Wind Turbine Efficiency, Part 3: The 40.3% That Got Away

You made it to Part 3! If you haven’t already please go back to read Part 1 and Part 2.

Let's continue. From calculus, we know that to find a maximum of a given single-variable function, we take the derivative, or the slope of the function, with respect to the variable and find where the derivative equals to zero. This is because the slope of a function is zero where the function changes from increasing to decreasing or decreasing to increasing output values (aka peaks and valleys). Equation 24 from Part 2 is rather ugly, however, so let’s set the derivative with respect to k=v2/v1 (the ratio of final and initial velocity) as our plan of attack (reminder: ve, v1 and v2 are all known constants in this expression). Let’s do this now.

            25.     P=1/4rAv1³(1-k²+k-k³) (substitution of k=v2/v1 into equation 24)

            26.     dP/dk=1/4rAv1³(0-2k+1-3k²)=1/4rAv1³(-2k+1-3k²)=0

            27.     -2k+1-3k²=0 ((1/4rAv1³) is a giant multiplicative non-zero constant term, so it can be
             dumped into the zero never to emerge again (except by integration))

            28.     k=1/3, -1 (solutions to equation 27, obtained by factoring the second-degree polynomial and
             letting each set of terms equal to 0 since if ab=0, either a=0 or b=0 makes the statement true)

Obviously, a negative value of k=v2/v1 does not make sense since this requires that the wind hit the turbine and flow backwards, so we will only keep the k=1/3 value. Plugging the value for k into equation 25, we get:

                                           29.     Pmax=1/4rAv1³(1-1/9+1/3-1/27)=16/27(1/2rAv1³)

To interpret this result, all that must be remembered is that the total power in the original cylinder of wind was found to be Pwind=1/2rAv1³ in equation 7. Substituting in this expression reveals the following relationship:

                                                                      30.     Pmax=16/27Pwind

In other words, only 16/27, or 59.3%, of the total power in a column of wind can ever be extracted by wind turbines (this is assuming 100% turbine internal efficiency relative to the 59.3% limitation). This means that there is an inherent limitation in the production efficiency of wind power relative to available energy to be harvested.

Fig. 4: Turbine efficiency cartoon (Wikimedia)

And there you have it, Betz's Law in only 30 steps.

So, knowing this, should we abandon wind power? The answer is a definite no. Wind turbines have an installation cost in both money and materials and also severe limitations as to practical operation, such as a decreasing efficiency in high wind velocities to prevent structural damage, but they are an important member of a small set of what I would consider to be true renewable energy strategies. I won’t talk about this now since I feel guilty about the density of the topic I just covered, but I will make this the topic of my next post.

If you have any questions, leave them in the comments section below and I’ll try to answer them as best I can.

Wind Turbine Efficiency, Part 2: Too Many V Terms

Welcome back! If you haven’t already, please read Wind Turbine Efficiency, Part 1: A Windy Cylinder of Power.

All calculations thus far have dealt with air in front of the wind turbine. We should take a look at what happens behind it as well. From fluid dynamics we know the following equations to be true through logical progression:

                               8.     V1=V2 (V1 is air volume before turbine, V2 is air volume after)

                               9.     dV1/dt=dV2/dt

                               10.     dV/dt=Av (equation 5)

                               11.     A1v1=A2v2

Equations 9-11 simply state that the volume of wind entering our cylinder from Part 1 must change at the same rate as the volume of air exiting the turbine from behind. This is true if we assume no changes in temperature or atmospheric pressure before to after the turbine (beyond those induced by the slowing wind, which we are calculating for now). From energy conservation, we know that if work is performed on the wind turbine, then the kinetic energy of the wind after the turbine, and accordingly the wind velocity, must be less than that before. In other words, v1>v2. The result is that A2>A1, so the wind after the turbine must effect a cone of area expanding away form the turbine blades.

Fig. 3: Air flow through a wind turbine (Danish Wind Industry Association)

Let’s try to piece apart the maximum power obtainable from the wind cylinder calculated above. Wind force is defined as follows:

                                     12.     F=ma=d(mv)/dt=(dm/dt)v+m(dv/dt) (force equation)

For simplicity’s sake, we are assuming that the wind before the turbine has velocity v1 and slows to velocity v2 after performing work on the turbine, both of which are know constant values. When wind blows through our wind cylinder, the mass of air, and as a result the effective length of the cylinder since base A is constant, changes with time. Therefore, we are not concerned with how force changes with velocity, so the m(dv/dt) term can go to zero and we can evaluate the change in wind force over the turbine as follows:

                                  13.     ΔF=(dm/dt)Δv=(dm/dt)(v1-v2)

                                  14.     ΔF=r(dV/dt)(v1-v2)=rAve(v1-v2) (from equations 4 and 5)

