CALCULATIONS IN NANOTECHNOLOGY TASNEEM 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. It is dominated by surface effects such as Van der Waals force attraction, hydrogen bonding, electronic charge, ionic bonding, covalent bonding, hydrophobicity, hydrophilicity, and quantum mechanical tunneling, to the virtual exclusion of macro-scale effects such as turbulence and inertia.For example, the vastly increased ratio of surface area to volume opens new possibilities in surface- based science, such as catalysis

Relationship between Nanoscience and Quantum Mechanics Bohr, Einstein, Planck, Wolgang Paulie, Heisenberg(position momentum), Schrodinger( wave function).

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 D[3,2]= 1 𝑛 𝐷 𝑖 3 𝑣 𝑖 / 1 𝑛 𝐷 𝑖 2 𝑣 𝑖 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]= 𝐷 𝑖 𝑣 𝑖 /𝑁 2.Surface area moment mean D[3,2] (Sauter Mean Diameter): D[3,2]= 1 𝑛 𝐷 𝑖 3 𝑣 𝑖 / 1 𝑛 𝐷 𝑖 2 𝑣 𝑖 3. Volume moment mean D[4, 3] (De Brouckere Mean Diameter)

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

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)

DCS DLS

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Fluid Particle Dynamics

Fluid dynamic mechanism → Gravitational force 𝑭 𝑮 = 𝝆 𝑷 𝝅 𝒅 𝒑 𝟑 𝒈 𝟔 → Buoyant force 𝑭 𝑩 = 𝝆 𝒂 𝝅 𝒅 𝒑 𝟑 𝒈 𝟔 → Drag force 𝑭 𝑫 =( 𝝆 𝒂 𝒗 𝟐 𝟐 𝒈 𝒄 ) 𝑨 𝑷 𝑪 𝑫 𝐹 𝑅 = 𝐹 𝐺 − 𝐹 𝐵 − 𝐹 𝐷 = 𝑚 𝑔 𝑐 𝑑𝑣 𝑑𝑡

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. 𝑭 𝑹 =𝟎 & 𝑭 𝑩 =𝟎 Solving, 𝑭 𝑮 = 𝑭 𝑫 Laminar regime 𝒗 𝒕 = 𝒈 𝝆 𝒑 𝒅 𝒑 𝟐 𝟏𝟖𝝁 Transition regime 𝒗 𝒕 = 𝟎.𝟏𝟓𝟑 𝒈 𝟎.𝟕𝟏 𝒅 𝒑 𝟏.𝟏𝟒 𝝁 𝟎.𝟒𝟑 𝒆 𝟎.𝟐𝟗 Turbulent regime 𝒗 𝒕 =𝟏.𝟕𝟒 ( 𝒈 𝒅 𝒑 𝒆 𝒑 𝒆 ) 𝟎.𝟓

Determination of flow regime To calculate 𝑣 𝑡 , 𝑎 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝐾 𝑑𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑒𝑠 𝑡ℎ𝑒 appropriate range of the fluid-particle dynamic laws that apply. K= 𝑑 𝑝 ( 𝑔 𝜌 𝑝 𝜌 𝜇 2 ) 1 3 →𝐾<3.3:𝑆𝑡𝑜𝑘 𝑒 ′ 𝑠 𝑙𝑎𝑤 𝑟𝑎𝑛𝑔𝑒:𝑅𝑒≤2.2→ Laminar regime →3.3<𝐾<43.6;𝐼𝑛𝑡𝑒𝑟𝑚𝑒𝑑𝑖𝑎𝑡𝑒 𝑙𝑎𝑤 𝑟𝑎𝑛𝑔𝑒, 2≤𝑅𝑒≤500→ Transition regime → 43.6<𝑘<2360;𝑁𝑒𝑤𝑡𝑜 𝑛 ′ 𝑠 𝑙𝑎𝑤 𝑟𝑎𝑛𝑔𝑒, 𝑅𝑒>500→ 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= 𝑣 3 𝜌 2 /𝑔𝜇 𝜌 𝑝 →𝑊<0.2222;𝑆𝑡𝑜𝑘 𝑒 ′ 𝑠 𝑙𝑎𝑤 → 0.2222<W<1514; Intermediate’s law → 1514< W; Newton’s law

Cunnigham correction factor At 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:

THE DEAD CAN DANCE TOO Brownian Motion 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 THE DEAD CAN DANCE TOO

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 K; Boltzmann t;abs temp d; aerodynamic dia of particle

Centrifugal force: The shape of the collector causes the gas to rotate 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 𝑑 𝑝 2 𝑣 𝜌 𝑝 18𝜇 𝑑 𝑐

η=4 𝑁 𝐹𝐷 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 𝑁 𝐹𝐷 is flux deposition number, Single collection efficiency due to any flux force is η=4 𝑁 𝐹𝐷

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

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