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In analytical chemistry, potentiometric titration is a technique similar to direct titration of a redox reaction. It is a useful means of characterizing an acid. No indicator is used; instead the electric potential is measured across the analyte, typically an electrolyte solution. To do this, two electrodes are used, an indicator electrode (the glass electrode and metal ion indicator electrode) and a reference electrode. Reference electrodes generally used are hydrogen electrodes, calomel electrodes, and silver chloride electrodes. The indicator electrode forms an electrochemical half-cell with the interested ions in the test solution. The reference electrode forms the other half-cell.
The overall electric potential is calculated as
is the potential drop over the test solution between the two electrodes. is recorded at intervals as the titrant is added. A graph of potential against volume added can be drawn and the end point of the reaction is halfway between the jump in voltage.
depends on the concentration of the interested ions with which the indicator electrode is in contact. For example, the electrode reaction may be
As the concentration of changes, the changes correspondingly. Thus the potentiometric titration involve measurement of with the addition of titrant. Types of potentiometric titration include acid–base titration (total alkalinity and total acidity), redox titration (HI/HY and cerate), precipitation titration (halides), and complexometric titration (free EDTA and Antical #5). | 0 | Chromatography + Titration + pH indicators |
A screw displacement (also screw operation or rotary translation) is the composition of a rotation by an angle φ about an axis (called the screw axis) with a translation by a distance d along this axis. A positive rotation direction usually means one that corresponds to the translation direction by the right-hand rule. This means that if the rotation is clockwise, the displacement is away from the viewer. Except for φ = 180°, we have to distinguish a screw displacement from its mirror image. Unlike for rotations, a righthand and lefthand screw operation generate different groups.
The combination of a rotation about an axis and a translation in a direction perpendicular to that axis is a rotation about a parallel axis. However, a screw operation with a nonzero translation vector along the axis cannot be reduced like that. Thus the effect of a rotation combined with any translation is a screw operation in the general sense, with as special cases a pure translation, a pure rotation and the identity. Together these are all the direct isometries in 3D.
In crystallography, a screw axis symmetry is a combination of rotation about an axis and a translation parallel to that axis which leaves a crystal unchanged. If φ = 360°/n for some positive integer n, then screw axis symmetry implies translational symmetry with a translation vector which is n times that of the screw displacement.
Applicable for space groups is a rotation by 360°/n about an axis, combined with a translation along the axis by a multiple of the distance of the translational symmetry, divided by n. This multiple is indicated by a subscript. So, 6 is a rotation of 60° combined with a translation of 1/2 of the lattice vector, implying that there is also 3-fold rotational symmetry about this axis. The possibilities are 2, 3, 4, 4, 6, 6, and 6, and the enantiomorphous 3, 4, 6, and 6.
Considering a screw axis n, if g is the greatest common divisor of n and m, then there is also a g-fold rotation axis. When n/g screw operations have been performed, the displacement will be m/g, which since it is a whole number means one has moved to an equivalent point in the lattice, while carrying out a rotation by 360°/g. So 4, 6 and 6 create two-fold rotation axes, while 6 creates a three-fold axis.
A non-discrete screw axis isometry group contains all combinations of a rotation about some axis and a proportional translation along the axis (in rifling, the constant of proportionality is called the twist rate); in general this is combined with k-fold rotational isometries about the same axis (k ≥ 1); the set of images of a point under the isometries is a k-fold helix; in addition there may be a 2-fold rotation about a perpendicularly intersecting axis, and hence a k-fold helix of such axes. | 1 | Crystallography |
"Litigation science" describes analysis or data developed or produced expressly for use in a trial versus those produced in the course of independent research. This distinction was made by the U.S. 9th Circuit Court of Appeals when evaluating the admissibility of experts.
This uses demonstrative evidence, which is evidence created in preparation of trial by attorneys or paralegals. | 0 | Chromatography + Titration + pH indicators |
Many alloys of elements that resemble each other chemically will form a structure at higher temperatures where the two elements occupy similar positions in the lattice at random. At lower temperatures ordering may occur where crystallographic positions are no longer equivalent because one element preferentially occupies one site and the other the other. This partial ordering process may lower the translation symmetry and result in a different, larger unit cell. | 1 | Crystallography |
Liquid chromatography-mass spectrometry (LC/MS) couples high resolution chromatographic separation with MS detection. As the system adopts the high separation of HPLC, analytes which are in the liquid mobile phase are often ionized by various soft ionization methods including atmospheric pressure chemical ionization (APCI), electrospray ionization (ESI) or matrix-assisted laser desorption/ionization (MALDI), which attains the gas phase ionization required for the coupling with MS. These ionization methods allow the analysis of a wider range of biological molecules, including those with larger masses, thermally unstable or nonvolatile compounds where GC-MS is typically incapable of analyzing.
LC-MS provides high selectivity as unresolved peaks can be isolated by selecting a specific mass. Furthermore, better identification is also attained by mass spectra and the user does not have to rely solely on the retention time of analytes. As a result, molecular mass and structural information as well as quantitative data can all be obtained via LC-MS. LC-MS can therefore be applied to various fields, such as impurity identification and profiling in drug development and pharmaceutical manufacturing, since LC provides efficient separation of impurities and MS provides structural characterization for impurity profiling.
Common solvents used in normal or reversed phase LC such as water, acetonitrile, and methanol are all compatible with ESI, yet a LC grade solvent may not be suitable for MS. Furthermore, buffers containing inorganic ions should be avoided as they may contaminate the ion source. Nonetheless, the problem can be resolved by 2D LC-MS, as well as other various issues including analyte coelution and UV detection responses. | 0 | Chromatography + Titration + pH indicators |
In a common FPLC strategy, a resin is chosen that the protein of interest will bind to by a charge interaction while in buffer A (the running buffer) but become dissociated and return to solution in buffer B (the elution buffer). A mixture containing one or more proteins of interest is dissolved in 100% buffer A and pumped into the column. The proteins of interest bind to the resin while other components are carried out in the buffer. The total flow rate of the buffer is kept constant; however, the proportion of buffer B (the "elution" buffer) is gradually increased from 0% to 100% according to a programmed change in concentration (the "gradient"). At some point during this process each of the bound proteins dissociates and appears in the eluant. The eluant passes through two detectors which measure salt concentration (by conductivity) and protein concentration (by absorption of ultraviolet light at a wavelength of 280 nm). As each protein is eluted, it appears in the eluant as a "peak" in protein concentration, and can be collected for further use. | 0 | Chromatography + Titration + pH indicators |
Although the most common perovskite compounds contain oxygen, there are a few perovskite compounds that form without oxygen. Fluoride perovskites such as NaMgF are well known. A large family of metallic perovskite compounds can be represented by RTM (R: rare-earth or other relatively large ion, T: transition metal ion and M: light metalloids). The metalloids occupy the octahedrally coordinated "B" sites in these compounds. RPdB, RRhB and CeRuC are examples. MgCNi is a metallic perovskite compound and has received lot of attention because of its superconducting properties. An even more exotic type of perovskite is represented by the mixed oxide-aurides of Cs and Rb, such as CsAuO, which contain large alkali cations in the traditional "anion" sites, bonded to O and Au anions. | 1 | Crystallography |
The Laves graph has been suggested as an allotrope of carbon, analogous to the more common graphene and graphite carbon structure which also have three bonds per atom at 120° angles. In graphene, adjacent atoms have the same bonding planes as each other, whereas in the Laves graph structure the bonding planes of adjacent atoms are twisted by an angle of approximately 70.5° around the line of the bond. However, this hypothetical carbon allotrope turns out to be unstable.
The Laves graph may also give a crystal structure for boron, one which computations predict should be stable. Other chemicals that may form this structure include SrSi (from which the "srs net" name derives) and elemental nitrogen, as well as certain metal–organic frameworks and cyclic hydrocarbons.
The electronic band structure for the tight-binding model of the Laves graph has been studied, showing the existence of Dirac and Weyl points in this structure. | 1 | Crystallography |
Twinning is a form of symmetrical intergrowth between two or more adjacent crystals of the same mineral. It differs from the ordinary random intergrowth of mineral grains in a mineral deposit, because the relative orientations of the two crystal segments show a fixed relationship that is characteristic of the mineral structure. The relationship is defined by a symmetry operation called a twin operation.
The twin operation is not one of the normal symmetry operations of the untwinned crystal structure. For example, the twin operation may be reflection across a plane that is not a symmetry plane of the single crystal.
On the microscopic level, the twin boundary is characterized by a set of atomic positions in the crystal lattice that are shared between the two orientations. These shared lattice points give the junction between the crystal segments much greater strength than that between randomly oriented grains, so that the twinned crystals do not easily break apart. | 1 | Crystallography |
When used as an indicator in an EDTA titration, the characteristic blue end-point is reached when sufficient EDTA is added and the metal ions bound to the indicator are chelated by EDTA, leaving the free indicator molecule.
Eriochrome Black T has also been used to detect the presence of rare earth metals. | 0 | Chromatography + Titration + pH indicators |
In crystal growth, a Knudsen cell is an effusion evaporator source for relatively low partial pressure elementary sources (e.g. Ga, Al, Hg, As). Because it is easy to control the temperature of the evaporating material in Knudsen cells, they are commonly used in molecular-beam epitaxy. | 1 | Crystallography |
A column is prepared by packing a solid adsorbent into a cylindrical glass or plastic tube. The size will depend on the amount of compound being isolated. The base of the tube contains a filter, either a cotton or glass wool plug, or glass frit to hold the solid phase in place. A solvent reservoir may be attached at the top of the column.
Two methods are generally used to prepare a column: the dry method and the wet method. For the dry method, the column is first filled with dry stationary phase powder, followed by the addition of mobile phase, which is flushed through the column until it is completely wet, and from this point is never allowed to run dry. For the wet method, a slurry is prepared of the eluent with the stationary phase powder and then carefully poured into the column. The top of the silica should be flat, and the top of the silica can be protected by a layer of sand. Eluent is slowly passed through the column to advance the organic material.
The individual components are retained by the stationary phase differently and separate from each other while they are running at different speeds through the column with the eluent. At the end of the column they elute one at a time. During the entire chromatography process the eluent is collected in a series of fractions. Fractions can be collected automatically by means of fraction collectors. The productivity of chromatography can be increased by running several columns at a time. In this case multi stream collectors are used. The composition of the eluent flow can be monitored and each fraction is analyzed for dissolved compounds, e.g. by analytical chromatography, UV absorption spectra, or fluorescence. Colored compounds (or fluorescent compounds with the aid of a UV lamp) can be seen through the glass wall as moving bands. | 0 | Chromatography + Titration + pH indicators |
In crystallography, interstitial sites, holes or voids are the empty space that exists between the packing of atoms (spheres) in the crystal structure.
The holes are easy to see if you try to pack circles together; no matter how close you get them or how you arrange them, you will have empty space in between. The same is true in a unit cell; no matter how the atoms are arranged, there will be interstitial sites present between the atoms. These sites or holes can be filled with other atoms (interstitial defect). The picture with packed circles is only a 2D representation. In a crystal lattice, the atoms (spheres) would be packed in a 3D arrangement. This results in different shaped interstitial sites depending on the arrangement of the atoms in the lattice. | 1 | Crystallography |
Plane-wave topography can be made to extract an additional wealth of information from a sample by recording not just one image, but an entire sequence of topographs all along the sample's rocking curve. By following the diffracted intensity in one pixel across the entire sequence of images, local rocking curves from very small areas of sample surface can be reconstructed.
