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Although the sulfide content in sample can be determined straight forwardly as described for sulfites, the results are often poor and inaccurate. A better, alternative method with higher accuracy is available, which involves the addition of excess but known volume of standard sodium arsenite solution to the sample, during which arsenic trisulfide is precipitated:
The excess arsenic trioxide is then determined by titrating against standard iodine solution using starch indicator. Note that for the best results, the sulfide solution must be dilute with the sulfide concentration not greater than 0.01 M. | 0 | Chromatography + Titration + pH indicators |
For an adsorption column, the column resin (the stationary phase) is composed of microbeads. Even smaller particles such as proteins, carbohydrates, metal ions, or other chemical compounds are conjugated onto the microbeads. Each binding particle that is attached to the microbead can be assumed to bind in a 1:1 ratio with the solute sample sent through the column that needs to be purified or separated.
Binding between the target molecule to be separated and the binding molecule on the column beads can be modeled using a simple equilibrium reaction K = [CS]/([C][S]) where K is the equilibrium constant, [C] and [S] are the concentrations of the target molecule and the binding molecule on the column resin, respectively. [CS] is the concentration of the complex of the target molecule bound to the column resin.
Using this as a basis, three different isotherms can be used to describe the binding dynamics of a column chromatography: linear, Langmuir, and Freundlich.
The linear isotherm occurs when the solute concentration needed to be purified is very small relative to the binding molecule. Thus, the equilibrium can be defined as:
:[CS] = K[C].
For industrial scale uses, the total binding molecules on the column resin beads must be factored in because unoccupied sites must be taken into account. The Langmuir isotherm and Freundlich isotherm are useful in describing this equilibrium. The Langmuir isotherm is given by:
:[CS] = (KS[C])/(1 + K[C]), where S is the total binding molecules on the beads.
The Freundlich isotherm is given by:
:[CS] = K[C]
The Freundlich isotherm is used when the column can bind to many different samples in the solution that needs to be purified. Because the many different samples have different binding constants to the beads, there are many different Ks. Therefore, the Langmuir isotherm is not a good model for binding in this case. | 0 | Chromatography + Titration + pH indicators |
The theory of high performance liquid chromatography-HPLC is basically the same as general chromatography theory. who received Nobel prize for it. The theory of chromatography has been used as the basis for system-suitability tests, as can be seen in the USP Phamacopaeia, which are a set of quantitative criteria, which test the suitability of the HPLC system to the required analysis at any step of it.
This relation is also represented as a normalized unit-less factor known as the retention factor, or retention parameter, which is the experimental measurement of the capacity ratio, as shown in the Figure of Performance Criteria as well. t is the retention time of the specific component and t is the time it takes for a non-retained substance to elute through the system without any retention, thus it is called the Void Time.
The ratio between the retention factors, k', of every two adjacent peaks in the chromatogram is used in the evaluation of the degree of separation between them, and is called selectivity factor, α, as shown in the Performance Criteria graph.
The plate count N as a criterion for system efficiency was developed for isocratic conditions, i.e., a constant mobile phase composition throughout the run. In gradient conditions, where the mobile phase changes with time during the chromatographic run, it is more appropriate to use the parameter peak capacity P as a measure for the system efficiency. The definition of peak capacity in chromatography is the number of peaks that can be separated within a retention window for a specific pre-defined resolution factor, usually ~1. It could also be envisioned as the runtime measured in number of peaks' average widths. The equation is shown in the Figure of the performance criteria. In this equation tg is the gradient time and w(ave) is the average peaks width at the base.
The parameters are largely derived from two sets of chromatographic theory: plate theory (as part of partition chromatography), and the rate theory of chromatography / Van Deemter equation. Of course, they can be put in practice through analysis of HPLC chromatograms, although rate theory is considered the more accurate theory.
They are analogous to the calculation of retention factor for a paper chromatography separation, but describes how well HPLC separates a mixture into two or more components that are detected as peaks (bands) on a chromatogram. The HPLC parameters are the: efficiency factor(N), the retention factor (kappa prime), and the separation factor (alpha). Together the factors are variables in a resolution equation, which describes how well two components peaks separated or overlapped each other. These parameters are mostly only used for describing HPLC reversed phase and HPLC normal phase separations, since those separations tend to be more subtle than other HPLC modes (e.g.', ion exchange and size exclusion).
Void volume is the amount of space in a column that is occupied by solvent. It is the space within the column that is outside of the column's internal packing material. Void volume is measured on a chromatogram as the first component peak detected, which is usually the solvent that was present in the sample mixture; ideally the sample solvent flows through the column without interacting with the column, but is still detectable as distinct from the HPLC solvent. The void volume is used as a correction factor.
Efficiency factor (N) practically measures how sharp component peaks on the chromatogram are, as ratio of the component peaks area ("retention time") relative to the width of the peaks at their widest point (at the baseline). Peaks that are tall, sharp, and relatively narrow indicate that separation method efficiently removed a component from a mixture; high efficiency. Efficiency is very dependent upon the HPLC column and the HPLC method used. Efficiency factor is synonymous with plate number, and the number of theoretical plates'.
Retention factor (kappa prime) measures how long a component of the mixture stuck to the column, measured by the area under the curve of its peak in a chromatogram (since HPLC chromatograms are a function of time). Each chromatogram peak will have its own retention factor (e.g., kappa for the retention factor of the first peak). This factor may be corrected for by the void volume of the column.
Separation factor (alpha) is a relative comparison on how well two neighboring components of the mixture were separated (i.e., two neighboring bands on a chromatogram). This factor is defined in terms of a ratio of the retention factors of a pair of neighboring chromatogram peaks, and may also be corrected for by the void volume of the column. The greater the separation factor value is over 1.0, the better the separation, until about 2.0 beyond which an HPLC method is probably not needed for separation.
Resolution equations relate the three factors such that high efficiency and separation factors improve the resolution of component peaks in an HPLC separation. | 0 | Chromatography + Titration + pH indicators |
A set of structure utilities has been included for various applications such as: the transformation of unit cells ([http://www.cryst.ehu.es/cryst/celltran.html CELLTRAN]) or complete structures ([http://www.cryst.ehu.es/cryst/transtru.html TRANSTRU]); strain tensor calculation ([http://www.cryst.ehu.es/cryst/strain.html STRAIN]); assignment of Wyckoff Positions ([http://www.cryst.ehu.es/cryst/wpassign.html WPASSIGN]); equivalent descriptions of a given structure ([http://www.cryst.ehu.es/cryst/equivstru.html EQUIVSTRU]); comparison of different structures with support for the affine normalizers of monoclinic space groups. [http://www.cryst.ehu.es/cryst/rel.html STRUCTURE RELATIONS] calculates the possible transformation matrices for a given pair of group-subgroup related structures. | 1 | Crystallography |
The theoretical plate height is given by
where L is the column length and N the number of theoretical plates. The relation between plate number and peak width at the base is given by | 0 | Chromatography + Titration + pH indicators |
Focusing on crystallographic data and applications of the group theory in solid state physics, the server is built on a core of databases and contains different shells. | 1 | Crystallography |
If half of the tetrahedral sites of the parent HCP lattice are filled by ions of opposite charge, the structure formed is the wurtzite crystal structure. If all the octahedral sites of the anion HCP lattice are filled by cations, the structure formed is the nickel arsenide structure. | 1 | Crystallography |
Radial chromatography is a form of chromatography, a preparatory technique for separating chemical mixtures. It can also be referred to as centrifugal thin-layer chromatography. It is a common technique for isolating compounds and can be compared to column chromatography as a similar process. A common device used for this technique is a Chromatotron.
Here the solvent travels from the center of the circular chromatography silica layered on a plate towards the periphery. The entire system is kept covered in order to prevent evaporation of solvent while developing a chromatogram.
The wick at the center of system drips solvent into the system which the provides the mobile phase and moves the sample radially to form the sample spots of different compounds as concentric rings.
Continuous annular chromatography uses a stationary phase which is filled into an annular gap. The eluent is continuously fed across the whole bed interface also the feed is continuously fed at the top of the stationary however only at a certain point and not a cross the whole bed. The stationary phase is then rotated with a certain rotation speed. The rotation speed, eluent and feed flow rates have to be defined precisely such that the collector vessels only collect the correct substance. The retention times are transformed into the respective retention angles. | 0 | Chromatography + Titration + pH indicators |
]In terms of thermodynamics, two types of polymorphic behaviour are recognized. For a monotropic system, plots of the free energies of the various polymorphs against temperature do not cross before all polymorphs melt. As a result, any transition from one polymorph to another below the melting point will be irreversible. For an enantiotropic system, a plot of the free energy against temperature shows a crossing point before the various melting points. It may also be possible to convert interchangeably between the two polymorphs by heating or cooling, or through physical contact with a lower energy polymorph.
A simple model of polymorphism is to model the Gibbs free energy of a ball-shaped crystal as . Here, the first term is the surface energy, and the second term is the volume energy. Both parameters . The function rises to a maximum before dropping, crossing zero at . In order to crystallize, a ball of crystal much overcome the energetic barrier to the part of the energy landscape.
Now, suppose there are two kinds of crystals, with different energies and , and if they have the same shape as in Figure 2, then the two curves intersect at some . Then the system has three phases:
* . Crystals tend to dissolve. Amorphous phase.
* . Crystals tend to grow as form 1.
* . Crystals tend to grow as form 2.
If the crystal is grown slowly, it could be kinetically stuck in form 1. | 1 | Crystallography |
In the Fajans method, named after Kazimierz Fajans, typically dichlorofluorescein is used as an indicator; the end-point is marked by the green suspension turning pink. Prior to the end-point of the titration, chloride ions remain in excess. They adsorb on the AgCl surface, imparting a negative charge to the particles. Past the equivalence point, excess silver(I) ions adsorb on the AgCl surface, imparting a positive charge. Anionic dyes such as dichlorofluorescein are attracted to the particles, and undergo a colour change upon adsorption, representing the end-point. Eosin (tetrabromofluorescein) is suitable for titrating against bromide, iodide, and thiocyanate anions, giving a sharper end-point than dichlorofluorescein. It is not suitable for titrating against chloride anions because it binds to AgCl more strongly than chloride does. | 0 | Chromatography + Titration + pH indicators |
The liquid chromatography marketplace is incredibly diverse. Five to ten firms are consistently market leaders, yet nearly half of the market is made up of small, fragmented companies. This section of the report will focus on the roles that a few companies have had in bringing monolith column technologies to the commercial market.
In 1998, start-up biotechnology company BIA Separations of Ljubljana, Slovenia, came into being. The technology was originally developed by Tatiana Tennikova and Frantisek Svec during a collaboration between their respective institutes. The patent for these columns was acquired by BIA Separations and Ales Podgornik and Milos Barut developed the first commercially available monolith column in the form of a short disc encapsulated in a plastic housing. Trademarked CIM, BIA Separations has since introduced full lines of reversed-phase, normal-phase, ion-exchange, and affinity polymeric monoliths. Ales Podgornik and Janez Jancar then went on to develop large scale tube monolithic columns for industrial use. The largest column currently available is 8L. In May 2008, LC instrumentation powerhouse Agilent technologies agreed to market BIA Separations’ analytical columns based on monolith technology. Agilent's commercialized the columns with strong and weak ion exchange phases and Protein A in September 2008 when they unveiled their new Bio-Monolith product line at the BioProcess International conference.
While BIA Separations was the first to commercially market polymeric monoliths, Merck KGaA was the first company to market silica monoliths. In 1996, Tanaka and coworkers at the Kyoto Institute of Technology published extensive work on silica monolith technologies. Merck was later issued a license from Kyoto Institute of Technology to develop and produce the silica monoliths. Promptly thereafter, in 2001, Merck introduced its Chromolith line of monolithic HPLC columns at analytical instrumentation trade show PittCon. Initially, says Karin Cabrera, senior scientist at Merck, the high flow rate was the selling point for the Chromolith line. Based on customer feedback, though, Merck soon learned that the columns were more stable and longer-lived than particle-packed columns. The columns were the recipients of various new product awards. Difficulties in production of the silica monoliths and tight patent protection have precluded attempts by other companies at developing a similar product. It has been noted that there are more patents concerning how to encapsulate the silica rod than there are on the manufacture of the silica itself.
