Melting of Linear Alkanes between Swollen Elastomers and Solid Substrates

Transcription

1 pubs.acs.org/langmuir Melting of Linear Alkanes between Swollen Elastomers and Solid Substrates Kumar Nanjundiah and Ali Dhinojwala* Department of Polymer Science, The University of Akron, Akron, Ohio 44325, United States *S Supporting Information ABSTRACT: We have measured the melting and freezing behavior of linear alkanes confined between cross-linked poly(dimethylsiloxane) (PDMS) elastomers and solid sapphire substrates. Small molecules are often used as lubricants to reduce friction or as plasticizers, but very little is directly known about the migration or changes in physical properties of these small molecules at interfaces, particularly the changes in transition temperatures upon confinement. Our previous studies highlighted striking differences between the crystal structure of confined and unconfined pentadecane crystals in contact with sapphire substrates. Here, we have used surface-sensitive infrared visible sum-frequency-generation spectroscopy (SFG) to study the melting temperatures (T m ) of alkanes in nanometer thick interfacial regions between swollen PDMS elastomers in contact with sapphire substrate. We find that confined alkanes show depression in T m compared to the melting temperature of unconfined bulk alkanes. The depression in T m is a function of chain length, and these differences were smallest for shorter alkanes and largest for 19 unit long alkanes. In comparison, the DSC results for swollen PDMS elastomer show a broad distribution of melting points corresponding to different sizes of crystals formed within the network. The T m for confined alkanes has been modeled using the combination of Flory Rehner and Gibbs Thomson models, and the depression in T m is related to the thickness of the confined alkanes. These findings have important implications in understanding friction and adhesion of soft elastomeric materials and also the effects of confinement between two solid materials. INTRODUCTION Small molecules are added in cross-linked rubber to improve processing, as plasticizers in thermoplastic polymers to improve mechanical properties, or as lubricants to reduce friction (for example in syringes). Often in these situations it is expected that small molecules may migrate to the grain boundaries or interfaces between two solid materials. Our understanding of the physical properties of molecules at buried interfaces is limited, particularly in organic soft materials. Recently, we have developed a simpler experimental design to study the physical properties of confined liquids by pressing cross-linked elastomers in contact with solid surfaces. This geometry, in combination with surface-sensitive infrared visible sumfrequency-generation spectroscopy (SFG), was used to study confinement of water, alkanes, and other small molecules between PDMS elastomers and sapphire substrates. 1 4 In our previous work with alkanes, we have observed dramatic differences in the structure of pentadecane crystals in contact with sapphire substrate in comparison to pentadecane bulk crystals. 1 Here, we report our measurements on the melting and freezing transitions of confined alkanes between PDMS hemispherical lenses swollen with alkanes pressed in contact with sapphire substrates. The Gibbs Thomson (GT) model, developed to explain the changes in T m of small crystals, considers the extra surface energy required when forming thin crystals in contact with the bulk liquid. 5 7 The difference in T m compared to the bulk melting temperature (T m 0 ) can be determined using the equation 0 a( σcs σls) Tm Δ Tm = Tm,conf Tm = dδhfρs (1) In eq 1, d is the thickness or the radius of the crystal, ΔH f is the latent heat, σ ls is the liquid solid interfacial energy, σ cs is the crystal solid interfacial energy, ρ s is the molar density of the solid, and a is a geometric factor determined by the shape of the confined crystals and is equal to 2 for rectangular slabs. This model has been widely used to explain the transition temperatures of small molecules confined in porous media Increased ordering and viscosity have been observed for liquids confined between two mica surfaces, and this has been used to infer the enhancement in T m or the glass transition temperature The friction and sliding forces are also affected by the changes in properties of liquids due to confinement. 14,15 If small molecules penetrate inside the elastomers (or solid), then there is an additional depression in T m due to the entropy Received: July 27, 2013 Published: September 4, American Chemical Society 12168

