Questions from class - Lecture 2 Flashcards
What is the definition of an ideal chain?
An ideal chain is a chain where there is no interaction between the monomers.
Which parameters are used to describe the conformation and size of a polymer?
Mean-square end to end: = C_∞nl^2
Contour length: R_max = nl
Radius of gyration: R_g^2 = 1/N*∑(r_i - r_cm)^2
How does the end-to-end distance depend on the degree of polymerization for an ideal chain?
R_max = n*l.
Mean-square end to end = C_∞ * nl^2
Proportional with n.
What is the characteristic ratio?
The characteristic ratio, denoted C_n, is the average value of C_i which is the sum over all the bond vectors for the i-th monomer.
The sum over all the bond vectors for the i-th monomer will converge to this number C_i, because the angle is only confined for monomers in close proximity.
What is the equivalent freely jointed chain?
A chain with same avgR^2 , same R_max, but that is divided into N freely-jointed bonds of length b (Kuhn-length).
What is the freely rotating chain and what is its end-to-end vector?
A chain where all the bond lengths and bond angles are fixed, but the torsion angles are free to rotate. All the angles have equal probability. In this case:
avgR^2 = N*b^2 * (1 + cos theta)/(1 - cos theta)
How is the hindered rotation model defined?
Here the torsion angles are not all equally probable. The probability of a given torsion angle is proportional to the Boltzmann factor, exp[-U(phi_i)/kT], where U(phi_i) is the energy barrier for the given torsion angle.
What is the definition of the radius of gyration?
The radius of gyration is defined as:
R_g^2 = 1/N * ∑(r_i - r_cm)^2,
which is the mean square average distance from the i-th monomer to the polymers centre of mass.
What is the relation between the radius of gyration and the end-to-end distance of an ideal chain?
R_g^2 = (Nb^2)/6 = avgR^2/6.
What is the free energy of an ideal chain?
F = U - TS, where U = 0 (because no interactions).
F = (3/2)kTR^2/(Nb^2)
