414
J. A. LAVELLE AND A. C. ZETTLEMOYER
Estimations of the Dispersion and Polar Force Contributions to Heats of Immersion and Interaction Energies of Organic Molecules with Rutile and Graphon Surfaces
by J. A. Lavelle and A. C. Zettlemoyer Center for Surface and Coatings Research, Lehigh University, Bethlehem, Pennsylvania (Received August 23,1966)
The theory of additivity of intermolecular forces as proposed by Fowkes has been applied to studies of the heats of immersional wetting of rutile and Graphon in organic liquids of varying polarity. For Graphon the average dispersion force contribution to the heat of immersion (hid) in a series of n-butyl derivatives was calculated to be 110 ergs/cm2. Dispersion forces alone are sufficient to account for the heat liberated in forming the Graphon-organic liquid interface. For rutile, hid was calculated to be 146 ergs/cma, but this value includes a minor contribution due to polarization of the liquid by the electrostatic field of the solid. The average electrostatic force field extending from the rutile surface was calculated to be 2.72 X lo5esu/cm2 in good agreement with previously reported values. For butanol and heptane on Graphon, the interaction energy was calculated to be due entirely to dispersion forces. Approximately 70% of the interaction energy for heptane on rutile was calculated to be due to dispersion forces and 30% due to polarization of the hydrocarbon by the rutile. For butanol on rutile, the major contribution to the adsorption energy is due to dipole-dipole interactions. The contribution due to hydrogen bonding of butanol with rutile is estimated to be less than 10% of the total interaction energy.
Introduction The heats of immersion of rutile and Graphon in organic liquids have been reported.'t2 For a series of n-butyl derivatives, the heats of immersion with rutile were shown to be an approximate linear function of the dipole moment of the wetting liquide2 For a polar solid interacting with a polar molecule, a major contribution to the total energy of interaction is due to the interaction of the dipole of the wetting liquid molecules with the electrostatic field of the solid as given by the equation
E,
=
-P F
(1)
where E, is the interaction energy between the permanent dipole of the liquid and the electrostatic field of the solid surface, p is the dipole moment of the adsorbate and, F is the average electrostatic field of the solid. The Journal of Physieal Chemistry
Zettlemoyer, et a l l 2assumed that contributions from the London dispersion forces to the net energy of adsorption were approximately constant. They attributed differences in heat of immersion values primarily to E,. The slope of the linear plot of net energy of interaction vs. dipole moment was taken to be a first approximation of the average electrostatic field strength of the rutile surface. This approach for obtaining F has been critically assessed in this l a b ~ r a t o r y . ~ Based on the theory of the additivity of intermolecular forces, Fowkes has recently developed an approach for estimating the dispersion force contribution to (1) F. H. Healey, J. J. Chessick, A. C. Zettlemoyer, and G. J. Young, J . Phys. Chem., 58,887 (1954). (2) J. J. Chessick, A. C. Zettlemoyer, F. H. Healey, and G. J. Young, Can. J . Chem., 33, 251 (1955). (3) 5. J. Chessick, J. Phys. Chem., 66, 762 (1962).
HEATSOF IMMERSION OF RUTILEAND GRAPHON IN ORGANIC LIQUIDS
heats of immersion.435 This theory suggests a method of checking the assumption that the dispersion force contribution was indeed constant for the systems rutileorganic liquids.
Application of Theory Assuming the additivity of intermolecular forces, the experimentally determined heats of immersional wetting per unit area can be expressed as the sum of the dispersion force contribution (hid), a polarization force contribution (hi"), and a contribution due to the interaction of the permanent dipole with the solid (hi') hi = h,d
+ hi* + hi'
(2)
The dispersion force contribution to heats of immersion is given by Fowkes5 as hi
d
= YL
- 2% /m YS Y L
y L d , the dispersion force component of the surface tension of the liquid, was taken to be equal to y ~ , the surface tension of the liquid. This assumption is not unreasonable since Fowkes has calculated Y L ~ values from contact angles and found for some polar organic molecules, such as bromonaphthalene, that the values are not too different from Y L . ~ The term 7sd is the dispersion force component of the surface free energy of the solid. The temperature dependence of Y~~ was estimated from the coefficient of thermal expansion using the relation that the surface tension increases as the power of the density. Thus d d y s d / d T is very small and generally amounts to about 2% of the total heat of immersion. The term ysd for Graphon is given by Fowkes as 108 ergs/cm2 . ~ of the values and for rutile as 143 e r g s / ~ m ~All needed for solving eq 3 for the dispersion force contribution to the hcat of immersion are therefore available. It is important to note that the ysd value for rutile as reported by Fowkes was obtained from heats of immersion with hydrocarbons and contains the contribution due to polarization of the liquids by the rutile surface. Heats of immersion calculated by eq 3, therefore, give values representing both the dispersion and polarization components of the heat of im. ~ the dismersion, but as Fowkes points O U ~ , ~both persion and polarization forces are proportional to the polarizability of the molecule and these two forces should be additive. Equation 2 may then be rewritten as
h,
=
hid+"
+ hi"
(4)
415
where hid+a is calculated from eq 3 neglecting any polarization contribution to y ~ ~ .