2 of mixing. For long chain molecules, the Flory Huggins equation 16,17 (FH) can be used to model the depression in T m. T m Δ Hf + αϕ2 = o ΔHf/ Tm Rln(1 ϕ ) R[1 (1/ r)] ϕ 2 2 (2) In eq 2, ϕ 2 is the polymer volume fraction, r is the ratio of the molar volume of a polymer chain with respect to that of a small molecule, and R is the gas constant. The interaction parameter, α, is = ε (ε 11 + ε 22 ), where ε are the pair pair interaction energies. The χ-parameter that is used in the polymer literature is equal to α/rt. Equation 2 predicts a depression in T m, particularly for high values of ϕ 2. In the case of swollen elastomers, the size of the crystals is also controlled by the elasticity of the network, and in this case, the melting temperature depends on the entropic effect, the size of the crystals, and an additional term due to the stiffness of the elastic network. The effects of elasticity on swelling was described by the Flory Rehner equation. 17 All of these terms can be combined together and the depression in T m can be written as follows: ΔHf aσ/( ρd) + αϕ s 2 Tm = 0 1/3 ΔHf/ Tm R ln(1 ϕ ) R[1 (1/ r)] ϕ Rx( ϕ ϕ /2) (3) In eq 3, most of the terms are similar to those defined in eqs 1 and 2, and the new term x is equal to Vρ/M. Here, V is the molar volume, ρ is the density, and M is the molecular weight between cross-links. This equation was first used to understand the swelling of natural rubber with benzene. 18 In elastomers (or cross-linked networks), a broad distribution of melting temperatures is observed, and it has been suggested that each of these melting temperatures corresponds to a crystal of a particular size. Using this assumption, eq 3 and the experimentally measured distribution in T m have been used to determine the distribution of pore sizes or porosity. This problem was revisited by McKenna and co-workers 19,20 recently to study the melting of benzene in natural rubber and other small molecules in PDMS and polyisoprene networks. 21,22 McKenna and co-workers concluded that these models were unable to predict the depression in T m, and the heat of fusion was used as a fitting function to model the depression in T m. 23 For soft swollen elastomers in contact with solid substrates, the situation is more complex because of the influence of the solid surface on the segregation of small molecules at the interface. We anticipate a depression in T m as predicted by eq 3 as well as the segregation of alkanes next to the sapphire substrate. In addition, we know from previous studies that the crystal structure for confined and unconfined alkanes is different, and this may also influence T m. 1 In this paper, we have compared the transition temperatures of alkanes in bulk elastomers (measured using DSC) with those upon confinement (measured using SFG). In addition, we have used linear reflectivity measurements to probe the intermediate length scale between the DSC and SFG measurements to understand whether the melting starts at the interface or in the bulk. The combination of these three techniques provides an intriguing picture of how the interfacial melting temperature is affected by the alkane chain length. These results have important implications in many industrial and biological areas where a small amount of liquid can be trapped between soft or hard boundaries. 2 2 EXPERIMENTAL SECTION Sample Preparation. The PDMS lenses were prepared using Sylgard 184 monomer from Dow Corning Inc. The recipe consisted of 1 part cross-linker to 10 parts monomer. The monomer and the crosslinker were mixed together, and the air bubbles were removed. The lenses were made by placing a drop of this mixture on a fluorinated glass surface under water. The lenses used in these experiments were 5 mm in diameter. The lenses were cured under water at room temperature for 24 h. The water was removed, and the lenses were dried using dry nitrogen. The lenses were further cured in a vacuum oven for 4 h at 60 C. The cured lenses can have some amount of uncross-linked PDMS oligomers that could potentially leach out during the experiments. 2,24 Therefore, the lenses were soaked in toluene to remove these un-cross-linked chains. The toluene was replaced every 3 days for 2 weeks. The lenses were then removed from toluene and dried under vacuum for 4 h prior to the experiments. The root-meansquare (rms) roughness of the of the surface of the PDMS film was 0.5 nm, measured using an atomic force microscope (Nanoscope IIIa multimode AFM manufactured by Digital Instruments). 2,24 The modulus of the PDMS lenses was 2 3 MPa measured using Johnson Kendall Roberts (JKR) experiments. The static contact angle of water was 110 on PDMS. The surface energy of the PDMS surface was mj/m 2 (determined using JKR measurements). 