MAGNITUDE IN SEDIMENTATION EQUILIBRIUM
WITH
RAYLEIGH OPTICS
film thickness but not the radioactivity. Atmospheric COz, the concentration of which was reduced but not eliminated in our experiments, may be involved here.
3075
Acknowledgment. The authors thank their colleagues in the analytical department in the Shell Development Company Laboratories at Emeryville, California, for a helpful radiochemical analysis.
Aberrations Peculiar to the Use of Rayleigh Optics with the Ultracentrifuge. Magnitude in Sedimentation Equilibrium
by P. A. Charlwood and M. V. Mussett National Institute for Medical Research, London, N.W.7, England
(Received February 23, 1966)
The surfaces of equal solute concentration in an ultracentrifuge cell are cylindrical, whereas the slits of a Rayleigh diaphragm are set parallel with a radius. I n general, therefore, there is a gradient of concentration in any plane perpendicular to the slits. The effect of this gradient on the positions of interference fringe minima has been calculated. Even when the additional complications of partial illumination of one (or both) Rayleigh slit(s) during the revolution of the rotor were taken into account, the aberrations proved to be, in the least favorable experimentally attainable situations, only about the same magnitude as the random errors of measuring fringe positions.
Introduction It has been recognized since Rayleigh optics were first adopted for ultracentrifuge work’ that the record is complicated by (a) the surfaces of equal solute concentration not being flat and perpendicular to the aperture slits, and (b) light reaching the photographic plate when the cell is not in the correct position for interference. The effect of (a) is equivalent to a gradient of concentration “across” the slit apertures, whereas the feature of primary interest is the gradient parallel to the slits. As a preliminary to developing methods of making differential measurements of molecular weights from equilibrium patterns, it seemed desirable to investigate the magnitudes of the aberrations arising from the above factors. The components of the optical system and their relative dispositions are shown schematically in section in Figure 1. The mirror which normally reflects the light through a right angle is omitted as being nonessential,
merely an experimental convenience. The rotor revolves in a plane which is perpendicular to the optical axis, the distance between this axis and the axis of rotation being about 7 cm in most machines. The light source slit and the slits of the Rayleigh diaphragm lie parallel with the plane of rotation and perpendicular to the section shown in Figure 1. The cell sectors and associated cell slit diaphragm move relative to the rest of the optical system so that only once in each revolution do the slits of the cell diaphragm become parallel with the slits of the Rayleigh diaphragm. The contributions produced at all other orientations are included in the following treatment.
Theory The symbols used will in most cases be defined as they occur in the mathematical development, but a complete (1) E. G . Richards and H. K. Schachman, J . A m . Chem. Soc., 79, 5324 (1957).
Volume 70, Number 10 October 1966
3076
(1)
P. A. CHARLWOOD AND M. V. MUSSETT
(2)
(3) (4) (6)(6)
(7)
(8)
(9)
Figure 1. Ragleigli interference optical system: (1)slit source, ( 2 ) collimating lens, (3) cell twin-slit diaphragm, (4) double-sector cell center, (5) Rayleigh double-slit diaphragm, (6) condensing lens, (7) camera lens, (8) cylindrical lens, (9) photographic plate. The optical axis is represented by the dashed line. Cell windows are not shown.
list is given for easy reference at the end of this section. All distances, unless it is stated to the contrary, are in centimeters. 1. Relation of Solute Concentration and Position at Equilibrium. It is assumed that equilibrium has been attained in an ideal, two-component system and that n, the difference between refractive index of solution and solvent, is proportional to solute concentration, so that d In n/d(r2) = IC. Here r is the distance from the axis of rotation and IC = M w 2 ( 1 - 8p)/2RT, the symbols in this expression having their usual significance. Consider the plane of rotation CYZ (Figure 2 ) which cuts the axis of rotation at C. Let Y be a point in the cell and YZC a right angle, the optical axis intersecting the plane of rotation at a point on CZ not very far from Z. If H is another point in the cell such that CZ = CH = h, then
-------------h-------------
1
L
Figure 2. Instantaneous position of one cell slit (width I ) relative to one of the Rayleigh slits (width m,edges, respectively, ys and ~4 from the optical axis). Rotation occurs in the plane YZC. Optical axis, which is perpendiculas to YZC, passes through a point on CZ near Z.
