Saturday, August 4, 2007

Chemistry - Methylene Blue Prank: Make your friends Pee Blue/Green

Methylene Blue is a common Indicator used in Chemistry. Methylene blue is highly stable in the human body, and if ingested, it resists the acidic environment of the stomach as well as the many hydrolytic enzymes present. It is not significantly metabolized by the liver, and is instead quickly filtered out by the kidneys. Meaning that you wee it out instead of pooing it out. In order to make someone pee blue you would have to add small amounts of methylene blue (generally a few drops of a stain solution sufficed) to coffee, cola, or another dark beverage. The stain's color was masked by the beverage, and its taste is fairly faint. Within a few hours, the methylene blue was removed by the prank victim's kidneys, which caused his or her urine to change color. The urine may become green if little methylene blue was added; larger amounts create a deep blue color. The prank is fairly harmless if small amounts of methylene blue are used, although allergies are possible.

WARNING: Make sure you know the risks and read all relevant MSDS sheets before trying this on yourself or others! Some people may be allergic to Methylene Blue dye.




Allergies with Methylene Blue are very rare. And the indicator is harmless in small doses (It is often used in medicine.) The only real danger is that other harmful chemicals could have contaminated the indicator (Mainly from High School chemistry kids not using the chemical properly.) But if you order your own online, or "borrow" some that has not been contaminated, there is no need to worry.

Have fun!

Pi - An Interesting Representation


While on Wikipedia I saw an interesting Representation of the value of Pi. Basically if a circle's diameter is 1 (Radius = 0.5) The circumference will be Pi according to the circumference equation (c = 2Pi*R). Or in other words, if you take a circle with a diameter of 1 and roll it, it will travel Pi units per rotation. When a circle's diameter is 1, its circumference is π.

Friday, August 3, 2007

Calculus - Product Rule

Equation



The equation is read: The derivative of (f * g) is equal to: the (derivative of f times g) + (f times the derivate of g).

Proof

Suppose




and that f and g are each differentiable at the fixed number x. Then



Now the difference




is the area of the big rectangle minus the area of the small rectangle in the illustration.










That L-shaped region can be split into two rectangles, the sum of whose areas is readily seen to be:



(The illustration disagrees with some special cases, since f(w) need not actually be bigger than f(x) and g(w) need not actually be bigger than g(x). Nonetheless, the equality of (2) and (3) is easily checked by algebra.)

Therefore the expression in (1) is equal to




If all four of the limits in (5) below exist, then the expression in (4) is equal to



Now



because f(x) remains constant as wx;



because g is differentiable at x;



because f is differentiable at x;

and now the "hard" one:



because g is continuous at x. How do we know g is continuous at x? Because another theorem says differentiable functions are continuous.

We conclude that the expression in (5) is equal to



Example
y = sin(x) * x

1. First, derive sin(x) and x separately. sin(x) represents f in the equation for the product rule and x represents g.
  • You should get cos(x) and 1 ( f' and g' respectively)
2. Now we have:
f = sin(x)
g = x
f' = cos(x)
g' = 1
3. Now plug in the variables into the Product Rule equation.
  • You should get: y' = cos(x)*x + sin(x)

Going Further

If you know the product rule you never have to use the quotient rule.
For example:

y = sin(x)/x

1. First, rewrite the equation into the Product rule form.
  • y = sin(x) * (1/x)
  • Tip: 1/x is equal to x^-1
2. Now derive sin(x) and 1/x separately. sin(x) represents f in the equation for the product rule and 1/x represents g.
  • You should get cos(x) and -x^-2 ( f' and g' respectively)
3. Now we have:
f = sin(x)
g = x^-1
f' = cos(x)
g' = -x^-2

4. Now plug in the variables into the Product Rule equation.
  • You should get: y' = cos(x)*(x^-1) + sin(x)*(-x^-2)
  • When simplified you should get: y' = 0




Chemisty - Aerogel


Aerogel is a low-density solid-state material derived from gel in which the liquid component of the gel has been replaced with gas. The result is an extremely low density solid with several remarkable properties, most notably its effectiveness as an insulator. It is nicknamed frozen smoke, solid smoke or blue smoke due to its semi-transparent nature and the way light scatters in the material; however, it feels like expanded polystyrene (Styrofoam) to the touch.