Although the required post-processing and numerical analysis is sometimes moderately demanding, the effort is often compensated by very comprehensive information on the sample's local properties. Quantities that become quantitatively measurable in this way include local scattering power, local lattice tilts (crystallite misorientation), and local lattice quality and perfection. Spatial resolution is, in many cases, essentially given by the detector pixel size.
The technique of sequential topography, in combination with appropriate data analysis methods also called rocking curve imaging, constitutes a method of microdiffraction imaging, i.e. a combination of X-ray imaging with X-ray diffractometry.
Literature: | 1 | Crystallography |
Amperometric titration refers to a class of titrations in which the equivalence point is determined through measurement of the electric current produced by the titration reaction. It is a form of quantitative analysis. | 0 | Chromatography + Titration + pH indicators |
The basic driving force for protein crystallization is to optimize the number of bonds one can form with another protein through intermolecular interactions. These interactions depend on electron densities of molecules and the protein side chains that change as a function of pH. The tertiary and quaternary structure of proteins are determined by intermolecular interactions between the amino acids’ side groups, in which the hydrophilic groups are usually facing outwards to the solution to form a hydration shell to the solvent (water). As the pH changes, the charge on these polar side group also change with respect to the solution pH and the protein's pKa. Hence, the choice of pH is essential either to promote the formation of crystals where the bonding between molecules to each other is more favorable than with water molecules. pH is one of the most powerful manipulations that one can assign for the optimal crystallization condition. | 1 | Crystallography |
Argentation chromatography is chromatography using a stationary phase that contains silver salts. Silver-containing stationary phases are well suited for separating organic compounds on the basis of the number and type of alkene groups. The technique is employed for gas chromatography and various types of liquid chromatography, including thin layer chromatography. Analytes containing alkene groups elute more slowly than the analogous compounds lacking alkenes. Separations are also sensitive to the type of alkene. The technique is especially useful in the analysis of fats and fatty acids, which are well known to exist in both saturated and unsaturated (alkene-containing) forms. For example, trans fats, undesirable contaminants in ultra-processed foods, are quantified by argentation chromatography. | 0 | Chromatography + Titration + pH indicators |
Coupled substitution is the geological process by which two elements simultaneous substitute into a crystal in order to maintain overall electrical neutrality and keep the charge constant. In forming a solid solution series, ionic size is more important than ionic charge, as this can be compensated for elsewhere in the structure. | 1 | Crystallography |
In Cartesian coordinates the 3 basis vectors are represented by a cell tensor :
The volume of the unit cell, , is given by the determinant of the cell tensor:
For the special case of a cubic, tetragonal, or orthorhombic cell, the matrix is diagonal, and we have that: | 1 | Crystallography |
Cibacron Blue F3GA, Procion Blue HB, or Reactive blue 2 is a purinergic receptor antagonist, such as P2Y purinoceptor, and also an ATP receptor channels antagonist. It has a formula of CHClNOS and a molecular weight of 774.2 g/mol. Cibacron blue is soluble in water and DMSO, however insoluble in ethanol. In water, saturated concentration is reached at 12.92 mM with the help of sonication. Cibacron Blue F3GA has a wide specificity for nucleotide-binding proteins or just a stereoselectivity electrostatic binding. It can be used to purify interferons, dehydrogenases, kinases, and serum albumin. For example, interferon purification from human gingival fibroblast extract using Cibacron Blue F3G-A on poly(2-hydroxyethyl methacrylate), the supporting matrix, in the form of cryogels. It has shown 97.6% purity of interferon. | 0 | Chromatography + Titration + pH indicators |
In crystallography, a Wyckoff position is any point in a set of points whose site symmetry groups (see below) are all conjugate subgroups one of another. Crystallography tables give the Wyckoff positions for different space groups. | 1 | Crystallography |
There are two types of twinning that can occur during growth, accidental and ones where the twinned structure has lower energy.
In accidental growth twinning an atom joins a crystal face in a less than ideal position, forming a seed for growth of a twin. The original crystal and its twin then grow together and closely resemble each other. This is characteristic enough of certain minerals to suggest that it is thermodynamically or kinetically favored under conditions of rapid growth.
Different from these are twins found in nanoparticles such as the image here, these fivefold or decahedral nanoparticles being one of the most common. These cyclic twins occur as they are lower in energy at small sizes. For the five-fold case shown, there is a disclination along the common axis which leads to an additional strain energy. Balancing this there is a reduction in the surface free energy, in large part due to more (111) surface facets. In small nanoparticles the decahedral and a more complicated icosahedral structure (with twenty units) are lower energy, but at larger energies single crystals become lower energy. However, they do not have to transform into single crystals and can grow very large, and are known as fivelings, documented as early as 1831 by Gustav Rose; further drawings are available in the Atlas der Kristallformen, and see also the article on fiveling<nowiki/>s. | 1 | Crystallography |
Meyer sets include
*The points of any lattice
*The vertices of any rhombic Penrose tiling
*The Minkowski sum of another Meyer set with any nonempty finite set
*Any relatively dense subset of another Meyer set | 1 | Crystallography |
Tashiro's indicator is a pH indicator (pH value: 4.4–6.2), mixed indicator composed of a solution of methylene blue (0.1%) and methyl red (0.03%) in ethanol or in methanol.
It can be used e.g. for the titration of ammonia in Kjeldahl analysis. | 0 | Chromatography + Titration + pH indicators |
HPLC has many applications in both laboratory and clinical science. It is a common technique used in pharmaceutical development, as it is a dependable way to obtain and ensure product purity. While HPLC can produce extremely high quality (pure) products, it is not always the primary method used in the production of bulk drug materials. According to the European pharmacopoeia, HPLC is used in only 15.5% of syntheses. However, it plays a role in 44% of syntheses in the United States pharmacopoeia. This could possibly be due to differences in monetary and time constraints, as HPLC on a large scale can be an expensive technique. An increase in specificity, precision, and accuracy that occurs with HPLC unfortunately corresponds to an increase in cost. | 0 | Chromatography + Titration + pH indicators |
Traditionally, the Cohn process incorporating cold ethanol fractionation has been used for albumin purification. However, chromatographic methods for separation started being adopted in the early 1980s. Developments were ongoing in the time period between when Cohn fractionation started being used, in 1946, and when chromatography started being used, in 1983. In 1962, the Kistler & Nistchmann process was created which was a spinoff of the Cohn process. Chromatographic processes began to take shape in 1983. In the 1990s, the Zenalb and the CSL Albumex processes were created which incorporated chromatography with a few variations.
The general approach to using chromatography for plasma fractionation for albumin is: recovery of supernatant I, delipidation, anion exchange chromatography, cation exchange chromatography, and gel filtration chromatography.
The recovered purified material is formulated with combinations of sodium octanoate and sodium N-acetyl tryptophanate and then subjected to viral inactivation procedures, including pasteurisation at 60 °C.
This is a more efficient alternative than the Cohn process for four main reasons:
1) smooth automation and a relatively inexpensive plant was needed,
2) easier to sterilize equipment and maintain a good manufacturing environment,
3) chromatographic processes are less damaging to the albumin protein, and
4) a more successful albumin end result can be achieved.
Compared with the Cohn process, the albumin purity went up from about 95% to 98% using chromatography, and the yield increased from about 65% to 85%. Small percentage increases make a difference in regard to sensitive measurements like purity. There is one big drawback in using chromatography, which has to do with the economics of the process. Although the method was efficient from the processing aspect, acquiring the necessary equipment is a big task. Large machinery is necessary, and for a long time the lack of equipment availability was not conducive to its widespread use. The components are more readily available now but it is still a work in progress and will possibly be ready in the future to help the world. | 0 | Chromatography + Titration + pH indicators |
Thymol blue (thymolsulfonephthalein) is a brownish-green or reddish-brown crystalline powder that is used as a pH indicator. It is insoluble in water but soluble in alcohol and dilute alkali solutions.
It transitions from red to yellow at pH 1.2–2.8 and from yellow to blue at pH 8.0–9.6. It is usually a component of Universal indicator.
At wavelength (378 - 382) nm, extinction coefficient > 8000 and at wavelength (298 - 302) nm , the extinction coefficient > 12000. | 0 | Chromatography + Titration + pH indicators |
Micellar liquid chromatography (MLC) is a form of reversed phase liquid chromatography that uses an aqueous micellar solutions as the mobile phase. | 0 | Chromatography + Titration + pH indicators |
Classical examples of polymorphism are the pair of minerals calcite and aragonite, both forms of calcium carbonate. Allotropy is the term used for elements, for example diamond versus graphite, and in metallurgy.
β-HgS precipitates as a black solid when Hg(II) salts are treated with HS. With gentle heating of the slurry, the black polymorph converts to the red form. | 1 | Crystallography |
Typical transparent media such as glasses are isotropic, which means that light behaves the same way no matter which direction it is travelling in the medium. In terms of Maxwell's equations in a dielectric, this gives a relationship between the electric displacement field D and the electric field E:
where ε is the permittivity of free space and P is the electric polarization (the vector field corresponding to electric dipole moments present in the medium). Physically, the polarization field can be regarded as the response of the medium to the electric field of the light. | 1 | Crystallography |
An interstitial defect refers to additional atoms occupying some interstitial sites at random as crystallographic defects in a crystal which normally has empty interstitial sites by default. | 1 | Crystallography |
Past winners of the Martin Medal are:
* Robert Kennedy (2019)
* Jean-Luc Veuthey (2018)
* Andreas Manz (2017)
* Ian Wilson & Peter Myers (2016)
* Pavel Jandera (2015)
* Nobuo Tanaka (2014)
* Günther Bonn & Frantisek Svec (2013)
* Edward S. Yeung (2012)
* Peter J. Schoenmakers (2011)
* Peter Carr (2010)
* Wolfgang F. Lindner (2009)
* Ron Majors & Johan Roeraade (2007)
* Jim Waters (2006)
* Vadim A. Davankov (2005)
* Terry Berger (2004)
* Jack Henion (2003)
* Paul R. Haddad & Werner Engewald (2002)
* John Michael Ramsey (2001)
* Klaus Mosbach & William S. Hancock (2000)
* Hans Poppe & Geoffrey Eglinton, FRS (1999)
* Albert Zlatkis (1998, awarded posthumously)
* Will Jennings & Joseph Jack Kirkland (1997)
* Milton L. Lee (1996)
* Milos Novotny & Shigeru Terabe (1995)
* Pat Sandra & Csaba Horvath (1994)
* Hans Engelhardt, Fred E. Regnier, & Klaus K. Unger (1993)
* Irving Wainer & James W. Jorgenson (1992)
* Dai E. Games, Barry L. Karger, Daniel W. Armstrong, & Dennis H. Desty (1991)
* Egil Jellum, William Pirkle, & Carl A. Cramers (1990)
* Jon Calvin Giddings, Udo. A Th Brinkman, J. F. K. Huber, Rudolf E. Kaiser, & Lloyd R. Snyder (1986)
* Ervin Kovats & John Knox (1985)
* C. E. Roland Jones & Arnaldo L. Liberti (1984)
* Gerhard Schomburg & Ralph Stock (1983)
* Edward R. Adlard, Leslie S. Ettre, Courtney S. G. Phillips, & Raymond P. W. Scott (1982)
* G. A. Peter Tuey & Georges Guiochon (1980)
* Ernst Bayer & C. E. H. Knapman (1978) | 0 | Chromatography + Titration + pH indicators |
Homoepitaxial growth of semiconductor thin films are generally done by chemical or physical vapor deposition methods that deliver the precursors to the substrate in gaseous state. For example, silicon is most commonly deposited from silicon tetrachloride (or germanium tetrachloride) and hydrogen at approximately 1200 to 1250 °C:
:SiCl + 2H ↔ Si + 4HCl
where (g) and (s) represent gas and solid phases, respectively. This reaction is reversible, and the growth rate depends strongly upon the proportion of the two source gases. Growth rates above 2 micrometres per minute produce polycrystalline silicon, and negative growth rates (etching) may occur if too much hydrogen chloride byproduct is present. (Hydrogen chloride may be intentionally added to etch the wafer.) An additional etching reaction competes with the deposition reaction:
:SiCl + Si ↔ 2SiCl
Silicon VPE may also use silane, dichlorosilane, and trichlorosilane source gases. For instance, the silane reaction occurs at 650 °C in this way:
:SiH → Si + 2H
VPE is sometimes classified by the chemistry of the source gases, such as hydride VPE (HVPE) and metalorganic VPE (MOVPE or MOCVD).