Figure 3. Effect of condensing lens (not shown) on image formation. The plane YZO is perpendicular to the plane of rotation YZC (Figure 2 ) , but parallel to the optical axis.
In (nY/nH) = Ic{(CY)~ - (CH)2) = IC{(y2 h2) - h2) = ky2
to the plane CYZ (Figure 2). The focal plane of the condensing lens, which passes through OX (Figure 3) is parallel with the plane of rotation CYZ, and therefore perpendicular to OZ. Light from a point Y in the cell makes a contribution to the light intensity at any point X of the line OX. If OX = x, compared with ideal focusing at 0, the path difference is seen from Figure 3 to be
and
(YX
+
ny = nHekyz= nH(1
+ ky2 + - .) 0
(1)
As the maximum value of ?cy2is about 0.1 under usable equilibrium conditions, higher terms inside the bracket will be neglected. 2. Interference Optical Theory. A number of the usual assumptions and approximations are made in the following. In the dimension primarily involved, the combined effect of the camera and cylindrical lenses (Figure 1) is merely to produce at the photographic plate a magnified image of the interference fringes which are formed in the focal plane of the condensing lens, so that what happens to the right of this focal plane need not be considered. (In the second dimension the combined effect of all three lenses is to focus between cell and photographic plate, thereby giving a true representation of radial distances.) Here the condensing lens (focal length g), cell diaphragm, and Rayleigh diaphragm are regarded as being very close The Journal of Physical Chemistry
- YO)
+ (y - x)21 - v p - q j = g ( d E 1 + (Y - x)2/g21 -
= d[g2
= g{ [l
4 1
+ (y - x)2/2g2*
+ y2/g21)
* ][l
+ y2/2g2* ‘1) *
To the usual degree of approximation, as g >> x,y (YX - YO) = [(y
- X)Z - y 2 p g
=
x2/% - XY/9 (2) The first term, being independent of y, does not contribute to the interference, but merely determines the phase of the resultant light. It enters into K (see below), but K is eliminated when the product +(z)+*(z) is taken in the singleslit arrangement. In a twinslit arrangement its effect again disappears when #(z)+*(z) is taken because the term independent of y which it gives rise to enters equally into K 1and Kz
MAGNITUDE IN SEDIMENTATION EQUILIBRIUM WITH RAYLEIGH OPTICS
(see eq 5 below). In working out the phase-difference function we must add the contribution arising from the solute refractive index increment (see section 1). The phase-difference function
+
(3) 4 = (2.lr/X) b H ( 1 kyz) - x!//gI taking the refractive index of air as unity and making the approximations stated above. Here p is the optical path length in the cell and X is the wavelength of the light. (Note: the term unity within the inner bracket gives rise to 2npn& on expansion. Although this is independent of y across one sector, it is retained because it enters into the theory of the twin-slit arrangement which is necessary when both cell sectors are involved.) The amplitude $(z) at X is proportional to Je-”“()ddy between appropriate limits.z For simplicity we take the proportionality constant as unity so that $0) = Je - io(U)dy. (i) Single-Slit Aperture (Difraction Pattern). If we have a slit with edges distant yl and yz from the axis of the optical system $(2)
=
3077
effect is similar to the above except that the integrals now extend over two intervals. It is important to ensure correct representation of the refractive index at the center of each slit, corresponding to the separate cell channels. With an extension of the above notation =
1
+
p p ( - i u z ) exp(-iKl)du [exp(-iu2)
P u t t i n g c cos u2 du = PI,
[cos u2du
=
exp(-iKz)du sin uzdu =
Q1,
Pz,and
(Pz- iQ2)
4%
exp( -iK2)
Hence
+ h*)- w/ol/+j Y
[e-2r’I~nH(I
(P1Q2 - PzQJsinLIIdA1Az = i ( z > (5) where A = :27rnHpk/X and B = -2rz/gX. Putting u = d Z ( y 4-B/2A) and K = (A/k - Bz/4A), dy = d u / d x and $(s) =
