Melting of Linear Alkanes between Swollen Elastomers and SolidSubstratesKumar 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 oflinear alkanes confined between cross-linked poly(dimethylsiloxane)(PDMS) elastomers and solid sapphire substrates. Small molecules areoften used as lubricants to reduce friction or as plasticizers, but very little isdirectly known about the migration or changes in physical properties ofthese small molecules at interfaces, particularly the changes in transitiontemperatures upon confinement. Our previous studies highlighted strikingdifferences between the crystal structure of confined and unconfinedpentadecane crystals in contact with sapphire substrates. Here, we haveused surface-sensitive infrared−visible sum-frequency-generation spectros-copy (SFG) to study the melting temperatures (Tm) of alkanes innanometer thick interfacial regions between swollen PDMS elastomers incontact with sapphire substrate. We find that confined alkanes showdepression in Tm compared to the melting temperature of unconfined bulk alkanes. The depression in Tm is a function of chainlength, and these differences were smallest for shorter alkanes and largest for 19 unit long alkanes. In comparison, the DSCresults for swollen PDMS elastomer show a broad distribution of melting points corresponding to different sizes of crystalsformed within the network. The Tm for confined alkanes has been modeled using the combination of Flory−Rehner and Gibbs−Thomson models, and the depression in Tm is related to the thickness of the confined alkanes. These findings have importantimplications in understanding friction and adhesion of soft elastomeric materials and also the effects of confinement between twosolid materials.

■ INTRODUCTION

Small molecules are added in cross-linked rubber to improveprocessing, as plasticizers in thermoplastic polymers to improvemechanical properties, or as lubricants to reduce friction (forexample in syringes). Often in these situations it is expectedthat small molecules may migrate to the grain boundaries orinterfaces between two solid materials. Our understanding ofthe physical properties of molecules at buried interfaces islimited, particularly in organic soft materials. Recently, we havedeveloped a simpler experimental design to study the physicalproperties of confined liquids by pressing cross-linkedelastomers in contact with solid surfaces. This geometry, incombination with surface-sensitive infrared−visible sum-frequency-generation spectroscopy (SFG), was used to studyconfinement of water, alkanes, and other small moleculesbetween PDMS elastomers and sapphire substrates.1−4 In ourprevious work with alkanes, we have observed dramaticdifferences in the structure of pentadecane crystals in contactwith sapphire substrate in comparison to pentadecane bulkcrystals.1 Here, we report our measurements on the meltingand freezing transitions of confined alkanes between PDMShemispherical lenses swollen with alkanes pressed in contactwith sapphire substrates.The Gibbs−Thomson (GT) model, developed to explain the

changes in Tm of small crystals, considers the extra surface

energy required when forming thin crystals in contact with thebulk liquid.5−7 The difference in Tm compared to the bulkmelting temperature (Tm

0 ) can be determined using theequation

σ σρ

Δ = − = −−Δ

T T Ta T

d H( )

m m,conf m0 cs ls m

0

f s (1)

In eq 1, d is the thickness or the radius of the crystal, ΔHf is thelatent heat, σls is the liquid−solid interfacial energy, σcs is thecrystal−solid interfacial energy, ρs is the molar density of thesolid, and a is a geometric factor determined by the shape of theconfined crystals and is equal to 2 for rectangular slabs. Thismodel has been widely used to explain the transitiontemperatures of small molecules confined in porousmedia.8−12 Increased ordering and viscosity have been observedfor liquids confined between two mica surfaces, and this hasbeen used to infer the enhancement in Tm or the glasstransition temperature.13−15 The friction and sliding forces arealso affected by the changes in properties of liquids due toconfinement.14,15

If small molecules penetrate inside the elastomers (or solid),then there is an additional depression in Tm due to the entropy

Received: July 27, 2013Published: September 4, 2013

Article

pubs.acs.org/Langmuir

© 2013 American Chemical Society 12168 dx.doi.org/10.1021/la402884g | Langmuir 2013, 29, 12168−12175

of mixing. For long chain molecules, the Flory−Hugginsequation16,17 (FH) can be used to model the depression in Tm.

αϕϕ ϕ

=Δ +

Δ − − − −T

H

H T R R r/ ln(1 ) [1 (1/ )]mf

f mo

22

2 2 (2)

In eq 2, ϕ2 is the polymer volume fraction, r is the ratio of themolar volume of a polymer chain with respect to that of a smallmolecule, and R is the gas constant. The interaction parameter,α, is = ε12 − 0.5(ε11 + ε22), where ε are the pair−pairinteraction energies. The χ-parameter that is used in thepolymer literature is equal to α/RT. Equation 2 predicts adepression in Tm, particularly for high values of ϕ2.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, thesize of the crystals, and an additional term due to the stiffness ofthe elastic network. The effects of elasticity on swelling wasdescribed by the Flory−Rehner equation.17 All of these termscan be combined together and the depression in Tm can bewritten as follows:

σ ρ αϕ

ϕ ϕ ϕ ϕ=

Δ − +Δ − − − − − −

TH a d

H T R R r Rx

/( )