Historically, Merck has been known for its superior chemical products, and, in liquid chromatography, for the purity and reliability of its particulate silica. Merck is not known for its LC columns. Five years after the introduction of its Chromolith line, Merck made a very strategic marketing decision. They granted a worldwide sublicense of the technology to a small (less than $100M in sales), innovative company well known for its cutting-edge column technology: Phenomenex. This was a superior strategic move for two reasons. As mentioned above, Merck is not well known for its column manufacturing. Furthermore, having more than one silica monolith manufacturer serves to better validate the technology. Having sublicensed the technology from Merck, Phenomenex introduced its Onyx product line in January 2005.
On the other side of monolith technologies are the polymerics. Unlike the inorganic silica columns, the polymer monoliths are made of an organic polymer base. Dionex, traditionally known for its ion chromatography capabilities, has led this side of the field. In the 1990s, Dionex first acquired a license for the polymeric monolith technology developed by leading monolithic chromatography researcher Frantisec Svec while he was at Cornell University. In 2000, they acquired LC Packings, whose competencies were in LC column packings. LC Packings/Dionex revealed their first monolithic capillary column at the Montreux LC-MS Conference. Earlier that year, another company, Isco, introduced a polystyrene divinylbenzene (PS-DVB) monolith column under the brand SWIFT. In January 2005, Dionex was sold the rights to Teledyne Isco's SWIFT media products, intellectual property, technology, and related assets. Though the core competencies of Dionex have traditionally been in ion chromatography, through strategic acquisitions and technology transfers, it has quickly established itself as the primary producer of polymeric monoliths. | 0 | Chromatography + Titration + pH indicators |
Blue MX-R or Reactive Blue 4 has a formula of CHClNOS and a molecular weight of 637.4 g/mol. It contains dichlorotriazine ring to the chromophore unlike Cibacron Blue F3GA. For a large scale protein purification, Blue MX-R can be used to purify protein such as lactate dehydrogenase (LDH). In fast-protein liquid chromatography (FPLC) using Blue MX-R immobilized on poly(glycidyl methacrylate-co-ethylene dimethacrylate) beads, it was seen to separate lysozyme and bovine serum albumin (BSA), purified lysozyme from chicken albumin. | 0 | Chromatography + Titration + pH indicators |
Other plasma processing methods exist, but generally do not provide the resolution or purity of chromatographic methods.
Two-phase liquid extraction may be performed using polyethylene glycol (PEG)-phosphate Aqueous two-phase systems, with a PEG-rich top layer and a phosphate-rich bottom layer. Although this method is somewhat useful for protein recovery, it does not work as well for the recovery of other blood components.
Membrane fractionation has the advantage of minimal protein loss yet high removal of pathological plasma components. This method incorporates processes such as thermofiltration and applying pulsate flow. The latest two-stage membrane system utilizes a high flow recirculation circuit that is effective for removal of LDL cholesterol. It may prove useful for patients that have clogged arteries and other cardiovascular problems involving cholesterol.
Batch adsorption, e.g. onto ion exchange media, is only useful when dealing with smaller samples of plasma, typically 200 mL or less. Batch adsorption recovers the product in a larger volume of elution buffer than does column chromatography or frontal chromatography, and the resulting more dilute product requires concentration, typically on a membrane system, which can lead to loss of product by irreversible adsorption to the membrane. | 0 | Chromatography + Titration + pH indicators |
Dual-flow, also known as dual, countercurrent chromatography occurs when both phases are flowing in opposite directions inside the column. Instruments are available for dual-flow operation for both Hydrodynamic and hydrostatic CCC. Dual-flow countercurrent chromatography was first described by Yoichiro Ito in 1985 for foam CCC where gas-liquid separations were performed. Liquid–liquid separations soon followed. The countercurrent chromatography instrument must be modified so that both ends of the column have both inlet and outlet capabilities. This mode may accommodate continuous or sequential separations with the sample being introduced in the middle of the column or between two bobbins in a hydrodynamic instrument. A technique called intermittent countercurrent
extraction (ICcE) is a quasi-continuous method where the flow of the phases is alternated "intermittently" between normal and reversed-phase elution so that the stationary phase also alternates. | 0 | Chromatography + Titration + pH indicators |
The main limitation in the use of MLC is the reduction in efficiency (peak broadening) that is observed when purely aqueous micellar mobile phases are used. Several explanations for the poor efficiency have been theorized. Poor wetting of the stationary phase by the micellar aqueous mobile phase, slow mass transfer between the micelles and the stationary phase, and poor mass transfer within the stationary phase have all been postulated as possible causes. To enhance efficiency, the most common approaches have been the addition of small amounts of isopropyl alcohol and increase in temperature. A review by Berthod studied the combined theories presented above and applied the Knox equation to independently determine the cause of the reduced efficiency. The Knox equation is commonly used in HPLC to describe the different contributions to overall band broadening of a solute. The Knox equation is expressed as:
:h = An^(1/3)+ B/n + Cn
Where:
*h = the reduced plate height count (plate height/stationary phase particle diameter)
*n = the reduced mobile phase linear velocity (velocity times stationary phase particle diameter/solute diffusion coefficient in the mobile phase)
*A, B, and C are constants related to solute flow anisotropy (eddy diffusion), molecular longitudinal diffusion, and mass transfer properties respectively.
Berthod's use of the Knox equation to experimentally determine which of the proposed theories was most correct led him to the following conclusions. The flow anisotropy in micellar phase seems to be much greater than in traditional hydro-organic mobile phases of similar viscosity. This is likely due to the partial clogging of the stationary phase pores by adsorbed surfactant molecules. Raising the column temperature served to both decrease viscosity of the mobile phase and the amount of adsorbed surfactant. Both results reduce the A term and the amount of eddy diffusion, and thereby increase efficiency.
The increase in the B term, as related to longitudinal diffusion, is associated with the decrease in the solute diffusion coefficient in the mobile phase, DM, due to the presence of the micelles, and an increase in the capacity factor, k¢. Again, this is related to surfactant adsorption on the stationary phase causing a dramatic decrease in the solute diffusion coefficient in the stationary phase, DS. Again an increase in temperature, now coupled with an addition of alcohol to the mobile phase, drastically decreases the amount of the absorbed surfactant. In turn, both actions reduce the C term caused by a slow mass transfer from the stationary phase to the mobile phase. Further optimization of efficiency can be gained by reducing the flow rate to one closely matched to that derived from the Knox equation. Overall, the three proposed theories seemed to have contributing effects of the poor efficiency observed, and can be partially countered by the addition of organic modifiers, particularly alcohol, and increasing the column temperature. | 0 | Chromatography + Titration + pH indicators |
Microdialysis takes advantage of a semi-permeable membrane, across which small molecules and ions can pass, while proteins and large polymers cannot cross. By establishing a gradient of solute concentration across the membrane and allowing the system to progress toward equilibrium, the system can slowly move toward supersaturation, at which point protein crystals may form.
Microdialysis can produce crystals by salting out, employing high concentrations of salt or other small membrane-permeable compounds that decrease the solubility of the protein. Very occasionally, some proteins can be crystallized by dialysis salting in, by dialyzing against pure water, removing solutes, driving self-association and crystallization. | 1 | Crystallography |
The set of translations and rotations together form the rigid motions or rigid displacements. This set forms a group under composition, the group of rigid motions, a subgroup of the full group of Euclidean isometries. | 1 | Crystallography |
Selected area (electron) diffraction (abbreviated as SAD or SAED) is a crystallographic experimental technique typically performed using a transmission electron microscope (TEM). It is a specific case of electron diffraction used primarily in material science and solid state physics as one of the most common experimental techniques. Especially with appropriate analytical software, SAD patterns (SADP) can be used to determine crystal orientation, measure lattice constants or examine its defects. | 1 | Crystallography |
Polymorphism is the occurrence of multiple crystalline forms of a material. It is found in many crystalline materials including polymers, minerals, and metals. According to Gibbs' rules of phase equilibria, these unique crystalline phases are dependent on intensive variables such as pressure and temperature. Polymorphism is related to allotropy, which refers to elemental solids. The complete morphology of a material is described by polymorphism and other variables such as crystal habit, amorphous fraction or crystallographic defects. Polymorphs have different stabilities and may spontaneously and irreversibly transform from a metastable form (or thermodynamically unstable form) to the stable form at a particular temperature. They also exhibit different melting points, solubilities, and X-ray diffraction patterns.
One good example of this is the quartz form of silicon dioxide, or SiO. In the vast majority of silicates, the Si atom shows tetrahedral coordination by 4 oxygens. All but one of the crystalline forms involve tetrahedral {SiO} units linked together by shared vertices in different arrangements. In different minerals the tetrahedra show different degrees of networking and polymerization. For example, they occur singly, joined together in pairs, in larger finite clusters including rings, in chains, double chains, sheets, and three-dimensional frameworks. The minerals are classified into groups based on these structures. In each of the 7 thermodynamically stable crystalline forms or polymorphs of crystalline quartz, only 2 out of 4 of each the edges of the {SiO} tetrahedra are shared with others, yielding the net chemical formula for silica: SiO.
Another example is elemental tin (Sn), which is malleable near ambient temperatures but is brittle when cooled. This change in mechanical properties due to existence of its two major allotropes, α- and β-tin. The two allotropes that are encountered at normal pressure and temperature, α-tin and β-tin, are more commonly known as gray tin and white tin respectively. Two more allotropes, γ and σ, exist at temperatures above 161 °C and pressures above several GPa. White tin is metallic, and is the stable crystalline form at or above room temperature. Below 13.2 °C, tin exists in the gray form, which has a diamond cubic crystal structure, similar to diamond, silicon or germanium. Gray tin has no metallic properties at all, is a dull gray powdery material, and has few uses, other than a few specialized semiconductor applications. Although the α–β transformation temperature of tin is nominally 13.2 °C, impurities (e.g. Al, Zn, etc.) lower the transition temperature well below 0 °C, and upon addition of Sb or Bi the transformation may not occur at all. | 1 | Crystallography |
The measurement of the angles can be used to determine crystal structure, see x-ray crystallography for more details. As a simple example, Bragg's law, as stated above, can be used to obtain the lattice spacing of a particular cubic system through the following relation:
where is the lattice spacing of the cubic crystal, and , , and are the Miller indices of the Bragg plane. Combining this relation with Bragg's law gives:
One can derive selection rules for the Miller indices for different cubic Bravais lattices as well as many others, a few of the selection rules are given in the table below.
These selection rules can be used for any crystal with the given crystal structure. KCl has a face-centered cubic Bravais lattice. However, the K and the Cl ion have the same number of electrons and are quite close in size, so that the diffraction pattern becomes essentially the same as for a simple cubic structure with half the lattice parameter. Selection rules for other structures can be referenced elsewhere, or derived. Lattice spacing for the other crystal systems can be found here. | 1 | Crystallography |
The dyes used in this type of chromatography are inexpensive and generally available as they are from textile industries called reactive dye. It contains chromophores that are often attached to a triazine ring. In textile industries, reactive dyes are used to dye material like cotton which is cellulose.
Commonly used reactive dyes for chromatography can be separated according to their color index name or functional group. Noted that each company has different trade names and slightly different formulas of the reactive dyes. Usually available commercially with sepharose as the supporting matrix in the form of packed columns. | 0 | Chromatography + Titration + pH indicators |
Pumps vary in pressure capacity, but their performance is measured on their ability to yield a consistent and reproducible volumetric flow rate. Pressure may reach as high as 60 MPa (6000 lbf/in), or about 600 atmospheres. Modern HPLC systems have been improved to work at much higher pressures, and therefore are able to use much smaller particle sizes in the columns (), or about 1200 atmospheres. The term "UPLC" is a trademark of the Waters Corporation, but is sometimes used to refer to the more general technique of UHPLC. | 0 | Chromatography + Titration + pH indicators |
Simple twinned crystals may be contact twins or penetration twins. Contact twins meet on a single composition plane, often appearing as mirror images across the boundary. Plagioclase, quartz, gypsum, and spinel often exhibit contact twinning. Merohedral twinning occurs when the lattices of the contact twins superimpose in three dimensions, such as by relative rotation of one twin from the other. An example is metazeunerite. Contact twinning characteristically creates reentrant faces where faces of the crystal segments meet on the contact plane at an angle greater than 180°.
A type of twinning involving 180° relationships is called hemitropism or hemitropy.
In penetration twins the individual crystals have the appearance of passing through each other in a symmetrical manner. Orthoclase, staurolite, pyrite, and fluorite often show penetration twinning. The composition surface in penetration twins is usually irregular and extends to the center of the crystal.
Contact twinning can arise from either reflection or rotation, whereas penetration twinning is usually produced by rotation.
