Thermodynamics of binary mixtures containing N-alkylamides

www.elsevier.com/locate/molliq

Journal of Molecular Liquids 115 (2004) 93–103

Thermodynamics of binary mixtures containing N-alkylamides

Juan Antonio Gonzalez*, Jose Carlos Cobos, Isaıas Garcıa de la Fuente

G.E.T.E.F., Departamento de Termodinamica y Fısica Aplicada, Facultad de Ciencias, Universidad de Valladolid, 47071, Valladolid, Spain

Received 23 October 2003; accepted 25 February 2004

Available online 8 July 2004

Abstract

N-alkylamide + organic solvent mixtures have been investigated in the framework of a purely physical theory [dispersive-quasichemical

(DISQUAC)]. The amides considered are n-methylformamide (NMF), n-methylacetamide (NMA), n-ethylacetamide (NEA), n-

methylpropanamide (NMPA), 2-pyrrolidone and caprolactam. The solvents are alkanes, benzene, toluene or 1-alkanols. The DISQUAC

interaction parameters are reported. The model describes consistently thermodynamic properties such as vapor– liquid equilibria (VLE),

excess molar Gibbs energies, GE, and excess molar enthalpies, HE, solid– liquid equilibria (SLE), or the concentration–concentration

structure factor, SCC(0). DISQUAC improves results from other models, such as the extended real associated solution model (ERAS) or

UNIFAC. Interactions present in the studied mixtures are discussed. Solutions with alkanes are characterized by strong dipole–dipole

interactions between amide molecules. n-Methylformamide + aromatic compound mixtures behave similarly to associated systems. The

heterocoordination observed in some solutions involving methanol where interactions between like molecules are almost cancelled by

interactions between unlike molecules may partially be ascribed to size effects. For other alcoholic solutions, the ability of the alcohol for the

breakage of the amide–amide interactions is prevalent over solvation effects.

D 2004 Elsevier B.V. All rights reserved.

Keywords: Amide; Mixture; Size effect; Dipolar; Interaction

1. Introduction

We are engaged in a systematic investigation of the

thermodynamic properties of solutions containing a com-

pound with a very high dipolar moment in gas phase (l),such as, sulfolane [1,2] (l = 4.81 D [3]); dimethyl sulfox-

ide [4] (l = 4.06 D [3]); 1-methyl pyrrolidin-2-one [5]

(NMP; l = 4.09 D [3]) or propylene carbonate (l = 4.94 D

[3]).

Amides, amino acids, peptides and their derivatives are

of interest because they are simple models in biochemistry.

n-Methylformamide (NMF) possesses the basic (–CO) and

acidic (–NH) groups of the very common, in nature, peptide

bond [6]. Thus, proteins are polymers of amino acids linked

to each other by peptide bonds. Cyclic amides are also of

importance because they are related to structural problems

in biochemistry. Consequently, the understanding of liquid

mixtures involving the amide functional group is necessary

as a first step to a better knowledge of complex molecules of

0167-7322/$ - see front matter D 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.molliq.2004.02.046

* Corresponding author. Tel.: +34-983-423757; fax: +34-983-423136.

E-mail address: [email protected] (J.A. Gonzalez).

biological interest [7,8]. For example, the aqueous solution

of N,N-dimethylformamide (DMF) is a model solvent rep-

resenting the environment of the interior of proteins. More-

over, DMF and NMP are used as highly selective extractants

for the recovery of aromatic and saturated hydrocarbons

from petroleum feedstocks [9]. NMP, an excellent dissoci-

ating solvent [10,11] suitable for the use in electrochemistry

[12] and organic synthesis requiring aprotic media [13], can

replace with toxicological and environmental advantages

solvents such as chlorinated hydrocarbons [14].

From a theoretical point of view, amides are also a very

interesting class of compounds. In pure liquid state, they

present a significant local order [15,16] as their quite high

heats of vaporization, DvapH, indicate [17] (Table 1). In the

case of N,N-dialkylamides, this is due to the dominance of

the general dipole–dipole interactions [16], which can be

ascribed to their very high effective dipole moments (l ;Table 1), a useful magnitude to examine the impact of

polarity on bulk properties [18,19]. For amides and N-

alkylamides, their self-association via H-bonds must be also

taken into account [16,20–22].

On the other hand, mixtures containing a polar compo-

nent of high polarity such as NMP and alkanes of benzene

Table 1

Physical constantsa of some pure amides at 298.15 K

Amide V/cm3 mo�1 DvapH/kJ mo�1 Pc/bar Tc/K l/D l

n-Methylformamide (NMF) 58.63b 56.19c 63.2d 730d 3.86b 1.93

n-Methylacetamide (NMA) 76.94b,e 59.4b,f 48.9d 690b 3.89g 1.70

n-Methylpropanamide (NMPA) 93.63b 64.89c 42.9d 685b 3.72g 1.47

2-Pyrrolidone (2-PY) 76.88b,e 56.6d 800d 3.8g 1.66

Dimethylformamide (DMF) 77.44b 46.88c 52.2b 596.6b 3.68g 1.60

Dimethylacetamide (DMA) 93.04b 50.24c 39.2b 637b 3.8g 1.51

n-Methylpyrrolidone (NMP) 96.63b 52.80c 46d 721.8h 4.09b 1.59

a V, molar volume; DvapH, enthalpy of vaporization; Pc, critical pressure, Tc, critical temperature; l, dipole moment in gas phase; l (effective dipole moment

[19])= [l2NA/(4peoVkBT )]1/2 where, NA is the Avogadro’s number; eo, permittivity of the vacuum; kB, Boltzmann constant.

b [3].c [17].d Calculated using the Joback’s method [61].e T= 303.15 K.f Range of T: (398.15–478.15 K).g [60].h [75].

