### 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. 430)**

**10.02 Cloud Point Curve for the System Water + Methylcellulose (p. 439)**

**10.03 Calculation of the Pressure for the System CO _{2 }+ PS Using PC-SAFT (p. 452)**

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 missing and cyclohexane (CH) having a molecular weight of missing is missing. 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 vapor pressure of the polymer solution. For the system polystyrene (PS) + hexane the vapor pressure was measured for two different polymer segment fractions at T = 298.15 K.

The experimental results are P

^{S }= 20.56 kPa for missing and P

^{S }= 20.4 kPa for missing. The vapor pressure of the pure solvent at T = 298.15 K is P

^{S}

_{0 }= 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:

missing

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

a) Calculate the vapor pressure of cyclohexane at 25, 50 and 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 M

_{PIB}= 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 correctly?

**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:

missing

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 T

_{C}= 306.65 K and the experimental critical segment fraction is missing.

The used PNIPAM was monodisperse having a segment number of r

_{PNIPAM}= 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 (M

_{P}

_{S}=70.3 kg/mol) and CO

_{2}(M

_{CO2}= 44.014 g/mol). The liquid composition is missing and the liquid density is missing. Calculate the pressure in the vessel at missing using PC-SAFT-EOS with k

_{ij}= 0.0587

.