24 Alkanes of chain length C15 C27 were purchased from TCI America Inc. with purity greater than 98 wt %. They were used as received without further purification. In addition, selective experiments were done with 99.5 wt % purity alkanes, and no differences in the SFG spectra or transition temperatures were observed due to differences in the purity of the alkane samples. The samples for SFG and optical reflectivity were prepared by soaking the PDMS lenses in liquid alkanes (C15 and C17). For longer alkanes, the PDMS lenses were soaked in alkanes at temperatures above T m and then cooled back to room temperature. However, this resulted in cracking of the lens surfaces due to fast crystallization. To overcome this problem, the longer alkanes were melt cast directly on the sapphire surface and brought in contact with the PDMS lens. Before starting the experiments, the samples were heated above T m to allow for the system to attain equilibrium. The equilibrium concentration of alkane inside the PDMS lens (determined by weighing the lens before and after alkane swelling) achieved by the two different routes was found to be equivalent. The sapphire prisms were first wiped with toluene using a soft tissue and sonicated in toluene for 1 h. Then, they were washed with copious amounts of water and blow-dried using dry nitrogen. Finally, the sapphire prisms were plasma cleaned using air plasma for a period of 5 min before the experiments. The SFG cell was washed in soap solution and sonicated in toluene for a period of 2 h. The cell was then washed with water and blow-dried using dry nitrogen. The cell was heated in an oven at 135 C for 10 min and cleaned using air plasma before the experiments. The RMS roughness of the sapphire prism was nm measured using AFM (20 μm 20 μm scan area). For the SFG measurements, the soaked lenses were placed in the cell and brought in contact with the sapphire prism. The lens deformed under pressure (pressure was estimated to be between 0.1 and 1 MPa based on the flattened contact area) and flattened, creating a uniform contact area of mm in diameter. The SFG experiments for bulk alkane in contact with the sapphire substrate were done by filling the cell with alkanes and using a Teflon gasket between the cell and the sapphire prism to prevent any leaks. The cell was also equipped with an attachment for heating and cooling, and the temperature was measured at two locations using thermocouples. The temperature was controlled using a Lakeshore 330 temperature controller. To maintain a uniform heating and cooling rate, a block of copper with circulating water was placed below the cell. This was maintained at a constant temperature of 10 C Differential Scanning Calorimetry. For DSC experiments, the PDMS lens and amount of alkane close to the equilibrium swelling concentration were placed in a DSC pan and hermitically sealed. DSC thermal analysis was done using a TA universal 2000 system. The 12169

3 samples were equilibrated above the melting temperature for 1 h in the DSC before starting the temperature scan. This was done to allow for the PDMS lens to swell in the alkanes. The equilibrium concentration was determined by swelling the lens in a vial of alkane and measuring the weight of the lens before and after swelling. 22 A heating and cooling rate of 0.5 K/min was used. Reflectivity Measurements. A helium neon (He Ne) laser was used for reflectivity measurements to determine the phase transition temperatures and thickness of the alkane layers next to sapphire surface. The measurements were done using sapphire prisms in an internal reflection geometry. The experimental design is shown in Figure 1. In this experiment, the laser s incident angle was close to the Figure 1. Experimental setup showing the sapphire prism in contact with a PDMS lens. In linear reflectivity measurements the He Ne beam was incident from one side of the prism, and the intensity of the light was monitored as a function of temperature. For thickness measurements, the prism was rotated and the intensity of the He Ne light was measured as a function of incident angles. For the SFG experiment, the infrared and visible light are superimposed from one side of the prism, and the SFG signal from the other side of the prism was detected as the infrared wavenumbers are scanned from 2700 to 3200 cm 1. This sample setup was also equipped with a heating and cooling stage. critical angle, and the He Ne laser intensity was measured as a function of temperature (using a rate of 0.2 C/min). A chopper and photodetector attached to an SR 850 lock-in amplifier was used to observe the reflected intensity from the contact area. This experiment was sensitive enough to pick up the changes in refractive index upon freezing or melting, and the transition temperatures were noted when there was an abrupt