## Problems and Solutions

Chapter 10

Polymer Thermodynamics

### Textbook Examples:

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10.01
Calculation of the Average Segment Number (p. 432)

10.02
Cloud Point Curve for the System Water
+ Methylcellulose (p. 440)

10.03
Calculation of the Pressure for the System CO_{2}
+ PS Using PC-SAFT (p. 454)

Mathcad (2001) - Solution as XPS

### Additional Problems:

P10.01
**Segment Mole Fraction in a Polymer Solution **

The mole fraction of a polymer solution made from monodisperse
polystyrene (PS) having a molecular weight of

P10.02
**Number-Average and Mass-Average Segment Number for a Wesslau
Distribution **

The polydispersity of polyethylene can often be described with
the help of the Wesslau distribution function:

Calculate the number-average and the mass-average segment number.

P10.03
**Vapor Pressure Using Flory-Huggins **

In the original Flory-Huggins theory a concentration independent
interaction parameter
^{S}
= 20.56 kPa
for^{S}
= 20.4 kPa
for ^{S}_{0}
= 20.56 kPa and
the segment number of PS is
_{PS}
= 100

P10.04
**Vapor Pressure and Heat of Vaporization for Styrene
Polymerization in Cyclohexane**

Polystyrene can be
produced by dissolving the monomer styrene in the solvent cyclohexane at
25°C. During polymerization the temperature increases to 85°C. The
dependence of vapor pressure of cyclohexane on temperature is given by:

where A=3.96988, B=1203.526 and C=-50.287.

a) Calculate the vapor pressure of cyclohexane at 25, 50 und
75°C.

b) Plot the calculated vapor pressure of the solvent in a
suitable diagram.

c) How much heat is removed by the evaporation of the
solvent, if you assume

cyclohexane vapor to behave as
an ideal gas, the liquid volume is negligible

small and the enthalpy of
evaporation does not depend on temperature?

d) Why is it desired that the polymerization temperature does
not exceed 85°C?

e) Discuss the influence of the polymer on the vapor pressure
of cyclohexane.

P10.05
**Vapor Pressure of a PIB Solution in Benzene (Flory-Huggins)**

The vapor pressure of polyisobutylene (PIB) with a number-average
molecular weight of
_{PIB}
= 45 kg/mol dissolved in benzene (B) (_{B}
= 78.11 g/mol

a) Calculate the activity of the solvent for this polymer
solution.

b) Calculate the Flory-Huggins interaction parameter

c) Is this mixture stabile, if you assume the Flory-Huggins
Equation describes

the system correct?

P10.06
**LLE in a Polymer-Solution **

The LLE of a polymer solution, consisting of polymer B and
solvent A should be modeled using Flory-Huggins theory, where the
χ

b) Derive the spinodal and the critical
conditions.

P10.07
**Parameters of the Koningsveld-Kleintjens Model From Lower
Critical Solution Temperature **

Linear poly-N-isopropylacrylamide (PNIPAM) dissolved in water
shows a lower critical solution temperature (LCST). For the calculation
of the liquid-liquid equilibrium with the help of the
Koningsveld-Kleintjens model the parameter γ_{C} = 306.65 K_{PNIPAM}
= 4000

P10.08
**Pressure Above a Polymer Solution Using PC-SAFT **

A vessel contains a mixture consisting of polystyrene_{P}
_{
S}
=
70.3
kg/mol_{2} (_{CO2}
= 44.014 g/mol_{ij}
= 0.0587