Flashcards in Chapter 2 - Size and shape of polymers Deck (17):

1

## Which interactions between monomers are included in our "ideal chain"-model?

### NO interactions are included in the model.

2

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

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

3

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

### = 0

4

## 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.

5

## What is C_∞?

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

6

## How does C_∞ depend on side groups?

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

7

## 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).

8

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

### R_max = Nb

9

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

### = Nb^2 = b*R_max = C_∞ * n * l^2

10

## 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

11

## 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.

12

## How is C_∞ defined for a freely rotating chain?

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

13

## How is C_∞ defined for a hindered rotating chain?

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

14

## 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.

15

## 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

16

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

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

17