J.A. Gonzalez et al. / Journal of Molecular Liquids 115 (2004) 93–10394

are located in the GE–HE diagram [23] in a range between

hydrogen bond associated and nonassociated mixtures [24].

An important result is that it is not possible to describe both

GE and HE of these systems by the Chemical Theory of

Solutions [24]. This confirms the transitional character of

mixtures containing a very polar component and makes

difficult their theoretical treatment.

Different theories have been applied in order to study

N-alkylamide + organic solvent mixtures. The Flory theory

[25] has been used to describe the HE of 1-alkanol + 2-

pyrrolidone systems [26]. However, the symmetry of the

HE curves is not well represented by this model [26].

Fig. 1 shows the dependence on the composition of the

energetic parameter, X12, of the Flory theory for some of

the mentioned solutions. The observed variation suggests

the existence of orientational effects. A better representa-

Fig. 1. Energetic parameter in the Flory theory, X12(Jcm�3), for N-

alkylamide(1) + 1-alkanol(2) mixtures. Solid lines refer to dependence of

X12 with the concentration. Dashed lines refer to values at x1 = 0.5.

tion of the experimental values for HE and VE (excess

molar volumes) for N-alkylamide + 1-alkanol mixtures [27]

can be obtained using the ERAS model [28], which

combines the real association solution model [29] with

the Flory equation of state [25]. Nevertheless, some dis-

crepancies between experimental and calculated values

were obtained for solutions involving methanol. This was

ascribed to association effects are less important than

dipolar interactions in such mixtures [27]. Investigations

in terms of the Kirkwood–Buff theory [30] reveal that

methanol does not form clusters with NMF or n-methyl-

acetamide (NMA) [31,32]. The ERAS model has been also

applied to study the following class of systems: NMP+ ar-

omatic compound [33], NMP or DMF+ 1-alkyne [34], or

NMP + 1-alkanol [35–37]. These theoretical treatments

were developed under the assumption that NMP and

DMF are self-associated compounds, what is not strictly

justified [16]. The poor results obtained for 1-alka-

nol +NMP mixtures were attributed to the existence of

strong dipole–dipole interactions between amide mole-

cules [5].

It should be also mentioned that, for practical purposes,

interaction parameters for mixtures involving monoalky-

lated amides such as NMA or n-ethylacetamide (NEA)

and organic solvents (alkanes, alcohols, aromatic com-

pounds or amines) are available in the framework of the

Dortmund version of the UNIFAC model [38].

In order to gain insight about the interactions present in

the mentioned solutions, one of the purposes of this paper is

to investigate N-alkylamide + organic solvent mixtures in

the framework of DISQUAC [39], a purely physical model

based on the rigid lattice theory developed by Guggenheim

[40]. The considered amides are NMF, NMA, n-methyl-

propanamide (NMPA), NEA, 2-pyrrolidone (2-PY) and

caprolactam. The solvents are alkanes, benzene, toluene

and 1-alkanols. This study is also developed in terms of the

concentration–concentration structure factor, SCC(0) [41], a

useful magnitude to analyze the solution structure.

J.A. Gonzalez et al. / Journal of Molecular Liquids 115 (2004) 93–103 95

2. Model

In the framework of DISQUAC, mixtures of N-alkyla-

mides with an organic solvent are regarded as possessing

four types of surface: (i) type m, NH–CO in secondary

amides; (ii) type a, aliphatic (CH3, CH2, H, in linear

secondary amides; toluene or 1-alkanols; (iii) type c, c-

CH2 in cycloalkanes or cyclic N-alkylamides (iv) type s

(s = b, C6H6 in benzene; s= p, C6H5 in toluene; s= h, OH in

1-alkanols).

2.1. Assessment of geometrical parameters

When DISQUAC is applied, the total molecular vol-

umes, ri, surfaces, qi, and the molecular surface fractions, ai,of the compounds present in the mixture are calculated

additively on the basis of the group volumes RG and

surfaces QG recommended by Bondi [42]. As volume and

surface units, the volume RCH4 and surface QCH4 of

methane are taken arbitrarily [43]. The geometrical param-

eters for the groups referred to in this work are listed in

Table 2.

2.2. General equations

The main features of DISQUAC are (i) the partition

function is factorized into two terms, in such way that the

excess functions are calculated as the sum of two contribu-

tions: a dispersive (DIS) term which represents the contri-

bution from the dispersive forces; and a quasichemical

(QUAC) term which arises from the anisotropy of the field

forces created by the solution molecules. Thus,

GE ¼ GE;COMB þ GE;DIS þ GE;QUAC ð1Þ

HE ¼ HE;DIS þ HE;QUAC ð2Þ

(ii) The interaction parameters are assumed to be

dependent on the molecular structure; (iii) The value

z = 4 for the coordination number is used for all the polar

Table 2

Relative group increments for molecular volumes, rG =VG/VCH4 and areas,

qG =QG/QCH4, calculated from Bondi’s [42] method (VCH4 = 17.12� 10� 6

m3 mol�1; ACH4 = 2.90� 10�5 m2 mol�1

Group rG qG Ref.

