Phase Behavior of Long-Chain n-Alkanes at One and between Two

Nobuo Maeda and Jacob N. Israelachvili. The Journal of Physical ... Takashi Yamamoto , Koji Nozaki , Aki Yamaguchi , Naohito Urakami. The Journal of ...
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5906

J. Phys. Chem. B 2001, 105, 5906-5913

Phase Behavior of Long-Chain n-Alkanes at One and between Two Mica Surfaces Nobuo Maeda*,† and Mika M. Kohonen‡ Department of Applied Mathematics, Research School of Physical Sciences and Engineering, Australian National UniVersity, Canberra ACT 0200, Australia

Hugo K. Christenson Department of Physics and Astronomy, The UniVersity of Leeds, Leeds LS2 9JT, United Kingdom ReceiVed: October 20, 2000; In Final Form: April 2, 2001

The phase behavior of long-chain n-alkanes (carbon number: m ) 14, 16-18) adsorbed at isolated mica surfaces and confined between two mica surfaces has been studied above and below the bulk melting points Tm. Using the Surface Force Apparatus we have measured the thickness of alkane films adsorbed from vapor (0.98 < p/p0 < 0.995), studied the formation and growth of capillary condensates between two surfaces, and monitored phase changes in both the adsorbed films and the condensates. By measuring the growth rate of the capillary condensates we have identified a transition in the lateral mobility of molecules in the adsorbed films. This transition to greater mobility occurs slightly above Tm for n-C16 to n-C18, but several degrees below Tm for n-C14, and is accompanied by a change in wetting properties and a measurable decrease in adsorbed film thickness for n-C17 and n-C18. Capillary condensates that form below Tm remain liquid, but may freeze (crystallize) if the degree of confinement is reduced by separation of the mica surfaces. We conclude that an increase in the area of the liquid-vapor interface relative to that of the liquid-mica interface facilitates freezing in the case of the longer chain alkanes (n-C16 to n-C18), which show surface ordering at the liquidvapor interface. n-C14, which does not show surface ordering at the liquid-vapor interface, does not freeze under the same conditions.

Introduction Gibbs phase rule states that in bulk two parameters, the pressure and temperature, are sufficient to determine the phasestate of a one-component system.1 However, this is valid only for ideal (infinitely large) systems. Any real system has interfacesseither the walls of a container or interfaces between the different phases of the substance under consideration. Intermolecular forces in the proximity of the wall or the interfaces differ from those in the bulk and there is an extra term in the free energy. This surface free energy term becomes important for systems with large ratios of the interfacial area to the volume and affects the phase-state of the substance. Some characteristic measure of confinement, e.g., the slit width or pore diameter, becomes another degree of freedom of the system with a consequent increase in complexity of the phase equilibria. This is of particular significance in porous media such as soils, clays, rocks, and many materials with practical and technological application. Examples of phase transitions induced by solid container walls are capillary condensation of wetting liquids from undersaturated vapor and capillary melting of incommensurable solids. In either case the free energy gain due to wetting of the solid pore walls by the liquid offsets the free energy cost due * Author to whom correspondence should be addressed. E-mail: [email protected]. † Current address: Department of Chemical Engineering and Materials, University of California, Santa Barbara, CA 93106. ‡ Current address: Abteilung Angewandte Physik, Universitaet Ulm, Albert Einstein Allee 11, D-89069 Ulm, Germany.

to condensing undersaturated vapor or melting solid below the bulk melting point.2-4 Most experimental work on the effects of confinement on phase behavior has been carried out with porous solids.4-6 Even among the most well-defined of these such as porous silica glasses (e.g., Vycor) the interpretation is often complicated by polydispersity of the pore size and interconnectivity effects. This leads to substantial hysteresis between condensation and evaporation for capillary condensation, and between freezing and melting in the case of capillary melting.4,5 Especially in the case of freezing-melting transitions the possibility of pore blockage which can lead to hindered equilibration is also of major concern. Recently, novel mesoporous materials such as MCM-41 with isolated, cylindrical pores, and graphitic microfibers with slitlike pores have been used in fundamental studies of phase behavior in confinement.6 Here, the pore size is very monodisperse, and interconnectivity is rare, which often almost eliminates hysteresis effects. Nevertheless, in all these cases the pore size in any one experiment is fixed, and can often not be varied over a wide range. Use of the surface force apparatus (SFA) to study the phase behavior of substances in confinement eliminates some of the problems encountered with porous media. The gap between the two mica surfaces effectively constitutes a single model pore of variable slit width, which can be varied from nanometers to micrometers. The large chamber volume and the presence of a single liquid-vapor interface ensure equilibration during capillary condensation, and only hysteresis due to the first-order nature of the vapor-liquid transition remains. A number of

