oral defense - dje
TRANSCRIPT
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Measuring Colloidal Charges in Low Polar Media from Statistics of Particle
Trajectories
Daniel J. EvansMarch 8, 2016
Committee:Professor David G. Grier, Advisor
Professor Paul M. ChaikinProfessor Alexander Y. Grosberg
Professor Andrew D. KentProfessor Neal Weiner
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Charging Phenomena
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Klinkenberg & van der Minne, Electrostatics in the Petroleum Industry (1958)
Charging Phenomena
Gas explosion at a Shell refinery in Pernis, Netherlands in 1954
Remedy: dope the liquid with metallic salts to increase conductivity
Caused by a large charge separation and buildup in a petroleum mixture which arced and ignited
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Ordered Structure in Colloids
Kose et al., J. Colloid Int. Sci. 55, 487 (1976)
Pusey &
van Megen, N
ature 320, 340 (1986)
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Density-Matching Fluids
Science 287, 2585 (2000) De Hoog (2001)
PM
MA in C
HB
-decalin
Applied Optics 40, 4152 (2001)
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Leunissen et al., PNAS 104, 2585 (2007)
PMMA in CXB
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Our Place in the Story
Saline: 0.9% NaClDrinking waterDeionized waterPurified CXBCXB-Dodecane
Bjerrum length:
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How do colloids become charged in low polar environments?
Primary Mystery
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Solvent (CXB-Dodecane)
Robert & Caserio, Basic Principles of Organic Chemistry (1977)
Br
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PMMA Spheres
Andrew Hollingsworth
12-octadecanoyloxyoctadecanoic acid(12-HSA ‘dimer’)
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Dense Suspension
Glass Bulk
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Optical TweezersA
shkin, Biophys. J. 61, 569 (1992)
propagation
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Blinking Experiments
Laser
Periscope
IntensityModifier
Half-wave plate
Beam block
Polarizingbeam splitter
BeamExpander
Telescope
PC
High-speed Camera
dichroicmirror
objectivelens
Illumination
sample
Microscope
shutter
SLM
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Detecting Particles
a) b)
c) d)
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Single Blink Trajectory
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Calculating Relative Separation
Relative separation vector rj connects particle centers
Temporal midpoint Rj (between tj and tj+1)
1 degree of freedom
Midpoint Method:
Time interval:
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Calculating Relative Velocity
mobility
Relative velocity in a low Reynold’s number system (no inertial terms):
Midpoint Method:
Breathing mode velocity parallel to R
1D velocity:
Time interval:
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Measuring Forces
Eliminating mobility term gives
Velocity and Diffusivity
or
Midpoint Method:
Sainis, Dufresne et.al, PRL 99, 018303 (2007)Time interval:
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Kernel Density Estimation
Density estimate P(x)
Kernel function
Data points Xj
Normalized histogram
σ
1-D Histogram vs. KDE
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Relative Separation Distribution
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Velocity Average
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Finding Diffusivity
Calculating with trajectory data:
Eliminate error by evaluating velocity variance at two different time intervals and solve for
Einstein relation for time interval
Measurement error
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Pair Diffusivity Average
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Pair Diffusivity Average
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Force Average
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Poisson-Boltzmann Equation
Boltzmann distribution:
Charge density of N ion species in an electrolyte:
Poisson equation:
concentration of ith species
electrostatic potential
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Poisson-Boltzmann Equation
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Debye-Hückel Approximation
Linearized PBE
Debye length:
Electroneutrality:
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Potential Near a Charged Sphere
Charge
Mjones1984
BCs:
Spherical Symmetry
or
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Pair Potential and Force
Pair electrostatic force:
or
1 2
Potential generated by sphere 1:
Integrate over surface of sphere 2 to find pair potential energy:
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Surface potential
Charge
Force
Fit Parameters
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Pair Potential
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Charge Renormalization
Alexander, Chaikin et al, J. Chem. Phys. 80, 5776 (1984)
Unfortunately, DH breaks down for
Renormalize charge and surface potential:
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Various Pair Potentials
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Charges
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Ionic Length Scale
Low ionic strength: Bulk distance between ions:
comparable to particle sizeIntegrate over one screening length:
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Ionic Length Scale
Low ionic strength: Bulk distance between ions:
comparable to particle sizeIon diffusion time scale:
Primitive model at risk
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Take-away
An interesting low-ionic strength model colloidal system
Low polar regime, no added dispersants, yet stable and highly charged
Particle interaction is still screened-Coulomb, consistent with DLVO theory
Yet the low ionic strength calls the assumptions of the primitive model into question
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Thanks
David GrierAndrew Hollingsworth
William IrvineDavid Ruffner
Bhaskar KrishnatreyaHenrique Moyses
Mark HannelChen Wang
Colm Kelleher
And the rest of NYU CSMR
NYUMRSEC
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Pair Potentials
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Charge TransportIons associate at length scales smaller than the Bjerrum length B where the ions’ electrostatic energy is kBT:
Ian Morrison AOT
Micelle structures one way for charges to separate
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CXB Electrolytesnet reaction
free radicals
Andrew Hollingsworth
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PHS Stabilizers are Polar…
Andrew Hollingsworth
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…and so are PMMA monomers
Andrew Hollingsworth
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Charging of Particles• Where do particle
charges come from?
• How are they present in solution?
• How are they screened?
Andrew Hollingsworth
Hsu, D
ufresne, Weitz, Langm
uir, 21, 4881 (2005)
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Single Blink Relative Separation
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Pair Diffusion
Einstein-Smoluchowski relation:
Pair diffusion with drift:
Mean Square Displacement (MSD) calculateswhere
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MSD (One Blink)