The reaction chamber where this process takes place may be heated by lamps located outside the chamber. A common technique used in compound semiconductor growth is molecular beam epitaxy (MBE). In this method, a source material is heated to produce an evaporated beam of particles, which travel through a very high vacuum (10 Pa; practically free space) to the substrate and start epitaxial growth. Chemical beam epitaxy, on the other hand, is an ultra-high vacuum process that uses gas phase precursors to generate the molecular beam.
Another widely used technique in microelectronics and nanotechnology is atomic layer epitaxy, in which precursor gases are alternatively pulsed into a chamber, leading to atomic monolayer growth by surface saturation and chemisorption. | 1 | Crystallography |
Anthocyanins occur in the flowers of many plants, such as the blue poppies of some Meconopsis species and cultivars. Anthocyanins have also been found in various tulip flowers, such as Tulipa gesneriana, Tulipa fosteriana and Tulipa eichleri. | 0 | Chromatography + Titration + pH indicators |
Mathematically, a wallpaper group or plane crystallographic group is a type of topologically discrete group of isometries of the Euclidean plane that contains two linearly independent translations.
Two such isometry groups are of the same type (of the same wallpaper group) if they are the same up to an affine transformation of the plane. Thus e.g. a translation of the plane (hence a translation of the mirrors and centres of rotation) does not affect the wallpaper group. The same applies for a change of angle between translation vectors, provided that it does not add or remove any symmetry (this is only the case if there are no mirrors and no glide reflections, and rotational symmetry is at most of order 2).
Unlike in the three-dimensional case, one can equivalently restrict the affine transformations to those that preserve orientation.
It follows from the Bieberbach theorem that all wallpaper groups are different even as abstract groups (as opposed to e.g. frieze groups, of which two are isomorphic with Z).
2D patterns with double translational symmetry can be categorized according to their symmetry group type. | 1 | Crystallography |
In an anisotropic medium, such as a crystal, the polarisation field P is not necessarily aligned with the electric field of the light E. In a physical picture, this can be thought of as the dipoles induced in the medium by the electric field having certain preferred directions, related to the physical structure of the crystal. This can be written as:
Here χ is not a number as before but a tensor of rank 2, the electric susceptibility tensor. In terms of components in 3 dimensions:
or using the summation convention:
Since χ is a tensor, P is not necessarily colinear with E.
In nonmagnetic and transparent materials, χ = χ, i.e. the χ tensor is real and symmetric. In accordance with the spectral theorem, it is thus possible to diagonalise the tensor by choosing the appropriate set of coordinate axes, zeroing all components of the tensor except χ, χ and χ. This gives the set of relations:
The directions x, y and z are in this case known as the principal axes of the medium. Note that these axes will be orthogonal if all entries in the χ tensor are real, corresponding to a case in which the refractive index is real in all directions.
It follows that D and E are also related by a tensor:
Here ε is known as the relative permittivity tensor or dielectric tensor. Consequently, the refractive index of the medium must also be a tensor. Consider a light wave propagating along the z principal axis polarised such the electric field of the wave is parallel to the x-axis. The wave experiences a susceptibility χ and a permittivity ε. The refractive index is thus:
For a wave polarised in the y direction:
Thus these waves will see two different refractive indices and travel at different speeds. This phenomenon is known as birefringence and occurs in some common crystals such as calcite and quartz.
If χ = χ ≠ χ, the crystal is known as uniaxial. (See Optic axis of a crystal.) If χ ≠ χ and χ ≠ χ the crystal is called biaxial. A uniaxial crystal exhibits two refractive indices, an "ordinary" index (n) for light polarised in the x or y directions, and an "extraordinary" index (n) for polarisation in the z direction. A uniaxial crystal is "positive" if n > n and "negative" if n . Light polarised at some angle to the axes will experience a different phase velocity for different polarization components, and cannot be described by a single index of refraction. This is often depicted as an index ellipsoid. | 1 | Crystallography |
The stationary phase or adsorbent in column chromatography is a solid. The most common stationary phase for column chromatography is silica gel, the next most common being alumina. Cellulose powder has often been used in the past. A wide range of stationary phases are available in order to perform ion exchange chromatography, reversed-phase chromatography (RP), affinity chromatography or expanded bed adsorption (EBA). The stationary phases are usually finely ground powders or gels and/or are microporous for an increased surface, though in EBA a fluidized bed is used. There is an important ratio between the stationary phase weight and the dry weight of the analyte mixture that can be applied onto the column. For silica column chromatography, this ratio lies within 20:1 to 100:1, depending on how close to each other the analyte components are being eluted. | 0 | Chromatography + Titration + pH indicators |
GPC is often used to determine the relative molecular weight of polymer samples as well as the distribution of molecular weights. What GPC truly measures is the molecular volume and shape function as defined by the intrinsic viscosity. If comparable standards are used, this relative data can be used to determine molecular weights within ± 5% accuracy. Polystyrene standards with dispersities of less than 1.2 are typically used to calibrate the GPC. Unfortunately, polystyrene tends to be a very linear polymer and therefore as a standard it is only useful to compare it to other polymers that are known to be linear and of relatively the same size. | 0 | Chromatography + Titration + pH indicators |
Another use for the procedure is the affinity purification of antibodies from blood serum. If the serum is known to contain antibodies against a specific antigen (for example if the serum comes from an organism immunized against the antigen concerned) then it can be used for the affinity purification of that antigen. This is also known as Immunoaffinity Chromatography. For example, if an organism is immunised against a GST-fusion protein it will produce antibodies against the fusion-protein, and possibly antibodies against the GST tag as well. The protein can then be covalently coupled to a solid support such as agarose and used as an affinity ligand in purifications of antibody from immune serum.
For thoroughness, the GST protein and the GST-fusion protein can each be coupled separately. The serum is initially allowed to bind to the GST affinity matrix. This will remove antibodies against the GST part of the fusion protein. The serum is then separated from the solid support and allowed to bind to the GST-fusion protein matrix. This allows any antibodies that recognize the antigen to be captured on the solid support. Elution of the antibodies of interest is most often achieved using a low pH buffer such as glycine pH 2.8. The eluate is collected into a neutral tris or phosphate buffer, to neutralize the low pH elution buffer and halt any degradation of the antibody's activity. This is a nice example as affinity purification is used to purify the initial GST-fusion protein, to remove the undesirable anti-GST antibodies from the serum and to purify the target antibody.
Monoclonal antibodies can also be selected to bind proteins with great specificity, where protein is released under fairly gentle conditions. This can become of use for further research in the future.
A simplified strategy is often employed to purify antibodies generated against peptide antigens. When the peptide antigens are produced synthetically, a terminal cysteine residue is added at either the N- or C-terminus of the peptide. This cysteine residue contains a sulfhydryl functional group which allows the peptide to be easily conjugated to a carrier protein (e.g. Keyhole limpet hemocyanin (KLH)). The same cysteine-containing peptide is also immobilized onto an agarose resin through the cysteine residue and is then used to purify the antibody.
Most monoclonal antibodies have been purified using affinity chromatography based on immunoglobulin-specific Protein A or Protein G, derived from bacteria.
Immunoaffinity chromatography with monoclonal antibodies immobilized on monolithic column has been successfully used to capture extracellular vesicles (e.g., exosomes and exomeres) from human blood plasma by targeting tetraspanins and integrins found on the surface of the EVs.
Immunoaffinity chromatography is also the basis for immunochromatographic test (ICT) strips, which provide a rapid means of diagnosis in patient care. Using ICT, a technician can make a determination at a patient's bedside, without the need for a laboratory. ICT detection is highly specific to the microbe causing an infection. | 0 | Chromatography + Titration + pH indicators |
Ordinary (non-time) crystals form through spontaneous symmetry breaking related to a spatial symmetry. Such processes can produce materials with interesting properties, such as diamonds, salt crystals, and ferromagnetic metals. By analogy, a time crystal arises through the spontaneous breaking of a time-translation symmetry. A time crystal can be informally defined as a time-periodic self-organizing structure. While an ordinary crystal is periodic (has a repeating structure) in space, a time crystal has a repeating structure in time. A time crystal is periodic in time in the same sense that the pendulum in a pendulum-driven clock is periodic in time. Unlike a pendulum, a time crystal "spontaneously" self-organizes into robust periodic motion (breaking a temporal symmetry). | 1 | Crystallography |
Non-aqueous acid–base titrations can be carried out advantageously by thermometric means.
Acid leach solutions from some copper mines can contain large quantities of Fe(III) as well as Cu(II). The "free acid" (sulfuric acid) content of these leach solutions is a critical process parameter. While thermometric titrimetry can determine the free acid content with modest amounts of Fe(III), in some solutions the Fe(III) content is so high as to cause serious interference. Complexation with necessarily large amounts of oxalate is undesirable due to the toxicity of the reagent. A thermometric titration was devised by diluting the aliquot with propan-2-ol and titration with standard KOH in propan-2-ol. Most of the metal content precipitated prior to the commencement of the titration, and a clear, sharp endpoint for the sulfuric acid content was obtained. | 0 | Chromatography + Titration + pH indicators |
This technique is also used for detection of illicit drugs in various samples. The most common method of drug detection has been an immunoassay. This method is much more convenient. However, convenience comes at the cost of specificity and coverage of a wide range of drugs, therefore, HPLC has been used as well as an alternative method. As HPLC is a method of determining (and possibly increasing) purity, using HPLC alone in evaluating concentrations of drugs was somewhat insufficient. Therefore, HPLC in this context is often performed in conjunction with mass spectrometry. Using liquid chromatography-mass spectrometry (LC-MS) instead of gas chromatography-mass spectrometry (GC-MS) circumvents the necessity for derivitizing with acetylating or alkylation agents, which can be a burdensome extra step. LC-MS has been used to detect a variety of agents like doping agents, drug metabolites, glucuronide conjugates, amphetamines, opioids, cocaine, BZDs, ketamine, LSD, cannabis, and pesticides. Performing HPLC in conjunction with mass spectrometry reduces the absolute need for standardizing HPLC experimental runs. | 0 | Chromatography + Titration + pH indicators |
The thermospray (TSP) interface was developed in 1980 by Marvin Vestal and co-workers at the University of Houston. It was commercialized by Vestec and several of the major mass spectrometer manufacturers. The interface resulted from a long-term research project intended to find a LC–MS interface capable of handling high flow rates (1 ml/min) and avoiding the flow split in DLI interfaces. The TSP interface was composed of a heated probe, a desolvation chamber, and an ion focusing skimmer. The LC effluent passed through the heated probe and emerged as a jet of vapor and small droplets flowing into the desolvation chamber at low pressure. Initially operated with a filament or discharge as the source of ions (thereby acting as a CI source for vapourized analyte), it was soon discovered that ions were also observed when the filament or discharge was off. This could be attributed to either direct emission of ions from the liquid droplets as they evaporated in a process related to electrospray ionization or ion evaporation, or to chemical ionization of vapourized analyte molecules from buffer ions (such as ammonium acetate). The fact that multiply-charged ions were observed from some larger analytes suggests that direct analyte ion emission was occurring under at least some conditions. The interface was able to handle up to 2 ml/min of eluate from the LC column and would efficiently introduce it into the MS vacuum system. TSP was also more suitable for LC–MS applications involving reversed phase liquid chromatography (RT-LC). With time, the mechanical complexity of TSP was simplified, and this interface became popular as the first ideal LC–MS interface for pharmaceutical applications comprising the analysis of drugs, metabolites, conjugates, nucleosides, peptides, natural products, and pesticides. The introduction of TSP marked a significant improvement for LC–MS systems and was the most widely applied interface until the beginning of the 1990s, when it began to be replaced by interfaces involving atmospheric pressure ionization (API). | 0 | Chromatography + Titration + pH indicators |
The subgroups discussed so far are not only infinite, they are also continuous (Lie groups). Any subgroup containing at least one non-zero translation must be infinite, but subgroups of the orthogonal group can be finite. For example, the symmetries of a regular pentagon consist of rotations by integer multiples of 72° (360° / 5), along with reflections in the five mirrors which perpendicularly bisect the edges. This is a group, D, with 10 elements. It has a subgroup, C, of half the size, omitting the reflections. These two groups are members of two families, D and C, for any n > 1. Together, these families constitute the rosette groups.
