Chain-Length Dependence of the Thermodynamic ... - ACS Publications

Review Cite This: J. Chem. Eng. Data 2019, 64, 2229−2246

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Chain-Length Dependence of the Thermodynamic Behavior of Homologous α,ω-Disubstituted Alkanes Jose ́ C. S. Costa* and Luís M. N. B. F. Santos

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CIQUPCentro de Investigaçaõ em Química da Universidade do Porto, Departamento de Química e Bioquímica, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre, 687, Porto, P-4169-007, Portugal ABSTRACT: The chain-length dependence of the thermodynamic properties associated with the solid-to-liquid, liquid-to-gas, and solid-to-gas phase equilibria is analyzed and discussed for homologous families of linear α,ω-disubstituted alkanes, R-(CH2)n-R series. A remarkable alternation on the melting properties exhibited by even and odd-numbered alkanes is clearly emphasized in their α,ω-disubstituted derivatives since the even members display increased properties due to their higher crystal packing density. The odd−even effect is also perceived in the values of ΔsubHo and ΔsubSo. Strong hydrogen bonding contributes to high boiling points and ΔvapHo values evidenced by alkane-α,ω-diols. Moreover, the anomalously low values of ΔsubHo and ΔvapHo reported for larger dicarboxylic acids suggest the formation, in the vapor phase, of hydrogen-bonded cyclic structures. Furthermore, the analysis of the ΔfusHo/ΔsubHo and ΔfusSo/ΔsubSo ratios is used to highlight the contribution of functional groups to the cohesive interaction preserved in the liquid phase after a fusion transition. The thermodynamic interpretation indicates a higher structuration in the liquid alkane-α,ω-diols and alkane-α,ω-dioic acids, which have lower ratios of ΔfusHo/ΔsubHo than corresponding nalkanes. In addition, the thermodynamic analysis supports that hydrogen bonding in the liquid phase of alkanamines or alkaneα,ω-diamines has a significant low contribution to the overall intermolecular interactions.

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INTRODUCTION A fundamental understanding of phase transitions and condensed matter systems, comprising hydrocarbons and derivatives, is of research interest in various fields of application such as the oil industry,1−4 thin films and coatings,5−8 polymer science and engineering,9−12 and thermal energy storage and phase change materials (PCMs),13−18 among others. In a previous contribution, the chain-length dependence of the thermodynamic properties associated with the fusion, vaporization, and sublimation processes was investigated for homologous series of linear hydrocarbons and monosubstituted alkanes.19 Experimental data on melting and boiling points, heat capacities, and enthalpies and entropies of phase transition were reviewed and discussed.19 An odd−even alternation was observed in several thermodynamic properties related to the solid state. From the data analysis, trends in molar and specific thermodynamic properties of phase transition allowed the prediction of various thermodynamic properties for a very-long-chain monosubstituted alkane.19 To progress further, the present work presents a literature survey and analysis of thermodynamic properties associated with the phase transition for an extended series of homologous families of disubstituted alkane derivatives, R−(CH2)n−R series: n-alkanes (R = CH3); alkane-α,ω-diols (R = OH); alkane-α,ω-dithiols (R = SH); alkane-α,ω-diamines (R = NH2); alkane-α,ω-dioic acids (R = COOH); alkane-α,ωdiamides (R = CONH2); alkane-α,ω-dinitriles (R = CN); alkane-α,ω-dichlorides (R = Cl); alkane-α,ω-dibromides (R = © 2019 American Chemical Society

Br); and alkane-α,ω-diiodides (R = I). Experimental data on the thermodynamic properties associated with the fusion, vaporization and sublimation equilibria are reviewed and analyzed altogether with the data obtained for the monosubstituted alkanes. There are some valuable reports regarding the determination of thermodynamic properties for a homologous series of disubstituted alkanes.20−65 For instance, Della Gatta et al. have been concerned with the thermodynamic behavior of model compounds of environmental interest by studying phase transitions and heat capacity between the condensed states.20,22−26 The authors have explored the solid-to-solid and solid-to-liquid phase transitions for homologous series of alkane-α,ω-diols,20 alkane-α,ω-diamines,22 alkane-α,ω-diamides,23 and alkane-α,ω-dinitriles.24 The interactions between molecules, geometric properties, and the odd−even alternation have been discussed in several papers.20−32 For example, Boese et al. used a geometric model to explain the melting point alternation in alkane-α,ω-dithiols.21 Most thermodynamic properties can be found in the research contributions of Acree,37,39 Chickos,40,52,61 and Domalski35 and the contribution methods of various groups were developed to predict the thermodynamic properties of hydrocarbons and derivatives.66−73 In comparison with the monosubstituted analogues,19 there is a lower number of works regarding the Received: February 3, 2019 Accepted: April 24, 2019 Published: May 2, 2019 2229

DOI: 10.1021/acs.jced.9b00125 J. Chem. Eng. Data 2019, 64, 2229−2246

Journal of Chemical & Engineering Data

Review

Table 1. Melting Points (Tmelting), Standard (po = 105 Pa) Molar Enthalpies (ΔfusHo, at the Melting Temperature and Derived for 298.15 K), Entropies (ΔfusSo), and Gibbs Energies of Fusion (ΔfusGo), for Homologous Series of Disubstituted Alkane Derivatives: Alkane-α,ω-diols, Alkane-α,ω-dithiols, Alkane-α,ω-diamines, Alkane-α,ω-dioic Acids, Alkane-α,ω-diamides, Alkane-α,ω-dinitriles, Alkane-α,ω-dichlorides, Alkane-α,ω-dibromides, and Alkane-α,ω-diiodidesa Tmelting disubstituted alkane derivative

K

1,2-ethanediol 1,3-propanediol 1,4-butanediol 1,5-pentanediol 1,6-hexanediol 1,7-heptanediol 1,8-octanediol 1,9-nonanediol 1,10-decanediol 1,11-undecanediol 1,12-dodecanediol 1,13-tridecanediol 1,14-tetradecanediol 1,15-pentadecanediol 1,16-hexadecanediol 1,17-heptadecanediol 1,18-octadecanediol 1,19-nonadecanediol 1,20-eicosanediol

260.633 249.034 293.635 248.035 314.720 290.520 331.620 318.720 345.820 334.120 352.920 350.320 359.220 361.220 366.020 367.336 371.536 373.936 376.136

1,2-ethanedithiol 1,3-propanedithiol 1,4-butanedithiol 1,5-pentanedithiol 1,6-hexanedithiol 1,7-heptanedithiol 1,8-octanedithiol 1,9-nonanedithiol 1,10-decanedithiol

232.021 194.221 219.321 200.721 252.221 235.121 274.121 255.721 293.221

1,2-ethanediamine 1,3-propanediamine 1,4-butanediamine 1,5-pentanediamine 1,6-hexanediamine 1,7-heptanediamine 1,8-octanediamine 1,9-nonanediamine 1,10-decanediamine 1,11-undecanediamine 1,12-dodecanediamine

284.337 262.422 295.122 285.022 312.322 298.522 324.822 308.122 332.922 313.622 340.522

propanedioic acid butanedioic acid pentanedioic acid hexanedioic acid heptanedioic acid octanedioic acid nonanedioic acid decanedioic acid undecanedioic acid dodecanedioic acid tridecanedioic acid tetradecanedioic acid hexadecanedioic acid

407.538 457.037 371.037 426.437 377.539 415.337 380.037 404.035 385.035 402.535 386.340 397.340 395.440

ΔfusHοm(Tmelting) kJ·mol

−1

Alkane-α,ω-diols 10.033 11.434 18.735 15.736 26.420 26.320 36.320 36.720 45.020 45.920 54.220 54.820 63.520 65.320 72.820

ΔfusHοm(298 K) −1

kJ·mol

ΔfusSοm(298 K) −1

ΔfusGοm(298 K)

J·K·mol

kJ·mol−1

10.3 12.0 18.8 16.5 26.1 26.5 35.5 36.2 43.7 44.8 52.5 53.0 61.3 62.9 70.0

± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

2.1 2.2 2.0 2.2 2.0 2.0 2.1 2.0 2.1 2.1 2.3 2.3 2.3 2.4 2.4

39.6 ± 8.1 47.9 ± 8.8 63.9 ± 6.8 66.3 ± 8.9 82.9 ± 6.4 91.1 ± 6.9 107.0 ± 6.4 113.5 ± 6.4 126.1 ± 6.5 134.0 ± 6.4 148.2 ± 6.6 151.0 ± 6.6 170.0 ± 6.7 173.4 ± 6.7 190.6 ± 6.8

