a. Consider the similarities and differences between a poly(ethylene-co-vinyl alcohol) random copolymer and a typical protein.

(i) Describe two ways that the copolymer and a protein are similar at the molecular level.

[2 marks]

(ii) Describe two ways that the copolymer and a protein are different at the molecular level.

[2 marks]

b. The repeat units in poly(ethylene) (or PE) and poly(vinyl alcohol) (or PVA) are shown in the figure below. Here, n represents the number of units in the polymer. Two surfaces of PE are placed into close contact. Considering the composition of the repeat units, state whether you expect the adhesion energy for PE to be greater than or less than for two PVA surfaces placed into close contact? Explain your reasoning.

[2 marks]

c. A spherical colloidal particle with a radius of R is a small distance D from a ceiling from which it is suspended. The particle and ceiling are both made from polyethylene. See the sketch of a side view below.

The interaction energy, W, between the particle and ceiling is given as

where H is the Hamaker constant for the polymer in air. The particle has a mass density of p. Write an expression for the largest diameter of particle for which the attractive van der Waals force will support the weight of the particle suspended from the ceiling.

[6 marks]

d. Using your result in part c, estimate the order of magnitude of the size of the largest particle that can be suspended from the ceiling by van der Waals forces. You can assume that the distance of separation, D, is 1 nm.

[3 marks]

e. PE and PVA are immiscible.

(i) How do you expect the 穴 interaction parameter for PE and PVA to compare to the

value of x for PE and the PE-PVA random copolymer? Explain your reasoning.

[2 marks]

(ii) A blend of PE and PVA is in the metastable region of the PE-PVA phase diagram. What would you expect to happen if a small amount of diblock copolymer of PE and PVA was added to the blend?

[1 mark]

(iii) There are Npe units of PE and Npva units of PVA in the diblock copolymer. Provide an estimate of the characteristic size of the copolymer when blended with PE and PVA, as in part (ii).

[2 marks]

2.

a. This question concerns bacteria growing in a growth medium. At a particular time, the

number of bacteria is measured and found to be 10¹⁰, and at the same time the oxygen consumption is measured and found to be 10¹⁷ oxygen molecules per second. Each oxygen molecule when consumed releases approximately 10^-19 J of energy. The doubling time of the bacteria, i.e. the time it takes a bacterium to grow and divide to produce one extra bacterium, is 1 hour.

(i) What is the power consumption of a growing bacterium? Estimate how much energy needs to be consumed by a bacterium to create one extra bacterium.

[3 marks]

(ii) If a bacterial cell is approximately 1 |im across, estimate the power consumption of a bacterium per unit volume. If a woman of mass 50 kg is recommended to consume

8 x10⁶ J of food per day, what is her power consumption per unit volume? Is it higher, lower, or approximately the same as for the bacteria?

[4 marks]

b. This question is about a cubic four-legged animal with edges of length, h, falling through the

air. Under gravity the falling animal will accelerate until it reaches a terminal velocity, v_F, which is approximately

J

2mg 切

where m is the mass of the animal, g is the acceleration due to gravity, and Pair 〜1 kg/m³ is the mass density of air. If the animal has a length of h = 1 m, then:

(i) Determine the terminal velocity of the animal. Then determine the terminal kinetic

energy of the animal.

[3 marks]

(ii) Assume that when the animal hits the ground it slows down from this terminal velocity to a stop, over a distance equal to h. Then estimate the acceleration of, and hence force on, the animal during this deceleration.

[3 marks]

(iii) The bones of an animal break at an applied compressive stress of approximately 107 Pa. Estimate whether or not this stress is exceeded when the animal hits the ground. You can assume the animal lands on four legs, each of which has a femur that is approximately 0.1h across.

[3 marks]

(iv) If h is doubled, by what factor does the force on the animal when it hits the ground, change?

[4 marks]

3.

a. Using a scaling relation, describe how the viscosity of a concentrated, linear polymer solution in a good solvent will change as the molecular weight of the polymer is increased above its entanglement molecular weight, Me.

[1 mark]

b. Colloidal particles are suspended in a concentrated solution of polymers in a good solvent. How will the self-diffusion coefficient of the particles change when the molecular weight of the polymer is doubled? (The molecular weight of both polymers is above Me.)

[3 marks]

where is the electrolyte concentration in the bulk solution, r is a function of the particle's surface potential, K_1 is the Debye screening length, and H is the Hamaker constant. The figure below (from J. Israelachvili (2011) p. 328) presents the pair interaction energy for three different spherical colloids (labelled as A, B and C) suspended in water.

(i) Of these three (A, B and C), which one is the most stable? Explain your answer in a

sentence (or more) considering the thermal energy of the particles at room temperature.

[2 marks]

The critical coagulation concentration (CCC) is defined as the concentration of electrolytes in the continuous phase at which the maximum of W(D) is exactly 0.

(ii) Which of the colloids (A, B or C) is at the CCC?

[1 mark]

(iii) Starting from the DLVO equation for W(D), derive an equation to determine when the energy barrier will be at a maximum. (A numerical answer is not expected here.)

[3 marks]

(iv) We define DCCC as the separation distance between particles when the maximum of W(D) is 0 and hence the system is at its CCC. Derive an equation for Dccc as a function of k.

[3 marks]