Interpreting freezing point depression of stearic acid and methyl stearate

Fluid Phase Equilibria 238 (2005) 149–156

Interpreting freezing point depression of stearic acid and methyl stearate M.J. Goff, G.J. Suppes ∗ , M.A. Dasari Department of Chemical Engineering, The University of Missouri-Columbia, Columbia, MO 65211, USA Received 30 September 2004; received in revised form 12 September 2005; accepted 13 September 2005 Available online 2 November 2005

Abstract Freezing point depressions of binary systems including either stearic acid (SA) or methyl stearate (MES) were evaluated based on differential scanning calorimetry melting scans. The second binary component included a solvent from the group acetic acid, acetone, 2-butanone, and hexane. Vapor pressure as a function of liquid composition and temperature was used to measure vapor/liquid equilibrium. Activity coefficients were calculated from this data and models fit to the data to determine how well the models fit the solid–liquid equilibrium models. The Gibbs/Duhem equation and polymorphism of the melt transitions indicated that freezing point depressions were due to a combination of: (1) a reduction of activity of the triglyceride derivative in solution albeit with activity coefficients > 1.0, (2) incorporation of the solvent into the solid matrix for at least some of the mixtures, and (3) substantially different physical properties between the solid and liquid phases of the SA and MES. Different melting phenomena were observed in differential scanning calorimetry (DSC) scans depending upon the heteroatom functionality of the solvent. The empirical Margules, NRTL, and Wilson activity coefficient models fit data for the solvent activity coefficients well, while the UNIQUAC model combined with the predictive abilities of UNIFAC could not accurately predict activity coefficients. Despite questions on the fundamental interpretation of the data, modeling the activity coefficients for the solvent is sufficient to approximate the effect the solvent will have on the melting point depression. Relatively simple experiments following the total pressure of mixtures as a function of composition and temperature can be used to obtain activity coefficient model parameters for the Margules, NRTL, UNIQUAC, and Wilson. © 2005 Elsevier B.V. All rights reserved. Keywords: Activity coefficient modeling; Crystallization; Fatty acid esters; Fatty acids; Freezing point depression; Phase change; Phase change materials; Phase equilibria

1. Introduction The ability to predict solid–liquid equilibrium data is extremely important when designing crystallizers and understanding fluid properties. Solid–liquid equilibrium (SLE) data is scarce, and accurate methods of predicting equilibrium are needed. Vapor–liquid equilibrium (VLE) data is readily available for a large number of binary systems. By correlating VLE data with activity coefficient models and using the correlations to predict solid–liquid equilibria (SLE), available VLE data can be used to compensate for the shortfall in SLE data. This paper evaluates the utility of activity coefficients obtained from VLE to predict SLE and the fundamental understanding of SLE of SA

∗

Corresponding author. E-mail address: [email protected] (G.J. Suppes).

0378-3812/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2005.09.018

and MES using solvents for freezing point depression. The performance of solvents on the freezing point depression of SA and MES is then compared to established freezing point depression theory. Freezing point depression of SA and MES in solvents is an important fundamental parameters in many areas of research and practical applications. The ability to accurately predict the effect of varying concentrations of solvents is needed to control cold flow properties of diesel fuels [1,2], vary the freezing points of mixtures for use as phase change materials, and for purifying substances both in the laboratory and in industry. For phase change materials it is important to know the correct amount of solvent required to achieve the desired freezing point depression. For solid–liquid separations using low concentrations of solvent, accurate knowledge of activity coefficients of the components can be used to develop separation schemes.

