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Research

2D NMR: Heteronuclear Single-Quantum Correlation Spectroscopy (HSQC)

Heteronuclear single-quantum correlation spectroscopy (HSQC) is a 2D NMR technique that reveals one-bond correlations between hydrogen and a heteronucleus. The HSQC experiment is similar to the heteronuclear correlation experiment (HETCOR) but is more sensitive. In the HSQC spectrum, the proton chemical shift is plotted on the horizontal F2 axis, while the 13C chemical shift is plotted on the vertical F1 axis. The corresponding proton and 13C spectra are also shown. The HSQC contour plot does not have any diagonal peaks. All the cross-peaks indicate the protons directly attached to each carbon in a molecule. Similar to the COSY spectrum, imaginary lines are drawn in horizontal and vertical directions to identify the correlated peaks.
For example, the HSQC spectrum of 2-chlorobutane has a carbon signal at 11 ppm that can be assigned to the shielded methyl group and correlated to the proton multiplet at 1.01 ppm. The carbon signal at 24.8 ppm arises from the deshielded methyl group, which correlates to the proton multiplet at 1.52 ppm. Similarly, the methylene carbon signal at 33.3 ppm and methine carbon signal at 60.4 ppm correlate to the multiplets at 1.72 and 3.96 ppm, respectively.&#160; HSQC is a very useful technique for structurally elucidating complex molecules and is routinely used in protein NMR studies.

Heteronuclear single-quantum correlation spectroscopy (HSQC) is a 2D NMR technique that reveals one-bond correlations between hydrogen and a ...

2D NMR: Overview of Heteronuclear Correlation Techniques

Heteronuclear correlation spectroscopy is an analytical technique that investigates the coupling between different types of nuclei, often a proton and an X-nucleus, such as carbon-13 or nitrogen-15. This method is commonly used in nuclear magnetic resonance (NMR) spectroscopy to gain insights into complex chemical compounds&#39; structural and compositional aspects. A typical heteronuclear correlation spectrum displays X-nucleus chemical shifts on one axis and a proton spectrum on the other axis. Cross-peaks reveal the connection between specific protons and X-nuclei.
The main heteronuclear correlation experiments include HETCOR, HSQC, HMQC, and HMBC. HSQC, HMQC, and HMBC record the proton spectrum, whereas the X-nucleus spectrum is recorded by standard heteronuclear correlation spectroscopy or HETCOR. The HETCOR-HMQC-HSQC group of experiments cannot detect X-nuclei without an attached proton. HETCOR is used when ultrahigh peak resolution is required along the X-nucleus axis.
The heteronuclear single quantum correlation technique, or HSQC, investigates proton-to-X-nucleus single bond correlations. In an HSQC experiment, polarization is transferred from a proton nucleus to a neighboring X-nucleus and then back to the proton nucleus. The signal from the proton nuclei is then recorded. HSQC generates a spectrum like that of heteronuclear multiple-quantum correlation spectroscopy or HMQC but uses a different suppression method, providing better X-nucleus resolution along the axis.
Heteronuclear multiple-bond correlation, or HMBC, is a proton-detected experiment, like HMQC but with a longer initial delay time. This experiment is used to observe long-range proton to X-nucleus connectivity separated by 2-3 bonds, with some experiments going out to 4 or 5 bonds. In an HMBC experiment, direct one-bond correlations are suppressed as part of the sequence. The spectra of HMBC give rise to cross peaks that correlate which protons are coupled to what other specific X-nucleus is more than one bond away. The gradient HMBC (gHMBC) pulse sequence offers better suppression of interfering signals, making it particularly useful for analyzing complex molecules with overlapping signals.

Heteronuclear correlation spectroscopy is an analytical technique that investigates the coupling between different types of nuclei, often a proton and an ...

2D NMR: Homonuclear Correlation Spectroscopy (COSY)

Homonuclear correlation spectroscopy, or COSY, is a 2-dimensional NMR technique that provides information about coupled protons. Typically, the geminal and vicinal coupling are observed. For example, consider the COSY spectrum of ethyl acetate, where its 1D proton NMR spectrum is plotted along the vertical and horizontal axes with their corresponding chemical shift scale. Three spots on the diagonal corresponding to the three peaks in the 1D proton spectrum are called diagonal peaks. The COSY spectrum is symmetric about the diagonal, with signals above and below the diagonal called cross-peaks or off-diagonal peaks. An imaginary line is drawn from diagonal peaks parallel to the horizontal axis, leading to a cross peak. A vertical line is then drawn from the same cross peak towards the diagonal peak to correlate the peaks. The off-diagonal peaks correlating the multiplets at 1.25 and 4.2 ppm indicate that the methyl protons are coupled to the methylene protons. The signal at 2 ppm is not associated with cross-peaks because the protons are not involved in homonuclear coupling. A COSY spectrum is useful when overlapping multiplets complicate the corresponding 1D spectrum.

Homonuclear correlation spectroscopy, or COSY, is a 2-dimensional NMR technique that provides information about coupled protons. Typically, the geminal ...

Insensitive Nuclei Enhanced by Polarization Transfer (INEPT)

Insensitive Nuclei Enhanced by Polarization Transfer (INEPT) is an advanced Nuclear Magnetic Resonance (NMR) technique specifically designed to detect and enhance the signals of low-abundance nuclei, such as carbon-13 and nitrogen-15, in small molecules. The fundamental principle behind INEPT is the transfer of polarization from a more abundant and highly polarizable nucleus, typically hydrogen-1, to the low-abundance nucleus of interest. This process effectively boosts the NMR signal of the low-abundance nuclei, making them more easily detectable.
The INEPT technique involves a series of carefully timed radiofrequency (RF) pulses applied to the sample. These RF pulses excite the more abundant nuclei, causing them to align their spins in a specific manner. Through the process of spin coupling, the polarization of the more abundant nuclei is then transferred to the low-abundance nuclei. As a result, the NMR signal of these low-abundance nuclei is significantly enhanced, allowing for a more detailed analysis of the molecular structure.
Various pulse sequences have been developed to improve the observability of these low-abundance nuclei when coupled to a high-receptivity nucleus. The INEPT pulse sequence combines a spin echo and selective population inversion, which includes 90&#176; and 180&#176; pulses on the high-sensitivity (the I spins) and low-sensitivity nuclei (the S spins), respectively. Coupling-constant-based delays between pulses facilitate magnetization transfer through space or bond interactions. Additional RF pulses and delays invert the low-gamma magnetization, producing an observable NMR signal. The net result is an enhanced NMR signal from low-gamma nuclei that would otherwise be challenging to detect.
Various pulse sequences have been developed to improve the detection of low-abundance nuclei when coupled with high-receptivity nuclei such as protons. The INEPT sequence yields enhanced signals for insensitive nuclei, with half of the CH group producing negative peaks and the other half positive peaks. This pattern allows for discrimination between different types of carbon-hydrogen bonds within the molecule.
Decoupling methods can be employed to enhance sensitivity and resolution in distinguishing various carbon-hydrogen bonds, making INEPT an invaluable tool in the chemical and pharmaceutical industries.

Insensitive Nuclei Enhanced by Polarization Transfer (INEPT) is an advanced Nuclear Magnetic Resonance (NMR) technique specifically designed to detect and ...

