Freezing transitions in mixed surfactant/alkane monolayers at the air–solution interface

Abstract

Mixed monolayers at the air–water interface of the cationic surfactant, hexadecyltrimethylammonium bromide (CTAB), with alkanes show a first-order freezing transition as a function of temperature. Sum-frequency spectra and ellipsometric measurements are consistent with a structure in which the high-temperature phase is liquid-like and the low-temperature phase has all-trans, upright chains. There are strong structural similarities between the low-temperature phase in the mixed monolayers and frozen monolayers at the alkane–air and alkane–CTAB solution interfaces. The difference between the surface freezing point T_s and the freezing point of the bulk alkane T_b ranges from 1 °C for alkane chain length m = 17, to 28 °C for m = 11. Surface freezing is more favourable in mixed monolayers at the air–water interface than at the bulk alkane–water interface for the same surfactant concentration. Long-chain alkanes do not wet water, but it is postulated that if they did, they would also show surface freezing analogously to alkanes on silica. The surfactant plays the dual role of enhancing wetting and surface freezing of the alkane on water.

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Introduction

Surface phase transitions in insoluble monolayers of organic molecules on the surface of water have been studied intensively in the century since the pioneering work of Pockels, Langmuir and Harkins.¹ The development of grazing incidence X-ray diffraction in the 1980's permitted the structural determination of a wide range of mesophases differing in the lattice distortion, direction of tilt of the hydrocarbon chains, and long-range correlations in the twist of the chains.² Many of these phases are metastable with respect to bulk 3-dimensional crystallites, but can be formed by careful spreading and compression of the amphiphile on the surface of water. In contrast to the rich phase behaviour of insoluble (Langmuir) monolayers, the adsorbed films of most soluble surfactants (Gibbs monolayers) have uninteresting phase diagrams, showing only a single fluid phase over the whole range of concentrations. There is no hard and fast distinction between soluble and insoluble monolayers: the classification depends as much on the timescale of the experiment as on the absolute solubility of the surfactant. It is therefore almost inevitable that surfactants exist that are sufficiently soluble to form monolayers at equilibrium with a bulk solution, yet which have strong enough intermolecular interactions to show a liquid–solid monolayer phase transition at the air–water interface. The simplest of these molecules are the normal alcohols, which for chain lengths m > 9 show a liquid–solid phase transition, analogous to the L₁–LS phase transition in Langmuir monolayers, at a temperature about 15 K above the bulk melting point of the alcohols.³ (Since the 1990s, phase transitions have been studied in a number of other sparingly soluble surfactants, such as monoethyleneglycol tetradecyl ether (C₁₄E₁),^4,5 monoethyleneglycol dodecyl ether (C₁₂E₁),⁵n-hexadecyl phosphate,^6–8n-dodecyl-γ-hydroxybutyric acid amide (DHBAA),^9,10 2-hydroxyethyl laurate (2-HEL),¹¹ and the catanionic surfactants dodecyltrimethylammonium dodecylsulfate (DTA.DS) and decyltrimethylammonium decylsulfate (DeTA.DeS).¹²

Common, short-chain, micelle-forming surfactants such as alkyltrimethylammonium bromides (C_nTABs) and sodium dodecylsulfate (SDS) do not, on their own, form monolayers in condensed phases. These ionic surfactants do, however, form 2D solid phases in the presence of n-alcohols. The best known example is SDS, which when mixed with dodecanol at very low levels (≪1%) forms a condensed monolayer. Since commercial samples of SDS are always contaminated with dodecanol, SDS solutions show anomalous properties, such as increased foam stability, due to the formation of mixed monolayers of SDS and dodecanol in a solid phase. We have previously studied mixtures of C_nTAB (n = 12, 14, 16) and SDS with dodecanol and characterised the 2D phase transition in these mixed monolayers by sum-frequency spectroscopy (SFS) and ellipsometry.^13,14

The focus of this paper is on freezing transitions in mixtures of C_nTABs with linear alkanes, neither of which will form a condensed monolayer on water on their own. C_nTABs form highly disordered, liquid-like monolayers at all coverages up to the saturation value, which is reached at the critical micelle concentration (cmc). Pure alkanes with chain lengths m > 7 do not spread on water, but instead form a lens in equilibrium with a dilute 2D gas of alkane molecules on the water surface.¹⁵ If surfactants are progressively added to the aqueous sub-phase a concentration is reached where the alkane undergoes a first-order wetting transition to form a mixed monolayer of surfactant and alkane, coexisting with a lens of alkane:^16,17 a situation known as ‘pseudo-partial wetting’¹⁸ or ‘frustrated complete wetting’.¹⁵

We have shown in a preliminary communication that upon cooling a mixed monolayer of C₁₆TAB and tetradecane in the pseudo-partial wetting regime, a further first-order phase transition is observed from a liquid-like, conformationally disordered monolayer to a highly conformationally ordered solid phase.¹⁹ We will refer to this change as a freezing transition. The discontinuous nature of the freezing transition is shown clearly by ellipsometric measurements of the coefficient of ellipticity, [small rho, Greek, macron] (see below for a definition), as a function of temperature (Fig. 1). The transition (indicated by a dashed line) occurs 12 °C above the bulk freezing point of tetradecane (T_b = 6 °C).

Fig. 1 Variation in the coefficient of ellipticity, [small rho, Greek, macron], with temperature, T, for the surface of a 0.60 mM solution of C₁₆TAB in H₂O in the presence of lenses of tetradecane: (solid symbols) heating cycles; (open symbols) cooling cycles. The triangles and circles refer to different samples.

In this paper, we use sum-frequency spectroscopy and ellipsometry to elucidate the structure of the phases on either side of the freezing transition and explore the chain length dependence in mixed monolayers of C₁₆TAB with alkanes CH₃(CH₂)_m−2CH₃ with m = 11–17 (denoted C_m). Qualitatively different behaviour is observed with longer alkanes, which will be the subject of a separate paper.

Although long-chain alkanes do not form frozen monolayers on water—for the simple reason that they do not spread—alkanes do have an unusual property that is of relevance to the phenomena we report here: they exhibit surface freezing.^20–22 For chain lengths m = 16–50, a monolayer of alkane molecules at the vapour–liquid interface freezes at a temperature, T_s, up to 3 °C above the bulk freezing point, T_b. For lower values of m, this frozen monolayer is in an upright rotator phase with hexagonally packed chains: the same structure as the LS phase in insoluble monolayers on water. A single monolayer of solid alkane persists down to the bulk freezing point. The connection to the work in this paper is made clearer by the fact that surface freezing is not observed at the pure water–alkane interface²³ but can be induced at the solution–alkane interface by the presence of the cationic surfactant, C₁₆TAB.²⁴ The entropy changes of the freezing transitions at the solution–alkane and alkane–air interfaces are in excellent agreement and ellipsometric measurements on the solution–alkane interface are well-explained by a frozen mixed monolayer in an upright, rotator phase, analogous to that observed at the alkane–air interface. A comparison of the freezing transitions in mixed monolayers of surfactant and alkane at the air–water and alkane–water interface concludes this paper.

