Paper 11
Explain how solvent quality affects PEG conformation (coil vs. helix), and how this is measured experimentally.
Good Solvent (e.g., water, ethanol):
Poor Solvent or Mixed Solvent (e.g., isobutyric acid, water/IBA):
SANS:
Optical Rotation via Polarimetry:
How can sin²ψ analysis be used to quantify lattice strain in nanostructured materials? What are the limitations?
Using Bragg peak shifts at multiple ψ tilts, the sin²ψ method quantifies in-plane and out-of-plane strain components by fitting strain as a function of sin²ψ. It assumes a uniform strain state and enables extraction of the full strain tensor via tensor rotation.
Limitations include:
– Assumes homogeneous strain—not valid for nanostructures with gradients
– Peak broadening and asymmetry from inhomogeneous strain distort results
– Loses accuracy in ultra-thin films or near interfaces
– Cannot resolve strain distributions, only average values.
This parameter, denoted χ, quantifies the thermodynamic incompatibility between blocks in a copolymer.
Flory-Huggins interaction parameter
After heat treatment at 650°C, this microstructural feature became more homogeneous, reducing internal stress and contributing to increased ductility.
cellular substructure and residual stress field
This type of chain in the amorphous region—responsible for stress transfer between lamellae—must degrade for fragmentation into nanoplastics to occur under quiescent conditions.
tie-molecules (including bridges and bridging entanglements)
How does chirality in a polymer-solvent system influence optical rotation? Compare with Ising model predictions.
Key Dependencies:
The Ising model, classically used for spin systems, has been adapted to describe chiral symmetry breaking and helix formation in polymers. Each monomeric unit can be considered to exist in one of two chiral states (e.g., left-handed or right-handed helix), analogous to spin-up or spin-down states.
1D Helical Ising-like Model:
H=−J∑sisi+1−h∑si
Predictions:
Chirality in polymer–solvent systems induces asymmetric chain conformations that manifest in measurable optical rotation. This effect is cooperative and nonlinear, as captured by the Ising model. The model explains why short PEGs show weak rotation (low J, low N), while longer, cooperative chains in a biased field exhibit macroscopic chiral signatures — an essential mechanism in helical amplification and chiral sensing.
What is the significance of direction-dependent peak broadening in XRD of thin films? How do you decouple strain effects?
Direction-dependent peak broadening indicates strain anisotropy or crystallite size anisotropy. In XRD, if broadening varies with diffraction angle, it's often due to strain gradients or coherent domain deformation.
To decouple strain and size effects:
Use the Williamson–Hall method, where:
Δq_total = Δq_size + Δq_strain
Size broadening ∝ 1/cosθ, strain broadening ∝ tanθ.
Plotting βcosθ vs sinθ allows separation of slope (strain) and intercept (size).
When the block volume fractions are nearly equal and χN is high, this type of bicontinuous morphology can form
gyroid (Ia3d) structure
Unlike traditional wrought steel, AM austenitic stainless steel exhibits this feature due to rapid solidification, which is partially preserved after sub-recrystallization heat treatments.
fine cellular-dendritic microstructure aligned along the build direction
This specific measurable event in tensile testing correlates with the onset of nanoplastic release during PET degradation and matches the induction period observed in light scattering data.
drop in maximum stress/failure strength
Discuss the entropic penalties of chain confinement in a poor solvent. Relate to polymer conformation transitions
Entropy Loss Sources:
As solvent quality worsens:
Flory-type Free Energy (for coil-to-globule transition):
F(R)=(3kBTR^2)/(2Nb^2)+kBT⋅χ⋅(N^2b^6)/R^3
Compare microdiffraction and GIXRD for probing strain localization. When is each technique preferable?
Microdiffraction (μXRD):
– Uses focused X-ray beams (~sub-micron)
– Probes local strain variation within grains or features
– Ideal for mapping strain heterogeneity in complex nanostructures
Grazing-Incidence XRD (GIXRD):
– Uses shallow incidence angles
– Probes surface-near layers (depth-sensitive)
– Best for thin films, surface stress, or layered structures
Use μXRD when spatial resolution is needed (e.g. intra-grain strain).
