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Litmus can be found in different species of lichens. The dyes are extracted from such species as Roccella tinctoria (South American), Roccella fuciformis (Angola and Madagascar), Roccella pygmaea (Algeria), Roccella phycopsis, Lecanora tartarea (Norway, Sweden), Variolaria dealbata, Ochrolechia parella, Parmotrema tinctorum, and Parmelia. Currently, the main sources are Roccella montagnei (Mozambique) and Dendrographa leucophoea (California).

Chromatography + Titration + pH indicators

Chromatography is a physical method of separation that distributes the components you want to separate between two phases, one stationary (stationary phase), the other (the mobile phase) moving in a definite direction. Cold ethanol precipitation, developed by Cohn in 1946, manipulates pH, ionic strength, ethanol concentration and temperature to precipitate different protein fractions from plasma. Chromatographic techniques utilise ion exchange, gel filtration and affinity resins to separate proteins. Since the 1980s it has emerged as an effective method of purifying blood components for therapeutic use.

Chromatography + Titration + pH indicators

Several GC–MS systems have left earth. Two were brought to Mars by the Viking program. Venera 11 and 12 and Pioneer Venus analysed the atmosphere of Venus with GC–MS. The Huygens probe of the Cassini–Huygens mission landed one GC–MS on Saturns largest moon, Titan. The MSL Curiosity rovers Sample analysis at Mars (SAM) instrument contains both a gas chromatograph and quadrupole mass spectrometer that can be used in tandem as a GC–MS. The material in the comet 67P/Churyumov–Gerasimenko was analysed by the Rosetta mission with a chiral GC–MS in 2014.

Chromatography + Titration + pH indicators

Shodex is the brand name of HPLC columns and is best known for polymer-based columns. The product range covers aqueous and organic Size Exclusion Chromatography columns for large (bio-)molecules, columns for the routine analysis of sugars and organic acids, and a variety of Reversed Phase and HILIC columns. Additionally they offer Ion Chromatography (IC) and Ion Exchange columns. Shodex HPLC Columns are manufactured in Japan by Resonac (formerly known as Showa Denko), one of the largest Japanese chemical companies and listed in the Nikkei 225 index. They produce around 260 different columns, most packed with polymer-based particles, and have been doing so since 1974. The portfolio includes standard analytical columns, semi-micro columns, and preparative columns. Also size exclusion chromatography calibration standards are available (Pullulan, Polystyrene, Polymethylmethacrylate) Shodex is distributed worldwide by the different sales offices and by a range of local distributors.

Chromatography + Titration + pH indicators

Microcrystallization (or microcrystal test) is a method for identifying lichen metabolites that was predominantly used before the advent of more advanced techniques such as thin-layer chromatography and high-performance liquid chromatography. Developed primarily by Yasuhiko Asahina, this approach relies on the formation of distinctive crystals from lichen extracts. Although now superseded by modern analytical methods, microcrystallization still holds importance for compound purification and analysis using X-ray crystallography.

Crystallography

The concept of using a post-column catalytic reactor to enhance the response of the FID was described by Kenneth Porter & D.H. Volman, for the reduction of carbon dioxide and carbon monoxide to methane using a nickel catalyst. This process was later refined by Johns & Thompson, and is now commonplace in many laboratories, colloquially referred to as a methanizer. This device is limited to the conversion of carbon dioxide and carbon monoxide to methane, and the nickel catalysts are poisoned by species such as sulfur and ethylene. The use of two reactors in series for the subsequent combustion and then reduction of organic molecules is described by Takuro Watanabes group and Paul Dauenhauers group using separate reactors for oxidation and reduction. The authors demonstrate the effectiveness of this technique in qualifying traceable standards and the analysis of mixtures without calibrations. The PolyArc reactor combines the combustion and reduction zones into a single microreactor using proprietary catalyst blends that efficiently convert organic molecules to methane.

Chromatography + Titration + pH indicators

Instrumentation of supercritical fluid chromatography SFC has a similar setup to an HPLC instrument. The stationary phases are similar, and are packed inside similar column types. However, there are special features in these systems, because of the need to keep the mobile phase at supercritical fluidic state over the entire system. Temperature is critical to keep the fluids in a supercritical state, so there should be a heat control tool in the system, similar to that of GC. Also, there should be a precise pressure control mechanism, a restrictor to keep the pressure above a certain point, because pressure is another essential parameter to keep the mobile phase in a supercritical fluid state, so it is kept at the required minimal level. A microprocessor mechanism is placed in the instrument for SFC. This unit collects data for pressure, oven temperature, and detector performance to control the related pieces of the instrument. CO utilized in carbon dioxide dedicated pumps, which require that the incoming CO and pump heads be kept cold, in order to maintain the carbon dioxide at a temperature and pressure fit for supercritical fluidic state, where it can be effectively metered at a specified flow rate range. The CO subsequently becomes supercritical fluid throughout the injector and the column oven, when the temperature and pressure it is subjected to, are raised above the critical point of the liquid, thus the supercritical state is achieved. Supercritical fluids combine useful properties of gas and liquid phases, as it can behave like both a gas and a liquid in various aspects. A supercritical fluid provides a gas-like characteristic when it fills a container and it takes the shape of the container. The motion and kinetics of the molecules are quite similar to gas molecules. On the other hand, a supercritical fluid behaves like a liquid because its density property is near liquid; thus, a supercritical fluid shows a similarity to the dissolving effect of a liquid. The result is that one can load masses, similar to those used in HPLC, on column per injection, and still maintain a high chromatographic efficiency similar to those attained in GC. Typically, gradient elution is employed in analytical SFC using a polar co-solvent such as methanol, possibly with a weak acid or base at low concentrations ~1%. The apparent plate count per analysis can be observed to exceed 500K plates per meter routinely with 5 um stationary phases. The operator uses software to set mobile phase flow rate, co-solvent composition, system back pressure and column oven temperature, which must exceed 40 °C for supercritical conditions needed to be achieved with CO. In addition, SFC provides an additional control parameter – pressure – by using an automated static and dynamic back pressure regulator. From an operational standpoint, SFC is as simple and robust as HPLC, but fraction collection is more convenient because the primary mobile phase evaporates leaving only the analyte and a small volume of polar co-solvent. If the outlet CO is captured, it can be re-compressed and recycled, allowing for >90% reuse of CO. Similar to HPLC, SFC uses a variety of detection methods including UV/VIS, mass spectrometry, FID (unlike HPLC) and evaporative light scattering.