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Solid–liquid equilibrium systems are often characterized by high activity coefficients, the formation of new intermolecular compounds between two SA or two MES molecules, and components with significantly different molecular properties. The size and volume of the molecular species, whether they be SA or MES crystallizing as single molecules or as multiple molecules that form intermolecular compounds often differ significantly, resulting in large deviations from ideality. Due to this non-ideal behavior, data for predicting activity coefficients are necessary to reduce uncertainties in experimental design. The most convenient method for predicting activity coefficient data is to use physically or empirically derived models. Group contribution models such as UNIFAC and analytical solution of groups (ASOG) have been used to predict VLE and SLE for components of similar size [3–5]. Successful prediction of SLE from VLE for components containing similar groups and sizes has been accomplished by adjusting the interaction of the structural groups on the activity coefficient using the ASOG method [6,7]. The lack of a free volume contribution to the phase behavior of liquid mixtures has limited the success of these models for mixtures with significant size differences between components. The Wilson equation has been shown to model SLE when large differences in size are present and group contribution methods are inadequate [8–10]. SLE phase diagrams for a large number of binary systems other than those involving SA and MES have been constructed using a new method employing DSC [8,11]. Construction of SLE curves directly from DSC requires the mixture be immiscible in the solid phase. The SLE data obtained from the DSC can then be used to calculate the activity coefficient of the SA and MES. The Wilson and UNIFAC models have been used to adequately model SLE data obtained from DSC [12] while others have investigated the UNIFAC and DISQUAC models on fitting SLE [9,13,14]. A more detailed description of obtaining accurate SLE is given elsewhere [15]. 2. Experimental 2.1. Materials Stearic acid 99% Aldrich (St. Louis, MO), MES 99% Aldrich, acetone 99% Fisher, acetic acid glacial ACS grade 99.7% Fisher, 2-butanone certified reagent Fisher, and hexane were all 99% pure from Aldrich.

and response to the instrument. The samples were analyzed by twice cycling the sample from a temperature about 10 ◦ C above the melting point of the mixture to a temperature about 40 ◦ C below the melting point of the mixture. 2.2.2. Method of analysis A TA Instruments (New Castle, DE) Q100 Series DSC with TA5000 Advantage Software Suite provided transition temperatures and latent heats. The refrigerated cooling system provided cooling and a 50 mL/min nitrogen purge preserved sample quality. A Denver Instrument A-200DS balance was used to measure the mass of components added to the 5 mm diameter aluminum hermetic pans. Measured masses had standard deviations of 0.094 mg. 2.2.3. SA and MES activity coefficient procedure Results for the freezing point depression were analyzed using the melting onset temperature and extrapolating these results to a scan rate of zero. This procedure is described in more detail in a previous paper [16] and by others [9,17]. The effect of different scan rates on the melting point tangent line and how this can be extrapolated to a scan rate of 0 ◦ C/min is shown in Fig. 1. The extrapolated onset point was reported as the freezing point for purposes of discussion and modeling. This improves the accuracy for determination of the melting points of the samples. Activity coefficients were calculated using the classic freezing point depression Eq. (1) [18]: γi =

1 −Hmi (Tmi − T ) exp xi RTmi T

where Hmi is the molar heat of fusion of pure component i, Tmi , the absolute melting temperature of pure component i, T, the absolute melting temperature of the mixture, and xi is the mole fraction of component i. 2.2.4. Solvent activity coefficient procedure Activity coefficients for solvent were determined by placing 2 mL samples into 2 mL brass capped tubes fitted with a Hamilton pressure gauge capable of reading pressure to the nearest 1.4 kPa (0.2 psi). The pressure gauge apparatus was placed into a pre-heated Fisher Isotemp® muffle furnace. Samples were left

2.2. Methods 2.2.1. DSC procedure Samples were prepared by mixing components 1 and 2 at the desired concentration and sealing them in vials. The vials were then placed in the oven to melt the sample and shaken to ensure adequate mixing of the mixture. Vial contents were then allowed to cool completely before opening the vial to limit the amount of solvent lost by evaporation. Samples were weighed into aluminum hermetic DSC pans and hermetically sealed to prevent solvent from evaporating during the analysis. Samples of ∼5 mg provided an optimal combination of mass accuracy

(1)

Fig. 1. Effect of different scan rates on the melting tangent point.

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in the oven for 1 h to allow the temperature inside the pressure gauge apparatus to reach equilibrium. Each composition was prepared at least twice and the average vapor pressure used to calculate the activity coefficient. At least 10 samples were prepared at mole compositions of less than 10 mol% solvent to obtain more data at near infinite solvent dilution. Pressure readings were taken at two temperatures for each sample. Samples with acetic acid, 2-butanone, and hexane were taken at 120 and 140 ◦ C while samples with acetone were taken at 100 and 120 ◦ C. Activity coefficients were determined assuming activity coefficients of one for MES and SA. This assumption provides for accurate estimates because all the vapor pressure data were collected at high concentrations of MES and SA, where the activity coefficients approximate one and because the vapor pressure of MES and SA are over two orders of magnitude less than solvent. Vapor pressures were calculated from the total pressure reading, allowing for calculation of solvent activity coefficients. Standard deviations for the activity coefficients are about 0.1. 2.2.5. Activity coefficient modeling Experimental activity coefficients obtained from freezing point depression and vapor pressure data were regressed using the Margules, NRTL, Wilson, and UNIQUAC models [19]. The Margules, NRTL, and Wilson were regressed in Excel through a least-square algorithm, while UNIQUAC was regressed using UNIFAC in ChemCad version 5.3.1. 3. Results and discussion Activity coefficients for SA and MES were calculated from the SLE results obtained by DSC. Solvent activity coefficients were calculated from VLE obtained through vapor pressure data. The activity coefficient data were fit to the Margules, NRTL, UNIQUAC, and Wilson activity coefficient models. The models were then used to predict the activity coefficients of the components to construct SLE curves. SLE and VLE binary mixtures of SA and MES methyl stearate and stearic acid (component 1) with solvents acetic acid, acetone, 2-butanone, and hexane were evaluated. All solvents led to freezing point depression. For the more volatile solvents, it took considerable experimental procedure development to prevent the solvent from evaporating from the small sample sizes prior to measurement of the freezing point depression. DSC pans and lids were tared on the balance together, the fatty acid deriva-