If several twin crystal parts are aligned by the same twin law they are referred to as multiple or repeated twins. If these multiple twins are aligned in parallel they are called polysynthetic twins. When the multiple twins are not parallel they are cyclic twins. Albite, calcite, and pyrite often show polysynthetic twinning. Closely spaced polysynthetic twinning is often observed as striations or fine parallel lines on the crystal face. Rutile, aragonite, cerussite, and chrysoberyl often exhibit cyclic twinning, typically in a radiating pattern.
For rotational twinning the relationship between the twin axis and twin plane falls into one of three types:
:#parallel twinning, when the twin axis and compositional plane lie parallel to each other,
:#normal twinning, when the twin plane and compositional plane lie normally, and
:#complex twinning, a combination of parallel twinning and normal twinning on one compositional plane. | 1 | Crystallography |
Metanil Yellow (Acid Yellow 36) is a dye of the azo class. In analytical chemistry, it is used as a pH indicator and it has a color change from red to yellow between pH 1.2 and 3.2.
Although it is an unpermitted food dye, because of its bright yellow color, Metanil Yellow has been used as an adulterant in turmeric powder and arhar dal, particularly in India.
Animal studies have suggested that Metanil Yellow is neurotoxic and hepatotoxic. | 0 | Chromatography + Titration + pH indicators |
Unresolved complex mixture (UCM), or hump, is a feature frequently observed in gas chromatographic (GC) data of crude oils and extracts from organisms exposed to oil.
The reason for the UCM hump appearance is that GC cannot resolve and identify a significant part of the hydrocarbons in crude oils. The resolved components appear as peaks while the UCM appears as a large background/platform. In non-biodegraded oils the UCM may comprise less than 50% of the total area of the chromatogram, while in biodegraded oils this figure can rise to over 90%. UCMs are also observed in certain refined fractions such as lubricating oils and references therein.
One reason why it is important to study the nature of UCMs is that some have been shown to contain toxic components, but only a small range of known petrogenic toxicants, such as the USEPA list of 16 polycyclic aromatic hydrocarbons (PAHs), tend to be routinely monitored in the environment.
Analysis of the hydrocarbon fraction of crude oils by GC reveals a complex mixture containing many thousands of individual components. Components that are resolved by GC have been extensively studied e.g. However, despite the application of many analytical techniques the remaining components have, until very recently, proved difficult to separate due to the large numbers of co-eluting compounds. Gas chromatograms of mature oils have prominent n-alkane peaks which distract attention from the underlying unresolved complex mixture (UCM) of hydrocarbons often referred to as the ‘hump’. Processes such as weathering and biodegradation result in a relative enrichment of the UCM component by removal of resolved components and the creation of new compounds. It has been shown that both resolved and unresolved components of oils are subject to concurrent biodegradation, i.e. it is not a sequential process, but due to the recalcitrant nature of some components, the rates of biodegradation of individual compounds greatly varies. The UCM fraction often represents the major component of hydrocarbons within hydrocarbon-polluted sediments (see reference therein) and biota e.g. A number of studies has now demonstrated that aqueous exposure to components within the UCM can affect the health of marine organisms, including possible hormonal disruption, and high concentrations of environmental UCMs have been strongly implicated with impaired health in wild populations. | 0 | Chromatography + Titration + pH indicators |
:The symmetry of a crystalline material has profound impacts on its emergent properties, including electronic band structure, electromagnetic behavior, and mechanical properties . Crystal symmetry is described and categorized by the crystal system, lattice, and space group of the material. Determination of these attributes is an important aspect of crystallography.
:Precession electron diffraction enables much more direct determination of space group symmetries over other forms of electron diffraction. Because of the increased number of reflections in both the zero order Laue zone and higher order Laue zones, the geometric relationship between Laue zones is more readily determined. This provides three-dimensional information about the crystal structure that can be used to determine its space group. Furthermore, because the PED technique is insensitive to slight misorientation from the zone axis, it provides the practical benefit of more robust data collection. | 1 | Crystallography |
Prior to entering politics, Jones was a high pressure liquid chromatographer. She worked at the Washington University School of Medicine and KV Pharmaceutical before becoming a sales director with Mary Kay. In April 2015, Jones was the first African-American elected to the Ferguson City Council, where she represented the city's first ward. In February 2020, Jones was selected to serve on the United States Environmental Protection Agency Local Government Advisory Committee.
In the 2017 municipal election, Jones ran for mayor, receiving 42.77% of the vote. It was the city's first election after the shooting of Michael Brown and subsequent Ferguson unrest.
In the June 2, 2020 mayoral election, Jones defeated fellow council member Heather Robinett. Jones succeeded incumbent James Knowles III, a Republican who was unable to seek re-election due to term limits. On June 17, 2020, Jones was sworn in as the first black and female mayor of Ferguson.
She is also a pastor in the African Methodist Episcopal Church. | 0 | Chromatography + Titration + pH indicators |
Anthocyanins generally are degraded at higher pH. However, some anthocyanins, such as petanin (petunidin 3-[6-O-(4-O-(E)-p-coumaroyl-O-α--rhamnopyranosyl)-β--glucopyranoside]-5-O-β--glucopyranoside), are resistant to degradation at pH 8 and may be used effectively as a food colorant. | 0 | Chromatography + Titration + pH indicators |
In aqueous solution, bromocresol green will ionize to give the monoanionic form (yellow), that further deprotonates at higher pH to give the dianionic form (blue), which is stabilized by resonance:
The acid dissociation constant (pK) of this reaction is 4.8. Tap water is sufficiently basic to give a solution of bromocresol green its characteristic blue-green color.
The acid and basic forms of this dye have an isosbestic point in their UV-Visible spectrum, around 515 nm, indicate that the two forms interconvert directly without forming any other substance.
An ethanol solution (0.04 wt%) of bromocresol green has been proposed for TLC staining and is suitable for visualisation of the compounds with functional groups whose pK is below 5.0 (carboxylic acids, sulfonic acids, etc.). These appear as yellow spots on a light or dark blue background; no heating is necessary. Bromophenol blue solution can be used for the same purpose.
The compound is synthesized by bromination of cresol purple (m-cresolsulfonphthalein). | 0 | Chromatography + Titration + pH indicators |
In normal-phase chromatography, the stationary phase is polar and the mobile phase is nonpolar. In reversed phase the opposite is true; the stationary phase is nonpolar and the mobile phase is polar. Typical stationary phases for normal-phase chromatography are silica or organic moieties with cyano and amino functional groups. For reversed phase, alkyl hydrocarbons are the preferred stationary phase; octadecyl (C18) is the most common stationary phase, but octyl (C8) and butyl (C4) are also used in some applications. The designations for the reversed phase materials refer to the length of the hydrocarbon chain.
In normal-phase chromatography, the least polar compounds elute first and the most polar compounds elute last. The mobile phase consists of a nonpolar solvent such as hexane or heptane mixed with a slightly more polar solvent such as isopropanol, ethyl acetate or chloroform. Retention decreases as the amount of polar solvent in the mobile phase increases. In reversed phase chromatography, the most polar compounds elute first with the more nonpolar compounds eluting later. The mobile phase is generally a mixture of water and miscible polarity-modifying organic solvent, such as methanol, acetonitrile or THF. Retention increases as the fraction of the polar solvent (water) in the mobile phase is higher. Normal phase chromatography retains molecules via an adsorptive mechanism, and is used for the analysis of solutes readily soluble in organic solvents. Separation is achieved based on the polarity differences among functional groups such as amines, acids, metal complexes, etc. as well as their steric properties, while in reversed-phase chromatography, a partition mechanism typically occurs for the separation by non-polar differences.
In the aqueous normal-phase chromatography the support is based on a silica with "hydride surface" which is distinguishable from the other silica support materials, used either in normal phase, reversed phase, or hydrophilic interaction chromatography. Most silica materials used for chromatography have a surface composed primarily of silanols (-Si-OH). In a "hydride surface" the terminal groups are primarily -Si-H. The hydride surface can also be functionalized with carboxylic acids and long-chain alkyl groups. Mobile phases for ANPC are based on organic solvents as bulk solvents (such as methanol or acetonitrile) with a small amount of water as a modifier of polarity; thus, the mobile phase is both "aqueous" (water is present) and "normal phase type" (less polar than the stationary phase). Thus, polar solutes (such as acids and amines) are more strongly retained, with the ability to affect the retention, which decreases as the amount of water in the mobile phase increases.
Typically the mobile phases are rich with organic solvents, with amount of the nonpolar solvent in the mobile phase at least 60% or greater to reach minimal required retention. A true ANP stationary phase will be able to function in both the reversed phase and normal phase modes with only the amount of water in the eluent varying. Thus a continuum of solvents can be used from 100% aqueous to pure organic. ANP retention has been demonstrated for a variety of polar compounds on the hydride based stationary phases. Recent investigations have demonstrated that silica hydride materials have a very thin water layer (about 0.5 monolayer) in comparison to HILIC phases that can have from 6–8 monolayers. In addition the substantial negative charge on the surface of hydride phases is the result of hydroxide ion adsorption from the solvent rather than silanols. | 0 | Chromatography + Titration + pH indicators |
The angles used for each facet play a crucial role in the outcome of a gem. While the general facet arrangement of a particular gemstone cut may appear the same in any given gem material, the angles of each facet must be carefully adjusted to maximize the optical performance. The angles used will vary based on the refractive index of the gem material. When light passes through a gemstone and strikes a polished facet, the minimum angle possible for the facet to reflect the light back into the gemstone is called the critical angle. If the ray of light strikes a surface lower than this angle, it will leave the gem material instead of reflecting through the gem as brilliance. These lost light rays are sometimes referred to as "light leakage", and the effect caused by it is called "windowing" as the area will appear transparent and without brilliance. This is especially common in poorly cut commercial gemstones. Gemstones with higher refractive indexes generally make more desirable gemstones, the critical angle decreases as refractive indices increase, allowing for greater internal reflections as the light is less likely to escape. | 1 | Crystallography |
The unit distance graph on the three-dimensional integer lattice has a vertex for each lattice point; each vertex has exactly six neighbors. It is possible to remove some of the points from the lattice, so that each remaining point has exactly three remaining neighbors, and so that the induced subgraph of these points has no cycles shorter than ten edges. There are four ways to do this, one of which is isomorphic as an abstract graph to the Laves graph. However, its vertices are in different positions than the more-symmetric, conventional geometric construction.
Another subgraph of the simple cubic net isomorphic to the Laves graph is obtained by removing half of the edges in a certain way. The resulting structure, called semi-simple cubic lattice, also has lower symmetry than the Laves graph itself. | 1 | Crystallography |
The relationship between fractional and Cartesian coordinates can be described by the matrix transformation :
Similarly, the Cartesian coordinates can be converted back to fractional coordinates using the matrix transformation : | 1 | Crystallography |
These are the Bravais lattice types in three dimensions:
* P – Primitive
* I – Body centered (from the German "Innenzentriert")
* F – Face centered (from the German "Flächenzentriert")
* A – Base centered on A faces only
* B – Base centered on B faces only
* C – Base centered on C faces only
* R – Rhombohedral | 1 | Crystallography |
Weakly dissociated acids yield sharp thermometric endpoints when titrated with a strong base. For instance, bicarbonate can be unequivocally determined in the company of carbonate by titrating with hydroxyl (ΔH=-40.9 kJ/mol). | 0 | Chromatography + Titration + pH indicators |
*CCP4i – CCP4 Graphical User Interface
*CCP4MG – CCP4 Molecular Graphics Project
*Coot – Graphical Model Building
*HAPPy – automated experimental phasing
*MrBUMP – automated Molecular Replacement
*PISA – Protein Interfaces, Surfaces and Assemblies
*MOSFLM GUI – building a modern interface to MOSFLM | 1 | Crystallography |
Sphere packing on the corners of a hypercube (with the spheres defined by Hamming distance) corresponds to designing error-correcting codes: if the spheres have radius t, then their centers are codewords of a (2t + 1)-error-correcting code. Lattice packings correspond to linear codes. There are other, subtler relationships between Euclidean sphere packing and error-correcting codes. For example, the binary Golay code is closely related to the 24-dimensional Leech lattice.
