Thermodynamics of Mixtures Containing Amines. X. Systems with

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Thermodynamics of Mixtures Containing Amines. X. Systems with Cyclic Amines or Morpholine Juan Antonio Gonz
alez* G.E.T.E.F., Departamento de Física Aplicada, Facultad de Ciencias, Universidad de Valladolid, 47071 Valladolid, Spain ABSTRACT: Cyclic amine or morpholine + organic solvent mixtures have been investigated in terms of DISQUAC and of the Kirkwood
Buff formalism. The amines considered are cyclohexylamine; (c-CH2)uNH (u = 2
7) and (c-CH2)uN
CH3 (u = 4,5). The organic solvents are alkanes and methanol or ethanol. The DISQUAC interaction parameters are reported. The model describes correctly a whole set of thermodynamic properties: vapor
liquid equilibria (VLE); excess Gibbs energies, GEm; excess enthalpies, HEm; excess heat capacities at constant pressure, CEP,m; and partial excess enthalpies at infinite dilution, HE,∞ 1 , as well as the main features of the Kirkwood
Buff integrals. In (c-CH2)uNH + C6H12 mixtures, amine
amine interactions become weaker with and of the effective dipole moment. Interactions increased u values. This is supported by the corresponding decrease of HEm and HE,∞ 1 between amine molecules are also weakened when passing from a primary cyclic amine to an isomeric tertiary cyclic amine. The existence of an aromatic ring in the amine, as in aniline or pyridine, leads to stronger amine
amine interactions. Dipolar interactions between morpholine molecules are stronger than those between piperidine molecules, and reveal the existence of proximity effects between the two groups of morpholine. In systems with alkanes, interactions between amine molecules are preferred to those between unlike molecules. In piperidine + methanol and pyrrolidine + ethanol systems, the mixture structure is close to random mixing.

1. INTRODUCTION Amines and oxaalkanes are very important molecules from a theoretical point of view. Primary and secondary amines are weakly self-associated.1
8 Their Trouton’s constants are close to the value of nonassociated species9 (92.05 J 3 mol
1 3 K
1). For example, these constants are 90.02 and 92.83 J 3 mol
1 3 K
1 for hexylamine and aniline, respectively.10 In the case of 1-alkanols,9 the Trouton’s constant is 110.88 J 3 mol
1 3 K
1. Ether molecules are formally obtained by replacing one or several CH2 groups in an alkane by O atoms (e.g., cyclohexane, oxane, 1,3-dioxane, 1,4dioxane, 1,3,5-trioxane). A large variety of homomorphic molecular species can be so obtained which differ in the number and relative positions of the functional group. Similarly, many different amine molecules may be constructed. Thus, the study of mixtures with oxaalkanes or amines makes possible the examination of the influence of some interesting effects on their thermodynamic properties. Linear amines, CH3(CH2)u
1NH2 or CH3(CH2)u
1NH(CH2)v
1CH3), or linear oxaalkanes, CH3
(CH2)u
1
O
(CH2)v
1
CH3, allow the study of the size and steric effects produced by alkylgroups attached to the amine or to the etheric groups; N,N,N-trialkylamines, the effect of a globular shape; aromatic amines or ethers, the effect of polarizability; cyclic amines or oxaalkanes, the ring strain. Proximity effects between two
O
groups may be investigated through solutions including linear acetals, CH3
(CH2)u
1
O
CH2
O
(CH2)v
1
CH3, while mixtures with linear polyoxaalkanes CH3
O
(CH2
CH2
O)u
1
CH3 are useful in the investigation of the effect of increasing the number of oxyethylene groups. From a practical point of view, amines and ethers are very important compounds. Thus, aniline, its derivatives, or piperidine are used in the manufacturing of dyes and of rubber vulcanization accelerators, or in the fabrication of pharmaceuticals and pesticides. The treatment of pyridine systems is a first step for a r 2011 American Chemical Society

