Nanoscience Instrumentation

Big machines for small particles

Size measurements

• Transmission electron microscopy
• Electron microscopy
• Dynamic light scattering
• Resonant mass measurement
• Flow particle imaging
• Laser diffractometry
• Nanopore sensing

Electron Microscopy

Optical vs. Electron Microscopy

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• Electron microscopes use electron beams focused by electromagnets to magnify and resolve microscopic specimens
• Transmission electron microscopes (TEM) generate high resolution cross-sections of objects
• Scanning electron microscopes (SEM) display enhanced depth to map the surface of objects in 3D

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• Electron microscopes have two key advantages when compared to light microscopes:
• They have a much higher range of magnification (can detect smaller structures)
• They have a much higher resolution (can provide clearer and more detailed images)��
• disadvantage of electron microscopes are that they cannot display living specimens in natural colors, can require complicated sample preparation, and they can damage samples

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Optical vs. Electron Microscopy

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Optical vs. Electron Microscopy

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Rayleigh resolution

• The numerical aperture (NA) of a lens represents the ability of the lens to collect diffracted light and is given by NA = n sin a in this expression n is the index of refraction of the medium surrounding the lens and a is the acceptance angle of the lens ( n = 1 for air)

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From this we can that an optical microscope with an NA is about 0.95 (about the maximum possible in air) for blue light has practical resolution of around 250 nm. So how do we look at smaller things?

We use electrons!

Wavelength of a 100 keV electron is 3.4 picometers!

SEM vs TEM

• TEM detects transmitted electrons
• Looks though materials
• SEM detects scattered electrons and X-rays
• 3D images of surface
• Technically not a microscope
• Both system allow elemental analysis
• SEM via characteristic x-ray emission
• TEM through electron diffraction

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Dynamic Light Scattering and Zeta Potential

Dynamic Light Scattering – the workhorse of nano-sizing

Works with a wide range of particle types and materials

Capable of measuring particle sizes between 0.3 nm and 2 μm

• Hydrodynamics (Fluid flow)
• Diffusion/Brownian motion
• Statistical mechanics
• Rayleigh (Mie) scattering
• Optical Interference

Exploits several important pieces of Physics:

Source: Wikipedia

Peculiarities of nanoparticles in solution�this is all from fluid dynamics, but we aren’t going to talk about that today

Relates microscopic energy to temperature

Nano-mechanics is in general stochastic rather than deterministic

Diffusion and Brownian Motion

Microscopic motion and resulting collisions cause molecules and particles in a fluid to wander randomly

For molecules, this motion is known as diffusion

For particles, it is known as Brownian motion

Random microscopic motion in fluids are responsible for many of their properties:

• Temperature
• Pressure
• Heat conduction
• Sound propagation
• Viscosity

Diffusion constant

© 2011 Houston Community College

Stokes-Einstein equation

Einstein and Smoluchowski showed, using statistical methods, that for a particle undergoing Brownian motion

mobility

Einstein-Stokes equation

If we can measure the diffusion constant of a particle, we have a measure of its size

Speckle

When laser light scatters off multiple particles, a pattern of constructive and destructive interference known as speckle appears

Since the speckle pattern changes when particles move, it can be used to infer particle diffusion and then we use its autocorrelation function to measure the rate of variation to get the velocity

DLS applicability and limitations

• Measure sizes across the entire nano range (0.3 nm to 2 μm)
• Works with metallic, dielectric, polymeric, biological particles – anything that scatters light
• Fast and accurate

• Works only within a certain range of concentrations (too low – no signal, too high, multiple light scattering)
• Assumes particles are spherical (produces equivalent “Stokes radius” for non-spherical particles
• Handles polydispersity poorly

• Particle size may be different from what is observed in TEM/SEM, due to surface functionalization
• Most particles are in the Rayleigh range, so a few large particles can overwhelm the signal from many smaller ones.

Zeta potential measurements

Next to size, charge is the most important property of a colloidal particle

• Provides stability as Coulomb forces prevent aggregation
• Drives aggregation of oppositely charged particles

In an external electric field, charged particles are subject to an

Electrophoretic force:

Zeta potential

Zeta potential measurements can be used to estimate colloidal stability

Electrophoretic mobility

When an electric field is applied, the electrophoretic force quickly equilibrates with the Stokes drag (the drag in the solution from friction)

Electrophoretic mobility

However, real life is more complicated…

Screening

The solvent always contains counter charges to those on the surface. They are attracted to the surface, giving rise to a double layer (DL).

The width of the DL is known as the Debye length:

Concentration of i^th charged species (mol/l)

Charge number of i^th charged species

Zeta potential

The double layer reduces the electro-phoretic potential in two ways:

1. Counter charges adsorbed onto the surface (the Stern layer) reduce the effective particle charge
2. Counter charges between the Stern layer and the hydrodynamic slipping plane further screen the particle charge

Source: Wikipedia

The DL directly affect the electrophoresis

The electrostatic force on the counter ions is opposite to the force on the particle, which give rise to additional drag. This force is known as the electrophoretic retardation force.

Two limits:

Smoluchowski approx

valid for all shapes

Hückel approx

Electrophoretic light scattering

The magnitude of the oscillation can then be retrieved for the speckle with heterodyne detection