text
stringlengths 107
11k
| label
int64 0
1
| label_text
stringclasses 2
values |
|---|---|---|
Column chromatography is an extremely time-consuming stage in any lab and can quickly become the bottleneck for any process lab. Many manufacturers like Biotage, Buchi, Interchim and Teledyne Isco have developed automated flash chromatography systems (typically referred to as LPLC, low pressure liquid chromatography, around ) that minimize human involvement in the purification process. Automated systems will include components normally found on more expensive high performance liquid chromatography (HPLC) systems such as a gradient pump, sample injection ports, a UV detector and a fraction collector to collect the eluent. Typically these automated systems can separate samples from a few milligrams up to an industrial many kilogram scale and offer a much cheaper and quicker solution to doing multiple injections on prep-HPLC systems.
The resolution (or the ability to separate a mixture) on an LPLC system will always be lower compared to HPLC, as the packing material in an HPLC column can be much smaller, typically only 5 micrometre thus increasing stationary phase surface area, increasing surface interactions and giving better separation. However, the use of this small packing media causes the high back pressure and is why it is termed high pressure liquid chromatography. The LPLC columns are typically packed with silica of around 50 micrometres, thus reducing back pressure and resolution, but it also removes the need for expensive high pressure pumps. Manufacturers are now starting to move into higher pressure flash chromatography systems and have termed these as medium pressure liquid chromatography (MPLC) systems which operate above . | 0 | Chromatography + Titration + pH indicators |
The electronic density functional is explicitly used in the calculation of the electronic ground state. Packages such as VASP have an option to calculate the electronic density of states per eV to facilitate the prediction of conduction bands and band gaps. | 1 | Crystallography |
In X-ray crystallography, crystallographic disorder describes the cocrystallization of more than one rotamer, conformer, or isomer where the center of mass of each form is identical or unresolvable. As a consequence of disorder, the crystallographic solution is the sum of the various forms. In many cases, the components of the disorder are equally abundant, and, in other cases, the weighting coefficients for each component differ. Disorder can entail a pair or several components, and usually arises when the forms are nearly equal in energy and the crystal lattice is sufficiently spacious to accommodate the various components. | 1 | Crystallography |
The Uhlenhuth test, or the antigen–antibody precipitin test for species, was invented by Paul Uhlenhuth in 1901 and could distinguish human blood from animal blood, based on the discovery that the blood of different species had one or more characteristic proteins. The test represented a major breakthrough and came to have tremendous importance in forensic science. The test was further refined for forensic use by the Swiss chemist Maurice Müller in the year 1960s. | 0 | Chromatography + Titration + pH indicators |
A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry. While crystals, according to the classical crystallographic restriction theorem, can possess only two-, three-, four-, and six-fold rotational symmetries, the Bragg diffraction pattern of quasicrystals shows sharp peaks with other symmetry orders—for instance, five-fold.
Aperiodic tilings were discovered by mathematicians in the early 1960s, and, some twenty years later, they were found to apply to the study of natural quasicrystals. The discovery of these aperiodic forms in nature has produced a paradigm shift in the field of crystallography. In crystallography the quasicrystals were predicted in 1981 by a five-fold symmetry study of Alan Lindsay Mackay,—that also brought in 1982, with the crystallographic Fourier transform of a Penrose tiling, the possibility of identifying quasiperiodic order in a material through diffraction.
Quasicrystals had been investigated and observed earlier, but, until the 1980s, they were disregarded in favor of the prevailing views about the atomic structure of matter. In 2009, after a dedicated search, a mineralogical finding, icosahedrite, offered evidence for the existence of natural quasicrystals.
Roughly, an ordering is non-periodic if it lacks translational symmetry, which means that a shifted copy will never match exactly with its original. The more precise mathematical definition is that there is never translational symmetry in more than n – 1 linearly independent directions, where n is the dimension of the space filled, e.g., the three-dimensional tiling displayed in a quasicrystal may have translational symmetry in two directions. Symmetrical diffraction patterns result from the existence of an indefinitely large number of elements with a regular spacing, a property loosely described as long-range order. Experimentally, the aperiodicity is revealed in the unusual symmetry of the diffraction pattern, that is, symmetry of orders other than two, three, four, or six. In 1982, materials scientist Dan Shechtman observed that certain aluminium–manganese alloys produced the unusual diffractograms which today are seen as revelatory of quasicrystal structures. Due to fear of the scientific community's reaction, it took him two years to publish the results for which he was awarded the Nobel Prize in Chemistry in 2011.
On 25 October 2018, Luca Bindi and Paul Steinhardt were awarded the Aspen Institute 2018 Prize for collaboration and scientific research between Italy and the United States, after they discovered icosahedrite, the first quasicrystal known to occur naturally. | 1 | Crystallography |
In physics, a phason is a form of collective excitation found in aperiodic crystal structures. Phasons are a type of quasiparticle: an emergent phenomenon of many-particle systems. Similar to phonons, phasons are quasiparticles associated with atomic motion. However, whereas phonons are related to the translation of atoms, phasons are associated with atomic rearrangement. As a result of this rearrangement, or modulation, the waves that describe the position of atoms in the crystal change phase -- hence the term "phason".
Phasons can travel faster than the speed of sound within quasicrystalline materials, giving these materials a higher thermal conductivity than materials in which the transfer of heat is carried out only by phonons. Different phasonic modes can change the material properties of a quasicrystal.
Within superspace representation, aperiodic crystals can be obtained by taking a section of a periodic crystal of higher dimension (up to 6D) and cutting at an irrational angle. While phonons change the position of atoms relative to the crystal structure in space, phasons change the position of atoms relative to the quasicrystal structure and the cut-through superspace that defines it. Therefore, phonon modes are excitations of the "in-plane" real (also called parallel or external) space, whereas phasons are excitations of the perpendicular (also called internal) space.
Models of describing phasons include hydrodynamic theory (which describes phasons as a continuous pattern of motion), and phasonic flips, where atoms collectively jump to new sites. Hydrodynamic analysis of quasicrystals predicts that, while the strain relaxation of phonons is relatively rapid, relaxation of phason strain is diffusive and is much slower. Therefore, metastable quasicrystals grown by rapid quenching from the melt exhibit built-in phason strain associated with shifts and anisotropic broadenings of X-ray and electron diffraction peaks. | 1 | Crystallography |
Light alone does not rapidly degrade methyl violet, but the process is accelerated upon the addition of large band-gap semiconductors, TiO or ZnO. | 0 | Chromatography + Titration + pH indicators |
Thin-layer chromatography (TLC) is a chromatography technique that separates components in non-volatile mixtures.
It is performed on a TLC plate made up of a non-reactive solid coated with a thin layer of adsorbent material. This is called the stationary phase. The sample is deposited on the plate, which is eluted with a solvent or solvent mixture known as the mobile phase (or eluent). This solvent then moves up the plate via capillary action. As with all chromatography, some compounds are more attracted to the mobile phase, while others are more attracted to the stationary phase. Therefore, different compounds move up the TLC plate at different speeds and become separated. To visualize colourless compounds, the plate is viewed under UV light or is stained. Testing different stationary and mobile phases is often necessary to obtain well-defined and separated spots.
TLC is quick, simple, and gives high sensitivity for a relatively low cost. It can monitor reaction progress, identify compounds in a mixture, determine purity, or purify small amounts of compound. | 0 | Chromatography + Titration + pH indicators |
Synthetic perovskites are possible materials for high-efficiency photovoltaics – they showed a conversion efficiency of up to 26.3% and can be manufactured using the same thin-film manufacturing techniques as that used for thin film silicon solar cells. Methylammonium tin halides and methylammonium lead halides are of interest for use in dye-sensitized solar cells. Some perovskite PV cells reach a theoretical peak efficiency of 31%.
Among the methylammonium halides studied so far the most common is the methylammonium lead triiodide (). It has a high charge carrier mobility and charge carrier lifetime that allow light-generated electrons and holes to move far enough to be extracted as current, instead of losing their energy as heat within the cell. effective diffusion lengths are some 100 nm for both electrons and holes.
Methylammonium halides are deposited by low-temperature solution methods (typically spin-coating). Other low-temperature (below 100 °C) solution-processed films tend to have considerably smaller diffusion lengths. Stranks et al. described nanostructured cells using a mixed methylammonium lead halide () and demonstrated one amorphous thin-film solar cell with an 11.4% conversion efficiency, and another that reached 15.4% using vacuum evaporation. The film thickness of about 500 to 600 nm implies that the electron and hole diffusion lengths were at least of this order. They measured values of the diffusion length exceeding 1 μm for the mixed perovskite, an order of magnitude greater than the 100 nm for the pure iodide. They also showed that carrier lifetimes in the mixed perovskite are longer than in the pure iodide. Liu et al. applied Scanning Photo-current Microscopy to show that the electron diffusion length in mixed halide perovskite along (110) plane is in the order of 10 μm.
For , open-circuit voltage (V) typically approaches 1 V, while for with low Cl content, V > 1.1 V has been reported. Because the band gaps (E) of both are 1.55 eV, V-to-E ratios are higher than usually observed for similar third-generation cells. With wider bandgap perovskites, V up to 1.3 V has been demonstrated.
The technique offers the potential of low cost because of the low temperature solution methods and the absence of rare elements. Cell durability is currently insufficient for commercial use. However, the solar cells are prone to degradation due to volatility of the organic [CHNH]I salt. The all-inorganic perovskite cesium lead iodide perovskite (CsPbI) circumvents this problem, but is itself phase-unstable, the low temperature solution methods of which have only been recently developed.
Planar heterojunction perovskite solar cells can be manufactured in simplified device architectures (without complex nanostructures) using only vapor deposition. This technique produces 15% solar-to-electrical power conversion as measured under simulated full sunlight. | 1 | Crystallography |
Protein crystallization is governed by the same physics that governs the formation of inorganic crystals. For crystallization to occur spontaneously, the crystal state must be favored thermodynamically. This is described by Gibb's free energy (∆G), defined as ∆G = ∆H- T∆S, which captures how the energetics of a process, ∆H, trades off with the corresponding change in entropy, ∆S. Entropy, roughly, describes the disorder of a system. Highly ordered states, such as protein crystals, are disfavored thermodynamically compared to more disordered states, such as solutions of proteins in solvent, because the transition to a more ordered state would decrease the total entropy of the system (positive ∆S). For crystals to form spontaneously, the ∆G of crystal formation must be negative. In other words, the entropic penalty must be paid by a corresponding decrease in the total energy of the system (∆H). Familiar inorganic crystals such as sodium chloride spontaneously form at ambient conditions because the crystal state decreases the total energy of the system. However, crystallization of some proteins under ambient conditions would both decrease the entropy (positive ∆S) and increase the total energy (positive ∆H) of the system, and thus does not occur spontaneously. To achieve crystallization of such proteins conditions are modified to make crystal formation energetically favorable. This is often accomplished by creation of a supersaturated solution of the sample. | 1 | Crystallography |
Despite the reduced efficiency verses reversed phase HPLC, hundreds of applications have been reported using MLC. One of the most advantageous is the ability to directly inject physiological fluids. Micelles have an ability to solubilize proteins which enables MLC to be useful in analyzing untreated biological fluids such as plasma, serum, and urine. Martinez et al. found MLC to be highly useful in analyzing a class of drugs called b-antagonists, so called beta-blockers, in urine samples. The main advantage of the use of MLC with this type of sample, is the great time savings in sample preparation. Alternative methods of analysis including reversed phase HPLC require lengthy extraction and sample work up procedures before analysis can begin. With MLC, direct injection is often possible, with retention times of less than 15 minutes for the separation of up to nine b-antagonists.
Another application compared reversed phase HPLC with MLC for the analysis of desferrioxamine in serum. Desferrioxamine (DFO) is a commonly used drug for removal of excess iron in patients with chronic and acute levels. The analysis of DFO along with its chelated complexes, Fe(III) DFO and Al(III) DFO has proven to be difficult at best in previous attempts. This study found that direct injection of the serum was possible for MLC, verses an ultrafiltration step necessary in HPLC. This analysis proved to have difficulties with the separation of the chelated DFO compounds and with the sensitivity levels for DFO itself when MLC was applied. The researcher found that, in this case, reverse phase HPLC, was a better, more sensitive technique despite the time savings in direct injection.