1
lz
exp(-iuz) exp(-iK)du
Intensity is proportional to t,b(z)$*(x) where $*(z) is the conjugate of t,b(z). Again taking the constant of proportionality as unity we have
where L = ( K 2- K1).This and the preceding section deal with a static situation. In practice the extent of slit illumination is a function of time, as rotation alters the cell orientation and position relative to the Rayleigh diaphragm. 3. Efects of Cell Motion on Aperture Sizes as a Function of Time. Let the distances of the edges of the Rayleigh slits from the optic axis be yl, yz, y3, and y4 as exemplified in Figure 2. Of course, (y4 y3) = (yz - y1) = m, the width of each slit, and the y3) - (yz distance between slit centers, p, is [(yk y1)1/2. We also define B = (yd y3 YZ y1)/4, which is zero if the diaphragm is in the symmetrical position. When the cell has rotated through an angle 0 (from a position symmetrical with respect to the optical axis) until one cell slit is in the orientation shown in Figure 2, the position of the point Y’ which lies on one O.Z(q 1) edge of it is given by ZY’ = h tan e sec e. Here I is the width of a cell slit and p the distance between centers of cell slits, the same as that between centers of Rayleigh slits (see above). In the optical systems used, e is always quite small when light passes. If ly41 > Iyll, the maximum value of jej is obtained by
+
+
+ + +
[c e x p ( -iuz)du][ ;[:[(cos
[exp(iuz)du]
=
1
uz - i sin uz)du X
[L * ( c o suz + i sin uz)du1
Putting
c +
[cos uzdu = P and - iQ)(P
sin uzdu = Q
iQ>/A = (Pz &?/A = t(z> (4) (ii) Twin.-Slit Aperture (Interference Pattern). The
$(z)$*(z) = ( P
+
+
+
(2) G. Joos, “Theoretical Physics,” Blackie and Son Ltd., London, 1934.
Volume 70,h‘umher 10
October 1966
P.A. CHARLWOOD AND M. V. MUSSETT
3078
Table I: Integration Limits for the Calculation of Terms of Eq 7 Subscript of P or Q
Upper limit
Lower limit
considering the position of the edge of the cell slit furthest from y4 when the cell is symmetrically situated relative to the optical axis. This distance is [0.5. 0.5. (q Z) ly4l1, so that 181 1 tan 161 (q Z)]/h. The relations above show that this is 0.5(Z m ) ] / h . This expresequivalent t o [/g] q sion, which is arrived a t by a similar process if lyll > /y41, has a maximum value of 0.1 radian when calculated from the fourth column of figures in Table 11. Thus, to a sufficient degree of accuracy
++ +
[IY~I +
+ +
ZY’ = h8
+
+ 0.5(q + I )
(6)
In other words, since e = wt (where w is the constant angular velocity), the rotational movement can be regarded, for a given value of h, as practically equivalent to a uniform translational displacement of the cell and its associated diaphragm across the stationary Rayleigh double slit.
part of the rotation there are four points formed by the intersections of ZY with the edges of the cell slits, or with one edge of each cell slit and one edge of each Rayleigh slit. The y coordinates of these four points, which are plotted in Figure 4(ii) a t the appropriate t ( = B / w ) , determine the limits ul, u2, u3, and u4 applicable a t that instant for the terms of eq 5. When only one Rayleigh slit is illuminated by reason of the cell position, the situation can be represented by Figure 4(i) or (iii). Then eq 4 is used, the integration limits again being fixed by erection of an ordinate at the correct value of t. The correspondence between Figure 4 and the physical situation can be visualized as follows. No light passes until, at the beginning of Figure 4(i)a, one edge of a cell slit reaches yl. The portion of the width of the Rayleigh slit illuminated then increases
Table II : Parameters Expressing Effects of Solvent in Both Channelsa 1
m Q
0.054 0,075 0.0
0.054 0.150 0.0
0.054 0.075 -0.2
0.054 0.150 -0.2
0,100 0.025 0.0
0.100 0.025 -0.2
I n all these cases A1 = A I = 0.001 and kl = k~ = 1 X 10-6.
