Phase Transition Thermodynamics of Bisphenols - The Journal of

Article pubs.acs.org/JPCA

Phase Transition Thermodynamics of Bisphenols José C. S. Costa,† Juan Z. Dávalos,*,‡ and Luís M. N. B. F. Santos*,† †

Centro de Investigaçaõ em Química, Departamento de Química e Bioquímica, Faculdade de Ciências da Universidade do Porto, P-4169-007 Porto, Portugal ‡ Instituto de Quimica-Fisica “Rocasolano”, CSIC, Serrano 119, 28006 Madrid, Spain S Supporting Information *

ABSTRACT: Herein we have studied, presented, and analyzed the phase equilibria thermodynamics of a bisphenols (BP-A, BP-E, BP-F, BP-AP, and BP-S) series. In particular, the heat capacities, melting temperatures, and vapor pressures at different temperatures as well as the standard enthalpies, entropies, and Gibbs energies of phase transition (fusion and sublimation) were experimentally determined. Also, we have presented the phase diagrams of each bisphenol derivative and investigated the key parameters related to the thermodynamic stability of the condensed phases. When all the bisphenol derivatives are compared at the same conditions, solids BP-AP and BP-S present lower volatilities (higher Gibbs energy of sublimation) and high melting temperatures due to the higher stability of their solid phases. Solids BP-A and BP-F present similar stabilities, whereas BP-E is more volatile. The introduction of −CH3 groups in BP-F (giving BP-E and BP-A) leads an entropic differentiation in the solid phase, whereas in the isotropic liquids the enthalpic and entropic differentiations are negligible.

1. INTRODUCTION Bisphenol A (BP-A), bisphenol E (BP-E), bisphenol F (BP-F), bisphenol AP (BP-AP), and bisphenol S (BP-S) are monomers used in the production of polycarbonate and epoxy resins, food cans, dental composites, sealants as well as many plastic consumer products.1−3 Due to an increase in the use of products based on epoxy resins and polycarbonate plastics, the concerns about the health/environmental potential risks of BP-A, BP-F, and BP-S (the most used bisphenols) are increasing, and several data on estrogenic and androgen activities, carcinogenicity, and toxicity has been published, mostly on BP-A, which presents the highest toxicity.4,5 Inappropriately, BP-A can be found in wastewaters, in lakes and rivers, and in soil and in air.6,7 Thus, from the ecotoxicology point of view, it is crucial to restrict the emissions from the industrial processes and commercial products.8,9 Despite the important controversies over the form and amount of BP-A to which humans are in contact, substantial data indicate that exposure of humans to BP-A is related to increased risk for cardiovascular disease, miscarriages, cancer, reproductive and sexual dysfunctions, altered immune system activity, metabolic problems and diabetes, and cognitive, hormonal, and behavioral development in young children.10,11 Despite the relevance and adverse effects of bisphenol derivatives, the volatility, thermal behavior, and thermodynamic stability of these compounds is not well explored and understood. This work is part of a systematic investigation of the energetics, and thermophysical properties of organic chemicals with biological, medicinal, and technological relevance.12−14 Taking into account the importance of this class of compounds, we have performed an extended thermodynamic study, © XXXX American Chemical Society

including vapor pressure measurements at different temperatures, heat capacity determinations and phase behavior analysis, to deepen the molecular understanding of the stability of the solid and liquid phases of BP-A, BP-E, BP-F, BP-AP, and BP-S. The structure of the studied compounds is depicted in Figure 1.

Figure 1. Structural configuration of bisphenol A (BP-A), bisphenol E (BP-E), bisphenol F (BP-F), bisphenol AP (BP-AP), and bisphenol S (BP-S).

