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Compound - dimethyl sulfoxide (DMSO)

Paper topic - a review of the theory and modeling of surface charge transport


 * SUMMARY ASSIGNMENT**


 * Paper title:** Possible Dual-Charge-Carrier Mechanism of Surface Conduction on g-Alumina
 * [Full Marks JCB]**


 * Authors:** Shuhui Cai, Monica Caldararu, Viorel Chihaia, Cornel Munteanu, Cristian Hornoiu, and Karl Sohlberg

[1] S. Cai, M. Caldararu, V. Chihaia, C. Munteanu, C. Hornoiu and K. Sohlberg, "Possible Dual-Charge-Carrier Mechanism of Surface Conduction on g-Alumina," J. Phys. Chem. C, vol. 111, pp. 5506, 2007. DOI: [|10.1021/jp068817n]
 * Source (using IEEE citing format):**


 * Introduction:**
 * g-Al2O3 is a very versatile compound with excellent catalytic attributes. It can be used directly as a catalyst or used as a support to fine tune preexisting catalytic methods.
 * Through the unusual presence of hydrogen, the structure of g-alumina was determined to be H3mAl2-mO3. At low temperatures, g-alumina acts like a Bronsted acid. At high temperatures, it acts like a Lewis acid.
 * This paper examines the role of hydrogen and water in charge transport. Additionally, it attempts to explain the temperature dependence of conductivity for g-alumina.


 * An observation:**
 * An experimental plot of surface conductance (G) vs. temperature for g-alumina shows three regions: (1) a brief increase in G upon heating from room temperature, (2) a decrease in G until 450K, and (3) an increase in G at temperatures above 450K. The cooling curve shows hysteresis at lower temperatures.


 * Hypothesis:**
 * In region (2), surface conductance is controlled by adsorbed water molecules and thus decreases with the evaporation of water. In region (3), surface conductance is controlled by proton hopping. Hysteresis is due to the slow reformation of water at the surface.
 * The hypothesis was tested by calculating the energy parameters of the dual-charge-carrier model and comparing them to experimental data.


 * Theory:**
 * The first paragraph identifies several important variables to be used in subsequent derivations.
 * The surface conductance of a dual-charge-carrier model is derived from the definition of conductivity and assumption that both charge-carriers do not interact.
 * Charge-carriers vibrate in potential wells along the surface. The probability that a charge-carrier escapes the potential barrier depends on the depth of the well and the kinetic energy of the molecule. The average drift velocity of the charge carrier can be determined using its vibrational frequency, the probability, and the distance between potential wells.
 * The charge carrier concentration is then derived in terms of the total number of charge-carrier sites and the surface coverage. This term along with the average drift velocity for each charge-carrier can be summed and rewritten in different thermodynamic parameters to yield the dual-charge-carrier model for surface conductance.


 * Linking the dual-charge-carrier model to alumina surface microstructure:**
 * The author proposes two possible structures for the surface of alumina.
 * The possible adsorption configurations for alumina at low temperature are as follows: (1) 2Al atoms coordinate covalently bonded to a water molecule, (2) 2Al atoms coordinate covalently bonded to a hydroxide, and (3) 2O atoms hydrogen bonded to the 2H atoms of a water molecule.
 * The possible adsorption configurations for alumina at high temperature are as follows: (1) H attached to O at Al-O surface at top of trench, (2) H attached to O at Al-O surface at bottom of bench, and (3) H attached to O at the oxygen terminated surface.
 * H atoms are known to hop along the surface of alumina. The path in which the oxygen atom separation is minimized determines the direction of hopping.
 * The next paragraph reiterates the possible water adsorption configurations alumina at low temperatures, stressing that hydrogen bonded water to the oxygen-terminated surface must also be considered.
 * The surface conductance model can be applied to the low and high temperature charge carriers, water/hydroxide and protons respectively. The following interpretations can now be made:
 * Initial increase in temperature increases mobility of water and thus increases conductance
 * Further increase in temperature increases evaporation of water and thus decreases conductance
 * Further increase in temperature increases H mobility and thus increases conductance
 * It is expected that the vibrational frequency of H atoms is greater than that of water because water is heavier.
 * The following must be true to validate the hypothesis: Dfw < DFw < DfH < DFH. The consequence of this condition is that water is desorbed before H becomes mobile.


 * Calculations:**
 * The author constructed two ideal models for the surface of g-alumina. The author then estimated the energy parameters using various first principle calculations and conditions.
 * The vibrational frequencies are then calculated using the PM3 Hamiltonian, a semi-empirical force field.