A new variable has been introduced in equation 14, namely the effective velocity ve, which corresponds to the wind velocity that the turbine experiences as part of work production (in other words, if the wind were to lose all kinetic energy after contacting the turbine, a wind velocity of ve would generate a quantity of power the same as from wind with velocity v1 slowing to v2). Concerning the power obtained from the change in force, we know that since the change in wind force is equal to the force exerted on the turbine, power can be calculated as follows concerning the wind contacting the turbine:

                         15.     W=FL (instantaneous work equation, L is analogous displacement here)

                         16.     dW/dL=F, therefore dW=FdL

                         17.     P=dW/dt=d/dt(FdL)=F(dL/dt)=Fve (power equation)

                         18.     P=rAve²(v1-v2) (from equation 14)

From expanding equation 4 to accept that the wind velocity after the turbine is not zero, we obtain the equation:

               19.    P=1/2(dm/dt)(v1²-v2²) (this is just the difference in kinetic energy with changing mass)

               20.    P=1/2rAve(v1²-v2²) (from equations 5 and 6, parallel to equation 7)

Now we have two different equations for power, one from the work equation and the other from the kinetic energy equation! Setting these equal to each other, we obtain the expression:

                   21.     P=1/2rAve(v1²-v2²)=rAve²(v1-v2)

                   22.   v=1/2(v1+v2) (simplification of equation 21 using (v1²-v2²)=(v1+v2)(v1-v2) identity)

This equation tells us what the relationship between the effective velocity ve and the initial and final wind velocities v1 and v2 are. Specifically, the relationship is that the effective velocity is the average of the initial and final wind velocities. Using this relationship, let’s redefine the kinetic energy-derived power equation in terms of v1 and v2 in preparation for calculating maximum power.

                            23.    P=1/2rAv(v1²-v2²)=1/2rA(1/2(v1+v2))(v1²-v2²) (from equation 20)

                            24.    P=1/4rAv1³(1-(v2/v1)²+(v2/v1)-(v2/v1)³) (simplification of equation 23)

Things are starting to get exciting! Read on to Part 3 to finally start calculating the external efficiency limitation of wind turbines, and let me know any questions in the comments below.

Wind Turbine Efficiency, Part 1: A Windy Cylinder of Power

When people think of renewable energy, probably what comes to mind is a mixture of solar panels, wave motion generators, geothermal plants, hydroelectric dams and wind turbines. Of these, the two most associated with the image of a sustainable society are probably solar panels and wind turbines. That’s why when I caught a glimpse of this wind farm while at the Jersey shore, I felt like I had been transported into some sort of futuristic society apart from our own. 

Fig. 1: Wind farm near Atlantic City (personal photo, hence the quality)

Assumedly, we all know that every energy-harvesting method has efficiency limitations, even though some people like to pretend they don’t. With solar panels, calculating efficiency can be complicated as it comes down to a matter of quantum efficiency, but the efficiency limitations of wind turbines, also called Betz’s Law, can be readily calculated with some physics. Let’s explore this.

(Note: though not particularly difficult conceptually, this derivation is math-heavy. I will do my best to explain the underlying logic as we go along. Also, this explanation will be separated into three parts so that your eyes don’t bleed from the endless stretch of math. Backbone calculations for Betz’s Law come from the Wikipedia article and this MIT presentation, but I hope you will find that my explanation, though lengthy, is more intuitive than these sources. Enjoy!)

Let’s start with calculating how much power there exists in a cylinder of wind with base area A corresponding to the arm span of the wind turbine.

Fig. 2: Cylinder with base A and wind influx at velocity v (MIT)

                          1.  KE=1/2 mv²  (kinetic energy equation)
                   2.   KE=W (work-energy equation)
                   3.   P=d/dt(W)=1/2(dm/dt)v²+mv(dv/dt)  (power equation, product rule)

For equation two, let’s assume all work is converted to electrical energy, not friction or blade deformation or other stuff. Now in equation three, what normally happens is that the dm/dt term, or the change in mass over time, is assumed to be zero, producing the familiar mv(dv/dt) or (d(mv)/dt)v or Fv term associated with power. Instead, let’s assume that the air cylinder has a constant known speed v1. Therefore, the term mv(dv/dt) goes to zero, and we are left with equation 4:

                                                                   4.  P=1/2(dm/dt)v1²

From fluid dynamics, we know that

                                                         5.  dm/dt=(m/V)(dV/dt)=r(dV/dt)

or that the mass per volume, density, multiplied by the change in volume over time is equal to the change in mass over time. Makes sense, right? This is essentially just dimensional analysis. With constant wind cylinder base A and changing length L, change in volume over time is defined as

                                                         6.  dV/dt=d/dt(AL)=A(dL/dt)=Av1

Combining equations 4, 5 and 6, we get the general power equation for a cylinder of wind to be

                                                                       7.  P=1/2rAv1³

where r is density, A is cylinder base area (also area of turbine span) and v is a constant wind velocity. 

I’ll stop the first post here since it’s a good spot to take a break. Read on to the next post to learn how to calculate the effective wind speed acting on a wind turbine, and let me know in the comments below if you have any questions.

