1196
IGNACIO TINOCO, JR.,AND MARKP. FREEUN
accord with Hardy’sg early views which stressed the importance of the existence of low adhesion and easy slippage in the interface defined by contact of the outermost terminal groups of the monolayers adsorbed on each of the two rubbing solid surfaces. Examination of the glass slide after many traverses at high loads reveals the presence of slight wear scars, which confirms previous work2 that even in the presence of a solid film, there is always some metal/glam contact. Unquestionably, however, the high resistance t o penetration of the solid monolayers is also essential to decrease greatly the real area of contact of metal and glass. The roughness of the two sliding surfaces would therefore be expected to have some effect on the durability and hence the wear preventive properties (9) W. B. Hardy, “Collected Scientific Papers,” Cambridge Univesity Press, 1936.
Vol. 61
of adsorbed films. Research on this point will be reported later. The results obtained by rotating the ball slider before each successive traverse over the filmcoated slide reveal that desorption from the glass slide to the steel ball takes place quite readily. The depletion of molecules from the slide causes a large increase in the area of contact between surface asperities of the two solids with a proportionate increase in the friction and wear. Where desorption from a rubbing surface is a controlling factor in film failure, it is necessary to have a source of supply of additional polar molecules nearby in order to replenish the film-depleted surface. The importance of film replenishment in keeping friction and wear to a minimum is illustrated in Table I1 by the durability behavior of a film of octanoic acid under a 1000 g. load both in the presence and absence of a surrounding pool of the liquid acid.
THE OPTICAL ACTIVITY OF ORIENTED COPPER HELICES. I. EXPERIMENTAL BY IONACIO TINOCO, JR.,AND MARKP. FREEMAN Contribution from the Department of Chemistry, University of California, Berkeley, California Rscsbbd M a y 8, 1867
The rotation of linearly polarized microwaves by copper helices has been measured as a function of wave length. The optical activity, both along the helical axis eS3,and perpendicular to the helical axis ell, has been obtained, The rotatory dispersion curves can be described by Drude equations; 038 contains positive terms, while e,1 contains negative terms. The optically active absorption wave lengths are simply related to the length of wire in the helix and are nearly equal for the two optical activities.
Introduction The current interest in the optical activity of helical has prompted us to study a model system of macroscopic helices. It is hoped that by measuring the rotation of microwaves by oriented helices whose dimensions can be varied systematically, present theories of the optical activity of helices*+‘ can be tested, and that new insight may be gained. Lindman’ found that the rotatory dispersion of a system of randomly oriented 9 cm. copper helices could be described in the wave length range from 12 t o 34 cm. by a one term Drude equation. That is, the wave length dependence of the optical rotation of the helices had the same form as that observed €or molecules. Recently Winkler8 attempted t o repeat this work and claimed that the optical rotation observed by Lindman was due t o anisotropic scattering and not to optical activity. We have therefore carefully tested for diffraction effects in our apparatus. Furthermore, unlike Lmdman and Winkler, we have studied oriented arrays of heli(1) J. T. Yang and P. Doty, J . A m . Cham. SOC.,79, 761 (1957). (2) C. Cohen and A. a. Szent-Gyorgyi, ibid., 79, 248 (1957). (3) P. Doty and R. D . Lundberg, Proc. Natl. Acad. Sci., U.S.,43, 213 (1957). (4) D. D. Fitta and J. G. Kirkwood, ibid.. 41, 33 (1956). 736 (1956). (5) W. Moffitt, ibid., a, (6) W. Kauzmann, “Quantum Chemistry,” Academic Press, Ino., New York. N. Y.,1957, p. 616. (7) K. F. Lindman, Ann. Phtiaik, 63, 621 (1920). (8) M. H.Winkler, THIEJOURNAL, 60, 1665 (1956).
