Cyberinfrastructure-enabled Molecular Products Design...

1

Cyberinfrastructure-enabled Molecular Products Design

and Engineering: Challenges and Opportunities

Venkat VenkatasubramanianLaboratory for Intelligent Process Systems

Purdue UniversityWest Lafayette, IN, USA

Venkat Venkatasubramanian, Keynote Lecture,European Congress in Chem. Engg, Copenhagen, Sept 2007 2

LIPS

OutlineMolecular Products Design

Data, Information and Knowledge Modeling Challenges

Cyberinfrastructure Ontological Informatics

Industrial Case StudiesLubrizol: Fuel Additives DesignCaterpillar: Rubber Products DesignExxonMobil: Catalyst DesignEli Lilly: Seromycin Formulation for MDR-TB

Summary

Venkat Venkatasubramanian, Plenary Lecture, Foundations of Computer-Aided Process Design, Princeton, July 2004.

Acknowledgements

Prof. J. F. Caruthers and Prof. W. N. DelgassDr. K. Chan (Bear Stearns), Dr. A. Sundaram (ExxonMobil), Dr. P. Ghosh (ExxonMobil), Dr. S. Katare (Dow), Dr. A. Sirkar (Intel), Dr. P. Patkar (ZS), Dr. S-H. Hsu (Purdue), S. Syal (Purdue), B. K. Balachandra (Purdue)

Funding AgenciesNSFDOEIndiana 21st Century Research and Technology FundGE, Bangalore, IndiaLubrizolCaterpillar ExxonMobilEquistarCummins

Materials Design


LIPS

Acknowledgements

Dr. C. Zhao (Bayer)Dr. A. Jain (United)Dr. S-H. Hsu (Purdue)L. Hailemariam (Purdue)P. Akkisetty (Purdue)P. Sureshbabu (Purdue)I. Hamdan (Purdue)M. Chaffee (Purdue)A. Shukla (Purdue)

Funding Agencies:NSF ERCIndiana 21st Century R&T FundEli LillyPfizerAbbott

Dr. Prabir BasuDr. Girish JoglekarProf. Ken MorrisProf. G. V. ReklaitisInformation Technology@Purdue

Pharmaceutical Engineering

Venkat Venkatasubramanian, Plenary Lecture,Foundations of Computer-Aided Process Design, Princeton, July 2004.

LUBRIZOL: Fuel Additive Design

EPA requirement: Minimize intake-valve deposits (IVD)Approach: Fuel Additives Performance measure

BMW Test for IVD Stipulated to be less than 100 mg over a 10,000 mile road test

Expensive and time-consuming testing

Around $8000 for a single datum

Problem: Design fuel-additives that meet desired IVD performance levels

Intake Valve and Manifold


About 1000 Rubber Parts in Failure Critical Functions

Tires, Treads, Hoses, Shock Absorbers, O-rings, Gaskets, Mounts …

Reliability and Warranty Problems

CATERPILLAR


QuantumChemistry

T̃ = 2ρR∂ ψ∂I 1

+ I 1∂ ψ∂I 2

⎧⎨⎩

⎫⎬⎭

I −∂ ψ∂I 2

C + I 3∂ ψ∂I 3

C−1⎡

⎣⎢⎤

⎦⎥••∂ C∂C

Constitutive Model

3D FiniteElementPart Model

Spring-DashpotApproximationwith ChemicalAging

Ax + S8k1⎯ →⎯⎯ Ax+8

Ax + R k2⎯ →⎯⎯ Bx

Bxk3⎯ →⎯⎯ Bx

*

etc.Time

To rq u eCure Curve

Kinetics Polymer Network Mechanical Response

Mixing+

Heat Transfer+

Mold Filling

Part Manufacturing

Overcure

Undercure

SC

N S SS

SS

S

S

S

Zn

NewMolecules

MaterialFormulation

Manufac-turing

Process

PartShapeDesign

SubAssemblyDesignFull

ProductDesign &Operation

Design &Operation ofComplexSub-Assembly

Engine

Over 1000 rubber parts infailure critical functions

Multi-Scale Modeling

Quantum Mechanics

Kinetics

Heat Transfer FEA

Mechanics FEA

Part Design CAD /CAM

Caterpillar’s Multi-Scale Modeling Challenge: Design of Formulated Rubber Parts


ExxonMobil’s Grand Challenge: Catalyst Design via Combinatorial Chemistry

Fundamental Chemistry

Reactionkinetics

Performancemeasures

time

Rat

e/S

elec

tivity

C

k 6

A

B

F

k1

HD

R

M

E G

N

k 3 k4k2

k7

k5

Reaction network

Electronic/Structural descriptors

d band centerElectronegativity

...

Quantum calculations

Catalyst StructuresSynthesis

Characterization

10/11/2005

9

Pharmaceutical Product Development and Engineering

• Two ProductsDrugsDocuments

Preliminary product recipe

Drug is converted into ParticlesDrug Synthesis

Raw Chemicals

Formulation

Process Development

Preliminary process recipe

Scale/up -Tech Transfer

Adjusted process recipe

Manufacturing

A Delayed Product


Molecular Products DesignGiven a set of desired performance specifications, how does one rationally and efficiently identify the optimal product structures and formulations?$200+ Billion/yr industry: Major Opportunity for ChEsAreas of Application

Engineering MaterialsFuel and Oil AdditivesPolymer CompositesRubber CompoundsCatalystsSolvents, Paints and Varnishes…..

PharmaceuticalsDrug Design

Agricultural ChemicalsPesticidesInsecticides

Zeolite!!


Different Products, But Common Challenges

Lots of DataUncertain/Noisy Data Complex chemistry, lots of speciesNonlinear systems and processesIncomplete, Uncertain, MechanismsCombinatorially large search spacesNeed Multi-scale ModelsHundreds of Differential and Algebraic Equations to formulate and solveLaborious and time consuming model development processLimited human expertise


Traditional Approach

Revise Design

No

Designer

Hypothetical Molecule

Synthesize

Evaluate

Design Objectives

Yes

Solution

Meets Design Objectives ?

Drawback: Protracted and Expensive Design CycleNeed a Rational, Automated Approach: Discovery Informatics

EUREKA!!!


LIPS

Need a New ParadigmCyberinfrastructure Methods and Tools

Ontology-based Discovery Informatics

Venkat Venkatasubramanian, Plenary Lecture,Chemical Process Control 7, Canada, Jan 2006 14

LIPS

Data, Information, and KnowledgeData

What’s going on?Raw, does not inform much

InformationHow are the variables related?

Correlations and relationshipsKnowledge

Why are they related?Develop Mechanistic understandingFirst-Principles Based Math ModelsHeuristics

Tower of Babel of Data, Information and Models

Venkat Venkatasubramanian, Plenary Lecture, Pharmaceutical Sciences World Congress, Amsterdam, April 2007 15

LIPS

What is an Ontology?Originated in Philosophy

Study of ExistenceNot to be confused with Epistemology: Theory of Knowledge and Knowing

Computer Science and Artificial IntelligenceA formal, explicit specification of a shared conceptualizationKnowledge representation in AI

Logic, Semantic Networks, Frames, Objects, OntologyWeb-driven development

Semantic Richness: Description Logic (DL) provides foundation for formal reasoningEasily create, share and reuse knowledgeSemantic Search

Venkat Venkatasubramanian, Plenary Lecture, Pharmaceutical Sciences World Congress, Amsterdam, Apr 2007 16

LIPS

Based on Set Theory and First-order Logic

An ontology is a 5-tuple ),,,, oc ArelHRC(:=Ο consisting of • Two disjoint sets C and R whose elements are called concept identifiers and

relation identifiers, respectively • A concept hierarchy CH : CH is a directed, transitive relation CCH C ×⊆ which

is called concept hierarchy or taxonomy. ),( 21 CCH C means that 1C is a subconcept of 2C .

