Water diffusivity in a mixed phase binary system: Effective water diffusion coefficients in tetradecanol–eicosanol mixtures

Fluid Phase Equilibria 379 (2014) 157–166

Contents lists available at ScienceDirect

Fluid Phase Equilibria journal homepage: www.elsevier.com/locate/fluid

Water diffusivity in a mixed phase binary system: Effective water diffusion coefficients in tetradecanol–eicosanol mixtures Devon R. Widmer, David F. Calhoun, Daniel Thurston, Annabel M. Edwards ∗ Department of Chemistry and Biochemistry, Denison University, 100 West College Ave, Granville, OH 43230, USA

a r t i c l e

i n f o

Article history: Received 9 May 2014 Received in revised form 17 July 2014 Accepted 17 July 2014 Available online 24 July 2014 Keywords: Water diffusion Solid–liquid equilibrium Fourier-transform infrared spectroscopy (FTIR) Differential scanning calorimetry Fatty alcohol mixtures

a b s t r a c t Fourier-transform infrared attenuated total reflection spectroscopy is used to measure the effective water diffusion coefficients in pure tetradecanol between 313 K and 338 K and in liquid and liquid–solid mixtures of tetradecanol (C14 H29 OH) and eicosanol (C20 H41 OH) at 313 K. The temperature dependent data in tetradecanol yields an activation energy for diffusion higher than that measured in pure alkanes. This is consistent with the critical role hydrogen bonds play in diffusion. Differential scanning calorimetry and infrared spectroscopy are used to construct the solid–liquid phase diagram for the tetradecanol–eicosanol system. Diffusion measurements in these mixtures are linked to the experimental phase diagram. Water diffusivity in liquid mixtures at low eicosanol concentrations (80 to 100 mol percent tetradecanol) suggests that the measured diffusion coefficient of water is independent of the mixture’s bulk viscosity. We find a six-fold decrease in water diffusivity when the solid fraction of the equilibrium mixture increases from zero to thirty percent. The decrease in water diffusivity results from a longer diffusion path length caused by solid portions of the mixture acting as barriers to diffusion. © 2014 Elsevier B.V. All rights reserved.

1. Introduction In nature, long-chain alcohols mixtures exhibit a complex phase behavior that depends on the chain lengths of the component molecules. These mixtures along with fatty-acid mixtures limit water transport in a broad range of systems, including plant and insect cuticles and atmospheric aerosols [1–4]. Longchain alcohols are significant industrially as materials for latent energy storage and are often found in pharmaceuticals, cosmetics, and various consumer products [5]. Fatty alcohols also serve as models for more complex amphiphilic molecules such as phospholipids. These relatively simple molecules have complex phase behavior [6]. The aim of this study is to use infrared spectroscopy and differential scanning calorimetry to investigate water diffusivity in mixed solid–liquid systems. We know of no other study that looks at water diffusion in a system where solid fraction varies with composition. We investigate the lesser studied wax mixture of two long-chain n-alcohols: tetradecanol (C14 H29 OH) and eicosanol (C20 H41 OH). Our interest in tetradecanol–eicosanol mixtures was motivated by experimental temperature constraints, the wealth of previous studies

∗ Corresponding author. Tel.: +1 7405878556. E-mail address: [email protected] (A.M. Edwards). http://dx.doi.org/10.1016/j.fluid.2014.07.021 0378-3812/© 2014 Elsevier B.V. All rights reserved.

on tetradecanol mixtures, and the composition of natural barrier layers. For example, the leaf cuticle often contains alcohols with chain lengths between 20 and 30 carbons [7]. We found that 313 K was an optimal experimental temperature because the tetradecanol–eicosanol mixture possesses both fully liquid and solid–liquid regions, depending on the mixture composition. Although the phase diagrams for other mixtures of long chain alcohols have been well characterized, to our knowledge the phase diagram for tetradecanol and eicosanol has not been previously investigated [8,9]. Studies of solute diffusion in complex solvent systems help elucidate the role of solvent properties on solute transport [10–12]. Tracer diffusion studies provide information on solute–solvent interactions at very low solute concentrations. Methods that probe self-diffusion follow the dynamics of an isotopically labeled solute in system containing the non-labeled solute [13]. This work investigates the mutual diffusion of water into tetradecanol–eicosanol mixtures. We quantify water’s diffusion rate using effective translational diffusion coefficients calculated from the time evolution of water’s concentration profile in the mixtures [14]. The viscosity and hydrogen-bond dynamics of the liquid component of the longchain alcohol mixtures influence the diffusive motion of individual water molecules. As the mole fraction of eicosanol increases, the mixtures contain solid domains in equilibrium with the liquid that present barriers to diffusion.

158

D.R. Widmer et al. / Fluid Phase Equilibria 379 (2014) 157–166

The diffusivity of a large solute molecule in a liquid solvent of smaller molecules is generally predicted within 20% by the Stokes–Einstein equation, D = kB T/Cr [13]. The diffusion coefficient (D) depends on the solute radius (r), solvent bulk viscosity (), and temperature (T) as well as a stick (C = 6) or slip (C = 4) condition that accounts for solute–solvent interactions. For small solute molecules moving through large solvent molecules and for systems that have strong solute–solvent interactions, no one model predicts all observed diffusion coefficients. Small changes to the Stokes–Einstein equation extend the equation’s ability to model experimentally determined diffusion coefficients [12,13,15–19]. For example, if water’s hydrodynamic radius is varied to reflect whether the solvent is hydrophobic, polar, or capable of forming hydrogen bonds, the Stokes–Einstein equation models water diffusion in a range of organic solvents [20]. The Stokes–Einstein equation is also modified by raising the solvent viscosity to a fractional power. This reduced-viscosity approach gives D = kB T/C˛ r where ˛ < 1 accounts for a smaller bulk viscosity effect on the translational motion of small solutes [11,16,19]. Solutes diffuse more slowly through solvents in which solute–solvent association occurs [15,18,20–22]. For example, the diffusion coefficient of water is roughly three times smaller in an alcohol than in an alkane with the same viscosity due to hydrogenbond interactions between the water and the hydroxyl group. Using the reduced-viscosity approach, Needham et al. used a single solute hydrodynamic radius (r) to fit water diffusivity data in a homologous series of straight chain alcohols (n = 4–8). The constant solute radius suggests that water molecules diffuse more slowly through alcohols not because they drag a partial solvation shell of alcohol molecules with them but because hydrogen-bond interactions cause water molecules to reside longer at each alcohol hydroxyl group [15]. Molecular dynamic simulations have further verified that hydrogen bonds play a significant role in determining water diffusivity. Water self-diffusion values in aqueous solutions of glycerol, ethylene glycol, or methanol correlate with long hydrogen-bond lifetimes [23]. Hydrogen bonds formed between water and glycerol molecules in dilute aqueous glycerol solutions lead to slower glycerol diffusive motions, greatly affecting the overall water diffusion rate [24]. Molecular dynamic simulations also demonstrate that water diffusion rates decrease in hydrogel polymer systems when hydrogen-bond dynamics are slower [25]. Fourier-transform infrared attenuated total reflection (FTIRATR) spectroscopy is a robust technique for quantifying the diffusivity of water and other small solutes in thin-film polymeric systems [26–30]. The diffusion coefficients determined by this method match values measured by a variety of other experimental methods [31]. The principle advantages of this technique include the capacity to measure the diffusivity of more than one solute at a time (as long as each solute has independent absorption bands in the infrared spectrum), the ability to monitor changes in polymer characteristics due to the permeation of the solute in to the polymer matrix, and the capability to investigate solute–solvent interactions [26,32]. FTIR-ATR has been used to investigate solute diffusion in a wide range of systems, including rubbery, glassy, or crystalline polymers, copolymers, polymer blends, polymer-clay composites, asphalt binders, and porous TiO2 films [26,33–36]. To our knowledge this technique has not been extended to the highly viscous liquid or mixed solid–liquid systems that are studied here. We utilize the ability of FTIR-ATR to provide information on both the solute and solvent to characterize water diffusivity into fully liquid and solid–liquid tetradecanol–eicosanol mixtures. The complex phase behavior of mixtures of long-chain alcohols has been examined in detail by several research teams. Long-chain alcohols exhibit two distinct ordered solid phases. In addition,