better understanding of the pyrrole ring, specially important for modeling typical binding sites on proteins.7 Mixtures containing ethers are also important because they are increasingly used as additives to gasoline owing to their octane-enhancing and pollution-reducing properties.11,12 Cyclic polyethers have attracted interest as model substances for biosystems, particularly in connection with precise molecular recognition, which is essential to living systems,13 separation techniques, or chemical analysis. On the other hand, morpholine is a cyclic molecule which contains both the amine and the ether group and is particularly suitable for extraction, extractive distillation, and solvent application in the petrochemical industry. The aim of this work is to gain insight into the interactions and structure of systems formed by cyclic amines or morpholine and organic solvents, through the application of the DISQUAC model,14,15 and of the Kirkwood
Buff formalism.16
18 The former is a purely physical model based on the rigid lattice theory developed by Guggenheim.19 The latter is concerned with the study of fluctuations in the number of molecules of each component, and of the cross fluctuations. The amines considered in this work are cyclohexylamine, aziridine, azetidine, pyrrolidine, piperidine, hexamethyleneimine, heptamethyleneimine, methylpyrrolidine, methyl-piperidine, and morpholine. The solvents are cycloalkanes, n-alkanes, and 1-alkanols. No interaction parameters for mixtures with cyclic amines are available in terms of UNIFAC (Dortmund);20
23 however, some DISQUAC interaction parameters for cyclic secondary amine + cycloalkane systems have been previously reported.24

Received: May 24, 2011 Accepted: July 12, 2011 Revised: June 23, 2011 Published: July 12, 2011 9810

dx.doi.org/10.1021/ie201120h | Ind. Eng. Chem. Res. 2011, 50, 9810–9820

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QUAC Table 1. Dispersive (DIS) and Quasichemical (QUAC) Interchange Coefficients, CDIS , for (s,t) Contacts in Cyclic st,l and Cst,l Amine or Morpholine + Organic Solvents Mixtures (l = 1, Gibbs Energy; l = 2, Enthalpy; l = 3, Heat Capacity)

amine

contacta (s,t)

CDIS st,1

CDIS st,2

CDIS st,3

CQUAC st,1

CQUAC st,2

CQUAC st,3

cyclohexylamine

(c,n)

2.7

4

4.5

5.5

(c-CH2)2NH

(a,n) (c,n)

2.05 9.5

3.7 9.1


4.5

4.5 8.5

5.5 19


5

(c-CH2)3NH or (c-CH2)4NH

(c,n)

8.75

8.


4.5

4.5

14


5

(c-CH2)5NH

(c,n)

52b

8


4.5

4.5

10


5

(a,n)

5.4

7.8


2.5c

4.5

10


5

(c-CH2)6NH

(c,n)

4.15

8


4.5

4.5

9.10


5

(c-CH2)7NH

(c,n)

4.15

8


4.5

4.5

4.5


5

(c-CH2)4N
CH3

(c,n)d

8

17.2

(c-CH2)5N
CH3

(c,n)d (a,n)e

3.7 5

11.9 16.3

Morpholine

(e,n)f

4.3

9

1

1

(e,n)g

10.5

23

1

1

(c-CH2)4NH

(h,n)


20.5


46


1.5

0.5

(c-CH2)5NH

(h,n)


16.8


46


1.5

0.5

a

Abbreviations: a, aliphatic in n-alkane, methyl-pyrrolidine, methyl-piperidine, or 1-alkanols; c, c-CH2 in cycloalkanes, cyclic amines, or morpholine; c e,
O
in morpholine; n, amine group in cyclic amines or morpholine; h,
OH in 1-alkanols. b For cyclopentane, CDIS an,1 = 3.8. For tetradecane, DIS DIS d e CDIS CDIS =
2.1. Interaction parameters determined assuming that in mixtures with cyclohexane, C = C = 0. (octane) =16.6; CDIS an,3 an,1 an,2 an,2(decane) an,2 f g = 17.3. In mixtures with cycloalkanes. In mixtures with n-alkanes.

2. THEORIES 2.1. DISQUAC. In the framework of DISQUAC, cyclic amine or morpholine +organic solvent mixtures are regarded as possessing the following types of surface: (i) type c, (c-CH2 or c-CH in cyclic molecules; (ii) type n, (amine group in cyclic amines or morpholine; (iii) type e, (
O
group in morpholine); (iv) type s, (s = a, aliphatic (CH3, CH2, in n-alkanes, 1-alkanols, or methyl derivatives of cyclic amines; s = h, hydroxyl (
OH in 1-alkanols)). 2.1.1. General Equations. The main features of DISQUAC are as follows: (i) The total molecular volumes, ri, surfaces, qi, and the molecular surface fractions, Ri, of the compounds present in the mixture are calculated additively on the basis of the group volumes RG and surfaces QG recommended by Bondi.25 As volume and surface units, the volume RCH4 and surface QCH4 of methane are taken arbitrarily.26 The geometrical parameters for the groups referred to in this work are given elsewhere.24,26,27 (ii) The partition function is factorized into two terms, in such a way that the excess functions are calculated as the sum of two contributions: a dispersive (DIS) term which represents the contribution from the dispersive forces; and a quasichemical (QUAC) term which arises from the anisotropy of the field forces created by the solution molecules. In the case of the Gibbs , represented by the energy, GEm, a combinatorial term, GE,COMB m Flory
Huggins equation26,28 must be considered. Thus COMB DIS QUAC þ GE, þ GE, GEm ¼ GE, m m m