Chromatography + Titration + pH indicators

Selective enzyme and antibody separation can be achieved with the use of specific end groups that conjugate with the specific compounds. This results in a formation of a polymer-enzyme conjugate which can be reversibly precipitated and dissolved by changing the temperature. Chen and Hoffman used N-Hydroxysuccinimide (NHS) ester functional end group on NIPAAm to conjugate selectively with β-D-glucosidase. They found that the conjugated enzyme could be repeatedly precipitated and dissolved in solution and still maintain sufficient enzymatic activity. In a study that was published in 1998, Hoshino et al. prepared a TRP with a maltose ligand, evaluated it with concanavalin A (Con A), and attempted to separate and purify α-glucosidase, a thermolabile compound. Since the goal is to selectively isolate a thermolabile enzyme, a TRP with a small LCST value is desired. To fit this condition, the selected TRP was poly(N-acryloylpiperidine)-cysteamine (pAP), which has an LCST of 4 °C. The terminally bound maltose moiety maintains affinity for both analytes, thus the modified TRP, pAPM, met critical conditions of external temperature requirements and affinity for both target analytes. The solubility properties changed from 4 °C (soluble) to 8 °C (insoluble). Several reagents were tested for the recovery of Con A by desorption which had higher binding affinities to Con A than maltose. These reagents were α-D-glucopyranoside, D-mannose, methyl α-D-mannopyranoside, and glucose. α-D-mannopyranoside was the most effective for desorbing Con A from pAPM at virtually 100% after 1 hour. As a control, pAPM was used to bind Con A from a crude extract, which found the pickup of several impurities but still managed to recover 80% of Con A. This exemplifies the need for selective moieties, maltose not residing among them. Finally, the application of pAPM was tested by attempting to separate α-glucosidase from yeast extract under low temperature conditions. In conclusion, the pAPM was found to recover 68% of α-glucosidase activity tested against, maltose being the selected desorption reagent. Another interesting development for AC was involved with antibody separation using another TRP-ligand combination. Anastase-Ravion et al. attached a dextran derivative to the classic PNIPAAm to result in a poly(NIPAAm)-DD, and used this stationary phase to separate polyclonal antibodies from subcutaneous rabbit serum. From the study, the dextran derivative of choice was carboxymethyl dextran benzylamide sulfonate/sulfate, and when bound to the TRP was labeled poly(NIPAAm)-CMDBS. The LCST for the poly(NIPAAm)-CMDBS was raised from 32 °C to 33 °C. To test the success of the affinity binding, the antibodies were eluted with glycine buffer (adjusted to pH 2.6 with HCl). Promising results were obtained in 2003 in a study that merged the newer developments in affinity chromatography with microfluidic devices. Upon the development of microfluidic technology, coupling it with affinity chromatography meant modifying channel surfaces, packing coated beads, or packing with coated porous material, neither of which allow for replenishing the columns. This produces limitations that prevent the packing material from being changed or the column being regenerated. The approach they took to address those challenges meant incorporating TRP particles as a reversibly immobilized stationary phase. What separates this development from other AC methods is that the beads on which the modified TRP are attached can reversibly adhere to the inner surfaces of the microfluidic channels. The formulation of the smart bead matrix is a little complex, but in general PNIPAAm is modified two times, first with NHS, then with polyethylene glycol-biotin (PEG-b) resulting in PEG-b/pNIPAAm beads. The inner surface of the microfluidic channels is composed of polyethylene terephthalate, to which the PEG-b/pNIPAAm beads reversibly bind above the LCST. When the sample solution is passed through the channels, the target analyte binds to the biotin ligand. The temperature can then be brought below the LCST to dissociate and become removed from the inner channels. This allows for a system adept to being reloaded with stationary phase under mild conditions. They successfully separated and eluted Streptavidin. Further application of these procedures allow for portable AC columns which can be packed on site and used for local or clinical analytical separations of complex biological fluids.