Two-Dimensional (2D) NMR: Overview

The 1D NMR spectrum of large and complex molecules like natural products has complicated splitting patterns and overlapping signals, which can be easily interpreted using 2-dimensional (2D) NMR. Unlike 1D NMR, 2D NMR has two frequency axes that provide the coupling information between the nucleus A and nucleus B in a molecule. The process from which 2D spectra are obtained has four steps.
The first step is the preparation period, during which nucleus A is excited with a radiofrequency pulse. The second step is the evolution or wait period t1, which is incremented systematically, and no data is observed during this period. The next step is the mixing period, in which a second radiofrequency pulse is introduced, which transfers the magnetization to the spins of nucleus B. In the last step, the magnetization of nuclear spins from B is detected during the acquisition time t2 for each t1. Time domains t1 and t2 are Fourier transformed into frequency domains f1 and f2, and these correspond to two dimensions of 2D spectra, while the third dimension is the intensity. In 2D experiments, coupling between the same kind of nucleus is called homonuclear 2D experiments, whereas coupling between two types of nucleus is called heteronuclear 2D experiments. 2D spectra can be displayed as stacked or contour plots. When presented as stacked plots, 2D spectra are difficult to interpret. The contour plot is the horizontal cross-section of a stacked plot where the size of the circles shows the signal intensity. Its interpretation is straightforward and it is preferred for data analysis.

The 1D NMR spectrum of large and complex molecules like natural products has complicated splitting patterns and overlapping signals, which can be easily ...

2D NMR: Overview of Homonuclear Correlation Techniques

Homonuclear correlation spectroscopy (COSY) is a powerful technique used in Nuclear Magnetic Resonance (NMR) spectroscopy to study the correlations between nuclei of the same type within a molecule. It provides information about scalar couplings between adjacent nuclei, which helps determine connectivity and structural information. There are several COSY variants, each with its unique strengths and experimental parameters.
COSY90 is the standard two-dimensional (2D) COSY experiment that utilizes a second 90-degree pulse to achieve high sensitivity and resolution. It excels in analyzing small to medium-sized molecules and provides information on directly coupled protons. COSY45, similar to COSY90, uses 45-degree pulses instead of 90-degree pulses. This results in reduced sensitivity but improved resolution.
Long-range COSY (LR-COSY) extends the COSY experiment to detect scalar couplings between nuclei further apart in the molecule. It achieves this by combining multiple pulse sequences and magnetization transfers.
Relayed COSY is a variant of COSY that adds extra pulses to the standard pulse sequence to produce cross-peaks between cross-peaks, showing specific molecular connections hidden by overlapping signals.
TOCSY (Total Correlation Spectroscopy), also known as HOHAHA (Homonuclear Hartmann-Hahn Spectroscopy), reveals all through-bond connectivity between all coupled nuclei. TOCSY is especially useful for analyzing molecules with overlapping signals and complex coupling patterns.
NOESY (Nuclear Overhauser Effect Spectroscopy) measures the nuclear overhauser effect, which arises from dipole-dipole interactions between nuclei. It provides information about spatial proximity and can be used to determine the three-dimensional structure of a molecule.
ROESY (Rotating-frame Overhauser Enhancement Spectroscopy) is similar to NOESY but employs a different mechanism to obtain through-space correlations. It provides information about spatial proximity and is particularly useful for studying molecules with weak NOE signals.
In conclusion, choosing a COSY variant depends on the molecule or reaction under investigation and the desired information. The right COSY variant can be determined based on molecular size, coupling complexity, and the need for spatial or long-range connectivity data.

Homonuclear correlation spectroscopy (COSY) is a powerful technique used in Nuclear Magnetic Resonance (NMR) spectroscopy to study the correlations ...

Double Resonance Techniques: Overview

Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or radiofrequency pulses to manipulate and observe two distinct nuclear spins. One important application of double resonance is spin decoupling, which selectively suppresses coupling with one type of nucleus while observing the NMR signal from another nucleus, simplifying the spectrum and enhancing resolution.
Spin decoupling is usually achieved by irradiating the sample atoms with a suitable radio frequency (rf) pulse sequence, effectively eliminating all the coupling with one nuclide. This simplifies the observed spectrum, making it easier to analyze and understand the relationships between different nuclei.
Double resonance experiments can be classified as heteronuclear or homonuclear, depending on whether the two sets of nuclei are of different isotopes or the same isotope, respectively. They can also be selective or nonselective, depending on whether the irradiating frequency covers only a portion or all of the resonance frequencies.
In nonselective heteronuclear decoupling, samples are exposed to an appropriate radiofrequency range to remove all coupling with one nuclide. However, increased external field strengths necessitate more powerful irradiation across broader frequency ranges. In certain instruments, continuous irradiation creates enough heat to cause damage to thermally sensitive samples.
To overcome these problems, modern methods using a series of pulses and exact timing delays, like J-modulated spin echo pulse sequences, can be employed to eliminate or adjust coupling effects within the spectrum.
For example, the attached proton transfer (APT) experiment applies a J-modulated spin echo pulse sequence to focus on the phase of detected carbon signals. Carbon atoms attached to an even number of protons exhibit positive signals in the spectrum, while those bonded to an odd number of protons appear as negative signals.
It utilizes a combination of a 180&#176; proton pulse and broadband decoupling to simplify spectral interpretation and assign multiplicities. The 180&#176; pulse is applied to the protons during the APT experiment. Its role is to refocus the spin coupling evolution that naturally occurs due to interactions between protons and carbons.
Specifically, after the 90&#176; pulse creates transverse magnetization, the 180&#176; pulse ensures that the effects of coupling are frozen during the initial period where the decoupler is turned off. This means the chemical shifts evolve only during the time 1/J&#8203; (the coupling constant period) after the first 180&#176; pulse.
By carefully timing this pulse sequence, the experiment isolates carbon multiplicities by utilizing the J-coupling between carbons and their attached protons. After the coupling evolution period (1/J&#8203;), broadband decoupling is turned on. This removes the J-coupling signals, collapsing multiplets into single peaks for each carbon resonance.
The decoupling ensures that carbon signals are free of splitting, allowing for a clear differentiation of signals based on phase (positive or negative) rather than splitting patterns.
The APT technique selectively enhances carbon signals, providing valuable information about carbon-proton connectivity, the number of attached hydrogen atoms, and the overall molecular structure.

Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or ...

&sup1;H NMR of Labile Protons:  Deuterium (&sup2;H) Substitution

This lesson illustrates the role of deuterium substitution in simplifying the NMR spectrum of compounds comprising labile protons. One method employed is the use of deuterium. Amongst the three isotopes of hydrogen, deuterium (2H) has a nucleus composed of one proton and one neutron. When the D2O solvent is added to a pure dry ethanol solution, its labile proton is substituted with deuterium.
<img alt="Figure1" src="/files/ftp_upload/12280/12280-PT_Figure_1.svg" style="text-align: center; height: 700px;" />
Figure 1. The comparison of the proton NMR spectra of pure dry ethanol and the same in D2O solvent.
The signals from deuterium are not observed in a proton NMR spectrum, as deuterium&#8211;proton coupling is negligible, and no spin-spin splitting occurs between them. As shown in Figure 1, the NMR spectra of pure ethanol and ethanol in deuterium, the disappearance of the triplet in the latter, confirms that it corresponds to the labile &#8211;OH proton. Furthermore, the methylene protons that initially showed up as a multiplet transform to a quartet, proving that the multiplet is due to the coupling with the &#8211;OH proton and the methyl protons.