long chain alcohols exhibit several distinct minimally disordered rotator phases just below the melting temperature [5,37]. The rotator phase is characterized by rotational disorder around the length of the carbon chain. These rotator phases are most distinctly seen on cooling due to a hysteresis of the rotator-crystal transition [37]. Differential scanning calorimety (DSC) and X-ray diffraction studies of binary mixtures of eicosanol (C20 H41 OH) with octadecanol (C18 H37 OH) or nonadecanol (C19 H39 OH) reveal a rich solid–liquid phase behavior for both mixtures [5,9,38,39]. Separate DSC studies of the solid–liquid phase behavior of five long-chain alcohol mixtures with the components differing in their carbon chain length by either four or six carbons demonstrate a eutectic composition rich in the shorter chain alcohol. The previously studied mixture closest to the tetradecanol–eicosanol system is a 1-dodecanol (C12 H25 OH) and 1-octadecanol (C18 H37 OH) mixture. This mixture as well as the others exhibited additional solid–solid transitions that hint at the rich phase behavior of these long-chain alcohols due to the stability of both a solid rotator phase and a solid crystalline phase [8]. Separate studies have compared the bulk and surface thermodynamics of dry and hydrated n-alcohols and alcohol mixtures with chain lengths from 12 to 26 carbons [6,37]. For a dry mixture of tetradecanol and octadecanol, the thermodynamics of the bulk depend on the stability of four separate regions of the phase diagram: the liquid phase, the solid rotator phase, the crystalline solid phase, and a mixed phase containing both rotator and crystalline solids [6]. Additionally, kinetic effects cause supercooling to occur during the formation of each bulk solid phase in dry mixtures but not in hydrated mixtures. Hydration increases both the surface and bulk freezing temperatures and the temperature range over which the rotator phase is stable. Using tetradecanol and eicosanol mixtures at 313 K, we show that the FTIR-ATR technique can be used to measure the diffusivity of water in a viscous liquid and a mixed solid–liquid system. We quantify the decrease in water diffusivity as the solid fraction of the mixture increases. By increasing the eicosanol mole fraction, we are able to investigate systems with varying amounts of solid at a single temperature. We are able to monitor any phase change that occurs in our system as a result of water diffusion, and we can link the measured effective diffusion coefficients to the relative solid fraction observed in each mixture. 2. Experimental methods 2.1. Waxes 1-Tetradecanol (99+%, Acros Organics) and 1-eicosanol (98%, Acros Organics), were melted in a nitrogen atmosphere and dried using activated molecular sieve type 3A (Fluka). The sieve was activated prior to each use by heating to 473 K for at least 4 h under vacuum [40]. To avoid water absorption from the atmosphere during mixing, the waxes were melted and mixed under nitrogen. The mixtures were stirred in a fully liquid state for at least 45 min prior to cooling and solidification under nitrogen. Octanol (99%, Acros Organics) was dried over activated molecular sieve prior to use. 2.2. Differential scanning calorimetry A Thermal Analysis Tzero Q20 differential scanning calorimeter calibrated using indium was used to record thermograms of the pure wax and wax mixtures. Thermograms were used to determine the temperature-composition phase diagram for the bulk tetradecanol–eicosanol system. Mixtures were made as described above and thoroughly ground using a mortar and pestle prior to sampling. The sample cell was purged with nitrogen during each

D.R. Widmer et al. / Fluid Phase Equilibria 379 (2014) 157–166

159

run and 1–3 mg of each sample was tested. Each sample was held for 20 min in a completely molten state and then at 278 K for an additional 20 min to define a consistent thermal history for each sample. Transition temperatures were taken from the heating curves collected at 1 K/min scan rates. Melting temperatures measured for pure tetradecanol and pure eicosanol (311 ± 1 K and 337 ± 1 K, respectively) match literature values within our stated uncertainty. 2.3. Infrared spectroscopy All FTIR measurements were made on a Nicolet 6700 (Thermo Electron) FTIR using p-polarized light and a mercury–cadmium–telluride detector. Additional details on sample preparation and the FTIR measurement parameters can be found in the supplemental information section. 2.3.1. Melting curves Melting curves were constructed from temperature dependent IR spectra collected in 1 K increments as the tetradecanol–eicosanol wax mixtures were heated through their melting points. The peak position of the CH2 symmetric stretching peak was then plotted as a function of temperature to create the melting curve. 2.3.2. Diffusion measurements Melted wax layers used in diffusion measurements were housed in a horizontal ATR heated trough plate flow cell from Pike Technologies. The aluminum top plate was modified to allow for thicker liquid layers and additional temperature control using a recirculating water bath. A Viton o-ring confined the melted wax to a consistent elongated oval shape on the ATR crystal. A known mass of pure wax or wax mixture was melted under nitrogen to a trapezoidal, germanium, multiple reflection ATR crystal. Visual inspection ensured that the liquid wax formed a continuous layer wetting the germanium crystal. Each sample was further dried once in the flow cell and then held at the experimental temperature for at least 40 min to reach complete temperature equilibration before water vapor was introduced into the cell. We chose the 313.0 ± 0.5 K as our main experimental temperature because it is just above the melting temperature of pure tetradecanol and easily accessible and regulated by our experimental setup. Water vapor was furnished by feeding nitrogen through a bubbler containing pure water (Millipore, 18.1 M conductivity) set in a thermostated bath at the experiment temperature and was introduced into the ATR cell through insulated lines. To avoid disturbing the alcohol layer water vapor was introduced at a low flow rate, 65 mL/min. Mass balance calculations based on the solubility of water in tetradecanol and the recorded water uptake curves indicate that this flow rate did maintain an interfacial alcohol layer saturated with water. To test for wax layer loss due to evaporation during drying and water vapor runs, nitrogen gas was run over the molten wax layer for 1.5 h and no evidence of more than 1.5% wax loss due to wax evaporation was observed. Gravimetric measurements before and after each run were consistent with minimal wax loss and expected water uptake. 2.4. Fits to water absorbance versus time data In the ATR setup, the infrared beam only samples approximately the bottom 0.05% of the millimeter thick wax layer. Therefore after water vapor is introduced over the dry layer, no water absorbance signal is initially observed. The length of the initial delay and the subsequent increase in water absorbance is governed by water’s diffusion rate through the wax layer. Fits to the time-dependent absorbance data for the water bending vibration were used to determine the effective diffusion coefficient (Deff ) of water in each