Analysis of pharmaceuticals by MLC is also gaining popularity. The selectivity and peak shape of MLC over commonly used ion-pair chromatography is much enhanced. MLC mimics, yet enhances, the selectivity offered by ion-pairing reagents for the separation of active ingredients in pharmaceutical drugs. For basic drugs, MLC improves the excessive peak tailing frequently observed in ion-pairing. Hydrophilic drugs are often unretained using conventional HPLC, are retained by MLC due to solubilization into the micelles. Commonly found drugs in cold medications such as acetaminophen, L-ascorbic acid, phenylpropanolamine HCL, tipepidine hibenzate, and chlorpheniramine maleate have been successfully separated with good peak shape using MLC. Additional basic drugs like many narcotics, such as codeine and morphine, have also been successfully separated using MLC.
Another novel application of MLC involves the separation and analysis of inorganic compounds, mostly simple ions. This is a relatively new area for MLC, but has seen some promising results. MLC has been observed to provide better selectivity of inorganic ions that ion-exchange or ion-pairing chromatography. While this application is still in the beginning stages of development, the possibilities exist for novel, much enhanced separations of inorganic species.
Since the technique was first reported on in 1980, micellar liquid chromatography has been used in hundreds of applications. This micelle controlled technique provides for unique opportunities for solving complicated separation problems. Despite the poor efficiency of MLC, it has been successfully used in many applications. The use of MLC in the future appears to be extremely advantages in the areas of physiological fluids, pharmaceuticals, and even inorganic ions. The technique has proven to be superior over ion-pairing and ion-exchange for many applications. As new approaches are developed to combat the poor efficiency of MLC, its application is sure to spread and gain more acceptance. | 0 | Chromatography + Titration + pH indicators |
In crystallography, a lattice plane of a given Bravais lattice is any plane containing at least three noncollinear Bravais lattice points. Equivalently, a lattice plane is a plane whose intersections with the lattice (or any crystalline structure of that lattice) are periodic (i.e. are described by 2d Bravais lattices). A family of lattice planes is a collection of equally spaced parallel lattice planes that, taken together, intersect all lattice points. Every family of lattice planes can be described by a set of integer Miller indices that have no common divisors (i.e. are relative prime). Conversely, every set of Miller indices without common divisors defines a family of lattice planes. If, on the other hand, the Miller indices are not relative prime, the family of planes defined by them is not a family of lattice planes, because not every plane of the family then intersects lattice points.
Conversely, planes that are not lattice planes have aperiodic intersections with the lattice called quasicrystals; this is known as a "cut-and-project" construction of a quasicrystal (and is typically also generalized to higher dimensions). | 1 | Crystallography |
A crystal structure is defined as the spatial distribution of the atoms within a crystal, usually modeled by the idea of an infinite crystal pattern. An infinite crystal pattern refers to the infinite 3D periodic array which corresponds to a crystal, in which the lengths of the periodicities of the array may not be made arbitrarily small. The geometrical shift which takes a crystal structure coincident with itself is termed a symmetry translation (translation) of the crystal structure. The vector which is related to this shift is called a translation vector . Since a crystal pattern is periodic, all integer linear combinations of translation vectors are also themselves translation vectors, | 1 | Crystallography |
The spacing d between adjacent (hkℓ) lattice planes is given by:
*Cubic:
*Tetragonal:
*Hexagonal:
*Rhombohedral (primitive setting):
*Orthorhombic:
*Monoclinic:
*Triclinic: | 1 | Crystallography |
Precession electron diffraction is typically conducted using accelerating voltages between 100-400 kV. Patterns can be formed under parallel or convergent beam conditions. Most modern TEMs can achieve a tilt angle, φ, ranging from 0-3°. Precession frequencies can be varied from Hz to kHz, but in standard cases 60 Hz has been used. In choosing a precession rate, it is important to ensure that many revolutions of the beam occur over the relevant exposure time used to record the diffraction pattern. This ensures adequate averaging over the excitation error of each reflection. Beam sensitive samples may dictate shorter exposure times and thus, motivate the use of higher precession frequencies.
One of the most significant parameters affecting the diffraction pattern obtained is the precession angle, φ. In general, larger precession angles result in more kinematical diffraction patterns, but both the capabilities of the beam tilt coils in the microscope and the requirements on the probe size limit how large this angle can become in practice. Because PED takes the beam off of the optic axis by design, it accentuates the effect of the spherical aberrations within the probe forming lens. For a given spherical aberration, C, the probe diameter, d, varies with convergence angle, α, and precession angle, φ, as
Thus, if the specimen of interest is quite small, the maximum precession angle will be restrained. This is most significant for conditions of convergent beam illumination. 50 nm is a general lower limit on probe size for standard TEMs operating at high precession angles (>30 mrad), but can be surpassed in C corrected instruments. In principle the minimum precessed probe can reach approximately the full-width-half-max (FWHM) of the converged un-precessed probe in any instrument, however in practice the effective precessed probe is typically ~10-50x larger due to uncontrolled aberrations present at high angles of tilt. For example, a 2 nm precessed probe with >40 mrad precession angle was demonstrated in an aberration-corrected Nion UltraSTEM with native sub-Å probe (aberrations corrected to ~35 mrad half-angle).
If the precession angle is made too large, further complications due to the overlap of the ZOLZ and HOLZ reflections in the projected pattern can occur. This complicates the indexing of the diffraction pattern and can corrupt the measured intensities of reflections near the overlap region, thereby reducing the effectiveness of the collected pattern for direct methods calculations. | 1 | Crystallography |
In powder samples there is a tendency for plate- or rod-like crystallites to align themselves along the axis of a cylindrical sample holder. In solid polycrystalline samples the production of the material may result in greater volume fraction of certain crystal orientations (commonly referred to as texture). In such cases the reflex intensities will vary from that predicted for a completely random distribution. Rietveld allowed for moderate cases of the former by introducing a correction factor:
where is the intensity expected for a random sample, is the preferred orientation parameter and is the acute angle between the scattering vector and the normal of the crystallites. | 1 | Crystallography |
Composition of isometries mixes kinds in assorted ways. We can think of the identity as either two mirrors or none; either way, it has no effect in composition. And two reflections give either a translation or a rotation, or the identity (which is both, in a trivial way). Reflection composed with either of these could cancel down to a single reflection; otherwise it gives the only available three-mirror isometry, a glide reflection. A pair of translations always reduces to a single translation; so the challenging cases involve rotations. We know a rotation composed with either a rotation or a translation must produce an even isometry. Composition with translation produces another rotation (by the same amount, with shifted fixed point), but composition with rotation can yield either translation or rotation. It is often said that composition of two rotations produces a rotation, and Euler proved a theorem to that effect in 3D; however, this is only true for rotations sharing a fixed point. | 1 | Crystallography |
Methyl orange has mutagenic properties. When methyl orange is put under oxidative stress, one of the double-bonded nitrogen atoms that connects the aromatic rings gets radicalized and can further break down into reactive oxygen species or anilines, which are carcinogenic and can mutate DNA. Various bacteria and enzymes can also cause this breakdown to occur. | 0 | Chromatography + Titration + pH indicators |
When the dimension of the lattice rises to four or more, rotations need no longer be planar; the 2D proof is inadequate. However, restrictions still apply, though more symmetries are permissible. For example, the hypercubic lattice has an eightfold rotational symmetry, corresponding to an eightfold rotational symmetry of the hypercube. This is of interest, not just for mathematics, but for the physics of quasicrystals under the cut-and-project theory. In this view, a 3D quasicrystal with 8-fold rotation symmetry might be described as the projection of a slab cut from a 4D lattice.
The following 4D rotation matrix is the aforementioned eightfold symmetry of the hypercube (and the cross-polytope):
Transforming this matrix to the new coordinates given by
: will produce:
This third matrix then corresponds to a rotation both by 45° (in the first two dimensions) and by 135° (in the last two). Projecting a slab of hypercubes along the first two dimensions of the new coordinates produces an Ammann–Beenker tiling (another such tiling is produced by projecting along the last two dimensions), which therefore also has 8-fold rotational symmetry on average.
The A4 lattice and F4 lattice have order 10 and order 12 rotational symmetries, respectively.
To state the restriction for all dimensions, it is convenient to shift attention away from rotations alone and concentrate on the integer matrices . We say that a matrix A has order k when its k-th power (but no lower), A, equals the identity. Thus a 6-fold rotation matrix in the equilateral triangle basis is an integer matrix with order 6. Let Ord denote the set of integers that can be the order of an N×N integer matrix. For example, Ord = {1, 2, 3, 4, 6}. We wish to state an explicit formula for Ord.
Define a function ψ based on Eulers totient function φ; it will map positive integers to non-negative integers. For an odd prime, p, and a positive integer, k, set ψ(p) equal to the totient function value,
φ(p), which in this case is p−p. Do the same for ψ(2) when k > 1. Set ψ(2) and ψ(1) to 0. Using the fundamental theorem of arithmetic, we can write any other positive integer uniquely as a product of prime powers, m = Π p; set ψ(m) = Σ ψ(p). This differs from the totient itself, because it is a sum instead of a product.
The crystallographic restriction in general form states that Ord consists of those positive integers m such that ψ(m) ≤ N.
For m>2, the values of ψ(m) are equal to twice the algebraic degree of cos(2π/m); therefore, ψ(m) is strictly less than m and reaches this maximum value if and only if m is a prime.
These additional symmetries do not allow a planar slice to have, say, 8-fold rotation symmetry. In the plane, the 2D restrictions still apply. Thus the cuts used to model quasicrystals necessarily have thickness.
Integer matrices are not limited to rotations; for example, a reflection is also a symmetry of order 2. But by insisting on determinant +1, we can restrict the matrices to proper rotations. | 1 | Crystallography |
Brown MX-5BR or Reactive Brown 10 has a formula of CHClCrNNaOS and a molecular weight of 1163.6 g/mol, containing two dichlorotriazine rings. Brown MX-5BR, for example, can be used to purify lysozyme, phosphinothricin acetyltransferase. It also shown that it can elute tryptophanyl-tRNA synthetase using Trp as eluant, however, tryptophanyl-tRNA and tyrosyl-tRNA synthetase are the only t-RNA that can be elute out using Brown MX-5BR. | 0 | Chromatography + Titration + pH indicators |
The compressive strength and hardness of diamond and various other materials, such as boron nitride, (which has the closely related zincblende structure) is attributed to the diamond cubic structure.
Similarly, truss systems that follow the diamond cubic geometry have a high capacity to withstand compression, by minimizing the unbraced length of individual struts. The diamond cubic geometry has also been considered for the purpose of providing structural rigidity though structures composed of skeletal triangles, such as the octet truss, have been found to be more effective for this purpose. | 1 | Crystallography |
The elementary reaction responsible for water quantification in the Karl Fischer titration is oxidation of sulfur dioxide () with iodine:
This elementary reaction consumes exactly one molar equivalent of water vs. iodine. Iodine is added to the solution until it is present in excess, marking the end point of the titration, which can be detected by potentiometry. The reaction is run in an alcohol solution containing a base, which consumes the sulfur trioxide and hydroiodic acid produced. | 0 | Chromatography + Titration + pH indicators |
Crystallization is largely over when reaches values close to 1, which will be at a crystallization time defined by , as then the exponential term in the above expression for will be small. Thus crystallization takes a time of order
i.e., crystallization takes a time that decreases as one over the one-quarter power of the nucleation rate per unit volume, , and one over the three-quarters power of the growth velocity . Typical crystallites grow for some fraction of the crystallization time and so have a linear dimension , or
i.e., the one quarter power of the ratio of the growth velocity to the nucleation rate per unit volume. Thus the size of the final crystals only depends on this ratio, within this model, and as we should expect, fast growth rates and slow nucleation rates result in large crystals. The average volume of the crystallites is of order this typical linear size cubed.
