Integrating Mixture Design within the Property Clustering Framework

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Integrating Mixture Design within the Property
Clustering Framework Charles C. Solvasona, Fadwa
T. Eljacka,b, Nishanth G. Chemmangattuvalappila,
Mario R. Edena aDepartment of Chemical
EngineeringAuburn University, Auburn,
USA bDepartment of Chemical EngineeringQatar
University, Doha, Qatar ECCE 6 2007 Copenhagen,
Denmark Chemical Product Design and Engineering
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Outline

• Mixture Design
• Motivation and Challenges
• Property Clustering
• Method Integration
• Case Study Polymer Blend of Spun Yarn
• Conclusions
• Future Direction

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Mixture Design

• What is Mixture Design?
• Mixture Design is a Design of Experiments (DOE)
  tool used to determine the optimum combination of
  chemical constituents that deliver a desired
  response using a minimum number of experimental
  runs.

Prediction
Experimentation Y f(X)
Interpretation / Model Selection
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Motivations and Challenges

• Mixture Design Limitations
• Suffers from combinatorial problems
• 7 components 25 independent ternary plots per
  property
• Evaluation of multiple effects is difficult

• New method of visualizing mixture designs
• Must handle combinatorial intensive problems
• Must be easy to visualize
• Must be universal in its application

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Property Clustering

• What is Property Clustering?
• Property Clustering is a variable transformation
  technique where response properties are
  transformed to conserved surrogate property
  clusters

• Property Clustering Benefits
• Can handle combinatorial intensive problems
• Compresses pure component effects
• Is universal in its application

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Method Integration

• Property Models
• Linear Mixing Model
• Linear Regression Model
• Adequate for experimental design range

• Method Differences
• Rethink of property operators as effects on
  response
• Regression terms B are positive AND negative,
  creating positive and negative clusters

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Method Integration

• Negative Clusters
• Reside outside ternary diagram
• Rules
• NP 2P
• NT P-1
• Type II Ck lt 0
• Type I Ck gt 1

• Positive AUP
• Must maintain monotonically increasing
  relationship for interstream mixing, therefore
  the AUP must be positive, AUP gt 0
• AUP is adjusted using property reference values

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Method Integration

• Component Effects
• Canonical Effects (Scheffe, 1958)
• Adequate prediction, poor effect evaluation
• Suffers from collinearity problems

Property Definitions
Regression Model

• Polynomial Effects (Cox, 1971)
• Same prediction capability with improved
  evaluation due to standard centering
• Suffers from only secondary collinearity problems

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Case Study 1

• Polymer Blend Study
• Optimization of a polymer blend of spun yarn for
  use in rope for modern racing sailboats

• Objective
• Optimize a ternary or smaller polymer blend to
  deliver the specified product attributes of high
  strength, low stretch, and high floatability

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Case Study 1

• Attribute Property Relationship
• Strength Knot Strength of Yarn (Cornell, 2002)
• Stretch Thread Elongation (Cornell, 2002)
• Floatability Specific Volume (Eden et. al, 2003)

• Property Targets Feasibility Range

• Polymer Candidates
• Polyethylene
• Polystyrene
• Polypropylene

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Case Study 1

• Visualization of the effect is not clear

• None of the experiments are in the feasibility
  region

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Case Study 1
Scheffe Canonical Clusters
Experimental Runs

• Visualization of the effect is clearer
• Easy to add more components or experiments on
  same diagram

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Case Study 1
Cox Polynomial Clusters

• Effect Guidelines
• Distance to standard indicates relative magnitude
• Clusters on opposite sides of standard indicate
  inverse relationship

• Main collinearity removed and the effects are
  clearer yet

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Case Study 1
Solution Verification
Effect Clarity
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Conclusions

• Mixture Design Visualization with Clusters
• Handles combinatorial explosion
• Gives good representation of combined effects of
  each component
• Requires the use of negative cluster space

• Opportunities
• How to deal with secondary collinearity
• How to select principal properties

One Answer Use Latent Variable Models
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Future Direction

• PCR and PLS Analysis
• Tools used for fitting rank deficient data by
  reducing properties down to their underlying
  orthogonal latent variables
• Primary tool in bioinformatics and chemometrics

• Need for compressed representation of principal
  properties Ergon, 2005

• Multivariate Methods in the Development of a New
  Tablet Formulation Gabrielsson, 2003