Chromatography + Titration + pH indicators

* Liquid chromatography: Traditional chromatography columns were made of glass. Modern columns are mostly made of borosilicate glass, acrylic glass or stainless steel. To prevent the stationary phase from leaking out of the column interior a polymer, stainless steel or ceramic net is usually applied. Depending on the application material- and size-requirements may change. * Gas chromatography (GC): Older columns were made of glass or metal packed with particles of a solid stationary phase. More recently, narrower diameter (capillary) columns have been made using fused silica coated on the inside with a film of the stationary phase material. GC columns are typically very long to take advantage of their low resistance to the flow of carrier gas. The materials of the column and the stationary phase must be suitable for GC operating temperatures, which may range as high as 300°C or more.

Chromatography + Titration + pH indicators

Simple: * Strontium titanate * Calcium titanate * Lead titanate * Bismuth ferrite * Lanthanum ytterbium oxide * Silicate perovskite * Lanthanum manganite * Yttrium aluminum perovskite (YAP) * Lutetium aluminum perovskite (LuAP) Solid solutions: * Lanthanum strontium manganite * LSAT (lanthanum aluminate – strontium aluminum tantalate) * Lead scandium tantalate * Lead zirconate titanate * Methylammonium lead halide * Methylammonium tin halide * Formamidinium tin halide

Crystallography

Malachite green is traditionally used as a dye. Kilotonnes of MG and related triarylmethane dyes are produced annually for this purpose. MG is active against the oomycete Saprolegnia, which infects fish eggs in commercial aquaculture, MG has been used to treat Saprolegnia and is used as an antibacterial. It is a very popular treatment against Ichthyophthirius multifiliis in freshwater aquaria. The principal metabolite, leuco-malachite green (LMG), is found in fish treated with malachite green, and this finding is the basis of controversy and government regulation. See also Antimicrobials in aquaculture. MG has frequently been used to catch thieves and pilferers. The bait, usually money, is sprinkled with the anhydrous powder. Anyone handling the contaminated money will find that on upon washing the hands, a green stain on the skin that lasts for several days will result.

Chromatography + Titration + pH indicators

α-Naphtholphthalein (CHO) is a phthalein dye used as a pH indicator with a visual transition from colorless/reddish to greenish blue at pH 7.3–8.7.

Chromatography + Titration + pH indicators

In one version of the laser spray interface, explosive vaporization and mist formation occur when an aqueous solution effusing from the tip of the stainless steel capillary is irradiated from the opposite side of the capillary by a 10.6 μm infrared laser. Weak ion signals could be detected when the plume was sampled through the ion sampling orifice. When a high voltage (3–4 kV) was applied to the stainless-steel capillary, strong ion signals appeared. The ion abundances were found to be orders of magnitude greater than those obtained by conventional electrospray ionization in the case of aqueous solutions. This approach to laser spray ionization is a hybrid of three basic techniques for the generation of gaseous ions from the condensed phase, i.e., energy-sudden activation, nebulization and the action of an electric field. Laser spray mass spectrometry can faithfully reflect the solution-phase characteristics of biomolecules. It has been successfully applied to evaluate the binding affinities of protein-DNA. Laser spray has better ionization efficiency than conventional electrospray ionization (ESI). In particular, the sensitivity became more than one order of magnitude higher in negative ion modes. It was also found that this technique has a potential benefit for the low concentration samples due to condensation effect of the formed droplet by the irradiation of laser. Higher the solvation energies of triply charged metal ions, stronger are the signals for ions.

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In 2007 Houser et al. developed the analogous parameter to distinguish whether the geometry of the coordination center is square planar or tetrahedral. The formula is: where: and are the two greatest valence angles of coordination center; is a tetrahedral angle. When is close to 0 the geometry is similar to square planar, while if is close to 1 then the geometry is similar to tetrahedral. However, in contrast to the parameter, this does not distinguish and angles, so structures of significantly different geometries can have similar values. To overcome this issue, in 2015 Okuniewski et al. developed parameter that adopts values similar to but better differentiates the examined structures: where: are the two greatest valence angles of coordination center; is a tetrahedral angle. Extreme values of and denote exactly the same geometries, however is always less or equal to so the deviation from ideal tetrahedral geometry is more visible. If for tetrahedral complex the value of parameter is low, then one should check if there are some additional interactions within coordination sphere. For example, in complexes of mercury(II), the Hg···π interactions were found this way.

Crystallography

Suppose that a plane wave (of any type) is incident on planes of lattice points, with separation , at an angle as shown in the Figure. Points A and C are on one plane, and B is on the plane below. Points ABCC' form a quadrilateral. There will be a path difference between the ray that gets reflected along AC' and the ray that gets transmitted along AB, then reflected along BC. This path difference is The two separate waves will arrive at a point (infinitely far from these lattice planes) with the same phase, and hence undergo constructive interference, if and only if this path difference is equal to any integer value of the wavelength, i.e. where and are an integer and the wavelength of the incident wave respectively. Therefore, from the geometry from which it follows that Putting everything together, which simplifies to which is Bragg's law shown above. If only two planes of atoms were diffracting, as shown in the Figure then the transition from constructive to destructive interference would be gradual as a function of angle, with gentle maxima at the Bragg angles. However, since many atomic planes are participating in most real materials, sharp peaks are typical. A rigorous derivation from the more general Laue equations is available (see page: Laue equations).

