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Homework assignments posted here are subject to correction in class or
through other means. Problems as assigned here are for your convenience
but are not a substitute for obtaining assignments in class.
Assignments as issued in class supercede these assignments unless otherwise
noted.
Homework Assignment: 1
2 3 4 5
6
Who's Who in Interfacial Engineering
Appendix A in chapter 1 lists a number of contributors to the current state
of knowledge in the fundamentals of interfaces. Select two of these
individuals and write at least a single paragraph for each summarizing i) the
contribution and ii) why it is important.
Since we should not have any
repetition in a class this size, you must get your selection approved by me BY
EMAIL ONLY. In the case of multiple requests for a single subject, the time
stamp on the received email will be used to determine who will be assigned
their preference.
Your submission should be in a Microsoft Word file
emailed to me prior to the start of class.
Remember, plagiarism can get
you expelled.
Assignment Objectives:
 | Describe the relevance and substance of historical contributions to
interfacial science |
Reading Assignments:
|
|
Tuesday (8/17): Ch. 1 Introduction, HW1
Assigned |
|
| Thursday (8/19): Ch.
2 pp. 13-24 Surface Tension & Capillary Rise |
|
|
Tuesday (8/24)
Ch. 2 pp. 24-27 Kelvin equation and vapor pressure, HW1 Due, HW2
Assigned |
|
|
Thursday (8/26) Ch. 2 pp. 27-350 Contact
angle and wettability |
Invisible Forces are Affecting This Assignment
Problems for Class Discussion
1. The
pressure inside an air bubble in water is (equal to, less than, greater than)
the hydrostatic pressure inside a droplet of water in air when they both have
the same diameter. Why?
2. The
capillary rise between two parallel plates of separation distance
d is (equal to, less than, greater
than) the capillary rise in a tube, diameter
d, of the same material. Why? (Hint:
think about the shape of the interface)
Problem 2.6
Problem 2.7
Problems for Submission
2.3
2.4
2.5
Assignment
Learning Objectives:
·
Perform analyses associated with surface phenomena including capillary rise and
interfacial curvature
Reading
Assignments:
| Tuesday (8/24):
Ch.2. pp. 24-27 Kelvin equation and vapor pressure, HW1 Due,
HW2 Assigned |
| Thursday (8/26):
Ch.2. pp. 27-35
Contact angle and wettability |
| Tuesday (8/31):
Ch.3. pp.
47-57 Adsorption |
Tension is sometimes only skin deep
Problems for Class Discussion
1. For
n-octane,
n-hexadecane and n-octanol
the surface tensions are 21.8, 30.0 and 27.5
, and the interfacial tensions on
water are 50.8, 52.1 and 8.5
respectively.
Comment on the long-term spreading behavior of the three hydrocarbons on water.
Yes, calculations are in order before commenting!
Problems for Submission
1. Estimate
the surface tension of water at room temperature assuming that
. Make sure you state all of your
assumptions. Suggest reasons for the deviation from the experimentally measured
value of 72.8
.
2. A highly
viscous silicon oil has a surface tension of about 20
. A small drop of water is placed
on a film of the oil. The contact angle measured immediately after the water is
placed on the film is 110 degrees. What is the interfacial tension between the
water and the oil?
3. The
pressure required to prevent liquid from entering a plug of finely divided solid
is twice as great for a liquid of surface tension 50
, which completely wets the solid,
as it is for a liquid of surface tension 72.8
, which as a finite contact angle
with the solid. Calculate this contact angle.
Assignment Objectives:
|
Perform analyses associated with surface phenomena including spreading and
wetting |
Reading Assignments:
Tuesday (8/28):
Ch.2. pp. 27-35
Contact angle and wettability, HW2 Due, HW3 Assigned
Thursday (9/02):
Ch.3. pp. 47-57
Adsorption
Tuesday (9/07):
Ch.3. pp. 47-57
Adsorption, HW3 Due, Lab1 Assigned
Why So Tense?
Problems for Class Discussion
1. The figures below represent capillaries
of varying construction and arrangement. The diameter of the capillary portion
is the same in each case, and all of the capillaries are constructed of glass,
except where otherwise indicated. The equilibrium rise for water is shown at
the left. Draw meniscuses in each figure to correspond to (a) the level
reached by water rising up the clean, dry tube and (b) the level to which the
water would recede after having been sucked up to the end of the capillary.
The meniscuses in the capillary may be assumed to be spherical in shape.
Problems for
Submission
1. Calculate the vapor pressure of water when present in a
capillary of 0.1 ÿm radius (assume zero contact angle). Express your result as
percent change from the normal value at 20 °C.
2. Now assume that the
effective radius of that capillary is reduced because of the presence of an
adsorbed film of water 100 Å thick. Show what the percent reduction in vapor
pressure should now be.
(Submission Problems 1 & 2 come from Adamson, p.