Results Tables I and I1 show the results of the calorimetrically determined heats of immersion of rutile and Graphon in organic liquids of varying polarity.' The calculated dispersion and polarization force component is given and the contributions due to permanent dipole interactions are obtained using eq 4.
Table I: van der Waals Components of the Heats of Immersional Wetting of Rutile (TiOz) at 25' (ergs/cmZ) hi, measd
Liquid
Heptane Octane Butylamine Butyl alcohol Butyl chloride Butyric acid Nitropropane Water" y ~ d=
-144 -140 -330 -410 -502 -506 -664 -550
hid+", calcd
- 144 - 147 - 145 - 139 - 143 - 143 - 15gb -65
f9 f5 f 40 =!= 1 f8 zt 11 f6 f 18
21.8 for water, ref 4.
hiM, eq 4
0 0 - 185 -271 -359 -363 -505 -485
Calculated for nitromethane.
Table I1 : Comparison of Calculated and Measured Heats of Immersional Wetting of Graphon a t 25" ( ergs/cm2) Liquid
Heptane Butylamine Butyl alcohol Butyl chloride Butyric acid Water" y~~ =
hi, measd
-103 -106 -114 -106 -115 -32.2
f3 f6 f5 f2 i.1 f0 . 1
hid,
calcd
-112 -112 - 107 -111 -110 -34.0
21.8 ergs/cm2.
Figure 1 is a plot of the net energy of adsorption (hi - hL) us. the dipole moment of the wetting liquid. The experimental values and the calculated dispersion and polarization values are shown. It is significant to note that the slope of the line is unchanged after subtracting the dispersion and polarization force component from the net interaction energy. The average electrostatic field strength ( F ) of the rutile surface is (4) F. M .Fowkea, A S T M Tech. Publ., 360, 20 (1963). (5) F. M.Fowkea, I d .Eng. Chem., 56, No. 12,40(1964). (6) F. M. Fowkes, Advances in Chemistry Series, No. 43,American Chemical Society, Washington, D. C., 1964,p 99.
Volume 71, Number 2 January 1967
416
J. A. LAVELLE-4ND A. C. ZETTLEMOYER
600
(7)
-3
>
Since the calculated average electrostatic force field for rutile was found to be the same as that calculated by Zettlemoyer, values for E, and E, are the same as previously reported, When the values of E, are subtracted from E d + , (obtained from h i d + , h ~ )E, d values for rutile systems are obtained. There is no detectable electrostatic force field for Graphon; therefore, the E d values may be calculated directly from hid. Table 111 shows E d values for Graphon in heptane and in butanol. These values were calcuE, from the lated by Zettlemoyer2 by subtracting E, net energy of adsorption. These values are compared with those obtained directly from calculated heats of immersion using the method of Fowkes. Considering the assumptions made, the agreement is quite good.
LOO
M
0
v
r:
2 0
300
l d
8
-P
H
w
+
200
4!
w
%
2
100
0
Table 111: Comparison of Calculated Dispersion Energies for 3
2
1
0
Heptane and n-Butyl Alcohol on Graphon ( ergs/cm2)
Dipole Mment System
Figure 1. Polar and dispersion force components of the net interaction energy as a function of dipole moment of various polar molecules on rutile: 0, experimental; A, E,; 0,E d f E,.
Heptane on graphon Butanol on graphon
calculated to be 2.72 X lo5 esu/cm2 as previously determined by Zettlemoyer2 and estimated by de Boer.'