This lesson illustrates the role of deuterium substitution in simplifying the NMR spectrum of compounds comprising labile protons. One method employed is ...

Nuclear Overhauser Enhancement (NOE)

Irradiation of a spin-active nucleus causes an increase or decrease in the signal intensity of neighboring nuclei that are not necessarily chemically bonded or involved in J-coupling. &#160;This phenomenon, called the Nuclear Overhauser Enhancement (NOE), results from through-space interactions between the nuclear spins. The NOE effect decreases with increasing internuclear distance and is generally not observed beyond 4 angstroms. In NOE, dipole-dipole interactions between neighboring spin-active nuclei result in the transfer of nuclear spin polarization. These interactions can cause an increase or decrease in the signal intensity, which results in a positive or negative NOE, respectively.
NOE can be applied to improve the signal intensity of less sensitive nuclei such as carbon-13. Proton-decoupled carbon-13 spectra show a positive NOE effect, where the carbon signal intensities are substantially increased compared to those in proton-coupled spectra.
Targeted irradiation of specific nuclei can also reveal through-space proximity, which helps confirm stereochemistry and verify spectral peak assignments. The NOE effect is also applied in 2D NMR experiments, such as Nuclear Overhauser Effect Spectroscopy (NOESY), to determine the 3D structure of proteins.

Irradiation of a spin-active nucleus causes an increase or decrease in the signal intensity of neighboring nuclei that are not necessarily chemically ...

&sup1;H NMR of Labile Protons: Temporal Resolution

Protons bonded to heteroatoms such as nitrogen and oxygen exhibit a range of chemical shift values. This is due to the varying degree of hydrogen bonding between the proton and the heteroatom in other molecules. The extent of hydrogen bonding affects the electron density around the proton, thereby giving different chemical shift values for the protons in the proton NMR spectrum.
The &#8211;OH proton in alcohols typically appears in the range of &#948; 2 to 5 ppm but can vary depending on the specific alcohol and conditions. This &#8211;OH proton undergoes rapid proton exchange with other molecules and is referred to as a labile proton. So, the exact &#948; value of the &#8211;OH proton and the spin-spin coupling involving the &#8211;OH proton and the other protons in the alcohol depends on the rate of the &#8211;OH proton exchange. The proton exchange rate, in turn, depends on multiple factors, including the purity of the alcohol sample, temperature, and solvent.
<img alt="Figure1" src="/files/ftp_upload/12279/12279-PT_Figure_1.svg" style="text-align: center; height: 350px;" />
Figure 1. The triplet of a &#8211;OH proton in the proton NMR spectrum of neat ethanol.
For example, the &#8211;OH proton exchange in a pure dry ethanol sample is very slow on the NMR time scale, giving enough time for the spin-spin coupling. Consequently, as depicted in Figure 1, the proton NMR spectrum of pure dry ethanol shows a triplet for the &#8211;OH proton due to the spin-spin coupling with adjacent methylene protons. The methylene protons are seen as a multiplet due to the coupling with the &#8211;OH proton and the methyl protons.
The presence of trace amounts of an acid or base increases the proton exchange rate. The proton exchange becomes rapid, and the NMR spectrometer only records an average of all the possible environments for the &#8211;OH proton.
<img alt="Figure2" src="/files/ftp_upload/12279/12279-PT_Figure_2.svg" style="text-align: center; height: 325px;" />
Figure 2. The broad singlet of a &#8211;OH proton in the proton NMR spectrum of neat ethanol.
As a result, as recorded in Figure 2, the &#8211;OH proton exhibits a broad singlet. The protons from the adjacent methylene group present a quartet where the splitting is caused only by the adjoining methyl group.

Protons bonded to heteroatoms such as nitrogen and oxygen exhibit a range of chemical shift values. This is due to the varying degree of hydrogen bonding ...

&sup1;H NMR of Conformationally Flexible Molecules: Variable-Temperature NMR

The axial and equatorial protons in cyclohexane can be distinguished by performing a variable-temperature NMR experiment. In this process, except for one proton, the remaining eleven protons are replaced by deuterium. The deuterium substitution avoids the possible peak splitting caused by the spin-spin coupling between the adjacent protons. The remaining proton flips between the axial and equatorial positions.
<img alt="Figure1" src="/files/ftp_upload/13016/13016-PT_Figure_1.svg" style="text-align: center; height: 480px;" />
Figure 1. The temperature-dependent proton NMR spectra of cyclohexane.
Figure 1 depicts the proton NMR spectrum of the deuterium substituted sample, recorded at various temperatures. At room temperature, the rapid ring flipping of cyclohexane results in a single sharp peak. As the temperature is lowered to &#8722;60&#176;C, the rate of chair-chair interconversion reduces, resulting in the broadening of the peak.
Further lowering of the temperature broadens the peak, forming a saddle that splits into two peaks. On reaching a temperature lower than &#8722;89&#176;C, two sharp, well-resolved peaks corresponding to the equatorial and axial protons are formed. The peaks corresponding to the equatorial and axial protons occur at &#948; 1.62 and 1.14, respectively. At such low temperatures, the rate of chair-chair interconversion is reduced significantly, enabling the detection of the two distinct sets of protons on the NMR time scale.

The axial and equatorial protons in cyclohexane can be distinguished by performing a variable-temperature NMR experiment. In this process, except for one ...

&sup1;H NMR of Conformationally Flexible Molecules: Temporal Resolution

At room temperature, the chair conformer of cyclohexane undergoes rapid ring flipping between two equivalent chair conformers at a rate of approximately 105 times per second. These two chair conformers are in equilibrium. The rapid ring flipping results in the interconversion of the axial proton to an equatorial proton and an equatorial to the axial proton. Such interconversions are too rapid and cannot be detected on the NMR timescale. Hence, the NMR spectrometer cannot distinguish between the axial and equatorial protons, resulting in a single peak at &#948; 1.4.
Similarly, NMR averages all the conformations of any molecule with rapid conformational equilibria. For example, the CH3 protons in bromoethane have a single resonance and coupling constant for splitting by the CH2 protons due to the rapid internal rotation of the carbon-carbon bond. Lastly, besides conformational equilibria, the time-averaging effect of NMR spectroscopy is also observed in some chemical reactions.

At room temperature, the chair conformer of cyclohexane undergoes rapid ring flipping between two equivalent chair conformers at a rate of approximately ...