ð1Þ

HmE ¼ HmE, DIS þ HmE, QUAC

ð2Þ

The equations used to calculate the DIS and QUAC contributions to GEm and HEm in the framework of DISQUAC are given elsewhere.24,27 The temperature dependence of the interaction parameters is expressed in terms of the DIS and QUAC interQUAC where s 6¼ t are two conchange coefficients,24,27 CDIS st,l ;Cst,l tact surfaces present in the mixture and l = 1 (Gibbs energy; CDIS/QUAC = gDIS/QUAC (To)/RTo); l = 2 (enthalpy, CDIS/QUAC = st,1 st st,2 DIS/QUAC DIS/ hst (To)/RTo)); l = 3 (heat capacity,CDIS/QUAC = c st,3 pst QUAC (To)/R)). To = 298.15 K is the scaling temperature, and R is the gas constant. 2.2. Kirkwood
Buff Formalism. The theory16
18 describes thermodynamic properties of solutions in an exact manner in the whole concentration range using the Kirkwood
Buff integrals: Z ∞ ðgij
1Þ4πr 2 dr ð3Þ Gij ¼ o

The radial distribution function, gij, denotes the probability of finding a molecule of species i in a volume element at the distance r of the center of a molecule of species j. So, this function provides information about the solution structure on the microscopic level. The Gij values can be interpreted as follows: Gij > 0 represents the excess of molecules of the i type in the space around a given molecule of species j. This means attractive interactions between molecules of i and j. Gij < 0 means that interactions of i
i and j
j are preferred to mutual interactions.29 The Kirkwood
Buff integrals are derived from experimental data of thermodynamic properties as chemical potential; partial molar volumes and isothermal compressibility factor. The resulting equations are17,30

(iii) The interaction parameters are assumed to be dependent on the molecular structure; (iv) The value z = 4 for the coordination number is used for all the polar contacts. This represents one of the more important shortcomings of the model and is partially removed via the hypothesis of considering structure-dependent interaction parameters.

Gii ¼ RTkT þ

Gij ¼ RTkT
9811

xj V̅ 2j xi VD

V̅ i V̅ j VD




V xi

ð4Þ

ði 6¼ jÞ

ð5Þ

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where xi and V i are the mole fraction and the partial molar volume of component i, respectively (i = 1, 2); V is the molar volume of the solution; and kT, the isothermal compressibility of the mixture. D is defined as ! x1 x2 ∂2 GEm ð6Þ D¼1 þ RT ∂x21

Table 2. Molar Excess Gibbs Energies, GEm, at Equimolar Composition and Temperature T for Cyclic Amine or Morpholine + Alkane, or +1-Alkanol Mixtures. Comparison of Experimental Results (expt) with DISQUAC (DQ) Calculations Using the Interchange Coefficients from Table 1 GEm (J mol
1)

σr (P)a

P, T

T (K) N

system

Using the Gij quantities, it is possible to estimate the so-called linear coefficients of preferential solvation:30
32

expt

DQ

expt

DQ ref

C6H13N + n-C8

333.15 11

479

479 0.004 0.007 84

(c-CH2)2NH + C6H12

363.15 11 298.15 18

708 1110

321 0.003 0.10 84 1102 0.004 0.013 85

(c-CH2)3NH + C6H12

298.15 11

620

625 0.004 0.021 85

(c-CH2)4NH + C6H12

298.15 11

533

536 0.004 0.005 85

313.15 13

515

504 0.003 0.007 86

333.15 18

478

463 0.003 0.008 86

(c-CH2)5NH + C5H10

298.15 14

302

303 0.014 0.017 87

3. ESTIMATION OF THE MODEL PARAMETERS The general procedure applied in the estimation of the DISQUAC interaction parameters has been explained in detail elsewhere.34 Final values of the fitted parameters in this work are collected in Table 1. Some important remarks are given as follows.