The Logic Behind an Era of Safe Canning

Canned food is something that most everyone is familiar with. From canned sardines to peaches to condensed milk, canning food is a useful preservation method for our favorite foods. Better food preservation in turn means that the foods we love are available year round. Iconically, the ridged metal can comes to mind, but there are other forms of canning that involve glass jars with metal lids used primarily for home canning but also seen sometimes in stores.

Fig. 1: A sample of canning styles (Best in Packaging)

Many families can their own excess garden goods at home to eat later; according to the CDC, 1 in 5 American households participate in home canning [1]. There are two main sterilization methods used in home canning, one involving boiling the cans and the other involving high temperatures as well as high pressure [2]. Heat kills bacteria, mold and other bad stuff for reasons previously discussed in Party Science, Part 3: The Tasty Grub. However, for the same reason that bacteria are killed by heat the flavor of the preserved food may be affected as well. Pressure kills bacteria possibly as an effect of the expansion of dissolve gases within bacterial cells [3]. Acidity is another factor that affects bacterial survival, and it has been found that acidic foods inhibit the growth of pathogenic bacteria enough to permit the use of High Pressure Processing (HPP) as the only additional sterilization technique while basic foods such as meats require heat treatment as well [4]. 

In our current era when canning is considered a generally understood science, it is uncommon to hear of botulism cases from canned foods, especially those produced commercially. Botulism is the name of an illness caused by Clostridium botulinum bacteria that generate botulinum toxin. There are eight different forms of botulinum toxin labeled types A through G (botulinum toxin C is divided into C1 and C2), of which type A is the most potent and types A, B and E are associated with human botulism. Botulinum toxin is one of the most poisonous known biological substances and also happens to be the active ingredient in Botox injections. Botulinum toxin binds to receptors on the presynaptic surface of neurons and is accepted into the neuron where it interacts with proteins related to acetylcholine vesicle transport to prevent the neurotransmitter’s release [5].

Fig. 2: Botulinum toxin mechanism of action (Student Pulse)

Symptoms of botulism are typically those related to an impaired nervous system, such as blurred vision, muscle weakness, slurred speech, drooping eyelids and difficulty swallowing. The presentation of these symptoms after possible botulism exposure is an emergency situation as antitoxins exist to treat botulism if administered promptly and progressed botulism may be fatal due to respiratory system paralysis [6]. 

But botulism and other canning-related illness cases today are rare and for the most part, the effects of canning have been positive for human survival during harsh times and the winter season. I for one love having corn, my favorite vegetable/grain thing, available all year round, and for that I am thankful we have this technology. How about you? Let me know what you think in the comments below, and check out this link to an instructional video if you are interested in canning your own foods at home. 

A Bit on That Shampoo Vitamin

Apart from the well-known vitamins like vitamin C and vitamin D, there are others that are only known in context or perhaps not known at all. Take vitamin K for example. Did you even know there was such a thing? If it weren’t for its bizarre role in blood clotting, I wouldn’t have either. Another one most people only know a bit about is vitamin E. I most associate this vitamin with shampoo because a number of soaps advertise its antioxidant properties as the secret to model-like hair. But questionable advertisement schemes aside, vitamin E does play roles in human health so let’s learn a little about it, shall we?

Though it sounds singular, vitamin E is actually a class of eight fat-soluble antioxidant compounds, all of which contain a chromane ring with a 2-hydrophobic side chain (four compounds with saturated side chains (tocopherols), three with trans double bonds (tocotrienols)) and a 6-hydroxyl group. Varying positions of methyl functional groups around the phenyl portion of the chromane ring is what separates the alpha-, beta-, gamma- and delta-tocopherols as well as the tocotrienol subtypes. 

Fig. 1: Vitamin E subtypes with sidegroup key (American Oil Chemists' Society)

All vitamin E forms exhibit antioxidant properties due to the 6-hydroxyl group’s ability to offer its hydrogen as humble tribute to wandering radical aggressors. The resulting vitamin E radical is stabilized by the electronic properties of the adjacent phenyl ring through delocalization as to be relatively unreactive. In plants, vitamin E is commonly found in chloroplasts where they protect against reactive oxygen species (ROS) produced as byproducts of photosynthesis. In humans, vitamin E plays a similar role. Vitamin E is known to incorporate into cell membranes where it is thought to protect against cellular damage caused by radicals present environmentally or resulting from metabolism by reacting with radicals before they are able to oxidize lipids and other cellular components. Regarding antioxidant ability, alpha-tocopherol has been shown to scavenge radicals faster than lipid substrates can be targeted [1]. 