/ ln(1 ) [1 (1/ )] ( /2)s

mf 2

2

f m0

2 2 21/3

2

(3)

In eq 3, most of the terms are similar to those defined in eqs 1and 2, and the new term x is equal to Vρ/M. Here, V is themolar volume, ρ is the density, and M is the molecular weightbetween cross-links. This equation was first used to understandthe swelling of natural rubber with benzene.18 In elastomers (orcross-linked networks), a broad distribution of meltingtemperatures is observed, and it has been suggested that eachof these melting temperatures corresponds to a crystal of aparticular size. Using this assumption, eq 3 and theexperimentally measured distribution in Tm have been usedto determine the distribution of pore sizes or porosity. Thisproblem was revisited by McKenna and co-workers19,20

recently to study the melting of benzene in natural rubberand other small molecules in PDMS and polyisoprenenetworks.21,22 McKenna and co-workers concluded that thesemodels were unable to predict the depression in Tm, and theheat of fusion was used as a fitting function to model thedepression in Tm.

23

For soft swollen elastomers in contact with solid substrates,the situation is more complex because of the influence of thesolid surface on the segregation of small molecules at theinterface. We anticipate a depression in Tm as predicted by eq 3as well as the segregation of alkanes next to the sapphiresubstrate. In addition, we know from previous studies that thecrystal structure for confined and unconfined alkanes isdifferent, and this may also influence Tm.

1 In this paper, wehave compared the transition temperatures of alkanes in bulkelastomers (measured using DSC) with those upon confine-ment (measured using SFG). In addition, we have used linearreflectivity measurements to probe the intermediate lengthscale between the DSC and SFG measurements to understandwhether the melting starts at the interface or in the bulk. Thecombination of these three techniques provides an intriguingpicture of how the interfacial melting temperature is affected bythe alkane chain length. These results have importantimplications in many industrial and biological areas where asmall amount of liquid can be trapped between soft or hardboundaries.

■ EXPERIMENTAL SECTIONSample Preparation. The PDMS lenses were prepared using

Sylgard 184 monomer from Dow Corning Inc. The recipe consisted of1 part cross-linker to 10 parts monomer. The monomer and the cross-linker were mixed together, and the air bubbles were removed. Thelenses were made by placing a drop of this mixture on a fluorinatedglass surface under water. The lenses used in these experiments were≈5 mm in diameter. The lenses were cured under water at roomtemperature for 24 h. The water was removed, and the lenses weredried using dry nitrogen. The lenses were further cured in a vacuumoven for 4 h at 60 °C. The cured lenses can have some amount of un-cross-linked PDMS oligomers that could potentially leach out duringthe experiments.2,24 Therefore, the lenses were soaked in toluene toremove these un-cross-linked chains. The toluene was replaced every 3days for 2 weeks. The lenses were then removed from toluene anddried under vacuum for 4 h prior to the experiments. The root-mean-square (rms) roughness of the of the surface of the PDMS film was≈0.5 nm, measured using an atomic force microscope (Nanoscope IIIamultimode AFM manufactured by Digital Instruments).2,24 Themodulus of the PDMS lenses was 2−3 MPa measured usingJohnson−Kendall−Roberts (JKR) experiments. The static contactangle of water was 110° on PDMS. The surface energy of the PDMSsurface was 20−23 mJ/m2 (determined using JKR measurements).24

Alkanes of chain length C15−C27 were purchased from TCIAmerica Inc. with purity greater than 98 wt %. They were used asreceived without further purification. In addition, selective experimentswere done with 99.5 wt % purity alkanes, and no differences in theSFG spectra or transition temperatures were observed due todifferences in the purity of the alkane samples. The samples for SFGand optical reflectivity were prepared by soaking the PDMS lenses inliquid alkanes (C15 and C17). For longer alkanes, the PDMS lenseswere soaked in alkanes at temperatures above Tm and then cooled backto room temperature. However, this resulted in cracking of the lenssurfaces due to fast crystallization. To overcome this problem, thelonger alkanes were melt cast directly on the sapphire surface andbrought in contact with the PDMS lens. Before starting theexperiments, the samples were heated above Tm to allow for thesystem to attain equilibrium. The equilibrium concentration of alkaneinside the PDMS lens (determined by weighing the lens before andafter alkane swelling) achieved by the two different routes was foundto be equivalent.

