Materials Thermodynamics Flashcards
State the 1st Law of Thermodynamics
dU = dQ - dW
If work is due to pressure forces dW = pdV
State the 2nd Law of Thermodynamics
s2-s1 = dQ/T + S_irreversible
What is the statistical interpretation of entropy
Entropy can be viewed as the no of microstates associated with a system.
dS = k_b ln(omega)
Recall the KE-Temperature Relationship
KE = 3/2 k_b T
How does stiffness vary depending on the material group?
Material stiffness is determined by the primary and secondary bonding.
- In Metals, ionic crystals and covalent solids stiffness is governed by the balance of electrostatic attraction and steric repulsion. This sets the atomic distance and rigidity.
- In foams cell-walls determine rigidity.
How does the polymer load response change when crossing the glass-transition temperature
- Below Tg, the thermal energy is insufficient to allow for the sliding of the polymer chains and so the stiffness is dependent on the rigidity of the chains.
- Above Tg, the polymers are viscoelastic (resist shear flow and strain linearly). The polymer chain is flexible and there is sufficient thermal energy for the polymer chains to flow. Over short time scales the chains become entangled and have an elastic response
What are Elastomers
Elastomers are formed of a cross-linked network of polymer chains. The cross-links are added to the polymer chain reducing monomer length. Thermosets are an example of elastomers
Outline the load response on Elastomers above and below the glass transition temperature
Elastomers do experience a drop in stiffness as they approach. Above Tg Elastomers remain solid and retain an elastic response. As the temperature rises further the stiffness of the elastomer network increases linearly l.
For T greater than Tg:
E = k_bT/ v_mn_c
v_m is the monomer volume
n_c is the no of monomers between cross-links
Qualitatively explain the micro-structural origin of the elastic response of polymers
First Law Thermodynamics dU = dQ - dW dW = -FdR So F = -T dS/dR This can be explained as stretching a polymer reduces the number of micro-states and thus the entropy of the system so dS/dR is negative.
Explain the origin of a restoring force when stretching a polymer chain.
As the temperature increases the Gibbs free energy function changes. This U and pV terms are unchanged however the TS term changes with the increasing temperature. Therefore there will be a large thermodynamic driving force to minimise G which results in a larger restoring force
What are the limitations of the Random Walk Model
- Assumes pin-joints between chains
- Does not take into account side-groups on the polymer chain
- Assumes chains are 2D so underestimates the number of configurations
What criteria define a phase
- Atomic Arrangement
2. Chemical Species Present
Derive an expression for the change in Gibbs free energy
G = U+pV-TS
dG = dU + pdV + Vdp - TdS - sdT
During Phase Transformations:
dp = dT = 0
Outline the relationship between the equilibrium state and Gibbs Free Energy
The equilibrium state corresponds to the minimum value of the Gibbs free energy. The thermodynamic driving force is set by the difference between the Gibbs energy at the current state and the minimum Gibbs energy. Note: a reaction is said spontaneous if dG is negative
Describe how the free energy change can be used to determine miscibility
If two materials are miscible then the entropy of mixing will be large and positive. This means the free energy will be lower than the unmixed case. The proportions of A and B corresponding to the lowest free energy is the equilibrium state.
Why are some materials immiscible
Some materials (e.g oil and water) do not mix. This is because the increase in internal energy due to mixing is larger than the increase in entropy due to the higher number of micro-states so the Gibbs free energy is positive
How do we take into account the difference in energy between atoms at the surface and in the bulk.
The difference is accounted for by the surface tension/energy.
When is it important to consider the effects of surface energy
When considering a large amount of material the energy of the interface is insignificant. However when nucleating one phase in another the process starts with only a few atoms so the surface energy is significant
Outline Homogeneous Nucleation
Homogenous nucleation occurs when a solid crystal forms in a liquid.
The Gibbs free energy function is the sum of the bulk free energy and the surface energy.
Minimising Gibbs free energy gives the critical radius below which the nucleus is unstable.
Explain the phenomenon of under-cooling
Under-cooling refers to reducing a material in the liquid phase to below its freezing point. The liquid does not solidify due to the absence of a seed crystal/impurity.
Outline heterogeneous nucleation
Heterogeneous nucleation is the reason why in practice solidification occurs close the melting point. The presence of impurities an anchorage point for growth.
The presence of these impurities reduces the contact angle which in turn reduces the number of atoms needed to reach the critical radius.
Define Osmosis
Osmosis occurs when a semi-permeable membrane is placed between high and low concentrations of solute. The membrane only allows the solvent to pass through.
Explain the relationship between entropy and osmotic pressure
Entropy drives the system toward equilibrium by controlling the pressure either side of the membrane. At equilibrium these membrane pressures are equal. These membrane pressures are known as osmotic pressures.
What is the formula for Osmotic Pressure
O_p= RTc
where c is the solute concentration
Outline the derivation of the critical radius for Homogenous and Heterogeneous Nucleation
See notes
What is the equation for the Gibbs Free Energy of the Bulk in terms of undercooling
dG = dH * (T_m - T)/T_m
How does the entropy of solid, liquid and gas compare? How does that affect the change in Gibbs free energy
Entropy of Gas > Entropy of Liquid > Entropy of Solid
The higher entropy of a gas reduces the Gibbs free energy faster.
How do the Gibbs free energies of solids, liquids and gases compare
Gibbs free energy of a solid > Gibbs free energy of a liquid > Gibbs free energy of a gas
Recall the diagram that shows the free energy of solid, liquid and gas phases vary with temperature
See Week 3 notes
Why does the system minimise the surface area of the interface
Atoms at the surface have a higher energy accounted for by the surface energy (gamma). This reduces as the area of the interface reduces.