Fig. 1. (a) Schematic representation of a wax layer on ATR crystal in flow cell. (b) Calculated absorbance curves for a model layer assuming a constant diffusion coefficient (Deff = 3 × 10−6 cm2 /s). The blue, solid line is Eq. (1) using a constant layer thickness (Lave = 850 ␮m). The red, dashed line is a calculated absorbance curve that accounts for a variable layer thickness due to the meniscus formed by the liquid layer. This meniscus absorbance curve is modeled by a series of rings with varying thicknesses but a constant diffusion coefficient (Deff = 3 × 10−6 cm2 /s). The inset shows that for the thicker regions of the layer near the outer edge the absorbance rises more slowly in time as compared with thinner regions near the center of the ATR crystal. For more information please see the supplemental information. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

wax mixture. The steps to obtain the fitting equation used in this work are outlined in the supplemental information with a more complete treatment available in several references in the polymer literature [26,32]. Briefly, we first solve the diffusion equation, ∂C(z, t)/∂t =





2

Deff ∂ C(z, t)/∂z 2 , under the assumption that Deff is not a function of the water concentration in the wax layer. The solution to the diffusion equation is a concentration profile dependent on the initial and boundary conditions of our system. Because the measured water signal arises only from the very bottom of the wax layer, the measured absorbance is directly related to the water concentration only at the wax-crystal interface (z = 0, see Fig. 1a). The concentration profile at z = 0 combined with Beer’s Law gives Eq. (1) that predicts how the absorbance increases as a function of time. The absorbance increase in time is shown in Fig. 1b. The two overlapping curves in Fig. 1b show that for a liquid layer with variable thickness, the average layer thickness can be used to model the increase in absorbance as water diffuses through the layer. We use the geometry of our setup and the mass of wax deposited on the ATR crystal to determine the average layer thickness (Lave ) of the layer. Our time-dependent absorbance data is fit with Eq. (1) resulting in the value for the two fitting parameters, the effective diffusion coefficient, Deff and the absorbance measured when the wax layer has fully equilibrated with the water vapor, Abseq .

 Abs(t) = Abseq

4 1− 

 ∞

n

(−1) exp n=0 2n + 1



−Deff 2 Lave



(2n + 1) 2

2  t

(1)

D.R. Widmer et al. / Fluid Phase Equilibria 379 (2014) 157–166

MATLAB was used to process all data including a linear background correction and fitting the experimental Abs(t) curves [41]. The uncertainty in the mass of wax used to create each layer is less than 1.5%. As shown in Table 2 the smallest error in Deff from measurements on multiple wax layers of the same composition is 0.2 × 10−6 cm2 /s. An uncertainty in Deff of 0.2 × 10−6 cm2 /s corresponds to a 2% difference in wax mass carried into Eq. (1) via Lave for Lave ≈ 950 ␮m and Deff ≈ 3 × 10−6 cm2 /s. Thus the uncertainty in the mass of the deposited layers does not limit our experimental precision.

(a) 2 Melting 1.5

Heat Flow / (W/g)

160

1 0.5 0 -0.5

Freezing

3. Results and discussion

-1

3.1. Tetradecanol–eicosanol solid–liquid phase diagram

300

310 320 Temperature / (K)

330

310 320 Temperature / (K)

330

(b) 2854

Wavenumber / (cm-1)

2853 2852 2851 2850 2849 2848

290

300

(c) 340 335 Temperature / (K)

The discussion below highlights results that compare the measured effective diffusion coefficient to the bulk phase state of the tetradecanol–eicosanol mixture. We present the measured phase diagram of the tetradecanol–eicosanol system before discussing water diffusivity in both fully liquid mixtures and solid–liquid mixtures. An analysis of DSC thermograms allows us to construct the binary solid–liquid phase diagram. Fig. 2a shows a full thermogram for a tetradecanol–eicosanol mixture with a tetradecanol mole fraction (XT ) of 0.73. The hysteresis observed in the lower cooling trace compared to the top heating trace arises from supercooling. For consistency in both the construction of the phase diagram and the diffusion studies, the temperatures of the different transitions are taken from the DSC heating trace (the top trace in Fig. 2a) and each wax mixture used in the water diffusivity studies is heated to the experimental temperature from a fully solid phase. The split freezing peak at 304 K in the cooling trace suggests that during complete solidification the solid rotator phase may form prior to mixture crystallization. However without X-ray diffraction data, we cannot fully determine whether the solid in the solid–liquid coexistence region is in the crystal or rotator form. The existence of the rotator phase in the mixtures will depend on the mixture composition and thermal history. Different mixtures of long-chain alcohols studied in the literature did not clearly point to whether we expect to observe the rotator or crystalline phase when we heat the tetradecanol–eicosanol mixture from a fully solid state [6,9]. Between the eutectic peak at 307 K and the highest temperature peak at 322 K, the XT = 0.73 mixture contains both liquid and solid phases. The thermogram trace (Fig. 2a) with a clear eutectic peak at 307 ± 1 K and a more complex series of bumps at higher temperatures is typical for mixtures with compositions rarer in tetradecanol than XT = 0.84. The eutectic composition, where the whole mixture melts at 307 ± 1 K, is XT = 0.88. The constant temperature eutectic peak is present in the thermogram of each mixture tested and plotted (circles) in the experimental phase diagram in Fig. 2c. The liquidus points (squares) in Fig. 2c are the temperatures at which each mixture tested is fully liquid. The temperature of the liquidus point for each mixture is found from the highesttemperature distinct peak in the melting trace of each mixture’s thermogram. In addition to the DSC data, phase transition temperatures in our system are measured using IR melting curves by plotting the position of the symmetric CH2 stretching peak as a function of temperature (Fig. 2b). As the solid wax mixture liquefies, the increase in gauche defects in the chains cause the CH2 stretching peaks to decrease in intensity and shift to higher wavenumbers. Thus the CH2 stretching peak position is used to monitor mixture melting. As shown in Fig. 2c and Table 1 when the end points of the broad IR melting curve data transitions are used, the IR data overlays the DSC data. Additional analysis of the IR melting curves is included in the supplemental information section.

290

A

330 325 320

C

315

310 305

B

300 0

0.2 0.4 0.6 0.8 Mole Fraction Tetradecanol (XT)

1

Fig. 2. (a) DSC thermogram (exotherm down) for a XT = 0.73 tetradecanol–eicosanol mixture. (b) Change in position of the CH2 symmetric stretching peak with temperature for a XT = 0.73 tetradecanol–eicosanol mixture. (c) Phase diagram from DSC thermograms (solid markers) and IR melting curves (open markers) for tetradecanol–eicosanol mixtures. The eutectic transition is shown with circles and the liquidus line with squares. The dashed line is fit using the ideal solution model. Region A is a fully miscible liquid mixture, region B is a fully solid region, and region C represents the two phase region where liquid and solid are both present.