The most biologically relevant form of vitamin E in humans is alpha-tocopherol, which is selectively ushered into use around the body by the alpha-tocopherol liver transfer protein, while gamma-tocopherol is suspected to hold importance as well though details are currently unknown [2]. A deficiency of vitamin E may result in neuromuscular and neurological problems, retinopathy or anemia, and excessive consumption of vitamin E may cause difficulty clotting [3]. Vitamin E is present in a number of vegetable oils, though processed vegetable oils contain lower tocopherol content due to damage during refining, leafy greens, nuts, seeds, sweet potatoes, avocadoes, eggs, liver and fortified breakfast cereals [4], many of which are typically present in a normal healthy diet. The recommended daily intake of vitamin E is 15 mg for adults, 11 mg for children ages 9-13 and 6-7 mg for children ages 1-8. Now you know stuff about this not well known vitamin, so go tell a friend and make sure they know too!

For more information on vitamin E, check out this description by the American oil chemists’ society (same as ref. 1). It’s a tad technical, but highly informative and an interesting read.

Party Science, Part 3: The Tasty Grub

If you haven't already, please check out Party Science, Part 1: The Beats and Party Science, Part 2: The Lights.

To me, a party isn’t a party unless there’s food involved. Cooking and eating food is something that we all participate in on a daily basis, and the best food is usually to be had at parties. Let’s continue with the final installment of Party Science, Part 3: the Tasty Grub.

The creation of good food is closely related to a number of chemical reactions that make plant matter easier to eat, degrade potential toxins and impart a level of yumminess. From molecular kinetics, we know that the kinetic energy of molecules is proportional to temperature by the following equation:

                       1. E=nCvT, Cv=4.179 J/g°C for water (Chemical Principles, Zumdahl)

Therefore, by increasing the temperature of a foodstuff during cooking, we are increasing the kinetic energy and average molecular translational/rotational speeds and vibrational frequency. The result: destruction! As kinetic energy overcomes the hydrogen bonding energy of proteins such as enzymes, they begin to unfold and denature, losing their conformation and functionality. A classic example of this process is the denaturation of runny raw egg white proteins to produce the rubbery cooked egg white more commonly eaten than the former (deviled eggs anyone?). The degradation of structural proteins also plays a role in softening meats like steak during cooking (this process can occur faster at lower temperatures if enzymes that degrade proteins, such as those in pineapples and papayas, are used in a marinade to lower the activation energy of protein degradation). With plants, heating can denature certain proteins or compounds that are toxic to humans, increasing edibility. Heat also encourages the hydrolysis of cellulose [1] and starches. We experience this process through the soft texture of a baked potato.

As I’m sure you know, cooking also adds flavor to raw foodstuffs through a number of processes. One such process is caramelization, wherein sucrose inverts to produce fructose and glucose molecules that then undergo various reaction pathways to produce volatile, colored and flavorful compounds [2]. This process is notable in flans and apple pies. Another is the Maillard reaction, wherein sugars react with amino acids to again undergo various reaction pathways to produce tasty molecules [3]. The Maillard reaction is best known through the browning of cooked meat.

Fig. 1: The Maillard Reaction (Lynne Swerhone)

So far what has been described are all processes that have been in play for thousands of years, but what can chemistry offer to change the ways we prepare food? Well, if you’ve ever warmed up some cheese dip, then you know of at least one. Microwave ovens use microwaves (unsurprisingly) to warm up food by introducing a fluctuating electric field component that a water molecule’s dipole continually attempts to reorient with [4]. Chemistry has also fostered advances in modern food art and molecular gastronomy. If you ever use fruit juice boba as an ice cream topping or in mixing drinks, those are made of fruit juice mixed with calcium salts and dropped in sodium alginate, a soluble cellulose salt derived from brown algae (Fig. 2). When the sodium ions are replaced by aqueous calcium ions, insoluble calcium alginate is generated to seal in the juice drop in a process called spherification.

Fig. 2: Sodium alginate spherification (Molecular Recipes)

Thermodynamics has also brought us freeze drying through knowledge of phase diagrams and water sublimation [4]. The product is various forms of fruit and vegetable snacks, a healthy substitute for traditional party chips.

In many ways, party food is made to impress. Science helps us explain our current cooking techniques, and a good knowledge of these can allow for improvements and new innovations to reinvent regular party foods. With the music playing, the party lights on and the food ready to be served, your party prep is done so invite your friends and enjoy!

Below I am posting a cool video on how to make mojito spheres using molecular gastronomy, so check it out! And please tell me your thoughts in the comments below.

Party Science, Part 2: The Lights

If you haven't already, please read Party Science, Part 1: the Beats.

So, now that we’ve got the beats, what’s next? How about we get some lights to set the mood. Today’s installment: the lights.

