FerroFluids

        Lets talk about something interesting today. That thing is the marvel of ferrofluids. Ferrofluids are basically magnetic particles suspended within a liquid median using a surfactant. This creates a part liquid, part solid substance that displays superparamagnetism. What? Well in much simpler terms, a ferrofluid is a combination of two states of matter. The solid is connected to the liquid using the surfactant, which basically connects the liquid to the solid. A simple example of this is how soap is able to attach oil with water. Besides that, the surfactant is also the thing that is used to keep the magnetic particles from attaching to each other. Now, we reach the biggest word, superparamagnetism. This word simply means that all the particles are so small that they only have one magnetic dipole, meaning they all ether have a south or north pole. Or just a pole in general since you cant have only a south pole. There are a lot of things that can be done with ferrofluids. In fact maybe you have seen one of those cool towers made from them. 

                                     Strangely symmetric aren't they?

And while those things are cool, they don't really have an practical applications. And knowing what the topic of this blog is, lets give an example of some of the interesting symmetrical stuff that is being test about ferrofluids. 

       The first article is titled Effect of MFD Viscosity and Porosity on Revolving Axi-symmetric Ferrofluid with  Rotating Disk. The name may seem complicated, but it is actually quite simple. First, MFD stands for magnetic field-dependent. To start with, when ferrofluid is rotated, it will usually always display y-axis symmetry or axi-symmetric characteristics. Just look at the pictures above if you don't believe me. So, some scientists decided to apply an outside magnetic field to a ferrofluid that was rotating and in symmetry in order to see 3 things. First, how would its viscosity change, its porosity change, and would the ferrofluid even stay symmetrical. While the last tenet doesn't need defining, the first two do. Viscosity is something's willingness to flow. Porosity is the empty space in something. At the end of the experiment, it was found that despite all the variables that were changed the ferrofluids tended to act in a similar manner no matter what. The thing that I take form this however, is that symmetry is very hard to get rid of, no matter the velocity of the spinning, viscosity, or porosity. 

        It is important to remember why this stuff is so symmetric. And just in case you were unable to gather why from the beginning of this post, I will restate it here. Ferrofluids are not just liquids. They have small magnetic solids just floating around in them. And all these things are very easily influenced by a magnetic field. A magnetic field itself, usually goes from north to south. When the ferrofluids are exposed to one, they are go to a position dictated by the field itself. The surfactant keeps them from getting to close, and there you go, constant y-axis symmetry. Thanks for reading. 

The Thermodynamics of Symmetrical Bodies

Boltzmann

Flasks with Cohorts

Albert Einstein's "Electrodynamics of Moving Bodies" did encompass symmetry into some mind blowing theories on space and time and what not. But let us remind ourselves, we are humble people in the pursuit of answers in chemistry. But I do conjure up Einstein's miracle year papers to prove my point of the importance of symmetry.  Boltzmann (the handsome devil whose picture is shown above) had a way to calculate entropy based on the number of macro states a substance (let's say gas) can occupy in a cohort. The flasks with their cohorts are also above. There is a way to calculate entropy; it is S=klnW. S is entropy, k is Mr. Boltzmann's constant, and W is the number of macro states. There is a ubiquitous correlation between symmetry and entropy. Entropy very much is a degree of symmetry. Because there are two types of symmetries( dynamic entropy and static entropy) there are two types of entropies, aptly named dynamic entropy and static entropy. 

Everybody, just relax. I'm going to explain the two. Dynamic symmetry is due to dynamic motion like the motion of one individual molecule and static symmetry is due to phase change. It is obvious, looking at the cohorts, that III has more macro states and greater symmetry (the one that has the statistically better chance at happening). A symmetry increase due to dynamic motion is just as apparent. An electron flying in its orbital leads one to conclude that the hydrogen atom is a symmetrical sphere. If the electron did not move as it did, the atom would not be seen as a sphere because of the definite spot of the electron.  