change in the laser intensity. In these experiments, we were able to pick up both the rotator crystal and rotator melt transition temperatures. Thickness Measurements. The He Ne laser was also used to measure the changes in laser intensity as a function of incidence angle in an internal reflection geometry using sapphire prisms (Figure 1). The reflected intensity is a function of the refractive indices and thickness of the confined alkanes. In these experiments the laser beam was 0.5 mm in diameter and p-polarized. A three-layer reflectivity model was used to fit the reflected intensity as a function of incident angles using the following Fresnel model (eq 4). I = [ t conj( t )] ( r conj( r )) out p (prismin) p (prismin) p p [ t conj( t )] p (prismout) p (prismout) (4) In eq 4, t p and r p are the transmission and reflection coefficients, respectively. The mathematical equations for calculating t p and r p for a three-layer film have been derived previously 25 and are provided in the Supporting Information. Equation 4 was only used to model the data above T m due to excessive scattering in the crystal state. SFG Measurements. The SFG measurements involve the spatial and temporal overlap of a high-intensity visible laser beam (of frequency ω 1 ) with a tunable infrared laser (of frequency, ω 2 ). The SFG measurements were performed on a picosecond Spectra-Physics laser system with a tunable infrared beam ( cm 1,1ps pulse width, 1 khz repetition rate, and a diameter of μm) and a visible beam (800 nm, 1 ps pulse width, 1 khz repetition rate, and a diameter of 1 mm). 26 The incident angle of the infrared beam was 1 2 higher than the visible beam. The SFG signal was collected using a photomultiplier tube connected to a 0.5 m long spectrometer. The full width half-maximum of the tunable infrared pulse was 5 10 cm 1. SFG spectra were collected from 2700 to 3200 cm 1. The sample geometry is shown in Figure 1. This novel approach of using a flexible elastomeric lens, which deforms against a flat solid surface, to study confined liquids offsets the need to have perfectly parallel surfaces. Different interfaces were probed using different incident angles, and the SFG spectra for sapphire/liquid alkane, sapphire/ crystal alkane, and PDMS/sapphire interfaces were measured at 8, 2, and 8, respectively. These angles were measured with respect to the surface normal of the face of the sapphire prism and were determined using the refractive indices of liquid alkanes, PDMS, and alkane crystals. The polarization of the probe beams (IR and visible) and that of the SFG beam (before it reaches the detector) was set in one of two ways: s-polarized, electric field parallel to the surface; or p-polarized, electric field perpendicular to the surface. The combination of polarizations of all three beams (e.g., SSP) is reported in the following sequence; polarization of the SFG beam, visible beam, and IR beam. In general, for the C H stretching modes of methyl and methylene groups, the vibrational assignments are transferable from one molecule to the next in the absence of connections to inductive noncarbon heteroatom. 27 Therefore, for the majority of the methyl and methylene groups observed in these studies, the vibrational frequencies established by Synder and co-workers, based on extensive IR and Raman measurements of bulk alkanes and polyethylene, apply Following the convention of Synder, methyl modes are labeled r and methylene modes are labeled d, with superscripts + and distinguishing between symmetric and asymmetric modes, relative to the respective group s symmetry axis. To obtain quantitative information, the spectra were fitted using the following Lorentzian equation. 31 I(SFG) χ + eff,nr q ω IR A ϕ qe i q ω iγ In eq 5, A q, Γ q, ω q, and ϕ q are the strength, damping constant, angular frequency of a single resonant vibration, and phase, respectively. χ eff,nr is the nonresonant part of the SFG signal. RESULTS AND DISCUSSION This section is divided into four subsections. In the first subsection, we discuss the results of the surface-sensitive SFG technique that provides direct information on the nanometerthick interfacial layers next to the sapphire substrates. In the second subsection, we discuss the bulk transition temperatures measured using DSC. In the third subsection, we show transition temperatures measured using linear reflectivity. Finally, in the fourth subsection, we discuss the thermodynamic models used to predict the transition temperatures for confined alkanes. SFG Results. Figure 2 shows the SFG spectra measured using SSP polarization for the confined liquid alkane/sapphire (left panel) and confined crystal alkane/sapphire (right panel) interfaces. The strength of the SFG