Crystallography

Native chemical ligation of unprotected peptide segments is used to prepare the protein's polypeptide chain, which is then folded to form a protein molecule. In native chemical ligation, a peptide C-terminal thioester reacts with a second peptide that has a cysteine residue at its N-terminus, to give a product with a peptide bond at the ligation site. Multiple unprotected peptide segments can be linked in this way to give the full length polypeptide chain, which is folded to give the target protein molecule. Once the chemical synthesis of an L-protein is achieved, the D-protein enantiomer can be manufactured using synthetic peptide building blocks made from D-amino acids and Gly. Convergent synthesis is most effective in preparing long polypeptide chains, by using peptide-hydrazides, where the hydrazide can be converted to a thioester for use in native chemical ligation. The hydrazide is stable to native chemical ligation reaction conditions, and can be converted in situ to a reactive peptide-thioester for the next native chemical ligation condensation reaction.

Crystallography

HPTLC comprises three modes: linear mode, circular mode, and anticircular mode. Among these modes, the anticircular mode stands out as the fastest in theory and practice within the realm of HPTLC. This mode achieves separation by allowing the mobile phase to enter the plate layer precisely along an outer circular path, after which it flows toward the center at a nearly constant speed. This approach maximizes sample capacity while minimizing time, layer, and mobile phase consumption, making it the most cost-effective HPTLC technique. The narrow spot-path unique to anticircular HPTLC facilitates automated quantification. When compared to the linear and circular modes, the anticircular mode demonstrates superior separation and significantly heightened sensitivity, especially at higher Rf-values.

Chromatography + Titration + pH indicators

The screw axis appears in the dual quaternion formulation of a spatial displacement . The dual quaternion is constructed from the dual vector defining the screw axis and the dual angle , where φ is the rotation about and d the slide along this axis, which defines the displacement D to obtain, A spatial displacement of points q represented as a vector quaternion can be defined using quaternions as the mapping where d is translation vector quaternion and S is a unit quaternion, also called a versor, given by that defines a rotation by 2θ around an axis S. In the proper Euclidean group E(3) a rotation may be conjugated with a translation to move it to a parallel rotation axis. Such a conjugation, using quaternion homographies, produces the appropriate screw axis to express the given spatial displacement as a screw displacement, in accord with Chasles’ theorem.

Crystallography

In analytical and organic chemistry, elution is the process of extracting one material from another by washing with a solvent: washing of loaded ion-exchange resins to remove captured ions, or eluting proteins or other biopolymers from a gel electrophoresis or chromatography column. In a liquid chromatography experiment, for example, an analyte is generally adsorbed by ("bound to") an adsorbent in a liquid chromatography column. The adsorbent, a solid phase, called a "stationary phase", is a powder which is coated onto a solid support. Based on an adsorbent's composition, it can have varying affinities to "hold onto" other molecules—forming a thin film on the surface of its particles. Elution then is the process of removing analytes from the adsorbent by running a solvent, called an "eluent", past the adsorbent-analyte complex. As the solvent molecules "elute", or travel down through the chromatography column, they can either pass by the adsorbent-analyte complex or displace the analyte by binding to the adsorbent in its place. After the solvent molecules displace the analyte, the analyte can be carried out of the column for analysis. This is why as the mobile phase, called an "eluate", passes out of the column, it typically flows into a detector or is collected by a fraction collector for compositional analysis. Predicting and controlling the order of elution is a key aspect of column chromatographic and column electrophoretic methods.

Chromatography + Titration + pH indicators

Bromothymol blue acts as a weak acid in a solution. It can thus be in protonated or deprotonated form, appearing yellow or blue, respectively. It is bright aquamarine by itself, and greenish-blue in a neutral solution. The deprotonation of the neutral form results in a highly conjugated structure, accounting for the difference in color. An intermediate of the deprotonation mechanism is responsible for the greenish color in neutral solution. The protonated form of bromothymol blue has its peak absorption at 427 nm thus transmitting yellow light in acidic solutions, and the deprotonated form has its peak absorption at 602 nm thus transmitting blue light in more basic solutions. Highly acidic Bromothymol blue is magenta in color. The general carbon skeleton of bromothymol blue is common to many indicators including chlorophenol red, thymol blue, and bromocresol green. The presence of one moderate electron-withdrawing group (bromine atom) and two moderate donating groups (alkyl substituents) are responsible for bromothymol blues active indication range from a pH of 6.0 to 7.6. While the conjugation is responsible for the length and nature of the color change range, these substituent groups are ultimately responsible for the indicators active range. Bromothymol blue is sparingly soluble in oil, but soluble in water, ether, and aqueous solutions of alkalis. It is less soluble in nonpolar solvents such as benzene, toluene, and xylene, and practically insoluble in petroleum ether.

Chromatography + Titration + pH indicators

A sample is introduced, either manually or with an autosampler, into a sample loop of known volume. A buffered aqueous solution known as the mobile phase carries the sample from the loop onto a column that contains some form of stationary phase material. This is typically a resin or gel matrix consisting of agarose or cellulose beads with covalently bonded charged functional groups. Equilibration of the stationary phase is needed in order to obtain the desired charge of the column. If the column is not properly equilibrated the desired molecule may not bind strongly to the column. The target analytes (anions or cations) are retained on the stationary phase but can be eluted by increasing the concentration of a similarly charged species that displaces the analyte ions from the stationary phase. For example, in cation exchange chromatography, the positively charged analyte can be displaced by adding positively charged sodium ions. The analytes of interest must then be detected by some means, typically by conductivity or UV/visible light absorbance. Control an IC system usually requires a chromatography data system (CDS). In addition to IC systems, some of these CDSs can also control gas chromatography (GC) and HPLC.

