PropertiesProperties ofof ComplexComplex Particle-LadenParticle-Laden PolymericPolymeric SolutionsSolutions
Dr. Dan J. Fry Adjunct / UHCL
4/6/09 1 WhatWhat’’ss inin thethe WorldWorld AroundAround You?You? .. Suspensions are ubiquitous in Nature!
Aggregation of nanoparticle suspensions, similar to those proposed for medical dispersion.
(Savara Pharmaceuticals) .. Polymers are equally ubiquitous!
4/6/09 2 HowHow CanCan OneOne HopeHope toto UnderstandUnderstand SuchSuch Complexities?Complexities? .. A good starting point is to look at relevant time, length, and energy scales.
.. In many cases one can prepare system in “limiting” cases.
.. In many cases the system behavior is non- linear. We must think geometrically: Factors of 10 - logarithmically
Power Law Scaling! 4/6/09 3 CharacteristicCharacteristic ResponseResponse TimesTimes
.. Inertial:
.. Turbulent:
.. Elastic:
.. Flow:
.. Diffusive:
4/6/09 4 ParticulateParticulate InteractionsInteractions
Diffuse Double Layer Interaction 2 VR = 2πεaψ 0 ln[1+ exp(−κD)] 12 10 -4 M NaCl 10 -2 10 M NaCl V , 10 -1 M NaCl 8 T 0.3 M NaCl V 6 R VA T
T k B T = 298K
B
4 / k = 30 ε ε0
V/ T a = 50nm V 2 ψ0 = 30mV
0
-2 Dipole-Dipole interaction A a VA = − -4 12π D 0.1 1 10 100 1000 D [nm]
4/6/09 5 Polymeric-Polymeric-NanotubeNanotube SuspensionsSuspensions . Brownian nature controlled by both tube concentration, flow velocity/shear rate (Reynolds number), and elastic contribution from suspending medium.
. High-molecular weight polymer suspensions can be made “visco-elastic”, in some cases non-Newtonian:
Response not proportional to how hard you “push”!
4/6/09 6 Polymeric-Polymeric-NanotubeNanotube SuspensionsSuspensions SWNT MWNT PIB - polysiobutylene, MW = 500 Solvent: 0.6% NaDDBS in D2O. Solvent: PIB/Boger Boger Fluid - constant-viscosity / elastic, η ~0.9*10-3 Pa s η~0.6 – 10 Pa s MW = 800 PIB mixed with 0.1% MW = Screens van der Waals attraction ρ = 0.91gm/cm3 4.7X106 PIB. between tubes. Newtonian to 100 s-1 Forms micelles.
1011 SWNT MWNT 1010 MWNT 109 L [mm] 0.5-1 10-12 108 d [nm] 12-15 50 107 106 (L/d) ~60 200 105 -4 - -4
Pe f 4.3*10 – 8.7*10 1.1*10 – 4 4 10 3.6*10-3 3 10 nL3 2 – 4 6 – 183 102 SWNT nL2d 0.03 – 0.06 0.3 – 0.9 101 0 10 Pe 0.2 - 100 104 – 4*1010 10-1 -2 -5 -3 10-2 Re 5*10 – 15 10 – 10 10-1 100 101 102 103 Shear rate [s-1] shear rate [ -1s ] 4/6/09 7 DefiningDefining ““LimitingLimiting”” BehaviorBehavior
.. Convenient to define dimensionless scale factors as ratios of time, length, and energy: In general these can be controlled experimentally!
. Stokes Number (ratio of particle response to turbulent response):
. Reynolds Number (ratio of inertial to viscous forces):
. Weisenberg Number (ratio of flow rate to elastic relaxation time):
. Rotational Peclet Number (ratio of flow time to rotation time): 4/6/09 8 Observation:Observation: LightLight ScatteringScattering isis OurOur EyesEyes intointo SystemSystem BehaviorBehavior .. RememberRemember geometricgeometric optics?optics? . What matters is the ratio of characteristic size to the wavelength of incident light.
Birefringence - Orientation dependent Small Angle Light Scat. (SALS) electric field decomposition. q(~1/λ) range: 0.58 – 4.9 µm-1
Length scale probed: 0.2 -1.7 µm Dichroism - Orientation dependent absorption
Q gives insight into structure size!
