1)        “I have read the special instructions and expectations outlined above. By submitting this work, I certify that the work represents solely my own independent efforts. I confirm that I am expected to   exhibit honesty and use ethical behaviour in all aspects of the learning process. I confirm that it is my responsibility to understand what constitutes academic dishonesty under the Academic Integrity          Policy.”

If you agree, then for question 1, in your solutions, please write: the following statement: I, (print your name) agree.

Signed (your name), and date.

2) In your own words, explain electrostatic double layer repulsion forces.

3) In your own words, explain DLVO theory.

4) In the case of spinodal decomposition, why does a specific wavelength emerge?

5) van der Waals forces between two atoms have a 1/d6 potential at small distances, yet when we discuss the interaction between two surfaces, we used 1/d2 .  Why is this?

6) The plot shown should look familiar and was used in the context of phase separation to obtain a       phase diagram. What is being plotted? This curve corresponds to a specific value of the control            parameter which determines if the curve has one minimum or two minima, is this for a high or low      value of the control parameter? How is this curve used to get the phase diagram (hint: you will want to

touch on the importance of the points a-d)?

PROBLEMS: (The following 3 questions are each worth 10 marks, for a total of 30)

7) Show any equations you need to explain the following:

A team uses the surface forces apparatus to measure the magnitude of the force, F, as a function of the gap, D, between two crossed cylinders with radius R. First, they plot F as a function ofD on a log-log  plot.  a) Sketch what the theory would predict for this plot. b) Next, they plot F/R as a function of 1/D2 . Why, what do they learn by doing this?  c) They repeat the same measurement for the force between    two spheres of radius R and make the same plots. How would the results of a) and b), be different?

8) You figured out a nice experiment! A small tube filled with liquid “a” joins two droplets of liquid “a”, as shown, such that the top droplet           (radius r) is in air, with surface tension ya , and the bottom droplet (radius

R) is in liquid “b” with interfacial tension yab . You are able to adjust the ratio of r/R. Now, you make a remarkable observation that the system is in an unstable equilibrium, for a specific ratio of r/R, with either the        entire volume going into the bottom droplet, or the entire volume going  into the top droplet. Explain. Provide any equations needed to explain    your observation. Knowing the surface tension, how might you use this  to obtain the interfacial tension? Note that the droplets are small, so        gravity is not playing a role

9) Amphiphiles in solution can self-assemble into bilayer sheets with the shape of a disk with radius R (see schematic cross-section of the disk below). Assume a head-group interfacial tension, γ, as shown. Assume a line tension for the edge of the disk, σ (in units of energy per unit length).  The change in the free energy upon aggregation for a unit area of a bilayer is given byf.

a) Calculate an expression for the critical radius, Rc, of a bilayer disk.

b) Calculate the critical change in the free energy, ΔFc, required to form a nucleus.

c) Assume an activated process.  How does the probability of forming such a disk scale with ΔFc .

d) Provide a schematic plot of the free energy as a function of the radius and label Rc   and ΔFc .

V

σ

2R