Chromatography + Titration + pH indicators

Sunset yellow FCF (also known as orange yellow S, or C.I. 15985) is a petroleum-derived orange azo dye with a pH dependent maximum absorption at about 480 nm at pH 1 and 443 nm at pH 13 with a shoulder at 500 nm. When added to foods sold in the United States it is known as FD&C Yellow 6; when sold in Europe, it is denoted by E Number E110.

Chromatography + Titration + pH indicators

The roots of liquid chromatography extend back over a century ago to 1900, when Russian botanist Mikhail Tsvet began experimenting with plant pigments in chlorophyll. He noted that, when a solvent was applied, distinct bands appeared that migrated at different rates along a stationary phase. For this new observation, he coined the term “chromatography,” a colored picture. His first lecture on the subject was presented in 1903, but his most important contribution occurred three years later, in 1906, when the paper “Adsorption analysis and chromatographic method. Applications on the chemistry of chlorophyll,” was published. Rivalry with a colleague who readily and vocally denounced his work meant that chromatographic analysis was shelved for almost 25 years. The great irony of the matter is that it was his rival's students who later took up the chromatography banner in their work with carotins. Greatly unchanged from Tswetts time until the 1940s, normal phase chromatography was performed by passing a gravity-fed solvent through small glass tubes packed with pellicular adsorbent beads. It was in the 1940s, however, that there was a great revolution in gas chromatography (GC). Although GC was a wonderful technique for analyzing inorganic compounds, less than 20% of organic molecules are able to be separated using this technique. It was Richard Synge, who in 1952 won the Nobel Prize in Chemistry for his work with partition chromatography, who applied the theoretical knowledge gained from his work in GC to LC. From this revolution, the 1950s also saw the advent of paper chromatography, reversed-phase partition chromatography (RPC), and hydrophobic interaction chromatography (HIC). The first gels for use in LC were created using cross-linked dextrans (Sephadex) in an attempt to realize Synges prediction that a unique single-piece stationary phase could provide an ideal chromatographic solution. In the 1960s, polyacrylamide and agarose gels were created in a further attempt to create a single-piece stationary phase, but the purity of and stability of available components did not prove useful for implementation in the HPLC. In this decade, affinity chromatography was invented, an ultra-violet (UV) detector was used for the first time in conjunction with LC, and, most importantly, the modern HPLC was born. Csaba Horvath led the development of modern HPLC by piecing together laboratory equipment to suit his purposes. In 1968, Picker Nuclear Company marketed the first commercially available HPLC as a “Nucleic Acid Analyzer.” The following year, the first international symposia on HPLC was held, and Kirkland at DuPont was able to functionalize controlled porosity pellicular particles for the first time. The 1970s and 1980s witnessed a renewed interest in separations media with reduced interparticular void volumes. Perfusion chromatography showed, for the first time, that chromatography media could support high flow rates without sacrificing resolution. Monoliths aptly fit into this new class of media, as they exhibit no void volume and can withstand flow rates up to 9mL/minute. Polymeric monoliths as they exist today were developed independently by three different labs in the late 1980s led by Hjerten, Svec, and Tennikova. Simultaneously, bioseparations became increasingly important, and monolith technologies proved beneficial in biotechnology separations. Though industry focus in the 1980s was on biotechnology, focus in the 1990s shifted to process engineering. While mainstream chromatographers were using 3μm particulate columns, sub-2μm columns were in research phase. The smaller particles meant better resolution and shorter run times; there was also an associated increase in backpressure. In order to withstand the pressure, a new field of chromatography came into being: UHPLC or UPLC- ultra high pressure liquid chromatography. The new instruments were able to endure pressures of up to , as opposed to conventional machines, which, as previously state, can hold up to . UPLC is an alternative solution to the same problems monolithic columns solve. Similarly to UPLC, monolith chromatography can help the bottom line by increasing sample throughput, but without the need to spend capital on new equipment. In 1996, Nobuo Tanaka, at the Kyoto Institute of Technology, prepared silica monoliths using a colloidal suspension synthesis (aka “sol-gel”) developed by a colleague. The process is different from that used in polymeric monoliths. Polymeric monoliths, as mentioned above, are created in situ, using a mixture of monomers and a porogen within the column tubing. Silica monoliths, on the other hand, are created in a mold, undergo a significant amount of shrinkage, and are then clad in a polymeric shrink tubing like PEEK (polyetheretherketone) to reduce wall effects. This method limits the size of columns that can be produced to less than 15 cm long, and though standard analytical inner diameters are readily achieved, there is currently a trend in developing nanoscale capillary and prep scale silica monoliths.

Chromatography + Titration + pH indicators

Crystal parting occurs when minerals break along planes of structural weakness due to external stress, along twin composition planes, or along planes of weakness due to the exsolution of another mineral. Parting breaks are very similar in appearance to cleavage, but the cause is different. Cleavage occurs because of design weakness while parting results from growth defects (deviations from the basic crystallographic design). Thus, cleavage will occur in all samples of a particular mineral, while parting is only found in samples with structural defects. Examples of parting include the octahedral parting of magnetite, the rhombohedral and basal parting in corundum, and the basal parting in pyroxenes.