For each compound, the melting temperature, and the thermodynamic parameters of fusion as well as the heat capacities of the solid phase, were measured by differential scanning calorimetry (DSC). The vapor pressures at different temperatures were measured using the Knüdsen effusion method combined with a quartz crystal microbalance (KEQCM),15 and from the results Received: June 1, 2014 Revised: August 24, 2014

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dx.doi.org/10.1021/jp505404w | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

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Table 1. Thermodynamic Parameters of Fusion at the Fusion Temperature and at T = 298.15 K, for the Bisphenol Derivatives Studieda compound BP-A BP-E BP-F BP-AP BP-S

Tfus, K 431.2 399.3 436.2 462.2 519.9

± ± ± ± ±

1.0 0.5 0.4 0.9 0.3

Δ1s Hom(Tfus), kJ·mol−1 31.6 27.9 36.8 42.5 41.4

± ± ± ± ±

0.7 0.7 0.7 1.9 1.0

Δ1s Som(Tfus), J·K−1·mol−1 73.3 69.9 84.4 92.0 79.6

± ± ± ± ±

Δ1s Hom(298.15 K), kJ·mol−1

1.6 1.8 1.6 4.1 1.9

24.4 22.4 29.3 33.6 29.3

± ± ± ± ±

1.0 0.9 1.0 2.1 1.5

Δ1s Som(298.15 K), J·K−1·mol−1 53.2 54.0 63.7 68.1 49.4

± ± ± ± ±

2.5 2.3 2.5 4.7 3.4

Δ1s Gom(298.15 K), kJ·mol−1 8.5 6.3 10.3 13.3 14.6

± ± ± ± ±

1.2 1.1 1.2 2.5 1.8

The uncertainties of the experimental results were assigned on the basis of independent experiments as 2σ, where σ is the standard deviation of the mean. The uncertainties of the parameters at T = 298.15 K were calculated by using the rules of propagation of uncertainty and considering Δ(ΔslCp) = 5 J·K−1 mol−1. a

methodology for the determination of the heat capacities are given as Supporting Information. 2.3. Vapor Pressure Measurements: Knüdsen/Quartz Crystal Effusion. The vapor pressures of BP-A, BP-E, BP-F, BP-AP, and BP-S as a function of temperature were measured by the mass loss combined Knüdsen/Quartz crystal effusion apparatus (KEQCM) described in detail by Santos et al.15 This technique is based on the simultaneous gravimetric and quartz crystal microbalance mass loss detection. It has the advantages of requiring smaller sample sizes and results in shorter effusion times and the possibility of achieving temperatures up to T = 650 K. The vapor pressures of the solid compounds studied were measured at different temperature intervals: bisphenol A, 374−400 K; bisphenol E, 371−394 K; bisphenol F, 376−398 K; bisphenol AP, 410−439 K; bisphenol S, 465−490 K. 2.4. Quantum Chemical Calculations. Quantum chemical calculations were carried out using the Gaussian 09 package.24 The full geometry optimizations of the compounds under investigation, and their most significant conformers as well as harmonic vibrational frequencies without scaling were performed using the density functional M05-2X method with the 6-311++G(d,p) basis set without symmetry restrictions.25 Additional details concerning the Quantum chemical calculations and statistical thermodynamics calculations are presented as Supporting Information.

obtained, the standard thermodynamic parameters of sublimation were determined. The relationship between structure and energetics will be discussed on the basis of the experimental results and quantum chemical calculations.

2. EXPERIMENTAL SECTION 2.1. Purification and Characterization of Bisphenol Derivatives. 2,2-Bis(4-hydroxyphenyl)propane (bisphenol A, CAS 80-05-7, mass fraction > 0.99); 1,1-bis(4-hydroxyphenyl)ethane (bisphenol E, CAS 2081-08-5, mass fraction = 0.99); 1,1-bis(4-hydroxyphenyl)methane (bisphenol F, CAS 620-92-8, mass fraction = 0.98), 1,1-bis(4-hydroxyphenyl)-1-phenylethane (bisphenol AP, CAS 1571-75-1, mass fraction = 0.99), and 4,4′sulfonyldiphenol (bisphenol S, CAS 80-09-1, mass fraction = 0.98) were purchased from Sigma-Aldrich Co. (CAS Registry Nos. supplied by the author.) All the samples were clean from volatile impurities by keeping under low pressures (p < 10 Pa) at T = 353 K during 48 h. The final purity of the samples was verified by gas chromatography analysis, using an HP 4890 apparatus equipped with an HP-5 column, cross-linked (5% diphenyl and 95% dimethylpolysiloxane) and a flame ionization detector. The mass fraction of the pure compounds was found to be 0.999 in all cases. The relative atomic masses used in this work were those recommended by the IUPAC Commission in 2007.16 2.2. Differential Scanning Calorimetry (DSC). For each bisphenol, the melting temperature and the thermodynamic parameters of fusion were studied by DSC (Perkin-Elmer, Pyris 1) provided with an intracooler unit, over the temperature range from T = 263 K until their melting temperatures. Temperature and power scales were calibrated17−19 at heating rates of 0.04 and 0.17 K/s, respectively. The temperature scale was calibrated by measuring the melting temperature of the recommended high-purity reference materials: hexafluorobenzene, tin, and indium.20 The power scale was calibrated with highpurity indium (mass fraction purity >0.99999) as reference material. Thermograms of samples hermetically sealed in aluminum pans were recorded in a nitrogen atmosphere, at a heating rate of 0.04 K/s. Heat capacities were determined by the “scanning method” following the experimental methodology previously described with synthetic sapphire as reference material.20−23 The thermograms allowed the determination of the melting temperatures as well as the molar enthalpies of fusion, with no phase transition observed until the solid−liquid transition. The hypothetical enthalpies, entropies, and Gibbs energies of fusion, at T = 298.15 K, were derived by a temperature adjustment using the variation in heat capacity associated with fusion process. The detailed experimental results concerning the calibration of the DSC and the experimental

