Chapter 5 - Polymer solutions and blends Flashcards
Write down the Flory-Huggins parameter.
chi = z/2 * (2u_AB - u_AA - u_BB)/kT
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
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.
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.
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.
What are the two ways of demixing?
i) Nucleation and growth
ii) Spinodial decomposition
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.
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.
What is the mean field approximation?
The mean field approximation assumes that the distribution of molecules is uniform with no fluctuations.
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.
What is the total energy of species A and B upon mixing?
U = zn/2 * (U_Aphi_A + U_Bphi_B),
where U_A = u_AAphi_A + U_ABphi_B.
and U_B = u_BBphi_B + U_ABphi_A,
z is the coordination number (number of nearest neighbors) and n is the total number of lattice sites.
What is the total energy of species A and B before mixing?
U_0 = zn/2 * (u_AAphi_A + u_BBphi_B)
z is the coordination number (number of nearest neighbors) and n is the total number of lattice sites.
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.
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.
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)
