod, 0.00001%. CU, 0.00005 %; heavy metals (as Pb), 0.00001 %, Fe, 0.000005%; Ni, 0.000005 %; substances reducing KMnOa (as SOZ)< 0.015%. (g) Cyclohexane, Matheson, Coleman and Bell, Spectro(11) A. C. Gilby, Wilkes Scientific Corp., South Norwalk, Conn., private communication, July 22, 1969.
Table I. Comparison of Water Refractive Indices Reported in the International Critical Tables and Calculated by the Reflection Method Water Refractive Index ICT Valuesa Reflection* 1.3330 (5893 A) 1.3308 (5900 A) 1,3345(5460) 1.3321 (5450) 1.3349 (5350) 1.3328 (5350) 1 337.5 (4800) 1 3354 (4800) 1.3385 (4350) 1.3404 (4341) 1.3424 (3950) 1.343'7 (3944) 1,3495(3400) 1.3504 (3404) 1.3652 (2750) 1.3664 (2749) 1.38813 (2313) 1.3886 (2300) 1.4257 (1990) 1.4231 (2000) At 20 "C. At 24 "C. I
Table 11. Comparison of Refractive Indices Obtained on Abbb (Bausch-Lomb) Refractometer and by the Reflectance Method Reflectance T "C Solvent Abbe n D n5900 Water 24 1.3321 1.3308 Trifluoroethanol 24 1.2921 1 .2907a WE) Trimethylphosphate 1.3949 24 1.3962 (TMP) Acetonitrile 24 1.3419 1.3449 24 1.3268 Methanol 1.3279 24 1.3620 Ethanol 1.3634 24 Acetic acid (glacial) 1.3698 1.3682 24 Cyclohexane 1.4245 1.4146 N-methylacetamide 32.5 1 ,4269 1.4138 (NMN N,N-dimethyl24 1 ,4286 formamide (DMF) 1 ,4250 Value reported by manufacturer on nonredistilled solvent. The value is too low to be determined on the Abbe.
quality. Water (rnax), 0.02%; evap. res. (inax), 0.0003 %; fluores. (max.:), 0.25 ppb as quinine base. (h) Water distilled, deionized, and finally redistilled in glass using the Corning Model AG-2 distillation apparatus with a quartz immersion heater; conductivity, 1.79 pmhos (i) N-methylacetamide (NMA), Eastman Organic Chemicals No. 4969, m.p. 29-31 "C. (j) N,N-dimethylformamide (DMF), Matheson, Coleman and Bell, Spectroquality. Water (max), 0.05 %; evap. res. (max), 0.0005'%,fluores, (rnax), 0.5 ppb as quinine base. RESULTS AND DISCUSSION
In order to check the method, refractive indices were obtained for water and compared to the values listed in the International Critical Tables. The main purpose of the comparison is to check the reliability of our values as a function of wavelength. As may be seen by reference to Table I, the difference in magnitudes is 2 parts in 1330 or less over the entire wavelength range. This provides confidence in the values in the ultraviolet region where the other solvents have no reported data. The values reported in Table I1 are a comparison of those obtained by the reflectance method. For the first seven solvents listed, the difference in the results are about 0.1 to 0.2%. From the results in Table I, this is the magnitude of error that can be expected over the entire wavelength range. The error is greater for the last three solvents. Because of the ANALYTICAL CHEMISTRY, VOL. 42, NO. 6, MAY 1970
597
~~
Table III. Wavelength range, A 6500-1900 6500-1900 6500-1900 6500-1900 6500-1900 6500-1900
~~
Coefficients for Dispersion Equation
Coefficients from ICT Fit5 c x 10" Solvent T "C A c x 10" T "C A 0.324187 Water 24 0.322294 9.07177 206 9.05038 5.67080 TFE 24 0.287163 ... ... *.. TMP 24 0.386166 8.72674 ... ... ... Acetonitrile 24 0.336344 8.57972 16.5 0.337543 8.43014 Methanol 24 0.319878 8.43749 14.5 0.323195 8.27689 Ethanol 24 0.354241 8.56959 18.35 0.353604 8.40524 Acetic acid 22.9 0.35834 9.31207 0.361686 9.09593 (glac.) 24 6500-1900 0.406638 6.71059 10.85 0.420141 Cyclohexane 24 6500-1900 8.95534 0.402647 9.42798 3oc 0.414517 9.95475 NMA 32.5 6500-4000 22.4 0.400343 20.1484 0.413443 12.7075 DMF 24 6500-4250 a Four wavelengths given 6563, 5893, 4861.5, and 4340.6 A. b "International Critical Tables," Vol. 111, 1930, p 13. c From our data at 6700, 6300, 5900, 5500, 5100, and 4700 A using the Abbe (Bausch-Lomb) Refractometer.