ces. The optical activity could therefore be measured both for light incident along the helical axis and for light perpendicular to the helical axis. The optical activity of a randomly oriented sample has been shown to be the weighted mean of these two activities. Experimental .The microwave polarimeter had three principal parts: a polarizer, a container for the systems studied and an analyzer. Each of these components was mounted separately on a 2 meter optical bench. The polarizer consisted of a section of x band (3 cm.) wave guide (25.4 cm. long) and a klystron oscillator. The polarization of the radiation was caused by the physical dimensions of this wave guide and the natural polarization of a klystron oscillator. For the type723 klystron (A = 3.0 to 3.65 cm.) theradiofre uency power was injected 10.3 cm. from the analyzer end of &e rectangular wave guide. This end was terminated in a horn and the wave guide was tuned with a shorting stub inserted in the other end. For the wave length region 2.4 to 3.4 cm., a Varian Associates type X-13 klystron was used and the power was injected into the end of the polarizer through a gyrator. For both of these oscillators the wave length was determined by use of an F-R Machine Works type X410A absorption wave meter mounted between the horn and the wave guide on either the polarizer or the analyzer. The highest frequency region (2.1 to 2.44 cm.) was covered by a Varian Associates type X-12 klystron. Thls was coupled to a 2 cm. wave guide by means of an adjustable attenuator and a Tee joint which was connected to the end of the polarizer by a tapered section of wave guide. The wave length was determined by a “magic tee” and reactance type wave meter (De Mornay Bonardi type F715-1) attached to the other leg of the input tee. The (9) I. Tinooo, Jr., and W. G. Hammerle, ibid., 60, 1619 (1956).
I
OPTICALACTIVITYOF
Sept., 1957
power supply used in each case was appropriate to the tube being used, but each had facilities for either external or internal 1000 cycle amplitude modulation of the oscillator. The container for the systems studied was a wooden box, lined with 1/4 inch s onge rubber, of inside dimensions 13 X 13 X 39 cm. was supported by two */z inch iron rods extending up from the optical bench and inserted into two Castalloy flanges on the box. As it was desired to minimize the interaction of direct radiation from the polarizer with the flanges, the container was placed adjacent to the horn. At the same time, to minimize scattered radiation picked up by the analyzer, its horn was as far away from the container as was consistent with adequate signal strength (about 48 cm.). The flanges were so placed on the box that the box could be: (a) turned end for end, (b) rotated 90 degrees about the long axis, c) rotated 90 degrees about the long axis and turned en for end. This made four equivalent positions for the box which helped to determine and eliminate undesirable container effects. The analyzer consisted of a section of rectangular 3 cm. wave guide 24.8 cm. long with a horn on one end and a crystal diode 3.75 cm. from the other end. Other than.the restrictions imposed by the dimensions of the wave guide, the analyzer was untuned. The 1000 cycle pulsating d.c. output of the crystal was am lified by a high “Q” 1000 cycle amplifier.10 The amplifier Bad an attenuator that diminished the input signal 5 db. per step. The output of the am lifier was measured on the a.c. scale of an RCA Senior VoLOhmyst vacuum tube voltmeter. The analyzer was firmly clamped in a cylinder of aluminum which turned in pillow blocks. A scale, graduated in degrees, was attached to the cylinder which was turned by a worm gear such that one turn of the worm corresponded to one degree. A dial attached to the worm gear read in 0.01 degree unit. The optical rotation was measured by turning the analyzer for minimum signal. Actually, three voltages were chosen arbitrarily and the angles on each side of the minimum corresponding to these voltages were averaged to give the minimum. Under conditions of no depolarization, this minimum could be reproduced to ztO.03 degree. The helices were made by winding No. 20 B. and S.copper wire on 6/32 in. steel drill stock with a pitch of 8 turns to the inch. When released this winding expanded to approximately 0.5 cm. diameter. Helices for this experiment were three turns cut from this winding; they were 1 cm. long. When straightened out, they were found to contain 4.7 cm. of wire. The helices were imbedded in the center of a 3 cm. cube of polystyrene foam“ (transparent at these frequencies) oriented with their axes normal to one (marked) face. For this experiment, 192 right-handed and 192 left-handed helices were assembled.
