Monday, February 15, 2021

Raman Spectroscopy & Perseverance Mars Rover

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Topic: Raman Spectroscopy

Have you ever wondered what life may have been like if it ever existed on Mars? On the 30th of July 2020, NASA undertook that ambitious goal by launching a rover called “Perseverance” equipped with the most advanced analytical technologies of the 21st century. (NASA, n.d.) On board the rover was an instrument called a Raman Spectrometer. Its purpose is to detect and identify organic compounds. (NASA, n.d.) By detecting for life characteristic compounds such as amino acids or complex organic substances, one may be able to deduce whether life was present. In addition, Raman Spectroscopy is used frequently in Chemistry and Forensics to ascertain the identity of unknown compounds. (AZO Materials 2018) This technology relies on many facets of optics, such as lenses, reflection, diffraction, and the inelastic scattering of photons. (P. J. Larkin 2011, 28-31)



Figure 1: Raman Spectrometer diagram (simplified)

Molecules can exist at different vibrational and rotational energy levels caused by the various vibrational and rotational modes due to their structure. (P. J. Larkin 2011, 17-21) When the monochromatic light from the laser source impinges on a chemical substance, it causes the molecule to adopt an energy equivalent to the energy of the laser source. This is called a virtual state since it is not an actual energy state of the molecule and is only transient. If the molecule in question goes back into its ground state (lowest energy at a particular temperature), then it would release a photon that has the same energy as the photon from the source. When this happens, the scattering is referred to as Rayleigh Scattering. It turns out this happens much of the time, however, in some cases the molecule may return to an energy level that is higher than the ground state i.e. (v = 1, 2, 3, etc.). When this occurs, the photons emitted are lower in energy and hence have a longer wavelength. The resultant spectral lines are called stokes lines. A third, even less likely case can occur where the molecules are already in an excited state. In that scenario the light from the source caused the molecules to be excited to a virtual state higher than previously. As the molecule goes to a lower energy level, for example the ground state, the energy of the emitted photon has a higher energy, thereby having a shorter wavelength. The lines caused by this secondary process is known as anti-stokes lines. (Mettler Toledo, n.d.) The resulting spectrum would appear as shown in figure 2 below.

Figure 2: Raman Spectrum (Illustrative)

The wavelengths of light produced by this process are characteristic of the molecule and the chemical bonds in such a molecule. As a result, it can be used as a unique signature to identify unknown substances and elucidate their structures. The laser produces a monochromatic (one wavelength) beam. The light from the laser is directed into a beam splitter. Half of the beam exits the beam splitter and is lost. The other half of the beam is directed into a convex lens which focuses the beam down to a very small high-intensity point via refraction. The light then hits the sample and is scattered. This light then goes through the lens and hits the beam splitter where half is reflected into the laser and the other half is directed through a filter. This filter, sometimes referred to as a notch filter, removes most of the Rayleigh Scatter light which has the same wavelength as the laser light. Therefore, the filter isolates the useful signals for analysis i.e., the Stokes and Anti-stokes wavelengths. The light is then focused to a point by another convex lens and then passes through a narrow slit. The beam of light expands from the slit due to diffraction where it is reflected off a plane mirror onto a reflective grating. The grating functions to split the light into its individual wavelengths via interference and diffraction.  These wavelengths are however uncollimated, so a concave mirror aids to focus this beam to form a spectrum on a detector. The detector is typically highly sensitive, such as a charged couple detector or a photomultiplier. The spectrum is then amplified and the intensities of each of the wavelengths are recorded.

Figure 3: Real Raman Spectrum of polystyrene (Renishaw n.d.)

            It is very important that the notch filter removes most of the Rayleigh light otherwise the signal would be overwhelmed with this wavelength intensity, thereby sequestering the other wavelengths. Raman spectrometers use detectors such as CCDs (Charged Coupled Devices). A CCD is a silicon (Si) multichannel array detector capable of detecting in UV, visible and near-infrared light. Various types of CCDs can be used that are optimized for specific wavelength ranges. The intensity of each wavelength is determined by these detectors, creating a spectrum of intensities as seen in figure (3). (Horiba, n.d.) These peaks are highly specific to the compound. The data from the CCDs are first amplified and filtered to remove noise in the signal. A computer then uses this information to plot a graph of intensity versus wavenumber (inverse of wavelength expressed in cm-1). These peaks are then compared to a database that has the wavenumbers for every organic functional group known. Alternatively, the entire spectrum can be compared with a known database of compounds to distinguish what compound it is.

