Volume 5  Number 7                            Dennis R. Dinger                                1 May 2007

Updates

The E-zine

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"... for Ceramists" Series Books

The paperback version of Characterization Techniques for Ceramists is available on the Books and Downloads page at the web site!    Retail price is $29.95 plus shipping and handling. The book has 256 pages and it covers 34 different characterization techniques that are commonly used by ceramists.  Order your copy NOW!

The book sets on the web site have also been revised to include this new book.  A 3-book set of paperbacks, including one each of Particle Calculations for Ceramists, Rheology for Ceramists, and Characterization Techniques for Ceramists, is now available for $64.85 plus shipping and handling.  This is a $10 saving off the total retail price of the 3 paperback books.  A 3-book set of downloads is also available for $52.85.  This, too, represents a $10 saving off the total retail price of the 3 downloadable books.  

The E-Book version of Characterization Techniques for Ceramists is available for downloading at the Books and Downloads page of the website for $24.95.  The download is a 2.889 Mb self-extracting Zip® file for the Windows® environment which unzips to the 2.998 Mb book in PDF file format.  Those of you who order the downloadable book will want to know that the PDF book is formatted to print on 5.5" X 8.5" paper (i.e., 8.5" X 11" sheets cut in half.)

The other two books, Rheology for Ceramists and Particle Calculations for Ceramists, continue to be available for purchase as downloadable E-books and as paperback books at the Books and Downloads page of the web site.

A Well-Controlled Inter-Particle Spacing -- WHY?

Introduction

In this article, we will consider a third fundamental question, "Who cares about inter-particle spacing anyway???!!!"  Better yet:  "What is inter-particle spacing???!!!"  

In the previous two articles in this series (Ceramic Processing E-zine, Volume 5, Numbers 4 & 5, 2007), we considered control of particle size distributions and solids contents.  When you put those two parameters together, you arrive at inter-particle spacing.  In this article, we will consider rolling those two parameters into one integrated parameter:  inter-particle spacing (IPS).

PSD Effects on Distribution Properties

Consider that as the particle size distribution (PSD) varies from batch to batch, the packing capability of the powder and the surface area of the powder vary as well.  As PSDs become finer and finer, surface areas per gram of powder increase.  As PSDs change in any manner, packing capabilities change.  

          Packing Capabilities

Broad PSDs usually pack well.  Narrow PSDs pack poorly.  

The ultimate narrow distribution is a monodispersion, which when randomly distributed, packs to a porosity of about 40vol%.  When packed in large orderly arrays, a monodispersion can pack to produce about 26% porosity.  But unless each particle is placed perfectly into its exact, ordered position in the array, randomness raises the porosity to about 40%.  Of course, monodispersions can pack to even higher porosities when the particle surfaces are rough, or when they are coated with relatively high viscosity binders.

As distributions are broadened, packed porosities can decrease below 40%, even under random packing conditions.  One way to think of broadening the distribution is to add particles to the distribution of the exact sizes that can fit into all existing pores.  As existing pores are filled with particles, the distribution broadens, porosities decrease, and packing factors increase.

Daily batch to batch PSD variations necessarily change the packing potential of distributions.  It happens all of the time.  It is impossible to make two totally identical particle size distributions in two successive batches.  When distributions can have 10²⁰⁺ particles per cubic centimeter, identical batches will not happen.  And as batch PSDs change, packing capabilities change.

          Surface Areas

Coarse PSDs have relatively small surface areas (< 1 m²/g).  Fine PSDs have relatively large surface areas (> 20 m²/g).  As PSD varies from batch to batch, surface areas of the powders vary as well.  When PSDs become finer, surface areas increase.  When PSDs coarsen, surface areas decrease.

Why is this important?  Most suspension additives attach to particle surfaces, so as surface areas change, the available surface areas on which the chemical additives can attach change as well.  As PSDs vary, surface areas available to the additives vary and additive coverage concentrations vary.  In most batches, constant additive percentages are used.  So as PSDs vary from batch to batch, surface areas change, and densities of coverage of the additives change as well.

For these reasons, batch to batch variations in PSD cause packing, powder surface areas, and additive surface coverage densities to change.

Two Locations for Water in Suspensions

There are two primary locations for water (or non-aqueous suspending fluids) in suspensions to reside.  (1) Water fills interparticle pores; and (2) water separates particles.  Pores are necessarily filled first.  Any water remaining after pores are filled can then separate particles.  

Particle separation directly affects viscosities and rheologies.  During shear, the closer particles are, the more they will collide, the higher will be the viscosity, and the more the dilatant character of the rheology.  During shear, the farther particles are from each other, the less they will collide, the lower will be the viscosity, and the more the shear-thinning character of the rheology.