This all assumes an exponent of , which is appropriate for the uniform (homogeneous) nucleation in three dimensions. Thin films, for example, may be effectively two-dimensional, in which case if nucleation is again uniform the exponent . In general, for uniform nucleation and growth, , where is the dimensionality of space in which crystallization occurs. | 1 | Crystallography |
Hydrostatic CCC or centrifugal partition chromatography (CPC) was invented in the 1980s by the Japanese company Sanki Engineering Ltd, whose president was Kanichi Nunogaki. CPC has been extensively developed in France starting from the late 1990s. In France, they initially optimized the stacked disc concept initiated by Sanki. More recently, in France and UK, non-stacked disc CPC configurations have been developed with PTFE, stainless steel or titanium rotors. These have been designed to overcome possible leakages between the stacked discs of the original concept, and to allow steam cleaning for good manufacturing practice. The volumes ranging from a 100 ml to 12 liters are available in different rotor materials. The 25-liter rotor CPC has a titanium rotor. This technique is sometimes sold under the name "fast" CPC or "high-performance" CPC. | 0 | Chromatography + Titration + pH indicators |
Reversed phase HPLC (RP-HPLC) is the most widespread mode of chromatography. It has a non-polar stationary phase and an aqueous, moderately polar mobile phase. In the reversed phase methods, the substances are retained in the system the more hydrophobic they are. For the retention of organic materials, the stationary phases, packed inside the columns, are consisted mainly of porous granules of silica gel in various shapes, mainly spherical, at different diameters (1.5, 2, 3, 5, 7, 10 um), with varying pore diameters (60, 100, 150, 300, A), on whose surface are chemically bound various hydrocarbon ligands such as C3, C4, C8,C18. There are also polymeric hydrophobic particles that serve as stationary phases, when solutions at extreme pH are needed, or hybrid silica, polymerized with organic substances. The longer the hydrocarbon ligand on the stationary phase, the longer the sample components can be retained. Most of the current methods of separation of biomedical materials use C-18 type of columns, sometimes called by a trade names such as ODS (octadecylsilane) or RP-18 (Reversed Phase 18).
The most common RP stationary phases are based on a silica support, which is surface-modified by bonding RMeSiCl, where R is a straight chain alkyl group such as CH or CH.
With such stationary phases, retention time is longer for lipophylic molecules, whereas polar molecules elute more readily (emerge early in the analysis). A chromatographer can increase retention times by adding more water to the mobile phase, thereby making the interactions of the hydrophobic analyte with the hydrophobic stationary phase relatively stronger. Similarly, an investigator can decrease retention time by adding more organic solvent to the mobile phase. RP-HPLC is so commonly used among the biologists and life science users, therefore it is often incorrectly referred to as just "HPLC" without further specification. The pharmaceutical industry also regularly employs RP-HPLC to qualify drugs before their release.
RP-HPLC operates on the principle of hydrophobic interactions, which originates from the high symmetry in the dipolar water structure and plays the most important role in all processes in life science. RP-HPLC allows the measurement of these interactive forces. The binding of the analyte to the stationary phase is proportional to the contact surface area around the non-polar segment of the analyte molecule upon association with the ligand on the stationary phase. This solvophobic effect is dominated by the force of water for "cavity-reduction" around the analyte and the C-chain versus the complex of both. The energy released in this process is proportional to the surface tension of the eluent (water: 7.3 J/cm, methanol: 2.2 J/cm) and to the hydrophobic surface of the analyte and the ligand respectively. The retention can be decreased by adding a less polar solvent (methanol, acetonitrile) into the mobile phase to reduce the surface tension of water. Gradient elution uses this effect by automatically reducing the polarity and the surface tension of the aqueous mobile phase during the course of the analysis.
Structural properties of the analyte molecule can play an important role in its retention characteristics. In theory, an analyte with a larger hydrophobic surface area (C–H, C–C, and generally non-polar atomic bonds, such as S-S and others) can be retained longer as it does not interact with the water structure. On the other hand, analytes with higher polar surface area (as a result of the presence of polar groups, such as -OH, -NH, COO or -NH in their structure) are less retained, as they are better integrated into water. The interactions with the stationary phase can also affected by steric effects, or exclusion effects, whereby a component of very large molecule may have only restricted access to the pores of the stationary phase, where the interactions with surface ligands (alkyl chains) take place. Such surface hindrance typically results in less retention.
Retention time increases with more hydrophobic (non-polar) surface area of the molecules. For example, branched chain compounds can elute more rapidly than their corresponding linear isomers because their overall surface area is lower. Similarly organic compounds with single C–C bonds frequently elute later than those with a C=C or even triple bond, as the double or triple bond makes the molecule more compact than a single C–C bond.
Another important factor is the mobile phase pH since it can change the hydrophobic character of the ionizable analyte. For this reason most methods use a buffering agent, such as sodium phosphate, to control the pH. Buffers serve multiple purposes: control of pH which affects the ionization state of the ionizable analytes, affect the charge upon the ionizable silica surface of the stationary phase in between the bonded phase linands, and in some cases even act as ion pairing agents to neutralize analyte charge. Ammonium formate is commonly added in mass spectrometry to improve detection of certain analytes by the formation of analyte-ammonium adducts. A volatile organic acid such as acetic acid, or most commonly formic acid, is often added to the mobile phase if mass spectrometry is used to analyze the column effluents.
Trifluoroacetic acid as additive to the mobile phase is widely used for complex mixtures of biomedical samples, mostly peptides and proteins, using mostly a UV based detectors. They are used rarely used in mass spectrometry methods, due to its residues it can leave in the detector and solvent delivery system, which interfere with the analysis and detection. However it can be highly effective in improving retention of analytes such as carboxylic acids, in applications utilizing other detectors such as UV-VIS, as it is a fairly strong organic acid. The effects of acids and buffers vary by application but generally improve chromatographic resolution when dealing with ionizable components.
Reversed phase columns are quite difficult to damage compared to normal silica columns, thanks to the shielding effect of the bonded hydrophobic ligands; however, most reversed phase columns consist of alkyl derivatized silica particles, and are prone to hydrolysis of the silica at extreme pH conditions in the mobile phase. Most types of RP columns should not be used with aqueous bases as these will hydrolyze the underlying silica particle and dissolve it. There are selected brands of hybrid or enforced silica based particles of RP columns which can be used at extreme pH conditions. The use of extreme acidic conditions is also not recommended, as they also might hydrolyzed as well as corrode the inside walls of the metallic parts of the HPLC equipment.
As a rule, in most cases RP-HPLC columns should be flushed with clean solvent after use to remove residual acids or buffers, and stored in an appropriate composition of solvent. Some biomedical applications require non metallic environment for the optimal separation. For such sensitive cases there is a test for the metal content of a column is to inject a sample which is a mixture of 2,2- and 4,4-bipyridine. Because the 2,2-bipy can chelate the metal, the shape of the peak for the 2,2-bipy will be distorted (tailed) when metal ions are present on the surface of the silica... | 0 | Chromatography + Titration + pH indicators |
The basic principle of displacement chromatography is: there are only a finite number of binding sites for solutes on the matrix (the stationary phase), and if a site is occupied by one molecule, it is unavailable to others. As in any chromatography, equilibrium is established between molecules of a given kind bound to the matrix and those of the same kind free in solution. Because the number of binding sites is finite, when the concentration of molecules free in solution is large relative to the dissociation constant for the sites, those sites will mostly be filled. This results in a downward-curvature in the plot of bound vs free solute, in the simplest case giving a Langmuir isotherm. A molecule with a high affinity for the matrix (the displacer) will compete more effectively for binding sites, leaving the mobile phase enriched in the lower-affinity solute. Flow of mobile phase through the column preferentially carries off the lower-affinity solute and thus at high concentration the higher-affinity solute will eventually displace all molecules with lesser affinities. | 0 | Chromatography + Titration + pH indicators |
In analytical chemistry, argentometry is a type of titration involving the silver(I) ion. Typically, it is used to determine the amount of chloride present in a sample. The sample solution is titrated against a solution of silver nitrate of known concentration. Chloride ions react with silver(I) ions to give the insoluble silver chloride:
: Ag (aq) + Cl (aq) → AgCl (s) (K = 5.88 × 10) | 0 | Chromatography + Titration + pH indicators |
An eluotropic series, which orders solvents by how much they move compounds, can help in selecting a mobile phase. Solvents are also divided into solvent selectivity groups. Using solvents with different elution strengths or different selectivity groups can often give very different results. While single-solvent mobile phases can sometimes give good separation, some cases may require solvent mixtures.
In normal-phase TLC, the most common solvent mixtures include ethyl acetate/hexanes (EtOAc/Hex) for less-polar compounds and methanol/dichloromethane (MeOH/DCM) for more polar compounds. Different solvent mixtures and solvent ratios can help give better separation. In reverse-phase TLC, solvent mixtures are typically water with a less-polar solvent: Typical choices are water with tetrahydrofuran (THF), acetonitrile (ACN), or methanol. | 0 | Chromatography + Titration + pH indicators |
*Winkler test for dissolved oxygen: Used to determine oxygen concentration in water. Oxygen in water samples is reduced using manganese(II) sulfate, which reacts with potassium iodide to produce iodine. The iodine is released in proportion to the oxygen in the sample, thus the oxygen concentration is determined with a redox titration of iodine with thiosulfate using a starch indicator.
*Vitamin C: Also known as ascorbic acid, vitamin C is a powerful reducing agent. Its concentration can easily be identified when titrated with the blue dye Dichlorophenolindophenol (DCPIP) which becomes colorless when reduced by the vitamin.
*Benedicts reagent: Excess glucose in urine may indicate diabetes in a patient. Benedicts method is the conventional method to quantify glucose in urine using a prepared reagent. During this type of titration, glucose reduces cupric ions to cuprous ions which react with potassium thiocyanate to produce a white precipitate, indicating the endpoint.
*Bromine number: A measure of unsaturation in an analyte, expressed in milligrams of bromine absorbed by 100 grams of sample.
*Iodine number: A measure of unsaturation in an analyte, expressed in grams of iodine absorbed by 100 grams of sample. | 0 | Chromatography + Titration + pH indicators |
If we attempt to build a densely packed collection of spheres, we will be tempted to always place the next sphere in a hollow between three packed spheres. If five spheres are assembled in this way, they will be consistent with one of the regularly packed arrangements described above. However, the sixth sphere placed in this way will render the structure inconsistent with any regular arrangement. This results in the possibility of a random close packing of spheres which is stable against compression. Vibration of a random loose packing can result in the arrangement of spherical particles into regular packings, a process known as granular crystallisation. Such processes depend on the geometry of the container holding the spherical grains.
When spheres are randomly added to a container and then compressed, they will generally form what is known as an "irregular" or "jammed" packing configuration when they can be compressed no more. This irregular packing will generally have a density of about 64%. Recent research predicts analytically that it cannot exceed a density limit of 63.4% This situation is unlike the case of one or two dimensions, where compressing a collection of 1-dimensional or 2-dimensional spheres (that is, line segments or circles) will yield a regular packing. | 1 | Crystallography |
Displacement chromatography is a chromatography technique in which a sample is placed onto the head of the column and is then displaced by a solute that is more strongly sorbed than the components of the original mixture. The result is that the components are resolved into consecutive "rectangular" zones of highly concentrated pure substances rather than solvent-separated "peaks". It is primarily a preparative technique; higher product concentration, higher purity, and increased throughput may be obtained compared to other modes of chromatography. | 0 | Chromatography + Titration + pH indicators |
A key choice that must be made is how many atoms to explicitly include in ones calculation. In Big-O notation, calculations general scale as O(N3) where N is the number of combined ions and valence electrons. For structure calculations, it is generally desirable to choose the smallest number of ions that can represent the structure. For example, NaCl is a bcc cubic structure. At a first guess, one might construct a cell of two interlocked cubes – 8 Na and 8 Cl – as ones unit cell. This will give the correct answer but is computationally wasteful. By choosing appropriate coordinates, one might simulate it with just two atoms: 1 Na and 1 Cl.
