J. Phys. Chem. 1991, 95, 431-437 monomer-aggregate equilibrium. However, it should be noted that the range of porphyrin concentrations utilized in this study for both the 'H NMR and ESR experiments was small (10-4-10-3 M) and the data therefore do not provide definitive evidence which would rule out the possibility that a stable aggregate of the tetracationic porphyrin (such as a true dimer) might be formed under
43 1
the above solution conditions. Nevertheless, the results in this work clearly demonstrate the presence of only monomers in SDS solutions.
Acknowledgment. The support of the National Science Foundation (Grant CHE-882298 1 ) is gratefully acknowledged.
Contribution of Hydrogen Bonds to Apparent Molecular Mobility in Supercooled o-Sorbitol and Some Polyols Motosuke Naoki* and Satoshi Katahira Physical Chemistry Section, Bioscience Department, Faculty of Engineering, Gunma University, Kiryu. Gunma 376, Japan (Received: January 24, 1990; In Final Form: July 5, 1990)
The dielectric relaxation in the supercooled D-sorbitol was measured and studied together with that in glycerol and isomeric butanediols. Apparent energies of activation incorporate the energies associated with the equilibrium rearrangements of hydrogen bonds. A macroscopic way to analyze the contribution from hydrogen bonds is proposed, which explains well the peculiar properties of the molecular mobilities in associated liquids. The contribution from hydrogen bonds plays a significant role in the pressure variation of the molecular mobility and alters considerably the apparent volume of activation. In the temperature variation of the molecular mobility, the contribution from hydrogen bonds is about 30%. The decomposition rates of hydrogen bonds with temperature and pressure are estimated.
Introduction Natures of the molecular mobilities are frequently discussed by expressing them in terms of the quantities with energy dimensions such as the energy of activation. If the molecular mobility is associated with the configurations of hydrogen bonds, we may apparently observe the equilibrium change in the energy due to the change in the configurations of hydrogen bonds as the energy of activation. That is, we usually determine the enthalpy of activation from temperature variations of the molecular mobility, but it may contain the energy pertaining to the change in the number of hydrogen bonds with temperature. Similarly, the magnitude of pressure variations of the molecular mobility expressed as the volume of activation may contain the energy pertaining to the change in the number of hydrogen bonds with pressure. Therefore, when natures of the molecular mobility are properly analyzed, information on the configurations of hydrogen bonds which associate intimately with the molecular mobility may be given. This is the object of the present work. In liquids of molecules with several hydrogen bonds, each molecule is bound by transient long chains and/or networks constructed by hydrogen bonds, and its molecular motion is highly depressed. Since the energy of hydrogen bonds in alcohols is only several times as large as the thermal energy near room temperature, some slight decomposition may always exist. Changes in the number of hydrogen bonds with temperature and pressure lead to reconstructions of the transient long chains and/or networks and will affect the molecular mobility. Other than this contribution, it may give rise to the contribution from conformations pertaining to the intramolecular rotations in itinerant chains and/or three-dimensional networks constructed by hydrogen bonds as well as in liquids of permanent linear or network polymers. Dielectric properties of alcohols and water have widely been studied, and many kinetic theories to explain their relaxations have been applied.' The model in which the factor determining the molecular mobility is the number of molecules with several successive hydrogen bonds4 might be an approximation for water, whose overall van der Waals intermolecular potential energy per ( I ) For instances, see refs 2-4. (2) Hassion, F. X.;Cole, R. H. J . Cfiem.Pfiys. 1955, 23, 1756. (3) Sagal, M. W. J. Cfiem.Pfiys. 1962, 36, 2437. (4) Bertolini, D.; Cassettari, M.; Salvetti, G. J. Chem. Pfiys. 1982, 76, 3285.
0022-3654/91/2095-0431$02.50/0
molecule is much lower than the energy of hydrogen bond (ca. 10%). The associated molecules of which corresponding molecular liquids boil near room temperature have usually almost the same magnitude of the van der Waals potential energy per molecule as that of one hydrogen bond. In this case, the size of each molecule also may be a significant factor determining the molecular mobility. In the present work, we propose a macroscopic way to analyze the contributions above by adopting a simple activation process and study the molecular mobility in D-sorbitol, together with that in glycerol obtained by Johari and Whalley5 and in butanediols by SagaL3
Experimental Section D-Sorbitol of the highest grade was purchased from several companies, and every sample was heated to 160 OC and supercooled to room temperature. The most stable and colorless sample (Nakarai Chemical Ltd.) was used. The original sample melted to a slightly milk-white liquid and showed small endothermic shoulders near 70 and 110 OC in the DSC (differential scanning calorimetry) chart. After drying under vacuum at 140 OC for 2 h, the sample became transparent and the shoulders in the DSC chart vanished. In the present experiment, after drying under vacuum at 140 OC over 3 h, the liquid sample was loaded into the pressure dielectric cell, the details of which are shown elsewhere.I2 Then the sample and the cell were evacuated for an hour to remove the bubbles on the electrodes, the temperature was lowered to room temperature, the supercooled liquid region where crystallization rarely occurs, and the cell was set in the pressure vessel. The vessel was cooled to 0 OC,and the pressure was set to the pressure intended, Le., 0.1 and 78.5 MPa. The temperature was raised in steps of about 2 "C and held with an accuracy of f0.03 OC inside the pressure vessel by controlling the temperature of the ethylene glycol/water bath to f0.05OC. Johari, G. P.; Whalley, E. Faraday Symp. Chem. SOC.1972, 6, 23. Naoki, M.; Matsushita, M. Bull. Chem. SOC.Jpn. 1983, 56, 2396. Atake, T.; Angell, C. A. J. Pfiys. Cfiem. 1979,83, 3218. Williams, G.; Watts, D. C. Trans. Faraday Soc. 1980, 66, 80. (9) Davidson, D. W.; Cole, R. H. J . Cfiem. Phys. 1951, 19. 1484. (IO) Angell, C. A.; Smith, D. L. J . Pfiys. Cfiem. 1982, 86, 3845. ( I 1) Angell, C. A,; Stell, R. C.; Sichina, W. J . Pfiys. Chem. 1982, 86,
(5) (6) (7) (8)
1540. (12) Naoki, M.; Endou, H.; Matsumoto, K. J. Pfiys. Cfiem.1987,91,4169.