 * Results:**
 * H mobility:**
 * The computed hopping barrier for a proton in configuration (1) is 0.35eV.


 * H abstraction:**
 * Over the experimental temperature range, protons remain bound to the surface.


 * H2O and OH mobility:**
 * The computed hopping barrier for chemisorbed water and hydrogen-bonded water are 1.09 and 0.2eV respectively.


 * H2O abstraction:**
 * The computed abstraction energy for water is -0.69eV.


 * Discussion:**
 * Chemisorbed water (1) is an invalid configuration because the model predicts that H atoms become mobile before water evaporates.
 * Additionally, chemisorbed hydroxide (2) is invalid because the model predicts that hydroxide will remain bound to the surface over the experimental temperature range.
 * Hydrogen-bonded water (3) is a possible configuration because the model predicts the lowest hopping barrier and abstraction energy. When experimentally determined thermodynamic parameters are applied to the model, a best-fit line is produced that is in good agreement with actual data.
 * The hopping barrier for H is slightly slower than expected for two possible reasons: (1) the optimization is not producing the minimum energy conformation or (2) proton tunneling. Experimental results better fit the model with a hopping barrier of H to be 0.46 ± 0.12eV.
 * A possible hypothesis for the charge transport in the low temperature system describes the hydrogen-bonded, chemisorbed water molecule as a charge vehicle as opposed to a charge-carrier, which may be a proton. Therefore, the decrease in conductance as temperature increases may be related to a loss of the charge vehicle as opposed to a loss of the charge-carrier.
 * An increase in the slope of the high temperature region can be explained by the mobilization of other higher energy H atoms.


 * Conclusion:**
 * A dual-charge-carrier model for the surface conductance of g-alumina was constructed, solved, and compared to experimental data with good agreement. It was determined that hydrogen bonded water was the likely charge-carrier for the low temperature region, whereas H atoms attached to the top of a trench were the likely charge-carrier for the high temperature region.

=**Describe 10 strategies for obtaining melting points**=

**1. Type 'melting point of __(insert compound here)' into google search bar**
This works well for common compounds like Benzene; however, this method can present problems for isomers, pharmaceuticals (whether a compound is a salt or a free base), and for names like chlorobenzene that could accumulate hits for benzene, nitrobenzene, etc.

In the latter case, the CAS number and the compound name can be placed in separate quotations in the google search bar

==**2. Determine the melting point experimentally using a melting point apparatus or a differential scanning calorimeter (DSC), which is also used to determine glass transition and crystallization temperatures**==

For a description of good practice to take a melting point, follow [|this link] to an informative 'after school special' on taking melting points (start at 10:47)

Tips for taking a melting point: 1. Heat rapidly until about 15C before the expected melting point 2. Heat the sample a few degrees per minute (~1-3C) until you reach the onset of melting 3. Record the temperature range of melting from onset to completion

**3. Obtain experimenta data from peer reviewed scientific journals; [|SciFinder] can be used to find melting points**
Here are step by step instructions on how to obtain a melting point using SciFinder: 1. Login and click 'Explore substances' 2. Input a 'substance identifier' (common name, CAS, SMILES) and click 'search' 3. Click on 'substance detail' and slide to the very bottom of the page for experimental melting points

**4. Reaxys can be used to expedite strategy 3**
In Reaxys, melting points can be obtained providing a structure or some identifier of that compound (name, InChI, CAS, or SMILES) and by selecting 'melting point' under substance data->physical data; Reaxys can be found at the following link [|Reaxys]

The image below shows the experimental melting points of Benzene using Reaxys ==**5. Scroll through the list of compounds in the open melting point data explorer (to expedite this process, type the first letter of the compound's name when the list opens); melting point values from different sources should appear automatically below the search bar**== [|open melting point data explorer] ==6. A substructure search, in the open melting point data explorer) can be run using SMARTS language with the option of filtering the results by melting point range; additionally information on SMARTS language can be found at the following link==

7. Type the systematic name, synonym, trade name, registry number, SMILES, or InChI of a compound in the [|ChemSpider] search bar
Melting point data can be found under the properties tab in one of two sections: experimental data or predicted - EPISuite

In experimental data, melting points are usually found with links leading to MSDS sheets In predicted - EPISuite, melting points (up to two predicted and one experimental) are found under the heading 'Boiling Pt, Melting Pt, Vapor Pressure Estimations (MPBPWIN v1.42):'

//-or-//

Draw the structure, load a chemical or image file, or convert one of the six identifiers listed in strategy number 6 to the structure of a compound in the ChemSpider 'structure' search bar

Chemical files include - MOL, SDF, CDX, SKC, etc Image files include - GIF, JPG, PNG, TIFF, etc

