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 particle’s 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. Keirnan: Need pic p23 And equations Size distributions • 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. Keirnan: Pic p 49 Average Diameters • Choice of average to define system can be very important • Number mean • Volume mean (cubic) • Sauter’s 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 • Coulomb’s laws

13. Coulomb’s 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 coulomb’s 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. Add table of restitution coef Restitution Coefficient • 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 Add table of settling velocity and size • 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 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/ download/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. Add equation Coulomb’s Law • Different Coulomb’s 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. Add voltage equation in terms of E p 39 from moore Potential • 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 = 2πrh

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. 80% Sand mixture Sand and glass beads

48. 80% Sand mixture Sand and glass beads

49. Sand and acrylic beads

50. Sand and acrylic beads Sand adhered to acrylic beads