Dielectric Thermal Analysis and Scanning Electron Microscopy

By the end you should be able to: Describe the working and applications of dielectric thermal analysis of polymers, and the principle, instrumentation and applications of the scanning electron microscope.

Dielectric thermal analysis (DETA)

What it measures

DETA measures the dielectric properties of a material — permittivity and loss — as a function of temperature and frequency, while an alternating electric field is applied.

The idea. Polar groups in a polymer try to rotate to follow an alternating field. Whether they can depends on how mobile the chains are, which depends on temperature. So the dielectric response is a direct probe of molecular mobility.

Working

The sample is placed between two electrodes forming a capacitor, an AC voltage is applied over a range of frequencies, and the temperature is ramped. Two quantities are recorded:

Permittivity $\varepsilon'$ — energy stored, the ability of dipoles to align with the field.
Loss factor $\varepsilon''$ — energy dissipated as heat when dipoles rotate against internal friction.

\tan\delta = \frac{\varepsilon''}{\varepsilon'}

is the dissipation factor.

Reading the result. A peak in $\varepsilon''$ occurs where the rate of dipole reorientation matches the frequency of the applied field — a relaxation. Its temperature identifies a transition:

The glass transition $T_g$ gives the largest peak, where large segments of chain become mobile.
Smaller peaks below $T_g$ come from local motions of side groups.

Because the peak position depends on frequency, scanning frequency as well as temperature gives the activation energy of the motion.

Applications

Determining $T_g$ and secondary transitions in polymers.
Cure monitoring of thermosets — the most important industrial use. As a resin cross-links, the chains become progressively less mobile and the ionic conductivity falls by orders of magnitude, so DETA follows cure in real time, inside the mould, using embedded sensors. Nothing else reports cure state non-destructively during processing.
Detecting moisture, since water is strongly polar and shows up clearly.
Assessing suitability of polymers as insulators, where a low loss factor is required.

Scanning electron microscopy (SEM)

Why electrons rather than light

Resolution is limited by wavelength — roughly $\lambda/2$ at best. Visible light is 400–700 nm, so an optical microscope cannot resolve below about 200 nm however good its lenses.

Electrons accelerated through a potential $V$ have a de Broglie wavelength

\lambda = \frac{h}{\sqrt{2meV}}

which at 20 kV is around 0.0087 nm — some fifty thousand times shorter than visible light. Practical SEM resolution is 1–10 nm, limited by lens aberrations and the interaction volume rather than by wavelength.

This is the de Broglie relation from Physics Module 2 doing practical work: the microscope exists because electrons are waves.

Principle

A finely focused beam of electrons is scanned across the specimen in a raster. At each point the beam interacts with the surface and produces several signals; a detector collects one of them, and its intensity sets the brightness of the corresponding point on the display.

The image is built point by point, not projected. There is no image plane and no magnifying lens after the specimen — magnification is simply the ratio of the display size to the scanned area, which is why it can be changed continuously over a huge range.

Signals produced:

Secondary electrons — low energy, escaping only from the top few nanometres. Give topographic contrast, and the characteristic three-dimensional appearance of SEM images.
Backscattered electrons — high energy, from deeper. Yield increases with atomic number, so they give compositional contrast: heavier elements look brighter.
Characteristic X-rays — used in EDX/EDS for elemental analysis.

Instrumentation

Electron gun — tungsten filament, LaB₆, or a field emission source for the highest resolution. Anode and accelerating voltage — typically 1–30 kV. Electromagnetic lenses — condenser lenses demagnify the beam; the objective focuses it onto the specimen. Scan coils — deflect the beam in a raster. Specimen chamber — under high vacuum, because electrons scatter off air molecules. Detectors — Everhart-Thornley for secondary electrons, solid-state for backscattered, EDX for X-rays.

Sample preparation, and its limitations

The specimen must be conducting and vacuum-compatible. Non-conducting samples accumulate charge, which deflects the beam and produces bright streaks and distortion — charging. The remedy is a thin sputtered coating of gold or carbon, a few nanometres thick.

The consequences are real limitations rather than inconveniences:

Wet or living samples cannot normally be imaged, since the vacuum removes the water. Biological specimens must be fixed, dehydrated and critical-point dried — which alters what you are trying to look at.
Coating obscures the true surface at the finest scale.
Only the surface is seen. SEM gives no interior information; that requires TEM on a thinned section.

Environmental SEM works at low pressure and can image moist samples, at some cost in resolution.

Applications

Surface morphology of materials; particle size and shape of nanomaterials — the standard characterisation for the materials of Module 2; fracture surface analysis in failure investigation; thin film and coating thickness; semiconductor inspection; and, with EDX, elemental mapping of a surface.