Use GIXRD when depth profiling or average surface strain is sufficient
This technique was used to refine structure factors from SAXS data and confirm unit cell parameters.
Le Bail refinement
This combination of mechanical property changes indicated that the 650°C treatment successfully mitigated process-induced anisotropy while enhancing performance.
the simultaneous increase in yield strength and uniform elongation with reduced strength anisotropy
These lamellar components persist in solution long after the amorphous phase has degraded, contributing to the long-term environmental presence of nanoplastics.
crystalline lamellae
Figure 1: Explain Guinier → Fractal → Porod transitions in the SANS data. What structural features do they indicate about PEG in IBA/H₂O?
PEG in D₂O (open circles):
PEG in d-IBA (solid circles):
PEG in D₂O (good solvent):
PEG in d-IBA (poor solvent):
Figure 2 shows the evolution of principal strains and stresses in damascene Cu lines as a function of temperature. Explain the origin of anisotropic strain behavior (ε₁ ≠ ε₂ ≠ ε₃), and describe how thermal expansion mismatch contributes to the observed compressive stress state.
Anisotropic strain (ε₁ ≠ ε₂ ≠ ε₃) arises from confinement of Cu lines in dielectric trenches, leading to directional constraint during thermal expansion.
Thermal expansion mismatch between Cu and surrounding materials (FSG, Si) induces biaxial compressive stress upon heating:
– Cu expands more than FSG/Si
– Lateral expansion (ε₁, ε₂) is constrained
– Vertical direction (ε₃) can partially relax
This mismatch generates triaxial thermoelastic stress, with suppressed plasticity due to stress cancellation in resolved directions.
This type of chain-end arrangement leads to six intersecting tubes and is stabilized by weak hydrogen bonding and PEO crystallization
medial packing
The increase in strength after 650°C treatment is attributed to this thermally-activated mechanism, which reduces energy barriers for dislocation motion without dissolving cellular walls.
recovery (as opposed to recrystallization)
According to this classic statistical model, successive fragmentation of lamellar stacks yields a lateral size distribution consistent with environmental nanoplastic samples.
Kolmogorov log-normal fragmentation model
Use partition function arguments to explain helix–coil transitions. What experimental features reflect this?
The helix–coil transition arises from a balance between enthalpic stabilization of helices and entropic favorability of coils in the partition function. Experimentally, it is reflected by a slope change in SANS (–1 to –5/3), p(r) profile shifts, temperature-dependent optical rotation (polarimetry), and a decrease in scattering invariant Q with heating.
An X-ray diffraction study shows FWHM variation as a function of ψ angle. Explain how ψ-dependent peak broadening can be used to assess anisotropic strain. What does an increase in FWHM with ψ imply about stress states in thin films?
ψ-dependent peak broadening reflects orientation-specific microstrain. By measuring FWHM at various ψ (tilt) angles, one detects how strain varies with lattice plane orientation.
An increase in FWHM with ψ indicates:
– Greater in-plane strain fluctuations than out-of-plane
– Suggests biaxial stress state, common in thin films
– Points to anisotropic defect distributions or interface-induced strain gradients
This analysis helps reveal strain anisotropy and gradients, even when average strain is undetectable.
Despite representing only ~1% of the chain, this modification dramatically alters copolymer phase behavior.
end group functionalization
This heat treatment led to a significant increase in yield strength of the AM stainless steel by reducing dislocation density and promoting stress relaxation without full recrystallization.
650°C heat treatment for 1 hour
The degradation-induced loss of mechanical integrity in semicrystalline polymers is predicted using this decay model for tie-molecule density as a function of reactive bond fraction nk∼(1−ϕ)ℓk
logarithmic decay model tied to the average number of cleavable bonds per chain type