Separation and Solubility of Cis and Trans Isomers ... - ACS Publications

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Separation and Solubility of Cis and Trans Isomers in Nanostructured Double-Decker Silsequioxanes Beth W. Schoen, Carl T. Lira, and Andre Lee* Department of Chemical Engineering and Materials Science, Michigan State University, Room 2527 Engineering Building, 428 South Shawn Lane, East Lansing, Michigan 48824, United States

ABSTRACT: A fractional crystallization method was used to separate the cis and trans isomers of three double-decker silsesquioxanes (DDSQs) with an aminophenyl moiety in a THF + hexanes solvent mixture. The experimental solubilities were fitted to the Schröder−van Laar equation with activity coefficients determined using the NRTL model by adjusting the binary interaction parameters. The ability to separate these cis and trans isomers was affected by the regioisomer (m- or p-aminophenyl) and the R moiety (cyclohexyl or methyl) coupled via silicon. For a given DDSQ compound, the variances between the solubilities of the cis and trans isomers depend on differences in thermal properties (Schröder−van Laar). Cis isomers were 33 times more soluble than trans isomers for p-aminophenyl (R = methyl) and 22 times more soluble for the analogous m-aminophenyl in a solution of THF and hexanes. For a more sterically hindered m-aminophenyl (R = cyclohexyl), the cis isomers were only 3.5 times more soluble, and the overall solubility was also the lowest. The magnitude of the binary interaction between DDSQ and nonsolvent (hexanes) was used to explain how quickly the solubility decreased as hexanes were added. The solubilities of the two m-aminophenyl structures decreased at similar rates, while the solubility of the p-aminophenyl structure decreased at a much lower rate since the magnitude of the binary interaction between p-aminophenyl and hexanes is smaller.

1. INTRODUCTION

DDSQs with various reactive chemical moieties have been prepared, and their cis and trans isomers have been partially isolated.31,32 Recently our group has identified cis and trans isomers using 1H NMR spectroscopy, and thus, the ratio of cis and trans isomers of compounds A, B, and C can now be accurately quantified.33 This allows for verification of purity and the development of a model representing the quantitative measurements and parameters needed for fractional crystallization of these isomers. Furthermore, it provides an opportunity to understand how these configurations influence the structure−property relationships of these DDSQs. Fractional crystallization provides a platform for larger quantities of material to be separated into fewer fractions compared with other methods such as chromatography.34−36 Furthermore, fractional crystallization provides a much lower energy demand as opposed to an energy-intensive thermal separation method such as distillation. Hence, it is accepted as

A recently developed class of nanostructured silsesquioxanes provides a unique opportunity to investigate and characterize the influence of cis and trans configurations on the physical and chemical properties of an inorganic−organic hybrid material (Figure 1). The cis and trans descriptors characterize the orientation of the X and R moieties with respect to the Si−O core of the silsesquioxane. This class of silsesquioxanes are formally known as double-decker silsesquioxanes (DDSQs) because they are composed of two “decks” of silsesquioxanes stacked on top of one another, forming a cagelike structure.1 Prior to the advent of DDSQs, the majority of cagelike silsesquioxanes did not incorporate cis and trans isomers.2−5 Of the few cagelike silsesquioxanes that did incorporate geometric isomers, none have been synthesized in large quantities.6,7 Cagelike silsesquioxanes have demonstrated superior properties over their organic counterparts in areas such as thermal and mechanical properties,8−11 solubility,12−14 flame retardance,15−23 oxidative resistance,24−27 and dielectric properties.28−30 © 2014 American Chemical Society

Received: November 25, 2013 Accepted: March 25, 2014 Published: April 4, 2014 1483

dx.doi.org/10.1021/je4010245 | J. Chem. Eng. Data 2014, 59, 1483−1493

Journal of Chemical & Engineering Data

Article

Additionally, the X moiety was changed from m-aminophenyl to p-aminophenyl while the R moiety was methyl.