−1.5 ± 3.2 −2.3 ± 3.4 −0.3 ± 2.9 −3.3 ± 3.5 1.4 ± 2.8 −0.7 ± 2.9 3.6 ± 2.8 2.3 ± 2.8 6.1 ± 2.9 4.9 ± 2.9 8.3 ± 3.0 8.0 ± 3.0 10.6 ± 3.1 11.2 ± 3.1 13.2 ± 3.2

22.7 12.6 28.1 30.0 39.9 37.0 50.4 36.0 56.9 47.6 65.8

± ± ± ± ± ± ± ± ± ± ±

2.0 2.1 2.0 2.0 2.0 2.0 2.1 2.0 2.1 2.0 2.2

79.9 ± 7.1 48.0 ± 8.0 95.4 ± 6.8 105.3 ± 7.1 127.9 ± 6.5 123.9 ± 6.7 155.1 ± 6.4 116.7 ± 6.5 170.6 ± 6.4 151.9 ± 6.5 192.8 ± 6.4

−1.1 ± 2.9 −1.7 ± 3.2 −0.3 ± 2.8 −1.4 ± 2.9 1.8 ± 2.8 0.0 ± 2.8 4.2 ± 2.8 1.2 ± 2.8 6.0 ± 2.9 2.4 ± 2.8 8.3 ± 2.9

22.3 31.5 20.1 33.1 26.3 26.7 31.0 38.4 37.5 47.8 46.8 53.4

± ± ± ± ± ± ± ± ± ± ± ±

3.0 3.8 2.5 3.3 2.6 3.1 2.6 2.9 2.6 2.9 2.7 2.8

54.4 ± 7.9 68.3 ± 9.6 53.8 ± 6.9 76.9 ± 8.6 69.3 ± 7.1 63.3 ± 8.2 81.1 ± 7.2 94.1 ± 7.8 96.7 ± 7.3 117.5 ± 7.8 120.2 ± 7.3 133.1 ± 7.6

6.1 ± 3.8 11.2 ± 4.7 4.0 ± 3.2 10.2 ± 4.1 5.7 ± 3.3 7.8 ± 3.9 6.8 ± 3.4 10.3 ± 3.7 8.7 ± 3.4 12.7 ± 3.7 11.0 ± 3.4 13.7 ± 3.6

Alkane-α,ω-dithiols

Alkane-α,ω-diamines 22.637 12.222 28.122 29.822 40.222 37.022 51.022 36.222 57.822 48.122 67.122 Alkane-α,ω-dioic Acids 23.138 33.037 20.937 34.937 27.639 28.837 32.737 40.835 39.735 50.635 49.440 56.540

2230



Review

Table 1. continued disubstituted alkane derivative

Tmelting

ΔfusHοm(Tmelting)

ΔfusHοm(298 K)

ΔfusSοm(298 K)

ΔfusGοm(298 K)

K

kJ·mol−1

kJ·mol−1

J·K·mol−1

kJ·mol−1

64.4 ± 9.2

9.6 ± 4.5

79.7 ± 9.5 98.5 ± 11.1 93.3 ± 9.2 109.2 ± 10.9 113.6 ± 9.4 131.0 ± 10.5 132.4 ± 9.4 145.9 ± 9.9 150.7 ± 10.0

12.8 20.6 14.4 22.3 18.0 25.5 21.1 25.6 27.1

10.7 ± 2.0

35.2 ± 6.6

0.2 ± 2.8

± ± ± ± ± ± ± ±

53.9 ± 9.1 66.6 ± 7.5 65.4 ± 9.3 83.7 ± 7.7 78.0 ± 8.7 101.6 ± 7.2 100.6 ± 7.9 117.0 ± 6.8

−2.8 −1.5 −3.6 −2.4 −3.6 −1.7 −3.2 −0.5

7.1 ± 2.4 9.4 ± 1.2

38.6 ± 10.3 39.2 ± 4.6

−4.4 ± 5.5 −2.3 ± 3.7

11.1 ± 2.0 15.3 ± 2.3

39.3 ± 7.1 63.8 ± 9.5

−0.6 ± 2.9 −3.7 ± 3.7

12.2 ± 2.0

43.8 ± 7.3

−0.8 ± 3.0

Alkane-α,ω-dioic Acids octadecanedioic acid

398.141

propanediamide butanediamide pentanediamide hexanediamide heptanediamide octanediamide nonanediamide decanediamide undecanediamide dodecanediamide tetradecanediamide

444.223 536 (dec.)23 454.023 499.123 446.823 493.223 450.423 484.323 451.223 466.123 469.323

propanedinitrile butanedinitrile pentanedinitrile hexanedinitrile heptanedinitrile octanedinitrile nonanedinitrile decanedinitrile undecanedinitrile dodecanedinitrile

305.035 331.235 244.235 275.024 241.724 268.924 251.124 281.224 266.124 294.224

dichloromethane 1,2-dichloroethane 1,3-dichloropropane 1,4-dichlorobutane 1,5-dichloropentane 1,6-dichlorohexane 1,8-dichlorooctane 1,10-dichlorodecane 1,12-dichlorododecane

178.235 237.235 174.242 234.542 201.242 260.242 265.242 288.843 302.245

dibromomethane 1,2-dibromoethane 1,3-dibromopropane 1,4-dibromobutane 1,5-dibromopentane 1,6-dibromohexane 1,8-dibromooctane 1,10-dibromodecane 1,11-dibromoundecane 1,12-dibromododecane

220.543 283.035 238.635 252.144 233.245 271.245 287.245 299.245 262.645 313.245

diiodomethane 1,2-diiodoethane 1,3-diiodopropane 1,4-diiodobutane 1,5-diiodopentane 1,6-diiodohexane 1,10-diododecane

279.246 354.245 253.245 279.144 282.245 282.647 307.245

Alkane-α,ω-diamides 29.923

28.8 ± 3.5

38.423 52.723 44.623 58.423 55.023 68.823 64.423 73.723 77.523 Alkane-α,ω-dinitriles 10.835

36.6 49.9 42.2 54.8 51.9 64.6 60.6 69.1 72.1

12.635 18.024 15.024 22.024 18.724 28.224 26.024 34.324 Alkane-α,ω-dichlorides 6.235 8.835

13.2 18.3 15.9 22.5 19.7 28.6 26.8 34.4

± ± ± ± ± ± ± ± ±

3.7 4.5 3.6 4.4 3.6 4.2 3.7 3.9 4.0

2.3 2.1 2.3 2.1 2.2 2.0 2.1 2.0

± ± ± ± ± ± ± ± ±

± ± ± ± ± ± ± ±

4.7 5.6 4.5 5.4 4.6 5.3 4.6 4.9 5.0

3.5 3.0 3.6 3.1 3.4 3.0 3.1 2.8

Alkane-α,ω-dibromides 11.035 14.635

Alkane-α,ω-diiodides 12.146

a

The uncertainties of the hypothetical thermodynamic properties of fusion at 298.15 K were calculated by the error propagation rules considering Δ(ΔfusH) = 2 kJ·mol−1 and Δ(ΔfusCp) = 20 J·K−1·mol−1; (dec.) decomposition.

Ribeiro da Silva,62 Verevkin,50,51,57,64 Chickos,52,61 and Della Gatta,53 among others, have determined thermodynamic

vaporization and/or sublimation equilibria for the disubstituted alkane derivatives. Nonetheless, Majer and Svoboda,55 2231



Review

Table 2. Boiling Points (Tboiling), Standard (po = 105 Pa) Molar Enthalpies (ΔvapHo), Entropies (ΔvapSo), Gibbs Energies of Vaporization (ΔvapGo), and Extrapolated Vapor Pressures (pliquid), at T = 298.15 K, for Homologous Series of Disubstituted Alkane Derivatives: Alkane-α,ω-diols, Alkane-α,ω-dithiols, Alkane-α,ω-diamines, Alkane-α,ω-dioic Acids, Alkane-α,ωdiamides, Alkane-α,ω-dinitriles, Alkane-α,ω-dichlorides, Alkane-α,ω-dibromides, and Alkane-α,ω-diiodidesa disubstituted alkane derivative

Tboiling

ΔvapGοm(298 K)b

ΔvapHοm (298 K)

ΔvapSοm (298 K)

Pliquid (298 K)c

K

kJ·mol−1

kJ·mol−1

J·K·mol−1

Pa

143.5 150.6 163.7 175.1 192.1 201.9 225.3 236.8 255.8 270.0 283.3 302.2 312.8 327.7 343.5

± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

5.8 4.4 7.5 7.5 9.4 6.6 1.9 4.8 8.4 5.4 6.0 5.4 7.0 5.4 7.8

(3.8−32) × 100 (1.5−73) × 100 (2.5−52) × 10−1 (8.5−170) × 10−2 (2.4−64) × 10−2 (2.0−10) × 10−2 (7.3−29) × 10−3 (2.4−12) × 10−3 (4.2−97) × 10−4 (2.8−14) × 10−4 (8.1−46) × 10−5 (3.3−17) × 10−5 (9.0−62) × 10−6 (3.9−20) × 10−6 (1.2−10) × 10−6