Crystal structure calculations rely on periodic boundary conditions. That is, the assumption is that the cell you have chosen is in the midst of an infinite lattice of identical cells. By taking our 1 Na 1 Cl cell and copying it many times along each of the crystal axes, we will have simulated the same superstructure as our 8 Na 8 Cl cell but with much reduced computational cost. | 1 | Crystallography |
Cresol red can also be used as an electrophoretic color marker to monitor the process of agarose gel electrophoresis and polyacrylamide gel electrophoresis. In a 1% agarose gel, it runs approximately at the size of a 125 base pair (bp) DNA molecule (it depends on the concentration of buffer and other component). Bromophenol blue and xylene cyanol can also be used for this purpose. | 0 | Chromatography + Titration + pH indicators |
A symmetry of a Euclidean graph is an isometry of the underlying Euclidean space whose restriction to the graph is an automorphism; the symmetry group of the Euclidean graph is the group of its symmetries. A Euclidean graph in three-dimensional Euclidean space is periodic if there exist three linearly independent translations whose restrictions to the net are symmetries of the net. Often (and always, if one is dealing with a crystal net), the periodic net has finitely many orbits, and is thus uniformly discrete in that there exists a minimum distance between any two vertices.
The result is a three-dimensional periodic graph as a geometric object.
The resulting crystal net will induce a lattice of vectors so that given three vectors that generate the lattice, those three vectors will bound a unit cell, i.e. a parallelepiped which, placed anywhere in space, will enclose a fragment of the net that repeats in the directions of the three axes. | 1 | Crystallography |
An isometry of the Euclidean plane is a distance-preserving transformation of the plane. That is, it is a map
such that for any points p and q in the plane,
where d(p, q) is the usual Euclidean distance between p and q. | 1 | Crystallography |
Comprehensive two-dimensional gas chromatography is an analytical technique that separates and analyzes complex mixtures. It has been utilized in fields such as: flavor, fragrance, environmental studies, pharmaceuticals, petroleum products and forensic science. GCxGC provides a high range of sensitivity and produces a greater separation power due to the increased peak capacity. | 0 | Chromatography + Titration + pH indicators |
The Freundlich adsorption isotherm is mathematically expressed as
In Freundlichs notation (used for his experiments dealing with the adsorption of organic acids on coal in aqueous solutions), signifies the ratio between the adsorbed mass or adsorbate and the mass of the adsorbent , which in Freundlichs studies was coal. In the figure above, the x-axis represents , which denotes the equilibrium concentration of the adsorbate within the solvent.
Freundlich's numerical analysis of the three organic acids for the parameters and according to equation
were:
Freundlich's experimental data can also be used in a contemporary computer based fit. These values are added to appreciate the numerical work done in 1907.
△ K and △ n values are the error bars of the computer based fit. The K and n values itself are used to calculate the dotted lines in the figure.
Equation can also be written as
Sometimes also this notation for experiments in the gas phase can be found:
: = mass of adsorbate
: = mass of adsorbent
: = equilibrium pressure of the gaseous adsorbate in case of experiments made in the gas phase (gas/solid interaction with gaseous species/adsorbed species)
and are constants for a given adsorbate and adsorbent at a given temperature (from there, the term isotherm needed to avoid significant gas pressure fluctuations due to uncontrolled temperature variations in the case of adsorption experiments of a gas onto a solid phase).
: = distribution coefficient
: = correction factor
At high pressure , hence extent of adsorption becomes independent of pressure.
The Freundlich equation is unique; consequently, if the data fit the equation, it is only likely, but not proved, that the surface is heterogeneous. The heterogeneity of the surface can be confirmed with calorimetry. Homogeneous surfaces (or heterogeneous surfaces that exhibit homogeneous adsorption (single site)) have a constant of adsorption. On the other hand, heterogeneous adsorption (multi-site) have a variable of adsorption depending on the percent of sites occupied. When the adsorbate pressure in the gas phase (or the concentration in solution) is low, high-energy sites will be occupied first. As the pressure in the gas phase (or the concentration in solution) increases, the low-energy sites will then be occupied resulting in a weaker of adsorption. | 0 | Chromatography + Titration + pH indicators |
Le Bail analysis is commonly a part of Rietveld analysis software, such as GSAS/EXPGUI. It is also used in ARITVE, BGMN, EXPO, EXTRACT, FullProf, GENEFP, Jana2006, Overlap, Powder Cell, Rietan, TOPAS and Highscore. | 1 | Crystallography |
The trihexagonal tiling exists in a sequence of symmetries of quasiregular tilings with vertex configurations (3.n), progressing from tilings of the sphere to the Euclidean plane and into the hyperbolic plane. With orbifold notation symmetry of *n32 all of these tilings are wythoff construction within a fundamental domain of symmetry, with generator points at the right angle corner of the domain. | 1 | Crystallography |
The first reaction of iodine with SO and water is as follows:
SO+I+2HO→HSO+2HI
As the reaction proceeds, all available SO will be consumed and the starch indicator added to the solution will bind with the unconsumed iodine, turning the solution black.
The second step of the reaction requires pretreating with solution with NaOH to release bound SO. The reaction with iodine can then be done.
HSO⇌HSO⇌SO | 0 | Chromatography + Titration + pH indicators |
Gas chromatography–mass spectrometry (GC–MS) is an analytical method that combines the features of gas-chromatography and mass spectrometry to identify different substances within a test sample. Applications of GC–MS include drug detection, fire investigation, environmental analysis, explosives investigation, food and flavor analysis, and identification of unknown samples, including that of material samples obtained from planet Mars during probe missions as early as the 1970s. GC–MS can also be used in airport security to detect substances in luggage or on human beings. Additionally, it can identify trace elements in materials that were previously thought to have disintegrated beyond identification. Like liquid chromatography–mass spectrometry, it allows analysis and detection even of tiny amounts of a substance.
GC–MS has been regarded as a "gold standard" for forensic substance identification because it is used to perform a 100% specific test, which positively identifies the presence of a particular substance. A nonspecific test merely indicates that any of several in a category of substances is present. Although a nonspecific test could statistically suggest the identity of the substance, this could lead to false positive identification. However, the high temperatures (300°C) used in the GC–MS injection port (and oven) can result in thermal degradation of injected molecules, thus resulting in the measurement of degradation products instead of the actual molecule(s) of interest. | 0 | Chromatography + Titration + pH indicators |
The equivalence point, or stoichiometric point, of a chemical reaction is the point at which chemically equivalent quantities of reactants have been mixed. For an acid-base reaction the equivalence point is where the moles of acid and the moles of base would neutralize each other according to the chemical reaction. This does not necessarily imply a 1:1 molar ratio of acid:base, merely that the ratio is the same as in the chemical reaction. It can be found by means of an indicator, for example phenolphthalein or methyl orange.
The endpoint (related to, but not the same as the equivalence point) refers to the point at which the indicator changes color in a colorimetric titration. | 0 | Chromatography + Titration + pH indicators |
Typical titrations require titrant and analyte to be in a liquid (solution) form. Though solids are usually dissolved into an aqueous solution, other solvents such as glacial acetic acid or ethanol are used for special purposes (as in petrochemistry, which specializes in petroleum.) Concentrated analytes are often diluted to improve accuracy.
Many non-acid–base titrations require a constant pH during the reaction. Therefore, a buffer solution may be added to the titration chamber to maintain the pH.
In instances where two reactants in a sample may react with the titrant and only one is the desired analyte, a separate masking solution may be added to the reaction chamber which eliminates the effect of the unwanted ion.
Some reduction-oxidation (redox) reactions may require heating the sample solution and titrating while the solution is still hot to increase the reaction rate. For instance, the oxidation of some oxalate solutions requires heating to to maintain a reasonable rate of reaction. | 0 | Chromatography + Titration + pH indicators |
In two-dimensional space there are 5 Bravais lattices, grouped into four lattice systems, shown in the table below. Below each diagram is the Pearson symbol for that Bravais lattice.
Note: In the unit cell diagrams in the following table the lattice points are depicted using black circles and the unit cells are depicted using parallelograms (which may be squares or rectangles) outlined in black. Although each of the four corners of each parallelogram connects to a lattice point, only one of the four lattice points technically belongs to a given unit cell and each of the other three lattice points belongs to one of the adjacent unit cells. This can be seen by imagining moving the unit cell parallelogram slightly left and slightly down while leaving all the black circles of the lattice points fixed.
The unit cells are specified according to the relative lengths of the cell edges (a and b) and the angle between them (θ). The area of the unit cell can be calculated by evaluating the norm , where a and b are the lattice vectors. The properties of the lattice systems are given below: | 1 | Crystallography |
* Orbifold signature:
* Coxeter notation (rhombic): [∞,2,∞]
* Coxeter notation (square): [(4,4,2)]
* Lattice: rhombic
* Point group: D
* The group cmm has reflections in two perpendicular directions, and a rotation of order two (180°) whose centre is not on a reflection axis. It also has two rotations whose centres are on a reflection axis.
*This group is frequently seen in everyday life, since the most common arrangement of bricks in a brick building (running bond) utilises this group (see example below).
The rotational symmetry of order 2 with centres of rotation at the centres of the sides of the rhombus is a consequence of the other properties.
The pattern corresponds to each of the following:
*symmetrically staggered rows of identical doubly symmetric objects
*a checkerboard pattern of two alternating rectangular tiles, of which each, by itself, is doubly symmetric
*a checkerboard pattern of alternatingly a 2-fold rotationally symmetric rectangular tile and its mirror image
;Examples of group cmm | 1 | Crystallography |
Scandium has the smallest atomic and ionic (3+) radii (1.62 and 0.885 Å, respectively) among the rare-earth elements. It forms several icosahedron-based borides which are not found for other rare-earth elements; however, most of them are ternary Sc-B-C compounds. There are many boron-rich phases in the boron-rich corner of Sc-B-C phase diagram, as shown in figure 17. A slight variation of the composition can produce ScB, ScBC, ScBC and ScBC; their crystal structures are unusual for borides and are very different from each other. | 1 | Crystallography |
In the Euclidean plane, reflections and glide reflections are the only two kinds of indirect (orientation-reversing) isometries.
For example, there is an isometry consisting of the reflection on the x-axis, followed by translation of one unit parallel to it. In coordinates, it takes
This isometry maps the x-axis to itself; any other line which is parallel to the x-axis gets reflected in the x-axis, so this system of parallel lines is left invariant.
The isometry group generated by just a glide reflection is an infinite cyclic group.
Combining two equal glide reflections gives a pure translation with a translation vector that is twice that of the glide reflection, so the even powers of the glide reflection form a translation group.
In the case of glide-reflection symmetry, the symmetry group of an object contains a glide reflection, and hence the group generated by it. If that is all it contains, this type is frieze group p11g.
Example pattern with this symmetry group:
A typical example of glide reflection in everyday life would be the track of footprints left in the sand by a person walking on a beach.
Frieze group nr. 6 (glide-reflections, translations and rotations) is generated by a glide reflection and a rotation about a point on the line of reflection. It is isomorphic to a semi-direct product of Z and C.
Example pattern with this symmetry group:
For any symmetry group containing some glide-reflection symmetry, the translation vector of any glide reflection is one half of an element of the translation group. If the translation vector of a glide reflection is itself an element of the translation group, then the corresponding glide-reflection symmetry reduces to a combination of reflection symmetry and translational symmetry. | 1 | Crystallography |
* Nano- and bio-organic materials: production, synthesis, structure and properties, diagnostic methods using X-ray and synchrotron radiation, electrons, neutrons and atomic force microscopy
* Fundamental aspects of the formation of crystalline materials and nanosystems, their real structure and properties
* Creation and study of new crystalline and functional materials | 1 | Crystallography |
Methyl violet is a family of organic compounds that are mainly used as dyes. Depending on the number of attached methyl groups, the color of the dye can be altered. Its main use is as a purple dye for textiles and to give deep violet colors in paint and ink. It is also used as a hydration indicator for silica gel. Methyl violet 10B is also known as crystal violet (and many other names) and has medical uses. | 0 | Chromatography + Titration + pH indicators |
Consider a line of atoms A-O-B, separated by distance a. Rotate the entire row by θ = +2π/n and θ = −2π/n, with point O kept fixed. After the rotation by +2π/n, A is moved to the lattice point C and after the rotation by -2π/n, B is moved to the lattice point D. Due to the assumed periodicity of the lattice, the two lattice points C and D will be also in a line directly below the initial row; moreover C and D will be separated by r = ma, with m an integer. But by trigonometry, the separation between these points is:
Equating the two relations gives:
This is satisfied by only n = 1, 2, 3, 4, 6. | 1 | Crystallography |
An antiphase domain (APD) is a type of planar crystallographic defect in which the atoms within a region of a crystal are configured in the opposite order to those in the perfect lattice system. Throughout the entire APD, atoms sit on the sites typically occupied by atoms of a different species. For example, in an ordered AB alloy, if an A atom occupies the site usually occupied by a B atom, a type of crystallographic point defect called an antisite defect is formed. If an entire region of the crystal is translated such that every atom in a region of the plane of atoms sits on its antisite, an antiphase domain is formed. In other words, an APD is a region formed from antisite defects of a parent lattice. On either side of this domain, the lattice is still perfect, and the boundaries of the domain are referred to as antiphase boundaries. Crucially, crystals on either side of an antiphase boundary are related by a translation, rather than a reflection (a crystal twin) or an inversion (an inversion domain). | 1 | Crystallography |
Anthocyanins are found in the cell vacuole, mostly in flowers and fruits, but also in leaves, stems, and roots. In these parts, they are found predominantly in outer cell layers such as the epidermis and peripheral mesophyll cells.
