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J. Phys. Chem. 1992, 96, 3478-3480
Effects of Confinement on the Glass Transition Temperature of Molecular Liquids J. Zhang, G. Liu, and J. Jonas* Department of Chemistry, School of Chemical Sciences and Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801 (Received: October 10, 1991; In Final Form: December 10, 1991)
Effects of confinement on the glass transition of several molecular liquids in porous silica glasses were investigated by differential scanning calorimetry. The glass transition temperature, T,, of liquid isopropylbenzene, glycerol, di-n-butyl phthalate, tert-butylbenzene,and n-butyl acetate confined to sol-gel silica glasses with pore radii in the range 18-1 52 A was determined. For all liquids the confinement lowers the T, observed, and the Kelvin equation and the Ehrenfest relation were used in a phenomenologicalway to describe the observed trends of the glass transition with the pore size. A linear relationship between T, and the inverse of the pore radius, R,was observed. The relative temperature depression of the liquid-glass transition (ATIT,) due to confinement was found to be much smaller than that observed for freezing point depression.
Introduction
Molecular level properties of confined fluids are of interest in many fields because of their importance in a variety of technological processes including catalysis, chromatography, oil recovery, and membrane separations. A considerable amount of progress in understanding the dynamic and thermodynamic properties of molecular liquids in restricted geometries has been made in recent years.'-3 In our laboratory, recent studiesb8 have concentrated on the problem of reorientational dynamics of molecular liquids confined to porous silica glasses prepared by the sol-gel process. It is well-known that the phase transition temperature of liquids confined in porous materials depends upon the pore size.*I9 For water the fact that the lowering of the freezing point is inversely proportional to the pore radius has been reported.9J0J2 Similar behavior for the molecular liquids confined in sol-gel porous glasses was observed by our group? Awschalom and WarnockZ0recently pointed out that both liquidsolid and solidsolid phase transition temperature depressions increase linearly with the inverse of the pore radius and suggested a simple model of geometrical supercooling to interpret these results. Strange et al.21have reported the effects of confinement on the liquid-teplastic crystal transition and the plastic-to-brittle crystal phase transition for cyclohexane confined to porous silica. ~~~~~~~
~
( I ) Molecular Dynamics in Restricted Geometries; Klafter, J., Drake, J. M., Eds.; Wiley: New York, 1989 and references therein. (2) Dynamics in Small Confining System; Drake, J . M., Klafter, J., Kopelman, R., Eds.; Extended Abstracts Proceedings of Symposium of 1990 Fall Meeting of the Materials Research Society, Boston, MA, 1990 and references therein. (3) Drake, J . M.; Klafter, J. Phys. Today 1990, 46. (4) Liu, G.; Li, Y.; Jonas, J . J . Chem. Phys. 1989, 90, 5881. (5) Liu, G.; Mackowiak, M.; Li, Y.; Jonas, J. Chem. Phys. 1990, 149, 165. (6) Mackowiak, M.; Liu, G.;Jonas, J . J . Chem. Phys. 1990, 93, 2154. (7) Liu, G.; Mackowiak, M.; Li, Y.; Jonas, J . J . Chem. Phys. 1991, 94, 239. (8) Liu, G.;Li, Y.; Jonas, J . J . Chem. Phys. 1991, 95. 6892. (9) Patrick, W. A.; Kemper, W . A . J . Chem. Phys. 1938, 42, 369. (IO) Antoniou, A . A . J . Phys. Chem. 1964, 68, 2754. ( I 1) Armitage, D.; Price, F. P. Chem. Phys. Leu. 1976, 44, 305. ( I 2) Rennie, G.K.; Clifford, J. J . Chem. Soc., Furuduy Trans. I 1977, 73, 680. (13) Litvan, G. G.Adu. Colloid Inrerface Sci. 1978, 9, 253. (14) Tell, J . L.; Maris, H . J . Phys. Rea. B 1983. 28, 5122. ( I 5 ) Hall, P. G.; Williams, R. T.;Slade, R. C. T.J . Chem. Soc., Faraday Trans. I 1985, 81, 847. (16) Awschalom, D. D.; Warnock, J . Phys. Rev. B 1987, 35, 6779. (17) Pfeifer. H.; Oehme, W.; Siegel, H . Z . Phys. Chem. (Munich) 1987, 152, 473. ( I 8) Peterson, B. J . Mol. Phys. 1987, 62, 2 15. (19) Ozeki, S.J . Phys. Chem. 1989, 93, 7226. (20) Awschalom, D. D.; Warnock, J . Molecular Dynamics in Restricted Geomerries; Klafter, J., Drake, J. M., Eds.; John Wiley: New York, 1989. (21) Dore. J . C.; Dunn, M.; Hasebe, T.; Strange, J. H . Colloids SurJ 1989, 36, 199.
