COMMUNICATIOXS TO THE EDITOR
1842 The noun, bond, seems likewise inappropriate because the attraction between the alkyl groups of two polymer chains has none of the characteristics that distinguish chemical bonds from van der Waals forces. Any “simple multiple proportions” between such groups result from regularities in the structures of the two chains, not from any valence forces between alkyl groups. The alkyl chains in micelles of soap are not bonded together by phobia for surrounding mater; they stick together just as strongly in absence of water. Major workers in this field are surely well aware of the fact that there is no true bond between alkyl groups of adjacent polymer chains, and are moreover competent to calculate the thermodynamic quantities involved in the interaction between such chains; why, then, should a terminology continue in use that misleads some into thinking that the “hydrophobic bond” represents a special concept that must be mastered in order to deal with these systems? Why not speak simply of alkyl interaction free energy, energy, or entropy? I do not find it necessary to invent “fluorophobic bonds” in order to handle the thermodynamics of the limited solubility of heptane in perfluoroheptane. I thank NBmethy, Scheraga, and ISautzmann for kindly replying in some detail to my request for their views on this matter. However, I do not agree with their statement that ‘(. . .hydrocarbons actually prefer a nonpolar environment to being surrounded by water.’’ I say rather that molecules of water “prefer” to be hydrogen-bonded together rather than separate to admit alkanes. I n order for these to dissolve, a large amount of water must be present per mole of alkane in order to supply sufficient entropy to offset the unfavorable balance of attractive energies. Gilbert Lewis during a seminar responded to a graduate student who had contradicted him saying, “That is an impertinent remark, but it is also pertinent.” It is in the latter sense only that I offer the above criticism. DEPARTMENT O F CHEMISTRY OF CALIFORRIA URIVERSITY BERKELEY, CALIFORNIA 94720
JOEL
stances, and that they therefore would actually favor mixing. As it was noted repeatedly before12-4 this is indicated by a direct calculation of the relevant energies of interaction, just as it is shown by the data cited by Hildebrand. However, the net free energy of solution, which determines solubility, is dominated by a large negative, i.e., unfavorable excess entropy term.2-6 It has been s h o ~ n that ~ - ~this entropy term arises owing to changes in the state of water and has to be attributed to increased ordering of water molecules, i.e., to an increase in hydrogen bonding. As a result, in spite of the favorable interaction energies, the free energy of solution is positive. This can be expressed by saying that, in over-all terms, ie., in A F ” , hydrocarbons actually prefer a nonpolar environment to being surrounded by water. This is implied in the use of the adjective “hydrophobic.” Because the source of immiscibility is an entropy factor, the water-hydrocarbon system differs qualitatively, and in a unique maimer from most systems of low miscibility. Thus the interactions in this system do represent a special concept. We do not wish to argue about the matter of nomenclature. However, it should be pointed out that the criticism of the use of the term “bond” in the present context, where it does not refer to a chemical bond but to a loose association, has been recognized repeatedly by various worlcers in the past, too. Yevertheless, the term “hydrophobic bond” has proven to be useful as shown by its frequent occurrence in recent physical, chemical, and biochemical nomenclature. H. Hildebrand, J . Phys. Chem., 72, 1841 (1968). (2) W. Kauzmann, Advan. Protein Chem., 14, 1 (1959). (3) G. Nemethy and H. A. Scheraga, J . Phys. Chem., 66, 1773 (1982). (4) G. NQmethy, Angew. Chem., I n t . Ed., 6 , 195 (1967). (5) H. S. Frank and M. J. Evans, J . Chem. Phys., 13, 507 (1945). (1) J.