• A function CCRrel ×→: that relates concepts non-taxonomically. The function dom: CR→ with ))((:)( 1 RrelRdom Π= gives the domain of R , and range:

CR→ with ))((:)( 2 RrelRrange Π= give its range. For ),()( 21 CCRrel = we also write ),( 21 CCR .

• A set of axioms oA , expressed in an appropriate logic language, e.g. first order logic

17

Ontology: A Simple Example

Excipient Properties

Material

API

Is aIs a

has

Concept Instance Property

RolesComposition

Range

hashas

Flow aid

Filler

Lubricant

Minimum

Maximum

Average

Is an instance of has

Contact angle

Moisture content

Is aMaterial

Composition

has

Web Ontology Language: OWL


Catalyst Design Problem – The Grand Challenge

Fundamental Chemistry

Reactionkinetics

Performancemeasures

time

Rat

e/S

elec

tivity

C

k 6

A

B

F

k1

HD

R

M

E G

N

k 3 k4k2

k7

k5

Reaction network

Electronic/Structural descriptors

d band centerElectronegativity

...

Quantum calculations

Catalyst StructuresSynthesis

Characterization


1 A° 100 A° 10 μm 1 cm10-15 s

10-12 s

10-6 s

1 s

102 s

Quantum Mechanics

DFT

Atomistic SimulationMolec. Dyn.

Statistical Mechanics

TST

Continuum Models

Transport Models

Elect.Struct. Thermo.

Props.

Molec. Struct.

Rate Consts.

Overall Rxn Rates

Conc.Profiles

Microscopic Mesoscopic Macroscopic

Modeling at different Length and Time Scales


Paraffin Aromatization

Identify a catalyst formulation for light paraffin aromatization that is superior to Ga/H-ZSM-5 in terms of:

Higher Benzene, Toluene, Xylene(B/T/X) selectivityHigher Hydrogen selectivity

Microkinetic model development for the kinetic description of the system


Previous Work

Microkinetic Analysis (Dumesic, 1993)First unified view of reaction engineering on catalytic surfacesIncomplete forward problemLacks clear view of the design perspective (inverse problem)

Empirical Catalyst Design (Baerns, 2000)First attempt to “design” catalystsCompletely based on “guided” experiments – time consuming and expensiveNo fundamental understanding of the system (forward problem)

Ertl, Rasmussen, Lauterbach: Surface Science StudiesSteve Jaffe: Composition based modeling of large systemsJens Norskov: Computation based studiesSymyx, Novodynamics, Lauterbach: Combinatorial HTE

Venkat Venkatasubramanian, Plenary Lecture, Foundations of Computer-Aided Process Design, Princeton, July 2004.

Reaction Network – Propane Aromatization on HZSM-5

• 31 gas phase species + 29 surface species + 271 reaction steps• Model with 31 ODEs, 29 algebraic equations • 13 parameters with up to 10 orders of magnitude bounds on each

Hydride transfer

Cx-y=β-scission/Oligomerization

Cx+ Cy

+

H2 Cx-y

Dehyd

rogen

ation Protolysis

Cx=

adso

rptio

n/de

sorp

tion adsorption/desorption

Cy=

H+

CxH+

Cx

initiation

Paraffin

Dehydro-cyclization

Aromatics

Cx ParaffinCx

= OlefinPx

= Poly-olefinCx

=c Cyclic-olefinActive siteH+


Ontological Informatics: Modeling Super Highway

• DAE System: 30 to 1000 species and 10 to 50 parameters• Parameter search space is highly nonlinear with numerous local minimaGA based pseudo global parameter estimatorFast and efficient coverage of the parameter space

• Optimization: Traditional least-squares and features-based objectives

ChemistryCompiler

Reaction Description Language Plus (RDL+)

EquationGenerator

Automatic generation of differential algebraic

equations (DAEs)

Parameter Optimizer

Solution of DAEsLeast squares

Features

Advanced Statistical Analyzer

Sensitivity AnalysisUncertainty AnalysisError Propagation

ReactionsGrouping

Chemistry Rules

time

Rat

e/S

elec

tivity

Performance Curves

Data

J.M. Caruthers, J.A. Lauterbach, K.T. Thomson, V. Venkatasubramanian, C.M. Snively, A. Bhan, S. Katare and G. Oskarsdottir, “Catalyst Design: Knowledge Extraction from High Throughput Experimentation”, In “Understanding Catalysis from a Fundamental Perspective: Past, Present, and Future”, A. Bell, M. Che and W.N. Delgass, Eds., Invited Paper for the 40th Anniversary Issue of the Journal of Catalysis, 2003.

Katare, S., Caruthers, J. M., Delgass, W. N., Venkatasubramanian, V., “An Intelligent System for Reaction Kinetic Modeling and Catalyst Design”, Ind. Eng. Chem. Res. and Dev., 2004.

Model Refinement Procedure

Crude modelsInitial data

Model screening

Infer new knowledge about models (mechanism) and data

Model discriminationModel enhancement

Enhanced modelsRicher data set

Planning new experiments

Add/Delete models

Add/Delete data

Model analysisData analysis

Chemistry Rules for Propane Aromatization on HZSM-5

Chemistry Rules Representative Chemical Reactions

1. Alkane adsorption

2. Alkane desorption

3. Carbonium ion protolysis

4. Carbonium ion dehydrogenation

5. Olefin adsorption

6. Olefin desorption

7. Aromatization

8. Beta-Scission

9. Hydride Transfer

10. Oligomerization

CH4 +

+ H2

+

+ +

+


Modeling Super Highway: Reaction Modeling Suite (RMS)

Reaction Network

Reaction Description Language PlusEnglish Language Rules

C

k 6

A

B

F

k1

HD

R

M

E G

N

k 3 k4k2

k7

k5

Mathematical Equations

1//

541

1

=++−+=

−=

CBA

AB

AA

BkDkCkdtdCCkdtdC

θθθ

100’s of DAE’s

...

Model Generator

Beta ScissionLabel-site c1+ (find positive carbon)Label-site c2 (find neutral-carbon attached-to c1+)Label-site c3 (find neutral-carbon attached-to c2)Forbid (primary c3)Forbid (less-than (size-of reactant) 9)Disconnect c2 c3)Increase-order-of (find bond connecting c1+ c2)Add-charge c3Subtract-charge c1+

Beta ScissionLabel-site c1+ (find positive carbon)Require (c1+ primary and product)set-k k1Label-site c2+ (find positive carbon)Require (c2+ secondary and product)set-k 20*k1Label-site c3+ (find positive carbon)Require (c2+ tertiary and product)set-k 60*k1

Chemistry

8. Beta Scissiontransforms a carbenium ion into a smaller carbenium ion and an olefin

Grouping

8. a. Formation of a secondary carbenium ion

is 20 times faster than a primary carbenium ion

b. Formation of a tertiary carbenium ion

is 60 times faster than a primary carbenium ion

...