H 0.20094 0.26552 [76]

CH3 0.79848 0.73103 [43]

CH2 0.59755 0.46552 [43]

c-CH2 0.58645 0.66377–0.0385m

(4VmV 8)

[77]

C6H6 (homogeneous

molecule)

2.8248 2.0724 [43]

C6H5 2.67752 1.83797 [43]

OH 0.46963 0.50345 [45]

NH–CO 1.15537 0.8931 This work

contacts. This represents one of the more important short-

comings of the model, and is partially removed via the

hypothesis of considering structure dependent interaction

parameters.

In Eq. (1), the combinatorial term, GE,COMB is repre-

sented by the Flory–Huggins equation [43,44]. For binary

mixtures, this term is

GE;COMB ¼ RT x1lnU1

x1þ x2ln

U2

x2

� �ð3Þ

where Ui ¼ xirix1r1þx2r2

is the volume fraction of component i

( = 1, 2). The dispersive terms in Eqs. (2) and (3) are given

by:

FE;DIS ¼ ðx1q1 þ x2q2Þn1n2f DIS12 ð4Þ

where FE,DIS =GE,DIS or HE,DIS; ni ¼ xiqix1q1þx2q2

is the surface

fraction of component i in the mixture and

f DIS12 ¼ � 1

2RsRtðas1 � as2Þðat1 � at2Þf DISst ð5Þ

where fstDIS = gst

DIS ( FE,DIS = GE,DIS) and fstDIS = hst

DIS

(FE,DIS =HE,DIS) are, respectively, the Gibbs dispersive

parameter and the dispersive enthalpic parameter for the

(s, t)-contact.

For the quasichemical part, we have:

GE;QUAC ¼ RTðx1lE;QUAC1 þ x2l

E;QUAC2 Þ ð6Þ

with

lE;QUACi ¼ zqiRsasiln

XsasiXsias

ð7Þ

The quantities Xs are the quasichemical contact surfaces,

determined by solving the system of k equations (k is the

number of contact surfaces) which is obtained by maximiz-

ing the configurational partition function [43]

XsðXs þ RtXtgstÞ ¼ as ð8Þ

being gst ¼ exp � gQUACst

zRT

� �. Here, gst

QUAC is the Gibbs qua-

sichemical parameter for the (s, t)-contact and R the gas

constant. The values of Xsi in Eq. (7) are obtained by solving

Eq. (8) for xi = 1 (pure component i). Finally,

HE;QUAC ¼ 1

2Riqixið ÞRsRt XsXt � RiniXsiXtið ÞgsthQUACst ð9Þ

Here, hstQUAC stands for the enthalpic quasichemical param-

eter for the (s, t)-contact. For CpE=(BHE/BT)P, the corres-

ponding heat capacity parameters, c p,stDIS/QUAC, must be

Bx1 P;T


considered. The temperature dependence of the interaction

parameters gst, hst, cpst, has been expressed in terms of the

DIS and QUAC interchange coefficients [45], Cst,lDIS;

Cst,lQUAC where s p t= a, b, c, m, h, p, and l = 1 [Cst,1

DIS/QUAC =

g stDIS/QUAC(To)/RTo]; l = 2 [Cst,2

DIS/QUAC = h stDIS/QUAC(To)/

RTo)], l = 3 [Cst,3DIS/QUAC = cpst

DIS/QUAC(To)/R)]. To = 298.15 K

is the scaling temperature.

The equation of the solid-equilibrium curve of a pure

solid component 1 including two first-order transitions is,

for temperature below that of the phase transition [46]:

�lnx1 ¼DHfus1

R

� �1

T� 1

Tfus1

� �þ DCpfus1

R

� �

� lnT

Tfus1

� �þ Tfus1

T� 1

� �þ DH trs1V

R

� �

� 1

T� 1

T trs1V

� �þ DH trs1W

R

� �1

T� 1

T trs1W

� �þ lnc1 ð10Þ

Conditions at which Eq. (10) is valid have been specified

elsewhere [47]. In Eq. (10), c1 is the activity coefficient

of component 1 in the solvent mixture, at temperature T,

and in this work, is calculated using DISQUAC. DHfus1,

Tfus1, DCpfus1 are, respectively, the molar enthalpy of

fusion, the melting temperature and the change of the

molar heat capacity during the melting process of com-

ponent 1. DHtrs1, Ttrs1 stand for the molar enthalpy of

transition and transition temperature, respectively. The

required physical constants were taken from the literature

[48].

2.3. Concentration–concentration structure factor

The mixture structure can be studied using this magni-

tude, SCC(0) [41], defined as

SCCð0Þ ¼RT

ðB2GM=Bx21ÞP;T¼ x1x2

Dð11Þ

being GM=GE +GE,id and

D ¼ 1þ x1x2

RT

B2GE

Bx21

� �P;T

ð12Þ

D is a function closely related to the thermodynamic

stability [18,49]. For ideal mixtures, GE,id = 0; Did = 1 and

SCC(0) = x1x2. As stability conditions require, SCC(0)>0,

and if the system is close to phase separation, SCC(0)

must be large and positive (l, when the mixture presents

a miscibility gap). In contrast, if compound formation

between components appears, SCC(0) must be very low

(0, in the limit). Thus, if SCC(0)>x1x2, i.e., D < 1, the

dominant trend in the system is the separation of the

components (homocoordination), and the mixture is less

stable than the ideal. If 0 < SCC(0) < x1x2 = SCC(0)id, i.e.,

D>1, the fluctuations in the system have been removed,

and the dominant trend in the solution is the compound

formation (heterocoordination). The system is more stable

than ideal.

