Functionalizing Surfaces Using Polymers

David TromblyCree, Inc On-siteJanuary 31, 2011

What is a polymer?

Homopolymer

Diblock copolymer

Random copolymer

Outlook for polymers research

Summary

• Applications where polymers are used to modify surfaces

• Modeling of polymers

• Example: drug delivery, design of patterned surfaces

Drug design

drugbloodprotein

uptake byimmunesystem

targetcells

effective drug

delivery!

SupportSupport

Hydrophilic grafts

Water purification

Russo, Macro, 2006

Less dispersed decline in material properties

More dispersed improvement in material properties

Polymer nanocomposites

Semiconductor devices

Equal surface energies

Perpendicular lamellae

High value semiconductor devices

Random copolymer brush

f

A B

f = volume fraction of A

B

A

Modeling of polymers

Muller-Plathe PhysChemPhys 2002

Scaling theories

Does not give spatial dependence of density

Alexander-de Gennes brush

31

N~h

gR12

gR12

Stretching results from excluded volume; increases stretching energy

6aN

R21

g

Basic Concepts

Random walk

Alexander: obtained scaling by assuming each blob is a random walk

de Gennes: obtained scaling by assuming equilibrium height is a balance of stretching and excluded volume energy

Major result:

h

1

z

Atomistic approaches

Self-consistent field theoryw(r)

q(r,s)

)s,(q)(w)s,(q6Nb

s)s,(q 2

2

rrrr

qc(r,s)

Blood protein

Polymer-coated drug

ρ(r)

Diffusion equation:

0qn

Flexible chain

Captures effects of curvature

w(r) = vρ(r) Bispherical coordinate

s

s

Numerical methods• Discretize space and

time and solve the equations on the mesh (finite differencing)

http://userpages.umbc.edu

• Proof of concept and scale up using density predictions

0

1

2

3

4

5

6

7

8

9

0 1 2 3 4 5 6 7

dEta = 0.5

dEta = 0.4

dEta = 0.3

Numerical methods

Problem: huge arrays are required

F

kT

brush

D

H

Numerical methods• Solution: keep fewer time points

0

2

4

6

8

10

12

0 1 2 3 4 5 6 7

dEta = 0.5

dEta = 0.4

dEta = 0.3

dEta = 0.2

dEta = 0.1

brush

D

H

F

kT

• This is the first publication in which grafted polymer systems were correctly modeled with bispherical coordinates!

0

5

10

15

20

25

0 1 2 3

Compression of brush from equilibrium height costs free energy

Larger bare particle Increased energy

drug

protein

R

R

455.0H

R

brush

drug

667.1R2g

max. value

Rprotein

Rdrug

= 0.25

Rprotein

Rdrug

= 1.0

Rprotein

Rdrug

= 4.0

Drug design: varying Rprotein/Rdrug

D/Hbrush = 0.09F

kT

brush

D

H

protein

drug

R0.25

R

protein

drug

R0.5

R

protein

drug

R1.0

R

protein

drug

R2.0

R

protein

drug

R4.0

R

0

2

4

6

8

10

12

0 1 2 3 4

Effect of varying σRg2

Energetic effects of compression are compounded by increasing brush density

2gR

1R

R

drug

protein

σRg2 = 0.417

max. value

σRg2 = 6.67

σRg2 = 1.667

455.0H

R

brush

drug D/Hbrush = 0.09

2gR 0.417

2gR 0.834

2gR 1.667

2gR 3.33

2gR 6.67 F

kT

brush

D

H

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 1 2 3 4

Less curvature more energy on compression

brush

drug

H

R

1R

R

667.1R

drug

protein

2g

Rdrug

Hbrush

= 0.251

Rdrug

Hbrush

= 0.828

D

Hbrush

≈ 0.1

Effect of varying Rdrug/Hbrush

drug

brush

R0.251

H

drug

brush

R0.455

H

drug

brush

R0.828

H

2 2drug g

F

4 R R kT

brush

D

H

Energy scaling

0.93 2.25

protein drug

drug g brush

R R DF ~ ln

R R H

Trombly and Ganesan, JPS(B), 2009

Semiconductor devices

Random copolymer brush

f = volume fraction of A

B

A

Problem:

w(r)

q(r,s)

qc(r,s)

Flexible chain Incompatible

!

Mansky, et al, Science, 1997f

A B

• How do you model the random chains?

• To mimic the experimental scenario, use conditional probabilities to create sequences of random chains

• Solve the equations, average the results

Semiconductor devices

• Can we use a simpler theory?• Assumption: the grafted chains

rearrange

Optimization

Summary• Applications of modification of surfaces using polymers

• Modeling of polymers

• Examples: drug delivery, design of patterned surfaces

Final work• Use the model to help experimentalists design

random copolymer brush systems for achieving perpendicular lamellae

• A high value goal that is of great industrial interest!

Acknowledgements

Dr. Venkat Ganesan, Ganesan research group (Victor, Manas, Landry, Paresh, Chetan Thomas), Daniel Miller, Margaret Phillips

Funding:

NSF (Award # CTS-0347381)Robert A. Welch FoundationPetroleum Research Fund of American Chemical Society

Texas Advanced Computing Center

Derjaguin approximation

Rgrafted

Rbare

D

l

Rgrafted

Rbare

D

r

l(θ)

θ

Standard Modified

Hbrush

Rdrug= 0.251 σRg^2 = 1.667 Hbrush

Rdrug= 0.251 σRg^2 = 1.667

Trombly and Ganesan, JPS(B), 2009

Derjaguin approximation

Hbrush

Rdrug

Hbrush

Rdrug= 0.828 σRg^2 = 1.667

= 0.828 σRg^2 = 1.667

• Modified approximation accurate for small grafted particle

• Increased agreement of the two approximations for larger grafted particle, but only qualitative agreement with SCFT

Trombly and Ganesan, JPS(B), 2009

Atomistic approaches

http://www.ipfdd.de/Software.1568.0.html?&L=1

Monte Carlo simulations Molecular dynamics simulations

Keep track of atoms’ positions and velocities.

1

10

0.1 1 10 100 1000 10000

R/Rg = 0.05

R/Rg = 0.1

R/Rg = 1

R/Rg = 10

R/Rg = 50

Spherical brush

Large sphere flat plate height and scaling of σ

Small sphere star polymer scaling of σ once coverage is enough to form brush

2gR

g

brush

RH

~0.3 ~0.18

Flat plate: Hbrush/Rg ~ σ0.33 Star polymer:

Hbrush/Rg ~ σ0.2

Star polymer

Flat plate

Energy scaling

brush

25.2

g

grafted

93.0

grafted

bare

HD

lnR

R

R

R~F

• Range and functional form agree with predictions from scaling for star polymers and from Derjaguin approximation

• Unable to explain exponents that collapse energy curves

Trombly and Ganesan, JPS(B), 2009