s21_NMR
Nuclear Magnetic Resonance of the Four Basic Alcohols
Ramona White and Alan Turnbull
Abstract
A test to confirm previously measured values for chemical shift and spin-lattice relaxation times of the four most basic alcohols through pulsed nuclear magnetic resonance spectroscopy was conducted. The beat frequency within the free induction decay envelope of each alcohol was obtained and converted by means of a fast Fourier transform into the frequency domain to calculate chemical shift.
Introduction
Nuclear magnetic resonance (NMR) spectroscopy is a technique used to probe the structure of molecules and measure the interaction between nuclear spin states when placed under a magnetic field. The goal of this experiment is to measure the number of unique hydrogen environments found in the four basic alcohols: methanol, ethanol, 1-propanol, and 1-butanol and obtain clarifying values for their chemical shifts, particularly the OH environment. Spin lattice relaxation times, commonly referred to as T1, were obtained for each compound and revealed the rate of approach to equilibrium upon magnetization.
Theory
When the samples are placed under a constant magnetic field, B0, and subjected to electromagnetic radiation of the resonant frequency ω0, the hydrogen nuclei absorb energy and “spin-flip” to align themselves antiparallel to the field. Over a finite period of time, the nuclei give off energy and precess around the magnetic field back to the lower energy, alpha state. Their precession frequency, ω0, is defined through the fundamental resonance condition
(4)
Methods and Experimental Setup
(3)
A precise measurement of this characteristic time T1 requires a two pulse sequence known as the inversion-recovery method. A 180° pulse inverts the magnetization along the -z axis, and before it can fully relax back to equilibrium, a 90° pulse rotates the magnetization to the xy plane where its relaxation can be detected. By solving the differential equation of formula 3 with this initial condition we arrive at an expression to calculate spin-lattice relaxation times using different values of t, the time delay between pulses.
(2)
where vsample is the resonant frequency of our alcohol samples and vTMS is the resonant frequency of TMS we detected through the fast Fourier transform (FFT). A chemical shift of zero is defined as the resonant frequency peak of TMS.
During the magnetization process energy flows from the nuclei to the surrounding lattice, reducing the magnetic energy of the spins. The time taken for this energy flow is characteristic of the particular sample. The rate for the z component of net magnetization to reach equilibrium along the z direction is proportional to the difference between the equilibrium value M0 and instantaneous magnetization Mz.
(1)
The TeachSpin PS2 Spectrometer measured their precession as they decay at their respective resonant frequencies in a fast induction decay (FID) signal. Our FID plots were fast Fourier transformed to decompose the signal into its individual frequency components. A compound does not just contain one resonant frequency, but a range of resonant frequencies for each local environment of hydrogen in the molecule. Because frequencies can vary depending on the strength of the applied magnetic field, it is standard convention in NMR spectroscopy to calculate chemical shift relative to TMS (tetramethylsilane) resonance[5]. Chemical shift is hence defined as
A sample of each of our alcohols was placed within a small test tube and lowered into the sample chamber between a permanent magnet with a field strength of 0.5±0.01 Tesla. The PS2 unit itself produced and altered the pulse frequency, centering around 21 MHz for the resonant frequency of a proton. The unit allowed for adjustments of the pulse frequency, length, number of sequential pulses, and time delay between them. When nuclei fell back from resonance, their precession about the xy plane induced an emf in the sample coil to be detected and displayed on the oscilloscope. Two signals were observed: the FID signal directly detected from the coil representing the magnetization precession after deacy, and the FID signal multiplied by the reference frequency, best described as an FID envelope.
Figure 2. Screenshot from the digital oscilloscope displaying the 180° - 90° pulse sequence.
Magnetization in the xy plane is measured as the amplitude of the yellow decay plot. In
calculating chemical shift, a Fourier transform was taken of the blue oscillating FID envelope
following the 90° pulse.
Spin-Lattice Relaxation Times
The necessary length of a 90° pulse for each sample was determined when the FID amplitude shown on the oscilloscope was maximized and magnetic moment precession in the xy plane was at its greatest; likewise the length of 180° pulse was double that duration, when the amplitude was minimized. T1 times were measured using the inversion-recovery method which applied an 180°-90° pulse sequence as seen in figure 2. The period, or time between the pulse sequence repeats, was set through the pulse programmer to be greater than or equal to three times the T1 time so the compound had enough time to reestablish thermal equilibrium.
For each alcohol, we recorded the magnetization of the 90°pulse, Mz, at different time delays between the two pulses, t. Plotting these values revealed an exponential decay curve fitting equation 4; our data for ethanol is graphed below.
Linearizing the decay function as
(5)
inserting our values, and applying a least squares fit allowed us to determine T1 times.
Chemical Shift
When measuring chemical shift, we applied a single 90° pulse to our samples at a frequency 5-6 kHz above resonance. To calculate chemical shift, each of our alcohol samples included one drop of TMS to allow for a reference peak in the FFT.