The sapphire prisms were first wiped with toluene using a soft tissueand sonicated in toluene for 1 h. Then, they were washed with copiousamounts of water and blow-dried using dry nitrogen. Finally, thesapphire prisms were plasma cleaned using air plasma for a period of 5min before the experiments. The SFG cell was washed in soap solutionand sonicated in toluene for a period of 2 h. The cell was then washedwith water and blow-dried using dry nitrogen. The cell was heated inan oven at 135 °C for 10 min and cleaned using air plasma before theexperiments. The RMS roughness of the sapphire prism was 10−15nm measured using AFM (20 μm × 20 μm scan area). For the SFGmeasurements, the soaked lenses were placed in the cell and broughtin contact with the sapphire prism. The lens deformed under pressure(pressure was estimated to be between 0.1 and 1 MPa based on theflattened contact area) and flattened, creating a uniform contact area of0.5−1 mm in diameter. The SFG experiments for bulk alkane incontact with the sapphire substrate were done by filling the cell withalkanes and using a Teflon gasket between the cell and the sapphireprism to prevent any leaks. The cell was also equipped with anattachment for heating and cooling, and the temperature wasmeasured at two locations using thermocouples. The temperaturewas controlled using a Lakeshore 330 temperature controller. Tomaintain a uniform heating and cooling rate, a block of copper withcirculating water was placed below the cell. This was maintained at aconstant temperature of 10 °C

Differential Scanning Calorimetry. For DSC experiments, thePDMS lens and amount of alkane close to the equilibrium swellingconcentration were placed in a DSC pan and hermitically sealed. DSCthermal analysis was done using a TA universal 2000 system. The

Langmuir Article

dx.doi.org/10.1021/la402884g | Langmuir 2013, 29, 12168−1217512169

samples were equilibrated above the melting temperature for 1 h in theDSC before starting the temperature scan. This was done to allow forthe PDMS lens to swell in the alkanes. The equilibrium concentrationwas determined by swelling the lens in a vial of alkane and measuringthe weight of the lens before and after swelling.22 A heating andcooling 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 transitiontemperatures and thickness of the alkane layers next to sapphiresurface. The measurements were done using sapphire prisms in aninternal reflection geometry. The experimental design is shown inFigure 1. In this experiment, the laser’s incident angle was close to the

critical angle, and the He−Ne laser intensity was measured as afunction of temperature (using a rate of 0.2 °C/min). A chopper andphotodetector attached to an SR 850 lock-in amplifier was used toobserve the reflected intensity from the contact area. This experimentwas sensitive enough to pick up the changes in refractive index uponfreezing or melting, and the transition temperatures were noted whenthere was an abrupt change in the laser intensity. In these experiments,we were able to pick up both the rotator−crystal and rotator−melttransition temperatures.Thickness Measurements. The He−Ne laser was also used to

measure the changes in laser intensity as a function of incidence anglein an internal reflection geometry using sapphire prisms (Figure 1).The reflected intensity is a function of the refractive indices andthickness of the confined alkanes. In these experiments the laser beamwas ≈0.5 mm in diameter and p-polarized. A three-layer reflectivitymodel was used to fit the reflected intensity as a function of incidentangles using the following Fresnel model (eq 4).

= ×

×

I t t r r

t t

[ conj( )] ( conj( ))

[ conj( )]

out p(prismin)

p(prismin)

p p

p(prismout)

p(prismout)

(4)

In eq 4, tp and rp are the transmission and reflection coefficients,respectively. The mathematical equations for calculating tp and rp for athree-layer film have been derived previously25 and are provided in theSupporting Information. Equation 4 was only used to model the dataabove Tm 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 (offrequency ω1) with a tunable infrared laser (of frequency, ω2). TheSFG measurements were performed on a picosecond Spectra-Physicslaser system with a tunable infrared beam (2000−3800 cm−1, 1 pspulse width, 1 kHz repetition rate, and a diameter of 100−200 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 beamwas 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 ≈5−10cm−1. SFG spectra were collected from 2700 to 3200 cm−1. Thesample geometry is shown in Figure 1. This novel approach of using aflexible elastomeric lens, which deforms against a flat solid surface, tostudy confined liquids offsets the need to have perfectly parallelsurfaces. Different interfaces were probed using different incidentangles, 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 thesurface normal of the face of the sapphire prism and were determinedusing the refractive indices of liquid alkanes, PDMS, and alkanecrystals. The polarization of the probe beams (IR and visible) and thatof the SFG beam (before it reaches the detector) was set in one of twoways: s-polarized, electric field parallel to the surface; or p-polarized,electric field perpendicular to the surface. The combination ofpolarizations of all three beams (e.g., SSP) is reported in the followingsequence; polarization of the SFG beam, visible beam, and IR beam. Ingeneral, for the C−H stretching modes of methyl and methylenegroups, the vibrational assignments are transferable from one moleculeto the next in the absence of connections to inductive noncarbonheteroatom.27 Therefore, for the majority of the methyl and methylenegroups observed in these studies, the vibrational frequenciesestablished by Synder and co-workers, based on extensive IR andRaman measurements of bulk alkanes and polyethylene, apply.28−30

Following the convention of Synder, methyl modes are labeled r andmethylene modes are labeled d, with superscripts + and −distinguishing between symmetric and asymmetric modes, relative tothe respective group’s symmetry axis. To obtain quantitativeinformation, the spectra were fitted using the following Lorentzianequation.31

∑χω ω

∝ +− − Γ

ϕ

IA

i(SFG)

e

q

qi

q qeff,NR

IR

2q

(5)

In eq 5, Aq, Γq, ωq, and ϕq are the strength, damping constant, angularfrequency of a single resonant vibration, and phase, respectively. χeff,NRis the nonresonant part of the SFG signal.

