J . Phys. Chem. 1989, 93, 6241-6246
6241
Water Structuring around Nonpolar Molecules As Determined by HPLC Rebecca Silveston and Bengt Kronberg* Institute f o r Surface Chemistry, P.O.Box 5607, S- I 1 4 86 Stockholm, Sweden (Received: September 19, 1988; In Final Form: February 23, 1989) The molar free energy, enthalpy, and entropy of transfer of toluene and ethylbenzene from a highly nonpolar liquid, viz., poly(dimethylsiloxane), into water have been deduced from HPLC measurements in the temperature range 3-85 OC. The HPLC system consisted of poly(dimethylsi1oxane)-coated glass beads as a stationary phase and water as a mobile phase. The results show a large and positive free energy, which is increasing with temperature, when the two probes are transferred from the polymer liquid into water. The entropy of transfer is large and negative, decreasing in magnitude with temperature. The enthalpy of transfer is continuously increasing with temperature, being negative at low temperatures and positive above ca. 12 "C. The results are interpreted in terms of water structuring around the nonpolar toluene and ethylbenzene molecules. The free energy and enthalpy of transfer are shown to consist of two contributions: one negative water structuring contribution and one positive contribution due to the large difference in chemical nature (van der Waals forces and hydrogen-bonding capability) that is enforced on the system in the transfer process. Water structuring is thus associated with large and negative entropy and enthalpy of transfer and a small and negative free energy of transfer. All three thermodynamic functions are decreasing in magnitude with temperature.
Introduction The interaction between nonpolar parts of molecules and water is an important factor in many physicochemical processes, such as surfactant micellization and adsorption' or protein denaturatiom2 Models of these processes usually involve the solubility of simple aliphatic or aromatic hydrocarbons in water, which is equivalent to the transfer of the hydrocarbon from its own nonpolar environment to the aqueous solution. At room temperature, this process is accompanied by a large and negative entropy of transfer, while the enthalpy of transfer is around zero, resulting in a large and positive free energy of transfer.' It is generally accepted that the large negative entropy is due to an increased "ordering" or "structuring" of water in the vicinity of a nonpolar solute. A very common conclusion is that the small solubility of nonpolar solutes in water is due to this structuring process. Lately, however, it has been pointed out that the relaxation of water molecules into a more structured state must also be accompanied by a large negative enthalpy, with the result that the structuring is associated with a small and negative free energy of The low solubility of nonpolar solutes, hence, is actually due to a large and positive contribution to the enthalpy of transfer, originating in the difference in chemical nature of the water and the nonpolar molecule. The latter positive contribution gives rise to a positive free energy of transfer, resulting in the low solubility of nonpolar molecules. An obvious way to verify this description and to obtain further insight into the thermodynamics of water structuring in the presence of nonpolar molecules is to study the effect of temperature on the transfer functions, since the structuring of water decreases rapidly with temperat~re.~-* In the present study, we utilize liquid-liquid chromatography as a means to obtain the thermodynamics of transfer. The stationary phase is a coating of a nonpolar liquid, viz., poly(dimethylsiloxane) (PDMS), on glass beads, and the mobile phase is pure water. The nonpolar molecules are toluene and ethylbenzene. Using this system, we obtain the thermodynamic functions for the transfer of the probe molecules from the nonpolar (1) Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological Membranes, 2nd ed.; Wiley-Interscience: New York, 1980. (2) Kauzmann, W. Adv. Protein Chem. 1959, 14, I . (3) Shinoda, K.; Fujihira, M . Bull. Chem. SOC.Jpn. 1968, 41, 2162. (4) Shinoda, K. J. Phys. Chem. 1977, 81, 1300. (5) Shinoda, K. Principles ofSolution and Solubility; Dekker: New York, 1978. (6) Shinoda, K.; Kobayashi, M.; Yamaguchi, N. J. Phys. Chem. 1987, 91, 5292. (7) Patterson, D.; Barbe, M . J . Phys. Chem. 1976, 80, 2345. (8) Costas, M.; Patterson, D. J. Chem. Soc., Faraday Trans. I 1985,8l, 2381. (9) Hvidt, A. Biochim. Biophys. Acta 1978, 537, 374. (10) Hvidt, A. Physiol. Chem. Phys. Med. N M R 1983, 1.5, 501. ( I I ) Hvidt, A. Annu. Rev. Biophys. Bioeng. 1983, 12, 1.
