che2165 - last tutorial
Post on 22-Nov-2014
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This tutorial will cover surface engineering and colloids contents only
1. the equations you will be provided in the final exam; 2. the solutions to mid-term exam questions; 3. a few previous year's final exam questions/solutions; 4. some working questions we did in the lectures and tutorials. 5. a guide to the preparation of the final exam.
1. Equa(on list for surface engineering sec(on
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l =γr(cosθ )t2η
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dldt
=rγ cosθ8ηt
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dldt
=rγ cosθ4ηl€
ΔP = γ1R1
+1R2
⎛
⎝ ⎜
⎞
⎠ ⎟
Washburn equa,ons
Laplace equa,on
Interfacial tension (or interfacial energy), it has two types of ques,ons
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γ12 = γ1 +γ 2 −WA = γ1 +γ 2 − 2 γ1dγ 2
d − 2 γ1pγ 2
p
Lecture 20
Lecture 20
Lecture 18 Type 1
Type 2
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WA = 2 γ1dγ 2
d + 2 γ1pγ 2
p( )
1. Equa(on list (con(nue)
€
γL 1+ cosθ( ) = 2 γ SdγL
d + γ SpγL
p( )Typical ques,on:
Lecture 21
γ θ γ γ γ γ l l d s d
l p
s p ( ) 1 2 2 + = + cos Green = given
Red = to find
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γ sd = γDIM
1+ cosθDIM( )2
4
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γ sp =
γW (1+ cosθW ) − 2 γWd γ s
d( )2
4γWp
These two equa,ons came from the top equa,on. They are NOT provided in the exam paper!!
Deriva,ons in lecture 21, Working Problem 2.
Solid surface energy
DIM as a probe liquid has γld = 0.
1. Equa(on list (con(nue)
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cosθobv(Cassie ) = f1 cosθ1 − f2WeNng of real surfaces
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f1 =1+ cosθobs
1+ cosθTypical ques,on:
2. Mid-‐term exam ques(ons
• Ques(on 2. The volume of a molecule to be 4.19 Å3 (assuming the molecule is spherical and 1 Å = 1×10-‐10 m). Calculate the polarizability of the molecule α and clearly indicate units. (7 marks)
• Ques(on 3. A) Calculate the surface area of 2.7 grams of calcium carbonate powder, assuming spherical par(cles, diameter = 1 micrometer, density = 2.7 g/cm3) (7 marks)
• B) If this calcium carbonate powder is dispersed in water to a very low concentra(on, calculate the terminal velocity of at which the dispersed par(cles seYle. The density and the viscosity of water are 1 g/cm3 and 1 cP, respec(vely. (7 marks)
• Ques(on 4. You are doing a microelectrophoresis experiment with 2 µm diameter latex colloids dispersed in a 0.5 mmol/L aqueous solu(on of NaCl at 25oC. It takes 10 s for the colloid to cover a distance of 150 µm in the microelectrophoresis cell, with a poten(al gradient of 15 V/cm.
• A) Calculate the colloid’s electrophore(c mobility (5 marks)
• B) Calculate the colloid’s Zeta poten(al. Define the units (8 marks)
3. Some previous years’ ques(ons and solu(ons
• 2010 ques(on 2. Calculate the interfacial tension between n-‐decane and water using the data in the table. (5 marks)
• Water n-‐decane
• Surface tension γ (mN/m) 72.8 23.9
• γd (mN/m) 21.8 23.9 • γp (mN/m) 51.0 0
2010 ques(on 3
• A capillary tube with an internal diameter of 200 μm is inserted into a water droplet, which is placed on a superhydrophobic surface. The internal and the external walls of the capillary tube have contact angles with water of 0º and 90º, respec(vely (See figure below). At the equilibrium state, if the water surface tension is 72.8 mN/m, the water droplet has a spherical shape and a diameter of 3 mm, calculate the capillary rise of water in the capillary tube (neglect the height of the water droplet). The density of water is 1000 kg/m3, the gravity constant is 9.8 m/s2. (12 marks)
Internal diameter d = 200 micrometers
Water droplet diameter D = 3 millimeters
d
D
hCapillary rise (h), neglect the size of the water droplet
2008 Ques(on 10
• 10. Calculate the surface energy of poly(methyl methacrylate) (PMMA) using the contact angle data of two liquids of known surface tension listed in the table. (8 marks)
• Water Diiodomethane
• Surface tension γ (mN/m) 72.8 50.8 • γd (mN/m) 21.8 50.8 • γp (mN/m) 51.0 0 • Contact angles with PMMA 68˚ 37˚
4. Some working problems in our lectures
CHE 2156 Dr Wei Shen
Working problem 6: Find out the ra(o of penetra(on velocity between water and isopropanol using the θ, γ and η
data below
θ(˚) γ(mN/m) η(mPa.s)
Water 35 72 1.0 Isopropanol ~0 23 2.27
Liquid penetra,on In paper (porous non-‐woven cellulose fibre matrix)
Problem 7: Find the water penetra(on distance in a cylindrical capillary at 0.5 sec.
θ Assuming contact angle is 30˚, surface tension of the liquid is 70 mN/m. Capillary diameter is 200 micrometers. Liquid viscosity is 1 mPa.s.
Is this approach correct?
2010 ques(on 8
• Given that average covalent bonds of polymeric materials is 500kJ/mol, if plasma surface modifica(on is used to modify the surface, calculate the temperature of hot electrons required to modify the surface. (7 marks)
Energies in a glow-‐discharge plasma vs typical bond energies
Energy eV In glow discharge
Electrons 0 -‐ 20 ions 0 – 2 UV/visible 3 -‐ 40
In covalent bonds C-‐H 4.3 C-‐N 2.9 C-‐Cl 3.4 C-‐F 4.4 C=O 8.0 C-‐C 3.4 C=C 6.1
k – Boltzmann constant = 1.38x10-‐23J/K or 8.625x10-‐4 eV/K Te – electron temperature
If Te = 104 – 105 K, then electron kine,c energy will be 2.07x10-‐19 – 2.07x10-‐18 J or 1.3 -‐ 13 eV
Average covalent bond energy is in the order of 500 kJ/mol or 5 eV
The way to prepare the final exam for CHE 2165
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