■ RESULTS AND DISCUSSIONThis section is divided into four subsections. In the firstsubsection, we discuss the results of the surface-sensitive SFGtechnique that provides direct information on the nanometer-thick interfacial layers next to the sapphire substrates. In thesecond subsection, we discuss the bulk transition temperaturesmeasured using DSC. In the third subsection, we showtransition temperatures measured using linear reflectivity.Finally, in the fourth subsection, we discuss the thermodynamicmodels used to predict the transition temperatures for confinedalkanes.

SFG Results. Figure 2 shows the SFG spectra measuredusing 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 tothe concentration and orientation of the interfacial molecules.The position of the SFG peaks is related to the chemicalidentity of interfacial molecules. The spectral peaks observed inFigure 2 correspond to symmetric CH3 (2880 cm−1),asymmetric CH3 (2960 cm−1), symmetric CH2 (2850 cm−1),and asymmetric CH2(2916 cm

−1) vibrations. The peaks around2935−2940 and 2900 cm−1 are assigned to symmetric methyland asymmetric methylene Fermi bands, respectively. Thepeaks associated with −SiCH3 (PDMS) are expected to bepresent at 2905 and 2965 cm−1. These peaks were not observedin the SFG spectra, suggesting that the PDMS−sapphireinterface is saturated with liquid or crystal alkanes. For shorter

Figure 1. Experimental setup showing the sapphire prism in contactwith a PDMS lens. In linear reflectivity measurements the He−Nebeam was incident from one side of the prism, and the intensity of thelight was monitored as a function of temperature. For thicknessmeasurements, the prism was rotated and the intensity of the He−Nelight was measured as a function of incident angles. For the SFGexperiment, the infrared and visible light are superimposed from oneside of the prism, and the SFG signal from the other side of the prismwas detected as the infrared wavenumbers are scanned from 2700 to3200 cm−1. This sample setup was also equipped with a heating andcooling stage.

Langmuir Article

dx.doi.org/10.1021/la402884g | Langmuir 2013, 29, 12168−1217512170

alkanes, the confined liquid spectra are much more orderedthan the bulk liquid alkane/sapphire interface (data shown inref 1). The confined liquid spectra for C27 are very similar tothe SFG spectra of unconfined bulk C27 (without the PDMSconfinement) in contact with the sapphire substrate. Table 1

provides the values of the amplitude strength (Aq) obtained byfitting the spectra to eq 5. The increase in signal intensity aftercrystallization is many orders of magnitude higher for C15 andC19, much larger changes in comparison to C21 and C27. TheSFG spectrum for C27 in the crystal state is similar to that ofthe bulk crystal/sapphire interface. The strong methylenesignals (d+) observed for C15 and C19 in the crystal statesuggest that the alkane molecules are oriented with the chainaxis parallel to the surface.1 The strong methyl signals (r+)

observed for C21 and C27 crystals indicate that the chain axisof the alkane molecule are oriented perpendicular to thesurface.A series of SFG spectra were collected at various temper-

atures during the cooling and heating cycles. The temperatureswere changed at a rate of 0.2 K/min and a 25 min waiting timewas provided to attain equilibration before collecting the SFGspectra at each temperature. The Tm of interfacial alkanemolecules was defined as the temperature at which the SFGspectra changed abruptly from the liquid to crystal spectra (therepresentative liquid and crystal spectra are shown in Figure 2).The Tm measured using SFG for different chain lengths areshown in Figure 3A. As a reference, we have also shown the Tmmeasured for bulk alkanes using DSC in Figure 3A. Thedifferences in Tm (ΔTm) between the confined and bulk alkanes(heating cycle) are shown in Figure 3B. It is interesting that theΔTm is a function of chain length and that these differences aresmaller for shorter alkanes. In comparison, C19 shows thelargest difference in ΔTm, and this difference decreases againwith increasing chain length.It is interesting to compare the differences in the structure

and transition temperatures of confined and unconfined alkanesin contact with the sapphire substrate. The SFG results forunconfined alkanes show strong methyl peaks below Tm.

1,32 Inaddition, the Tm of unconfined alkanes are similar to the bulktransition temperatures. The confined alkane spectra for all ofthe alkane crystals, except the longest one, C27, are verydifferent from the spectra for the unconfined alkanes. However,the transition temperatures for C15 and C17 are similar to bulkTm and for C19−C27 are lower than bulk Tm. It appears thatthe transition temperatures are not entirely correlated with thedifferences in the structure between the crystal or liquid alkanesupon confinement.

