Thermodynamic Properties of Diamondoids

G. R. Vakili-Nezhaad

1.1. Introduction

Diamondoid hydrocarbons are ringed compounds that have a diamondlike structure consisting of a number of six-member carbon rings fused together [1,2]. They have high melting points and low strain energy, which highlights their relative stability [1,3]. The first diamondoid isolated from petroleum, adamantane, was later synthesized and this molecule and its derivatives show a number of unusual chemical and physical properties [1,3]. Adamantane derivatives have shown promise in pharmaceutical applications [1,4], and have been used as templates for crystallization of zeolite catalysts [1,5], and the synthesis of high-temperature polymers [6], so interest in this molecule and higher diamondoids has both pure and applied roots. Recently, interest in higher diamondoids has been renewed by molecular simulation studies suggesting possible applications in nanotechnology [1,7-9], and use as seed crystals in CVD diamond production [10]. Besides the attractions of diamondoids due to their applications to nanotechnology, these organic nanostructures cause severe problems in oil and gas production. Therefore for reducing the problems due to the precipitation of diamondoids in the petroleum production process of knowledge of the phase behavior of these components with hydrocarbons is important.

Considering the above, in this chapter we focus on the following main subjects. First, thermodynamic properties of pure diamondoids (adamantane and diaman-tane) are considered. Second, solubilities of diamondoids and phase behavior of the binary systems are given in detail.

1.2. Pure Component Thermodynamic Properties

In this section thermodynamic properties of light diamondoids such as adamantane and diamantane are presented.

Based on the temperature-dependence of the heat capacity of adamantane in the condensed state between 5 and 600 K taken from the results of measurements [11,12] presented this dependency as shown in Figure 1.1. The smoothed values of

Figure 1.1. The temperature dependence of the heat capacity in the condensed state for adamantane.

the molar heat capacity and the standard thermodynamic functions of adamantane in the interval from 340 to 600 are listed in Table 1.1. Thermodynamic quantities associated with the phase transitions of the compound are given in Table 1.2. The enthalpy of sublimation of adamantane was determined in a series of calorimetric experiments which can be seen in Table 1.3 [12]. Also the experimental saturated vapor pressures over crystal adamantane are given in Table 1.4 [12].

Table 1.1 Molar thermodynamic functions for adamantane.

T (K)

Cs,m1R

ASm IR

AHm/RT

®m IR

Crystal I

340

26.26

26.64

13.66

12.98

360

28.41

28.21

14.42

13.78

380

30.27

29.79

15.21

14.58

400

31.98

31.39

16.01

15.38

420

33.61

32.99

16.81

16.18

440

35.24

34.59

17.61

16.98

460

36.91

36.19

18.41

17.78

480

38.65

37.80

19.22

18.59

500

40.46

39.42

20.03

19.39

520

42.32

41.04

20.85

20.19

540

44.18

42.67

21.68

20.99

543.2

44.48

42.93

21.81

21.12

Liquid

543.2

44.48

46.02

24.81

21.21

560

45.99

47.40

25.42

21.98

580

47.65

49.04

26.16

22.88

600

49.05

50.68

26.90

23.78

Table 1.2 Temperatures, the molar enthalpies, and entropies of phase transitions of adamantane.

Transition Ttoms(K) AHm (Jmol-1) ASm (JK-1mol-1) Reference

CrII^CrI 208.60 3376 16.19 Kabo et al., 1998

CrI^I 543.20 13958 ± 279 25.7 ± 0.5 Kabo et al., 2000

The entropy of crystal adamantane from the low-temperature measurements based on the work of Chang and Westrum (1960) is ASm (cr I; 303.54 K) = (199.27 ± 0.40) JK-1 mol-1. Thermodynamic parameters of sublimation AcrI Hm(303.54 K) = (58.52 ± 0.15) kJ mol-1 and AcrISm(303.54 K) = (192.79 ± 0.49) JK-1mol-1 were calculated on the basis of results given in Table 1.3 and the mean value AcrICp = -44.35 JK-1 mol-1. The experimental standard entropy of adamantane in the gas state Sm(g; 303.54 K) = (324.62 ± 0.76) JK-1 mol-1 was obtained using the value of Psat = (30.4 ± 1.5) Pa (Table 1.4).

The entropy of gaseous adamantane at T = 303.54 K, Sm(g) = (324.83 ± 1.62) JK-1mol-1 determined from the above-mentioned data is in very good agreement with the experimental value [12]. Thermodynamic functions of adamantane in the ideal gas state between 100 and 1000 K are given in Table 1.5 [12].