Mass Spectrometry: Carboxylic Acid, Ester, and Amide Fragmentation

The fragmentation patterns observed for compounds such as carboxylic acids, esters, and amides in the mass spectra include &#9082;-cleavage and McLafferty rearrangement. Fragmentation by &#9082;-cleavage preferentially occurs at the carbon-carbon bond at the &#9082;-position next to the carboxylic group to generate a neutral radical and a cation. Long chain compounds with hydrogen at their &#947;-carbon undergo McLafferty rearrangement to give a radical cation and a neutral alkene.
For example, the fragmentation of butyramide is demonstrated in Figure 1. The molecular ion peak of butyramide, which contains one nitrogen atom, shows an odd mass-to-charge ratio of 87. Fragmentation of butyramide molecular ion by &#9082;-cleavage produces a cation at a mass-to-charge ratio 44. In addition to &#9082;-cleavage, butyramide molecular ion also undergoes fragmentation via McLafferty rearrangement. The base peak at the mass-to-charge ratio 59 arises due to McLafferty rearrangement.
<img alt="Figure1" src="/files/ftp_upload/13051/13051_PT_Figure_1.svg" style="text-align: center; height: 250px;" />

The fragmentation patterns observed for compounds such as carboxylic acids, esters, and amides in the mass spectra include &#9082;-cleavage and McLafferty ...

Chemical Ionization (CI) Mass Spectrometry

The molecular ion peak of a molecule in the mass spectrum provides vital information for molecular identification. However, conventional electron impact ionization can lead to the rapid dissociation of some molecular ions before they reach the detector. A milder ionization method is required to increase the lifetime of such ionized analyte molecules. Chemical ionization (CI) is a gas-phase protonation reaction useful for mass-analyzing analyte molecules that are easily protonated to yield the corresponding conjugate acid. In this process, the sample is mixed with an excess reagent gas, which ensures the electron impact occurs primarily on the reagent gas. The charged species formed from the reagent protonates the analyte molecule, producing a relatively stable protonated analyte (conjugate acid) compared to the molecular ion. This results in an M+1 peak in the mass spectrum. The conjugate acid may then undergo fragmentation that generates additional signals.
For example, the CI of di-sec-butyl ether in methane gas illustrates this process. When the ether is mixed with excess methane gas as a reagent, electron impact occurs on methane rather than the ether. The resulting methane radical cation can react with another methane molecule to generate a methane radical and a methanium ion. The methanium ion is a source of gas-phase protons, which can protonate the ether to form its conjugate acid. The sequential reactions during the chemical ionization of di-sec-butyl ether are depicted in Figure 1.
<img alt="Figure1" src="/files/ftp_upload/12300/12300_PT_Figure_1.svg" style="text-align: center; height: 175px;" />
Figure 1: Chemical ionization of di-sec-butyl ether methane mixture.
This conjugate acid of the ether (m/z = 131) is relatively more stable than the molecular ion (m/z = 130) of ether formed via the conventional electron impact ionization. In the traditional route, the molecular ion undergoes fragmentation via &#945; cleavage, giving a signal at m/z = 101. Figure 2 illustrates the reactions that occur during electron impact ionization directly on di-sec-butyl ether.
<img alt="Figure2" src="/files/ftp_upload/12300/12300_PT_Figure_2.svg" style="text-align: center; height: 175px;" />
Figure 2: Electron impact ionization of di-sec-butyl ether and fragmentation of the molecular ion.
So, the mass spectra of di-sec-butyl ether ionized via CI feature an M+1 peak at m/z = 131. On the other hand, mass spectra of di-sec-butyl ether ionized via electron impact ionization do not show any peak at the m/z value of its molecular weight. Figures 3a and 3b show the mass spectra of di-sec-butyl ether ionized via the electron impact and chemical ionization methods, respectively.
<img alt="Figure3" src="/files/ftp_upload/12300/12300_PT_Figure_3.svg" style="text-align: center; height: 225px;" />
Figure 3:&#160;a) No m/z = 130 peak is visible in the mass spectrum obtained via electron impact ionization of di-sec-butyl ether. b) The m/z = 131 peak is clearly visible in the mass spectrum obtained via chemical ionization of di-sec-butyl ether.

The molecular ion peak of a molecule in the mass spectrum provides vital information for molecular identification. However, conventional electron impact ...

Mass Spectrometry: Alkyl Halide Fragmentation

Chlorine isotopes exist as 35Cl and 37Cl in a 3:1 ratio, while bromine isotopes exist as 79Br and 81Br in a 1:1 ratio. The mass spectrum of alkyl halides typically produces two distinct molecular ion peaks, the molecular ion peak, [M], and the molecular ion plus two, [M + 2] peak. The relative heights of these two peaks are proportional to the isotopic abundance ratios of the halide. For example, 2&#8208;chloropropane and 1&#8208;bromopropane display two peaks with relative peak heights in a 3:1 and 1:1 ratio, respectively.
Alkyl halides typically lose a non-bonding electron from the halogen to form molecular ions. The base peak results from the heterolytic cleavage of the carbon&#8211;halogen bond, where the bonding electrons go to the most electronegative atom, forming a cation and halogen atom. Interestingly, the &#9082;-cleavage is observed only in alkyl chlorides, not alkyl bromides. In alkyl chlorides, the&#160; C&#8211;Cl and C&#8211;C bonds exhibit similar strengths, while in alkyl bromides, the C&#8211;Br bond is weaker than the C&#8211;C bond. Consequently, the alkyl chlorides form a stable cation, where the positive charge is shared between the two atoms.
While less commonly discussed, fluoroalkanes and iodoalkanes exhibit unique fragmentation behavior. Fluoroalkanes, due to the strength of the C&#8211;F bond and the presence of only one isotope (19F), show limited fragmentation and lack isotopic peaks. Iodoalkanes, with their weak C&#8211;I bond and a single isotope (127I), predominantly fragment by losing iodine, resulting in simpler spectra with less isotopic splitting.

Chlorine isotopes exist as 35Cl and 37Cl in a 3:1 ratio, while bromine isotopes exist as 79Br and 81Br in a 1:1 ratio. The mass spectrum of alkyl halides ...

Electrospray Ionization (ESI) Mass Spectrometry

Higher molecular weight biomolecules are nonvolatile compounds that may decompose before ionizing or vaporizing during mass analysis with conventional electron impact ionization methods. Accordingly, electrospray ionization (ESI) is the favored method for vaporizing and ionizing biomolecules as it circumvents rapid fragmentation and enables the recording of mass signals for the entire biomolecule.
ESI utilizes electrical energy to transfer ions from the liquid phase of the sample into the gaseous phase. The analyte biomolecule is premixed with an ionic liquid&#8212;a nonmolecular compound serving as the ionization source. The solution is sprayed through a high-voltage capillary to generate a fine aerosol. The voltage difference applied between the capillary and the entrance of the analysis chamber causes the movement of charged droplets toward the analysis chamber. The ionic liquid from the aerosol evaporates during this movement, leaving behind a variably protonated or ionized analyte molecule. These charged species are detected in the mass spectrum at an m/z value equivalent to the sum of the analyte molecule&#39;s molecular mass and the ions&#39; molecular weight from the ionic liquid associated with the analyte molecule.
The position of mass signals varies depending on the type of cations present in the ionic liquid. For example, the presence of sodium ions in the ionic liquid leads to an (M+23) peak in the mass spectra, while the presence of a proton results in an (M+1) peak.

Higher molecular weight biomolecules are nonvolatile compounds that may decompose before ionizing or vaporizing during mass analysis with conventional ...