8
6
Results Scattering Effects.-We chose the interaction of a system of 1 cm. helices with microwaves as a model for the optical activity of molecules. However, because of the dimensions of the helices, their interparticle distances, and the wave lengths used, other effects are possible. For example, the system might act as a birefringent or dichroic crystal, or as a diffraction grating. There also could be secondary scattering effects due to reflection of the radiation from the box, flanges, supports, etc. All these effects might cause an apparent rotation of the plane of polarization of the microwaves which was not due to optical activity. To eliminate birefringence (which would change the incident radiation from linearly to elliptically polarized) and dichroism (which would rotate the plane of polarization), the helices were arranged to be analogous to a uniaxial crystal with light incident parallel to the optic axis.12 To measure the (10) F. Harris, Thesis. University of California, 1953. (11) Suggested by Professor R. J. Myers. (12) F. A. Jenkins and H. E. White, “Fundamentals of Physioal Optics,” McGmw-Hill Book Co., Inc.. New York, N. Y., 1950, p. 496.
~RIENTEDCOPPER HELICES
1197
optical activity along the helical axis (e33),the helices were simply oriented with their axes parallel to the direction of propagation of the radiation. To measure the optical activity perpendicular to the helical axis (h= 822)) the helices were oriented perpendicular to the propagation direction, but with their axes alternately parallel and perpendicular to the direction of the incident plane of polarization. 375 365
k
\\ I
I
I
I
I
I
1
I
I
1
-160 -120 -80 -40 0 40 80 120 160 Excess R. H. helices. Fig. 1.-The optical rotation of cop er helices us. the excess number of right handed helices. $he closed circles 0 represent dilution with blank polystyrene cubes; the open circles 0 represent dilution with left handed helices.
Diffraction and secondary scattering effects are more difficult to eliminate, but suitable tests may be made to evaluate them. It was found at h = 3 cm. that the angle of rotation of a full box of parallel helices was independent (within 10%) of the distance of the box from the polarizer. Scattering effects should be critically dependent on the relative locations of the three polarimeter components. A more extensive test of scattering effects was made by dilution experiments. Two types of dilutions were made. In one, the right handed helices were replaced by left handed helices (or vice versa). The scattering effects therefore remained essentially constant, but the angle of rotation changed. In the other, the helices were replaced by blank polystyrene cubes, thus decreasing both the rotation and the scattering effects. For each dilution the box was initially considered to be full of cubes and the positions for inserting diluent cubes were determined by random numbers. The angle of rotation at each dilution was measured for the four positions of the box described in the Experimental section. The results, obtained a t h = 3.16 cm., are shown in Fig. 1. The mean of the four angles is plotted us. the excess number of right handed helices. The closed circles represent dilution with blank cubes; while the open circles represent dilution with other helices. The closed circle at zero on the abscissa represents the box filled with blanks; while the open circle a t zero represents a racemic mixture. The negative numbers on the abscissa represent an excess number of left handed helices. The good agreement between the two types of dilution is convincing evidence that secondary scattering effects are unimportant in this experiment. The straight line obtained shows that interparticle diff ractioii cffects are also negligible.
1198
IGNACIO TINOCO, JR.,AND MARKP. FREEMAN
20 0
-20 -40 r'
M
4 v e,
-60
-80 - 100 - 120 - 140 2.0 2.2 2.4
2.8 3.0 3.2
2.6
3.4 3.6
X (cm.).
Fig. 2.-The rotatory dispersion for right handed helices oriented parallel to the direction of propagation of the radiation. The circles are experimental points; the solid line is eq. 2.
AXES PARALLEL T O DIRECTION OF PROPAGATION
bb
5
0
I t.
-
-5
-
I
1
I \
m AXES PERPENDICULAR TO D I R E C T I O N OF PROPAGATION
- 10
-
- 15 -20 2.6
2.8
3.0
3.2
3.4
3.0
A (em.).