In the framework of the DISQUAC model

D

x1x2¼ 1

SCCð0Þ

¼ 1

x1x2þ 1

RT

B2GE;COMB

Bx21

� �P;T

þ 1

RT

B2GE;int

Bx21

� �P;T

ð13Þ

where GE,int =GE,DIS +GE,QUAC and

B2GE;COMB

Bx21

� �P;T

¼ RTðr1 � r2Þ2

ðx1r1 þ x2r2Þ2ð14Þ

B2GE;int

Bx21

� �P;T

¼ � 2q21q22g

DIS12

ðx1q1 þ x2q2Þ3� 1

x1

BlE;QUAC

Bx1

� �P;T

ð15Þ

The BlE;QUAC� �

derivatives are calculated numerically.

3. Estimation of the interaction parameters

Table 3 summarizes the types and number of contacts

present in each investigated solution, the references where

the already known interchange coefficients are available,

and the assumptions/restrictions applied during the fitting

procedure.

The general procedure applied in the estimation of the

interaction parameters is as follows. First, the experimental

database for the systems under study is carefully analyzed to

select those systems which will be used in the fitting

procedure of the parameters. Second, the parameters are

fitted to reproduce as well as possible the concentration

dependence of the experimental GE and HE data of those

systems selected for the adjustement. This is made by means

of a Marquardt algorithm [50] which minimizes the objec-

tive function:

FðCDIS=QUACst;1 ;C

DIS=QUACst;2 ;C

DIS=QUACst;3 Þ

¼X

ðGEcalc � GE

expÞ2=NG þ

XðHE

calc � HEexpÞ

2=NH

ð16Þ

where the sums are taken over NG and NH, the number of

experimental data points for GE and HE, respectively. Third,

when required data are not available, or are considered to be

Table 3

Contacts present in the investigated systems. The type of data used and assumptions/restrictions applied during the fitting procedure of the interaction

parameters are included

Systema Contactsb Interaction parameters Fitted to Assumptions– restrictions Ref.

Linear N-alkylamide

+ n-Cn

(a, m) DIS and QUAC VLE, HE QUAC parameters

independent of the amide

This work

Linear N-alkylamide (a, c) DIS Neglected [1, 78]

+ c-Cn (a, m) DIS and QUAC Previously

determined

in this work

(c, m) DIS and QUAC VLE, HE C am,lQUAC =C cm,l

QUAC This work

NMF+ benzene,

or + toluene

(a, s)

s = b or p

C ab,1DIS = 0.289;

C ab,2DIS = 0.576;

C ab,3DIS =� 0.585

C ap,1DIS = 0.39;

C ap,2DIS = 0.59;

C ap,3DIS =� 0.35

[79]

(a, m) DIS and QUAC Previously

determined

in this work

(s, m) DIS and QUAC SLE, HE QUAC parameters

independent of the

aromatic compound

This work

Cyclic amide + c-Cn (c, m) DIS and QUAC VLE QUAC parameters

equal to those for

linear amides

This work

Cyclic amide + n-Cn (a, c) DIS Neglected [1,78]

(c, m) DIS and QUAC Previously

determined

in this work

(a, m) DIS and QUAC VLE C am,lQUAC =C cm,l

QUAC This work

NMF or (a, h) DIS and QUAC [45,47]

NMA+1-alkanol (a, m) DIS and QUAC Previously

determined

in this work

(h, m) DIS and QUAC VLE, HE C hm,1QUAC independent of

the mixture compounds

This work

2-PY+ 1-alkanol (a, c) DIS Neglected [1,78]

(a, h) DIS and QUAC [45,47]

(a, m) DIS and QUAC Previously

determined

in this work

(c, h) DIS and QUAC [80]

(c, m) DIS and QUAC Previously

determined

in this work

(h, m) DIS and QUAC VLE, HE C hm,1QUAC independent of

the mixture compounds

This work

a For symbols, see Table 1.b Type a, CH3, CH2, H, in linear secondary amides; toluene or 1-alkanols; type c, c-CH2 in cycloalkanes or cyclic N-alkylamides; type b, C6H6 in benzene;

type p, C6H5 in toluene; type h, OH in 1-alkanols; type m, NH–CO in secondary amides.


unreliable, the corresponding interchange coefficients are

estimated by interpolation or extrapolation of the well-

known parameters, taking into consideration their overall

variation with the molecular structure of the mixture com-

pounds. This procedure increases markedly the predictive

ability of the model.

In the present case, the fitting of the interaction

parameters is somewhat difficult as part of the treated

systems (those with alkanes) show miscibility gaps. DIS-

QUAC is a mean field theory and LLE calculations are

developed under the basic and wrong assumption that GE

is an analytical function close to the critical point. The

instability of a systems is given by (B2GM/Bx12)P,T and

represented by the critical exponent c>1 in the critical

exponents theory [18]. According to this theory, mean

field models (c = 1) provide LLE curves which are too

high at the upper critical solution temperature (UCST) and

too low at the LCST [18] (lower critical solution temper-

ature). Thus, one must keep the Csm,1DIS/QUAC (s = a, c)

coefficients between certain limits in order to provide

Table 4

Dipersive (DIS) and quasichemical (QUAC) interchange coefficients, C st,lDIS

and C st,lQUAC, for (s, t) contacts investigated in this work

Systema Contactb (s, t) C st,1DIS Cst,2

IS Cst,1QUAC Cst,2

QUAC

NMF; NEF+ n-Cn (a, m) 0.55 1 8. 6.5

NMA; NEA+ n-Cn (a, m) 0.20 1 8. 6.5

NMPA; NEP+ n-Cn (a, m) � 0.40 1 8. 6.5

NMF; NEF+ c-Cn (c, m) 0.75 1.15 8. 6.5

NMA; NEA+ c-Cn (c, m) 0.50 1.15 8. 6.5

NMPA; NEP+ c-Cn (c, m) 0.15 1.15 8. 6.5

2-PY+ n-Cn (a, m) � 1.1 1.15 8. 6.5

2-PY+ c-Cn (c, m) � 0.85 1.15 8. 6.5

Caprolactam+ n-Cn (a, m) 0.6 1.15 8. 6.5

Caprolactam+ c-Cn (c, m) 0.85 1.15 8. 6.5

NMF+ benzene (b, m) � 0.45 0.48 7.1 2.5

NMF+ toluene (p, m) � 0.70 0.40 7.1 2.5

NMF+MeOH (h, m) 0.62 � 2.7 0.3 2.