Crystallography

Although malachite green has almost no fluorescence in aqueous solution (quantum yield 7.9x10), several research groups have developed technologies to detect malachite green. For example, Zhao et al., demonstrated the use of malachite green aptamer in microcantilever based sensors to detect low concentration of malachite green.

Chromatography + Titration + pH indicators

Mixtures of complex acids can be resolved by thermometric titration with standard NaOH in aqueous solution. In a mixture of nitric, acetic and phosphoric acids used in the fabrication of semi-conductors, three endpoints could be predicted on the basis of the dissociation constants of the acids: The key to determine the amount of each acid present in the mixture is the ability to obtain an accurate value for the amount of phosphoric acid present, as revealed by titration of the third proton of HPO. Figure 10 illustrates a titration plot of this mixture, showing 3 sharp endpoints.

Chromatography + Titration + pH indicators

Retention uniformity is calculated from the following formula: where n is the number of compounds separated, R are the Retention factor of the compounds sorted in non-descending order.

Chromatography + Titration + pH indicators

Translations, denoted by T, where v is a vector in R have the effect of shifting the plane in the direction of v. That is, for any point p in the plane, :or in terms of (x, y) coordinates, A translation can be seen as a composite of two parallel reflections.

Crystallography

Rigid unit modes (RUMs) represent a class of lattice vibrations or phonons that exist in network materials such as quartz, cristobalite or zirconium tungstate. Network materials can be described as three-dimensional networks of polyhedral groups of atoms such as SiO tetrahedra or TiO octahedra. A RUM is a lattice vibration in which the polyhedra are able to move, by translation and/or rotation, without distorting. RUMs in crystalline materials are the counterparts of floppy modes in glasses, as introduced by Jim Phillips and Mike Thorpe.

Crystallography

D designates compounds of arbitrary stoichiometry. Originally, D1-D10 were set aside for stoichiometry AB, D11-D20 for stoichiometry AB for n > 3, D31-D50 for (AB), and D51 up for the AB for arbitrary m and n.

Crystallography

The advent of displacement chromatography can be attributed to Arne Tiselius, who in 1943 first classified the modes of chromatography as frontal, elution, and displacement. Displacement chromatography found a variety of applications including isolation of transuranic elements and biochemical entities. The technique was redeveloped by Csaba Horváth, who employed modern high-pressure columns and equipment. It has since found many applications, particularly in the realm of biological macromolecule purification.

Chromatography + Titration + pH indicators

In a crystal, the constitutive particles are arranged periodically, with translational symmetry forming a lattice. The crystal structure can be described as a Bravais lattice with a group of atoms, called the basis, placed at every lattice point; that is, [crystal structure] = [lattice] [basis]. If the lattice is infinite and completely regular, the system is a perfect crystal. For such a system, only a set of specific values for can give scattering, and the scattering amplitude for all other values is zero. This set of values forms a lattice, called the reciprocal lattice, which is the Fourier transform of the real-space crystal lattice. In principle the scattering factor can be used to determine the scattering from a perfect crystal; in the simple case when the basis is a single atom at the origin (and again neglecting all thermal motion, so that there is no need for averaging) all the atoms have identical environments. Equation () can be written as : and . The structure factor is then simply the squared modulus of the Fourier transform of the lattice, and shows the directions in which scattering can have non-zero intensity. At these values of the wave from every lattice point is in phase. The value of the structure factor is the same for all these reciprocal lattice points, and the intensity varies only due to changes in with .

Crystallography

Bragg diffraction (also referred to as the Bragg formulation of X-ray diffraction) was first proposed by Lawrence Bragg and his father, William Henry Bragg, in 1913 after their discovery that crystalline solids produced surprising patterns of reflected X-rays (in contrast to those produced with, for instance, a liquid). They found that these crystals, at certain specific wavelengths and incident angles, produced intense peaks of reflected radiation. Lawrence Bragg explained this result by modeling the crystal as a set of discrete parallel planes separated by a constant parameter . He proposed that the incident X-ray radiation would produce a Bragg peak if reflections off the various planes interfered constructively. The interference is constructive when the phase difference between the wave reflected off different atomic planes is a multiple of ; this condition (see Bragg condition section below) was first presented by Lawrence Bragg on 11 November 1912 to the Cambridge Philosophical Society. Although simple, Bragg's law confirmed the existence of real particles at the atomic scale, as well as providing a powerful new tool for studying crystals. Lawrence Bragg and his father, William Henry Bragg, were awarded the Nobel Prize in physics in 1915 for their work in determining crystal structures beginning with NaCl, ZnS, and diamond. They are the only father-son team to jointly win. The concept of Bragg diffraction applies equally to neutron diffraction and approximately to electron diffraction. In both cases the wavelengths are comparable with inter-atomic distances (~ 150 pm). Many other types of matter waves have also been shown to diffract, and also light from objected with a larger ordered structure such as opals.

Crystallography

Friedels salt plays a main role in the binding and retention of chloride anions in cement and concrete. However, Friedels salt remains a poorly understood phase in the CaO–AlO–CaCl–HO system. A sufficient understanding of the Friedel's salt system is essential to correctly model the reactive transport of chloride ions in reinforced concrete structures affected by chloride attack and steel reinforcement corrosion. It is also important to assess the long-term stability of salt-saturated Portland cement-based grouts to be used in engineering structures exposed to seawater or concentrated brine as it is the case for radioactive waste disposal in deep salt formations. Another reason to study AFm phases and the Friedel's salt system is their tendency to bind, trap and to immobilise toxic anions, such as , , and , or the long-lived radionuclide I, in cementitious materials. Their characterization is important to conceive anion getters and to assess the retention capacity of cementitious buffer and concrete barriers used for radioactive waste disposal.