0 1991 American Chemical Society
Naoki and Katahira
432 The Journal of Physical Chemistry, Vol. 95, No, 1. 1991 51
r - - - - I ’ ’ O
I
1
T
41
3’ W
4
2
20
11
I
i
I
01 280
1
1
10
1
300
2 90 T
/
310
K
Figure 2. Variations of the dielectric relaxation magnitude (At), the
dielectric constant at high-frequency extreme (e-), and the distribution parameter of the Williams-Watts decay function (0)for D-sorbitol. Empty symbols are for 0.1 MPa and closed symbols for 78.5 MPa. I
I
2
3
1
log
4 f / Hz
I
5
Figure 1. Examples of the complex dielectric constants of D-sorbitol as a function of logarithmic frequency. Empty circles are for 0.1 MPa and
closed circles for
78.5
0 1
MPa.
At each temperature step, the electric capacitance and dissipation factor were measured in a frequency range of 0.1-100 kHz by a General Radio 1620-A capacitance measuring assembly. The dielectric cell was not a type of simple parallel plates, and the geometrical dielectric constant in a vacuum, Co, and its dependence on temperature and pressure were determined by the measurements of the electric capacitance C and dissipation factor D for two reference samples of benzene (Uvasol grade, Merck) and methylene chloride (UV grade, Wako Chemical Co.) over the present experimental range by CO = [I/(tM
- tB)][CM/(I + DM2) - cB/(l + DeZ)] (1)
where the subscripts B and M indicate benzene and methylene chloride, respectively, and t B and cM are the static dielectric constants of which values were referred to the existing literature data.’*Is The dielectric constant t‘ and loss t” of D-sorbitol were determined by e’
=
eB
+ (I/cO)[c/(I+ D2)- cB/(1 + DeZ)]
e”=(I/cO)[cD/(I +@)-CBDB/(l +OB2)]
(2)
(3)
The data of benzene were always referred to correct the instrumental stray capacitance and conductance. The experimental uncertainties in the absolute value of the dielectric constant were
*o.
I%.
Experimental Results Examples of e’ and e” are shown as a function of logarithmic frequency in Figure I . The static dielectric constant, to, and the dielectric constant at the high-frequency extreme, e,, were obtained from extrapolations of the complex plane plots of e’ and e”, i.e., for to, by using the double-decay function proposed by Williams and Watts,* and for e,, by adjusting a skewed arc (@= 0.14) by Davidson and Cole.9 The dielectric magnitude, At eo - e,, and t, are shown as a function of temperature in Figure 2 and AE as ~~
(13) Vjj, J . K.; Scaife. G. S.J . Chem. Phys. 1976, 64, 2226. (14) Sinner. J . F.;Cussler, E. L.; Fuoss, R. M . J . Phys. Chem. 1968, 7 2 , 1057. ( 1 5 ) HandBook of Chemistry and Physics, 54th ed.; CRC Press: Boca Raton, FL, 1973-1974; p E-56.
2 01
086
1
I
1
I
090
088 Tg
/
I
1
092
1
Io
0%
T
Figure 3. Logarithmic frequencies of the maximum dielectric loss and the dielectric relaxation magnitude as a function of reciprocal temperature reduced by the glass transition temperature for D-sorbitol. Empty symbols are for 0.1 MPa and closed symbols for 78.5 MPa.
a function of reciprocal temperature in Figure 3 where the temperature is reduced by the glass transition temperature, T . The dilatometric Tg is 264.0 K, and TBat 78.5 MPa calculatei from the data obtained by Atake and Angel1 (dT,/dp = 0.043 K/MPa)’ is 267.4 K. Since the dielectric dispersion of D-sorbitol is very broad as shown in Figure 1 (the half-width of t” of sorbitol is about 3.4 decades, compared with a typical width, e.g., for o-terphenyl of about 2.1 decades), the experimental errors inherent in the extrapolation of the complex plane plots are about 7% in At. At increases with temperature and decreases with pressure even if it is plotted as a function of Tg/T in Figure 3. The variations of At with temperature and pressure are not similar to those of the molecular liquids represented by the logarithmic frequency of the maximum loss, logf,,, which are approximately superposed by Tg/T. Generally, At for molecular liquids and several alcohols decreases with increasing temperature approximately as 1 / T due to the thermal scattering of molecular orientations. As is discussed in the following sections, the number of hydrogen bonds in D-
Molecular Mobility in Supercooled D-Sorbitol
The Journal of Physical Chemistry, Vol. 95, No. 1 , 1991 433
TABLE I: Vogel Parameters of D-Sorbitol in Eq 1
p. MPa
A
B, K
To,K
STD
T region, K
0.1
31.41 39.61 32.929
1350.2 2513.3 1741
228.0 210.4 224
0.018 0.043
285.2-298.6 289.5-302.9 272-309"
78.5 0.1
OAngell and Smith (ref IO).