For further details on these connections, see the book Sphere Packings, Lattices and Groups by Conway and Sloane. | 1 | Crystallography |
In many cases, an initial set of phases are determined, and the electron density map for the diffraction pattern is calculated. Then the map is used to determine portions of the structure, which portions are used to simulate a new set of phases. This new set of phases is known as a refinement. These phases are reapplied to the original amplitudes, and an improved electron density map is derived, from which the structure is corrected. This process is repeated until an error term (usually ) has stabilized to a satisfactory value. Because of the phenomenon of phase bias, it is possible for an incorrect initial assignment to propagate through successive refinements, so satisfactory conditions for a structure assignment are still a matter of debate. Indeed, some spectacular incorrect assignments have been reported, including a protein where the entire sequence was threaded backwards. | 1 | Crystallography |
Consider the series of delta functions given by
The Patterson function is given by the following series of delta functions and unit step functions | 1 | Crystallography |
Stereographic projection plots can be carried out by a computer using the explicit formulas given above. However, for graphing by hand these formulas are unwieldy. Instead, it is common to use graph paper designed specifically for the task. This special graph paper is called a stereonet or Wulff net, after the Russian mineralogist George (Yuri Viktorovich) Wulff.
The Wulff net shown here is the stereographic projection of the grid of parallels and meridians of a hemisphere centred at a point on the equator (such as the Eastern or Western hemisphere of a planet).
In the figure, the area-distorting property of the stereographic projection can be seen by comparing a grid sector near the center of the net with one at the far right or left. The two sectors have equal areas on the sphere. On the disk, the latter has nearly four times the area of the former. If the grid is made finer, this ratio approaches exactly 4.
On the Wulff net, the images of the parallels and meridians intersect at right angles. This orthogonality property is a consequence of the angle-preserving property of the stereographic projection. (However, the angle-preserving property is stronger than this property. Not all projections that preserve the orthogonality of parallels and meridians are angle-preserving.)
For an example of the use of the Wulff net, imagine two copies of it on thin paper, one atop the other, aligned and tacked at their mutual center. Let be the point on the lower unit hemisphere whose spherical coordinates are (140°, 60°) and whose Cartesian coordinates are (0.321, 0.557, −0.766). This point lies on a line oriented 60° counterclockwise from the positive -axis (or 30° clockwise from the positive -axis) and 50° below the horizontal plane . Once these angles are known, there are four steps to plotting :
#Using the grid lines, which are spaced 10° apart in the figures here, mark the point on the edge of the net that is 60° counterclockwise from the point (1, 0) (or 30° clockwise from the point (0, 1)).
#Rotate the top net until this point is aligned with (1, 0) on the bottom net.
#Using the grid lines on the bottom net, mark the point that is 50° toward the center from that point.
#Rotate the top net oppositely to how it was oriented before, to bring it back into alignment with the bottom net. The point marked in step 3 is then the projection that we wanted.
To plot other points, whose angles are not such round numbers as 60° and 50°, one must visually interpolate between the nearest grid lines. It is helpful to have a net with finer spacing than 10°. Spacings of 2° are common.
To find the central angle between two points on the sphere based on their stereographic plot, overlay the plot on a Wulff net and rotate the plot about the center until the two points lie on or near a meridian. Then measure the angle between them by counting grid lines along that meridian. | 1 | Crystallography |
Proteins can be engineered to improve the chance of successful protein crystallization by using techniques like Surface Entropy Reduction or engineering in crystal contacts. Frequently, problematic cysteine residues can be replaced by alanine to avoid disulfide-mediated aggregation, and residues such as lysine, glutamate, and glutamine can be changed to alanine to reduce intrinsic protein flexibility, which can hinder crystallization.. | 1 | Crystallography |
Methyl violet 10B has six methyl groups. It is known in medicine as Gentian violet (or crystal violet or pyoctanin(e)) and is the active ingredient in a Gram stain, used to classify bacteria. It is used as a pH indicator, with a range between 0 and 1.6. The protonated form (found in acidic conditions) is yellow, turning blue-violet above pH levels of 1.6.
Methyl violet 10B inhibits the growth of many Gram positive bacteria, except streptococci. When used in conjunction with nalidixic acid (which destroys gram-negative bacteria), it can be used to isolate the streptococci bacteria for the diagnosis of an infection. | 0 | Chromatography + Titration + pH indicators |
This shell contains applications which are essential for problems involving group-subgroup relations between space groups. Given the space group types of G and H and their index, the program [http://www.cryst.ehu.es/cryst/subgroupgraph.html SUBGROUPGRAPH] provides graphs of maximal subgroups for a group-subgroup pair G > H, all the different subgroups H and their distribution into conjugacy classes. The Wyckoff position splitting rules for a group-subgroup pair are calculated by the program [http://www.cryst.ehu.es/cryst/wpsplit.html WYCKSPLIT]. | 1 | Crystallography |
Most traditional HPLC is performed with the stationary phase attached to the outside of small spherical silica particles (very small beads). These particles come in a variety of sizes with 5 µm beads being the most common. Smaller particles generally provide more surface area and better separations, but the pressure required for optimum linear velocity increases by the inverse of the particle diameter squared.
According to the equations of the column velocity, efficiency and backpressure, reducing the particle diameter by half and keeping the size of the column the same, will double the column velocity and efficiency; but four times increase the backpressure. And the small particles HPLC also can decrease the width broadening. Larger particles are used in preparative HPLC (column diameters 5 cm up to >30 cm) and for non-HPLC applications such as solid-phase extraction. | 0 | Chromatography + Titration + pH indicators |
A separation in which the mobile phase composition remains constant throughout the procedure is termed isocratic (meaning constant composition). The word was coined by Csaba Horvath who was one of the pioneers of HPLC.
The mobile phase composition does not have to remain constant. A separation in which the mobile phase composition is changed during the separation process is described as a gradient elution. For example, a gradient can start at 10% methanol in water, and end at 90% methanol in water after 20 minutes. The two components of the mobile phase are typically termed "A" and "B"; A is the "weak" solvent which allows the solute to elute only slowly, while B is the "strong" solvent which rapidly elutes the solutes from the column. In reversed-phase chromatography, solvent A is often water or an aqueous buffer, while B is an organic solvent miscible with water, such as acetonitrile, methanol, THF, or isopropanol.
In isocratic elution, peak width increases with retention time linearly according to the equation for N, the number of theoretical plates. This can be a major disadvantage when analyzing a sample that contains analytes with a wide range of retention factors. Using a weaker mobile phase, the runtime is lengthened and results in slowly eluting peaks to be broad, leading to reduced sensitivity. A stronger mobile phase would improve issues of runtime and broadening of later peaks but results in diminished peak separation, especially for quickly eluting analytes which may have insufficient time to fully resolve. This issue is addressed through the changing mobile phase composition of gradient elution.
By starting from a weaker mobile phase and strengthening it during the runtime, gradient elution decreases the retention of the later-eluting components so that they elute faster, giving narrower (and taller) peaks for most components, while also allowing for the adequate separation of earlier-eluting components. This also improves the peak shape for tailed peaks, as the increasing concentration of the organic eluent pushes the tailing part of a peak forward. This also increases the peak height (the peak looks "sharper"), which is important in trace analysis. The gradient program may include sudden "step" increases in the percentage of the organic component, or different slopes at different times – all according to the desire for optimum separation in minimum time.
In isocratic elution, the retention order does not change if the column dimensions (length and inner diameter) change – that is, the peaks elute in the same order. In gradient elution, however, the elution order may change as the dimensions or flow rate change. if they are no scaled down or up according to the change
The driving force in reversed phase chromatography originates in the high order of the water structure. The role of the organic component of the mobile phase is to reduce this high order and thus reduce the retarding strength of the aqueous component. | 0 | Chromatography + Titration + pH indicators |
Inoculate MacConkey's (Glucose phosphate broth) with pure culture of test organism. Incubate the broth at 35 °C for 48–72 hours.
After incubation add 5 drops of methyl red directly into the broth, through the sides of the tube. | 0 | Chromatography + Titration + pH indicators |
A crystal can be described as a lattice of atoms, which in turn this leads to the reciprocal lattice. With electrons, neutrons or x-rays there is diffraction by the atoms, and if there is an incident plane wave with a wavevector , there will be outgoing wavevectors and as shown in the diagram after the wave has been diffracted by the atoms.
The energy of the waves (electron, neutron or x-ray) depends upon the magnitude of the wavevector, so if there is no change in energy (elastic scattering) these have the same magnitude, that is they must all lie on the Ewald sphere. In the Figure the red dot is the origin for the wavevectors, the black spots are reciprocal lattice points (vectors) and shown in blue are three wavevectors. For the wavevector the corresponding reciprocal lattice point lies on the Ewald sphere, which is the condition for Bragg diffraction. For the corresponding reciprocal lattice point is off the Ewald sphere, so where is called the excitation error. The amplitude and also intensity of diffraction into the wavevector depends upon the Fourier transform of the shape of the sample, the excitation error , the structure factor for the relevant reciprocal lattice vector, and also whether the scattering is weak or strong. For neutrons and x-rays the scattering is generally weak so there is mainly Bragg diffraction, but it is much stronger for electron diffraction. | 1 | Crystallography |
The Cauchy–Born rule or Cauchy–Born approximation is a basic hypothesis used in the mathematical formulation of solid mechanics which relates the movement of atoms in a crystal to the overall deformation of the bulk solid. It states that in a crystalline solid subject to a small strain, the positions of the atoms within the crystal lattice follow the overall strain of the medium. The currently accepted form is Max Borns refinement of Cauchys original hypothesis which was used to derive the equations satisfied by the Cauchy stress tensor. The approximation generally holds for face-centered and body-centered cubic crystal systems. For complex lattices such as diamond, however, the rule has to be modified to allow for internal degrees of freedom between the sublattices. The approximation can then be used to obtain bulk properties of crystalline materials such as stress-strain relationship.
For crystalline bodies of finite size, the effect of surface stress is also significant. However, the standard Cauchy–Born rule cannot deduce the surface properties. To overcome this limitation, Park et al. (2006) proposed a surface Cauchy–Born rule. Several modified forms of the Cauchy–Born rule have also been proposed to cater to crystalline bodies having special shapes. Arroyo & Belytschko (2002) proposed an exponential Cauchy Born rule for modeling of mono-layered crystalline sheets as two-dimensional continuum shells. Kumar et al. (2015) proposed a helical Cauchy–Born rule for modeling slender bodies (such as nano and continuum rods) as special Cosserat continuum rods. | 1 | Crystallography |
One path to the reciprocal lattice of an arbitrary collection of atoms comes from the idea of scattered waves in the Fraunhofer (long-distance or lens back-focal-plane) limit as a Huygens-style sum of amplitudes from all points of scattering (in this case from each individual atom). This sum is denoted by the complex amplitude in the equation below, because it is also the Fourier transform (as a function of spatial frequency or reciprocal distance) of an effective scattering potential in direct space:
Here g = q/(2) is the scattering vector q in crystallographer units, N is the number of atoms, f[g] is the atomic scattering factor for atom j and scattering vector g, while r is the vector position of atom j. The Fourier phase depends on one's choice of coordinate origin.
For the special case of an infinite periodic crystal, the scattered amplitude F = M F from M unit cells (as in the cases above) turns out to be non-zero only for integer values of , where
when there are j = 1,m atoms inside the unit cell whose fractional lattice indices are respectively {u, v, w}. To consider effects due to finite crystal size, of course, a shape convolution for each point or the equation above for a finite lattice must be used instead.
Whether the array of atoms is finite or infinite, one can also imagine an "intensity reciprocal lattice" I[g], which relates to the amplitude lattice F via the usual relation I = FF where F is the complex conjugate of F. Since Fourier transformation is reversible, of course, this act of conversion to intensity tosses out "all except 2nd moment" (i.e. the phase) information. For the case of an arbitrary collection of atoms, the intensity reciprocal lattice is therefore:
Here r is the vector separation between atom j and atom k. One can also use this to predict the effect of nano-crystallite shape, and subtle changes in beam orientation, on detected diffraction peaks even if in some directions the cluster is only one atom thick. On the down side, scattering calculations using the reciprocal lattice basically consider an incident plane wave. Thus after a first look at reciprocal lattice (kinematic scattering) effects, beam broadening and multiple scattering (i.e. dynamical) effects may be important to consider as well. | 1 | Crystallography |
The simplicity and efficiency of MEKC have made it an attractive technique for a variety of applications. Further improvements can be made to the selectivity of MEKC by adding chiral selectors or chiral surfactants to the system. Unfortunately, this technique is not suitable for protein analysis because proteins are generally too large to partition into a surfactant micelle and tend to bind to surfactant monomers to form SDS-protein complexes.