The similarity of the phase diagram from the IR heating curves verifies that the phase behavior of the wax in the ATR setup mimics the behavior observed in the DSC. We are thus able to use Fig. 2c to map out the phase state of the wax mixtures used in our water diffusivity studies. Additionally, this overlap strengthens our assumption that the fraction of the layer sampled by the ATR is thick enough to represent true bulk behavior of the mixture. Fig. 2c is consistent with phase diagrams for other long chain nalcohols [8]. A eutectic mixture exists at high mole fractions of the shorter chain alcohol and the position of the solid–liquid or liquidus

D.R. Widmer et al. / Fluid Phase Equilibria 379 (2014) 157–166

161

Table 1 Comparison of composition and temperature data used to create the phase diagram in Fig. 2c. DSC data taken from peak position of DSC thermograms and IR data taken from change in position of symmetric CH2 stretching peak as a function of temperature. DSC Data

Overall mixture mole fraction C14 H29 OH (XT )

IR Data

DSC Data

Liquidus transition temperature* (K) 337.4 ± 1.0 334.9 ± 1.0 332 ± 3

0.00 0.20 0.25 0.25 0.32 0.43 0.43 0.58 0.59 0.61 0.67 0.69 0.70 0.73 0.76 0.80 0.80 0.84 0.88 0.88 0.89 0.89 0.93 0.96 1.00 * ‡

327.2 326.4 326.5 323.5 323.9 324.4 322.0 315.9 314.2 313.6 309.8

± ± ± ± ± ± ± ± ± ± ±

Eutectic transition temperature* (K) 335 332 332 327

333.1 ± 1.0 330.8 ± 1.0

± ± ± ±

2 2 2 2

327 ± 2 328 ± 2 326 ± 2

1.0 1.0 2.0 1.0 1.0 1.0 2.0 2.0 1.0 1.0 1.0

318.0 ± 1.0

307.7 ± 0.6 308.6 ± 0.6 311.4 ± 1.0

IR Data

305.6 ± 0.5 306.6 ± 0.3 305.9 ± 0.6 306.1 ± 0.3 306.7 306.4 306.7 306.6 306.6 306.7 306.4 306.7 306.9 306.2 306.8 307.0 306.6 306.6 307.1 306.9 306.3

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.3 0.3 0.4 0.3 0.5 0.3 0.4 0.3 0.4 0.4 0.3 0.2 0.2 0.3 0.2 0.6 0.6

307.5 ± 0.5 307.0 ± 0.5 307.0 ± 0.5

308.0 ± 0.5

307.0 ± 0.5 306.0 ± 0.5 308.0 ± 0.5

307.0 ± 0.5‡

311.0 ± 1.0

Stated experimental uncertainties represent relative uncertainties from the width of DSC transition peak or the slope of the IR melting curve. Only one clear transition shows on the IR melting curve, this point represents an overlap of both the liquidus and eutectic transition.

line, Eq. (2), is well fit by the ideal solution model following Raoult’s law. T=

T=

Sf,E TE Sf,E + Rln(1 − XT ) Sf,T TT Sf,T + Rln(XT )

for XT < 0.88

(2)

for XT > 0.88

In these equations XT is the mole fraction of tetradecanol in the mixture and TT , Sf,T and TE , Sf,E are the fusion temperatures and entropies of fusion for pure tetradecanol and pure eicosanol, respectively. The entropies of fusion are calculated from enthalpy of fusion literature values [42]. The ideal solution model assumes that the two alcohols exhibit no miscibility in the solid phase but crystallize separately as pure tetradecanol and pure eicosanol. For the tetradecanol–eicosanol system, this assumption is supported by the similarity between the calculated and experimental points in Fig. 2c and by data from comparable systems. Carareto et al. observe solid phase miscibility in mixtures of alcohols differing by six carbons only at mixture compositions very rich in the longer chain component [8]. Ventola and coworkers similarly find only complete miscibility in long chain alcohols that differ in length by one carbon (pentadecanol–hexadecanol, hexadecanol–heptadecanol, and heptadecanol–octadecanol) [38]. An exception is reported for the tetradecanol–octadecanol mixture by Sirota and coworkers who find that the hydrogen-bond interactions between each alcohol create solid phase mixtures of tetradecanol and octadecanol [6]. 3.2. Water diffusivity in pure tetradecanol In the solid–liquid mixtures, we expect water to diffuse only through the liquid portion of each mixture. Therefore, we initially characterize water diffusion in pure tetradecanol and fully liquid tetradecanol–eicosanol mixtures. Then by increasing the eicosanol

mole fraction in the mixtures, we study systems with an increasing solid fraction. As water diffuses into the wax layer, the water absorption bands increase as the characteristic alcohol absorption bands decrease until the bottom most wax layer becomes saturated with water (Fig. 3a). The change in the alcohol bands is due to the infrared beam sampling fewer alcohol molecules in the wet versus dry film due to the mutual diffusion of the alcohol molecules out of the effective penetration depth of the IR beam, changes in the refractive index of the wax layer due to water absorption, and changing hydrogen-bond interactions between the alcohol-hydroxyl groups and water. This behavior is also seen in studies of water diffusion into poly(vinyl alcohol) films studied by Sammon and coworkers where polymer film swelling is the corollary to the diffusion of the alcohol observed here. The changes in the OH stretching region of the IR spectrum due to both diffusion and changes in the alcoholhydroxyl stretch render this region of the spectrum undesirable for quantitative analysis of water diffusion. Sammon and coworkers found that an analysis of the growth of the water bending peak allows for quantitative diffusion measurements as the water bending vibration is less influenced by the local environment of the water molecules [30]. Fig. 3b highlights the increase in the bending vibration for water diffusion into liquid tetradecanol at 313 K. Absorbance versus time curves are constructed for the integrated bending peak and for individual wavenumbers in the bending peak (Fig. 3c). Fits to both the integrated data and individual wavenumbers give values for the diffusion coefficient within the stated error bars except for runs with very low water signal in which the integrated peak is overwhelmed by background water vapor bands. Fig. 3c plots the rise in the integrated bend peak as a function of time and the fit to Eq. (1) with L = 912 ␮m and Deff = 3.3 × 10−6 cm2 /s. The robustness of the fit indicates Fickian diffusion of water at both short and long times. Multiple experiments were conducted at varying tetradecanol layer thicknesses to confirm the consistency of our technique. From these

162

D.R. Widmer et al. / Fluid Phase Equilibria 379 (2014) 157–166

(a)

2.5

-3

ln (Deff in cm2 /s x 10 6 )

x 10

6 4

Absorbance

Positive Water Peaks

2 0 -2

2

1.5

Negative Tetradecanol Peaks

-4 4000

(b) 2.5

x 10

1 3500

3000 2500 2000 Wavenumber / (cm-1 )

1500

-3

3

3.05 3.1 3.15 1 / Temperature / (K)

3.2 x 10

-3

Fig. 4. Arrhenius behavior of the Deff with temperature. Line is best fit to the data. The slope equals −Ea /R with Ea = 36 kJ/mol and R = 0.08314 kJ/mol K. Here Ea represents the activation energy for water diffusion.