(c-CH2)5NH + C6H12

298.15 15

366

369 0.008 0.008 85

(c-CH2)5NH + C7H14 (c-CH2)5NH + C8H16

298.15 11 298.15 13

381 372

370 0.004 0.006 87 356 0.004 0.010 87

(c-CH2)6NH + C6H12

298.15 11

305

302 0.008 0.010 85

(c-CH2)5NH + n-C7

298.42

6

512

524 0.005 0.007 88

(c-CH2)4N
CH3+ C6H12 298.15 10

114

114 0.002 0.004 85

Cyclohexylamine or Secondary Cyclic Amine + Cycloalkane. These systems are built by one contact (c,n). The corre-

(c-CH2)5N
CH3+ C6H12 298.15 12

41

42 0.002 0.004 85

(c-CH2)5N
CH3 + n-C7 298.42

5

53

54 0.003 0.003 88

morpholine + C8H16

363.15 16

912

916 0.003 0.007 89

morpholine + n-C7

393.15 20 303.15

839 1206

840 0.004 0.010 89 1171 88

morpholine + n-C8

353.35 14

1060

1048 0.003 0.016 89

383.35 15

952

967 0.002 0.011 89

δii ¼ xi xj ðGii
Gij Þ δij ¼ xi xj ðGij
Gjj Þ

ð7Þ ði 6¼ jÞ

which are useful quantities to determine the local mole fractions, xij, of the i species around the central j molecule.30,33

sponding interaction parameters were obtained from available data on VLE, HEm, and CEpm. Cyclohexylamine or Piperidine + n-Alkane. These mixtures are characterized by three contacts: (a,c), (a,n), and (c,n). The (a,c) contacts are described by DIS parameters only which are known from VLE, HEm and CEpm measurements of cyclohexane + n-alkane mixtures.28 As the interaction parameters for the (c,n) contacts have been obtained previously, only those for the (a,n) contacts must be now determined. Calculations were carried out = CQUAC . This general rule is valid for assuming that CQUAC an,l cn,l many other solutions as, linear oxaalkane,35 linear alkanone,36 linear organic carbonate,37 alkanoic acid anhydride,38 haloalkane,39,40 linear monocarboxylic acids,41 alkanol,42
46 alkoxyethanol,47 sulfolane,48 amide,49
51 or amine10,52 + n-alkane, or + cyclohexane. Tertiary Cyclic Amine + Alkane. These solutions are built by three contacts: (a,c), (a,n), and (c,n). The CDIS ac,l coefficients have been neglected as in previous DISQUAC applications methylcyclohexane has been treated as a n-alkane.10,37 Note the low HEm of the methylcyclohexane + heptane system (36 J 3 mol
1 at 298.15 K and equimolar composition53). The interaction parameters for the (a,n) and (c,n) contacts are assumed to be merely dispersive, as in N,N,N-trialkylamine + alkane systems.54 In the case of cyclohexane mixtures, for simplicity, the interaction parameters for (a,n) contacts have been also neglected. Morpholine + Alkane. The mixtures with cycloalkanes are characterized by three contacts (c,e), (c,n), and (e,n). The CDIS ce,l and CQUAC coefficients are known35 from the study of cyclic ce,l ether + cycloalkane mixtures, and those for the (c,n) contacts have been obtained from data for piperidine systems (see above). Thus, only the interaction parameters for the (e,n) contacts must be fitted. There are six contacts in morpholine + n-alkane systems: (a,c), (a,e), (a,n), (c,e), (c,n), and (e,n). Interaction parameters for the contacts (a,c), (a,e), (a,n), (c,e), (c,n) are known, as the CDIS ae,l and interchange coefficients were obtained in a previous CQUAC ae,l work35 from cyclic ether + n-alkane data. However, it was

(c-CH2)4NH + ethanol

a

313.15 15
1063
1070 0.006 0.021 86 333.15 15


905

(c-CH2)5NH + methanol 298.15 11


831


928 0.004 0.019 86
825 0.008 0.025 72

318.15 11


693


673 0.005 0.021 72

Standard relative deviation, eq 8.

assumed that the different molecular environment (cycloalkane, n-alkane) modify the CDIS en,l coefficients. A similar procedure was applied for systems of alkoxyethanols, and n-alkane, cyclohexane, 1-alkanol or ether.47,55 Pyrrolidine, or Ppiperidine +1-Alkanol. The contacts (a,c), (a,n), (a,h), (c,n), (c,h), and (h,n) are present in these solutions. and CDIS,QUAC are The interchange coefficients CDIS,QUAC ah,l ch,l known from the treatment of 1-alkanol + n-alkane,27 or + cycloalkane42,44 mixtures, respectively. Thus, only the interaction parameters for (h,n) contacts must be fitted.