Again we’ll start with a simple question: what is light? Simple question, not so simple answer. To skip a lot of gritty stuff, let’s just start with the premise that light is a form of electromagnetic radiation consisting of orthogonal electric and magnetic field components and behaving as a transverse wave while also as a particle… yeah. Anyways, there are many types of light bulbs that we can use for different effects. For typical houselights, incandescent bulbs with tungsten filaments that utilize blackbody radiation were used until recent years. Currently, compact fluorescent light bulbs (CFLs) are popular for efficiency reasons with LEDs on the rise. CFLs work by ionizing argon gas and mercury vapor with tungsten filaments by thermal electron emission to produce UV radiation. The UV radiation is then converted to visible white light by phosphors either on the bulbs or on their housing [1]. LEDs utilize the junction between semiconductor material doped with electron rich or electron poor elements relative to the semiconductor valence number (p-n junction) to produce light as the electrons from the negatively-doped material fall into lower-energy electron "holes" in the positively-doped material. With these typical lights we have some basic lighting. Now what are we going to do about colorful lights for that true party feel? The college DIY option would be to put colored plastic or something over house lights to get the same effect as a colored bulb at a fraction of the cost!

Fig. 1: Procedure for colored lamp perfection (Dornob)

But how does doing this produce colored light? The first thing to notice is that the colored filter is, in fact, colored (huh, imagine that). What this indicates to us is that whatever the material is made of or coated with, it is only transmitting light that comprises the observed color. In other words, the material is absorbing a portion of the visible spectrum of light and we see a net color as a result of this absence. This could be due to a number of factors, for example the presence of transition metal compounds or conjugated organics, but the general property that allows a material to absorb light is a possible electron energy state transition corresponding to a frequency in the visible spectrum. When applied, the colored filter acts on the white light emitted from the light source, filtering out the characteristic absent spectrum and producing a net color. And with our bargain colored lights in place, how about we go for a special effect to top it all off. Let's use some blacklights. Blacklights are fluorescent lamps tubed in black-coated glass to absorb most visible light and coated in phosphors that permit only UVA light (not UVB, which causes sunburn, or UVC, which is filtered out by our atmosphere naturally and would give you super sunburn, a.k.a. cancer) to exit. The UVA radiation produced interacts with phosphors in white clothing from laundry detergents, with natural phosphors in teeth and nails and with fluorescent clothing to produce the psychedelic colors that are associated with blacklights [2]. With beats and lights, our party is going strong.

Below I’ve posted a video of Russian hip hop artist Kristina Si that depicts multiple types of lights employed at a party. Take notes people. 

Party Science, Part 1: The Beats

Who doesn’t like to party, am I right? Going to your favorite concerts, dancing at clubs, or just chilling with friends, partying helps us all to relieve the stresses of daily life and maybe make a few lasting memories. Living in the time we do, we have the technology to throw some epic shindigs, and not to get preachy, but from the flashing lights to the music beats, a lot of what allows us to party in the way we do is realized through science. I want to take the next couple posts or so to talk about some of the basic aspects of party science. Today we’ll cover the beats.

What is sound anyway? In its basic form, sound is the perception of longitudinal waves propagating in the air around us. Take the drum for instance. A stereotypical drum consists of some sort of membrane adjacent to an echo chamber. When struck, the membrane implodes at the point of compression, but nearby surface immediately works to restore equilibrium by pulling up on the impact point while the impact point pulls the surrounding membrane down [1]. The result is a wave propagating across the membrane. What does this mean for the air around the drum membrane? when the membrane implodes, air under the membrane is put into pressure and triggers movement away from the drum surface, only to feel the opposite reaction when the membrane at that point fluctuates outward.

Fig. 1: Production of longitudinal waves in a drum (University of Leicester)

This air movement creates a series of propagating low- and high-pressure zones comprising the longitudinal sound waves that have communicated human culture for thousands of years. On string instruments, the concept is the same. When plucked, the string oscillates and sends those vibrations to the instrument belly, causing air fluctuations by the face of the string instrument, say, a guitar, to produce music that has colored many cultures with Spanish influence [2]. However, the way this effect is experienced differs with modern music like dubstep, electric, house or other computer-altered music types that don’t come from physical musical instruments per se. With this sort of music, the component properties of previously recorded sounds are altered with the help of computer software. For example, a gradual increase in sound frequency and tempo is the sensation often used to foreshadow a dubstep drop. How do you send these synthetic beats out to awaiting ears? The answer is with a speaker, what some would consider a crucial part of any party. The basic speaker consists of a membrane or cone attached to an electromagnetic coil (solenoid) next to a permanent magnet. When current is sent through the solenoid, a magnetic field is produce down the length of the coil oriented towards or away from the electromagnet at a given moment if the field is envisioned as a vector pointing down the coil center. As the current fluctuates, the membrane is moved towards and away from the magnet, creating sound waves. When worked in reverse, with sound waves generating current, the device is called a microphone. The single waveform current signal generated can then be broken down using Fourier analysis into component frequencies with corresponding amplitudes (aka that bar diagram widget that moves when your music plays). To generate music, the speaker current is controlled by programs that mathematically synthesize waveforms from music files and divvy up the responsibilities of producing a net sound effect between available speakers. In the end, if executed properly with a location that offers the right amount of acoustic bounce back, say in a closed room among friends or in the middle of Miami skyscrapers like in the video of Hardwell below, you’ve got the basis of a good time.