0022-3654/89/2093-6241$01.50/0
PDMS liquid into water. The chromatographic method has the advantage of being fast and accurate as compared to solubility measurements for these molecules, that have a very low solubility in water. We have used the concept of splitting the enthalpy and free energy of transfer into two contributions each. This splitting has been performed by several authors previo~sly.~-'~ However, the exact definition of what each contribution includes and the physical model of water during the transfer from a hydrophobic environment to water are still under discussion. We choose to split the free energy and enthalpy in terms of a temperature-dependent and -independent contribution, as this best describes our experimental results.
Thermodynamic Background The partitioning, K', of the probe between the stationary phase (PDMS) and the mobile phase (water) is defined at any temperature as the ratio of the probe concentration in the two phases. The concentration units should be expressed in moles of solute (nl) per unit volume, i.e., nlP/V' for the polymer phase and nlw/P for the aqueous phase. Here, VP and P are the volumes of the two phases. The partitioning is related to the retention volume of the probe, VR, throughI5
where Pkis the retention volume of the marker, Le., a nonretarding molecule such as a salt. The chemical potential of the probe, pl,in the stationary phase is expressed as (hI - p I o ) / R T=
In a1 = In GI
+ In y l
(2)
where p l o is the chemical potential of the pure probe and a, is the activity of the probe in the liquid. We have adopted the conventionI6 of using the volume fraction 4 as the concentration variable in expressing the activity coefficient, 7,i.e. Yl
= U'/Gl
(3)
The use of mole fraction instead of volume fraction in eq 2 and 3 is correct only when dealing with molecules of the same size. (12) Lumry, R.; Battistel, E.; Jolicoeur, C. Faraday Symp. Chem. SOC. 1982, No. 17, 93. (1 3 ) Lumry, R. In Bioenergetics and Thermodynamics; Model Systems; Braibant, A. Ed.; Reidel: Dordrecht, The Netherlands, 1980; p 405. ( 1 4) Ben-Naim, A. J . Phys. Chem. 1965, 69, 3240. (15) Scott, R. P. W. Contemporary Liquid Chromatography; Wiley-Interscience: New York, 1976. (16) Patterson, D.; Tewari, Y. B.; Schreiber, H. P.; Guillet, J. E. Macromolecules 1971, 4, 356.
0 1989 American Chemical Society
6242
The Journal of Physical Chemistry, Vol. 93, No. 16, 1989
TABLE I: Transfer Functions Gtr, Htr,and TS" for the Transfer of the Two Probes from PDMS into Water (kJ/mol) toluene
ethylbenzene
71°C
G"
ffr
TS'
G"
ffr
TS"
5 IO 15
15.1 15.5 15.8 16.0 16.2 16.4 16.8 17.1 17.4 17.6 17.8
-6.1 -1.4 0.9 2.1 3.4 4.5 6.0 7.5 9.1 10.4 11.8
-2 1.2 -16.9 -14.9 -13.9 -1 2.8 - I 1.9 -10.8 -9.6 -8.3 -7.2 -6.0
17.7 18.1 18.4 18.7 18.9 19.2 19.6 20.0 20.3 20.6 20.9
-3.3 -1.9 0.6 2.2 3.8 5.4 7.5 9.0 9.9 10.9 12.0
-21.0 -20.0 -17.8 -16.4 -1 5.2 -13.8 -12.1 -11.0 -10.4 -9.6 -8.8
20 25 30 40 50 60 70 80
50
. v
40
0
0.01
0,02
0.03
0.04 0.05 0.06
AMOUNTOFPDMS / ( g )
However, the use of mole fractions is definitely not suitable as a measure of concentration when dealing with polymer solutions. In this situation, the entropy of mixing is more appropriately described by the Flory-Huggins theory, using volume, segment, or weight fractions.16-" We therefore believe that the volume, or weight, fraction is the best concentration variable, especially since the polymer molecular weight is only approximately known.I6 When equilibrium conditions prevail, eq 2 can be applied to the polymer (p) and water (w) phases to give
In y I w- In ylP = In (4)P/QIw) = In K = G t r / R T
Silveston and Kronberg
(4)
and thus we have