In all that follows, attention is confined to a fixed value of h, ie., in Figure 2 to a section through ZY parallel with the axis of rotation. When the cell rotation corresponds with Figure 2, the instantaneous contribution to the light intensity at any point X (Figure 3) is given by eq 5 with the limits for the integrals defined by the y coordinates of the cell slits (such as ZY’). However, if ZY’ exceeds y4, then u4 is fixed by y4 and not by ZY’. Thus a t any moment during this The JOUTTUI~ of Physical Chemistry
ka+b#c4
kaq&b#ca
)CO~b#CY
(ii)
(iii)
v
(i) ___j
t
(=e/u)
Figure 4. Extent of Rayleigh slit aperture effective a t r = h during cell rotation. Shaded and plain are= correspond, respectively, to the two cell channels. The intervals a, b, c are common to the three situations within the limits of accuracy of approximations used. Situations (i) and (iii) produce the fogging effects, and (ii) the interference fringes of interest.
MAGNITUDE I N SEDIMENTATION EQUILIBRIUM WITH RAYLEIGH OPTICS
until at the end of the interval 4(i)a it covers the range yl to (yl I ) at which stage the second edge of the same cell slit has reached yl. In 4(i)b the region transmitting light is defined by the edges of the cell slit, which are distance I apart but moving relative to yl and yz. The interval (i)c is rather similar to 4(i)a in reverse. During 4(ii) the first cell slit passes across the other Rayleigh slit while the second cell slit scans the first Rayleigh slit. Finally, during 4(iii) the second cell slit traverses the second Rayleigh slit. 4. Light Intensity ut Any Point, Integrated over a Complete Scan. As the relative intensity, I(x), at the point X is given by t(x) (eq 4 or 5) at any instant, the total effect is obtained by taking &(x)dt over the requisite time interval. Since, as explained above, the limits of the integrals used t o evaluate E(x) are themselves functions of time, a double integration is involved. Because e varies directly with t, the resultant intensity may be taken as j((X,e)de. As an example of what is involved, we consider the time interval (i)a (Figure 4), throughout which eq 4 applies with the lower limits of P and Q constant at .\/&(yl B/2A1). As the upper limits increase from a l ( y l B,/2A1) to v‘X(y1 1 B/2A1) during this time, in terms of the previous convention for the origin of 8 they would be written as a 1 [ h O 0.5(q I) B/2A1] with 0 increasing from [yl - 0.5(q l ) ] / h to [yl - 0.5(q - Z)]/h. It is permissible and more convenient for subsequent collection of like terms to 0.5(m change the origin of 8 by the constant {yl q ) ) / h so that the upper limits become .\/&[he 0.5(m I ) B/2A1 yl] with 0 now increasing from -(m 1)/2h to - ( m - I)/2h during 4(i)a. If we denote E(x,e) thus obtained as f5a, the contribution to the total light reaching x: is
+
+
+
+ +
+
+
+
+ + +
+
+
+
+
I n a similar manner we get f4a and Ida(x) from 4(iii)a. It is necessaqy to apply eq 5 to the interval 4(ii)a, thereby obtaining tla = (Pla2 Qla2)/A1,tza= (Pza2 Q2a2)/A2)E3a =: 2[(P1aPza QlaQ2a) COS L - (PlaQza PzaQla) sin L ] , / m 2and corresponding contributions to I(x). For brevity
+
+
+
I(x) =
S
3079
- (m--E)/Zh
-(m+L)/2h (m-Z)/2h
+ (b(Z,e)de +
Ea(x:,We
- (m--E)/Zh
(m+-1)/2h
m-Z)/2h
fc(x,’%de (7)
The integration limits for all the P’s and Q’s are given in Table I. The “fogging” contribution, which is given by 5 terms with subscripts containing 4 and 5 , can be calculated separately if it is desired. For l > m separate sets of equations might be written, but the accuracy of computer calculations makes it possible to use the same set by employing a subterfuge (see below).