signals is proportional to the concentration and orientation of the interfacial molecules. The position of the SFG peaks is related to the chemical identity of interfacial molecules. The spectral peaks observed in Figure 2 correspond to symmetric CH 3 (2880 cm 1 ), asymmetric CH 3 (2960 cm 1 ), symmetric CH 2 (2850 cm 1 ), and asymmetric CH 2 (2916 cm 1 ) vibrations. The peaks around and 2900 cm 1 are assigned to symmetric methyl and asymmetric methylene Fermi bands, respectively. The peaks associated with SiCH 3 (PDMS) are expected to be present at 2905 and 2965 cm 1. These peaks were not observed in the SFG spectra, suggesting that the PDMS sapphire interface is saturated with liquid or crystal alkanes. For shorter q q 2 (5) 12170

4 Figure 2. SFG spectra taken in the SSP polarization (s-polarized SFG and visible and p-polarized IR beams) for PDMS swollen with liquid alkanes (bottom to top, C15, C19, C21, and C27) in contact with a sapphire substrate above (left) and below (right) T m. The spectra were fitted using eq 5 with peak assignments described in the main text. alkanes, the confined liquid spectra are much more ordered than the bulk liquid alkane/sapphire interface (data shown in ref 1). The confined liquid spectra for C27 are very similar to the SFG spectra of unconfined bulk C27 (without the PDMS confinement) in contact with the sapphire substrate. Table 1 Table 1. A q Values Obtained by Fitting SSP Spectra to Eq 5 for Confined Alkanes of Varying Chain Length in Liquid and Crystal States d + r + r fr r c15 confined liquid c19 confined liquid c21 confined liquid c27 confined liquid c15 confined crystal c19 confined crystal c21 confined crystal c27 confined crystal provides the values of the amplitude strength (A q ) obtained by fitting the spectra to eq 5. The increase in signal intensity after crystallization is many orders of magnitude higher for C15 and C19, much larger changes in comparison to C21 and C27. The SFG spectrum for C27 in the crystal state is similar to that of the bulk crystal/sapphire interface. The strong methylene signals (d + ) observed for C15 and C19 in the crystal state suggest that the alkane molecules are oriented with the chain axis parallel to the surface. 1 The strong methyl signals (r + ) observed for C21 and C27 crystals indicate that the chain axis of the alkane molecule are oriented perpendicular to the surface. A series of SFG spectra were collected at various temperatures during the cooling and heating cycles. The temperatures were changed at a rate of 0.2 K/min and a 25 min waiting time was provided to attain equilibration before collecting the SFG spectra at each temperature. The T m of interfacial alkane molecules was defined as the temperature at which the SFG spectra changed abruptly from the liquid to crystal spectra (the representative liquid and crystal spectra are shown in Figure 2). The T m measured using SFG for different chain lengths are shown in Figure 3A. As a reference, we have also shown the T m measured for bulk alkanes using DSC in Figure 3A. The differences in T m (ΔT m ) between the confined and bulk alkanes (heating cycle) are shown in Figure 3B. It is interesting that the ΔT m is a function of chain length and that these differences are smaller for shorter alkanes. In comparison, C19 shows the largest difference in ΔT m, and this difference decreases again with increasing chain length. It is interesting to compare the differences in the structure and transition temperatures of confined and unconfined alkanes in contact with the sapphire substrate. The SFG results for unconfined alkanes show strong methyl peaks below T m. 1,32 In addition, the T m of unconfined alkanes are similar to the bulk transition temperatures. The confined alkane spectra for all of the alkane crystals, except the longest one, C27, are very different from the spectra for the unconfined alkanes. However, the transition temperatures for C15 and C17 are similar to bulk T m and for C19 C27 are lower than bulk T m. It appears that the transition temperatures are not entirely correlated with the differences in the structure between the crystal or liquid alkanes upon confinement. DSC Results. Figure 4 shows the DSC thermal data during the heating and cooling cycles for PDMS swollen with liquid alkanes. For bulk alkanes, there are two main transitions. One is liquid-to-rotator, and the other is from rotator-to-crystal state. The relatively sharp peaks in Figure 4B at lower temperature are associated with rotator-to-crystal transitions. 