Change in Gibbs free energy can measure whether some process is spontaneous or not. If it is negative, it is spontaneous, if it positive then it is not, and if it is zero then it is at equilibrium. This is the max entropy. At this state, the substance is most susceptible to some internal or external constraints. Constraints like this include polarity and isotropicity. When these changes happen, because of a force or field, the symmetry is reduced as well as the entropy. Our friends in Basel, Switzerland have come up with the perfect platitude: Any system evolves spontaneously toward a maximal symmetry. It is analogous to saying that when I heat up a gas, the entropy is increased because of the higher number of possible arrangements these molecules can be in. But, contrary to common sense and intuition and thermodynamically speaking, the symmetry increases because individually each molecule has more energy and that little electron is moving a lot faster allowing the nuclei of the molecules to look more like spheres. But there are real irking (I like the work irk) constrains like I just mentioned. The van't Hoff factor (bringing these gas molecules closer together and restricting their degrees of freedom) are the constrains that reduce the symmetry. The point is that that these gas molecules are indistinguishable from one another and that is why the apparent disorder has nothing to do with our discussion on symmetry. I can attest to the fault reasoning that symmetry is disorder. We can say a sphere is perfectly symmetrical because if we rotate it an infinite number of ways, it is distinguishable from all views.  Mathematically, it boils down to this equation: S=lnN! where N! is the total permutation symmetry number.  We have all heard about the heat death of the universe, where the universe (as entropy inexorably increases) will stop at the point where entropy of the universe is maximum. This goes along with the Big Crunch Theory of the death of the universe where the reverse of the Big Bang will happen, essentially. In the fist scenario, the entropy of the universe is max. and in the second, the symmetry of the universe is max. (as everything will be in the singularity). Both are end of universe scenarios (how poetic).  Hope you have enjoyed this look into the relationship between entropy and symmetry (for a while, people have been asking me what's their story, you know are they dating or something but it hasn't been until now that their relationship has been explained in terms of end of time scenarios). 

Symmetrical Hydrogen Bonds v2

In one of our prior posts, we left off without mentioning how symmetrical "hydrogen bonds" are created. We mentioned that "hydrogen bonds" are incredibly strong, but these symmetriacl "hydrogen bonds" are even superior in strength. This post will serve to detail what makes a "hydrogen bond" symmetrical, and how they are formed.

Symmetric "Hydrogen Bond"

Symmetrical "hydrogen bonds" have the potential to be one of the strongest bonds, but what makes a regular "hydrogen bond" symmetrical? A study conducted at Yale University in October of 2012 by Schley involved analyzing iridium (III) alkoxides to determine what gives rise to a symmetrical "hydrogen bond". Utilizing x-ray diffraction, he found, along with his coleagues, that very short hydrogen bonds with O···O distances of 2.4 angstroms exist. After a series of calculations, Shley uncovered that a shorter O···O bond distance will give rise to a symmetrical hydrogen bond.



Symmetrical "Hydrogen Bonds" in Iridium (III) Aloxides

One method which attempts to prove that hydrogen bonds are asymmetric is called the NMR, nuclear magnetic resonance, method. It is illustrated with 3-hydroxy-2-phenylpropenal and then applied to
dicarboxylate monoanions. Resulting from this analysis is that the intramolecular "hydrogen bonds" are asymmetric, although can become symmetric in a crystal structure.


3-hydroxy-2-phenylpropenal

Another article by Charles Perrin states that symmetrical "hydrogen bonds" can occur only in a crystal. He supports this claim by stating that a disorded environment, in solution, will produce an asymmetric bond. However, crystals, such as when water is in its solid phase existing as ice, can guarantee symmetry. So does this mean that symmetric hydrogen bonds can occur only in the solid phase, and never in the gas or liquid phase?


