Paint & Coatings Industry - March 2008 - (Page 61)

design to calculate the properties, so that a comparison can be made later.) The design points, along with the design limits, are shown in Figure 3. The design space in Figure 3 is bigger than it should be, so that later the mixture design space can be compared to that of the slack, factorial design space. When the regression equation is analyzed for the mixture design it would have the following form. Property = aAA + aBB + aCC + aABAB + aACAC + aBCBC (2) Figure 6. The property range is from about 45 to 140, just as in Figure 2. The mixture design response equation was given in Equation 2. As already stated, the following equality holds: A+B+C=1 (3) Equation 3 can be rearranged to give the following: C=1–A–B (4) If C in Equation 2 is substituted with Equation 4, a slack equation is obtained: If all the coefficients were significant, one would interpret them by saying, for example, when A is increased the Property is increased by aAA units. In addition of course, when A is increased either B or C or both are decreased and then the Property will be changed by the change in a BB and/or aCC. One would also see a change in the contributions of the interaction terms AB, AC and BC. The comments for increasing B or C would be similar. The response surface for the mixture design is shown in Figure 4. Wait a minute! This response surface only has properties varying between from about 45 to 70. The slack, factorial design had performance varying between about 45 and 140. Let’s look at what is happening in the slack, factorial design. When You Put A Lot Of Energy Into Your Business It’s Good To Know Blackmer Vane Pumps Will Never Let Your Energy Go To Waste. Energy-efficient sliding vane pumps could save you up to 40% on your electric consumption. ■ Self-adjusting sliding vane technology eliminates energyrobbing slip If your paint & coatings processes could benefit from lower electric consumption and higher flow performance Interpretation of the Slack Equation The slack, factorial design space of Figure 1 can be redrawn in terms of mixture coordinates as in Figure 5. The design space is twice as large as that of the desired design space. The grey area is the additional design space introduced by using the uncontrolled slack variable C in a slack, factorial design. Although the desired range for C was to be 0.3 to 0.4, because the maximum range of A and B each went to 0.4, C had to go to as low as 0.2. The formulations in the grey area may or may not work or be desired. If the experiments do work, the response surface would be like that in PCI02084Blck.indd 1 Better Get Blackmer (616) 241-1611 www.blackmer.com 1809 Century Avenue SW Grand Rapids, MI 49503-1530 Process | Energy | Transport | Military • Marine Visit ads.pcimag.com PA I N T & C O A T I N G S I N D U S T R Y 1/8/08 11:54:09 AM 61 http://www.blackmer.com http://www.blackmer.com http://www.blackmer.com http://ads.pcimag.com

Table of Contents Feed for the Digital Edition of Paint & Coatings Industry - March 2008

Viewpoint Industry News Calendar of Events Company News Mergers and Acquisitions Names in the News Marketplace Quarterly Stock Watch Reaching Strict VOC Requirements With Outstanding Durability for Industrial Maintenance and Marine Coatings A Unique Fungicide for Wood-Filled Plastic deSigns of the Times: Slacking Off! From Rocks to Nanos Shear-Free Dispersion Process Fluorinated Oxetane Oligomers as Versatile Intermediates for Polymer Modification The Effects of TPO Composition on Adhesion and Proposed Chemical Mechanism Supplier Showcase Color Management Materials Watch Products Classifieds Advertiser Index

Paint & Coatings Industry - March 2008

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