2

Absorbance

1.5 1 0.5 0 -0.5 1800

1750

1700

1650

1600

1550

1500

Wavenumber / (cm-1 )

(c)

Peak Area

0.15

0.1

0.05

Integrated H2O bend peak Fit, Deff = 3.3 x 10-6 cm2/s

0

0

1000

2000 3000 4000 Time / (s)

5000

6000

Fig. 3. (a) Selected spectra showing the change in FTIR signal after water vapor is introduced over pure tetradecanol at 313 K. The spectra shown are taken at 9, 19, 49, 99, 149, 249, and 299 s after water was introduced into the flow cell. (b) Water bend vibration increasing in time as water diffuses through the tetradecanol layer. (c) Fit to the increase in the water bend vibration using Eq. (1). Fit parameters: L = 931 ␮m, Abseq = 0.14, Deff = 3.3 × 10−6 cm2 /s.

runs, the effective diffusion coefficient of water in tetradecanol at 313.0 ± 0.5 K is determined to be 3.1 ± 0.2 × 10−6 cm2 /s with the error bars representing the 95% confidence interval. The success of fitting the pure tetradecanol data to Eq. (1) confirms the validity of the assumptions made for our system including: the top most wax layer rapidly saturates with water, no water adsorbs to the surface of the crystal, and excellent thermal control. The Fickian behavior also indicates that our initial assumption that Deff does not change with increasing water concentration is valid at the relatively low water concentrations studied here [30,43]. To confirm our ability to observe valid water diffusion coefficient using liquids in our FTIR-ATR setup, we measured water diffusion in octanol at 295 K. We find our measured value falls within the range measured by a previous group [15].

To further characterize water diffusion in liquid tetradecanol, we measure the diffusion coefficient of water in tetradecanol at temperatures from 313 to 338 K, a temperature range accessible by our current instrument configuration. As expected the measured diffusion coefficient rose with increasing temperature as shown by Fig. 4. Over this narrow temperature range, we observe Arrhenius behavior with a corresponding activation energy of 36 kJ/mol for water diffusion through tetradecanol. To our knowledge, this is the first activation energy reported for water diffusion in a long-chain alcohol or acid system. Water diffusion coefficients measured in hexadecane (C16 H34 ) from 298 to 318 K give an activation energy of 14 kJ/mol [44]. The higher value measured in tetradecanol reflects the energy needed to break hydrogen bonding interactions between the molecule and an alcohol hydroxyl group. Adding the approximate energy of a hydrogen bond between water and methanol (15–20 kJ/mole) to the hexadecane value is in good agreement with our measured value [45,46]. This result further shows the crucial role water-alcohol hydrogen bonds play in governing water diffusion through liquid alcohols. Needham and coworkers showed that the slower water diffusion rate in linear alcohols, as compared to similar viscosity linear alkanes, is due to longer water residence times at the polar hydroxyl group. Our measurements show this longer residence time is paralleled with an increased activation energy for diffusion that is on the order of the strength of a hydrogen bond. We next explore how water’s diffusion coefficient changes when a portion of the tetradecanol molecules are replaced by longer eicosanol molecules. 3.3. Water diffusion coefficient in liquid tetradecanol–eicosanol mixtures Table 2 shows the measured diffusion coefficient of water at 313 K in several mixtures of tetradecanol and eicosanol. Above XT = 0.80, the mixture is completely liquid and the measured diffusion coefficients do not vary within experimental error. In addition, the position of the alcohol CH2 symmetric stretching band shows that a mixture with a composition of XT = 0.80 that had been heated to 333 K and directly cooled to 313 K remains a supercooled liquid. Water diffusivity in this supercooled mixture (Deff = 3.2 × 10−6 cm2 /s) is consistent with other fully liquid mixtures. Thus the measured diffusivity of water remains unchanged even though the viscosity of the mixture increases approximately 20% [47]. Several studies have observed a decreased dependence on bulk viscosity for small solutes diffusing in larger solvent systems [15,16,20]. In alkane solvents, this decreased dependence is explained to arise from similar local chain motions evidenced by

D.R. Widmer et al. / Fluid Phase Equilibria 379 (2014) 157–166

163

Table 2 Measured effective diffusion coefficient of water vapor (Deff ) in liquid and solid–liquid mixtures of tetradecanol and eicosanol at 313.0 ± 0.5 K. Overall mixture mole fraction C14 H29 OH (XT )

Deff (cm2 /s)a

1 0.95 0.88 eutectic composition 0.80 0.70 0.60

3.1 3.2 3.5 1.7 1.3 0.5

± ± ± ± ± ±

0.2 × 10−6 0.4 × 10−6 0.4 × 10−6 0.4 × 10−6 0.1 × 10−6 0.1 × 10−6

Number of runs

Percent solid in mixtureb

Liquid mole fraction C14 H29 OH (XT liq )b

Maximum water concentrationc (M)

6 4 6 2 2 3

All liquid All liquid All liquid 8% 19% 31%

1 0.95 0.88 0.87 0.87 0.87

0.96 0.94 0.92 0.92 0.92 0.92

a The reported uncertainty in Deff for pure C14 H29 OH represents the 95% confidence interval calculated from the values measured in different runs. For the mixtures, the reported uncertainty represents one standard deviation of the values measured in different runs. A new wax layer was used for each run. b The percent solid and composition of the liquid present in the solid–liquid mixtures is calculated from the phase diagram in Fig. 2c. c During a measurement, the water composition of the mixture increases from zero toward the maximum water concentration that is approximated from water’s saturation point (one water molecule per four alcohol molecules as described in Ref. [37]). The measured Deff values are calculated assuming Deff does not change with water concentration (see Section 2.4).

(a) Absorbance at 1640 cm -1

comparable isomerization rates of both shorter (C8 ) and longer (C20 ) alkane chains [16,48]. Simulations of water diffusion in dodecane (C12 H26 ) and C96 H194 at high temperatures (443 K), show only a one percent decrease in the calculated diffusion coefficient when ten percent of the C12 alkane is replaced with C96 alkane. When twenty percent of the C12 molecules are replaced with C96 molecules the water diffusion coefficient measured from the simulations drops by 17% [49]. The similar water diffusion coefficient values for the different compositions of the fully liquid tetradecanol–eicosanol mixtures is thus not surprising based on the reduced role viscosity plays on small solute diffusion in longchain systems and the similarity of chain length between the two alcohols [19]. We have shown that FTIR-ATR can be used to measure the diffusion coefficient of water in liquid long chain alcohols. We now ask how water’s diffusive motion changes when this liquid is dispersed in a mixture that contains solid fractions in dynamic equilibrium.