2. MATERIALS AND METHODS 2.1. Solvents and Reagents. Tricyclo[7.3.3(3,7)]octasiloxane-5,11,14,17-tetraol-1,3,5,7,9,11, 14,17-octaphenyl (Ph8tetrasilanol-POSS) was obtained from Hybrid Plastics (Hattiesburg, MS). Tetrahydrofuran (THF), hexanes, diethyl ether, magnesium turnings, triethylamine, trichloromethylsilane, cyclohexyltrichlorosilane, 3-[bis(trimethylsilyl)amino]phenylmagnesium chloride, and 4-[bis(trimethylsilyl)amino]phenylmagnesium bromide were obtained from Sigma-Aldrich when used for synthetic procedures and solvent separations. Triethylamine was obtained from J.T.Baker Chemicals (Pleasant Prairie, WI) when used for column chromatography. Dichloromethane was obtained from Macron Chemicals (Nashville, TN). The solvents were distilled under nitrogen and degassed using freeze−pump−thaw methods for synthetic procedures and employed without further processing when used for separation studies. SiliaFlash P60 silica gel was purchased from SiliCycle UltraPure Silica Gels (Quebec City, Quebec, Canada). Silica gel 60 F254 (0.2 mm thick, SigmaAldrich) precoated plastic plates were used for thin-layer chromatography (TLC). 2.2. Synthesis. The three structures studied in this work and the notation is described herein. The DDSQs are abbreviated as DDSQ(X)(R), where X and R are the organic moieties attached to the D-group silicon atoms (silicon atoms bonded to two oxygen atoms; Figure 1).38 The first set of cis and trans isomers, [(m-aminophenyl)methylsilyl]-bridged octaphenyl-DDSQ, is designated as DDSQ(m-AP)(Me) and represented by the shorthand notation A (Figure 2a). The second set of isomers, [(m-aminophenyl)cyclohexylsilyl]-

Figure 1. (top) Trans and (bottom) cis isomers of DDSQ(X)(R).

an appropriate economic approach for an industrial scale.37 A fractional crystallization method involving the variation of solvent polarity was used to separate the cis and trans isomers of compounds A, B, and C. For the precipitates, molar ratios of the individual isomers were obtained using 1H NMR data.33 The experimental solubility results were modeled using the nonrandom two-liquid (NRTL) activity coefficient method. Activity coefficients, thermodynamic properties, and structural characteristics all contributed to the solubility model for the solution of mixed isomers. In this work, solubility, separation, and chemical properties were studied for isomers of three different DDSQ molecules. The R moiety was varied from methyl to cyclohexyl while the X moiety was m-aminophenyl.

Figure 2. (left) Trans and (right) cis isomers of compounds (a) A, (b) B, and (c) C. 1484



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Scheme 1. Synthesis of Compounds A, B, and Ca

a

Y = Br or Cl; R = Me or Cy; X = p- or m-aminophenyl.

Figure 3. Flowchart describing the fractional crystallization/isomer separation procedure for the trans and cis isomers of compounds A, B, and C.

structures A, B, and C was studied individually. The solvent polarity was varied by changing the ratio of solvent (THF) to “nonsolvent” (hexanes) using the procedure outlined in Figure 3. The purities of the individual isomers were confirmed using 1 H NMR and differential scanning calorimetry (DSC) data. A typical example of the separation procedure for compounds A, B, and C is as follows: solid DDSQ for one of the variants A, B, and C [varying between 0.1 g and 1.1 g (0.077 mmol and 0.81 mmol)] was placed in a round-bottom flask. The ratio of isomers in the initial sample varied. Minimal THF was added to the flask at 25 °C until the solid completely dissolved. Hexanes

bridged octaphenyl-DDSQ, is designated as DDSQ(m-AP)(Cy) and represented by shorthand notation B (Figure 2b), and the third set, [(p-aminophenyl)methylsilyl]-bridged octaphenyl-DDSQ, is designated as DDSQ(p-AP)(Me) and represented by the shorthand notation C (Figure 2c). All of the compounds were synthesized by capping the DDSQ tetrasilanol with dichlorosilanes (Scheme 1). Details of synthetic procedures were based on the literature.32,39 These procedures generated mixtures of cis and trans isomers. 2.3. Separation. A fractional crystallization method was used to separate the cis and trans isomers. Each of the 1485



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equilibrated at 40 °C for 60 s and subsequently heated to 350 °C at a constant heating rate of 10 °C/min. 2.6. Modeling. The solubilities measured in these experiments were modeled by the Schröder−van Laar equation (eq 1):41,42