10.1021/jp003874g CCC: $20.00 © 2001 American Chemical Society Published on Web 05/31/2001

Phase Behavior of Long-Chain n-Alkanes applications of the SFA to capillary condensation have been described in the literature.7-11 We have recently used capillary-condensation experiments with the SFA as a means of studying freezing and melting phenomena in a single pore.12-14 With vapor in the chamber in equilibrium with bulk solid, liquid will condense between the surfaces at small separations. The unfavorable interfacial free energy between the mica and the solid phase of the condensed substance shifts the equilibrium phase state of the condensate to liquid below the bulk melting point. Such experiments have been carried out with alcohols such as tert-butyl alcohol, neopentanol, and menthol, chosen because their bulk melting points are close to room temperature.12,13 The size of the condensate decreases with decreasing temperature, and is inversely proportional to the temperature below the bulk melting point. The behavior is analogous to the inverse relationship between melting-point depression and pore size found in many porousmedia studies. With the SFA we are thus able to study the equilibrium between bulk solid, vapor, and condensed liquid in a pore. This is equivalent to determining a line of triple points in the system. While capillary condensates in the annular wedge formed around mica surfaces in contact have not been observed to freeze, even at 40 °C below Tm, observations have been made of (i) direct condensation of solid from vapor outside the liquid condensate, and (ii) freezing of liquid condensates on separation of the surfaces.12,13 We have recently described such observations with n-octadecane condensed from vapor between mica surfaces.14 Freezing occurred more easily as the degree of confinement of the alkane was reduced. A few degrees below Tm freezing occurred only after the condensates had snapped when the surfaces were taken far apart, at lower temperatures the liquid necks would freeze while still joining the surfaces while at the lowest temperatures studied solidification occurred immediately upon separation from contact. There was thus a qualitative correlation between the ease of freezing and the relative areas of the liquid-vapor interface compared to the mica-liquid interface. On lowering the temperature after condensation of liquid around the surfaces at contact, slow growth of crystallites from the liquid-vapor interface into the vapor could be observed.14 In contrast, in similar experiments with for example tert-butyl alcohol the condensates are observed to evaporate until the equilibrium size at the lower temperature is reached.12,13 These results suggest that the liquid-vapor interface of the capillary condensates of n-alkanes promotes nucleation of solid, either in the liquid or directly from vapor. Normal alkanes are very common compounds in science and engineering, and are widely used in lubricants and fuels. Polymers, surfactants, and liquid crystals as well as many biological molecules such as lipids, all contain structural units of n-alkanes. They are known to exhibit rich bulk phase behavior. For n-alkanes with odd carbon numbers and even carbon numbers of m g 20, rotator phases are found at temperatures between the liquid and crystalline phases.15-17 In the rotator phase there is rotational freedom about the long axis of the molecules, although the positional order of the bulk triclinic (for m even) or orthorhombic (m odd) lattice structure is preserved. Most intriguing, however, are the surface properties of some of the long-chain n-alkanessthey are one of the few substances that exhibit surface ordering or surface “freezing”. The interface between vapor and bulk liquid n-alkanes for 16 e m e 50 (also for m ) 15 according to some reports18,19) remains ordered up to a few degrees above the bulk melting