15

-4

10 5 Absorbance at 1640 cm-1

0

Fit, Deff = 1.3 x 10-6 cm2/s

-5

(b)

3.4. Water diffusion coefficient in solid–liquid tetradecanol–eicosanol mixtures

2.5

As more eicosanol is added to the tetradecanol–eicosanol mixture, the mixture crosses into the two phase region and both liquid and solid are present. As shown in Fig. 5a, Eq. (1) fits the experimental data indicating that Fickian diffusion continues to describe the dynamics of the system. As the fraction of solid in the mixture increases from zero to thirty-one percent, the measured effective diffusion coefficient decreases six-fold and the equilibrium water absorbance of the mixture decrease three-fold (Table 2 and Fig. 6). A decrease in both the rate and measured signal indicate water is traveling only through the liquid portions of the layer. The loss of water signal ultimately limits the composition range over which we can study how solid mixture fractions change water’s diffusion path. Below a mixture composition of XT = 0.60, the water signal is too low to collect data that can be reliably fit. The values in Table 2 are average values of water’s diffusion coefficient across separate experiments. The thermogram in Fig. 2a showing a hysteresis between the melting and solidification peaks reminds us that the phase of the mixture sensitively depends on thermal history. Thus for comparison, values in Table 2 are measured under identical conditions: each mixture is heated to a fully liquid layer and then cooled to a fully solid layer before heating the mixture to 313 K. To demonstrate that the variation in water diffusivity is due to the phase or solid fraction of the layer, we also measure Deff on layers that have been prepared by an alternate protocol: the layers are heated to a fully liquid layer and then directly cooled to 313 K. Therefore two mixtures with the same tetradecanol:eicosanol molar ratio have different amounts of solid phase present at 313 K due to varied thermal histories. The position of the symmetric CH2 stretching peak provides a

2.0 Deff / 10-6 (cm2/sec)

x 10

0

2000

4000 Time / (s)

6000

8000

1.5 1.0 0.5

Increasing Liquid Percent 0.0 2850.5 2851.5 2852.5 2853.5 2849.5 CH2 Symmetric Stretching Peak Position / (cm-1) Fig. 5. (a) Fit using Eq. (2) to the increase in absorbance at 1640 cm−1 for water diffusion into a 70:30 tetradecanol:eicosanol mole fraction mixture. Fit parameters: L = 944 ␮m, Abseq = 0.0013, Deff = 1.3 × 10−6 cm2 /s. (b) Correlation between Deff and CH2 symmetric stretching peak. The composition of mixtures is indicated by the color/shape: red squares are XT = 0.60, blue diamonds are XT = 0.70, and green triangles are XT = 0.80. Filled symbols indicate samples cooled to a solid state before heating to 313 K. Open symbols indicate samples directly cooled to 313 K.

measure of the relative solid fraction of each mixture. As shown in Fig. 5b, the measured effective diffusion coefficient scales with the position of the CH2 symmetric stretching peak. Mixtures with a larger solid fraction have CH2 symmetric stretching peaks at lower wavenumbers and also have lower measured effective diffusion

164

D.R. Widmer et al. / Fluid Phase Equilibria 379 (2014) 157–166

Deff / 10-6 (cm2/s)

(a) 4 3 2 1

0 0%

10%

20%

30%

40%

Percent Solid in Mixture

(b) 0.2

Abseq

0.15 0.1

0.05

0 0%

10%

20%

30%

40%

Percent Solid in Mixture Fig. 6. (a) Deff and (b) Abseq plotted against the calculated percent solid in the mixture assuming an ideal mixture and the phase diagram presented in Fig. 2c. The Abseq value for the fully liquid mixture (solid fraction = 0) represents the average of two measurements on a fully liquid layer with XT = 0.80.

coefficients. The scatter in the data seen in Fig. 5b is a combination of the uncertainties of this experimental method along with the difficulty of characterizing a metastable system. The difference spectra that we collect are very sensitive to slight changes in the solid fraction of the layer. For several of the mixtures, we observe evidence for small increases in the amount of solid in the mixture during the course of water diffusion. Hydration increases the bulk freezing temperatures of long chain alcohols because of the higher solubility of water in the rotator phase [37]. Thus the observed small increase in solid fraction is expected given interactions between the water molecules and OH groups that stabilize the solid over the liquid. We do not observe a correlation between the magnitude of the decrease in CH2 symmetric stretching peak wavenumber and the composition of the mixture or the initial peak position. The average decrease is less than 0.5 cm−1 . The correlation in Fig. 5b between Deff and the position of the CH2 symmetric stretching peak also supports the assumption that the lowest layer of the wax imaged by the IR has a similar phase structure as the entire layer. The overlap of the DSC and IR points in the phase diagram in Fig. 2c also confirms that the phase behavior of the lowest wax layer matches the bulk behavior observed in the DSC. Thus we do not see evidence for long-range ordering or different phase change dynamics caused by the alcohols interacting with the hydrophilic germanium surface. The amount of the solid fraction in each mixture is estimated using the experimental phase diagram in Fig. 2c and the ratio of the different segments of the tie line at 313 K. This ratio provides a measure of the solid fraction of each layer in addition to the relative information provided by the CH2 symmetric stretching peak position. With this approach we model the system as an ideal mixture

and assume the solid present in the solid–liquid two-phase region (labelled C in Fig. 2c) is pure eicosanol. The liquidus line intersects with a tie line at 313 K at XT = 0.87. Thus at 313 K regardless of the overall mixture composition, the liquid portion of the twophase region in an ideal mixture has a composition of XT liq = 0.87. The percent of the mixture that is solid or liquid changes as the overall mixture composition changes but the composition of the liquid portion does not. For a mixture with an overall composition of XT = 0.60, the left hand segment of the tie line runs from XT = 0 to XT = 0.60 and corresponds to the liquid fraction of the mixture. The right hand side of the tie line runs from XT = 0.60 to XT = 0.87 and corresponds to the solid fraction of the mixture. Thus at 313 K for a mixture with an overall composition of XT = 0.60, the solid pure eicosanol is 31% of the mixture (0.27/0.87 = 0.31). The calculated percent solid of each mixture is listed in Table 2. An increase in the solid fraction of the mixture leads to a decrease in water diffusivity and the equilibrium water absorbance signal. Fig. 6a plots the effective diffusion coefficient versus the solid fraction of each mixture and Fig. 6b plots the decrease in the measured Abseq value. The decrease in water content is due to an increasingly solid mixture and a mixture with a smaller ratio of hydroxyl to methylene groups. The combined decrease in water content and diffusivity suggest water molecules are present only in the liquid portion of each mixture and this liquid portion is surrounded by barriers to diffusion. As observed in our experiments, water diffusion is still Fickian but slower because of an increase in tortuosity of the path length caused by solid domains. Both solid forms, crystalline and rotator would cause barriers to diffusion. Water is insoluble in the crystalline-solid form. Although water is two times more soluble in the solid-rotator phase than in the liquid phase, water absorption and diffusion into the rotator phase is expected to be much slower than the timescale of our experiments [37]. Similar results have been seen in polymeric systems. Breen and coworkers describe the decrease in water and acetone diffusivity in poly(vinyl alcohol)-clay nanocomposites as due to the increased diffusion path length experienced by each solute [50]. In our measurements, the diffusivity falls faster than the increase in the solid mixture fraction. For example, the diffusivity drops to one sixth the original value in a mixture that is less than one third solid. A larger number of smaller crystalline domains will increase the tortuosity of the mixture more than a smaller number of larger domains. Simulations are planned to model the effect of solid domain size and distribution on the observed diffusion coefficient. 4. Conclusion The effective diffusion coefficient for water in fully liquid and solid–liquid mixtures of tetradecanol and eicosanol is determined using FTIR-ATR experiments. By correlating water diffusivity with the relative solid fraction of the mixture, this work provides an additional example of the utility of the FTIR-ATR technique to simultaneously measure diffusivity and properties of the solvent that influence solute diffusion. For pure tetradecanol, we find an activation energy for water diffusion that confirms the importance of hydrogen-bonding interactions between water and the alcohol solvent. For the fully liquid mixtures, our results show that the water diffusivity appears to be independent of mixture composition up to 20% mole fraction eicosanol. By further increasing the eicosanol fraction in the mixture, we are able to observe that a mixture with approximately 30% solid content decreased the diffusivity of water by a factor of six, independent of temperature effects, from 3.1 × 10−6 cm2 /s to 0.5 × 10−6 cm2 /s. The magnitude of this decrease can be explained by water diffusing through the liquid portions of the mixture but following a more tortuous path due to the presence of solid domains in either the rotator or crystalline phase acting as barriers to diffusion.