The detected FID signal is in the form
(6)
where T2 is the spin-spin relaxation time, another time constant characteristic to each type of compound that represents the decay of the FID. Taking a Fourier transform directly of this signal would reveal a resonant frequency peak from the cosine function, convoluted with the exponential decay function frequencies. To remove the effects of the exponential decay and enhance resolution, we multiplied the FID by an exponential growth function with time constant a. Countering the decay with only a rising exponential would result in steeply rising noise, hence the weighting function W(t) also included a falling Gaussian function with time constant b.
(7)
Frequency spectra contain a range of line widths, so the best method of determining a and b was experimentally on our LabView program, varying them until resolution and signal-to-noise ratio were optimized.
The FIDs were transported directly from the spectrometer to a National Instrument NI 6034E data acquisition device (DAQ) using a 68-pin cable and National Instrument Terminal Block BNC-2110. On Labview, we multiplied the FID by our weighting function, averaged the signal from one pulse with five other identical pulses, and then took an FFT to arrive at frequency distributions to determine chemical shift from. (Screenshot of Labview program left at bottom.) The FFT revealed these beat frequencies, the difference between actual resonance and the frequency of the applied pulse. Chemical shift was calculated using formula 2 with our detected resonant frequency peaks of each spectrum.
Results
Table I. Chemical Shift and T1 times of the Four Basic Alcohols
Our T1 times reveal how fast the net magnetization vector recovers to its ground state in each sample. Although T1 varies with magnet strength and temperature, through comparison to other publications we remain confident in the identification of each alcohol. Our results confirm an negative correlation between relaxation time T1 and molecular weight.
By counting the number of chemical shift values in each molecule and recognizing an extra peak from noise in our ethanol spectrum, we confirmed the number of local hydrogen environments: two in methanol, three in ethanol, four in 1-propanol, and five in 1-butanol.
Figure 3. Full structural formula of ethanol C2H6O where each local hydrogen environment is boxed in.
Because there are 3 environments, the FFT reveals three resonant frequency peaks to the right of TMS.
Due to resolution limitations, we were unable to discern sub-peaks within our spectra and assign environment names to each peak. Because the OH environment only consists of one hydrogen, it appears as the shortest peak relative to the other peaks in the spectra. We were able to identify the chemical shift of the OH peak in pure concentrations to be 2.60 ppm in methanol, 2.31 in ethanol, and 2.64 ppm in both 1-butanol and 1-propanol with ± 0.47 ppm of error. In methanol the OH resonant frequency is less than that in the other samples, because it is shielded more by the neighboring three hydrogen instead of two. This study concludes that the OH peak in solventless alcohols should appear around 2.5 ppm, a value previously disagreed upon in NMR literature.
Figure 4. Frequency spectrum of 1-propanol with drop of TMS. Blue star indicates
TMS peak at 5880 Hz and green circles identify beat frequencies of 5894.5, 5918,
5936, and 5969.5 Hz we calculated chemical shift values from.
Future Suggestions
In future NMR investigations calculating chemical shift we would suggest using a solvent in order to improve the resolution of the signals and detect peak splitting. Deuterium compounds are often used in NMR studies, as their spin values do not allow it’s resonant frequency to appear on a spectrometer tuned to proton resonance. Resolution would also improve by using a stronger magnet and higher spectrometer frequency to have a wider spread of resonant frequencies. Our instrument frequency of 21.1 MHz established a chemical shift of 1 ppm to be 21.1 Hz, but if a 300 MHz signal was applied the chemical shift would scale as 1 ppm to 300 Hz and peaks would be better detectable. As a last improvement, measuring spin-spin relaxation time T2 would help identify the most accurate time constant values to be used in the weighting functions, constants we identified experimentally.
Citations
[1] TeachSpin, Inc. Pulsed/CW NMR Spectrometer PS2-A/B/C: Instructor’s Manual. Buffalo, NY (1996).
[2] R.J. Abraham, M. Mobli, Modelling 1H NMR Spectra of Organic Compounds: Theory, Applications and NMR Prediction Software. Wiley, Chichester (2008).
[3] J. Stoltenberg, D. Pengra, R. Van Dyck and O. Vilches, “Pulsed Nuclear Magnetic Resonance.” UCSB Physics (2006).
[4] G. Morris, “NMR Data Processing.” Manchester, UK, University of Manchester School of Chemistry (1999).
[5] A. Srinivasa Rao, V. Arulmozhi and S. Rajalakshmi, Mutual Interactions between Hydrogen Bond in Alcohols - NMR Study. Pondicherry Central University, India (1993).
[6] Spectral Database for Organic Compounds, SDBS. National Institute of Advanced Industrial Science and Technology, Japan. [online] Available at:
<https://sdbs.db.aist.go.jp/sdbs/cgi-bin/cre_index.cgi> [Accessed 20 April 2021].
[7] W. Reusch, “Hydroxyl Proton Exchange and the Influence of Hydrogen Bonding.” Michigan State University, MI (2013).
Labview Program