108.5 119.0 123.3 129.6 135.8 146.6

± ± ± ± ± ±

5.0 5.0 5.0 5.0 6.0 6.0

(2.5−19) × 102 (1.2−9.0) × 102 (2.2−17) × 101 (8.8−66) × 100 (1.5−26) × 100 (7.7−130) × 10−1

116.3 124.5 131.7 134.3 142.4 148.2 156.5

± ± ± ± ± ± ±

5.0 1.5 7.1 6.7 10.0 10.0 6.4

(5.7−43) × 102 (2.2−12) × 102 (7.4−42) × 101 (2.8−14) × 101 (7.2−81) × 100 (2.9−32) × 100 (1.8−9.2) × 100

161.9 158.9 182.8 176.5 209.4 219.7 239.4 226.2 222.3 179.7

± ± ± ± ± ± ± ± ± ±

8.2 13.1 7.7 9.2 7.6 12.8 8.3 10.8 8.8 11.4

(1.5−34) × 10−3 (2.4−400) × 10−4 (2.8−50) × 10−4 (6.9−250) × 10−5 (2.6−46) × 10−5 (1.5−220) × 10−6 (1.7−41) × 10−6 (4.7−310) × 10−7 (9.6−280) × 10−7 (1.5−130) × 10−6

1,2-ethanediol 1,3-propanediol 1,4-butanediol 1,5-pentanediol 1,6-hexanediol 1,7-heptanediol 1,8-octanediol 1,9-nonanediol 1,10-decanediol 1,11-undecanediol 1,12-dodecanediol 1,13-tridecanediol 1,14-tetradecanediol 1,15-pentadecanediol 1,16-hexadecanediol

471.248 486.748 503.245 515.245 523.245

22.6 25.6 28.2 30.9 33.7 36.2 39.0 41.5 43.9 46.8 49.7 52.1 55.0 57.4 59.7

± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

1,2-ethanedithiol 1,3-propanedithiol 1,4-butanedithiol 1,5-pentanedithiol 1,6-hexanedithiol 1,7-heptanedithiol 1,8-octanedithiol

419.248 442.245 468.748

12.3 14.2 18.3 20.6 24.0 25.7

± ± ± ± ± ±


389.748 412.955 431.748 452.248 477.748 497.248

10.3 13.1 15.7 18.3 20.6 22.9 25.0

± ± ± ± ± ± ±

542.745

propanedioic acid butanedioic acid pentanedioic acid hexanedioic acid heptanedioic acid octanedioic acid nonanedioic acid decanedioic acid undecanedioic acid dodecanedioic acid

40.8 42.9 45.2 47.8 51.1 55.6 57.5 59.5 58.7 56.3

propanediamide propanedinitrile butanedinitrile pentanedinitrile hexanedinitrile heptanedinitrile octanedinitrile

Alkane-α,ω-diols 2.649 65.4 ± 2.050 2.0e 70.5 ± 1.551 3.7e 77.0 ± 3.052 e 3.7 83.1 ± 3.052 53 4.1 91.0 ± 3.052 2.0e 96.4 ± 0.352 1.753 106.2 ± 1.652 e 2.0 112.1 ± 1.452 53 3.9 120.2 ± 3.052 2.0e 127.3 ± 1.220 53 2.2 134.2 ± 1.220 e 2.0 142.2 ± 1.220 53 2.4 148.2 ± 1.220 2.0e 155.1 ± 1.220 53 2.6 162.1 ± 1.220 Alkane-α,ω-dithiols 2.554 44.7 ± 2.055 2.554 49.7 ± 2.055 54 2.5 55.1 ± 2.055 54 2.5 59.3 ± 2.055 3.554 64.5 ± 3.0d 3.554 69.4 ± 3.0d

491.748 539.248 559.248 568.248

16.9 17.7 22.3 23.7

Alkane-α,ω-diamines 2.556 45.0 ± 2.055 54 2.1 50.2 ± 2.055 54 2.1 55.2 ± 0.357 54 2.0 58.3 ± 0.257 3.0e 63.1 ± 0.257 e 2.5 67.1 ± 0.257 54 2.0 71.7 ± 0.657 75.5 ± 0.357 80.2 ± 0.357 84.7 ± 0.457 89.2 ± 0.657 Alkane-α,ω-dioic Acidsd ± 3.9 89.1 ± 3.0 ± 6.3 90.3 ± 5.0 ± 3.6 99.7 ± 2.8 ± 4.5 100.5 ± 3.5 ± 3.6 113.6 ± 2.7 ± 6.2 121.1 ± 4.9 ± 3.9 128.9 ± 3.0 ± 5.2 126.9 ± 4.1 ± 4.2 125.0 ± 3.3 ± 5.5 109.8 ± 4.4 Alkane-α,ω-diamidesd 97.6 ± 3.6 Alkane-α,ω-dinitriles

± ± ± ±

2.558 2.558 2.558 2.558

66.5 71.0 75.4 78.5 2232

± ± ± ±

2.058 3.0e 2.058 2.058

166.4 ± 5.0 178.3 ± 5.0 183.8 ± 5.0

(4.0−30) (2.9−22) (4.6−34) (2.6−19)

× × × ×

101 101 100 100



Review


Tboiling

ΔvapGοm(298 K)b

ΔvapHοm (298 K)

ΔvapSοm (298 K)

Pliquid (298 K)c

K

kJ·mol−1

kJ·mol−1

J·K·mol−1

Pa

± 2.058 ± 2.058

189.1 ± 5.0 193.7 ± 5.0

(1.2−9.1) × 100 (5.4−41) × 10−1

± ± ± ± ± ± ± ± ± ±

2.055 2.055 2.055 2.055 2.055 2.059 2.059 2.059 3.0e 2.060

130.9 137.2 143.6 150.3 154.7

± ± ± ± ±

5.0 5.0 5.0 5.0 5.0

(2.1−16) (3.6−27) (8.2−62) (1.9−14) (5.8−44)

× × × × ×

106 105 104 104 103

± ± ± ± ±

2.055 2.055 2.055 2.055 3.055

138.6 143.4 145.6 152.1 163.7

± ± ± ± ±

5.0 5.0 5.0 5.0 5.6

(2.1−16) (5.6−42) (7.0−52) (1.6−12) (4.3−32)

× × × × ×

105 104 103 103 102

± ± ± ±

2.061 2.061 2.061 2.061

139.3 ± 5.0 146.0 ± 5.0

nonanedinitrile decanedinitrile dichloromethane 1,2-dichloroethane 1,3-dichloropropane 1,4-dichlorobutane 1,5-dichloropentane 1,6-dichlorohexane 1,7-dichloroheptane 1,8-dichlorooctane 1,9-dichlorononane 1,10-dichlorodecane

313.055 356.655 394.055 427.148 453.248 477.248 500e 514.248 533.248

dibromomethane 1,2-dibromoethane 1,3-dibromopropane 1,4-dibromobutane 1,5-dibromopentane 1,6-dibromohexane 1,7-dibromoheptane 1,8-dibromooctane 1,9-dibromononane

370.155 404.855 440.548 470.248 495.548 516.245 536.248 544.248 559.745

diiodomethane 1,2-diiodoethane 1,3-diiodopropane 1,4-diiodobutane

453.258 473.258

Alkane-α,ω-dinitriles 81.9 25.6 ± 2.558 27.6 ± 2.558 85.3 Alkane-α,ω-dichlorides −10.0 ± 2.558 29.0 −5.7 ± 2.558 35.2 −2.0 ± 2.558 40.8 1.6 ± 2.558 46.4 4.6 ± 2.558 50.7 56.3 61.2 65.6 69.4 73.1 Alkane-α,ω-dibromides −4.3 ± 2.558 37.0 −1.1 ± 2.558 41.7 4.1 ± 2.558 47.5 7.7 ± 2.558 53.1 11.0 ± 2.558 59.8

Alkane-α,ω-diiodides 4.1 ± 2.558 45.6 6.3 ± 2.558 49.8 54.1 59.0

(7.0−53) × 103 (2.9−22) × 103

a

The uncertainties of the hypothetical thermodynamic properties of vaporization at 298.15 K were calculated by the error propagation rules considering Δ(ΔvapCp) = 20 J·K−1·mol−1. bValues derived from the dependence of vapor pressure with the vaporization temperature and by heat capacity correction to 298.15 K. cExtrapolated vapor pressures from the Gibbs energies of vaporization. dValues derived from the combination of fusion and sublimation results. eInter/extrapolated values.