Crystallography

A uniform structure is identified by each sphere having the same number of contacting neighbours. This gives each sphere an identical neighbourhood. In the example image on the side each sphere has six neighbouring contacts. The number of contacts is best visualised in the rolled-out contact network. It is created by rolling out the contact network into a plane of height and azimuthal angle of each sphere. For a uniform structure such as the one in the example image, this leads to a regular hexagonal lattice. Each dot in this pattern represents a sphere of the packing and each line a contact between adjacent spheres. For all uniform structures above a diameter ratio of , the regular hexagonal lattice is its characterising feature since this lattice type has the maximum number of contacts. For different uniform structures the rolled-out contact pattern only varies by a rotation in the plane. Each uniform structure is thus distinguished by its periodicity vector , which is defined by the phyllotactic triplet .

Crystallography

When an excess of Ba is added to a non-ionic surfactant of the alkyl propylene oxide derivative type, a pseudo-cationic complex is formed. This may be titrated with standard sodium tetraphenylborate. Two moles tetraphenylborate react with one mole of the Ba/ non-ionic surfactant complex.

Chromatography + Titration + pH indicators

When a crystal is composed of crystallites with varying lattice orientation, topographic contrast arises: In plane-wave topography, only selected crystallites will be in diffracting position, thus yielding diffracted intensity only in some parts of the image. Upon sample rotation, these will disappear, and other crystallites will appear in the new topograph as strongly diffracting. In white-beam topography, all misoriented crystallites will be diffracting simultaneously (each at a different wavelength). However, the exit angles of the respective diffracted beams will differ, leading to overlapping regions of enhanced intensity as well as to shadows in the image, thus again giving rise to contrast. While in the case of tilted crystallites, domain walls, grain boundaries etc. orientation contrast occurs on a macroscopic scale, it can also be generated more locally around defects, e.g. due to curved lattice planes around a dislocation core.

Crystallography

Two-dimensional chromatography represents the most thorough and rigorous approach to evaluation of the proteome. While previously accepted approaches have utilized elution mode chromatographic approaches such as cation exchange to reversed phase HPLC, yields are typically very low requiring analytical sensitivities in the picomolar to femtomolar range. As displacement chromatography offers the advantage of concentration of trace components, two dimensional chromatography utilizing displacement rather than elution mode in the upstream chromatography step represents a potentially powerful tool for analysis of trace components, modifications, and identification of minor expressed components of the proteome.

Chromatography + Titration + pH indicators

If the crystal diffracts to high resolution (<1.2 Å), the initial phases can be estimated using direct methods. Direct methods can be used in x-ray crystallography, neutron crystallography, and electron crystallography. A number of initial phases are tested and selected by this method. The other is the Patterson method, which directly determines the positions of heavy atoms. The Patterson function gives a large value in a position which corresponds to interatomic vectors. This method can be applied only when the crystal contains heavy atoms or when a significant fraction of the structure is already known. For molecules whose crystals provide reflections in the sub-Ångström range, it is possible to determine phases by brute force methods, testing a series of phase values until spherical structures are observed in the resultant electron density map. This works because atoms have a characteristic structure when viewed in the sub-Ångström range. The technique is limited by processing power and data quality. For practical purposes, it is limited to "small molecules" and peptides because they consistently provide high-quality diffraction with very few reflections.

Crystallography

Sunset yellow FCF is known as FD&C yellow No. 6 in the US and is approved for use in coloring food, drugs, and cosmetics with an acceptable daily intake of 3.75 mg/kg.

Chromatography + Titration + pH indicators

Anthocyanins fluoresce, enabling a tool for plant cell research to allow live cell imaging without a requirement for other fluorophores. Anthocyanin production may be engineered into genetically modified materials to enable their identification visually.

Chromatography + Titration + pH indicators

This parameter is often used in biomechanics, when describing the motion of joints of the body. For any period of time, joint motion can be seen as the movement of a single point on one articulating surface with respect to the adjacent surface (usually distal with respect to proximal). The total translation and rotations along the path of motion can be defined as the time integrals of the instantaneous translation and rotation velocities at the IHA for a given reference time. In any single plane, the path formed by the locations of the moving instantaneous axis of rotation (IAR) is known as the centroid, and is used in the description of joint motion.