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Glass transitions are different from crystalline solid phase transitions in that they are kinetic p r o c e ~ s e s . ~Experimental ~*~~ glass transitions occur over a range of temperatures, and the fictive glass transition temperature measured by differential scanning calorimetry (DCS) strongly depends on both the cooling rate and the heating rate.22s23By studying the glass transition of confined liquids in porous solids, one may obtain not only dynamic but also kinetic information about the confined liquids. In spite of the fact that the heat capacity9J4and freezing point of liquids in porous materials have been extensively studied, reports about the measurement of the glass transition temperatures of liquids in porous systems are scarce in the l i t e r a t ~ r e . ~ ~ , ~ ~ In this work, the glass transition temperatures, T,,of molecular liquids isopropylbenzene, glycerol, tert-butylbenzene, di-n-butyl phthalate, and n-butyl acetate confined in the sol-gel prepared porous silica glasses with varying pore sizes were investigated by DSC. The molecular liquids were selected by considering the following points: (a) The liquid should easily form a glass phase without crystallization at a chosen cooling rate. (b) The substance should be a liquid at room temperature to make the loading procedure easy. (c) For the convenience of temperature measurement, the glass transition point should be in the range of the DSC measurement technique, far away from the freezing point and other phase transition points, and the liquid should produce relatively great change in heat capacity at the transition. The goal of this work was to investigate the effects of confinement on the glass transition of the molecular liquid studied and then to provide basic experimental data which could be used to test the existing glass transition theories. For all liquids the confinement lowers the T, observed, and the Kelvin equation and the Ehrenfest relation were used in a phenomenological way to describe the observed trends of the glass transition of the cohfined liquids with the pore size. In agreement with the results reported by Jackson and M ~ K e n n a , a* ~linear relationship between T, and the inverse of the pore radius, R, was also observed. The relative temperature depression due to confinement of the liquid-glass transition (ATIT,) was found to be much smaller than that observed for freezing point depression. Experimental Section Reagent grade isopropylbenzene,tert-butylbenzene, and n-butyl acetate were purchased from Aldrich Chemical Company Inc., reagent grade di-n-butyl phthalate was purchased from Sigma (22) Owen, A . E. In Amorphous Solid and the Liquid Stare; March, N . H.. Street, R. A., Tosi, M., Eds.; Plenum Press: New York, 1985. (23) Jackle, J . Rep. f r o g . Phys. 1986, 49, 171. (24) Jackson, C. L.; McKenna, G.B.J . Non-Crysr. Solids 1991,131,221. (25) Jackson, C. L.; McKenna, G.B. In Dynamics in Small Confining System; Drake, J. M., Klafter, J., Kopelman, R., Eds.; Extended Abstracts Proceedings of Symposium of 1990 Fall Meeting of the Materials Research Society, Boston, MA, 1990.
0 1992 American Chemical Society
Effects of Confinement on Tg of Liquids TABLE I: Glass Transition Temperature, T, of Molecular Liquids Confined to Porous Silica Glasses liquid R,A I/R,A-' T.,K isopropylbenzene bulk 0.000 130.7' 129.4 62 0.016 127.4 36 0.028 126.0 18 0.056 192.1b glycerol bulk 0.000 191.6 152 0.007 191.1 62 0.016 36 0.028 189.9 177.7c di-n-butyl phthalate bulk 0.000 176.5 62 0.016 172.0 29 0.034 168.9 19 0.053 141.6d tert- butylbenzene bulk 0.000 140.2 62 0.016 139.5 37 0.027 137.4 19 0.053 122.3' n-butyl acetate bulk 0.000 121.8 57 0.017 121.1 37 0.027 116.5 18 0.056 '127 K, ref 28. b190 K ref 29. c176K, ref 30. d142 K. ref 30. K,ref 31.
'118
Chemical Company, Inc., and reagent grade glycerol was purchased from Fisher Scientific Co. The liquids were used without further treatment. The porous silica sample was made by the sol-gel glass process.8 The Brunauer-Emmett-Teller (BET) method was applied to measure the surface area, average pore radius, and the pore size distributions on the AUTOSORB- 1 BET instrument (Quantachrom Corp.). The specific pore radii of the glass samples prepared ranged from 18 to 152 A. Typical glasses prepared by this process have a narrow pore size distribution,* a porosity of approximately 7095,a surface area ranging from 200 to 400 m2/g, and a high pore interconnectivity. As we discussed in our earlier study: typical adsorption and desorption isotherms for N2 indicated the high degree of pore uniformity within the sample and were consistent with the narrow pore size distribution. The isotherms were type IV according to the isotherm classification scheme of Brunauer, Deming, Deming, and Teller (BDDT). This type of isotherm is characteristic of a mesoporous material having pores of approximately cylindrical cross section. The liquid-glass sample was loaded into an aluminum DSC volatile sample pan. The sample mass was determined on a microbalance weight, and a typical sample pan contained about 8 mg of silica glass and known amounts of liquid which could be calculated from the total pore volume. The filled pan was then sealed with an aluminum cover and placed on the sample cell of the DSC measurement station, and a similar but empty pan was used as the reference on the other side cell. The pan containing the same amount of silica glass without liquid was also used as a reference, but no difference was found. The DSC instrument was calibrated using cyclohexane. Both phase transition and melting of cyclohexane were observed and calibrated according to the literature values.26 In the DSC experiments, first the sample was heated to room temperature (25 "C) and held at that temperature until the stable heat flow of DSC was obtained. Then the sample was quenched through the glass transition temperature region at the cooling rate of 200 OC/min. After a stable heat flow was established, the sample was heated at a rate of 25 OC/min to room temperature. The glass transition temperature TBwas determined from the DSC heat flow versus temperature curve.*' (26) 1135. (27) (28) (29) 602.
