ACS MeetingAugust 2007

Structure and Properties of Polyethylene Nanofibers from Molecular Dynamics Simulations

Sezen Curgul, Krystyn J. Van Vliet, Greg C. Rutledge*

Department of Materials Science and Engineering*Department of Chemical Engineering

Massachusetts Institute of Technology

Introduction

Electrospinning: A versatile method to produce fibers with diameters in the nano range

Advantages Small diameters (10 nm-10 mm) High surface area (1-100 m2/g) High porosity (ca. 90%) Small fiber-to-fiber distance

Motivation

Numerous applications postulated for nanofibers, but little fundamental investigation of the nanofiber properties

Difficulty of characterization on the nanoscale

Life science applications• Drug delivery carrier• Haemostatic devices• Wound dressing

Cosmetic skin masks• Skin cleansing• Skin healing• Skin therapy

Military protection clothing• Minimal impedance to air• Trapping aerosols• Anti-bio / -chemical gases

Nanosensors• Thermal sensor• Piezoelectric sensor• Biochemical sensor• Florescence chemical sensor

Industrial applications (electronic/optical)• Micro/nano electronic devices• Electrostatic dissipation• Electromagnetic interference shielding• Photovoltaic devices (nano-solar cell)• LCD devices• Higher efficiency catalyst carriers

Tissue engineering scaffolds• Membranes for skin• Tubes for blood vessels• 3D scaffolds for bone and cartilage regeneration

Filtration media• Liquid filtration• Gas filtration• Molecular filtration

Polymer nanofibers

Burger C, Hsiao BS, Chu B, Annu. Rev. Mater. Res. 2006, 36, 333

Objectives Evaluate the fiber properties (including structural,

mechanical, thermal) at the molecular level as a function of fiber size

Understand the origin of transition from bulk-like behavior to nanomaterial behavior: How small is “nano”?

Approach Constructing the simulation

Step I: Equilibrium simulation in bulk using Periodic Boundary Conditions

Step II: Increase box size in 2 directions. The system remains periodic only in Z-dimension

x

y

z

Molecular Dynamics Simulation

Polyethylene: the prototypical chain-like molecule (C50-C300)

Total system size: 200 to 150,000 C atoms

Compute engine: LAMMPS from Sandia National Laboratory

Structural characterization NVT ensemble, 495 K

Radial density profiles Radial density profile is

obtained by:

Where

Fiber radius calculated by Gibbs dividing surface method

z

0 2 4 6 8 10 12 14 16 180.0

0.2

0.4

0.6

0.8

De

nsi

ty (

g/c

m3 )

Distance from fiber center (nm)

1000 x C150 1000 x C100 500 x C100 150 x C100 50 x C100 20 x C150 15 x C100 3 x C200

GDS

0.75

2n r

rr L

1

r rN

ii r

n r r r dr

0

02 rdrrrr GDSstep

Diameters from 2.0 to 23 nm

Interfacial thickness: Distance over which density decreases from 90% of its bulk value to 10%:~ 0.78-1.39 nm

Increases slightly with fiber size*

*Manuscript submitted to Macromolecules

Interfacial Excess Energy Gibbs Dividing Surface applied

to energy profile Calculate interfacial excess

energy

Eint=0.022±0.002 J/m2

(similar to thin film PE simulations1 and experiments2)

Eint NOT dependent on fiber size*

0 2 4 6 8 10 12 14 160

100

200

300

400

500

600

700

800

En

erg

y d

en

sity

(J/

cm3 )

Distance from fiber center (nm)

1000 x C150 1000 x C100 500 x C100 150 x C100 50 x C100 20 x C150 15 x C100 3 x C200

LrEEE GDSGDStotalint 2

Etotal 2L E r rdr0

LrEE GDScoreGDS2

0.0 0.5 1.0 1.5 2.0 2.50

200

400

600

800

En

erg

y d

en

sity

(J/

cm3 )

Distance from fiber center (nm)

4xC50 4xC100 10xC50 3xC200 2xC300 4xC150 6xC100 12xC50

0 2 4 6 8 10 12

560

580

600

620

640

E

core

(J/c

m3 )

Rfiber

(nm)

1He D,Reneker DH, Mattice WL, Comp. Th. Poly. Sci.. 1997, 7, 19

2Polymer Handbook, Wiley 1999, 4th edition.

Ecore dependson fiber size!!!

*Manuscript submitted to Macromolecules

Molecular Conformations

Measure of chain size: Radius of gyration

Chains are confined*

Confinement increases as Fiber size decreases Molecular weight increases Effect notable up to 2-4xRg

0 1 2 3 4 5 6 70.4

0.6

0.8

1.0

Rfiber

/Rg,bulk

Rg/

Rg

,bu

lk

C50 C100 C150

*Manuscript submitted to Macromolecules

Glass Transition Temperature (Tg)

Determination Slow cooling (effective rate =1.97x1010 K/s)

from 495 K down to 100 K Re-equilibrate at several temperatures to

determine fiber radius and core density vs T*

*Manuscript submitted to Macromolecules

150 200 250 300 350 400 450 500

0.75

0.80

0.85

0.90

0.95

30 x C150

De

nsi

ty (

g/c

m3 )

Temperature (K)

150 200 250 300 350 400 450 5002.75

2.80

2.85

2.90

2.95

3.00

3.05

3.10

30 x C150

Rfib

er (n

m)

Temperature (K)

Tg

Fiber vs film Tg’s

Tg depends significantly on fiber radius or thin film thickness

Observed in amorphous thin films experimentally and theoretically1-4

Tg more depressed for nanofiber than the thin film*

0.5 1.0 1.5 2.0 2.5 3.0

100

120

140

160

180

200

220

240

260

FIBER THIN FILM

Tg

(K

)

