Particles and Nanoparticles

1
Particles and Nanoparticles
2
Nanoparticles for drug delivery

• Nanoparticles offer many benefits
• Improved dissolution for low solubility drugs
• Increased Bioavailability
• Ability to cross barriers
• Targeted drug delivery

3
Particle behavior

• All particles are subjected to many factors
• Body forces (gravity, fluid drag)
• Friction
• Inelastic contact/collisions
• Others are only significant at small scales
• Electrostatics
• Van der Waals forces
• Casimir effect
• Most result in attractive/cohesive forces

4
Particle size and behavior

• Size may be the most important factor for
  particle behavior
• Segregation
• Agglomeration
• Thermodynamics
• What is a particles size?

5
Size

• Difficult to determine
• Depends on method
• Light scattering, sieving, etc.
• Not obvious what the size of a non-spherical
  particle is

6
Size distributions
Keirnan Need pic p23 And equations

• Normal (Gaussian)
• Log-Normal
• Most systems of fine particles
• Rosin-Rammler
• Milled materials, irregular particles

Fan and Zhu, Principals of gas-solid flows. p 19
7
Average Diameters
Keirnan Pic p 49

• Choice of average to define system can be very
  important
• Number mean
• Volume mean (cubic)
• Sauters mean
• Particle with the same surface area per unit
  volume
• Geometric mean
• Log d

Rhodes, Principles of Powder Technology. P 46
8
What about particle shape

• Most particles are not spherical
• Shape is almost as important as size
• Anisotropic behavior
• Higher (or lower) packing density
• What is the size of a non-spherical particle?

Add examples of particle shapes- needle, disk,
ellipsoid, and some of the things size changes
9
Equivalent radius

• Volume
• Hydrodynamic
• Others

Use table from notes/book
10
Nanoparticle shape

• Platelets can orient themselves in blood stream
• Get stuck to vessel walls
• Rods
• Micelles can change shape
• When subjected to shear
• Tend to loose contents in the process

V. Torchilin, Nanoparticulates as Drug Carriers.
2006
11
Interactions between particles

• Many forces act on particles of all sizes
• Friction
• Gliding
• Rolling
• Inelastic collision
• Body forces

12
Friction

• Leonardo Da Vinici (1500s) found that a force
  proportional to the force holding two objects
  together is needed to set them in motion
• Friction depends only on force
• Not on surface area
• Coulombs laws

13
Coulombs Laws

• The force of traction required to set the system
  in motion is proportional to the total weight of
  the individual components.
• The force of traction T is independent of the
  surface area of the solids in contact.
• There is a difference between static friction
  when the solids are initially at rest and dynamic
  friction when the solids are already in motion.

Eq. P 19
Coefficient of static and dynamic friction p19
14
Surface properties

• Friction is still in many respects a mystery and
  not well understood
• Microscopic studies suggest that ordinary solids
  have a rugged topography
• For sliding protrusions must deform to allow
  relative motion

15
Gliding and Rotations

• As solids move the point I will move and trace
  out a curve on each particle
• The motion of any point M on S is described by
• The relative velocity at I and rotation

Eq. p22
16
Motions

• The angular velocity vector w is broken up into
  two orthogonal components
• Where wt corresponds to rotation in the plane of
  the figure
• wn describes spinning about a vertical axis
• The motion can be broken up into 3 types of
  motion
• Is the gliding velocity
• Is the angular speed due to spinning
• Is the angular speed due to rolling

Eq bottom p22
17
Rolling without gliding

• Vg 0
• The instantaneous axis of rotation passes though
  I and is a straight line aligned with vector w
• Particles act like cogwheels

18
Frustrated rolling

• For a dense pile all particles are in intimate
  contact and rotation may be entirely inhibited

19
Gliding without rolling

• w 0
• Can occur for smooth or nearly frictionless
  particles
• Can also occur when rotations are precluded for
  geometric reasons
• Particle motion can be approximated by coulombs
  law
• Two particles will glide on each other only if
  their tangential force is greater than muN

fix
20
Collisions

• Momentum is conserved during particle collision
• Energy is not conserved.
• Some energy is lost to heat and noise

Fig. And mo balance
21
Restitution Coefficient
Add table of restitution coef

• Some energy is always lost in collisions of real
  particles
• After a collision at U (with a stationary
  object) the particle rebounds with a smaller
  velocity eU
• where e is the restitution coefficient
• Experimentally it is observed that e can be a
  function of velocity