J. Phys. Chem. B, Vol. 105, No. 25, 2001 5907 point (Tm).20 The surface tension of these n-alkanes thus shows a maximum a few degrees above Tm, instead of the usual monotonic decrease with temperature.18,19 The formation of an ordered monolayer at the liquid-vapor interface with the structure of the hexagonally packed bulk rotator-like phase has been inferred from X-ray reflection studies.19,20 Subsequently, ellipsometry,21 nonlinear optics,22 and Gibbs adsorption isotherm23 studies have independently confirmed the presence of these ordered monolayers. Unlike the case with surface melting of solids below the melting point, the order in the surface monolayer does not propagate gradually into the bulk alkane as the temperature is lowered toward the bulk melting point. A simulation study suggests that the molecules in the monolayers can hardly move along the surface whereas motion perpendicular to the surface seems to be less restricted.24 The increased mechanical strength of the surface frozen layers has been inferred from the longer lifetimes of foams25 and bubbles26 in long-chain n-alkanes below the surface ordering transition temperature Tsf. Surface ordering of long-chain n-alkanes occurs not only at the free liquid-vapor interface but also in thin films adsorbed on a solid substrate. Thin films of long-chain n-alkanes adsorbed on silica substrates undergo a surface phase transition, accompanied by a change in thickness and wetting properties a few degrees above the bulk melting point.27 We have recently studied films of n-hexadecane and noctadecane formed on mica by vapor adsorption.28 Using a novel application of the SFA to study the growth rate of capillary condensates we were able to identify a transition in film mobility with temperature of the adsorbed layers of alkanes. At this transition, which occurs about 2 degrees above Tm, the mobility of molecules in the alkane films increases by over an order of magnitude. At the same temperature, an experimentally significant decrease in adsorbed film thickness was measured with n-octadecane, but could not be found for n-hexadecane. These results suggested the occurrence of an order-disorder transition of the adsorbed alkane films on mica, akin to that found at the surface of bulk alkanes19,20 and with adsorbed films on silica.27 In this paper we present a continuation and an extension of our previous work on long-chain n-alkanes confined to a single mica surface and between two mica surfaces above and below the bulk melting point. We extend previous studies with n-octadecane and n-hexadecane to include n-heptadecane and n-tetradecane, and present information on film mobility from the growth rates of capillary condensates, adsorbed film thickness, and the phase state of capillary condensates. In particular, we here report the observation of a surface phase transition for n-tetradecane (n-C14) films on mica, a substance which does not exhibit surface ordering at the liquid-vapor interface. In contrast to the longer-chain alkanes, however, thin adsorbed films of n-C14 on mica substrates appear to undergo a transition at a temperature several degrees below Tm. Materials and Methods The simplified SFA used in this study has been described previously.13,14 Briefly, two back-silvered, molecularly smooth mica surfaces are glued with a thermosetting epoxy resin (Epikote 1004, Shell Chemical Co.) to cylindrically polished silica disks of radius of curvature R ≈ 2 cm. The disks are mounted in a crossed-cylinder configuration, with one of the disks on a rigid support of effective spring constant k ≈ 105 N/m, and the other at the end of a piezoelectric cylinder (see Figure 1). Calcium hydride was used as a drying agent in the chamber.

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Maeda et al.

Figure 2. Thickness d of the adsorbed film of n-C18 at 30.0 °C as a function of time after the liquid is introduced into the measuring chamber. d initially increases and then approaches a constant value of ≈3.5 nm after ≈40 h.

Figure 1. Schematic picture of the simplified Mark IV SFA. The monochromator can be replaced by a video recorder to directly inspect the surfaces via optical microscopy. The entire setup is housed in a temperature-controlled cabinet and room.

The interference fringes (fringes of equal chromatic order: FECO29) are recorded with a cooled CCD camera (Photometrics PXL). The CCD consists of a 512 × 512 pixel array, and exposure times of 100 to 3000 ms are employed. The fringes are analyzed using software from Digital Optics that fits a quadratic function to the intensity profile distributed over several pixels and finds the intensity peak with a maximum accuracy of about 0.05 pixels. The analysis yields the surface separation H and the refractive index n of the medium between the surfaces, as well as the shapes of the surfaces and the lateral dimensions of capillary condensates around the contact zone. From n one calculates the thickness d of adsorbed films on the mica surfaces using

d)

H(n - 1) 2(nf - 1)

