The next method of particle size analysis we will consider in this series is the electrical resistance technique, sometimes known as the Coulter Method. 

Instrument Capabilities

Electrical resistance instruments cover the particle size range from about 0.4 micrometers up to about 1200 micrometers.  Using this technique, particles must be suspended in dilute sample solutions.

How Does the Electrical Resistance Method Work?

This technique uses two electrodes mounted on either side of a fine orifice to measure the electrical resistance of the suspension passing through the orifice.  As individual particles pass between the electrodes, the resistance rises and falls are captured by the control computer. 

     Volume Measurements

The electrical resistance measured when a particle passes through the orifice increases as a function of the volume of  particle between the electrodes.  The resistance measurement is insensitive to most materials properties, so slurries of individual materials, as well as suspensions containing varied body compositions, can be measured.

Unlike sedimentation techniques, which require that all particles be the same density, the electrical resistance technique can handle most mixtures of particles of varying densities and compositions.  This technique can therefore analyze the particle size distributions of whole-body slips in single analyses.

     Extreme Dilution Required

The requirement for this technique is that particles MUST pass through the orifice individually.  If suspensions are partially flocculated and flocs pass between the electrodes, the total volumes of the flocs will be analyzed as if they are large single particles.

For this reason, samples for analysis must not only be deflocculated and well-dispersed to allow particles to travel independently, but the samples must also be sufficiently dilute so the independent particles can pass between the electrodes individually.  This requirement usually forces sampling, dilution, more sampling, more dilution, etc., until the final dilute, dispersed samples are ready to be analyzed.

This forces lab technicians to pay particular attention to their sampling and preparation techniques.  It is very easy to produce non-representative samples when original samples must be repeatedly dispersed, diluted, and resampled.  It is very easy to use a pipette to carefully draw samples out of the upper layers of a beaker, only to leave all of the coarse particles in the bottom of the beaker with the mixing pellet.  I watched once as this was being done.  The technician very carefully pulled the final sample out of a beaker with a pipette, but actually, he very carefully pulled a non-representative sample due to his placement of the pipette in the sample beaker.

Considerations When Using This Technique

Although these instruments can measure particle sizes into the sub-micron range, other techniques which can go finer, such as the photon correlation method, may still need to be employed to cover the far reaches of the sub-micron particle size region.

Then too, even though these instruments can measure up into the 1000 micron range, boulders in that size range tend to settle quickly, so this should be considered when measuring coarse particles.  The instrument manufacturer should have taken care of this, but it doesn't hurt to pay attention to how well the larger particles are kept in suspension and actually measured.  Coarse particles may remain suspended when flow rates are high, but as flow rates decrease, more and more particles can begin to settle out of suspension.

Once again, other techniques such as sieve analysis may need to be employed to cover particle sizes larger than the instruments' upper size limits.

For particularly broad distributions, electrical resistance results will need to be combined with finer and coarser measurement results.  All such results will be based on fundamentally different definitions of particle size.  Photon correlation results depend on frequency shifts of scattered radiation; electrical resistance techniques depend on volumes of particles (which are then used to calculate particle diameters);  and sieve analyses depend on the size of particles that can fit through screen orifices.  Combining the results of three diverse techniques (such as these) will typically show two discontinuities -- one in each size range where the results have been combined (i.e., in the zone of overlap.)

The final method of particle size analysis we will consider in this series is microscope techniques. 

Instrument Capabilities

Microscopes allow particle size analysis of relatively large particles down to sub-micron particles.  Capabilities depend on the resolution of the microscope used.  Optical microscopy allows analysis from coarse particles in the millimeter range down into the micrometer range.  Scanning electron microscopes allow analysis of similarly large particles, but SEMs can resolve particles well down in the sub-micron range.  (Some SEMs can resolve particles as fine as ~20nm.)

How Does This Technique Work?

To use microscopes for particle size analysis, one simply measures and tabulates the sizes and numbers of particles in the field of view.  The measuring and counting can be done by hand directly through the microscope, or on photo-micrographs of the dispersed particles.  Measuring and counting can also be done automatically in computer-controlled microscopes.  Many scanning electron microscopes offer this option, especially when beam control techniques are possible.  Some optical microscopes with mounted video cameras can also automatically perform such analyses.

