© Copyright 2003 by the American Chemical Society
VOLUME 107, NUMBER 4, JANUARY 30, 2003
LETTERS Surface Induced Glass Transition in a Confined Molecular Liquid Ranko Richert* and Min Yang Department of Chemistry and Biochemistry, Arizona State UniVersity, Tempe, Arizona 85287-1604 ReceiVed: September 10, 2002; In Final Form: NoVember 27, 2002
The structural relaxation of a glass-forming simple liquid, 3-methylpentane, is studied by triplet state solvation dynamics as a function of the distance from the surface in porous silica. By bonding the optical probes to the pore surface, we observe interfacial dynamics which are 3 orders of magnitude slower compared with the bulk, equivalent to a surface induced glass transition. Consistent with length scales of cooperativity, these effects disappear for distances from the surface exceeding a few nanometers.
Various disordered materials are being considered for nanotechnological applications, including many glass-forming molecular and polymeric systems. Although processing techniques are approaching nanometer dimensions, our understanding of the features involved in glass-formation in submicron confining geometries has remained incomplete. For materials to perform in nanotechnological applications, it is therefore desirable to improve our knowledge of how geometrical confinement alters the behavior of disordered condensed matter relative to bulk samples.1 Such finite size and boundary effects are also important for the performance of thin film lubricants, for improving the efficiency of retrieving oil trapped in porous rocks, for modeling how aquifers promote the transport of undergroundwater, and for the transport of matter in cells and membranes. Surface force apparatus experiments performed by Israelachvili2 and Granick3 as well as simulations by Landman4 have revealed a drastic increase in the viscosity if the liquid is compressed to a few molecular layers between flat surfaces. Molecular ordering at the atomically smooth mica interface is made responsible for this effect. In contrast, porous sol-gel glasses exhibit a highly irregular internal structure and a distribution of surface curvatures, similar to natural porous materials.5 Using subpicosecond optical birefringence in porous glass samples, * To whom correspondence should be addressed.
Warnock and co-workers have identified an interfacial layer whose orientational time scale is higher than the bulk value, but the change amounts to a factor of ≈3 only.6 In a more detailed study, Loughnane et al. have assigned slow dynamics in CS2 to the surface layer in silicate nanopores, where the time scale for orientation is a factor of ≈10 above the bulk value.7 The prominent features of supercooled liquids are the complex behavior regarding the time and temperature dependence of their structural R relaxation.8 At the glass transition temperature Tg, the time scale associated with viscous flow reaches τg ) 100 s, resulting in the glassy or amorphous solid state for T < Tg. Relaxations of glass-forming materials often exhibit a Kohlrausch-Williams-Watts (KWW) type correlation function
Φ(t) ) exp[-(t/τKWW)β] )
∫0∞ gKWW(τ)e-t/τ dτ
(1)
with lower values of β reflecting wider probability densities gKWW(τ) of the relaxation times τ. In these systems, the temperature dependence τKWW(T) commonly follows the Vogel-Fulcher-Tammann (VFT) expression
log10(τKWW/s) ) A + B/(T - T0)
(2)
An important feature of glass-formers is their cooperative nature of the molecular motion, whose increasing length scale ξ(T) is often made responsible for the pronounced slowing down of
10.1021/jp022039r CCC: $25.00 © 2003 American Chemical Society Published on Web 12/31/2002
896 J. Phys. Chem. B, Vol. 107, No. 4, 2003
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the dynamics as T approaches Tg.9 This length scale with ξ(Tg) ≈ 3 nm can be considered the distance required by two molecules to relax independently. Therefore, the penetration of boundary effects into the liquid will be more pronounced in the viscous regime of a liquid relative to the fluid regime. Jackson and McKenna have studied how nanometer scale geometrical confinement affects the Tg of organic glass-forming materials.10 Subsequently, numerous experimental techniques have been applied in order to quantify how confinement changes the behavior of supercooled liquids and polymers.11-16 Geometrical restriction on the scale of nanometers is often found to modify the dynamics of molecular motion, and it is customary to compare the results with the bulk in terms of a confinement induced glass transition