Table IV. Comparison of Dispersion Equation Values to Experimental Values
z
z
Reflec., Disp. Eq., Reflec., Disp. Eq., Solvent T , "C "C n5900 " c n5900 Differencea "C nzzoo "C n2200 Differencea TFE 24 1.2921 1.2919 0.012 1.3263 1.3253 0.077 TMP 24 1.3962 1.3961 0.007 1.4714 1.4711 0.023 Acetonitrile 24 1.3449 1.3448 0.008 1.4118 1,4088 0.209 Methanol 24 1.3279 1.3278 0.004 1.3889 1.3874 0.110 Ethanol 24 1.3634 1.3632 0.017 1.4320 1,4305 0.109 Acetic acid (glac.) 24 1.3682 1.3682 0.002 1.4433 1.4437 -0.030 Cyclohexane 24 1.4146b 1.4146 -0.004 1.4714 1.4721 0.044 NMA 32.5 1.4138* 1.4139 -0.001 1.4286b 1.4279 0.054 DMF 24 1.425ob 1 ,4249 0.006 1.4661b 1.4506 1.060 Water 24 1.3308 1.3309 -0.009 1* 3974 1.3966 0.052 Error is indication of least squares dispersion fit to our reflection values of refractive index. (-) means equation above reflection value. (+) means equation below reflection value. * See text. Q
high refractive indices of DMF, NMA, and cyclohexane, the critical angle for each of these is large and outside the physical limitations of the Wilkes' unit. Thus the refractive indices determined by reflection are in error as indicated by the values in Table 11. The error is due to the fact that the high angle scan cannot be run at an incident angle greater than the critical angle, and hence errors cannot be minimized by the program TABLE (see appendix). As was stated earlier, the angle of incidence for any one scale reading varies with the refractive index of the prism. For example, a scale reading on the Wilkes' unit of 83 equalsea true angle of incidence of 70' at 5000 A, whereas at 2000 A, 70" equals a scale reading of 86. The Wilkes unit is physically limited to a scale reading of 90 which is approximately 73" at 2000 A. Even at this scale reading, the window available to the incident beam is on the order of 1 to 2 mm in width and makes the optimization of energy-the initial adjustmentsvery difficult. To get the incident beam at the sample-prism interface, at the outset it is necessary to translate the prism parallel to the incident beam such that making further fine adjustment is not possible. The data are most concisely presented in terms of the constants defined in Equation 1 (see Table 111). Also included in the table are the constants obtained from fitting the long wavelength data in the International Critical Tables. The accuracy of the equation, in which the constants were obtained by a least squares fitting procedure, is shown in Table IV where the experimectal and curve fitted values are compared a t 5900 and 2200 A. In the cases of DMF and NMA the comparisons are at 4000 and 4250 A rather than 2200 A. The 598
ANALYTICAL CHEMISTRY, VOL. 42, NO. 6, MAY 1970
values calculated from the dispersion equation differ from the experimental values by less than the experimental error. ACKNOWLEDGMENT
We thank A. Ruiter and D. Mayers for purifying the trifluoroethanol and trimethylphosphate and A, c. Gilby for the program titled TABLE, APPENDIX
Calculation of the optical constants (preliminary and final scans). All terminology is that of W. N. Hansen (9). See this reference for further details. The reflectivity at a plane boundary between two isotropic homogeneous phases, in which one phase (here the prism) is transparent are given by the Frensel equations.