were added dropwise until a white suspension persisted. The precipitate (designated ppt1) was isolated by filtration and dried under a stream of nitrogen. The first precipitate, ppt1, was usually predominantly the trans isomer, since that isomer is less soluble. Depending on the initial cis:trans ratio and the solvent ratio, some cis isomer can be present. Within this filtrate, the trans isomer was at the solubility limit, but the cis isomer was not always at the solubility limit. The filtrate solvent mixture of THF and hexanes was removed under vacuum, leaving a solid cake (designated ppt2). For collection of this precipitate, hexanes were added to create a pourable suspension. The solid (ppt2) was collected by filtration and dried under a stream of nitrogen. In general, the average recovery of total material in all experiments was greater than 90 % for all three compounds. By material balance, the quantities of DDSQ and solvent in the supernatant of the first precipitation were the compositions used in solubility modeling. Cases where the cis isomer was below the solubility limit are noted below. 2.4. Chromatographic Purification. The thermal properties of the pure isomers of A, B, and C were important in modeling the saturation curves. In order to obtain accurate values, the highest feasible purity of each isomer was desired. The solid trans isomer can be isolated easily by selectively precipitating the trans isomer while maintaining a solution undersaturated in the cis isomer. However, the cis isomer is more difficult to isolate in high purity by precipitation. Hence, chromatography columns were utilized to further purify the cis isomers from selected ppt2 solids (mixtures with high cis fractions). Flash silica gel chromatography was performed using SiliaFlash P60 silica gel with particle sizes of 0.043 mm to 0.063 mm (230 mesh to 400 mesh) at room temperature. The column had a length of 203 mm and a diameter of 31.8 mm. The column was packed according to methods described by Still et al.40 To prevent loss of the stationary phase through the bottom, the column was plugged with cotton. Silica gel was packed approximately three-quarters of the total length of the column. A thin layer of sand (approximately 6.35 mm) was positioned above and below the silica gel in order to provide an even base for the stationary phase and prevent concentration and streaking of the bands as they came off the column and were collected. Solid DDSQ (0.2 g to 1.0 g) was dissolved in minimal dichloromethane and loaded on the top of the column bed. The mobile phase was 1 % triethylamine in dichloromethane. Silica gel 60 F254 (0.2 mm thick) precoated plastic plates were used for TLC, and spots were visualized by dipping the plates in dichloromethane and viewing them under shortwave ultraviolet light. 2.5. Characterization. 2.5.1. NMR Spectroscopy. 1H NMR spectra of compounds A, B, and C were measured at 25 °C on a Varian UNITY Inova 600 spectrometer equipped with a 5 mm pulsed field gradient (PFG) switchable broadband probe and operating at 599.80 MHz. The 1H NMR data were acquired using a recycle delay of at least 20 and 32 scans to ensure accurate integration. The 1H chemical shifts were referenced to that of residual protonated solvent in CDCl3 (7.24 ppm). 2.5.2. Differential Scanning Calorimetry. The melting behavior was studied using a TA Instruments Q2000 differential scanning calorimeter equipped with a mechanical cooling system under a nitrogen atmosphere. Samples were placed in a Q-zero aluminum pan and sealed with a lid to evaluate the cis and trans isomers. Samples were first

ln(xiγi) = −

ΔHm ⎡ T ⎤ ⎥ ⎢1 − RT ⎣ Tm ⎦

(1)

where xi is the mole fraction of isomer i that remains in the saturated solution at a given temperature (T = room temperature in this work), Tm and ΔHm are the temperature and enthalpy of its melting transition, respectively, and R is the universal gas constant. The activity coefficient γi quantifies deviations from an ideal solution (γi = 1).43 For a given temperature, the solution of eq 1 [i.e., the righthand side (RHS)] is a constant that depends only on the Tm and ΔHm of the pure substance. The left-hand side of eq 1 is associated with the mole fraction of the substance soluble in the given solvent system and its activity coefficient. For ideal solubility (γ = 1.00), the solubility of the substance in the solvent depends only on the experimental temperature. When γ is less than 1.00, the solubility of the substance in that solvent is greater than the ideal solubility, and when γ is greater than 1.00, the solubility in that solvent is less than the ideal solubility. It is recognized that the structures of compounds A, B, and C are much larger in comparison with the solvent molecules (THF and hexanes). Therefore, it is expected that these solutions are nonideal. The activity coefficient model used to fit the experimental data was a simplified version of the NRTL model (eq 2):44 ln γi =

∑j xjτjiGji ∑k xkGki

Gij = exp( −αijτij);

+

∑ j

⎡ ∑ x τ G ⎤ ⎢τij − m m mj mj ⎥ ∑k xkGkj ⎥⎦ ∑k xkGkj ⎢⎣ xjGij

τij = aij +

bij T

;

τii = 0;

Gii = 1 (2)

where γi is the activity coefficient of solute i, xj (j ≠ i) are the mole fractions of the remaining constituents in this quaternary system, τij is an intermediate parameter representing the binary interaction parameters aij and bij, and αij is the nonrandomness parameter. For the THF + hexanes binary pair, a full set of parameters are available from Aspen Plus version 7.3.45 For the limited data collected in this work at a single temperature, the number of parameters was reduced by equating the ij interactions for some pairs and by setting some parameters equal to zero. For each of the three DDSQ structures, since the cis and trans isomers possess the same functional groups, the cis−trans binary energy interaction parameters are assumed to be the same as the cis−cis and trans−trans parameters, and thus, τct = τtc = 0. For the same reason, the cis−hexanes interaction is assumed to be the same as the trans−hexanes interaction and the cis−THF interaction is assumed to be the same as the trans−THF interaction. These assumptions resulted in the simplifications acis,H = atrans,H and acis,T = atrans,T. These parameters will thus be abbreviated aDDSQ,H and aDDSQ,T without distinction of the cis and trans isomers. It was further assumed that the nonrandomness parameters α for DDSQ− THF interactions and DDSQ−hexanes interactions are equal to 1486