Recent applications of MEKC include the analysis of uncharged pesticides, essential and branched-chain amino acids in nutraceutical products, hydrocarbon and alcohol contents of the marjoram herb.
MEKC has also been targeted for its potential to be used in combinatorial chemical analysis. The advent of combinatorial chemistry has enabled medicinal chemists to synthesize and identify large numbers of potential drugs in relatively short periods of time. Small sample and solvent requirements and the high resolving power of MEKC have enabled this technique to be used to quickly analyze a large number of compounds with good resolution.
Traditional methods of analysis, like high-performance liquid chromatography (HPLC), can be used to identify the purity of a combinatorial library, but assays need to be rapid with good resolution for all components to provide useful information for the chemist. The introduction of surfactant to traditional capillary electrophoresis instrumentation has dramatically expanded the scope of analytes that can be separated by capillary electrophoresis.
MEKC can also be used in routine quality control of antibiotics in pharmaceuticals or feedstuffs. | 0 | Chromatography + Titration + pH indicators |
The symbol of a space group is defined by combining the uppercase letter describing the lattice type with symbols specifying the symmetry elements. The symmetry elements are ordered the same way as in the symbol of corresponding point group (the group that is obtained if one removes all translational components from the space group). The symbols for symmetry elements are more diverse, because in addition to rotations axes and mirror planes, space group may contain more complex symmetry elements – screw axes (combination of rotation and translation) and glide planes (combination of mirror reflection and translation). As a result, many different space groups can correspond to the same point group. For example, choosing different lattice types and glide planes one can generate 28 different space groups from point group mmm, e.g. Pmmm, Pnnn, Pccm, Pban, Cmcm, Ibam, Fmmm, Fddd, and so on. In some cases, a space group is generated when translations are simply added to a point group. In other cases there is no point around which the point group applies. The notation is somewhat ambiguous, without a table giving more information. For example, space groups I23 and I23 (nos. 197 and 199) both contain two-fold rotational axes as well as two-fold screw axes. In the first, the two-fold axes intersect the three-fold axes, whereas in the second they do not. | 1 | Crystallography |
A method for detecting arsenious oxide, simple arsenic, in corpses was devised in 1773 by the Swedish chemist, Carl Wilhelm Scheele. His work was expanded upon, in 1806, by German chemist Valentin Ross, who learned to detect the poison in the walls of a victim's stomach.
James Marsh was the first to apply this new science to the art of forensics. He was called by the prosecution in a murder trial to give evidence as a chemist in 1832. The defendant, John Bodle, was accused of poisoning his grandfather with arsenic-laced coffee. Marsh performed the standard test by mixing a suspected sample with hydrogen sulfide and hydrochloric acid. While he was able to detect arsenic as yellow arsenic trisulfide, when it was shown to the jury it had deteriorated, allowing the suspect to be acquitted due to reasonable doubt.
Annoyed by that, Marsh developed a much better test. He combined a sample containing arsenic with sulfuric acid and arsenic-free zinc, resulting in arsine gas. The gas was ignited, and it decomposed to pure metallic arsenic, which, when passed to a cold surface, would appear as a silvery-black deposit. So sensitive was the test, known formally as the Marsh test, that it could detect as little as one-fiftieth of a milligram of arsenic. He first described this test in The Edinburgh Philosophical Journal in 1836. | 0 | Chromatography + Titration + pH indicators |
The simplest wallpaper group, Group p1, applies when there is no symmetry other than the fact that a pattern repeats over regular intervals in two dimensions, as shown in the section on p1 below.
The following examples are patterns with more forms of symmetry:
Examples A and B have the same wallpaper group; it is called p4m in the IUCr notation and *442 in the orbifold notation. Example C has a different wallpaper group, called p4g or 4*2 . The fact that A and B have the same wallpaper group means that they have the same symmetries, regardless of details of the designs, whereas C has a different set of symmetries despite any superficial similarities.
The number of symmetry groups depends on the number of dimensions in the patterns. Wallpaper groups apply to the two-dimensional case, intermediate in complexity between the simpler frieze groups and the three-dimensional space groups. Subtle differences may place similar patterns in different groups, while patterns that are very different in style, color, scale or orientation may belong to the same group.
A proof that there are only 17 distinct groups of such planar symmetries was first carried out by Evgraf Fedorov in 1891 and then derived independently by George Pólya in 1924. The proof that the list of wallpaper groups is complete only came after the much harder case of space groups had been done. The seventeen possible wallpaper groups are listed below in . | 1 | Crystallography |
In chemistry, water(s) of crystallization or water(s) of hydration are water molecules that are present inside crystals. Water is often incorporated in the formation of crystals from aqueous solutions. In some contexts, water of crystallization is the total mass of water in a substance at a given temperature and is mostly present in a definite (stoichiometric) ratio. Classically, "water of crystallization" refers to water that is found in the crystalline framework of a metal complex or a salt, which is not directly bonded to the metal cation.
Upon crystallization from water, or water-containing solvents, many compounds incorporate water molecules in their crystalline frameworks. Water of crystallization can generally be removed by heating a sample but the crystalline properties are often lost.
Compared to inorganic salts, proteins crystallize with large amounts of water in the crystal lattice. A water content of 50% is not uncommon for proteins. | 1 | Crystallography |
A lattice system is a group of lattices with the same set of lattice point groups. The 14 Bravais lattices are grouped into seven lattice systems: triclinic, monoclinic, orthorhombic, tetragonal, rhombohedral, hexagonal, and cubic. | 1 | Crystallography |
Similar assays can be performed for research purposes, detecting concentrations of potential clinical candidates like anti-fungal and asthma drugs. This technique is obviously useful in observing multiple species in collected samples, as well, but requires the use of standard solutions when information about species identity is sought out. It is used as a method to confirm results of synthesis reactions, as purity is essential in this type of research. However, mass spectrometry is still the more reliable way to identify species. | 0 | Chromatography + Titration + pH indicators |
Until 1980, laser-heated crystal growth used only two laser beams focused over the source material. This condition generated a high radial thermal gradient in the molten zone, making the process unstable. Increasing the number of beams to four did not solve the problem, although it improved the growth process.
An improvement to the laser-heated crystal growth technique was made by Fejer et al., who incorporated a special optical component known as a reflaxicon, consisting of an inner cone surrounded by a larger coaxial cone section, both with reflecting surfaces. This optical element converts the cylindrical laser beam into a larger diameter hollow cylinder surface. This optical component allows radial distribution of the laser energy over the molten zone, reducing radial thermal gradients. The axial temperature gradient in this technique can go as high as 10000 °C/cm, which is very high when compared to traditional crystal growth techniques (10–100 °C/cm). | 1 | Crystallography |
In the laboratory, it is used to detect the presence of alkaline phosphatase activity by hydrolysis of PNPP. In basic conditions, presence of hydrolytic enzymes will turn reaction vessel yellow.
4-Nitrophenol is a product of the enzymatic cleavage of several synthetic substrates such as 4-nitrophenyl phosphate (used as a substrate for alkaline phosphatase), 4-nitrophenyl acetate (for carbonic anhydrase), 4-nitrophenyl-β--glucopyranoside and other sugar derivatives which are used to assay various glycosidase enzymes. Amounts of 4-nitrophenol produced by a particular enzyme in the presence of its corresponding substrate can be measured with a spectrophotometer at or around 405 nm and used as a proxy measurement for the amount of the enzyme activity in the sample.
Accurate measurement of enzyme activity requires that the 4-nitrophenol product is fully deprotonated, existing as 4-nitrophenolate, given the weak absorbance of 4-nitrophenol at 405 nm. Complete ionization of the alcohol functional group affects the conjugation of the pi bonds on the compound. A lone pair from the oxygen can be delocalized via conjugation to the benzene ring and nitro group. Since the length of conjugated systems affects the color of organic compounds, this ionization change causes the 4-nitrophenol to turn yellow when fully deprotonated and existing as 4-nitrophenolate.
A common mistake in measuring enzyme activity using these substrates is to perform the assays at neutral or acidic pH without considering that only part of the chromophoric product is ionized. The problem can be overcome by stopping the reaction with sodium hydroxide (NaOH) or other strong base, which converts all product into 4-nitrophenoxide; final pH must be > ca. 9.2 to ensure more than 99% of the product is ionised. Alternatively enzyme activity can be measured at 348 nm, the isosbestic point for 4-nitrophenol/4-nitrophenoxide. | 0 | Chromatography + Titration + pH indicators |
Thymolphthalein is a phthalein dye used as an acid–base (pH) indicator. Its transition range is around pH 9.3–10.5. Below this pH, it is colorless; above, it is blue. The molar extinction coefficient for the blue thymolphthalein dianion is 38,000 M cm at 595 nm.
Thymolphthalein is also known to have use as a laxative and for disappearing ink. | 0 | Chromatography + Titration + pH indicators |
Researchers began questioning the nature of "tail states" in disordered semiconductors in the 1950s. It was found that such tails arise from the strains sufficient to push local states past the band edges.
In 1953, the Austrian-American physicist Franz Urbach (1902–1969) found that such tails decay exponentially into the gap. Later, photoemission experiments delivered absorption models revealing temperature dependence of the tail.
A variety of amorphous crystalline solids expose exponential band edges via optical absorption. The universality of this feature suggested a common cause. Several attempts were made to explain the phenomenon, but these could not connect specific topological units to the electronic structure. | 1 | Crystallography |
The process of separating mixtures of chemical compounds by passing them through a column that contains a solid stationary phase that was eluted with a mobile phase (column chromatography) was well known at that time. Chromatographic separation was considered to occur by an adsorption process whereby compounds adhered to a solid media and were washed off the column with a solvent, mixture of solvents, or solvent gradient. In contrast, Martin and Synge developed and described a chromatographic separation process whereby compounds were partitioned between two liquid phases similar to the separatory funnel liquid-liquid separation dynamic. This was an important departure, both in theory and inder equilibrium conditions. Martin and Synge initially attempted to devise a method of performing a sequential liquid-liquid extraction with serially connected glass vessels that functioned as separatory funnels. The seminal article presenting their early studies described a rather complicated instrument that allowed partitioning of amino acids between water and chloroform phases. The process was termed "counter-current liquid-liquid extraction." Martin and Synge described the theory of this technique in reference to continuous fractional distillation described by Randall and Longtin. This approach was deemed too cumbersome, so they developed a method of absorbing water onto silica gel as the stationary phase and using a solvent, such as chloroform, as the mobile phase. This work was published in 1941 as "a new form of chromatogram employing two liquid phases." The article describes both the theory in terms of the partition coefficient of a compound, and the application of the process to the separation of amino acids on a water-impregnated silica column eluted with a water:chloroform:n-butanol solvent mixture. | 0 | Chromatography + Titration + pH indicators |
A crystal system is a set of point groups in which the point groups themselves and their corresponding space groups are assigned to a lattice system. Of the 32 point groups that exist in three dimensions, most are assigned to only one lattice system, in which case the crystal system and lattice system both have the same name. However, five point groups are assigned to two lattice systems, rhombohedral and hexagonal, because both lattice systems exhibit threefold rotational symmetry. These point groups are assigned to the trigonal crystal system.
In total there are seven crystal systems: triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic. | 1 | Crystallography |
In order to visualize functional relations and provide better understanding of experimental data, the graphical interface emphasize user interactivity and functional interconnection. There are two visualization tools in the suite: one depicting single material while another being focused on intergrowths of two different materials. | 1 | Crystallography |
Compounds that were historically given the formulae REAlB and REB have the MgAlB structure with an orthorhombic symmetry and space group Imma (No. 74). In this structure, rare-earth atoms enter the Mg site. Aluminium sites are empty for REB. Both metal sites of REAlB structure have partial occupancies of about 60–70%, which shows that the compounds are actually non-stoichiometric. The REB formula merely reflects the average atomic ratio [B]/[RE] = 25. Yttrium borides form both YAlB and YB structures. Experiments have confirmed that the borides based on rare-earth elements from Tb to Lu can have the REAlB structure. A subset of these borides, which contains rare-earth elements from Gd to Er, can also crystallize in the REB structure.
Korsukova et al. analyzed the YAlB crystal structure using a single crystal grown by the high-temperature solution-growth method. The lattice constants were deduced as a = 0.58212(3), b = 1.04130(8) and c = 0.81947(6) nm, and the atomic coordinates and site occupancies are summarized in table I.