Aston, J. G.;Szasz, G.J.; Fink, H . L. J . Am. Chem. Sot. 1943. 65, Perkin-Elmer, DSC-7Instruction Manuals. Johari, G.P.; Goldstein, M. J . Chem. Phys. 1970, 53, 2372. Jeong, J. H.; Nagel, S. R.; Bhattacharya, S.Phys. Reu. A 1986,34,
The Journal of Physical Chemistry, Vol. 96, No. 8, 1992 3479
Results and Discussion The DSC experimental data of the glass transition temperatures for the molecular liquids isopropylbenzene, glycerol, di-n-butyl phthalate, tert-butylbenzene, and n-butyl acetate confined to porous silica glasses with different pore radii are given in Table I. One should note that the error of the glass transition temperature measurement by DSC increases with decreasing pore size because of the decrease of the signal-to-noise ratio, and for the smallest porous glass sample in the experiments, the error in the temperature measurement is about f l 0C.27 Table I shows that the T i s for all liquids studied exhibit the same trend with confinement-the smaller the pore radius R, the lower the T4 of the confined liquid. This is true for all glassforming liquids studied in this work independent of the chemical properties and strength of interactions with the pore surface.8 In most studies of the phase transitions of the liquids confined in porous materials, the depression of the freezing point below the normal one has been related to the existence of the capillary effects on the confined l i q ~ i d , ' ~ Jand ~ J thus ~ * ~the ~ Kelvin equation has been used in combination with the Clausius-Clapeyron equation. Therefore, a linear relation between the depression of the phase transition point and the inverse of the pore radius has been obtained to explain the experimental observations. For the glass transitions of confined liquids, the negative pressure on the confined liquids due to the existence of the menisci is also considered as an important factor in the depression of the glass transition. Using the Kelvin equation for an idealized cylindrical pore of radius R, the pressure reduction on the liquid inside the pore compared with the vapor pressure can be written as3* A P = 2Aa/R
(1)
where Au is the difference between the gas-wall and the liquidwall interfacial energies. The Clausius-Clapeyron equation cannot be used to describe a glass transition since it is not a phase transition. However, if we focus on the thermodynamic properties of a confined substance, measured far away from the transition point, the glass transition temperature can be related to the pressure of the liquid by an equation of irreversible thermodynamics known as the second Ehrenfest r e l a t i ~ n ~ * - ~ ~
In the above equation Pa and AC,, are the respective changes of the thermal expansion coefficient and heat capacity at constant pressure which occur at Tg. The Ehrenfest relation was extended to the glass transition phenomena by Davies and and the validity of the equation for glass transitions has been widely The Ehrenfest relation has been used successfully to explain many pressure-related experimental glass transition data.22-23,37J8In a phenomenological way, we apply the Ehrenfest relation to a glass transition of a liquid in confined geometries. Combining the Ehrenfest relation with the Kelvin equation, we get an equation relating the decrease in the glass transition temperature to the pore radius R, as follows Aa2Aa
AT =
vT"w
(3)
(30) Carpenter, M. R.; Davies, D. B.; Matheson, A. J. J . Chem. Phys. 1967, 46, 2451. (31) Ceccorulli, G.; Pizzoli, M.; Scandola, M. Polymer 1987, 28, 2077. (32) Surface Tension and Absorption; Defay, R., Prigogine, I., Eds.;
Wiley: (33) (34) (35) (36) (37) (38) 4423.