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composition of each precipitate that will be discussed in sections 3.1.1 to 3.1.3. The trans isomer was often predominant in ppt1 samples, while the cis isomer was predominant in ppt2 samples with exceptions discussed below. Solubilities were determined on the basis of composition data from the solid obtained in step 8 of Figure 3 and are summarized in Table 2. The mole fractions were determined using the material balance on the total mass of each solvent and the mass of DDSQ with 1H NMR analysis. Samples that were fully saturated with both isomers were evaluated for the quantity of each isomer that remained in solution (ppt2) as the quality of the solvent was varied from polar (THF-rich) to nonpolar (hexanes-rich) (Figure 4a−c). As the solution became hexanes-rich, less of each isomer remained in solution. The cis isomer predominated throughout the range of solvents used. 3.1.1. Compound A. From the 18 experiments for compound A summarized in Table 1, the highest purity of the trans isomer (ppt1) was obtained in experiment 11, when 0.447 g (3.34·10−4 mol) of A was placed in a mixture with a nonsolvent:solvent (hexanes:THF) molar ratio of 5:10 (9:13 v/ v) to yield 0.369 g (2.76·10−4 mol) of > 99 % trans isomer. The highest purity of cis isomer was obtained in ppt2 of experiment 5, when 0.710 g (5.31·10−4 mol) of A was placed in a mixture with a nonsolvent:solvent molar ratio of 9:10 (7:4 v/v) to yield 0.327 g (2.45·10−4 mol) of > 99 % cis isomer. Generally, the average recovery of total material in all of the experiments was (92 ± 9) %. Experiments with A using a starting material (SM) with an approximately 1:1 cis:trans ratio and a supernatant fully saturated with both isomers displayed a high trans purity in A ppt1 and a high cis purity in A ppt2, according to the 1H NMR results (experiments 1−5). Those using a supernatant fully saturated with trans isomer and undersaturated with cis isomer displayed high trans purity in A ppt1 and a lower cis purity in A ppt2 (experiments 6−8). Additional separations were then carried out using the products from the first eight experiments as the SM (experiments 9−18). Experiments using the first ppt1 (with a higher trans ratio) as the SM mostly displayed a supernatant fully saturated with trans isomers and undersaturated with cis isomers for the conditions tested and exhibited a high trans purity in ppt1 and a much lower cis purity in ppt2 (experiments 9−12). An attempt was then made to obtain the highest-purity cis isomer with experiments using an SM with a higher cis ratio (experiments 13−18). These experiments contained a supernatant fully saturated with both isomers and displayed a low trans purity in A ppt1 and a high cis purity in A ppt2. The ratio of isomers in the SM did not have an effect on the solubility of the isomers. For all of the experiments employing a supernatant fully saturated with cis isomers, the average percentage of cis isomers in A ppt2 was (90 ± 5) %. 3.1.2. Compound B. From the five experiments for compound B in Table 1, the highest purity of the trans isomer (B ppt1) was obtained in experiment 1, when 0.328 g (2.22· 10−4 mol) of B was placed in a mixture with a nonsolvent:solvent molar ratio of 6:7 (3:2 v/v) to yield 0.257 g (1.75·10−4 mol) of 36 % trans isomer. The highest purity of the cis isomer (ppt2) was obtained in experiment 3, when 0.270 g (1.82·10−4 mol) of B was placed in a mixture with a nonsolvent:solvent molar ratio of 1:1 (1:1 v/v) to yield 0.058 g (3.91·10−5 mol) of 91 % cis isomer. Generally, the average recovery of total material in all of the experiments was (94 ± 3) %.

zero. These simplifications reduced the binary NRTL equation to the two-suffix (one-parameter) Margules equation (eq 3):43 ln γ1 = x 2 2[τ12 + τ21] ≡ ln γ1 = x 2 2[2τ12] ln γ2 = x12[τ21 + τ12] ≡ ln γ2 = x12[2τ12]

(3)

This equation is shown as a binary in order to help the reader understand how the binary contribution to the multicomponent model simplifies with these assumptions.