NMF+EtOH (h, m) 0.62 � 1.44 0.3 2.

NMF+z 1-PrOH (h, m) 0.62 � 1.27 0.3 2.

NMA+MeOHc (h, m) � 1.3 � 0.85 0.3 0.3

NMA+EtOHc (h, m) � 0.75 0.68 0.3 0.3

NMA+z 1-PrOHc (h, m) 0.3 0.80 0.3 0.3

2-PY+MeOH (h, m) � 0.70 18.35 0.3 � 8

2-PY+EtOH (h, m) 1.0 � 8.2 0.3 4.5

2-PY+z 1-PrOH (h, m) 2.0 � 7.0 0.3 4.5

a For symbols, see Table 1; n-ethylformanide (NEF); n-ethylacetamide

(NEA), n-ethylpropanamide (NEP); methanol (MeOH); ethanol (EtOH); 1-

propanol (1-PrOH).b For contacts, see Table 3.c C st,3

DIS =� 2.0;C st,3QUAC =� 3.0.

Table 5

Excess molar Gibbs energies, GE, at equimolar composition and

temperature T for N-alkylamide + organic solvent mixtures

Systema T/K Nb GE/J mol�1 rr( P)c Ref.

Exp.d DQe Exp. DQ

NMA+ n-C8 363.15 10 0.023 0.28 (0.32) [55]

383.15 10 0.050 0.32 (0.38) [55]

398.15 10 0.002 0.059 (0.096) [51]

NMA+ n-C10 413.15 41 0.008 0.033 (0.045) [54]

NMPA+ n-C8 363.15 13 1520 1613 0.022 0.066 (0.13) [55]

383.15 13 1550 1631 0.011 0.071 (0.13) [55]

NEA+ n-C10 363.15 12 0.019 0.075 (0.18) [55]

383.15 12 0.020 0.046 (0.14) [55]

NMA+ c-C8 398.15 34 0.047 0.080 (0.046) [51]

Caprolactam+ 363.15 10 1770 1747 0.017 0.13 [55]

n-C8 383.15 10 1820 1772 0.073 0.093 [55]

Caprolactam+ 363.15 9 0.006 0.043 [55]

n-C10 383.15 9 0.006 0.037 [55]

Caprolactam+ 383.15 8 0.057 0.076 [55]

n-C12 403.15 8 0.033 0.055 [55]

423.15 9 0.055 0.059 [55]

NMF+MeOH 313.15 25 99 103 0.011 0.057 [81]

NMF+EtOH 313.15 21 195 193 0.007 0.013 [82]

NMA+MeOH 313.15 17 � 263 � 259 0.004 0.014 (0.064) [83]

398.55 36 � 490 � 276 0.004 0.10 (0.015) [59]

NMA+EtOH 313.15 23 � 113 � 104 0.002 0.007 (0.030) [84]

2-PY+MeOH 313.15 21 � 171 � 172 0.004 0.031 [85]

2-PY+EtOH 313.15 20 70 69 0.006 0.015 [85]

a For symbols, see Tables 1 and 4.b Number of experimental data.c Eq. (17).d Experimental value.e DISQUAC result (between parenthesis are given UNIFAC results


not very high calculated UCSTs. The final parameters are

collected in Table 4.
calculated with parameters from the literature [38]).
Fig. 2. HE for N-alkylamide(1) + organic solvent(2) mixtures. Points refer to

experimental results: (.) NMA(1) + c-C8(2) at 398.15 K [51], (n)

NMF(1) + benzene(2) at 298.15 K [86]. Solid lines refer to DISQUAC

calculations.

4. Results

4.1. DISQUAC results

Tables 5–8 compare DISQUAC calculations for VLE,

HE, SLE and SCC(0) with experimental values for the

investigated systems. Figs. 2–6 show this comparison in

graphical way for some selected mixtures. For the sake of

major clarity, Tables 5 and 6 list deviations for pressure (P)

and HE defined respectively as:

rrðPÞ ¼ 1=NX Pexp � Pcalc

Pexp

� �2" #1=2

ð17Þ

and

devðHEÞ ¼ 1

N

X HEexp � HE

calc

AHEexpðx1 ¼ 0:5ÞA

" #28<:

9=;

1=2

ð18Þ

In Eqs. (17) and (18), N stands for the number of experi-

mental data.

DISQUAC represents quite accurately the thermody-

namic properties of the systems under study. It is remark-

able that the model can be applied over a wide range of

temperature as the results for the NMF+ benzene system

show (Tables 6 and 7). Nevertheless, DISQUAC fails

when describing VLE data for solutions with alkanes

Fig. 3. HE for N-alkylamide(1) + 1-alkanol(2) mixtures. Points refer to

experimental results: (x) NMA(1) +methanol(2) (T= 398.15 K [59]), (.)NMF(1) +methanol(2), (n) NMF(1) + ethanol(2), (z) NMF(1) + 1-prop-

anol(2) (T= 313.15 K [70]), (E) NMF(1) + 1-butanol(2) (T= 313.15 K

[88]). Solid lines refer to DISQUAC calculations.