(1)

where nf is the (bulk) refractive index of the alkane in question. Temperature control is achieved with a two-stage method. The room temperature is controlled to (0.2 °C in the range 15-35 °C using a compressor and a stageless heating unit. A second heating unit inside a wooden cabinet around the SFA is supplied with a fan and a heating unit, which is set at 0-1 °C above the temperature of the room. In this manner control to (0.05 °C may be achieved. The actual temperature is measured with a thermocouple placed inside the SFA (at the same height as but ≈5 mm away from the mica surfaces). Due to a small heating effect by the light beam the temperature at the mica surfaces is about 0.1 °C hotter than that of the bulk reservoir at the bottom of the SFA. For measurements at temperatures below 15 °C a separate cooling unit is connected to the wooden cabinet. Coolant at a temperature down to -20 °C is passed through a metal heat exchanger inside the cabinet. To avoid condensation of water and build-up of ice on the heat exchanger dry air is passed

through the cabinet. The lowest temperature achieved inside the SFA in this manner was ≈ -3.5 °C. At these lower temperatures there is a larger temperature gradient in the chamber, of the order of a few tenths of a degree, although the surfaces remain warmer than the reservoir. Measurements of the contact wavelengths of the fringes (which defines the mica thickness and the zero of separation) in an atmosphere of dry nitrogen were carried out at the uppermost and the lowermost temperatures in the range of interest, to account for the thermal expansion of mica (approximately 2 × 10-5 K-1). The contact wavelengths at intermediate temperatures were calculated by linear interpolation. After measurements in dry nitrogen the liquid n-alkanes (Sigma or Aldrich, 99+%) were injected onto the bottom of the chamber, usually at the highest temperature in the range of interest. We did not observe any noticeable difference between as-received and distilled samples for n-C18 and n-C16 and hence used only as-received samples for n-C17 and n-C14. After the injection the system was left to equilibrate for several days due to the very low vapor pressure of the samples (≈3 × 10-4 mmHg at 31 °C in case of n-C1830). Measurements of the film thickness at an isolated surface, the surface separation at which jumps into contact occur, and the size of capillary condensates as a function of time in contact were then carried out at each temperature. Subsequently, at least 11 h was allowed for reequilibration on changing the temperature. Measurements were carried out both on decreasing and increasing the temperature. The surfaces were occasionally monitored with optical microscopy from above during the course of the experiment, and the reservoir inspected visually through a window in the SFA. Results The thickness d of adsorbed films on effectively isolated mica surfaces in vapor of n-C18 at T ) 30 °C is shown as a function of time in Figure 2. It appears that after some 40 h the film thickness has reached its final value, and we are thus confident that we have allowed sufficient time for equilibration in the experiments by allowing several days to elapse. The relative vapor pressure calculated from the maximum condensate size and the Kelvin equation was g0.97. Figure 3 shows the measured film thickness as a function of temperature above and below Tm (dashed line) for n-C17 at p/p0 g 0.98. Note the decrease in d at about 25 °C, from 3.3 ( 0.2 nm to 2.4 ( 0.2 nm. Similar results were obtained for n-C18, where d decreased from 3.5 ( 0.5 nm to 2.8 ( 0.5 nm at 3031 °C (Tm ) 28.2 °C), at p/p0 g 0.97.28 The change in film thickness appeared to occur at lower temperatures on cooling

Phase Behavior of Long-Chain n-Alkanes

Figure 3. Thickness d of the adsorbed film of n-C17 as a function of temperature, calculated using the symmetrical three-layer interferometer model (eq 1) and refractive index of the bulk liquid. The bulk melting point (22 °C) is indicated with a dashed line. There is a significant decrease in d around 25 °C.

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Figure 5. Volume of the capillary condensates of n-C17 as a function of time at various temperatures. The first measurement was obtained 1 min after the surfaces were brought into contact and the data are shown for the first 60 min only. There is a significant increase in the condensate growth rate at about 25 °C. The solid line is the condensate growth rate calculated by the film drainage model (eq 3), using A ) 1.2 × 10-20 J, η ) 4 mPas, γ ) 27.5 mN/m. The dashed line is the condensate growth rate calculated by the vapor diffusion model (eq 2), using p0 ) 3.2 × 10-4 mmHg, p/p0 ) 0.995, Df ) 0.042 cm2 s-1.