3. RESULTS AND DISCUSSION 3.1. Separation of the Cis and Trans Isomers of A, B, and C. Sections 3.1.1 to 3.1.3 describe the recoveries and purities of the samples. Within each section, the discussion starts with the conditions providing the highest purity of the cis and trans fractions. Table 1 provides a summary of the Table 1. Isomers of Compounds A, B, and C Obtained from Fractional Crystallization/Solubility Experiments and Their Purities As Determined by 1H NMR Spectroscopy expt

SMa

1 2 3 4 5 6b 7b 8b 9b 10b 11b 12b 13 14 15 16 17 18

1:1 1:1 1:1 1:1 1:1 1:1 1:1 4:6 2:8 2:8 1:9 2:8 8:2 9:1 9:1 9:1 9:1 8:2

1 2 3 4 5

7:3 8:2 8:2 6:4 8:2

1 2 3 4b 5b 6b 7b 8b 9 10 11 12

1:1 1:1 1:1 1:1 1:1 > 9:1 > 9:1 > 9:1 > 9:1 3:7 3:7 3:7

ppt1 (% trans) Compound A 84 90 58 59 96 85 93 95 97 96 99 91 35 20 12 15 7 33 Compound B 36 31 15 29 20 Compound C 71 68 78 82 88 92 92 99 8 3 7 32

ppt2 (% cis) 90 95 86 92 99 77 83 75 31 60 16 93 86 91 89 85 85 84 84 86 91 73 85 99 95 96 87 86 71 63 39 87 88 92 97

a

Approximate cis:trans ratio in the starting material. bUndersaturated in the cis isomer. 1487



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Table 2. Experimental Data from Material Recovered in Step 8 of Figure 3 for Compounds A, B, and C compd A

a

xH:xTa 0.123 0.137 0.205 0.220 0.240 0.240 0.286 0.308 0.342 0.347 0.362 0.411 0.521 0.539 0.616 0.899 1.155 1.361

xcis

xtrans −3 b

1.45·10 1.35·10−2 2.60·10−2 2.64·10−2 2.55·10−2 2.52·10−4 b 6.03·10−3 b 1.46·10−2 3.06·10−3 b 1.54·10−3 b 3.97·10−3 b 1.61·10−2 3.35·10−3 6.98·10−3 3.47·10−3 4.29·10−3 7.75·10−4 5.32·10−4

−3

3.27·10 1.50·10−3 4.29·10−3 4.92·10−3 4.50·10−3 1.37·10−3 1.84·10−3 2.59·10−3 1.04·10−3 1.02·10−3 8.07·10−4 1.92·10−3 2.35·10−4 6.90·10−4 1.96·10−4 4.33·10−5 6.45·10−5 8.49·10−5

compd

xH:xTa

B

0.264 0.370 0.616 0.880 0.994

5.45·10−3 2.51·10−3 1.79·10−3 8.22·10−4 8.68·10−4

9.90·10−4 9.46·10−4 1.74·10−4 1.61·10−4 1.37·10−4

C

0.123 0.513 0.603 0.616 0.689 0.822 0.880 1.115 1.155 1.174 1.369 1.400

4.86·10−4 b 0.00785 2.75·10−4 b 0.00574 2.59·10−4 b 0.00463 0.00591 8.21·10−4 b 0.00452 7.45·10−4 b 0.00142 0.00152

7.47·10−4 4.46·10−4 1.59·10−4 2.68·10−4 1.03·10−4 1.61·10−4 8.34·10−5 1.34·10−4 5.99·10−4 1.09·10−4 1.30·10−4 2.27·10−4

xcis

xtrans

Hexanes to tetrahydrofuran mole fraction ratio. bUndersaturated isomer.

Figure 4. Experimental (□, cis; ○, trans) and modeled (solid line, cis; dashed line, trans) solubility limits in hexanes:THF (xH:xT) solutions for isomers of compounds (a) A, (b) B, and (c) C.

The SM for all of the B experiments was majority cis isomer because of a more complicated synthetic procedure that provided not only a lower reaction yield but also additional byproducts and required further purification. One of the byproducts had a similar solubility as the trans isomer, and in

order to purify B, some trans isomer was lost with the byproduct. However, since fraction ppt2 (majority cis isomer) was the principal solid and the experimental data from compound A demonstrated that the ratio of isomers in the SM did not have any effect on the solubility of the isomers, 1488