Notation a, b, c particular time intervals during cell rotation A = 2irn~pk/X B = -2?r~/Xg focal length of condensing lens g fixed distance from axis of rotation to plane of interest in h cell I integrated light intensity k = MwZ(1 - op)/2RT K = ( A / k - B2/4A) 1 width of slit in cell window holder L = (Kz - KI) M molecular weight of solute width of slit in Rayleigh diaphragm m n difference between refractive index of solution and solvent (corresponding to any value of T ) optical path length in cell P P,Q Fresnel-type integrals f cos u2du and f sin uzdu, respee tively distance between centers of a pair of slits P r distance from axis of rotation (general) gas constant R time t T absolute temperature U = 1/A(y B/2A) partial specific volume of solute 0 coordinate in image plane (“across” fringes) 2 coordinate in Rayleigh diaphragm plane (perpendicular to Y slits) A distance between consecutive fringe minima A* displacement of fringe system e angle of rotation x wavelength of light in air instantaneous contribution to intensity 5 density of solution P phase-difference function 9 amplitude function w angular velocity
+
*
Computer Programs and Calculations
5
where Ea(z,e)
ts,,. By similar reasoning Ib(x)
= a=l
and Io(x) can be defined so that in summary
The computer was programmed in EMA (extended mercury autocode) to calculate the integrals of eq 7 by Gaussian quadrature for specified values of the constants and a series of values of x. This involves values of P and Q corresponding to particular values of 0. The P and Q terms were themselves computed Volume 70,Number 10 October 1866
P. A. CHARLWOOD AND 11.V. MUSSETT
3080
by Gaussian quadrature. Comparison of typical calculations using six- and eight-point quadrature showed that the six-point was sufficiently accurate. The main restrictions in the basic derivation are that 1 6 m and the separations (q) between centers of slits are identical in the two pairs. The case 1 > m was dealt with as follows. If we calculate I(s) for I’ almost identical with m, say I’ = m [ l - (I - m) X lO-5/2m], then is very small, corresponding to a change in 0 of (I - m) X 10-6/2h. If the computer is instructed to sum Is($),I&), and 1O61b(r), we get I ( z ) for I > m with adequate accuracy. To obtain the effect of uniform solvent in one sector we can make one of the k’s extremely small, but the corresponding A should be reduced so that Al/kl = Az/kz. This saves working out different types of integrals which are required when k = 0 exactly. To compaae fringe patterns with those obtained with uniform solvent in both channels a similar procedure can be used. The program makes possible the calculation of I ( s ) for symmetrical (g = 0), asymmetrical (fj = -0.2), or intermediate positions of the Rayleigh diaphragm, for different slit widths, and as just mentioned, for solvent us. solvent, solution us. solvent, or one solution vs. another. Positions of interference minima, located in computer results, were compared with what would be obtained for a static situation if there were opposite each cell slit uniform solution having the refractive index obtaining a t the center of the actual slit. The interval (in x) between consecutive minima js given by the usual expression for a double slit A = Xg/q
(8)
The displacement of the band system from the symmetrical position is given by A* = Xg[Ai/ki
- Az/kz
+ A~(yz+ y1)’/4 Az(Y4 + ?h)2/41/2?l
(9)