92; Discussion problem 1 from Adamson, p. 40)
| Review concepts of spreading and capillarity |
| Use the Kelvin equation to estimate vapor pressure |
Reading Assignments:
| Tuesday (9/07): Ch.3. pp. 47-57 Adsorption, HW3 Due, HW4
Assigned, Term paper assigned |
| Thursday (9/12): Ch.3. pp. 47-57 Adsorption, Lab1 Assigned |
| Tuesday (9/14): Ch.8 pp. 153-171 Bubbles, Foams, and Films, HW4
Due, HW5 Assigned |
Spread your work out to form a monolayer
Problems for Class Discussion
1. From
Benjamin Franklin's experiment (see link on website along with the introduction
to Chapter 4 in Adamson’s text), estimate an approximate value for Avogadro's
number; make your calculation clear.
The answer is a little off-- would more accurate measurements on Franklin's part
helped?
Problems for Submission
1. The plot of
surface tension versus the natural logarithm molar concentration for a
surfactant in water at 20 °C is linear with a slope of -7.25 mJ m-2.
Calculate the area per surfactant molecule at the surface in inverse square
nanometers.
2. When 2.0 g
of finely divided bone charcoal is immersed in 100 cm3 of a 10-4
M dye solution and brought to
equilibrium, the molar concentration of the dye solution drops to 0.4 x 10-4
M. When an additional 2.0 g is added,
the concentration drops to 0.2 x 10-4
M. Calculate the specific surface area of the powder in square
meters per gram, assuming the adsorption obeys the Langmuir isotherm. The
effective surface area of the dye molecule is 65 Å2.
Assignment Objectives:
| Perform calculations required to analyze monolayers and interpret
results from Langmuir isotherms |
| Apply the Gibbs adsorption isotherm to analyze experimental results |
| Review concepts of spreading and capillarity |
Reading Assignments:
| Tuesday (9/14):
Ch.8 pp.
153-171 Bubbles, Foams, and Films, HW4 Due, HW5 Assigned |
| Thursday (9/16):
Ch.8 |
|
Tuesday (9/21):
Ch.4 pp.
61-68 Surfactants, HW5 Due, HW6 Assigned |
|
Thursday (9/23):
Term Paper Memo Due |
|
Friday (10/1):
Lab01 Report Due |
|
Thursday (10/05):
Midterm Exam, Chapters 1-3, 8
|
Not Enough for Surface Tension Headache
From your textbook:
1. The effective area of the amphphile headgroup at the surface of
a micelle (increases, decreases, remains the same). Why?
2. The surfactant number (increases, decreases, remains the same)
as salt is added to a surfactant solution. Why?
Problems for Submission
1. The surface tensions of aqueous solutions of sodium dodecyl
sulfate (SDS) at 25 °C at different concentrations are:
|
c (mM)
|
0
|
2
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
12
|
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g (mN/m)
|
72.0
|
62.3
|
52.4
|
48.5
|
45.2
|
42.0
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40.0
|
39.8
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39.6
|
39.5
|
Estimate the surface excess and the area per surface
SDS molecule at three concentrations: 3, 7, 10 mM.
Assignment Objectives:
| Predict the behavior of systems containing aggregates |
Reading Assignments:
| Tuesday (9/21): Ch.4 pp. 61-68 Surfactants, HW5 Due, HW6
Assigned |
| Thursday (9/23): Term Paper Memo Due
|
| Tuesday (9/28): Ch. 4, HW6 Due
|
| Thursday (9/30): Ch. 5 pp. 80-92
|
| Friday (10/1): Lab01 Report Due
|
| Tuesday (10/05): Midterm Exam, Chapters 1-3, 8
|
Aggregate This
1. The surface
tensions of aqueous solutions of the nonionic surfactant CH3(CH2)9(OCH2CH2)5OH
at 25 °C at different concentrations c are:
|
c (mM)
|
0
|
0.01
|
0.03
|
0.1
|
0.2
|
0.5
|
0.8
|
1
|
2
|
3
|
|
g (mN/m)
|
72.0
|
63.9
|
56.2
|
47.2
|
41.6
|
34.0
|
30.3
|
29.8
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29.6
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29.5
|
Determine the
critical micelle concentration (CMC). What is the surface area per surfactant
molecule at the CMC?
2. CMCs and
aggregation umbers for the nonionic surfactant dodecyldimethylamine oxide (n-C12H25(Me)2N+
O-) (M.W. ~ 229) are given in the following table.
|
T(°C)
|
CMC (g/l)
|
N0
|
|
1
|
0.0284
|
77
|
|
27
|
0.0210
|
76
|
|
40
|
0.0183
|
78
|
|
50
|
0.0175
|
73
|
(a)
Calculate the area per head group assuming that the micellar radius equals the
length of the fully extended hydrocarbon chain. (b) Using the equilibrium model,
calculate the values of
DGmic
for micellization at 25 and 40 °C.
From Interfacial Engineering.