D.R. Widmer et al. / Fluid Phase Equilibria 379 (2014) 157–166

Acknowledgements This work was supported by a Camille and Henry Dreyfus Faculty Start-up award and a Research Corporation Cottrell College Science (CC19817) award to AME and Denison University startup funds. We thank C. French Cudjoe for help with DSC experiments and G. Nathanson and E. Edwards for helpful discussion of the manuscript. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.fluid.2014.07.021. References [1] L. Carreto, A.R. Almeida, A.C. Fernandes, W.L.C Vaz, Thermotropic mesomorphism of a model system for the plant epicuticular wax layer, Biophys. J. 82 (2002) 530–540. [2] D. Donaldson, V. Vaida, The influence of organic films at the air-aqueous boundary on atmospheric processes, Chem. Rev. 106 (2006) 1445–1461. [3] J.J. Najera, A.B. Horn, Infrared spectroscopic study of the effect of oleic acid on the deliquescence behaviour of ammonium sulfate aerosol particles, Phys. Chem. Chem. Phys. 11 (2009) 483–494. [4] P. Papagiannakopoulos, X. Kong, E.S. Thomson, N. Markovic, J.B.C Pettersson, Surface transformations and water uptake on liquid and solid butanol near the melting temperature, J. Phys. Chem. C 117 (2013) 6678–6685. [5] L. Ventola, M. Ramirez, T. Calvet, X. Solans, M.A. Cuevas-Diarte, P. Negrier, et al., Polymorphism of n-alkanols: 1-heptadecanol, 1-octadecanol, 1-nonadecanol, and 1-eicosanol, Chem. Mat. 14 (2002) 508–517. [6] E. Sloutskin, E.B. Sirota, H. Kraack, O. Gang, A. Doerr, B.M. Ocko, et al., Surface and bulk phase behavior of dry and hydrated tetradecanol:octadecanol alcohol mixtures, J. Chem. Phys. 116 (2002) 8056–8066. [7] S. Merk, A. Blume, M. Riederer, Phase behaviour and crystallinity of plant cuticular waxes studied by Fourier-transform infrared spectroscopy, Planta 204 (1998) 44–53. [8] N.D.D Carareto, M.C. Costa, M.P. Rolemberg, M.A. Kraehenbuehl, A.J.A Meirelles, The solid–liquid phase diagrams of binary mixtures of even saturated fatty alcohols, Fluid Phase Equilib. 303 (2011) 191–192. [9] L. Ventola, T. Calvet, M.A. Cuevas-Diarte, H.A.J. Oonk, D. Mondieig, Solid–solid and solid–liquid equilibria in the n-alkanols family: C18 H37 OH–C20 H41 OH system, Phys. Chem. Chem. Phys. 6 (2004) 3726–3731. [10] L. Zhu, T. Cai, J. Huang, T.C. Stringfellow, M. Wall, L. Yu, Water self-diffusion in glassy and liquid maltose measured by Raman microscopy and NMR, J. Phys. Chem. B 115 (2011) 5849–5855. [11] H. Park, T. Chang, S. Lee, Diffusion of small probe molecule in oligomers, J. Chem. Phys. 113 (2000) 5502–5510. [12] B.A. Kowert, M.B. Watson, N.C. Dang, Diffusion of squalene in n-alkanes and squalane, J. Phys. Chem. B 118 (2014) 2157–2163. [13] E.L. Cussler, Diffusion Mass Transfer in Fluid Systems, third ed., Cambridge University Press, New York, NY, 2011. [14] J. Crank, The Mathematics of Diffusion, Clarendon Press, Oxford, 1970. [15] J.T. Su, P.B. Duncan, A. Momaya, A. Jutila, D. Needham, The effect of hydrogen bonding on the diffusion of water in n-alkanes and n-alcohols measured with a novel single microdroplet method, J. Chem. Phys. 132 (2010) 044506. [16] B.A. Kowert, M.B. Watson, Diffusion of organic solutes in squalane, J. Phys. Chem. B 115 (2011) 9687–9694. [17] R. Murarka, S. Bhattacharyya, B. Bagchi, Diffusion of small light particles in a solvent of large massive molecules, J. Chem. Phys. 117 (2002) 10730–10738. [18] E. Hawlicka, Self-diffusion in multicomponent liquid systems, Chem. Soc. Rev. 24 (1995) 367–377. [19] T.C. Chan, W.K. Tang, Diffusion of aromatic compounds in nonaqueous solvents: a study of solute, solvent, and temperature dependences, J. Chem. Phys. 138 (2013) 224503. [20] A.J. Easteal, Tracer diffusion of water in organic liquids, J. Chem. Eng. Data 41 (1996) 741–744. [21] J. Schmidt, J. Skinner, Brownian motion of a rough sphere and the Stokes–Einstein law, J. Phys. Chem. B 108 (2004) 6767–6771. [22] J. Lu, R. Kong, T. Chan, Effects of molecular association on mutual diffusion: a study of hydrogen bonding in dilute solutions, J. Chem. Phys. 110 (1999) 3003–3008. [23] N. Zhang, W. Li, C. Chen, J. Zuo, L. Weng, Molecular dynamics study on water self-diffusion in aqueous mixtures of methanol, ethylene glycol and glycerol: investigations from the point of view of hydrogen bonding, Mol. Phys. 111 (2013) 939–949. [24] C. Chen, W.Z. Li, Y.C. Song, L.D. Weng, N. Zhang, Concentration dependence of water self-diffusion coefficients in dilute glycerol–water binary and glycerol–water–sodium chloride ternary solutions and the insights from hydrogen bonds, Mol. Phys. 110 (2012) 283–291. [25] Y. Wu, S. Joseph, N.R. Aluru, Effect of cross-linking on the diffusion of water, ions, and small molecules in hydrogels, J. Phys. Chem. B 113 (2009) 3512–3520.