sorbitol is considered to decrease only weakly as the temperature and pressure increase. Therefore, the origin of the dielectric dispersion of D-sorbitol may not be interpreted by the change in the number of hydrogen bonds alone. Changes in the electric field surrounding each molecule need to be considered in detail. The dielectric loss reduced by its maximum, are apparently superposed, and the resulting master curve is shown in Figure 4, in which the Williams-WattsE and the Davidson-Cole9 equations are drawn. The two empirical distribution equations do not represent well the relaxation spectrum in the supercooled sorbitol. Variations of the distribution parameter in the Williams-Watts equation with temperature and pressure are small as shown in Figure 2. For smoothing the dependence of logf,,, on temperature in Figure 3, the parameters of the following Vogel equation were determined by the least-squares regression
1
-2
0
-1
2
1
log ul7
Figure 4. Master curve of the reduced dielectric loss against log UT (= logf/jm,) for D-sorbitol. Empty symbols are for 0.1 MPa and closed symbols for 78.5 MPa. Solid line is the Williams-Watts equation with j3 = 0.37, and broken line is the Davidson-Cole equation with j3 = 0.1 3.
1
300,
(4)
In4=A-B/(T-To)
where the average mobility 4 is taken as 4 = 2?rf,,. The resulting values of the parameters are listed in Table I. The present experimental range is very narrow, and extrapolations of the Vogel equation, i.e., the physical significances of the parameters A, B, and To,are meaningless. Equation 4 has been used to calculate the energics of activation. A simple activation process is expressed by
4 = 4- exp(-G*/RT)
(5)
where G* is the Gibbs energy of activation. The usual activation variables derived from eq 5, here designated as the "apparent" activation variables, are expressed byI2 H*app = papp
-R[a In 4 / 8 ( 1 / 7 9 1 p
(6)
= -RT(a In 4 / a ~ ) ~
E*app
=
H*app
(7)
-ppapp
(8)
E* v,app = E * a p p - pi p a p p = -R[a In + / a ( l / 791Y
0285
(9)
where pi is the internal pressure, Htappthe apparent enthalpy of activation, Papp the apparent volume of activation, ESaPPthe the apparent apparent internal energy of activation, and energy of activation at constant volume. They are plotted in Figure 5, and thcir representative values are listed in Table 11, where those for glycerol5 and butanediols3 are also listed. Vapp is about half of the van der Waals volume, VvdW,of the D-sorbitol molecule 96 cm3/mol). For o-terphenyl and poly(viny1 chloride), (V,, E*app falls on a single curve, when it is plotted as a function of T/Tg.I2In Figure 6, E*app,which is equal to Hlappat 1 atm, is
-
290
2 95 0
300
0
305
T / K
Figure 5. Apparent activation variables as a function of temperature for D-sorbitol. Empty symbols are for 0.1 MPa and closed symbols for 78.5
MPa. compared with that from the other dielectric Vogel equationlo listed in Table I and the calorimetric data" obtained by Angel1 et al. The ratio p i p , p/E*app is a macroscopic measure of the intermolecular confPgurational contribution related to the partitioning of molecules in configurational space in molecular liquids.12
TABLE 11: Representative Values of Activation Quantities and Changes in Number of Hydrogen Bonds for D-Sorbitol, Glycerol,"and Butanediols and n-Butane at 300 K, 0.1 MPab
D-sorbitol H*app/kcalmol-' Pap/cm3mol-l Pi f a p p / E * a p p
( E app (vapp
- E*m)/E*app - pin)/P a p p
[S*JA*
+ (at/avPi/~-~
(dt/ap),/MPa-'
78.5 MPa, 294 K 61.7 f 12.5
0.16 f 0.01 0.31 f 0.07 -3.4 i 0.7 -0.0023 f 0.0003
0.13 h 0.01 0.35 f 0.04
-0.0026 f 0.0005
-0.001 5 f 0.0003 1,2-Bdiolb
H*,p,/kcal mol-' [s*,/A*
glycerol4
0.1 MPa, 294 K 53.3 f 8.2 44 f 2
+ (a~/ar),i/~-l
"Johari and Whalley (ref 5). bSagal (ref 3).
10.4 -0.0021
1,3-Bdiolb 10.1 -0.0018
0.1 MPa, 217.5 K 25.3 19.1 0.08 0.23 -4.2 -0.0022 -0.0016 1 ,4-Bdiolb
7.9
1470 MPa, 258.2 K 16.1 -5.2 -0.0017 n-Bolb 7.3
434
The Journal of Physical Chemistry, Vol. 95, No. 1. 1991
\
The quantity A * ihas been introduced after the equilibrium differential form of the Gibbs energy. The last term in eq 12 means that the Gibbs energy of activation increases as the number of hydrogen bonds increases. We may be allowed to interpret this term in another way. When a molecule has a hydrogen bond with other molecules, the molecule is trapped in a deeper well by the amount of lAIil and more energy may be required to escape from the trap. It should be noted that the summation in eq 12 is not necessarily identical with that in eq 10. So long as we monitor the change in hydrogen bonds by the molecular mobility, we can hardly obtain information on the intramolecular hydrogen bonds, which may not be closely related to the molecular mobility. In the practical experiments, we cannot fix the number of hydrogen bonds externally and we always observe the apparent activation variables in eqs 6-9; Le., T o r p only is fixed, but ti is free. From eq 12, the apparent variables are expressed as
'\ '\
loot
t
ot
100
Naoki and Katahira
,
I
105
1.10 T / Tg
1
115
120
Figure 6. Apparcnt internal energy of activation as a function of temperature reduced by the glass transition temperature for D-sorbitol. Circles are the present experiment: (0),0.1 MPa; ( O ) , 78.5 MPa. Squares (0)are the DSC experiments, and the broken line is eq I obtained by Angel1 et al. (refs IO and 1 I ) . The thick solid line indexed by E', is the molecular contribution of the activation energy.