Figure 4. Thickness d of the adsorbed film of n-C14 as a function of temperature, calculated using the symmetrical three-layer interferometer model (eq 1) and refractive index of the bulk liquid. Different symbols are from different experiments. The bulk melting point (5.9 °C) is indicated with a dashed line. No significant change in d is observed over the temperature range studied.

than on heating (not shown). For n-C16 at p/p0 g 0.98 (Tm ) 18.2 °C) no clear transition could be determined from 16 to 25 °C, within error. Figure 4 shows the results of similar measurements with n-C14, where the measurements were extended down to temperatures of 7 degrees below Tm at 5.9 °C. p/p0 was estimated to be g0.99. No obvious change in d over the entire temperature range could be identified. The larger scatter at the lower temperatures is most likely related to larger temperature fluctuations when the heat exchanger is used (see Materials and Methods section). As the surfaces approach they are pulled into contact by the formation of a capillary condensate, which is liquid for all alkanes at all temperatures over the experimental range. The critical surface separation at which capillary condensation occurs was for all alkanes constant, within error, over the experimental range and found to be 14 ( 4 nm. After the inward jump, the surfaces come to a separation of typically 1.0 ( 0.2 nm, and if a load is applied to the surfaces, this separation may be seen to shift inward to about 0.5 nm. If the surfaces are left in contact after the inward jump, a capillary condensate grows slowly around the contact zone. Figure 5 shows the measured condensate volume as a function of time in vapor of n-C17 at a selection of different temperatures.

Figure 6. Volume of the capillary condensates of n-C14 as a function of time at various temperatures. The first measurement was obtained 1 min after the surfaces were brought into contact and the data are shown for the first 60 min only. There is a significant increase in the condensate growth rate at about 1 °C. The solid line is the condensate growth rate calculated by the film drainage model (eq 3), using A ) 1.2 × 10-20 J, η ) 4 mPas, γ ) 26.5 mN/m. The dashed line is the condensate growth rate calculated by the vapor diffusion model (eq 2), using p0 ) 4 × 10-3 mmHg, p/p0 ) 0.995, Df ) 0.04 cm2 s-1.

As can be seen, the rate of condensate growth increases drastically between 24 and 25 °C, the same range at which the thickness transition was observed. There is some hysteresis, with the transition occurring at slightly higher temperatures on heating than on cooling (not shown). Similar results were obtained earlier with n-C18 and n-C16,28 with a transition to more rapid film growth a few degrees above Tm. The solid and dashed lines in Figure 5 will be discussed in the next section. Figure 6 shows the condensate volumes as a function of time in vapor of n-C14 at different temperatures. As can be seen, the rate of condensate growth increases drastically at about 1 °C, in this case well below Tm. The solid and dashed lines in Figure 6 will be discussed in the next section. To facilitate comparisons between the investigated alkanes Figure 7 shows the condensate volume V after an elapsed time of 1 h at each temperature. In each case, the volume shows a

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Maeda et al. have here been qualitatively confirmed with n-C17 over the equivalent temperature range below Tm, and for (Tm - T) g 7 °C for n-C16. By contrast, the behavior with n-C14 appears to be quite different. No freezing of the liquid bridge was ever observed, down to 7 °C below Tm. Discussion

Figure 7. Volume of the capillary condensates of n-alkanes (C14, C16, C17, C18) after 1 h in contact (V1hr) as a function of temperature. Different symbols refer to different n-alkanes, diamonds for C14, triangles for C16, squares for C17, and circles for C18. The bulk melting points of the n-alkanes are indicated by vertical, dashed lines. There is a significant increase in the volume of the capillary condensates for each n-alkane, at ≈1 °C for C14, ≈19 °C for C16, ≈25 °C for C17, and ≈31 °C for C18.