3. RESULTS 3.1. Solid−Liquid Equilibrium: Molar Heat Capacities, Melting Temperatures, and Thermodynamic Properties of Fusion. For BP-A, BP-E, BP-F, BP-AP, and BP-S, the experimental fusion temperatures, Tfus, and standard molar enthalpies of fusion at Tfus, ΔfusH, were measured by differential scanning calorimeter (the molar entropies of fusion were derived as Δ1s Hom/Tfus). The detailed experimental results concerning the fusion equilibrium are given as Supporting Information. For each compound, the hypothetical molar enthalpy of fusion, at T = 298.15 K, was calculated according to eq 1: ΔslHmo(T ) = ΔslHmo(Tfus) + ΔslC po,m(T − Tfus)

(1)

The hypothetical molar entropy of fusion, at T = 298.15 K, was calculated according to eq 2: ΔslSmo(T ) = ΔslHmo(Tfus)/Tfus + ΔslC po,m ln(T /Tfus)

(2)

The value of ΔlsCp = 54.4 J·K−1·mol−1 (variation in molar heat capacity associated with fusion process) was used, which is in according to the equation proposed by Sidgewick26 and recommended by Chickos,27 and the uncertainty interval was taken as ±5 J·K−1·mol−1. B



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The hypothetical molar Gibbs energy of fusion, at T = 298.15 K, was calculated according to eq 3: ΔslGmo(T ) = ΔslHmo(T ) − T ΔslSmo(T )

(3)

Table 1 presents the experimental fusion temperatures, Tfus, the results of the standard molar enthalpies, ΔlsHom, and entropies, ΔlsSom, of fusion at the fusion temperature, and the derived hypothetical standard molar enthalpies, entropies, and Gibbs energies of fusion, ΔlsGom, at T = 298.15 K, for the compounds studied. Table 2. Experimental Data of Vapor Pressures for Solids Bisphenol A, Bisphenol E, Bisphenol F, Bisphenol AP, and Bisphenol S T/K

p/Pa

373.10 375.62 378.09 380.59

0.0475 0.0628 0.0852 0.110

370.09 373.09 376.08

0.0723 0.101 0.145

375.40 377.99 379.99 382.97 384.37

0.0616 0.0842 0.106 0.15 0.175

409.92 412.98 415.89 418.88

0.0434 0.0624 0.0870 0.124

465.06 467.94 470.25 472.88

0.140 0.178 0.221 0.276

T/K

p/Pa

Bisphenol A 383.09 0.148 385.57 0.191 388.09 0.254 390.64 0.340 Bisphenol E 379.08 0.206 382.05 0.288 385.07 0.393 Bisphenol F 385.43 0.195 387.00 0.234 389.01 0.294 390.43 0.340 Bisphenol AP 421.92 0.163 424.88 0.224 427.91 0.305 430.88 0.411 Bisphenol S 475.34 0.348 478.01 0.427 480.33 0.513 482.98 0.637