DSC Results. Figure 4 shows the DSC thermal data duringthe heating and cooling cycles for PDMS swollen with liquidalkanes. For bulk alkanes, there are two main transitions. One isliquid-to-rotator, and the other is from rotator-to-crystal state.The relatively sharp peaks in Figure 4B at lower temperatureare associated with rotator-to-crystal transitions.33 The longeralkane molecules are less soluble in PDMS, and we had excessliquid alkanes in the DSC samples. This resulted in observingthe freezing and melting of the excess alkane in addition to thetransition temperatures of liquid alkanes inside the swollenPDMS. However, for C15, there was a negligible quantity ofexcess C15, and the freezing and melting transitions correspondto C15 inside the swollen PDMS. The broad thermal peaksobserved in the DSC cooling and heating scans are associatedwith the size distribution of the crystal (Gibbs−Thomson effectshown in eq 1). The broad thermal peaks have been reportedfor melting of small molecules in networks19,21,22 and glasseswith well-defined porosity.20,23 The distribution of crystal sizesdetermined using the combination of Gibbs−Thomson andFlory−Rehner equation is provided in the SupportingInformation. The DSC data during the cooling cycle are afunction of nucleation rates, and we have not used thetransition temperatures measured in the cooling cycle for anyquantitative comparisons. Our focus here is on the comparisonbetween the bulk and interfacial melting temperatures. We haveplotted the surface Tm measured using SFG as vertical dashedlines in Figure 4. For C15, the freezing transition at theinterface occurs before the freezing of the liquid alkanes in theswollen PDMS network. In comparison with longer alkanes, itis observed that a large fraction of the alkane molecules are

Figure 2. SFG spectra taken in the SSP polarization (s-polarized SFGand visible and p-polarized IR beams) for PDMS swollen with liquidalkanes (bottom to top, C15, C19, C21, and C27) in contact with asapphire substrate above (left) and below (right) Tm. The spectra werefitted using eq 5 with peak assignments described in the main text.

Table 1. Aq Values Obtained by Fitting SSP Spectra to Eq 5for Confined Alkanes of Varying Chain Length in Liquid andCrystal States

d+ r+ rf r r−

c15 confined liquid 12 213 315 −120c19 confined liquid 16 132 256 −100c21 confined liquid 28 78 366 −216c27 confined liquid 75 26 74 −12c15 confined crystal 898 361 170c19 confined crystal 821 265 147c21 confined crystal 131 220 133c27 confined crystal 11 159 122

Langmuir Article

dx.doi.org/10.1021/la402884g | Langmuir 2013, 29, 12168−1217512171

frozen inside the PDMS elastomer before the alkane moleculesfreeze at the PDMS−sapphire interface. A similar conclusioncan be reached by observing the melting transitions during theheating cycle. It is important to note that the DSC peaks areextremely broad, and we do not have one bulk transitiontemperature to compare with the transition temperaturesobserved at the interface.Reflectivity Results.We have measured the intensity of the

reflected He−Ne light as a function of the incident angle toprobe the freezing of the alkanes next to a sapphire substrate.The results for PDMS lenses swollen with liquid alkanes incontact with the sapphire prism are shown in Figure 5. There isa sharp drop in intensity corresponding to the critical angleexpected for PDMS in contact with sapphire. These results canbe modeled using either a two-layer model consisting of asapphire prism in contact with PDMS or an alkane film or athree-layer model with an alkane layer between a PDMS lens

and a sapphire substrate (eq 4). Because of the similarity in therefractive indices of PDMS and liquid alkanes, we were unableto measure the thickness of the alkane liquid in contact with thesapphire substrate. On cooling below Tm, the critical angles arevery different, indicating a change in refractive index due to thecrystallization of alkanes. As a comparison, we have measuredthe reflected intensity as a function of incident angles for bulkalkane in contact with a sapphire substrate (unconfined), andthe critical angles are similar to those measured for confinedalkanes below Tm. This indicates that the alkane molecules havecrystallized next to the sapphire substrate. For longer chainlengths, we were also able to use these experiments to observeboth the liquid-to-rotator and rotator-to-crystal transitiontemperatures. From the combination of linear reflectivity andSFG results we can confirm that the interface between PDMSand sapphire is saturated with alkane liquid (or alkane crystalsbelow Tm).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 andcooling cycles (Figure 6). The confined alkane was held at 5 °C

Figure 3. (A) Transition temperatures measured during heating (red circles) and cooling (blue circles) cycles by SFG and for bulk alkanes usingDSC (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 smallerthan the size of the symbols. (B) The differences in Tm 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) forPDMS saturated with different length of alkane chains (C15, C19,C21, and C27). The red vertical dashed lines represent the transitiontemperature measured using SFG, and the black vertical dotted linesrepresent the transition temperature measured using a He−Ne laser(linear reflectivity) that probes much thicker interfacial layer than theSFG technique.

Figure 5. Reflected intensity versus incident angle measured forPDMS lenses soaked with alkanes in contact with the sapphiresubstrate. 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 athree-layer reflectivity model (eq 4) with 100 nm thick alkane layer(solid red line) and 10 nm thick alkane layer (dashed red line).