Matrix-Assisted Laser Desorption Ionization (MALDI)

Matrix-assisted laser desorption ionization (MALDI) is a powerful analytical technique used in mass spectrometry. It enables the identification and characterization of various biomolecules, including proteins, peptides, nucleic acids, and carbohydrates. MALDI spectrometry is widely employed in biological and medical research, as well as in fields like pharmacology and biochemistry.
The analyte of interest, a biomolecule or a mixture of biomolecules, is mixed with a suitable matrix material. The matrix is usually an organic compound, such as a small organic acid or a crystalline substance, that facilitates ionization. This analyte-matrix mixture is then deposited onto a target surface, inserted into the mass spectrometer, and dried. During drying, the matrix forms small crystals that incorporate the analyte molecules within their structure.
Once the sample is prepared, a pulsed laser is directed onto the target surface. The matrix molecules absorb the laser beam energy, causing them to heat up and vaporize rapidly. This process is known as laser desorption. As the matrix molecules vaporize, they carry the embedded analyte molecules. The vaporized analyte molecules become ionized through a process called proton transfer. The proton transfer occurs between the matrix and the analyte molecule. The matrix molecule donates a proton to the analyte molecule, resulting in the formation of protonated ions. The analyte ions are then accelerated by an electric field and further separated based on their mass-to-charge ratio in a time-of-flight mass analyzer.
The mass spectrum obtained from MALDI spectrometry provides valuable information about the mass and relative abundance of the analyzed biomolecules.

Matrix-assisted laser desorption ionization (MALDI) is a powerful analytical technique used in mass spectrometry. It enables the identification and ...

Mass Spectrometry: Aldehyde and Ketone Fragmentation

In mass spectrometry, the fragmentation of aliphatic aldehydes and ketones generally occurs through three key mechanisms: &#945;-cleavage, inductive cleavage, and the McLafferty rearrangement.
<ol>
	<li>&#945;-Cleavage 
	&#945;-Cleavage is a common fragmentation in carbonyl compounds where the bond adjacent to the carbonyl group is broken. This process produces an alkyl radical and an acylium cation, which is often detected in the mass spectrum due to its stability.</li>
	<li>Inductive Cleavage 
	In inductive cleavage, fragmentation yields an acyl radical and an alkyl cation. This occurs when electrons are drawn toward the carbonyl, weakening adjacent bonds and resulting in a distinctive fragmentation pattern. For example, in the mass spectrum of 5-methyl-2-hexanone, inductive cleavage produces an alkyl cation at a mass-to-charge (m/z) ratio of 71.</li>
	<li>McLafferty Rearrangement 
	The McLafferty rearrangement is a specific fragmentation pattern for carbonyl compounds with &#947;-hydrogen (hydrogen on the third carbon from the carbonyl group). The molecule undergoes a six-membered cyclic transition in this rearrangement, yielding a radical cation and a neutral alkene. For 5-methyl-2-hexanone, this rearrangement results in a peak at m/z 58.</li>
</ol>
Example: Fragmentation of 5-methyl-2-hexanone 
In the mass spectrum of 5-methyl-2-hexanone, the molecular ion undergoes these fragmentation patterns:
<ol style="list-style-type: circle;">
	<li>Inductive cleavage produces an alkyl cation at m/z 71.</li>
	<li>&#945;-Cleavage results in the base peak at m/z 43.</li>
	<li>McLafferty rearrangement creates a distinct peak at m/z 58.</li>
</ol>
An additional diagnostic feature in aldehydes is the M&#8722;1 peak, which arises due to the &#945;-cleavage of the aldehyde proton. In mass spectrometric analysis, this peak can help identify aldehydes, specifically among other carbonyl compounds.
Understanding these fragmentation pathways is crucial for interpreting mass spectra, particularly in identifying functional groups and distinguishing between similar compounds.

In mass spectrometry, the fragmentation of aliphatic aldehydes and ketones generally occurs through three key mechanisms: &#945;-cleavage, inductive ...

Mass Spectrometry: Alcohol Fragmentation

Alcohols (R-OH) ionize to lose one non-bonded electron from the oxygen atom, forming molecular ions. Due to their tendency to fragment rapidly, the intensity of the molecular ion peak in the mass spectrum is weak or sometimes absent. The fragmentation patterns for alcohols occur in two ways, i.e. &#9082;-cleavage and dehydration. During &#9082;-cleavage, the bond at the &#9082;-position adjacent to the hydroxyl group cleaves to give a resonance-stabilized cation and a radical. However, intramolecular dehydration involves losing a water molecule from an alcohol, forming an alkene cation, which shows a peak at M&#8722;18. Consider the fragmentation of butanol as shown below. &#9082;-cleavage produces a base peak at a mass-to-charge ratio of 31. In the case of dehydration, the fragmentation forms an alkene radical cation at a mass-to-charge ratio of 56.
<img alt="Figure1" src="/files/ftp_upload/13046/13046-PT_Figure_1.svg" style="text-align: center; height: 175px;" />

Alcohols (R-OH) ionize to lose one non-bonded electron from the oxygen atom, forming molecular ions. Due to their tendency to fragment rapidly, the ...

Mass Spectrometry: Amine Fragmentation

Amines can be identified using mass spectroscopy based on their characteristic fragmentation patterns. The molecular ions of amines undergo fragmentation via &#9082;-cleavage. The &#9082;-cleavage of the carbon-carbon bonds in amines generates an alkyl radical and resonance-stabilized nitrogen-containing cation.
In amines, the number of nitrogen atoms affects the mass of the molecular ion, which is described by the nitrogen rule of mass spectrometry. This rule states that a compound containing a single or an odd number of nitrogen atoms produces a molecular ion with an odd molecular weight, while a compound with no or an even number of nitrogen atoms generates a molecular ion with an even molecular weight.
For example, the mass spectrum of 3-methyl-1-butanamine, which contains one nitrogen atom, displays a molecular ion having an odd mass-to-charge ratio of 87. Fragmentation of this molecular ion via &#9082;-cleavage produces a base peak, which features a mass signal at a mass-to-charge ratio of 30, corresponding with the loss of the 2-methyl propyl radical.
Similarly, the fragmentation of triethylamine via &#9082;-cleavage generates a cation at a mass-to-charge ratio of 86. The molecular ion peak shows an odd mass-to-charge ratio of 101, as shown below.
<img alt="Figure1" src="/files/ftp_upload/13048/13048_PT_Figure_1.svg" style="text-align: center; height: 105px;" />

Amines can be identified using mass spectroscopy based on their characteristic fragmentation patterns. The molecular ions of amines undergo fragmentation ...

Mass Spectrometry: Cycloalkene Fragmentation

The molecular ions of cycloalkenes undergo fragmentation via a retro-Diels&#8211;Alder reaction.

The reaction proceeds via the cleavage of two carbon-carbon bonds in the cycloalkene to yield ethene. The remaining part of the cycloalkene structure is a dienyl radical cation with a molecular weight of 28 u lower than the molecular ion. This fragmentation pathway is similar to the fragmentation of cycloalkanes releasing ethene, differing only in the resultant radical cation. An alkyl species forms from the cycloalkane, whereas a dienyl species originates from the cycloalkene.