Crystal Structure of Water

A paper entitled "A neutron scattering study of strong-symmetric hydrogen bonds in potassium and cesium hydrogen bistrifluoroacetates: Determination of the crystal structures and of the single-well potentials for protons" demonstrates how "hydrogen bonds" are stronger when in their symmetric, crystalline form. Potassium and cesium hydrogen bistrifluoroacetates emphasize the covalent element of the O···O bond as well as the ionic nature of the hyrogen proton bond. The resulting of this combination of pairing is an incredibly strong bond.


A Hydrogen Bistrifluoroacetates

As a result of these three different studies, we are left with a symmetric "hydrogen bond's" whose strength exceeds that of a regular "hydrogen bond". There are three elements that must be met if we wish for this "hydrogen bond" to be symmetric:

1. "Hydrogen bonding" must occur in the molecule (this is sort of assumed if we are talking about symmetric "hydrogen bonding"
2. The O···O bond distance must be as small as possible
3. The molecule containing the hydrogen bonding should be in a crystal form

Strong Symmetric "Hydrogen Bond"

With all of these conditions met, a regular, rather strong, "hydrogen bond" becomes an incredibly powerful symmetrical "hydrogen bond"



Math? In Chemistry?

As you might have picked up from before, there are several kinds of symmetric molecules! That brings up a huge question-- how do we classify them? How do we differentiate one from another?

Well, that's the purpose of applying group theory in the world of molecules!

Wait a second! Isn't group theory a very advanced mathematical concept? Yes, but it can be applied here in a more simple fashion. This post will cover the basics.

We've touched upon this in one of our earliest blog posts, but it's never bad to repeat something that's so important, right?

In this case, one phrase is crucial to understanding the various types of symmetry:

"A Symmetry operation is an operation which brings an object into a new orientation which is equivalent to the old one."

So for example, in the BF3 molecule below,

we can rotate the shape around the center by 120 degrees. That would change where the atoms go, but it would still maintain the same form. So that rotation would here be a symmetry operation.

There are 5 main symmetry operations involved with molecules:

1) The identity (E)

This is what several people would call a "trivial" operation. Basically, it's doing nothing to the molecule-- that would, of course, keep it in the same form. So every molecule has at least this symmetry operation.

2) Rotation (Cn)

In this operation, we rotate the molecule around certain axes in order to get the same shape back. The axis, depending on the angle that the molecule is rotated by, is called Cn. For example,

as the picture suggests, a rotation by 360/2 degrees around the C2 axis would bring the molecule to the exact same shape! Similarly, rotation by 360/3 degrees around C3 and rotation by 360/4 degree around C4 would both preserve symmetry. 

I hope you realized the pattern: an axis used to rotate the molecule by 360/n degrees is called the Cn axis.

In addition, the operation itself is also called Cn. 

Here are some more examples:

In this famous H2O molecule, we can see that rotating it by 180 degrees around the axis in the middle would make it the same shape! Hence, this molecule has rotational symmetry.

This time, we have something more complicated! There are two different types of rotational axes in this molecule of benzene (C6H6). We can rotate it by 60 degrees around the center C6 axis or by 180 degrees around the C2 axis to get the same hexagonal shape.

Another thing to note here is this-- how many C2 axes do you think there are? I'll give you a moment to think.

Well if you answered 6, you're correct! There are three that intersect through opposite sides-- such as the one shown in the picture, and there are three more that intersect through opposite vertices! That makes 6 whole axes of just C2. This just shows you that a molecule doesn't need to just have one type of rotational symmetry.

Oh, and one more thing-- the Cn axis with the highest value of "n" is called the principal axis.

3) Reflection (σ)

Reflection is also relatively straight forward-- it's just reflecting the molecule across certain planes.

There are three types associated with this symmetry operation: 

          1) Vertical (σv): In this case, the plane of reflection is parallel to the principal axis. Here's an example:

In this ammonia molecule, the plane shown in yellow contains the principal axis. Since reflecting it across that plane would result in the same shape, this molecule is vertically reflective. (That specific reflection is also called σv.)

