Flashcards in Chapter 2 - Size and shape of polymers Deck (17)
Which interactions between monomers are included in our "ideal chain"-model?
NO interactions are included in the model.
What are typical fluctuations of bond lengths and bond angles in a polymer?
Bond length: ±0,05Å. Bond angle: ~3-5%
What is the value of (average angle between i-th and j-th monomer) in the freely jointed chain model?
What is the characteristic ratio, and how is it defined?
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 C_∞?
C_∞ is the characteristic ratio in the limiting case where N goes to ∞. Long chains can be approximated with C_∞.
How does C_∞ depend on side groups?
The bulkier the side groups, the higher value of C_∞.
What is an equivalent freely jointed chain?
A chain with same , same R_max, but that is divided into N freely-jointed bonds of length b (Kuhn-length).
What is the contour length of a equivalent freely jointed chain?
R_max = Nb
What is the mean-square end-to-end-distance of an equivalent freely jointed chain?
= Nb^2 = b*R_max = C_∞ * n * l^2
What is the Kuhn length, and how is it defined?
The Kuhn length is the length of each segment in an equivalent freely jointed chain with length b, and is defined as:
b = / = (C_∞*n*l^2)/R_max
What assumption is made in the freely rotating chain-model?
That all bond lengths and bond angles are fixed, and that all torsion angles are equally probable.
How is C_∞ defined for a freely rotating chain?
C_∞ = (1 + cos theta)/(1 - cos theta)
How is C_∞ defined for a hindered rotating chain?
C_∞ = (1 + cos theta)/(1 - cos theta) * (1 + )/(1 - )
What is the probability of a given torsion angle in the hindered rotating chain model proportional to?
It 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 radius of gyration, how is it mathematically defined?
The average square distance between monomors at position R_i and the polymers centre of mass.
R_g^2 = 1/N * ∑(R_i - R_cm)^2
What is the radius of gyration of an ideal linear chain given as?
R_g^2 = (N*b^2)/6