shift ∆Tg. The lacking consensus regarding even the sign of ∆Tg implies that both accelerated as well as frustrated dynamics are being observed in nanoconfined materials relative to their bulk counterparts.17 It is especially with supercooled liquids that the results regarding confinement effects are apparently controversial and poorly understood. Near Tg, the typical changes observed upon confining a glassformer are a broader and more symmetric probability density of relaxation times, g(τ), a more Arrhenius-like temperature dependence τ(T), and occasionally a bifurcation into slower and faster components.1 For highly supercooled liquids or polymers, sluggish interfacial dynamics have been suggested,18,19 but a direct experimental observation of spatially distributed dynamics within a pore remained lacking. A more detailed picture emerges from a recent MD simulation of an 80:20 binary Lennard-Jones liquid within a pore, where the dynamics is observed to slow gradually from bulklike behavior at the center of the pore to highly frustrated particle mobility near the boundary.20 In the supercooled state, the interfacial relaxation time of this model liquid is around 3 orders of magnitude slower than the bulk value. In this study, we provide insight into the spatial distribution of the dynamics of a simple glass-forming liquid, 3-methylpentane (3MP) in its viscous regime, geometrically confined to the 7.5 nm diameter pores of sol-gel processed silica. To this end, triplet state solvation dynamics21 is employed in order to assess the structural relaxations in bulk and confined 3MP, a nonpolar glass-forming branched alkane with Tg ) 77 K. The liquid is doped with chromophores and their time-resolved S0 r T1 (0-0) emission spectra are analyzed in order to obtain the average emission energy 〈ν〉 as a function of time. Normalization according to 〈ν(t ) 0)〉 f 1 and 〈ν(t ) ∞)〉 f 0 yields the Stokes-shift correlation function C(t), which reflects the shear modulus G(t) of the solvent surrounding the probe in the present case of nonpolar solvation.22,23 Equation 2 is useful for characterizing G(t)/G∞ ) C(t) by its time scale τ and exponent β. The time-integrated effect is directly related to the shear viscosity η
η)
∫0∞ G(t) dt ) G∞∫0∞ C(t) dt ) G∞〈τ〉
(3)
where 〈τ〉 is the average time scale of G(t)/G∞ ≈ C(t) and G∞ ) G(t ) 0) is the high-frequency modulus. GelSil type porous silica with average pore diameter 7.5 nm is cleaned in 2-propanol and 30% H2O2 prior to drying at 200 °C in a vacuum for 48 h. At room temperature, 3MP wets a flat silica surface subject to the same cleaning procedure. Dilute (2 × 10-4 mol/mol) solutions of naphthalene (NA) or quinoxaline (QX) in 3MP are imbibed into GelSil samples. Timeresolved emission spectra are recorded as a function of temperature for both solutes in bulk and confined 3MP. Figure
Figure 1. (a) Average emission energy at t ) 100 ms versus temperature for various solute/solvent combinations in the bulk (circles) and in pores of 7.5 nm diameter (diamonds). Triangles are obtained after replacing the solvent by Argon gas. (b) Average steady-state emission energy of quinoxaline (QX, solid circles) and naphthalene (NA, open circles) in various bulk solvents, sorted according to polarity in terms of ETN. Comparing both sides demonstrates that QX in porous silica experiences the polarity of alcohol, implying its position at the interfacial OH groups.
1a shows the average emission energy 〈ν〉 at a fixed time versus temperature for the solutes NA (open symbols) and QX (solid symbols) in bulk 3MP (circles) and in the confined 3MP (diamonds), with the decreasing 〈ν〉 for T g 80 K being the signature of solvent responses. Although the step heights ∆ν for QX are similar for the bulk and confined case, the curve for QX/3MP in pores is lower in energy by ≈745 cm-1. To rationalize this feature, Figure 1b shows steady-state energies 〈ν〉 of NA and QX in solvents of different polarity. The ground (µG) and excited (µE) state dipole moments of the two probes (µG ) 0, µE ≈ 0 for NA and µG ) 0.44 D, µE ) 1.75 D for QX) determine their sensitivity to polarity. Figure 1b demonstrates that 〈ν〉 as low as 20 600 cm-1 for QX is achieved only in highly polar environments, e.g., in the presence of the -OH groups in alcohol.24 For the QX/3MP sample in porous silica, this implies that all QX chromophores are positioned at the silanol groups which populate the silica surface.15 After replacing the solvent by Argon gas, the triangles labeled QX/Ar in Figure 1a are obtained. The absence of a step in 〈ν〉 for QX/Ar indicates the removal of all 