I n all this work parameters typical of the optical system of the Beckman-Spinco ultracentrifuge were used, q, h, and g being taken as 0.4, 7.0, and 62.5 cm, respectively, and X as 546 mp. Then A = 0.008536 cm. (In practice the plate image is magnified in this direction by about 3.4 because of the cylindrical lens, but this is unimportant from the point of view of the present investigation, as previously mentioned.) It is not at present possible experimentally to measure the positions of intensity minima to better than about 0.02 of a fringe. It should, therefore, be sufficient to calculate I ( z ) in the neighborhood of the anticipated The Journal of Physical C h m k t r y
minima a t intervals of 2 of 0.0002 cm in general. This enables the minima to be located wit,hin *0.0001 cm. The typical portions of central bands of fringes which are shown in Figures 5 and 6 were, however, computed mainly at rather wider intervals (0.0005 cm in s). The size of A is governed by the magnitude of the refractive index gradient “across” the Rayleigh diaphragm. For a given optical system, with light of fixed wavelength, A is proportional to pnalc. When interference optics are used it is not possible to exceed a certain value of A without completely losing resolution of the fringes. I n the calculations a maximum permissible value of A of 66 was usually taken, which is not far from the limit found when using the steep gradients of the method of Y p h a n t i ~ . ~More fre10. The stipulation quently in equilibrium work A made earlier that = Az/lc2need not hold in practice, but saves modifying the program to take account of the rather arbitrary difference of refractive index between the centers of channels. The values taken for other parameters are given in Tables II-IV. The speed of the ultracentrifuge in equilibrium experiments is usually selected to give lc
-
Table 111: Parameters Corresponding to Occupation of One Channel by Solution, Other by Solvent” 1
0.054 o,075
o,o
0.054 o,075 -o,2
0.054 0.100 o,150 o,025 -o,2 o,o
‘ In all these cwes A I = GO, A B = 6 k* = 3 x 10-8.
x
0.100
o,025
-o,
0,100
o.025 -o,2
10-4, kl = 0.3, and
values of the magnitudes shown. The usual cell slits have I = 0.054 cm, and the Rayleigh diaphragms m = 0.075 or 0.15 cm. Of course, the number of minima in the central band of fringes is determined by the smaller of 1 and m (in conjunction with q). Calculations have generally been confined to the eight minima nearest the center of the main band, the ones which would be used in practice for measurement.
Results and Discussion I n most cases the computer results gave the positions of minima within =kO.OOOl cm-in s of the values calculated from the simple eq 8 and 9. The exceptions are shown in Table V. Even these departures are only about the same size as experimental errors involved in measuring positions of fringe minima. I n practice the Rayleigh diaphragm is not in the same plane as the (3) D. A. Yphantis, Biochemistry, 3, 297 (1964).
MAGNITUDE IN SEDIMENTATION EQUILIBRIUM WITH RAYLEIGH OPTICS
3081
Table IV: Parameters Used for Calculating Differential Effects” (9
c
Ai Az kl kz
60 60 0.3 0.33
60 60 0.3 0.3
66 60 0.33 0.3
(ii)
J
10 10 0.1 0.11
10 10 0.1 0.1
1 m
11 10 0.11 0.1
0.054 0.075
0.054 0.054
0.100 0.025
” Each column of set (i) waa combined in turn with each column of set (ii), giving a total of 18 combinations, all also having g = 0. One other combination waa used, obtained by taking the first column of each set with = 0.1.
Table V: Comparison of Positions of Intensity Minima Obtained by Computer and from Simple Formulas“ 0.001 0.001 1 x 10-8 1 x 10-6 0.100 0.025 -0.2 +0.0213 A0.0215 A0.0299 A0.0301
Ai Az kl k2 1 m
B X X* X X* X X*
60 6 X lo-‘ 0.3 3 x 10-8 0.054 0.150 -0.2 - 0.0043 -0.0041 0.0128 0.0130 0.0213 0.0215
60 60 0.3 0.33 0.054 0.054 0.0 0.0460 0.0462 0,0546 0.0548
60 60 0.3 0.33 0.054 0.075 0.1 - 0.0328 - 0.0331
60 60 0.3 0.33 0.054 0.075 0.0 0.0375 0.0377
66 60 0.33 0.3 0.054 0.075 0.0 0.0302 0.0304
x and x* are respectively the positions of minima as given by eq 8 and 9 and by computer.