G t r / R T = In (p- P k ) / P+ In [VIP(co)/VIW(m)] ( 5 ) where Gtr is the molar free energy of transfer of the probe from the stationary polymer phase to the mobile aqueous phase and VIP(,,) and VIW(m) are the partial molar volumes of the probe at infinite dilution in the polymer and aqueous phases, respectively. In this derivation, we have ignored any pressure effects. Were these to be included, then a term involving the pressure times the difference in the partial molar volume at infinite dilution of the probe in the two liquids would appear in eq 5. This term is negligible according to L o ~ k e . l ~ *In' ~our system, we find it contributes approximately only 0.1 kJ/mol to the free energy of transfer and is hence neglected in our calculations of the free energy of transfer since it is within experimental error. As seen from eq 5 , a knowledge of the partial molar volume of the probe at infinite dilution in the two phases needs to be known. The partial molar volume of benzene and toluene in water has been determined by Makhatadze and Privalov20 in the temperature range 5-80 OC. We have calculated the partial molar volume of benzene and toluene in the PDMS phase using the Prigogine-Flory theory21s22for nonpolar polymer solutions (eq 20 in ref 23) in this temperature range. The ratio of these quantities, as it appears in eq 5 , was found to be constant and equal to 1.13 for these two solutes in this temperature range. There is therefore reason to assume that the value of this ratio is valid also for ethylbenzene. Nevertheless, it is a small correction of about 0.3 kJ/mol applied to P, which is on the order of 15-20 kJ/mol (see Table I ) . I n the calculations of G" this correction is included. The enthalpy of transfer is determined from the temperature dependence of Gtr, Le., from the van't Hoff plot of Gtr/T versus l ! T . Finally, the entropy of transfer is determined from the fundamental relation GIr = IPr - TS". Experimental Section Column Preparation. The stationary phase consisted of poly(dimethy1siloxane) (PDMS), a secondary standard from (17) Karger, B. R.; Snyder, L. R.; Horvath, C. An Introduction to Separation Science; Wiley: New York, 1973; Chapter 2. (18) Locke, D. C. Adc. Chromatogr. 1968, 8, 47. (19) Locke, D. C.;Martire, D. E. Anal. Chem. 1967, 39, 921. (20) Makhatadze, G . I.; Privalov, P. L. J . Chem. Thermodyn. 1988, 20, 405. (21) Flory, P. J . Discuss. Faraday SOC.1970, 49, 7. (22) Patterson, D.; Delmas, G . Discuss. Faraday SOC.1970, 49, 98. (23) Chahal, R. S . ; Kao, W.-P.; Patterson, D. J . Chem. Soc., Faraday Trans. 1 1973, 69, 1834.
Figure 1. Dependence of retention volume of toluene on different loadings of P D M S in the HPLC columns.
Aldrich Chemical Co. (MW = 600000), coated onto nonporous glass beads (30-60 pm). The beads were prewashed with 1 M reagent-grade HNO, followed by water and chromatographic grade toluene. The PDMS was deposited onto the glass beads from a slurry of the beads in a 0.1% toluene solution. After 24 h of stirring, the toluene was evaporated in a Rotavapor and the dried beads were slurried with chromatographic grade methanol. The slurry was packed with a Magnus Scientific Instruments Co. slurry packer at 5000 psi into a 25 cm X 4.6 mm (id.) stainless steel column with methanol as the packing fluid. When the packing of the column was completed, the methanol was rinsed with deaerated water. The total amount of PDMS in the column was 0.0126 i 0.0005 g. Column Characterization. The amount of PDMS deposited onto the glass beads was determined by means of differential thermal analysis (DTA; Mettler Model TA 2000). Upon cooling, the PDMS crystallizes at -90 "C, and upon heating, melting occurs at -45 0C.24*25Hence, the PDMS sample was allowed to equilibrate at -90 "C and then heated at a constant rate of 5 OC/min. The heat absorbed in the endothermic transition at -45 "C was used to measure the amount of PDMS in the sample through a calibration with known amounts of PDMS. The mobile phase, water, was purified through the following steps: decalcination, prefiltration with activated charcoal, reverse osmosis, treatment with two mixed-bed ion exchangers, activated charcoal, and Organex, and finally a filtration through a 0.2-nm cationic nylon filter. All purification units came from Millipore Inc., except the final filter, which was delivered by Cuno Inc. The water was deaerated with helium. The probes, injected into a 20-ml loop, were dilute solutions of chromatographic grade toluene and ethylbenzene (both from Merck). The eluent was detected with a Waters 410 Millipore refractive index meter. The column temperature was controlled to 3~0.5"C. The flow rate was maintained at 1.0 f 0.05 mL/min giving a pressure of 750 f 100 psi. Analysis of the column performance gave about 400 theoretical plates, corresponding to a height equivalent to a theoretical plate (HETP) of 0.08 cm.