3MP, whereas QX remains hydrogen-bonded to the surface with an accordingly low emission energy. In contrast to QX, the probe molecule NA is nonpolar and not susceptible to hydrogen bonding. Therefore, NA remains dissolved in 3MP also in porous silica. For a sphere of radius R, the probability density for a particles distance r from the center is p(r) ) 3r2/R3 in the continuum limit and the average distance 〈r〉 of a chromophore from the pore wall is thus estimated to be 〈r〉 ) R/4 ≈ 0.94 nm for the 7.5 nm diameter pores. It is precisely this difference in the spatial distribution of QX and NA which is exploited in order to assess the dynamics of the bulk (NA/3MP and QX/3MP), confined (NA/ 3MP), and interfacial (QX/3MP) situation of a viscous liquid. Fitting eq 1 to the respective C(t) data results in the time scales τ(T) compiled in Figure 2 for bulk (τbulk), confined (τconf), and interfacial (τintf) 3MP. The dynamics observed in bulk 3MP are independent of the solute used, NA or QX. In both cases, the C(t) traces are well described by a KWW type decay of eq 1 with βbulk ) 0.42 and by a VFT type temperature dependence
Letters
Figure 2. Temperature dependence of the solvent relaxation time in 3-methylpentane (3MP) for the bulk liquid (QX/3MP, solid circles; NA/3MP, open circles), for 3MP confined to 7.5 nm pores (NA/3MP, open diamonds), and for the interfacial layer of 3MP at the pore wall (QX/3MP, solid diamonds). The solid lines are VFT curves with B ) 464 K, T0 ) 52 K, and A ) -16.8, -15.2, and -13.5, in the order from top to bottom curve. The dotted line indicates the τ ) 100 s criterion for determining Tg. The dashed curve is obtained by shifting the VFT line for the bulk case by ∆Tg ) +5.2 K.
τ(T) of eq 2 with Abulk ) -16.8, B ) 464 K, and T0 ) 52 K. This is the typical behavior of a molecular glass-forming liquid. Assuming that NA is homogeneously distributed within the pores, the confined NA/3MP case reflects the dynamics averaged over the pore volume. According to the data in Figure 2, this situation is characterized by a broader distribution g(τ) of relaxation times, i.e., a smaller exponent βconf ) 0.22, and by VFT parameters Aconf ) -15.2, B ) 464 K, and T0 ) 52 K. The third curve in Figure 2 corresponds to the interfacial layer of 3MP at the pore boundary as probed by QX attached to the interfacial -OH groups. This interfacial case differs from both the bulk and confined liquid case and is characterized by βintf ) 0.25, Aintf ) -13.5, B ) 464 K, and T0 ) 52 K. On the basis of the τ(Tg) ) 100 s criterion for identifying Tg, we find Tg,bulk ) 76.7 K for the bulk liquid, Tg,conf ) 79.0 K for 3MP confined to the 7.5 nm pores, and Tg,intf ) 81.9 K for the interfacial 3MP. Obviously, the surface induces a glass transition of 3-methylpentane at a temperature at which the more remote or bulk material remains in the equilibrium liquid phase. In terms of a glass transition shift relative to the bulk liquid, the above observations are summarized by ∆Tg,conf ) +2.3 K and ∆Tg,intf ) +5.2 K for the confined and interfacial liquid, respectively. However, the different τ(T) traces of Figure 2 do not coincide after shifting by ∆Tg on the temperature scale, as indicated by the dashed curve which corresponds to the bulk VFT fit shifted by ∆Tg ) +5.2 K. Instead, the VFT fits indicate that the changes are accounted for by adjusting the preexponential parameter A only. Therefore, the effect of nanopores is more appropriately described by ∆A or equivalently by a temperature invariant relaxation time ratio. Comparing the average time scale within the pore with that in the bulk leads to τconf/τbulk ) 40, whereas the relaxation time within the interfacial layer is slower by a factor of τintf/τbulk ) 2000. Assuming that the simple relation between 〈τ〉 and η in eq 3 is valid also for the surface dynamics, the viscosity η of the interfacial layer is around 3 orders of magnitude larger than that of the unperturbed liquid, thereby strongly exceeding the interfacial effects observed on the ns to ps time scale.6,7,18 Immobilizing the probe QX itself is not responsible for this
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Figure 3. Probability densities g(ln τ) of relaxation times τ, based on the KWW type solvent relaxations. In the order of increasing peak τ, the curves are for the bulk liquid (QX/3MP and NA/3MP, circles, β ) 0.42), for 3MP confined to 7.5 nm pores (NA/3MP, open diamonds, β ) 0.22), and for the interfacial layer of 3MP at the pore wall (QX/ 3MP, solid diamonds, β ) 0.25). The dashed line is calculated as described in the text.