Retro-Diels&#8211;Alder reactions of cycloalkenes are also similar to the McLafferty-rearrangement-type fragmentation observed in acyclic alkenes with hydrogen on the &#947; carbon. In both cases, cleavage occurs at two positions, yielding an ethene molecule and an alkenyl species. In acyclic alkenes, the cleavage occurs at one carbon-carbon bond and a carbon-hydrogen bond, along with rearranging hydrogen from one carbon to another. In cyclic alkenes, cleavage occurs at two carbon&#8211;carbon bonds without any atomic rearrangement. Figure 1 depicts the fragmentation of cyclohexene via a retro-Diels&#8211;Alder reaction.
<img alt="Figure1" src="/files/ftp_upload/13044/13044-PT_Figure_1.svg" style="text-align: center; height: 90px;" />
Figure 1: Fragmentation of cyclohexene via a retro-Diels&#8211;Alder reaction.
In addition to the retro-Diels&#8211;Alder reaction, branched cycloalkenes exhibit fragmentation via cleavage of the side chain to form a cycloalkene cation. For example, the fragmentation of 1-methyl-1-cyclohexene via a retro-Diels&#8211;Alder reaction and side-chain cleavage are shown in Figure 2.
<img alt="Figure2" src="/files/ftp_upload/13044/13044-PT_Figure_2.svg" style="text-align: center; height: 225px;" />
Figure 2: Fragmentation of 1-methyl-1-cyclohexene via (top) a retro-Diels&#8211;Alder reaction; (bottom) side-chain cleavage.
The corresponding signals of the isoprenyl radical cation and the cyclohexenyl cation are evident in the mass spectrum of 1-methyl-1-cyclohexene shown in Figure 3.
<img alt="Figure3" src="/files/ftp_upload/13044/13044-PT_Figure_3.svg" style="text-align: center; height: 250px;" />
Figure 3: Mass spectrum of 1-methyl-1-cyclohexene.

The molecular ions of cycloalkenes undergo fragmentation via a retro-Diels&#8211;Alder reaction.

The reaction proceeds via the cleavage of two ...

Mass Spectrometry: Alkyne Fragmentation

The fragmentation of alkynes preferentially occurs at the carbon&#8211;carbon bond between the &#945; and &#946; carbon of the alkyne bond to generate a 3-propynyl cation (or propargyl cation). In terminal alkynes, there is the only type of fragmentation that yields the 3-propynyl cation. The unsubstituted 3-propynyl cation exhibits a peak at a mass-to-charge ratio of 39. In internal alkynes, the 3-propynyl cation is substituted. For example, 2-pentyne fragments into methyl-substituted 3-propynyl cation, which subsequently features as a mass signal at the mass-to-charge ratio of 56. The 3-propynyl cation is resonance-stabilized, and the corresponding mass signal is intense in the mass spectrum of alkynes. Figure 1 shows the fragmentation of 1-pentyne into an ethyl radical and a resonance stabilized 3-propynyl cation.
<img alt="Figure1" src="/files/ftp_upload/13045/13045-PT_Figure_1.svg" style="text-align: center; height: 115px;" />
Figure 1: Fragmentation of 1-pentyne molecular ion to yield the 3-propynyl cation.
Another fragmentation pathway observed in terminal alkynes is the loss of hydrogen from the terminal sp carbon. This results in a mass signal with a mass-to-charge ratio of one unit less than the molecular ion. This M&#8211;1 peak is very intense and becomes the base peak in the mass spectra of many alkynes, so it can be used to identify alkynes.
<img alt="Figure2" src="/files/ftp_upload/13045/13045-PT_Figure_2.svg" style="text-align: center; height: 275px;" />
Figure 2: The mass spectrum of 1-pentyne.

The fragmentation of alkynes preferentially occurs at the carbon&#8211;carbon bond between the &#945; and &#946; carbon of the alkyne bond to generate a ...

Mass Spectrometry: Aromatic Compound Fragmentation

Upon ionization, aromatic compounds generate a molecular ion that is observed as a prominent peak in their mass spectra. For example, the molecular ion peak for benzene appears at a mass-to-charge ratio of 78, while toluene is observed at a mass-to-charge ratio of 92. The molecular ion benzene is highly stable and does not readily undergo further fragmentation due to the significant amount of energy required to disrupt the aromatic stability of the benzene ring. In contrast, the molecular ion of alkyl&#8208;substituted benzenes, such as toluene, can undergo fragmentation by losing a hydrogen atom, forming a benzylic carbocation. This carbocation can rearrange to form the resonance-stabilized tropylium cation, which appears in the mass spectra as a strong peak. In the case of toluene, this strong peak is observed at a mass-to-charge ratio of 91.

Upon ionization, aromatic compounds generate a molecular ion that is observed as a prominent peak in their mass spectra. For example, the molecular ion ...

Mass Spectrometry: Long-Chain Alkane Fragmentation

The molecular ions of linear alkanes prefer to fragment at the carbon-carbon bond away from the end of the chain since the cleavage of an inner bond creates a stable carbocation and a stable radical. Consequently, the mass signals of linear alkanes feature intense peaks in the middle of the mass-to-charge ratio plot with weaker peaks on either end. The fragmentation of each carbon-carbon bond with the release of a methyl group in each splitting leads to prominent peaks in the mass spectra separated by 14 u. Smaller mass signals near each prominent peak result arise from secondary fragmentation at the carbon-hydrogen bond.
For example, consider the fragmentation pattern of n-hexane shown in Figure 1 and the corresponding mass spectra in Figure 2.
<img alt="Figure1" src="/files/ftp_upload/12299/12299-PT_Figure_1.svg" style="text-align: center; height: 500px;" />
Figure 1: Fragmentation of n-hexane molecular ion.
<img alt="Figure2" src="/files/ftp_upload/12299/12299-PT_Figure_2.svg" style="text-align: center; height: 275px;" />
Figure 2: Mass spectrum of n-hexane.
The signals at a mass-to-charge ratio of 71, 57, 43, 29, and 15 indicate that the cleavage can occur at all carbon-carbon bonds in the molecule. However, the relative abundance of these peaks varies. The difference between molecular ion signal and signal at 71 indicates the separation of methyl groups (M.W. = 15 u) group from molecular ions. Further release of a CH2 group from that fragment (M.W. = 14 u) results in a signal at 57. The signals at 43, 29, and 15 are due to the subsequent releases of CH2 groups. The abundance of signals at 15 and 71 is minimal due to the least probability for the formation of unstable methyl carbocation or a methyl radical, respectively. The base peak at 43 indicates the most preferred fragmentation, which yields a pair of stable carbocation and radical.

The molecular ions of linear alkanes prefer to fragment at the carbon-carbon bond away from the end of the chain since the cleavage of an inner bond ...

Newton's Laws of Motion

Source: Andrew Duffy, PhD, Department of Physics, Boston University, Boston, MA
This experiment examines at various situations involving two interacting objects.
First, the experiment examines the forces that two objects apply to one another while they collide. The objects are wheeled carts that have variable masses. The purpose of this experiment is to discover when the force the first cart exerts on the other is the same magnitude as the force the second cart exerts back on the first, as well as when these two forces have different magnitudes.
Second, it examines the forces that two objects exert on one another when one cart is pushing or pulling the second one. Again, the focus is on exploring the situations in which the two forces have the same magnitude and in which they have different magnitudes.

Newton&#039;s Laws of Motion and Collision Experiments

חוקי התנועה של ניוטון

Source: Andrew Duffy, PhD, Department of Physics, Boston University, Boston, MA
This experiment examines at various situations involving two interacting ...