151

Fig. 2. Activity coefficients of SA and MES (component 1) in solvent at the melting point of the mixture.

tive and solvent mixture were added to the sample pan, and the lid immediately placed on top of the sample pan to prevent any evaporative loss during the weighing process. 3.1. Activity of MES and SA Activity coefficients for SA and MES at different compositions are provided in Fig. 2. The activity coefficients of SA and MES increase with decreasing compositions of the other component, as expected. Activity coefficients increase at about the same rate for both SA and MES, and the activity coefficients for SA are consistently higher than those for MES in the same solvent. Activity coefficients for SA and MES at infinite dilution and at a composition of 50 mol% are provided in Table 1. The data at 50 mol% were calculated from DSC measurements, and the infinite dilution values were extrapolated from experimental data using the model that had the best fit with the data. These data suggest that the carboxylic acid group of SA lead to greater positive deviations from ideal behavior for the solvents of this study. 3.2. Activity of solvents Activity coefficients for the solvents at infinite dilution (extrapolated values from Wilson equation) and at a composition of 50 mol% are provided in Table 1. Table 2 contains the complete set of activity coefficient as calculated from VLE experimental data.

Table 1 Freezing depression for 50 mol% SA and MES (component 1) and activity coefficients Component 1

Component 2

x1 Mole fraction

x1 Volume fraction

Freezing depression T (◦ C)

γ1∞

γ2∞

γ10.5

γ20.5

MES

Acetic acid Acetone 2-Butanone Hexane

0.50 0.51 0.50 0.50

0.87 0.83 0.83 0.73

12.47 7.85 10.54 10.28

1.69 1.47 1.47 1.84

4.94 1.65 2.43 2.63

0.70 1.03 0.90 0.93

1.06 1.00 1.07 1.09

SA

Acetic acid Acetone 2-Butanone Hexane

0.50 0.50 0.50 0.50

0.85 0.82 0.77 0.70

12.24 6.35 8.96 9.02

1.84 1.36 1.79 1.82

4.36 2.14 2.58 2.64

0.84 1.25 1.11 1.10

1.06 1.01 1.07 1.07

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Table 2 Activity coefficient data of solvents (component 2) at 120 ◦ C for acetone systems and 140 ◦ C for all others MES/acetic acid

MES/acetone

x1 (mol)

γ2

0.00 0.05 0.05 0.12 0.23 0.44 0.80 0.82 0.94 0.95 0.97

1.00 1.06 1.06 1.11 1.17 1.18 1.79 1.97 3.67 4.02 3.83

SA/acetic acid

MES/2-butanone

x1 (mol)

γ2

0.00 0.44 0.43 0.86 0.90 0.90 0.91 0.93 0.95 0.95

1.00 1.00 1.08 1.23 1.26 1.28 1.30 1.27 1.26 1.21

SA/acetone

MES/hexane

x1 (mol)

γ2

x1 (mol%)

γ2

0.00 0.30 0.53 0.53 0.80 0.84 0.90 0.94 0.95 0.95 0.97

1.00 1.02 1.16 1.04 1.62 1.80 1.86 1.81 1.89 1.90 2.10

0.00 0.58 0.64 0.70 0.76 0.80 0.84 0.93 0.94 0.94 0.95 0.96

1.00 1.01 1.07 1.14 1.22 1.32 1.44 1.51 1.60 1.97 2.88 2.81

SA/2-butanone

SA/hexane

x1 (mol)

γ2

x1 (mol)

