4/6/094/6/09 11

Properties of ComplexProperties of ComplexParticle-LadenParticle-Laden

Polymeric SolutionsPolymeric Solutions

Dr. Dan J. FryDr. Dan J. FryAdjunct / UHCLAdjunct / UHCL

4/6/094/6/09 22

WhatWhat’’s in the World Around You?s in the World Around You? Suspensions are ubiquitous in Nature!Suspensions are ubiquitous in Nature!

Polymers are equally ubiquitous!Polymers are equally ubiquitous!

Aggregation ofAggregation of nanoparticle nanoparticle suspensions, suspensions, similar to those proposed for similar to those proposed for

medical dispersion.medical dispersion.

(Savara Pharmaceuticals)

4/6/094/6/09 33

How Can One Hope to Understand SuchHow Can One Hope to Understand SuchComplexities?Complexities?

A good starting point is to look at relevant time,A good starting point is to look at relevant time,length, and energy scales.length, and energy scales.

In many cases one can prepare system inIn many cases one can prepare system in““limitinglimiting”” cases. cases.

In many cases the system behavior is non-In many cases the system behavior is non-linear.linear.

We must think geometrically: Factors of 10 - logarithmically

Power Law Scaling!

4/6/094/6/09 44

Characteristic Response TimesCharacteristic Response Times

Inertial:Inertial:

Turbulent:Turbulent:

Elastic:Elastic:

Flow:Flow:

Diffusive:Diffusive:

4/6/094/6/09 55

Particulate InteractionsParticulate Interactions

0.1 1 10 100 1000

-4

-2

0

2

4

6

8

10

12

T = 298Kε = 30ε0a = 50nmψ0 = 30mV

10 -4 M NaCl 10 -2 M NaCl VT, 10 -1 M NaCl 0.3 M NaCl VR VA

VT /

kBT

D [nm]

( )[ ]DaVR κψπε −+= exp1ln2 20

−=DaAVA π12

Dipole-Dipole interaction

Diffuse Double Layer Interaction

V/k B

T

4/6/094/6/09 66

Polymeric-Polymeric-NanotubeNanotube Suspensions Suspensions Brownian nature controlled by both tube concentration,Brownian nature controlled by both tube concentration,

flow velocity/shear rate (Reynolds number), and elasticflow velocity/shear rate (Reynolds number), and elasticcontribution from suspending medium.contribution from suspending medium.

High-molecular weight polymer suspensions can beHigh-molecular weight polymer suspensions can bemade made ““viscovisco-elastic-elastic””, in some cases non-Newtonian:, in some cases non-Newtonian:

Response not proportional to how hard you “push”!

4/6/094/6/09 77

Polymeric-Polymeric-NanotubeNanotube Suspensions SuspensionsSWNT

Solvent: 0.6% NaDDBS in D2O.η ~0.9*10-3 Pa sScreens van der Waals attractionbetween tubes.Forms micelles.

MWNT

Solvent: PIB/Bogerη~0.6 – 10 Pa sρ = 0.91gm/cm3

Newtonian to 100 s-1

SWNT MWNT

L [mm] 0.5-1 10-12

d [nm] 12-15 50

(L/d) ~60 200

f 4.3*10-4 – 8.7*10-4

1.1*10-4 –3.6*10-3

nL3 2 – 4 6 – 183

nL2d 0.03 – 0.06 0.3 – 0.9

Pe 0.2 - 100 104 – 4*1010

Re 5*10-2 – 15 10-5 – 10-3

PIB - polysiobutylene, MW = 500Boger Fluid - constant-viscosity / elastic,MW = 800 PIB mixed with 0.1% MW =4.7X106 PIB.

10-1 100 101 102 10310-2

10-1

100

101

102

103

104

105

106

107

108

109

1010

1011

Pe

shear rate [ s-1 ]

SWNT

MWNT

Shear rate [s-1]

4/6/094/6/09 88

Convenient to define dimensionless scaleConvenient to define dimensionless scalefactors as ratios of time, length, and energy:factors as ratios of time, length, and energy:

Stokes Number Stokes Number (ratio of particle response to turbulent response)(ratio of particle response to turbulent response)::

Reynolds Number Reynolds Number (ratio of inertial to viscous forces):(ratio of inertial to viscous forces):

WeisenbergWeisenberg Number Number (ratio of flow rate to elastic relaxation time)(ratio of flow rate to elastic relaxation time)::

RotationalRotational Peclet Peclet Number Number (ratio of flow time to rotation time)(ratio of flow time to rotation time)::

Defining Defining ““LimitingLimiting”” Behavior Behavior

In general these can be controlled experimentally!

4/6/094/6/09 99

Observation: Light Scattering is OurObservation: Light Scattering is OurEyes into System BehaviorEyes into System Behavior

Remember geometric optics?Remember geometric optics? What matters is the ratio of characteristic size to theWhat matters is the ratio of characteristic size to the

wavelength of incident light.wavelength of incident light.

Small Angle Light Scat. (SALS)q(~1/λ) range: 0.58 – 4.9 µm-1

Length scale probed: 0.2 -1.7 µm

Birefringence - Orientation dependent electric field decomposition. Dichroism - Orientation dependent absorption

Q gives insight into structure size!