4. RESULTS 4.1. DISQUAC Results. Results from the DISQUAC model are compared with experimental data for VLE, GEm, HEm, CEPm, and Kirkwood
Buff integrals or linear coefficients of HE,∞ 1 preferential solvation in Tables 2
7. Comparisons for selected mixtures are plotted in Figures 1
7. For the sake of clarity, relative deviations for the pressure (P) and HEm are defined as

σ r ðPÞ ¼ 9812

8 azetidine > pyrrolidine > piperidine > ... (Tables 4 and 6). This reveals that interactions between amine molecules become weaker when the size of these compounds are increased. The corresponding decrease of the effective dipole moment of cyclic amines (Table 8), a useful magnitude to examine the impact of polarity on bulk properties,34,59
62 may explain the mentioned variation
1 E of HEm and HE,∞ 1 . The large positive values of TSm/(J 3 mol ) E E (= Hm
Gm) of these cyclohexane mixtures are remarkable: 510 (aziridine) < 802 (azetidine) > 664 (pyrrolidine) > 461 (piperidine)> 422 (hexamethyleneimine) (all values calculated using experimental data listed in Tables 2 and 4) and reveal that amine
amine interactions are mainly of dipolar type. Note that for the typical associated solution 1-pentanol + hexane, GE63 m =
1 and TSEm =
566 J 3 mol
1. 1041 J 3 mol
1 ;HE64 m = 475 J 3 mol = For the system diethylamine + hexane at 303.15 K, HE,65 m 672 J 3 mol
1; GEm = 222 J 3 mol
1 (DISQUAC value) and TSEm = 450 J 3 mol
1, which is lower than the value for the pyrrolidine + cyclohexane mixture. That is, dipolar interactions are less important in systems with linear secondary amines. On the other hand, in cyclohexane solutions, HEm and HE,∞ 1 changes in the order: cyclohexylamine > hexamethyleneimine > Table 6. Partial Molar Excess Enthalpies at Infinite Dilution and 298.15 K for Cyclic Amine(1) or Morpholine(1) + Cyclohexane(2) Mixtures. Comparison of Experimental Valuesa (expt) with DISQUAC (DQ) Results Obtained Using Interaction Parameters Listed in Table 1

amine cylohexylamine

HE,∞ (kJ 3 mol
1) 1

HE,∞ (kJ 3 mol
1) 2

expt

DQ

expt

DQ

ref 90

5.46

5.74

2.74

2.65

12.03

14.85

6.09

6.46

85

azetidine pyrrolidine

6.90 6.95

7.49 6.85

5.08 3.95

5.24 4.13

85 85

piperidine

4.68

4.87

2.98

2.79

85

hexamethyleneimine

3.85

4.32

2.44

2.35

85

heptamethyleneimine

2.15

2.50

1.22

1.47

85

N-methylpyrrolidine

1.22

1.00

0.68

0.96

85.

N-methylpiperidine

0.54

0.65

0.33

0.56

85

Morpholineb

9.65

10.09

6.14

6.83

95

aziridine

Obtained from the fitting of the experimental data to a Redlich
Kister equation. b Value at 308.15 K.

a

N-methylpiperidine (Tables 4 and 6). Therefore, interactions between amine molecules are weakened when passing from a primary amine to an isomeric tertiary amine. The same trend is observed in mixtures containing linear amines. Thus, for systems involving heptane, HEm/(J 3 mol
1) = 1064 (hexylamine66)> 454 (dipropylamine67) > 112 (triethylamine68). It is noteworthy that for the cyclohexylamine solution, TSEm = 235 J 3 mol
1, value calculated using GEm = 614 J 3 mol
1 obtained from DISQUAC, which indicates that amine self-association is in this case more important than in piperidine (see above). HEm results for systems with the aromatic amines aniline, or pyridine and cyclohexane are much higher than those involving cyclohexyamine, piperidine, or N-methylpiperidine. Thus, HEm/(J 3 mol
1) = 1880 (aniline;69 T = 308.15 K); 1438 (pyridine70). In addition, aniline is not miscible with alkanes at room temperature and equimolar compostion. The upper critical solution temperature (UCST) of the aniline + heptane system is 342.7 K.71 Therefore, it may be concluded then that the presence of the aromatic ring leads to an enhancement of the amine
amine interactions. The HEm/(J 3 mol
1) of mixtures including methanol changes in the sequence:
3150 (piperidine)72 <
711 (pyridine)73 <
170 (aniline),74 which may be ascribed in some extent to the fact that the positive contribution to HEm from the disruption of amine
amine interactions upon mixing increases in the order aniline > pyridine > piperidine. HEm of morpholine + alkane systems is much higher than that of the corresponding piperidine solutions (Table 4). Moreover, E,∞ (piperidine + C6H12) HE,∞ 1 (morpholine + C6H12) > H1 (Table 6). It may be then concluded that interactions between morpholine molecules are stronger than those between piperidine molecules. These large differences between HEm and HE,∞ 1 values of morpholine and piperidine solutions cannot be merely explained by the larger effective dipole moment of morpholine (Table 8). Proximity effects related to the presence of the N and O atoms in the same molecule should be also taken into consideration, as such effects lead to an enhancement of dipolar interactions between morpholine molecules. This is supported by the higher TSEm values of morpholine mixtures. For the system with cyclohexane, at 308.15 K, GEm = 1029 J 3 mol
1 (DISQUAC value) and TSEm = 823 J 3 mol
1; higher values than that previously reported for the corresponding mixture with piperidine. It is remarkable that systems with the ether and amine groups placed in different molecules are characterized by lower HEm values (in J 3 mol
1): 627 (diethylamine +1,4-dioxane75), 712 (diproylamine +1,4-dioxane75), 523 (butylamine +1,4-dioxane76).