Fig. 5. SLE for NMF(1) + organic solvent mixtures(2). Points refer to

experimental results [48]: (.) benzene, (n) ethanol. Solid lines refer to

DISQUAC calculations. Dashed lines refer to ideal mixtures.


(Table 5). This is due to (i) the large difference between

vapor pressures of pure compounds which leads to large

values of the dP/dx slope, (ii) the system temperature is

much lower than the corresponding UCST. It is remarkable

that fitting equations such as NRTL or UNIQUAC cannot

describe the big changes in dP/dx that occur at high

dilution and near the miscibility gap with the required

accuracy [51]. The poor results provided by DISQUAC

merely underline that it is not possible to represent VLE

and LLE simultaneously with the same set of interaction

parameters [52]. One should keep in mind that critical

Fig. 4. HE at 303.15 K for 2-PY(1) + 1-alkanol(2) mixtures. Points refer to

experimental results [26]: (z) methanol, (E) ethanol, (n) 1-propanol, (x)1-butanol, (.) 1-pentanol. Solid lines refer to DISQUAC calculations.

effects on the thermodynamic properties of fluids are

observed in practice over a large range of temperature

and densities around the critical point [53]. When the

system temperature approaches to the UCST, DISQUAC

results are improved, and the heterogeneous azeotropes are

quite well described. For example, for the NMA+ n-C10

system, at 413.15 K, Paz = 49.24 kPa and x1az = 0.226 [54].

At the same temperature, the calculated results are

Paz = 46.25 kPa and x1az = 0.231; for the caprolactam + n-

C12 mixture at 423.15 K; Paz = 16.08 kPa and x1az = 0.113

[55]. The theoretical results at 423.15 K are Paz = 15.76

kPa and x1az = 0.096.

It should be mentioned that the critical points are

described, as usually [1,56], in the correct range of

Fig. 6. SCC(0) at 313.15 K for linear secondary amide(1) +methanol(2)

mixtures. Points refer to experimental results from VLE measurements

[81,83,85]: (n) NMF, (.) NMA, (E) 2-PY. Solid lines refer to DISQUAC

calculations. Dashed line refer to ideal mixture.

Table 7

Solid– liquid equilibria for n-methylformamide + organic solvent mixtures

[48]

Solvent Na D(T)b/K rr(T)c

C6H6 19 0.68 0.003

C7H8 20 2.5 0.011

MeOH 18 1.2 0.008

EtOH 17 0.9 0.059

a Number of data points.b D(T) =SjTexp� Tcalcj/N.c rrðTÞ ¼ 1=N

P Texp�TcalcTexp

� �2� �1=2

.


temperature and composition. For the NMPA+ n-C8 sys-

tem, UCST= 361.25 K and x1c = 0.267 [55]. DISQUAC

predicts UCST= 365.9 K and x1c= 0.324. The NMF+ n-C6

solution shows a miscibility gap, at 363.15 K for

0.065 < x1 < 0.997 [57]. DISQUAC yields the inmiscibility

for 0.063 < x1 < 0.971. Nevertheless, the calculated LLE

curves (and also the calculated HE curves) close to the

UCST are, as usually, more rounded than the experimental

ones (Fig. 2; see Ref. [56] and references herein). This is

due to calculations which are developed assuming that the

excess functions are analytical close to the critical points,

while the thermodynamic properties are, really, expressed

in terms of scaling laws with universal critical exponents

and universal scaling functions [18].

4.2. Comparison with other models

In a recent work [27], ERAS has been applied to

mixtures with 1-alkanols. The mean deviation for HE

Table 6

Excess molar enthalpies, HE, at equimolar composition and temperature T

for N-alkylamide + organic solvent mixtures

Systema T/K Nb HE/J mol�1 Dev(HE)c Ref.

Exp.d DQe Exp. DQ

NMF+C6H6 298.15 17 417 424 0.006 0.046 [86]

15 383 0.017 0.10 [87]

NMF+C7H8 298.15 17 447 454 0.004 0.042 [86]

NMF+

MeOH

313.15 17 259 257 0.008 0.042 [70]

NMF+EtOH 313.15 17 601 596 0.007 0.012 [70]

NMF+

1-PrOH

313.15 17 730 742 0.009 0.025 [70]

NMF+

1-BuOH

313.15 17 831 808 0.007 0.026 [88]

NMA+ 313.15 13 � 76 � 79

(� 356)

0.009 0.060

(2.95)

[58]

MeOH

398.25 21 � 270 � 267

(� 268)

0.004 0.056

(0.023)

[59]

NMA+

EtOH

313.15 13 195 194

(202)

0.008 0.046

(0.133)

[58]

NMA+

1-PrOH

313.15 12 274 273

(238)

0.009 0.062

(0.080)

[58]

NMA+

1-BuOH

313.15 14 314 305

(281)

0.010 0.079

(0.079)

[58]

2-PY+

MeOH

303.15 10 22 21 0.136 0.81 [26]

2-PY+EtOH 303.15 11 495 517 0.005 0.061 [26]

2-PY+

1-PrOH

303.15 10 831 833 0.004 0.053 [26]

2-PY+

1-BuOH

303.15 10 953 965 0.002 0.022 [26]

2-PY+

1-PeOH

303.15 10 1060 1180 0.002 0.051 [26]

a For symbols, see Tables 1 and 4. 1-BuOH, 1-butanol; 1-PeOH, 1-

pentanol.b Number of data points.c Eq. (18).d Experimental value.e DISQUAC result (between parenthesis are given UNIFAC results

calculated with parameters from the literature [38]).