Figure 4. Suggested trend for τ(r)/τbulk based upon τbulk/τbulk ) 1 for r ) 0 (QX and NA in bulk 3MP), τconf/τbulk ) 40 for r ) 〈r〉 ≈ R/4 ) 0.94 nm (NA/3MP in pores), and τintf/τbulk ) 2000 for r ) R ) 3.75 nm (QX/3MP in pores). The line is an empirical interpolation only. The inner scale shows the distance d from the interface for a spherical geometry.
sluggish dynamics at the interface, because even in the bulk liquid QX hardly rotates on the time scale of the solvent response.25 The spatially resolved dynamics is shown in more detail in Figure 3 in terms of the probability densities g(ln τ) ) τ g(τ) based upon the values of β and τ for the bulk, confined, and interfacial situation. Clearly, the interfacial and bulk relaxation time distributions are separated, whereas the intermediate curve associated with the pore volume average covers both the fastest and slowest relaxation times. In particular, observing that 45% of the g(ln τ) area for the confined case overlaps with the range of τ values observed in the bulk suggests that a fraction of the liquid within the pore behaves bulk like, most likely originating from the pore center. As illustrated in Figure 4, we can now assign relative relaxation times as a function of the distance r (0 e r e R) from the center: τ(r ) 0) ) τbulk, τ(r ) 〈r〉 ) R/4) ) τconf ) 40τbulk, and τ(r ) R) ) τintf ) 2000τbulk, i.e., at the interface. These three points are interpolated empirically by ln(τ(r)/s) ≈ exp[2.15 × (r/R)1.2] - 1, which is used to calculate the convolution of a position dependent τ with weight p(r) dr
898 J. Phys. Chem. B, Vol. 107, No. 4, 2003 ) 3r2/R3 dr with the probability density g(ln τ) of the bulk 3MP. This average over all positions within the pore leads to the dashed line included in Figure 3 and agrees well with much of the distribution obtained for NA/3MP in the 7.5 nm pores associated with the pore volume averaged dynamics. Therefore, the random position of NA within the pore together with the τ(r) curve of Figure 4 are sufficient for rationalizing the broader and shifted probability density associated with the pore volume average. Picosecond reorientational dynamics of wetting and nonwetting liquids in porous glasses has been studied by Fourkas and co-workers, who made changes in the hydrodynamic volume and the reduced dimensionality rather than viscosity responsible for the inhibited surface dynamics.7,18 Because the present work focuses on the time scales of mechanical solvation in a deeply supercooled material, modes other than purely orientational motion play an important role and the layer affected by the interface is significantly thicker. Still, the extent to which our results on the increased relaxation time are paralleled by an accordingly high viscosity near the pore boundary requires further clarification. It would also be interesting to determine whether the dramatic slowing down of the interfacial liquid dynamics is as sensitive to the surface curvature as in the case of the above-mentioned optical Kerr effect experiments.7,18 The observation of a large relaxation time gradient in a simple liquid near a silica surface bears a series of implications. The behavior of a wetting liquid which acts as viscous lubricant changes dramatically within the first few nanometers distance from the surface, even in the absence of atomically smooth surface conditions, specific interactions with the surface, or external pressure. Consistent with experimental findings, such a spatial variation of the dynamics results in the broadening of relaxation time distributions. Observing the most pronounced confinement effects at the surface suggests that the boundaries dominate in altering the properties of the liquid and that pure finite size effects are of minor importance. Within this picture, a surface induced glass transition combined with the cooperative nature of molecular motion in viscous liquids is sufficient for explaining the tentative distance dependence τ(d) of Figure 4. Particles at distances d > 2-3 nm away from the