Supercooling and Nucleation of Fatty Acids: Influence of Thermal

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B: Liquids, Chemical and Dynamical Processes in Solution, Spectroscopy in Solution

Supercooling and Nucleation of Fatty Acids: Influence of Thermal History on the Behavior of the Liquid Phase John A Noel, Laurent Kreplak, Nuwansiri Nirosh Getangama, John R. de Bruyn, and Mary Anne White J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b10568 • Publication Date (Web): 03 Dec 2018 Downloaded from http://pubs.acs.org on December 14, 2018

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The Journal of Physical Chemistry

Supercooling and Nucleation of Fatty Acids: Influence of Thermal History on the Behavior of the Liquid Phase

John A. Noël,a Laurent Kreplak,b,c Nuwansiri Nirosh Getangama,d John R. de Bruynd and Mary Anne Whitea,b,c,*

a Department b

of Chemistry, Dalhousie University, Halifax, Nova Scotia, B3H 4R2, Canada

Department of Physics and Atmospheric Science, Dalhousie University, Halifax, Nova Scotia, B3H

4R2, Canada c

Clean Technology Research Institute, Dalhousie University, Halifax, Nova Scotia, B3H 4R2, Canada

d Department

of Physics and Astronomy, University of Western Ontario, London, Ontario, N6A 3K7,

Canada

*Corresponding author; email: [email protected]

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Abstract

Saturated fatty acids are an exceptionally important class of liquids, used in many consumer products and suggested as phase change materials (PCMs) for thermal energy storage, in part because they crystallize with minimal supercooling. Here we investigate fatty acid nucleation to understand why crystallization is so facile, as a step toward identifying potential mechanisms for the suppression of supercooling in other PCMs. We find that fatty acid supercooling can be induced only if the liquid is first heated above a material-dependent threshold temperature. NMR spin-lattice relaxation time studies show that the average mobility of the alkyl chains in the fatty acids increases more rapidly with temperature above the supercooling threshold temperature, and NMR T1 hysteresis also set in at that temperature. Measurements of the real portion of the dielectric constant as a function of temperature show that a liquid fatty acid heated far above its melting point behaves with an apparent temperature upon cooling that is higher than the actual temperature, when compared to its behaviour at the same temperature upon heating. Our results suggest that molecular clusters in the liquid fatty acids break apart when the liquids are heated above their threshold temperature, and do not immediately reform on cooling. The breakup of clusters leads to an increase in the mobility of the fatty acid molecules. Since the clusters do not reform quickly on subsequent cooling, nucleation does not occur, and substantial supercooling results.


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1. INTRODUCTION Fatty acids are an exceptionally important class of liquids, used in the production of lubricants, soaps, cosmetics and foodstuffs. Recently fatty acids have been suggested as phase change materials for thermal energy storage. Understanding the role of their thermal history on phase stability and metastability, and concomitant changes in physical properties, is of intrinsic interest to all these fields. Phase change materials (PCMs) have considerable potential to capture and store thermal energy.1,2,3 PCMs store heat primarily through the enthalpy change of a phase transition, typically melting. Melting of the PCM stores energy, and crystallization of the PCM releases the stored energy. Selection of a PCM for an application is primarily based on the melting temperature, Tfus, falling within the required temperature range. If the operational temperature range does not include the melting temperature, the PCM will not change phase, and most of the thermal energy storage capacity will not be accessed. Materials with high values of enthalpies of fusion, ΔfusH, are preferred, as these maximize the thermal energy storage density of the system. Two structural motifs for organic molecular materials have been identified as most promising for use as PCMs at ambient and moderate temperature (~ 20 to ~ 150 °C) with regard to their enthalpies of fusion, namely those with long alkyl chains (e.g., paraffins, fatty acids, fatty esters, etc.), and those with extensive hydrogen-bonding networks in the solid phase (e.g., sugar alcohols).4,5 PCMs have been investigated for use in a variety of applications including: moderation of temperature swings within buildings,6 thermal energy storage for solar thermal systems,7 temperature-regulating fabrics, off-peak energy storage, and thermal managements of electronics including tablet computers,8 batteries,9 and photovoltaic panels.10 In many of these applications,