[Sdev(HE)/number of systems] between experimental

results and values calculated using ERAS is 0.259, while

DISQUAC provides 0.10. The large deviation obtained

from ERAS is due to the fact that the model fails when

representing HE for NMA or 2-PY+methanol systems. In

addition, GE is also poorly described, because ERAS

overestimates the chemical contribution to this excess

function. In contrast, VE is accurately represented. The

difficulty to describe simultaneously HE, GE, VE has been

interpreted assuming that dipolar interactions are more

important than association effects [27] (see below). For

similar reasons to those stated above, the Dortmund

version of UNIFAC also represents poorly VLE for the

systems with alkanes. In addition, the temperature depen-

dence of HE is not correctly described as the model

predicts that this magnitude increases with temperature.

At equimolar composition, for the NMA+methanol sys-

tem UNIFAC yields � 356 and � 268 J mo�1 at 313.15

and 398.15 K, respectively. The experimental values are

(in the same order) � 77 J mo�1 [58] and � 270 J mo�1

[59].

5. Discussion

5.1. N-alkylamide + alkane

As already mentioned, N-alkylamides such as NMF,

NMA, 2-PY or caprolactam are not miscible with alkanes

at room temperature (see above). This reveals strong

dipole–dipole interactions between amide molecules,

which can be explained in terms of their large values for

l and l (Table 1). For example, l (NMF) = 3.86 D [3];l-

(NMF) = 1.93 and l (NMA)= 3.89 D [60]; l (NMA) = 1.70

(Table 1). It is interesting to compare these values with

those for methanol: l = 1.7 D [61] and l = 1.02 [19]. The

UCSTs for the methanol + n-C6 or + n-C8 systems are

306.75 K [62] and 339.3 K [63], respectively. It is then

possible to conclude that dipole–dipole interactions are

stronger in solutions with amides and particularly in those

containing NMF. Accordingly to this behaviour, SCC(0) is

large and positive (Fig. 7). Note that the maximum of this

function is shifted to the region where the critical compo-

sition is encountered.

Fig. 7. DISQUAC calculations for SCC(0) of the mixtures: (1)

NMPA(1) + n-C8(2) at 383 K, (2) NMA(1) + c-C8(2) at 460 K, (3)

Table 8

Thermodynamic functionsa for N-alkylamide + 1-alkanol systems

Systemb GE,COMB/ TSE/ TSE,int/ DISQUAC

contributions

to SCC(0)�1,c

SCC(0)

J mol�1 J mol�1 J mol�1

Comb. Interac. Exp.d DQe

NMF+MeOH � 90 160 70 0.268 � 0.566 0.26 0.270

NMF+EtOH � 7 406 400 0.021 � 0.602 0.301 0.292

NMF+ 1-PrOH � 6 474 468 0.018 � 0.792 0.310

NMF+ 1-BuOH � 40. 504 464 0.121 � 1.10 0.331

NMA+MeOH � 191 187 � 4 0.545 0.179 0.208 0.211

NMA+EtOH � 49 308 259 0.147 0.174 0.230 0.231

NMA+1-PrOH � 4. 189 185 0.012 � 0.260 0.266

NMA+1-BuOH � 4 185 181 0.011 � 0.396 0.277

2-PY+MeOH � 212 186 � 26 0.62 0.141 0.217 0.224

2-PY+EtOH � 62 412 350 0.193 � 0.398 0.257 0.263

2-PY+ 1-PrOH � 9 675 666 0.028 � 0.435 0.278

2-PY+ 1-BuOH � 1. 828 827 0.002 � 0.295 0.270

2-PY+ 1-PeOH � 16 979 963 0.051 � 0.198 0.260

a GE,COMB [Eq. (3)]; TSE =HE�GE and TSE,int =HE�(GE�GE,COMB) at

313.15 K except for systems including 2-PY (T= 303.15 K). Experimental

results taken from references given in Tables 5 and 6. In absence of

experimental GE, values calculated using DISQUAC.b For symbols, see Tables 1, 4 and 5.c See Eqs. (13)– (15); values at 313.15 K.d Experimental values at 313.15 K calculated using VLE data from

references given in Table 5.e DISQUAC result.


5.2. NMF+aromatic compound

For the mixture containing benzene, DISQUAC predicts

GE (x1 = 0.5; 298.15 K) = 1142 J mo�1. Therefore, GE>HE

(Table 6) and TSE (x1 = 0.5; 298.15 K) =� 725 J mo�1.

This is a typical feature of associated solutions as well as

the fact that the HE curve is shifted to low mole fractions

of the self-associated compound (Fig. 2). Thus, for the 1-

pentanol + n-hexane system, GE (x1 = 0.5; 298.15 K) = 1041

J mo�1 [64]; HE (x1 = 0.5; 298.15 K) = 475 J mo�1 [65]

and TSE (x1 = 0.5; 298.15 K) =� 566 J mo�1. Therefore,

the solution structure is rather ordered, and this may

explain the importance of the interactions between the

very common amide and aromatic groups in proteins,

which seem to achieve a significant stabilization energy

[66].