γ2

x1 (mol)

γ2

x1 (mol)

γ2

0.00 0.16 0.33 0.58 0.85 0.85 0.88 0.89 0.92 0.93 0.94 0.95

1.00 1.04 1.11 1.26 1.45 1.48 2.35 2.21 3.60 3.19 3.78 3.16

0.00 0.21 0.45 0.75 0.81 0.85 0.91 0.91 0.94 0.95 0.97 0.99

1.00 1.09 1.16 1.22 1.19 1.30 1.33 1.57 1.65 1.48 1.87 1.98

0.00 0.54 0.70 0.88 0.89 0.93 0.93 0.93 0.95 0.95

1.00 1.00 1.01 1.03 1.26 1.33 1.55 1.62 2.36 1.69

0.00 0.59 0.85 0.89 0.91 0.92 0.93 0.95 0.95 0.96 0.98 0.99

1.00 1.01 1.97 2.28 2.27 2.01 2.08 2.10 2.36 2.42 2.91 3.06

The dipole moments of the solvents are: hexane = 0, acetic acid = 1.7, acetone = 2.88, and 2-butanone = 2.78 Debye [20]. Stearic acid has a dipole moment of 1.76 Debye, while the value for MES is based on extrapolated values from lower molecular weight fatty acids and methyl esters (e.g. hexanoic acid at 1.13 Debye and methyl hexanoate at 1.7 Debye), the dipole moment of MES is about 1.99 Debye. The dipole moment of MES is closer to that of acetic acid and acetone, which explains the lower activity coefficients of these solvents in the MES binaries relative to the SA binaries. The dipole moment of stearic acid is smaller than that of MES and therefore closer to that of hexane and explains the lower activity coefficient of SA in hexane compared with MES in hexane. The high activity coefficients of acetic acid in the SA and MES is not fully understood, but could be caused by the fact that acetic acid has a greater density than the other solvents. Also, the impact of local compositions is believed to impact the data. Stearic acid and MES are known to crystallize with their polar groups aligned, so if the solvent molecules are preferentially attracted to the polar groups, greater localized solvent concentrations different from the bulk concentration will impact the SLE data. Acetic acid showed the highest activity coefficients of all the solvents with infinite dilution activity coefficients in excess of 4. However, even at 50 mol%, the activity coefficients of acetic acid were about 1.2 for both systems. This relatively low activity coefficient could be explained by the like–like interactions of acetic acid next to the carboxylate group (or methyl

ester group) of the SA and MES. At higher concentrations of acetic acid, the like-dislike interactions of the acid group with the aliphatic tails of the SA and MES leads to much higher activity coefficients. The large size and complexity of the SA and MES leads to interactions that tend to be a strong function of composition. 3.3. Activity coefficient modeling Binary interaction parameters were calculated for the Margules, NRTL, and Wilson models based on the activity coefficients obtained from VLE data and are summarized in Table 3. Experimental solvent activity coefficient data used for model fitting are summarized in Table 2. Fig. 3 shows the four models fit to the SA/acetone system and represents the fit obtained for the other seven binary pairs. The models fit the data for the activity coefficients of solvent well, but could not accurately model the activity coefficients for SA and MES. UNIQUAC regression using ChemCad tended to underestimate the activity coefficient of both components, giving activity coefficients less than one. UNIQUAC has difficulties modeling the phase behavior of two components with such large differences in size and physical properties using group contribution methods. One of the greatest limitations is caused by the difference in polarity for SA and MES between the solid and liquid phases. Stearic acid [21] and methyl stearate [22] crystallize as dimers by

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Table 3 Model parameters Model Margules A12 A21

MES/acetic acid 0.83 1.49

Wilson λ12 λ21

5032 476

NRTL δg12 δg21 α12

4461 1084 0.70

Model Margules A12 A21

MES/acetone 0.26 0.34

0.39 0.86

2100 1900

SA/acetic acid 0.73 1.24

MES/2-butanone

673 447 1.20 SA/acetone

MES/hexane 0.46 0.80

3058 311

3329 215

2643 437 0.55

2719 874 1.47

SA/2-butanone

0.54 0.63

0.61 0.89

SA/hexane 1.10 1.00

Wilson λ12 λ21

3974 2041

2537 1628

3034 503

2748 1797

NRTL δg12 δg21 α12

4258 1394 1.36

2106 935 2.3

2778 602 1.32

3058 1483 0.92

forming hydrogen bonds in the case of stearic acid and the interaction of the polar ester groups in methyl stearate. This makes the molecules larger in the solid-state, resulting in decreased polarity for the dimers because the polar groups are protected by the long aliphatic chain of the fatty acid. A small molecule such as acetic acid can disrupt the crystallization process more than a larger molecule. Such a large difference in apparent size and polarity of the molecules between the solid and liquid states accounts for the discrepancy when attempting to model activity coefficients. Activity coefficients of SA and MES are close to one, except at near infinite dilutions where they increase slightly. This poses a problem when modeling because these commonly used models are not effective at fitting data with high activity coefficients for one component with an activity coefficient near one for the other component over most of the composition range. This is due to the