Most frequently occurring in nature are the glycosides of cyanidin, delphinidin, malvidin, pelargonidin, peonidin, and petunidin. Roughly 2% of all hydrocarbons fixed in photosynthesis are converted into flavonoids and their derivatives, such as the anthocyanins. Not all land plants contain anthocyanin; in the Caryophyllales (including cactus, beets, and amaranth), they are replaced by betalains. Anthocyanins and betalains have never been found in the same plant.
Sometimes bred purposely for high anthocyanin content, ornamental plants such as sweet peppers may have unusual culinary and aesthetic appeal. | 0 | Chromatography + Titration + pH indicators |
In 1833, Adam August Krantz (who studied pharmacy and later "Geognosie" at the Bergakademie Freiberg) founded the Krantz company in Bonn. Four years later, Krantz moved to Berlin and sold minerals, fossils, rocks and basically acquired a monopoly in the production of crystal models made of pear wood or walnut. Ever since its foundation, the firm was always in contact with renowned scientists and important collectors. Hence in 1880, Krantz proposed a series of 743 pear wood models compiled for teaching purposes by the crystallographer Paul Groth. Seven years later, a supplementary collection of 213 models was available.
At the onset of the 20th century, Friedrich Krantz (a nephew of August Krantz, with a degree in mineralogy) supported by his teacher the crystallographer Carl Hintze, offered a collection of 928 models including most of the Groth models. Later, and along with many other productions, a Dana collection of 282 models was manufactured. Krantz offered a choice of collections of wooden models in different sizes (5, 10, 15–25 cm). In addition, he sold a variety of glass models having the crystallographic axes illustrated by colored silk threads or with the holohedral form made of cardboard inside. Also available were models in massive cut and polished glass (colored and uncolored), cardboard models, wire crystal models, crystal lattice models, models with rotating parts, etc.
Over the years, Krantz published numerous detailed catalogues of the collections he offered; they constitute a precious documentation. | 1 | Crystallography |
Closely related is mmCIF, macromolecular CIF, which is intended as an successor to the Protein Data Bank (PDB) format. It is now the default format used by the Protein Data Bank.
Also closely related is Crystallographic Information Framework, a broader system of exchange protocols based on data dictionaries and relational rules expressible in different machine-readable manifestations, including, but not restricted to, Crystallographic Information File and XML. | 1 | Crystallography |
4-Nitrophenol irritates the eyes, skin, and respiratory tract. It may also cause inflammation of those parts. It has a delayed interaction with blood and forms methaemoglobin which is responsible for methemoglobinemia, potentially causing cyanosis, confusion, and unconsciousness. When ingested, it causes abdominal pain and vomiting. Prolonged contact with skin may cause allergic response. Genotoxicity and carcinogenicity of 4-nitrophenol are not known. The in mice is 282 mg/kg and in rats is 202 mg/kg (p.o.). | 0 | Chromatography + Titration + pH indicators |
Though many people conceptualize images and diffraction patterns separately, they contain principally the same information. In the simplest approximation, the two are simply Fourier transforms of one another. Thus, the effects of beam precession on diffraction patterns also have significant effects on the corresponding images in the TEM. Specifically, the reduced dynamical intensity transfer between beams that is associated with PED results in reduced dynamical contrast in images collected during precession of the beam. This includes a reduction in thickness fringes, bend contours, and strain fields. While these features can often provide useful information, their suppression enables a more straightforward interpretation of diffraction contrast and mass contrast in images. | 1 | Crystallography |
The concept of Voronoi decomposition was investigated by Peter Gustav Lejeune Dirichlet, leading to the name Dirichlet domain. Further contributions were made from Evgraf Fedorov, (Fedorov parallelohedron), Georgy Voronoy (Voronoi polyhedron), and Paul Niggli (Wirkungsbereich).
The application to condensed matter physics was first proposed by Eugene Wigner and Frederick Seitz in a 1933 paper, where it was used to solve the Schrödinger equation for free electrons in elemental sodium. They approximated the shape of the Wigner–Seitz cell in sodium, which is a truncated octahedron, as a sphere of equal volume, and solved the Schrödinger equation exactly using periodic boundary conditions, which require at the surface of the sphere. A similar calculation which also accounted for the non-spherical nature of the Wigner–Seitz cell was performed later by John C. Slater.
There are only five topologically distinct polyhedra which tile three-dimensional space, . These are referred to as the parallelohedra. They are the subject of mathematical interest, such as in higher dimensions. These five parallelohedra can be used to classify the three dimensional lattices using the concept of a projective plane, as suggested by John Horton Conway and Neil Sloane. However, while a topological classification considers any affine transformation to lead to an identical class, a more specific classification leads to 24 distinct classes of voronoi polyhedra with parallel edges which tile space. For example, the rectangular cuboid, right square prism, and cube belong to the same topological class, but are distinguished by different ratios of their sides. This classification of the 24 types of voronoi polyhedra for Bravais lattices was first laid out by Boris Delaunay. | 1 | Crystallography |
*A web application for determining molecular geometry indices on the basis of 3D structural files can be found [http://kchn.pg.gda.pl/geom/ here]. | 1 | Crystallography |
The Lely method, also known as the Lely process or Lely technique, is a crystal growth technology used for producing silicon carbide crystals for the semiconductor industry. The patent for this method was filed in the Netherlands in 1954 and in the United States in 1955 by Jan Anthony Lely of Philips Electronics. The patent was subsequently granted on 30 September 1958, then was refined by D. R. Hamilton et al. in 1960, and by V. P. Novikov and V. I. Ionov in 1968. | 1 | Crystallography |
There are 2 regular complex apeirogons, sharing the vertices of the trihexagonal tiling. Regular complex apeirogons have vertices and edges, where edges can contain 2 or more vertices. Regular apeirogons p{q}r are constrained by: 1/p + 2/q + 1/r = 1. Edges have p vertices arranged like a regular polygon, and vertex figures are r-gonal.
The first is made of triangular edges, two around every vertex, second has hexagonal edges, two around every vertex. | 1 | Crystallography |
The main compartment of the titration cell contains the anode solution plus the analyte. The anode solution consists of an alcohol (ROH), a base (B), sulfur dioxide () and KI. Typical alcohols that may be used include ethanol, diethylene glycol monoethyl ether, or methanol, sometimes referred to as Karl Fischer grade. A common base is imidazole.
The titration cell also consists of a smaller compartment with a cathode immersed in the anode solution of the main compartment. The two compartments are separated by an ion-permeable membrane.
The Pt anode generates from the KI when current is provided through the electric circuit. The net reaction as shown below is oxidation of by . One mole of is consumed for each mole of . In other words, 2 moles of electrons are consumed per mole of water.
The end point is detected most commonly by a bipotentiometric titration method. A second pair of Pt electrodes is immersed in the anode solution. The detector circuit maintains a constant current between the two detector electrodes during titration. Prior to the equivalence point, the solution contains but little . At the equivalence point, excess appears and an abrupt voltage drop marks the end point. The amount of charge needed to generate I and reach the end point can then be used to calculate the amount of water in the original sample. | 0 | Chromatography + Titration + pH indicators |
LC–MS is widely used in the field of bioanalysis and is specially involved in pharmacokinetic studies of pharmaceuticals. Pharmacokinetic studies are needed to determine how quickly a drug will be cleared from the body organs and the hepatic blood flow. MS analyzers are useful in these studies because of their shorter analysis time, and higher sensitivity and specificity compared to UV detectors commonly attached to HPLC systems. One major advantage is the use of tandem MS–MS, where the detector may be programmed to select certain ions to fragment. The measured quantity is the sum of molecule fragments chosen by the operator. As long as there are no interferences or ion suppression in LC–MS, the LC separation can be quite quick. | 0 | Chromatography + Titration + pH indicators |
High through-put methods exist to help streamline the large number of experiments required to explore the various conditions that are necessary for successful crystal growth. There are numerous commercial kits available for order which apply preassembled ingredients in systems guaranteed to produce successful crystallization. Using such a kit, a scientist avoids the hassle of purifying a protein and determining the appropriate crystallization conditions.
Liquid-handling robots can be used to set up and automate large number of crystallization experiments simultaneously. What would otherwise be slow and potentially error-prone process carried out by a human can be accomplished efficiently and accurately with an automated system. Robotic crystallization systems use the same components described above, but carry out each step of the procedure quickly and with a large number of replicates. Each experiment utilizes tiny amounts of solution, and the advantage of the smaller size is two-fold: the smaller sample sizes not only cut-down on expenditure of purified protein, but smaller amounts of solution lead to quicker crystallizations. Each experiment is monitored by a camera which detects crystal growth. | 1 | Crystallography |
Methyl red displays pH dependent photochromism, with protonation causing it to adopt a hydrazone/quinone structure.
Methyl Red has a special use in histopathology for showing acidic nature of tissue and presence of organisms with acidic natured cell walls.
Methyl Red is detectably fluorescent in 1:1 water:methanol (pH 7.0), with an emission maximum at 375 nm (UVA) upon excitation with 310 nm light (UVB). | 0 | Chromatography + Titration + pH indicators |
Physical properties of interest to materials science among perovskites include superconductivity, magnetoresistance, ionic conductivity, and a multitude of dielectric properties, which are of great importance in microelectronics and telecommunication. They are also some interests for scintillator as they have large light yield for radiation conversion. Because of the flexibility of bond angles inherent in the perovskite structure there are many different types of distortions which can occur from the ideal structure. These include tilting of the octahedra, displacements of the cations out of the centers of their coordination polyhedra, and distortions of the octahedra driven by electronic factors (Jahn-Teller distortions). The financially biggest application of perovskites is in ceramic capacitors, in which BaTiO is used because of its high dielectric constant. | 1 | Crystallography |
Bromothymol blue may be used for observing photosynthetic activities, or as a respiratory indicator (turns yellow as CO is added). A common demonstration of BTB's pH indicator properties involves exhaling through a tube into a neutral solution of BTB. As CO is absorbed from the breath into the solution, forming carbonic acid, the solution changes color from green to yellow. Thus, BTB is commonly used in science classes to demonstrate that the more that muscles are used, the greater the CO output.
Bromothymol blue has been used in conjunction with phenol red to monitor the fungal asparaginase enzyme activity with phenol red turning pink and bromothymol blue turning blue indicating an increase in pH and therefore enzyme activity. However, a recent study suggests that methyl red is more useful in determining activity due to the bright yellow ring formed in the zone of enzyme activity.
It may also be used in the laboratory as a biological slide stain. At this point, the bromothymol is already blue, and a few drops of BTB are used on a water slide. The specimen is mixed with blue BTB solution and fixed to a slide by a cover slip. It is sometimes used to define cell walls or nuclei under the microscope.
