Molecular Modeling and Engineering of VegetableMolecular Modeling and Engineering of Vegetable--Oil Based LubricantsOil Based Lubricants

Mary Jo Biddy*, Mike J. Mary Jo Biddy*, Mike J. TupyTupy††, John , John CurroCurro**, and Juan J. de Pablo* **, and Juan J. de Pablo*

*Department of Chemical and Biological EngineeringUniversity of Wisconsin – Madison

†Cargill Inc. Wayzatta, MN

** Sandia National LaboratoriesAlbuquerque, NM

Funding Acknowledgements:

- DOE Computational Science Graduate Fellowship- Cargill Inc.

Introduction: Vegetable Oils as LubricantsIntroduction: Vegetable Oils as Lubricants

Alternative to petroleum-based products

Environmentally acceptable lubricants

Use agricultural feed-stockBiodegradableMinimal health and safety risksEasier disposalVegetable oils: corn, soybean, canola, cocoa

Vegetable oil-based lubricants provide improved lubricity compared to petroleum-based products

FairFairThermal stability

Very goodGoodLubricating properties

GoodFairLow volatility

PoorFairOxidation stability

PoorPoorLow T properties

GoodFairViscosity / Temperature

VegetableMineralProperty

AGRI-PureTM

Introduction: Definition of Fatty Acids and TriglyceridesIntroduction: Definition of Fatty Acids and Triglycerides

Oleic acid (O) C18:1

Linolenic acid (Le) C18:3

Stearic acid (S) C18:0

Linoleic acid (Li) C18:2

Palmitic acid (P) C16:0

carbon oxygen hydrogen

Aliphatic groupsGlycerol

backbone Aliphatic groups

Triglyceride Force FieldTriglyceride Force Field• Polar group of TAG: ester linkage• Model molecule: methyl acetate• Force field parameters:

Quantum Mechanics(Gaussian MP2/aug-cc-pVDZ)

φ

ΔE

Θ−Θeq

ΔEΔE

r - req

Intramolecular Potentials

( )2( )

2r

bond eqKU r r r= − ( )2

( )2bend eq

KU r θ θ θ= − ( )3

0

( ) 1 costorsion ii

U r iν φ=

= −⎡ ⎤⎣ ⎦∑

rqq

rrrU '4)(

612

+⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−⎟

⎠⎞

⎜⎝⎛=

σσε

Intermolecular PotentialLennard-Jones plus

Coulomb interactions

Sum, A. K., Biddy, M.J., Tupy, M.J., and de Pablo, J.J., J. Phys. Chem. B 107(51) 14443, December 2003.

Force Field TestingForce Field Testing

ΔH (kJ/mol)ρ (g/cm3)Liquid properties

0.825 / 0.825

0.870 / 0.870

0.886 / 0.895

calc. / exp.

52.2 / ―

48.6 / ―

35.8 / 35.4

calc. / exp.

C17H34O2Methyl palmitate

C13H26O2Methyl laurate

C6H12O2Methyl pentanoate

at 25o C

32.60.934Experimental

30.10.897OPLS

33.50.932This work

ΔH (kJ/mol)ρ (g/cm3)

Methyl Acetate

NERDmethyl acetate

0.8

0.9

1.0

1.1

1.2

0.8 0.9 1.0 1.1 1.2

Experimental Density* [g/cc]

Cal

cula

ted

Den

sity

[g/c

c]Physical Properties of TriglyceridesPhysical Properties of Triglycerides

0.9310.902

80100

TrilinoleninTrilinolenin

0.9300.890

80100

TrilinoleinTrilinolein

ρ (g/cc)T (oC)

OOO

Tripropanoin(20oC)Tributyrin (20oC)

Tricaproin (20oC)

LLL (80oC)SSS (80oC)

OOO (80oC)PPP (80oC)

0.80

0.84

0.88

0.92

0.96

1.00

0 30 60 90 120

Temperature [oC]

Den

sity

[g/c

c]

* Experimental numbers include correlation results

Viscosity PredictionsViscosity Predictions

0

2

4

6

8

10

12

14

16

18

20

0 5 10 15 20

LLL 100oC

LLL 80oC

OOO 100oC SSS 100oC

SSS 80oCPPP 80oC

PPP 100oC

Experimental* Viscosity (cSt)

Cal

cula

ted

Vis

cosi

ty (c

St)

* Experimental numbers include correlation results

Green-Kubo Relation

Simulation Details:

• NVT MD Simulation• 40 molecules• Periodic Boundary

Conditions• Reaction Field Correction

Vegetable Oil Property Predictions: Canola OilsVegetable Oil Property Predictions: Canola Oils

8.4238.3 + 0.9100Mid Oleic

191/20138.9540 + 440

High Oleic

Low Oleic

36 + 5

8.7 + 0.9

37 + 4

9.6 + 0.9

Viscosity (cSt)Simul. Exp.

39.93

8.59

35.56

8.07

165/156

248/213

VISim/Exp

100

Temperature(oC)

40

100

40

These vegetable oils are a combination of the triglycerides OOO, OLiO, OLeO, POO, and SOO

Pour PointPour Point

• Accepted industrial standard• It is the temperature at which an oil no longer

flows• Why is this measurement important?