Fig. 3. Modeling of activity coefficient data for SA/acetone system at 140 ◦ C.

mathematical limitations of the models and does not allow these models to fit data with great differences in activity coefficients. To better understand the difficulties encountered in modeling the data the thermodynamic consistency of the data was evaluated using the Gibbs/Duhem equation. For a binary system the Gibbs/Duhem equation reduces to x1

d ln γ1 d ln γ2 + x2 =0 dx1 dx1

Rearranging the equation yields: d ln γ2 x1 d ln γ1 =− dx1 x2 dx1 The slope of the ln γ 1 curve at every composition is of opposite sign to the slope of the ln γ 2 curve. For the case when two components are present in equal amounts, the slopes of the two curves will have the same slope, but opposite sign. This explains why the models have a difficult time fitting data from binary mixtures when one component has high activity coefficients and the other component has relatively low activity coefficients close to one. The inability of the activity coefficient models to accurately fit SA and MES data does not adversely impact the predicted SLE, and will be discussed later. For these binary systems, the Gibbs/Duhem equation will not allow the activity coefficient of both components to simultaneously decrease or increase. This creates a modeling problem when a SA and MES has an activity coefficient < 1.0 over some composition range while the solvent always has an activity coefficient > 1.0. Further discussion on this topic is provided after a discussion of the solid–liquid equilibrium and the certainty of the activity coefficients obtained from that data.

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154

Fig. 4. Freezing point depression of 85 wt.% SA in solvent.

between the solid and liquid phases, and large differences in size that result in localized concentration of the polar solvents near the polar end of the SA and MES. It is this complex behavior of the solid phase that makes interpretation of the data difficult and makes interpretation of the Gibbs/Duhem equation less than straight forward. The actual activity coefficients (as opposed to those calculated from freezing point depression) are believed to be consistent with the Gibbs/Duhem equation. At least part of the freezing point depressions reported in Table 1 are due to a modification of the solid structure due to incorporation of the solvent into the solid matrix (as evidenced by the different shapes of the DSC peaks of Fig. 4). In the calculation of the activity coefficients of Fig. 2, the freezing point depression was incorrectly interpreted as a solution phenomenon when it was actually a solid-state phenomenon.

3.4. Freezing point depression

3.5. SLE phase diagrams

All of the solvents depressed the freezing points of SA and MES. The melting point is interpreted as the intercept of the inflection tangent with the base line. For example, the freezing point of stearic acid is 66.98 ◦ C. Table 1 summarizes the freezing point depressions for 50 mol% SA and MES in solvent. The greatest impact on freezing point depression was observed for solvents in MES. Fig. 4 shows the effect of different solvents on the decrease in melting point for SA. Acetone caused the least freezing point depression while maintaining the sharpest DSC peak. Solvents with the greatest impact on freezing point depression tended to broaden the DSC peak the most. Acetic acid caused the greatest freezing point depression as well as broadening of the endotherm peak. The two endotherms (two peaks) for the acetic acid system of Fig. 4 provide evidence that acetic acid is interacting directly with the acid group in the solid matrix. Different crystalline structures of the heteroatom groups in a TG derivative are typically a source of polymorphism. Sato has measure three polymorphs and two polytypes for stearic acid in n-hexane, with the least soluble form being favored at temperatures above 23 ◦ C [23]. This explains why only one endotherm is present when hexane is used as the solvent. Methyl stearate is also known to be polymorphous with the transition temperatures being so close together that it is nearly impossible to distinguish the two from each other using a DSC [24]. The DSC scans highlight an important aspect of SLE for large molecules; namely, complex molecules can undergo polymorphism with different parts of the large molecule responding differently to changing environments (e.g. a changing solvent matrix). While the SA and MES–solvent systems are binary systems, certain aspects of the phase behavior are more consistent with a ternary systems. Specifically, the ability of a solvent to interact differently with the heteroatom groups of the SA and MES as compared to the aliphatic chain. In these systems, VLE (especially the smaller molecules) tends to behave like a binary system. However, the SLE (especially the larger molecule solid phases) tends to behave like ternary systems due to polymorphism, differences in polarity