Fig. 3.-(Bottom) The rotatory dispersion for right handed helices oriented perpendicular to the direction of propagation of the radiation. The open circles represent the rotation of right handed helices; the closed circles represent the rotation of left handed helices multiplied by minus one. The solid line is eq. 3. (Top) The long wave length portion of Fig. 2.
It was of interest to see how the precision compared if one box position were used instead of the mean of all four. It was found that the mean deviation from a straight line if all four positions were measured was 0.6', while the mean deviation for one position was 0.9'. We therefore used only this one
Vol. 61
position in the rotatory dispersion measurements. We conclude from the above studies that the rotation angles measured are due to the optical activity of the helices. There is perhaps a 10% uncertainty in the angles caused by the various scattering effects. Rotatory Dispersion.-The optical rotation as a function of wave length for the box full of right handed helices all oriented with their axes parallel to the direction of propagation of the incident radiation is shown in Fig. 2. Only one orientation of the box was studied. There are two optically active absorption bands clearly visible and there is evidence for a third band at the short wave length side. In Fig. 3 (bottom) the rotatory dispersion for the full box of right-handed helices all oriented perpendicular to the direction of propagation is shown. The angles of rotation for both right-handed (open circles) and left-handed (closed circles) helices are shown on the same figure with the angles for the left-handed helices multiplied by minus one. Only one active absorption band is seen, but there is evidence for another from the fact that the curve is not symmetrical around zero. In Fig. 3 (top) the long wave length portion of Fig. 2 is replotted for comparison. It is interesting to note that the rotatory dispersions near the critical wave lengths are just reversed for the two orientations of the helices. The optical activity along the helical axis approaches a minimum on the long wave length side of the critical wave length, while the optical activity perpendicular to the helical axis approaches a maximum on this same side. Also, the critical wave lengths for the two orientations are slightly different. The angle of zero rotation used in all the previous figures was obtained by studying a racemic mixture as a function of wave length. This angle of rotation was nearly independent of wave length except from 2.3 to 2.4 em. We attributed a small positive change in this region to small differences in the right and left handed helices which only became significant when the individual rotations became very, large. Cotton Effect.-The state of polarization of the radiation received by the analyzer was also determined as a function of wave length. Incident plane polarized light will in general become eliptically polarized after passage through an optically active medium. The results are shown in Fig. 4. The ratio ( l / p ) of the minimum amplitude to the maximum amplitude of the received radiation (the square root of the corresponding intensities) is plotted vs. wave length. The value of l / p can vary from 0 for linearly polarized radiation to 1 for circularly polarized radiation. The top half of the figure is for helices oriented with their axes parallel to the direction of propagation and the bottom half is for the perpendicular helices. It is seen that the value of l / p approaches a maximum a t the same critical wave lengths observed in the rotatory dispersion curves. Discussion A rotatory dispersion curve is commonly described by a Drude equation of the form
1
1199
OPTICAL ACTIVITY OF ORIENTED COPPERHELICES
Sept., 1957
This equation is not valid very close to an optically active absorption band (A = A,) because it does not consider energy dissipation. Although eq. 1 predicts an infinite rotation a t the absorption band, experimentally it has been found's that the rotation goes through a maximum on one side of the band then passes through a minimum on the other side. If only one term in the Drude equation is important the rotation passes through zero a t the center of the band. Lindman' had previously found a critical wave length for copper helices a t i 2L where L was the length of the wire in the helix. We find that the data in Fig. 2 can be described by a three term Drude equation with Xj = 2L/j ( j an integer). The three values (indicated by vertical lines in the figure) are ha = 3.15 em., h4 = 2.36 em., and hg = 1.89 em. The first two values were directly measured and the third was inferred. These values correspond to L = 4.72 em., which is very close to the actual length of wire in each helix. The solid line shown in Fig. 2 and the top half of Fig. 3 is a plot of