Bromothymol is used in obstetrics for detecting premature rupture of membranes. Amniotic fluid typically has a pH > 7.2, bromothymol will therefore turn blue when brought in contact with fluid leaking from the amnion. As vaginal pH normally is acidic, the blue color indicates the presence of amniotic fluid. The test may be false-positive in the presence of other alkaline substances such as blood or semen, or in the presence of bacterial vaginosis. | 0 | Chromatography + Titration + pH indicators |
Swansea University has had a long established history of development and innovation in mass spectrometry and chromatography. | 0 | Chromatography + Titration + pH indicators |
Real-life crime scene investigators and forensic scientists warn that popular television shows do not give a realistic picture of the work, often wildly distorting its nature, and exaggerating the ease, speed, effectiveness, drama, glamour, influence and comfort level of their jobs—which they describe as far more mundane, tedious and boring.
Some claim these modern TV shows have changed individuals' expectations of forensic science, sometimes unrealistically—an influence termed the "CSI effect".
Further, research has suggested that public misperceptions about criminal forensics can create, in the mind of a juror, unrealistic expectations of forensic evidence—which they expect to see before convicting—implicitly biasing the juror towards the defendant. Citing the "CSI effect," at least one researcher has suggested screening jurors for their level of influence from such TV programs. | 0 | Chromatography + Titration + pH indicators |
* Paper form: It is a strip of coloured paper which changes colour to red if the solution is acidic and to blue, if the solution is basic. The strip can be placed directly onto a surface of a wet substance or a few drops of the solution can be dropped onto the universal indicator using dropping equipment. If the test solution is of a dark colour, it is preferable to use a paper universal indicator, such as Hydrion paper.
* Solution: The main components of a universal indicator, in the form of a solution, are thymol blue, methyl red, bromothymol blue, and phenolphthalein. This mixture is important because each component loses or gains protons depending upon the acidity or alkalinity of the solution being tested. It is beneficial to use this type of universal indicator in a colorless solution. This will increase the accuracy level of indication. | 0 | Chromatography + Titration + pH indicators |
In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, and the space is usually three-dimensional Euclidean space. However, sphere packing problems can be generalised to consider unequal spheres, spaces of other dimensions (where the problem becomes circle packing in two dimensions, or hypersphere packing in higher dimensions) or to non-Euclidean spaces such as hyperbolic space.
A typical sphere packing problem is to find an arrangement in which the spheres fill as much of the space as possible. The proportion of space filled by the spheres is called the packing density of the arrangement. As the local density of a packing in an infinite space can vary depending on the volume over which it is measured, the problem is usually to maximise the average or asymptotic density, measured over a large enough volume.
For equal spheres in three dimensions, the densest packing uses approximately 74% of the volume. A random packing of equal spheres generally has a density around 63.5%. | 1 | Crystallography |
The surface advances by the lateral motion of steps which are one interplanar spacing in height (or some integral multiple thereof). An element of surface undergoes no change and does not advance normal to itself except during the passage of a step, and then it advances by the step height. It is useful to consider the step as the transition between two adjacent regions of a surface which are parallel to each other and thus identical in configuration—displaced from each other by an integral number of lattice planes. Note here the distinct possibility of a step in a diffuse surface, even though the step height would be much smaller than the thickness of the diffuse surface. | 1 | Crystallography |
The Kovats index applies to organic compounds. The method interpolates peaks between bracketing n-alkanes. The Kovats index of n-alkanes is 100 times their carbon number, e.g. the Kovats index of n-butane is 400. The Kovats index is dimensionless, unlike retention time or retention volume. For isothermal gas chromatography, the Kovats index is given by the equation:
where the variables used are:
* , the Kováts retention index of peak i
* , the carbon number of n-alkane peak heading peak i
* , the retention time of compound i, minutes
* , the air peak, void time in average velocity , minutes
The Kovats index also applies to packed columns with an equivalent equation: | 0 | Chromatography + Titration + pH indicators |
Okano’s group expanded on their success by using different modifiers to enhance hydrophobicity through the attachment of butyl methacrylate (BMA), a hydrophobic comonomer. For simplification the resultant polymer has been labeled as IBc (isopropylacrylamide butyl methacrylate copolymer). The polymers were synthesized using radical telomerization with varying BMA content. Where pure PNIPAAm was unable to resolve hydrophobic steroids at any temperature, IBc-grafted silica stationary phases were able to resolve steroid peaks with increasingly retarded retention times in correlation to both increased BMA content and increased temperature. They went on to develop a method to separate phenylthiohydantoin(PTH)-amino acids using their IBc stationary phase with a stronger emphasis of implementing environmentally friendly conditions using a purely aqueous phase in HPLC. Another group separated catechins using PNIPAAm. | 0 | Chromatography + Titration + pH indicators |
The columns used in FPLC are large [mm id] tubes that contain small [µ] particles or gel beads that are known as stationary phase. The chromatographic bed is composed by the gel beads inside the column and the sample is introduced into the injector and carried into the column by the flowing solvent. As a result of different components adhering to or diffusing through the gel, the sample mixture gets separated.
Columns used with an FPLC can separate macromolecules based on size (size-exclusion chromatography), charge distribution (ion exchange), hydrophobicity, reverse-phase or biorecognition (as with affinity chromatography). For easy use, a wide range of pre-packed columns for techniques such as ion exchange, gel filtration (size exclusion), hydrophobic interaction, and affinity chromatography are available. FPLC differs from HPLC in that the columns used for FPLC can only be used up to maximum pressure of 3-4 MPa (435-580 psi). Thus, if the pressure of HPLC can be limited, each FPLC column may also be used in an HPLC machine. | 0 | Chromatography + Titration + pH indicators |
Fischer and Jandera studied the effect of changing the concentration of methanol on CMC values for three commonly used surfactants. Two cationic, hexadecyltrimethylammonium bromide (CTAB), and N-(a-carbethoxypentadecyl) trimethylammonium bromide (Septonex), and one anionic surfactant, sodium dodecyl sulphate (SDS) were chosen for the experiment. Generally speaking, the CMC increased as the concentration of methanol increased. It was then concluded that the distribution of the surfactant between the bulk mobile phase and the micellar phase shifts toward the bulk as the methanol concentration increases. For CTAB, the rise in CMC is greatest from 0–10% methanol, and is nearly constant from 10–20%. Above 20% methanol, the micelles disaggregate and do not exist. For SDS, the CMC values remain unaffected below 10% methanol, but begin to increase as the methanol concentration is further increased. Disaggregation occurs above 30% methanol. Finally, for Septonex, only a slight increase in CMC is observed up to 20%, with disaggregation occurring above 25%.
As has been asserted, the mobile phase in MLC consists of micelles in an aqueous solvent, usually with a small amount of organic modifier added to complete the mobile phase. A typical reverse phase alkyl-bonded stationary phase is used. The first discussion of the thermodynamics involved in the retention mechanism was published by Armstrong and Nome in 1981. In MLC, there are three partition coefficients which must be taken into account. The solute will partition between the water and the stationary phase (KSW), the water and the micelles (KMW), and the micelles and the stationary phase (KSM).
Armstrong and Nome derived an equation describing the partition coefficients in terms of the retention factor, formally capacity factor, k¢. In HPLC, the capacity factor represents the molar ratio of the solute in the stationary phase to the mobile phase. The capacity factor is easily measure based on retention times of the compound and any unretained compound. The equation rewritten by Guermouche et al. is presented here:
:1/k¢ = [n • (KMW-1)/(f • KSW)] • CM +1/(f • KSW)
Where:
*k¢ is the capacity factor of the solute
*KSW is the partition coefficient of the solute between the stationary phase and the water
*KMW is the partition coefficient of the solute between the micelles and the water
*f is the phase volume ratio (stationary phase volume/mobile phase volume)
*n is the molar volume of the surfactant
*CM is the concentration of the micelle in the mobile phase (total surfactant concentration - critical micelle concentration)
A plot of 1/k¢ verses CM gives a straight line in which KSW can be calculated from the intercept and KMW can be obtained from the ratio of the slope to the intercept. Finally, KSM can be obtained from the ratio of the other two partition coefficients:
:KSM = KSW/ KMW
As can be observed from Figure 1, KMW is independent of any effects from the stationary phase, assuming the same micellar mobile phase.
The validity of the retention mechanism proposed by Armstrong and Nome has been successfully, and repeated confirmed experimentally. However, some variations and alternate theories have also been proposed. Jandera and Fischer developed equations to describe the dependence of retention behavior on the change in micellar concentrations. They found that the retention of most compounds tested decreased with increasing concentrations of micelles. From this, it can be surmised that the compounds associate with the micelles as they spend less time associated with the stationary phase.
Foley proposed a similar retentive model to that of Armstrong and Nome which was a general model for secondary chemical equilibria in liquid chromatography. While this model was developed in a previous reference, and could be used for any secondary chemical equilibria such as acid-base equilibria, and ion-pairing, Foley further refined the model for MLC. When an equilibrant (X), in this case surfactant, is added to the mobile phase, a secondary equilibria is created in which an analyte will exist as free analyte (A), and complexed with the equilibrant (AX). The two forms will be retained by the stationary phase to different extents, thus allowing the retention to be varied by adjusting the concentration of equilibrant (micelles).
The resulting equation solved for capacity factor in terms of partition coefficients is much the same as that of Armstrong and Nome:
:1/k¢ = (KSM/k¢S) • [M] + 1/k¢S
Where:
*k¢ is the capacity factor of the complexed solute and the free solute
*k¢S is the capacity factor of the free solute
*KSM is the partition coefficient of the solute between the stationary phase and the micelle
*[M] may be either the concentration of surfactant or the concentration of micelle
Foley used the above equation to determine the solute-micelle association constants and free solute retention factors for a variety of solutes with different surfactants and stationary phases. From this data, it is possible to predict the type and optimum surfactant concentrations needed for a given solute or solutes.
Foley has not been the only researcher interested in determining the solute-micelle association constants. A review article by Marina and Garcia with 53 references discusses the usefulness of obtaining solute-micelle association constants. The association constants for two solutes can be used to help understand the retention mechanism. The separation factor of two solutes, a, can be expressed as KSM1/KSM2. If the experimental a coincides with the ratio of the two solute-micelle partition coefficients, it can be assumed that their retention occurs through a direct transfer from the micellar phase to the stationary phase. In addition, calculation of a would allow for prediction of separation selectivity before the analysis is performed, provided the two coefficients are known.
The desire to predict retention behavior and selectivity has led to the development of several mathematical models. Changes in pH, surfactant concentration, and concentration of organic modifier play a significant role in determining the chromatographic separation. Often one or more of these parameters need to be optimized to achieve the desired separation, yet the optimum parameters must take all three variables into account simultaneously. The review by Garcia-Alvarez-Coque et al. mentioned several successful models for varying scenarios, a few of which will be mentioned here. The classic models by Armstrong and Nome and Foley are used to describe the general cases. Foley's model applies to many cases and has been experimentally verified for ionic, neutral, polar and nonpolar solutes; anionic, cationic, and non-ionic surfactants, and C8, C¬18, and cyano stationary phases. The model begins to deviate for highly and lowly retained solutes. Highly retained solutes may become irreversibly bound to the stationary phase, where lowly retained solutes may elute in the column void volume.
Other models proposed by Arunyanart and Cline-Love and Rodgers and Khaledi describe the effect of pH on the retention of weak acids and bases. These authors derived equations relating pH and micellar concentration to retention. As the pH varies, sigmoidal behavior is observed for the retention of acidic and basic species. This model has been shown to accurately predict retention behavior. Still other models predict behavior in hybrid micellar systems using equations or modeling behavior based on controlled experimentation. Additionally, models accounting for the simultaneous effect of pH, micelle and organic concentration have been suggested. These models allow for further enhancement of the optimization of the separation of weak acids and bases.
One research group, Rukhadze, et al. derived a first order linear relationship describing the influence of micelle and organic concentration, and pH on the selectivity and resolution of seven barbiturates. The researchers discovered that a second order mathematical equation would more precisely fit the data. The derivations and experimental details are beyond the scope of this discussion. The model was successful in predicting the experimental conditions necessary to achieve a separation for compounds which are traditionally difficult to resolve.
Jandera, Fischer, and Effenberger approached the modeling problem in yet another way. The model used was based on lipophilicity and polarity indices of solutes. The lipophilicity index relates a given solute to a hypothetical number of carbon atoms in an alkyl chain. It is based and depends on a given calibration series determined experimentally. The lipophilicity index should be independent of the stationary phase and organic modifier concentration. The polarity index is a measure of the polarity of the solute-solvent interactions. It depends strongly on the organic solvent, and somewhat on the polar groups present in the stationary phase. 23 compounds were analyzed with varying mobile phases and compared to the lipophilicity and polarity indices. The results showed that the model could be applied to MLC, but better predictive behavior was found with concentrations of surfactant below the CMC, sub-micellar.