(If you want to see an interactive, 3-D version of this, click here.)

          2) Horizontal (σh): In this case, the plane is perpendicular to the principal axis. 

Before, we saw that benzene molecules have an C6 rotation axis, which is the principal axis in this case. So the plane shown here would count as the horizontal plane, since it's perpendicular to that axis. And clearly we can see that reflecting the molecule across this plane gets us the same shape. 

          3) Dihedral (σd): This one's a bit more complicated. In this case, the plane is parallel to the principal axis and bisects the angle between two C2 axes. It's best explained with an example:

In this picture, imagine the C2 axes connecting opposite vertices. We see that the plane bisects the angle formed by two of these axes. Since the plane is also parallel to the principal axis, this reflection counts as a dihedral reflection.

Lastly, notice how the dihedral plane was also the vertical plane! The two do not have to be distinct-- rather, all dihedral planes are actually vertical planes, since dihedral planes must also be parallel to the principal axis.

So far, we've covered 3 out of 5 symmetry operations. We'll continue on with our journey at another time.

Starting the new year off with a BOOM!

Hey y'all! I hope that you all had a nice winter break.

We're starting the first post of the year with a bang! 
More specifically, we're gonna discuss what makes the bang: explosive molecules such as the well-known TNT (Trinitrotoluene).

(Structure of a TNT molecule)

(Structures of a) methenamine and other explosive compounds; b) RDX; c) HMX; d) HMTD; e) PETN)

(A 3-D representation of a PETN molecule)

First, as we mentioned above, these are all explosive molecules! All of these materials have at one point been used in warfare, due to their ability to explode readily.

In fact, PETN was used in the recent and infamous incident of the Underwear Bombing in 2009! The terrorist, Umar Farouk Abdulmutallab, was found with 80 grams of PETN sewn into his underwear. 

(The device used in the bombing attempt of 2009. The PETN molecules can be seen in the center.)

But hold on! All of the molecules shown above are remarkably symmetric!! Aren't symmetric molecules supposed to be stable by themselves? Why would they want to explode? And especially why spontaneously?

Well first of all, stability is not the only factor in predicting whether a molecule spontaneously goes into reaction. In fact, that's determined by what's called the Gibbs free energy, notated with the letter G. It basically refers to the amount of energy that can be used to do work, and the equation for this energy is described below:

The ΔH represents enthalpy, the T represents temperature, and the ΔS represents entropy. 

In general, if ΔG is negative, the reaction is endergonic, which implies that it is also spontaneous! That's what determines it.

In the case of explosives, we see two things:

1) All of the explosive molecules mentioned before are exothermic, meaning that they have negative changes in enthalpy. 

2) All of them also have positive values of entropy! 

The specific values of enthalpy and entropy for TNT and PETN can be seen below (click on the image to see a bigger picture):

And because of these values, ΔG is VERY negative! This reveals exactly why these symmetric molecules explode so viciously and spontaneously.

But wait-- shouldn't aren't symmetric molecules very "ordered"? They don't look disordered, but why are their entropies so high?

Sadly, if you were thinking that, you've fallen into a trap. If anything, entropy measures how complicated (in a sense) a system is. In this case, we see that these molecules are all actually very complicated, especially compared to their decomposition into fairly simple gases!

For example, PETN starts one of its forms of decomposition in the following way:

(This process, in which nitrogen dioxide is separated, happens rapidly throughout its decomposition.)

Its ultimate forms of decomposition can be seen below:

We can see that eventually, the entire, complicated molecule turns into mere carbon dioxide, carbon monoxide, water, hydrogen gas, nitrogen gas, and other basic molecules!

Lastly, what's even more shocking is that these symmetric molecules aren't even as stable as we thought! Although they are perfectly symmetric, they are actually restricted in movement! Thus, when they are triggered, they rearrange themselves rapidly, releasing these more stable products. 