...

...

...


Results

Over prediction of C2s and under prediction of aromaticsSpace time x 104 [hr]

Wt %

C2H6 C3H6

C3H8 Aromatics

Data*

* Lukyanov et. al., Ind. Eng. Chem. Res. , 34, 516-523, 1995

Model


Results – Model Refinement

Refined model adds alkylation step to convert lighter alkanes to higher onesSpace time x 104 (hr)

Wt %

C2H6 C3H6

C3H8 Aromatics

DataOriginal ModelRefined Model

GA Based Pseudo Global Parameter Estimator

S.no. Name Esposito & Floudas (2000) Global optimizer

GA based procedure

υ Objective CPU s reported

min max

υ Objective Time taken

(CPU s)

Scaled CPU s

Time taken *671/211 (% Saving)

1 First order

irreversible chain reaction

5.0035 1.0000 1.18584x10-6 2.92

20.05 5.0122 0.9976 9.25418x10-6 0.24 0.76 (74)

2a First order

reversible chain reaction

4.0000 2.0000 40.013 20.007

1.8897x10-7 568.44 6164.3

3.9813 1.9759 39.787 19.887

8.1313x10-6 0.45 1.43 (100)

2b Same as 2a but with error in data

4.021 2.052 39.45 19.62

1.586x10-3 272.91 1899.82

4.001 2.027 39.22 19.50

1.589x10-3 0.5 1.59 (99)

3 Catalytic

cracking of gas oil

12.214 7.9798 2.2216

2.65567x10-3 79.77 1185

12.246 7.9614 2.2351

2.68017x10-3 0.38 1.21 (98)

4 Bellman’s problem

4.5704x10-6

2.7845x10-4 22.03094 36.16 12222

4.5815x10-6 2.7899x10-4 22.2885 3.54 11.26 (69)

5 Methanol-to-hydrocarbon

process

5.1981 1.2112

0 0 0

0.10652

1361.8 19125

5.2212 1.2320

1.6363x10-31 4.0059x10-12

0.004665

0.10586 2.08 6.61 (100)

6 Lotka-Volterra Problem

3.2434 0.9209 1.24924x10-3 367.26

9689.67 3.1434 0.9583 2.39784x10-3 0.56 1.78 (100)

Our zeolite model31 ODEs, 29 Algebraic equations

13 parameters9 concentration curves

Performance comparison on test problems – worst case: 3 ODEs/5 parameters

Reasonable comparisonto experimental data

2 hours on a Sun 400 MHz solaris machine


Ontological Informatics for Catalyst Design: Summary

Chemistry Rules

High Throughput Experimental

Data

Reaction Knowledge

Base

Kinetic Modeling Toolkit

(Reaction Modeling Suites)

Chemistry Rules

High Throughput Experimental

Data

Reaction Knowledge

Base

Kinetic Modeling Toolkit

(Reaction Modeling Suites)

Represents reaction chemistries explicitlyCustomizable for different catalyst chemistries Results

Real-time evaluation of 100s of reaction pathways and 1000s of DAEsSaved months of model development effortImproved mechanistic understanding and first principles models

Molecule Ontology

Reaction Mechanism

Ontology

Reaction Ontology Chemistry

Knowledge Base

Molecule Classification

Reaction Classification

Reaction Network

Generator

Correctness and Consistency Checking

Proposed Mechanism

Graphical User Interface

Chemistry Ontology

Application

Ontology

Molecule Ontology

Reaction Mechanism

Ontology

Reaction Ontology

Molecule Ontology

Reaction Mechanism

Ontology

Reaction Ontology Chemistry

Knowledge Base

Molecule Classification

Reaction Classification

Reaction Network

Generator

Correctness and Consistency Checking

Proposed Mechanism

Graphical User Interface

Chemistry Ontology

Application

Ontology

Application

Proposed Framework for Knowledge Extraction from HTE – Kinetic Modeling

Reaction Modeling Suite

Automatic processing of data


Automatic processing of data

Model RefinementRules Features mapping

Suggestions for location of new rules

New HTE for Model Discrimination via Experimentation

Experiments in new composition regimesMeasure critical variables identifiedHigh Throughput

Experiments

time

Rat

e/S

elec

tivity

Performance Curves

FTIRGC...

Chemistry RulesReactionsLumping

Chemistry RulesReactionsLumping

Feature Extractor/Analyzer

Feature Extractor/Analyzer

Inverse Model

Genetic Algorithms

SelectionRecombination

Catalyst Library

HTE

Target Catalyst

Model Revision

Compare Performance

Catalyst Design Challenge

Target Catalyst Performancetime

Rat

e/Se

lect

ivity

Forward Model

Hybrid Model

Physical ModelStatistics/Neural-Nets

A + S A-Sk1

C + R Dk2

A-S +Dk3

time

Rat

e/Se

lect

ivity

Kinetics AI/Systems Tools Catalyst Performance

F

Pseudo Global Optimizer

Pseudo English Rule Compiler

Statistical Analyzer

Feature Extractor

Catalyst

{k}



LUBRIZOL: Fuel Additive Design

EPA requirement: Minimize intake-valve deposits (IVD)Approach: Fuel Additives Performance measure

BMW Test for IVD Stipulated to be less than 100 mg over a 10,000 mile road test

Expensive and time-consuming testing

Around $8000 for a single datum

Problem: Design fuel-additives that meet desired IVD performance levels

Intake Valve and Manifold

Fuel + Oil (Liquid + Vapor Mixture)

Additive Componentthat keeps it in solution

Additive Component that bindsto deposit “precursors”

Fuel-Additive Molecules

High-Boiling Deposit Forming Precursors

Fuel-Additives : A Functional Description

Component “length” directlyindicative of stability of additive

Breakage of this bond removes “dirt” carrying capacity totally

Chemical nature of this component (polar/non-polar) controls “dirt” removingcapacity

Breaking of these bonds control “length”

The first-principle model tracks the structural distribution of fuel-additive with time due to reactive degradation

FirstFirst--Principles Model for Additive DegradationPrinciples Model for Additive Degradation

Performance

Pattern RecognitionNeural Networks

RegressionAb Initio Methods Group Contribution

TopologicalTechniques

MolecularMechanics

Material/MoleculeFormulation

Primary Model

Structural Descriptors

Secondary Model

General Framework of Predictor ModelsGeneral Framework of Predictor Models

Modeling DegradationModeling Degradation

Dynamic in natureModeled as first-order irreversible reactions for additive degradationRate constants in proportion to rates of pure thermal degradation

Distribution of molecular species differing in structureIdentified by effective "length"Population balance model tracks distribution with time

From Stability to IVDFrom Stability to IVD

Define "amount of active additive"The fraction of the additive species that remains active (i.e.

intact viable structure) in the fuel at any point of time

A dynamic quantity decreasing with timeDepends on additive distribution

Solubility correlated to IVD via regressionLinear modelsNeural-Network modelsInput descriptors are the amounts of active additive at

different times

If A goes higher, B should go higher .....If C goes higher, D should go lower .....