The increase of the HE, when passing from benzene to

toluene, may be attributed to the aliphatic part of the latter,

which leads to a larger number of broken dipole–dipole

interactions between the NMF molecules.

5.3. Secondary amide + 1-alkanol

For a given amide, HE (x1 = 0.5) increases with the

chain length of the 1-alkanol (Table 6), which may be due

to (a) interactions between unlike molecules become

weaker; (b) the increase of the aliphatic surface of the

alcohol leads to a larger positive contribution to HE from

the disruption of the amide–amide interactions. This is

supported by the fact that the maxima of the HE curves are

skewed to higher mole fractions of the amide when the

length of the 1-alkanol increases (Figs. 3 and 4). A similar

behaviour is encountered in 1-alkanol + tertiary amide

[36,37,67,68], or + dimethylsulfoxide [68] mixtures and

marks the importance of the dipole–dipole interactions in

the investigated solutions.

methanol(1) + n-C6(2) at 383 K.

It turns out to be more difficult to compare HE for

systems formed by a given amide and different 1-alkanols.

From the experimental data, it seems that interactions

between unlike molecules are stronger in solutions with

NMA than in mixtures with NMF or 2-PY (Table 6). On the

other hand, in systems involving methanol or ethanol, the

mentioned interactions are stronger in solutions with 2-PY

than in those with NMF. The opposite trend is observed for

mixtures with the remainder alcohols.

The fact that, for a fixed 1-alkanol, HE (NMA) <HE

(NMF) has been ascribed in great part to the larger proton

accepting ability of NMA than of NMF [69,70]. However,

the observed variation of HE may be due to the fact that the

positive contribution to this magnitude from the disruption

of dipole–dipole interactions between amide molecules is

larger for NMF than for NMA (see above).

The major importance of dipolar interactions in alcoholic

solutions over association/solvation effects is supported by

(a) TSE>0 (Table 8). The systems with lower TSE values are

characterized by quite large negative combinatorial entro-

pies (Table 8). (b) The decrease of HE with the increase of

the temperature for the NMA +methanol system (i.e.,

CpE < 0; Table 6) and the gain of entropy of mixing of this

solution (at equimolar composition and 313.15 K, TSE = 187

J mol-1, while at 398.5, TSE = 220 J mol-1). Such behaviour

is a general feature of nonpolar mixtures [71,72]. It is also

observed in those solutions where the endothermic break-

ening upon mixing of the dipole–dipole interactions be-

tween like molecules is cancelled by formation of dipole–


dipole interactions between unlike molecules [71,72]. (c)

dVE/dT < 0 encountered in 2-PY+ 1-alkanol systems [73],

characteristic of solutions where strong free volume effects

are present [74].

Inspection of Table 8 reveals that SCC(0) values at

equimolar composition are not far from 0.25 (ideal behav-

iour). Note the quite low GE (x1 = 0.5) values for systems

such as NMF+methanol, + ethanol or for 2-PY+ ethanol,

which can be ascribed to a certain enthalpic–entropic

compensation in the studied solutions. On the other

hand, the mixtures wich show heterocoordination

(NMA or 2-PY+methanol) are characterized by SCC(0)

curves which are nearly symmetrical (Fig. 6), indicating

that the interactions between unlike molecules are of the

1:1 type.

From Table 8, we can also conclude the following: (i)

The contribution to SCC�1 (0) from the ideal combinatorial

Gibbs energy (1/x1x2) is always much higher than those

from the combinatorial entropy or from the interaction term.

(ii) The contribution to SCC�1 (0) from the combinatorial

entropy is always positive (Eq. 14). Thus, heterocoordina-

tion is also due, in some extent, to the difference in size of

the mixture components. This is particularly important for

those systems where interactions between like molecules

and unlike molecules are balanced (e.g., NMA or 2-

PY +methanol). In accord with this conclusion, studies on

the basis of the Kirkwood–Buff theory for NMA, or

NMF+methanol, or + ethanol [31,32] yield that the local

mole fractions differ only slightly ( < 1%) from the bulk

values and that the amide and the alcohol do not form

clusters. (iii) The interactional contribution to SCC�1 (0) is

negative for those systems characterized by homocoordina-

tion, where the greater ability of the longer 1-alkanols for

the breakage of the amide–amide interactions is prevalent

over other solvation effects. The same occurs in solutions

with alkanes.

6. Conclusions

N-alkylamides + organic solvent mixtures have been

investigated in terms of the purely physical theory DIS-

QUAC. The corresponding interaction parameters are

reported. The model describes consistently thermodynamic

properties such as VLE, HE, SLE or SCC(0). Solutions

with alkanes are characterized by strong dipole–dipole

interactions between amide molecules. NMF+ aromatic

compound mixtures behave similarly to associated sys-

tems. In NMA+methanol, or 2-PY+methanol, or + eth-

anol solutions, interactions between like molecules are

almost cancelled by interactions between unlike mole-

cules. The heterocoordination observed for these mixtures

[SCC(0) < 0.25] may be partially ascribed to size effects.

For other alcoholic solutions, the ability of the alcohol for

the breakage of the amide–amide interactions is prevalent

over solvation effects.

Acknowledgements

This work was supported by the Programa Nacional de

D.G.I. del Ministerio de Ciencia y Tecnologıa ‘‘Proyectos

I+D del Programa Nacional de Procesos y Productos

Quımicos’’, Project ref. PPQ2001-1664, y Union Europea

(F.E.D.E.R) and by the Consejerıa de Educacion y Cultura

of Junta de Castilla y Leon, under Project VA039/01.

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Thermodynamics of binary mixtures containing N-alkylamides