4/6/094/6/09 1010

512X512CCD Array

HH

vorticity axis

gradient axisHe-Ne Laser

632.8/670 nm hν ~ 1.9eV

CCD Camera connectedto monitor and VHS recorder.

Horizontal (H) polarizationaligned with flow field.

Vertical (V)polarizationaligned with vorticityaxis.

0 50 100 150 200 2500

50

100

150

200

250

2 s-10 50 100 150 200 250

0

50

100

150

200

250

58 s-1

0 50 100 150 200 2500

50

100

150

200

250

94 s-1

0 50 100 150 200 2500

50

100

150

200

250

153 s-1

θ

xz

Observational SetupObservational Setup

Modulate incoming polarization to determine

orientation.

4/6/094/6/09 1111

102 103 104 105

10-3

10-2

10-1

100

101

-2.6

-1.8

100 % C2H2

S(q)

q(cm-1)

15 12 10 7 5 4 3 2 1

Intensity of scattered light, I(q) = NS(q)(Kim et al.)

h

4/6/094/6/09 1212

40 µm

•Nanotubes have an attractive interparticle potential and floc (aggregate) inquiescence.

•Because of the packing nature of high aspect ratio tubes, and the viscoelasticnature of the background fluid, aggregate structure tends to be more compactthan diffusion-limited aggregation.

Clustering in the Presence of ShearClustering in the Presence of Shear

4/6/094/6/09 1313

•Light scattering patterns don’t show a strong flowalignment.

•“Bulge” in vv and hh light scattering patterns at longtimes implies some degree of separation into twocharacteristic length scales.

•Through microscopy we see small tubes close toshear cell walls, larger tubes towards center of cell.

•Jefferey orbits of longer MWNTs drives flow alignedtubes into bulk.

•Tube-Tube interactions drive shorter tubes to wallwhere they align with the vorticity direction.

Size SegregationSize Segregation

4/6/094/6/09 1414

flow vorticity

flow

gradientvorticity

0 20 40 60 80 100 120 140 160 1800

50

100

150

200

250

n(θ)

tilt angle, θ [degrees]

bulk wall

0.1% by wt MWNT in PIB/Boger

Orientation SegregationOrientation Segregation

4/6/094/6/09 1515

2−∝ φRoR DD

3

]8.0)/[ln(3LdLTkDD B

RoR πη−

==

Semi-dilute limit: tube-tube interaction begins toplay a role and excluded volume restricts rotarydiffusion coefficient.

Dilute limit forrigid rods :

2φγγ

&&∝=

RDPe

a

Excluded volume via Doi-Edwards:

d2

““ClassicalClassical”” Rigid-Rod Approximation Rigid-Rod Approximation

4/6/094/6/09 1616

1 10 100-5

-4

-3

-2

-1

0

1

2

3

4

5

Δn',

Δ n'' X

106

shear rate [ s-1]

Δn'' Δn' Pure PIB/Boger

0 100 200 300 400-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

gap: d = 0.37mmλ = 670nm

shear off

Δn'

x 106

time, t [sec]

NaDDBS 2% in D2O

shear on - 10 s-1

Universal ScalingUniversal Scaling

4/6/094/6/09 1717

•By definition, a liquid cannot sustain anon-zero shear stress.

•Some particulate suspensions areunique in that they exhibit a transitionfrom liquid to solid behavior - they jam,or develop a yield stress.

•The degree to which they jam isdependent on particulateconcentration and how hard you pushon them.

Shear stressYield Stress: JammingYield Stress: Jamming

4/6/094/6/09 1818

•(c-d)Below a critical shear stress (rate)there is not sufficient energy to breakthe contact bonds between tubesformed by overlapping orbits.

•(c-d)When the system size (shear cellgap) becomes comparable to tubeorbits they are confined and floc end-to-end in x-z plane along z.

•(c-d)Stripped pattern results fromband growth at expense of smallerclusters.

•(b) Increasing concentration φ resultsin a cavitated network.

Shear-Induced Phase TransitionShear-Induced Phase Transition

4/6/094/6/09 1919

Future ApplicationsFuture Applications Magnetic Viruses: biologically functionalizedMagnetic Viruses: biologically functionalized

magnetic magnetic nanoparticlesnanoparticles:: DNA removed from virus interior. Casing is then usedDNA removed from virus interior. Casing is then used

as a template for Feas a template for Fe33OO44 particle. particle.

Biohazard Detoxification: poly(lactic-glycolic acid)Biohazard Detoxification: poly(lactic-glycolic acid)nanospheres nanospheres carrying surface receptors tocarrying surface receptors toremove invaders from blood.remove invaders from blood.

PEG Shell / Drug Emulsion: delivery of time-PEG Shell / Drug Emulsion: delivery of time-sensitive contents to circulatory system of strokesensitive contents to circulatory system of strokevictim.victim.

4/6/094/6/09 2020

Amit Chakrabarti (Kansas State University)Chris Sorensen (Kansas State University)Flint Pierce (Kansas State University)Erik Hobbie (NIST)Ben Langhorst (NIST)Howard Wang (Michigan Technological University)Eric Grulke (University of Kentucky)H. Kim (Kyunghee University)

AcknowledgementsAcknowledgements