T/K

p/Pa

393.09 395.56 398.05 400.54

0.436 0.566 0.718 0.916

388.07 391.08 394.03

0.541 0.749 1.024

393.01 395.49 397.31 398.92

0.454 0.598 0.703 0.831

434.05 436.94 439.93

0.576 0.798 1.019

Figure 2. Experimental plots of ln(p/Pa) versus (1/T)/K−1 for the bisphenol derivatives studied: ○, BP-A; □, BP-E; △, BP-F; ◇, BP-AP; ∗, BP-S.

and at the vapor pressure at the mean temperature, Δgs Sm(⟨T⟩;p⟨T⟩)), were calculated by eq 5. Δsg Sm(⟨T ⟩,p(⟨T ⟩)) = Δsg Hmo(⟨T ⟩)/⟨T ⟩

The standard molar enthalpies of sublimation, at T = 298.15 K, Δgs Hom, were determined by eq 6: Δsg Hmo(T ) = Δsg Hmo(⟨T ⟩) + (T − ⟨T ⟩)Δsg C po,m

Δsg Smo(T ) = Δsg Sm(⟨T ⟩,p(⟨T ⟩)) + Δsg C po,m(T ) ln(T /⟨T ⟩) − R ln(po /p(⟨T ⟩)) 5

(7)

Δgs Cp

where p = 10 Pa. is the variation in molar heat capacity associated with sublimation process, obtained by a temperature adjustment using the difference between the heat capacities of the gas and solid phases, at T = 298.15 K, calculated by eq 8:

0.762 0.918 1.108

Δsg C po,m = C po,m(g) − C po,m(s)

(8)

Table 4 presents the values of the standard molar heat capacities at T = 298.15 K in the solid, Cop,m(s), and gas, Cop,m(g), phases, the derived standard heat capacities of sublimation, Δgs Cop,m at T = 298.15 K, and calculated absolute entropies, Som, of solid, liquid, and gas phases for the compounds studied. For all the bisphenols, Cop,m(s) was obtained from the DSC results and Cop,m(g) and Som(g) were derived based in statistical thermodynamics using the harmonic vibration frequencies and optimized structures derived from quantum chemical calculations. The standard molar Gibbs energies of sublimation were calculated through eq 9 where the parameters are referenced to T = 298.15 K.

3.2. Solid−Gas Equilibrium: Vapor Pressures and Thermodynamic Properties of Sublimation. Table 2 presents the vapor pressures at several temperatures obtained using the combined Knüdsen/Quartz crystal effusion apparatus for BP-A, BP-E, BP-F, BP-AP, and BP-S. The standard molar enthalpies of sublimation at the mean temperature of the sublimation experiments, ⟨T⟩, were derived for the compounds studied, using the integrated form of the Clausius−Clapeyron according to eq 4: ln(p /Pa) = a − b[(1/T )/K −1]

(6)

The standard molar entropies of sublimation, at T = 298.15 K, Δgs Som, were calculated using eq 7:

o

485.35 487.69 490.26

(5)

(4)

Δsg Gmo(T ) = Δsg Hmo(T ) − T Δsg Smo(T )

where a is a constant and b = Δgs Hom(⟨T⟩)/R. The plots of ln(p/Pa) = f(1/T) for the compounds studied herein are shown in Figure 2. Table 3 presents the parameters of the Clausius− Clapeyron equation, the calculated standard deviations, and the standard molar enthalpies and entropies of sublimation at the mean temperature, ⟨T⟩. The standard molar enthalpies of sublimation at the mean temperature were determined by the parameter b, of the Clausius−Clapeyron equation, and the molar entropies of sublimation at the mean temperature, ⟨T⟩,

(9)

Table 5 lists the derived standard molar enthalpies, entropies, and Gibbs energies of sublimation, and the extrapolated vapor pressures, at T = 298.15 K, for the compounds studied, calculated through eq 10. ⎛ Δ g G o (T ) ⎞ p(T ) = po × exp⎜ − s m ⎟ ⎝ RT ⎠ o

(10)

