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54 Cards in this Set
- Front
- Back
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What does the freely jointed chain method state as the contour length? |
contour length = nL Simplest measure of the chain - chain length along the backbond |
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For a freely jointed chain, what is the root mean square end to end distance?
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^1/2=(nl^2)^0.5 |
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What are the two main things which the freely jointed chain model discounts? |
1) Bond angle restrictions
2) rotation hindered by steric effects |
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What does the Valence angle model include? |
- introduction of bond angle restrictions - allow free rotation about bonds (still neglecting steric effects) |
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The model which is based upon the Valence angle model, but that includes steric effects is... |
rotational isomeric state theory |
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What is the characteristic ratio? |
A measure of the stiffness of a chain. Cinfinity = /nl^2 |
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Two things which the freely jointed chain, valence angle and rotational isomeric state models all ignore are |
1) long range intramolecular interactions 2) polymer-solvent interactions |
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What happens when the expansion parameter, alpha is i) polymer-polymer interactions are more favourable than polymer-solvent interactions ii) polymer solvent interactions are more favourable than polymer polymer interactions iii) Polymer-polymer and polymer-solvent interactions are approximately equivalent |
i) alpha < 1, chains contract, poor solvent ii) alpha>1, chains expand, good solvent iii) alpha =1, theta condition |
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What is the theta temperature |
Temperature at which the expansion parameter, alpha is equal to 1. At a temperature above the theta temperature, good solvent and temperature below the theta temperature, poor solvent |
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Define Radius of gyration |
Average distance of chain segments from centre of the chain |
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How are the mean square end to end distance, Re and the radius of gyration, Rg related? |
Re^2=6*Rg^2 |
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How do polymers scale with N in the melt/theta solvent? |
Rg proportional to (N^0.5)b |
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How to polymers scale with N in a good solvent? |
Rg proportional to (N^(3/5))b |
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State the Einstein equation for diffusion |
D=kT/constant |
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Describe the principles of Rouse diffusion |
- Low molecular weight polymers - Consider polymer as collection of beads joined by springs |
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State 3 assumptions of the Rouse model for diffusion |
1) beads only interact through springs 2) particles can diffuse collectively through a fluid which drains through beads 3) Each particle can be treated independently |
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What is the Rouse time |
tauR = R^2/D |
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For Rouse diffusion , how are the diffusion coefficient D and N related? |
D proportional to 1/N |
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Describe the basics of the Tube model of diffusion |
-Chains can move only in limited directions -Regard each entanglement that a polymer chain experiences as a constraint - constraints around a polymer chain define a tube - polymers can only diffuse along its tube/primitive path of length L |
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Describe the concept of Reptation diffusion |
High molecular weights Regard diffusion as occurring by propagation of defect along the primitive path. |
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what is the Reptation time? |
Time for polymer to escape from its tube. |
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How is the diffusion coefficient, D related to N in the reptation model? |
D proportional to N^-2 |
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Name 2 methods to measure diffusion |
1) Neutron reflectometry 2) Ion beam analysis |
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What are the limits of the reptation model? |
Ignores: -constraint release (the polymer chains are constantly moving) - contour length fluctuations (tube length is not constant)@ |
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Name 4 properties of a material which crystallisation can impact upon |
1) Mechanical strength 2) Optical clarity 3) Density 4) Solubility |
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DSC |
Differential Scanning Calorimetry |
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How can crystallinity be measured? |
DSC - measure difference between sample and reference heat required to sustain same heating rate for each. with known sample mass, can locate and quantify transitions. X-RAY DIFFRACTION - regular crystalline order in solids gives rise to Bragg peaks. ratio of crystalline peak to amorphous hump gives fractional crystallinity. |
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What factors can effect crystallinity? |
-Increasing molecular weight decreases rate of crystallisation |
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What is plotted on a Hoffman Weeks plot? |
Plot Tm as a function of Tc Plot Tm=Tc and extrapolate to equilibrium Tm* |
