914
F. R. MCFE~LY AND G. A. SOMORJAI In cmc =
-
___ ( " @ ) + K
(4) 1 + K , kT where m is the number of carbon atoms in the chain, w is the free energy difference per methylene group between micellar state and singly dispersed state, K and K , are the experimental constants, T is the absolute temperature, and k is the Boltzmann constant. K, and K are determined experimentally from the change of cmc with the concentration of the gegenions and the change of cmc with the number of carbon atoms in a paraffin chain. The free energy difference of transferring a -CH2- group from aqueous environment to micellar aggregate is estimated to be 1.08kT for ordinary surfact a n t ~ and ~ ' that for -CF2- is extimastedto be 1.6kT from __.
the change of the cmc values with the fluorocarbonchain length. As the K value in eq 4 does not change much with the kinds of surfactants, the cmc of a fluorinated surfactant is close to that of an ordinary surfactant whose hydrocarbon chain length is about 1.5 times longer than the fluorocarbon ~ h a i n . ~ 9 (27) P 37-42, eq (1.44)and (1.45)in ref 19. (28) K. Shinoda, Bull. Chem. SOC. Jap., 26, 101 (1953). (29) Tables of surface tension and solubility data will appear following these pages in the microfilm edition of this volume of the journal. Single copies may be obtained from the Business Operations Office, Books and Journals Division, American Chemical Society, 1155 Sixteenth St., N.W., Washington, D. C. 20036,by referring to author, title of article, volume, and page number. Remit check or money order for $3.00 for photocopy or $2.00 for microfiche.
Studies of the Vaporization Kinetics of Hydrogen-Bonded Liquids by F. R. McFeely and G. A. Somorjai* Inorganic Materials Research Division, Lawrence Berkeley Laboratory, and Department of Chemistry, University of California, Berkeley, California 947.80 (Received July $3,1971) Publication costs assisted by the U . S . Atomic Energu Commission
The vacuum evaporation rates of glycerol, ethylene glycol, and triethylene glycol have been measured in the temperature range 5-50' using a microbalance. The activation enthalpies of vaporization of the three liquids were found to be different from their enthalpies of vaporization. The vacuum evaporation rates for glycerol and triethylene glycol were about one-third of the maximum rate that can be calculated from the vapor pressures, and one-twentieth of the maximum rate for diethylene glycol. It appears that breaking one or more hydrogen bonds at the surface is the rate-limiting step in the mechanism of vaporization of these largely hydrogen-bonded liquids.
Introduction To date there have been many studies of the vaporization kinetics of single crystal surfaces. These investigations have revealed a variety of vaporization mechanisms.I For some of the solids the desorption of loosely bound surface species was rate limiting (most metals). For other compounds, bond-breaking at well-defined surface sites, surface chemical reactions, association or dissociation were rate limiting. I n cases where desorption of molecules at the vaporizing surface was not the rate limiting step, the observed vaporization rate was frequently found to be less than the maximum possible rate, J,,,c, that can be calculated from the kinetic theory of gases. The vaporization coefficient av = Jobsd/Jmaxhas been used to indicate the magnitude of the deviation of the observed rate, J 0 b s d , from the maximum rate. I n contrast, the vaporization kinetics of liquids have not been investigated. WyllieZhas measured the vacThe Journal of Physical Chemistry, Vol. 76, No. 6, 1078
uum vaporization rates of several liquids at one temperature and has thus obtained values for the vaporization coefficient cyv. However the lack of information about the activation enthalpy of vaporization, AH,*, which can only be obtained from studies of the vaporization rates as a function of temperature, precludes any deduction of the vaporization mechanism. We have studied the vacuum vaporization rates of glycerol (CH20HCHOHCH20H), diethylene glycol (CHZOHCH~OCH~CH~OH), and triethylene glycol (CHZOHCH~OCH~CH~OCH~CH~OH) in the temperature ranges 18-50', 5-30', and 10-40°, respectively. From the data the vaporization rates and AH,* for each' liquid were obtained. The experimental results indicate that the breaking of a specific number of hydrogen bonds may be the rate limiting step in each case. (1) G.A. Somorjai and J. E. Lester, Progr. Solid State Chem., 4, 1 (1967). (2) G.Wyllie, Proc. Roy. Sac., Ser. A , 197,383 (1949).
