Problems and Solutions
Chapter 10
Polymer Thermodynamics

Textbook Examples:

XPS-file display is available in Internet Explorer. In case of Firefox, select Internet Explorer when asked for the software to open the file.

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 CO2 + PS Using PC-SAFT (p. 454)

Mathcad (2001) - Solution (zip)
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  and cyclohexane (CH) having a molecular weight of  is . Calculate the segment mole fraction of PS in this polymer solution.

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  occurs. This interaction parameter can be estimated using the vapour pressure of the polymer solution. For the system polystyrene (PS) + hexane the vapour pressure was measured for two different polymer segment fractions at T = 298.15 K. The experimental results are  PS = 20.56 kPa forand   PS = 20.4 kPa for . The vapor pressure of the pure solvent at T = 298.15 K is PS0 = 20.56 kPa and the segment number of PS is rPS = 100. Can the original Flory-Huggins theory be applied for this polymer solution?

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 MPIB = 45 kg/mol dissolved in benzene (B) (MB = 78.11 g/mol) was measured as function of polymer concentration at 313.15 K. The vapor pressure of benzene at this temperature is 24.3 kPa. For a polymer segment fraction of 0.4 the vapor pressure was 22.6 kPa.
    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-function is given by:
       
       a) Calculate the segment-based activity coefficients of the polymer and of the solvent.
       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 and the function β(T) are required. The experimental critical temperature is TC = 306.65 K and the experimental critical segment fraction is . The used PNIPAM was monodisperse having a segment number of rPNIPAM = 4000. Calculate the parameter γ and  β(T).

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

A vessel contains a mixture consisting of polystyrene (MP S = 70.3 kg/mol) and CO2 (MCO2 = 44.014 g/mol ). The liquid composition is  and the liquid density is . Calculate the pressure in the vessel at  using PC-SAFT-EOS with kij = 0.0587.