Translations do not fold back on themselves, but we can take integer multiples of any finite translation, or sums of multiples of two such independent translations, as a subgroup. These generate the lattice of a periodic tiling of the plane.
We can also combine these two kinds of discrete groups — the discrete rotations and reflections around a fixed point and the discrete translations — to generate the frieze groups and wallpaper groups. Curiously, only a few of the fixed-point groups are found to be compatible with discrete translations. In fact, lattice compatibility imposes such a severe restriction that, up to isomorphism, we have only 7 distinct frieze groups and 17 distinct wallpaper groups. For example, the pentagon symmetries, D, are incompatible with a discrete lattice of translations. (Each higher dimension also has only a finite number of such crystallographic groups, but the number grows rapidly; for example, 3D has 230 groups and 4D has 4783.) | 1 | Crystallography |
Crystal optics is the branch of optics that describes the behaviour of light in anisotropic media, that is, media (such as crystals) in which light behaves differently depending on which direction the light is propagating. The index of refraction depends on both composition and crystal structure and can be calculated using the Gladstone–Dale relation. Crystals are often naturally anisotropic, and in some media (such as liquid crystals) it is possible to induce anisotropy by applying an external electric field. | 1 | Crystallography |
The acceptable daily intake (ADI) is 0–4 mg/kg under both EU and WHO/FAO guidelines.
Sunset yellow FCF has no carcinogenicity, genotoxicity, or developmental toxicity in the amounts at which it is used.
It has been claimed since the late 1970s, under the advocacy of Benjamin Feingold, that sunset yellow FCF causes food intolerance and ADHD-like behavior in children, but there is no scientific evidence to support these broad claims. It is possible that certain food colorings may act as a trigger in those who are genetically predisposed, but the evidence is weak. | 0 | Chromatography + Titration + pH indicators |
In geometry, a glide reflection or transflection is a geometric transformation that consists of a reflection across a hyperplane and a translation ("glide") in a direction parallel to that hyperplane, combined into a single transformation. Because the distances between points are not changed under glide reflection, it is a motion or isometry. When the context is the two-dimensional Euclidean plane, the hyperplane of reflection is a straight line called the glide line or glide axis. When the context is three-dimensional space, the hyperplane of reflection is a plane called the glide plane. The displacement vector of the translation is called the glide vector.
When some geometrical object or configuration appears unchanged by a transformation, it is said to have symmetry, and the transformation is called a symmetry operation. Glide-reflection symmetry is seen in frieze groups (patterns which repeat in one dimension, often used in decorative borders), wallpaper groups (regular tessellations of the plane), and space groups (which describe e.g. crystal symmetries). Objects with glide-reflection symmetry are in general not symmetrical under reflection alone, but two applications of the same glide reflection result in a double translation, so objects with glide-reflection symmetry always also have a simple translational symmetry.
When a reflection is composed with a translation in a direction perpendicular to the hyperplane of reflection, the composition of the two transformations is a reflection in a parallel hyperplane. However, when a reflection is composed with a translation in any other direction, the composition of the two transformations is a glide reflection, which can be uniquely described as a reflection in a parallel hyperplane composed with a translation in a direction parallel to the hyperplane.
A single glide is represented as frieze group p11g. A glide reflection can be seen as a limiting rotoreflection, where the rotation becomes a translation. It can also be given a Schoenflies notation as S, Coxeter notation as [∞,2], and orbifold notation as ∞×. | 1 | Crystallography |
In elution mode, solutes are applied to the column as narrow bands and, at low concentration, move down the column as approximately Gaussian peaks. These peaks continue to broaden as they travel, in proportion to the square root of the distance traveled. For two substances to be resolved, they must migrate down the column at sufficiently different rates to overcome the effects of band spreading. Operating at high concentration, where the isotherm is curved, is disadvantageous in elution chromatography because the rate of travel then depends on concentration, causing the peaks to spread and distort.
Retention in elution chromatography is usually controlled by adjusting the composition of the mobile phase (in terms of solvent composition, pH, ionic strength, and so forth) according to the type of stationary phase employed and the particular solutes to be separated. The mobile phase components generally have lower affinity for the stationary phase than do the solutes being separated, but are present at higher concentration and achieve their effects due to mass action. Resolution in elution chromatography is generally better when peaks are strongly retained, but conditions that give good resolution of early peaks lead to long run-times and excessive broadening of later peaks unless gradient elution is employed. Gradient equipment adds complexity and expense, particularly at large scale. | 0 | Chromatography + Titration + pH indicators |
The Ripper Method, developed in 1898, is an analytical chemistry technique used to determine the total amount of sulfur dioxide (SO) in a solution. This technique uses iodine standard and a starch indicator to titrate the solution and determine the concentration of free SO. The titration is done again with a new sample of the solution, but the sample is pretreated with sodium hydroxide (NaOH) to release bound SO. The result of these two titrations can then be used to determine the bound, free, and total amount of SO in the solution. Instead of using a starch indicator, an electrode can be used to determine the presence of free iodine. This technique is widely used in wine making. | 0 | Chromatography + Titration + pH indicators |
In the hard sphere model, the particles are described as impenetrable spheres with radius ; thus, their center-to-center distance and they experience no interaction beyond this distance. Their interaction potential can be written as:
This model has an analytical solution in the Percus–Yevick approximation. Although highly simplified, it provides a good description for systems ranging from liquid metals to colloidal suspensions. In an illustration, the structure factor for a hard-sphere fluid is shown in the Figure, for volume fractions from 1% to 40%. | 1 | Crystallography |
Before ion-exchange chromatography can be initiated, it must be equilibrated. The stationary phase must be equilibrated to certain requirements that depend on the experiment that you are working with. Once equilibrated, the charged ions in the stationary phase will be attached to its opposite charged exchangeable ions, such as Cl or Na. Next, a buffer should be chosen in which the desired protein can bind to. After equilibration, the column needs to be washed. The washing phase will help elute out all impurities that does not bind to the matrix while the protein of interest remains bounded. This sample buffer needs to have the same pH as the buffer used for equilibration to help bind the desired proteins. Uncharged proteins will be eluted out of the column at a similar speed of the buffer flowing through the column with no retention. Once the sample has been loaded onto to the column, and the column has been washed with the buffer to elute out all non-desired proteins, elution is carried out at specific conditions to elute the desired proteins that are bound to the matrix. Bound proteins are eluted out by utilizing a gradient of linearly increasing salt concentration. With increasing ionic strength of the buffer, the salt ions will compete with the desired proteins in order to bind to charged groups on the surface of the medium. This will cause desired proteins to be eluted out of the column. Proteins that have a low net charge will be eluted out first as the salt concentration increases causing the ionic strength to increase. Proteins with high net charge will need a higher ionic strength for them to be eluted out of the column.
It is possible to perform ion exchange chromatography in bulk, on thin layers of medium such as glass or plastic plates coated with a layer of the desired stationary phase, or in chromatography columns. Thin layer chromatography or column chromatography share similarities in that they both act within the same governing principles; there is constant and frequent exchange of molecules as the mobile phase travels along the stationary phase. It is not imperative to add the sample in minute volumes as the predetermined conditions for the exchange column have been chosen so that there will be strong interaction between the mobile and stationary phases. Furthermore, the mechanism of the elution process will cause a compartmentalization of the differing molecules based on their respective chemical characteristics. This phenomenon is due to an increase in salt concentrations at or near the top of the column, thereby displacing the molecules at that position, while molecules bound lower are released at a later point when the higher salt concentration reaches that area. These principles are the reasons that ion exchange chromatography is an excellent candidate for initial chromatography steps in a complex purification procedure as it can quickly yield small volumes of target molecules regardless of a greater starting volume.
Comparatively simple devices are often used to apply counterions of increasing gradient to a chromatography column. Counterions such as copper (II) are chosen most often for effectively separating peptides and amino acids through complex formation.
A simple device can be used to create a salt gradient. Elution buffer is consistently being drawn from the chamber into the mixing chamber, thereby altering its buffer concentration. Generally, the buffer placed into the chamber is usually of high initial concentration, whereas the buffer placed into the stirred chamber is usually of low concentration. As the high concentration buffer from the left chamber is mixed and drawn into the column, the buffer concentration of the stirred column gradually increase. Altering the shapes of the stirred chamber, as well as of the limit buffer, allows for the production of concave, linear, or convex gradients of counterion.
A multitude of different mediums are used for the stationary phase. Among the most common immobilized charged groups used are trimethylaminoethyl (TAM), triethylaminoethyl (TEAE), diethyl-2-hydroxypropylaminoethyl (QAE), aminoethyl (AE), diethylaminoethyl (DEAE), sulpho (S), sulphomethyl (SM), sulphopropyl (SP), carboxy (C), and carboxymethyl (CM).
Successful packing of the column is an important aspect of ion chromatography. Stability and efficiency of a final column depends on packing methods, solvent used, and factors that affect mechanical properties of the column. In contrast to early inefficient dry- packing methods, wet slurry packing, in which particles that are suspended in an appropriate solvent are delivered into a column under pressure, shows significant improvement. Three different approaches can be employed in performing wet slurry packing: the balanced density method (solvent's density is about that of porous silica particles), the high viscosity method (a solvent of high viscosity is used), and the low viscosity slurry method (performed with low viscosity solvents).
Polystyrene is used as a medium for ion- exchange. It is made from the polymerization of styrene with the use of divinylbenzene and benzoyl peroxide. Such exchangers form hydrophobic interactions with proteins which can be irreversible. Due to this property, polystyrene ion exchangers are not suitable for protein separation. They are used on the other hand for the separation of small molecules in amino acid separation and removal of salt from water. Polystyrene ion exchangers with large pores can be used for the separation of protein but must be coated with a hydrophilic substance.
