NANO 202 / CENG 212 Intermolecular & Surface Forces Homework Packet. Assignment numbers correspond to the class number written on the syllabus and should be done immediately after the class indicated Assignment 1 1) Rank the following gases by increasing value of the van der Waals parameter a:

a) Cl2, Br2, H2, F2, O2, N2 b) Rn, Kr, Xe c) CO, N2 d) N2, NH3, N2H4, (CH3)2CO e) C2H6, C2H2, C2H4 f) Do you expect these interactions to be stronger in a vacuum or in a solvent?

2) Find an expression for the self-energy μi for a molecule confined to a two-dimensional

surface—that is, the sum of the interaction energies with all of the other molecules on the surface. The number density is ρ and the molecules interact via a potential function defined by w(r) = –C/rn. Verify that n > 2 for the interaction to be short-ranged.

Assignment 2

3) The entropy of vaporization is a constant for most substances, Svap ~80 J mol–1 (Trouton’s

rule). a) Plot the latent heat or enthalpy of vaporization, Lvap = Hvap, as a function of TB for at least

three substances from the upper section of the following table (ie, pentane – bromine). Verify that these substances follow Trouton’s rule.

Substance TB (K) Lvap (kJ mol-1) Pentane 309 25.8 Hexane 342 28.9 Heptane 372 31.8 Ethylene oxide 284 25.5 Benzene 353 30.7 Diethyl ether 308 26.5 Tetrachloromethane 350 29.8 Mercury 630 59.1 Bromine 332 30.0

Water 373 40.7 Formic acid 374 23.1

b) Now plot the values for water and formic acid. Do they follow Trouton’s rule? Speculate as to why or why not.

Assignment 3 1) Calculate the separation, r, in nanometers, beyond which the force between a barium ion and

a bromide ion falls below kT (at room temperature in vacuum). 2) Estimate the radius of the potassium ion, K+, given the following values for the solubility of

potassium chloride at 298K in the following solvents (15 pts.) • water (0.166 mol K+ / mol water, εwater = 78.5) • methanol (0.0044 mol K+ / mol methanol, εmethanol = 32.6) • acetone (1.4 × 10-6 mol K+ / mol acetone, εacetone = 20.7)

Assignment 4 In class, we mentioned that the dipole of carbon monoxide (CO) is oriented such that the partial negative charge resides on the carbon atom. The carbonyl group, C=O, as occurs in ketones, carboxylic acids, aldehydes, esters, and peptides, has its partial negative charge on the oxygen atom. If the internuclear distance between C and O is 1.2 × 10–10 m and the dipole moment is 2.4 D (1 Debye = 3.336 × 10–30 C m), calculate (a – d) using the following formulae,

u = ql

where u is the dipole moment and l is the distance between the two charges, +q and –q, and

V =14πε0

qr

is the electrical potential (voltage) at an arbitrary point from a charge (assume r >> l). The voltage at an arbitrary point away from the dipole can be represented by the sum of the potentials due to each of the charges that make up the dipole. a) Calculate the effective charges +q and –q on the carbon and oxygen atoms.

b) Calculate the potential 9.0 × 10–10 m from the dipole along its axis, with the oxygen being

the nearer atom.

c) Calculate the potential 9.0 × 10–10 m from the dipole perpendicular to its axis.

d) What would the potential be if only the oxygen atom were charged?

Assignment 5 The dielectric constant (ε) of a solvent reflects its ability to screen the electric fields of solubilized ions and dipoles and thus attenuates intermolecular forces. The greater the tendency of solvent molecules to orient in the presence of an electric field, the greater the dielectric constant. In general, this ability increases with the density of dipoles and with any specific intermolecular forces within the solvent. Using these criteria, the chemical structures, and the dipole moment (in units of Debye, 1 D = 3.336 × 10-30 C m), rank the following groups of solvents in order of decreasing ε.

a) Water H2O (1.85 D), formamide HC(=O)NH2 (3.70 D), dimethylformamide

HC(=O)N(CH3)2 (3.86 D)

b) Methanol CH3OH (1.69 D), isopropanol (CH3)2CHOH (1.66 D), ethanol CH3CH2OH (1.69 D)

c) Acetonitrile CH3CN (3.92 D), acetone (CH3)2C=O (2.9 D), dimethylsulfoxide (CH3)2SO (3.96 D)

d) Carbon tetrachloride CCl4 (0 D), dichloromethane CH2Cl2 (1.6 D), chloroform CHCl3