sharp increase over a narrow temperature range of 0.5-1.5 °C above Tm for n-C16, and 2-3 °C above Tm for n-C17 and n-C18, but about 5 °C below Tm for n-C14. After measurements of the condensate size, the surfaces were separated and the refractive index of the resulting liquid bridges determined. The results were found to agree with the corresponding bulk literature values,31 e.g., 1.432-1.437 for n-C16 and 1.432-1.436 for n-C18. Above Tm when the surfaces are separated a large distance the liquid bridge snaps and droplets are formed on each of the opposing mica surfaces. The appearance of these droplets when viewed from above through the microscope eyepiece shows that an apparent change in wetting occurs at the same temperature as a transition in surface mobility and (for some of the alkanes) in adsorbed film thickness. Figure 8 shows both the appearance of the FECO and optical microscope photographs of n-alkane droplets on mica surfaces below (Figure 8a) and above (Figure 8c) this transition temperature Tt. Above Tt, when the condensate growth rate is fast, the droplets spreads over the surfaces quickly, suggesting a small contact angle. Below Tt the droplets have a larger contact angle and do not spread. They stay on the surfaces in coexistence with the adsorbed thin films for hours until they finally evaporate. Rough values of the contact angle of these droplets can be estimated via the FECO from the width of the droplets and surface separation at which they coalesce if the surfaces are rapidly brought together again. Assuming that the two droplets are both identical spherical caps, the contact angle below Tt was estimated to be 16° ( 6° for n-C18. This value is slightly higher than the 10° reported for n-C20 on silica.27 At temperatures close to the transition the droplets on either surface may split abruptly into several smaller droplets as the bridge snaps (Figure 8b). When the surfaces are separated below Tm the phase state of the condensate and its variation with surface separation depends on the temperature and the particular alkane in question. This has been extensively studied for n-C18, and the results reported elsewhere.14 Briefly, the lower the temperature the more easily solidification occurs; within 2 °C of Tm the liquid does not freeze before the condensate has snapped, at T-depressions of 2-4 °C freezing takes place immediately after a jump out from contact is observed, and at still lower temperatures the entire bridge freezes during the separation process. These phenomena

The results of the present study will be discussed with appropriate reference to earlier published observations on the freezing and melting of n-C18 condensed between mica surfaces,14 and our initial study of n-C16 and n-C18 films adsorbed on mica.28 Adsorbed Film Thickness. Previous measurements over the range 17-30 °C failed to detect any experimentally significant change in d for n-C18 as they stopped just short of the apparent transition which we have found here.14 This transition in adsorbed film thickness identified for n-C17 and n-C18 is a clear indication that the nature of these films changes a few degrees above the bulk melting point. The lack of a clear transition with either n-C14 or n-C16 shows that we are at the limit of what the interferometry technique can resolve. The film thicknesses measured below the transitions (where such can be identified) appear to be slightly greater than the length of an extended alkane molecule (all trans configuration). While we can obviously only speculate about the structure of the adsorbed films, one possibility is that there is a disordered region next to the mica surface with more ordered parallel chains perpendicular to the surface above it. Capillary Condensation Transition. The separation Hc at which the capillary-condensation transition occurs is in rough agreement with previous work on a number of liquids, where d values of 3 nm typically give Hc values in the range 12-15 nm. A theoretical model based on the coalescence of adsorbed films on the opposing surfaces due to van der Waals forces has been shown to be accurate for adsorbed films of d g 5 nm. The reasons for the deviations toward greater Hc from this filmthickening model for the thinner films have been discussed in detail in a number of recent publications.8,9 The present work merely confirms these deviations without shedding further light on the matter. As found with other liquids there is no change in behavior at the bulk transition Tm. The transition in surface mobility and adsorbed film thickness at Tt does not show up in the Hc values either. This is not surprising in view of the experimental accuracy. Growth Rates of Capillary Condensates. When the surfaces are pulled together by capillary condensation of n-alkane from vapor, they remain separated by a thin film of liquid. This “contact” separation is consistent with previous results from measurements of solvation forces between mica surfaces in bulk n-C14 and n-C16, which show that very large applied loads would be required to remove the last layer or two of molecules from between the surfaces.32 As the n-alkanes layer parallel to the mica surfaces under these conditions, the experimental data typically show that two layers of alkyl chains remain between the surfaces at contact. During the jump-in caused by the capillary condensation, the films adsorbed on the isolated surfaces are squeezed out and the liquid collects in the annular condensate around the flattened contact zone. In the context of our suggested structure of the surface films on isolated surfaces the jump-in would see the removal of most or all of the outer, ordered region from between the surfaces. The change in subsequent growth rate of the capillary condensates found with temperature is the clearest