The two experimental techniques used in this paper are sum-frequency spectroscopy and ellipsometry; a brief introduction to these two techniques is provided here.

Sum-frequency spectroscopy (SFS) is a form of surface-sensitive non-linear vibrational spectroscopy in which pulsed visible (frequency ω_vis) and infrared laser beams (ω_IR) are overlapped at a surface and light is emitted coherently at the sum of the two incident frequencies: ω_SF = ω_vis + ω_IR.^25–31

Within the electric dipole approximation, the intensity of the sum-frequency (SF) signal, I(ω_SF), depends on the intensities of the visible and IR beams and the square of the second-order susceptibility tensor, χ⁽²⁾:

I(ω_SF) ∝ |χ⁽²⁾|²I(ω_vis)I(ω_IR) (1)

χ⁽²⁾ is a material property that is related to the molecular hyperpolarisibility, β, of the molecules at the surface by where N is the number density of the molecules, f is a factor to account for the difference between the electric field of the incident light and the local electric field, and the angle brackets indicate that the molecular hyperpolarisability has to be averaged over the orientations of all the molecules at the interface.

Three key features of SFS are highlighted here. First, χ⁽²⁾ is a third-rank tensor, which vanishes by symmetry in centrosymmetric or isotropic environments. Therefore, there will be no SF signal from the bulk fluids on either side of a gas–liquid interface but only from molecules at the interface that have net orientation and hence break the symmetry of the bulk phases. Second, β is negligible except in the vicinity of a vibrational resonance that is both IR- and Raman-active. Varying the frequency of the infrared laser and recording the SF signal as a function of ω_IR yields a vibrational spectrum. Third, the hyperpolarisability, β, is also a third-rank tensor which is zero by symmetry for a centrosymmetric molecule. An all-trans hydrocarbon chain is locally centrosymmetric (the middle of each C–C bond is a centre of inversion) and therefore the methylene vibrations in an all-trans chain are SF-inactive. Gauche defects break the symmetry and give rise to SF-allowed CH₂ vibrations, provided that the overall symmetry of the interface is not isotropic (in which case β is non-zero but <β> vanishes). As a consequence of this orientational averaging, chemical groups that have a strong preferred orientation generally give stronger SF signals than those that have a broad distribution of orientations.

In ellipsometry, a polarised laser beam is reflected from an interface and the change in the state of polarisation is measured. In the form of ellipsometry used in this paper, the measured quantity is the coefficient of ellipticity, [small rho, Greek, macron], which is defined as the imaginary part of r_p/r_s at the Brewster angle, where r_p and r_s are the complex amplitude reflection coefficients for p- and s-polarised light, respectively. The Brewster angle is defined as the angle where the real part of r_p/r_s is zero. The coefficient of ellipticity is a sensitive function of the profile of the optical dielectric constant (ε = n², where n is the refractive index) through the interface. For a thin isotropic film between two semi-infinite media with dielectric constants ε₁ and ε₂, [small rho, Greek, macron] is given by the Drude equation:³²

where λ is the wavelength of the light and z is the coordinate normal to the interface. Since hydrocarbons have a higher dielectric constant than water or air, ellipsometry is very sensitive to the accumulation of surfactants or alkanes at the air–water interface. In reflectometry experiments, it is common to model a complex interface as a series of stratified, homogeneous layers and to use an optical matrix method to account for the effect of each layer on the reflectivity.³³ A similar device can be used in ellipsometry, in which case one simply adds the contributions to [small rho, Greek, macron] from each layer.

Monolayers on water are more accurately described as being optically uniaxial, with the extraordinary axis along the surface normal. In this case, the Drude equation has to be modified to read

where ε_e and ε_o are respectively the dielectric constants perpendicular and parallel to the interface.^34,35 In frozen surface phases of hydrocarbon chains, the term due to the anisotropy can make a major, or even dominant, contribution to the coefficient of ellipticity.

Experimental

Materials

Hexadecyltrimethylammonium bromide (C₁₆TAB: Fluka, >99%) was recrystallised three times from an acetone–methanol mixture. Recrystallised, fully-deuterated hexadecyltrimethylammonium bromide (d-C₁₆TAB) was a gift from Dr R. K. Thomas, University of Oxford. Tetradecyltrimethylammonium bromide (C₁₄TAB), recrystallised three times from acetone with a small amount of ethanol, was kindly provided by Prof. P. D. I. Fletcher, University of Hull. Alkanes, C_m, with m = 11–16 (Aldrich, 99+%) or 17 (Sigma, 99%) were percolated 2–3 times through neutral alumina before use. Deuterated tetradecane (d-C₁₄: Cambridge Isotope Laboratories, 98% D) was percolated once through neutral alumina. Solutions for ellipsometry were prepared in H₂O (Elga, UHQ) and for sum-frequency spectroscopy in D₂O (Aldrich, 99.9%).

Ellipsometry

Ellipsometric measurements were performed on a Picometer Ellipsometer (Beaglehole Instruments, Wellington, NZ) equipped with a HeNe laser at 632.8 nm. Surfactant solutions were held in a 5 cm diameter glass dish in a sealed thermostatted cell with fused silica windows for the laser beams to pass through. Around 1 µL of alkane at room temperature was added to the surfaces of samples using a glass syringe with a stainless steel needle. The temperature was varied in discrete intervals with an equilibration time of ca. 45 min between each measurement. Increments of 1–2 °C were used away from the transition and <1 °C close to the transition. The temperature of the sample was measured directly to a precision of 0.1 °C with a thermocouple that was fixed in position throughout the experiment. Measurements were recorded every 1 s and averaged over 50 s. Readings were considered to be stable if [small rho, Greek, macron] varied by less than 2 × 10⁻⁵ over a period of 10 min. The precision of the averaged values of [small rho, Greek, macron] was typically better than ±1 × 10⁻⁵.

