16. Aggregation and Self-Assembly

Question 1

What is an aggregate?

Answer 1

A collection of many particles into a solid due to attractive forces between the particles.

Question 2

What does the shape/dimensionality of an aggregate depend on?

Answer 2

The nature of molecular interactions.

Question 3

What causes aggregates to form?

Answer 3

When the change in free energy, dU, is negative upon the addition of a molecule or particle.

Question 4

What does the chemical potential of an aggregate depend on?

Answer 4

• The shape of the aggregates
• The number of particles in the aggregate

Question 5

Give the equation for the chemical potential of an aggregate

Answer 5

µ = chemical potential
U = free energy
N = number of particles

Question 6

Describe a 1 dimensional aggregate

Answer 6

A linear aggregate where all N particles/molecules are joined together in a line

Question 7

Give the equation for the total free energy of a 1D aggregate

Answer 7

U = free energy
N = number of particles
µ = chemical potential

Question 8

Give the equation for the change in free energy of a 1D aggregate

Answer 8

U = free energy
N = number of particles
µ = chemical potential

Question 9

Is it energetically favourable for a 1D aggregate to grow?

Answer 9

Yes, it is always energetically favourable.

Question 10

Describe a 2 dimensional aggregate

Answer 10

A disk-like aggregate. The number of circumference atoms increases as the size of the atom increases.

Question 11

Give the equation for the change in free energy of a 2D aggregate

Answer 11

U = free energy
N = number of particles
µ = chemical potential
γ = excess surface energy of unbonded particles around the circumference
v = molecular/particle volume

Question 12

Is it energetically favourable for a 2D aggregate to grow?

Answer 12

Yes, above a critical value of N. Above this, µ < 0 and below this µ > 0.

Question 13

Describe a 3 dimensional aggregate

Answer 13

A spherical/droplet-shaped aggregate. The number of surface atoms increases as the size of the aggregate increases.

Question 14

Give the equation for the change in free energy of a 3D aggregate

Answer 14

U = free energy
N = number of particles
µ = chemical potential
γ = excess surface energy of unbonded particles
v = molecular/particle volume

Question 15

Is it energetically favourable for a 3D aggregate to grow?

Answer 15

Yes, above a critical value of N. Above this, µ < 0 and below this µ > 0.

Question 16

How do you find the critical aggregation number?

Answer 16

By setting the equation for the change in free energy of an aggregate to 0 and solving for N.

Question 17

How do 2D and 3D aggregates begin to grow?

Answer 17

Homogeneous nucleation

Question 18

Define homogeneous nucleation

Answer 18

The probability of producing a stable nucleus by chance due to fluctuations.

Question 19

Give the equation for the probability of homogeneous nucleation

Answer 19

P = probability
Nc = critical aggregation number
Uc = critical energy
kB = Boltzmann’s constant
T = temperature

Question 20

Give the equation for the critical energy of a 2D aggregate

Answer 20

Uc = critical energy
µ = chemical potential
Nc = critical aggregation number

Question 21

Give the equation for the critical energy of a 3D aggregate

Answer 21

Uc = critical energy
µ = chemical potential
Nc = critical aggregation number

Question 22

Define heterogeneous nucleation

Answer 22

When impurities act as nucleation sites, lowering the energy barrier, Uc, to nucleation.