When the value of pip, /Elappe x d s 0.5, the free volume model is a good approximation?6 Values of the ratio for D-sorbitol listed in Table I1 are even smaller than those of polymers (ca. 0.2-0.3). The contribution of the spatial configurations of molecules seems to be trivial, and only little free space to move into is apparently required for the molecular motions in associated liquids. This is not likely near the glass transition temperature, because the Brownian motion requires numerous microstates, Le., free spaces of almost the same size or larger than the molecule, for the cooperative rearrangements of the configurations of many molecules. This apparently unnatural result for associated liquids is due to the fact that the experiment observes the molecular mobility only from its variations with temperature and pressure. When some chemical configuration such as hydrogen bonds changes simultaneously with temperature and pressure, the energy accompanying the chemical configuration also appears as the energy of activation for the molecular mobility.
Activation Process in Associated Liquids For molecules with several groups that are capable of hydrogen bonding, the first and second laws of the thermodynamics give17 dE = T d S - p dV -
(10)
where ti is the extent of the hydrogen bonding and Ai is the affinity of each hydrogen bond defined by Ai = -(aE/aFi)s,v,j#i = -(ac/a[i)rqp,j#i
(1 1)
Since the attractive (negative) hydrogen-bond energy increases as ti increases, Ai is positive with a value of about 2.5-5 kcal/mol of hydrogen bonds for alcohols. With analogy to the equilibrium thermodynamic functions, the internal energy of activation E', the enthalpy of activation H', the entropy of activation S * , and the volume of activation vl are defined. The displacement of the Gibbs energy of activation is expressed as dC* = -S* d T
+ r" d P - Z A * i &
(12)
where A l i is the affinity of activation, the magnitude of which is equal to Ai, but its sign is opposite (-5 to -2.5 kcal/mol of hydrogen bonds):
A*i = -Ai
(13)
(16) Naoki, M.; Koeda, S. J . Phys. Chem. 1989, 93, 948. (17) Prigogine, 1.; Defay, R. Thermodynamique Chimique; Editions Desoer: Liege, 1950.
where y is the thermal-pressure coefficient. H*,VI, E*, and E l y are the activation variables at constant ti. As the temperature increases, the number of hydrogen bonds decreases, and this and E*, ( A l i is negdecrease raises the values of Hlapp,Etapp, ative). When the number of the hydrogen bonds Jecreases with and Elvapp increase. In these pressure, VIappdecreases and E*app cases, the apparent intermolecular configurational contribution, piVapp/E*,,,,should be much smaller than that at constant ti. The isochronous T-p relation expressed by which corresponding to the pressure dependence of Tg,dTg/dp, may also be very small. These reveal the origin of the general nature of the molecular mobility in associated liquids, Le., large Htapp,I8 approaches of HIappto Arrhenius type,I9 small small piVtapp/E*app,5920 and small (13T/ap),+.~ The small ( d T / d p ) , (=dT,/dp) may be understood as follows. As the liquid is compressed with increasing pressure, intermolecular free spaces decrease and the number of microstates available for each molecule decreases. Then the molecular mobility governed by the spatial configuration of microstates (which is sometimes called the configurational entropy or the free volumeI6) will decrease. This is the case in molecular liquids and those with permanent long chains or networks. In associated liquids, however, the hydrogen bonds will partially decompose with increasing pressure when ( a t i / d p ) Tis negative. The latter factor raises the molecular mobility, cancels the former factor, and reduces the increase of Tg against pressure. Equation 15 may well explain the unusual pressure dependences of ionic conductance in aqueous alkali-metal halides21*22 (as the pressure increases, the conductance increases, reaches a maximum, and then decreases) in terms of decrease and extinction of hydrogen bonds with pressure. As the hydrogen bonds partially decompose with increasing pressure, the seams of the networks of hydrogen bonds may increase and the ions trapped by the networks will become more mobile. In much higher pressure regions, almost all of the hydrogen bonds will have broken out , decrease; Le., Pap? may increase and approach and ( a t i / ~ , )may P.Then the mobility of the ions will decrease to the one under high pressure (with little free spaces) without hydrogen bonds. VIapp,5318
(18) Pingel, N.; Poser, U.;Wiirflinger, A. J . Chem. Soc., Faroday Trans. I 1984, 80.3221. (19) Stillinaer, F. H . J . Chem. Phvs. 1988, 89, 6461. (20) MacK&e, J. D. J. Chem. Phys. 1958, 28, 1037. (21) Horne, R. A.; Myers, B. R.; Frysinger, G.R. J . Chem. Phys. 1963, 39,
2666.