The precise value of the phase transition temperature is sensitive to impurities: freshly percolated alkanes and freshly recrystallised surfactants tended to give higher values of T_s. To provide an indication of reproducibility, multiple repeat measurements on the C₁₆TAB + C₁₄ system gave a range of values of T_s = 16.7–18.8 °C. Experiments in which one of the components was deuterated gave transition temperatures 2–3 °C lower. This difference may be ascribed partially to the lower purity of the deuterated compounds, but also reflects the thermodynamics of the phase transition: deuterated alkanes have lower melting points than normal alkanes.³⁶

Sum-frequency spectroscopy

Sum-frequency spectroscopy (SFS) was carried out as described previously.^29,37 A pulsed fixed-frequency visible beam (532 nm, s-polarised, 4 ns pulse length, 20 Hz repetition rate, 1 mm diameter, 10 mJ pulse⁻¹) was overlapped with a tunable infrared beam (3000–2800 cm⁻¹, p-polarised, ∼1 ns pulse length, 0.4 mm diameter, 0.4–0.7 mJ pulse⁻¹) at the air–water interface. The beams were directed onto the surface at θ_vis = 55° and θ_IR = −50° (the negative sign indicating that two laser beams were counter propagating). The beams were incident at a point away from the centre of the sample and the sample was rotated at 2 rpm to reduce the effect of local heating by the IR laser beam. The use of D₂O rather than H₂O as a subphase further reduces local heating and decreases the non-resonant background signal from the subphase. The s-polarised sum-frequency (SF) light was emitted in a narrow beam at a well defined angle θ_SF = 37–38° depending on the IR wavelength and was detected with a liquid nitrogen-cooled CCD camera (Princeton Instruments). The SF signal from the sample was referenced to a signal obtained simultaneously from a GaAs crystal. After background subtraction, sample spectra were normalised to the reference spectra and fitted as described elsewhere.^37,38

Samples were held in a 6 cm glass dish in a thermostatted cell covered by a lid with slits for entry and exit of the laser beams. The temperature of samples was measured with a thermocouple before each spectrum to a precision of ±0.1 °C. Over the course of a spectrum the temperature of the sample varied by <0.5 °C.

Results

Sum-frequency spectroscopy (SFS)

In our preliminary communication, we presented SF spectra of the surface of a solution of C₁₆TAB in the presence of tetradecane, above and below the freezing transition. Since both the surfactant and alkane contained hydrocarbon chains, these spectra did not distinguish between the two species. Here we use selective deuteration to look separately at the conformational order in the two components in the monolayer.

Fig. 2 shows SF spectra in the C–H stretching region (2800–3000 cm⁻¹) of monolayers of (A) h-C₁₆TAB + h-C₁₄ (denoted h + h), (B) h-C₁₆TAB + d-C₁₄ (denoted h + d), (C) d-C₁₆TAB + h-C₁₄ (denoted d + h) and (D) h-C₁₆TAB alone, where h indicates a normal, protonated molecule and d a fully deuterated molecule. Fig. 2(A) thus contains contributions from both the surfactant and the alkane, while Fig. 2(B) shows just the surfactant and Fig. 2(C) just the alkane. The assignment of the peaks in Fig. 2 is well-established.^39,40 The strongest peak at 2878 cm⁻¹ is assigned to the symmetric methyl stretch (r⁺) and the peak at 2937 cm⁻¹ is a Fermi resonance of the r⁺ mode with overtones of the methyl modes (r⁺_FR). The behaviour of the r⁺_FR peak parallels that of the r⁺ peak and will not be discussed further. The peak at 2850 cm⁻¹, which is observed principally above T_s, is the symmetric methylene stretch (d⁺). The antisymmetric methylene (d⁻) and methyl (r⁻) stretches are weak in SSP-polarised spectra: the latter appears as a shoulder on the high frequency side of the r⁺_FR mode. Previous SF studies on monolayers of partially deuterated C₁₄TAB have shown that the vibrations of the trimethylammonium headgroup are not detected.⁴¹

Fig. 2 SF spectra at the air–solution interface of a 0.60 mM solution of C₁₆TAB in D₂O in the presence of lenses of tetradecane. T > T_s (grey lines) and T < T_s (black lines). (A) h-C₁₆TAB and h-tetradecane, (B) h-C₁₆TAB and d-tetradecane, (C) d-C₁₆TAB and h-tetradecane, and (D) h-C₁₆TAB without tetradecane at 15 °C. The visible and sum-frequency fields were s-polarised and the IR field was p-polarised (denoted SSP).

For quantitative analysis of SF spectra, the spectra need to be deconvoluted into their constituent peaks. Each peak is assigned a line strength, S_ν, resonant frequency, ω_ν, and two linewidths corresponding to homogeneous and inhomogeneous broadening; these parameters are then minimised subject to some constraints. The detailed fitting procedure is described elsewhere,³⁸ here we will merely discuss the line strengths, S, that are deduced from the fits (See Table 1). For an isolated peak, the SF intensity, I ∝ S²; however, interference between neighbouring peaks and with the weak non-resonant background from the subphase can significantly alter the shape and intensity of peaks in an SF spectrum.

Table 1 Line strengths, S, of the r⁺ and d⁺ peaks in the SSP-polarised spectra (shown in Fig. 2) of a 0.60 mM C₁₆TAB solution in D₂O in the presence of lenses of tetradecane. Column 4 contains the sums of the line strengths in columns 2 and 3; column 8 contains the sum of the line strengths in columns 6 and 7. The repeatability in S(r⁺) is ∼10%. In the solid phase, S(d⁺) is sensitive to noise and to the details of the fitting procedure and is indicative only

	Below Ts				Above Ts				Pure
	h + d	d + h	Sum	h + h	h + d	d + h	Sum	h + h	C16TAB
S(r^+)	3.2	1.8	5.0	4.4	1.8	0.0	1.8	2.2	1.2
S(d^+)	0.1	0.3	0.4	0.25	1.4	0.0	1.4	1.4	1.1

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h + h Spectra. Above T_s, the ratio of line strengths, S(d⁺)/S(r⁺) = 0.6. This value is characteristic of a monolayer with a high degree of conformational disorder in the chains.³⁷ When the temperature of the sample was lowered through the phase transition, the strength of the r⁺ peak in the h + h spectrum doubled, whilst the d⁺ peak, while still detectable, decreased by a factor of five. The spectrum below T_s resembles that of a monolayer of dodecanol on water in its solid phase,^3,37 which is known to be in an upright rotator phase with an area per chain of 21 Ų.⁴² The weakness of the d⁺ peak indicates that the number of gauche defects in the solid phase of the monolayer is very low. It is reasonable therefore to approximate the chains in the solid phase as being all-trans. For the r⁺ mode in SSP-polarised spectra, <β> ∝ 〈cosθ〉, to a good approximation, where θ is the angle between the C₃ axis of the methyl group and the surface normal. We are more interested in the mean tilt, ϕ of the alkyl chain from the surface normal. If the chain is free to rotate about its long axis, then 〈cosθ〉 = 〈cosϕ〉cosα where α is the angle between the chain axis and the terminal C–C bond.³ Consequently, from eqns. (1) and (2), S(r⁺) ∝ N〈cosϕ〉. To distinguish between an increase in the number density of molecules, N, contributing to the spectrum in the frozen phase and a decrease in the mean chain tilt, ϕ, we need to look at the spectra of selectively deuterated mixtures.

