NOTES
668 conclude that the substrates are in a better hydrogen bonding environment on the surface of the anionic and cationic micelles than on the surface of the zwitterionic micelle. These data do suggest that a more extended investigation into the properties of the micellar surface employing fluorine magnetic resonance may yield information important for the interpretation of kinetic data for reactions occurring in micellar systems.
( I ) . Sphere-Sphere. (The molecules have radii rl and r2). The molar covolume is U1,2
=
4n 3 (rl + r2)*N
(9) Sphere-Rod. (The sphere has radius rl; the rod has cylindrical half-length 12, cylindrical radius r2, and hemispherical ends of radius r2). The covolume is most simply obtained from the volume that the center of a sphere cannot enter, i.e.
On the Interaction of Solute Molecules with Porous Networks by A. G. Ogston Department of Physical Biochemistry, John Curtin School of Medical Research, Australian National University, Canberra, A.C.T. Australia (Received June 30,1969)
Giddings, Kucera, Russell and Myers1 have given an elegant and penetrating account, on the basis of statistical mechanics, of “exclusion” interactions between rigid molecules and inert porous networks. Because the network is considered as random (whatever forms of surface compose it), their treatment does not appear to demand that it need also be rigid, since variation of the distribution of its elements with time would not affect the time-average of interactions of molecules with it. The treatment is not, therefore, so asymmetrical with regard to the distinction between “network” and “molecules” as might appear at first sight. In such a context as gel chromatography, there is of course a very practical distinction between solute and gel. Nevertheless, the findings of Edmond, Farquhar, Dunstone and Ogston2 and of Ogston and Silpananta3 show that real cross-linked gels (specifically Sephadex) have thermodynamic properties, both in themselves and in their interactions with solute molecules, very similar to those of equivalent solutions of uncross-linked molecules. This opens the possibility of treating gel-solute interactions by the same (symmetrical) approach as is used for solute-solute interactions and, consequently, of comparing results obtained on both types of system by experimental methods appropriate to each. A basis for this treatment is provided by Flory’s4 “dilute solution” theory; by this, the molecular covolume of a pair of molecules, whose interaction is purely entropic, can be identified with their molar second virial coefficient (interaction between like molecules) or the corresponding molar interaction coefficient (interaction between unlike mo~ecules).5 The chemical potentials of solutes vary with exponentials of the products of these coefficients and the relevant concentrati~n.~ Molar covolumes are easily evaluated in simple cases. The Journal of Physical Chemistry
However, the same result can be arrived at (i) by considering the probability of placement of a sphere of radius (rl r2)in a, random arrangement of thin rods of length 212;6(ii) with rather greater difficulty, by considering the average limitation of the rotation of a rod r2) and (rl rz 12) whose center lies between (rl from the center of a sphere; or (iii) by considering the rod to be generated by movement of a sphere of radius r2 through distance 212 in a random distribution of spheres of radius rl. (It can be shown that the probability of “collision” in this case, for unit swept volume, is the same as for the infinitesimal radial expansion of a sphere of radius r2, so that the argument of ref 6 can be applied). The last method is of special interest because it shows that the movement of the sphere need not be rectilinear; therefore, the r‘rodJ7need not be straight or stiff, provided that multiple exclusion of a sphere by parts of the same rod does not occur. (3) Rod-Rod. (Each rod is as in 9, with radii rl, r2 and cylindrical half-lengths Ill 12). Route 2 (ii) could no doubt be followed in this case also, though with greater difficulty still, but it is easily solved by route (iii). One rod is considered to be generated by movement through distance 211 of a sphere of radius (rl r2) in a random suspension of thin rods of length 212. Application of the argument of ref 6 then leads directly to
+
+
+ +
+
{ + r2)hlz +
U I , =~ 2n(r1
2n(rl+
r2)2(11+
22)
+
( r l + r2)3}
N
(3)
Equation 3 is (like expression 1) symmetrical, as it should be. Putting ll = 0 reduces eq 3 to eq 2, and putting l2 also = 0, reduces eq 2 to eq 1. Putting rl = and M. N. Myers, J , (1)J, c. Giddings, E. Kuoera, c, p. phgs. Chern., 72,4397 (1gcis). (2) E. Edmond, S. Farquhar, J. R. Dunstone, and A. G. Ogston, Biochm. J * * loss 755 (lgeS)* (3) A. G. Ogston and p. SilPanant% ibid.3 in Press. (4) P. J. Flory, “Principles of Polymer Chemistry,” Cornel1 University Press, Ithaca, N. Y., 1953. (5) E. Edmond and A. G. Ogston, Riochem. J., 1 0 9 , m 1 ( 1 9 6 s ) . (6) A. G. Ogston, Trans. Faraday Soc., 54, 1754 (1958).