It is seen to give a very good description of the data. For the perpendicular helices we find a good agreement with the data (solid line in Fig. 3) for 6
I
~2
970
- (3.05)s + X2 - (9.14)2
(3)
The Xj are now chosen as 2L'/j ( j an odd integer). The values are Xa = 3.05 em., XI = 9.14 cm., L' = 4.57 em.; the value of L' is still very close to the length of wire in a helix. It may seem artificial to pick XI = 9.14 cm. as a critical wave length. However, it was found that no two term Drude equation would fit the data if the second critical wave length were less than 3.05 em. Also, both the rotatory dispersion and the depolarization curves failed to indicate the presence of an optically active adsorption band a t Xq = 2.28 em. Therefore we have assumed that Xj for even j do not correspond to active absorption bands for this orientation. If we want to keep hj simply related to the length of the wire in the helix, we are left with XI as chosen. However, any value for a critical wave length longer than 5 em. would fit the data as well. A quantum mechanical derivation by RosenfeldI4 of the theory of optical activity of systems much smaller than the wave length of light shows that a better representation of the data for theoreticaI calculations is given by (4)
The molecular rotation [e] is the actual angle e (degrees) divided by the path length (decimeters) and also divided by the number of molecules per unit volume (cm.-9. The refractive index of the solvent is n. Although this derivation is not implicitly applicable to our system, it should be interesting to (13) See, for example, C. Djeraasi, W. Closson and A. E. Lippman, J . Am. Chem. Soc., 18, 3163 (1956). (14) L.Rosenfeld, 2. Phyeik;, 118, 161 (1928).
0.2 0.1
e
00.3
\
,
b
\
4
3.0 3.2 3.4 3.6 (cm.). Fig. 4.-The Cotton effect for erpendicular helices (bottom) and parallel helices (top). %he reciprocal of the axial ratio of the elliptically polarized light is plotted vs. wave length. 2.6
2.8
examine the behavior of the various parameters when this equation is fitted to our data. In this work we took the refractive index as 1 because the polystyrene foam is mostly air. The path length was 3.5 dm. and the concentration for the full box was 0.0401 helices/cm.3. We can therefore write the following equations for the molecular rotation of the right handed helices in the wave length region 2.0 em. < X < 3.6 em. Radiation incident parallel to the helical axis [ess] = - X'
2.2(3.15)2 (3.15)'
-
- X'24.2(2.36)' - (2.36)'
-
106(1.89)' - (1.89)' (5)
X'
Radiation incident perpendicular to the helical axis
The parameters in eq. 5 and 6 are listed in Table I. TABLE I THE OPTICALLYACTIVE ABSORPTIONBANDSAND THE CORRESPONDING ROTATORY STRENGTHS OF COPPER HELICES PARALLEL [e,] AND PERPENDICULARTO THE DIRECTION OF PROPAGATION OF THE RADIATION j = 1 9.14 j = 2 4.57 j = 3 3.05 j = 4 2.28 j = 5 1.83
9.44 4.72 3.15 2.36 1.89
82.7 0 4.6 0 ?
? ? - 2.2 - 24.2 - 106
The optical rotation of a molecule in solution, or equivalently, the optical rotation of a random orientation of particles, is the mean of the three principal optical activitie~.~ [el11 ieZ2i [osai [eo] = (7)
+
3
+
Although these data cannot be compared directly with Lindman's results,' we note that in the wave length region corresponding to j = 1 for his helices,
1200
J. T.LAW
his results fit a positive Drude term. We would expect this behavior from the trends seen in Table I. The negative terms are decreasing while the positive terms are increasing with increasing wave length. However, no generalizations should be made until more is known about the effect of helix pitch and diameter. For example, a helical antenna of these dimensions would be expected to be in the normal mode (radiating normal to the helical axis) at the longest wave lengths studied and would be expected to radiate in the axial mode at the shortest wave lengths.15 To what extent this should affect the optical activity is not yet known, but presumably the effects are related. Conclusions We have found that the optical rotation of 1 em. copper helices can be described by a Drude equation. For right handed helices the optical activity along the helical axis has negative Drude terms while the optical activity perpendicular to the heli(15) John D. Kraus. "Antennas," McGraw-Hill Book Co.. Inc., New York, N. Y..1950, p. 176.