properties (fusion) at θ = 298.15 K. For the analysis and discussion, the value of ΔfusCop is considered constant within the temperature range (θ to the melting point). The hypothetical value of the Gibbs energies of fusion at the reference temperature θ (ΔfusGo), used to evaluate the solid phase stability over the liquid, is expressed by eq 3.19 ÄÅ ÉÑ ÅÅ θ ÑÑÑ o o Å Å ÑÑ ΔfusG (θ ) = ΔfusH (Tm)ÅÅ1 − ÅÅÇ Tm ÑÑÑÖ ÉÑ ÄÅ ÑÑ ÅÅ i ij θ yzyzz Ñ Å jj oÅ + ΔfusC pÅÅθ jjj1 − lnjjj zzzzzz − (Tm)ÑÑÑ ÑÑ ÅÅ jT z ÑÑÖ ÅÅÇ k k m {{ (3)

properties for some α,ω-disubstituted alkanes, which are reviewed and discussed in this work. On the basis of the reviewed data, the gradual introduction of methylene moieties (−CH2−) on the relative stability of the crystalline and liquid phases of homologous series of disubstituted alkane derivatives is investigated according to the chain length dependence of the thermodynamic properties of phase transition: molar and specific enthalpies, entropies, and Gibbs energies of fusion, vaporization, and sublimation. Following the methodology of our previous work, all properties were converted to a reference temperature of θ = 298.15 K, which enables a comparison between all data.19 Considering the solid-to-liquid phase transition, enthalpies (ΔfusHo) and entropies (ΔfusSo) of fusion were converted to a hypothetical temperature of θ = 298.15 K according to eqs 1 and 2, respectively.19 ΔfusH o(θ ) = ΔfusH o(Tm) + ΔfusC po(θ − Tm) ΔfusS o(θ ) =

ΔfusH o ji θ zy + ΔfusC po lnjjj zzz jT z Tm k m{

Considering the liquid-to-gas and solid-to-gas phase transitions, Gibbs energies associated with the vaporization or sublimation processes (Δvap;subGo) were calculated from the respective enthalpies and entropies of phase transition by the fundamental thermodynamic relation {ΔG(θ) = ΔH(θ) − θ·ΔS(θ)}. The enthalpies and entropies of phase transition were obtained from the literature by the dependence of vapor pressures with temperature, using the integrated form of the Clausius−Clapeyron equation, following the procedures presented in previous works.19,74,75 The standard (po = 105 Pa) enthalpies (Δvap;subHo) and entropies (Δvap;subSo) of vaporization or sublimation at the reference temperature θ

(1)

(2)

The enthalpies and entropies obtained at the melting temperature (Tm) were reviewed from the literature and the difference between the molar heat capacity of the condensed phases (ΔfusCop) was used to derive the thermodynamic 2233



Review

Table 3. Standard (po = 105 Pa) Molar Enthalpies (ΔsubHo), Entropies (ΔsubSo), Gibbs Energies of Sublimation (ΔsubGo), and Extrapolated Vapor Pressures (psolid), at T = 298.15 K, for Homologous Series of Disubstituted Alkane Derivatives: Alkaneα,ω-diols, Alkane-α,ω-diamines, Alkane-α,ω-dioic Acids, Alkane-α,ω-diamides, Alkane-α,ω-dinitriles, Alkane-α,ω-dichlorides, Alkane-α,ω-dibromides, and Alkane-α,ω-diiodidesa disubstituted alkane derivative

ΔsubGοm(298 K)

ΔsubHοm(298 K)

ΔsubSοm(298 K)

Psolid 298 Kb

kJ·mol−1

kJ·mol−1

J·K·mol−1

Pa

183.1 198.5 227.6 241.3 275.0 293.0 332.3 350.3 381.9 404.0 431.5 453.2 482.8 501.1 534.1

± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

10.0 9.9 10.1 11.6 11.4 9.6 6.7 8.0 10.6 8.4 8.9 8.5 9.7 8.6 10.4

(3.7−110) × 100 (1.7−41) × 100 (1.9−86) × 10−1 (1.8−110) × 10−1 (9.5−520) × 10−3 (1.5−250) × 10−2 (8.8−130) × 10−4 (5.2−83) × 10−1 (2.4−120) × 10−5 (2.2−36) × 10−5 (1.5−31) × 10−6 (6.9−120) × 10−7 (6.8−160) × 10−8 (2.2−43) × 10−8 (3.2−89) × 10−9

196.2 172.4 227.1 239.6 270.3 272.1 311.5

± ± ± ± ± ± ±

8.7 8.2 9.8 9.7 11.9 12.1 9.0

(5.1−110) × 102 (2.2−47) × 102 (4.7−83) × 101 (2.6−46) × 101 (2.2−61) × 100 (1.8−50) × 100 (1.9−31) × 10−1

216.3 227.2 236.6 253.4 278.7 283.0 320.5 320.3 319.0 297.2 286.7

± ± ± ± ± ± ± ± ± ± ±

2.062 8.962 3.462 3.462 2.762 9.862 4.262 7.462 4.962 8.362 8.262

(4.2−8.8) × 10−4 (6.1−190) × 10−6 (1.2−4.4) × 10−4 (3.5−13) × 10−6 (6.6−19) × 10−6 (1.1−53) × 10−7 (2.3−12) × 10−7 (1.4−26) × 10−8 (5.9−41) × 10−8 (1.5−43) × 10−8 (1.1−29) × 10−8

c

± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

1,2-ethanediol 1,3-propanediol 1,4-butanediol 1,5-pentanediol 1,6-hexanediol 1,7-heptanediol 1,8-octanediol 1,9-nonanediol 1,10-decanediol 1,11-undecanediol 1,12-dodecanediol 1,13-tridecanediol 1,14-tetradecanediol 1,15-pentadecanediol 1,16-hexadecanediol

21.1 23.3 27.9 27.6 35.1 35.5 42.7 43.8 50.0 51.7 58.0 60.1 65.5 68.6 72.9


9.2 ± 3.8 11.4 ± 3.8 15.4 ± 3.6 16.9 ± 3.5 22.5 ± 4.1 23.0 ± 4.1 29.2 ± 3.5

propanedioic acid butanedioic acid pentanedioic acid hexanedioic acid heptanedioic acid octanedioic acid nonanedioic acid decanedioic acid undecanedioic acid dodecanedioic acid hexadecanedioic acid

46.9 54.1 49.3 58.0 56.8 63.4 64.3 69.8 67.4 69.0 69.9

± ± ± ± ± ± ± ± ± ± ±

4.2 4.0 4.7 5.1 5.0 3.5 3.3 3.4 4.9 3.5 3.7 3.6 3.9 3.7 4.1

0.9 4.2 1.6 1.6 1.3 4.8 2.0 3.6 2.4 4.1 4.1

propanediamide propanedinitrile butanedinitrile pentanedinitrile hexanedinitrile heptanedinitrile octanedinitrile nonanedinitrile decanedinitrile

9.6 ± 1.558

dichloromethane 1,2-dichloroethane

−14.5 ± 6.1 −8.0 ± 4.5

14.1 16.2 18.7 21.3 22.0 25.8

± ± ± ± ± ±

4.3 3.9 4.4 4.0 4.2 3.9

Alkane-α,ω-diols 75.7 ± 2.9 82.5 ± 2.7 95.8 ± 3.6 99.6 ± 3.7 117.1 ± 3.6 122.9 ± 2.0 141.7 ± 2.6 148.3 ± 2.5 163.9 ± 3.7 172.1 ± 2.4 186.7 ± 2.6 195.2 ± 2.6 209.5 ± 2.6 218.0 ± 2.7 232.1 ± 2.7 Alkane-α,ω-diaminesc 67.7 ± 2.8 62.8 ± 2.9 83.1 ± 2.0 88.3 ± 2.0 103.0 ± 2.0 104.1 ± 2.0 122.1 ± 2.2 111.5 ± 2.0 137.1 ± 2.1 132.3 ± 2.1 155.0 ± 2.3 Alkane-α,ω-dioic Acids 111.4 ± 0.762 121.8 ± 3.362 119.8 ± 1.262 133.6 ± 1.362 139.9 ± 1.062 147.8 ± 3.862 159.9 ± 1.662 165.3 ± 2.962 162.5 ± 1.962 157.6 ± 3.362 155.4 ± 3.362 Alkane-α,ω-diamides 126.4 ± 0.563 Alkane-α,ω-dinitrilesc 78.4 ± 1.064 70.0 ± 1.065 79.8 ± 3.0 89.3 ± 3.6 91.3 ± 3.0 101.0 ± 2.9 101.6 ± 3.0 113.9 ± 2.8 Alkane-α,ω-dichloridesc 36.1 ± 3.7 44.6 ± 3.1