the PCM acts passively, as external crystallization triggers are not feasible. Thus, it is important both for the PCM to melt within the temperature range of the application, and also to crystallize within that same temperature range. If not, on subsequent cycles the material cannot access most of its thermal energy storage capacity. As such, supercooling (cooling of the liquid phase below the equilibrium melting temperature of the material) can present an obstacle for otherwise potentially useful PCMs. Fatty acids are especially promising as PCMs. The saturated, linear fatty acids have high values of ΔfusH (~ 180 J g-1)11 and a range of discrete melting points depending on the length of the alkyl chain.12,13 Furthermore, Tfus can be fine-tuned through the use of eutectic mixtures.12 (Note that a sharp melting point is preferable, to enhance storage over a narrow temperature range. Such a sharp melting point can include eutectics, but off-eutectic compositions can lead to phase separation and broad, shifted melting points after many melt-freeze cycles.) Fatty acids have been shown to cycle thermally without degradation,11 are non-toxic, and can be produced sustainably.14 In general fatty acids crystallize with little supercooling. In contrast to the fatty acids, some other organic materials such as sugar alcohols require significant supercooling for the crystallization of the solid phase: liquid erythritol is often observed to supercool > 80 K without crystallization.15 However, sugar alcohols also have exceptionally high values of ΔfusH, 324 J g-1 for erythritol, for example.16 As such, suppression of supercooling in sugar alcohol PCMs is an attractive target as it would allow them to be used in a wider range of applications. While supercooling in some PCMs can be mitigated through the use of nucleating aids, no such aid has yet been reported for the sugar alcohols. In the present work, the nucleation behavior of saturated fatty acids is examined with the goal of understanding why they do not generally supercool, and the longer-term objective of


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identifying potential mechanisms to promote nucleation in PCMs that intrinsically exhibit extensive supercooling, such as sugar alcohols. Fatty acids are known to exist as dimers in the solid phase with pairs of molecules hydrogen bonded through their carboxylic headgroups.17 Near-IR spectroscopy shows that the fatty acids remain associated as dimers in the liquid phase, even to quite elevated temperature.17,18 In addition to the presence of dimers in the liquid phase, there is evidence to suggest that there is further ordering in the liquid phase of fatty acids. In the 1920’s, Morrow detected diffraction peaks corresponding to two different molecular spacings in the X-ray scattering patterns of molten fatty acids.19 He determined that these spacings did not correspond to any of the crystalline phases of the fatty acids, or to crystallites. One of the spacings increased linearly with chain length, and was ascribed to the length of the fatty acid. The second spacing was essentially invariant to chain length, with a value of ~ 4.5 Å.19 On the basis of this spacing, Morrow postulated the existence of “distinct space arrays” in the liquid phase and viewed them as quasi-liquid crystalline, or cybotactic groups.19,20 More recently, Iwahashi and coworkers have proposed the existence of fatty acid clusters in the liquid phase of fatty acids.18,21,22,23 On the basis of NMR, viscosity, density, and X-ray diffraction measurements of octanoic acid and some saturated and unsaturated 18-carbon acids, they proposed that rod-like fatty acid dimer pairs aggregate like ‘bundles of straw’ and that these clusters are randomly aligned within the overall isotropic liquid phase.18,21 They further suggested that the clusters of fatty acid dimers have an interdigitated structure, with the terminal methyl group of one molecule in the same plane as the carbonyl carbon of the adjacent molecule. Iwahashi et al.22 and Yoshimoto and Sato24 have shown that the crystallization temperature of cis-9-octadecenoic acid can be influenced by its thermal history. Both groups



found that when cis-9-octadecenoic acid (Tfus = 13.2 °C) was heated to temperatures below 40 °C, it crystallized at ~ 10 °C, but when heated to 50 °C or above, it required cooling to ~ 4 °C before crystallization was initiated.22,24 They attributed the onset of increased supercooling to a change in the ordering of the liquid phase, possibly from a change in the clustering behavior of the fatty acid molecules. This suggestion implies that the fatty acid clusters in the liquid phase promote nucleation of the solid phase. Yoshimoto and Sato24 also showed that when cis-9octadecenoic was heated to 80 °C and then incubated at 20 °C for 20 h or longer, it again crystallized at ~ 10 °C. The incubation at 20 °C reversed the influences of the 80 °C heating cycle, suggesting that the liquid phase had reverted to its initial ordering. In the present studies, the generality of the induction of supercooling is explored for saturated fatty acids, and the influence of temperature and thermal history on the behavior of the liquid phase is investigated by use of DSC, NMR, and dielectric constant measurements. Specifically, the role of order in the liquid phase of fatty acids on their nucleation is studied, providing new physical insights concerning temperature-dependent structure in liquid fatty acids.

2. MATERIALS AND EXPERIMENTAL METHODS 2.1 DSC. Thermal cycling of PCMs was performed using differential scanning calorimetry (DSC; TA Instruments DSC Q200), calibrated with the melting of indium before each set of measurements. DSC experiments were made using a 2 K min-1 scanning rate under a 25 mL min-1 flow of helium. Sample masses were ~ 3 to 8 mg, and samples were measured in crimped aluminum DSC pans. Melting and crystallization temperatures were taken as the onset temperature. The procedure, shown schematically in Figure 1, was as follows: the sample was 6 ACS Paragon Plus Environment

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heated past its Tfus to a temperature higher than Tfus, and held isothermally at that temperature for 60 min. The sample was then cooled until crystallization occurred. The process was then repeated with increasing holding temperatures. Octanoic acid (Sigma, > 99 %), dodecanoic acid (Aldrich, 98 %), tridecanoic acid (Sigma, > 98 %) and hexadecanoic acid (Alfa Aesar, 95 %) were investigated using the above procedure. During each heat treatment, DSC thermograms were recorded to determine melting and crystallization temperatures.