Force and Acceleration

Source: Nicholas Timmons,&#160;Asantha Cooray, PhD, Department of Physics &#38; Astronomy, School of Physical Sciences, University of California, Irvine, CA

The goal of this experiment is to understand the components of force and their relation to motion through the use of Newton&#39;s second law by measuring the acceleration of a glider being acted upon by a force.
Nearly every aspect of motion in everyday life can be described using Isaac Newton&#39;s three laws of motion. They describe how objects in motion will tend to stay in motion (the first law), objects will accelerate when acted upon by a net force (the second law), and every force exerted by an object will have an equal and opposite force exerted back onto that object (the third law). Almost all of high school and undergraduate mechanics is based on these simple concepts.

Force, Acceleration and Acceleration Measurement of a Glider

כוח ותאוצה

Source: Nicholas Timmons,&#160;Asantha Cooray, PhD, Department of Physics &#38; Astronomy, School of Physical Sciences, University of California, Irvine, ...

Vectors in Multiple Directions

Source: Nicholas Timmons, Asantha Cooray, PhD, Department of Physics &#38; Astronomy, School of Physical Sciences, University of California, Irvine, CA

This experiment demonstrates how vectors add and subtract in multiple directions. The goal will be to analytically calculate the addition or subtraction of multiple vectors and then to experimentally confirm the calculations.
A vector is an object with both magnitude and direction. The magnitude of a vector is simply denoted as the length, while the direction is typically defined by the angle it makes with the x-axis. Because forces are vectors, they can be used as a physical representation of vectors. By setting up a system of forces and finding which additional force will create an equilibrium between the forces, a system of vectors can be experimentally verified.

Vectors Addition and Subtraction

וקטורים בכיוונים מרובים 

Source: Nicholas Timmons, Asantha Cooray, PhD, Department of Physics &#38; Astronomy, School of Physical Sciences, University of California, Irvine, CA

...

Kinematics and Projectile Motion

Source: Ketron Mitchell-Wynne, PhD,&#160;Asantha Cooray, PhD, Department of Physics &#38; Astronomy, School of Physical Sciences, University of California, Irvine, CA
This experiment demonstrates the kinematics of motion in 1 and 2 dimensions. This lab will begin by studying motion in 1 dimension, under constant acceleration, by launching a projectile directly upward and measuring the maximum height reached. This lab will verify that the maximum height reached is consistent with the kinematic equations derived below.
Motion in 2 dimensions will be demonstrated by launching the ball at an angle &#952;. Using the kinematic equations below, one can predict the distance to where the projectile will land based upon the initial speed, total time, and angle of trajectory. This will demonstrate kinematic motion with and with out acceleration in the y- and x-directions, respectively.

Kinematics, Projectile Motion and Motion in Two Dimension

קינמטיקה ותנועת קליעים

Source: Ketron Mitchell-Wynne, PhD,&#160;Asantha Cooray, PhD, Department of Physics &#38; Astronomy, School of Physical Sciences, University of ...

Newton's Law of Universal Gravitation

Source: Ketron Mitchell-Wynne, PhD,&#160;Asantha Cooray, PhD, Department of Physics &#38; Astronomy, School of Physical Sciences, University of California, Irvine, CA
Legend states that Isaac Newton saw an apple fall from a tree. He noticed the acceleration of the apple and deduced that there must have been a force acting upon the apple. He then surmised that if gravity can act at the top of the tree, it can also act at even larger distances. He observed the motion of the moon and the orbits of the planets and eventually formulated the universal law of gravitation. The law states that every particle in the universe attracts every other particle with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. This force acts along the line joining the two particles.
Gravitational acceleration g, which is the acceleration an object on the surface of the Earth experiences due to the Earth&#39;s gravitational force, will be measured in this lab. Accurately knowing this value is extremely important, as it describes the magnitude of the gravitational force on an object at the surface of the Earth.

Law of Gravitation and Measuring Gravitational Acceleration

חוק הכבידה האוניברסלית של ניוטון 

Conservation of Momentum

Source: Nicholas Timmons,&#160;Asantha Cooray, PhD, Department of Physics &#38; Astronomy, School of Physical Sciences, University of California, Irvine, CA

The goal of this experiment is to test the concept of the conservation of momentum. By setting up a surface with very little friction, collisions between moving objects can be studied, including their initial and final momenta.
The conservation of momentum is one of the most important laws in physics. When something is conserved in physics, the initial value is equal to the final value. For momentum, this means that the total initial momentum of a system will be equal to the total final momentum. Newton&#39;s second law states that the force on an object will be equal to the change in the object&#39;s momentum with time. This fact, combined with the idea that momentum is conserved, underpins the workings of classical mechanics and is a powerful problem-solving tool.

Momentum Conservation and Momentum Before/After Collisions

שימור המומנטום

Friction

Source: Nicholas Timmons,&#160;Asantha Cooray, PhD, Department of Physics &#38; Astronomy, School of Physical Sciences, University of California, Irvine, CA

The goal of this experiment is to examine the physical nature of the two types of friction (i.e., static and kinetic). The procedure will include measuring the coefficients of friction for objects sliding horizontally as well as down an inclined plane.
Friction is not completely understood, but it is experimentally determined to be proportional to the normal force exerted on an object. If a microscope zooms in on two surfaces that are in contact, it would reveal that their surfaces are very rough on a small scale. This prevents the surfaces from easily sliding past one another. Combining the effect of rough surfaces with the electric forces between the atoms in the materials may account for the frictional force.
There are two types of friction. Static friction is present when an object is not moving and some force is required to get that object in motion. Kinetic friction is present when an object is already moving but slows down due to the friction between the sliding surfaces.

Friction: Static and Kinetic

חיכוך 

Hooke's Law and Simple Harmonic Motion

Source: Ketron Mitchell-Wynne, PhD,&#160;Asantha Cooray, PhD, Department of Physics &#38; Astronomy, School of Physical Sciences, University of California, Irvine, CA
Potential energy is an important concept in physics. Potential energy is the energy associated with forces that depend upon the position of an object relative to its surroundings. Gravitational potential energy, which is discussed in another video, is the energy associated that is directly proportional to the height of an object above the ground. Similarly, it is possible to define spring potential energy, which is directly proportional to the displacement of a spring from its relaxed state. A stretched or compressed spring has potential energy, as it has the ability to do work upon an object. The &#8220;ability to do work&#8221; is often quoted as the fundamental definition of energy.
This video will demonstrate the potential energy stored in springs. It will also verify the restoring force equation of springs, or Hooke&#8217;s Law. The spring constant is different for springs of different elasticities. Hooke&#8217;s law will be verified and the spring constant measured by attaching varying weights to a suspended spring and measuring the resulting displacements.