(22) MacFarlane, D. R.; Scheirer, J.; Smedley, S. 1. J . Phys. Chem. 1986, 90, 2168.
The Journal of Physical Chemistry, Vol. 95, NO.1, 1991 435
Molecular Mobility in Supercooled D-Sorbitol
Intramolecular Conformational Contribution When molecular chains lengthen by successive hydrogen bondings, some rotating microstates around the bonds of neighboring atoms inevitably arise. These intramolecular degrees of freedom raise the equilibrium conformational entropy. However, when a molecule moves from one position to another position where some lower density, higher energy space is located, the neighboring atoms should take some particular conformational state to move the molecule into the space intended. That is, some additional negative intramolecular conformational entropy of activation, SI,, is required for the molecular motions in long-chain liquids. S*, increases as the region of the Brownian motion increases (as the temperature decreases), and the experimental energy of activation of polymers increases steeply near the glass transition temperature.I2 We assume a similar situation for the transient long chains and/or networks constructed by hydrogen bonds. We separate H* in eq 14,the enthalpy of activation at constant ti, into the intramolecular conformational contribution of TS*, and the molecular contribution of H*,, which is the enthalpy of activation for the reference rigid molecule without any intramolecular effects: HIapp zz H * ,
+ T[S*,+ CA*i(dti/d77,]
(19)
Similarly, we may separate v1 in eq 15 into the conformational contribution of v1, (S*,) and the molecular contribution of v1,, which is the volume of activation for the reference rigid molecule. For polymers, the conformational contribution is expressed as a function of temperature only in the zeroth approximation at the low-density region,23 but it is essentially a function of ti in associated liquids, especially when & approaches to zero. However, the dependence of S*, and VS, (S*,) on ti may not be so strong in the region of large ti. As seen in the following section, the change in ti is very small in our experimental range, and we may be allowed to approximate S*, to be independent of pressure. Then we have from Vr (S*,) z 0
p m - EA*i(a€i/dp)T
(20) Equations 19 and 20 reveal the natures of the molecular mobility in polymer liquids: large activation energies24 and the and ( d T / d ~ between )~ those intermediate values of p i p a p/E*app of molecular liquids and o! associated l i q ~ i d s . ~ , ' ~ , ~ ~ Strictly speaking, the separation of H* into H * , and TS*,and the assumption of v1, (S*r)z 0 do not hold true. The internal energy shifts with the rearrangements of the intramolecular rotational states? e.g., the difference between gauche and trans conformations is about 0.5 kcal/mol in n-butane. The volume (S*,) is not zero. also shifts with the rotational states27and This conformational contribution is significant for polymers, especially for their rubber elasticity, but may not be for the molecular mobility in associated liquids because the shifts of the internal energy and volume pertaining to the intramolecular rotational states are much smaller than the energies and volume of activavapp
are 95.8, 51.4,and 135.0 cm3/mol for D-sorbitol, glycerol, and o-terphenyl, respectively. The value of E * , ( = H * , at 0.1 MPa) is shown in Figure 6. The contribution of hydrogen bonds to the energy of activation represented by (Elap- E*,)/Elappis approximately 30% for D-sorbitol and 20% For glycerol, and that - Vm)/ VIapp is -340% for to the volume of activation by ( vapp D-sorbitol and -500% for glycerol, as shown in Table 11. It should be emphasized that the hydrogen bonds have strong effects upon the pressure variation of the molecular mobility rather than its temperature variation. o-Terphenyl is neither rigid nor similar to D-sorbitol and glycerol. For simple molecular liquids corresponding to the latter polyols, however, it is very difficult to get each stable supercooled liquid for which measurements of pressure effects on dielectric dispersion are relatively easy. This problem is avoided in the analysis of butanediols in the next section. D-Sorbitol has six hydroxyl groups and glycerol, three. Formally, each hydroxyl group is capable of two hydrogen bondings, but in reality two of each are impossible due to the steric hindrance for the molecules longer than propanol. Then the number of hydrogen bonds of each molecule may be assumed to be six for D-sorbitol and three for glycerol. The possibility of intramolecular hydrogen bonds should be excluded, which may be very high between the hydroxyl groups separated by four carbon atoms. Unfortunately, we have no information on it and assume that all hydroxyl groups have an equivalent affinity of hydrogen bonding A*
=
HIappH * ,
vr
Changes in Number of Hydrogen Bonds in D-Sorbitol and Glycerol H*, and Vtm in eqs 19 and 20 are the ones for the rigid molecule of the same size without any hydrogen bonds. We have referred to o-terphenyl (0-TP) and calculated values of H * , and VSm from those of o-TP reduced by each van der Waals volume, i.e., H * , = [Vvdw/VVd~(O-TP)]H*(O-TP)and pm = [V,dw/ Vvdw(o-TP)]P(o-TP). Following Bondi's method,30values of Vvdw (23) Naoki, M.; Tomomatsu, T. Macromolecules 1980, 13, 322. (24) McCrum, N. G.;Read, B. E.; Williams, G . Anelastic and Dielectric Effects in Polymeric Solids; Wiley: New York, 1967. (25) Naoki, M.;Owada, A. Polymer 1984, 25, 75. (26) Flory, P. J.; Hoeve, C. A.; Ciferri, A. J . Polym. Sci. 1959, 34, 337. (27) Allen, G.;Bianchi, U.: Price, C. Trans. Faraday Soc. 1%3,59, 2493. (28) Flory, P. J. Statistical Mechanics of Chain Molecules; Interscience Publishers: New York, 1969. (29) Wolf, F. P.; Allen, G.Polymer 1975, 16, 209. (30) Bondi, A. Physical Properties of Molecular Crystals, Liquids, and Glasses; Wiley: New York, 1968.
