Fluid Phase Equilibria 337 (2013) 6–10
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Fluid Phase Equilibria
j o ur nal homep age: www.elsevier.com/locate/fluid
Comparison between three predictive methods for the calculation of polymer
solubility parameters
Ismael Díaz
b,∗
, Eduardo Díez
a
, Javier Camacho
a
, Salvador León
b
, Gabriel Ovejero
a
a
Grupo de Catálisis y Procesos de Separación (CyPS), Departamento de Ingeniería Química, Facultad de C. Químicas, Universidad Complutense de Madrid, Avda. Complutense s/n,
28040 Madrid, Spain
b
Departamento de Ingeniería Química Industrial y del Medio Ambiente, Escuela Técnica Superior de Ingenieros Industriales, Universidad Politécnica de Madrid, C/José Gutiérrez
Abascal 2, 28006 Madrid, Spain
a r t i c l e i n f o
Article history:
Received 20 June 2012
Received in revised form
18 September 2012
Accepted 21 September 2012
Available online 28 September 2012
Keywords:
Molecular dynamics
COSMO-SAC
Group contribution
Polymer
Bisphenol-A polycarbonate
Ethylene-co-vinyl acetate
Polyvinyl alcohol
a b s t r a c t
Solubility parameters (SP) of three polymers have been estimated and compared with both experimental
values. The methods employed for the estimation are: traditional group contribution procedures (Fedors
and van Krevelen), molecular dynamics simulation to calculate cohesive energy density and extension
of the COSMO-SAC thermodynamic model to polymer mixtures. The aim of the paper is accurately pre-
dicted polymer solubility parameters showing differences between methods. Selected polymers have
been polyvinyl alcohol (PVA), ethylene-co-vinyl acetate (EVA) and bisphenol-A polycarbonate (PC).
© 2012 Elsevier B.V. All rights reserved.
1. Introduction
Polymer materials are extremely important in current way of
life; adhesives, pipes, wrappings or multimedia devices are exam-
ples of items that are mainly composed of polymer materials,
widely produced all around the world [1]. Therefore, polymer
processing has been an important research topic in the last decades.
Many of the steps involved in polymer production processes are
equilibrium staged steps, such as steam stripping or solvent devola-
tization; this makes polymer–solvent compatibility a key aspect to
accurately model these processes. In fact, the behaviour of the poly-
mer is very important to be properly analyzed because, in many
cases, it determines the design of the separation steps. However,
polymer solution properties are quite different from conventional
mixtures and they require using specific thermodynamics mod-
els. Historically, the most widely employed model has been the
well-known Flory–Huggins [2,3] model, based on the determina-
tion of the so-called Flory–Huggins interaction parameter,
12
,
that accounts for the compatibility of component 1 (solvent)
and 2 (polymer). From the regular solution theory developed by
∗
Corresponding author. Tel.: +34 91 336 5341; fax: +34 91 394 4114.
E-mail address: idiaz@quim.ucm.es (I. Díaz).
Hildebrand [4,5]
12
can be related to the solubility parameters of
both components by the simple expression:
12
=
V
1
RT
(ı
1
- ı
2
)
2
(1)
Solubility parameters can be calculated, following regular solu-
tion theory, from the values of cohesive energy density, c (energy
to separate molecules in the condensed phase):
ı
1
=
√
c =
H
1,v
- RT
V
1
(2)
where H
1,v
is the vaporization energy. Later on, with Eq. (1), the
value of
12
can be determined from the molar volume of the sol-
vent (V
1
) and the solubility parameter of the pure components.
This implies that the value of the interaction parameter
12
of a
polymer-containing mixture can be easily determined for a wide
range of solvents if the value of the polymer solubility parameter
is known.
Many efforts have been made to develop both experimental
techniques and prediction methodologies. Among the first ones, the
most important techniques are swelling [6], inverse gas chromatog-
raphy [7,8] or intrinsic viscosity [9] measurements. Among the
prediction methods, van Krevelen [10] and Fedors [11,12] devel-
oped both group contribution methods that are widely employed
0378-3812/$ – see front matter © 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.fluid.2012.09.028