Results In order to assure that the probe molecules are penetrating into the PDMS phase and not just adsorbing onto the polymer surface, we have studied the retention at different PDMS loading on the glass beads,26 Figure 1. These results show that the probes are penetrating into the polymer liquid and adsorption onto the polymer surface is not of importance with the size of the glass beads used in this study. It was also necessary to measure the dependence of the specific retention volume on the probe concentration in order to find out whether the true retention volume at infinite dilution was being measured in this HPLC setup. Figure 2 shows that the specific (24) Helmer, J. D.; Polanteer, K. E. J . Appl. Polym. Sci. 1969, 13, 21 13. (25) Lee, C. L.; Johanson, 0. K.; Flaningam, 0. L.; Hahn, P. Polym. Prepr. ( A m . Chem. Soc., Diu. Polym. Chem.) 1969, 10, 131 I . (26) Gray, D.G . Prog. Polym. Sci. 1977, 5 , 1 .
The Journal of Physical Chemistry, Vol. 93, No. 16, 1989 6243
Water Structuring around Nonpolar Molecules
a 30
f
5
950
r-
' 7 v
20
i
TOLUENE
I
1
...... . . 9
IO
0
u-
g
a
600
I
0
(0
I
1
2
I
3
I
I
4
I
5
6
1
0
I
7
6
.'
-IO
CONCENTRATION / (mmoles/L )
Figure 2. Concentration dependence of the specific retention volume of
toluene. The arrow indicates the solubility limit.
i
730 ETHYLBENZENE
280
:\
300
320
TEMPERATURE /
b 30
I
340
I
360
1
(K I
ETHYLBENZENE
TOLUENE
.\
E
0
I
,
,
,
,
0
20
40
60
80
TEMPERATURE /
(
I
"C )
Figure 3. Specific retention volume of toluene and ethylbenzene as a
function of temperature. retention volume is totally independent on toluene concentration. The retention time difference between an unretarded marker, sodium nitrate, and the probe solutions, toluene or ethylbenzene, was measured from 2.6 to 85.0 "C. The retention volumes were found to be independent of the flow rate of the mobile phase, thus ensuring that equilibrium conditions prevail. The retention times were converted to volumes by simply multiplying with the flow rate. Since the flow rate was found to fluctuate slightly with time, it was deemed necessary to measure the flow rate for each run. Figure 3 shows the effect of temperature on the specific retention volume for the two probes toluene and ethylbenzene. The retention volumes are strongly temperature dependent with a maximum around 15 O C . There is also a large difference in retention volume of the two probes. The free energy, Qr, enthalpy, W ,and entropy, S',of transfer were obtained according to the procedure in Thermodynamic Background. The results are shown in Table I and Figure 4, where GIr, ff', and TS" are plotted as a function of the temperature. (Note that Table I is a representation of interpolated values at specific temperatures and not those obtained at the experimental temperatures.) The figure reveals that the free energy of transfer is large and positive, corresponding to a low solubility of the probe in water. The entropy of transfer, however, is strongly negative and decreases in magnitude with increasing temperature. The enthalpy of transfer, finally, is negative at low temperatures and positive at high temperatures. It is also apparent from the shape of the ff' and TS" curves in Figure 4 that the heat capacity of transfer from the PDMS phase to the aqueous phase at constant pressure, Cpt', is positive and decreases with temperature.
Discussion The large and negative entropy of transfer of hydrophobic solutes from a hydrophobic environment to water is generally attributed to an increased structuring of the water molecules in the proximity of the nonpolar solute^.'^^^-^^ As seen in Figure ~
~
~~
tr
100
~
(27) Frank, H. S.; Evans, M J . J . Chem. Phys. 1945, 13, 507.
-30
280
300
320
340
TS
382
TEMPERATURE / ( K )
Figure 4. Transfer functions Gtr, IF', and TS",for the transfer of (a) toluene and (b) ethylbenzene from PDMS to water as a function of temperature.
4, this structuring decreases as the temperature is increased.