Langmuir Article

dx.doi.org/10.1021/la402884g | Langmuir 2013, 29, 12168−1217512172

above the bulk Tm before starting the scans. Any temperature atwhich there was an abrupt change in the He−Ne intensity wasdesignated as a transition temperature. The two-step changes inintensity during the heating cycle correspond to crystal-to-rotator and rotator-to-liquid transition temperatures. Thetransition temperatures (rotator-to-crystal) measured usingthe linear reflectivity measurements are plotted as short dashedlines in Figure 4. The differences between the transitiontemperatures measured using He−Ne experiments and bulk Tmare shown in Figure 3B. For C15 and C17, the Tm measuredusing the SFG and the He−Ne beam are very similar to eachother. For longer alkanes, in the heating cycle, the melting ofthe interface layer precedes the melting of the thick alkane layernext to the sapphire substrate. The cooling cycle for longeralkanes also shows that the interfacial layer freezes before thethicker layers of alkanes are frozen next to the sapphiresubstrates.Thermodynamic Models. To understand the melting

temperatures of confined alkanes, there are two main effectsthat we need to consider. The first effect is the depression of Tmas a function of concentration. The second consideration is thatthe thickness (or size) of the confined crystal will affect the Tm(eqs 2 and 3).To understand the first effect, we can use the Flory−Rehner

model to calculate the solubility of alkanes in PDMSelastomers.17 The chemical potentials inside and outside thenetwork are labeled as μ′ and μ″, respectively. At equilibrium,these two chemical potentials should be equal.

μ μ ϕ ϕ α ϕ

ϕ ϕ

′ = ° + + − − + −

+ −

⎜ ⎟⎡⎣⎢

⎛⎝

⎞⎠⎤⎦⎥RT

r

RTx

ln (1 ) 11

(1 )

[ /2]

1 1 12

21/3

2 (6)

μ μ″ = ° (7)

In eqs 6 and 7, the parameters are same as described in eq 3. Inaddition, μ° is the chemical potential of the pure liquid (orsolvent). Table 2 provides the values of the parameters used fordetermining the equilibrium swelling ratios, and the results forC27 are shown as a black solid line in Figure 7. There are arange of values for Hilderbrand solubility parameters reportedin the literature for PDMS, and we have used a value from therange that matches the swelling results measured for PDMSlenses swollen in C27. In Figure 7, left of the solid linecorresponds to the one-phase region and to the right a two-phase region, where the two phases are a pure solvent phase

and an elastomer phase swollen in alkane. Here, theconcentrations were chosen such that the systems were alwaysin the two-phase region.We have calculated the melting temperatures using eq 2 for

an infinitely thick crystal (thickness is infinity in eq 2) (shownas black dashed line) and variable concentration of alkanes inthe swollen PDMS. The correction term due to elasticity is verysmall, and the results calculated using eqs 2 or 3 are similar.There is a significant depression in Tm when the concentrationof alkane is lower than the equilibrium concentration. However,for PDMS with excess alkanes the Tm should be similar to thebulk Tm. For C27, the equilibrium swelling concentration was≈4−5 vol %. The melting transition temperatures measuredusing DSC (red), SFG measurements (black), and opticalreflectivity (blue) are also shown in Figure 7. The Tm ofconfined C27 crystals measured using SFG and linearreflectivity do not match the predictions for a thick crystallayer 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 nmthick alkane crystal layer next to the sapphire substrate (reddashed line in Figure 7). We would like to emphasize that weare assuming the validity of eq 2 or 3 to estimate the filmthickness. Similarly, we can estimate the thicknesses that matchthe melting temperatures of the other alkanes, and the resultsare shown in Table 3. It is important to note that the values ofthe interfacial surface energies are not known and that this canintroduce errors in the thicknesses estimated using eq 2 or 3. Inaddition, the thickness calculations for C15 and C17 willstrongly depend on the reference bulk melting temperature. Asa comparison, we have also discussed the DSC analysis forcrystal size inside the PDMS network (see Figure S2 in theSupporting Information). The GT model with thin crystalsprovide a plausible explanation for depression in Tm observedusing SFG and linear reflectivity measurements.Although the thickness of the confined alkane films may

explain the depression in Tm, there are some importantanomalies that need to be mentioned. First, we have observedlarger differences in the structure of the interfacial molecules forshorter alkanes (C15−C19) in comparison to longer alkanes(C21−C27). However, these differences did not entirelycorrelate with the magnitude of the melting point depression.Second, the changes in the critical angles upon coolingindicates that there are much thicker alkane crystals next tothe sapphire substrate compared to the thickness valuescalculated using the depression in Tm (Table 3). Severalpotential explanations may resolve this anomaly. First, upon

Figure 6. Scan of He−Ne reflected intensity with temperature for C27alkane confined between PDMS lens and sapphire substrate.