8. In the ChemInfo Validation spreadsheet, type the name of the compound and use the 'getMP' function
If you want a very crude approximation, you can use the 'getPredictedMP' function; it would be beneficial to know what compounds were used to develop this model in order to tell whether it's applicable for the compound of interest (here is a link to this model)

To access the spreadsheets from 2009, 2010, and 2011 follow these links: 2009/2010 [|2011]

There is also a web-based interfaced which can be accessed by following this link [|ChemInfo Validation]; simply scroll down the list of common names and the select melting point (if it appears in the list)

9. Obtain MSDS's from physical collections kept by the University; at Drexel, these are kept in yellow bins in the hallways of every floor of Disque
To search MSDS sheets online, follow this link [|MSDS Index]

10. Search through the index of reference books for melting points and scan those pages for the compound; listed below are some common chemistry reference books
- CRC Handbook of Chemistry and Physics (Drexel students have access to an e-book version; to access it, follow this link [|CRC Handbook]) - Merck (Drexel students also have access to this; to access it, follow this link [|Merck Index]) - Chemistry textbooks

=A review of the theory and modeling of surface charge transport=

Robert Wexler Drexel University Chemistry Information Retrieval - CHEM367 Submitted December 3, 2011

Contents
(I) Introduction (II) Theory (III) An empirical approach (IV) A physics approach

**Introduction**
Surface charge transport has vital applications to the health and transportation of human beings. For example, semiconducting compounds such as tin (II) oxide can be used to detect hydrogen, hydrogen sulfide, nitrous oxide, carbon monoxide, and various hydrocarbons to name a few (1). Thus if the exhaust from an automobile or some other gasoline powered machine is allowed to accumulate in a closed setting, the carbon monoxide produced from incomplete combustion can be detected through its surface interactions with a tin (II) oxide gas sensor. Tin (II) oxide and other semiconducting compounds such a titanium dioxide, gallium (III) oxide, cerium (IV) oxide, etc. can be used to detect the ratio of air (oxygen) to fuel at an engine's point of ignition using surface conductivity measurements (1). Surface charge transport also has important applications in organic synthesis. For example, insulating compounds such as gamma-alumina can be used for heterogeneous catalysis and as drying agents due to surface charge mobility and water storage respectively (2, 3). Currently, the full potential of surface charge transport and its applications has not yet been realized because its mechanism of action is still largely unknown (4). In this minireview, the available surface charge transport mechanisms will be discussed and separated into two main categories: empirical and physically based formulae.

**Theory**
In order to understand surface charge transport, it is important to develop a basic understand of quantum mechanics, modes of conductivity, and band theory. Additionally, it would be beneficial to the reader to assume that the terms surface charge transport and surface conductivity are interchangeable.

**A Brief History of Quantum Mechanics**
Prior to the development of quantum mechanics, it was widely known that electromagnetic radiation was a wave phenomena. 19th century chemists and physicists found that a description of black body radiators using classical Newtonian mechanics predicted infinitely intense radiation. This was coined the 'ultraviolet catastrophe' (5). In 1887, Heinrich Hertz discovered that the amount of electrons released from a metal exposed to electromagnetic radiation was not dependent of the intensity of the radiation but rather the wavelength. This phenomena is known as the photoelectric effect. In 1900, Max Planck hypothesized that the oscillating centers in black body radiators cannot absorb and emit any energy value but rather quantized bits called quanta (6). Combining all of these discoveries, Albert Einstein clairvoyantly proposed that all electromagnetic radiation comes in packets of energy quanta, which later were referred to as photons (7).

In 1909, Rutherford performed his famous gold foil experiment affirming the existence of electrons and a positively charged atomic nucleus (8). In 1913, the hydrogen line spectra mystery was finally solved by Neils Bohr who suggested that the wavefunction of hydrogen must have an integer number of wavelengths (9). In 1925, Louis de Broglie discovered that the momentum (p) of a given particle could be determined by Planck's constant and the wavelength of the particle. This discovered suggested wave-particle duality; light can act both like a wave and a particle (7). Combining all of these discoveries, Erwin Schrodinger proposed that the wavefunctions for a particle (eigenfuctions) and their associated energies (eigenenergies) can be related using the following expression

[1]

where E is the total energy of the allowed wavefunctions, psi is the wavefunction, and H is the Hamiltonian which operates on the wavefunction to give the eigenenergies. The Hamiltonian is the sum of the potential (V) and kinetic energy (T) of the particle. The kinetic energy term can be determined using the formula T = p^2 / (2 * m) where the m is the mass of the particle and p is the momentum operator, which is defined by a quantum mechanical postulate

[2]

where h bar is Planck's constant divided by 2 * Pi, i is the square root of negative one, and the upside down triangle (nabla symbol) is the differential of the spatial coordinates. The potential energy function can be and has been described as many things such as an infinite well, a parabolic potential, etc. The combination of equations [1] and [2] gives a more complete form of the time-independent Schrodinger equation.