New York, 1966. Davies, R. 0.;Jones, G.0. Adu. Phys. 1953, 2, 370. Goldstein, M. J . Chem. Phys. 1963, 39, 3369. Nose, T. Polym. J . 1971, 2, 445. Goldstein, M. J . Phys. Chem. 1973, 77, 667. Atake, T.; Angell, C. A. J . Phys. Chem. 1979.83, 3218. Naoki, M.; Matsumoto, K.; Matsushita, M. J. Phys. Chem. 1986, 90,
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J . Phys. Chem. 1992,96, 3480-3485
R (A) BULK
62
36
18
-194 1
2 ' .00. d l . 0 2 .0J .04 .05 . 0 6
1/R
'
(Ae1)
Figure 1. Pore size dependence of the experimental T, of the studied molecular liquids confined to porous silica glasses. The Tgvalues for bulk liquids are also given (1 /R = 0): A, isopropylbenzene; V, glycerol; W, di-n-butyl phthalate; 0 , ten-butylbenzene;0, n-butyl acetate.
Since the depression of the glass transition temperature of the liquids in the pores is relatively small, in this limited range Aa, ACp, and Au can be assumed to be constant, and eq 3 gives us a linear relation between the depression of the glass transition temperature and the inverse of pore radius. This agrees with our experimental results for the depression of the glass transition temperature of all molecular liquids studied, as shown in Figure 1 which plots T , vs the reciprocal of the radius R . Figure 1 shows that the decrease of the glass transition temperature of confined liquids compared to the glass transition temperature in the bulk changes linearly with the inverse of the pore radius R. It is worth mentioning that linear regression gives the following correlation coefficients for the plots shown in Figure 1: 0.973,0.992,0.993,0.993,and 0.969. It is interesting to compare the behavior of the glass transition temperature of confined liquids to that observed for the freezing
points. One notes that the depression ratio of the glass transition, AT/T,, is relatively small (below 5% for the smallest pore size) compared with the freezing point depression ratio, AT/Tf (above 20% for the same pore size). These results show that the confinement effect on the glass transition of confined liquids is much weaker than the confinement effect on crystallization of confined liquids. In order to give a specific example, we note that Strange et a1.*' reported that the melting point of cyclohexane is lowered by about 40 K and the solid-solid phase transition by about 20 K when cyclohexane is confined to porous silica glass with a pore diameter of 90 A. The idea that the depression of glass transition points is the result of the capillary effect on the confined liquids can be tested by calculating the AT from the previous data. For example, according to the experimental data given in ref 39,the interfacial tension of glycerol, Au, is estimated to be 70 dyn/cm above the glass transition point. The pressure decrease of the glycerol confined to a 36-Asize pore, AP,is about 0.4kbar obtained by using the Kelvin equation. It is also known that dT,/dP = 4 K/kbarm for glycerol, so the depression of the glycerol glass transition temperature, AT, is determined to be approximately 2 K. This agrees surprisingly well with our experimental results (see Table I or Figure 1) in spite of the approximative nature of our interpretation. The main result of our experimental study using DSC is the finding that the glass transition temperature, T,, of several molecular liquids is lowered when the liquid is confined with a porous silica glass. It is also interesting to note that the effects of confinement on T are much smaller when compared to the analogous effects on the freezing point temperature or on the solidsolid phase transition?' The experimental observationz4of a linear dependence of the glass transition temperature, T,, and the inverse of the pore radius ( 1 / R )was phenomenologically interpreted in terms of the Kelvin equation and the Ehrenfest relation. Acknowledgment. This work was supported in part by the National Science Foundation Grant NSF DMR 89-20538. Our thanks are due to P. G. Wolynes for bringing this problem to our attention and to N. Goldenfeld and G. B. McKenna for helpful comments. (39) Glycerol; Miner, C. S.,Dalton, N. N., Eds.;Reinhold: New York, 1953. (40) DiMarzio, E. A.; Gibbs, J. H.; Fleming, P. D., 111; Sanchez, 1. C. Macromolecules 1976, 9, 763.
Dipole Relaxation near Boundaries M. Urbakh* and J. Klafter* School of Chemistry, Tel- Aviu University, 69978, Ramat- Aviu, Tel-Aviv, Israel (Received: November 1 1 , 1991)
The influence of a solid-liquid interface on the relaxation of a point dipole embedded in the liquid side is discussed. The dielectric friction of a dipole as a function of its distance from a boundary is calculated. The calculations are carried out assuming a nonlocal dielectric function of the liquid, characterized by a typical correlation length which may depend on temperature. The corrections to the relaxation of a dipole due to the presence of a boundary are shown to be small. Larger correctionscan be introduced by postulatingstructural changes in the nature of the liquid near the boundary. As a demonstration we apply the proposed formalism in the study of temperature and pore size dependence of a dipole relaxation.
1. Introduction A large number of experimental and theoretical studies have
dressed, i.e., changes in freezing and viscosity as well as chemical reactions and energy-transfer AIS0 traIlSlatiOna1
been devoted to the understanding of the role of spatial restrictions in modifying the properties of embedded liquids and molecules. Both thermodynamical and dynamical questions have been ad-
( I ) Klafter, J., Drake, J. M., Eds. Molecular Dynamics in Restricted Geometries; Wiley: New York, 1989.
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