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)