Vol. 61
cal axis has positive Drude terms. At long wave lengths the positive terms seem to dominate. The optically active absorption bands are simply related to the length of the wire in the helix. The critical wave lengths along and perpendicular to the helical axes are nearly, but not quite, equal. Except for the dependence on the length of the helix, these phenomena are similar to those found for helical polypeptide~.~A better model for helical polypeptides which should remove this exception would be helices made of alternating lengths of conductor and insulator. The conductor would correspond to the polarizable amide bond and the insulator would correspond to the insulating =CHR group. A quantitative comparison of these results with theories of optical activity of helices4-6 will be made later. Acknowledgment.-We wish to thank Professors Gwinn, Harris, McGarvey, Myers and O'Konski, Dr. Mahan and Mr. Maki. Their loan of equipment and their helpful suggestions made this work feasible.
THE HIGH TEMPERATURE OXIDATION OF SILICON BYJ. T.LAW Bell Telephone Laboratories, Incorporated, Murray Hill,New Jersey Received May 0, 1067
The oxidation kinetics of silicon have been studied over a range of temperatures from 1000 to 1300'K. and at pressures from 10-sto5 X 10-2mm. Under alltheconditions investigated, therate followed a parabolic equation n = ZK(t/n) e, where the rate constant K was markedly pressure dependent. A possible interpretation of this is given in terms of the boundary layer theory. The removal of the oxide film by flashing has been studied as a function of flashing temperature. The rate of evaporation of silicon was found t o be decreased by almost two orders of magnitude in the presence of a 300 A. film.
+
Introduction At present there is considerable interest in the problem of obtaining atomically clean germanium and silicon surfaces. One of the most difficult species to remove from any surface is oxygen, but it is even more difficult to demonstrate conclusively how much chemisorbed oxygen or oxide film is still present after a given treatment. If the oxidation process of silicon has a rate that is determined by the oxide film thickness we then have a tool for measuring fairly directly the amount of oxide remaining after a given treatment. All we need do is measure the rate before and after a certain treatment, and if the oxidation kinetics are known we can then deduce any change in film thickness. Since all surface cleaning techniques depend on high vacuum conditions we would prefer to carry out the oxidation measurements at fairly low oxygen pressures (ca. lo-' mm.). To date no kinetic data are available a t pressures below 200 mm. At atmospheric pressure, McAdam and Geil' measured the thickness of the oxide film as a function of time by an optical method. They found that over the temperature range investigated, 873 to 1273"K., the results could be described by a parabolic rate law (1) D. J. McAdam and G. W. Geil, J . Research NaU. Bur. Standards, 28, 503 (1942).
dn/dt = K / n (1) where n is the number of molecules of oxygen reacted at time t and K is the rate constant. Brodsky and Cubicciotti2 reported data in the temperature range 1220 to 1420°K. and at an oxygen pressure of 200 mm. Under these conditions the oxidation rates could be described by a logarithmic law of the form
n = b log ( 1
+ at)
(2)
where a and b are constants. At the lowest and highest temperatures investigated, the data could be fitted equally well by a parabolic equation. It therefore appears possible that a parabolic law is followed from 873 to 1420°K. Let us consider for a' moment the basis of a paraboIic oxidation law. If the film is sufficiently thick that electric fields across it are small, then the diffusion of reactants through the oxide layer will be controlled by the concentration gradient from the gas-oxide interface to the metal-oxide interface. This gradient is pr?portional to l/n so that the rate of growth, dnldt, 1s also proportional to l/n if the rate-determining step is the diffusion of reactants through the oxide layer. I n the derivation of this equation by Cabrera and MottS it was assumed that local thermo(2) M. (1951).
B. Brodsky and D. Cubicciotti, J. A m . Chem. SOC.,73,3497
(3) N. Cnbrera ancl N. F. Mott, Repts. Proe. Thus., 12, 103 (1048).
-