All of this shows exactly why and how explosives create the BANG that we know of.

(Explosion caused by TNT)

What a shocking turn of events-- who knew symmetry wasn't always the desired form of molecules?

Symmetrical Hydrogen Bonds

In one of the first blog posts, we questioned the importance of symmetry in chemistry and gave multiple ways how symmetry is involved in basically every aspect of chemistry. In this blog post, we are going to focus on one of these ways: the symmetrical "hydrogen bond". The symmetrical "hydrogen bond" has the potential to be over forty times stronger than a regular "hydrogen bond", but you are probably wondering why "hydrogen bonds" are so important. After mentioning "hydrogen bonding" multiple times, you have probably noticed that I put it in quotations. This is because hydrogen bonding is not actually bonding, but rather an attraction between molecules.

"Hydrogen Bonding"
The red atoms represent oxygen
The yellow atoms represent hydrogen

What are "hydrogen bonds"? "Hydrogen bonds" are an intermolecular force (a special case of covalent bonding) which are essential to basically all biological systems, and are formed when an atom contains a hydrogen bonded to a fluorine, oxygen, nitrogen, and sometimes chlorine. One can even argue that without "hydrogen bonding", many creatures would cease to exist! "Hydrogen bonding" explains many of the extraordinary properties of water such as its surface tension, ability to act as a universal solvent, cohesion, capillary action, and much more. As seen in the image on the right, the water molecules are sticking together, known as cohesion. The water molecules are polar, as the hydrogen is pseudo-positive and the oxygen is pseudo-negative, and each molecule is attracted to each other (the hydrogen of one is attracted to the oxygen of the other). This causes an incredibly strong "bond" to be formed, illustrated by the dotted line connecting the red (oxygen) and yellow (hydrogen) atoms together, known as "hydrogen bonding".

A property of a hydrogen bond, cohesion, is seen here. The water molecules
are sticking together on top of this penny creating a dome-like shape.

Neon Atom

Boron Atom

"Hydrogen bonds" are also responsible for the stabilization of large macromolecules such as proteins and nucleic acids, key for all living specimens. So as you can tell, "hydrogen bonds" are incredibly important, and an even stronger bond could create an even more versatile molecule! A symmetrical "hydrogen bond", seen below, is exactly what it sounds like: a molecule with symmetry (it can be any kind of symmetry) of hydrogen bonds. In prior posts, we have discussed how molecules which are symmetric are more stable. Stable molecules, contain strong bonds, so they are incredibly difficult to "separate". Just to make this a little more clear, I will give you an example. We can say that neon, a noble gas, has symmetry within its second energy level, while boron, does not. From this information, it would seem that neon should have a higher first ionization energy, the energy required to rip off an electron, because this atom wants to be stable and symmetric. So when we look up in a table and find that neon has a first ionization energy of 2081 kJ/mol and boron has one of 800.6 kJ/mol we are not surprised. Therefore, if a "hydrogen bond" is symmetric, it should require more energy to split it; thus, becoming stronger. 

Symmetrical "Hydrogen Bond"

Just to recap, we went over what a "hydrogen bond" is, and why it is important for virtually all living creatures on earth. We then discussed how symmetry leads to stability and stronger bonds/ attractive forces. This then takes me to the point where I can begin talking about the symmetrical hydrogen bond, but I will leave you pondering the implications of a symmetrical hydrogen bond until a future blog post.

   

Group Theory-- A Brief Introduction

In one of our first posts, we briefly introduced the concept of mathematical group theory and how that relates to chemistry. Specifically, different symmetric molecules with different types of symmetryies are placed in different "groups," which have special mathematical and chemical properties of their own.

Before we begin on our chemathical journey, check out this introductory video! It offers a lot of information and explanations to group theory.

We hope you enjoy! We'll discuss more in depth about this topic in upcoming posts! (: