Reference no: EM131248341
Nanomechanics Problem Set
1) Debye length:
The physiological concentration of ions in a cell is close to 150 mmol/L. Calculate the Debye length for a NaCl solution at 150 mmol/L in water at 25oC. What would be the value of the Debye length if you add 10 mmol/L of spermine chloride (making tetravalent cations and four Cl- ions per molecule, or 10 mmol/L of spermidine chloride (with trivalent cations and three Cl- ions per molecule? Imagine you are making an arti?cial cell by creating lipid vesicles with CaCl2 at 150 mmol/L instead of NaCl inside it. Calculate the Debye screening length in your arti?cial vesicle-based cell. For a complex ionic solution the Debye length is given by
λD = (4πλB∑izi2ni)-1/2
where zi, ni are the ion valency and number concentration of ion type i, respectively. Do not forget to express the concentrations in 1/m3.
2) DLVO interactions:
Consider a solution of lysozyme proteins in 1 mmol/L monovalent salt bu?er. The charge on proteins at these conditions is 10e, the Hamaker constant H = 10kBT. The shape of the molecule can be approximated by a sphere with radius of 1.7 nm. What is the potential barrier for the molecule aggregation? Will the solution be stable at these conditions? Will it be stable at 10 mmol/L salt, 100 mmol/L salt concentration?
3) Charge of λ-DNA:
Assume the DNA has one elementary charge per 0.17 nm and that the charge is spread homogeneously along its length. What is the e?ective valence of λ-DNA before and after Manning condensation is taken into account? How does it vary with temperature? Formulate the condition of overcharging of double-stranded DNA molecule by counterions. Assume that DNA double helix is a cylinder of radius 1 nm with charge density of -1e per 0.17 nm spread homogeneously over its surface. Calculate the charge coupling parameter for monovalent, divalent, and trivalent counterions and discuss their ability to overcharge or condense the molecule. Repeat the calculation with the effective charge density after the Manning condensation.
4) Overcharging:
Test the condition of overcharging of the following polyions:
(a) double-stranded DNA molecule; Assume that DNA double helix is a cylinder of radius 1 nm with charge density of -1e per 0.17 nm spread homogeneously over its surface.
(b) SDS micelle of radius 2.2 nm and the charge -60e.
(c) latex bead of radius 2 m and surface charge density -0.02 μC/cm2;
Calculate the charge coupling parameter = 2πσλ2Bz3 for monovalent, divalent, and trivalent counterions and discuss their ability to overcharge the polyion. The overcharging boundary value of is 10.
Attachment:- Assignment.rar
Improvement in managing the quality of the food served
: Explain three areas of improvement in managing the quality of the food served and/or the services rendered at the food court chain - Describe three initiatives for the food court chain to undertake to overcome the three quality issues.
|
The magnitude of the marginal revenue product of labor
: A hospital is a monopsonist in the market for nursing services in a city. At its profit-maximizing input combination, the elasticity of supply for nursing services is +1. What does this tell you about the magnitude of the marginal revenue product ..
|
Scale versus riskiness tradeoff
: Scale versus riskiness tradeoff:- Interpret this condition in terms of a "cost of bringing 1 unit of investment to completion."
|
Define global pattern of atmospheric heating and circulation
: Describe global patterns of atmospheric heating and circulation. What mechanisms produce high precipitation in the tropics? What mechanisms produce high precipitation at temperate latitudes? What mechanisms produce low precipitation in the tropi..
|
Calculate the charge coupling parameter
: Calculate the charge coupling parameter = 2πσλ2Bz3 for monovalent, divalent, and trivalent counterions and discuss their ability to overcharge the polyion. The overcharging boundary value of is 10
|
Do you think that the benefits of volume reduction
: Primary concerns for MSW incinerators are air contamination from gases and fly ash and soil/water contamination from bottom ash. How can gases and fly/bottom ash emissions from an incinerator be monitored and controlled to limit environmental hea..
|
Plan for either at work or in your personal life
: Think about the last event you had to plan for either at work or in your personal life. Did you have a process? How did having or not having a process impact the outcome of the event?
|
What is the maximum amount of profit the firm can earn
: A monopolist serves a market in which the demand is P = 120 - 2Q. It has a fixed cost of 300. Its marginal cost imarginal cost is 10 for the first 15 units (MC = 10 when 0 ≤ Q ≤ 15). If it wants to produce more than 15 units, it must pay overtime..
|
Why it difficult to base climate on a single season weather
: Click here-"http://climate.nasa.gov/climate_resources/42/" to watch the NASA video Temperature Puzzle. Many people are quick to dismiss global warming after a cold winter or a late summer. After watching the video, how would you respond to this pe..
|