Rfiber

, h1/2

(nm)

1 Keddie JL, Jones RAL,Cory RA Europhysics Letters 1994, 27, 59

2Fukao K, Miyamoto Y, Phys.Review E 2000, 61, 1743

3Ellison CJ, Torkelson JM, Nature Materials 2003, 2, 695

4Fryer DS, Nealy PF,de Pablo J, J.Journal of Vac. Sci. Tech 2000, 18, 3376 *Manuscript submitted to Macromolecules

Modeling of Tg depression in nanofibers

Layer model1: A volume-averaged formulation for thin films

Derivation of formula for nanofibers*: Surface material with thickness ξ(T)

and Tg=Tg,surf

Core material with Tg=Tg,bulk

1Forrest JA, Mattsson J, Phys Rev. E., 2000, 61, R53.*Manuscript submitted to Macromolecules

2

, , ,

2 g g

g g bulk g bulk g surf

T TT T T T

R R

, , ,1 2

g

g g bulk g bulk g surf

TT T T T

h

ξ, Tg=Tg,surf

ξ, Tg=Tg,surf

Tg=Tg,bulk

Tg=Tg,bulk

Cooperativity Length Scale Cooperativity length scale ξ(T) with

decreasing temperature is given by

where Tref=Tg,bulk=280 K1

Thin film*: Tg,surf=155±5K ξ (Tg,bulk) = 0.45 ± 0.18 nm

Nanofiber* Tg,surf=150±7K ξ (Tg,bulk) = 0.35 ± 0.2 nm

Statistically indifferent ξ in nanofibers and thin films

Single ξ~ 4nm regardless of geometry, compared to CRR=0.46 nm2

0.5 1.0 1.5 2.0 2.5 3.0

80

120

160

200

240

280

FILM FIBER

Tg

(K)

R, h1/2

(nm)

ref refT T T T

1Capaldi FM, Boyce MC,Rutledge GC, Polymer., 2004, 45, 1391.

2Solunov CA, European Polymer Journal, 1999, 35, 1543.

120 160 200 240 2800.0

0.2

0.4

0.6

0.8

1.0

1.2

(n

m)

Temperature (K)

FILM FIBER

*Manuscript submitted to Macromolecules

Molecular Weight Dependence of Tg

3 different molecular weights (MW)

C150, MW = 2100 g/mol C100, MW = 1400 g/mol C50, MW = 700 g/mol

Depression in Tg NOT DEPENDENT on Molecular Weight

Agreement with amorphous thin polymer films of low to moderate molecular weight

Layer theory VALID for this molecular weight range

0.5 1.0 1.5 2.0 2.5 3.0

100

120

140

160

180

200

220

240

260

280

C50 C100 C150

Tg

(K)

Fiber radius (nm)

Mechanical Properties Determination of Young’s

modulus (E)

Apply constant strain rate up to a predetermined strain along the long axis of the fiber (compression and tension, small elongation ±5%)

Noise in stress data, stress is averaged for several different initial configurations using weighted least squares method

Calculate Young’s modulus as initial slope to stress-strain curve

-0.06 -0.04 -0.02 0.00 0.02 0.04 0.06-80

-60

-40

-20

0

20

40

60

30 x C150

Szz

_a

vera

ge

(M

Pa

)

Strain

Displacement rate = 0.049 m/sec Fiber diameter = 6.148 nm

Dependence of E on fiber radius

2.0 2.2 2.4 2.6 2.8 3.0 3.2

600

700

800

900

1000

1100

1200

1300

1400

1500

0.08 m/sec 0.04 m/sec 0.02 m/sec 0.01 m/sec

Mod

ulus

(M

Pa)

Rfiber (nm)

2.0 2.2 2.4 2.6 2.8 3.0 3.2

700

800

900

1000

1100

1200

0.08 m/sec 0.04 m/sec 0.02 m/sec 0.01 m/sec

Mod

ulus

(M

Pa)

Rfiber (nm)

Simulation temperatures: Well below Tg

Modulus decreases with decreasing fiber size at 150K and 100K

Similar results found in experimental studies of thin films1

150 K

100 K

1Stafford CM, Vogt BD,Harrison C, Julthongpiput D, Huang R Macromolecules, 2006, 39, 5095.

Strain rate vs. Temperature Modulus decrease due to the action of relaxation processes which

Speed up at high temperature Rendered irrelevant by high strain rates

Surface relaxations faster than bulk (Small fibers are more “surface” than bulk) Small fibers: Temperature effect wins (despite high strain rates) Large fibers: Temperature competing against high strain rates

100 110 120 130 140 150

600

675

750

825

900

975

1050

1125

1200

1275

1350

1425

15xC100 30xC100 30xC150

Mod

ulus

(MP

a)

Temperature (K)

90 100 110 120 130 140 150 160500

600

700

800

900

1000

1100

1200

1300

15xC100 30xC100 30xC150

Mod

ulus

(M

Pa)

Temperature (K)

100 110 120 130 140 150500

600

700

800

900

1000

1100

1200

1300

15xC100 30xC100 30xC150

Mod

ulus

(M

Pa)

Temperature (K)

100 110 120 130 140 150500

600

700

800

900

1000

1100

1200

15xC100 30xC100 30xC150

Mod

ulus

(M

Pa)

Temperature (K)

Strain rate decreasing

8x 1x2x4x

Conclusions Structural characterization

Bulk-like behavior at center Confined chains towards the surface No dependence of interfacial excess energy on fiber size

Thermal characterization Tg depression as fiber size decreases (similar to thin films) Cooperativity length scales with previous literature

Mechanical characterization Young’s modulus decreases as fiber size decreases Temperature and strain rate are competing for large fibers

Acknowledgements

Rutledge and Van Vliet groups at MIT Dupont-MIT Alliance