The best solubility is obtained when the solubility
parameters of polymer and solvent are close to each
other. For polymers the so called radius of solubility
KE-100.3410 Polymer properties
sphere (RAO) can be calculated. The liquids inside
Exercise 5:
the sphere act as solvents and outside the sphere as
Polymer solubility and gas permeation
non-solvents.
RA 
Exercise 5.1
 2
 2 D , s    P , P   P , s    H , P   H ,s 
2
D,P
2
2
Polymer solubility in different solvents can be estimated using solubility parameters
i. According to the Hansen model, the overall solubility parameter can be obtained as
    
2
D
2
P
2
H
where P refers to polymer and S to solvent.
RA
RA
 1 for solvent and
 1 for non-solvent. Estimate using the Hansen
RAO
RAO
where D, P, and H are the dispersive, polar, and hydrogen bonding parameters. In
model whether PVC is soluble in the monomer vinyl chloride when the following
table 3-3 Hansen solubility parameters for some common solvents are listed.
parameters for PVC are known D = 18.2 MPa1/2, P = 7.5 MPa1/2, H = 8.3 MPa1/2 and
RAO = 3.5 and for vinyl chloride: D = 15.4 MPa1/2, P = 8.1 MPa1/2, H = 2.4 MPa1/2.
Choose the best solvent from the table for PVC.
Exercise 5.2
The solubility parameter is related to cohesive energy-density Ecoh or the molar energy
of vaporization of a pure liquid Ev:
i  E
coh
i

Eiv
Vi
where Ev is defined as the energy change upon isothermal vaporization of the
saturated liquid to the ideal gas state at infinite dilution and Vi is the molar volume of
the liquid. The solubility parameter of a polymer has to be determined indirectly or
calculated by group-contribution methods. Calculation of  by a group-contribution
method requires the value of a molar attraction constant Fi, for each chemical group in
the polymer repeating unit. Values of Fi have been obtained by regression analysis of
Exercise 5.3
physical property data for a large number of organic compounds. The solubility
Poly(vinyl alcohol) film (thickness 0.20 mm) is laminated in between two LDPE films
parameter of a polymer is then calculated from these molar attraction constants and
(thickness of each film 0.2 mm). Oxygen transfer coefficient for LDPE is 2.210-13
the molar volume of the polymer.
(cm3(STP)cm)/(cm2sPa) and for PVOH 6.6510-16 cm3(STP)cm)/(cm2sPa).
i 
F F
i 1
Vi
i

i 1
i
Mi
a)
What is the oxygen transfer coefficient for the laminate at 25°C?
b)
A product is packed in this laminate material. The gas volume of the package
is 20 cm3 and surface area is 250 cm2. How long is shelf life of the product
i
when the oxygen concentration in the packet must not exceed 1.0 mol-%?
Some values of the molar attraction constants are shown in the table. Calculate the
Oxygen concentration is 0.0 mol-% just after the packaging.
solubility parameters using Van Krevelen constants for
a) Polyisobutylene, density 0.924 g/cm3
c)
What would be the shelf life of a product packed in a similar LDPE
packaging at room temperature?
b) Polystyrene, density 1.04 g/cm3
c) Polycarbonate, density 1.20 g/cm3
Exercise 5.4
Plastic soft drink bottles are made of poly(ethylene terephthalate) in Finland. Empty
1.5 dm3 bottle is filled to 2.0 bar CO2 pressure at 25°C and the cap is closed tightly.
Carbon dioxide transfer coefficient for PET is P(CO2, 25°C) = 0.11810-13
cm3(STP)cm/(cm2sPa). How long time does it take for CO2 pressure to drop one
tenth?
Exercise 5.5
Calculate the change in free energy of mixing when 10% solution of polystyrene (Mn
= 10000 g/mol) in cyclohexane at 34 oC is prepared. Flory-Huggins parameter is
0.50; density of cyclohexane is 0.7785 g/cm3 and density of styrene 1.06 g/cm3
Exercise 5.6*
Is 1000 g of polystyrene miscible with 1000 g polybutadiene at150 oC, when the
molecular weights of both polymers are 1105 g/mol? What is the upper limiting
molecular weight that the polymers are still miscible at that temperature? Would
increasing the temperature enhance the miscibility when the molecular weights are
1105 g/mol? Solubility parameter for PS is  18.6 (MPa)1/2 and density  = 1.06
g/cm3. Solubility parameter for polybutadiene is  17.2 (MPa)1/2 and density  =
1.01 g/cm3. Can assume that coordination value is z = 6.