A final type of model based on molecular properties of a solute is a branch of quantitative structure-activity relationships (QSAR). QSAR studies attempt to correlate biological activity of drugs, or a class of drugs, with structures. The normally accepted means of uptake for a drug, or its metabolite, is through partitioning into lipid bilayers. The descriptor most often used in QSAR to determine the hydrophobicity of a compound is the octanol-water partition coefficient, log P. MLC provides an attractive and practical alternative to QSAR. When micelles are added to a mobile phase, many similarities exist between the micellar mobile phase/stationary phase and the biological membrane/water interface. In MLC, the stationary phase become modified by the adsorption of surfactant monomers which are structurally similar to the membranous hydrocarbon chains in the biological model. Additionally, the hydrophilic/hydrophobic interactions of the micelles are similar to that in the polar regions of a membrane. Thus, the development of quantitative structure-retention relationships (QRAR) has become widespread.
Escuder-Gilabert et al. tested three different QRAR retention models on ionic compounds. Several classes of compounds were tested including catecholamines, local anesthetics, diuretics, and amino acids. The best model relating log K and log P was found to be one in which the total molar charge of a compound at a given pH is included as a variable. This model proved to give fairly accurate predictions of log P, R > 0.9. Other studies have been performed which develop predictive QRAR models for tricyclic antidepressants and barbiturates. | 0 | Chromatography + Titration + pH indicators |
The Tensorial Anisotropy Index A extends the Zener ratio for fully anisotropic materials and overcomes the limitation of the AU that is designed for materials exhibiting internal symmetries of elastic crystals, which is not always observed in multi-component composites. It takes into consideration all the 21 coefficients of the fully anisotropic stiffness tensor and covers the directional differences among the stiffness tensor groups.
It is composed of two major parts and , the former referring to components existing in cubic tensor and the latter in anisotropic tensor so that This first component includes the modified Zener ratio and additionally accounts for directional differences in the material, which exist in orthotropic material, for instance. The second component of this index covers the influence of stiffness coefficients that are nonzero only for non-cubic materials and remains zero otherwise.
where is the coefficient of variation for each stiffness group accounting for directional differences of material stiffness, i.e. In cubic materials each stiffness component in groups 1-3 has equal value and thus this expression reduces directly to Zener ratio for cubic materials.
The second component of this index <math>
A^A | 1 | Crystallography |
Methyl yellow, or C.I. 11020, is an organic compound with the formula CHNCHN(CH). It is an azo dye derived from dimethylaniline. It is a yellow solid. According to X-ray crystallography, the CN core of the molecule is planar.
It is used as a dye for plastics and may be used as a pH indicator. In aqueous solution at low pH, methyl yellow appears red. Between pH 2.9 and 4.0, methyl yellow undergoes a transition, to become yellow above pH 4.0. | 0 | Chromatography + Titration + pH indicators |
Silver ions form alkene complexes. The binding is reversible, but sufficient to impede the elution of the alkene-containing analytes. | 0 | Chromatography + Titration + pH indicators |
Difference density maps are usually calculated using Fourier coefficients which are the differences between the observed structure factor amplitudes from the X-ray diffraction experiment and the calculated structure factor amplitudes from the current model, using the phase from the model for both terms (since no phases are available for the observed data). The two sets of structure factors must be on the same scale.
It is now normal to also include maximum-likelihood weighting terms which take into account the estimated errors in the current model:
where m is a figure of merit which is an estimate of the cosine of the error in the phase, and D is a "σ" scale factor. These coefficients are derived from the gradient of the likelihood function of the observed structure factors on the basis of the current model. A difference map built with m and D is known as a mFo – DFc map.
The use of ML weighting reduces model bias (due to using the model's phase) in the 2 Fo–Fc map, which is the main estimate of the true density. However, it does not fully eliminate such bias. | 1 | Crystallography |
Symmetries in nature lead directly to conservation laws, something which is precisely formulated by Noether's theorem.
The basic idea of time-translation symmetry is that a translation in time has no effect on physical laws, i.e. that the laws of nature that apply today were the same in the past and will be the same in the future. This symmetry implies the conservation of energy. | 1 | Crystallography |
In solid state physics, a superstructure is some additional structure that is superimposed on a higher symmetry crystalline structure. A typical and important example is ferromagnetic ordering.
In a wider sense, the term "superstructure" is applied to polymers and proteins to describe ordering on a length scale larger than that of monomeric segments. | 1 | Crystallography |
Confusion between inversion domains and antiphase domains is common, even in the published literature, and particularly in the case of GaAs grown on silicon. (Similar defects form in GaN on silicon, where they are correctly identified as inversion domains). An example is illustrated in the diagram below.
Figure 4. Highlighted area showing an inversion domain, incorrectly called an antiphase domain, in GaAs on Si.
The shaded region, B, is an example of an APD. In the figure, GaAs is grown on a misoriented surface of Si (details are not discussed here). The misorientation causes the Ga and As atoms in region B to be on opposite sites compared to the crystal matrix. The presence of the APD results in Ga sites 1, 1’, 2, 2’, 3, 3’ being bonded to Ga atoms in the APD to form an APB.
In mixed oxidation state materials like magnetite, antiphase domains and antiphase domain boundaries can occur as a result of charge-ordering even though there are no changes in atom locations. For example, the reconstructed magnetite (100) surface contains alternating Fe pairs and Fe pairs in the first subsurface layer. An antiphase domain boundary can form if two subsurface Fe pairs meet when two terraces grow together. | 1 | Crystallography |
Booth designed an electromechanical computer, the ARC (Automatic Relay Computer), in the late 1940s (1947-1948). Later on, they built an experimental electronic computer named SEC (Simple Electronic Computer, designed around 1948-1949) - and finally, the APE(X)C (All-Purpose Electronic Computer) series.
The computers were programmed by Kathleen. | 1 | Crystallography |
Ion chromatography (or ion-exchange chromatography) is a form of chromatography that separates ions and ionizable polar molecules based on their affinity to the ion exchanger. It works on almost any kind of charged molecule—including small inorganic anions, large proteins, small nucleotides, and amino acids. However, ion chromatography must be done in conditions that are one pH unit away from the isoelectric point of a protein.
The two types of ion chromatography are anion-exchange and cation-exchange. Cation-exchange chromatography is used when the molecule of interest is positively charged. The molecule is positively charged because the pH for chromatography is less than the pI (also known as pH(I)). In this type of chromatography, the stationary phase is negatively charged and positively charged molecules are loaded to be attracted to it. Anion-exchange chromatography is when the stationary phase is positively charged and negatively charged molecules (meaning that pH for chromatography is greater than the pI) are loaded to be attracted to it. It is often used in protein purification, water analysis, and quality control. The water-soluble and charged molecules such as proteins, amino acids, and peptides bind to moieties which are oppositely charged by forming ionic bonds to the insoluble stationary phase. The equilibrated stationary phase consists of an ionizable functional group where the targeted molecules of a mixture to be separated and quantified can bind while passing through the column—a cationic stationary phase is used to separate anions and an anionic stationary phase is used to separate cations. Cation exchange chromatography is used when the desired molecules to separate are cations and anion exchange chromatography is used to separate anions. The bound molecules then can be eluted and collected using an eluant which contains anions and cations by running a higher concentration of ions through the column or by changing the pH of the column.
One of the primary advantages for the use of ion chromatography is that only one interaction is involved the separation, as opposed to other separation techniques; therefore, ion chromatography may have higher matrix tolerance. Another advantage of ion exchange is the predictability of elution patterns (based on the presence of the ionizable group). For example, when cation exchange chromatography is used, certain cations will elute out first and others later. A local charge balance is always maintained. However, there are also disadvantages involved when performing ion-exchange chromatography, such as constant evolution of the technique which leads to the inconsistency from column to column. A major limitation to this purification technique is that it is limited to ionizable group. | 0 | Chromatography + Titration + pH indicators |
In liquid crystals, homeotropic alignment is one of the ways of alignment of liquid crystalline molecules. Homeotropic alignment is the state in which a rod-like liquid crystalline molecule aligns perpendicularly to the substrate. In the polydomain state, the parts also are called homeotropic domains. In contrast, the state in which the molecule aligns to a substance in parallel is called homogeneous alignment.
There are various other ways of alignment in liquid crystals. Because homeotropic alignment is not anisotropic optically, a dark field is observed between crossed polarizers in polarizing optical microscopy.
By conoscope observation, however, a cross image is observed in the homeotropic alignments. Homeotropic alignment often appears in the smectic A phase (S).
In discotic liquid crystals homeotropic alignment is defined as the state in which an axis of the column structure, which is formed by disc-like liquid crystalline molecules, aligns perpendicularly to a substance. In other words, this alignment looks like a state in which columns formed by piled-up coins are arranged in an orderly way on a table.
In practice, the homeotropic alignment is usually achieved by surfactants and detergent for example lecithin, some esilanes or some special polyimide (PI 1211). Generally liquid crystals align homeotropically at an air or glass interface. | 1 | Crystallography |
The number of theoretical plates, or separation efficiency, in capillary electrophoresis is given by:
where is the number of theoretical plates, is the apparent mobility in the separation medium and is the diffusion coefficient of the analyte. According to this equation, the efficiency of separation is only limited by diffusion and is proportional to the strength of the electric field, although practical considerations limit the strength of the electric field to several hundred volts per centimeter. Application of very high potentials (>20-30 kV) may lead to arcing or breakdown of the capillary. Further, application of strong electric fields leads to resistive heating (Joule heating) of the buffer in the capillary. At sufficiently high field strengths, this heating is strong enough that radial temperature gradients can develop within the capillary. Since electrophoretic mobility of ions is generally temperature-dependent (due to both temperature-dependent ionization and solvent viscosity effects), a non-uniform temperature profile results in variation of electrophoretic mobility across the capillary, and a loss of resolution. The onset of significant Joule heating can be determined by constructing an "Ohms Law plot", wherein the current through the capillary is measured as a function of applied potential. At low fields, the current is proportional to the applied potential (Ohms Law), whereas at higher fields the current deviates from the straight line as heating results in decreased resistance of the buffer. The best resolution is typically obtained at the maximum field strength for which Joule heating is insignificant (i.e. near the boundary between the linear and nonlinear regimes of the Ohm's Law plot). Generally capillaries of smaller inner diameter support use of higher field strengths, due to improved heat dissipation and smaller thermal gradients relative to larger capillaries, but with the drawbacks of lower sensitivity in absorbance detection due to shorter path length, and greater difficulty in introducing buffer and sample into the capillary (small capillaries require greater pressure and/or longer times to force fluids through the capillary).
The efficiency of capillary electrophoresis separations is typically much higher than the efficiency of other separation techniques like HPLC. Unlike HPLC, in capillary electrophoresis there is no mass transfer between phases. In addition, the flow profile in EOF-driven systems is flat, rather than the rounded laminar flow profile characteristic of the pressure-driven flow in chromatography columns as shown in figure 5. As a result, EOF does not significantly contribute to band broadening as in pressure-driven chromatography. Capillary electrophoresis separations can have several hundred thousand theoretical plates.
The resolution () of capillary electrophoresis separations can be written as:
According to this equation, maximum resolution is reached when the electrophoretic and electroosmotic mobilities are similar in magnitude and opposite in sign. In addition, it can be seen that high resolution requires lower velocity and, correspondingly, increased analysis time.