33 The longer alkane molecules are less soluble in PDMS, and we had excess liquid alkanes in the DSC samples. This resulted in observing the freezing and melting of the excess alkane in addition to the transition temperatures of liquid alkanes inside the swollen PDMS. However, for C15, there was a negligible quantity of excess C15, and the freezing and melting transitions correspond to C15 inside the swollen PDMS. The broad thermal peaks observed in the DSC cooling and heating scans are associated with the size distribution of the crystal (Gibbs Thomson effect shown in eq 1). The broad thermal peaks have been reported for melting of small molecules in networks 19,21,22 and glasses with well-defined porosity. 20,23 The distribution of crystal sizes determined using the combination of Gibbs Thomson and Flory Rehner equation is provided in the Supporting Information. The DSC data during the cooling cycle are a function of nucleation rates, and we have not used the transition temperatures measured in the cooling cycle for any quantitative comparisons. Our focus here is on the comparison between the bulk and interfacial melting temperatures. We have plotted the surface T m measured using SFG as vertical dashed lines in Figure 4. For C15, the freezing transition at the interface occurs before the freezing of the liquid alkanes in the swollen PDMS network. In comparison with longer alkanes, it is observed that a large fraction of the alkane molecules are 12171

5 Figure 3. (A) Transition temperatures measured during heating (red circles) and cooling (blue circles) cycles by SFG and for bulk alkanes using DSC (heating cycle, black crosses) as a function of the number of carbon units in the alkane chain. The error bars for the data measured are smaller than the size of the symbols. (B) The differences in T m between the confined alkane and bulk measured using SFG (squares) and linear reflectivity (circles) plotted as a function of the number of carbon units in the alkane chain. Figure 4. DSC (A) cooling (blue) and (B) heating scans (red) for PDMS saturated with different length of alkane chains (C15, C19, C21, and C27). The red vertical dashed lines represent the transition temperature measured using SFG, and the black vertical dotted lines represent the transition temperature measured using a He Ne laser (linear reflectivity) that probes much thicker interfacial layer than the SFG technique. frozen inside the PDMS elastomer before the alkane molecules freeze at the PDMS sapphire interface. A similar conclusion can be reached by observing the melting transitions during the heating cycle. It is important to note that the DSC peaks are extremely broad, and we do not have one bulk transition temperature to compare with the transition temperatures observed at the interface. Reflectivity Results. We have measured the intensity of the reflected He Ne light as a function of the incident angle to probe the freezing of the alkanes next to a sapphire substrate. The results for PDMS lenses swollen with liquid alkanes in contact with the sapphire prism are shown in Figure 5. There is a sharp drop in intensity corresponding to the critical angle expected for PDMS in contact with sapphire. These results can be modeled using either a two-layer model consisting of a sapphire prism in contact with PDMS or an alkane film or a three-layer model with an alkane layer between a PDMS lens Figure 5. Reflected intensity versus incident angle measured for PDMS lenses soaked with alkanes in contact with the sapphire substrate. The data for unconfined C15 bulk crystal (no PDMS) (squares), C15 confined liquid (crosses), and C15 confined crystal (triangles). The intensity profile for the C15 confined liquid is fit to a three-layer reflectivity model (eq 4) with 100 nm thick alkane layer (solid red line) and 10 nm thick alkane layer (dashed red line). and a sapphire substrate (eq 4). Because of the similarity in the refractive indices of PDMS and liquid alkanes, we were unable to measure the thickness of the alkane liquid in contact with the sapphire substrate. On cooling below T m, the critical angles are very different, indicating a change in refractive index due to the crystallization of alkanes. As a comparison, we have measured the reflected intensity as a function of incident angles for bulk alkane in contact with a sapphire substrate (unconfined), and the critical angles are similar to those measured for confined alkanes below T m. This indicates that the alkane molecules have crystallized next to the sapphire substrate. For longer chain lengths, we were also able to use these experiments to observe both the liquid-to-rotator and rotator-to-crystal transition temperatures. From the combination of linear reflectivity and SFG results we can confirm that the interface between PDMS and sapphire is saturated with alkane liquid (or alkane crystals below T m ). The melting and freezing transition temperatures were measured by observing changes in the intensity of the He Ne light as a function of temperature during the heating and cooling cycles (Figure 6). The confined alkane was held at 5 C 12172