Cellulose based medium can be used for the separation of large molecules as they contain large pores. Protein binding in this medium is high and has low hydrophobic character. DEAE is an anion exchange matrix that is produced from a positive side group of diethylaminoethyl bound to cellulose or Sephadex.
Agarose gel based medium contain large pores as well but their substitution ability is lower in comparison to dextrans. The ability of the medium to swell in liquid is based on the cross-linking of these substances, the pH and the ion concentrations of the buffers used.
Incorporation of high temperature and pressure allows a significant increase in the efficiency of ion chromatography, along with a decrease in time. Temperature has an influence of selectivity due to its effects on retention properties. The retention factor (k = (t − t)/(t − t)) increases with temperature for small ions, and the opposite trend is observed for larger ions.
Despite ion selectivity in different mediums, further research is being done to perform ion exchange chromatography through the range of 40–175 °C.
An appropriate solvent can be chosen based on observations of how column particles behave in a solvent. Using an optical microscope, one can easily distinguish a desirable dispersed state of slurry from aggregated particles. | 0 | Chromatography + Titration + pH indicators |
Crystal twinning occurs when two or more adjacent crystals of the same mineral are oriented so that they share some of the same crystal lattice points in a symmetrical manner. The result is an intergrowth of two separate crystals that are tightly bonded to each other. The surface along which the lattice points are shared in twinned crystals is called a composition surface or twin plane.
Crystallographers classify twinned crystals by a number of twin laws, which are specific to the crystal structure. The type of twinning can be a diagnostic tool in mineral identification. There are three main types of twinning. The first is growth twinning which can occur both in very large and very small particles. The second is transformation twinning, where there is a change in the crystal structure. The third is deformation twinning, in which twinning develops in a crystal in response to a shear stress, and is an important mechanism for permanent shape changes in a crystal. | 1 | Crystallography |
Phenol red exists as a red crystal that is stable in air. Its solubility is 0.77 grams per liter (g/L) in water and 2.9 g/L in ethanol. It is a weak acid with pK = 8.00 at .
A solution of phenol red is used as a pH indicator, often in cell culture. Its color exhibits a gradual transition from yellow (λ = 443 nm) to red (λ = 570 nm) over the pH range 6.8 to 8.2. Above pH 8.2, phenol red turns a bright pink (fuchsia) color.
In crystalline form, and in solution under very acidic conditions (low pH), the compound exists as a zwitterion as in the structure shown above, with the sulfate group negatively charged, and the ketone group carrying an additional proton. This form is sometimes symbolically written as and is orange-red. If the pH is increased (pK = 1.2), the proton from the ketone group is lost, resulting in the yellow, negatively charged ion denoted as HPS. At still higher pH (pK = 7.7), the phenol's hydroxy group loses its proton, resulting in the red ion denoted as PS.
In several sources, the structure of phenol red is shown with the sulfur atom being part of a cyclic group, similar to the structure of phenolphthalein. However, this cyclic structure could not be confirmed by X-ray crystallography.
Several indicators share a similar structure to phenol red, including bromothymol blue, thymol blue, bromocresol purple, thymolphthalein, and phenolphthalein. (A table of other common chemical indicators is available in the article on pH indicators.) | 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 crystallographic point groups that exist in three dimensions, most are assigned to only one lattice system, in which case both the crystal and lattice systems have the same name. However, five point groups are assigned to two lattice systems, rhombohedral and hexagonal, because both exhibit threefold rotational symmetry. These point groups are assigned to the trigonal crystal system. | 1 | Crystallography |
4-Nitrophenol (also called p-nitrophenol or 4-hydroxynitrobenzene) is a phenolic compound that has a nitro group at the opposite position of the hydroxyl group on the benzene ring. | 0 | Chromatography + Titration + pH indicators |
These are the crystallographic groups of a cubic crystal system: 23, 432, , 3m, and . All of them contain four diagonal 3-fold axes. These axes are arranged as 3-fold axes in a cube, directed along its four space diagonals (the cube has symmetry). These symbols are constructed the following way:
* First position – symmetrically equivalent directions of the coordinate axes x, y, and z. They are equivalent due to the presence of diagonal 3-fold axes.
* Second position – diagonal 3 or axes.
* Third position – diagonal directions between any two of the three coordinate axes x, y, and z. These can be 2, m, or .
All Hermann–Mauguin symbols presented above are called full symbols. For many groups they can be simplified by omitting n-fold rotation axes in positions. This can be done if the rotation axis can be unambiguously obtained from the combination of symmetry elements presented in the symbol. For example, the short symbol for is mmm, for is mm, and for is mm. In groups containing one higher-order axis, this higher-order axis cannot be omitted. For example, symbols and can be simplified to 4/mmm (or mm) and 6/mmm (or mm), but not to mmm; the short symbol for is m. The full and short symbols for all 32 crystallographic point groups are given in crystallographic point groups page.
Besides five cubic groups, there are two more non-crystallographic icosahedral groups (I and I in Schoenflies notation) and two limit groups (K and K in Schoenflies notation). The Hermann–Mauguin symbols were not designed for non-crystallographic groups, so their symbols are rather nominal and based on similarity to symbols of the crystallographic groups of a cubic crystal system. Group I can be denoted as 235, 25, 532, 53. The possible short symbols for I are m, m, mm, m. The possible symbols for limit group K are ∞∞ or 2∞, and for K are ∞ or m or ∞∞m. | 1 | Crystallography |
Conductometric titration is a type of titration in which the electrolytic conductivity of the reaction mixture is continuously monitored as one reactant is added. The equivalence point is the point at which the conductivity undergoes a sudden change. Marked increase or decrease in conductance are associated with the changing concentrations of the two most highly conducting ions—the hydrogen and hydroxyl ions. The method can be used for titrating coloured solutions or homogeneous suspension (e.g.: wood pulp suspension), which cannot be used with normal indicators.
Acid-base titrations and redox titrations are often performed in which common indicators are used to locate the end point e.g., methyl orange, phenolphthalein for acid base titrations and starch solutions for iodometric type redox process. However, electrical conductance measurements can also be used as a tool to locate the end point.
Example: titration of an HCl solution with the strong base NaOH. As the titration progresses, the protons are neutralized to form water by the addition of NaOH. For each amount of NaOH added equivalent amount of hydrogen ions is removed. Effectively, the mobile H cation is replaced by the less-mobile Na ion, and the conductivity of the titrated solution as well as the measured conductance of the cell fall. This continues until the equivalence point is reached, at which one obtains a solution of sodium chloride, NaCl. If more base is added, an increase in conductivity or conductance is observed, since more ions Na and OH are being added and the neutralization reaction no longer removes an appreciable amount of H. Consequently, in the titration of a strong acid with a strong base, the conductance has a minimum at the equivalence point. This minimum can be used, instead of an indicator dye, to determine the endpoint of the titration. The conductometric titration curve is a plot of the measured conductance or conductivity values as a function of the volume of the NaOH solution added. The titration curve can be used to graphically determine the equivalence point.
For reaction between a weak acid and a weak base in the beginning conductivity decreases a bit as the few available H ions are used up. Then conductivity increases slightly up to the equivalence point volume, due to contribution of the salt cation and anion.(This contribution in case of a strong acid-strong base is negligible and is not considered there.) After the equivalence point is achieved the conductivity increases rapidly due to the excess OH ions. | 0 | Chromatography + Titration + pH indicators |
The diffraction from a crystalline material, and thus the intensity of the diffracted beam, changes with the type and number of atoms inside the crystal unit cell. This fact is quantitatively expressed by the structure factor. Different materials have different structure factors, and similarly for different phases of the same material (e.g. for materials crystallizing in several different space groups). In samples composed of a mixture of materials/phases in spatially adjacent domains, the geometry of these domains can be resolved by topography. This is true, for example, also for twinned crystals, ferroelectric domains, and many others. | 1 | Crystallography |
ScBCSi (x = 0.030, y = 0.36 and z = 0.026) has a cubic crystal structure with space group F3m (No. 216) and lattice constant a = 2.03085(5) nm. This compound was initially identified as ScBC (phase I in the Sc-B-C phase diagram of figure 17). A small amount of Si was added into the floating zone crystal growth and thus this phase is a quaternary compound. Its rare cubic structure has 26 sites in the unit cell: three Sc sites, two Si sites, one C site and 20 B sites; 4 out of 20 B sites are boron-carbon mixed-occupancy sites. Atomic coordinates, site occupancies and isotropic displacement factors are listed in table VIII.
In the unit cell, there are three independent icosahedra, I1, I2 and I3, and a B polyhedron which are formed by the B1–B4, B5–B8, B9–B13 and B14–B17 sites, respectively. The B polyhedron has not been observed previously and it is shown in figure 23. The icosahedron I2 has a boron-carbon mixed-occupancy site B,C6 whose occupancy is B/C=0.58/0.42. Remaining 3 boron-carbon mixed-occupancy sites are bridge sites; C and Si sites are also bridge sites.
More than 1000 atoms are available in the unit cell, which is built up by large structure units such as two supertetrahedra T(1) and T(2) and one superoctahedron O(1). As shown in figure 24a, T(1) consists of 4 icosahedra I(1) which have no direct bonding but are bridged by four B and C20 atoms. These atoms also form tetrahedron centered by the Si2 sites. The supertetrahedron T(2) that consists of 4 icosahedra I(2) is the same as shown in figure 18b; its mixed-occupancy sites B and C6 directly bond with each other. The superoctahedron O(1) consists of 6 icosahedra I(3) and bridge sites B, C18, C1 and Si1; here Si1 and C1 exhibit a tetrahedral arrangement at the center of O(1). The B polyhedra also arrange octahedrally, without the central atom, as shown in figure 24c where the B and C19 atoms bridge the B polyhedra to form the octahedral supercluster of the B polyhedra.
Using these large polyhedra, the crystal structure of ScBCSi can be described as shown in figure 25. Owing to the crystal symmetry, the tetrahedral coordination between these superstructure units is again a key factor. The supertetrahedron T(1) lies at the body center and at the edge center of the unit cell. The superoctahedra O(1) locate at the body center (0.25, 0.25, 0.25) of the quarter of the unit cell. They coordinate tetrahedrally around T(1) forming a giant tetrahedron. The supertetrahedra T(2) are located at the symmetry-related positions (0.25, 0.25, 0.75); they also form a giant tetrahedron surrounding T(1). Edges of both giant tetrahedra orthogonally cross each other at their centers; at those edge centers, each B polyhedron bridges all the super-structure clusters T(1), T(2) and O(1). The superoctahedron built of B polyhedra is located at each cubic face center.
Scandium atoms reside in the voids of the boron framework. Four Sc1 atoms form a tetrahedral arrangement inside the B polyhedron-based superoctahedron. Sc2 atoms sit between the B polyhedron-based superoctahedron and the O(1) superoctahedron. Three Sc3 atoms form a triangle and are surrounded by three B polyhedra, a supertetrahedron T(1) and a superoctahedron O(1). | 1 | Crystallography |
Chemical bleaching is achieved by oxidation or reduction. Oxidation can destroy the dye completely, e.g. through the use of sodium hypochlorite (NaClO, common bleach) or hydrogen peroxide. Reduction of methyl violet occurs in microorganisms but can be attained chemically using sodium dithionite. | 0 | Chromatography + Titration + pH indicators |
Retention uniformity, or R, is a concept in thin layer chromatography. It is designed for the quantitative measurement of equal-spreading of the spots on the chromatographic plate and is one of the Chromatographic response functions. | 0 | Chromatography + Titration + pH indicators |
Affinity chromatography can be used in a number of applications, including nucleic acid purification, protein purification from cell free extracts, and purification from blood.