Figure 1. Schematic of the DSC thermal cycling procedure.

An octanoic acid-in-water emulsion also was cycled using this method. To prepare the emulsion, a 4 volume % solution of TWEEN 65 (polyoxyethylenesobitan tristearate, Fluka AG) in water was first prepared following the procedure of Whitman et al.25 TWEEN 65 is a surfactant that can be used to suspend droplets of hydrophobic liquid in an aqueous solution. Liquid octanoic acid was added to the TWEEN 65 solution at volume ratio of 1:5. The mixture was shaken for 60 seconds, and then sonicated for 3 minutes.

2.1 Dielectric Measurements. Measurements of the complex dielectric constant were made using a Solartron Analytical Modulab MTS with a 129610A Cryostat. Samples of octanoic 7 ACS Paragon Plus Environment


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acid (Sigma, > 99 %) and dodecanoic acid (Aldrich, 98 %) enclosed between parallel copper plates with a 2.08 mm separation were scanned from 1 x 106 Hz to 1 x 10-1 Hz with a sinusoidal alternating potential of 4 V RMS. The sample volume was 0.65 mL. Measurements were made at increments of 10 K (octanoic acid) or 15 K (dodecanoic acid) on heating. When the desired maximum temperature was reached, the sample was held at that temperature for 1 h before it was cooled. Dielectric measurements were made at the same temperatures on cooling.

2.3 NMR Relaxation Time Measurements. NMR 13C spin-lattice relaxation time, T1, measurements for were made using a Bruker Avance 500 MHz NMR spectrometer, and the inversion recovery method. A 180°-τ-90° pulse sequence was used with 16 values of τ ranging from 1 ms to 40 s. A 40 s delay was implemented between pulse sequences, and eight replicate scans were acquired for each value of τ. The acquired intensities, I, were plotted as a function of τ, and fit to: 𝜏

(

𝐼 = 𝐼0 1 ― 2𝜗𝑒

),

𝑇1

[1]

where I0 is the intensity acquired from a 90° pulse and ϑ is a fitting parameter to determine T1 for each 13C nucleus in the fatty acid chain. Measurements were performed on ~ 0.5 mL of neat octanoic acid (Sigma, > 99 %) in a 5 mm glass tube, with a 2 mm glass capillary filled with D2O (Aldrich, 99 % D) inserted inside of it to provide a signal lock while keeping the fatty acid pure. The temperature was varied from 27 °C to 87 °C and back to 27 °C, with a heating gas flow rate of 800 L h-1 using a BVT-3200 temperature controller. Measurements were made at temperature increments of 15 K.


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3. RESULTS AND DISCUSSION The influence of thermal cycling on crystallization of fatty acids was remarkable. When saturated linear fatty acids were melted and heated to a temperature moderately above their Tfus, then held at that temperature for 60 min, crystallization occurred upon cooling with relatively minor supercooling. In contrast, increasing the holding temperature to a temperature above a fatty acid-dependent threshold, led to significant supercooling. DSC thermograms of the thermal cycling of dodecanoic acid are shown in Figure 2. The results of the thermal cycling of dodecanoic and octanoic acids are given in Figure 3, along with previous results for the unsaturated fatty acid, cis-9-octadecenoic acid22, which are shown for comparison. Similar thermal cycling results for tridecanoic acid and hexadecanoic acid are presented in the Supplemental Information. Our results demonstrate that the induced supercooling phenomenon observed for one unsaturated fatty acid22 also occurs for saturated fatty acids.



Figure 2. DSC thermograms showing the results of thermal cycling experiments on dodecanoic acid. Dodecanoic acid exhibited increased supercooling when heated for 1 h to 125 °C or higher.