2234

230.7 ± 3.7 220.3 245.3 243.7 267.5 267.1 295.3

± ± ± ± ± ±

10.4 9.3 10.6 9.2 10.0 8.8

169.5 ± 16.0 176.3 ± 10.8

(1.1−3.8) × 103 (6.0−200) × 101 (3.0−71) × 102 (9.2−310) × 100 (3.8−94) × 100 (2.6−77) × 100 (6.2−140) × 10−1 (3.0−390) × 106 (4.2−150) × 105



Review


ΔsubGοm(298 K)

ΔsubHοm(298 K)

ΔsubSοm(298 K)

Psolid 298 Kb

kJ·mol−1

kJ·mol−1

J·K·mol−1

Pa

c

1,2-dibromoethane 1,3-dibromopropane

−1.7 ± 3.9 0.4 ± 4.4

diiodomethane

3.2 ± 3.9

Alkane-α,ω-dibromides 52.8 ± 2.8 62.8 ± 3.1 Alkane-α,ω-diiodidesc 57.8 ± 2.9

182.8 ± 8.7 209.3 ± 10.7

(4.1−92) × 104 (1.4−51) × 104

183.1 ± 8.9

(5.6−130) × 103

a

The uncertainties of the hypothetical thermodynamic properties of sublimation at 298.15 K were calculated by the error propagation rules. Extrapolated vapor pressures from the Gibbs energies of sublimation. cValues derived from the combination of fusion and vaporization results.

b

were derived by eqs 4 and 5, respectively.19Δvap;subHo (⟨T⟩) was obtained from the Clausius−Clapeyron equation and the difference between the molar heat capacity of the gas and liquid/solid phases (Δvap;subCpo) was used to derive the thermodynamic properties (vaporization and sublimation) at θ = 298.15 K. The thermodynamic properties of the phase transition can be interrelated according to eq 6, for which θ is the reference temperature.19

(CH2)n−NH2, measured by DSC, were obtained from another investigation of Della Gatta et al., who interpreted and discussed the solid-to-liquid phase transition based on the crystal structures of the alkane-α,ω-diamines, and their corresponding intermolecular interactions.22 Melting properties of alkane-α,ω-dioic acids, HOOC−(CH2)n−COOH, were mostly reviewed from the contributions of Acree, Domalski, and Chickos, who compiled several data sets on the enthalpy of fusion and melting point for organic compounds.35,37,39,40 The thermodynamic properties of fusion for alkane-α,ω-diamides, H2NCO-(CH2)n-CONH2, and alkane-α,ω-dinitriles, NC(CH2)n-CN, were also obtained from the research works of Della Gatta et al, who have explored fusion and solid-to-solid transitions and investigated the odd−even effect in a homologous series.23,24 Concerning the alkane-α,ω-dihalides, melting temperatures are reported from several authors and values for the enthalpies of fusion are scarce in the literature.35,42−47 Table 2 lists the reviewed values of the boiling points and the thermodynamic properties of vaporization, derived at θ = 298.15 K, for homologous series of disubstituted alkane derivatives. Most of the boiling points were obtained from a handbook of data on organic compounds recommended by Weast and Grasselli.48 For the alkane-α,ω-diols, Gibbs energies of vaporization (ΔvapGo), at θ = 298.15 K, were derived by the combination of enthalpies (ΔvapHo) and entropies (ΔvapSo) of phase transition, which had been determined by Della Gatta from the temperature dependence of vapor pressure measured by the torsion-effusion and Knudsen-effusion methods.53 On the basis of the volatility studies, the same approach aimed at determining ΔvapGo, at θ = 298.15 K, was carried out for all compounds. As demonstrated in a previous work, the conversion of thermodynamic properties to θ = 298.15 K by a heat capacity correction could be associated with a significant error. Nevertheless, this issue is not so relevant for the values of ΔvapGo.19 Accurate values of ΔvapHo, at θ = 298.15 K, for the diols were obtained from the experimental measurements delivered by Chickos, Verevkin, and Della Gatta,20,51,53 and the values of ΔvapSo, at θ = 298.15 K, were derived by the combination of ΔvapGo and ΔvapHo. Predicted values for the vapor pressures of the liquid phase, at 298.15 K, were extrapolated from the Gibbs energies of vaporization. For the alkane-α,ω-dithiols, ΔvapGo was derived from the temperature dependence of vapor pressure listed in the Yaws Handbook of Vapor Pressure.54 High accuracy values of ΔvapHo, at θ = 298.15 K, were taken from the critical review and data compilation published by Majer and Svoboda.55 The thermodynamic properties of vaporization for the alkane-α,ωdiamines were reviewed from the same data compilations, altogether with experimental determinations of the vapor pressure and enthalpy of vaporization of linear aliphatic

Δ vap;subH o(θ ) = Δ vap;subH o(⟨T ⟩) + Δ vap;subC po(θ − ⟨T ⟩) i θ yz zz + Δ vap;subC po lnjjjj z k ⟨T ⟩ {

(4)

o

Δ vap;subS o(θ ) =

Δ vap;subH (⟨T ⟩) ij po yz zz − R lnjjj j p⟨T ⟩ zz k { ⟨T ⟩

(5)

Δsub[H o ; S o ; Go](θ ) = Δ vap[H o ; S o ; Go](θ ) + Δfus[H o ; S o ; Go](θ )

(6)

From the data analysis, trends in melting and boiling points, and trends in molar/specific thermodynamic properties of fusion, vaporization and sublimation are plotted for the homologous series of α,ω-disubstituted alkanes studied. In some cases, the relative stability of the solid and liquid phases is analyzed and discussed by comparing altogether mono- and disubstituted alkane derivatives. In addition, insights on the contribution of the functional groups for the cohesive interaction preserved in the liquid phase as well as the odd− even alternation detected for the thermodynamic properties related to the solid state are highlighted along this work.

■

DATA ANALYSIS AND DISCUSSION Table 1 lists the thermodynamic properties of fusion for homologous series of disubstituted alkane derivatives. Reviewed values of the melting temperatures and associated enthalpies of fusion as well as the thermodynamic properties, derived at θ = 298.15 K, are presented. Melting properties of alkane-α,ω-diols were mostly reviewed from the contribution of Della Gatta et al., who measured the temperatures and enthalpies of fusion for homologous series of linear alkane-α,ωdiols, HO−(CH2)n−OH, by differential scanning calorimetry (DSC).20 For the congeners, alkane-α,ω-dithiols, melting points of nine compounds, HS−(CH2)n−SH, were obtained from the contribution of Boese et al., who explored the melting point alternation by understanding the crystal-packing behavior of alkyl chains and −SH groups.21 There are no data available regarding the determination of enthalpies of fusion for alkane-α,ω-diols. Melting temperatures, enthalpies, and entropies of fusion of 10 alkane-α,ω-diamines, H2N− 2235



Review

Figure 1. Trends in melting (A) and boiling points (B) for homologous series of disubstituted alkane derivatives: alkane-α,ω-diols (blue ◆); alkane-α,ω-dithiols (blue ◇); alkane-α,ω-diamines (green ■); alkane-α,ω-dioic acids (red ▲); alkane-α,ω-diamides (orange -); alkane-α,ωdinitriles (gold □); alkane-α,ω-dichlorides (yellow ∗); alkane-α,ω-dibromides (red ×) and alkane-α,ω-diiodides (purple +). Trends for the isoelectronic linear alkanes are depicted for comparison (gray ●).