Hooke&#039;s Law, Simple Harmonic Motion and Measuring Spring Displacement and Oscillation Period

חוק הוק ותנועה הרמונית פשוטה

Equilibrium and Free-body Diagrams

Source: Ketron Mitchell-Wynne, PhD, Asantha Cooray, PhD, Department of Physics &#38; Astronomy, School of Physical Sciences, University of California, Irvine, CA
Equilibrium is a special case in mechanics that is very important in everyday life. It occurs when the net force and the net torque on an object or system are both zero. This means that both the linear and angular accelerations are zero. Thus, the object is at rest, or its center of mass is moving at a constant velocity. However, this does not mean that no forces are acting on the objects within the system. In fact, there are very few scenarios on Earth in which no forces are acting upon any given object. If a person walks across a bridge, they exert a downward force on the bridge proportional to their mass, and the bridge exerts an equal and opposite upward force on the person. In some cases, the bridge may flex in response to the downward force of the person, and in extreme cases, when the forces are great enough, the bridge may become seriously deformed or may even fracture. The study of this flexing of objects in equilibrium is called elasticity and becomes extremely important when engineers are designing buildings and structures that we use every day.

Equilibrium and Free-body Diagrams and Torques in Equilibrium

שיווי משקל ודיאגרמות גוף חופשי

Source: Ketron Mitchell-Wynne, PhD, Asantha Cooray, PhD, Department of Physics &#38; Astronomy, School of Physical Sciences, University of California, ...

Torque

Source: Nicholas Timmons,&#160;Asantha Cooray, PhD, Department of Physics &#38; Astronomy, School of Physical Sciences, University of California, Irvine, CA

The goal of this experiment is to understand the components of torque and to balance multiple torques in a system to achieve equilibrium. Much like how a force causes linear acceleration, torque is a force that causes a rotational acceleration. It is defined as the product of a force and the distance of the force from the axis of rotation. If the sum of the torques on a system is equal to zero, the system will not have any angular acceleration.

Torque and Establishment of Rotational Equilibrium

מומנט

Rotational Inertia

Source: Nicholas Timmons,&#160;Asantha Cooray, PhD, Department of Physics &#38; Astronomy, School of Physical Sciences, University of California, Irvine, CA

Inertia is the resistance of an object to being accelerated. In linear kinematics, this concept is directly related to the mass of an object. The more massive an object, the more force is required to accelerate that object. This is seen directly in Newton&#39;s second law, which states that force is equal to mass times acceleration.
For rotation, there is a similar concept called rotational inertia. In this case, rotational inertia is the resistance of an object to being rotationally accelerated. Rotational inertia is dependent not only upon mass, but also upon the distance of mass from the center of rotation.
The goal of this experiment is to measure the rotational inertia of two rotating masses and to determine the dependence upon mass and distance from the axis of rotation.

Rotational Inertia and Moment of Intertia

אינרציה סיבובית

Angular Momentum

Source: Nicholas Timmons,&#160;Asantha Cooray, PhD, Department of Physics &#38; Astronomy, School of Physical Sciences, University of California, Irvine, CA

Angular momentum is defined as the product of the moment of inertia and the angular velocity of the object. Like its linear analog, angular momentum is conserved, meaning that the total angular momentum of a system will not change if there are no external torques on the system. A torque is the rotational equivalent of a force. Because it is a conserved, angular momentum is an important quantity in physics.
The goal of this experiment is to measure the angular momentum of a rotating rod and to use the conservation of angular momentum to explain two rotational demonstrations.

Principle, Conservation and Measurement of Angular Momentum

מומנטום זוויתי

Energy and Work

Source: Ketron Mitchell-Wynne, PhD,&#160;Asantha Cooray, PhD, Department of Physics &#38; Astronomy, School of Physical Sciences, University of California, Irvine, CA
This experiment demonstrates the work-energy principle. Energy is one of the most important concepts in science and is not simple to define. This experiment will deal with two different kinds of energy: gravitational potential energy and translational kinetic energy. Gravitational potential energy is defined as the energy an object possesses because of its placement in a gravitational field. Objects that are high above the ground are said to have large gravitational potential energy. An object that is in motion from one location to another has translational kinetic energy. The most crucial aspect of energy is that the sum of all types of energy is conserved. In other words, the total energy of a system before and after any event may be transferred to different kinds of energy, wholly or partly, but the total energy will be the same before and after the event. This lab will demonstrate this conservation.
Energy can be defined as &#34;the ability to do work,&#34; which relates mechanical energy with work. Flying projectiles that hit stationary objects do work on those stationary objects, such as a cannonball hitting a brick wall and breaking it apart or a hammer driving a nail in to a piece of wood. In all cases, there is a force exerted on a body, which subsequently undergoes displacement. An object in motion has the ability to do work, and thus it has energy. In this case, it is kinetic energy. In this experiment, gravity will be doing work on gliders.
The transfer of the potential energy of gravity to translational kinetic energy will be demonstrated in this experiment by sliding a glider down air tracks at various angles (i.e., heights), starting from rest. The potential energy of an object is directly proportional to its height. The net work done on an object is equal to the change in its kinetic energy; here, the glider will start from rest and then gain kinetic energy. This change in kinetic energy will be equal to the work done by gravity and will vary depending upon the starting height of the glider. The work-energy principle will be verified by measuring the starting height and the final velocity of the glider.

Energy, Work and Measurement of Mechanical Energy

אנרגיה ועבודה

Enthalpy

Source: Ketron Mitchell-Wynne, PhD,&#160;Asantha Cooray, PhD, Department of Physics &#38; Astronomy, School of Physical Sciences, University of California, Irvine, CA
When a pot of water is placed on a hot stove, heat is said to &#34;flow&#34; from the stove to the water. When two or more objects are placed into thermal contact with each other, heat spontaneously flows from the hotter objects to the colder ones, or in the direction that tends to equalize the temperature between the objects. For example, when ice cubes are put in a cup of room-temperature water, heat from the water flows to the ice cubes and they begin to melt. Often, the term &#34;heat&#34; is used inconsistently, usually to simply refer to the temperature of something. In the context of thermodynamics, heat, like work, is defined as a transfer of energy. Heat is energy transferred from one object to another because of a difference in temperature.
Furthermore, the total energy of any isolated thermodynamic system is constant-that is, energy can be transferred to and from different objects within the system and can be transformed to different types of energy, but energy cannot be created or destroyed. This is the first law of thermodynamics. It is very similar to the conservation of energy law discussed in another video, but in the context of heat and thermodynamic processes. In the case of ice cubes in water, if the first law of thermodynamics was invalid, then one might expect that adding ice cubes to an isolated room-temperature cup of water would cause the water to boil, which would imply the creation of energy.

Enthalpy; Heat Transfer and the First Law of Thermodynamics

אנטלפיה

Entropy

Source: Ketron Mitchell-Wynne, PhD,&#160;Asantha Cooray, PhD, Department of Physics &#38; Astronomy, School of Physical Sciences, University of California, Irvine, CA
The second law of thermodynamics is a fundamental law of nature. It states that the entropy of a system always increases over time or remains constant in ideal cases when a system is in a steady state or undergoing a &#34;reversible process.&#34; If the system is undergoing an irreversible process, the entropy of the system will always increase. This means that the change in entropy, &#916;S, is always greater than or equal to zero. The entropy of a system is a measure of the number of microscopic configurations the system can attain. For example, gas in a container with known volume, pressure, and temperature can have an enormous number of possible configurations of the individual gas molecules. If the container is opened, the gas molecules escape and the number of configurations increases dramatically, essentially approaching infinity. When the container is opened, the entropy is said to increase. Therefore, entropy can be considered a measure of the &#34;disorder&#34; of a system.

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