5

where p = 10 Pa and T = 298.15 K. C



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Table 3. Sublimation Results for the Bisphenol Derivatives Studied, Where a and b Are from the Clausius−Clapeyron Equation, ln(p/Pa) = a − b·(T/K), and b = Δgs Hom(⟨T⟩)/R; R = 8.314 462 1 J·K−1·mol−1a BP-A BP-E BP-F BP-AP BP-S

b, K

r2

⟨T⟩, K

p(⟨T⟩), Pa

16216 ± 61 16149 ± 67 16596 ± 55 18934 ± 127 18787 ± 119

0.9999 0.9999 0.9999 0.9996 0.9996

386.84 382.07 387.49 424.93 477.83

0.222 0.284 0.247 0.226 0.416

a

compound 40.4 41.0 41.4 43.1 38.4

± ± ± ± ±

0.2 0.2 0.1 0.3 0.2

Δgs Hom(⟨T⟩), kJ·mol−1 134.8 134.3 138.0 157.4 156.2

± ± ± ± ±

Δgs Som(⟨T⟩;p(⟨T⟩)), J·K−1·mol−1

0.5 0.6 0.5 1.1 1.0

348.5 351.4 356.1 370.5 326.9

± ± ± ± ±

1.8 2.0 1.7 2.4 2.1

The uncertainties of the parameters a and b were obtained by the least-squares method from the fitting. The uncertainties of the thermodynamic parameters were calculated by using the rules of propagation of uncertainty.

a

Table 4. Solid and Gas Phase Heat Capacities at T = 298.15 K and the Difference between the Heat Capacities of the Gas and Solid Phases and Solid, Liquid, and Gas Phase Absolute Entropies at T = 298.15 K, for the Bisphenol Derivatives Studied (All Values in J·K−1·mol−1)a compound BP-A BP-E BP-F BP-AP BP-S

Cop,m(s) 302 277 247 367 281

± ± ± ± ±

Δgs Cop,m

Cop,m(g)

3 3 3 3 3

267 239 216 324 249

± ± ± ± ±

−35 −38 −31 −43 −32

10 10 10 10 10

± ± ± ± ±

Som(s)

10 10 10 10 10

272 247 222 323 268

± ± ± ± ±

Som(1)

10 10 10 11 11

325 300 286 391 317

± ± ± ± ±

Som(g)

11 11 11 12 12

521 501 479 600 507

± ± ± ± ±

10 10 10 10 10

was fitted to the second-order polynomial from DSC results: Cop,m(s) = aT2 + bT + c, and the uncertainty was estimated as ±3 J·K−1·mol−1. The uncertainties of Cop,m(g) and Som(g) were estimated as ±10 J·K−1·mol−1. The uncertainties of Δgs Cop,m, and absolute entropies, were calculated by using the rules of propagation of uncertainty. a o Cp,m(s)

Table 5. Values of the Standard Molar Enthalpies, Δgs Hom, Entropies, Δgs Som, and Gibbs Energies, Δgs Gom, of Sublimation for the Bisphenol Derivatives Studied, at T = 298.15 K and Extrapolated Vapor Pressures of the Solid Phase at T = 298.15 Ka compound BP-A BP-E BP-F BP-AP BP-S

Δgs Hom(298.15 K), kJ·mol−1 137.9 137.4 140.8 162.8 162.0

± ± ± ± ±

Δgs Som(298.15 K), J·K−1·mol−1

1.0 1.0 1.0 1.6 2.1

249.4 254.5 257.0 277.5 239.2

± ± ± ± ±

Δgs Gom(298.15 K), kJ·mol−1

p(298.15 K), Pa

± ± ± ± ±

(4.1−12.8) × 10−7 (9.5−29.0) × 10−7 (3.3−9.9) × 10−7 (4.0−21.5) × 10−10 (4.5−35.8) × 10−12

3.2 3.2 3.1 4.3 5.2

63.6 61.5 64.2 80.1 90.7

1.4 1.4 1.4 2.1 2.6

a

The uncertainties of the thermodynamic parameters of sublimation at T = 298.15 K were calculated by using the rules of propagation of uncertainty. The uncertainties of the estimated p(298.15 K) are presented as a pressure interval due to the asymmetry effect of the error propagation in the pressure results.