Table 1.3 The results of calorimetric of the enthalpy of sublimation for adamantane.0

No.

m (g)

T (K)

/ AVdr (mVs)

Type of Cell

A H (J)

A Hm (kJ mol-1)

1

0.05016

306.14

4790.37

A

20.50

58.40

2

0.06792

305.86

6498.38

A

29.17

58.51

3

0.07126

306.52

6854.55

A

30.77

58.82

4

0.07615

309.06

7211.37

A

32.37

57.91

5

0.09246

309.14

8852.84

A

39.74

58.55

6

0.07291

309.47

6953.20

A

31.21

58.32

7

0.06815

308.11

6494.41

A

29.15

58.28

8

0.11800

308.40

11278.84

A

50.63

58.45

9

0.06363

309.04

5702.89

B

26.95

57.70

10

0.08484

309.09

7659.34

B

36.19

58.12

11

0.07283

309.37

6611.68

B

31.24

58.45

12

0.10855

308.51

9819.18

B

46.40

58.24

13

0.04533

306.08

4104.92

B

18.52

58.29

14

0.07410

305.81

6703.16

B

30.25

58.24

15

0.05741

306.50

5226.57

B

23.58

58.61

a The calorimetrically measured enthalpy change AH and molar enthalpies AHm were calculated from

expressions: AH = K-1 /rr=0 AVdT; AH m = AH (M/m), where m is the mass of a specimen; M is the molar mass; K is the calorimetric constant (Ka = 228.78 mVsK-1 and Kb = 211.62 mVsK-1); AV is the thermocouple potential difference corresponding to the temperature difference between the cell and the calorimetric thermostat at time ; is the experiment duration; T is the temperature of the calorimeter. The value of m is corrected for the mass of saturated vapor in the free volume of the ampoule immediately before the experiment.

Table 1.4 Saturated vapor pressures Psat over crystal adamantane.

T (K)

r (s)

Am (mg)

Psat(Pa)

303.58

5454

19.57

30.37

303.52

3054

10.87

30.14

303.46

3054

11.06

30.65

303.53

3054

10.90

30.21

303.56

3054

10.72

29.71

303.59

3054

11.24

31.15

Am is the sample mass decrease; t is the duration of effusion.

Am is the sample mass decrease; t is the duration of effusion.

At this point we present the phase diagrams of adamantane and diamantane according to the work of Reiser et al. [13].

The results of the phase boundary experiments are summarized in Figure 1.2 for adamantane. The equation representing adamantane has been presented by the least squares linear regression method. The result of this regression can be expressed in the following form.

with the correlation coefficient of 0.997. Also the equation representing the solid-vapor pressure curve that has been obtained by the least squares method can be written as ln P(kPa) = -6570/T + 18.18 483 < T < 543 K. (1.2)

The correlation coefficient of this curve is 0.995. The dashed lines in Figure 1.2 also provide Boyd's vapor pressure correlations.

ln P(kPa) = -6324.7/ T + 17.827 366 < T < 443. (1.3)

ln P(kPa) =-9335.6/ T - 15.349 log T + 65.206 313 < T < 443. (1.4)

Table 1.5 Standard molar thermodynamic functions for adamantane in the ideal gas state.

T (K)

Cp / R

AS/ R

A H/ R

$/R

A fH

A fG

100

5.144

28.26

4.225

24.04

-98.57

-40.54

200

10.38

33.29

5.887

27.40

-117.1

24.76

298.15

17.73

38.75

8.530

30.22

-134.6

98.16

300

17.88

38.86

8.587

30.27

-134.9

99.61

303.54

18.17

39.07

8.697

30.37

-135.4

102.5

400

26.01

45.12

11.93

33.19

-150.1

180.2

500

33.23

51.73

15.49

36.23

-162.1

264.2

600

39.24

58.33

18.97

39.37

-171.1

350.3

700

44.19

64.77

22.23

42.54

-177.5

437.8

800

48.31

70.94

25.24

45.71

-181.9

526.5

900

51.76

76.84

28.00

48.84

-184.4

614.6

1000

54.68

82.45

30.52

51.92

-185.3

703.5

Figure 1.2. Phase diagram of adamantane.

The results of Cullick, Magouirik, and Ng [14] are also presented as the solid line in Figure 1.2.

ln P(kPa) =-7300/T - 4.376log T + 31.583 323 < T < 499. (1.5)

The phase diagram for diamantane, Figure 1.3, has been generated in a similar manner to that of the adamantane diagram. The fundamental distinction between these systems is that three solid phases of diamantane, Si ,S2, and S3 were observed. The equation representing the liquid-vapor curve is ln P(kPa) =-5680/ T + 14.858 516 < T < 716. (1.6)

The correlation coefficient of this curve is 0.989. The equation for the S3 vapor pressure curve of diamantane has been obtained using the least squares linear regression method which can be read as lnP(kPa) =-7330/T + 18.00 498 < T < 516K. (1.7)

This equation had a correlation coefficient of 0.986. The solid curves in Figure 1.3 are based on the correlations of Cullick et al. [14] and they can be written in the following forms.

ln P(kPa) = 18.333 - 7632.5/T 353 < T < 493 K. (1.8)

ln P(kPa) = 190.735 - 18981.3/T - 55.4418 log T 332 < T < 423 K. (1.9)

1/t x 103 (1/k) Figure 1.3. Phase diagram of diamantane.

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