Phase Behavior of Long-Chain n-Alkanes

J. Phys. Chem. B, Vol. 105, No. 25, 2001 5911

Figure 8. Optical microscope pictures of n-octadecane droplets left on the isolated mica surfaces after the liquid bridge has snapped at T < Tt (a), T ≈ Tt (b), and T > Tt (c). At T < Tt a single droplet is left on either mica surface, with a finite contact angle of θ ≈ 10°-22°. At T ≈ Tt, the bridge splits into a number of small droplets. At T > Tt, a single, spreading droplet is left on either surface.

evidence we have of a transition in the structure of the adsorbed alkane films. Recent measurements with vapors of liquids such as pentane, hexane, cyclohexane, and water have shown that for these liquids of high vapor pressure (20-500 mmHg) the growth rates of capillary condensates appear to be largely controlled by vapor diffusion from the reservoir into the annular wedge around the contact zone.33,34 Following the results of that study, the dashed lines in Figures 5 and 6 represent condensate growth rates calculated assuming that material transfer to the condensate occurs solely by diffusion through the vapor phase. The size of the condensate is described in terms of the radius of curvature of the liquid-vapor interface, r, which, to a very good approximation, is given by half the separation between the mica surfaces at the location of the meniscus.7-13 Under steady-state conditions the growth is described by the following equation:33,34

[

( )]

-γVm dr DMwp0 p ) G(r) - exp dt RgTF p0 RgTr

(2)

where D is the diffusion coefficient, Mw is the molecular weight, p0 is the saturation vapor pressure, p is the actual vapor pressure, Rg is the gas constant, F is the density, γ is the surface tension, Vm is the molar volume of the liquid, and G is a function characterizing the geometry of the contacting mica surfaces. The volume of the condensate is related to r by the equation V ) 4πRr2, where R (≈2 cm) is the radius of curvature of the mica surfaces.14 Clearly, while this model appears to give results that are reasonably close to the growth rates measured below the transition temperatures for both n-C14 and n-C17 (as was found previously for n-C16 and n-C18), it underestimates them by over an order of magnitude above the transition temperature. The films adsorbed to the mica surfaces outside the liquid-vapor interface of the condensates provide an alternative route of material transport into the condensates. Assuming that the disjoining pressure, Π, of the adsorbed films can be described by Π ) A/6πd3 where A is the Hamaker constant,35 a simple calculation gives the following equation for the rate of change of r due to flow of liquid along the mica surfaces:28,34

dr 2(dr - d)Df I(t:Df,R) ) dt π2Rr

(3)

where Df ) A/6πηd, η is the viscosity, d is the adsorbed film thickness, dr is the film thickness calculated by equating the Laplace pressure in a meniscus with radius of curvature r to the disjoining pressure of the film, R is the annular radius of

the growing meniscus, and I is an integral, the values of which have been tabulated. The solid lines in Figures 5 and 6 represent the predicted rate of growth assuming material transfer to the condensate occurs solely by flow of liquid along the mica surfaces. The curves were calculated using eq 3, based on the measured values of d, R and R, and estimated values of A and the bulk viscosity η (given in the figure captions). (A more detailed discussion of the modeling of film drainage will be provided in a forthcoming publication.34) As can be seen, the measured growth rates above the transition are consistent with a mechanism dominated by material transport in the adsorbed films. Evidently, the decrease in adsorbed film thickness identified for n-C17 and n-C18 is accompanied by a transition to much greater mobility of the adsorbed molecules, and a similar transition occurs for n-C14 and n-C16 as well. This is consistent with a picture of greater disorder of the alkane chains above the transition. n-C14 is not believed to show surface ordering at the alkanevapor interface.19,20 Our results suggest that there is no intrinsic difference between the transitions experienced by the n-C14 film below Tm and that found for the longer-chain alkanes above Tm. There is indeed no reason a transition in surface behavior should automatically be related to the bulk phase behavior in the same manner. The lack of surface ordering on bulk n-C14 is simply due to the transition being pre-empted by bulk freezing. This does not occur with the adsorbed layers on mica, and the surface transition simply shifts toward lower temperatures with decreasing alkyl-chain length, as expected. Disordering of the alkyl chains would occur at lower temperatures as the chain length decreases.19,20 Wetting Behavior of Surfaces. Additional support for a transition comes from observations of the wetting behavior of the droplets formed on rupture of the liquid bridges on separation. The higher contact angle observed below the transition is consistent with a surface presenting a larger relative concentration of methyl groups at the surface. The more disordered layer above the transition would have a greater fraction of methylene groups, leading to a smaller contact angle of the alkane droplets, as observed. Our suggested picture of the structure of the adsorbed alkane films above and below Tt would thus appear as in Figure 9, which also shows the situation between two mica surfaces at all T in the experimental range. Hysteresis. All features connected with the transition showed temperature hysteresis. We could not accurately quantify this hysteresis, but it appeared to be of the order of a degree. The observations suggest a first-order transition, as in surface freezing of bulk liquid n-alkanes.26 Although the equilibrium properties of the ordered surface monolayers on the bulk alkanes have been rather well documented by now, the kinetics of