Table 6. Summary of the Values of the Thermodynamic Properties of Phase Transition at T = 298.15 K for the Bisphenol Derivatives compound

ΔHom(298.15 K), kJ·mol−1

BP-A BP-E BP-F BP-AP BP-S

24.4 22.4 29.3 33.6 29.3

± ± ± ± ±

1.0 0.9 1.0 2.1 1.5


137.9 137.4 140.8 162.8 162.0

± ± ± ± ±

1.0 1.0 1.0 1.6 2.1


113.6 115.0 111.5 129.3 132.7

± ± ± ± ±

1.4 1.3 1.4 2.6 2.5

ΔSom(298.15 K), J·K−1·mol−1 Solid−Liquid Equilibrium 53.2 54.0 63.7 68.1 49.4 Solid−Gas Equilibrium 249.4 254.5 257.0 277.5 239.2 Liquid−Gas Equilibrium 196.2 200.6 193.3 209.4 189.8 D

ΔGom(298.15 K), kJ·mol−1

± ± ± ± ±

2.5 2.3 2.5 4.7 3.4

8.5 6.3 10.3 13.3 14.6

± ± ± ± ±

1.2 1.1 1.2 2.5 1.8

± ± ± ± ±

3.2 3.2 3.1 4.3 5.2

63.6 61.5 64.2 80.1 90.7

± ± ± ± ±

1.4 1.4 1.4 2.1 2.6

± ± ± ± ±

4.0 3.9 4.0 6.3 6.2

55.1 55.2 53.9 66.8 76.1

± ± ± ± ±

1.9 1.8 1.8 3.3 3.1



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Table 7. Specific Heat Capacities and Absolute Entropies at T = 298.15 K and Specific Enthalpies and Entropies of Sublimation for the Bisphenol Derivatives Studieda compound BP-A BP-E BP-F BP-AP BP-S

Cop(s), J·K−1·g−1 1.32 1.29 1.23 1.26 1.12

± ± ± ± ±

Cop(g), J·K−1·g−1

0.01 0.01 0.01 0.01 0.01

1.17 1.12 1.08 1.12 0.99

± ± ± ± ±

0.04 0.05 0.05 0.03 0.04

So(s), J·K−1·g−1 1.19 1.15 1.11 1.11 1.07

± ± ± ± ±

0.02 0.03 0.03 0.02 0.02

So(g), J·K−1·g−1 2.28 2.34 2.39 2.07 2.03

± ± ± ± ±

0.04 0.05 0.05 0.03 0.04

Δgs Ho, kJ·g−1 0.604 0.641 0.703 0.561 0.647

± ± ± ± ±

0.004 0.005 0.005 0.006 0.008

Δgs So, J·K−1·g−1 1.09 1.19 1.28 0.96 0.96

± ± ± ± ±

0.01 0.02 0.02 0.02 0.02

a The uncertainties of the specific thermodynamic parameters of sublimation, heat capacities, and absolute entropies at T = 298.15 K were calculated by using the rules of propagation of uncertainty.

Figure 3. Phase diagrams of the bisphenol derivatives studied showing the corresponding solid−gas (s−g), liquid−gas (l−g), and solid−liquid (s−l) equilibrium lines. Melting temperatures (corresponding triple point temperatures, TP) are depicted for each compound.

3.3. Liquid−Gas Equilibrium: Thermodynamic Properties of Vaporization. The hypothetical thermodynamic parameters of vaporization, at T = 298.15 K, were derived from the fusion and sublimation results according eqs 11, 12, and 13. Δgl Hmo(T ) = Δsg Hmo(T ) − ΔslHmo(T )

Δgl Smo(T ) = Δsg Smo(T ) − ΔslSmo(T )

(12)

Δgl Gmo(T ) = Δsg Gmo(T ) − ΔslGmo(T )

(13)

Table 6 presents the derived standard molar enthalpies, entropies, and Gibbs energies of fusion, sublimation, and

(11) E



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Figure 4. Thermodynamic parameters of phase equilibria (enthalpies, entropies, and Gibbs energies of fusion/sublimation/vaporization), and absolute molar entropies of BP-A, BP-E, BP-F, BP-AP, and BP-S.

