MatSE 443

Introduction to the Materials Science of Polymers

Penn State University

Introduction to the Materials Science of Polymers

Penn State University

PC Painter and MM Coleman Essentials of Polymer Science(DEStech Publications) |

## Chapter 11

**This is an important chapter!**

**Concepts that you must know:**

- Thermodynamics of Mixing:
- At the outset you must realize that the free energy of mixing, the entropy of mixing, and the enthalpy of mixing, are all
,*differences**i.e.*they describe the thermodynamic__energy change__between a mixed and a demixed system. Secondly, you must understand that these properties are calculated per volume. __entropy of mixing__Follow through how Flory-Huggings start from**S**= k_{B}ln**W**and derive the entropy of mixing enumerating the arrangements of black/white "balls" on a lattice. Equations 11.9, 11.12, and 11.13 are all the same relation written for different units; can you explain the differences?__enthalpy of mixing__Understand the definition of the chi parameter (eq.11.22). Also, based on this definition, you should appreciate how it can be applied to the FH lattice model (eq.11.25), how it connects to solubility parameters (eq.11.37), and the 'empirical' relation of eq.11.39.- *Implicit in all the above are a number (3 important ones) of assumptions the Flory-Huggins theory is based on. You should be able to pin-point them while reading through the derivation.
- Based on the above you should be able to explain to a layman: why entropy always favors mixing, what is the temperature dependance (and where it comes from), why small molecules typically mix and polymers typically don't mix
- Phase Behavior: Concepts of chemical potential, spinodal, binodal, and critical point; and how all these are connected back to the free energy of mixing.
- Chi at the critical point, incl. the empirical relation (eq.11.55), and Theta temperature for a solution (definition and physical meaning).

**Exercises:**

- * Make sure that you go through the derivations in the text, with the emphasis inidentifying physical meanings and assumptions.
- **Derive eq.11.48 by differentiating the Flory-Huggins equation (see footnote.41 on pg.348)

**Interactive Module:**

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The files are extremely small (typically half a minute with a modem) and can be run directly from this web-page.

- Start by choosing M
_{A}=M_{B}=1 (mixture of two 'monomers'), and span the whole range of available chi values. Notice how entropy remains the same (the blue curve only seems to move because the y-axis changes), and how the enthalphy changes. Can you relate these two behaviors back to the FH equation? - Set the chi to a small positive value (0.3-0.5), and increase the M
_{A}. What do you notice for the enthalpy/entropy, as far as their dependence on M_{A}is concerned? Can you explain this by pointing to the correct term in the FH equation? - Do the same for any other value of chi (positive or negative). Do the M
_{A}dependances change? - Can you calculate why such a sharp change when changing from M
_{A}=1 to a slightly higher number, and the insencitivity to M_{A}between values of 60 to 10,000? - What happens if both M
_{A}and M_{B}are larger than 1? Comment on both the entropy and the enthalpy contributions to the FH free energy of mixing.