Expert Rules/ HeuristicsFundamental Physics/Chemistry

)v(t

ρ•∇−=∂ρ∂

)(P)v(vt

)v(τ•∇+∇−=ρ∇•+

∂ρ∂

How to integrate diverse scientific knowledge/information into

a single unified knowledge architecture ?

Forward Problem Approaches

Empirically speaking, a polynomial expansion fits my data............

Data-driven/empirical models


Modeling Philosophy

All models are wrong….… but some are useful!

-- George Box(U. Wisconsin)

Hybrid ModelsCombine First-principles and Data-driven models

Hybrid Model for IVD PredictionHybrid Model for IVD Prediction

Time

Am

ount

of A

ctiv

e A

dditi

ve

τ0 τ2 τi τN

Additive A

Additive B

Intake-Valve Deposit

ComputerComputer--Aided Design of FuelAided Design of Fuel--AdditivesAdditives

Hybrid Model

Additive Performance

Intake ValveDeposit

Additive StructureFuel PropertyEngine Conditions

Genetic Algorithms

.

.

SelectionRecombination

Physical Model

Statistical/Neural-Net Correlation

Previous Approaches to Inverse Problem

Previous MethodologiesRandom SearchHeuristic EnumerationMath ProgrammingKnowledge-Based SystemsGraph Reconstruction

DisadvantagesCombinatorial Complexity

Nonlinear Search Spaces Local Minima Traps

Difficulties in Knowledge AcquisitionDifficulties in using high-level chemical/bio-chemical knowledge

Overview of Genetic AlgorithmsOverview of Genetic Algorithms

DefinitionGenetic Algorithms are stochastic, evolutionary search procedures based on Darwinian model of natural selection

Essential ComponentsGenetic Operators

CrossoverMutation

Reproductive PlanFitness Proportionate Selection

Genetic Algorithms for Product DesignGenetic Algorithms for Product Design

Global SearchDiversity of solutionsHigh potential for noveltyGlobal Optima

Development is de-coupled from forward problemRobust to non-linearity

Population based searchAbility to provide several near-optimal solutions

Captures transparently the rich chemistry of the design problem

Overview of Genetic AlgorithmsOverview of Genetic Algorithms

Select Operator

Molecular DesignsInitial Population

Calculate Fitness

Select Parent(s)

MutationCrossover

Apply Operator

Create New Population

Genetic Algorithms (GA)Genetic Algorithms (GA)

GAs are stochastic evolutionary search procedures based on the Darwinian model of natural selection

Initial Population (random)

Fitness Calculn, Parent Selectn

OperatorsNew

Population

“ Survival of the fittest ”

Evolution

Single-point Crossover

Genetic Operators: CrossoverGenetic Operators: Crossover

]nO C

OCO[O

H

H

C

H

H

C

O

H

H

C

H

H

C

CH3

CH3

C O CO[ ]n

O O CO

CO]n[

CH3

CH3

C O CO

O ]n[Parent #1 Parent #2

Offspring #1 Offspring #2

Main-chain and Side-chain Mutation

Mainchain MutationCH

HCH

H

n

CH

H

Parent: Offspring:

CH

H

n

CH

H

CH

HCF

H

n

Parent:

CH

HCH

n

Offspring:

Sidechain Mutation

Replace F by

Replace CH 2by

Mutation OperatorsMutation Operators

Fitness Function for GA-based CAMD

α = 0.0001

α = 0.01α = 0.001

α = 0.0005

Fitness (F) = exp - α Pi – PPi,max – Pi,min

2

Fractional Error (FE) = Pi – P

P

Polymer Design Case Study

• Base Groups

• Target Properties•

••

•

• Density Glass Transition Temperature

Thermal Expansion Coefficient Specific Heat Capacity

Bulk Modulus

15 Side-chain Groups

3 -C2H5 -nC H3 7 -iC H3 7

-Cl -Br -OH

-H

tC4H9

-OCH3-CN-

-CH

-F

3-C-O

O CH - 3-C-O

CH --C-O

NH--NH

X

X

X

17 Main-chain Groups>C< -S- -SO2- -O- -NH-

O-C-O

-C-O

-C-O

-O O--C-O

O--C-O

-C-O

NH- -O-C-O

NH-

Target Properties

Target PolymerDensity (gm/cm3)

2.96x10-4 1152.67 5.18x109

TP2: 1377.82 2.51x109

TP3: 1135.10 5.40x109

1073.96 5.39x109

TP5: 995.95 5.31x109

TP6: 1016.55 6.12x109

TP7:

1.34

1.18

1.21

1.19

1.28

1.25

1.06

350.75

225.24

420.83

406.83

472.00

421.12

322.55 1455.90 3.85x109

C

O

O C

O

O C

H

H

C

H

H n

C

H

H

C

F

F

C

H

H

C

H

CH 3 n

C

O

OO

CH 3

C

CH 3 n

CH

S O3

C

CH 3

O

n

O

n

SO 2 O

O O C

O n

C

H

H

C

H

H

C

H

H

C

H

H

C

H

H

C

O n

N

H

Glass Transition

(K)

Thermal Expansion

1/K

HeatCapacityJ/kg K

BulkModulusK N/m3

TP1:

2.81x10-4

2.90x10-4

2.90x10-4

2.90x10-4

2.98x10-4

2.89x10-4

TP4:

Polymer Design Case Study: Results

Legend: Success Rate; Average Conv. Generation; Number with fitness >0.99

Target Polymer

C

O

O C

O

O C

H

H

C

H

H n

C

H

H

C

F

F

C

H

H

C

H

CH 3n

C

O

OO

CH 3

C

CH 3 n

S O

CH 3

C

CH 3

O

n

O

n

SO 2 O

O O C

O n

C

H

H

C

H

H

C

H

H

C

H

H

C

H

H

C

O n

N

H

C

O

O C

O

O C

H

H

C

H

H n

CH 3

CH 3

O

CH 3

O

n

60%240213

48%5226

12%19374

0%-

589

48%232142

32%632168

100%64198

88%109161

4%86870

12%184282

36%4116

0%-

163

0%-

861

32%400175

8%548199

100%61217

68%210162

8%382144

Random MC, SC Random MC, SCFeasibility Constraints

Near Optimal DesignsPolymer Design Overall Error Fitness

Target Polymer: #4

3

S On

CC H 3

C HO 0% 1.0

Case 1: Standard GA

0.74% 0.995n

H HCH

O CO

CH

n

2C H 5 OC

C NO O O C O 1.18% 0.991

Case 2: Modified GA, StabilityHO H O

0.25% 0.999nC H 3

CH

C OO C

1.10% 0.991

Case 3: Modified GA, Stability & Complexity

O C HSC O C

2 5

H n

O CO

CH

H n

0.21% 0.999

HC 3 O O

nC

C H 3O C O C 0.83% 0.995

Advantages of GAs for Product Design

Global SearchDiversity of solutionsHigh potential for noveltyGlobal Optima

Development is de-coupled from forward problemRobust to non-linearity

Population based searchAbility to provide several near-optimal solutions

Captures transparently the rich chemistry of the design problem

•••

Powerful generic method with some drawbacksNo convergence guaranteesPerformance sensitive to parametersPerformance dependent on search space structure

Drawbacks of GAs

Evolutionary Design of FuelEvolutionary Design of Fuel--AdditivesAdditives

• Knowledge Based

Initial Population• Random

No

Termination Criteria• Last Generation ?• Fitness = 1.0 ?