z
-nAHB
(21)
where n is the actiue number of hydrogen bondings per molecule (n = 6 for D-sorbitol and n = 3 for glycerol) and AHBis the affinity of one hydrogen bond. AHBfor alcohols is distributed from 2.5 to 5 kcal/mol. Here we adopt 4 kcal/mol for AHBfollowing the value of 4 kcal/mol for ethanol and 3.8 kcal/mol for acetic acid in each gas state. One may count the loss of the van der Waals energy by each hydrogen bonding. The overall van der Waals energy for the hydroxyl group is estimated as about 0.92 kcal/mol from the heat of vaporization, and the loss of van der Waals energy for each coordination site of hydroxide (one hydrogen bonding) is about 0.1 kcal/mol, which is of no account for the present rather rough estimation. Changes in the number of hydrogen bonds estimated from the following equations
+ T[S*, + A*(dt/aT),]
vapp 2 v m
- A*(%/~P)T
( 19')
(20')
are shown in Figures 7 and 8 and Table 11, where [ is the overall for the caloriextent of hydrogen bonding. The values of Vapp metric and dielectric data by Angel1 et al. were calculated from and dTi/dp7 by assuming dTg/dp = their data on H*applo,'l (dT/do), in ea 18. . Plots of the temperature dependence, -[S*,/A* + (dt/d7'),1, in Figure 7 scatter near Tgdue to the intramolecular conformational contribution which depends on the primary structure of each molecule, whereas plots of the pressure dependence, ( d t / d ~ ) can ~, be superposable within the experimental errors (Figure 8). Therefore, the rate of the decomposition of hydrogen bonds with pressure is the same in D-sorbitol and glycerol when the temperature is reduced by Tg, and the neglect of the pressure dependence of s*,may be a good approximation in the present experimental region. This is also the evidence that the pressure dependences of the molecular mobility in D-sorbitol and glycerol at constant [ are almost identical with each other. The apparent difference in the volume of activation occurs from the masking of the difference in the amount of the pressure decomposition of hydrogen bonds. Johari and Whalley reported that the volume of activation of glycerol unusually increases with p r e ~ s u r e .From ~ eq 20', when the rate of the decomposition of hydrogen bonds decreases, Vapp increases (A* is negative). When the rate goes to zero due to the vitrification in lower temperatures or due to that all of the hyI
.,T.
436 The Journal of Physical Chemistry, Vol. 95, No. 1 , 1991
Naoki and Katahira
3.0r-----
A.
01 100
i
1
1
I
1 20
1.10
I
t
I
1.30
01
T / Tg
Figure 7. Rate of the change in hydrogen bonds with temperature and the conformational entropy of activation as a function of temperature reduced by the glass transition temperature. Circles are the present experiments for o-sorbitol: (0),0.1 MPa; (O), 78.5 MPa. Squares (0) are the DSC experiments, and broken line is eq 1 obtained by Angell et al. for D-sorbitol (refs 10 and I I ) . Triangles (A)are for glycerol obtained by Johari and Whalley (ref 5).
drogen bonds have completely been decomposed in higher temmay approach its maxiperatures under higher pressures, Papp mum value of Vt, which may be similar to the van der Waals volume (5 I .4 cm3/mol). Therefore, the apparently unusual increase of Papp with pressure is revealed as the masking by the change in the number of hydrogen bonds, and this may be a common phenomenon for molecules constructing transient long chains and/or networks of hydrogen bonds in the liquid state. From the present experiment, we cannot separate the term ( a l / d T ) , from the analysis of the energy of activation. However, the energy of activation of polymers rapidly approaches that of molecular liquids as the temperature increases.]* Therefore, S*, may be expected to reduce rapidly with temperature and to vanish at higher temperatures. The value of -(af/8r), may be separated from -T[S’, + A’(al/dT),] at TIT, > 1.15. D-Sorbitol and glycerol deviate in the region of TIT, < 1 .I as shown in Figure 7. The conformation around the hydrogen bond (0-He-0 bond) is almost free rotation. The more restricted conformation is required for D-sorbitol, whose permanent chain is longer than that of glycerol, and the former lS*rlmay be larger than the latter. In the analysis above, there are ambiguities in the distribution and value of the affinity of the active hydrogen bonds. If one intramolecular hydrogen bond exists steadily in D-sorbitol, (a[/ aT), may be calculated larger by about 17% than that in Table I I and Figures 7 and 8. If the Brownian motion requires the breakage of hydrogen bonds only, but not the complete separation of 0-0 pairs, 1.4’1 may be about 2.6 kcal/mol, as suggested by Walrafen et and (al/aT), may be larger by about 50%. Furthermore, all of the hydrogen bonds may not be equivalent and IA’I might be somewhat smaller due to steric hindrances. Therefore, the present quasi-quantitative analysis may give the minimum rates of the decomposition of hydrogen bonds. Considering the experimental errors in the energies of activation, these ambiguities are not large. There have been many spectroscopic studies on the hydrogen bond’s equilibrium. Barkatt and Angel13*studied absorptions of 1435 and 1580 nm pertaining to the O H group in the near-IR spectrum for sorbitol and gave the enthalpy of the hydrogen bond’s equilibrium as 2.6 f 0.1 kcal/mol. From this, (a(/dT), may be estimated as 2.7 X at 290 K (TIT, = 1.09), which agrees with the present result. Walrafen et aIs3’observed the direct Raman shift of 175 and 53 cm-’ pertaining to the hydrogen bonds in water, analyzed the scattering intensity, and obtained the enthalpy of hydrogen bond’s equilibrium as 2.6 f 0.1 kcal/mol, (31) Walrafen. G . E.: Fisher, M. R.; Hokmabadi, M . S.; Yang. W. H. J . Chem. Phys. 1986, 85, 6970. (32) Barkatt, A,: Angell, C. A. J . Chem. Pkys. 1979, 70,901.