When you watch this video, think about how the sounds are being synthesized. Is wave frequency/amplitude being altered? Are the sounds natural or computer generated? Let me know your thoughts in the comments (and don’t feel obligated to watch the entire video, it’s long).

Experiment: Extraction of Plant Pigment as Food Coloring

My favorite drink to buy during Wawa lunch runs is Vitamin Water. Besides the extra boost of vitamins to supplement my college diet, I like that they use natural plant dyes rather than synthetic ones. To stop the kindling of a debate about whether synthetic dyes are bad for consumers, I would like to state that I don’t believe synthetic and natural chemicals are different; as a chemistry student, I assert that synthetically produced chemicals, if synthesized and refined properly, are the same as ones obtained naturally (aside from possibly isotope content, but I don’t see why that should matter). The problem with synthetic dyes at the moment is that some cannot hold their ground against investigations related to carcinogenic or other deleterious health effects, whether related to the compounds themselves or to manufacturers’ procedures. As for plant dyes, most have been consumer tested by humans for thousands of years. What’s more, natural plant dyes often have antioxidant properties. The biological role of antioxidants is another controversial topic, but suffice it to say that reactive oxygen species (ROS) and other reactive species are produced within your body continuously through processes such as metabolism and have been linked to tissue damage and cancer generation at high levels. Therefore, consuming a normal amount (not a 1,000mg vitamin C tablet every hour) of antioxidants through food can’t hurt and may even have health benefits. The point of bringing up this topic is to introduce the first home experiment I am posting on this blog. I am going to demonstrate how to extract plant pigments for use as food coloring.

Materials:

• High ethanol content liquor (vodka)
• 40% (80 proof) vodka used
• Higher proof makes volume reduction easier due to lower boiling point of ethanol 
• Pyrex glass container for extraction
• Liquid measuring cup used
• Frying pan for water bath
• Plant matter
• Tested: canned beets, spinach, watermelon, blackberries
• Worked: canned beets, blackberries

Procedure:

• The frying pan was filled 3/4 way up with water, then heated over medium heat until small bubbles formed.
• Plant matter was added to the Pyrex container with enough vodka to cover it, then the container was placed into middle of the frying pan bath.
• The reaction was left for approx. 30 min (until the color of the vodka no longer appeared to be changing and alcohol could no longer be smelled).

Fig. 1: Coloring extraction setup

• The reaction mixture was transferred to a ceramic bowl, then the plant matter was removed before letting the colored solution cool to room temperature.

Fig. 2: Coloring concentration

• The ceramic bowl was covered and the coloring solution was set to concentrate overnight. The bowl was swirled occasionally to recollect dried dye along the waterline.

Results:
Of the tested plants, the canned beets and blackberries were the only two to work. Both produced a similar hue of purple-red coloring. When the blackberry coloring was used on cream cheese frosting, the result was a light purple-red pastel frosting with a slightly runnier textured due to inadequate dye concentration prior to use and to mixing (Fig. 3). Adding a teaspoon of the dye to a cup water imparted a moderate red coloring which soon thinned (Fig. 4). in both instances, no blackberry taste was conferred (same for beets).

Fig. 3: Blackberry colored cream cheese frosting

Fig. 4: Blackberry colored water

Explanations:
For setup considerations, Pyrex and ceramic containers were used to hold the dye solution as a precaution against possible dye discoloration due to reactions with the container. Low boiling water was used to roughly manage the reaction temperature while reducing the chance of degradation, due to heat in this instance. Coloring concentration was performed prior to testing as a precaution against changes in food texture due to the addition of large quantities of water. The concentrating bowl was covered to prevent dust from depositing in the coloring solution and to lessen the chances of dye degradation due to interaction with ambient light. Vodka was used for extraction rather than water to lower the external polarity relative to the plant material's internal environment. The result is a polarity gradient across the membrane of the plant cells that aided in the migration of relatively non-polar dye molecules outward from within the plant cells while trapping other more polar molecules, one such molecule type being sugars, that would confer flavor. In this way, the coloring produced by this method differs from the juice of the tested plants. Dye color consistency should be considered when using the blackberry coloring, as anthocyanin pigments respond to changes in pH with changes in color. Color degradation over time is another consideration, and coloring soon before consumption is recommended (when added to water, the coloring soon reduced in intensity, an effect which may be reduced or enhanced by the contents of what is being colored) The produced colorings will contain ethanol at low concentrations, a consideration more than a concern. 

I was only able to produce purple-red coloring, but it is likely that other untested plant materials will be able to produce differing colors. I will be leaving which plants can color be extracted from in this method as an open question, so if you find any others please let me know in the comments!