New Generation

ProbabilisticSelect Operator

Select Parent(s)Fitness Proportionate

Apply Operator

Crossover Mutation

Elitist PolicyRetain k best in population

Calculate Fitness (F)Structure ---> Hybrid Model

Fitness <---- Additive Performance

Head LinkerBranch Tail

Yes

Stop

StartIVDdesired< IVDlimit;Maximize Solubility

Objective

Branch Crossover

L

JSite 2

Branch A

Parent-1

N

K

Parent-2

L

N

K

Branch A moved to site-2 to ensure feasibility of offspring-1

Offspring-1

J

Offspring-2

Genetic Operators: Branch CrossoverGenetic Operators: Branch Crossover

Run Rank/Identifier Fitness Predicted IVD(PLS-NN Model) Structural Description

1, I-1 0.997 11.4 mg Novel Structure. Infrequently used linker.

2, I-2 0.996 11.5 mg Novel Structure. Same tails as beststructure, different heads and linkersI

6, I-6 0.993 12.0 mgVariant of structure found in the BMWdatabase. Same head and linkers, differenttails

1, II-1 0.999 10.1 mg Novel Structure. Different from I-1.Infrequently used linker component.

2, II-2 0.989 12.6 mgSlight variant of additive structure foundin BMW and HONDA databases.Different tails but same head and linker

II

4, II-4 0.983 13.2 mg Minor variation of structure II-2 above.Slight modification of the head

1, III-1 1.00 8.9 mg Novel Structure. Different from I-1 andII-1. Commonly used components

2, III-2 0.994 11.9 mg Variant of III-1. One linker and tailmodified.III

3, III-3 0.993 12.1 mgVariant of structure II-2 above. Slightmodification of head. A linker and tailinserted.

Evolutionary Design of Fuel Additives: ResultsEvolutionary Design of Fuel Additives: ResultsObjective: Determine a structure with IVD < 10 mgDosage: 50 PTB; Population Size: 25; Generations: 25Objective: Determine a structure with IVD < 10 mgDosage: 50 PTB; Population Size: 25; Generations: 25

School of Chemical Engineering, Purdue University

Tires, Treads, Hoses, Shock Absorbers, O-rings, Gaskets, Mounts ……..

Rubber Parts in Service


Rubber Formulation

Accelerator Activator

Rubber

Retarder

Filler

Antidegradants Oils

Sulfur

Mixing (~ hrs)

Part

Curing (~ hrs) Therm

al History

Final Vulcanized Part

Chemical Environment

Deformational Environment

Thermal Environment

Application (~ yrs)

Given the Desired Property/Performance of

Interest, what is the Optimal Rubber Formulation?

Problem Definition

Rubber Formulation


Rubber

Retarder

Filler

AntidegradantsOilsSulfur

Which materials to include?

How much of them to include?

What should be the processing conditions?


What are Sulfur-Vulcanized Elastomers?

Rubber Formulation


Rubber

Retarder

Filler


Accelerated Sulfur Vulcanization

SS S

S

Vulcanization

+ S8

School of Chemical Engineering, Purdue UniversityAIChE Annual Meeting, Reno 2001

OBJECTIVE OF THIS WORK

• Understand the Mechanistic Details of Accelerated-Sulfur-Vulcanization.

• Provide a Mathematical Description of the Kinetics of Accelerated-Sulfur Vulcanization consistent with Mechanistic Chemistry

Rubber Formulation

Accelerator Activator Retarder

Rubber Filler

Sulfur Oils Antidegradants

NC

SS N O

NR

ZnO/Stearic-Acid

BenzothiazoleSulfenamide

S8


COMPLEXITY OF VULCANIZATION REACTIONS

W.Scheele (1956) 1 Perhaps no-where in chemistry is there encountered a field which even in its literature alone shows so many uncertainties and (possibly only apparent) contradictions as that of the vulcanization of rubber.

L.Bateman (1963) 2 Whilst it has long been appreciated, albeit intuitively, that sulfur vulcanization is a very complex chemical process, the actual complexity as revealed in the studies described above is probably far in excess of what has ever been envisaged.

1W. Scheele, O. Lorenz and W. Dummer, Rubber Chemistry and Technology, 29, 1 (1956)

2 L. Bateman, C.G. Moore, M. Porter and B. Saville, “The Chemistry and Physics of Rubber-Like Substances”, L Bateman, Ed., Maclaren & Sons Ltd., London, 1963, pp 449.

P.J. Nieuwenhuizen (1997) 3 It must be considered remarkable that despite all the effortsand progress in the field of vulcanization during the past decade, one has to conclude that the statements of Scheele and Bateman, made 30 to 40 years ago, are still true to a great extent.

3 P.J. Nieuwenhuizen, Rubber Reviews, Rubber Chemistry and Technology, 29, 70 (1997)


SCHEMATIC OF A VULCANIZATION CURVE

Temporal Evolution of Crosslinks

Time

0

Con

cent

ratio

n of

Cro

sslin

ks, ν

Curing Phase

Reversion Phase

Induction Phase

A SS

SS

S

S S S

Time Scale ~YearsTime Scale ~ Hrs


CAMD Sub-Problems

Structure Space

Pro

perty

INVERSE PROBLEM(Given Properties, Predict

Structure/Formulation)

Properties/ Performance( P1, P2, ……..PN )

FORWARD PROBLEM(Given Structure, PredictProperties/Performance)

Material Structure/Formulation

NeuralNetwork

Hybrid Models

Fundamental Models


THE

OV

ERA

LL F

OR

WA

RD

MO

DEL




Engine


Mixing+

Heat Transfer+

Mold Filling

Part Manufacturing

Overcure

Undercure

Manufac-turing

Process

MaterialFormulation

Ax + S8k1⎯ →⎯⎯ Ax+8

Ax + R k2⎯ →⎯⎯ Bx


*

etc.Time

Torque Cure Curve


T̃ = 2ρR∂ ψ∂I 1

+ I 1∂ ψ∂I 2

⎧⎨⎩

⎫⎬⎭

I −∂ ψ∂I 2

C + I 3∂ ψ∂I 3

C−1⎡

⎣⎢⎤

⎦⎥••∂ C∂C

Constitutive Model



PartShapeDesign

QuantumChemistry

SC

N S SS

SS

S

S

S

Zn

NewMolecules


Accelerator Activator+

Active Accelerator Complex

S8

Active Sulfurating Agent

Rubber Bound Intermediate(Crosslink Precursor)

Rubber Bound persulfenyl radical

Polysulfidic crosslinks

Aged Network

DesulfurationDegradation

NC

SS Sx S C

S

NAx

Bx

C

C

CH Sx S CS

N

Bx•

C

C

CH Sx*

Vux

C

C

CH Sx C

C

C

NC

SS N O (ZnO + Stearic Acid)

2-morpholinothiobenzothiazole

Schematic of a Vulcanization Curve


Accelerator Activator+

Active Accelerator Complex

S8

Active Sulfurating Agent

NC

SBt =

BtS-NR2 BtSH + R2NH

BtS-NR2 + BtSH BtSSBt + R2NH

BtS-SBt + S8 BtS-S-SBt + S7 BtS-S2-SBt + S6 •••

BtS-Sx-SBt + BtS-Sy-SBt BtS-Sz-SBt + BtS-Sw-SBt

NC

SS Sx S C

S

N

NC

SS N O

NC

SS Sx S

NC

SZn

L

L

Without Activator With Activator

Ax = BtS-Sx-SBt

Accelerator Chemistry

BtS-SBt + S8 BtS-S8-SBt


CROSSLINKING CHEMISTRY (I)