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Figure 3. Supercooling at crystallization (Tfus – Tcryst), where Tcryst is the “normal” crystallization temperature for a sample that had not been heated much past the melting point, as a function of the holding temperature, Thold, relative to the melting temperature, Tfus, for dodecanoic and octanoic acid as measured in the present work, and for cis-9-octadecenoic as measured by Iwahashi et al.22

Iwahashi et al. suggested that molecular clusters existed in liquid cis-9-octadecenoic acid, and that the clusters disintegrated as the temperature was increased.21,22 We propose that the onset of supercooling is linked to the thermally induced disappearance of molecular clusters in the liquid, and that above the threshold temperature the overall molecular ordering in the liquid phase is changed. We further hypothesize that the molecular clusters in the liquid phase promote nucleation of the crystalline phase of the fatty acids: when the clusters are destroyed after 11 ACS Paragon Plus Environment


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sufficient heating, there is an increased barrier to nucleation. Greater supercooling is required for bulk crystallization after heating above the threshold temperature. Such increased supercooling increases the driving force for nucleation, namely the chemical potential difference, Δμ, between the solid and liquid phases:26 ∆μ = ∆fus𝐻(

𝑇fus ― 𝑇 𝑇fus

) .

[2]

Another way that the influence of heating a fatty acid above its supercooling threshold temperature can be examined is by measuring the time required for crystallization to be initiated at a given magnitude of supercooling. To investigate this, dodecanoic acid (Tfus = 43 °C) was heated to either 50 °C (below its threshold temperature) or 120 °C (above its threshold temperature) and held at that temperature for 60 min before cooling to 41 °C. At 41 °C, liquid dodecanoic acid would be supercooled by 2 K. As seen in Figure 4, when the fatty acid was held at 50 °C, crystallization occurred nearly immediately on cooling to 41 °C, whereas when held at 120 °C, the supercooled liquid persisted at 41 °C for more than 1 h before crystallization occurred. This experiment was carried out in triplicate, and was reproducible.


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Figure 4. DSC thermograms comparing the time required for crystallization initiation in liquid dodecanoic acid cooled to 41 °C (i.e., 2 K supercooling) after having been heated to, and held for 1 h at, 50 °C or 120 °C. Curves are offset vertically by 1 W g-1 for clarity. The time required for crystallization to be initiated is related to the probability of forming a critical nucleus. In both cases described above, the same mass of fatty acid was supercooled by the same amount (2 K) and both experienced the same driving force (Δμ) for nucleation. Our results indicate that when the fatty acid was heated to 120 °C there was a greater barrier to be overcome to form a critical crystal nucleus, and hence a longer nucleation time. Thus, the probability of there being a critical nucleus present at any given time was lower for the fatty acid heated to 120 °C than for dodecanoic acid heated only to 50 °C. Presuming that clusters of fatty acid molecules were present in the liquid phase when dodecanoic acid was heated to 50 °C, and that they were not present (or greatly reduced in size or number) when heated to 120 °C, we conclude that the presence of fatty acid clusters lowers the barrier to nucleation and thereby increases the probability of forming a critical crystal nucleus at a given temperature.



The argument in the previous paragraph assumes homogeneous nucleation. Nonetheless, it is possible that nucleation could have been initiated heterogeneously on the surface of the aluminum DSC pan. To determine the influence of the aluminum DSC pans on crystallization, an octanoic acid-in-water emulsion was tested using the same cycling protocol outlined in Figure 1. In this sample, the fatty acid was not in direct contact with the surface of the aluminum DSC pan: each droplet of octanoic acid was surrounded by water (Figure 5 inset). As such it was possible to decouple the influence of the surface of the pan from the crystallization temperature. It is assumed that the droplets of octanoic acid were large enough that molecular ordering within the droplet approximated that of the bulk liquid. As shown in Figure 5, the octanoic acid-inwater exhibited the same supercooling behavior as neat octanoic acid when subjected to the same thermal cycling regime. We can thus conclude that the nucleation described in this work was initiated homogeneously and that the surfaces of the aluminum DSC pans did not influence the nucleation of the fatty acids. Therefore, the crystallization threshold effects observed are intrinsic properties of the fatty acids. Knowledge of the degree of motion within individual molecules (intramolecular mobility) could give insights into the overall degree of ordering within the liquid phase. A fatty acid molecule that is part of a cluster could be expected to be more constrained than a fatty acid molecule in the bulk liquid. For the liquid as a whole, the average mobility of atoms in the fatty acid alkyl chains over all molecules in the liquid would increase as the number of molecules held within clusters decreased.