Figure 3 shows the crystal structure of YAlB viewed along the x-axis. The large black spheres are Y atoms, the small blue spheres are Al atoms and the small green spheres are the bridging boron sites; B clusters are depicted as the green icosahedra. Boron framework of YAlB is one of the simplest among icosahedron-based borides – it consists of only one kind of icosahedra and one bridging boron site. The bridging boron site is tetrahedrally coordinated by four boron atoms. Those atoms are another boron atom in the counter bridge site and three equatorial boron atoms of one of three B icosahedra. Aluminium atoms are separated by 0.2911 nm and are arranged in lines parallel to the x-axis, whereas yttrium atoms are separated by 0.3405 nm. Both the Y atoms and B icosahedra form zigzags along the x-axis. The bridging boron atoms connect three equatorial boron atoms of three icosahedra and those icosahedra make up a network parallel to the (101) crystal plane (x-z plane in the figure). The bonding distance between the bridging boron and the equatorial boron atoms is 0.1755 nm, which is typical for the strong covalent B-B bond (bond length 0.17–0.18 nm); thus, the bridging boron atoms strengthen the individual network planes. On the other hand, the large distance between the boron atoms within the bridge (0.2041 nm) suggests weaker interaction, and thus the bridging sites contribute little to the bonding between the network planes.
The boron framework of YAlB needs donation of four electrons from metal elements: two electrons for a B icosahedron and one electron for each of the two bridging boron atoms – to support their tetrahedral coordination. The actual chemical composition of YAlB, determined by the structure analysis, is YAlB as described in table I. If both metal elements are trivalent ions then 3.99 electrons can be transferred to the boron framework, which is very close to the required value of 4. However, because the bonding between the bridging boron atoms is weaker than in a typical B-B covalent bond, less than 2 electrons are donated to this bond, and metal atoms need not be trivalent. On the other hand, the electron transfer from metal atoms to the boron framework implies that not only strong covalent B-B bonding within the framework but also ionic interaction between metal atoms and the framework contribute to the YAlB phase stabilization. | 1 | Crystallography |
The material matrix has a symmetry with respect to a given orthogonal transformation () if it does not change when subjected to that transformation.
For invariance of the material properties under such a transformation we require
Hence the condition for material symmetry is (using the definition of an orthogonal transformation)
Orthogonal transformations can be represented in Cartesian coordinates by a matrix given by
Therefore, the symmetry condition can be written in matrix form as
For a transversely isotropic material, the matrix has the form
where the -axis is the axis of symmetry. The material matrix remains invariant under rotation by any angle about the -axis. | 1 | Crystallography |
These planar defects are similar to stacking faults in that they are often created through slip of atomic planes and dislocation motion, but the degree of translation varies. In stacking faults, the region of stacking mismatch is bounded by two partial dislocations, and an extended dislocation is formed. For anti-phase domains which only exhibit chemical disorder, the region is bounded by two complex stacking faults, which exhibit both stacking and chemical disorder. Thus, it takes 4 partial dislocations to fully restore the order of the crystal. These can be seen in Figure 1 and 2 below. The width of these regions is determined by the force balance between the like-signed partial dislocations’ repulsion and the regions surface energy. As the anti-phase boundary surface energy increases, the degree of separation between the partial dislocations will decrease to compensate.
Figure 1: This figure depicts two layers of atoms in a Ni3Al crystal, a binary alloy that often exhibits anti-phase boundaries. For visualization purposes, the atoms in the bottom layer are shown as larger than the top layer, but this is not actually the case. The translation of the top layer can be broken down into two steps, indicated by the small arrows 1 and 2. (b) The partial sliding of the top layer by the short vector 1 leads to the formation of a complex stacking fault. (c) The complete sliding of the top layer with the translation magnitude given by a unit lattice translation (1+2), resulting in the formation of an anti-phase boundary. If the top plane slips by two complete lattice spacings (1, 2, 3, and 4), a superdislocation is formed, and this is required for the perfect crystal structure to be restored. It is expected that this superdislocation, consisting of two perfect lattice translations, dissociates into four different partial dislocations with two on each side.
Figure 2: An antiphase boundary created by four partial dislocations (1,2,3,4), surrounded by complex stacking faults. Outside of these shaded regions, the crystal is perfect. | 1 | Crystallography |
For each particular lattice, a conventional cell has been chosen on a case-by-case basis by crystallographers based on convenience of calculation. These conventional cells may have additional lattice points located in the middle of the faces or body of the unit cell. The number of lattice points, as well as the volume of the conventional cell is an integer multiple (1, 2, 3, or 4) of that of the primitive cell. | 1 | Crystallography |
Immobilized metal ion affinity chromatography (IMAC) is based on the specific coordinate covalent bond of amino acids, particularly histidine, to metals. This technique works by allowing proteins with an affinity for metal ions to be retained in a column containing immobilized metal ions, such as cobalt, nickel, or copper for the purification of histidine-containing proteins or peptides, iron, zinc or gallium for the purification of phosphorylated proteins or peptides. Many naturally occurring proteins do not have an affinity for metal ions, therefore recombinant DNA technology can be used to introduce such a protein tag into the relevant gene. Methods used to elute the protein of interest include changing the pH, or adding a competitive molecule, such as imidazole. | 0 | Chromatography + Titration + pH indicators |
The chief advantage over direct amperometry is that the magnitude of the measured current is of interest only as an indicator. Thus, factors that are of critical importance to quantitative amperometry, such as the surface area of the working electrode, completely disappear from amperometric titrations.
The chief advantage over other types of titration is the selectivity offered by the electrode potential, as well as by the choice of titrant. For instance, lead ion is reduced at a potential of -0.60 V (relative to the saturated calomel electrode), while zinc ions are not; this allows the determination of lead in the presence of zinc. Clearly this advantage depends entirely on the other species present in the sample. | 0 | Chromatography + Titration + pH indicators |
Metals, and specifically rare-earth elements, form numerous chemical complexes with boron. Their crystal structure and chemical bonding depend strongly on the metal element M and on its atomic ratio to boron. When B/M ratio exceeds 12, boron atoms form B icosahedra which are linked into a three-dimensional boron framework, and the metal atoms reside in the voids of this framework. Those icosahedra are basic structural units of most allotropes of boron and boron-rich rare-earth borides. In such borides, metal atoms donate electrons to the boron polyhedra, and thus these compounds are regarded as electron-deficient solids.
The crystal structures of many boron-rich borides can be attributed to certain types including MgAlB, YB, REBSi, BC and other, more complex types such as REBCSi. Some of these formulas, for example BC, YB and MgAlB, historically reflect the idealistic structures, whereas the experimentally determined composition is nonstoichiometric and corresponds to fractional indexes. Boron-rich borides are usually characterized by large and complex unit cells, which can contain more than 1500 atomic sites and feature extended structures shaped as "tubes" and large modular polyhedra ("superpolyhedra"). Many of those sites have partial occupancy, meaning that the probability to find them occupied with a certain atom is smaller than one and thus that only some of them are filled with atoms. Scandium is distinguished among the rare-earth elements by that it forms numerous borides with uncommon structure types; this property of scandium is attributed to its relatively small atomic and ionic radii.
Crystals of the specific rare-earth boride YB are used as X-ray monochromators for selecting X-rays with certain energies (in the 1–2 keV range) out of synchrotron radiation. Other rare-earth borides may find application as thermoelectric materials, owing to their low thermal conductivity; the latter originates from their complex, "amorphous-like", crystal structure. | 1 | Crystallography |
The injection loop is a segment of tubing of known volume which is filled with the sample solution before it is injected into the column. Loop volume can range from a few microliters to 50 ml or more. | 0 | Chromatography + Titration + pH indicators |
Recognizing the habit can aid in mineral identification and description, as the crystal habit is an external representation of the internal ordered atomic arrangement. Most natural crystals, however, do not display ideal habits and are commonly malformed. Hence, it is also important to describe the quality of the shape of a mineral specimen:
* Euhedral: a crystal that is completely bounded by its characteristic faces, well-formed. Synonymous terms: idiomorphic, automorphic;
* Subhedral: a crystal partially bounded by its characteristic faces and partially by irregular surfaces. Synonymous terms: hypidiomorphic, hypautomorphic;
* Anhedral: a crystal that lacks any of its characteristic faces, completely malformed. Synonymous terms: allotriomorphic, xenomorphic. | 1 | Crystallography |
Phenol red was used by Leonard Rowntree and John Geraghty in the phenolsulfonphthalein test to estimate the overall blood flow through the kidney in 1911. It was the first test of kidney function and was used for almost a century but is now obsolete.
The test is based on the fact that phenol red is excreted almost entirely in the urine. Phenol red solution is administered intravenously; the urine produced is collected. By measuring the amount of phenol red excreted colorimetrically, kidney function can be determined. | 0 | Chromatography + Titration + pH indicators |
IEC/RP MMC combines the advantages of RPLC and IEC. For example, WAX/RP has increased separation power and degree of freedom in adjusting the separation selectivity when compared with single WAX or RPLC. | 0 | Chromatography + Titration + pH indicators |
Bromophenol blue (3′,3″,5′,5″-tetrabromophenolsulfonphthalein, BPB), albutest is used as a pH indicator, an electrophoretic color marker, and a dye. It can be prepared by slowly adding excess bromine to a hot solution of phenolsulfonphthalein in glacial acetic acid. | 0 | Chromatography + Titration + pH indicators |
The coupling of chromatography with MS is a well developed chemical analysis strategy dating back from the 1950s. Gas chromatography (GC)–MS was originally introduced in 1952, when A. T. James and A. J. P. Martin were trying to develop tandem separation – mass analysis techniques. In GC, the analytes are eluted from the separation column as a gas and the connection with electron ionization (EI) or chemical ionization (CI) ion sources in the MS system was a technically simpler challenge. Because of this, the development of GC-MS systems was faster than LC–MS and such systems were first commercialized in the 1970s. The development of LC–MS systems took longer than GC-MS and was directly related to the development of proper interfaces. Victor Talrose and his collaborators in Russia started the development of LC–MS in the late 1960s, when they first used capillaries to connect an LC columns to an EI source. A similar strategy was investigated by McLafferty and collaborators in 1973 who coupled the LC column to a CI source, which allowed a higher liquid flow into the source. This was the first and most obvious way of coupling LC with MS, and was known as the capillary inlet interface. This pioneer interface for LC–MS had the same analysis capabilities of GC-MS and was limited to rather volatile analytes and non-polar compounds with low molecular mass (below 400 Da). In the capillary inlet interface, the evaporation of the mobile phase inside the capillary was one of the main issues. Within the first years of development of LC–MS, on-line and off-line alternatives were proposed as coupling alternatives. In general, off-line coupling involved fraction collection, evaporation of solvent, and transfer of analytes to the MS using probes. Off-line analyte treatment process was time-consuming and there was an inherent risk of sample contamination. Rapidly, it was realized that the analysis of complex mixtures would require the development of a fully automated on-line coupling solution in LC–MS.
The key to the success and widespread adoption of LC–MS as a routine analytical tool lies in the interface and ion source between the liquid-based LC and the vacuum-base MS. The following interfaces were stepping-stones on the way to the modern atmospheric-pressure ionization interfaces, and are described for historical interest. | 0 | Chromatography + Titration + pH indicators |
Recently, CBED was applied to study graphene and other 2D monolayer crystals and van der Waals structures. For 2D crystals, the analysis of CBED patterns is simplified, because the intensity distribution in a CBED disk is directly related to the atomic arrangement in the crystal. The deformations at a nanometer resolution have been retrieved, the interlayer distance of a bilayer crystal has been reconstructed, and so on, by using CBED. | 1 | Crystallography |
Gel permeation chromatography is conducted almost exclusively in chromatography systems. The experimental design is not much different from other techniques of High Performance liquid chromatography. Samples are dissolved in an appropriate solvent, in the case of GPC these tend to be organic solvents and after filtering the solution it is injected onto a column. The separation of multi-component mixture takes place in the column. The constant supply of fresh eluent to the column is accomplished by the use of a pump. Since most analytes are not visible to the naked eye a detector is needed. Often multiple detectors are used to gain additional information about the polymer sample. The availability of a detector makes the fractionation convenient and accurate. | 0 | Chromatography + Titration + pH indicators |
The determination of trace acids in organic matrices is a common analytical task assigned to titrimetry. Examples are Total Acid Number (TAN) in mineral and lubricating oils and Free Fatty Acids (FFA) in edible fats and oils. Automated potentiometric titration procedures have been granted standard method status, for example by ASTM for TAN and AOAC for FFA. The methodology is similar in both instances. The sample is dissolved in a suitable solvent mixture; say a hydrocarbon and an alcohol which also must contain a small amount of water. The water is intended to enhance the electrical conductivity of the solution. The trace acids are titrated with standard base in an alcohol. The sample environment is essentially hostile to the pH electrode used to sense the titration. The electrode must be taken out of service on a regular basis to rehydrate the glass sensing membrane, which is also in danger of fouling by the oily sample solution.