Considerations When Using Microscopy to Analyze Particle Size Distributions

     Preferred Orientations

When analyzing spherical particles with microscopy, spheres can be expected to take random orientations on mounting slides or stubs.  Non-spherical particles, however, tend to preferentially lie on one of their large flat outer surfaces -- in many cases, their largest flattest outer surface.  Just as a coin dropped onto the floor will tend to lie in an orientation with a head or a tail (rather than an edge) facing up, clay plates will also tend to lie on one of their broad, flat faces.  Other non-spherical particles will orient themselves similarly.  Cubes will tend to sit on one of their six faces.  Fibers will lie flat, rather than standing upright.  Etc.

Microscopes will generally provide views of the broadest cross-sectional areas of particles.  They also tend to hide the thicknesses of the particles.  Regardless of the angle of view, generally two dimensional views will be presented to the viewer.

When a scanning electron microscope is equipped with an energy dispersive X-ray analyzer and with a beam control system, the unit can be calibrated to give indications of the thicknesses of particles.  Electron beams can cause X-ray generation from both the particle and the underlying mounting stub.  When particles are especially small and/or thin, a lot of X-rays will be generated by the electron beam within the mounting stub.  As particles increase in size and thickness, more X-rays will be generated within the particle and fewer X-rays will be generated within the mounting stub.  The intensity of X-rays generated within the mounting stub that reach the EDX sensor can therefore be calibrated to give an indication of the thickness of the particle targeted by the electron beam.

For optical microscopy, other methods must be employed.  In some cases, particles are illuminated by a linear beam at an angle to the viewing surface and to the observer's line of sight.  The horizontal distance between the line across the top of the particle and the extension of the line on the mounting slide beside the particle (plus the knowledge of the angle of the light beam relative to the slide surface) can indicate the thickness of the particle.  This is cumbersome to apply to a bazillion particles, but it can be done.  This technique is more typically used to determine the thicknesses of layers, rather than thicknesses of particles.

Randomly oriented particles will not usually occur on mounting slides or stubs.  If random orientations are required, one must disperse particles in mounting monomers, polymerize the dispersions, section and polish them, and then analyze the random cross-sections.  Note, however, that random orientations of non-spherical particles are associated with the analysis of cross-sections, rather than the overhead views of particles mounted on slides or stubs that are normally associated with microscopy techniques.

     Acceptable Quality of Dispersion?

Samples must be dispersed on mounting slides and stubs so all particles are free and clear of one another.  When this is not the case, particles lying on the surfaces of other particles or particles lying underneath other particles will not be properly analyzed.  When this is not the case, particles that are side-by-side and touching one another will appear to be single, larger particles.

     Poor Sampling Statistics -- Are Results Representative?

Microscopy techniques used for particle size distribution analyses are usually characterized by poor sampling statistics.  How many particles are necessary to define a representative sample of the original sample material?  The answer, unfortunately, is usually much larger than the number of particles we are willing to view, size, and tabulate. 

            Sufficiently Large Overall Numbers of Particles Analyzed??

How many particles are in a ton of material?  The answer could be 10²⁰ or larger.  How many particles must we collect to have a representative sample of such a large material?  1%?  0.01%?  0.0001%?  etc?  0.0001% of  10²⁰ is  10¹⁴.  If we say that 0.0001% is sufficient to define a representative sample, are we then going to be willing to measure and size 10¹⁴ particles of that material in a microscope?  I don't think so.

I remember from college that we were told we could achieve a reasonable particle size analysis of a powder by measuring 100 particles on a photomicrograph.  Is 0.0000000000000001% of a sample  truly representative?  I'd be willing to bet most of you would answer, "No."  That would be correct.  But that's the kind of statistical significance we use when we attempt to measure particle size distributions using microscopy techniques.

            Sufficiently Large Numbers of Fines, Relative to the Numbers of Coarse??

Similarly, we need to (or at least we should) analyze many more fields of view as magnifications increase if we want to obtain reasonable results.  If we analyze a square centimeter area to view the relatively large particles, how many fields of view must we analyze at higher magnifications to achieve similar results?

Using microscopes to analyze particle size distributions is definitely not a manual operation (or at least it shouldn't be.)  Even with automatic analyzers, one should realize that it will take long analysis times and require many fields of view to achieve reasonable analysis results.  It is doubtful that samples will be uniformly (i.e., homogeneously) dispersed across microscope slides and stubs, so unless relatively large numbers of fields of view are taken randomly across the surface, results will be non-uniform (i.e., inhomogeneous -- skewed -- biased -- etc.)