THE ROCKEFELLER UNIVERSITY NEW YORK, NEW YORIC 10021
GEORGE K~GMETHY
DEPARTMENT OF CHEMISTRY CORNELL UNIVERSITY H. HILDEBRAND ITHACA, NEWYORK 14850
HAROLD A. SCHERAGA
DEPARTMENT OF CHEMISTRY
WALTER KAUZMANN
RECEIVED JANUARY 18, 1968
PRINCETON UNIVERSITY PRINCETON, NEWJERSEY 08540 RECEIVED FEBRUARY 17, 1968
Comments on the Communication “A Criticism of the Term ‘Hydrophobic Bond’ ”
The Internal Pressure of Simple Liquids
by Joel H. Hildebrand
Sir: Hildebrand’s discussion’ of the nature of the forces of interaction governing the solubility of hydrocarbons is incomplete. It is certainly true, as he states, that van der Waals interactions in themselves are on the balance favorable between the two subThe Journal of Physical Chemistry
Sir: Any general theory of the liquid state must involve expressions for the interaction potentials between the molecules, thermal energy, and volume. Much progress is being made in this field, but the expressions obtained are generally complex and difficult to handle. For many purposes ?t is, therefore,
1843
COMMUNICATIONS TO THE EDITOR
constant B in front of R to correspond with the fact convenient to employ simpler, semiempirical models that more that three degrees of freedom interact with which can provide a useful description of experimental volume in a typical liquid. The equation then becomes results together with some insight into molecular processes. Pr--..-Vo One such group of theories which is being found a BR increasingly useful in describing the properties of liquids such as viscosity and P V T properties is those This equation is then further modified for use at low associated with the concept of free volume. Recently,’ volumes and high pressure by introducing the concept i t has been found possible to combine together some of a “molecular compressibility” Po. When this is free-volume concepts with the van der Waals equation done we obtain, as explained in ref 1, the approximate to provide certain relations applicable to P V T berelation havior at low or moderate volumes. Naturally these relations give slightly different results to those obtained PT - VO) 2/30 _ -by other treatments, so that it is of interest to consider a BR +TY them in relation to the most discriminating experiwhere a is the coefficient of thermal expansion, PT is mental data. the coefficient of isothermal compressibility, V is the It now appears that some suitable results are provolume, Vo is the assumed molar volume at O’K, P o is ) ~ T~rturro.~ vided by the work of Bianchi, et ~ 1 . and the isothermal compressibility of the close-packed They measured the quantity molecules at O’K, B is a constant related to the external degree of freedom of the molecule, and R is the gas constant. V
v-
(v
where Pi, the internal pressure, is given by the usual equation
p -__
(:F)T -
It can be shown (eq A) that putting (dP/dT) = a/PT, we obtain, when P is small compared with Ta//3T
-P
= T(g) V
Bianchi carried lout direct measurements of (dP/dT) on several liquids over a temperature range of 20-60” and as a result values of (d In Pi/dT) vere obtained to an accuracy estimated at f10%. I n his discussion of this quantity, Bianchi2 starts from the concept that the intermolecular energy U can be represented by a term of the type a/Vn, i.e., that it is dependent on volume only. From this he concludes that (d In Pi/dlT), should be zero. To a certain extent their results confirm this conclusion in that the value of (d In Pi/dT), is very small, but the experiments also show that it is actually negative and quite measurable. We shall now consider this result in relation to the van der Waals equation as applied to liquids. Starting from the conventional van der Waals equation
we first substitute Pi for a/Vz and secondly introduce a
This equation may then be tested by using available P V T data to provide a , PT, and (da/aT), at low pressures and then calculating PO. These may then be compared with values obtained by other means. Measurements for (d In Pi/dT)v for carbon tetrachloride and benzene were published by Bianchi, et a1.,2 and values for n-octane and acetone were provided by Turtur1-0.~ I n carrying through the calculation according to eq I, it is essential t o use the values for a, PT and (da/dT), which relate to the average volumes used in the (d In Pi/dT), measurements. No great accuracy can be claimed for the quantity (da/dT),, but smooth curves of a against T (constant v) with a negative slope were obtained, and (da/dT), was given by the slope at the relevant (1) R. N. Haward, Trans. Faraday SOC.,62, 828 (1966). (2) U. Bianchi, G. Agalio, and A. Turturro, J.Phys. Chem., 69,4392 (1965). (3) A. Turturro, private communications.
Volume 72,Number 6 May 1868
CO~WKJSICATIONS TO THE EDITOR
1844 Table I: The Estimation of 0°K compressibility ( P O )from Eq I
Liquid
Benzene” n-Octaneb Carbon tetrach 1oride‘ Acetoned
Temp, QC
(d In Pi/dOt,
(daldT) V I
PO, cm2/dyne
PO, cm2/dynea
OK-1
OK-2
(this paper)
(ref I )
41 45 38.4
-0 52 x 10-3 -0.93 X -0.46 x 10-3
4.4 5.9 7.5
10-8 10-8 10-6
9
32.5
-0.36 X
1 . 6 x 10-6
15
x x x
x x 3.2 x 8
10-12 10-l2 1O-l2
X
4.6
x
pa, cm%/dyne (adiabatic) (ref 4 )
1 1 . 9 x 10-12 14.9 X
8.3
x
12.7
x
10-l2
a Data from R. E . Gibson and J. F. Kincaid, J . Amer. Chem. Soc., 60, 513 (1938). The Tait equation with their constants waa used for interpolation where necessary. Data of H. ,If. Eduljee, D. M. Newitt, and K. E. Weale, J . Chem. Soc., 3086 (1951). Tait equation used as above. Data from R. E. Gibson and 0. H. Loeffler, J . Amer. Chem. Soc., 63, 898 (1941) (as above). Data from International Critical Tables, T’ol. 111, interpolated by computed cubic equation. Difficulty was found in fitting these results either to a Tait or Huddleston equation.