0 -0.025
3 -0.02
-0.015
-x
0.00 001 0.02 (cm.) Figure 5. Intensity variation, I(x), aa a function of x for A1 = 110, Az = 100, ki = 0.66, kz = 0.6, 1 = 0.054, m = 0.075, and B = 0. Arrows indicate positions of intensity minima calculated by means of eq 8 and 9. Lower curve indicates fogging contribution.
-0.01
4x
cell slits, but the effects of this, and of other approximations made in the theory, could hardly alter the general findings. It must be concluded that, with existing equipment, the “fogging” effects and aberrations considered here, which are of a different type from those discussed by Yphantisla have a negligible influence on results. I n
-0.005
0.005
0.025
0.015
(cm)
Figure 6. Intensity variation, I ( s ) ,as a function of x for A i = A2 = 0.001, kl = kz = 1 X 1 = 0.195, m = 0.15, and B = -0.2. Arrows indicate positions of intensity minima expected from eq 8.
experiments carried out with wedge-centerpiece cells and interference optics, there is an additional term, linear in y, entering into the expressions which form the basis for the calculations (sect,ion 2i). Although no computations for this type of case have been carried out, it seems obvious from the results of the present work t.hat these effects also must be negligible. Similarly, our original intention to investigate the consequences of errors in slit-width fabrication waa deemed Volume 70.Number 10
October 1966
NORMAN COHENAND JULIAN HEICKLEN
3082
Acknowledgments. We are much indebted to Mr. F. Hussein and also to Dr. L. J. Gosting for helpful criticisms of the manuscript. We also thank Mr. S.
superfluous. The results of cell misalignment can be calculated in the normal, elementary way because of the relatively small magnitude of the aberrations established in this work.
Gresswell for assisting in some preliminary calculations.
The Production of Perfluorocyclopropane in the Reaction of Oxygen Atoms with Tetrafluoroethylene
by Norman Cohen and Julian Heicklen Aerospace Corporation, El Segundo, California (Received February 28, 1966)
The reaction of O(*P) with C2F4 proceeds by the reaction scheme
+ C2F4 -%- CF2O + CF2 0 + C2F4 C2F40*
0
2CF2 -% C2F4 CF2
-!-
C2F4
3 CyClO-CaF6
+ CzF4-%-
C2F40*
CzF40*
CF20 4- CyclO-caF~ CF20
+ CF2
+
where C2F40* is an excited intermediate. The ratio k6/(kll ICs) is 0.15 at 22' and drops slightly as the temperature is raised. The CF2 radicals produced give the same values for k3/kz'" as do singlet CF2 radicals produced in another system.
Introduction In recent reports from this laboratory,'l2 it has been shown that the reaction of triplet oxygen atoms with C2F4yields CF20as the sole oxygen-containing product independent' of conditions for temperatures from 23 to 125". However, at room temperature the cyclo-CaF~ formed was about 0.15 that of the CFzO for C2F4 pressures up to 30 mm. This invariance with pressure is contrary to that expected from the sequence of reactions
0
+ C2F4 +CF20 + CF2 (singlet)
The Journal of Physical Chemktry
(1)
CF2
2CF2 +CzF4 ---j cyCIO-C~F6
+ C2F4
(2) (3)
Therefore, two possible alternatives were suggested'?a
0
+ C2F4 +CF20 + CF2 (triplet) 0 + CzF4 + C2F40*
(1) D. Saunders and J. Heicklen,
(4) (5)
J. Am. Chem. SOC., 87, 2088 (1966). (2) D.Saunders and J. Heicklen, J . Phys. Chem., 70, 1950 (1966). (3) J. Heicklen, N. Cohen, and D. Saunders, ibid., 69, 1774 (1965).