Iggy Azalea and the Scientific World View

Possibly my favorite Iggy Azalea music video is of her song "Fancy." My interest in the video has nothing to do with whether or not I am, indeed, fancy, but has to do instead with that in portraying an extravagant high school she unknowingly created a snapshot of the scientific wealth of our society. To show you what I mean, I am posting below a walkthrough of the many scientific fields and concepts related to major symbols in just the first minute of her music video:

• Shiny night gown – polymer chemistry (spun polyester, dyed synthetics), petroleum engineering (plastic input extraction)
• Tablet – materials science (circuit components), computer science (HTML, CSS, OS), electrical engineering, math (image processing)
• Sunglasses – materials science (polymer optical properties), physics (light wave polarization, optical refraction)
• White board – polymer chemistry (plastic surface), organic chemistry (marker ink)
• Paper air planes – ecology (responsible (assumedly) forestry), paper chemistry (lignin removal, cellulose bleaching), aerodynamics (gliding flight, airfoil), psychology (motives to throw airplanes in class)
• Plaid shirt – textile chemistry (cellulose extraction and bleaching, softening, dyeing, cotton anti-static/anti-wrinkling), mechanical engineering (industrial looms), computer science (pattern programming)
• Fuzzy hats – polymer chemistry, mechanical engineering (machined faux-fur weaving)
• Lunch table – materials science (metallic corrosion), polymer chemistry (blue anti-rust coating)
• Lunch – organic chemistry (food coloring, gelatin protein matrix, pesticides/insecticides, Maillard reaction), agricultural chemistry (fertilizer), polymer chemistry (plastic trays, PETE bottles, HDPE bottle caps, PS utensils, jello cups), materials science (plastic-metal laminate jello lids)
• Cheerleaders – biochemistry (ATP/ADP, insulin signaling, neuronal action potential, calcium ion muscle contractions), human physiology (muscular/cardiovascular systems), physics (inertia, statics)
• Stadium complex – materials science (metallurgy for light posts, optical materials for lamps, concrete), structural engineering (stadium structure)
• Pink designer shirt – economics (brand-name price factor), sociology (brand choice)

If my bizarre method of enjoying this Iggy Azalea music video speaks to anything beyond my personality, recognizing that each scene contains a collection of scientific triumphs demonstrates that science is not just a complex skill set that takes forever to build, it is a way of thinking as any other profession is. And even if the average person does not possess the full scientific skill set, which is a fair expectation, the scientific way of thinking, namely recognizing the everyday role of scientific principles and applying the scientific method and philosophy when confronted with problems, is a learnable world-view for the average person.

How Soap Helps Us Clean

Ever wonder why it is that we use soap to clean our cars, dishes, bodies and hands? Aside from dyes, perfumes and other additives, soap contains molecules called surfactants. Surfactants are complex molecules that have hydrophobic "tail" regions consisting of long carbon chains and hydrophilic "head" regions that are charged or polar. Some of the oldest soaps were made by heating water washed through wood ash (called caustic soda, lye, or sodium hydroxide) with a fat source [1]. Fat sources can be triglycerides from animal fat, fatty acids from plants or other sources of similar molecules often possessing a carboxylic acid (hence the term "fatty acid") or fatty acid-derived ester group as in triglycerides. The chemical reaction that results is called "saponification" and involves the cleavage of triglyceride fatty acids by hydroxide ions forming glycerol and neutralization of the fatty acids to form salts of the fatty acids.

Fig. 1: Saponification mechanism for fatty acid-derived esters in triglycerides (University of Malta)

An example of the type of fatty acid salt that results from saponification is sodium oleate;

Fig. 2: Sodium oleate (Exporters India)

This surfactant molecule is formed by reacting sodium hydroxide with oleic acid, better known as olive oil. So how do these surfactants help to clean dishes? Let’s think about what types of foods are the worst to clean after cooking dinner. Sugary syrups from cranberry sauce, jams and the like are a breeze to clean; just rinse the dishes and bam, they’re clean. This is because sugars are water soluble. The oily pan used to fry meat, however, is a mess and gives your hands that slick feeling everybody hates. Oil is hydrophobic and will likely stick to your pan better than it does to the water running over it. Here is where soap helps. Above a critical concentration, surfactants tend to form clumps in water called "micelles" so that all of the hydrophobic tails are collected inward (a bilayered micelle is a lysosome, and a lysosome with its hydrophobic tails pointed outward containing a water layer of varying thickness is a bubble).

Fig. 3: Surfactant organization forms in water (Wikipedia)

Exactly at what concentration these micelles form is dictated by thermodynamics in balancing the loss of entropy from organizing the surfactant molecules against the higher energy of associating water and the hydrophobic tail regions [3]. When soap is applied to the oily pan surface, the hydrophobic tails embed in the oil and form it into small droplets. The oil is then escorted by the hydrophilic head regions into the surrounding water and down the drain when rinsed. It is this ability to make hydrophobic substances pseudo-hydrophilic that makes soap so useful to us. What about washing cars and our bodies. While the circumstances are radically different and accordingly warrant different surfactants, the mechanism is the same. Soap helps to escort away hydrophilic bits in dirt, grime and bird poop on cars and dead cells and human oils on our bodies, helping to keep things in line with our modern sense of cleanliness.

