Unit 2, Part 3: Characterizing Nanostructure Size

Dr. Brian Grady-Lecturerbpgrady@ou.edu

Outline

• Discrete Nanostructures– Size and Shape

• Spheres– Size from microscopy and light scattering

• Not Spheres– Size from microscopy

– Composition• ICP/AAS for bulk concentration• XPS for surface concentration

– Arrangement of atoms• Bonds-Raman, IR, NMR• X-ray diffraction

Nanostructure Size

• If discrete particles, then in general particles are all the same general shape (all spheres or all ellipsoids or all cubes etc.)

• If particles are not spheres, then unless the particles are all the same size it is almost impossible to determine anything about size characteristics without microscopy

How to use microscopy to determine nanoparticle size

• How electron microscopy works: third unit• Typically, use a dilute suspension of the solids in

a solvent and directly deposit the nanoparticles in the solvent on the grid that will go in the microscope– Trial and error to get particles not sitting on top of one

another, yet having enough particles to get a representative image

• Take picture, and measure size either with a ruler or with image analysis software– Figure 100 or so particles require to be quantified for

decent statistics.

vv

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vv

vv

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Too concentrated

v

vv

Too dilute

vvv

vv

vv

vv

About correct

Problems with Microscopy

• Very labor intensive– Trial and error to concentration of nanoparticles and

drop volume– Quantifying image is difficult

• Image analysis programs are difficult to work correctly, typically have to confirm results

• No image analysis program: a lot of measuring with a magnifying glass

• Tends to undercount really small particles• Can you get single particle dispersion• Does particle size get altered during drying

(electron microscopy requires dry samples)

Non-spherical particles

• If non-spherical particles are uniform in size, x-ray or light scattering (depending on particle size) can be used to quantify size distribution for some shapes

• Probably the most common thing to do is to show an electron micrograph, and say this is the general shape and size of these non-spherical particles, and leave it at that. Work-benefit ratio to be more quantitative, with the inherent error especially with small particles, isn’t usually high enough.

Spherical Particles

• There is one other commonly used method to determine particle size, and the particle size distribution, for spherical nanoparticles: light scattering

• Requires that the material be dispersed in a solvent and that all nanoparticles exist individually– The machine automatically figures out the correct concentration

to have the best signal to noise; assumes individually dispersed particles

– Can check assumption of individual dispersion by looking at particle size distribution or by changing concentration manually and making sure the result stays the same (always a good idea for an unknown material).

Particle size distribution• Most spherical nanoparticle size distributions are fit well by

the log normal distribution (slightly asymmetric):

Y=A*exp(-0.5(log(R)-log(Ro))2/b2)

– Two parameters b (the width of the distribution) and Ro (the average radius). A is set by the fact that the area under the curve is 1.

Normal Distribution

Log-Normal distribution

Two types of light scattering

• Static light scattering (also called Mie Scattering or just light scattering) and dynamic light scattering (also called photon correlation spectroscopy or quasi-elastic light scattering)

• Static light scattering measures scattered intensity as a function of angle (just like xrd) while dynamic light scattering measures variation in time of scattered intensity at a fixed scattering angle.

• Difficult to tell which machine is which (can’t without reading the manual!)

Light Scattering (also called Static Light Scattering)

• Light scattering: measurement of intensity as a function of angle. – Use a laser– Scattering from a dispersed set of spheres is called Mie Scattering

(Mie figured out the mathematics that relate size and refractive index to observed scattering pattern)

– Very complicated mathematics. Why?• Light is polarized from a laser, x-rays are not• Light can be transmitted at an interface but change direction (index of

refraction), x-rays cannot (in a practical sense anyway).

• Light can be reflected at an interface, x-rays cannot in a practical sense• Light scattering is due to the spheres themselves, not the arrangement

of spheres in space (i.e. atoms don’t cause peaks in x-ray scattering, the way in which they are arranged do!)

• Multiple scattering is a problem– How get a distribution? Have to assume some functional form of the

distribution and then compare the calculated scattering pattern with the measured pattern. If all the sizes are the same (monodisperse system), then the problem is trivial

Dynamic Light Scattering

• Measures the variation of light intensity with time (pick an angle, typically either 90 or 175 degrees) and measure the variation in intensity with time (time increment is pretty short; usually microseconds)

• Variation in time is caused by diffusion of particles which changes scattering angle slightly

Dynamic Light Scattering (cont.)

• A particular shape of the distribution does not need to be assumed; can calculate in theory the distribution from first principles

• You are NOT actually measuring particle size; you are actually measuring diffusion constant. Hence you must use some relationship between diffusion constant and particle size (Stokes-Einstein law)

• There is a great deal of mathematics that goes into converting that variation in intensity to diffusion constant.

(k is the Boltzmann’s constant, T is temperature, r is the radius of the sphere and is the viscosity of the fluid)

Why nothing “scientific” to read on DLS

• The mathematics are just too complicated

• I have given you two things; both written for the new person (i.e. not really at a high enough level for a college course)

Light Scattering vs. DLS

• You will be doing light scattering in the lab; however you will also be presented with results from a DLS system (http://www.bic.com/90Plus.html) (you can’t do it yourself since it is at the Health Sciences Center)

• Light scattering has higher upper limit to minimum particle size (20-50 nm, depending on particle). – Without the ability to change the polarization of incoming light,

the upper limit on light scattering is around 500 nm.

• DLS machines lower limit is 0.5 nm to 5 nm, depending on particle.

Problems with Light Scattering

• Machines are essentially a black box, and will give you an answer no matter what almost. If you have non-spherical particles, this machine will still give you an answer. Can have multiple scattering, that can be an issue.

• Materials that settle quickly cannot be measured easily (although our light scattering machine does pump the material in a circle to reduce this problem)

• Works with colored materials; but not as well.