915
VAPORIZATION KINETICSOF HYDROGEN-BONDED LIQUIDS
Experimental Section The vacuum vaporization experiments were carried out using a Cahn microbalance mounted in a vacuum chamber. The weight change of the balance was displayed on a recorder as a function of time so that the weight of the vaporizing sample could be monitored continuously. The balance could measure weight changes of less than 10 pg. The liquid that was to be vaporized (spectrograde for glycerol, and reagent grade for the two glycols) was placed in a cylindrical aluminum sample holder and Torr for a was maintained a t a pressure of 5-50 X period of up to 5 hr to remove dissolved gases and other more volatile impurities (water, etc.), Since degassing of the liquid samples was carried out in the vaporization chamber the samples could be transferred onto the microbalance in 30 sec thus eliminating any possibility of recontamination. The sample was then placed on the balance and the chamber evacuated by means of an oil diffusion pump to an ambient pressure of -5 X 10-6 Torr. At this pressure, the flux of vaporized or ambient molecules striking the vaporizing liquid surface is negligible. During the experiments the temperature of the liquid was monitored by a 0.005-in. copper-constantan thermocouple placed in the liquid. We were able to place the thermocouple directly on the vaporizing surface where it was held by the surface tension. I n order to assure that there would be no surface cooling the total vaporization rates were kept lower than rates reported in single crystal vaporization studies where no temperature gradients across the vaporizing sample could be found.3 [During the vaporization of NaCl crystal surmol/cm2 min were meafaces rates as high as 4.8 X mol/cm2 min, the rate sured as compared to 0.7 X measured for glycerol at 34", and only the two highest temperature rate measurements for diethylene glycol exceeded the NaCl vaporization rate. Although the activation enthalpy of sublimation of NaCl was much higher than for any of the liquids in this study the temperature of the solid surface was within 0.25" of the bulk temperature. 1 While diethylene glycol cooled from 22' to 5" and triethylene glycol to 10" due to heat loss by vaporization, the temperature measured by the thermocouple was found to be independent of its position in the crucible. It therefore appears that under the given experimental conditions there was no detectable temperature gradient between the surface and the bulk and that we therefore had an accurate measure of the temperature of the vaporizing surface. The liquid was heated by radiation from a coil of nichrome resistance wire placed near the sample. The liquid was maintained at a constant temperature within A0.2" by means of a variable gain feedback control unit. Reproducible steady state vaporization rates a t as many as five different temperatures could be measured before the sample surface receded significantly
,
10.0
\
I
\
\
I
I
',\rh~~=?\.O
M o x i m u m rate kcnl /mole
\
t 0.1
3.1
3.2
3.3
IO"
34
T 'K
Figure 1. Key: -, vacuum Vaporization rate of glycerol; - _ ,_maximum rate;6 +, determination by Heideger and Boudart.
into the holder. The evaporation rates were measured by both starting at low temperature and increasing the temperature and also by starting at high temperature and decreasing the temperature. The vacuum evaporation rates were reproducible regardless of the thermal history of the sample. Fifty vaporization rates were measured with the various glycerol samples, forty were made using diethylene glycol, and thirty-five using triethylene glycol in the indicated temperature ranges.
Results Figure 1 shows a plot of the logarithm of the evaporation rate (mg/cm2 min) as a function of the reciprocal temperature for glycerol. The solid line indicates the experimental vacuum vaporization rate, while the dotted line represents the maximum rate predicted by the kinetic theory of gases using the well-known Langmuir equation4 J(mg/cm2 min) = P , , / ( ~ ~ M R '" T) using the equilibrium vapor pressure data of Stedman.5 Here Peq is the equilibrium vapor pressure, M is the molecular weight of thevapor (assumed to be monomer), and R and T have their usual meaning. The isolated point on the graph represents the vacuum vaporization rate of glycerol as calculated from the data obtained at a single temperature by Heideger and Boudart.'j Figures 2 and 3 give the vacuum vaporization rates of diethylene and triethylene glycol, along with the maximum rates calculated from the equilibrium vapor pressure data of Gallaugher and Hibbert.' The equi(3) J. E. Lester, Ph.D. thesis, University of California, Berkeley, 1967. (4) I. Langmuir, J. Amer. Chem. Soc., 3 5 , 931 (1913). (5) D . F. Stedman, Trans. Faraday Soc., 24,289 (1928). (6) W. J. Heideger and M. Boudart, Chem. Eng. Sci., 17, 1 (1962). (7) A. F. Gallaugher and J. Hibbert, J . Amer. Chem. SOC.,59, 2523 (1937). The Journal of Physical Chemistry, Vol. 76, No. 6, 1972
916
F. R. MCFEELY AND G. A. SOMORJAI ~~
~~
Table I: The Heat of Vaporization, AH,,, the Activation Enthalpy of Vaporization, AH,*, and the Evaporation Coefficient, a,,(30O0K),for Giycerol, Diethylene Glycol, and
Triethylene Glycol
Glycerol Diethylene glycol Triethylene glycol
-
AH”,
AH”*,
kcal/mol
kcal/mol
aV(3000K)
21.0 12.5 17.0
17.1 16.8 18.4
0.34 0.05
0.46
10.0
m u u m evaporation rate
1.0
3.3
3.5
3.4
3.6
I O / T’K
Figure 2. Key: -, vacuum vaporization rate of diethylene glycol; - - -, maximum rate.’ 10.0
I
\
I
\
\
Maximum rate
t
Vacuum evaporatio
-
0.I
1
1
librium heats of vaporization, AH,, and the experimentally determined activation enthalpies, AH,* for all three Iiquids are summarized in Table I, along with a,(300°K), the ratio of the observed vacuum evaporation rate to maximum rate for each of the liquids at 300°K. It should be noted that a, is not constant throughout the studied temperature range due to the difference in AH, and AH,*.