(1.06)

e) Tetrahydrofuran —CH2CH2CH2CH2O— (5-member ring, 1.63 D), diethyl ether CH3CH2OCH2CH3 (1.15 D)

f) Benzene C6H6 (0 D), hexane C6H14 (0 D), carbon tetrachloride CCl4 (0 D)

Assignment 6 1) Write the name of the dominant intermolecular or interatomic interaction represented by the

symbol (—) and circle the interactions whose potentials are >10 kT at 298 K in a vacuum. The choices are dispersion (London), orientational (Keesom), inductive (Debye), covalent, ion-dipole, ion-induced dipole, hydrophobic, and coulombic. (1 pt. each)

a) NH3—NH3 b) K+—I− c) Xe—Kr d) CH3CH2—CH2CH3 e) C2H6—C2H6 in vacuum f) C1000H2002—C1000H2002 g) Cs+—H2O h) (CH3)2CO—(CH3)2CO i) CH4—CH4 in water j) Cl−—CH4

2) Calculate the strength of interaction (in units of kT) between a chloromethane molecule and a neon atom at room temperature (300K) that are 1 nm apart.

Assignment 7 1) Explain why the melting temperature of 2-methyl pentane is lower than that of n-hexane,

while the boiling temperatures are similar.

2) Draw the two isomers of 3-hexene and explain why the melting temperatures are different. Assignment 8 Reconcile the fact that the Debye force is always attractive with the hydrophobic force, which suggests a repulsive interaction between water and a non-polar solute. Assignment 9 Consider the diagram below, which represents a droplet of pure water (γLG = 72.8 J m-2) on the surface of an unknown polymer in air.

a) Is the unknown polymer most likely polyethylene [(CH2)2]n, Teflon [(CF2)2]n, or cellulose

(C6H10O5)n?

b) Which material listed in (a) would make the best microfluidic device driven by capillary flow?

Assignment 10 All intermolecular and surface forces have one of three fundamental origins: electrostatic, entropic, and ________. Please respond to the following questions. (1 pt. each)

a) What is the third fundamental origin represented by the “_________” above?

b) What is the origin of the Debye interaction? c) What is the origin of the steric repulsive force?

d) What is the origin of the dispersion interaction?

e) What is the origin of the hydrophobic force?

Assignment 11 Calculate the interaction energy per unit area between two silicon surfaces (A = 20 × 10-20 J) at a separation D = 0.5 nm in air. Use this result to estimate the force between a silicon AFM tip with the surface of a silicon wafer, below (scale bar = 5 nm). (5 pts.)

Assignment 12 A sphere composed of polyvinylchloride (PVC, A = 7.5 × 10-20 J, ρ = 1300 kg m-3, rVDW ~ 0.17 nm) is adhered to the underside of a smooth sheet of the same material against the force of gravity. The largest radius, R, of sphere that will remain adhered to the surface against the force of gravity is 1.5 mm. On which planet are we most likely to be: Earth, Mercury (the smallest of the planets), or Jupiter (the largest of the planets)? (5 pts.) Assignment 13 Consider a biocolloidal dispersion of vesicles with radius R = 100 nm in a 100 mM NaCl solution (κ–1 = 0.95 nm). The surface potential ψ0 and thus the stability of the biocolloid can be adjusted by changing the pH. Assume that the interaction takes place at physiological temperature, T = 310 K.

a) Write down a function for the DLVO interaction in terms of R, the double-layer

interaction constant Z, the Hamaker constant A, the Debye parameter κ, and the distance between particles D. (3 pts.)

b) When the interparticle separation equals the Debye length, show that the colloid is stable

when the surface potential ψ0 = 34.5 mV, and unstable when ψ0 = 14.5 mV. Note: in Israelachvili’s formula for the double-layer interaction, ψ0 is in mV, not V. (5 pts.)

c) At large separations (D >> κ-1), is the DLVO interaction dominated by the electrostatic double-layer or the van der Waals component? Is the force attractive or repulsive? (2 pts.)

Assignment 14 Write the name of the intersurface or interparticle force that is responsible for the effects described in (a) through (j). The choices are covalent bonding, coulombic, van der Waals, capillary, electric double layer, DLVO, steric repulsive, oscillatory solvation, and depletion. Assume standard temperature and pressure unless otherwise indicated. (1 pt. each)

a) The force experienced between two smooth mica surfaces when brought from a distance of 2 nm to contact in n-hexane.

b) The attractive force experienced between two smooth mica surfaces when brought from

of 2 nm to contact in liquid 8-methyloctadecane: CH3—(CH2)6—CH(CH3)—(CH2)9—CH3

c) The attractive force experienced between two mica surfaces each with a value of rms roughness of 1 nm when brought from a distance of 2 nm to contact in n-hexane.

d) An epoxy-based adhesive polymerized by a condensation reaction against an OH-

terminated silica surface.

e) A fully cured, smooth, epoxy sphere stuck to an OH-terminated silica surface in a vacuum.

f) The repulsive force of two chitosan hydrochloride surfaces in water at neutral pH.

g) The attractive force of two epoxy beads separated by 2 nm in a solution of polystyrene

random coils whose Flory radii are 3 nm.

h) The attractive force between chitosan and graphene oxide at neutral pH.

i) The increase in adhesive force of a single gecko spatula as a function of relative humidity.

j) The use of a polymer brush on the surfaces of colloidal particles to prevent aggregation.