Assignment Objectives:
| Determine the CMC for an amphiphile solution |
| Describe micellar structure based on geometric considerations |
| Perform calculations involving the thermodynamic behavior of micelles,
including relaxation phenomena |
Reading Assignments:
| Tuesday (9/28): Ch. 4, HW6 Due
|
| Thursday (9/30): Ch. 5 pp. 80-92
|
| Friday (10/1): Lab01 Report Due
|
| Tuesday (10/05): Midterm Exam, Chapters 1-3, 8
|
This assignment is aggregating
From Interfacial Engineering:
1.
The following table gives the measured critical micelle concentration (CMC)
of an SDS solution as a function of the concentration of sodium chloride in
the solution. The table also gives the measured mean aggregation numbers.
|
cNaCl
(M)
|
CMC (mM)
|
N0
|
|
0.00
|
8.1
|
58
|
|
0.01
|
5.7
|
64
|
|
0.03
|
3.1
|
71
|
|
0.10
|
1.5
|
93
|
|
0.30
|
0.71
|
123
|
Assuming spherical micelle geometry, calculate for all five salt
concentrations: (a) the volume of hydrocarbon core inside a micelle; (b) the
effective radius of the hydrocarbon core; (c) the cross-sectional area per
chain at the aggregate surface; (d) the area per charge assuming it is
located 0.3 nm outside the hydrocarbon core.
2.
In pressure-jump experiments on micellar solutions of sodium hexadecyl
sulfate (SHS) at 45 °C, one observes a fast relaxation process that varies
with SHS concentration as follows:
|
T(°C)
|
CMC (g/l)
|
N0
|
|
1
|
0.0284
|
77
|
|
27
|
0.0210
|
76
|
|
40
|
0.0183
|
78
|
|
50
|
0.0175
|
73
|
The
CMC is 0.52 mM and the aggregation number N=100. Determine the rate constant
for a monomer leaving the micelle,
. Estimate the standard deviation of the micelle
size distribution. What is the value of the association rate constant?
Calculate the average lifetime of a monomer in the micelle.
Assignment Objectives:
|
Predict the behavior of amphiphiles based on geometry
|
|
Perform calculations involving the relaxation behavior of micelles
|
Reading Assignments:
| Tuesday (10/12): Ch. 6, HW7 Due
|
| Thursday (10/14): Ch. 6 T |
| uesday (10/19): Ch. 6, HW8 Due
|
The Force is Strong in this One
From Interfacial Engineering:
Problems for Class Discussion
1. What are
the three material properties that determine the theoretical Hamaker
constant? Would you expect the experimental value for the Hamaker constant
to be (equal to, less than, or greater than) the theoretical value for
water? For benzene? Why?
2. Is the
force of attraction between two identically shaped tine particles of quartz
placed in vacuum (equal to. less than, greater than) the force of attraction
when they are placed in water? Why?
3. Assuming
they are uncharged, do dust particles and mist droplets attract or repel
each other in air?
4. Would you
expect tiny spheres of polystyrene and PTFE (polytetrafluoroethylene) in
octane to attract or repel themselves? Each other?
Problems for Submission
1. Calculate
the different van der Waals energy contributions for interaction between an
ethanol and benzene molecule, based on the data below:
|
Compound
|
Dipole
moment
(Debye)
|
Polarizability
(10-30
m3)
|
Ionization
potential
(eV)
|
|
Ethanol
|
1.69
|
5.49
|
10.49
|
|
Benzene
|
0
|
10.3
|
9.24
|
2.
Estimate the Hamaker constant for water assuming hn to be about 10 eV. Then calculate the
approximate force of attraction between two spheres of ice of radius 1
mm and 100 Å apart.
Assignment Objectives:
| Compare the relative strengths of intermolecular forces under
different sets of conditions (phase, solvents, composition, etc.) |
| Calculate forces between macroscopic bodies |
| Compare relative attractions of bodies in different media |
Reading Assignments:
|
Thursday (10/21):
Ch. 7
|
|
Tuesday (10/26):
Ch. 7, HW9 Due
|
See Class Handouts From your textbook:
4.12, 4.13, 4.14, 4.15
Assignment Objectives:
| Describe the rate of coagulation processes |
| Describe the potential requirements for a stable colloid |
| Explain the role of the zeta potential for characterizing colloidal sols |
| Apply principles of electrokinetics to characterizing colloids |
Reading Assignments:
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|
Thursday (11/06) Review Remainder of Chapter 4 |
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Friday (11/07) Milestone 2 for Term Paper Due (5PM) |
|
|
Tuesday (11/11) Review Chapter 8,
HW9 Due |
|
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Thursday (11/13) Review Chapter 10 |
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Tuesday (11/18) No class meeting, AIChE Annual Meeting |
|
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Thursday (11/20) No class meeting, AIChE Annual Meeting,
HW10 Due |
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Tuesday (11/25) EXAM 2 |
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Thursday (11/27 ) No class meeting, Thanksgiving |
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Tuesday (12/02) A primer on measuring interfacial area |
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Thursday (12/04 ) Term Paper Presentations |
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Tuesday (12/09) Term Paper Due (10 AM) |
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