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Supercooling, (Tfus - Tcryst) / K

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10

8

Neat Octanoic Acid Octanoic Acid - in - Water Emulsion 6 0

20

40

60

80

(Thold - Tfus ) / K

Figure 5. Supercooling at crystallization (Tfus – Tcryst), where Tcryst is the normal crystallization temperature, as a function of the holding temperature, Thold, relative to the melting temperature, Tfus, for neat octanoic acid and an octanoic acid-in-water emulsion using TWEEN 65 as a surfactant. The latter system, shown schematically in the inset, was determined for three hold temperatures. A test of our hypothesis that clusters in the liquid structure break apart when liquid fatty acids are heated above their threshold temperature, and that the clusters do not immediately reform on cooling, is to see if the average intramolecular mobility of molecules in the liquid phase increases at the threshold temperature (corresponding to the loss of clusters) but does not immediately revert to its initial state on cooling (as the clusters do not rapidly reform). One parameter by which the intramolecular mobility can be probed is through the spin-lattice relaxation time, T1, measured using NMR spectroscopy.27 As the temperature is increased, it is 15 ACS Paragon Plus Environment


anticipated that T1 would rise because there is more thermal motion of the molecules, decreasing the efficiency of the dipolar relaxation. However, a change in the liquid phase structure, such as a change from a liquid containing clusters to one without clusters, also would allow increased motion of carbon nuclei within the alkyl chains of the fatty acids. In most organic compounds, T1 relaxation occurs through dipolar reactions between carbon nuclei and attached protons. The efficiency of this relaxation process depends on the angle between the line between the two nuclei and the magnetic field vector.27 As the nuclei tumble through space, this angle changes. Spin-lattice relaxation is most efficient when the frequency of molecular motion matches the Larmor frequency of the transition. In the unclustered state, the frequencies of molecular motions would be more influenced by changes in temperature, and the rate of change of T1 with respect to temperature would thereby increase as the range of motions available to the nuclei increases. In this work, changes in T1 are attributed to increased motion of carbon nuclei within individual alkyl tails as clusters dissociate rather than increased frequency of motion of molecules as a whole (although this is not precluded). Values of T1 previously have been measured for cis-9-octadecenoic acid as a function of temperature on heating, and a change in slope was observed around 55 °C,22 which is close to the threshold temperature for supercooling in that fatty acid. The present results test the generality of that finding. The spin-lattice relaxation time of neat liquid octanoic acid was measured here using the inversion recovery method as a function of temperature from 27 °C to 87 °C and back to 27 °C. (NMR spectra shown in the Supporting Information.) The highest values of T1 were observed for the carbonyl carbon. Its relaxation was least efficient because it has no directly bonded protons through which dipolar relaxation could occur. The next highest T1 was for the methyl carbon. 16 ACS Paragon Plus Environment

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Although it has three directly bonded protons, it is also the most mobile carbon in the molecule, which decreases the efficiency of its relaxation because the frequency of its motion is much greater than the Larmor frequency. As the liquid fatty acid was heated mildly, T1 for the carbon nuclei in the alkyl chain increased linearly with temperature (Figure 6), as anticipated due to the increase in thermal motion in the system. Above 57 °C, the rate of change of T1 with respect to temperature increased. For example, the slope corresponding to C8 increased from 0.076 s K-1 to 0.099 s K-1 at 57 °C. Unclustered molecules would be more greatly influenced by changes in temperature due to less inhibited motion of methylene groups within the alkyl chains, so this change in slope, which occurs close to the threshold temperature for supercooling (Figure 3), likely indicates a reduction in the number of clusters in the liquid phase. The change in behavior of T1 at 57 °C supports the idea that the number of clusters in liquid octanoic acid has been greatly reduced at this temperature. Thus, this temperature might represent the limit of metastability for the clusters; while there may be a gradual decline in their size or number with increasing temperature, above the temperature limit to their metastability, their size and number rapidly decreases.



Figure 6. Spin-lattice relaxation times, T1, of the 13C nuclei of octanoic acid as function of temperature on heating. The dashed lines are linear fits to the data. The blue lines fit the lowtemperature region and the red lines fit the high-temperature region. Results for C4 and C5 are not shown as their peaks in the NMR spectrum could not be resolved.

There was no hysteresis in the curve of T1 vs. T on cooling down to 57 °C (Figure 7). Hysteresis was observed below 57 °C, however, with lower values of T1 than on heating in the region below this threshold temperature, suggesting that the molecular clusters did not reform upon cooling into the low-temperature region.


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Figure 7. Spin-lattice relaxation times, T1, of the (a) 13C nuclei of octanoic acid as function of temperature on heating and on cooling, and (b) a magnified view of the behavior of C8 in the hysteretic region, and after 2 hours at the lowest temperature. C4 and C5 are not shown as their peaks in the NMR spectrum could not be resolved. Lines are guides to the eye. 19 ACS Paragon Plus Environment