have devised a method of separating these two major contributions. The interaction energy due to dispersion forces is estimated by the heat of vaporization of a compound in which methyl groups are substituted for the hydroxyl groups. For example the dispersion force contribution for glycerol is taken to be the AH, of 3methylpentane. The hydrogen bonding contribution is then accounted for using a semiempirical parameter, 6(OH), the hydrogen bond energy increment per OH group. For the purposes of our analysis we chose 8(OH) = 4.3 kcal/mol since that is the average reported value of the hydrogen bond energies for alcohols given by Pimente19 and since that value fits the data well. The predicted enthalpies of vaporization with varying hydrogen bonding contributions (assuming the additivity of hydrogen bond energies) are shown in Table I1 along with the experimental enthalpies and activation enthalpies of vaporization. The homologous compounds used to estimate the dispersion force contribution to A H , were, for glycerol, 3-methylpentane, for diethylene glycol, dipropyl ether, and for triethylene glycol, dipropoxyethane. The heats of vaporization of 3-methylpentane and dipropyl ether are given by Jordan.10 Unfortunately we could find no reliable data for dipropoxyethane, but judging by the variations in heats of vaporization of similar compounds we can be reasonably confident that its heat of vaporization is Table 11: Comparison of the Enthalpies and Activation Enthalpies of Vaporization with the Enthalpies of Vaporization Calculated by Adding Different Hydrogen Bond Contributions to the Enthalpy of Vaporization of the Homologous Molecules A H H AHH
Glycerol Diethylene glycol Triethylene glycol
AHH+
AHH
b(0H)
2S(OH)
38(OH)
8.7
12.3 13.0
16.6 17.3
>8.7
>13.0
>17.3
8.0
+
AHH+
20.9 ...
AHV
AH”*
21.0 17.1 12.5 16.8 17.0 18.4
Discussion In the three organic liquids studied, the energy binding a molecule to its neighbors at the liquid surface is primarily due to hydrogen bonding and attractive interactions through dispersion forces. Bondi and Simkins The Journal of Physical Chemistry, Vol, 76, No. 6 , 1979
(8) A. Bondi and P. J. Simkin, AIChE J . , 3,473 (1957). (9) G. C. Pimentel and A. L. McClellan, “The Hydrogen Bond,” W. H. Freeman, San Francisco, Calif., 1960. (10) T. E. Jordan, “Vapor Pressures of Organic Compounds.” Interscience, New York, N. Y.,1954.
VAPORIZATION KINETICSOF HYDROGEN-BONDED LIQUIDS greater than that of dipropyl ether by no more than 1-2 kcal/mol. Inspection of Table I1 reveals that the three liquids studied have vaporization energy requirements that are distinctly different. For glycerol, which exhibits the strongest total hydrogen bonding, AH,* < AH,. Thus the activation enthalpy of vaporization is less than the total enthalpy of vaporization. It is apparent from Table I1 tahatthe enthalpy of vaporization reflects the breaking of three hydrogen bonds. It is also apparent that the activation enthalpy corresponds to the breaking of only two hydrogen bonds. It is assumed that the molecules vaporize as monomers. For the vaporization of diethylene glycol AH,* > AH,. There is strong experimental evidence that this molecule exists in a ringlike form caused by internal hydrogen bonding.
Its enthalpy of vaporization AH, = 12.5 kcal/mol is appreciably smaller than that for ethylene glycol (17.0 kcal/mol) .7 Similarly the entropy of vaporization at the boiling point indicates weaker association in liquid diethylene glycol (AS, = 24.14 e.u.)' than in liquid ethylene glycol (AS, = 29.0 e.u.)? or triethylene glycol (AS, = 30.9 e.u.) .' Thus vaporization near equilibrium is likely to require the breaking of only one hydrogen bond per molecule, in addition to overcoming the attractive dispersion forces between the molecules in the liquid. The activation enthalpy of vaporization, however, indicates a much greater energy requirement (16.8 kcal/mol) for breaking the molecule away at the vaporizing surface. This larger energy requirement would indicate that two hydrogen bonds must be broken before the molecule could vaporize into vacuum. For triethylene glycol (CH,OHCHzOCH&H,OCH,CH20H) the activation enthalpy of vaporization is only slightly larger (18.4 kcal/mol) than the heat of vaporization (>17.0 kcal/mol) .' Also this liquid has a large evaporation coefficient. The breaking of two hydrogen bonds is clearly necessary for vaporization to occur, both in equilibrium and in vacuum. The less than unity evaporation coefficient indicates that although the energetics of vaporization far from equilibrium are not much different from the equilibrium case, the surface concentration of molecules that may vaporize is less than their surface concentration a t equilibrium. Since the presence of minute impurities a t the vaporizing surface that could block the vaporization cannot be ruled out, a more detailed analysis of this effect would not be useful. Studies of the vaporization of ice single crystalsll have revealed that the breaking of one hydrogen bond
917
can be a rate limiting step in the sequence of reaction steps leading to the vaporization of water molecules. At low temperatures ( 5-SO"), AH,* = AH, = 12.2 kcal/mol and a, = 1. This value reflects the energy necessary to break two hydrogen bonds. However, above -45" AH,* approaches the values of 'lzAH, and a,