[3]

Schrodinger's equation can be applied to any atom or molecule and, when solved, gives its energy levels; this greatly builds upon Bohr's model that only gives the energy levels of hydrogen (10).

**What is Conductivity?**
Resistance measures how easily a current moves through a material and has units of ohms. The inverse of resistance, measured in mhos (how whimsical), is conductivity; lower resistance means higher conductivity. Concerning conductivity, there are four main types of materials: metals, semiconductors, insulators, and superconductors (7). Conductors have low resistance to the flow of charged particles. Some examples of conductors are silver, gold, and copper. Copper is commonly used for electrical wiring because of its excellent conductivity and affordability. Semiconductors have medium resistance to the flow of charged particles. Some examples of semiconductors are silicon, germanium, and other group IV elements (7). Silicon is widely-know for its use in integrated circuits, an essential component of computers, cell phones, CDs, DVDs, and many more (11). Semiconductors have two main subgroups: intrinsic and extrinsic. Intrinsic semiconductors are pure, natural semiconductors (silicon, germanium, gallium arsenide) whereas extrinsic semiconductors use impurities called dopants to improve the conductivity of intrinsic semiconductors (7). Insulators have high resistance to the flow of charged particles. Some examples of insulators are wood, glass, plastics, and ceramics. Lastly, superconductors have zero resistance to the flow of charged particles. Some examples of superconductors are yttrium barium copper oxide, bismuth strontium calcium copper oxide, among others. Superconductors could be used to improve the efficiency of energy transmission and levitated transportation (12). At the moment, superconductor applications are few because superconducting materials must be supercooled to obtain zero resistance. Thus, an exciting avenue of research today pertains to developing higher temperature superconductors. The reason for the conductive behavior of metals, semiconductors, and insulators will be discussed in the next section.

**A Taste of Band Theory**
Quantum mechanics can be used to describe the conductive behavior of metals semiconductors, and insulators. Let's go back to the very basics: all matter is made up of protons, neutrons, and electrons thanks to Ernest Rutherford and J.J. Thomson respectively (13). An electron can be considered both a wave and a particle due to de Broglie's wave-particle duality. With a wavefunction, Schrodinger's equation can now be solved for the possible energy levels of the electrons. These energy levels can be described by the quantum numbers n, l, ml, and ms organizing the electron configuration of each atom into atomic orbitals that portray the probabilistically favored location of an electron. When two atoms react to form a diatomic molecule, the atomic orbitals combine to form a molecular orbital. This is called linear combination of atomic orbitals (LCAO) and the number of atomic orbitals is equal to the number of molecular orbitals. If the wavefunctions reinforce each other, a bonding molecular orbital is formed. However if the wavefunctions cancel each other, a node of zero electron density or antibonding orbital is formed (14). Figure 1 shows wavefunction reinforcement and canceling in the hydrogen atom.

Figure 1. The molecular orbital of hydrogen showing the atomic orbitals (far right and left) and the bonding (bottom) and antibonding (top) molecular orbitals

As the number of atoms in the molecule increases to a solid, the energy levels overlap to form bands. The highest occupied and lowest unoccupied energy band are known as the valence and conduction band respectively; the energy gap between these bands are called band gaps. Metals, semiconductors, and insulators have characteristic band gaps allowing one to determine a compound's conductive nature using its band diagram. Figure 2 shows an example of a band diagram for a metal, semiconductor, and insulator.

Figure 2. Depiction of the band diagrams for metals, semiconductors, and insulators

Figure 2 shows that the energy bands of metals overlap. Basically, this could mean either one of two things: the bandgap between the valence and conduction bands is very small allowing electrons to jump to higher energy levels or there are less electrons than available energy levels (14). Figure 2 also depicts that there is a large band gap between the valence and conduction band for insulators. At room temperature, an electron does not have enough energy to overcome the band gap's energy barrier. However, the conductivity of insulators is known to increase as the temperature of the system increases (2). In between metals and insulators, semiconductors have a much smaller band gap between the valence and conduction band allowing some conductivity at room temperature. However, the conductivity of semiconductors can be greatly improved by doping, which is adding small amounts of impurities; the dopant only makes up a very small percentage of the solid in order to maintain the integrity of the original crystal lattice. For example if the conductive properties of elemental silicon want to be improved, it can be doped with a group III or V element such as Boron or Arsenic respectively (7). If the three-valence electron element Boron is added, there is a mobile electron deficiency, a positive hole, in the lattice which increases the conductivity. Doped semiconductors with holes are known as p-type (positive-type) and those with extra electrons are n-type (negative-type). Figure 3 shows n and p-type Silicon semiconductors.

