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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
Charging Phenomena
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
Ordered Structure in Colloids
Kose et al., J. Colloid Int. Sci. 55, 487 (1976)
Pusey &
van Megen, N
ature 320, 340 (1986)
Density-Matching Fluids
Science 287, 2585 (2000) De Hoog (2001)
PM
MA in C
HB
-decalin
Applied Optics 40, 4152 (2001)
Leunissen et al., PNAS 104, 2585 (2007)
PMMA in CXB
Our Place in the Story
Saline: 0.9% NaClDrinking waterDeionized waterPurified CXBCXB-Dodecane
Bjerrum length:
How do colloids become charged in low polar environments?
Primary Mystery
Solvent (CXB-Dodecane)
Robert & Caserio, Basic Principles of Organic Chemistry (1977)
Br
PMMA Spheres
Andrew Hollingsworth
12-octadecanoyloxyoctadecanoic acid(12-HSA ‘dimer’)
Dense Suspension
Glass Bulk
Optical TweezersA
shkin, Biophys. J. 61, 569 (1992)
propagation
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
Detecting Particles
a) b)
c) d)
Single Blink Trajectory
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:
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:
Measuring Forces
Eliminating mobility term gives
Velocity and Diffusivity
or
Midpoint Method:
Sainis, Dufresne et.al, PRL 99, 018303 (2007)Time interval:
Kernel Density Estimation
Density estimate P(x)
Kernel function
Data points Xj
Normalized histogram
σ
1-D Histogram vs. KDE
Relative Separation Distribution
Velocity Average
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
Pair Diffusivity Average
Pair Diffusivity Average
Force Average
Poisson-Boltzmann Equation
Boltzmann distribution:
Charge density of N ion species in an electrolyte:
Poisson equation:
concentration of ith species
electrostatic potential
Poisson-Boltzmann Equation
Debye-Hückel Approximation
Linearized PBE
Debye length:
Electroneutrality:
Potential Near a Charged Sphere
Charge
Mjones1984
BCs:
Spherical Symmetry
or
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:
Surface potential
Charge
Force
Fit Parameters
Pair Potential
Charge Renormalization
Alexander, Chaikin et al, J. Chem. Phys. 80, 5776 (1984)
Unfortunately, DH breaks down for
Renormalize charge and surface potential:
Various Pair Potentials
Charges
Ionic Length Scale
Low ionic strength: Bulk distance between ions:
comparable to particle sizeIntegrate over one screening length:
Ionic Length Scale
Low ionic strength: Bulk distance between ions:
comparable to particle sizeIon diffusion time scale:
Primitive model at risk
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
Thanks
David GrierAndrew Hollingsworth
William IrvineDavid Ruffner
Bhaskar KrishnatreyaHenrique Moyses
Mark HannelChen Wang
Colm Kelleher
And the rest of NYU CSMR
NYUMRSEC
Pair Potentials
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
CXB Electrolytesnet reaction
free radicals
Andrew Hollingsworth
PHS Stabilizers are Polar…
Andrew Hollingsworth
…and so are PMMA monomers
Andrew Hollingsworth
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)
Single Blink Relative Separation
Pair Diffusion
Einstein-Smoluchowski relation:
Pair diffusion with drift:
Mean Square Displacement (MSD) calculateswhere
MSD (One Blink)