VLE data were obtained and modeled for binary systems to determine if these systems follow freezing point depression theory (Eq. (1)) and to better understand how VLE data can be used to predict freezing point depression. Fig. 5 summarizes the SLE for the SA/acetone system. The model curves of Fig. 5 are constructed using activity coefficients obtained from their respective model. Standard deviations for the temperature in the T–x diagram arising from errors in activity coefficient measurements are about 0.5 ◦ C. At a standard deviation of ±0.21 ◦ C for DSC measurements, the data have a standard deviation far less than their variance from the model prediction. The UNIQUAC model fits the solid–liquid equilibrium data very well, however, the activity coefficients predicted by the model are not physically possible, as there should be no maximum or minimum in the activity coefficient curves. UNIQUAC did not predict the correct solid–liquid equilibrium for the other binary systems, and provided a prediction between those of the ideal prediction that of the other three models (Margules, NRTL, and Wilson). Use of the Margules, NRTL, and Wilson activity coefficient models improved accuracy of SLE calculations over ideal behavior. The UNIQUAC model predicts activity coefficients less than one, predicting that the temperature at which pure SA and MES

Fig. 5. Solid–liquid equilibrium predicted and experimental values for SA/acetone.

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4. Conclusion

Fig. 6. Mixture of 70 wt.% MES/citric acid.

begins to freeze out of solution is less than that predicted for the ideal case. The experimental data and models are above the temperature predicted using ideal freezing point depression theory because the activity coefficients are greater than unity. For mixtures containing more than about 5 mol% SA and MES, corresponding to the eutectic composition, freezing point depression is only influenced by the activity coefficient of SA and MES. As long as the concentration range of interest is with a mole concentration of more than this composition, it is only necessary to obtain activity coefficients of the SA and MES. Therefore, increases in the activity coefficients of SA and MES increase the freezing point and the activity coefficient of the solvent does not directly impact the freezing point. Mixtures composed of components with similar functional groups have lower activity coefficients (in this case, close to 1) and provide the greatest freezing point depression.

Freezing point depression can be achieved by mixing solvents with SA and MES. DSC of the melt transition indicates that the freezing point depression is due in part to incorporation of the solvent into the solid matrix leading to a solid that has a lower freezing point. The activity coefficients of the SA and MES in solution are greater than 1.0, and it can be difficult to achieve significant freezing point depression without selecting solvents that actually modify the solid crystalline structure. This is especially the case for mixtures with larger molecules where substantial similarity in molecular structure is needed to provide freezing point depression. The Margules, NRTL, and Wilson activity coefficient models fit data for the solvent activity coefficients well, while the UNIQUAC model could not accurately predict activity coefficients. Because of the difficulty of distinguishing between “solution” and “solid-state” phenomena for mixtures with SA and MES, activity coefficients calculated from depressions in freezing points may readily be lower than the actually activity coefficients of the SA and MES in solution. Inaccuracies in the calculation of the activity coefficients can lead to erroneous interpretations that the Gibbs/Duhem equation is being violated. Despite questions on the fundamental interpretation of the data, modeling the activity coefficients for the solvent is sufficient to approximate the effect the solvent will have on the depression. Relatively simple experiments following the total pressure of mixtures as a function of composition and temperature can be used to obtain activity coefficient model parameters. References

3.6. Mixtures with larger molecules The DSC of Fig. 6 summarizes the solid–liquid transition for a mixture of 70 wt.% MES and citric acid as compared to these pure components. Whereas all the solvents provides a freezing point depression, this mixture of two larger molecules provided no freezing point depression. This behavior is consistent with a mechanism of freezing point depression for SA and MES where localized interaction of a small molecule on a TG derivative leads to a substantially different SLE transition. Two larger molecules are less susceptible to this type of behavior and thus have a greater tendency to have substantially separate freezing phenomenon. 3.7. Application of freezing point depression Modeling of activity coefficient data provides insight into trends and can be used as an effective tool to screen possible solvents for use in determining the solvent and quantity required to obtain a certain freezing point depression. This allows a single SA and MES to meet a range of PCM temperature requirements, and more importantly, the amount of solvent required to achieve the desired operating temperature.

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