Trajectory Control of PbSe- -Fe2O3 Nanoplatforms under

Viscous Flow in the presence of magnetic field

Lioz Etgar, Arie Nakhmani, Allen Tannenbaum, Efrat Lifshitz, and Rina Tannenbaum

Nanoscience and Nanotechnology Program Technion-Israel Institute of Technology

PbSe QDs

-Fe2O3 NPs

Organic molecules

Drug molecules

How do we create functionalized conjugate structures?

Conjugate structure of -Fe2O3 Nanoparticles and PbSe Quantum

DotsTEM/HRTEM micrographs-

1.3nm

Etgar L.; Lifshitz E.; Tannenbaum R. J. Phys. Chem C, 2007, 111(17), 6238-6244.

The motion of these conjugate structures:• In a viscous flow • In the presence of an external magnetic field

Is of crucial importance, since this property should provide us with new insights into the behavior of the conjugate structures as a potential in-vivo drug delivery system.

Motivation

Studying the NQDs-NPs conjugates under different fluid flow rates

(capacitances) and at different fluid viscosities (which will mimic

the viscosity of blood), while applying an external magnetic field.

Goals

All the flow experiments were conducted with nanoplatform

suspensions in aqueous poly(ethylene glycol) (PEG) solutions

and recorded by a CCD camera. The resulting video films were analyzed by a unique software

package (developed specifically for this propose), which

calculates the velocity, direction and trajectories of each

NQDs-NPs conjugate nanostructure separately.

Methods

Conjugate structures

N

P

d

x

y

Flow measurement set-up

The forces which act on the nanoplatforms

1. Magnetic force.

2. Viscous drag force (fluidic force).

3. Nanoplatform-blood cell interactions.

4. Gravitational force.

5. Buoyancy force.

6. Inertial force.

7. Van der Walls inter-nanoplatform forces.

The inertial force and the inter-nanoplatform interactions can be

neglected if the total volume occupied by the nanoplatforms per unit

volume of fluid is very small.

Buoyancy force Gravitational force

Several orders of magnitude smaller than the other forces.

62.19 10 pN61.84 10 pN

Thus, we consider mainly the magnetic and fluidic forces, while

the nanoplatform-blood interactions are already taken into

consideration by measuring the transport of the nanoplatforms in

fluids with different viscosities.

The forces which act on the nanoplatforms

(cont.)

Fluidic force

6f p p fF R ( v v )

pR

pv

fv

fluid viscosity

conjugate radius

conjugate velocity

fluid velocity.

6 ( 0)fx p px fxF R v v

6 ( )fy p py fyF R v v

By considering a motion in the x-y plane,the components of the fluidic force are:

N

P

d

x

y

Magnetic force

0

3( )

( 3)mp

m mp mp a amp

F N V H H

mpmH70 104

Nanoplatform permeability

Permeability of the air

aH

1)( 0 mpmp

Nmp Total number of nanoplatforms

The applied magnetic field

Nanoplatform susceptibility

Vmp Nanoplatforms volume

2 40

2 2 3

3 ( )

3 2(( ) )

mp mp mp s magmx

mp

N V M R x dF

x d y

2 40

2 2 3

3

3 2(( ) )

mp mp mp s magmy

mp

N V M R yF

x d y

Ms is the saturation magnetization of the specific magnet, in this case it

equals to 1106 A/m.

Ffx

Conjugate structures

N

P

d

x

y

Fmx

Fy(total)=Ffy+Fmy

Flow measurement set-up

6 ( 0)fx p px fxF R v v

6 ( )fy p py fyF R v v

2 40

2 2 3

3 ( )

3 2(( ) )

mp mp mp s magmx

mp

N V M R x dF

x d y

2 40

2 2 3

3

3 2(( ) )

mp mp mp s magmy

mp

N V M R yF

x d y

6BK TDrh

Nanosight LM10

1.25cP 0.05ml/hr

1.25cP 0.3ml/hr

3.71cP 0.3ml/hr

4.13cP 0.7ml/hr+Magnet

6.35cP 0.2ml/hr

Representative films

Graphical user interface (GUI) was developed in MATLAB

Software package

Representative images of the original visualization of the nanopaltforms

during flow

Results

0.0 0.2 0.4 0.6 0.8 1.00.0

0.1

0.2

0.3

R

adia

n

Volumetric flow rate [mL/h]

1.25cP 1.73cP 2.13cP 3.71cP 4.13cP 6.35cP

The influence of an external magnetic field on the nanoplatform trajectories.

PEG solutions with different viscosities:

1.25 cP 1.73 cP 2.13 cP 3.71 cP 4.13 cP 6.35 cP

Flow rates: 0.03 mL/hr0.05 mL/hr

0.1 mL/hr 0.2 mL/hr0.3 mL/hr0.5 ml/hr0.7 mL/h 0.9 mL/hr

Constant magnetic Constant magnetic fieldfield

Etgar L., Arie Nahmani, Allen Tannenbaum, Efrat Lifshitz, Rina Tannenbaum. Submitted to Physical Review B, 2008.

Force balance on the nanoplatforms during their flow

X

y

d

Results (cont.)

Fy(Total)=Ffy+Fmy

Fmx

Ffx

0.0 0.3 0.6 0.9 1.2

0.00

0.02

0.04

0.06

Ffx [

pN

]

Volumetric flow rate [mL/h]

1.25cP 1.73cP 2.13cP 3.71cP 4.13cP 6.35cP F

mx

F fx [

pN

]

0.0 0.3 0.6 0.9 1.2

0.10

0.15

0.20

0.25

0.30

Fy

(to

tal)

[pN

]

Volumetric flow rate [mL/h]

1.25cP 1.73cP 2.13cP 3.71cP 4.13cP 6.35cP

F y(t

ota

l) [

pN

]

Summary

1. We studied the motion of these conjugate structures:• In viscous flows• Under the presence of an external magnetic field

2. Developed quantitative relationships between particle size, fluid viscosity, fluid flow rates and magnetic field strengths, and their effect on the particle trajectories and particle cohesion.

3. Even at low magnetic fields (~1 Tesla), the trajectories of the particles can be controlled, fact which validates the fundamental drug targeting and delivery strategy using magnetic nanoparticles as the active targeting nanoplatforms.