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having all of the SMs for experiments with B composed of majority cis isomer helped ensure that the cis isomer was not undersaturated. It was determined that these experiments contained a supernatant that was fully saturated with both isomers and displayed a low trans purity in ppt1 and a high cis purity in ppt2. The average percentage of cis isomer in ppt2 was (84 ± 7) %. 3.1.3. Compound C. From the 12 experiments for compound C in Table 1, the highest purity of the trans isomer (ppt1) was obtained in experiment 8, when 0.322 g (3.34·10−4 mol) of C was placed in a mixture with a nonsolvent:solvent molar ratio of 7.5:5.5 (9:4 v/v) to yield 0.0273 g (2.04·10−5 mol) of > 99 % trans isomer. The highest-purity cis fraction (ppt2) was obtained in experiment 1, when 0.331 g (2.48·10−4 mol) of C was placed in a mixture with a nonsolvent:solvent molar ratio of 7.5:8.5 (1:0.7 v/v) to yield 0.131 g (9.79·10−5 mol) of > 99 % cis isomer. Generally, the average recovery of total material in all of the experiments was (96 ± 5) %. As with A, experiments using an SM with an approximately 1:1 cis:trans ratio and a supernatant fully saturated with both isomers displayed a moderately high trans purity in ppt1 and a high cis purity in ppt2, according to the 1H NMR results (experiments 1−5). Additional separations were then carried out using the products from the first five experiments as the SM (experiments 6−12). Experiments using an SM with a higher trans content mostly displayed a supernatant fully saturated with trans isomers and undersaturated with cis isomers for the conditions tested and exhibited a high trans purity in ppt1 and a much lower cis purity in ppt2 (experiments 6−8). An attempt was then made to obtain the highest-purity cis isomer with experiments using an SM with a higher cis ratio (experiments 9−12). These experiments contained a supernatant fully saturated with both isomers and displayed a low trans purity in ppt1 and a high cis purity in ppt2. Similarly to the meta species A, it was demonstrated that the ratio of isomers in the SM did not have an effect on the solubility of the isomers for the para species. For all of the experiments employing a supernatant fully saturated with cis isomer, the average percentage of cis isomer in ppt2 was (93 ± 5) %. 3.2. Chromatography Results. Chromatography columns were used to obtain the highest purity of each isomer. There were up to 60 fractions (5 mL to 10 mL each) from one chromatography column. TLC plates and 1H NMR spectra were used to identify the pure fractions. The trans isomer eluted before the cis isomer for all of the materials. There was sufficient separation in the order of elution to achieve complete separation of the two isomers. 3.3. DSC Results. When the cis and trans isomers of compounds A, B, and C were heated, a sharp endothermic peak was observed, which is representative of a melting transition. From this transition, the onset of melting (Tm) and the total heat of fusion (ΔHm) were determined. Tm was calculated by extrapolating the slope from the peak width at half height to the baseline, and ΔHm was found as the total area of the melting endotherm (Figure 5). These values are shown in Table 3 and were used to fit the experimental data. 3.4. Results of Model Fitting. THF−hexanes binary interaction parameters were taken from the VLE regression sets in Aspen Plus version 7.3 (aH,T = aT,H = 0, bH,T = −15.0959 K, bT,H = 233.6258 K, and αT,H = 0.3).41,43,45 Only the binary parameters aij for cis/trans−hexanes and cis/trans−THF interactions (aDDSQ,H and aDDSQ,T, respectively) were adjusted to fit xi values along the saturation curves. Since all of the data

Figure 5. Example of a melting endotherm (trans-A) showing the melting temperature Tm and heat of fusion ΔHm as determined by DSC at a heating rate of 10 °C/min.

Table 3. Melting Temperatures and the Total Heats of Fusion for Compounds A, B, and C As Determined by DSC at a Heating Rate of 10 °C/min compd

Tm (°C)

ΔHm (kJ·mol−1)

cis-A trans-A cis-B trans-B cis-C trans-C

289.5 312.0 265.9 270.0 272.6 309.3

42 56 39 46 38 58

were collected at room temperature only, the temperature dependence was ignored (i.e., bDDSQ,H = bDDSQ,T = 0). Thus, for the interactions between DDSQ and each solvent, τDDSQ,H = aDDSQ,H and τDDSQ,T = aDDSQ,T. Therefore, a negative value of aij provides a negative value of τij and γ < 1.00, while a positive value of aij provides a positive value of τij and γ > 1.00. As the magnitude of aij increases, the solution becomes less ideal. For large negative values of aij, the material is more soluble than in an ideal solution; for large positive values of γ, the solvent is a “nonsolvent”, and the material is less soluble than in an ideal solution. The model results are compared to the experimental observations as shown in Figure 4a−c for compounds A, B, and C, respectively. The scatter seen in Figure 4a−c can be attributed to the experimental uncertainties due to the small sample sizes used. The relative uncertainty that provides the most error (according to differential error analysis) is from the solid composition obtained by 1H NMR analysis (Table 1). The experimental measurements in Table 1 lie within the computed confidence intervals of ± 5 %. For example, the point in Figure 4 with a solid xH:xT ratio of 0.899 has a 500 % relative error (% RE), as determined by the error in the composition of the trans isomer (Table 4). The % RE is very high for this data point because 99 % of the 326 mg sample is the cis isomer. Therefore, the mass of the trans isomer is only 3.3 mg, or 1 % of the sample, which is below is threshold of detection for 1H NMR spectroscopy. The ± 5 % confidence interval, as discussed previously, is applied to the entire sample mass, yielding a confidence interval of approximately ± 16 mg, which is 5 times larger than the mass of the trans isomer. Clearly, as the mass of a component decreases, the relative uncertainty for that component increases significantly, which explains the larger 1489