diamines reported by Verevkin et al.57 The vaporization properties for alkane-α,ω-dioic acids and alkane-α,ω-diamides were derived by the combination of fusion and sublimation results, which will be further discussed. For the alkane-α,ωdinitriles, ΔvapGo and ΔvapHo, at θ = 298.15 K, were derived from the properties reported by Stephenson and Malanowski, who presented a compilation on the thermodynamics of organic compounds, including the temperature dependence of vapor pressure.58 ΔvapGo values for homologous series of alkane-α,ω-dihalides were derived from the same data compilation.58 Accurate values of ΔvapHo, at θ = 298.15 K, for alkane-α,ω-dichlorides, alkane-α,ω-dibromides, and alkaneα,ω-diiodides were reviewed from the reports of Majer and Svoboda as well as from Chickos et al.55,61 The fusion and vaporization data are combined in Table 3 which lists the calculated values for the thermodynamic properties of sublimation, at θ = 298.15 K, for the homologous series of alkane-α,ω-diols, alkane-α,ω-diamines, alkane-α,ωdinitriles, alkane-α,ω-dichlorides, alkane-α,ω-dibromides, and alkane-α,ω-diiodides. For the alkane-α,ω-dioic acids, ΔsubHo, ΔsubSo, and ΔsubGo were obtained from the investigation of Ribeiro da Silva et al., who have used the Knudsen mass-loss technique to measure the vapor pressures in the solid phase of dicarboxylic acids.62 The reported studies on thermodynamic properties of vaporization and sublimation for the alkane-α,ωdiamides were found to be very scarce. For the homologous series studied, predicted values for the hypothetical vapor pressures of the crystalline phase, at 298.15 K, were extrapolated from the Gibbs energies of sublimation. Allowing a comparison between all data, trends (chain length dependence) in melting and boiling temperatures, trends in molar and specific thermodynamic properties associated to the solid− liquid phase transition, trends in molar and specific thermodynamic properties associated to the liquid−gas phase transition, and trends in molar and specific thermodynamic properties associated with the solid−gas phase transition are plotted for the homologous series of disubstituted alkane derivatives. In all graphical representations the trends for the isoelectronic linear alkanes are depicted for comparison. Figure 1 represents the trends in melting (Tmelting) and boiling (Tboiling) temperatures for a homologous series of disubstituted

alkane derivatives. The odd−even alternation observed for the linear alkanes and their monosubstituted derivatives is also observed in all homologous series of α,ω-disubstituted alkanes. The α,ω-disubstituted alkanes show an alternation in their melting temperatures with even members (even number of methylene groups) exhibiting systematically higher values than odd members. As demonstrated in our previous review, the Tmelting values for the isoelectronic linear alkanes with an even number of carbons can be plotted by a polynomial fit that is higher than the curve obtained for the odd-numbered alkanes.19 The odd−even effect has been investigated by different authors. Several researchers have interpreted the melting point alternation regarding the literature data on crystal structures of the α,ω-derivatives, and their corresponding intermolecular interactions.20−32 Commonly, the higher fusion temperatures of even-numbered compounds can be a consequence of a more efficient packing of their alkyl chains, as observed for linear alkanes, alkane-α,ω-diols, alkane-α,ωdiamines, alkane-α,ω-diamides, and alkane-α,ω-dioic acids.20,22−26,31 Boese et al. have explored the structural properties of even- and odd-numbered alkane-α,ω-dithiols by investigating the crystal packing arrangements of hydrocarbon chains. The authors have concluded that the even-numbered dithiols have higher melting points than the odd members due to a more efficient crystal packing.21 According to Figure 1, alkane-α,ω-diamides and alkane-α,ω-dioic acids are the homologous series with higher values of Tm. The melting points of the homologous series of alkane-α,ω-diols and alkane-α,ω-diamines are close, while the homologous series of alkane-α,ω-dithiols exhibit lower values. Considering the same functional groups, the same differentiation had been observed for the monosubstituted alkane derivatives.19 Comparing the three homologous series of alkane-α,ω-dihalides, the dihalogenated alkanes with the higher-size halogen have higher values of the melting point due to a larger dispersive interaction, which is in nice agreement with the previous data reported for monohalogenated derivatives.19 Analyzing the trends obtained for the boiling points, a polynomial growth of Tboiling along the series is depicted in all α,ω-disubstituted alkanes. There are no data available regarding the trends of Tboiling for diamides and diacids, which are probably very high, and, therefore, the data for the 2236



Review

Figure 2. Trends in molar (A) and specific (B) enthalpies of fusion, molar (C) and specific (D) entropies of fusion, and molar (E) and specific (F) Gibbs energies of fusion, at θ = 298.15 K, for homologous series of disubstituted alkane derivatives: alkane-α,ω-diols (blue ◆); alkane-α,ωdiamines (green ■); alkane-α,ω-dioic acids (red ▲); alkane-α,ω-diamides (orange -); alkane-α,ω-dinitriles (gold □); alkane-α,ω-dichlorides (yellow ∗); alkane-α,ω-dibromides (red ×) and alkane-α,ω-diiodides (purple +). Trends for the isoelectronic linear alkanes are depicted for comparison (gray ●).

bonding contributes to the higher boiling points exhibited by the liquid phases of mono-ols and diols.76−78 Although the melting temperatures of the dithiols are clearly lower than observed for diamines and diols, the larger size of the sulfur atoms leads to more pronounced dispersive interactions, which are reflected in the magnitude of their boiling points. As expected, the alkane-α,ω-dihalides constituted by larger-size

alkane-α,ω-nitriles appear in Figure 1 as the series with the higher magnitude in the boiling point. Contrary to that observed in the melting behavior, there is a clear differentiation between the boiling points of alkane-α,ω-diols and alkane-α,ωdiamines: higher Tboiling is observed for the series of diols. This is in nice agreement with the differentiation observed between linear alkanols and alkanamines.19 The strong hydrogen 2237



Review

Figure 3. Trends in molar (A) and specific (B) enthalpies of vaporization, molar (C) and specific (D) entropies of vaporization and molar (E) and specific (F) Gibbs energies of vaporization, at θ = 298.15 K, for homologous series of disubstituted alkane derivatives: alkane-α,ω-diols (blue ◆); alkane-α,ω-dithiols (blue ◇); alkane-α,ω-diamines (green ■); alkane-α,ω-dioic acids (red ▲); alkane-α,ω-diamides (orange -); alkane-α,ωdinitriles (gold □); alkane-α,ω-dichlorides (yellow ∗); alkane-α,ω-dibromides (red ×) and alkane-α,ω-diiodides (purple +). Trends for the isoelectronic linear alkanes are depicted for comparison (gray ●).

halogen display higher values of Tboiling. The differentiation in terms of melting and boiling temperatures can be further analyzed by a discussion on the contributions of the enthalpies and the entropies of phase transition. The magnitude of the melting point can be interpreted as an indication of the relative stability of a solid phase in terms of its fusion process. In fact, the melting temperature of a compound

is a consequence of enthalpic and entropic contributions, as indicated by the thermodynamic relation Tm = ΔfusHo/ΔfusSo. Hence, high values for the enthalpies and low values for the entropies (of fusion) contribute to the higher stability of the solid phase of a material relative to its solid-to-liquid transition. In addition to the melting point magnitude, the relative stability of a solid phase in terms of the fusion process can be 2238



Review

Figure 4. Trends in molar (A) and specific (B) enthalpies of sublimation, molar (C) and specific (D) entropies of sublimation and molar (E) and specific (F) Gibbs energies of sublimation, at θ = 298.15 K, for homologous series of disubstituted alkane derivatives: alkane-α,ω-diols (blue ◆); alkane-α,ω-diamines (green ■); alkane-α,ω-dioic acids (red ▲); alkane-α,ω-diamides (orange -); alkane-α,ω-dinitriles (gold □); alkane-α,ωdichlorides (∗); alkane-α,ω-dibromides (red ×) and alkane-α,ω-diiodides (purple +). Trends for the isoelectronic linear alkanes are depicted for comparison (gray ●).

discussed by analyzing the derived values of ΔfusGo, at 298.15 K, as both properties are due to enthalpic and entropic contributions. Trends in molar and specific enthalpies, entropies, and Gibbs energies of fusion, at 298.15 K, are represented by Figure 2. As expected, the trends observed in ΔfusGo are similar to those observed in Tm, allowing an evaluation of the relative stability of the solid phase: higher values of ΔfusGo are exhibited for the homologous series of

alkane-α,ω-diamides, and alkane-α,ω-dioic acids; identical values of ΔfusGo are observed between alkane-α,ω-diols and alkane-α,ω-diols. When compared with the analogues isoelectronic linear alkanes, the higher melting point of most homologous series of disubstituted alkane derivatives is driven by an enthalpy− entropy compensation: comparatively to n-alkanes, higher values of ΔfusHo and lower/identical values of ΔfusSo are 2239