Table 2. Values of Parameters Used To Compute Eq 3

chain length (n) bulk Tm (K) ΔHf (J/mol)34 Va (cm3/mol)

15 283.1 34 574 278.017 294.9 40 124 309.519 304.9 45 580 341.621 313.2 47 697 374.923 320.4 53 127 408.927 331.7 61 145 475.9

aThe interaction parameter α was determined using solubilityparameters.17 The equation is given by α = V(δalkane − δpdms)

2,where δalkane = n/(0.155643 + 0.112683n) (cal0.5/cm1.5).35 The valueof δpdms is taken as 13.41 MPa0.5.36

Langmuir Article

dx.doi.org/10.1021/la402884g | Langmuir 2013, 29, 12168−1217512173

heating, the crystal layer equilibrates with the surroundingreservoir, and the thickness of the crystal decreases withincreasing temperature. Therefore, the transition temperaturesare indicating a much thinner layer than suggested by thecritical angle measurements. The other plausible explanation isthat the size of the crystals that grow near the sapphiresubstrate depend on the length of the alkanes. As observed inthe bulk DSC data, there are distribution of crystals that areformed inside the PDMS network (Figure S2). Perhaps for C15larger crystals nucleate next to the sapphire surface comparedto those for C19. A direct analysis of the structure andthickness of the alkane crystals next to the sapphire substrates isplanned using tomographic techniques.

■ SUMMARYIn summary, we have measured the melting and freezingtransition temperatures of confined alkanes between PDMSelastomers and sapphire substrates. The difference in themelting temperatures of confined crystals with respect to thebulk transitions is a function of chain length. The combinationof the Flory−Rehner and Gibbs−Thomson models is used tocalculate the crystal size next to the sapphire substrate. Theunderstanding of crystal size and melting temperatures next tothe sapphire substrate has important implications in the areas ofnanocomposites, friction, and lubrication.

■ ASSOCIATED CONTENT*S Supporting InformationEquations for fitting the reflectivity data. This material isavailable free of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: ali4@uakron.edu (A.D.).NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSWe acknowledge funding from National Science Foundation(DMR-0512156 and DMR-1105370). We thank Yu Zhang withthe help in analyzing the DSC results showed in the SupportingInformation. We also thank Emmanuel Anim-Danso and MikeHeiber for helpful discussions.

■ REFERENCES(1) Nanjundiah, K.; Dhinojwala, A. Confinement-induced ordering ofalkanes between an elastomer and a solid surface. Phys. Rev. Lett. 2005,95, 154301/1−154301/4.(2) Yurdumakan, B.; Harp, G. P.; Tsige, M.; Dhinojwala, A.Template-induced enhanced ordering under confinement. Langmuir2005, 21, 10316−10319.(3) Kurian, A.; Prasad, S.; Dhinojwala, A. Direct measurement ofacid- base interaction energy at solid interfaces. Langmuir 2010, 26,17804−17807.(4) Nanjundiah, K.; Hsu, P. Y.; Dhinojwala, A. Understanding rubberfriction in the presence of water using sum-frequency generationspectroscopy. J. Chem. Phys. 2009, 130, 024702−024702.(5) Evans, R.; Marconi, U. M. B. Phase equilibria and solvation forcesfor fluids confined between parallel walls. J. Chem. Phys. 1987, 86,7138−48.(6) Gibbs, J.; Bumstead, H.; Van Name, R.; Longley, W. The CollectedWorks of J. Willard Gibbs; Longmans, Green, and Co.: London, 1931;Vol. 1.

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 themelting temperature as a function of concentration calculated for an infinitely thick (black short dashed line) and for a 50 nm thick (red short dashedline) C27 alkane crystal. We have used a = 2 and σ = 70 mJ/m2 for calculating the depression of Tm. The horizontal red, blue, and black dashed linescorrespond to the Tm measured using DSC for 100% C27, He−Ne reflectivity measurements, and SFG measurements, respectively. The inset showsa schematic representation of chemical potentials involved in the system.

Table 3. Thickness of Confined Alkanes Calculated UsingSFG and He−Ne Measurements

chain length (n) thickness (nm) (SFG) thickness (nm) (He−Ne)