Table 7. Kirkwood
Buff Integrals, Gij, and Linear Coefficients of Preferential Solvation, δij, at Equimolar Compositions and Temperature T for Cyclic Amine(1) or Morpholine(1) + Organic Solvent(2) Mixtures. DISQUAC Values are Given in Parentheses system

T (K)

G11 (J cm
3)

G22 (J cm
3)

G12 (J cm
3)

δ11 (J cm
3)

δ12 (J cm
3)

0.6 (13.9) 26.5 (23.6)


145.6 (
138.2)
62.9 (
64.6)


197 (
207)
162.8 (
160.6)

49.4 (55.2) 47.3 (46)


12.8 (
17.2)
25 (
24)

cyclohexylamine + n-C8a (c-CH2)4NH + C6H12b

333.15 298.15

(c-CH2)5NH + C6H12c

298.15


53 (
46.4)


77.7 (
72.1)


137.3 (
143.4)

21.1 (24.3)


14.9 (
17.8)

(c-CH2)5NH + n-C7d

298.42

62.5 (53)


105.1 (
108.5)


203.3 (
197.5)

66.4 (62.6)


24.5 (
22.2)

(c-CH2)5NH + n-C14e

298.15

(180)

(
281.2)

(
204)

(96)

(19.3)

morpholine + n-C8f

353.35

447.1 (407.7)


63.1 (
74.1)


369.8 (
348.9)

204.2 (
189.2)


76.7 (
68.79)

methanol + (c-CH2)5NHg

298.15


52.6 (
46.3)


121.7 (
120.2)


30 (
33.2)


5.6 (
3.3)

22.9 (21.8)

ethanol + (c-CH2)4NHh

313.15


90.2 (
86)


116.1 (
114)


33.2 (
36.1)


14.2 (
12.5)

20.7 (19.5)

a

VLE, ref 84; VEm, ref 96. b VLE, ref 85; VEm = 0. c VLE, ref 85; VEm, ref 61. d VLE, ref 88; VEm, ref 62. e VEm, ref 62. f VLE, ref 89; VEm = 0. g VLE and VEm, ref 72. h VLE, ref 86; VEm = 0. 9814

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Figure 1. VLE for cyclic amine(1) + alkane(2) mixtures at temperature T. Points are the experimental results: (b) pyrrolidine(1) + cyclohexane(2) at T = 313.15 K;85 (9) cyclohexylamine(1) + octane(2) at T = 333.15 K.84 Solid lines are the DISQUAC calculations.

Figure 2. VLE for morpholine(1) + cyclooctane(2) mixtures at temperature T. Points are the experimental results:89 (b) T = 353.15 K; (9) T = 383.15 K. Solid lines are the DISQUAC calculations.

Supermolecule calculations show the existence of proximity effects in morpholine.77 Thus, the different hydrogen bonding between water and the amine and ether groups in morpholine and in molecules that contain only one of these groups has been ascribed to the mentioned proximity effects.77 Similar trends are encountered in systems with 1-alkanols or isomeric 2-alkoxyethanols and alkane.47 The effective dipole moments of 2-alkoxyethanols are higher than those of the isomeric 1-alkanols47 (e.g., μ̅ (2-methoxyethanol) = 0.879; μ ̅ (1butanol) = 0.664). The larger μ ̅ values of 2-alkoxyethanols together with the presence of the
O
and
OH groups in the same molecule lead to an enhancement of the dipolar interactions between 2-alkoxyethanol molecules, and to a weakening of the effects related to the intermolecular self-association

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Figure 3. HEm of cyclic amine(1) + cyclohexane(2) mixtures at 298.15 K. Points are the experimental results: (b) cyclohexylamine;90 (9) pyrrolidine;85 (2) aziridine.85 Solid lines are the DISQUAC calculations.