Review

similar contributions can be noted when analyzing the increment of the ΔvapGo value (at 298.15 K and expressed in kJ·mol−1) per −CH2− group: n-alkanes, 2.9; alkane-α,ω-diols, 2.6; alkane-α,ω-dioic acids, 2.8; alkane-α,ω-diamines, 2.5. Having the highest values of ΔvapGo, the homologous series of dioic acids have low volatility because of the increased relative stability of the liquid phase. Although there are no data available, similar reasoning could be expected for the diamides. The volatility of the liquid phase is higher for the homologous series of n-alkanes and their halogenated derivatives (among them higher for the smaller halogens) and lower for alkaneα,ω-diols. The homologous series of alkane-α,ω-diamines, alkane-α,ω-dinitriles, and alkane-α,ω-dithiols display similar volatilities in their isotropic liquid phases (at 298.15 K). The analysis of the trends in the specific thermodynamic properties indicates that for a very-long-chain compound ΔvapHo, ΔvapSo, and ΔvapGo will converge for the typical values reported previously for the polyethylene.19 The differentiation in the specific properties of disubstituted alkanes (with shorter chains) is very similar to that observed for monosubstituted congeners. To exemplify the thermodynamic differentiation, the following relation is observed in the specific enthalpies of vaporization: ΔvapHo (diols) > ΔvapHo (diamines) > ΔvapHo (dithiols) > ΔvapHo (alkanes) ≈ ΔvapHo (dichlorides) > ΔvapHo (dibromides) > ΔvapHo (diiodides). The value of ≈360 J·g−1 (a typical value for the polyethylene)19 is obtained for all members of alkanes and α,ω-dichlorides. Interestingly, because of the large size of the iodine atom, a constant value of ΔvapSo ≈ 0.55 J·K−1·g−1 (polyethylene) was observed for all members of n-iodoalkanes, which are very close to the values of ΔvapSo ≈ 0.52 J·K−1·g−1 obtained for 1,2-diiodoethane and 1,3diiodopropane. Although there is relevant cohesive energy in the liquid phases of diols, dinitriles, or dioic acids, the differentiation between odd or even members is not evidenced in the magnitude of the thermodynamic properties. The knowledge of the thermodynamic properties associated with the solid−gas transition is used to better evaluate and understand the relative stability of a solid phase since, by a general point of view, all intermolecular forces are broken between the molecules along their sublimation. Figure 4 represents the trends in the thermodynamic properties of sublimation for α,ω-disubstituted alkanes. Ribeiro da Silva et al. have discussed the atypically low values for the sublimation enthalpies of larger dicarboxylic acids in terms of partial cyclization in the gas phase, which contributes for a higher than expected volatility in the solid phase.62 A comparison of the alkane-α,ω-diols with the alkaneα,ω-diamines shows that the thermodynamic properties of sublimation (ΔsubHo, ΔsubSo, and ΔsubGo) are higher for the diols. This differentiation is contrary to observed in the fusion properties, in which the diamines present higher values of ΔfusHo and ΔfusSo. These indications reveal that a high percentage of hydrogen bonding in diamines is broken along the fusion process. As expected and according to the values of ΔsubGo, the homologous series of dicarboxylic acids (with lower than eight methylene groups) presents higher cohesive forces in the solid phase. The magnitude of cohesive forces in alkane-α,ω-diols is lower than that observed for the diacids but higher than evidenced for homologous series of diamines and dinitriles. Concerning the condensed phases of halogenated compounds, the high dispersive interaction of the larger halogen groups justifies the higher values of ΔsubGo for alkaneα,ω-diiodides. The odd−even alternation observed in fusion

observed for alkane-α,ω-diamides, alkane-α,ω-dioic acids, and alkane-α,ω-diols. Comparing to the other series, alkane-α,ωdiamines display higher values of ΔfusS, which probably indicates that hydrogen bonding in alkanamines and alkaneα,ω-diamines is not so relevant in the liquid phase (when compared with the diols or dicarboxylic acids). This observation will be highlighted below. Curiously, both ΔfusHo and ΔfusSo parameters are lower for the alkane-α,ω-dinitriles evidencing the high contribution of the nitrile group (very polar) in the cohesive interaction preserved in the liquid phase.77,78,80 According to Saum, the −CN groups associate in pairs by a strong dipole interaction, leading to partial dimerization and longer-range association in dinitriles.79 The analysis of the specific thermodynamic properties indicates that all properties become diluted when the disubstituted alkane gains an ever-larger alkyl chain. Compared with the monoderivatives analogues, the odd−even alternation in all properties is even more emphasized, whereby the even members of the homologous series evidence an increased value of their thermodynamic properties due to a more efficient crystal packing. In addition, especially for the values of Tm and ΔfusGo, the odd−even alternation also becomes diluted for larger alkyl chains. More detailed highlights concerning the relative stability of the condensed phases will be presented below after evaluating the vaporization and sublimation phase equilibria. Concerning the vaporization properties, trends in molar and specific enthalpies, entropies, and Gibbs energies of vaporization, at 298.15 K, are represented by Figure 3. With the exception of alkane-α,ω-dioic acids, all thermodynamic properties of vaporization for the disubstituted alkanes show a regular growth along the series. The thermodynamic properties of vaporization (and sublimation) are anomalously low for larger dioic acids such as the dodecanedioic acid and hexadecanedioic acid. Some authors have associated this finding with the possibility of formation, in the vapor phase of long-chain diacid molecules, of a hydrogen-bonded cyclic structure.62,81−83 The strong hydrogen-bonding of the terminal groups in alkane-α,ω-diols is expressed in high values of ΔvapHo, ΔvapSo, and ΔvapGo. A comparison between alkane-α,ωdiamines and alkane-α,ω-diols indicates that the fusion enthalpies are higher for the diamines while the vaporization enthalpies are clearly higher for the diols. This observation supports the fact that along the solid−liquid transition, the cohesive energies of alkanols, especially hydrogen bonding, are more preserved in the liquid phase. The dinitriles exhibit higher enthalpies of vaporization than the analogue series of diamines due to the high polar characteristics of the −CN group that contribute to increased cohesive energies of the liquid phase.79 As observed in the fusion equilibria and in nice harmony with the previous data reported for the monohalogenated alkanes, there is a clear increase of the enthalpic contribution for the higher size halogens.19 On the basis of the gradient of ΔvapHo (values at 298.15 K and expressed in kJ· mol−1) the enthalpic contribution yielded by the introduction of an additional methylene group can be analyzed and discussed. For the homologous series, the data points of which are available to make extrapolations and interpretations, similar enthalpic contributions as observed for the monoderivative alkanes (≈ 5 kJ·mol−1) are obtained: alkane-α,ωdiamines, 4.3; alkane-α,ω-dithiols, 4.9; alkane-α,ω-dichlorides, 4.9; alkane-α,ω-diiodides, 4.9. Curiously, the results indicate that this contribution is higher for alkane-α,ω-diols. Nevertheless, because of enthalpic and entropic compensations, 2240



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Figure 5. Trends in melting temperatures for homologous series (A) of alkane-α,ω-diols (blue ◆) and n-alkanols (blue ◇), homologous series (B) of alkane-α,ω-diamines (green ■) and alkanamines (green □), homologous series (C) of alkane-α,ω-dioic acids (red ▲) and alkanoic acids (red △), and homologous series (D) of alkane-α,ω-diamides (orange -) and alkanamides (orange □). Trends for the isoelectronic linear alkanes are depicted for comparison (gray ●).

properties is also reflected in the values ΔsubHo, ΔsubSo, and ΔsubGo. To better evaluate the odd−even effect in the melting properties of homologous series of mono- and disubstituted alkane derivatives, Figure 5 represents the trends in melting temperatures (as a function of the number of carbons) for alkanols and alkane-α,ω-diols, alkanamines, and alkane-α,ωdiamines, alkanoic acids, and alkane-α,ω-dioic acids, and alkanamides and alkane-α,ω-diamides. In each graphical representation, trends for the isoelectronic linear alkanes are depicted for comparison. As clearly noted, the presence of functional groups in both chain extremities enhances the melting point as well as the odd−even alternation. Moreover, in both mono- and disubstituted alkanes, the members of the series with an even number of methylene moieties exhibit systematically higher melting temperatures compared to odd ones. The odd−even effects observed in several thermophysical properties in alkanes and endsubstituted derivatives have been explored by different authors.20−32 The alternation between even and odd members is correlated with the density and can be explained in terms of a simple geometrical model.27 According to the investigation of Boese et al., the higher melting points and densities for the even members of diols and diamines can be explained by the interplay between hydrogen bonding and hydrophobic interactions.78 These interactions occur in nice harmony for

the even members, leading to a dense crystal packing.78 In the case of odd members, they lead to geometrical restrictions contributing to a lower efficient packing. The same authors have explored the melting point alternation for other homologous series such as alkane-α,ω-dithiols,21 and alkaneα,ω-dioic acids.83 Concerning the diacids, the crystal packing and geometry requirements of odd members enforce some relevant restrictions on the molecular conformation, leading to a lower than expected melting point. Della Gatta et al. explored the melting behavior of alkane-α,ω-diamides and discussed the odd−even alternation displaying by the temperature of melting and associated thermodynamic properties.23 By identical reasons presented for the diacids, the consonance among dispersive interactions and hydrogen bonding in the even members of diamides contribute to a more efficient crystal packing density.23,83 Hence, the differentiation of the molecular/supramolecular features observed for odd or even members of homologous series is reflected in different physical and chemical properties associated with the condensed phases. The odd−even effect has been also observed in different materials such as perfluorinated alkyl substances,75 aromatic compounds,74 polymers,84,85 and ionic liquids,86 among others. An evaluation of the cohesive energies of a solid or liquid phase can be accessed by the interpretation of the enthalpies of sublimation and vaporization, respectively. In this context, Figure 6 represents the trends in ΔvapHo and ΔsubHo (as a 2241