6 Table 2. Values of Parameters Used To Compute Eq 3 chain length (n) bulk T m (K) ΔH f (J/mol) 34 V a (cm 3 /mol) a The interaction parameter α was determined using solubility parameters. 17 The equation is given by α = V(δ alkane δ pdms ) 2, where δ alkane = n/( n) (cal 0.5 /cm 1.5 ). 35 The value of δ pdms is taken as MPa Figure 6. Scan of He Ne reflected intensity with temperature for C27 alkane confined between PDMS lens and sapphire substrate. above the bulk T m before starting the scans. Any temperature at which there was an abrupt change in the He Ne intensity was designated as a transition temperature. The two-step changes in intensity during the heating cycle correspond to crystal-torotator and rotator-to-liquid transition temperatures. The transition temperatures (rotator-to-crystal) measured using the linear reflectivity measurements are plotted as short dashed lines in Figure 4. The differences between the transition temperatures measured using He Ne experiments and bulk T m are shown in Figure 3B. For C15 and C17, the T m measured using the SFG and the He Ne beam are very similar to each other. For longer alkanes, in the heating cycle, the melting of the interface layer precedes the melting of the thick alkane layer next to the sapphire substrate. The cooling cycle for longer alkanes also shows that the interfacial layer freezes before the thicker layers of alkanes are frozen next to the sapphire substrates. Thermodynamic Models. To understand the melting temperatures of confined alkanes, there are two main effects that we need to consider. The first effect is the depression of T m as a function of concentration. The second consideration is that the thickness (or size) of the confined crystal will affect the T m (eqs 2 and 3). To understand the first effect, we can use the Flory Rehner model to calculate the solubility of alkanes in PDMS elastomers. 17 The chemical potentials inside and outside the network are labeled as μ and μ, respectively. At equilibrium, these two chemical potentials should be equal. 1 2 μ = μ + RT ϕ + ϕ ln (1 ) 1 + α ϕ (1 ) 1 1 r 1 1/3 + RTx[ ϕ ϕ /2] 2 2 (6) μ = μ (7) In eqs 6 and 7, the parameters are same as described in eq 3. In addition, μ is the chemical potential of the pure liquid (or solvent). Table 2 provides the values of the parameters used for determining the equilibrium swelling ratios, and the results for C27 are shown as a black solid line in Figure 7. There are a range of values for Hilderbrand solubility parameters reported in the literature for PDMS, and we have used a value from the range that matches the swelling results measured for PDMS lenses swollen in C27. In Figure 7, left of the solid line corresponds to the one-phase region and to the right a twophase region, where the two phases are a pure solvent phase and an elastomer phase swollen in alkane. Here, the concentrations were chosen such that the systems were always in the two-phase region. We have calculated the melting temperatures using eq 2 for an infinitely thick crystal (thickness is infinity in eq 2) (shown as black dashed line) and variable concentration of alkanes in the swollen PDMS. The correction term due to elasticity is very small, and the results calculated using eqs 2 or 3 are similar. There is a significant depression in T m when the concentration of alkane is lower than the equilibrium concentration. However, for PDMS with excess alkanes the T m should be similar to the bulk T m. For C27, the equilibrium swelling concentration was 4 5 vol %. The melting transition temperatures measured using DSC (red), SFG measurements (black), and optical reflectivity (blue) are also shown in Figure 7. The T m of confined C27 crystals measured using SFG and linear reflectivity do not match the predictions for a thick crystal layer next to a sapphire substrate. To explain the experimental results, we need to take into account the thickness dependence of the melting temperature (Gibbs Thomson) in addition to the entropic effect of mixing. The SFG results matches the predictions if we assume a 50 nm thick alkane crystal layer next to the sapphire substrate (red dashed line in Figure 7). We would like to emphasize that we are assuming the validity of eq 2 or 3 to estimate the film thickness. Similarly, we can estimate the thicknesses that match the melting temperatures of the other alkanes, and the results are shown in Table 3. It is important to note that the values of the interfacial surface energies are not known and that this can introduce errors in the thicknesses estimated using eq 2 