Assignment 15 Consider a suspension of cylindrical silicon dioxide nanowires with dimensions l = 10 μm, d = 25 nm interacting in a 200 mM aqueous solution of KCl. (ASiO2–water–SiO2 = 1.4 × 10–20 J) The wires have been chemically modified to have a surface potential ψ0 = 5 mV. Assume the nanowires interact with their long axes arranged in parallel and are initially at a separation D = 5 nm. Useful quantity: tanh2 (5/103) = 0.00235

a. Calculate the DLVO force exerted by the nanowires on each other (10 pts.)

b. Calculate the average spacing (s) of polymer “mushrooms” (i.e., in the low-coverage regime) with Rg = 1 nm required produce a repulsive pressure between the nanowires at D = 5 nm. You may assume for simplicity that the force calculated in (a) acts over a total area of contact of 10–15 m2. (20 pts.)

Assignment 16 Consider the diagram from class 10, along with your responses to the questions. The diagram represents a droplet of pure water (γLG = 72.8 J m-2) on the surface of an unknown polymer in air.

a) Calculate the value of γLS, the interfacial energy between pure water and the polymer. (3

pts.)

b) Calculate the height a column of pure water would rise in a capillary tube (d = 0.5 mm) of this polymer. (3 pts.)

Assignment 17 Why does soap feel slippery?

Assignment 18 1) Consider again the droplet of water from worksheets 10 and 17. The critical micelle

concentration of sodium dodecyl sulfate (SDS) in water is 8 mM.

a) SDS is added to the water for a final bulk concentration of 8 mM. Does the contact angle increase, decrease, or remain the same? Why?

b) The concentration of SDS is increased to from 8 mM to 10 mM. Does the contact angle

increase, decrease, or remain the same? Why? 2) Consider the gradual addition of an unknown surfactant to water in an open beaker in air.

a) Identify on the chart below the plots corresponding to the concentration of monomers X1,

the concentration of monomers in large aggregate XN, the concentration of aggregates XN/N, and the critical micelle concentration (CMC). (3 pts.)

a) Calculate the critical micelle concentration in mole fraction units given that the radius of

a surfactant molecule is r = 1 nm and its interfacial free energy is γi = 10 mJ m-2. (4 pts.)

b) If the concentration of the unknown surfactant in the bulk is equal to the critical micelle concentration, what happens to X1, XN, and XN/N if small droplets of olive oil are dispersed in the solution in the moments before they rise to the surface because of buoyancy. (3 pts.)

Jurin equation:

ℎ =2𝛾!" cos𝜃𝜚𝑔𝑅

Young-Dupré equation: 𝑊!" = 𝛾!"(1+ cos𝜃) Debye length:

𝜅!! =  0.304[𝑋]

 nm,        𝑋 ≡ 𝑜𝑛𝑒  𝑡𝑜  𝑜𝑛𝑒  𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑙𝑦𝑡𝑒

Alexander-de Gennes equation (brush regime):

𝑃 𝐷 =𝑘𝑇𝑠!

2𝐿𝐷

!!+

𝐷2𝐿

!!  𝑓𝑜𝑟  𝐷 < 2𝐿

Formation of aggregates: XN = N{exp[α(1 – 1/Np)]}N α ≈ 4πr2γi / kT Debye length:

𝜅!! =  0.304[𝑋]

,        𝑋 ≡ 𝑜𝑛𝑒  𝑡𝑜  𝑜𝑛𝑒  𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑙𝑦𝑡𝑒

𝑋! = 𝑋!𝑒!!!!!"

Δ𝜇! ≈𝑒!

4𝜋𝜀!𝜀(𝑎! + 𝑎!)

Gvap = Hvap – TBS Hvap = Uvap + PV µl

i ~ 6w(σ) ΔG = (Gfinal – Ginitial) = 0 at equilibrium

(mushroom regime) P(D) = 36(kT/s2Rg)e–D/Rg N m–2 (mushroom regime)