Since the temperature dependence of the entropy is directly related to the heat capacity ( d P / d T = Cpt'/T),we conclude that the decreasing heat capacity with increasing temperature, observed in Figure 4, is also due to a diminishing water structuring around the hydrophobic solutes. Thus, through the definition of heat capacity of transfer, C p p dff'/dT, we also conclude that the enthalpy of transfer (and its temperature dependence) must reflect these structural effects. Concerning the entropy of transfer, it contains two contributions: a combinatorial contribution and a contribution from the structuring of water. As discussed further in Appendix I, the combinatorial contribution is close to zero in this system. Thus, Str can be considered as being only a reflection of the water structuring. As will be seen in the text below, the enthalpy and free energy of transfer are split into two contributions. One contribution is due to the water structuring and is designated H> and G,", representing the relaxation of water molecules into a more ordered state close to the nonpolar solute molecule, Le., solvation.*" This contribution is very temperature dependent and vanishes at temThe other contribution to the peratures around 160 0C.44*29930 enthalpy and free energy of transfer, H$ and G,", is attributed (28) Franks, F.; Reid, D. S. In Warer-a Comprehemioe Treatise; Franks,
F., Ed.; Plenum Press: New York, 1973; Vol. 2, Chapter 5 .
(29) Ramadan, M. S.; Evans, D. F.; Lumry, R. J . Phys. Chem. 1983.87, 4538.
(30) Evans, D. F.; Ninham, B. W. J . Phys. Chem. 1986, 90, 226.
6244
The Journal of Physical Chemistry, Vol. 93, No. 16. 1989
Silveston and Kronberg
TEMPERATURE 1 ( K ) h
0
Y
-
g
.
100
200
300
400
,
a
500
I
600
0.00
7
. Y,
e
-0.02
-0.06 c
. 9
-0.04
L
1
i
-10
Y3
.
u.
D
c: -20
9Q
z
f
transfer for toluene as a function of temperature, showing the origin of the enthalpy-entropycompensation. The full drawn curve is fitted with the use of eq 7. Figure 5. Entropy of
to the hydrogen-bonding connectivity,l* that is the large difference in the chemical nature that the probe experiences in the transferring This difference in chemical nature can be described in terms of (i) differences in van der Waals forces and (ii) a decrease in hydrogen-bonding interactions upon the introduction of a nonpolar solute into the Thus, the major contribution to Hob arises from the strong attraction between water molecules that must be overcome in the transfer Strictly, if HOfris partly attributed to hydrogen-bonding interactions, it ought to have some temperature dependence. This temperature dependence should be in the same order of magnitude as the temperature dependence of the enthalpy of vaporization. In the small temperature interval studied here, the enthalpy of vaporization changes with about 755, while the change in enthalpy of transfer is far more dramatic. Thus, we can safely consider the structuring contribution to the enthalpy of transfer to be the major cause of its temperature dependence. Thus, we have G" = Got' + Gir = Hot'
+ Hstr - TS"
(6a)
and
! -30
1
1
I
300
320
I
1
.
v
-10
9
$! L?
E z
-20
4
E
-30 260
280
340
360
380
TEMPERATURE / ( K )
Ho'r = GOtr
(6b)
We will now analyze the entropy of transfer in order to obtain information on G: and H:. Figure 5 shows that the entropy of transfer is a rapidly decreasing function of temperature. It was found that the temperature dependence is exponential; i.e., the entropy can be described by S = Ae-TfT
(7) where A and T are constants. Experimentally, T was found to be 60 f 5 K for both probes whereas A was found to be -6.5 f 0.1 kJ/(mol K) for toluene and -7.9 f 0.1 kJ/(mol K) for ethylbenzene. The structuring contribution to the free energy, G:, at any temperature T, is equal to the area under the P - T curve in Figure 5; i.e.
The quantity TS' corresponds to the area of the rectangle in this figure. The enthalpy of transfer due to water structuring, H F , corresponds to the total area in the figure; i.e.
or with the use of eq 7
G," = T s t r H:' = ( T + 7)s''
(loa)
(1 Ob) Figure 6 shows the temperature dependence of the TS", Gstr, and H," quantities. The figure reveals that the structuring contribution to the enthalpy of transfer, H:, is large, negative, and
Figure 6. Water structuring contributionsto the transfer functions, i.e., G,", H C , and TS", for the transfer of (a) toluene and (b) ethylbenzene from PDMS to water, as a function of temperature.