where θ and pθ are the derived temperature and pressure at the triple point. ΔHoθ is the standard molar enthalpy of phase transition and ΔCop,m is the variation in molar heat capacity associated with sublimation/vaporization process. The lines relative to the solid−gas transition was represented from the experimental vapor pressure measurements, using the derived Δgs Hom at ⟨T⟩. The liquid−gas transition lines were estimated from the combination of the experimental sublimation and fusion results, assuming Δg1Hom(⟨θ⟩) = Δgs Hmo(⟨θ⟩) − Δ1s Hom(⟨θ⟩), where Δgs Hom(⟨θ⟩) was calculated by eq 6 by replacing T for the temperature of the triple point. The solid−liquid lines were drawn schematically assuming equal triple point and standard melting temperatures. Hence, these lines should be regarded only as an approximation when the phase diagrams are analyzed. Deviations from these extrapolations are important, because large ranges of pressures are considered. From the phase diagrams it can be seen that solids BP-A and BP-F present similar volatilities, and therefore their crystal packings are probably similar. There are entropic and enthalpic contributions to justify the same volatility of these compounds (as verified in the Gibbs energies of sublimation). On the one hand, solid BP-E is more volatile (lower Gibbs energies of sublimation) than its congeners (BP-A and BP-F) due to an entropic differentiation due to its lower molecular symmetry, which also contributes for its lower triple point temperature.31−34 On the other hand, the thermodynamic stabilities of the liquid phases of BP-A, BP-E, and BP-F are very similar. As evidenced, the introduction of −CH3 groups in BP-F (giving BP-E and BP-A) is responsible for the entropic differentiation observed in solid phase, whereas in the liquid phase the enthalpic and entropic differentiations seem to be

vaporization at T = 298.15 K, for all the compounds. The entropies of the gas phase were derived from the quantum chemical calculations, and the entropies of the solid and liquid phases were calculated through eqs 14 and 15 (Table 4). Smo(s) = Smo(g) − Δsg Smo

(14)

Smo(l) = Smo(g) − Δgl Smo

(15)

Calculated values of specific heat capacities, absolute entropies, enthalpies, and entropies of sublimation are listed in Table 7.

4. DISCUSSION 4.1. Phase Diagrams of Bisphenol Derivatives. On the basis of the experimental results presented herein, the phase diagrams for BP-A, BP-E, BP-F, BP-AP, and BP-S are schematically represented in Figure 3. For each compound, the vapor pressures for the solid phase were calculated according to the Clarke and Glew equation28 (16), considering the calculation for the variation in molar heat capacity associated with sublimation process (Table 4). For the liquid phase, the value of −80 J·K−1·mol−1was estimated as the variation in molar heat capacity between the gas and liquid phases, which is a typical value of Δg1Cop,m for organic compounds as evidenced for biphenyl.29,30 R ln K p = −ΔGθo /θ + ΔHθo[(1/θ) − (1/T )] + ΔC po,m[(θ /T ) − 1 + ln(T /θ )]

(16)

θ is the triple point; T is the variable temperature; R is the gas constant; Kp = p/pο; and ΔGoθ is the standard molar Gibbs energy at triple point, calculated as {ΔGoθ = −R·⟨θ⟩·ln (pθ/po)}, F



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in solid and liquid phases seem to be similar. The higher melting point and lower volatility of solid and liquid BP-S (higher Δgs Gom and Δgl Gom) are justified by the lower values of Δgs Som and Δgl Som (higher molecular symmetry and low flexibility).