Conclusions

Microscopic techniques certainly allow us to view, size, and count particles sampled from our batches.  Microscopic techniques are very useful to analyze individual particles to learn their morphologies, relative surface properties, compositions, etc.  Due to statistical limitations, microscopic techniques are poor means to measure particle size distributions.

When all else fails, by all means, use microscopes to analyze particle size distributions.  When other methods are available, however, microscopy should not be anyone's first choice for this type of analysis.  But when all other methods are inadequate to the task, use microscopy -- and be aware of its limitations.

.... More Feedback is Requested, Please ....

Last month, I requested feedback on new topics for books in the  ... for Ceramists  series.  Here is a possible book subject I want to throw out to see what you think (in hopes I'll actually be able to draw some comments and get some feedback from some of you.) 

Processing Methods for Ceramists

This book would be organized similar to Characterization Techniques.  In this case, each chapter will be devoted to the devices associated with a particular processing method.  For example, the table of contents might look something like this:

Section 1 Blunging
     1 Low Intensity Mixers
          Production Blunger Impellors
          Production Blunger Tanks
     2 High Intensity Mixers
          Batch vs Continuous
     3 Holding Tanks
Section 2 Dry & High-Solids Mixing
     4 Muller Mixers
     5 Ribbon Mixers
     6 Littleford Mixers
     7 V-Blenders
     8 Sigma-Blade Mixers
     9 Hobart Mixers
Section 3 Slurry Pumping
   10 Diaphragm Pumps
   11 Piston Pumps
   12 Rotational Pumps
Section 4 Crushing
   13 Jaw Crushers
   14 Roll Crushers
   15 Hammer Mills
Section 5 Milling
   16 Tumbling Ball Mills
   17 Stirred Ball Mills
   18 Rod Mills
   19 Jet Mills
   20 Sweco Mills
   21 Batch vs Continuous
Section 6 Preparatory Processing
   22 Filter Presses
   23 Delaminators
   24 Sieves (Lawns)
   25 Spray Dryers
           Rotational Atomizers
           Mechanical Atomizers
   26 Ferro Filters
   27 Storage Tanks and Hoppers
           Mass Flow
           Funnel Flow
   28 Dust Collectors
Section 7 Forming
   29 Dry Presses
   30 Isostatic Presses
   31 Extruders
   32 Tape Casters
   33 Pelletizers
   34 Calendars
   35 Ram Presses
   36 Roller Formers
   37 Injection Molders
   38 Slip Casters
   39 Pressure Casters
   40 Glaze Applicators
          Spraying
          Dipping
          Waterfalls
Section 8 Green Machining
   41 Manual Operations
   42 CNC Machines
Section 9 Drying and Firing
   43 Dryers
          Batch vs Continuous
   44 Kilns
          Tunnel Kilns
          Periodic Kilns
          Frit Melters
          Electric Kilns
          Gradient Kilns
          Fast-Firing Kilns
   45 Burners
          Gas & LP Gas Firing
   46 Heat Recovery
Section 10 Process Controlling
   47 Computers
   48 Dedicated Controllers
   49 Sensors
          Thermocouples
          Pressure Sensors
          Displacement Transducers -- LVDTs and RCDTs
   50 Robots
Section 11 Finishing
   51 Grinders
   52 Polishers
   53 Tumblers
           Vibratory
           Barrel
 

I'd appreciate feedback and comments:

How does this sound? 

Is a book like this needed? 

Can you suggest some other topics that should be given separate chapters?  

Should some of these topics be deleted? 

Any comments, generally????

Obviously, this type of book will require the help of equipment manufacturers -- but my experiences when preparing the Characterization book were positive in this regard.

As the list of chapters lengthens, it's possible that this topic will eventually need a Book I and Book 2 so all subjects can be covered adequately.

We had a course like this (40 years ago at Alfred University) that we nicknamed "Steam Shovel" because it started with equipment at the mine site and went on from there.  I'm not familiar with any modern textbooks for ceramists or materials engineers that attempt to cover these types of subjects in this way. 

I think a book like this would be useful not only as an undergraduate text, but as a handy reference in industry -- especially if the information in each chapter is practical and useful to all. 

Let me know what you think of this idea.    

Thanks.

Miscellany

Suggested topics for future issues of this E-zine .... Please continue to send your ideas or questions for future topics.  Thanks.  Until next time ...

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103 Augusta Rd, Clemson, SC 29631   (864) 654-5731

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