decreasing in magnitude with increasing temperature, as predicted by Patterson and Barbe through thermodynamic rea~oning.~ This contradicts the commonly held opinion that the structuring of water is not associated with an enthalpy change. The basis of this notion is that the experimentally observed total enthalpy of transfer is close to zero at room temperature, as is also found in this work (Figure 4). The temperature dependence of the thermodynamic quantities, however, results in another interpretation first suggested by Shinoda3v4and Patterson' and confirmed by our experimental results. Figure 6 also reveals that the free energy associated with water structuring, G:, is negative; i.e., structuring lowers the free energy of the system. This seems quite logical since otherwise structured water would not form spontaneously. We also note in Figure 6 that there is an enthalpy-entropy compensation; Le., IfP'I = lTS"l >> ICtrl. Such compensation is expected in every system where structure is broken or formed.' The reason for this enthalpy-entropy compensation can be seen in Figure 5, where the rapid decrease in SV with temperature gives rise to the small area under the 9'-T curve compared to the large area of the TS" rectangle, shown in this figure. Figure 5 is therefore an experimental confirmation that the enthalpy-entropy compensation is found in the rapidly decreasing water structuring with increasing temperature, causing the GP to be small compared to TS'. Analytically, this statement is shown by the small value of T compared to T in eq 10. The enthalpies of transfer in Figure 6 differ considerably from the enthalpies shown in Figure 4. Figure 7 shows that the dif-
The Journal of Physical Chemistry, Vol. 93, No. 16, 1989 6245
Water Structuring around Nonpolar Molecules
.
40 I
Y 7
v
...... . . . .
1
e
30
I
I
I
I
18.9
I
I
22.0
20 10
>
-
260
280
300
320
340
4 5 + L
360
5
TEMPERATURE / ( K )
Figure 7. HC as deduced from Figure 5 (ethylbenzene is not shown in Figure 5) and Figure 2 (i.e., Hotr = Wr - H Ir ) as a function of temper-
0 -10
10
15
20
25
30
FREE ENERGY OF TRANSFER / ( kJ/mol)
ature.
Figure 8. Enthalpy of transfer versus the free energy of transfer for toluene and ethylbenzene. Assuming a linear relationship, the HC
ference between the experimental enthalpies of transfer, R',and the enthalpies obtained from Figure 5, Le., H$ (=IFr- H,"), is approximately independent of temperature. This difference is attributed to all contributions other than structuring, Le., difference in van der Waals forces, etc. The values obtained are 18.8 f 0.5 and 22.0 f 0.5 kJ/mol for toluene and ethylbenzene, respectively. For the sake of clarity, we repeat that this analysis rests on two assumptions. The first is that the entropy of transfer is only due to water structuring. This implies (i) that the combinatorial entropy of transfer is approximately zero and (ii) that other temperature-dependent contributions, should they exist, alter the free energy insignificantly compared to the effect by water structuring. The second assumption in this analysis is that the T ) is continued at higher approximate exponential behavior of Sr( temperatures. We emphasize that if either of these two assumptions is in error, it would not significantly alter the temperature dependence or relative magnitudes of G:, H:, and 9' nor the interpretation given here. An alternative route to obtain the different contributions without using eq 7 is to use the enthalpy-entropy compensation phenomenon that is common in aqueous systems. Hence, a plot of enthalpy versus entropy should be linear, and an extrapolation to the intercept, 9' = 0, in such a plot will give the desired H$. However, it has been ~ h o w n ~that ' * ~the ~ enthalpy versus entropy plots for a set of data that have been obtained from the same measurements not only reflect physicochemical phenomena but also may be strongly influenced by statistical effects, due to the extensive compensation of errors that may occur. This problem can be circumvented, however, by plotting the enthalpy versus the free energy. Such a plot is shown in Figure 8. The plot displays a linear correlation, and we obtain How from extrapolation '= Rr, of the experimental line to its intersection with the line 0 Le., when S" = 0. The values for H$ obtained are 19 f 1 and 22 f 1 kJ/mol for toluene and ethylbenzene, respectively, which coincide with the values obtained from eq 6, 7, and 10, as shown in Figure 7 . Since eq 7 is an empirical fit of experimental data, it is obvious that it can be used to predict the relationship shown in Figure 8. As a check, Gf' and IF' can be developed in terms of T, 7,and A , from eq 6 , 7, and IO, giving
contribution to the enthalpy of transfer can be obtained by extrapolation to the G" = flrline.
GI' = Hot' + rAe-T/'
(1la)
and
IF' = H$
+ ( T + r)Ae-T/'
(1lb)
A plot of ( 1 1 b) versus (1 1a), at different temperatures, has only a slight positive curvature that can be approximated as linear. The accuracy of our data is not sufficient to discern whether a linear relationship or a curve with a slight positive curvature, as predicted
by eq 11, is the best fit in Figure 8. Using the Flory-Huggins expression for the chemical potential of the probe in the two phases, we find that the solubility of the probe, expressed in mole fraction, xl, can be written as
where is the interaction parameter of the probe with the polymer and V , and V, are the molar volumes of the probe and water, respectively. Since both and the molar volumes change monotonically with temperature, the maximum of the specific retention volume, shown in Figure 3, corresponds to a minimum in the solubility. For a number of hydrocarbons, toluene and ethylbenzene included, it is found that a minimum in the solubility occurs at about 290 K,33coinciding with the maximum in Figure 3. Thus, these HPLC measurements predict the same temperature dependence of hydrocarbon solubility as is found experimentally. This temperature dependence was given the interpretation3s4 in terms of water structuring, adopted in this paper.