By using affinity chromatography, one can separate proteins that bind to a certain fragment from proteins that do not bind that specific fragment. Because this technique of purification relies on the biological properties of the protein needed, it is a useful technique and proteins can be purified many folds in one step. | 0 | Chromatography + Titration + pH indicators |
4-Nitrophenol can be prepared by nitration of phenol using dilute nitric acid at room temperature. The reaction produces a mixture of 2-nitrophenol and 4-nitrophenol. | 0 | Chromatography + Titration + pH indicators |
Foods and beverages contain numerous aromatic compounds, some naturally present in the raw materials and some forming during processing. GC–MS is extensively used for the analysis of these compounds which include esters, fatty acids, alcohols, aldehydes, terpenes etc. It is also used to detect and measure contaminants from spoilage or adulteration which may be harmful and which is often controlled by governmental agencies, for example pesticides. | 0 | Chromatography + Titration + pH indicators |
Reversed-phase liquid chromatography (RP-LC) is a mode of liquid chromatography in which non-polar stationary phase and polar mobile phases are used for the separation of organic compounds. The vast majority of separations and analyses using high-performance liquid chromatography (HPLC) in recent years are done using the reversed phase mode. In the reversed phase mode, the sample components are retained in the system the more hydrophobic they are.
The factors affecting the retention and separation of solutes in the reversed phase chromatographic system are as follows:
a. The chemical nature of the stationary phase, i.e., the ligands bonded on its surface, as well as their bonding density, namely the extent of their coverage.
b. The composition of the mobile phase. Type of the bulk solvents whose mixtures affect the polarity of the mobile phase, hence the name modifier for a solvent added to affect the polarity of the mobile phase.
C. Additives, such as buffers, affect the pH of the mobile phase, which affect the ionization state of the solutes and their polarity.
In order to retain the organic components in mixtures, the stationary phases, packed within columns, consist of a hydrophobic substrates, bonded to the surface of porous silica-gel particles in various geometries (spheric, irregular), at different diameters (sub-2, 3, 5, 7, 10 um), with varying pore diameters (60, 100, 150, 300, A). The particle's surface is covered by chemically bonded hydrocarbons, such as C3, C4, C8, C18 and more. The longer the hydrocarbon associated with the stationary phase, the longer the sample components will be retained. Some stationary phases are also made of hydrophobic polymeric particles, or hybridized silica-organic groups particles, for method in which mobile phases at extreme pH are used. Most current methods of separation of biomedical materials use C-18 columns, sometimes called by trade names, such as ODS (octadecylsilane) or RP-18.
The mobile phases are mixtures of water and polar organic solvents, the vast majority of which are methanol and acetonitrile. These mixtures usually contain various additives such as buffers (acetate, phosphate, citrate), surfactants (alkyl amines or alkyl sulfonates) and special additives (EDTA). The goal of using supplements of one kind or another is to increase efficiency, selectivity, and control solute retention. | 0 | Chromatography + Titration + pH indicators |
Paracetamol powder has poor compression properties, which poses difficulty in making tablets. A second polymorph was found with more suitable compressive properties. | 1 | Crystallography |
*This test is done to ascertain the nature of fluid in the vagina during pregnancy especially when premature rupture of membranes (PROM) is suspect. This test involves putting a drop of fluid obtained from the vagina onto paper strips containing nitrazine dye. The strips change color depending on the pH of the fluid. The strips will turn blue if the pH is greater than 6.0. A blue strip means it's more likely the membranes have ruptured.
This test, however, can produce false positives. If blood gets in the sample or if there is an infection present, the pH of the vaginal fluid may be higher than normal. Semen also has a higher pH, so recent vaginal intercourse can produce a false reading.
* To perform a fecal pH test for diagnosing intestinal infections or other digestive problems
* In civil engineering, to determine the carbonatation spread in concrete structures and therefore assess the state of the rebar's passivation film. | 0 | Chromatography + Titration + pH indicators |
The problem of close-packing of spheres was first mathematically analyzed by Thomas Harriot around 1587, after a question on piling cannonballs on ships was posed to him by Sir Walter Raleigh on their expedition to America.
Cannonballs were usually piled in a rectangular or triangular wooden frame, forming a three-sided or four-sided pyramid. Both arrangements produce a face-centered cubic lattice – with different orientation to the ground. Hexagonal close-packing would result in a six-sided pyramid with a hexagonal base.
The cannonball problem asks which flat square arrangements of cannonballs can be stacked into a square pyramid. Édouard Lucas formulated the problem as the Diophantine equation or and conjectured that the only solutions are and . Here is the number of layers in the pyramidal stacking arrangement and is the number of cannonballs along an edge in the flat square arrangement. | 1 | Crystallography |
The standard addition approach involves spiking the same sample extract with several known concentrations of analyte. This technique is more robust and effective than using matrix matched standards but is labor-intensive since each sample must be prepared several times to achieve a reliable calibration. | 0 | Chromatography + Titration + pH indicators |
When a second phase of mass fragmentation is added, for example using a second quadrupole in a quadrupole instrument, it is called tandem MS (MS/MS). MS/MS can sometimes be used to quantitate low levels of target compounds in the presence of a high sample matrix background.
The first quadrupole (Q1) is connected with a collision cell (Q2) and another quadrupole (Q3). Both quadrupoles can be used in scanning or static mode, depending on the type of MS/MS analysis being performed. Types of analysis include product ion scan, precursor ion scan, selected reaction monitoring (SRM) (sometimes referred to as multiple reaction monitoring (MRM)) and neutral loss scan. For example: When Q1 is in static mode (looking at one mass only as in SIM), and Q3 is in scanning mode, one obtains a so-called product ion spectrum (also called "daughter spectrum"). From this spectrum, one can select a prominent product ion which can be the product ion for the chosen precursor ion. The pair is called a "transition" and forms the basis for SRM. SRM is highly specific and virtually eliminates matrix background. | 0 | Chromatography + Titration + pH indicators |
Many beam HREM images of extremely thin samples are only directly interpretable in terms of a projected crystal structure if they have been recorded under special conditions, i.e. the so-called Scherzer defocus. In that case the positions of the atom columns appear as black blobs in the image (when the spherical aberration coefficient of the objective lens is positive - as always the case for uncorrected TEMs). Difficulties for interpretation of HREM images arise for other defocus values because the transfer properties of the objective lens alter the image contrast as function of the defocus. Hence atom columns which appear at one defocus value as dark blobs can turn into white blobs at a different defocus and vice versa. In addition to the objective lens defocus (which can easily be changed by the TEM operator), the thickness of the crystal under investigation has also a significant influence on the image contrast. These two factors often mix and yield HREM images which cannot be straightforwardly interpreted as a projected structure. If the structure is unknown, so that image simulation techniques cannot be applied beforehand, image interpretation is even more complicated. Nowadays two approaches are available to overcome this problem: one method is the exit-wave function reconstruction method, which requires several HREM images from the same area at different defocus and the other method is crystallographic image processing (CIP) which processes only a single HREM image. Exit-wave function reconstruction provides an amplitude and phase image of the (effective) projected crystal potential over the whole field of view. The thereby reconstructed crystal potential is corrected for aberration and delocalisation and also not affected by possible transfer gaps since several images with different defocus are processed. CIP on the other side considers only one image and applies corrections on the averaged image amplitudes and phases. The result of the latter is a pseudo-potential map of one projected unit cell. The result can be further improved by crystal tilt compensation and search for the most likely projected symmetry. In conclusion one can say that the exit-wave function reconstruction method has most advantages for determining the (aperiodic) atomic structure of defects and small clusters and CIP is the method of choice if the periodic structure is in focus of the investigation or when defocus series of HREM images cannot be obtained, e.g. due to beam damage of the sample. However, a recent study on the catalyst related material Cs[NbWO] shows the advantages when both methods are linked in one study. | 1 | Crystallography |
Orcein, also archil, orchil, lacmus and C.I. Natural Red 28, are names for dyes extracted from several species of lichen, commonly known as "orchella weeds", found in various parts of the world. A major source is the archil lichen, Roccella tinctoria. Orcinol is extracted from such lichens. It is then converted to orcein by ammonia and air. In traditional dye-making methods, urine was used as the ammonia source. If the conversion is carried out in the presence of potassium carbonate, calcium hydroxide, and calcium sulfate (in the form of potash, lime, and gypsum in traditional dye-making methods), the result is litmus, a more complex molecule. The manufacture was described by Cocq in 1812 and in the UK in 1874. Edmund Roberts noted orchilla as a principal export of the Cape Verde islands, superior to the same kind of "moss" found in Italy or the Canary Islands, that in 1832 was yielding an annual revenue of $200,000. Commercial archil is either a powder (called cudbear) or a paste. It is red in acidic pH and blue in alkaline pH. | 0 | Chromatography + Titration + pH indicators |
Column chromatography in chemistry is a chromatography method used to isolate a single chemical compound from a mixture. Chromatography is able to separate substances based on differential adsorption of compounds to the adsorbent; compounds move through the column at different rates, allowing them to be separated into fractions. The technique is widely applicable, as many different adsorbents (normal phase, reversed phase, or otherwise) can be used with a wide range of solvents. The technique can be used on scales from micrograms up to kilograms. The main advantage of column chromatography is the relatively low cost and disposability of the stationary phase used in the process. The latter prevents cross-contamination and stationary phase degradation due to recycling. Column chromatography can be done using gravity to move the solvent, or using compressed gas to push the solvent through the column.
A thin-layer chromatograph can show how a mixture of compounds will behave when purified by column chromatography. The separation is first optimised using thin-layer chromatography before performing column chromatography. | 0 | Chromatography + Titration + pH indicators |
Oligocrystalline material owns a microstructure consisting of a few coarse grains, often columnar and parallel to the longitudinal ingot axis. This microstructure can be found in the ingots produced by electron beam melting (EBM). | 1 | Crystallography |
Ab initio or first principles calculations are any of a number of software packages making use of density functional theory to solve for the quantum mechanical state of a system. Perfect crystals are an ideal subject for such calculations because of their high periodicity. Since every simulation package will vary in the details of its algorithms and implementations, this page will focus on a methodological overview. | 1 | Crystallography |
In crystallography, the dyakis dodecahedron only exists in one crystal, which is pyrite. Pyrite has other forms other than the dyakis dodecahedron, including tetrahedra, octahedra, cubes and pyritohedra. Though the cube and octahedron are in the cubic crystal system, the dyakis dodecahedron and the pyritohedon are in the isometric crystal system and the tetrahedron is in the tetrahedral crystal system. Though the dyakis dodecahedron has 3-fold axes like the pyritohedron and cube, it doesn't have 4-fold axes but it does have order-4 vertices, as when the dyakis dodecahedron is rotated 90 or 270° along an order-4 vertex, it is not the same as before, because the order-4 vertices act as 2-fold axes, as when they are rotated a full turn or 180°, the polyhedron looks the same as before. | 1 | Crystallography |
Mass spectrometry (MS) is an analytical technique that measures the mass-to-charge ratio (m/z) of charged particles (ions). Although there are many different kinds of mass spectrometers, all of them make use of electric or magnetic fields to manipulate the motion of ions produced from an analyte of interest and determine their m/z. The basic components of a mass spectrometer are the ion source, the mass analyzer, the detector, and the data and vacuum systems. The ion source is where the components of a sample introduced in a MS system are ionized by means of electron beams, photon beams (UV lights), laser beams or corona discharge. In the case of electrospray ionization, the ion source moves ions that exist in liquid solution into the gas phase. The ion source converts and fragments the neutral sample molecules into gas-phase ions that are sent to the mass analyzer. While the mass analyzer applies the electric and magnetic fields to sort the ions by their masses, the detector measures and amplifies the ion current to calculate the abundances of each mass-resolved ion. In order to generate a mass spectrum that a human eye can easily recognize, the data system records, processes, stores, and displays data in a computer.