Rubber Bound Intermediate(Crosslink Precursor)

Active Sulfurating AgentN

CS

S Sx S CS

N

CH

HC

C

CH

3

H

S

N C

S

S

N C

S

x S

S

CH

C CH

S

S

x

N

C

S S

+

N C

S

S

H

N C

S

SH

(R.34)

C

C

CH Sx S CS

N

Ax Bx

Rubber

Crosslinking Chemistry (I)


Rubber, RH

BtS•

S8S8

S7RS-Sy+1

•

RS-Sy+8•

S8

S8

S7Bt Sz+1•S8

S8

(Regene ra tio n o f

S ul fu rat in g Sp ec ie s)

Bt Sz+8•

+ Bt-SH

+ Bt-Sz•

Crosslink PrecursorRSx –SBt, RSx-Zn-SBt

Crosslink PrecursorRSx –SBt, RSx-Zn-SBt

CrosslinksRSSy -RCrosslinksRSSy -R

Rubber, RH

Sulfurating SpeciesBtS-Sx-SBt, BtS-Zn-Sx-SBt

Sulfurating SpeciesBtS-Sx-SBt, BtS-Zn-Sx-SBt

Persulfenyl RadicalRS-Sy

•Persulfenyl RadicalRS-Sy

•

Rubber, RH Bt Sz+2•

Rubber, RH

RS-Sy

Cyclic SulfideBtSZnSBt

Main- Chain Modification, Conjugated Dienes/Trienes, Inactive thiols

RSSy-1R + BtSZnSSBt

(Desulfuration) (Degradation)

ZnOBtSZnSBt

BtS-ZnSx-SBt

(Scorch Delay)

CDB + Pthalimide (Retarder Action)

S8… S7 S8BtS-SBt

BtSNR2

BtSSSBtBtSSxSBt BtSS8SBtBtS-SBt BtSSxSBt

+ BtSSySBt

BtS-SBtBtSSxSBt + BtSSySBt

+ CTP-R2NH

Lumped S8 Pickup

Sequential S8 Pickup

Both

Mechanisms

BtSH 820 Reactions, 107 Species


Equations for MBTS and other sulfurating species

[ ]

{ } { }{ } { }{ }{ }{ }{ }{ }{ }{ }⎥

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

++++++

++++++++++++

++++++++++

++++++++

++++++

++++++

+−+−−

−−−−=

∑∑

∑

=

∗

=

∗

=

278695104113122131

768594103112121

26758493102111

65748392101

2564738291

54637281

24536271

4352612

34251

32412

231212

1

A-A

16

2rr0DESULF

20E-E

16

1rr0BST-A0R-A

80S-A

14

2rr0A-AMBT-MBSMBS0

]A[5.0]A][A[]A][[A]A][[A ]][A[A]][A[A]][A[A2

]A][A[]A][[A]A][[A ]][A[A]][A[A]][A[A2]A[5.0]A][[A]A][[A ]][A[A]][A[A]][A[A2

]A][A[]A][[A ]][A[A]][A[A]][A[A2]A[5.0]A][[A ]][A[A]][A[A]][A[A2

]A][[A ]][A[A]][A[A]][A[A2]0.5[A ]][A[A]][A[A]][A[A2

]][A[A]][A[A]][A[A2][A5.0]][A[A]][A[A2

]][A[A]][A[A2][A5.0]][A[A2 ]][A[A2][A

k

Vu][Ak][Ek.50B][Ak][Ak

][S][AkA1)(r][Ak[MBS][MBT]k[MBS]kAdtd

][E][EkA][A2k

Vu][AkA][A2k][S][Ak][A2k][Adtd

10E-E

13

1rr1A-A

16

2rr0DESULF

14

2rr0A-A81S-A1R-A1

∗∗

=

==

+−

++−−=

∑

∑∑

POPULATION BALANCE EQUATIONS


POPULATION BALANCE EQUATIONS

[ ] ⎥⎦

⎤⎢⎣

⎡+−−−= ∑

=

16

1ii0R114A81A31C11 Vu][Ak]A[]MBTS[k2]S[][Ak][Ak2A

dtd

[ ] [ ][ ] ][AkA1)(i][Ak][S][AkMBSMBTkAdtd

0C1

14

2ii0A480A3A20 −⎥⎦

⎤⎢⎣

⎡−−−= ∑

=

⎥⎦

⎤⎢⎣

⎡−⎥

⎦

⎤⎢⎣

⎡− ∑∑

==

16

1ii01R

16

1ii0C4 Vu]A[k*B][Ak

[ ]⎩⎨⎧

>≤≤

++−⎩⎨⎧

>≤≤

−−=7i]S[6i2,0

]A[k]A[][Ak1)(i7i,0

6i2],S[]A[k ][Ak2A

dtd

8i3Ai0A4

8i3AiC1i


Equations for Crosslink Precursors

[ ] )*][Ek][MBTSk(Bdtd

1C7C10 +=

[ ] *][Ek]B[k)1i(][Ak2*]B][A[kBdtd

1iC7i2CiC1i0A4i ++−−+−=


[ ]

[ ]

jconcanditimeatPointDataalExperiment

ConstantsRate

cdtdts

kkkk

ji

P

q

i

m

j ji

jiji

=

=≥

=

=⎥⎥

⎦

⎤

⎢⎢

⎣

⎡ −∑∑= =

exp,

321

2

1 1exp,

exp,,

k

k0k

)k,,(

..

......,,k,)k(

min

ν

νφν

ν

νν

m time points, q concentrations

RATE-CONSTANT DETERMINATION

FACTS

Total of 820 different reactions 107 Coupled Ordinary Nonlinear Differential Equations9 Optimizable Rate Constants


B2•

Example Writing Population Balance Equations

kB

C

C

HC S S C

S

N

S

S * C

S

N

+

C

C

CH S 2*

+

C

C

CH S*

* C

S

N

SS

kA

B2

E•

E2•

Potential Breaking Sites

B•

[ ] ( )[ ]

[ ] [ ] [ ] [ ]

[ ] [ ] [ ] [ ]2B22B

2A2A2

B0BB

A0AA2BA2

BkEdtd,BkB

dtd

BkEdtd,BkB

dtd

RTEexpkk,

RTEexpkk,BkkB

dtd

==

==

⎟⎠⎞

⎜⎝⎛−=⎟

⎠⎞

⎜⎝⎛−=+−=

••

••



Population Balance Equations

[ ]

y

13

1x

x13

1yxA-A

16

2rr0DESULF

20E-E

16

1rr0BST-A0R-A

8

1yy0S-A

14

2rr0A-AMBTMBS-0

AAk

Vu][Ak][Ek21B][Ak ][Ak

][S][AkA1)(r][Ak[MBS][MBT]kAdtd

∑∑

∑∑

∑∑

=

−

=

=

∗

=

∗

==

+

−+−−

−−−=

][E][EkA][Ak2

Vu][AkA][A2k][S)][A - ][A(k][A2k][Adtd

10E-E

13

1rr1A-A

16

2rr0DESULF

14

2rr0A-A

8

1 y y01S-A1R-A1

∗∗

=

===

+−

++−−=

∑

∑∑∑

]A][[Ak

][E][EkA][Ak2]][A[Ak1)(x

A][A2k][S)][A- ][A(k][A2k][Adtd

r-x

1-x

1rrA-A

x0E-E

x14

1rrxA-Ax0A-A

14

1xrr0A-A

8

1yy1-xxS-AxR-Ax

∑

∑

∑∑

=

∗∗−

=

+==

+

+−−−

+−−=

x = 0

x = 1

2 ≤ x ≤ 13


Final Set of Population Balance Equations

( )

( )

( )

( )

( )( )

( )⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

∗

∗

∗

∗

∗

EBxBxAxkkkkfAxkf

SAkf

VuBxkkf

BxBxAxkkkf

BxBxAxkkkf

Axkkkkf

EMBT

S

Vu

Bx

Bx

Ax

xx

,,,,,,,,

,,...