At the start of the experiment, the initial value for T1 at T = 27 °C for C8 was 3.61 ± 0.03 s. After heating to 87 °C and cooling back to 27 °C, the value of T1 for C8 was 3.41 ± 0.02 s. (A similar decrease was observed for the other carbon centers.) When the spin-lattice relaxation time was remeasured after the octanoic acid sample had been held for 2 h at 27 °C, the values of T1 had increased towards their original values: for C8, for example, the value of T1 had risen to 3.50 ± 0.02 s. The recovery of the values of T1 toward their initial values indicates that the liquid slowly evolved from the high-temperature, unclustered state back to the low-temperature, clustered state. Our results suggest that, given sufficient time the clusters in the liquid fatty acid that had been destroyed by the increased temperature can reform at lower temperatures. This finding is supported by the supercooling results of Yoshimoto and Sato24 for cis-9-octadecenoic acid: they found that a sample that had been heated past its threshold temperature and then incubated at 20 °C for at least 20 h required only minor supercooling for nucleation to occur. Each measurement of T1 took approximately 90 min. On cooling, this could have been sufficient time for some recovery of the fatty acid clusters. This phenomenon can be observed for C1, the carbon nucleus with the greatest hysteresis. While the high-temperature slope is initially maintained below 57 °C, the slope decreases at lower temperatures, indicative of a return to the low-temperature liquid ordering. Further information on dynamics comes from our dielectric studies. The real portion of the dielectric constant relative to the permittivity of free space, ε’(ω)/ε0, was used as a probe of the overall mobility of fatty acid molecules in the liquid phase. We hypothesize that the fatty


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acid molecules in the liquid phase would be more mobile if no clusters were present than if clusters exist. When the frequency of the applied electric field is low, the molecular dipoles can reorient to align with the field, resulting in relatively high values of ε’/ε0. At sufficiently high frequencies, however, the molecular dipoles do not have time to orient themselves with the rapidly oscillating field, and ε’(ω)/ε0 decreases. The ability of the molecular dipoles to align with the field will depend on the molecular mobility and so will be influenced by changes in the degree of clustering in the fatty acids studied here. Results of measurement of ε’(ω)/ε0 for dodecanoic acid on heating are shown in Figure 8, and data for cooling are in Figure 9. Similar curves for octanoic acid are presented in the Supplemental Information. Figure 8 shows that the ε’(ω)/ε0 data shifted toward higher frequency as the temperature was increased. This shift indicates that the mobility of the fatty acid molecules, on average, increased as the temperature was raised. On the basis of Figure 8 alone it cannot be said whether this change was due to a change in the liquid phase structure, or whether it was due solely to change in viscosity or some other thermal effect.



62 °C Heating 77 °C Heating 92 °C Heating 107 °C Heating 122 °C Heating 132 °C Heating

10

ε'(ω)/ε0

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8

6

0.1

1

10

100

1000

10000

100000

Frequency / Hz

Figure 8. The real portion of the dielectric constant of dodecanoic acid (Tfus = 43 °C), relative to the permittivity of free space ε0, as a function of frequency on heating.


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62 °C Heating 77 °C Heating 92 °C Heating 107 °C Heating 122 °C Heating 132 °C Heating

132 °C t = 30 min 132 °C t = 45 min 122 °C Cooling 107 °C Cooling 92 °C Cooling 77 °C Cooling

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ε'(ω)/ε0

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8

6

0.1

1

10

100

1000

10000

100000

Frequency / Hz

Figure 9. The real portion of the dielectric constant of dodecanoic acid (Tfus = 43 °C) relative to the permittivity of free space ε0 as a function of frequency on heating, then over the isothermal holding period at 132 °C, and then on cooling. The fatty acid was held a 132 °C for 60 min between the heating and cooling cycles. Measurements made on heating are represented by circles; measurements made on cooling are represented by squares, with the same colour for a given temperature.



After being held for 1 h at the maximum temperature (132 °C in the case of dodecanoic acid, which melts at 43 °C), the fatty acids were cooled. The holding temperature was above the threshold temperature for supercooling for the respective fatty acids. On cooling, ε’(ω)/ε0 showed considerable hysteresis (Figure 9). This is more easily visualized in Figure 10, which shows the values of ε’(ω)/ε0 for dodecanoic acid at a single frequency (1 Hz) as a function of temperature on heating and on cooling, and after holding at the high temperature for 30 minutes.

Figure 10. Real portion of the dielectric constant of dodecanoic acid (Tfus = 43 °C) relative to the permittivity of free space at 1 Hz as a function of temperature on heating and on cooling. The fatty acid was held a 132 °C for 60 min between the heating and cooling cycles.