Y
((x2
+
Y;1'2
+ x)'"]
X =
p
f
E2K2,
y = 2n2K
Rg =
ll a = cos 8, p = sin28 - n2, y = I11
8
=
+
(n2cos8 - n 2 sn28)2 n2cos0 n2 - sin28)2
+
(8)
combining Equations 7 and 8 with 6 and rearranging to
angle of incidence (9)
17 =
n2 - = real part of the relative refractive index of
absorbing phase =
K
the attenuation index of the absorbing phase
For a partially polarized beam, the observed reflectivity at angles of incidence greater than the critical angle is given by Robs
=
R l + YRII l + Y
=
1 -
or (In 10)A =
2P
+ 27s
K--
(1
I f 7
(s-P)2K2+
+2y
...
(4)
where A is the absorbance Using only the first two terms of Equation 4 and solving for K , we have
2P
+ 2ys
4Y (S
K =
=
Q (1
P
=
2n2cy/[(l
Q
=
2n4cy/[p1ycy2n4 p)]
- n2)pl’2]
and cy, defined above. It may be noted that the reflection method is applicable to absorbing samples whereas the critical angle method is not (12). However, for all solvents in the ranges reported, the calculated values of K varied from 0 to 0,044 with typical values of the order of It should also be noted that the absorption values are so low as to be cornputationally inaccurate by the equations used. For angles of incidence smaller than the critical angle, the reflectivity is still Rl.
+ YRll
I + r
(6)
but Rl and R Iare ~ defined by Equations 41 and 42 of Reference 9, the first terms of which are given below (Equations 8 and 9). =
(cos0 (cos0
- f(n)/f’(n)
(10)
(5)
+
Rl
noid
Once the desired accuracy (approx. 3 parts in 10 is reached), the final n is used in computing K from Equation 5. If the K 0.02, the second terms of Equations 41 and 42 of Reference 9 are used with the first order K from Equation 5 to correct the reflectivity for absorption; the interative procedure is repeated to compute a corrected n, and Equation 5 used to compute a new K . The initial guess for n for subsequent wavelengths is that computed for the previous one. Each n must now be multiplied by the refractive index of the prism to obtain the refractive index of the sample, n2. The computed K is multiplied by n2, and the optical constants n2 and n2K are used for the program TABLE. The
- P)2
+ 2p/n2)
where S
=
nnew =
+ 2ys
2P
Robs
A general iterative procedure is used for obtaining n, the relative refractive index. The initial approximation for n used here is n sampleln prism at the sodium D line. Subsequent interations are based on
- n 2 + sin2)02 + n 2 - sin28)2
(7)
(12) N. J. Harrick, “Internal Reflection Spectroscopy,” Interscience Publishers, New York, 1967, p. 19.
preceding description outlined the principles of REFRAC. TABLE analyzes the data, n2 and n 2 K for optimizing conditions (Le,, least error), and REFRAC is used again after scans are made at optimum angles of incidence. The program, DISPER, is a least squares fit of a general dispersion equation. n
=
1
+ AX2/(X2- C )
(10)
X is in centimeters. where A
=
G/{ 1
- [ZX4( N - 22n + h2)/
(2x2
G
=
-~~2n)2]}
- 22X2n + ZX2n2)/(ZX2n- ZX2)1 + {[ZX4 - ZX4n) ( N - 22n
+ 2 n 2 ) / [ ( Z X 2-
Z X Z ~}) ~ ]
+
C = (2X4 AZX4 - ZX4n)/(ZX2 - ZX2n) N = Number of observations All computer programs REFRAC and DISPER are available from us. They are written in G E Time-share BASIC language and can be supplied in either hardcopy or punched paper tape. The program, TABLE, should be obtained directly from the authors of Reference (5). RECEIVED for review January 7,1970. Accepted February 27, 1970.
ANALYTICAL CHEMISTRY, VOL. 42, NO. 6, M A Y 1970
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