A recent thermometric titrimetric procedure for the determination of FFA developed by Cameiro et al. (2002) has been shown to be particularly amenable to automation. It is fast, highly precise, and results agree very well with those obtained by the official AOAC method. The temperature change for the titration of very weak acids such as oleic acid by 0.1 mol/L KOH in propan-2-ol is too small to yield an accurate endpoint. In this procedure, a small amount of paraformaldehyde as a fine powder is added to the titrand before the titration. At the endpoint, the first excess of hydroxyl ions catalyzes the depolymerization of paraformaldehyde. The reaction is strongly endothermic and yields a sharp inflection. The titration plot is illustrated in Figure 13. The speed of this titration coupled with its precision and accuracy makes it ideal for the analysis of FFA in biodiesel feedstocks and product. | 0 | Chromatography + Titration + pH indicators |
Titrations are often recorded on graphs called titration curves, which generally contain the volume of the titrant as the independent variable and the pH of the solution as the dependent variable (because it changes depending on the composition of the two solutions).
The equivalence point on the graph is where all of the starting solution (usually an acid) has been neutralized by the titrant (usually a base). It can be calculated precisely by finding the second derivative of the titration curve and computing the points of inflection (where the graph changes concavity); however, in most cases, simple visual inspection of the curve will suffice. In the curve given to the right, both equivalence points are visible, after roughly 15 and 30 mL of NaOH solution has been titrated into the oxalic acid solution. To calculate the logarithmic acid dissociation constant (pK), one must find the volume at the half-equivalence point, that is where half the amount of titrant has been added to form the next compound (here, sodium hydrogen oxalate, then disodium oxalate). Halfway between each equivalence point, at 7.5 mL and 22.5 mL, the pH observed was about 1.5 and 4, giving the pK.
In weak monoprotic acids, the point halfway between the beginning of the curve (before any titrant has been added) and the equivalence point is significant: at that point, the concentrations of the two species (the acid and conjugate base) are equal. Therefore, the Henderson-Hasselbalch equation can be solved in this manner:
Therefore, one can easily find the pK of the weak monoprotic acid by finding the pH of the point halfway between the beginning of the curve and the equivalence point, and solving the simplified equation. In the case of the sample curve, the acid dissociation constant K = 10 would be approximately 1.78×10 from visual inspection (the actual K is 1.7×10)
For polyprotic acids, calculating the acid dissociation constants is only marginally more difficult: the first acid dissociation constant can be calculated the same way as it would be calculated in a monoprotic acid. The pK of the second acid dissociation constant, however, is the pH at the point halfway between the first equivalence point and the second equivalence point (and so on for acids that release more than two protons, such as phosphoric acid). | 0 | Chromatography + Titration + pH indicators |
There are two distinct uniform colorings of a trihexagonal tiling. Naming the colors by indices on the 4 faces around a vertex (3.6.3.6): 1212, 1232. The second is called a cantic hexagonal tiling, h{6,3}, with two colors of triangles, existing in p3m1 (*333) symmetry. | 1 | Crystallography |
Calcium in a blood sample should be estimated when required medically. Calcium should be precipitated out of 0.1 mL of the blood sample serum as calcium oxalate. After that, the decomposition of the calcium oxalate should occur by heat. Then, the sample should be estimated colorimetrically by o-cresolphthalein complexone. The required liquid complexone is made by dissolving 10 mg o-cresolphthalein complexone in 50 mL alkaline borate, and then 50 mL of 0.05 N HCl are added to make the solution's pH 8.5. This method for calcium determination is efficient and effective, requiring a minimal amount of blood serum sample and a reasonable amount of time. | 0 | Chromatography + Titration + pH indicators |
The allows for visualization of two misoriented materials and their interface such as crystal twins or grain boundaries. The user interface provides three views: two smaller views, each depicting one unit cell of selected material and orientation, and a larger view depicting an appropriate interface of the two structures. The interface can be visualized in four modes:
* 3D model of both unit cells,
* wire-frame model of both unit cells,
* cross section of the interface,
* bulk representation (up to several hundred atoms).
All three views in the user interface are functionally interconnected. If the content of one view is rotated by the user, the other views follow. If a crystallographic plane or direction is selected in one view, it is shown in other views and corresponding crystallographic indices are stated. The tool also allows to highlight coincident site lattice or calculate the list of planes and directions which are parallel or nearly parallel in the two misoriented materials. | 1 | Crystallography |
Mathematically, the points of the diamond cubic structure can be given coordinates as a subset of a three-dimensional integer lattice by using a cubic unit cell four units across. With these coordinates, the points of the structure have coordinates satisfying the equations
There are eight points (modulo 4) that satisfy these conditions:
All of the other points in the structure may be obtained by adding multiples of four to the coordinates of these eight points. Adjacent points in this structure are at distance apart in the integer lattice; the edges of the diamond structure lie along the body diagonals of the integer grid cubes. This structure may be scaled to a cubical unit cell that is some number of units across by multiplying all coordinates by .
Alternatively, each point of the diamond cubic structure may be given by four-dimensional integer coordinates whose sum is either zero or one. Two points are adjacent in the diamond structure if and only if their four-dimensional coordinates differ by one in a single coordinate. The total difference in coordinate values between any two points (their four-dimensional Manhattan distance) gives the number of edges in the shortest path between them in the diamond structure. The four nearest neighbors of each point may be obtained, in this coordinate system, by adding one to each of the four coordinates, or by subtracting one from each of the four coordinates, accordingly as the coordinate sum is zero or one. These four-dimensional coordinates may be transformed into three-dimensional coordinates by the formula
Because the diamond structure forms a distance-preserving subset of the four-dimensional integer lattice, it is a partial cube.
Yet another coordinatization of the diamond cubic involves the removal of some of the edges from a three-dimensional grid graph. In this coordinatization, which has a distorted geometry from the standard diamond cubic structure but has the same topological structure, the vertices of the diamond cubic are represented by all possible 3d grid points and the edges of the diamond cubic are represented by a subset of the 3d grid edges.
The diamond cubic is sometimes called the "diamond lattice" but it is not, mathematically, a lattice: there is no translational symmetry that takes the point (0,0,0) into the point (3,3,3), for instance. However, it is still a highly symmetric structure: any incident pair of a vertex and edge can be transformed into any other incident pair by a congruence of Euclidean space. Moreover, the diamond crystal as a network in space has a strong isotropic property. Namely, for any two vertices of the crystal net, and for any ordering of the edges adjacent to and any ordering of the edges adjacent to , there is a net-preserving congruence taking to and each -edge to the similarly ordered -edge. Another (hypothetical) crystal with this property is the Laves graph (also called the K crystal, (10,3)-a, or the diamond twin). | 1 | Crystallography |
The temperature of the system can be estimated by use of the Equipartition Theorem, with three degrees of freedom for each ion. Since ionic velocities are generally recorded at each step in the numerical simulation, the average kinetic energy of each ion is easy to calculate. There exist schemes which attempt to control the temperature of the simulation by, e.g. enforcing each ion to have exactly the kinetic energy predicted by the Equipartition Theorem (Berendsen thermostat) or by allowing the system to exchange energy and momentum with a (more massive) fictitious enclosing system (Nose-Hoover thermostat).
The net force on each ion is generally calculated explicitly at each numerical step. From this, the stress tensor of the system can be calculated and usually is calculated by the numerical package. By varying the convergence criteria, one can either seek a lowest energy structure or a structure that produces a desired stress tensor. Thus, high pressures can be simulated as easily as ambient pressures. | 1 | Crystallography |
A further occurrence of ordered columnar arrangement on the macroscale are foam structures confined inside a glass tube. They can be realised experimentally with equal-sized soap bubbles inside a glass tube, produced by blowing air of constant gas flow through a needle dipped in a surfactant solution. By putting the resulting foam column under forced drainage (feeding it with surfactant solution from the top), the foam can be adjusted to either a dry (bubbles shaped as polyhedrons) or wet (spherical bubbles) structure.
Due to this simple experimental set-up, many columnar structures have been discovered and investigated in the context of foams with experiments as well as simulation. Many simulations have been carried out using the Surface Evolver to investigate dry structure or the hard sphere model for the wet limit where the bubbles are spherical.
In the zigzag structure the bubbles are stacked on top of each other in a continuous w-shape. For this particular structure a moving interface with increasing liquid fraction was reported by Hutzler et al. in 1997. This included an unexpected 180° twist interface, whose explanation is still lacking.
The first experimental observation of a line-slip structure was discovered by Winkelmann et al. in a system of bubbles.
Further discovered structures include complex structures with internal spheres/foam cells. Some dry foam structures with interior cells were found to consist of a chain of pentagonal dodecahedra or Kelvin cells in the centre of the tube. For many more arrangements of this type, it was observed that the outside bubble layer is ordered, with each internal layer resembling a different, simpler columnar structure by using X-ray tomography. | 1 | Crystallography |
*[http://www-ssrl.slac.stanford.edu/absorb.html The SSRL Absorption Package] —
*[http://www.gwyndafevans.co.uk/chooch.html CHOOCH] —
*[http://www.hwi.buffalo.edu/SnB/ Shake-and-Bake] (SnB) —
*[http://shelx.uni-ac.gwdg.de/SHELX/ SHELX] — | 1 | Crystallography |
Ion suppression in LC-MS and LC-MS/MS refers to reduced detector response, or signal:noise as a manifested effect of competition for ionisation efficiency in the ionisation source, between the analyte(s) of interest and other endogenous or exogenous (e.g. plasticisers extracted from plastic tubes, mobile phase additives) species which have not been removed from the sample matrix during sample preparation. Ion suppression is not strictly a problem unless interfering compounds elute at the same time as the analyte of interest. In cases where ion suppressing species do co-elute with an analyte, the effects on the important analytical parameters including precision, accuracy and limit of detection (analytical sensitivity) can be extensive, severely limiting the validity of an assay's results. | 0 | Chromatography + Titration + pH indicators |
In crystallography, polymorphism describes the phenomenon where a compound or element can crystallize into more than one crystal structure. The preceding definition has evolved over many years and is still under discussion today. Discussion of the defining characteristics of polymorphism involves distinguishing among types of transitions and structural changes occurring in polymorphism versus those in other phenomena.
It is also useful to note that materials with two polymorphic phases can be called dimorphic, those with three polymorphic phases, trimorphic, etc. | 1 | Crystallography |
Beyond the most common perovskite symmetries (cubic, tetragonal, orthorhombic), a more precise determination leads to a total of 23 different structure types that can be found. These 23 structure can be categorized into 4 different so-called tilt systems that are denoted by their respective Glazer notation.
The notation consists of a letter a/b/c, which describes the rotation around a Cartesian axis and a superscript +/—/0 to denote the rotation with respect to the adjacent layer. A “+” denotes that the rotation of two adjacent layers points in the same direction, whereas a “—” denotes that adjacent layers are rotated in opposite directions. Common examples are aaa, aaa and aaa which are visualized here. | 1 | Crystallography |
Separation by capillary electrophoresis can be detected by several detection devices. The majority of commercial systems use UV or UV-Vis absorbance as their primary mode of detection. In these systems, a section of the capillary itself is used as the detection cell. The use of on-tube detection enables detection of separated analytes with no loss of resolution. In general, capillaries used in capillary electrophoresis are coated with a polymer (frequently polyimide or Teflon) for increased flexibility. The portion of the capillary used for UV detection, however, must be optically transparent. For polyimide-coated capillaries, a segment of the coating is typically burned or scraped off to provide a bare window several millimeters long. This bare section of capillary can break easily, and capillaries with transparent coatings are available to increase the stability of the cell window. The path length of the detection cell in capillary electrophoresis (~ 50 micrometers) is far less than that of a traditional UV cell (~ 1 cm). According to the Beer-Lambert law, the sensitivity of the detector is proportional to the path length of the cell. To improve the sensitivity, the path length can be increased, though this results in a loss of resolution. The capillary tube itself can be expanded at the detection point, creating a "bubble cell" with a longer path length or additional tubing can be added at the detection point as shown in figure 2. Both of these methods, however, will decrease the resolution of the separation. This decrease is almost unnoticeable if a smooth aneurysm is produced in the wall of a capillary by heating and pressurization, as plug flow can be preserved. This invention by Gary Gordon, US Patent 5061361, typically triples the absorbance path length. When used with a UV absorbance detector, the wider cross-section of the analyte in the cell allows for an illuminating beam twice as large, which reduces shot noise by a factor of two. Together these two factors increase the sensitivity of Agilent Technologiess Bubble Cell CE Detector six times over that of one using a straight capillary. This cell and its manufacture are described on page 62 of the June 1995 issue of the Hewlett-Packard Journal'.