Fix equation
22
Body Forces

• Gravity
• Fg mg
• Fluid Drag
• When Fd Fg particle is at terminal velocity
• Settling velocity
• Stokes Law
• Brownian motion
• Movement of particles due to thermal agitation
• Nanoparticles can not settle due to Brownian
  motion

Add table of settling velocity and size
Add equations
23
Cohesive forces

• Many forces can lead to the agglomeration of
  smaller particles
• As the size and mass of particle s decrease many
  of these forces become more and more important

Table of forces and sizes from blue book
24
Moisture Cohesion

• Liquid on particles surfaces can lead to
  capillary forces
• Force depends on amount of water available to
  create liquid bridge
• More water means larger bridge
• Too much water and the surface tension no longer
  holds the particles together

Middleman, fundamentals of polymer processing,
1977
25
Electrostatics

• Important on both large and small scales
• Increases as surface area/volume ratio decreases
• On contact materials of differing composition
  transfer charges
• Tribocharging
• Can lead to large forces

26
Industrial Electrostatics

• Some industries utilize electrostatics
• Spray coating
• Xerography
• Filtration
• For others can cause large problems
• Pharmaceuticals
• Dust explosions

27
Dust explosions

• Wheat flower can produce more energy than TNT
• Dust lofted into the air can be ignited by
  electrostatic sparks
• Especially troublesome in grain silos and mining
  industry
• Over the last 10 years there have been 115 grain
  explosions in the US
• Killing about 10 workers
• Robert W. Schoeff, Kansas State
  University

Masson, http//www-old.ineris.fr/en/recherches/ do
wnload/blaye_report.pdf
http//www.geaps.com/proceedings/2004/Hajnal.cfm
28
Geophysical Processes

• Charging may be important for geophysical
  processes
• Especially those in dry environments
• Sand transport (Kanagy et al. 1994)
• Volcano Plumes (Miura et al. 1996)
• Lightning (Desch et al. 2002)

www.spaceweather.com/swpod2005/18aug05/young1.jpg
29
Tribocharging

• Particles in contact
• Differing electronic structure
• Energy levels are not equal
• In conductors this is pretty straight forward
• Nonconductors are more complex but seem to charge
  by similar mechanisms
• Electrons move to equalize potential energy

30
Conduction bands

• In all compounds bonding electrons are found in
  separate energy levels
• In macroscopic materials energy levels are so
  close together that electrons seem to exist in
  energy bands
• If there are energy states easily available to
  electrons then the material is a conductor
• If there is a large energy gap then it is a
  insulator

31
Contact between conductors

• Potential energy of the top bands are not equal
• Electrons move from A to B to equalize energy
  levels
• Electrons are free to move in a conductor
• Produce an electric field which raises the
  potential energy as well
• Flow of electrons stops when energy levels are
  equal

Harper
32
Nonconductors

• Electrons can not move in a nonconductor
• No free energy levels for electrons to fill
• How do nonconductors charge?
• Several possibilities
• Contamination
• Very difficult to produce total pure substances
• Even a small number of impurities can produce
  many localized energy levels for electrons near
  the surface
• Electrons may fill these energy levels in a
  similar way to conductors
• Charges adhered to surface may also be transferred

33
Separation

• Electrons and holes set up electric field
• Increases energy needed to cross
• Eventually energy levels equalize
• On separation
• For conductors
• Most electrons fallow the electric potential and
  travel back to original substance
• For nonconductors
• Some electrons travel back but most remain
• Tribocharging of nonconductors usually produces
  much higher charges than for conductors

34
Coulombs Law
Add equation

• Different Coulombs Law from friction law
• Electric force given by
• Coulombs
• Measurement of charge
• 1 mole of electrons produces 1 coulomb of charge
• Force of an infinite plane

35
Electric Field

• Force felt by a unit of charge
• E F/q (N/C or V/m)
• Lines of force originate on positive charges and
  end on negative charges
• Each line is at a constant field intensity
  (constant force)

36
Potential
Add voltage equation in terms of E p 39 from
moore

• Energy necessary to bring charge from infinity
  some point
• Constant potential surfaces
• Perpendicular to field lines
• Conducting surfaces are constant potential
  surfaces
• Electrons can move so equalize their energy
• Electric field tends to concentrate around sharp
  edges

37
Measuring electric charges

• Faraday Cup
• Electric field inside a conductor
• Net charge
• Induced measurements
• Online measurements
• Depend on distance
• Change electric field