Raman spectroscopy has had limited application in its early developments due to the low efficiency of normal Raman scattering, however, new developments of optical instruments, lasers, and nanotechnology have allowed greater sensitivities and resolutions. (S. Weng et al. 2019, 2) One such advancement to Raman spectroscopy is coherent anti-stokes Raman spectroscopy. One of the major drawbacks of Raman spectroscopy is that fluorescence can occur in molecules and often have a greater intensity than the stokes and anti-stokes lines, hence increasing the noise in the spectrum which makes identification difficult or impossible. Coherent anti-stokes Raman spectroscopy addresses this issue by using two pulsed lasers. The frequency is kept constant with one laser and the second laser tuned so that the frequency difference between the two lasers equals the frequency of a Raman-active mode of interest. (Teledyne, n.d.) In addition, it enhances the weak Raman signal by using a four-wave mixing process. (Semrock, n.d.) Another advancement in Raman spectrometry is Fourier-transform Raman spectroscopy which uses a neodymium-doped yttrium aluminum garnet (Nd: YAG) laser which has a wavelength of 1064 nm as the light source. This eliminates the fluorescence interference problem and reduces the laser damage to samples caused by higher frequency light. (S. Weng et al. 2019, 2)

The Raman spectrometer is an important analytical instrument, which for the first time is being used on another planet (Mars). (NASA, n.d.) Only speculation remains at what ‘Perseverance’ would find on Mars when it touches down, however, it would surely alter humanity’s understanding of life itself, our origins and help scope for the possibility of becoming a multi-planetary species. Raman spectrometry is a vital tool in chemistry and forensics, used to determine the identities of compounds and the composition of mixtures and works by using light to excite the vibrational or rotational modes of molecules from virtual states. This requires innovative uses of optics which focuses the light, filters it, reflects it, diffracts it, and collects it onto sensitive detectors to be measured. The Raman spectrometer still has a lot of areas for development. Within these areas of improvement are the filters and lasers i.e., to create much more efficient narrower filters and to have lasers of higher intensities.

References

AZO Materials. 2018. “Raman Spectroscopy and its Most Common Applications.” Accessed 10, December 2020. https://www.azom.com/article.aspx?ArticleID=16150.

Horiba. n.d. “Instrument Presentation.” Accessed 8, December 2020. https://www.horiba.com/en_en/ramanspectrometerpresentation/.

Mettler Toledo. n.d. “Raman Spectroscopy.” Accessed 9, December 2020. https://www.mt.com/us/en/home/applications/L1_AutoChem_Applications/Raman-Spectroscopy.html.

NASA. n.d. “Instruments.” Accessed 9, December 2020. https://mars.nasa.gov/mars2020/spacecraft/instruments/.

NASA. n.d. “Mars 2020.” Accessed 1, December 2020. https://mars.nasa.gov/mars2020/.

P. J. Larkin. 2011. Infrared and Raman Spectroscopy: Principles and Spectral Interpretation. USA: Elsevier.

Princeton Instruments. n.d. “Raman Spectroscopy.” Accessed 5, December 2020. https://www.princetoninstruments.com/learn/raman.

Renishaw. n.d. “Raman Spectra Explained.” Accessed December 5, 2020https://www.renishaw.com/en/raman-spectra-explained—25807.

S. Weng, et al. “Recent advances in Raman technology with applications in agriculture, food and biosystems: A review.” Artificial Intelligence in Agriculture 3, no. 1-10 (October) https://doi.org/10.1016/j.aiia.2019.11.001.

Semrock. n.d. “Coherent anti-stokes Raman Scattering.” https://www.semrock.com/coherent-anti-stokes-raman-scattering-cars.aspx.

Sunday, February 14, 2021

Non-rigorous Proof of the Power Rule of Derivatives

 

Non-rigorous Proof of the Power Rule of Derivatives

By Clement Charles

 Using the binomial expansion to prove the power rule, which is the generalized rule for derivatives of powers (including polynomials).


Consider the function:

Where .

Recall the definition of the derivative is:

Therefore, the derivative of the function is:

By the binomial expansioncan be expressed as:

In summation notation:

Therefore, the limit becomes:

Factoring an h:

Recast this equation:

NB:

For:

Since terms for k > 1 are 0, it means that the expression can be reduced to:

NB:

And:

So that:

Friday, February 12, 2021

An introduction to tesla coils-Nikola Tesla's dream


Picture by: PBS

 A tesla coil is a device invented by Nikola Tesla capable of generating extremely large voltages at a high frequency. Nikola developed this device in his search for a means of providing wireless energy to everyone at no cost. Although this purpose was never realized due to its impracticality and inability to turn a profit; the physics involved in the tesla coil is truly remarkable.

A tesla coil is basically a transformer, where the secondary coil is a tower consisting of many turns of wire (approx. 2000 turns) and a primary coil which contains few turns of a thick wire. An alternating current is applied to the primary coil, and due to Faraday’s law of induction, a current is induced in the secondary coil. The current in the secondary coil, however, is at a much higher voltage than the primary coil due to the significant increase in the number of turns in a thinner gauge wire. The current supplied to the primary coil is created by a high-frequency resonant circuit. The secondary coil is specifically tuned to the high frequency of the primary coil. This is done by adding a metallic toroid, seen at the tops of tesla coils which acts as a capacitor. The charge at the toroid becomes so incredibly high that the electrons become free and ionizes the air in a beautiful light show.


(NB: This is a repost from my previous blog)

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Raman Spectroscopy & Perseverance Mars Rover

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