temperature. The results obtained are given in Table I. The results obtained here may be conveniently compared with those given in ref 1 and by Kudryavtsev and Samgina14whose modulus is, however, adiabatic and not isothermal. I n view of the several approximations and of the rather crude model used, the agreement between the results seems reasonable. Differences from the results of Kudryavtsev cannot be due to their use of an adiabatic measurement since they generally obtained higher values of Po. In the case of acetone and octane the lower value given by the van der Waals equation1 is probably due to use of high pressure (5000-7000 atm) at the point where the equation is applied to determine Po. (This is calculated from the intercept where V = Vo.) Bridgman’s measurements at very high pressures (10,000-40,000 atm)5 certainly indicate that PO must be nonlinear with pressure over a wide range. Recently, studies of the effect of pressure on viscosity have also led to proposals that the molar volume at 0°K has a finite ~ompressibility.~~7 Hogenboom, et al.,’ have proposed that V ofor ann-C(15) alkane should be assigned a compressibility equivalent to that of the solid near the melting point, Le., PO 25 X 10l2. This value is higher than any proposed here, but the coinpressibility of the solid may well be above that of the smaller molar volume at 0°K since it does contain some free space. Nevertheless, the higher figure agrees with the requirements of the viscosity theories. However, the fact that a value of ,Boof the right order can be obtained by this method does suggest that the approach used may have some validity. Physically speaking, it appears that U is not a specific function of V . As the temperature rises a t constant volume, so does the total pressure on the molecules. I n this way the occupied volume is reduced and some eIastic energy is stored.
Universita, Genova, Italy, for his assist’ancein carrying out this work.
Acknowledgment. The authors wish to thank Dr. A. Turturro of the Institute di Chimica Industriale,
(2) D. J. Le Roy, B. A. Ridley, and K. A. Quickert, Faraday Society Discussion on the Molecular Dynamics of the Chemical Reactions of Gases, Toronto, 1967.
T h e Journal of Physical Chemistry
(4) B. B. Kudryavtsev and G. A. Samgina, Russ. J . Phys. Chem., 39, 478 (1985). ( 5 ) P. W. Bridgman, Pioc. Am. Acad. Arts Sci., 76, 72 (1948). (6) 8 . J. Matheson, J . Chem. Phys., 44, 895 (1966). (7) D. L. Hogenboom, (1987).
W.Webb, and A. J. Dixon, ibid.,
46, 2586
DEPARTMENT OF POLYMER A N D FIBRE SCIEXCE R. N. H.\WARD THEUNIVERSITY OF NANCHESTER INSTITUTEB. 11.PARKER OF SCIENCE A N D TECHNOLOGY MANCHESTER I, ENGLASD
RECEIVED FEBRUARY 7 , 1968
Comment on “Quantum Theoretical Treatment
of Equilibrium Chemical Rate Processes”
Sir: I n a recent Kote under the above title, Yao and Zwolinski‘ proposed a modified formulation of transition state theory in which the usual kT/h term in the expression for the rate constant is replaced by ~ e - ~ ~ / ~ ’ ‘ ~ / (1 - e-hv’kT), equivalent to multiplying it by the factor (hn/2kT)/sinh(hv/2kT), in which i; is the frequency of passage across the barrier and v is the absolute magnitude of the imaginary frequency i v of a harmonic oscillator corresponding to an inverted parabolic potential along the reaction path. Their approach is similar in some respects to that used by us2 in which the kT/h term is multiplied by the factor (hv/2kT)/sin (hv/2kT). I n both cases the correction factor derives from the extraction from the statistical mechanical expression for the equilibrium constant of a partition function Qso* corresponding to motion in the reaction coordinate. However, whereas our expression2 gives the (1) S. J. Yao and B. J. Zwolinski, J . Phys. Chem., 72, 373 (1968).