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The hysteresis in ε’(ω)/ε0 indicates that the molecular dipoles become more mobile, on average, with heating, and remained so on cooling. The NMR resultssuggest that the mobility of the carbon atoms within the fatty acid alkyl chains increases above the threshold temperature for supercooling (i.e., the temperature at which clusters are broken up). These results suggest that the increase in mobility of the fatty acid dipoles seen in the dielectric response is due to an increase in the mobility of the molecules as a whole. Note that no measurable hysteresis was observed when the fatty acid was heated only to temperatures below its supercooling threshold temperature. We infer that the increase in ε’(1 Hz)/ε0 on heating was at least partially due to the destruction of clusters, and the hysteresis on cooling arose from clusters not reforming. A similar trend was found for octanoic acid. A time-temperature superposition28 was performed on the ε’(ω)/ε0 curves measured on heating to create a master curve to describe ε’(ω)/ε0 at any temperature. Briefly, the ε’(ω)/ε0 curves measured on heating were shifted along the frequency axis by a temperature-dependent factor α(T) to bring all the curves in line with a reference curve, chosen here to be the one taken at the lowest temperature on the heating run (62 °C for dodecanoic acid and 22 °C for octanoic acid). There was no shift in the ε’(ω)/ε0 direction. With all the ε’(ω)/ε0 curves measured on heating overlaid, the value of ε’(ω)/ε0 at each frequency was averaged to produce the master curve (Figure 11 for dodecanoic acid; see Supplementary Information for octanoic acid results).



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Figure 11. Master curve for the real part of the dielectric constant of dodecanoic acid (Tfus = 43 °C), relative to the permittivity of free space, created by shifting the individual ε’(ω) curves (Figure 9) by a factor α(T) to bring them in line with the reference curve, chosen as the curve from the measurement made at 62 °C.

The purpose of the master cure was to determine if there was any difference between the behavior on heating and cooling. The natural logarithms of the values of α(T) used to create the master curve were plotted as a function of (1/T – 1/T0) and fit to the Arrhenius-type expression (Figure 12):28 ln [𝛼(𝑇)] =

𝐸𝑎 1 𝑅

(

1

)

𝑇 ― 𝑇0

,


[3]

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where Ea is the activation energy for the dipolar reorientation, R is the gas constant, and T0 is the reference temperature (62 °C = 335 K for dodecanoic acid). With the value of Ea (50 ± 3 kJ mol-1 for dodecanoic acid and 48 ± 3 kJ mol-1 for octanoic acid) determined from the fit, the values of α(T) needed to bring the ε’(ω) curves measured on cooling in line with the master curve can be inserted into a modified version of Equation 3 to determine the apparent temperature, TA, of the fatty acid on cooling: ln [α(𝑇)] =

0

𝐸𝑎 1

(

1

𝑅 𝑇A

)

― 𝑇0

.

[4]

Ea ≈ 50 kJ mol-1

-1

ln[α(T)]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-2

-3

-4 -0.0006

-0.0004

-0.0002

0

[(1/T) - (1/T0)] / K-1

Figure 12. Natural logarithm of the values of α(T) used to create the master curve for dodecanoic acid (Tfus = 43 °C) from the ε’(ω)/ε0 curves measured on heating as a function of (1/T – 1/T0). The dashed line is a fit to Equation 3. 27 ACS Paragon Plus Environment


The apparent temperature for each measurement made on cooling for both dodecanoic and octanoic acid was determined using Equation 4. (For the measurements made on heating, the real temperature, T, is equal to TA in all cases because the master curve was made from the heating curves.) On cooling from temperatures above the supercooling threshold temperature, the fatty acids had TA > T (Figure 13); i.e., the dielectric response of the fatty acids at temperature T on cooling was the same as the response observed on heating at the higher temperature TA. For example, for dodecanoic acid on cooling, at T = 67 °C, TA was 102 °C. This result indicates that fatty acid clusters were eliminated on heating above the threshold temperature for supercooling, leading to a liquid with increased mobility, on average, and that the clusters did not reform immediately on cooling. As such, the liquid fatty acid molecules were more mobile at a given temperature on cooling than they were at the same temperature on heating.

Figure 13. Apparent temperature, TA, of liquid (a) dodecanoic acid (Tfus = 43 °C) and (b) octanoic acid (Tfus = 17 °C) as a function of the actual temperature, T, on heating and on cooling. The fatty acids were held for 1 h at the maximum temperature before cooling. 28 ACS Paragon Plus Environment

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From the point of view of supercooling, a fatty acid that is melted and heated to temperatures below the threshold temperature crystallizes with minimal supercooling (~ 2 K for dodecanoic acid). However, when a fatty acid has been melted and heated above its threshold temperature for supercooling, on cooling the dielectric response behaves as though it were at a higher temperature than the actual temperature. Thus, when the fatty acid reaches the normal crystallization temperature (T = Tcryst), it could still have mobility and ordering similar to a higher-temperature or less-supercooled liquid, and further supercooling could be required to bring TA = Tcryst.