h + d Spectra. The spectra in Fig. 2(B) were acquired with C₁₄D₃₀ in the place of C₁₄H₃₀, and so contain no direct contributions from alkane molecules. Above T_s, the SF spectrum is very similar to that of C₁₆TAB in the absence of alkane (Fig. 2(D)). The d⁺ and r⁺ modes are comparable in intensity, again confirming that the chains are conformationally highly disordered. Below T_s, the d⁺ mode weakens greatly while the line strength of the r⁺ mode increases by 50%. There are two reasons for ascribing the increase in S(r⁺) principally to an increase in <cos ϕ> (i.e., a decrease in tilt) rather than an increase in the number density of surfactant molecules, N_surf, at the interface. First, interfacial tension measurements on surface freezing at the bulk tetradecane–C₁₆TAB(aq) interface have shown that N_surf does not change greatly at the phase transition temperature. Second, surface tension and neutron reflection measurements made above T_s show that for cationic surfactants at the air–water interface, N_surf remains approximately constant when alkanes are added, at least for high concentrations of surfactant;^43,44 the maximum value of N_surf is limited by repulsions (both steric and electrostatic) between the trimethylammonium headgroups.

d + h Spectra. The d + h spectra only contain a contribution from the alkane. Above T_s there is no SF signal detectable above the noise level. It is known from tensiometry, ellipsometry and neutron reflectometry on related systems that oil is present in the mixed monolayer, but the alkane molecules have no preferred orientation and are therefore sum-frequency inactive. With no signal from the alkane in the liquid phase, we would expect the line strengths in the h + h and h + d spectra to be the same: to within experimental precision, they are.

Below T_s, the d + h spectrum shows a sharp r⁺ mode and only a very weak d⁺ mode. The value of S(r⁺) is ∼60% of that of the same mode in the h + d spectrum. At first sight this result is very surprising: the low value of the ratio S(d⁺)/S(r⁺) would indicate a chain that was predominantly all-trans; but tetradecane in an all-trans configuration is centrosymmetric and hence sum-frequency inactive. The electric fields at ω_SF from the two methyl groups are π out-of-phase and should cancel out in the far field. It is conceivable that <cos θ> might be different for the two ends of the alkane molecule; for example, if there were a greater population of chain defects at one end of the chain. Comparison of the Figs. 2(A) and (B) show that the CH₃ groups of C₁₆TAB and C₁₄ contribute with the same phase and consequently the methyl group of the tetradecane at the outer side of the monolayer makes a larger contribution than the opposite terminus. Chain disorder tends to increase towards the air side of a monolayer, which would result in a larger contribution to the SF field from the inner methyl group, in contradiction to experiment. We believe that the net signal from the tetradecane molecules arises from a break-down in the electric dipole approximation, which assumes that the electric fields do not vary over the dimension of the molecule. Electric quadrupole SF transitions, which depend on gradients in the fields, are permitted for centrosymmetric molecules. As a result of the rapid changes in the dielectric constant across the interface, the local fields experienced at the air–monolayer and monolayer–water interfaces are significantly different. This effect has been observed previously by Sefler et al. for liquid eicosane (C₂₀) below T_s, where a single frozen layer of eicosane molecules exists on the surface.⁴⁵ The experimental data of Sefler et al. can be rationalised if the contribution of the lower methyl group to the sum-frequency field is 50–60% of that from the upper methyl group. If a similar degree of cancellation occurs in the mixed C₁₆TAB + alkane monolayers, the composition of the mixed monolayer in the solid phase may be estimated from the line strengths of the methyl groups, with the tetradecane line strength corrected to allow for the (negative) contribution of the lower methyl group. We then find that the mixed monolayer contains 40–50% surfactant, which is in the same range as in mixed monolayers of C_nTAB + dodecanol and SDS + dodecanol.^13,14

Ellipsometry

The coefficient of ellipticity is plotted as a function of T for the C₁₆TAB + C₁₄ system in Fig. 1. A sharp phase transition is observed at a temperature of 18.5 °C. Careful heating and cooling cycles show that there is negligible hysteresis in the transition. Fig. 3 gathers together data for C₁₆TAB + C_m monolayers with m = 11–17. In Fig. 3, the difference between heating and cooling cycles has been suppressed for clarity. The concentration of C₁₆TAB was c = 0.60 mM except for m = 11, where we used 0.30 mM. The surfactant is below its Krafft temperature in all these experiments (T_K = 25 °C) and crystals of C₁₆TAB appeared at the lowest temperatures when c = 0.60 mM was used.

Fig. 3 Coefficient of ellipticity, [small rho, Greek, macron], against temperature, T, for the air–solution interfaces of C₁₆TAB solutions in H₂O in the presence of lenses of alkane with chain lengths, m (labelled on figure). c = 0.30 mM (m = 11) and 0.60 mM (m = 12–17).

For every system there was a discontinuous change in [small rho, Greek, macron](T) corresponding to a first-order transition between a liquid monolayer and a solid monolayer. Within error, the heating and cooling curves for each alkane were identical and the discontinuities occurred at the same temperatures, T_s(m) (marked by dashed vertical lines). The values of T_s(m) increased with increasing m and were always above the bulk melting point, T_b(m), of the alkane: just below T_s the solid monolayer was in equilibrium with a liquid lens. The transition temperatures are reported in Table 2.

Table 2 Calculated thickness of the hydrocarbon layer, d_c, of C₁₆TAB + C_m and C₁₄TAB + C_m monolayers in the liquid and solid phase at the transition temperature, T_s (eqns. (12) and (13)). Values of the surface excess of surfactant, Γ, and surface tension, σ, used to calculate d_c

n	m	c/mM	T s/°C	Γ/µmol m^−^2	σ/mN m^−1	d c(l)/Å	d c(s)/Å
a Approximated as Γ at 25 °C in the absence of oil.^50 b From neutron reflection results at 25 °C.^43 c Approximated as σ^aw at 25 °C for C16TAB + C12.^49 d At 25 °C.^43
16	11	0.30	2	2.8^a	45^c	12	18
16	12	0.60	10	3.4^a	40^c	12	18
16	13	0.60	14	3.4^a	40^c	11	19
16	14	0.60	18	3.4^a	40^c	12	21
16	15	0.60	19	3.4^a	40^c	11	20
16	16	0.60	22	3.4^a	40^c	11	21
16	17	0.60	22	3.4^a	40^c	11	20
14	12	1.20	0	2.7^b	43^d	9	16

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We also measured the phase transition in a shorter homologue of C₁₆TAB for one alkane. For dodecane lenses on a C₁₄TAB solution (c = 1.2 mM), [small rho, Greek, macron](T) decreased discontinuously at T_s = 0.2 °C from −1.9 × 10⁻³ to −2.8 × 10⁻³. Comparing C₁₆TAB + C₁₄ with C₁₆TAB + C₁₂, or C₁₆TAB + C₁₂ with C₁₄TAB + C₁₂ shows that reducing the chain length by two carbons lowered T_s by around 10 °C regardless of whether the length of the alkane or the surfactant chain were altered.