The mass spectrum can be used to determine the mass of the analytes, their elemental and isotopic composition, or to elucidate the chemical structure of the sample. MS is an experiment that must take place in gas phase and under vacuum (1.33 * 10 to 1.33 * 10 pascal). Therefore, the development of devices facilitating the transition from samples at higher pressure and in condensed phase (solid or liquid) into a vacuum system has been essential to develop MS as a potent tool for identification and quantification of organic compounds like peptides. MS is now in very common use in analytical laboratories that study physical, chemical, or biological properties of a great variety of compounds. Among the many different kinds of mass analyzers, the ones that find application in LC–MS systems are the quadrupole, time-of-flight (TOF), ion traps, and hybrid quadrupole-TOF (QTOF) analyzers. | 0 | Chromatography + Titration + pH indicators |
Vectors and planes in a crystal lattice are described by the three-value Miller index notation. This syntax uses the indices h, k, and ℓ as directional parameters.
By definition, the syntax (hkℓ) denotes a plane that intercepts the three points a/h, a/k, and a/ℓ, or some multiple thereof. That is, the Miller indices are proportional to the inverses of the intercepts of the plane with the unit cell (in the basis of the lattice vectors). If one or more of the indices is zero, it means that the planes do not intersect that axis (i.e., the intercept is "at infinity"). A plane containing a coordinate axis is translated so that it no longer contains that axis before its Miller indices are determined. The Miller indices for a plane are integers with no common factors. Negative indices are indicated with horizontal bars, as in (13). In an orthogonal coordinate system for a cubic cell, the Miller indices of a plane are the Cartesian components of a vector normal to the plane.
Considering only (hkℓ) planes intersecting one or more lattice points (the lattice planes), the distance d between adjacent lattice planes is related to the (shortest) reciprocal lattice vector orthogonal to the planes by the formula | 1 | Crystallography |
Applications in macroscopic engineering have been suggested, building quasi-crystal-like large scale engineering structures, which could have interesting physical properties. Also, aperiodic tiling lattice structures may be used instead of isogrid or honeycomb patterns. None of these seem to have been put to use in practice. | 1 | Crystallography |
In geometry, the trihexagonal tiling is one of 11 uniform tilings of the Euclidean plane by regular polygons. It consists of equilateral triangles and regular hexagons, arranged so that each hexagon is surrounded by triangles and vice versa. The name derives from the fact that it combines a regular hexagonal tiling and a regular triangular tiling. Two hexagons and two triangles alternate around each vertex, and its edges form an infinite arrangement of lines. Its dual is the rhombille tiling.
This pattern, and its place in the classification of uniform tilings, was already known to Johannes Kepler in his 1619 book Harmonices Mundi. The pattern has long been used in Japanese basketry, where it is called kagome. The Japanese term for this pattern has been taken up in physics, where it is called a kagome lattice. It occurs also in the crystal structures of certain minerals. Conway calls it a hexadeltille, combining alternate elements from a hexagonal tiling (hextille) and triangular tiling (deltille). | 1 | Crystallography |
Bromocresol purple is used in medical laboratories to measure albumin. Use of BCP in this application may provide some advantage over older methods using bromocresol green. In microbiology, it is used for staining dead cells based on their acidity, and for the isolation and assaying of lactic acid bacteria.
In photographic processing, it can be used as an additive to acid stop baths to indicate that the bath has reached neutral pH and needs to be replaced.
Bromocresol purple milk solids glucose agar is used as a medium used to distinguish dermatophytes from bacteria and other organisms in cases of ringworm fungus (T. verrucosum) infestation in cattle and other animals. | 0 | Chromatography + Titration + pH indicators |
In gas chromatography, the Kovats retention index (shorter Kovats index, retention index; plural retention indices) is used to convert retention times into system-independent constants. The index is named after the Hungarian-born Swiss chemist Ervin Kováts, who outlined the concept in the 1950s while performing research into the composition of the essential oils.
The retention index of a chemical compound is retention time interpolated between adjacent n-alkanes. While retention times vary with the individual chromatographic system (e.g. with regards to column length, film thickness, diameter and inlet pressure), the derived retention indices are quite independent of these parameters and allow comparing values measured by different analytical laboratories under varying conditions and analysis times from seconds to hours. Tables of retention indices are used to identify peaks by comparing measured retention indices with the tabulated values. | 0 | Chromatography + Titration + pH indicators |
To begin HPTLC, a stationary phase has to be determined to separate different compounds within a mixture. Around 90% of all pharmaceutical separations are performed on normal phase silica gel; however, other stationary phases such as alumina can be used for samples with dissociating compounds and cellulose for ionic compounds. The reverse-phase HPTLC method (similar methodology to reverse-phase TLC) is used for compounds with high polarity. After the selection of the stationary phase, plates are generally washed with methanol and dried in an oven to remove excess solvent.
Selection for the mobile phase is one of the most important processes of HPTLC and follows a trial and error pathway. However, the PRISMA system stands as a guideline for finding the optimal mobile phase. The mobile phase is dependent on the absorptivity of the stationary phase and the composition of the compound of interest. The compound is first tested with solutions such as diethyl ether, ethanol, dichloromethane, chloroform for normal phase HPTLC, or solutions such as methanol, acetonitrile, and tetrahydrofuran for reverse phase HPTLC. The retardation factors (Rf) of the compounds with the selected solvent are then analyzed and the solvent that gives the largest Rf is chosen to be the mobile phase for the compound. Then, the mobile solvent strength is tested against hexane (for normal HPTLC) and water (for reverse-phase HPTLC) to determine the need for adjustment.
Notable HPTLC devices such as the Linomat 5 and the Automatic TLC Sampler 4 (ATS 4) by CAMAG function very similarly by having the automated spray-on sample application technique. This automated spray-on technique is useful to overcome the uncertainty in droplet size and position when the sample is applied to the TLC plate by hand. Additionally, automation provides high resolution and narrow bands since the solvent evaporates immediately as the sample makes contact with the plate. One approach to automation has been the use of piezoelectric devices and inkjet printers for applying the sample. Alternatively, the Nanomat 4 and ATS 4 by CAMAG are manually operated where the sample is applied via spot application using a capillary pipette.
Upon chromatographic detection, HPTLC plates are usually developed in saturated twin-trough chambers with filter paper for optimal outcomes. However, flat-bottom chambers and horizontal-development chambers are also used for specific compounds. A general mechanism for the HPTLC device goes as follows. A fitted filter paper is placed in the rear trough of the chamber and the mobile phase is poured through the rear trough to ensure complete solvent absorption of the filter paper. The chamber is then tilted to ~45° so both troughs are equal in solvent volume and left alone to equilibrate for ~20 mins. Finally, the HPTLC plate is placed in the chamber to develop. Between each sample reading, the mobile phase and filter paper are changed to ensure the best outcomes.
The spot capacity (analogous to peak capacity in HPLC) can be increased by developing the plate with two different solvents, using two-dimensional chromatography. The procedure begins with development of a sample loaded plate with first solvent. After removing it, the plate is rotated 90° and developed with a second solvent. | 0 | Chromatography + Titration + pH indicators |
A screw axis (helical axis or twist axis) is a line that is simultaneously the axis of rotation and the line along which translation of a body occurs. Chasles' theorem shows that each Euclidean displacement in three-dimensional space has a screw axis, and the displacement can be decomposed into a rotation about and a slide along this screw axis.
Plücker coordinates are used to locate a screw axis in space, and consist of a pair of three-dimensional vectors. The first vector identifies the direction of the axis, and the second locates its position. The special case when the first vector is zero is interpreted as a pure translation in the direction of the second vector. A screw axis is associated with each pair of vectors in the algebra of screws, also known as screw theory.
The spatial movement of a body can be represented by a continuous set of displacements. Because each of these displacements has a screw axis, the movement has an associated ruled surface known as a screw surface. This surface is not the same as the axode, which is traced by the instantaneous screw axes of the movement of a body. The instantaneous screw axis, or instantaneous helical axis (IHA), is the axis of the helicoidal field generated by the velocities of every point in a moving body.
When a spatial displacement specializes to a planar displacement, the screw axis becomes the displacement pole, and the instantaneous screw axis becomes the velocity pole, or instantaneous center of rotation, also called an instant center. The term centro is also used for a velocity pole, and the locus of these points for a planar movement is called a centrode. | 1 | Crystallography |
In crystallography, a fractional coordinate system (crystal coordinate system) is a coordinate system in which basis vectors used to the describe the space are the lattice vectors of a crystal (periodic) pattern. The selection of an origin and a basis define a unit cell, a parallelotope (i.e., generalization of a parallelogram (2D) or parallelepiped (3D) in higher dimensions) defined by the lattice basis vectors where is the dimension of the space. These basis vectors are described by lattice parameters (lattice constants) consisting of the lengths of the lattice basis vectors and the angles between them .
Most cases in crystallography involve two- or three-dimensional space. In the three-dimensional case, the basis vectors are commonly displayed as with their lengths denoted by respectively, and the angles denoted by , where conventionally, is the angle between and , is the angle between and , and is the angle between and . | 1 | Crystallography |
Sphere packing in a cylinder is a three-dimensional packing problem with the objective of packing a given number of identical spheres inside a cylinder of specified diameter and length. For cylinders with diameters on the same order of magnitude as the spheres, such packings result in what are called columnar structures.
These problems are studied extensively in the context of biology, nanoscience, materials science, and so forth due to the analogous assembly of small particles (like cells and atoms) into cylindrical crystalline structures.
The book "Columnar Structures of Spheres: Fundamentals and Applications" serves as a notable contributions to this field of study. Authored by Winkelmann and Chan, the book reviews theoretical foundations and practical applications of densely packed spheres within cylindrical confinements. | 1 | Crystallography |
Nucleation can be either homogeneous, without the influence of foreign particles, or heterogeneous, with the influence of foreign particles. Generally, heterogeneous nucleation takes place more quickly since the foreign particles act as a scaffold for the crystal to grow on, thus eliminating the necessity of creating a new surface and the incipient surface energy requirements.
Heterogeneous nucleation can take place by several methods. Some of the most typical are small inclusions, or cuts, in the container the crystal is being grown on. This includes scratches on the sides and bottom of glassware. A common practice in crystal growing is to add a foreign substance, such as a string or a rock, to the solution, thereby providing nucleation sites for facilitating crystal growth and reducing the time to fully crystallize.
The number of nucleating sites can also be controlled in this manner. If a brand-new piece of glassware or a plastic container is used, crystals may not form because the container surface is too smooth to allow heterogeneous nucleation. On the other hand, a badly scratched container will result in many lines of small crystals. To achieve a moderate number of medium-sized crystals, a container which has a few scratches works best. Likewise, adding small previously made crystals, or seed crystals, to a crystal growing project will provide nucleating sites to the solution. The addition of only one seed crystal should result in a larger single crystal. | 1 | Crystallography |
An important application of mosaic crystals is in monochromators for x-ray and neutron radiation. The mosaicity enhances the reflected flux, and allows for some phase-space transformation.