4. CONCLUSIONS Saturated fatty acids are promising PCMs; in general, they require only minor supercooling for nucleation of the crystalline phase. However, fatty acids can be made to supercool more extensively by heating above a fatty acid-dependent supercooling threshold temperature. Such knowledge is essential to avoid unintended supercooling of a fatty acid phase change material, as supercooling could prevent it from releasing stored thermal energy. We propose that the observed onset of supercooling is due to a change in the ordering of fatty acid molecules within the liquid phase, and specifically the loss on heating of dynamic molecular clusters. Our conclusion is based on NMR and dielectric results. NMR T1 experiments showed that, on average, the alkyl chains of fatty acid molecules in the liquid phase became more mobile as temperature was increased, with a change in temperature derivative of T1 at the supercooling threshold temperature, indicating even more mobility. We postulate that the additional mobility arises from the breakup of molecular clusters



that restricted the motion of their contained molecules, as thermal hysteresis onset in T1 corresponds to the thermal hysteresis onset in crystallization. Through variable-temperature measurements of the real portion of the dielectric constant we showed that the dielectric response of the fatty acids heated above their supercooling threshold temperature behaves on cooling as though they are at a higher temperature than the actual temperature. Again, above the supercooling threshold temperature, the mobility of molecules in the liquid phase at a given temperature was higher on cooling than at the same temperature on heating. We attribute the hysteretic increase in the mobility of the fatty acid molecules to the loss on heating of fatty acid clusters that restrict mobility, with little cluster reformation on cooling. The detailed nature of the clusters and their role in crystallization of fatty acids are yet to be discerned. The present evidence links the presence of clusters to the formation of critical nuclei for crystallization, and hence shows their important role in determining the phase behavior of liquid fatty acids.

Supporting Information Supporting Information includes thermal cycling results for tridecanoic acid and hexadecanoic acid, dielectric constant results for octanoic acid and selected NMR spectra from the T1 experiments.

Acknowledgements J. A. N. acknowledges funding from Dalhousie Research in Energy, Advanced Materials and Sustainability (DREAMS), an NSERC CREATE program, and an NSERC CGS-D scholarship. M. A. W., J. R. de B. and L. K. acknowledge support from NSERC of Canada and the Canada Foundation for 30 ACS Paragon Plus Environment

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Innovation. M. A. W. also acknowledges support from the Clean Technologies Research Institute at Dalhousie University. The authors thank Dr. Mike Lumsden and NMR-3 at Dalhousie University for assistance with the NMR experiments.

References Cited: 1 Noël,

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Iwahashi, M.; Kasahara, Y.; Minami, H.; Matsuzawa, H.; Suzuki, M.; Ozaki, Y. Molecular behaviors of n-fatty acids in liquid state. J. Oleo Sci. 2002, 51, 157-164. 19 Morrow, R. M. The diffraction of x-rays in liquid normal monobasic fatty acids. Phys. Rev. 1928, 31, 10-15. 20 Stewart, G .W.; Morrow, R. M. Molecular space array in liquid primary normal alcohols. Proc. Nat. Acad. Sci. 1927, 13, 222-223. 21 Iwahashi, M.; Kasahara, Y. Dynamic molecular movements and aggregation structures of lipids in a liquid state. Curr. Opin. Colloid Interf. Sci. 2011, 16, 359-366. 22 Iwahashi, M.; Yamaguchi, Y.; Kato, T.; Horiuchi, T.; Sakurai, I.; Suzuki, M. Temperature dependence of molecular conformation and liquid structure of cis-9-octadecenoic acid. J. Phys. Chem. 1991, 95, 445451. 23 Iwahashi, M.; Kasahara, Y.; Matsuzawa, H.; Yagi, K.; Nomura, K.; Terauchi, H.; Ozaki, Y.; Suzuki, M. Self-diffusion, dynamical molecular conformation, and liquid structures of n-saturated and unsaturated fatty acids. J. Phys. Chem. B 2000, 104, 6186-6194. 24 Yoshimoto, N.; Sato, K. Preheating effects of melt on nucleation and growth of oleic acid polymorphs. Jpn. J. Appl. Phys. 1994, 33, 2746-2749. 25 Whitman, C. A.; Mysyk, R.; White, M. A. Investigation of factors affecting crystallization of cyclopentane clathrate hydrate. J. Chem. Phys. 2008, 129, 174502. 26 Boistelle R. Fundamentals of nucleation and crystal growth. In Crystallization and polymorphism of fats and fatty acids; Garti, N.; Sato. K. Eds.; Marcel Dekker, Inc.: New York, 1988. 27 Balci, M. Basic 1H- and 13C-NMR spectroscopy; Elsevier: Amsterdam, 2005. 28 Dealy, J.; Plazek, J. Time-temperature superposition – a users guide. Rheol. Bull. 2009, 78, 16-31. 18


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TOC Graphic: 160

Apparent Temperature / °C

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Cooling

120

80

Heating

40 40

60

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140

Temperature / °C


Supercooling and Nucleation of Fatty Acids: Influence of Thermal

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