Figure 3. n and p-type Silicon semiconductors on the right and left respectively

Band theory is an excellent model to describe the conductivity of bulk metals, semiconductors, and insulators. However, when the material is made into thin films, the surface interactions dominate and conductivity does not follow the patterns of bulk samples often times performing better (15). As was stated in the introduction, the mechanism of surface charge transport has yet to be sufficiently explained. In the next two sections, I will discuss two different methods of experimentation that hope to elucidate this mechanism.

An empirical approach
Currently, there are many empirical investigations into the surface conductivity of the semiconductor tin oxide because it is commonly used in gas detectors (1, 4, 16-18). Sberveglieri splits gas sensors into two main categories: air to fuel ratio sensors for engines and toxic gas sensors (1). The latter sensor commonly employs doped and un-doped thin film tin oxide. Experimental observation shows the following relationship between conductivity and the partial pressure of detectable gas

[4]

where G is the conductivity, G0 is the initial conductivity, gamma is constant characteristic of the semiconducting material, Pgas is the partial pressure of the detectable gas, and m is an exponential parameter that depends on the gas being detected (1). For hydrogen, carbon monoxide, and methane, the m value is positive and thus the surface conductivity of thin film tin oxide increases as partial pressure the gas increases.

Kissine et al. show that different gases have different effects on the surface conductivity of thin film tin oxide. Data suggests that a basic power law can be used to approximate the surface conductivity of tin oxide

[5]

where the variables are the same as in Sberveglieri's paper (18). Utilizing some surface physics, a more involved equation is produced

[6]

where sigma is the surface conductivity, ni and n are parameters of tin oxide, mu_n is the electron mobility, and mu_p is the hole mobility. The n parameter is dependent upon the partial pressures of the detectable gases present. Results show that increasing oxygen pressure decreases surface conductivity and increasing ethanol pressure increases surface conductivity. When the two gases are combined, the surface conductivity is even lower than that of pure oxygen (18). Kissine attempts to describe the latter trend by defining the ethanol and oxygen donor-like and acceptor-like impurities respectively. It is possible that semiconductor activity between ethanol and oxygen take away from the surface conductivity of thin film tin oxide (18).

Clarke shows that the presence of oxygen has an opposite effect on the surface conductivity of the semiconductor Germanium (19). In the experiment, Germanium was exposed to different component gases of the atmosphere; oxygen showed a sizable increase in the surface conductivity. This unexpected phenomena could be explained by oxygen adding energy levels to the surface through which conduction is allowed (19).

A physics approach
Rather than fit surface conductivity to an empirical function, some scientist seek to describe its mechanism using solid state and surface physics (2, 3, 20-24). One model used to describe surface charge transport in gamma-alumina suggests a dual charge-carrier mechanism (2). At lower temperatures, the surface conductivity of gamma-alumina is controlled by water molecules whereas, at higher temperatures, it is controlled by mobile protons. The general trend is that as gamma-alumina is heated from room temperature to 450K, the surface conductivity decreases because absorbed and adsorbed water molecules evaporate (3). As gamma-alumina is heated from 450 to 673K, the surface conductivity increases because protons become mobile (20). Using solid state and surface physics, the following expression is derived to describe this trend in surface conductivity

[7]

where G is the surface conductivity, B is a constant, v is velocity of the charge-carrier, and n is the charge-carrier concentration. This model is in good agreement with experimental data by suggesting that, at lower temperature, hydrogen bonded water is the charge-carrier whereas, at higher temperature, protons becomes a charge-carrier migrating along a water scaffold (2). Cai also determined the entropic parameters of the dual charge-carrier model in gamma-alumina by treating equation [7] with thermodynamics.

Using a different approach, Geistlinger describes surface charge transport for gallium (III) oxide using quantum mechanical treatments. Ultimately, it is suggested that the Volkenstein theory is an excellent basis to described chemisorption (22, 23).

Conclusions
There are many different methods that seek to describe the trends and mechanism of surface charge transport. Some are empirical in nature and others are derived directly from solid state and surface physics. Nonetheless, development in this field is crucial in order to systematically develop gas detectors, catalysts, computer chips, and, in general, surface conductivity-based applications.