Photochemistry and Dipole-Dipole interactions

So in summary, the cosine terms will simplify to 1 in this case.- The ionic charge screening refers to the fact that the presence of ions in the solution will alter the electric field and therefore the dipole-dipole interaction. To take this into account, you can use the Poisson-Boltzmann equation as you have mentioned.- You are on the right track with finding the number of particles per cubic meter in the solution. Keep in mind that this is the concentration of ions, but you will also need the concentration of molecules (the photo-active molecules in this case) in order to calculate the total number of molecules in the solution.- Once you have all the necessary values, you can plug them into the expression for
  • #1
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Let me begin by saying that this question had a disclaimer, saying that part a should NOT be done exactly, but in a back of the napkin manner. The idea is to make reasonable assumptions and approximations in order to obtain an answer.

Homework Statement


Suppose that a certain chemical synthesis of molecular aggregates is driven by light (photochemistry). Infrared photon absorption changes a large molecule's arrangement from almost nonpolar into a polarized configuration. These newly polarized molecules are then attracted to one another to form aggregates ("supramolecular assembly"). In free space, their dipolar electric potentials have the usual relation to distance away from the dipole (polarized molecule). However, chemistry is rarely performed in free-space...
Assume instead that the synthesis is performed in a 6.0 milli-Molar aqueous solution of NaCl (salt water) at room temperature. While water's dielectric constant will alter the field, the ionic concentrations will also vary to effectively screen the dipolar field.Part a. What is the distance dependence of the interaction energy for two dipoles (assumed to be aligned) in this aqueous environment? (Here, you may simplify things by also assuming the distance dependent terms from the dipole-dipole interaction and from the ionic charge screening can simply be multiplied together.

Part b. Assume that the dipole's magnitude can be approximated as half an electron's charge separated by 3.8 nm. Make a rough estimate of the distance at which two polarized molecules' attractive potential will be greater than thermal energy, kBT = 25 meV.

Part c. Assume these photo-active molecules have a Stoke's radius of 2.4 nm. Under continuous
IR exposure (you may assume that exactly half of the large molecules are excited to the excited polar configuration), what is the approximate concentration (molecules per unit volume) of these molecules such that it takes them on average 55 seconds to diuse far enough to fall within the bonding distance of another polarized molecule (which you calculated in Part b)?

Homework Equations


Relevant to this are the Stokes-Einstein equation for part C
[tex]D = \frac{k_{B}T}{4 \pi \eta a}[/tex]
The interaction energy between two dipoles (in vacuum)
2m6v9l5.jpg


The Attempt at a Solution



Part a:
This is actually the part I have the most difficulties with. I've already found the expression for the distance dependence of two dipoles (as given in the equations section) in vacuum, so that goes like 1/r^3. However, I'm quite unsure about the cosine terms. The question says the dipoles are aligned, so I'd say that means that θ1=θ2 (or does it mean that the negative of the one faces the positive of the other?. The phi I do not know.
Furthermore, I know (from my book, Lindsay's introduction to nanoscience) that this energy is reduced by an amount equal to the inverse of the dielectric constant of the medium they are immersed in, so that of water. However, this is where I get lost. The question clearly indicates that I have to do something with ionic charge screening, but I am clueless as to what this entails.
What I have done already (and I am NOT sure if it is of any use) is the following:
The solution is 6 milli molar. This means that per liter, there are 0.06 moles of NaCl in the solution. 1 mole is 6.02214×10^23 particles, so 6 milli molar is 3.61×10^22 particles per liter and 3.61×10^25 molecules per cubic meter.

So from here on, I do not know what to do. Any hints would be very much appreciated.

Edit: Upon closer inspection of the book, I did find a section that talks about this screening. It is described by the Poisson Boltzman equation, which (in the taylor approximation) can be solved
flk4mf.jpg


This is a good thing, as it uses the molarity. I'm not sure how to exactly proceed here. I can work out what all the factors are in this, ending up with a new expression for the energy, but I still don't know how to handle the angles and such. And should I still divide by the dielectric moment of water, if I'm using this equation (which already takes it into account)?