Production

Silica aerogel is made by drying a hydrogel composed of colloidal silica in an extreme environment. Specifically, the process starts with a liquid alcohol like ethanol which is mixed with a silicon alkoxide precursor to form a silicon dioxide sol gel (silica gel). Then, through a process called supercritical drying, the alcohol is removed from the gel. This is typically done by exchanging the ethanol for liquid acetone, allowing a better miscibility gradient, and then onto liquid carbon dioxide and then bringing the carbon dioxide above its critical point. A variant on this process involves the direct injection of supercritical carbon dioxide into the pressure vessel containing the aerogel. The end result removes all liquid from the gel and replaces it with gas, without allowing the gel structure to collapse or lose volume.

Aerogel composites have been made using a variety of continuous and discontinuous reinforcements. The high aspect ratio of fibers such as fiberglass have been used to reinforce aerogel composites with significantly improved mechanical properties.

Resorcinol-formaldehyde aerogel (RF aerogel) is made in a way similar to production of silica aerogel.

Carbon aerogel is made from a resorcinol-formaldehyde aerogel by its pyrolysis in inert gas atmosphere, leaving a matrix of carbon. It is commercially available as solid shapes, powders, or composite paper.

Uses

There are a variety of tasks for which aerogels are used. Commercially, aerogels have been used in granular form to add insulation to skylights. After several trips on the Vomit Comet, one research team has shown that producing aerogel in a weightless environment can produce particles with a more uniform size and reduce the Rayleigh scattering effect in silica aerogel, thus making the aerogel less blue and more transparent. Transparent silica aerogel would be very suitable as a thermal insulation material for windows, significantly limiting thermal losses of buildings.

Its high surface area leads to many applications, such as a chemical absorber for cleaning up spills (see adsorption). This feature also gives it great potential as a catalyst or a catalyst carrier. Aerogel particles are also used as thickening agents in some paints and cosmetics.

Aerogels are being tested for use in targets for the National Ignition Facility.

Aerogel performance may be augmented for a specific application by the addition of dopants, reinforcing structures, and hybridizing compounds. Using this approach, the breadth of applications for the material class may be greatly increased.

Commercial manufacture of aerogel 'blankets' began around the year 2000. An aerogel blanket is a composite of silica aerogel and fibrous reinforcement that turns the brittle aerogel into a durable, flexible material. The mechanical and thermal properties of the product may be varied based upon the choice of reinforcing fibers, the aerogel matrix, and opacification additives included in the composite. NASA used aerogel to trap space dust particles aboard the Stardust spacecraft. The particles vaporize on impact with solids and pass through gases, but can be trapped in aerogels. NASA also used aerogel for thermal insulation of the Mars Rover and space suits.

Aerogels are also used in particle physics as radiators in Cherenkov effect detectors. ACC system of the Belle detector, used in the Belle Experiment at KEKB, is a recent example of such use. The suitability of aerogels is determined by their low index of refraction, filling the gap between gases and liquids, and their transparency and solid state, making them easier to use than cryogenic liquids or compressed gases. Their low mass is also advantageous for space missions.

Resorcinol-formaldehyde aerogels (polymers chemically similar to phenol formaldehyde resins) are mostly used as precursors for manufacture of carbon aerogels, or when an organic insulator with large surface is desired. They come as high-density material, with surface area about 600 m²/g.

Metal-aerogel nanocomposites can be prepared by impregnating the hydrogel with solution containing ions of the suitable noble or transition metals. The impregnated hydrogel is then irradiated with gamma rays, leading to precipitation of nanoparticles of the metal. Such composites can be used as eg. catalysts, sensors, electromagnetic shielding, and in waste disposal. A prospective use of platinum-on-carbon catalysts is in fuel cells.

Aerogel can be used as drug delivery system due to its biocompatibility. Due to its high surface area and porous structure, drugs can be adsorbed from supercritical CO2. The release rate of the drugs can be tailored based on the properties of aerogel.

Carbon aerogels are used in the construction of small electrochemical double layer supercapacitors. Due to the high surface area of the aerogel, these capacitors can be 2000 to 5000 times smaller than similarly rated electrolytic capacitors.

Dunlop tennis has recently incorporated Aerogel into the mold of its new series of racquets. Dunlop have also used it in squash racquets

 
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