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Figure 6. Trends in molar enthalpies of vaporization and sublimation, at θ = 298.15 K, for homologous series (A and B) of alkane-α,ω-diols (blue ◆) and alkanols (blue ◇), homologous series (C and D) of alkane-α,ω-diamines (green ■) and alkanamines (green □), and homologous series (E and F) of alkane-α,ω-dioic acids (red ▲) and alkanoic acids (red △). Trends for the isoelectronic linear alkanes are depicted for comparison (gray ●).

following enthalpic contributions are predicted: R = OH, 48; R = NH3, 37; R = COOH, 64. As expected, the higher enthalpic contribution is obtained with the carboxyl group. Owing to their cyclization in the gas phase, the larger diacids were not considered for this extrapolation. The higher boiling points and higher enthalpies of vaporization evidenced by the diacids are caused by a strong hydrogen bonding in the liquid phase that can occur between two molecules to produce dimers. In agreement with some comments already done along this work, the hydrogen bonding in liquid alkanols is stronger than that observed for alkanamines. Curiously, compared to

function of the number of carbon atoms) for homologous series of alkanols and alkane-α,ω-diols, alkanamines, and alkane-α,ω-diamines as well as for alkanoic acids and alkaneα,ω-dioic acids. The contribution of the terminal groups for the intermolecular interaction in the liquid phase of mono- and disubstituted alkanes can be predicted by extrapolation of the linear plots of ΔvapHo (at 298.15 K, in kJ·mol−1) to n (carbons) = 0. For the monosubstituted alkanes [R−(CH2)n−CH3], enthalpic contributions can be derived, as reported in previous work: R = OH, 34; R = NH3, 17; R = COOH, 40. Concerning the disubstituted alkane derivatives [R−(CH2)n−R], the 2242



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Figure 7. Trends in ΔfusHo/ΔsubHo and trends in ΔfusSo/ΔsubSo (properties derived at θ = 298.15 K) for homologous series (A and B) of alkanols (blue ◇), alkanamines (green □) and alkanoic acids (red △), and homologous series (C and D) of alkane-α,ω-diols (blue ◆), alkane-α,ωdiamines (green ■), and alkane-α,ω-dioic acids (red ▲). Trends for the isoelectronic linear alkanes are depicted for comparison (gray ●).

The contribution of the functional groups in the cohesive interaction preserved along the fusion process can be accessed by analyzing the ratio of ΔfusHo/ΔsubHo and ΔfusSo/ΔsubSo. To accomplish this analysis, Figure 7 represents the trends of those ratios (values at 298.15 K) for homologous series of alkanes, alkanols, alkanamines, alkanoic acids, alkane-α,ω-diols, alkane-α,ω-diamines, and alkane-α,ω-dioic acids. Lower ratios suggest that a relevant cohesive interaction is preserved in the liquid phase contributing to a more organized/structured liquid. The comparison with the isoelectronic linear alkanes allows inferring about the contribution of the terminal groups of each homologous series. The ratio between fusion and sublimation enthalpies increases with a successive introduction of methylene groups into the alkyl chain converging to a constant value in a very large compound. As observed, a high percentage of intermolecular interaction is preserved in the liquid phase of linear alkanes, since along the solid to liquid transition, those interactions decrease by about 40% (ΔfusHo/ΔsubHo ≈ 0.4) for the larger members of the series. The strong contribution of the hydroxyl group in the cohesive energy conserved in the liquid phase is well expressed by lower values of ΔfusHo/ ΔsubHo. For instance, the ratios in n-hexadecanol and 1,16hexadecanediol were found to be ≈0.35 and ≈0.30, respectively, whereas a ratio of ≈0.4 is observed for nhexadecane. The intermolecular interaction preserved in the

that of the alkanamines, the enthalpic contribution is doubled with the presence of two amino groups (diamines) in the extremities of the alkyl chains. The same observation could not be observed for diols and diacids. In addition, the gradient of the plots of ΔvapHo for n-alkanes, n-alkanamines, and n-alkanols were found to be 4.9, 4.7, and 4.6 (values in kJ·mol−1), respectively, whereas, for homologous series of alkane-α,ωdiamines and alkane-α,ω-diols, the gradients are obtained as 4.3 and 7.2, respectively. Compared to homologous series of linear alkanes, alkanols, alkanamines, and diamines, the higher than expected gradient obtained for the diols could be associated with supramolecular features arising from the presence of two terminal hydroxyl groups capable of making strong intermolecular interactions. Probably, the cohesive interaction when both hydroxyl groups coexist is lower than expected for shorter chains. According to Chickos et al. the intramolecular hydrogen bonding in diols has a minimal influence on the vaporization enthalpies.52 In nice agreement with the melting properties, the odd−even alternation in ΔsubHo values is more pronounced for the disubstituted derivatives, appearing to be further noted for alkane-α,ωdiamines. Despite there being clear odd−even alternation, it is possible to note that the gradient in ΔsubHo is higher for alkane-α,ω-diols and approximately similar for alkanes, alkanols, alkanamines, and alkane-α,ω-diamines. 2243



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ORCID

liquid phase is even more pronounced in alkanoic acids and alkane-α,ω-dioic acids. In addition, for larger compounds, the ratio of ΔfusHo/ΔsubHo decreases with the existence of functional groups in both extremities of the alkyl chain. The homologous series of alkanamines and alkane-α,ω-diamines have similar or even higher ratios than corresponding nalkanes, arising from the higher fusion enthalpies of the amines/diamines. These findings support the idea that hydrogen bonding in the liquid phase of the diamines is less relevant than in the alcohols or carboxylic acids due to the extensive hydrogen bonding disruption in the fusion process, which is also highlighted by higher enthalpies and entropies of fusion. The same conclusions can be obtained from the ratio of ΔfusSo/ΔsubSo. As perceived, very similar ratios are derived for amines, diamines, and corresponding isoelectronic linear alkanes, indicating less structuration in the liquid. The higher cohesive energies/hydrogen bonding in the liquid phase of alkanols, diols, acids, and diacids are well expressed by the lower values of ΔfusSo/ΔsubSo, which contribute to a more organized liquid. Compared to homologous n-alkanes, the structuration of diols and diacids leads to a lower entropy in the liquid and, hence, the lower entropy of fusion (Figure 2).

José C. S. Costa: 0000-0002-7134-8675 Luís M. N. B. F. Santos: 0000-0003-3040-0358 Funding

The authors thank Fundacão para a Ciência e Tecnologia (FCT), and FEDER (COMPETE 2020) for financial support to CIQUP, Faculty of Science, University of Porto (Projects UID/QUI/00081/2013 and NORTE-01-0145-FEDER000028, Sustainable Advanced Materials, SAM). Dr. José Costa also thanks FCT and the European Social Fund for the award of the postdoctoral fellowship (SFRH/BPD/116930/ 2016). Notes

The authors declare no competing financial interest.

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CONCLUSION An extended analysis of the thermodynamic behavior of different homologous series of α,ω-disubstituted alkanes was discussed based on the chain-length dependence of the thermodynamic properties associated with the phase transition. A clear odd−even alternation was found in the melting properties (Tm, ΔfusHo, and ΔfusSo) and is explained by a better crystal packing density of the even members of the homologous series. Compared to monosubstituted alkane congeners, the presence of functional groups in both chain extremities was found to improve the relative stability of condensed phases, and the odd−even effect displayed in the solid-state properties becomes even more pronounced. The high relative stability of the condensed phases was noted for the families whose nature of functional groups allowsthe formation of strong hydrogen-bonding interactions such as alkane-α,ω-dioic acids, and alkane-α,ω-diols. The lower than expected ΔvapHo values for larger dioic acids was attributed to the intramolecular hydrogen bonding in the gas-phase. Concerning the alkane-α,ω-dihalides, the homologous series with higher-size halogens display higher values of melting and boiling points as well as higher enthalpies/entropies of phase transition due to the more pronounced dispersive interaction of the larger functional groups. The large dipole moment of the nitrile group is reflected by increased values of Tb and ΔvapHo in liquid alkane-α,ω-dinitriles. The thermodynamic interpretation of ΔfusHo/ΔsubHo and ΔfusSo/ΔsubSo was used to compare the liquid organization and structuration among all the series studied by inferring the intermolecular interaction preserved in the liquid along the fusion process. The hydrogen-bonding in the liquid phase of alkane-α,ω-diamines was found to have a significantly lower contribution to the overall intermolecular interactions in comparison with that of the diols and dioic acids.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. 2244



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