Flashcards in Chapter 5 - Polymer solutions and blends Deck (24):

1

## Write down the Flory-Huggins parameter.

### chi = z/2 * (2u_AB - u_AA - u_BB)/kT

2

## What is a dilute solution? What is the characteristic length scale?

###
The case when the concentration is far below the critical concentration.

Characteristic length scale is R_g prop. N^3/5

3

## What is a semidilute solution?

### The case when the concentration is approximately the same as the critical concentration, that is when the chains begin to touch.

4

## What is a concentrated solution? What is the characteristic length scale?

###
When the concentration is above the critical concentration, that is there is considerable overlap between different chains.

The characteristic length scale is the mesh size.

5

## How does the phase separation temperature depend on the molar mass of the polymer?

### The phase separation temperature goes up with increasing molar mass of the polymer.

6

## What are the two ways of demixing?

###
i) Nucleation and growth

ii) Spinodial decomposition

7

##
In which of the following cases is there an entropy gain of mixing?

i) Regular solution

ii) Polymer solution

iii) Polymer blend

### In all of them. But because the polymer chains take up a much bigger volume than small molecules, the entropy gain is less for polymer solutions, and even less for polymer blends.

8

## What is the mathematical expression for entropy gain for mixing?

###
∆S = -k * [((phi_A)/(N_A) * ln phi_A) + ((phi_b)/(N_B) * ln phi_B)]

phi_i = fraction of species i.

N_i = number of lattice sites species i takes up.

9

## What is the mean field approximation?

### The mean field approximation assumes that the distribution of molecules is uniform with no fluctuations.

10

## What is the probability of that the neighbor of a given molecule is A or B respectively in the mean field approximation?

### The probability is directly proportional to the volume fractions phi_A and phi_B.

11

## What is the total energy of species A and B upon mixing?

###
U = zn/2 * (U_A*phi_A + U_B*phi_B),

where U_A = u_AA*phi_A + U_AB*phi_B.

and U_B = u_BB*phi_B + U_AB*phi_A,

z is the coordination number (number of nearest neighbors) and n is the total number of lattice sites.

12

## What is the total energy of species A and B before mixing?

###
U_0 = zn/2 * (u_AA*phi_A + u_BB*phi_B)

z is the coordination number (number of nearest neighbors) and n is the total number of lattice sites.

13

## What is the energy gain upon mixing?

###
∆U = U - U_0 = zn/2 * (1-phi)*phi * [2u_AB - u_AA - u_BB],

where phi is the volume fraction of one of the reaction species, and (1-phi) the volume fraction of the other.

14

## What is the interpretation of the value of the Flory-Huggins interaction parameter?

###
If chi > 0 there is repulsion between species A and B.

If chi < 0 there is attraction between species A and B.

15

## What is the total free energy change of mixing per molecule, and what is the entropic and enthalpic term?

###
∆F = kT * (phi/N_A * ln phi + (1-phi)/N_B * ln (1-phi) + chi*phi(1-phi)

The entropic term is:

phi/N_A * ln phi + (1-phi)/N_B * ln (1-phi)

The enthalpic term is:

chi*phi(1-phi)

16

## What is UCST behavior?

###
UCST = upper critical solution temperature

For the relation chi = A + B/T, when B > 0, chi decreases with increasing T. The UCST is the highest temperature of the two-phase region.

17

## What is LCST behavior?

###
LCST = lower critical solution temperature

For the relation chi = A + B/T, when B < 0, chi increases with increasing T. The LCST is the lowest temperature of the two-phase region.

18

## What is the binodal line?

### It is the line between the stable and metastable phase. Also known as the coexistence curve. Between the binodal and spinodal line, the two-phase can coexist with the mixed phase.

19

## What is the spinodal line?

### It is the line between the metastable and the unstable phase. That is, on the inside of this curve the solution will always be unstable, and be phase-separated.

20

## What is the critical point?

### This is the point where the spinodal and binodal line has the same value.

21

## What is the criterium for a stable mix?

### That the second derivative of the free energy as a function of composition is greater than 0.

22

## What is the criterium for an unstable mix?

### That the second derivative of the free energy as a function of composition is less than 0.

23

## How can you determine the interaction parameter?

### By using light scattering.

24