To interpret the values of [small rho, Greek, macron] quantitatively, we need to construct a model for the dielectric profile through the interface, which we describe in the following section. Readers who are not interested in the details of the model may wish to skip to Fig. 4 below and the Discussion.

Modelling ellipsometry of mixed surfactant/alkane monolayers

We divide the interface up into five parallel homogeneous layers: air; hydrocarbon chains of the surfactant + alkane (denoted by the subscript c); hydrated headgroups (subscript h); electrical double layer containing counterions (subscript i); and the bulk aqueous solution (approximated as pure water). The Drude equation (eqn. (3) or (4) as appropriate) is then used to calculate the contribution of each of the three internal layers to the coefficient of ellipticity. Roughness is incorporated by including an additional contribution to the coefficient of ellipticity from capillary waves (subscript r). We therefore write

[small rho, Greek, macron] = [small rho, Greek, macron]_r + [small rho, Greek, macron]_i + [small rho, Greek, macron]_h + [small rho, Greek, macron]_c (5)

Our approach is to estimate all the physical quantities involved in the calculation of the coefficient of ellipticity, other than the thickness of the chain region, which can then be determined by comparison of the model with the experimental values of [small rho, Greek, macron]. While the number of assumptions and approximations may appear to be large, the calculated coefficients of ellipticity are rather insensitive to the precise values of most of the parameters in the model. Two parameters to which [small rho, Greek, macron] displays particular sensitivity are the density of the hydrocarbon chain region in the liquid phase and the anisotropy of the hydrocarbon chains in the solid phase. We have shown previously that ellipsometric data of C₁₆TAB monolayers can only be understood if the chain region has a density very close to that of a liquid hydrocarbon.⁴⁶ The anisotropy in the hydrocarbon chains was determined ellipsometrically with similar assumptions to those in this paper; consequently errors in the assumptions are likely to cancel out.⁴⁷ The model we use to calculate each of the terms in eqn. (5) is described below.

Roughness. The contribution from roughness, [small rho, Greek, macron]_r, is proportional to √T and inversely proportional to √σ, where σ is the surface tension of the solution.⁴⁸ The value of [small rho, Greek, macron] of pure water at 25 °C, 0.4 × 10⁻³, is ascribed entirely to capillary wave roughness. For pure water at 298 K, σ = 72 mN m⁻¹. We estimated [small rho, Greek, macron]_r of a solution from where σ^aw is in mN m⁻¹ and T is in K. Given the rather weak dependence of [small rho, Greek, macron]_r on σ, we approximated the surface tensions of C₁₆TAB solutions in the presence of alkanes by the literature values for C₁₆TAB in the presence of dodecane at the same concentrations at 25 °C.⁴⁹ For C₁₄TAB solutions in the presence of dodecane σ was taken from ref. 43 (see Table 2).

Counterions. The counterion layer (i) and headgroup layer (h) were assumed to be isotropic and homogeneous. The integral in the Drude eqn. (3) can therefore be replaced by the thickness, d_j of the j^th layer.

The optical dielectric constant, ε = n², where n is the refractive index at the wavelength of the laser. For water, ε_w is a function of temperature. A third-order polynomial fit to literature values⁵¹ of ε_w in the range 0–40 °C was used to calculate ε_w at each transition temperature:

ε_w(T) = 3.715 × 10⁻⁸T³ − 7.803 × 10⁻⁶T² + 4.996 × 10⁻⁵T + 1.7756 (8)

where T is the temperature in °C.

For layers containing more than one component (e.g., water + ions, or water + headgroups), ε_j can be estimated by means of the Lorentz–Lorenz effective medium approximation (EMA) in terms of the dielectric constants and volume fractions, ϕ, of the individual components {α, β, …}.

The values of the dielectric constants and molar volumes of different components are listed in Table 3.

Table 3 Dielectric constants, ε, and molar volumes, V_m used in the modelling of [small rho, Greek, macron]

	V m/cm^3 mol^−1	ε
a Calculated from the ionic radius.^53 b Calculated from values of refractive index (ε = n^2), ^51 or density (Vm = 1/ρ).^51 c V m(TMA) = Vm(N^+(CH3)3Br^−) − Vm(Br^−) where Vm(N^+(CH3)3Br^−) = 81.3 cm^3 mol^−1.^57 d Calculated with eqn. (11) with values of Rm from ref. 53. e Calculated with eqn. (11) with Rm equal to a sum of molar atomic refractivities.^51
Air	—	1.00^b
H2O	—	1.77^b
Br^−	19.0^a	6.29^d
TMA	62.3^c	2.38^e
Undecane	211^b	2.07^b
Dodecane	228^b	2.02^b
Tridecane	244^b	2.03^b
Tetradecane/tetradecyl	260^b	2.04^b
Pentadecane	276^b	2.05^b
Hexadecane/hexadecyl	293^b	2.06^b
Heptadecane	310^b	2.06^b

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To calculate [small rho, Greek, macron]_i (and [small rho, Greek, macron]_h) we need to know the surface excess of surfactant, Γ (≅N_surf/N_A where N_A is Avogadro's number). For C₁₆TAB, we approximated Γ in the presence of an alkane at T_s by its value at 298 K in the absence of the alkane.⁵⁰ The similarity between the SF spectra for pure C₁₆TAB and for C₁₆TAB + d-C₁₄ (Fig. 2) together with previous neutron reflection⁴³ and surface tension¹⁷ data for mixed C_nTAB + alkane monolayers suggests that the presence of oil does not greatly affect the surface excess of C₁₆TAB. For C₁₄TAB, Γ has been measured directly by neutron reflection in the presence of dodecane at 25 °C;⁴³ these values of Γ were employed as estimates for the surface excess of C₁₄TAB at T_s. The values of Γ used in the modelling are listed in Table 2.

Charge neutrality requires that the surface excess of bromide counterions is equal to that of the surfactant. The bromide ions are treated as a homogeneous layer in water with a thickness equal to the Debye length, r_D. The counterion term, [small rho, Greek, macron]_i is, in fact, quite insensitive to the choice of thickness of the layer or the concentration profile within the layer. A solution of a 1 ∶ 1 ionic surfactant with ions of charge +1 and −1 at concentration c (moles per unit volume) has a Debye length

where ε_r is the relative permittivity of the solution, ε₀ is the permittivity of a vacuum, R is the molar gas constant, T is the temperature and F is the Faraday constant.⁵² The surfactant solutions used had Debye lengths of 8–17 nm. The volume fraction of bromide ions in the layer, ϕ_Br⁻, was calculated from the concentration of ions in the layer and the ionic radius.⁵²ε_Br⁻ was calculated from the molar refractivity, R_m, ⁵³ and the molar volume, V_m (from the ionic radius⁵³) using the Clausius–Mossotti equation:

The dielectric constant of the counterion layer, ε_i, was then found from eqn. (9), with ϕ_w = 1 − ϕ_Br⁻. Values of ε_i and d_i = r_D were substituted into eqn. (7) to obtain [small rho, Greek, macron]_i.