negligible for the three compounds. Solids BP-AP and BP-S present clearly lower volatilities than the other bisphenols, which is probably due to the higher energy of their crystal packing and high molecular symmetry of BP-S. As expected, both compounds present high triple point temperatures due to the thermodynamic stability of their solid phases. 4.2. Enthalpies, Entropies, and Gibbs Energies of Phase Transition. An evaluation of the thermodynamic parameters of phase equilibria (enthalpies, entropies, and Gibbs energies of fusion/sublimation/vaporization) was carried out to better evaluate the stability of solid and liquid phases of each compound (Table 6). Melting points, molar and specific heat capacities, enthalpies, entropies, and Gibbs energies of phase transition, as well as the calculated absolute entropies of the solid, liquid, and gas phases corroborate the understanding of the relative thermodynamic stability of the condensed phases of each compound. The quantum chemical calculations allowed the determination of the heat capacities and gas phase entropies of the most stable conformer. The computed energies and enthalpies for the stable conformations of the molecules studied and the activations barriers of BP-A, BP-E, BP-F, and BP-AP rotamers due to the rotation of their phenolic moiety rings were determined in a previous work.14 The scheme of Figure 4 represents a comparison for the thermodynamic parameters of phase equilibria for all the compounds studied. The solids BP-A and BP-F present similar volatilities (similar Δgs Gom) as verified in their phase diagrams, whereas solid BP-E presents a slightly lower stability of its crystalline phase. It is also verified a lower value of Δ1s Gom for BP-E, which is in accord with its lower melting temperature. The thermodynamic parameters of fusion refer to the hypothetical states corrected to T = 298.15 K, thus allowing a direct comparison of the fusion parameters for all the compounds. To compare the phase stabilities, the analysis of melting temperatures (Tm) becomes important, because they are related to enthalpic and entropic contributions, as indicated by the relation Tm = Δs1Hmo(Tm)/Δs1Smo(Tm). BP-A and BP-F exhibit molecular structures with symmetry (C2 point group in the gas phase) and seems to present a better crystal packing, contributing to the higher melting temperatures and higher Gibbs energies of fusion and sublimation (lower volatilities, higher solid phase stability). Although BP-A presents lower Δgs Hom (probably due to lower cohesive energies) and lower entropy of sublimation than its congener BP-F, the stabilities of their solid phases are similar due to an enthalpic and entropic compensation. Isotropic liquids BP-A, BP-E, and BP-F have very similar similar thermodynamic parameters contributing to the same volatility (similar Δgl Gom), as verified in the phase diagrams (Figure 3). The increments verified in the values of the absolute entropies and heat capacities of the solid phase due to the introduction of a −CH3 group from BP-F, giving BP-E and BP-A, are ≈25−30 J·K−1·mol−1 (Table 4). The knowledge of the specific values of heat capacities, absolute entropies, enthalpies, and entropies of sublimation are of scientific and industrial interest with many applications (Table 7). For example, the specific heat capacities are useful for the determination of thermal diffusivities of materials, which are helpful properties for the design and development of new polymers (namely polycarbonates) with well-defined thermal properties.35,36 Solid phases of BP-AP and BP-S are very thermodynamically stable (clear higher melting points and lower volatilities than the congeners BP-A, BP-E, and BP-F). Curiously, BP-AP and BP-S present similar values of Δgs Hom, Δ1s Hom, and Δg1Hom, and therefore their cohesive energies

5. CONCLUSIONS Phase transition thermodynamics including vapor pressures measurements of bisphenol A, bisphenol E, bisphenol F, bisphenol AP, and bisphenol S were presented. The thermodynamic properties of phase equilibria (fusion, sublimation and vaporization) were analyzed as well as the phase diagrams of each bisphenol derivative. Herein, it was shown that solids BP-A and BP-F present similar thermodynamic stabilities, whereas BP-E is more volatile. The introduction of −CH3 groups in BP-F (giving BP-E and BP-A) is responsible for the entropic differentiation observed in the solid phase, whereas the isotropic liquids BP-A, BP-E, and BP-F are very similar. Of all the bisphenols, solids BP-AP and BP-S present lower volatilities and higher melting temperatures due to the higher stability of their solid phases.

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ASSOCIATED CONTENT

S Supporting Information *

S1. DSC measurements: molar heat capacities at constant pressure, melting temperatures, standard enthalpies and entropies of fusion. S2. KEQCM measurements: vapor pressure determinations and thermodynamic parameters of sublimation. S3. Additional results of quantum chemical calculations. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*J. Z. Dávalos. E-mail: [email protected]. *L. M. N. B. F. Santos. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Thanks are due to Fundaçaõ para a Ciência e Tecnologia (FCT), Lisbon, Portugal, and to the European Social Fund for ́ financial support to Centro de Investigaçaõ em Quimica, University of Porto (strategic project PEst C/QUI/UI0081/ 2013). The support of the Spanish MICINN Project CTQ2009-13652 is also gratefully acknowledged. José C. S. Costa acknowledges FCT and the European Social Fund (ESF) under the third Community Support Framework (CSF) for the award of Ph.D. Research Grant SFRH/BD/74367/2010.

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REFERENCES

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