• The temperature at which oil can be pumped and adequate oil pressure can be maintained in an engine ranges from 5 to 20oC above the pour point.

• The lower the pour point temperature the better

• The typical pour point of a commercial petroleum-based oil formulation is around -35 to -40oC.

Experimental Measurement of Pour PointExperimental Measurement of Pour Point

• A sample of lubricant is chilled in a test jar to a set of defined temperatures.

• At each temperature the test jar is tilted horizontally.• If the fluid does not flow within 5 seconds, then this is

the experimentally determined pour point.• The recorded pour point is 3°C higher than the

experimentally determined point.

Can we use molecular simulations to predict what seems to be a qualitative measurement?

Elastic ConstantsElastic Constants• We have investigated pour points using elastic constants to better

understand oil gel behavior.• The expression for the elastic constant is divided into three parts:1

• Young’s Modulus

Where λ = Cxxyy and μ = Cxyxy

• A typical Young’s Modulus value below Tg:2– 3 GPa for PVC with a Tg of 82oC– 3.3 GPa for Nylon with a Tg of 50oC– 3.3 GPa for PMMA with a Tg of 105oC

STRESSijlm

KINETICijlm

BORNijlmijlm CCCC −+=

1. Yoshimoto, K., Papakonstantopolous, G.J., Lutsko, J.F., and de Pablo, J.J., Phys. Rev. B 71(18) 184108, May 2005.

2. Bower, D. An Introduction to Polymer Physics.3. Gillmore et. al., Journal of Polymer Science Part B, 37(16) 2287, August 1999

μλμ )μ 2λ 3 (E

++

=

Example of StorageModulus of Gelatin near gel point3

-39 -36 -33 -30 -27 -24 -21 -18 -15 -120.1

1

ExperimentalPour Point

-21oC

Temperature (ºC)

You

ng's

Mod

ulus

(GPa

)

Simulation Results─ Guide for the Eye

Low Oleic Canola Oil Pour PointLow Oleic Canola Oil Pour Point

A large increase in the Young’s moduli at the pour point temperature is observed for all of the canola oils.

Pour Point Predictions: Pour Point DepressionPour Point Predictions: Pour Point Depression

• Test pour point of low oleic canola oil in the presence of isobutyl oleate

• Biodegradable pour point depressant

• Experimental Pour point of – 30oC• Force field already developed and

structure already known

• Two concentrations 20% and 60% (w/w) of isobutyl oleate

Asadauskas, S. et. al.; J. Am. Oil. Chem. Soc.1999, 76, 313.

-39 -36 -33 -30 -27 -24 -21 -18 -150.1

1

Pour Point Depression Predictions: Pure DepressantPour Point Depression Predictions: Pure Depressant

Temperature (oC)

You

ng’s

Mod

ulus

(GPa

)

Experimental Pour Point

-30oC

The pour point temperature of the pour point depressant is accurately predicted at -30oC.

-36 -33 -30 -27 -24 -21 -18 -150.01

0.1

1

Pour Point Depression Predictions: 20% w/w DepressantPour Point Depression Predictions: 20% w/w Depressant

Temperature (oC)

You

ng’s

Mod

ulus

(GPa

)

Predicted Pour Point

-24oC

The pour point was lowered by 3oC by adding the pour point depressant.

ExperimentalPour Point of

Low Oleic Canola Oil-21oC

-36 -33 -30 -27 -24 -21 -18 -150.01

0.1

1

Pour Point Depression Predictions: 60% w/w DepressantPour Point Depression Predictions: 60% w/w Depressant

Temperature (oC)

You

ng’s

Mod

ulus

(GPa

)

Predicted Pour Point

-27oC

The pour point temperature is depressed by 6oC by adding a greater amount of depressant.

Experimental Pour Point of

Low Oleic Canola Oil-21oC

Triglycerides Triglycerides –– SelfSelf--Assembly?Assembly?

Ordering of TriglyceridesOrdering of Triglycerides

Carbonyl Carboncharge 0.65

Molecule1

Molecule2

Attraction Carbonyl Oxygencharge -0.5

0 5 10 15 200.0

0.5

1.0

1.5

2.0

2.5

-18°C -27°C -30°C -39°C

Distance (A)

Rad

ial D

istri

butio

n Fu

nctio

nPour Point Prediction of Pure DepressantPour Point Prediction of Pure Depressant

0 1 2 3 40

20

40

60

80

100

120

140

-18°C -27°C -39°C

Time (ns)M

ean

Squa

re D

ispl

acem

ent (

nm2 )

Radial Distribution Function between Head Carbons

Mean Square Displacement of Center of Mass

• Experimental pour point of isobutyl oleate is -30oC• Very little change in structure near this pour point

temperature• A deviation in <r2> suggests a gel is forming• High <r2> values suggest the system is liquid like

Trajectory of Particles for 20% Pour Point DepressantTrajectory of Particles for 20% Pour Point Depressant

Low Oleic Oil Pour Point Depressants

Trajectory of C=O on glycerol backbone

-27oC

Final Trajectory of Pour Point DepressantFinal Trajectory of Pour Point Depressant

Low Oleic Oil Pour Point Depressants

Vegetable Oils: Castor Oil Vegetable Oils: Castor Oil

• Has a long history of being recognized as a lubricant• Is the only vegetable oil with a high content of hydroxyl

fatty acids

Ricinoleic fatty acid

9RRO4RLiLi3ROO

69RRR12RRLi

PercentageTriglyceride

Composition from Firestone, David, Physical and Chemical Characteristics of Oils,Fats and Waxes, (AOCS, Washington DC, 1999).