Headgroups. The layer containing the headgroups was modelled as a mixture of trimethylammonium (TMA) groups and water according to eqn. (9). The number of TMA groups per unit area, Γ, was estimated as described above. For the thickness of the layer, d_h, we make use of neutron reflection measurements by Thomas and co-workers on monolayers of C₁₆TAB at the air–water interface. They described the headgroup layer by a Gaussian distribution of width 14 Å.^54–56 This roughness includes both the intrinsic roughness of the monolayer and a capillary wave roughness of 9 Å.⁵⁵ After deconvoluting the capillary wave roughness, the intrinsic roughness is 11 Å. The roughness defined by Thomas and co-workers corresponds to the full width of the distribution at 1/e of the maximum; the corresponding rms roughness is a factor of √8 smaller. We used twice the rms width (8 Å) as an estimate of the thickness of the headgroup layer for both C₁₄TAB and C₁₆TAB solutions.

To estimate ε_TMA, values of the molar volume, V_m, and molar refractivity, R_m, are required. The molar volume of N(CH₃)₃Br is quoted as 81.3 cm³ mol⁻¹ (135 ų per molecule) by Thomas and co-workers;⁵⁷V_m(Br⁻) from the ionic radius is 19.0 cm³ mol⁻¹,⁵³ giving V_m(TMA) = 62.3 cm³ mol⁻¹. To a good approximation molar refractivities are additive. The molar refractivity of the trimethylammonium headgroup, R_m(TMA), was estimated as a sum of molar atomic refractivities of C, H and N for a secondary amine (in the absence of reference values for quaternary amines),⁵¹ε_TMA was calculated from R_m(TMA) and V_m(TMA) using eqn. (11), ε_h from the Lorentz–Lorenz EMA (eqn. (9)), and finally [small rho, Greek, macron]_h from eqn. (7), with d_h = 8 Å.

The calculated values of [small rho, Greek, macron]_r, [small rho, Greek, macron]_i, and [small rho, Greek, macron]_h are shown in Table 4.

Table 4 Calculated values of [small rho, Greek, macron]_r, [small rho, Greek, macron]_i, and [small rho, Greek, macron]_h for mixed monolayers of C_nTAB + alkane for the conditions in Table 2. The experimental values of the coefficient of ellipticity [small rho, Greek, macron]_exp used to calculate [small rho, Greek, macron]_c are given

	n	m	[small rho, Greek, macron] r	[small rho, Greek, macron] h	[small rho, Greek, macron] i	[small rho, Greek, macron] exp	[small rho, Greek, macron] c
High T	16	11	0.49	−0.48	−0.52	−2.34	−1.82
	16	12	0.52	−0.58	−0.62	−2.52	−1.84
	16	13	0.53	−0.58	−0.62	−2.42	−1.74
	16	14	0.53	−0.58	−0.62	−2.57	−1.90
	16	15	0.53	−0.58	−0.62	−2.39	−1.72
	16	16	0.53	−0.58	−0.62	−2.41	−1.74
	16	17	0.53	−0.58	−0.62	−2.39	−1.72
	14	12	0.50	−0.46	−0.50	−1.91	−1.45
Low T	16	11	0.49	−0.48	−0.52	−3.19	−2.68
	16	12	0.52	−0.58	−0.62	−3.46	−2.78
	16	13	0.53	−0.58	−0.62	−3.52	−2.84
	16	14	0.53	−0.58	−0.62	−3.80	−3.13
	16	15	0.53	−0.58	−0.62	−3.78	−3.10
	16	16	0.53	−0.58	−0.62	−3.79	−3.12
	16	17	0.53	−0.58	−0.62	−3.70	−3.03
	14	12	0.50	−0.46	−0.50	−2.79	−2.32

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Chain region: liquid phase. In the liquid phase, we assume that the chain layer, comprising the hydrocarbon chains of both the surfactant and the oil, is isotropic and has the average density of liquid alkane of chain length n and m at 25 °C.⁵¹ One could use the density at T_s, but the correction would be small given the other approximations made in the analysis. The dielectric constant, ε_c, was taken as that of a 1 ∶ 1 mixture (by volume) of C_n and C_m, from eqn. (9) and the dielectric constants in Table 3. ε_c does not vary greatly with n or m.

From eqn. (7), the thickness of the hydrocarbon layer in the liquid phase, d_c(l), is given by

where [small rho, Greek, macron]_c = [small rho, Greek, macron]_exp − [small rho, Greek, macron]_h − [small rho, Greek, macron]_i − [small rho, Greek, macron]_r, (Table 4). The calculated values of d_c(l) are tabulated in Table 2. The parameter in the model that has the greatest influence on d_c(l) is the dielectric constant of the chain region. We have assumed the ‘oil-film’ model, which gave good agreement for monolayers of both cationic (C_nTAB) and non-ionic (C_nE_m) surfactants.^46,58 If the density of the chain region is less than that of a liquid alkane, the thicknesses will be larger than the calculated values. It is, however, unclear why oil molecules would spread from an oil droplet into an interphase of significantly lower density. The headgroup and counterion contributions are roughly linear functions of surface excess: a 10% error in Γ would change the calculated thickness by less than 1 Å.

Chain region: solid phase. In the solid phase, SF spectra suggest that the monolayer is similar to a frozen monolayer of dodecanol on the air–water interface, which is in an upright rotator phase with an area per molecule, A = 20.9 Ų, at 25 °C.⁵⁹ The uniaxial dielectric constants of a solid monolayer of dodecanol, determined from ellipsometric measurements as a function of the refractive index of the aqueous subphase, are ε_e = 2.23 and ε_o = 2.12.⁴⁷ We use these values for the hydrocarbon chain in the low temperature phase of the mixed C₁₆TAB + alkane monolayers. From eqn. (4), we can calculate the thickness of the hydrocarbon layer in the solid phase, d_c(s), as where [small rho, Greek, macron]_c is estimated as for the liquid phase. Values of d_c(s) are shown in Table 2.

For the C_nTAB + C_m monolayers, the isotropic contribution to [small rho, Greek, macron]_c is negative and the anisotropic contribution is approximately half as large as the isotropic contribution but of opposite sign. For a given value of [small rho, Greek, macron]_c, inclusion of the anisotropic contribution leads to an increase in the modelled thickness; neglecting anisotropy would lead to errors in the thickness of up to 40%.