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Table 4. % Relative Errors (% RE) Determined by a ± 5 % Confidence Interval in 1H NMR Measurements % RE

% RE

compd

xH:xT

cis

trans

compd

xH:xT

cis

trans

A

0.123 0.137 0.205 0.220 0.240 0.240 0.286 0.308 0.342 0.347 0.362 0.411 0.521 0.539 0.616 0.899 1.155 1.361

16 6 6 6 6 32 7 6 7 8 6 6 5 5 5 5 5 6

7 50 35 32 33 6 21 33 20 13 30 47 76 56 93 500 65 36

B

0.264 0.370 0.616 0.880 0.994

5 7 5 5 6

83 18 56 59 37

C

0.123 0.513 0.603 0.616 0.689 0.822 0.880 1.115 1.155 1.174 1.369 1.400

8 5 8 5 7 5 5 6 6 6 5 6

13 93 14 112 18 148 359 36 43 39 60 39

scatter in the experimental trans data points. Another feasible cause of error is the experimental masses and volumes of all four components, which provide % REs of < 10 for the trans isomer and < 1 for the cis isomer. Additional causes of error in the experimental values and the model may be attributed to the magnitude of Tm with respect to the experimental temperature, variation in the room temperature, the accuracy of ΔHm, and the filtration method. It is important to recognize that although the % RE in xi is large at times, the trends in the activity coefficients for the cis and trans isomers of different DDSQ compounds and the binary interaction coefficients of DDSQ compounds with THF and hexanes are minimally affected. Activity coefficients as a function of the mole fraction of solvent (THF or hexanes) for all three DDSQ compounds investigated are presented in Figure 6a,b, respectively. The adjustable parameters representing the interactions between the DDSQ compounds and the solvent (aDDSQ,T and aDDSQ,H) are summarized in Table 5. For compounds A, B, and C, the solubilities in 100 % THF (left side of Figure 7) are higher than the ideal values (Table 6). From the model, ln(γsolute−solvent) < 0 and ln(γsolute−nonsolvent) > 0, which confirms that THF is a good solvent and hexanes are a nonsolvent for these three DDSQ compounds. The γsolute values are highly nonideal for all of the conditions tested, since xsolvent is very close to 1.00 and the saturated solutions are close to infinite dilution for DDSQ. The relation between the activity coefficients and the binary interaction parameters is most obvious in eq 3 for a binary: since τij = aij and xsolvent is very close to 1, ln γ∞ i = 2aij. The magnitude of the binary interaction parameter of DDSQ and THF (aDDSQ,T) combined with the RHS of the Schröder− van Laar equation (eq 1) can be used to explain the overall solubilities of compounds A, B, and C. For all three compounds investigated, the solubility of the cis species is always greater than that of the trans species in a solvent with a fixed ratio of THF to hexanes. The experimental saturation curves for the cis and trans species in a THF/hexanes mixture, as shown in Figure 4a−c, appear to exhibit the same slope. This observation validates the assumption that the interaction parameters for each isomer with the solvent are the same (aDDSQ,T = aDDSQ,H).

Figure 6. Activity coefficients of the solutes vs the mole fraction of (a) the nonsolvent (hexanes) and (b) the solvent (THF), when each compound is considered a binary. When the natural logarithm of the activity coefficient is larger than zero, the interaction is between the DDSQ and hexanes. When the natural logarithm of the activity coefficient is less than zero, the interaction is between the DDSQ and THF.

Table 5. Binary Interaction Parameters for Compounds A, B, and C with Hexanes and THF compound

aDDSQ,H

aDDSQ,T

A B C

1.7904 2.1676 0.1474

−3.4085 −1.5328 −1.7338

However, the magnitude of the separation between the cis and trans saturation curves for each compound (Figure 7) varies and is dependent on the physical melting characteristics, which are given by the ratio of the ideal solubilities for the two isomers (Table 6). Isomers of compound C exhibited the largest magnitude of separation in their saturation curves (Figure 7). The cis isomer of compound C was 33 times more soluble than the trans isomer, a partitioning threshold of 33:1. The separation of the saturation curves of the isomers of compound A was slightly closer; the cis isomer was 22 times more soluble than the trans isomer. The isomers of compound B exhibited the smallest magnitude of separation in their saturation curves; the cis isomer was only 3.5 times more soluble than the trans isomer. The isomers of C exhibit the largest differences in Tm and ΔHm and the isomers of B exhibit 1490



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respectively) and different values of aDDSQ,T (−3.4085 and −1.5328, respectively) but coincidentally have similar solubilities in THF. This further confirms that the Schröder−van Laar equation and binary interaction coefficients are both necessary when determining solubility.