NOTES
669
rz and 11
= lZ gives the covolumes for self-interaction of spheres or rods. These expressions should also hold good for systems in which rods are cross-linked to form a gel, provided that the randomness of their distribution is unaffected and that the cross links themselves do not contribute significantly to the exclusion. A fascinating consequence of these expressions is that they show that any system of two solutes which interact only entropically will satisfy the conditions for “incompatible” phase separation provided only that the molecules are of different size. This condition is6 PI1 pzz
- p21z < 0
With spheres, for example, this condition is satisfied by the algebraically necessary condition
+
( ~ T J ~ ( ~ -Y (rl ~ ) ~ rJ6 < 0
which depends only on the ratio Yi/% not on their absolute magnitude. Similar relationships Can be shown to hold for the sphere-rod and rod-rod Cases. Ogston and Silpananta3 have shown that incompatible phase separation occurs in a Sephadex-polyethylene glycol system under conditions similar to those under which it occurs in a dextran-polyethylene glycol system.
photolyzed with 2537-A uv light at 77°K for approximately 1 min. The photolysis produces a dark blue color due to the electron. At this point, an esr spectrum is taken of the sample to ensure that photolysis of the organic solute is minimal. The sample is then photobleached a t 77°K with light from an infrared lamp for approximately 4 min. The electrons become mobile, attach to the solute, and the esr spectrum of the anion can be then observed. A Varian V4510 esr spectrometer equipped with a dual cavity and Fieldial magnetic field regulator was employed in this work. Measurements of hyperfine splittings and g values were made vs. potassium peroxylamine disulfonate (AN = 13.0 G and g = 2.0056).
Results Photolysis of the deuterated alkaline glass containing produces mainly the electron. sodium acetate (10 d) Photobleaching results in a radical whose esr spectrum shows a large doublet splitting (ca. 27 G) (Figure la). A small amount of methyl radical is formed in the
An Electron Spin Resonance Study of Acetate Dianion and Acetamide Anion’ Ijy Michael D. Sevilla Atomics International Division of North American Rockwell Corporation, Canoga Park, California 01804 (Received June SO, 1969)
Reactions of the electron with amino acids and dipeptides are under investigation in this laboratory through use of electron spin resonance (esr) spectroscopy.2 To elucidate the structure of the anion radicals formed it was desirable to investigate model compounds for these systems. Acetate ion and acetamide were chosen because the acetate dianion should have a n-electronic structure similar to anions of amino acids3 and the acetamide anion should closely approximate the electronic structure of an anion of the peptide bond. These species were prepared through electron attachment in an alkaline glass. They are found to exhibit interesting properties owing to restricted rotation of their methyl groups which are described in this note.
Experimental Section The experimental procedure was essentially that of Ayscough, Collins, and Dainton4 as modified by Holroyd and Glass.6 In this method a deoxygenated 8 N NaOD (92% DzO) solution containing 5 d K4Fe(CN)a and 1-10 d solute is cooled to 77°K. The glass formed is
Figure 1. First derivative esr spectra of the acetate dianion in a deuterated alkaline glass at various temperatures: A, spectrum taken immediately after photobleaching, T = 85°K. (The very weak outer lines are due to the methyl radical); B, spectrum after warming to 150°K; C, spectrum at 180°K; D, spectrum after cooling to 150°K; E, spectrum a t 85°K. After first warming to 180°K repeated cycling results in reproducible spectra.
(1) This work was supported by the Division of Biolom and Medicine of the U. 8. Atomic EnergV Commission. (2) M. D. Sevilla, Abstracts, The 158th National Meeting of the American Chemical Society, New York, N . Y., 1969. (3) (a) J. W. Sinclair and M. W. Hanna, J . Phys. Chem., 71, 84 (1967); (b) P. B. Ayscough and A. K. Roy, Trans. Faraday SOC., 64, 582 (1968).
(4) P. B. Ayscough, R. G. Collins, and F. 8. Dainton, Nature, 205, 965 (1965). (5) R. A. Holroyd and J. W. Glass, Znt. J . Radiat. Biol., 14, 445 ( 1968).
Volume 74, Number 3 February 6, 1070