Pyrolitic graphite (PG) can be produced in form of mosaic crystals (HOPG: highly ordered PG) with controlled mosaicity of up to a few degrees. | 1 | Crystallography |
The distribution constant (or partition ratio) (K) is the equilibrium constant for the distribution of an analyte in two immiscible solvents.
In chromatography, for a particular solvent, it is equal to the ratio of its molar concentration in the stationary phase to its molar concentration in the mobile phase, also approximating the ratio of the solubility of the solvent in each phase.
The term is often confused with partition coefficient or distribution coefficient. | 0 | Chromatography + Titration + pH indicators |
*Karl Fischer titration: A potentiometric method to analyze trace amounts of water in a substance. A sample is dissolved in methanol, and titrated with Karl Fischer reagent (consists of iodine, sulfur dioxide, a base and a solvent, such as alcohol). The reagent contains iodine, which reacts proportionally with water. Thus, the water content can be determined by monitoring the electric potential of excess iodine. | 0 | Chromatography + Titration + pH indicators |
In manufacturing, the simulated moving bed (SMB) process is a highly engineered process for implementing chromatographic separation. It is used to separate one chemical compound or one class of chemical compounds from one or more other chemical compounds to provide significant quantities of the purified or enriched material at a lower cost than could be obtained using simple (batch) chromatography. It cannot provide any separation or purification that cannot be done by a simple column purification. The process is rather complicated. The single advantage which it brings to a chromatographic purification is that it allows the production of large quantities of highly purified material at a dramatically reduced cost. The cost reductions come about as a result of: the use of a smaller amount of chromatographic separation media stationary phase, a continuous and high rate of production, and decreased solvent and energy requirements. This improved economic performance is brought about by a valve-and-column arrangement that is used to lengthen the stationary phase indefinitely and allow very high solute loadings to the process.
In the conventional moving bed technique of production chromatography the feed entry and the analyte recovery are simultaneous and continuous, but because of practical difficulties with a continuously moving bed, the simulated moving bed technique was proposed. In the simulated moving bed technique instead of moving the bed, the feed inlet, the solvent or eluent inlet and the desired product exit and undesired product exit positions are moved continuously, giving the impression of a moving bed, with continuous flow of solid particles and continuous flow of liquid in the opposite direction of the solid particles.
True moving bed chromatography (TMBC) is only a theoretical concept. Its simulation, SMBC, is achieved by the use of a multiplicity of columns in series and a complex valve arrangement, which provides for flow of the feed mixture and solvent, and "eluent" or "desorbent" feed at any column. The valving and piping arrangements and the predetermined control of these allow switching at regular intervals the sample entry in one direction, the solvent entry in the same direction but at a different location in the continuous loop, whilst changing the fast product and slow product takeoff positions to also move in the same direction, but at different relative locations within the loop.
Ref 3 explains that the advantage of the SMBC is high production rate, because a system could be near continuous, whilst its disadvantage is that it only performs one cut in mixtures. Thus, it is well-suited for separation of a binary mixture. With multiple cuts, analogous to a series of distillation columns, multiple compounds can be separated from a mixture of more than two compounds. With regard to efficiency it compares with the simple chromatography technique like continuous distillation does with batch distillation. | 0 | Chromatography + Titration + pH indicators |
Paper chromatography is one method for testing the purity of compounds and identifying substances. Paper chromatography is a useful technique because it is relatively quick and requires only small quantities of material. Separations in paper chromatography involve the principle of partition. In paper chromatography, substances are distributed between a stationary phase and a mobile phase. The stationary phase is the water trapped between the cellulose fibers of the paper. The mobile phase is a developing solution that travels up the stationary phase, carrying the samples with it. Components of the sample will separate readily according to how strongly they adsorb onto the stationary phase versus how readily they dissolve in the mobile phase.
When a colored chemical sample is placed on a filter paper, the colors separate from the sample by placing one end of the paper in a solvent. The solvent diffuses up the paper, dissolving the various molecules in the sample according to the polarities of the molecules and the solvent. If the sample contains more than one color, that means it must have more than one kind of molecule. Because of the different chemical structures of each kind of molecule, the chances are very high that each molecule will have at least a slightly different polarity, giving each molecule a different solubility in the solvent. The unequal solubility causes the various color molecules to leave solution at different places as the solvent continues to move up the paper. The more soluble a molecule is, the higher it will migrate up the paper. If a chemical is very non-polar it will not dissolve at all in a very polar solvent. This is the same for a very polar chemical and a very non-polar solvent.
It is very important to note that when using water (a very polar substance) as a solvent, the more polar the color, the higher it will rise on the papers. | 0 | Chromatography + Titration + pH indicators |
The first electron crystallographic protein structure to achieve atomic resolution was bacteriorhodopsin, determined by Richard Henderson and coworkers at the Medical Research Council Laboratory of Molecular Biology in 1990. However, already in 1975 Unwin and Henderson had determined the first membrane protein structure at intermediate resolution (7 Ångström), showing for the first time the internal structure of a membrane protein, with its alpha-helices standing perpendicular to the plane of the membrane. Since then, several other high-resolution structures have been determined by electron crystallography, including the light-harvesting complex, the nicotinic acetylcholine receptor, and the bacterial flagellum. The highest resolution protein structure solved by electron crystallography of 2D crystals is that of the water channel aquaporin-0. In 2012, Jan Pieter Abrahams and coworkers extended electron crystallography to 3D protein nanocrystals by rotation electron diffraction (RED). | 1 | Crystallography |
Shortly after the invention of the laser by Theodore Maiman in 1960, it was quickly recognized that a laser could act as a point source to evaporate source material in a vacuum chamber for fabricating thin films. In 1965, Smith and Turner succeeded in depositing thin films using a ruby laser, after which Groh deposited thin films using a continuous-wave CO laser in 1968. Further work demonstrated that laser-induced evaporation is an effective way to deposit dielectric and semiconductor films. However, issues occurred with regard to stoichiometry and the uniformity of the deposited films, thus diminishing their quality compared to films deposited by other techniques. Experiments to investigate the deposition of thin films using a pulsed laser at high power densities laid the foundation for pulsed laser deposition, an extremely successful growth technique that is widely used today.
Experiments utilizing continuous-wave lasers continued to be performed throughout the latter half of the twentieth century, highlighting the many advantages of continuous-wave laser evaporation including low power densities, which can reduce surface damage to sensitive films. It proved challenging to achieve congruent evaporation from compound sources using continuous-wave lasers, and film deposition was typically limited to sources with high vapor pressures due to the low continuous wave power densities available.
In 2019, the evaporation of sources using continuous-wave lasers was rediscovered at the Max Planck Institute for Solid State Research and dubbed "thermal laser epitaxy". This new technique uses elemental sources illuminated by high-power continuous-wave lasers (typically with peak powers around 1 kW at a wavelength of 1000 nm), thus allowing the deposition of low-vapor-pressure materials such as carbon and tungsten while avoiding issues with congruent evaporation from compound sources. | 1 | Crystallography |
Before MMC was considered as a chromatographic approach, secondary interactions were generally believed to be the main cause of peak tailing.
However, it was discovered afterwards that secondary interactions can be applied for improving separation power. In 1986, Regnier’s group synthesized a stationary phase that had characteristics of anion exchange chromatography (AEX) and hydrophobic interaction chromatography (HIC) on protein separation.
In 1998, a new form of MMC, hydrophobic charge induction chromatography (HCIC), was proposed by Burton and Harding.
In the same year, conjoint liquid chromatography (CLC), which combines different types of monolithic convective interaction media (CIM) disks in the same housing, was introduced by Štrancar et al.
In 1999, Yates’ group [11] loaded strong-cation exchange (SCX) and reversed phase liquid chromatography (RPLC) stationary phases sequentially into a capillary column coupled with tandem mass spectrometry (MS/MS) in the analysis of peptides, which became one of the most efficient technique in proteomics afterwards.
In 2009, Geng’s group first achieved online two-dimensional (2D) separation of intact proteins using a single column possessing separation features of weak-cation exchange chromatography (WCX) and HIC (termed as two-dimensional liquid chromatography using a single column, (2D-LC-1C). | 0 | Chromatography + Titration + pH indicators |
Hydrion is a trademarked name for a popular line of compound pH indicators, marketed by Micro Essential Laboratory Inc., exhibiting a series of color changes (typically producing a recognizably different color for each pH unit) over a range of pH values. Although solutions are available, the most common forms of Hydrion are a series of papers impregnated with various mixtures of indicator dyes. It is considered a "universal indicator". | 0 | Chromatography + Titration + pH indicators |
A microbatch usually involves immersing a very small volume of protein droplets in oil (as little as 1 µl). The reason that oil is required is because such low volume of protein solution is used and therefore evaporation must be inhibited to carry out the experiment aqueously. Although there are various oils that can be used, the two most common sealing agent are paraffin oils (described by Chayen et al.) and silicon oils (described by D’Arcy). There are also other methods for microbatching that don't use a liquid sealing agent and instead require a scientist to quickly place a film or some tape on a welled plate after placing the drop in the well.
Besides the very limited amounts of sample needed, this method also has as a further advantage that the samples are protected from airborne contamination, as they are never exposed to the air during the experiment. | 1 | Crystallography |
For the special case of simple cubic crystals, the lattice vectors are orthogonal and of equal length (usually denoted a), as are those of the reciprocal lattice. Thus, in this common case, the Miller indices (hkℓ) and [hkℓ] both simply denote normals/directions in Cartesian coordinates.
For cubic crystals with lattice constant a, the spacing d between adjacent (hkℓ) lattice planes is (from above)
Because of the symmetry of cubic crystals, it is possible to change the place and sign of the integers and have equivalent directions and planes:
*Indices in angle brackets such as ⟨100⟩ denote a family of directions which are equivalent due to symmetry operations, such as [100], [010], [001] or the negative of any of those directions.
*Indices in curly brackets or braces such as {100} denote a family of plane normals which are equivalent due to symmetry operations, much the way angle brackets denote a family of directions.
For face-centered cubic and body-centered cubic lattices, the primitive lattice vectors are not orthogonal. However, in these cases the Miller indices are conventionally defined relative to the lattice vectors of the cubic supercell and hence are again simply the Cartesian directions. | 1 | Crystallography |
The water content of most compounds can be determined with a knowledge of its formula. An unknown sample can be determined through thermogravimetric analysis (TGA) where the sample is heated strongly, and the accurate weight of a sample is plotted against the temperature. The amount of water driven off is then divided by the molar mass of water to obtain the number of molecules of water bound to the salt. | 1 | Crystallography |
There are three modes of formation of twinned crystals.
* Growth twins are the result of an interruption or change in the lattice during formation or growth due to a possible deformation from a larger substituting ion. Parallel growth describes a form of crystal growth that produces the appearance of a cluster of aligned crystals. Close examination reveals that the cluster is actually a single crystal. This is not twinning, since the crystal lattice is continuous throughout the cluster. Parallel growth likely takes place because it reduces system energy.
* Annealing or transformation twins are the result of a change in crystal system during cooling as one form becomes unstable and the crystal structure must re-organize or transform into another more stable form.
* Deformation or gliding twins are the result of stress on the crystal after the crystal has formed. Because growth twins are formed during the initial growth of the crystal, they are described as primary, whereas transformation or deformation twins are formed in an existing crystal and are described as secondary. | 1 | Crystallography |