Conclusions Liquid-liquid chromatography is a useful tool to obtain accurate thermodynamic quantities for the transfer of probe molecules from one liquid to another. The heat capacity of transfer of toluene and ethylbenzene from PDMS into water is positive and decreases with temperature. The entropy of transfer is large and negative and decreases in magnitude with temperature. The enthalpy of transfer can be split into one temperatureindependent term, which is due to the difference in chemical nature, and one temperature-dependent term, which originates in the structuring of water around the nonpolar solutes. The enthalpy of transfer due to water structuring alone is large and negative and decreases in magnitude with temperature. The free energy of transfer, due to water structuring, is small and negative and decreases in magnitude with temperature. Acknowledgment. We gratefully acknowledge financial support from the Swedish Board for Technical Development.
Appendix I In this appendix, we will discuss the combinatorial part of the entropy of transfer. In the PDMS phase, the chemical potential of the probe can be expressed in terms of the Flory-Huggins theory. Thus, the combinatorial part of the chemical potential of the probe is In @ l P + (1 - Vi/ V,)( 1 - C$~P), giving the following expression for the chemical potential at infinite dilution in a polymer of infinitly high molecular weight (plP - p l o ) / R T = In 4 1 P
(31) Exner, 0. Prog. Phys. Org. Chem. 1973, I O , 411. (32) Krug, R. R.; Hunter, W. G.; Grieger, R. A. J . Phys. Chem. 1976,80, 2335, 2341.
+ 1 + pIPE/RT
(AI)
(33) Gill, S . J.; Nichols, N. F.; Wadso, I. J . Chem. Thermodyn. 1976, 8, 445.
J . Phys. Chem. 1989, 93, 6246-6250
6246
where p i p E is the excess, noncombinatorial part of the chemical potential . The chemical potential of a hydrophobic molecule in an aqueous solution is normally expressed in terms of the mole fraction, Le., with use of the regular solution theory ( p l w-
p I o ) / R T = In x l w+ wIwE/RT
(A21
This approach is, however, questionable on two points. Firstly, the molecules are assumed to have the same size, and secondly, the molecules are assumed to be randomly mixed. The former point is easily taken into account by the use of Flory-Huggins theory. Even though this theory overestimates the combinatorial entropy, it is probably better than regular solution theory. The latter point has been discussed by Costas and Patterson,8 who point out that not all of the volume is available to the hydrophobic molecule due to the network formation by hydrogen bonding. They propose that a term, In m, should be added to the combinatorial entropy in the expression of the chemical potential, where m is the number of water molecules that form a cage around the hydrophobic molecule. Thus, using the Flory-Huggins expression
for the chemical potential at infinite dilution of the probe, we have the following: (ylw- p l o ) / R T = In
+ ( 1 - V i / V w )+ In m + p l w E / R T (A31
Equating the chemical potentials of the probe in the polymer and in the water gives Gtr/RT = (plWE - pIPE)/RT = In 41P/41w- In m
+ Vl/Vw (A41
Hence, the free energy, and thus the entropy, of transfer should be corrected for by including the two last terms in eq A4. These two terms are of opposite signs and cancel if m = exp(Vl/Vw), which in these systems would give a number between 100 and 200 for m. In any case, the correction is not crucial and would at the most be on the order of about 3-6 kJ/mol. That would displace G" and 9' curves by the same amount but not alter the general conclusions. Registry No. H,O, 7732-18-5; PhMe, 108-88-3; PhEt, 100-41-4.