4/6/09 9 ObservationalObservational SetupSetup
0 50 100 150 200 250 0 Horizontal (H) polarization 50 2 s-1
100 0 50 100 150 200 250 HH 0
gradient 150 aligned with flow field. 50 58 s-1 z 200 axis 100
He-Ne Laser 250 0 50 100 150 200 250 150 0 -1 632.8/670 nm x 200 50 94 s 250 100
hν ~ 1.9eV 0 50 100 150 200 250 150 0
200 50 153 s-1
250 100
150 θ 200 Vertical (V) 250 polarization vorticity aligned with vorticity axis axis.
512X512 CCD Array CCD Camera connected to monitor and VHS recorder. Modulate incoming polarization to determine orientation.
4/6/09 10 100 % C2H2
15 h
1 12 10 10 7
0 -2.6 5 10 4 3
2 -1 10S(q) 1
10-2 -1.8
10-3
102 103 104 105 q(cm-1)
Intensity of scattered light, I(q) = NS(q) (Kim et al.) 4/6/09 11 ClusteringClustering inin thethe PresencePresence ofof ShearShear
40 µm
•Nanotubes have an attractive interparticle potential and floc (aggregate) in quiescence.
•Because of the packing nature of high aspect ratio tubes, and the viscoelastic nature of the background fluid, aggregate structure tends to be more compact than diffusion-limited aggregation.
4/6/09 12 SizeSize SegregationSegregation
•Light scattering patterns don’t show a strong flow alignment.
•“Bulge” in vv and hh light scattering patterns at long times implies some degree of separation into two characteristic length scales.
•Through microscopy we see small tubes close to shear cell walls, larger tubes towards center of cell.
•Jefferey orbits of longer MWNTs drives flow aligned tubes into bulk.
•Tube-Tube interactions drive shorter tubes to wall where they align with the vorticity direction.
4/6/09 13 Orientation Segregation Orientation Segregation 250 0.1% by wt MWNT in PIB/Boger bulk wall 200
) 150 θ n(
100
flow vorticity 50
0 0 20 40 60 80 100 120 140 160 180 vorticity tilt angle,θ [degrees] gradient
flow
4/6/09 14 ““ClassicalClassical”” Rigid-RodRigid-Rod ApproximationApproximation Dilute limit for 3k T[ln(L / d) − 0.8] D = D = B rigid rods : R Ro πηL3
Semi-dilute limit: tube-tube interaction begins to a play a role and excluded volume restricts rotary diffusion coefficient.
Excluded volume via Doi-Edwards:
2d
−2 DR ∝ DRoφ
γ& 2 Pe = ∝ γ&φ DR
4/6/09 15 UniversalUniversal ScalingScaling
5
4 Δn'' Pure PIB/Boger Δn' 3
2
6 1
n'' X 10 0 Δ
-1n', Δ -2
-3
-4
-5 1 10 100 shear rate [ -1s]
2.0
NaDDBS 2% in2 OD 1.5
1.0
6 shear off shear on - 10 -1s 0.5 n' x 10 Δ
0.0
-0.5 gap: d = 0.37mm λ = 670nm -1.0 0 100 200 300 400 time, t [sec]
4/6/09 16 YieldYield Stress:Stress: JammingJamming Shear stress
•By definition, a liquid cannot sustain a non-zero shear stress.
•Some particulate suspensions are unique in that they exhibit a transition from liquid to solid behavior - they jam, or develop a yield stress.
•The degree to which they jam is dependent on particulate concentration and how hard you push on them.
4/6/09 17 Shear-InducedShear-Induced PhasePhase TransitionTransition
•(c-d)Below a critical shear stress (rate) there is not sufficient energy to break the contact bonds between tubes formed by overlapping orbits.
•(c-d)When the system size (shear cell gap) becomes comparable to tube orbits they are confined and floc end- to-end in x-z plane along z.
•(c-d)Stripped pattern results from band growth at expense of smaller clusters.
•(b) Increasing concentration φ results in a cavitated network.
4/6/09 18 FutureFuture ApplicationsApplications .. Magnetic Viruses: biologically functionalized magnetic nanoparticles: . DNA removed from virus interior. Casing is then used
as a template for Fe3O4 particle.
.. Biohazard Detoxification: poly(lactic-glycolic acid) nanospheres carrying surface receptors to remove invaders from blood.
.. PEG Shell / Drug Emulsion: delivery of time- sensitive contents to circulatory system of stroke victim. 4/6/09 19 AcknowledgementsAcknowledgements
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)
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