4. CONCLUSION The cis and trans isomers of a series of DDSQ(X)(R) compounds were successfully separated using a fractional crystallization method. The Schröder−van Laar equation (eq 1), and the NRTL model (eq 2) were used to fit the experimental data. The model was simplified to reduce the number of adjustable parameters. The NRTL model parameters are consistent with the solubility trends, suggesting that they have physical meaning. In this paper, the solubilities of the cis and trans isomers were represented using the same binary interaction coefficients for DDSQ + solvent and DDSQ + nonsolvent for each isomer. The two isomers of each compound do not interact differently with a given solvent even though they have different solubilities. The difference in the solubilities of the cis and trans isomers is due to the purecomponent properties (RHS), not the DDSQ + solvent and DDSQ + nonsolvent interactions. Among the different compounds, the differences in solubility are due to both the Schrö der−van Laar equation and the binary interaction coefficients. Overall it was determined that changing the R group from a methyl group to a bulkier cyclohexyl moiety (i.e., A to B) decreases the solubility of the compound and also decreases the partitioning threshold between the cis and trans isomers. The differences in Tm and ΔHm are consistent with the change in the isomeric partitioning threshold of these compounds. Additionally the solubilities of the meta structures, compounds A and B, decrease at similar rates with increasing content of hexanes, which was verified by the interaction parameters with hexanes. Changing the X group from meta to para (i.e., A to C) leads to an increase in the partitioning threshold and a decrease in the rate of solubility. Overall, the models show that the assumptions were valid over the range of experiments, and the determined saturation curves can be used for the separation of the cis and trans isomers of compounds A, B, and C.

Figure 7. Modeled solubility limits in a hexanes:THF (xH:xT) solution for the cis and trans isomers of compounds A, B, and C. The three upper curves represent the cis isomers, and the lower three curves represent the trans isomers.

Table 6. Solutions of the Schröder−van Laar Equation (RHS) at Room Temperature and the Corresponding Solubility Limits Based on Ideal Solution Assumptions (γ = 1.00) for Compounds A, B, and C compound

RHS

xideal

cis-A trans-A cis-B trans-B cis-C trans-C

−7.97 −11.08 −7.03 −8.37 −6.96 −11.42

3.47·10−4 1.54·10−5 8.83·10−4 2.32·10−4 9.54·10−4 1.10·10−5

the smallest difference, which is consistent with these solubility data.46,47 For compounds B and C, the cis isomers, which are the more soluble species, approached the same solubility in THF (left side of Figure 7). This is because they have very similar values for their binary interaction parameters with THF (aB,T = −1.5328 and aC,T = −1.7338) and similar Tm and ΔHm values (RHSs of approximately −7). cis-A possesses a higher solubility in THF than the other two compounds because its value of aA,T is most negative (aA,T = −3.4085) and the Tm and ΔHm values (RHS of approximately −8) are larger than those of the other compounds. The slopes of the saturation curves in Figure 7 are very different for cis-B and cis-C, which results from their different binary interaction coefficients with the nonsolvent (hexanes) (aB,H = 2.1676 and aC,H = 0.1474). The magnitude of aDDSQ,H provides information on how quickly the solubility decreases as hexanes are added to THF. Since aC,H is so close to zero, the interaction of cis-C and hexanes is nearly ideal. Therefore, the solubility of cis-C with the addition of hexanes does not decrease as rapidly as with the other compounds, and the lower solubility is largely due to dilution of the more polar THF solvent. The slope of the saturation curve of cis-A is similar to that of cis-B because they have similar values for their interaction with hexanes (aA,H = 1.7904). For compounds A and C, the trans isomers, which are the less soluble species, have similar values for Tm and ΔHm (RHSs of approximately −11), but since aA,T (−3.4085) has a larger magnitude than aC,T (−1.7338), trans-A is more soluble in THF than trans-C is. Additionally, trans-A and trans-B have different Tm and ΔHm values (RHSs of approximately −11 and −8,

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AUTHOR INFORMATION

Corresponding Author

*Phone: (517)355-5112. Fax: (517)432-1105. E-mail: leea@ msu.edu. Notes

The authors declare no competing financial interest.

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REFERENCES

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