The anisotropy of the hydrocarbon chain region is dependent on the tilt of the hydrocarbon chains. If the axis of the hydrocarbon chain were tilted from vertical by an angle ϕ = 15°, the anisotropy in the dielectric constants would decrease by 0.01 and the modelled thicknesses would be ∼1 Å smaller. A tilt of 56° from vertical would give ε_e = ε_o = 2.16 (the same as a completely disordered layer) and modelled thicknesses of 12–14 Å (30% shorter than with vertical chains). A large tilt is not consistent, however, with results from SFS. The intensity of the SF signal, I_SF ∝ N²〈β〉², from eqns. (1) and (2). For close-packed chains, N ∝ cosϕ, while in SSP-polarised spectra, 〈β(r⁺)〉 ∝ 〈cosϕ〉, Consequently, I_SF(ϕ) ≈ I_SF(ϕ = 0)(cosϕ)⁴ and is hence very sensitive to tilt. Comparing C₁₆TAB + C₁₄ and pure dodecanol monolayers in the low-T phase, we find that I_SF(r⁺) for the surfactant–alkane mixture is ∼60% that of dodecanol. After correcting for the effect of the lower methyl group of the alkane, as discussed above, one infers that the tilts are very similar in the two monolayers.

The uniaxial dielectric constants are also very sensitive to the density of chains in the monolayer. If the area per molecule were chosen to be that of a crystalline phase (18.7 Ų) rather than a rotator phase (20.9 Ų), the Clausius–Mossotti equation would give values of ε_e = 2.43 and ε_o = 2.29, and the modelled thicknesses would be ∼40% smaller (11–12 Å). These thicknesses are significantly less than the extended chain lengths of alkane and surfactant and therefore not consistent with a crystalline layer of vertical or near vertical chains.

Interpretation of ellipsometric thicknesses. The thickness of the chain region in the liquid phase of the monolayers of C₁₆TAB + C_m is constant at a value of 11–12 Å for all values of m (Fig. 4). Aveyard et al. observed that the extent of mixing of oil molecules with the surfactant in mixed monolayers decreased with increasing chain length.^49,60,61 However, the volume per alkane molecule increases with chain length, so the overall thickness does not appear to vary significantly. It is perhaps surprising that the C₁₆TAB + C₁₁ monolayer should have the same thickness as the other systems given that the concentration of surfactant, and consequently its surface excess, is lower. Our previous work on mixed monolayers of C₁₂TAB + C₁₆ has shown that the thickness is almost independent of Γ in the pseudo-partial wetting regime: the decrease in the number of surfactant molecules is compensated by an increase in the number of oil molecules.¹⁷ The mixed monolayer of C₁₄TAB + C₁₂ was ∼2 Å thinner than C₁₆TAB, probably as a consequence of the shorter surfactant chains.

Fig. 4 Modelled thicknesses, d, of C₁₆TAB + C_m monolayers at the air-solution interface in the liquid phase (open circles) and solid phase (filled circles) at the transition temperature; and also of liquid and solid phase C₁₄TAB + C₁₂ monolayers (open and filled triangles). Values of d are plotted against the alkane chain length, m. The extended lengths of C_m, C₁₆ and C₁₄ are marked by dashed, solid and dotted lines respectively.

Fig. 4 compares the experimentally determined thicknesses with the extended chain lengths of C₁₆ and C₁₄ alkyl chains and C_m alkanes. For C₁₆TAB + C_m monolayers with m = 14–17, the calculated thicknesses are very close to the extended chain length of C₁₆ (solid line in Fig. 4). For m = 11–13, d_c(s) lies between the extended chain lengths of the alkane (dashed line) and the surfactant. For C₁₄TAB + C₁₂, the thickness also lies between the extended length of C₁₄ (dotted line in Fig. 4) and C₁₂. The ellipsometric data are thus consistent with a structure of the low-T phase comprising a monolayer of vertically oriented chains with the packing density of a rotator phase.

Discussion

Sum-frequency spectroscopy is a powerful technique for studying chain conformation in surfactant systems and provides clear evidence of the microscopic structural changes occurring at the phase transition. The conformation of the hydrocarbon chains changes from that characteristic of a liquid to that of a solid at the phase transition. The nature of the long-range correlations within the ‘solid’ monolayer is not addressed by spectroscopic techniques: to demonstrate that these monolayers show (quasi-) long-range translational order will require X-ray diffraction experiments, which are planned for the future. Isotopic substitution allows us to distinguish between the two components of the monolayer, to establish the conformational order in each and, within the solid phase, to estimate the composition of the monolayer. SFS is limited in the amount of quantitative information that it can provide about the composition or thickness of the surface film, partly due to uncertainty in the local electric fields experienced by the interfacial molecules (which we addressed earlier in the context of the non-vanishing signal from the alkane molecules) and partly because SFS is insensitive to molecules in an isotropic environment. Consequently, it provides no information on the composition of the high T, liquid phase.

Conversely, ellipsometry is sensitive to both species at the interface regardless of the symmetry of the phase. It is also extremely sensitive (capable of detecting changes in coverage of <1% of a monolayer) and has good spatial resolution (<10 µm with imaging optics). However, the information content of ellipsometry is poor and it is only in conjunction with other measurements, such as SFS, neutron reflectometry or surface tensiometry, that one can build models to predict the coefficient of ellipticity of the air–water interface that do not have so many variable parameters as to be practically useless. While it is rare for ellipsometry alone to yield a unique structure, it can provide support for one structure and disprove another. Here we have used ellipsometry to determine the thickness of the high-T phase, knowing from SFS that it is liquid-like. We find that the thickness of the chain region of the monolayers is independent of chain length and about half the length of the fully extended surfactant chain (d_c = 11–12 Å). In the solid phase, we showed that ellipsometry is consistent with an ordered mixed monolayer of densely packed upright chains, as inferred from SFS. Alternative models of tilted chains or multilayers would not be consistent with the combined SFS and ellipsometry data.³

We commented in the introduction on the connection between solid–liquid phase transitions in the mixed monolayers studied here and surface freezing at the pure alkane–air interface. While most solids exhibit surface melting, where the surface melts at a lower temperature than the bulk, alkanes and some related chain molecules (such as alcohols) are unusual in exhibiting surface freezing. For shorter chain lengths, 16 ≤ m < 44, the monolayers are rotator phases (lacking long-range correlations between the chain twists), while for longer chains, 44 ≤ m ≤ 50, they are crystalline.²² Rotator phases form even when a rotator structure is not a stable phase of the bulk alkane (e.g., even chain length alkanes with m < 20):⁶² the presence of the interface stabilises rotator phases compared to crystalline phases.