165

[26] Y. Elabd, M. Baschetti, T. Barbari, Time-resolved Fourier-transform infrared/attenuated total reflection spectroscopy for the measurement of molecular diffusion in polymers, J. Polym. Sci., B: Polym. Phys. 41 (2003) 2794–2807. [27] G. Fieldson, T. Barbari, The use of FTIR-ATR spectroscopy to characterize penetrant diffusion in polymers, Polymer 34 (1993) 1146–1153. [28] K. Ichikawa, T. Mori, H. Kitano, M. Fukuda, A. Mochizuki, M. Tanaka, Fouriertransform infrared study on the sorption of water to various kinds of polymer thin films, J. Polym. Sci., B: Polym. Phys. 39 (2001) 2175–2182. [29] S. Morita, M. Tanaka, Y. Ozaki, Time-resolved in situ ATR-IR observations of the process of sorption of water into a poly(2-methoxyethyl acrylate) film, Langmuir 23 (2007) 3750–3761. [30] L.M. Doppers, C. Sammon, C. Breen, J. Yarwood, FTIR-ATR studies of the sorption and diffusion of acetone/water mixtures in poly(vinyl alcohol), Polymer 47 (2006) 2714–2722. [31] S.U. Hong, T.A. Barbari, J.M. Sloan, Diffusion of methyl ethyl ketone in polysiobutylene: comparison of spectroscopic and gravimetric techniques, J. Polym. Sci., B: Polym. Phys. 35 (1997) 1261–1267. [32] D.T. Hallinan Jr., M.G. De Angelis, M.G. Baschetti, G.C. Sarti, Y.A. Elabd, Non-Fickian diffusion of water in Nafion, Macromolecules 43 (2010) 4667–4678. [33] D. Murphy, M.N. Depinho, An ATR-FTIR study of water in celluloseacetate membranes prepared by phase inversion, J. Membr. Sci. 106 (1995) 245–257. [34] M. Hase, R. Scheffelmaier, S. Hayden, D. Rivera, Quantitative in situ attenuated total internal reflection Fourier-transform infrared study of the isotherms of poly(sodium 4-styrene sulfonate) adsorption to a TiO2 surface over a range of cetylpyridinium bromide monohydrate concentrations, Langmuir 26 (2010) 5534–5543. [35] T. Karbowiak, E. Ferret, F. Debeaufort, A. Voilley, P. Cayot, Investigation of water transfer across thin layer biopolymer films by infrared spectroscopy, J. Membr. Sci. 370 (2011) 82–90. [36] K.L. Vasconcelos, A. Bhasin, D.N. Little, Measurement of water diffusion in asphalt binders using Fourier-transform infrared-attenuated total reflectance, Transp. Res. Rec. 2179 (2010) 29–38. [37] E.B. Sirota, X.Z. Wu, The rotator phases of neat and hydrated 1-alcohols, J. Chem. Phys. 105 (1996) 7763–7773. [38] L. Ventola, T. Calvet, M.A. Cuevas-Diarte, M. Ramirez, H.A.J. Oonk, D. Mondieig, et al., Melting behaviour in the n-alkanol family. Enthalpy-entropy compensation, Phys. Chem. Chem. Phys. 6 (2004) 1786–1791. [39] L. Ventola, T. Calvet, M.A. Cuevas-Diarte, X. Solans, D. Mondieig, P. Negrier, et al., Solid state equilibrium in the n-alkanols family: the stability of binary mixed samples, Phys. Chem. Chem. Phys. 5 (2003) 947–952. [40] D. Bradley, G. Williams, M. Lawton, Drying of organic solvents: quantitative evaluation of the efficiency of several desiccants, J. Org. Chem. 75 (2010) 8351–8354. [41] MATLAB release 2011, the MathWorks, Inc., Natick, MA, USA. [42] Source for tetradecanol enthalpy of fusion: E.S. Domalski and E.D. Hearing, Condensed Phase Heat Capacity Data in NIST Chemistry WebBook, NIST Standard Reference Database Number 69, Eds. P.J. Linstrom and W.G. Mallard, National Institute of Standards and Technology, Gaithersburg MD, 20899, http://webbook.nist.gov, (retrieved April 26, 2014). Values from the following three sources were averaged for the eicosanol enthalpy of fusion: (1) Hopfe, D. Thermophysical Data of Pure Substances. Data Compilation of FIZ CHEMIE, Germany, p. 33 (1990) accessed from Wiley Infotherm, http://www.infotherm.com, (retrieved November 21, 2013). (2) Ventola L., Ramirez M., Calvet T., Solans X., Cuevas-Diarte M.A., et al., Chem. Mat. 14, 2002, 508–517. (3) Van Miltenburg, J.C., Oonk, H.A.J., Ventola, L. J. Chem. Eng. Data 46, 2001, 90–97. [43] We note that these assumptions did not hold in every liquid system we initially investigated. Our experiments on water uptake into glycerol show that water did not rapidly saturate the top most liquid layer due to water’s miscibility with glycerol and the low water flow rate. The glycerol data could be fit with a model in which the concentration of water in the top-most layer increases during the course of water diffusion through the layer as described in Crank, J. The Mathematics of Diffusion, Clarendon Press, Oxford, 1970. [44] P. Schatzberg, Diffusion of water through hydrocarbon liquids, J. Polym. Sci., C: Polym. Sym. 10 (1965) 87–92. [45] I.A. Sedov, B.N. Solomonov, Gibbs free energy of hydrogen bonding of aliphatic alcohols with liquid water at 298 K, Fluid Phase Equilib. 315 (2012) 16–20. [46] B. Solomonov, I. Sedov, Quantitative description of the hydrophobic effect: the enthalpic contribution, J. Phys. Chem. B 110 (2006) 9298–9303. [47] Due to its high melting point, no known relevant viscosity data for eicosanol exists. Considering a corollary system, 1-decanol and 1-hexadecanol at 328 K, the viscosity (␩) and density (␳) of decanol and hexadecanol are 4.07 cP and 805.9 kg m−3 and 814.13 and 9.03 cP, respectively (Matsuo S, Makita T, Int. J. Thermophys. 10, 1989, 833 and 885). The Kendall and Moore model for the kinematic viscosity of a mixture (v = /), (vmix )1/3 =

n i

xi (v)

1/3

where xi is the

mole fraction in the mixture has been shown to predict the viscosities of binary mixtures of long-chain molecules (Goncalve et al., Viscosities of fatty mixtures: Experimental data and prediction, J. Chem. Eng. Data 52, 2007, 2000–2006). Using the Kendall and Moore model we find the predicted viscosity for 80:20 decanol:hexadecanol mixture is 4.9 cP or 23% higher than pure decanol. Similarly, we would expect a higher viscosity for the 80:20 tetradecanol:eicosanol mixture.

166

D.R. Widmer et al. / Fluid Phase Equilibria 379 (2014) 157–166

[48] Y. Zhang, R. Venable, R. Pastor, Molecular dynamics simulations of neat alkanes: the viscosity dependence of rotational relaxation, J. Phys. Chem. 100 (1996) 2652–2660. [49] Z.A. Makrodimitri, D.J.M. Unruh, I.G. Economou, Molecular simulation of diffusion of hydrogen, carbon monoxide, and water in heavy n-alkanes, J. Phys. Chem. B 115 (2011) 1429–1439.

[50] A.F. Breen, C. Breen, F. Clegg, L. Doeppers, L. Khairuddin, M. Labet, C. Sammon, J. Yarwood, FTIR-ATR studies of the sorption and diffusion of acetone:water mixtures in poly(vinyl alcohol)-clay nanocomposites, Polymer 53 (2012) 4420–4428.