CALCULATIONS IN

NANOTECHNOLOGYTASNEEM KAPADIA

60011115023

NANOTECHNOLOGY

Nanotechnology is the understanding and control of matter at dimensions of roughly 1 to 100 nanometers.

This is the world of atoms, molecules, macromolecules, quantum dots, and macromolecular assemblies.

Relationship between Nanoscience and Quantum Mechanics

Particle size Distribution

Particle size influences many properties of particulate materials and is a valuable indicator of quality and performance. It determines:

appearance and gloss of paint

flavor of cocoa powder

reflectivity of highway paint

hydration rate & strength of cement

properties of die filling powder

absorption rates of pharmaceuticals

appearances of cosmetics

Particle size distribution

Number weighted distributions: Particle size doesn’t matter only number of particles

Volume weighted distributions: The relative contribution will be proportional to (size)3, distribution represents the composition of the sample in terms of its volume/mass, and therefore its potential $ value.

Intensity weighted distributions: Dynamic light scattering techniques will give the contribution of each particle in the distribution relating to the intensity of light scattered by the particle. For example, using the Rayleigh approximation, the relative contribution for very small particles will be proportional to (size)6.

Mean, Median & Mode mean – ‘average’ size of a population

median – size where 50% of the population is below/above

mode – size with highest frequency.

1.Number length mean D[1,0]:

D[1,0]=

2.Surface area moment mean D[3,2] (Sauter Mean Diameter):

D[3,2]=

3. Volume moment mean D[4, 3] (De Brouckere Mean Diameter)

It is one of the fundamental parameters known to affect dispersion stability. Its measurement brings detailed insight into the causes of dispersion, aggregation or flocculation, and can be applied to improve the formulation of dispersions, emulsions and suspensions.

ZETA POTENTIAL

Zeta potential is a measure of the magnitude of the electrostatic or charge repulsion or attraction between particles in a liquid suspension.

Particle size measurement methods

Dynamic Light Scattering (DLS) Differential Centrifugal

Sedimentation (DCS) Transmission Electron Microscopy

(TEM) Scanning Electron Microscopy (SEM) Asymmetric flow- field flow

fractionation (AFFF) Particle Tracking Analysis (PTA)

DLS

DCS

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Fluid Particle Dynamics

Fluid dynamic mechanismF

→ Gravitational force

→ Buoyant force

→ Drag force

Terminal Particle Settling Velocity If particle is not accelerating, velocity must be

constant. This velocity where all the forces balance out, is called terminal settling velocity.

Solving,

Laminar regime

Transition regime

Turbulent regime

Determination of flow regimeTo calculate appropriate range of the fluid-particle dynamic laws that apply.

K=

Laminar regime

Transition regime

Turbulent regime

Larocca and Theodore defined a dimensionless value W that would enable one to calculate diameter of a particle if terminal velocity is known.

W=

0.2222<W<1514; Intermediate’s law

1514< W; Newton’s law

Cunnigham correction factorAt very low reynold numbers, when the particle size is comparable with the mean free path of fluid molecules, the medium is no longer continuous. The particles fall between the molecules at a faster rate than explained by aerodynamics. To allow this slip, Cunningham introduced a factor to Stoke’s equation,

Where, Cunningham correction factor

The modified stoke’s- Cunningham equation is

On further simplification with kinetic theory of gases:

Brownian Motion

THE DEAD CAN DANCE TOO

• Particles suspended in a gas or liquid seem to move around randomly as they are pushed to and fro by collisions with the atoms that comprise the gas or liquid.

• Brownian motion of a particle in the fluid is a result of thermal fluctuations surrounding the particle

Particle collection mechanism

The overall collection/removal process for particulates in a fluid takes place in 4 steps:

Application of external force velocity directs of retrieval section,

Retention at the retrieval area,

As particles get accumulated, they are subsequently removed,

Ultimate disposition completes the process.

Particle collection mechanism and efficiency

Brownian motion :Diffusion occurs when smaller particles having Brownian motion hit the surface of the fibers

Centrifugal force:

The shape of the collector

causes the gas to rotate. The

Heavier particles move

towards the wall and lose

kinetic energy and hence

Fall down and get separated.

The drift velocity, number of

Rotations and residence time

affects the efficiency.

Interception: Interception occurs when particles do not depart from the streamlines. The inertia or Brownian motion of particles is negligible. Particles following streamlines arrive at the fibers and get "intercepted" on the fiber surface.

Interception parameter NR=Dp (particle diameter)/Df (fiber diameter)

Inertia impaction: This occurs when particles cannot adjust to the "sudden" change of streamlines near fibers, and, due to inertia, depart from the streamlines and impact on the fiber surface.

Inertia impaction parameter, Ni= C

Thermophoretic and diffusiophoretics forces:

These are classified as flux forces because they are dependent on temperature and concentration gradients respectively. the thermal and diffusiophoretic forces, acting on a body suspended in a gas not in equilibrium, originates from interaction of gas molecules with solid surface.

Thermal: moves from hot to cold

Diffusiophoretics: moves in the direction of heavier partices in the fluid

The gas solid interaction is defined by ‘Ratio of mean free path length to particle radius’ called Knudsen number Kn.

Ratio is flux deposition number,

Single collection efficiency due to any flux force is

Gravity: When the only significant force acting on a particle is the gravity, then this mode of deposition is called sedimentation, or gravitational settling.

Electrostatic attraction:The charged particles are subjected to a strong electrical field to overcome the drag force of the fluid. Combined effect of direct impaction, interception and electrostatic attraction.

Electrostatic force, Fe=q Ep,

where, q:particle charge Ep: collection field intensity

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