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Maeda et al. a consequence of the absence of surface ordering in this liquid. Clearly, kinetic effects are involved in these freezing phenomena, but we are not in a position to provide any information on these. Conclusions Our results show that n-C16, n-C17, and n-C18 films adsorbed on isolated mica surfaces undergo a first-order transition at a temperature a few degrees above Tm, whereas n-C14 films undergo the same transition at a temperature approximately 5 °C below Tm. The transition is accompanied by an increase in lateral mobility of the molecules in the films and a change in the wetting properties, together with a measurable decrease in adsorbed film thickness for n-C17 and n-C18. This is in agreement with the surface ordering (surface freezing) of n-alkanes observed at the bulk liquid-vapor interface and wetting transition of n-alkanes on silica surfaces. The freezing and melting behavior of these n-alkanes confined between mica surfaces is influenced by surface ordering of the alkane-vapor interface, and this leads to easier nucleation of solid with n-C16, n-C17, and n-C18 than with n-C14.

Figure 9. Schematic illustration of the proposed structure of the adsorbed alkane films. At low temperatures (T < Tt) the film region next to the mica substrate is disordered with a more ordered, outer layer of all-trans chains perpendicular to the surface. Bulk alkane forms a finite contact angle on the film (top). At higher temperatures (T > Tt) the outer film region becomes more disordered and the film thins slightly. Bulk alkane spreads on the film (middle). Between two mica surfaces at small surface separations (H ≈ 1 nm) alkane chains order parallel to the surfaces for all temperatures in the range of study (bottom).

formation of such monolayers has so far received little attention. The matter is complicated by the possible role played by impurities. Apparently, impurities seem necessary to nucleate the ordered surface layers, although the nature of the impurities seems to be unimportant.20 The lack of nucleation sites on the atomically flat mica surfaces means that the temperature must be lowered below the (equilibrium) transition point to induce surface freezing of the films. Freezing and Melting Behavior. Previous observations with n-C18 have shown how liquid bridges freeze as the surfaces are separated from contact, even at temperature depressions as small as 2 °C.14 This is in stark contrast to results with most other liquids that have been studied under similar conditions. tertButyl alcohol does not freeze down to 13 °C below Tm12,13 and menthol remains liquid at 40 °C below Tm.36 With neo-pentanol it appears that direct condensation of solid from vapor will occur at temperature depressions of 12-18 °C and more, but at higher temperatures liquid bridges do not freeze on separation of the surfaces. Freezing for relatively smaller ∆T has here been confirmed for bridges of n-C16 and n-C17, whereas n-C14 remains liquid 7 °C below Tm. We conclude that liquids that exhibit surface ordering at the liquid-vapor interface are more liable to freeze when the liquid-vapor interfacial area is increased on separation. The presence of ordered surface monolayers facilitates the nucleation of crystalline or rotator phases, and prevents substantial supercooling of bulk long-chain alkanes. The mica-condensate interface would in all cases be expected to inhibit crystallization or freezing. Unfortunately, we have not been able to quantitatively relate the observations of freezing to the relative magnitudes of the interfacial areas before and after separation. The lack of freezing with n-C14 is then simply

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