An X-ray reflectivity study by Tikhonov et al. found no interfacial freezing at the pure water–docosane (C₂₂) interface.²³ Lei and Bain showed that interfacial freezing at the aqueous solution–alkane interface can be induced by the presence of C₁₆TAB.²⁴ The transitions were identified from jumps in the coefficient of ellipticity, [small rho, Greek, macron](T), of the solution–alkane interface and from discontinuous changes in the gradient of σ(T). The coefficients of ellipticity of the solid monolayers were successfully modelled with mixed monolayers of vertically oriented alkane and surfactant chains with an area per chain equal to that of a solid monolayer of dodecanol at the air–water interface, 21 Ų. The entropy change for the monolayer phase transition (determined from ∂σ/∂T) was in good agreement with the value expected from frozen monolayers at the alkane–air interface and with the melting of bulk rotator phases. The corresponding surface freezing range, ΔT = T_s − T_b, decreased with increasing alkane chain length, from 14 °C for C₁₃ to 6 °C for C₁₄ and 3 °C for C₁₅. With hexadecane, the interface did not freeze.

Fig. 5 compares T_s(m) for the mixed C₁₆TAB + C_m films at the air–solution interface with the bulk melting points, T_b, of the alkanes. Although T_s decreases with decreasing m, T_b decreases faster with the result that the ΔT = T_s − T_b increases from 1 °C for m = 17, to 28 °C for m = 11. The presence of a long-chain surfactant at the interface thus greatly increases the surface freezing range of an alkane. This may be a general phenomenon for alkanes at a variety of interfaces.

Fig. 5 Comparison of the surface phase transition temperatures of mixed C₁₆TAB + C_m monolayers at the air–solution interface, T_s (open squares) with the melting points of the bulk alkanes, T_b (filled circles) and the surface freezing temperatures at the interface between C₁₆TAB solutions and bulk alkanes (open triangles).

It is instructive to compare the low-T phase of mixed C₁₆TAB + C_m monolayers at the air–water and alkane–water interfaces. In both cases, the same structure comprising upright, all-trans chains, can explain the available structural evidence. For C₁₆TAB + C₁₄, the compositions of the solid phase inferred from SFS (air–water) and tensiometry (alkane–water) are in agreement. The equivalence of the entropy change at the alkane–water interface with that at the alkane–air interface (where the structure has been determined unequivocally by X-ray diffraction)²² provides indirect support for the postulated structure. The fact that C₁₆TAB + C₁₆ monolayers undergo liquid–solid phase transitions at the air–water interface but not at the alkane–water interface suggests that the solid monolayers are more stable at the air–water interface. This increased stability is seen more generally in the values of ΔT, which are 6 °C higher for the monolayers at the air–water interface (see Fig. 5).

Several explanations for surface freezing in alkanes have been proposed, based upon capillarity,²² fluctuations of the molecules normal to the plane,^63,64 and conformational disorder of molecules within the surface-frozen monolayer,⁶⁵ but no consensus has emerged. The reason for increased stability of frozen C₁₆TAB + C_m monolayers at the air–water interface compared to the alkane–water interface is also unclear. One possible explanation lies in the change in surface entropy on freezing.²⁴ At the alkane–solution interface, the alkane molecules lose three degrees of translational freedom upon freezing but the surfactant molecules only lose two, as they are already constrained to the interface. On freezing at the air–solution interface, both surfactant and alkane molecules are already constrained to the interface, so the change in surface entropy on monolayer freezing is less negative than at the alkane–solution interface. The monolayer transition temperature, T_s = ΔH_s/ΔS_s, where ΔH_s is the change in surface enthalpy on freezing and ΔS_s is the change in surface entropy on freezing (both negative). If the enthalpic interactions at the two interfaces are comparable, then T_s will be higher at the air–water interface.

Alkanes (16 ≤ m ≤ 50) also exhibit surface-freezing behaviour at the air–silica interface.^66–68 At temperatures above T_s the alkanes wet the solid surface. Surface-freezing coincides with a dewetting transition, since liquid alkanes do not wet low-energy (methyl-terminated) faces of their own solids. Below T_s (but above T_b) the SiO₂ is covered by a frozen monolayer of vertically oriented alkane molecules in equilibrium with liquid alkane lenses.⁶⁷ The variation of T_s with m closely matches that seen at the air–alkane interface.

No effect similar to alkanes on SiO₂ can be observed for alkanes on water for the simple reason that long-chain alkanes do not wet water. One can pose the hypothetical question of whether a metastable monolayer of an alkane on water would show surface freezing. The probable answer is yes. For the bulk tetradecane–C₁₆TAB solution interface, one can extrapolate the plot of T_s against surface excess, Γ, back to Γ = 0 and find that T_s for the pure tetradecane–water interface is only 1–2 °C below T_b. For C₁₆TAB–tetradecane, the surface freezing temperature at the air–solution interface is 6 °C higher than at the alkane–solution interface, from which we infer that T_s would be above T_b for an alkane monolayer on pure water. Thus surfactant is needed to allow the alkane to spread on water (pseudo-partial wetting), but is not essential for the alkane to show surface freezing.

Conclusions

Monolayers of pure C₁₆TAB at the air–solution interface do not show any phase transitions between condensed phases. In the presence of an alkane, with a chain length 11 ≤ m ≤ 17, a first-order phase transition is observed. This phase transition can be described in two different ways. Either, one can view the alkane as permitting the surfactant to crystallise, by filling in the free volume between the surfactant chains, or one can view the surfactant as inducing a surface freezing transition in a monolayer of the alkane. The latter perspective permits a comparison with surface freezing in alkanes at other interfaces. The same structural model for the low-T phase, consisting of a (mixed) monolayer of all-trans, upright chains in a rotator phase, explains the existing structural and spectroscopic information at the air–water, alkane–air and alkane–water interfaces. The frozen phase is significantly more stable at the air–water interface than at the alkane–water interface. Although a pure alkane monolayer cannot be studied on the surface of water, since long-chain alkanes do not wet water, we predict that if such a monolayer existed it too would show surface freezing, analogously to alkane monolayers on silica. A feature of the mixed monolayers of C₁₆TAB + alkanes on water is that the alkane can freeze in the monolayer at temperatures well above (ΔT < 30 °C) the bulk melting point; a characteristic that might prove useful for controlling the surface properties of oil–water–surfactant systems.

Acknowledgements

KMW would like to thank the EPSRC for a studentship. LQ would like to thank the Pao Yu-Kong & Pao Zhao-Long Foundation for support.

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Footnotes

† Current address: Department of Chemistry, Zhejiang University, Hangzhou. 310027 P. R. China

‡ Current address: Department of Chemistry, University of Durham, South Road, Durham, UK DH1 3LE. E-mail: c.d.bain@durham.ac.uk

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