38
Charging and particles

• Charges on a particle
• May not be constant or even the same sign
• Surface chemistry
• Quartz crystal faces each charge differently
• Charge distribution may depend on
• Particle size
• Temperature
• Hot spot formation can lead to increased
  electron mobility and even charge transfer
  amongst like materials

39
Break down

• Break down potential
• Cosmic rays and radiation produce ions in air
• In high electric field these ions accelerate
• If field high enough ions impact molecules and
  produce more ions
• Several types of break down
• Corona
• Spark
• Brush

Keirnan LaMarche need pics Should we bring in
the VDG?
40
Maximum particle charge

• Breakdown limits maximum particle charge
• But need ions to initiate break down
• If high field is localized to a small area there
  will be an insufficient number of ions present
• Will need a larger electric field to initiate
  break down

Add graph from harper
Harper p 15
41
Charging during flow

• To better understand how particles charge as they
  flow
• Our group examined the charging of grains as they
  flow through a tube
• Easy to control surface area
• Simple flow

42
Charging and surface area
A 2prh
43
Constant surface area
44
Charge distribution
45
Forces on Particles

• 10x larger charge on particles at the walls of
  the cylinder than at the center
• Force proportional to charge
• F q1(q2k/r2)
• It is possible to separate the charged particles
  from the uncharged particles at the center
• Could lead to segregation

46
Mixtures of particles

• Tested bidisperse mixtures
• Sand mixed with
• 4mm glass beads (charge positive)
• 3mm acrylic beads (charge negative)
• Sand segregated at the walls of cylinder
• Should produce a measurable difference in charging

47
Sand and glass beads
48
Sand and glass beads
49
Sand and acrylic beads
50
Sand and acrylic beads
Sand adhered to acrylic beads
51
Permanent charges

• Crystal structure often has charges or is polar
• In air these charges attract ions and are become
  balanced
• In solution these charges play a larger role
• Zeta potential

52
Electrostatics and size

• As size of particles decrease
• The surface area per unit volume increases
• More surfaces to tribocharge and therefore
  greater forces
• Maximum possible charge per particle increases

53
Controlling ES

• Not easy
• Static eliminators
• Produce ions to eliminate charges
• Ions have to be able to reach charges
• New charges are produced as soon as material
  moves
• High humidity
• Makes particles more conductive
• Can cause agglomeration on its own

54
Dielectrophoresis

• Movement of particles due to induced polarization
• Can move non-charged particles
• Gets weaker as particle size decreases
• Can separate larger particles from smaller
• Used in biological sciences

55
Polarization

• In electric field molecules can become polar
• Electronic polarization
• Atomic polarization
• Interfacial polarization
• others

Figures showing types
56
Non-uniform field
Keirnan LaMarche Add pic from book p 340

• In uniform field forces are balanced
• When the field is non-uniform
• one side of particle interacts with more field
  lines
• Feels a force toward increasing field density
• Sign of the charge is not important
• Can use AC fields

57
Dielectrophoretic separation

• The force felt on particles decreases as volume
  decreases
• The relative force of most effects increases as
  size decreases
• Larger particles will be attracted to nonuniform
  fields more than smaller ones
• Can this be used to separate larger particles
  from smaller ones?
• Already used for separations in biological systems

Pohl p370
58
Van der Waals forces

• Several intermolecular forces
• London forces - Caused by induced polarization on
  molecular scale
• As molecules approach their electron clouds can
  shift
• Produce temporary dipoles which attract
• Keesom forces - molecular dipole interactions
• Forces between molecules with permanent dipoles

59
Forces on nanoparticles
Keirnan LaMarche Add figure with distance and
interaction time from nanopart book

• Causes agglomeration
• Intermolecular force
• Short distances and relatively weak

60
Thermodynamics and size

• As particle size shrinks sever important changes
  can happen
• Crystal structure
• Surface energy
• stability
• Solubility

61
Surface energy
62
Solubility?

• Less stable particles dissolve easier
• Technically increases solubility
• But larger particles are more stable
• Oswald ripening larger nanoparticles grow at the
  expense of smaller ones

63
Entropy and agglomeration

• Depletion effect - Entropic mechanism
• Agglomerates larger particles (nanoparticles) to
  give more room for more mobile particles
  (proteins or polymers)
• Area around particles where centers of smaller
  particles can not enter
• If larger particles are in contact no small
  particles can enter region
• Forces due to collisions are unbalanced
• Forces particles together

64
Casimir Effect

• Another force that acts to attract objects on
  small scales
• Arises from quantum fluctuations
• Difference in number allowed in between particles
  and outside of them