100
1
I
120
110 T
/
I
I30
135
Tg
Figure 8. Rate of the change in hydrogen bonds with pressure as a function of temperature reduced by the glass transition temperature. Circles are the present experiments for o-sorbitol. Squares (0)are the DSC experiments,and ( 0 )is eq 1 obtained by Angell et al. for D-sorbitol (refs 10 and 1 1 ) . Triangles are for glycerol obtained by Johari and Whalley (ref 5): (A),0.1 MPa; (A), elevated pressures of 500-2000 MPa.
which gives (d(/dT), to be 2.6 X I O-3. They proposed a two-step process for the vaporization of water, i.e., the breakage of the hydrogen bond with 2.6 kcal/mol and the complete separation of non-hydrogen-bonded 0-0 pairs with 3.2 kcal/mol. In quantitative analysis, it may be a problem whether the affinity governing the molecular mobility is only the breakage of hydrogen bond (IA’I 2.6 kcal) or the complete separation (vaporization) (IA*I 4-5 kcal/mol).
- -
n-Butanol and Butanediols In the above section, the variations of number of hydrogen bonds have been estimated by regarding the energy and volume of activation of o-terphenyl as the ones of the reference rigid molecule. Without this assumption, we may analyze the contributions of hydrogen bonds in isomeric diols. Saga1 presented dielectric relaxations of n-butanol (n-Bol), 1,2-butanediol (1,2-Bdiol), 1,3-butanediol (l,3-Bdiol), and 1,4butanediol (1,4-Bdi01).~ Values of HIappare listed in Table TI. These alcohols may be divided into two categories with respect to Hlapp.1,ZBdiol and IJ-Bdiol belong to the first category (their HIapp are around 10 kcal/mol), and 1 ,4-Bdiol and n-Bo1 belong to the second category (their HIappare around 7.5 kcal/mol). Considering the high possibility of intramolecular hydrogen bonding in 1 ,Cbutanediol, the difference of about 2.5 kcal/mol in H*app between these two categories should be related to the number of active hydrogen bondings for each molecule which constructs long chains and affects the molecular mobility. That is, 1,2-Bdiol and 1,3-Bdiol may have two active hydrogen bondings, but 1,4-Bdiol and n-Bo1 only one. When we apply eq 19’ to the diols which are the same molecular size (the same HI,) and subtract Htapp of 1,4-Bdiol from that of each 1,2-Bdiol and 1,3Bdiol, we may get T[S*, A * ( e ( / d r ) ] for each active hydrogen bonding. By adopting A* = -4 kcalp”l, we have -[S*,/A* (d[/aT),] at 300 K for 1,2-Bdiol and I,3-Bdiol, which are listed in Table 11. Since the temperature studied is higher than the melting temperature of each diol, the conformational contribution may be very small and the resulting values may be almost equal
+
to
+
(wan,.
Conclusion
Associated liquids differ in molecular mobility from their corresponding molecular liquids. These differences have been revealed to be due to the masking effects of the equilibrium change in the configuration of hydrogen bonds. When the hydrogen bonds decompose partially, the intermolecular ties (hydrogen bonds) may become loosened. Then the molecular mobility will increase. The energy associated with the equilibrium change in the number of hydrogen bonds is apparently incorporated in the energy required
J . Phys. Chem. 1991, 95, 437-444 for molecular motions. A separation of the contribution from hydrogen bonds has been tried by using a simple activation process. The hydrogen bonds decompose with increasing pressure. This plays a role in raising the molecular mobility at higher pressures. On the other hand, the compression reduces the number of available microstates of each molecule in the configurational space and depresses the molecular mobility. In the molecular motions in the associated liquids, these two factors are of the same order and the slight difference in their magnitude may produce various peculiar properties of the associated liquids. The hydrogen bonds decompose with increasing temperature. This raises the molecular mobility similarly to the thermal energy. This decomposition of hydrogen bonds requires the increase in the apparent activation energy and may bring and camouflage the apparcnt activation process close to the Arrhenius type. The
431
molecular mobility at a constant number of hydrogen bonds in associated liquids may not particularly differ from that in permanent polymer or network liquids. Assuming that the origin of the molecular mobility in associated liquids at a constant number of hydrogen bonds is the same as that in o-terphenyl, the decomposition rate of hydrogen bonds with temperature and pressure is quasi-quantitatively estimated with some ambiguities in the number of active hydrogen bonds and in the value of the affinity of each hydrogen bond. These ambiguities, however, may be of no great importance in the rather rough estimation of the present study. The use of o-terphenyl as a reference is avoided in the analysis on butanediols, and almost the same results are given. The present results with respect to the temperature dependence of the number of hydrogen bonds agree with spectroscopic studies.