Remember:  Carrier fluid (1)  fills pores, and (2) separates particles.

InterParticle Spacing (IPS)

This leads to IPS considerations.  As PSD and packing change, the IPS in suspensions changes as well.  

As packing potential decreases, more porosity is defined between the particles in the batch.  As porosities increase, more of the available water is required to fill those pores and less is available to separate particles.  So when porosities increase, at constant solids content, particles move closer together.  As packing potential improves, less porosity is defined, less water is required to fill those pores, more water is available to separate particles, and the particles are farther apart.

Now consider a process with varying PSD that precisely controls solids contents and batch viscosities.  As PSD narrows, packing potentials worsen, porosities increase, more fluid is tied up filling pores, less fluid remains to separate particles, particles move closer together, suspension viscosities increase, higher deflocculant concentrations (or lower flocculant concentrations) are required to achieve final target viscosities, and final process suspensions become more and more dilatant and less and less shear-thinning.

If the opposite happens and PSD broadens, packing potentials improve, porosities decrease, less fluid is necessary to fill pores, more fluid remains to separate particles, particles move farther apart, suspension viscosities decrease, higher flocculant concentrations (or lower deflocculant concentrations) are required to achieve final target viscosities, and final process suspensions become less and less dilatant and more and more shear-thinning.

Processing Properties

Suspension properties and especially forming properties vary considerably as rheologies change.  When everything else is 'constant', rheological properties will have the biggest effect on forming properties of process bodies.  For this major reason, PSD variations combined with precise control of solids contents and a final viscosity target will necessarily produce fluctuating rheological properties.  Forming properties are functions of viscosity and rheology --- not viscosity alone.  

As a result, when PSD varies but solids content and final viscosity are precisely controlled, the PSD variations will be the direct cause of rheology and forming property variations. 

Better Batch Controls????

If it were possible to perfectly control PSD and solids contents, that is what everyone would do (and should do).  But it is impossible to control PSD perfectly.  Since PSD will vary from batch to batch, what is the next best control?

Solids contents are relatively easy to precisely control, but even with today's computerized particle size analyzers, it is still impossible to control PSD perfectly.  With today's computerized particle size analyzers, however, it is possible to precisely measure body PSDs, and then to calculate expected packing factors, porosities, and interparticle spacings from them.

Constant Batch-to-Batch Properties

This author suggests that it is better to target control of IPS and solids contents from batch to batch, than to control PSD and solids content. 

First of all, most processes do not actually CONTROL particle size distributions.  Process conditions such as unit operations' times are precisely controlled under the assumption that they control PSDs.  But that is not correct.  For example, when ball milling times are held precisely constant, particle size distributions are still NOT being controlled precisely.  Powder feed sizes and individual particle mechanical properties vary, so no two batches will be identical, nor will any two batches even mill identically.  Constant milling times DO NOT GUARANTEE constant PSDs.  Most processes, however, proceed under such assumptions.  Then, when PSDs are finally measured, it is to CHECK the results, not to CONTROL the results.  Most process systems, therefore, do not really control PSD.  PSD variations occur all the time from batch to batch -- and most 'controls' are actually 'checks' to determine how close to the desired values the batches actually came.. 

Although PSDs cannot easily be controlled, existing PSDs can be precisely measured.  Solids contents can be controlled very precisely.  

The result in most process systems is that they have fluctuating PSDs at constant solids contents.  When the final control to achieve the target process viscosity is to adjust flocculant or deflocculant concentrations, batch rheological properties will vary as described above:  batch to batch PSD variations will then produce rheologies from extreme dilatancy to extreme pseudoplasticity (shear-thinning behavior).  

IPS Controls

When IPS controls are instituted, more constant batch to batch forming properties will result.  To control IPS, it is not necessary to precisely control PSD.  Yes -- we certainly do our best to hold PSDs constant from batch to batch.  But with IPS control, we accept the PSD achieved with each batch.  We measure it and use it to calculate the solids content necessary to achieve constant IPS.  Then, we control the solids content (which we CAN do precisely) to the calculated optimum value.  When the particles are always the same distance from one another from batch to batch, we have a better chance of achieving desired rheological properties by controlling additive concentrations to adjust final process viscosities.

Either we assume constant PSD (recognizing that it is not constant) as we control solids content to achieve final process viscosities at varying rheologies, or we accept and measure the actual PSDs (as they fluctuate) so we can calculate and set the solids content to maintain constant IPS.  Constant IPS should achieve final process viscosities at relatively constant rheological properties.  Additive concentrations will vary as PSDs vary because surface area varies as PSD varies.  But variable additive concentrations should produce relatively constant rheological properties when the distances between particles are constant --- which, after all, is the goal when IPS is controlled.