,,,...

,,,,,...

,,,,,...

,,,,...

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

5251427

16

80015

634

4323

4212

4102011

8

ddt Initial Conditions:

Ax(>0)(0) = Bx(0) = B*x(0) = Vux(0) = MBT(0) = E(0) = 0

A0(0) = [MBS]0 S8(0) = [Sulfur]0

Most simple kinetic model that explains all the important features of sulfur vulcanization.

Total of 820 different reactions considered with 107 coupled ordinary nonlinear differential equations and 9 optimizable rate-constants.


Population Balance Model - Predictions

Open Symbols = Experimental DataSolid Line = Model PredictionsOpen Symbols = Experimental DataSolid Line = Model Predictions

T = 330 FT = 330 F

Effect of Accelerator and Sulfur

(1.0, 4.0)(0.5, 4.0)

(0.5, 2.0)

+ (1.0, 2.0)

(0.75, 2.0)x

Legend


Population Balance Model – Different Temperatures

T = 310 FT = 310 F T = 298 FT = 298 F

Open Symbols = Experimental DataSolid Line = Model PredictionsOpen Symbols = Experimental DataSolid Line = Model Predictions


QuantumChemistry

T̃ = 2ρR∂ ψ∂I 1

+ I 1∂ ψ∂I 2

⎧⎨⎩

⎫⎬⎭

I −∂ ψ∂I 2

C + I 3∂ ψ∂I 3

C−1⎡

⎣⎢⎤

⎦⎥••∂ C∂C

Constitutive Model



Ax + S8k1⎯ →⎯⎯ Ax+8

Ax + R k2⎯ →⎯⎯ Bx


*

etc.Time

To rq u eCure Curve


Mixing+

Heat Transfer+

Mold Filling

Part Manufacturing

Overcure

Undercure

SC

N S SS

SS

S

S

S

Zn

NewMolecules

MaterialFormulation

Manufac-turing

Process

PartShapeDesign




Engine


THE

CA

TER

PILL

AR

GR

AN

D C

HA

LLEN

GE


Spatial Profile of the State-of-Cure for theThermal History in the Mold

T he r

mal P

r of ile

85-87

89-91

91-93

93-95

95-97

> 99

97-99

87-89

Cur e

Pro

file

Actual Part Design


Result Summary Vulcanization

Vulcanization Chemistry

MathematicalQuantification

Insights into Actual Part Design

Mechanistic Evaluation

• Evaluated all possiblemechanisms critically for accelerated sulfur vulcanization

• Identified the simplest set of reactions that describe all the important aspects of cure.

• Developed Population Balance Model based on mechanistic details to describe the different aspects of cure.

• Single set of parameters that predicts cure details for all formulations at all temperatures.

• Model extended for retarders, filled systems and other accelerator and elastomer classes.

• Incorporation of PopulationBalance model with a finiteelement code to predict spatial cure profile.

• Identification of undercuredand overcured regionsvisually.


QuantumChemistry

T̃ = 2ρR∂ ψ∂I 1

+ I 1∂ ψ∂I 2

⎧⎨⎩

⎫⎬⎭

I −∂ ψ∂I 2

C + I 3∂ ψ∂I 3

C−1⎡

⎣⎢⎤

⎦⎥••∂ C∂C

Constitutive Model



Ax + S8k1⎯ →⎯⎯ Ax+8

Ax + R k2⎯ →⎯⎯ Bx


*

etc.Time

To rq u eCure Curve


Mixing+

Heat Transfer+

Mold Filling

Part Manufacturing

Overcure

Undercure

SC

N S SS

SS

S

S

S

Zn

NewMolecules

MaterialFormulation

Manufac-turing

Process

PartShapeDesign




Engine


THE

OV

ERA

LL F

OR

WA

RD

MO

DEL


CAMD Framework

The solution of INVERSE PROBLEM involves searching for the optimal rubber formulation that has the desired macroscopic performance.

Prediction

P1 P2 P3 ... Pn

Structure or Formulation Product Performance

Design

Inverse Problem

Prediction

P1 P2 P3 ... Pn

Structure or Formulation

Design

Inverse Problem

Forward Problem

RubberAcceleratorSulfurActivatorFillerRetarder

Cure-StateModulusStress-StrainStiffness


Genetic Algorithms (GA)

GAs are stochastic evolutionary search procedures based on the Darwinian model of natural selection


Fitn

ess

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−

−−= ∑

2

mini,maxi,

desi,i

PPPP

(F)Fitness αexp

Initial Population (random)

Formulation = [1 4 0.1 30 330]



Fitn

ess

“ Survival of the fittest ”

New Population

Evolution

Genetic Algorithms (GA, contd)

Operators


Formulation Representation

Binary Representation

Rubber Formulation


Rubber

Retarder

Filler


Rubber Formulation

Accelerator ActivatorAccelerator Activator

Rubber

Retarder

Rubber

Retarder

FillerFiller

AntidegradantsOilsSulfur AntidegradantsOilsSulfurSulfur

0 01 1 •• •1 0 01 1

Phr of Different Ingredients


Genetic Operators

Parent 1 Parent 2

Offspring 1 Offspring 2

0 01 1 10 0 01 1 1 01 1 01 0 01 0

0 01 1 0 1 00 00 1 01 1 1 1 10 01

0 01 1 10 0 01 1 1 01 1 01 0 01 0

0 01 1 0 1 00 000 01 1 0 10 01 1 0 1 00 00 00 00 1 01 1 1 1 10 011 01 1 1 1 10 01 10 01

Formulation

Fitn

ess

Crossover

0 01 1 10 0 01 1

1 01 1 10 0 01 1

0 01 1 10 0 01 1

1 01 1 10 0 01 1

Mutation


Tmax (time to reach max cure) = 16 min

Vumax (crosslink @ Tmax) = 71.5 mol/m3

Stress (100% Elongation) = 0.92 MPa

Stress (200% Elongation) = 1.65 MPa

Optimal FormulationsDesired Property

Inverse Problem (Results)

• Binary Representation

• Fitness Proportionate Selection

• Crossover Probability = 0.8, Mutation Probability = 0.2

• Population Size = 40, Number of Generations = 40, Elitism = 10%

[1.75 1.25 0.05 0 315]

[0.50 4.00 0.10 0 310]

[1.75 1.50 0.05 0 310]

[0.75 2.75 0.10 0 315]