or 3. In addition, the thickness calculations for C15 and C17 will strongly depend on the reference bulk melting temperature. As a comparison, we have also discussed the DSC analysis for crystal size inside the PDMS network (see Figure S2 in the Supporting Information). The GT model with thin crystals provide a plausible explanation for depression in T m observed using SFG and linear reflectivity measurements. Although the thickness of the confined alkane films may explain the depression in T m, there are some important anomalies that need to be mentioned. First, we have observed larger differences in the structure of the interfacial molecules for shorter alkanes (C15 C19) in comparison to longer alkanes (C21 C27). However, these differences did not entirely correlate with the magnitude of the melting point depression. Second, the changes in the critical angles upon cooling indicates that there are much thicker alkane crystals next to the sapphire substrate compared to the thickness values calculated using the depression in T m (Table 3). Several potential explanations may resolve this anomaly. First, upon 12173

7 Figure 7. Plot of the equilibrium concentration of C27 in PDMS as a function of temperature (black line). The plot also has the prediction for the melting temperature as a function of concentration calculated for an infinitely thick (black short dashed line) and for a 50 nm thick (red short dashed line) C27 alkane crystal. We have used a = 2 and σ = 70 mj/m 2 for calculating the depression of T m. The horizontal red, blue, and black dashed lines correspond to the T m measured using DSC for 100% C27, He Ne reflectivity measurements, and SFG measurements, respectively. The inset shows a schematic representation of chemical potentials involved in the system. Table 3. Thickness of Confined Alkanes Calculated Using SFG and He Ne Measurements chain length (n) thickness (nm) (SFG) thickness (nm) (He Ne) heating, the crystal layer equilibrates with the surrounding reservoir, and the thickness of the crystal decreases with increasing temperature. Therefore, the transition temperatures are indicating a much thinner layer than suggested by the critical angle measurements. The other plausible explanation is that the size of the crystals that grow near the sapphire substrate depend on the length of the alkanes. As observed in the bulk DSC data, there are distribution of crystals that are formed inside the PDMS network (Figure S2). Perhaps for C15 larger crystals nucleate next to the sapphire surface compared to those for C19. A direct analysis of the structure and thickness of the alkane crystals next to the sapphire substrates is planned using tomographic techniques. SUMMARY In summary, we have measured the melting and freezing transition temperatures of confined alkanes between PDMS elastomers and sapphire substrates. The difference in the melting temperatures of confined crystals with respect to the bulk transitions is a function of chain length. The combination of the Flory Rehner and Gibbs Thomson models is used to calculate the crystal size next to the sapphire substrate. The understanding of crystal size and melting temperatures next to the sapphire substrate has important implications in the areas of nanocomposites, friction, and lubrication ASSOCIATED CONTENT *S Supporting Information Equations for fitting the reflectivity data. This material is available free of charge via the Internet at AUTHOR INFORMATION Corresponding Author * ali4@uakron.edu (A.D.). Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS We acknowledge funding from National Science Foundation (DMR and DMR ). We thank Yu Zhang with the help in analyzing the DSC results showed in the Supporting Information. We also thank Emmanuel Anim-Danso and Mike Heiber for helpful discussions. REFERENCES (1) Nanjundiah, K.; Dhinojwala, A. Confinement-induced ordering of alkanes between an elastomer and a solid surface. Phys. Rev. Lett. 2005, 95, / /4. (2) Yurdumakan, B.; Harp, G. P.; Tsige, M.; Dhinojwala, A. Template-induced enhanced ordering under confinement. Langmuir 2005, 21, (3) Kurian, A.; Prasad, S.; Dhinojwala, A. Direct measurement of acid- base interaction energy at solid interfaces. Langmuir 2010, 26, (4) Nanjundiah, K.; Hsu, P. Y.; Dhinojwala, A. Understanding rubber friction in the presence of water using sum-frequency generation spectroscopy. J. Chem. Phys. 2009, 130, (5) Evans, R.; Marconi, U. M. B. Phase equilibria and solvation forces for fluids confined between parallel walls. J. Chem. Phys. 1987, 86, (6) Gibbs, J.; Bumstead, H.; Van Name, R.; Longley, W. The Collected Works of J. Willard Gibbs; Longmans, Green, and Co.: London, 1931; Vol. 1.

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