interface are no longer affected, consistent with typical length scales ξ ≈ 3 nm reported for the cooperativity near Tg.8 Accordingly, an analogous distance dependence τ(d) is expected near a single surface without additional spatial restriction. Cooling the liquid subject to geometrical confinement in order to form a glass will result in solidification which sets in at the interface, whereas lower temperatures are required to traverse the glass transition of the inner pore liquid. By the same token, the material near the interface is immobile on the time scale of viscous flow near the center of the pore, thereby confining the liquid further. At the “bottlenecks” which interconnect the pores, such immobile layers may eventually prohibit liquid flow among pores and create a crossover from an isobaric (constant pressure) to an isochoric (constant volume) path. This situation will occur
Letters when the spatial extent ξ of cooperativity competes with the smallest lengths scale of the confining geometry, where ξ depends on the material and temperature. Because Tg and the behavior of the liquid near Tg depend on the thermodynamic path, a crossover to the isochoric condition might contribute to the apparent inconsistency regarding confinement effects of some supercooled liquids,17 whereas this does not apply to o-terphenyl.26 The present findings support previous interpretations of dynamics in porous materials which have invoked a frustrated interfacial layer18,27 and attempts to exploit such measurements for assessing the length scale of cooperativity.28 Because the present sample material, 3-methylpentane, exhibits the typical properties of other branched alkanes and oils, the current findings are relevant also for the performance of lubricants on the nanometer scale and for the transport properties of oil in porous rocks. References and Notes (1) Molecular Dynamics in Restricted Geometries; Drake, J. M., Klafter, J., Eds.; Wiley: New York, 1989. (2) Horn, R. G.; Israelachvili, J. N. J. Chem. Phys. 1981, 75, 1400. Israelachvili, J. N.; McGuiggan, P. M. Science 1988, 241, 795. (3) Van Alsten, J.; Granick, S. Phys. ReV. Lett. 1988, 61, 2570. Granick, S. Science 1991, 253, 1374. (4) Gao, J.; Luedtke, W. D.; Landman, U. J. Chem. Phys. 1997, 106, 4309. (5) Drake, J. M.; Klafter, J. Phys. Today 1990, 43, 46. (6) Warnock, J.; Awschalom, D. D.; Shafer, M. W. Phys. ReV. B 1986, 34, 475. (7) Loughnane, B. J.; Scodinu, A.; Fourkas, J. T. J. Phys. Chem. B 1999, 103, 6061. (8) Ediger, M. D.; Angell, C. A.; Nagel, S. R. J. Phys. Chem. 1996, 100, 13200. (9) Angell, C. A.; Ngai, K. L.; McKenna, G. B.; McMillan, P. F.; Martin, S. W. J. Appl. Phys. 2000, 88, 3113. (10) Jackson, C. L.; McKenna, G. B. J. Non-Cryst. Solids 1991, 131133, 221. (11) Zhang, J.; Liu, G.; Jonas, J. J. Phys. Chem. 1992, 96, 3478. (12) Huwe, A.; Kremer, F.; Behrens, P.; Schweiger, W. Phys. ReV. Lett. 1999, 82, 2338. (13) Schu¨ller, J.; Mel’nichenko, Yu. B.; Richert, R.; Fischer, E. W. Phys. ReV. Lett. 1994, 73, 2224. (14) Barut, G.; Pissis, P.; Pelster, R.; Nimtz, G. Phys. ReV. Lett. 1998, 80, 3543. (15) Wendt, H.; Richert, R. J. Phys.: Condens. Matter 1999, 11, A199. (16) Forrest, J. A.; Dalnoki-Veress, K.; Stevens, J. R.; Dutcher, J. R. Phys. ReV. Lett. 1996, 77, 2002. (17) McKenna, G. B. J. Phys. IV France 2000, 10, 53. (18) Loughnane, B. J.; Farrer, R. A.; Scodinu, A.; Reilly, T.; Fourkas, J. T. J. Phys. Chem. B 2000, 104, 5421. (19) Streck, C.; Mel’nichenko, Yu. B.; Richert, R. Phys. ReV. B 1996, 53, 5341. (20) Scheidler, P.; Kob, W.; Binder, K. Europhys. Lett. 2000, 52, 277. (21) Richert, R. J. Chem. Phys. 2000, 113, 8404. (22) Berg, M. Chem. Phys. Lett. 1994, 228, 317. (23) Wendt, H.; Richert, R. J. Phys. Chem. A 1998, 102, 5775. (24) Richert, R.; Wagener, A. J. Phys. Chem. 1991, 95, 10115. (25) Yang, M.; Richert, R. Chem. Phys. 2002, 284, 103. (26) Simon, S. L.; Park, J.-Y.; McKenna, G. B. Eur. Phys. J. E 2002, 8, 209. (27) Park, J.-Y.; McKenna, G. B. Phys. ReV. B 2000, 61, 6667. (28) Richert, R. Phys. ReV. B 1996, 54, 15762.