[3.00 0.75 0.10 0 315]

[2.75 1.00 0.25 0 330]

0.9999

0.9999

0.9996

0.9994

0.9991

0.9990

15

16

17

13

17.5

10.5

69.92

71.57

75.75

67.88

65.34

70.46

0.91

0.92

0.97

0.88

0.85

0.93

1.63

1.65

1.75

1.58

1.52

1.67

Formulation Fitness Tmax Vumax σ100 σ200

Example 2


[1.75 1.25 0.05 0 315]

[0.50 4.00 0.10 0 310]

[1.75 1.50 0.05 0 310]

[0.75 2.75 0.10 0 315]

[3.00 0.75 0.10 0 315]

[2.75 1.00 0.25 0 330]

0.9999

0.9999

0.9996

0.9994

0.9991

0.9990

15

16

17

13

17.5

10.5

69.92

71.57

75.75

67.88

65.34

70.46

0.91

0.92

0.97

0.88

0.85

0.93

1.63

1.65

1.75

1.58

1.52

1.67

Formulation Fitness Tmax Vumax σ100 σ200

0 10 20 30 40 50 600

10

20

30

40

50

60

70

80

1

2

3

Time, min

Con

cent

ratio

n of

Cro

sslin

ks, m

ol/m

3

New Formulations

BEST THREE FORMULATIONS

Solution Found in 24th generation.

i.e.only 960 out of a total of 131072 formulations were searched

~ 0.73 %


Interactive Software Used At Caterpillar on a Daily Basis

10/11/2005

1

Pharmaceutical Product Development and Engineering

• Two ProductsDrugsDocuments

Preliminary product recipe

Drug is converted into ParticlesDrug Synthesis

Raw Chemicals

Formulation

Process Development

Preliminary process recipe

Scale/up -Tech Transfer

Adjusted process recipe

Manufacturing

A Delayed Product


LIPS

• Prescription drug recalls• 176 in 1998• 248 in 2001• 354 in 2002

• Schering-Plough Corp. recalled 59 million asthma inhalers in 1999 and 2000 -- unknown number were shipped empty.•Semiconductor Manufacture 6 σ•Chemicals 5 to 5.5 σ•Pharma 2.5 σ


LIPS

Pharma Industry’s Scale-up Challenge

engineering

pharmaceutical

4

Purdue Ontology for Pharmaceutical Engineering (POPE)

Information

Deci

sion

tree

s an

d he

uris

tics

Mathem

atical models

ModLABOntoMODEL


LIPS

Ontologies Developed So Far in Our ProjectEquipment ontology

Standards referenced: STEP, AP231, FIATECHGeneral recipe ontology

RecipeElement, UnitProcedure, Operation etc. Standards referenced: ISA S88, S95, OntoCAPE

Process safety ontologyDeviation, Cause, Consequence etc.

Material ontology for pharmaceutical product developmentFlow property, Angle_of_Fall, Carrs_Index etc.

Reaction mechanism ontologyMolecule, Atom, Bond, Reaction etc. Referenced: Chemistry Development Kit

Model ontologyGuideline ontology

Referenced: GuideLine Interchange Format

Venkat Venkatasubramanian, PSWC, April 2007, Amsterdam 6

LIPS

Material Property Ontology in Protégé

Venkat Venkatasubramanian, PSWC, April 2007, Amsterdam 7

LIPS

Experiment Ontology

Experiment Data Files

Experimental Methods Details


LIPS

Guideline Ontology for Dosage Form Formulation

Follows GLIF (Guideline Interchange Format), A standard ontology for clinical guidelines

9

Model Ontology


SuperModel

Model Container Model Container

Model Model

hasModelContainers

hasModel hasModelhasModelIndex hasModelIndex

Equation

Partial Differential

Integral

Algebraic

DAE

Function Evaluation

Assumptions

Universal Constants Dependent Var Independent Var Model Parameters

Variable Link

Variable

Variable

Simple Variable

Array Variable

SizeOfListVariable

Link

hasInitialGuess

hasVar PointsToValue

PointsToValuehasVar

hasEqn

hasAssumptions

hasUnivConstants hasDepVar hasIndepVar hasModelParms

hasVar

hasSymbol

hasML

Text Input


LIPS

Integrated Model-based Decision SupportRecipe Process Information Repository

Material Form in XForms Recipe Network

Used by PHASuite

Used by Batches/Batch+


LIPS

Integrating with Mathematical Knowledge

User created model instance

Model Ontology Equations in MathML

• Variables linked through URI

Process Description (instances of Process Ontology)

Automatically generated Mathematica statements

Interface

Mathematica Notebook

Access ontology instances

Mathem

atica K

ernel

Rich ClientWeb Applications

13

Literature Experiments

Experiment Report Data

Intelligent Systems for PreformulationFormulationProcess Monitoring and Control

Tools for Organic Solids Mfg.Optimization, Simulation, Safety Analysis, Scheduling

Multiscale models for synthesis mehtods

Modeling and Analysis Crystalline Structure

Unit Operation modelsDEM/CFD/FEM

Process modelingFirst Principles Process Model

Organic composites:Physical, chemical, and powder

properties

Equipment: blender, tabletting press, roller compactor, fluid bed

Process:Crystallization, Granulation, Drying,

Size Reduction etc.

Knowledgerelationships

Systematic functionalization

Control methodology for spatial structure of organic composites

Material synthesis method development

Determine structure-function-performance relationships

Instruments

Cyberinfrastructure for Real-time Decision Support for Design, Control, and Optimization

Dissolution Problems

Spatial Structure

Process Monitoring and Control

Tools for Design and Manufacturing

Modeling

User

Ontological Informatics Infrastructure

Material Science

Experiments

Process

DEM

Experiment Report Physical PropertiesPowder Properties

eLabNotebookBlender

Literature Experiments

Experiment Report Data

Intelligent Systems for PreformulationFormulationProcess Monitoring and Control

Tools for Organic Solids Mfg.Optimization, Simulation, Safety Analysis, Scheduling

Multiscale models for synthesis mehtods

Modeling and Analysis Crystalline Structure

Unit Operation modelsDEM/CFD/FEM

Process modelingFirst Principles Process Model

Organic composites:Physical, chemical, and powder

properties

Equipment: blender, tabletting press, roller compactor, fluid bed

Process:Crystallization, Granulation, Drying,

Size Reduction etc.

Knowledgerelationships

Systematic functionalization

Control methodology for spatial structure of organic composites

Material synthesis method development

Determine structure-function-performance relationships

Instruments

Tools for Design and Manufacturing

Modeling

User

Ontological Informatics Infrastructure

Material Science

Experiments


LIPS

SummaryReviewed Modeling and Informatics Challenges in Molecular Products Design and EngineeringNeed for Cyberinfrastructure Concepts, Methods, and ToolsOntological approach for information and knowledge modeling

Beyond ERP, SAP, Oracle, Expert Systems etc.This is not just programming! Nor can it be done by CS folks alone!

POPE: Purdue Ontology for Pharmaceutical EngineeringConceptual foundation for next the generation, integrated, decision support tools environment

This is only a beginning….Miles to go before we sleep….Huge opportunities for Process/Product Systems Engineers

15

Thank You for Your Attention!

Any Questions?

Cyberinfrastructure-enabled Molecular Products Design...

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