Besides diffusion and Joule heating (discussed above), factors that may decrease the resolution in capillary electrophoresis from the theoretical limits in the above equation include, but are not limited to, the finite widths of the injection plug and detection window; interactions between the analyte and the capillary wall; instrumental non-idealities such as a slight difference in height of the fluid reservoirs leading to siphoning; irregularities in the electric field due to, e.g., imperfectly cut capillary ends; depletion of buffering capacity in the reservoirs; and electrodispersion (when an analyte has higher conductivity than the background electrolyte). Identifying and minimizing the numerous sources of band broadening is key to successful method development in capillary electrophoresis, with the objective of approaching as close as possible to the ideal of diffusion-limited resolution. | 0 | Chromatography + Titration + pH indicators |
Consider the scattering of a beam of wavelength by an assembly of particles or atoms stationary at positions . Assume that the scattering is weak, so that the amplitude of the incident beam is constant throughout the sample volume (Born approximation), and absorption, refraction and multiple scattering can be neglected (kinematic diffraction). The direction of any scattered wave is defined by its scattering vector . , where and ( ) are the scattered and incident beam wavevectors, and is the angle between them. For elastic scattering, and , limiting the possible range of (see Ewald sphere). The amplitude and phase of this scattered wave will be the vector sum of the scattered waves from all the atoms
For an assembly of atoms, is the atomic form factor of the -th atom. The scattered intensity is obtained by multiplying this function by its complex conjugate
The structure factor is defined as this intensity normalized by
If all the atoms are identical, then Equation () becomes and so
Another useful simplification is if the material is isotropic, like a powder or a simple liquid. In that case, the intensity depends on and . In three dimensions, Equation () then simplifies to the Debye scattering equation:
An alternative derivation gives good insight, but uses Fourier transforms and convolution. To be general, consider a scalar (real) quantity defined in a volume ; this may correspond, for instance, to a mass or charge distribution or to the refractive index of an inhomogeneous medium. If the scalar function is integrable, we can write its Fourier transform as . In the Born approximation the amplitude of the scattered wave corresponding to the scattering vector is proportional to the Fourier transform . When the system under study is composed of a number of identical constituents (atoms, molecules, colloidal particles, etc.) each of which has a distribution of mass or charge then the total distribution can be considered the convolution of this function with a set of delta functions.
with the particle positions as before. Using the property that the Fourier transform of a convolution product is simply the product of the Fourier transforms of the two factors, we have , so that:
This is clearly the same as Equation () with all particles identical, except that here is shown explicitly as a function of .
In general, the particle positions are not fixed and the measurement takes place over a finite exposure time and with a macroscopic sample (much larger than the interparticle distance). The experimentally accessible intensity is thus an averaged one ; we need not specify whether denotes a time or ensemble average. To take this into account we can rewrite Equation () as: | 1 | Crystallography |
The Gran plot is based on the Nernst equation which can be written as
where E is a measured electrode potential, E is a standard electrode potential, s is the slope, ideally equal to RT/nF, and {H} is the activity of the hydrogen ion. The expression rearranges to
depending on whether the electrode is calibrated in millivolts or pH. For convenience the concentration, [H], is used in place of activity. In a titration of strong acid with strong alkali, the analytical concentration of the hydrogen ion is obtained from the initial concentration of acid, C and the amount of alkali added during titration.
where v is the initial volume of solution, c is the concentration of alkali in the burette and v is the titre volume. Equating the two expressions for [H] and simplifying, the following expression is obtained
A plot of against v will be a straight line. If E and s are known from electrode calibration, where the line crosses the x-axis indicates the volume at the equivalence point, . Alternatively, this plot can be used for electrode calibration by finding the values of E and s that give the best straight line. | 0 | Chromatography + Titration + pH indicators |
Laser spray ionization refers to one of several methods for creating ions using a laser interacting with a spray of neutral particles or ablating material to create a plume of charged particles. The ions thus formed can be separated by m/z with mass spectrometry. Laser spray is one of several ion sources that can be coupled with liquid chromatography-mass spectrometry for the detection of larger molecules. | 0 | Chromatography + Titration + pH indicators |
RHEED is an extremely popular technique for monitoring the growth of thin films. In particular, RHEED is well suited for use with molecular beam epitaxy (MBE), a process used to form high quality, ultrapure thin films under ultrahigh vacuum growth conditions. The intensities of individual spots on the RHEED pattern fluctuate in a periodic manner as a result of the relative surface coverage of the growing thin film. Figure 8 shows an example of the intensity fluctuating at a single RHEED point during MBE growth.
Each full period corresponds to formation of a single atomic layer thin film. The oscillation period is highly dependent on the material system, electron energy and incident angle, so researchers obtain empirical data to correlate the intensity oscillations and film coverage before using RHEED for monitoring film growth.
Video 1 depicts a metrology instrument recording the RHEED intensity oscillations and deposition rate for process control and analysis. | 1 | Crystallography |
ScBSi has a tetragonal crystal structure with space group P422 (No. 92) or P422 and lattice constants of a, b = 1.03081(2) and c = 1.42589(3) nm; it is
isotypic to the α-AlB structure type. There are 28 atomic sites in the unit cell, which are assigned to 3 scandium atoms, 24 boron atoms and one silicon atom. Atomic coordinates, site occupancies and isotropic displacement factors are listed in table VI.
The boron framework of ScBSi is based on one B icosahedron and one B unit. This unit can be observed in β-tetragonal boron and is a modification of the B unit of α-AlB (or B unit in early reports). The B unit is a twinned icosahedron made from B13 to B22 sites with two vacant sites and one B atom (B23) bridging both sides of the unit. The twinned icosahedron is shown in figure 18a. B23 was treated as an isolated atom in the early reports; it is bonded to each twinned icosahedra through B18 and to another icosahedron through B5 site. If the twinned icosahedra were independent without twinning then B23 would be a bridge site linking three icosahedra. However, because of twinning, B23 shifts closer to the twinned icosahedra than another icosahedron; thus B23 is currently treated as a member of the twinned icosahedra. In ScBSi, the two B24 sites which correspond to the vacant sites in the B unit are partially occupied; thus, the unit should be referred to as a B cluster which is occupied by about 20.6 boron atoms. Scandium atoms occupy 3 of 5 Al sites of α-AlB, that is Sc1, Sc2 and Sc3 correspond to Al4, Al1 and Al2 sites of α-AlB, respectively. The Al3 and Al5 sites are empty for ScBSi, and the Si site links two B units. This phase also exists without silicon.
Figure 19a shows the network of boron icosahedra in the boron framework of ScBSi. In this network, 4 icosahedra form a supertetrahedron (figure 18b); its one edge is parallel to the a-axis, and the icosahedra on this edge make up a chain along the a-axis. The opposite edge of the supertetrahedron is parallel to the b-axis and the icosahedra on this edge form a chain along the b-axis. As shown in figure 19, there are wide tunnels surrounded by the icosahedron arrangement along the a- and b-axes. The tunnels are filled by the B units which strongly bond to the surrounding icosahedra; the connection of the B units is helical and it runs along the c-axis as shown in figure 19b. Scandium atoms occupy the voids in the boron network as shown in figure 19c, and the Si atoms bridge the B units. | 1 | Crystallography |
The main advantages of this technique are the high pulling rates (60 times greater than the conventional Czochralski technique) and the possibility of growing materials with very high melting points. In addition, LHPG is a crucible-free technique, which allows single crystals to be grown with high purity and low stress.
The geometric shape of the crystals (the technique can produce small diameters), and the low production cost, make the single-crystal fibers (SCF) produced by LHPG suitable substitutes for bulk crystals in many devices, especially those that use high-melting-point materials. However, single-crystal fibers must have equal or superior optical and structural qualities compared to bulk crystals to substitute for them in technological devices. This can be achieved by carefully controlling the growth conditions. | 1 | Crystallography |
A sculpture titled Bamboozle, by Jacobus Verhoeff and his son Tom Verhoeff, is in the form of a fragment of the Laves graph, with its vertices represented by multicolored interlocking acrylic triangles. It was installed in 2013 at the Eindhoven University of Technology. | 1 | Crystallography |
Water is particularly common solvent to be found in crystals because it is small and polar. But all solvents can be found in some host crystals. Water is noteworthy because it is reactive, whereas other solvents such as benzene are considered to be chemically innocuous. Occasionally more than one solvent is found in a crystal, and often the stoichiometry is variable, reflected in the crystallographic concept of "partial occupancy". It is common and conventional for a chemist to "dry" a sample with a combination of vacuum and heat "to constant weight".
For other solvents of crystallization, analysis is conveniently accomplished by dissolving the sample in a deuterated solvent and analyzing the sample for solvent signals by NMR spectroscopy. Single crystal X-ray crystallography is often able to detect the presence of these solvents of crystallization as well. Other methods may be currently available. | 1 | Crystallography |
If the illuminated area selected by the aperture covers many differently oriented crystallites, their diffraction patterns superimpose forming an image of concentric rings. The ring diffractogram is typical for polycrystalline samples, powders or nanoparticles. Diameter of each ring corresponds to interplanar distance of a plane system present in the sample. Instead of information about individual grains or the sample orientation, this diffractogram provides more of a statistical information for instance about overall crystallinity or texture. Textured materials are characteristic by a non-uniform intensity distribution along the ring circumference despite crystallinity sufficient for generating smooth rings. Ring diffractograms can be also used to discriminate between nanocrystalline and amorphous phases.
Not all the features depicted in the diffraction image are necessarily wanted. The transmitted beam is often too strong and needs to be shadowed with a beam-stopper in order to protect the camera. The beam-stopper typically shadows part of the useful information as well. Towards the rings center, the background intensity also gradually increases lowering the contrast of diffraction rings. Modern analytical software allows to minimize such unwanted image features and together with other functionalities improves the image readability it helps with image interpretation. | 1 | Crystallography |
In crystallography, an anti-structure is obtained from a salt structure by exchanging anion and cation positions.
For instance, calcium fluoride, CaF, crystallizes in a cubic motif called the fluorite structure. The same crystal structure is found in numerous ionic compounds with formula AB, such as ceria (CeO), zirconia (cubic ZrO), uranium dioxide (UO). In the corresponding anti-structure, called the antifluorite structure, anions and cations are swapped, such as beryllium carbide (BeC) or lithium oxide (LiO), potassium sulfate (KSO).
Other anti-structures include:
* anti-SnO: TiN
* anti-PbCl: CoP
* anti-CdCl: CoN
* anti-CdI: CsO
* anti-NbS: HfS
* anti-ReO: CuN
* anti-LaF: CuP, CuAs | 1 | Crystallography |
In physics, the phase problem is the problem of loss of information concerning the phase that can occur when making a physical measurement. The name comes from the field of X-ray crystallography, where the phase problem has to be solved for the determination of a structure from diffraction data. The phase problem is also met in the fields of imaging and signal processing. Various approaches of phase retrieval have been developed over the years. | 1 | Crystallography |
Although there is a large number of simple known ABX perovskites, this number can be greatly expanded if the A and B sites are increasingly doubled / complex AA’BB’X. Ordered double perovskites are usually denoted as ABB’O where disordered are denoted as A(BB’)O. In ordered perovskites, three different types of ordering are possible: rock-salt, layered, and columnar. The most common ordering is rock-salt followed by the much more uncommon disordered and very distant columnar and layered. The formation of rock-salt superstructures is dependent on the B-site cation ordering. Octahedral tilting can occur in double perovskites, however Jahn–Teller distortions and alternative modes alter the B–O bond length. | 1 | Crystallography |
Affinity purification of albumin and macroglobulin contamination is helpful in removing excess albumin and α-macroglobulin contamination, when performing mass spectrometry. In affinity purification of serum albumin, the stationary used for collecting or attracting serum proteins can be Cibacron Blue-Sepharose. Then the serum proteins can be eluted from the adsorbent with a buffer containing thiocyanate (SCN). | 0 | Chromatography + Titration + pH indicators |
* Positions of the CBED disks are the same as the positions of the Bragg peaks and are given approximately by the relation:
where is the distance between the crystallographic planes , is the Bragg angle, is an integer, and is the wavelength of the probing electrons.
* The beam convergence semi-angle - is controlled by the C2 aperture. The probing beam convergence semi-angle, , is of the order of milliradians, ranging from 0.1˚ to 1˚. For small convergence semi-angle, the CBED disks do not overlap with each other, whereas for larger semi-convergence angles, the disks overlap.
* The diameter of a CBED disk is given by the beam convergence semi-angle :
* Defocus : The distance between the crossover of the probing beam and the position of the specimen is called the defocus distance . The sample can be moved along the axis. At a defocus distance, both the direct space and reciprocal space information are visible in the CBED pattern. | 1 | Crystallography |