15 200 19017 300 19019 20 2621 26 3523 30 4627 50 85

Langmuir Article

dx.doi.org/10.1021/la402884g | Langmuir 2013, 29, 12168−1217512174

(7) Thomson, J. J. Applications of Dynamics to Physics and Chemistry;Macmillan: New York, 1888.(8) Watanabe, A.; Iiyama, T.; Kaneko, K. Melting temperatureelevation of benzene confined in graphitic micropores. Chem. Phys.1999, 305, 71−74.(9) Radhakrishnan, R.; Gubbins, K. E.; Watanabe, A.; Kaneko, K.Freezing of simple fluids in microporous activated carbon fibers.Comparison of simulation and experiment. J. Chem. Phys. 1999, 111,9058−9067.(10) Meyer, R. R.; Sloan, J.; Dunin-Borkowski, R. E.; Kirkland, A.;Novotny, M. C.; Bailey, S. R.; Hutchison, J. L.; Green, M. L. H.Discrete atom imaging of one-dimensional crystals formed withinsingle-walled carbon nanotube. Science 2000, 289, 1324−1326.(11) Wilson, M. The formation of low-dimensional ionic crystallitesin carbon nanotubes. J. Chem. Phys. 2002, 116, 3027−3041.(12) Alba-Simionesco, C.; Coasne, B.; Dosseh, G.; Dudziak, G.;Gubbins, K. E.; Radhakrishnan, R.; Sliwinska-Bartkowiak, M. Effects ofconfinement on freezing and melting. J. Phys. (Paris) 2006, 18, R15−R68.(13) Christenson, H. K. Confinement effects on freezing and melting.J. Phys. (Paris) 2001, 13, R95−R133.(14) Hu, H. W.; Carson, G. A.; Granick, S. Relaxation time ofconfined liquids under shear. Phys. Rev. Lett. 1991, 66, 2758−61.(15) Granick, S. Motions and relaxations of confined liquids. Science1991, 253, 1374−9.(16) Flory, P. J.; John Rehner, J. Statistical mechanics of cross-linkedpolymer networks II. Swelling. J. Chem. Phys. 1943, 11, 521−526.(17) Flory, P. J. Principles of Polymer Chemistry; Cornell UniversityPress: Ithaca, NY, 1953.(18) Kuhn, W.; Peterli, E.; Majer, H. Freezing point depression ofgels produced by high polymer network. J. Polym. Sci. 1955, 16, 539−548.(19) Jackson, C. L.; McKenna, G. B. On the anamolous freezing andmelting of solvent crystals in swollen gels of natural rubber. RubberChem. Technol. 1990, 64, 760−68.(20) Jackson, C. L.; McKenna, G. B. The melting behavior of organicmaterials confined in porous solids. J. Chem. Phys. 1990, 93, 9002−11.(21) Qin, Q.; McKenna, G. B. Melting of solvents nanoconfined bypolymers and networks. J. Polym. Sci., Part B: Polym. Phys. 2006, 44,3475−3486.(22) Wu, J.; McKenna, G. B. Anomalous melting behavior ofcyclohexane and cyclooctane in poly(dimethyl siloxane) precursorsand model networks. J. Polym. Sci., Part B: Polym. Phys. 2008, 46,2779−2791.(23) Xu, B.; Di, X.; Mckenna, G. B. Melting of pentaerythritoltetranitrate (PETN) nanoconfined in controlled pore glasses. J. Therm.Anal. Calorim. 2013, 113, 539−543.(24) Yurdumakan, B.; Nanjundiah, K.; Dhinojwala, A. Origin ofhigher friction for elastomers sliding on glassy polymers. J. Phys. Chem.C 2007, 111, 960−965.(25) Born, M.; Wolf, E. Principles of Optics, 7th ed.; CambridgeUniversity Press: Cambridge, UK, 1999.(26) Harp, G. P.; Rangwalla, H.; Yeganeh, M. S.; Dhinojwala, A.Infrared-visible sum frequency generation spectroscopy study ofmolecular orientation at polystyrene/comb-polymer interfaces. J. Am.Chem. Soc. 2003, 125, 11283−11290.(27) Colthup, N.; Daly, L. H.; Wiberley, S. E. Introduction to Infraredand Raman Spectroscopy, 2nd ed.; Academic Press: New York, 1975; p544.(28) MacPhail, R. A.; Strauss, H. L.; Snyder, R. G.; Elliger, C. A.Carbon-hydrogen stretching modes and the structure of n-alkyl chains.2. Long, all-trans chains. J. Phys. Chem. 1984, 88, 334−41.(29) Snyder, R. G.; Strauss, H. L.; Elliger, C. A. C-H stretchingmodes and the structure of n-alkyl chains. 1. Long, disordered chains.J. Phys. Chem. 1982, 86, 5145−5150.(30) Snyder, R. G. Group-moment interpretation of the infraredintensities of crystalline normal paraffins. J. Chem. Phys. 1965, 42,1744−63.

(31) Gautam, K. S.; Schwab, A. D.; Dhinojwala, A.; Zhang, D.;Dougal, S. M.; Yeganeh, M. S. Molecular structure of polystyrene atthe air/polymer and solid/polymer interfaces. Phys. Rev. Lett. 2000, 85,3854−3857.(32) Yeganeh, M. S. Phase transitions at n-alkane/solid interfaces.Phys. Rev. E 2002, 66, 041607/1−041607/4.(33) Gang, H.; Gang, O.; Shao, H. H.; Wu, X. Z.; Patel, J.; Hsu, C. S.;Deutsch, M.; Ocko, B. M.; Sirota, E. B. Rotator phases and surfacecrystallization in α-eicosene. J. Phys. Chem. B 1998, 102, 2754−2758.(34) Dirand, M.; Bouroukba, M.; Briard, A.; Chevallier, V.; Petitjean,D. Temperatures and enthalpies of (solid + solid) and (solid + liquid)transitions of n-alkanes. J. Chem. Thermodyn. 2002, 34, 1255−77.(35) Hoy, K. L. Tables of Solubility Parameters; Union Carbide Corp.:Tarrytown, NY, 1975.(36) Barton, A. F. M. Handbook of Polymer-Liquid InteractionParameters and Solubility Parameters; CRC Press: Boca Raton, FL,1990.

Langmuir Article

dx.doi.org/10.1021/la402884g | Langmuir 2013, 29, 12168−1217512175