Dynamic Study of Aqueous Solutions of 2-Propanol and Ethanol in the Presence of Anionic and Cationic Surfactants by Ultrasonic Methods Sadakatsu Nishikawa* and Fumiharu Matsuo Department of Chemistry, Faculty of Science and Engineering, Saga University, Saga 840, Japan (Received: March 1, 1990; In Final Form: July 3, 1990)
Ultrasonic absorption, velocity, and density have been measured in aqueous solutions of 2-propanol (from 1 to 8 mol dm") in the presence of an anionic surfactant, sodium dodecyl sulfate (SDS) (from 1.5 to 300 mmol d d ) , and a cationic surfactant, cetyltrimethylammonium bromide (CTAB) (from 5 to 10 mmol d ~ n - ~at) ,25 OC along with electric conductivity. A simple and handy procedure for an analysis of the absorption spectra associated with Debye type relaxations has been shown, which is useful when it is not specified whether the observed absorption is due to single- or double-relaxation processes. Following the analysis, single- and double-relaxation absorptions have been found in the aqueous solution of 2-propanol with SDS. On the other hand, only a single-relaxation process has been observed in the solutions with CTAB. The relaxation process observed at around 70-120 MHz in these solutions has been characteristic of a perturbation of an equilibrium associated with the alcohol-water interaction, and the rate and thermodynamic constants have been determined from the concentration dependence of the ultrasonic parameters. The results have been compared to each other and have been discussed under considerations of the effects of the surfactant structures and also of the interactions between the alcohol and surfactants. In addition, another relaxation process has been newly found in the lower frequency range (4.5-23 MHz) in solutions with 30, 60, 100, and 300 mmol dm" SDS, and it has been speculated to be due to an exchange process of alcohols between the bulk and micelle phases from the concentration dependence of the relaxation frequency. A single-relaxation process has also been observed in aqueous solutions of ethanol with SDS at around 100 MHz. The cause of it has been estimated to be due to the exchange process of ethanol between the SDS micelle and bulk phases from the concentration dependence of the relaxation frequency. From these results, the exchange process has been speculated to be strongly dependent on the size of the hydrophobic groups of alcohol molecules and the stiffness of the micelle formed by surfactant molecules.
Introduction
Recent interests in nonelectrolyte aqueous solutions are increasing because of the applicabilities as good solvent~.'-~On the other hand, clarifications of dynamic properties for aqueous solutions of nonelectrolytes have not been made so much because the various processes are proceeding very rapidly in aqueous media. Also, the low solubilities of many nonelectrolytes with hydroxyl group into water have limited the investigation of such properties. Surface-active agents may be used to dissolve such low-soluble nonelectrolytes by their solubilization abilities. The ultrasonic absorption method is one of the best tools to study the dynamic properties of liquids and has been applied to the clarification for the solution characteristics of nonelectrolytes. Wyn-Jones' groups4 have been studying the solution properties ( I ) Mittal, K. L., Ed. Micellization, Solubilization and Microemulsions; Plenum: New York, 1977. (2) Acree, W. E., Jr.; Bertrand, G. L. J. Solution Chem. 1983, 12, 755. (3) Johnson, I.; Olofsson, G. J . Colloid Interface Sci. 1987, 155, 56. (4) (a) Hall, D. G.; Jobling, P. L.; Wyn-Jones, E.; Rassing, J. E. J. Chem. Soc., Faraday Trans. 2 1977, 73, 1582. (b) Gormally, J.; Sztuba, B.; WynJones, E.; Hall, D. G. J. Chem. Soc., Faraday Tram. 1985, 14,953. (c) Kelly, G.; Takisawa, N.; Bloor, D. M.; Hall, D. G.; Wyn-Jones, E. J. Chem. Soc., Faraday Trans. I 1985,85. 4321.
0022-3654/91/2095-0437$02.50/0
of aqueous solutions of some alcohols, the solubilities of which are limited, with various surface-active agents, and they have attributed the observed relaxation process at a few megahertz or less frequency range of the sound to an interconversion of both solutes between micelle and bulk phase. Quite recently, Zana and MichelsShave reported that there exists another relaxation process in aqueous solution of 1-butyl alcohol at room temperature, and it is due to an aggregation of the alcohol at around 0.9 mol dm-3. Furthermore, it is well established that in the aqueous solution of soluble or miscible alcohols at room temperature, such as ethanol?' 1-propanol,8s92-propanol,Ioand 2-methyl-2-propanol,11*12 (5) Zana, R.; Michels, B. J. Phys. Chem. 1989, 93, 2643. (6) Takagi, K.; Negishi, K. Jpn. J. Appl. Phys. 1975, 14, 953. (7) Emery, J.; Gasse, S.Acustica 1979, 43, 205. (8) Nishikawa, S.;Mashima, M.; Yasunaga, T. Bull. Chem. Soc. Jpn. 1975, 48, 66 1. (9) Madigosky, W. M.; Warfield, R. W. J. Chem. Phys. 1987,86, 1491. (10) Nishikawa, S.; Mashima, M.; Yasunaga, T. Bull. Chem. Soc. Jpn. 1976, 49, 1413.
( I I ) Blandamer, M. J.; Parke, D. E. L.;Hidden, N. J.; Symons, M. C. R. Trans. Faraday Soc. 1968, 64, 2691. (12) Nishikawa, S.; Mashima, M.; Maekawa, M.; Yasunaga, T. Bull. Chem. Soc. Jpn. 1975, 48, 2353.
0 1991 American Chemical Society