Vegetable Oil Property Predictions: Castor OilVegetable Oil Property Predictions: Castor Oil

Viscosity Indexsimul. /exp.

Viscosity (cSt)**simul. /exp.

Density (kg/m3)

Temp (oC)

135/91256 + 23/252951 + 440

27 + 2 /19.9924 + 5100

** Triglyceride composition not given for experimental data.

-39 -36 -33 -30 -27 -24 -21 -18 -15 -120.1

1

Castor Oil Pour PointCastor Oil Pour Point

ExperimentalPour Point of Castor Oil is

-27oC

You

ng’s

Mod

ulus

(GPa

)

Temperature (oC)

-39 -36 -33 -30 -27 -24 -21 -18 -15 -120.1

1

Castor Oil Pour Point Castor Oil Pour Point –– no Double Bondno Double Bond

-39 -36 -33 -30 -27 -24 -21 -18 -15 -120.1

1

Predicted Pour Point is

-24oCYou

ng’s

Mod

ulus

(GPa

)Temperature (oC)

Predicted Pour Point is

-27oC

You

ng’s

Mod

ulus

(GPa

)

Temperature (oC)

Pure Castor Oil No Double Bond

-39 -36 -33 -30 -27 -24 -21 -18 -15 -120.1

1

-39 -36 -33 -30 -27 -24 -21 -18 -15 -120.1

1

Castor Oil Pour Point Castor Oil Pour Point –– no Hydroxyl Groupno Hydroxyl Group

Predicted Pour Point is

-18oCYou

ng’s

Mod

ulus

(GPa

)Temperature (oC)

Predicted Pour Point is

-27oC

You

ng’s

Mod

ulus

(GPa

)

Temperature (oC)

Pure Castor Oil No Hydroxyl Group

Current Work: Ordering of Triglycerides in Low Oleic Canola OilCurrent Work: Ordering of Triglycerides in Low Oleic Canola Oil

Carbonyl Carbon and Oxygen Atoms500 molecules

-30oC

0 10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

-3°C -30°C

Rad

ial D

istri

butio

n Fu

nctio

nDistance (A)

Intermolecular Radial Distribution Function between Carbonyl Carbons

**Systems simulated at Sandia National Laboratories using LAMMPS

SummarySummary

• Successfully developed force-field parameters from ab initio calculations

• Accurate force-field for triglycerides and esters

• Good agreement with measured densities and viscosities for both triglycerides and vegetable oils

• Flexible and inexpensive tool for examining different molecular structures

• Accurate modeling method for the prediction of pour points

AcknowledgementsAcknowledgements

• Professor de Pablo• Dr. Mike Tupy• Dr. John Curro• Dr. Amadeu Sum• Yioryos Papakonstantopoulos• Dr. Manolis Doxastakis• de Pablo Group• Sandia National Laboratories for supercomputing work • Funding sources:

DOE CSGF and Cargill

Viscosity Index DefinitionViscosity Index Definition

[ ]

( )Y

UHN

NantiI

logloglog

10000715.0/)1)log((V

−=

+−=

Where:Η is the viscosity of a reference oil with VI of 100 at 40oCwhose viscosity matches the oil at 100oCU is the viscosity of the oil at 40oC Y is the viscosity of the oil at 100oC

Force Field DevelopmentForce Field Development

• Calculate physical properties of methyl acetate

• Use MD NPT to determine density and heat of vaporization

• Long-range correction for reaction field (continuum dielectric constant εRF)

0.053.8350.6253CH3

-0.502.8400.7922O=

0.653.3120.7185C

-0.403.4720.6736-O-

0.203.8300.6347CH3

q (a.u.)σ (Å)ε (kJ/mol)

rqq

rrrU '4)(

612

+⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−⎟

⎠⎞

⎜⎝⎛=

σσεIntermolecular Potential

Lennard-Jones plus Coulomb interactions

Elastic ConstantsElastic Constants• We have investigated pour points using elastic constants

to better understand oil gel behavior.• The expression for the elastic constant is divided into

three parts:

22

2 1 −⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

−∂∂

= rrV

rrVχ

Yoshimoto, K., Papakonstantopolous, GJ, Lutsko, JF, and de Pablo, JJ, Phys. Rev. B 71(18) 184108, May 2005.

[ ] ( )

( ) ( )rqqgqqqqqV

TnkTk

VC

mljio

jniljlimblmijlmijb

oijlm

;,1

2

βααβαβαββα

αβαβχ

δδδδττττ

∑≠

+

++−−=

Stress Fluctuations Kinetic Term

Born Term

where