Chapter 2 - Size and shape of polymers

Question 1

Which interactions between monomers are included in our “ideal chain”-model?

Answer 1

NO interactions are included in the model.

Question 2

What are typical fluctuations of bond lengths and bond angles in a polymer?

Answer 2

Bond length: ±0,05Å. Bond angle: ~3-5%

Question 3

What is the value of (average angle between i-th and j-th monomer) in the freely jointed chain model?

Answer 3

= 0

Question 4

What is the characteristic ratio, and how is it defined?

Answer 4

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.

Question 5

What is C_∞?

Answer 5

C_∞ is the characteristic ratio in the limiting case where N goes to ∞. Long chains can be approximated with C_∞.

Question 6

How does C_∞ depend on side groups?

Answer 6

The bulkier the side groups, the higher value of C_∞.

Question 7

What is an equivalent freely jointed chain?

Answer 7

A chain with same , same R_max, but that is divided into N freely-jointed bonds of length b (Kuhn-length).

Question 8

What is the contour length of a equivalent freely jointed chain?

Answer 8

R_max = Nb

Question 9

What is the mean-square end-to-end-distance of an equivalent freely jointed chain?

Answer 9

= Nb^2 = b*R_max = C_∞ * n * l^2

Question 10

What is the Kuhn length, and how is it defined?

Answer 10

The Kuhn length is the length of each segment in an equivalent freely jointed chain with length b, and is defined as:

b = / = (C_∞nl^2)/R_max

Question 11

What assumption is made in the freely rotating chain-model?

Answer 11

That all bond lengths and bond angles are fixed, and that all torsion angles are equally probable.

Question 12

How is C_∞ defined for a freely rotating chain?

Answer 12

C_∞ = (1 + cos theta)/(1 - cos theta)

Question 13

How is C_∞ defined for a hindered rotating chain?

Answer 13

C_∞ = (1 + cos theta)/(1 - cos theta) * (1 + )/(1 - )

Question 14

What is the probability of a given torsion angle in the hindered rotating chain model proportional to?

Answer 14

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.

Question 15

What is the radius of gyration, how is it mathematically defined?

Answer 15

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

Question 16

What is the radius of gyration of an ideal linear chain given as?

Answer 16

R_g^2 = (N*b^2)/6

Question 17

What is the relationship between the entropy of an ideal chain and the end-to-end distance?

Answer 17

The entropy decreases with R^2.

Less possible conformations as the chain is stretched out - fully stretched, only one conformation exists