Fluorescence detection can also be used in capillary electrophoresis for samples that naturally fluoresce or are chemically modified to contain fluorescent tags. This mode of detection offers high sensitivity and improved selectivity for these samples, but cannot be utilized for samples that do not fluoresce. Numerous labeling strategies are used to create fluorescent derivatives or conjugates of non-fluorescent molecules, including proteins and DNA. The set-up for fluorescence detection in a capillary electrophoresis system can be complicated. The method requires that the light beam be focused on the capillary, which can be difficult for many light sources. Laser-induced fluorescence has been used in CE systems with detection limits as low as 10 to 10 mol. The sensitivity of the technique is attributed to the high intensity of the incident light and the ability to accurately focus the light on the capillary. Multi-color fluorescence detection can be achieved by including multiple dichroic mirrors and bandpass filters to separate the fluorescence emission amongst multiple detectors (e.g., photomultiplier tubes), or by using a prism or grating to project spectrally resolved fluorescence emission onto a position-sensitive detector such as a CCD array. CE systems with 4- and 5-color LIF detection systems are used routinely for capillary DNA sequencing and genotyping ("DNA fingerprinting") applications.
In order to obtain the identity of sample components, capillary electrophoresis can be directly coupled with mass spectrometers or surface-enhanced Raman spectroscopy (SERS). In most systems, the capillary outlet is introduced into an ion source that utilizes electrospray ionization (ESI). The resulting ions are then analyzed by the mass spectrometer. This setup requires volatile buffer solutions, which will affect the range of separation modes that can be employed and the degree of resolution that can be achieved.
The measurement and analysis are mostly done with a specialized.
For CE-SERS, capillary electrophoresis eluants can be deposited onto a SERS-active substrate. Analyte retention times can be translated into spatial distance by moving the SERS-active substrate at a constant rate during capillary electrophoresis. This allows the subsequent spectroscopic technique to be applied to specific eluants for identification with high sensitivity. SERS-active substrates can be chosen that do not interfere with the spectrum of the analytes. | 0 | Chromatography + Titration + pH indicators |
A deformation twin embryo forms in BCC metal by accumulating stacking faults, with a variant selection governed by the local stress state. Variation of the stress field close to twins inferred from HR-EBSD experimental and crystal plasticity finite element ([https://damask.mpie.de/index.html CPFE]) simulation data indicated that twins nucleate on sites with maximum strain energy density and twin resolved shear stress; thus, reducing the total elastic energy after formation. This relaxation depends on the twin thickness and is a deciding factor in the spacing between twins. Experimental and three-dimensional analysis has focussed on the (stored) strain energy density measured along a path. This highly localised stress field can provide a sufficient driving force for concurrent twin nucleation and inter/intra-granular crack nucleation.
Deformation twin growth can be perceived as a two-step process of i) thickening that is mediated by the interaction between the residual and mobile twin partials at the coherent twin-parent interface, and ii) dislocation mobility along the twin shear direction. The twin propagates when the homogeneous shear stress reaches a critical value, and a twin-parent interface advances inside the parent grain [240]. The propagating deformation twin generates a stress field due to its confinement by the surrounding parent crystal, and deformation twins develop a 3D oblate spheroid shape (which appears in 2D sections as a bi-convex lens) with a mixed coherent and non-coherent interface (Figure b).
Kannan et al. found, using in-situ ultra-high-speed optical imaging, that twin nucleation in single-crystal magnesium is stress-driven accompanied by instantaneous propagation at a speed of 1 km/s (initially) that prioritises volume lateral thickening over forward propagation, past a critical width where growth is then become faster along the shear direction. Barnett also indicated that growth is due to twin tip extension. Furthermore, elastic simulations of the local stress field surrounding the ellipsoidal twin tip find that the field can be described using its lens angle () and that the stress field magnitude increases with twin thickness.
In practice, plastic accommodation occurs in the parent crystal; thus, it also depends on the material’s yield stress, the anisotropic elastic stiffness of the parent crystal lattice, and the deformation twinning shear magnitude. This can also be accompanied by long-range diffusion of elements and elemental segregation (e.g., Cr and Co in single crystal Ni-based superalloy MD2), which occurs at the twin boundary to facilitate twin growth by lowering the critical stacking fault energy. A linear variation has been observed between twin thickness, stacking fault energy and grain size, and to a lesser degree, the stress state of the twinning grain (Schmid Factor). The twin thickness saturated once a critical residual dislocations’ density reached the coherent twin-parent crystal boundary.
Significant attention has been paid to the crystallography, morphology and macro mechanical effects of deformation twinning. Although the criterion for deformation twin growth is not entirely understood, it is a tip-controlled phenomenon linked to the interaction between the residual and mobile twin partials at the twin interface; thermodynamically, this involves the elastic energy of the strained lattice, the interface and volume free-energy of the twin, and the dissipated energy of the growth mechanism. To fully understand the interactions between microstructure (i.e., grain size, texture), temperature and strain rate on deformation twinning, it is crucial to characterise the (high) local stress and strain field associated with twin thickening and propagation. This is especially important for materials where cleavage fracture can be initiated by twinning (e.g., iron-silicon, the ferrite phase of age-hardened duplex stainless-steel, and single-crystal magnesium) as a stress-relieving mechanism.
Early studies of deformation twins arrested within grains of niobium and iron visualised the highly local strain concentration at the twin tip using an etch-pit procedure. More recently, high-resolution electron backscatter diffraction (HR-EBSD) has been used to investigate the strain singularity ahead of a twin tip in hexagonal close-packed (HCP) zirconium alloy. A deformation twin in commercial purity titanium was characterised similarly and then quantified using a local Schmid factor (LSF) at the twin tip, as described in equation below.
where σ is the stress tensor, S is the Schmid tensor, P is its symmetric part, d is the shear direction and n is the shear plane normal for ith slip system. The authors concluded that conditions at the twin tip control thickening and propagation in a manner analogous to the operation of dislocation sources ahead of a crack-tip. In the analysis, a broad region of high LSF ahead of the twin tip favoured propagation, whereas a narrow region of high LSF promoted thickening. Since then, it has been argued that the LSF firmly controls the twin variant selection, as twinning has strong polarity.
The LSF novelty – compared to other criteria to describe conditions at the twin – lies in combining a geometrical criterion with the deformation field in the parent grain to provide an approximate indication of the local twin mode (i.e., thickening or propagation). However, the LSF analysis does not take advantage of the available full-field data, relies on global information on the applied stress, and does not consider the energy balance that drives twin growth. There have been few in-situ experiments to quantify the strain field ahead of a propagating deformation twin. Such observations might validate geometrical or hybrid geometrical-energy-based criteria for growth. Nanoscale testing (i.e., transmission electron microscopy) may not represent the behaviour in bulk samples due to plasticity starvation, i.e., large surface area to volume ratio, so a suitable analysis method is needed.
Lloyd described the stress concentration field ahead of the twin tip using a two-dimensional dislocation-based model within a single magnesium grain. Wang and Li, who considered microscopic phase-field (MPF) models of cracks, noted that the stress fields were similar for dislocations, deformation twinning and martensitic transformations, with differences only in the traction of the created surface, i.e., there is 100% traction recovery for dislocations and a traction-free surface for a crack. They highlighted that the stress field singularity regulates the advancement of the crack-tip and dislocations. This stress concentration can be characterised using a path-independent line integral, as shown by Eshelby for dislocations considering the contribution from the surface traction and ellipsoidal inclusions, and Rice for cracks and stress concentrations with traction-free surfaces. Furthermore, Venables noted that the oblate spheroid shape of the twin tip is the ideal example of an ellipsoid inclusion or a notch. | 1 | Crystallography |
A post column oxidation-reduction reactor is a chemical reactor that performs derivatization to improve the measurement of organic molecules. It is used in gas chromatography (GC), after the column, and before a flame ionization detector (FID), to make the detector response uniform for all organic molecules.
The reactor converts the carbon atoms of organic molecules in GC column effluents into methane before reaching the FID. The resulting detector response is uniform on a per-carbon basis and avoids the need for response factors and calibration standards for each molecule. It can improve the response of the FID to many molecules with poor/low response including carbon monoxide (CO), carbon dioxide (CO), hydrogen cyanide (HCN), formamide (CHNO), formaldehyde (CHO) and formic acid (CHO), because these molecules are converted to methane. | 0 | Chromatography + Titration + pH indicators |
A monolithic HPLC column, or monolithic column, is a column used in high-performance liquid chromatography (HPLC). The internal structure of the monolithic column is created in such a way that many channels form inside the column. The material inside the column which separates the channels can be porous and functionalized. In contrast, most HPLC configurations use particulate packed columns; in these configurations, tiny beads of an inert substance, typically a modified silica, are used inside the column. Monolithic columns can be broken down into two categories, silica-based and polymer-based monoliths. Silica-based monoliths are known for their efficiency in separating smaller molecules while, polymer-based are known for separating large protein molecules. | 0 | Chromatography + Titration + pH indicators |
Kennedy was born on November 11, 1962, in Sault Ste. Marie, Michigan. He earned a Bachelor of Science degree in chemistry at the University of Florida in 1984 and a Ph.D. from the University of North Carolina-Chapel Hill (UNC) in 1988 while working under James Jorgenson. He was an NSF post-doctoral fellow at UNC from 1989-1991 with R. Mark Wightman. | 0 | Chromatography + Titration + pH indicators |
Zeta potential titrations are titrations in which the completion is monitored by the zeta potential, rather than by an indicator, in order to characterize heterogeneous systems, such as colloids. One of the uses is to determine the iso-electric point when surface charge becomes zero, achieved by changing the pH or adding surfactant. Another use is to determine the optimum dose for flocculation or stabilization. | 0 | Chromatography + Titration + pH indicators |
Desalting is used to remove salts from protein solutions, phenol or unincorporated nucleotides from nucleic acids or excess crosslinking or labeling reagents from conjugated proteins. Buffer exchange is used to transfer a protein solution into a buffer system appropriate for downstream applications such as ion exchange, electrophoresis or affinity chromatography. | 0 | Chromatography + Titration + pH indicators |
The French police officer Alphonse Bertillon was the first to apply the anthropological technique of anthropometry to law enforcement, thereby creating an identification system based on physical measurements. Before that time, criminals could be identified only by name or photograph. Dissatisfied with the ad hoc methods used to identify captured criminals in France in the 1870s, he began his work on developing a reliable system of anthropometrics for human classification.
Bertillon created many other forensics techniques, including forensic document examination, the use of galvanoplastic compounds to preserve footprints, ballistics, and the dynamometer, used to determine the degree of force used in breaking and entering. Although his central methods were soon to be supplanted by fingerprinting, "his other contributions like the mug shot and the systematization of crime-scene photography remain in place to this day." | 0 | Chromatography + Titration + pH indicators |
The mobile phase is composed primarily of supercritical carbon dioxide, but since CO on its own is too non-polar to effectively elute many analytes, cosolvents are added to modify the mobile phase polarity. Cosolvents are typically simple alcohols like methanol, ethanol, or isopropyl alcohol. Other solvents such as acetonitrile, chloroform, or ethyl acetate can be used as modifiers. For food-grade materials, the selected cosolvent is often ethanol or ethyl acetate, both of which are generally recognized as safe (GRAS). The solvent limitations are system and column based. | 0 | Chromatography + Titration + pH indicators |
The FCC lattice is a Bravais lattice, and its Fourier transform is a body-centered cubic lattice. However to obtain without this shortcut, consider an FCC crystal with one atom at each lattice point as a primitive or simple cubic with a basis of 4 atoms, at the origin and at the three adjacent face centers, , and . Equation () becomes
with the result
The most intense diffraction peak from a material that crystallizes in the FCC structure is typically the (111). Films of FCC materials like gold tend to grow in a (111) orientation with a triangular surface symmetry. A zero diffracted intensity for a group of diffracted beams (here, of mixed parity) is called a systematic absence. | 1 | Crystallography |