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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

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Homework #1 (Due 8/21/12)

Who's Who in Interfacial Engineering

You ahve been given a list of 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:

bulletDescribe the relevance and substance of historical contributions to interfacial science

Reading Assignments:

bullet

Tuesday (8/14):           Ch.1     Introduction, HW1 Assigned

bullet

Thursday (8/16):         Ch.2     pp. 23-46 Surface tension

bullet

Tuesday (8/21):           Ch.2.    pp. 46-76 Curvature and tension measurement

bullet

Thursday (8/23):         Ch.2.    pp. 76-103 Kelvin equation and vapor pressure

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Homework #2 (Due 8/28/12)

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)

3. Explain why it is possible to make sandcastles only in partially wet sand and not in either fully immersed or completely dry sand.

4. Why do construction workers spray water when they are working with very dusty materials?

 

 

Problems for Submission

2.3, 2.4, 2.9, 2.10

Assignment Learning Objectives:     

         Perform analyses associated with surface phenomena including capillary rise and interfacial curvature

 

Reading Assignments:

bullet

Thursday (8/23):         Ch.2.    pp. 76-103 Kelvin equation and vapor pressure

bullet

Tuesday (8/28):           Ch.3.    pp. 107-147 Gibbs adsorption

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Homework #3 (Due 9/4/12)

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 m 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 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)

bulletReview concepts of spreading and capillarity
bulletUse the Kelvin equation to estimate vapor pressure

Reading Assignments:

bullet

Thursday (8/30):         Ch.3.    pp. 148-171     Micelles and other amphiphile structures

bullet

Tuesday (9/4):             Ch.3.    pp. 171-207     Monolayers

Homework #4 (Due 9/11/12)

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:

bullet 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

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Homework #5 (Due 09/18/12)

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 Adamsons 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 2.

Assignment Objectives:

bulletPerform calculations required to analyze monolayers and interpret results from Langmuir isotherms
bulletApply the Gibbs adsorption isotherm to analyze experimental results
bulletReview concepts of spreading and capillarity

Reading Assignments:

bulletT
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Homework #6 (Due 9/27/12)

Not Enough for Surface Tension Headache

Problems for Discussion:

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

g (mN/m)

72.0

62.3

52.4

48.5

45.2

42.0

40.0

39.8

39.6

39.5

 Estimate the surface excess and the area per surface SDS molecule at three concentrations: 3, 7, 10 mM.

2. 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

29.6

29.5

Determine the critical micelle concentration (CMC). What is the surface area per surfactant molecule at the CMC?

3. 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.

4. 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.

 

5. 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:

bulletPredict the behavior of systems containing aggregates
bulletDetermine the CMC for an amphiphile solution
bulletDescribe micellar structure based on geometric considerations
bulletPerform calculations involving the thermodynamic behavior of micelles, including relaxation phenomena

Reading Assignments:

bulletTuesday (9/18):           Introduction to molecular forces
bulletThursday (9/20):         Term Paper Memo Due
bulletTuesday (9/25):           Career Fair, no class meeting, watch videos
bulletThursday (9/27):         Review HW6
bulletTuesday (10/02):         Midterm Exam, Chapters 1-4
bulletThursday (10/4):         Fall Break
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The Force is Strong in this One

From Interfacial Engineering:

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?

 

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 apart.

 

Assignment Objectives:

bulletCompare the relative strengths of intermolecular forces under different sets of conditions (phase, solvents, composition, etc.)
bullet Calculate forces between macroscopic bodies
bulletCompare relative attractions of bodies in different media

Reading Assignments:

bullet

Thursday (10/21):            Ch. 7

bullet

Tuesday (10/26):              Ch. 7, HW9 Due

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See Class Handouts From your textbook:

4.12, 4.13, 4.14, 4.15

Assignment Objectives:

bulletDescribe the rate of coagulation processes
bulletDescribe the potential requirements for a stable colloid
bulletExplain the role of the zeta potential for characterizing colloidal sols
bulletApply principles of electrokinetics to characterizing colloids

Reading Assignments:

bullet Thursday (11/06) Review Remainder of Chapter 4
bullet Friday (11/07) Milestone 2 for Term Paper Due (5PM)
bullet Tuesday (11/11) Review Chapter 8, HW9 Due
bullet Thursday (11/13) Review Chapter 10
bullet Tuesday (11/18) No class meeting, AIChE Annual Meeting
bullet Thursday (11/20) No class meeting, AIChE Annual Meeting, HW10 Due
bullet Tuesday (11/25) EXAM 2
bullet Thursday (11/27 ) No class meeting, Thanksgiving
bullet Tuesday (12/02) A primer on measuring interfacial area
bullet Thursday (12/04 ) Term Paper Presentations
bullet Tuesday (12/09) Term Paper Due (10 AM)

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