So there you have it, a summary of how we utilize soap. If you guys have any topics you would like to hear about or this article tickled your fancy, leave a comment so I can hear your thoughts. 

The Dazzling Chemistry of Fireworks

Yesterday was the Fourth of July, and millions of people all over America gathered in parks and along waterways to witness one of the most dazzling examples of ancient science; fireworks. The invention of gunpowder in China ca. 600-900 CE resulted in the creation of the first fireworks, later buffed up to the colorful sky-flowers we know today by Italian fireworks makers in the 1830s [1]. While waiting for a fireworks display at the Philadelphia Museum of Art, I found myself wondering how is it that we humans have come to create this technology. The first step was to devise a method of controlling highly exothermic and expansive (due to gas formation) chemical reactions and initiate them on purpose through the use of chemical oxidizers (originally saltpeter, KNO3) that contribute oxygen to combustion reactions, allowing them to burn in containers without oxygen flow or even in vacuums. But the role of gunpowder in history has had many uses beyond fireworks and isn’t what makes this specific variety of chemical explosions so addicting. What gives fireworks their characteristic hues are the metal ions that exist along with the crafted gunpowder in fireworks shells. Italian fireworks makers discovered that the use of KClO3 rather than saltpeter could increase the temperature of the combustion reaction, allowing for the light-emitting potential of metal ions to be unleashed [2]. When calculating the standard enthalpy of reaction for the following decompositions;

1.     2KNO3 --> K2O + N2 + 2.5O2

2.     2KClO3 --> 2KCl + 3O2

it can be observed that the decomposition of KClO3 is more exothermic than that of KNO3 (625 kJ/mol for KNO3 and -89.6 kJ/mol for KClO3 based on standard enthalpies of formation found on Wikipedia), the former also generating 0.5 more moles of O2 gas than the latter. The extra oxygen gas contributes to the exothermic nature of the combustion through the formation of CO2 and SO2 gas (-393.5 kJ/mol for CO2 and -296.81 kJ/mol for SO2 based on Wikipedia values), the same source of energy from which coal power plants operate, according to the following equations:

3.     C + O2 --> CO2

4.     S + O2 --> SO2

The color that a given metal salt produces when heated is characteristic of the metal element and can be calculated based on the following equations [3,4];

5.     E=hv 

6.     c=lv (v=fl modified for light)

7.     E=hc/l (from equations 5. and 6.)

8.     E=-Rhc(1/(nf)^2-1/(ni)^2) (Rydberg Formula*)

*note: UC Davis source seems to consolidate the Rydberg Formula hc term into the Rydberg constant, as evidenced by their subsequent derivation eliminating the hc term against the value of R.

Fig. 1: Sodium electron orbital energy diagram (Whitman College)

From the above electron orbital energy diagram for sodium, it can be seen that the transition between the highest occupied molecular orbital (HOMO), the 3s orbital, and the lowest unoccupied molecular orbitals (LUMO), the 3p set, corresponds to an emission of light in the 589nm wavelength region, or yellow light. This fact is experimentally verified since the yellow color of fireworks is often produced by sodium salts. It is in this fashion that the colors each metal element produces can be understood. So why metals? Well, the emission of light in various visible colors is reliant on electron energy state transitions as we just discussed, and electron band structure properties for metals tell us that the Fermi level, or highest occupied energy level (HOMO energy level), lies in the middle of an electron band in metals, meaning that there are higher electron energy levels to which metal electrons may be excited [5]. So metals are used simply because in our universe these are the elements that are capable of light-producing electron transitions.

Of course other factors must go into fireworks to achieve such controlled chemical acrobatics as producing tailed explosions or glittery rain, but with bang and color you have the basic makings of this recreational technology that is also a marvel of modern chemistry. 

I plan to do experiments inspired by daily events or questions that arise, so comment if this post has brought up any topics you would like to hear more about or want to see experiments on. Thanks!

Dear Readers,

As a university student studying chemistry and material science, I find it unsettling that Americans don't take more interest in science matters. Modern science is the reason that we can cruise in fancy cars, see our parents halfway around the planet and expect to live well into the end of a century in more than one regard. Discoveries and innovations in science fields have the potential to completely revolutionize our way of life for the better, and if I were to want the american public to better understand one thing about science, it would be that science is for everyone. The way the sciences are currently perceived, they seem like unattainable fields coded in math and jargon intended for only a select few, an intellectual elite. But this is the fault of our society, not of science itself. Science is for people like you, me and the other millions of people who are looking to make their lives and the lives of others better. Science is for those of us who want to know more about how this world we live in ticks and what lies before and after what living in the present can offer. It is for those of us who are searching for meaning somewhere in this full yet empty universe into which we were all thrown blind. Science for us all, the Everyday Thinkers.

                                                                                                          -Alex