Figure 4. HEm of cyclic amine(1) + alkane(2) mixtures at temperature T. Points are the experimental results: (1) piperidine(1) + cyclohexane(2)85 (T = 298.15 K); (b) piperidine(1) + octane(2)92 (T = 303.15 K); (2) morpholine(1) + cyclohexane(2)95 (T = 308.15 K); (9) morpholine(1) + octane(2)92 (T = 303.15). Solid lines are the DISQUAC calculations.

of these compounds.47 As consequence, the upper critical solution temperatures of the 2-alkoxyethanol + heptane mixtures (319.74 K for the 2-methoxyethanol mixture78) are much higher than those of the systems containing the homomorphic 1-alkanols. In addition, the TSEm curves of the 2-alkoxyethanol mixtures are s-shaped as GEm and HEm are of the same order of magnitude,47 while TSEm values are large and negative for mixtures with 1-alkanols due to GEm ≈ 2HEm (see above). 5.1. Kirkwood-Buff Integrals. The positive δ11 and negative δ12 values encountered for cyclic amine + alkane systems indicate that interactions between amine molecules are preferred to those 9815

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Figure 5. Molar excess functions at 298.15 K for the methanol(1) + piperidine(2) system. Points are the experimental results:72 (9) F = G, Gibbs energy; (b) F = H, enthalpy. Solid lines are the DISQUAC calculations.

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Figure 7. Linear coefficients of preferential solvation, δij, of cyclic amine(1) + organic solvent(2) mixtures at temperature T. Dashed lines are the experimental results (see Table 7): (a) δ11; (b) δ12 of morpholine(1) + octane(2) at 353.15 K; (c) δ11; (d) δ12 of ethanol(1) + pyrrolidine(2) at 313.15 K. Solid lines are the DISQUAC calculations.

Table 8. Physical Constants of Some Cyclic Amines and Morpholine Va (cm3 3 mol
1) Pcb (bar) Tcc (K) μd (D)

Amine

115.02f

cyclohexylamine

j

426g g

̅μ

e

614.9h

1.33i

0.475

g

2.19i

1.162

aziridine

52

67

534.6

pyrrolidine

83.24k

56.1h

568.6h

1.58i

0.663

piperidine

99.37l

46.5h

594.1h

1.19i

0.457

N-methylpiperidine

122.30m

40g

585.7g

0.80i

0.277

morpholine

87.52n

54.7o

618o

1.56i

0.638

a

Molar volume at 298.15 K. b Critical pressure. c Critical temperature. d 2 1/2 Dipole moment. e Effective dipole moment μ ̅ = [μ NA/(4πεoVkBT)] where NA is the Avogadro’s number; εo is the permittivity of the vacuum; kB is the Boltzmann constant. f Reference 97. g Calculated according to Joback’s method, ref 98. h Reference 99. i Reference 100. j Reference 101. k Reference 102. l Reference 61. m Reference 103. n Reference 104. o Reference 98. Figure 6. CEP,m of piperidine(1) + n-alkane(2) systems at 298.15 K. Points are the experimental results:62 (2) heptane; (b) decane; (9) dodecane. Solid lines are the DISQUAC calculations.

between unlike molecules. The rather large positive δ11 values of the morpholine + cyclooctane mixture at 353.15 K are noticeable (Table 7, Figure 7), as reveal that strong interactions between morpholine molecules exist, even at high temperatures. On the other hand, interactions between amine molecules are increasingly preferred when the chain length of the alkane is increased in solutions with piperidine (Table 7). The mixtures examined including 1-alkanols are characterized by rather low |δij| values (Table 7, Figure 7), which are similar to those encountered for 1-alkanol + amide,32,56 or + pyridine79 systems. This has been interpreted assuming that molecules of the same kind have no tendency to form aggregates in the solution.32,56 Thus, despite the strong interactions between

unlike molecules (see the large and negative HEm of the methanol + piperidine system, Table 4, Figure 5), it may be concluded that the distribution of the molecules in the solution is nearly random. 5.2. The DISQUAC Interaction Parameters. Some comments on the dependence with the molecular structure of the interaction parameters are necessary. It is well-known that the segmentation into groups, for example, of cycloalkanes into c-CH2 groups is not strictly justified, and it seems more appropriate to treat each cyclic molecule as an independent entity.24 In the (c-CH2)uNH + cyclohexane series, this may explain in some extent the quite different interactions parameters for aziridine, and in piperidine + cycloalkane systems, the different CDIS cn,1 coefficient for the cyclopentane solution. Despite this, it is (l = 1,3) noteworthy that, for the former mixtures, the CQUAC cn,l coefficients are independent of the amine for u > 2; a behavior rather usual in the framework DISQUAC, as is encountered 9816