Intrinsic Potential Energy Barrier for Twisting in the trans-Stilbene S, State in Hydrocarbon Solvents Jack Sakiel* and Ya-Ping Sun Department of Chemistry, The Florida State University, Tallahassee, Florida 32306-3006 (Received: January 17, 1989; In Final Form: March 30, 1989)
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Rate constants for It* Ip* twisting in the SI state of trans-stilbene in the n-alkane solvent series (H(CH2),H, n = 5-16) are treated by transition-state theory. In contrast to claims in the literature, observed activation enthalpies, AH*obad, increase with increasing n and depend linearly on E,, the solvent viscous flow activation energy: A H * , , = A H * , + aE, with A H * t = 2.85 f 0.04 kcal/mol and a = 0.39 f 0.02. This behavior is consistent with a medium-enhanced isomerization barrier model proposed earlier. Entropies of activation are also linearly dependent on E, since an isokinetic relationship exists between them and the activation enthalpies. It is concluded that A H * , , the intrinsic barrier to It* 'p* twisting, is independent of alkane solvent.
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introduction Extensive research efforts in the laboratories of photochemists and spectroscopists during the past 30 years on the trans s cis photoisomerization of the stilbenes have been The mechanism of this reaction is now well-understood and is often the starting point of discussions on cis-trans photoisomerization generally. The complementarity of trans-stilbene fluorescence and photoisomerization was established relatively early by studies, primarily in Fischer's laboratory, of the temperature dependence cis quantum of fluorescence quantum yields, &, and of trans yields, 4tc,4"and later, with the advent of laser pulse excitation, the temperature dependence of 7f.7-9Comparative quenching studies of excited stilbene singlet and triplet states obtained by
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( I ) Saltiel, J.; D'Agostino, J.; Megarity, E. D.; Metts, L.; Neuberger, K. R.; Wrighton, M.; Zafiriou, 0. C. Org. Phofochem. 1973, 3, 1. (2) Saltiel, J.; Charlton, J. L. In Rearrangements in Ground and Excited States; de Mayo, P., Ed.; Academic; New York, 1980; Vol. 3, p 25. (3) Saltiel, J.; Sun, Y.-P. Manuscript in preparation. (4) Malkin, S.; Fischer, E. J . Phys. Chem. 1964, 68, 1153, and earlier papers in this series. ( 5 ) Dyck, R. H.; McClure, D. S . J . Chem. Phys. 1962, 36, 2336. ( 6 ) Gegiou, D.; Muszkat, K . A.; Fischer, E. J . Am. Chem. SOC.1968, 90, 12. (7) Sumitani. M.; Nakashima. N.; Yoshihara, K.; Nagakura, S. Chem. Phys. f e l t . 1977, 5 1 , 183. (8) Taylor, J. R.; A d a m , M. C.; Sibbett, W. Appl. Phys. f e l t . 1979, 35, 590. (9) Good, H. P.; Wild, U . P.; Haas, E.; Fischer, E.; Resewitz, E.-P.; Lippert, E. Ber. Bunsen-Ges. Phys. Chem. 1982, 86, 126.
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direct and by sensitized excitation, respectively, established that intersystem crossing from transoid geometries, It*, is at best a minor process at ambient temperatures.'*I2 The currently accepted mechanism for trans cis photoisomerization is that twisting about the central bond occurs as an activated process in the lowest excited singlet state surface to a twisted intermediate, Ip*, which upon decay partitions itself nearly equally between trans and cis ground-state geometries. This mechanism was proposed by Saltiel following the observation that perdeuteration of the stilbene molecule has essentially no effect on the photoisomerization kinetics.13 It has k e n confirmed by numerous laser pulsed excitation studies, some of which will be considered in detail below. The origin of the barrier to It* Ip* torsional distortion has been the subject of theoretical discussions, and though the notion that it originates in a crossing,I4possibly avoided,I5 between the lowest 'B, state and a higher IA, state enjoys wide popularity, no convincing experimental proof of this hypothesis is available. Other possibilities are that the barrier is primarily inherent in the en-
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( I O ) Hammond, G . s.;Saltiel, J.; Lamola, A. A,; Turro, N. J.; Bradshaw, J. S.; Cowan, D. 0.;Counsell, R. C.; Vogt, V.; Dalton, C. J. Am. Chem. SOC. 1964, 86, 3 197. ( I 1 ) Saltiel, J.; Megarity, E. D. J . Am. Chem. SOC.1972, 94, 2742. (12) Saltiel, J.; Marinari, A,; Chang, D. W. L.; Mitchener, J. C.; Megarity, E. D. J . Am. Chem. SOC.1979, 101, 2982. (13) Saltiel, J. J . A m . Chem. SOC.1967, 89, 1036; 1968, 90, 6394. (14) Orlandi, G . ; Siebrand, W. Chem. Phys. Letr. 1975, 30, 352. (15) Birks, J. B. Chem. Phys. Lett. 1978, 43, 430
0 I989 American Chemical Society