Part B
What I've done here (lacking a solution for A as of now) is the following.
Assuming that the dipole’s magnitude can be approximated as half an electron charge separated by 3.8 nm, the magnetic dipole moment is equal to μ=qx = 0.5×e×3.8×10^-9 = 3.04381x10^-28 C m.

Then, I want to do something with the equation I obtain in A, and just set it equal to the 25 meV and solve for r. That much I can do of course, but without anything from A I get stuck here.

Part C
Using the Einstein Stokes relation I get that, given is that the synthesis is performed at room temperature, T = 293 K, the viscosity of water at room temperature is 1.002 ×10^(-3) Pa s and the stokes radius is 2.4 nm, that the diffusion constant D = 8.9242×10^(-11) m² s^(-1).

Now, beyond this I will need a value of r from question B. However, that does not finish the question, I have to do something with the concentration. This, I also do not know how to do as of yet. I half expect having to do something with an expectation value, as the question asks to do this on average, but I have yet to figure this out. However, I'd first and foremost like to solve A, so that is what my question is about primarily.

Thank you in advance
 
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  • #2
for your help.First of all, it's great that you have already done some research and have attempted to solve the problem on your own. Here are some hints to help you with part a:

- The dipoles are assumed to be aligned, so this means that the angle between them is 0 degrees. This means that the cosine terms in the dipole-dipole interaction equation will simplify to 1.
- The phi term is the angle between the dipole moment and the direction of the electric field. In this case, since the dipoles are aligned, phi will also be 0 degrees and the cosine term will again simplify to 1.
- The ionic charge screening refers to the effect of the ions in the solution on the interaction between the dipoles. In a high ionic concentration solution like salt water, the ions will shield the electric field of the dipoles, reducing the strength of the interaction. This can be taken into account by using the Poisson Boltzmann equation, which you have already mentioned.
- When using the Poisson Boltzmann equation, you will need to know the concentration of the ions in the solution, as well as the temperature and dielectric constant of water. These values can be found from a chemistry textbook or online.
- Once you have the expression for the interaction energy in the aqueous environment, you can compare it to the interaction energy in vacuum to see how it changes. Remember that the interaction energy in vacuum is proportional to 1/r^3, so you will want to see how the aqueous environment affects this dependence.

For part b, you are on the right track with using the interaction energy equation from part a and setting it equal to the thermal energy. You can then solve for r to find the distance at which the attractive potential will be greater than thermal energy.

For part c, you will need to use the diffusion constant that you calculated and the value of r that you found in part b to solve for the concentration. You can use the Einstein-Stokes equation as you have mentioned, but you will also need to take into account the fact that only half of the molecules are excited to the polar configuration. You can do this by multiplying the concentration by a factor of 2.

I hope these hints help you to solve the problem. Remember to keep track of your units and to check your final answer to make sure it makes sense. Good luck!
 

1. What is photochemistry?

Photochemistry is the branch of chemistry that deals with the study of chemical reactions and processes that are initiated by the absorption of light.

2. What are dipole-dipole interactions?

Dipole-dipole interactions are attractive forces between two molecules that have permanent dipole moments. This means that one molecule has a slightly positive end and the other has a slightly negative end, and they are attracted to each other.

3. How are photochemistry and dipole-dipole interactions related?

In photochemistry, light is used to excite molecules and initiate chemical reactions. Dipole-dipole interactions can play a role in these reactions by influencing the orientation and stability of the excited molecules.

4. What types of molecules exhibit dipole-dipole interactions?

Molecules that have polar covalent bonds, such as water (H2O) and ammonia (NH3), exhibit dipole-dipole interactions. This is because the unequal sharing of electrons in these bonds results in a separation of charge and the formation of a dipole moment.

5. How do dipole-dipole interactions affect the properties of molecules?

Dipole-dipole interactions can affect a molecule's boiling and melting points, as well as its solubility in polar solvents. They can also influence the strength of intermolecular forces and the stability of a molecule's structure.

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