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Table A1. Physical Constants of Pure Amines Needed for Kirkwood
Buff Calculationsa RPb amine


3

(10

cyclohexylamine pyrrolidine

1.05f 1.22i

piperidine

0.96l

morpholine

3 K)

n,o

0.955

kSc
1

(TPa )

kTe

CPd
1

(J 3 mol


1

3K )

(TPa
1)

575.1g 626j

200h 160.2k

764 857

965j

177.4m

1061

o

164.8p

620

496

a

For cyclohexane, heptane, octane, methanol and ethanol data are taken from ref 99. b Isobaric thermal expansion ecoefficient. c Adiabatic compressibility. d Isobaric heat capacity. e Isothermal compressibility, kT = kS + (TRp2V)/(Cp,m). f Reference 97. g Reference 105. h Estimated according to the Chueh
Swanson method in ref 98. i Reference 102. j Reference 106. k Reference 107. l Reference 108. m Reference 61. n Reference 109. o Reference 110. p Reference 111.

when investigating alcoholic solutions such as alkanol + alkane;27,42
46 1-alkanol + cyclic ether,80 + amide,49
51 or in alkoxyethanol + alkane mixtures.47 On the other hand, the CDIS cn,l (l = 2,3) coefficients remain also constant for u > 2. Thus, the different behavior of (c-CH2)uNH + cyclohexane systems is QUAC coefficients which decrease merely described by CDIS cn,1 and Ccn,2 with increasing u values. In the case of the enthalpic parameter, the observed variation may be ascribed to an increasing steric effect, which weakens dipolar interactions between amine molecules.81 The CDIS cn,1 variation is somewhat different to that encountered in many other applications, where the increase of the dispersive interaction parameters is typically ascribed to increasing inductive effects.81 For N-methylpiperidine + n-alkane mixtures, CDIS an,2 coefficients depend on the chain length of the n-alkane (Table 1). This reveals the existence of the so-called Patterson effect in such systems, which is ascribed to the order destruction of longer alkanes during the mixing process with nonpolar or weakly polar molecules, of globular or plate-like shapes28,54,82,83 (e.g., benzene, cyclohexane, triethylamine). In the case of piperidine solutions, the mentioned effect are of minor importance due to the large contribution to HEm from the breaking of the polar amine
amine interactions. However, a different CDIS an,3 coefficient is needed for an accurate description of the CEP,m of the piperidine + tetradecane system. This merely reveals the close relation between CEP,m and the third interchange coefficients with the molecular structure of the considered solutions. The same trend has been encountered, e.g., when investigating 1-alkanol27 or pyridine10 + n-alkane systems in terms of DISQUAC.

6. CONCLUSIONS DISQUAC describes correctly a whole set of thermodynamics properties: VLE, GEm, HEm, CEP,m, HE,∞ 1 , and the main features of the Kirkwood
Buff integrals for the investigated solutions. In (c-CH2)uNH + C6H12 mixtures, amine
amine interactions become weaker when the size of the amines is increased. This is supported by the decrease of HEm, HE,∞ 1 , and of the effective dipole moment. Interactions between amine molecules are weakened when passing from a primary cyclic amine to an isomeric tertiary cyclic amine. The existence of an aromatic ring in the amine, as in aniline or pyridine, leads to stronger amine
amine interactions. Proximity effects between the two groups of morpholine leads to stronger interactions between these molecules than those between piperidine molecules. In

systems with alkanes, interactions between amine molecules are preferred to those between unlike molecules. In piperidine + methanol and pyrrolidine + ethanol systems, the mixture structure is close to random mixing.

’ APPENDIX See Table A1 for the physical constants of the pure amines needed for the Kirkwood
Buff calculations. ’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Fax: +34-983-423136. Tel: +34-983423757.

’ ACKNOWLEDGMENT The author gratefully acknowledges the financial support received from the Consejería de Educaci
on y Cultura of Junta de Castilla y Le
on, under Project VA052A09 and from the Ministerio de Ciencia e Innovaci
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