The Contributions of van der Waals Forces to the Adsorption Energy With the assumption that vertical, lateral, and other internal interactions of the molecules in the adsorbed state are the same as in the liquid state, the total energy of interaction between adsorbed polar molecules and a heteropolar surface is given by2 E.4
- EL = E d
+ E, f E,
(5)
where E A - ELis the net integral energy of adsorption, Ed is the contribution due to London dispersion forces, E, is the contribution due to polarization of the molecule by the field of the solid, and E, is defined by eq 1. The various expressions developed for these energies have been summarized by de Boer? The most useful forms of these equations for the purpose of this paper are The Journal of Physical Chemistry
Zettlemoyer, et a1.2
Method of Fowkes
67 66
64
68
Table IV shows the various calculated interaction energies for the rutile-heptane and rutile-butanol systems. For heptane on rutile, the quantity E d + , obtained by the method of Fowkes is 95 ergs/cm2. E,, as calculated from eq 7, is 30 ergs/cm2 and upon subtracting this quantity from Ed+,, an E d value of 65 ergs/cm2 is obtained. This value compares favorably wit,h the 62 ergs/cm2 obtained by Zettlemoyer.2 For n-butyl alcohol on rutile, E, (obtained from ENET- Ed+,) is 271 ergs/cm2. This result represents an energy liberation of 25 ergs/cm2 in excess of that calculated from eq 1. This excess in the polar contribution is attributed to a hydrogen bonding interaction of the butanol with the rutile surface ( E H B ) . Based on this assumption, E d has a value of 70 ergs/ cm2, which is consistent with the magnitude of the other E d values. When 25 ergs/cm2 is subtracted from E d given by Zettlemoyer, who did not assess the hydrogen-bonding contribution, a value of 69 ergs/ ~
(7) J. H. de Boer, Aduan. Colloid Sci., 3 , 1 (1950).
HEATSOF IMMERSION OF RUTILEAND GRAPHON IN ORGANIC LIQUIDS
Table IV: Comparison of Calculated Interaction Energies for Heptane and n-Butyl Alcohol on Rutile (ergs/cmz) EHB
Method
0
0 0
Zettlemoyer2 Fowkes
21 21
246 246
0 25
21
246
25
Zettlemoyer Corrected for H bonding Fowkes
System
Ed
Ea
Heptane on rutile Heptane on rutile
62 65
30 30
Butanol on rutile Butanol on rutile
94 69
Butanol on rutile
70
E,
0
cm2is obtained for E d . This result is in excellent agreement with our E d value of 70 ergs/cm2. When allowance is made for hydrogen bonding, better agreement of Zettlemoyer’s original E d value with the assumption that Ed is approximately constant is obtained. When 20-25 ergs/cm2 as the hydrogen bonding contribution is subtracted from the E , values in Table I, the slope of the linear curve in Figure 1 is not significantly altered. I n fact, it can be argued that this procedure gives a better fit for butanol and butyric acid. From studies of water adsorption on high-area rutile (72 mz/g), Micales has estimated the minimum number of hydroxyl sites to be about 1 X 1014 sites/cm2. The proposed mechanism for this adsorption is that one water molecule reacts with one oxygen atom on the rutile surface to give two hydroxyl sites. Thus the minimum number of oxygen sites per cm2 of surface is about 5 X l O I 3 . Allowing 5 kcal/mole for the energy
417
liberated during the formation of a hydrogen bond at these sites, a value of 17 ergs/cm2 is estimated for the minimum contribution of hydrogen bonding to the total interaction energy. This result is in the range of the value of 20-25 ergs/cm2 that we suggest is involved in the interacting of butanol with rutile.
Heats of Immersion in Water As shown in Table I, the polar contribution (hi’) to the heat of immersion of rutile in water is considerably higher than one would predict on the basis of its dipole moment. This result is strong evidence for the presence of an additional polar interaction between water and rutile most probably in the form of hydrogen bonding. In Table 11, the excellent agreement between measured and calculated heats of immersion for Graphon in water indicate that only dispersion force interactions are operative at this interface. Indirectly, then, the value of 21.8 ergs/cm2 calculated by Fowkes6 as the dispersion component of the surface t,ension of water appears to be an excellent approximation. Acknowledgment. The authors wish to express their appreciation to F. M. Fowkes for his aid in determining the temperature coefficient of -ysd for rutile and to the Technical Association of the Graphic Arts and the Litho Chemical and Supply Co. for their financial support in the form of the Thomas R. Caton Fellowship for J. A. L. ( 8 ) F. J. Micale, Ph.D. Thesis, Lehigh University, 1965.
Volume 71 Number 8 January 1987 ~