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Describe the main features of homogeneous nucleation |
- spatially and temporally random - many nuclei short lived - energy barrier must be overcome for nucleation |
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Describe the main features of heterogeneous nucleation |
- occurs at specific sites (impurities/particles) - starts simultaneously at all sites - if all interfaces are same distance from nucleation sites, heterogeneous |
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How can the kinetics of crystallisatoin be measured? |
DILATOMETRY Measure the volume change. Place polymer in dilatometer with contacting, bot penetrating liquid. Melt polymer then place in thermostatted bath at T Measure contraction volume vs time. |
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State 3 assumptions of Avrami analysis
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1) Volume is unaffected 2) Nuclei remain fixed in space with respect to each other 3) Single process governs crystallisation |
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Fibrils |
HOMO 2 HET 1 |
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Disc |
HOMO 3 HET 2 |
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Spherulite |
HOMO 4 HET 3 |
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Sheaf |
HOMO 6 HET 5 |
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Define the following terms in the Avrami equation: k n (V/Vo) (wmelt/w0) |
k = growth rate of the crystal n = Avrami exponent V = volume at time t V0 = initial volume wmelt/w0 = time dependent fraction of molten polymer remaining |
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State 7 assumptions of Flory Huggins theory |
1) All sites are occupied 2) Occupation is random and governed solely by chain connectivity 3) Lattice sites are all the same size 4) Chain flexibility is unaltered by mixing state 5) Interactions are isotropic 6) Interaction parameter has no compositional dependence 7) Only nearest neighbour interactions are considered |
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Define the terms |
delta G = free energy of mixing N= degree of polymerisation phi = volume fraction chi = Flory Huggins interaction parameter |
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What must be true for phase separation to be spontaneous? |
second derivative of delta G wrt phi is gtreater than 0 |
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Why are small drops less stable than large drops in a two phase blend? |
Due to interfacial tension |
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What is spinodal decomposition?
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When phase separation is thermodynamically favourable. No energy barrier to overcome for demixing. |
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What is Nucleation and Growth? |
When phase separation is thermodynamically favourable. There is an energy barrier, so the process requires nucleation to occur before phase separated domains can grow. |
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Define b, z and w in the width of interface equation |
b = Kuhn Step length
z = depth of interface w = interfacial width |
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How is the R related to the molecular weight M in the scaling relationship for polymers? |
R=k (M^0.5) often useful to use units in question to figure this out |
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How is diffusion related to molecular weight for: a) Rouse diffusion b) Reptation c) Reptation accounting for contour length fluctuations and contstraint release |
a) D = k M^-1 b) D = k M^-2 c) D = k M^-2.3 |
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give the equation relating distance travelled over time and the diffusion coefficient.
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<x> = 2(Dt/pi)^0.5 |
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Why is one measure of percentage crystallinity better than the other? |
The second accounts for the increase in crystallinity due to recrystallisation before the melting transition is reached. |
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When does spinodal decomposition occur? |
Spinodal decomposition occurs when a UCST blend is cooled into the 2 phase region of the phase diagram. |
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What does the binodal represent? |
The final equilibrium concentration of the blend after undergoing spinodal decomposition. |
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What is the critical value (with reference to a phase diagram)? |
Value at which phase separation is spontaneous. |
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Describe the three main stages of spinodal decomposition in a polymer blend |
Spinodal decomposition is the name of phase separation process that occurs when a UCST blend is quenched from the one phase into the two phase region of the phase diagram. Proceeds in 3 distinct stages: EARLY STAGE Immediately after quenching, have regions rich in component A and regions rich in component B. Co-continuous morphology with characteristic length scale. Amount of A in A rich and B in B rich increase, while characteristic length scale remains fixed. INTERMEDIATE STAGE At some point, structure begins to coarsen (i.e. characteristic length scale increases) During this stage amount of A in A rich and B in B rich still increase. LATE STAGE Amount of A in A rich and B in B rich have reached equilibrium phase separated value and remain fixed. Characteristic length scale still increases, until eventually bulk phase separation has occurred. |
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What information can be obtained from the Avrami exponent? |
Gives information on the morphology of crystals and the mechanism of nucleation. |