Crystallography

In crystallography, the R-factor (sometimes called residual factor or reliability factor or the R-value or R) is a measure of the agreement between the crystallographic model and the experimental X-ray diffraction data. In other words, it is a measure of how well the refined structure predicts the observed data. The value is also sometimes called the discrepancy index, as it mathematically describes the difference between the experimental observations and the ideal calculated values. It is defined by the following equation: where F is the so-called structure factor and the sum extends over all the reflections of X-rays measured and their calculated counterparts respectively. The structure factor is closely related to the intensity of the reflection it describes: The minimum possible value is zero, indicating perfect agreement between experimental observations and the structure factors predicted from the model. There is no theoretical maximum, but in practice, values are considerably less than one even for poor models, provided the model includes a suitable scale factor. Random experimental errors in the data contribute to even for a perfect model, and these have more leverage when the data are weak or few, such as for a low-resolution data set. Model inadequacies such as incorrect or missing parts and unmodeled disorder are the other main contributors to , making it useful to assess the progress and final result of a crystallographic model refinement. For large molecules, the R-factor usually ranges between 0.6 (when computed for a random model and against an experimental data set) and 0.2 (for example for a well refined macro-molecular model at a resolution of 2.5 Ångström). Small molecules (up to ca. 1000 atoms) usually form better-ordered crystals than large molecules, and thus it is possible to attain lower R-factors. In the Cambridge Structural Database of small-molecule structures, more than 95% of the 500,000+ crystals have an R-factor lower than 0.15, and 9.5% have an R-factor lower than 0.03. Crystallographers also use the Free R-Factor () to assess possible overmodeling of the data. is computed according to the same formula given above, but on a small, random sample of data that are set aside for the purpose and never included in the refinement. will always be greater than because the model is not fitted to the reflections that contribute to , but the two statistics should be similar because a correct model should predict all the data with uniform accuracy. If the two statistics differ significantly then that indicates the model has been over-parameterized, so that to some extent it predicts not the ideal error-free data for the correct model, but rather the error-afflicted data actually observed. The quantities and are similarly used to describe the internal agreement of measurements in a crystallographic data set.

Crystallography

Combinations of chromatographic methods can be used to purify a target molecule. The purpose of purifying proteins with FPLC is to deliver quantities of the target at sufficient purity in a biologically active state to suit its further use. The quality of the end product varies depending the type and amount of starting material, efficiency of separation, and selectivity of the purification resin. The ultimate goal of a given purification protocol is to deliver the required yield and purity of the target molecule in the quickest, cheapest, and safest way for acceptable results. The range of purity required can be from that required for basic analysis (SDS-PAGE or ELISA, for example), with only bulk impurities removed, to pure enough for structural analysis (NMR or X-ray crystallography), approaching >99% target molecule. Purity required can also mean pure enough that the biological activity of the target is retained. These demands can be used to determine the amount of starting material required to reach the experimental goal. If the starting material is limited and full optimization of purification protocol cannot be performed, then a safe standard protocol that requires a minimum adjustment and optimization steps are expected. This may not be optimal with respect to experimental time, yield, and economy but it will achieve the experimental goal. On the other hand, if the starting material is enough to develop more complete protocol, the amount of work to reach the separation goal depends on the available sample information and target molecule properties. Limits to development of purification protocols many times depends on the source of the substance to be purified, whether from natural sources (harvested tissues or organisms, for example), recombinant sources (such as using prokaryotic or eukaryotic vectors in their respective expression systems), or totally synthetic sources. No chromatographic techniques provide 100% yield of active material and overall yields depend on the number of steps in the purification protocol. By optimizing each step for the intended purpose and arranging them that minimizes inter step treatments, the number of steps will be minimized. A typical multistep purification protocol starts with a preliminary capture step which often utilizes ion exchange chromatography (IEC). The media (stationary phase) resin consists of beads, which range in size from being large (good for fast flow rates and little to no sample clarification at the expense of resolution) to small (for best possible resolution with all other factors being equal). Short and wide column geometries are amenable to high flow rates also at the expense of resolution, typically because of lateral diffusion of sample on the column. For techniques such as size exclusion chromatography to be useful, very long, thin columns and minimal sample volumes (maximum 5% of column volume) are required. Hydrophobic interaction chromatography (HIC) can also be used for first and/ or intermediate steps. Selectivity in HIC is independent of running pH and descending salt gradients are used. For HIC, conditioning involves adding ammonium sulfate to the sample to match the buffer A concentration. If HIC is used before IEC, the ionic strength would have to be lowered to match that of buffer A for IEC step by dilution, dialysis or buffer exchange by gel filtration. This is why IEC is usually performed prior to HIC as the high salt elution conditions for IEC are ideal for binding to HIC resins in the next purification step. Polishing is used to achieve the final level of purification required and is commonly performed on a gel filtration column. An extra intermediate purification step can be added or optimization of the different steps is performed for improving purity. This extra step usually involves another round of IEC under completely different conditions. Although this is an example of a common purification protocol for proteins, the buffer conditions, flow rates, and resins used to achieve final goals can be chosen to cover a broad range of target proteins. This flexibility is imperative for a functional purification system as all proteins behave differently and often deviate from predictions.

Chromatography + Titration + pH indicators

Columnar structures have also been studied intensively in the context of nanotubes. Their physical or chemical properties can be altered by trapping identical particles inside them. These are usually done by self-assembling fullerenes such as C60, C70, or C78 into carbon nanotubes, but also boron nitride nanotubes Such structures also assemble when particles are coated on the surface of a spherocylinder as in the context of pharmaceutical research. Lazáro et al. examined the morphologies of virus capsid proteins self-assembled around metal nanorods. Drug particles were coated as densely as possible on a spherocylinder to provide the best medical treatment. Wu et al. built rods of the size of several microns. These microrods are created by densely packing silica colloidal particles inside cylindrical pores. By solidifying the assembled structures the microrods were imaged and examined using scanning electron microscopy (SEM). Columnar arrangements are also investigated as a possible candidate of optical metamaterials (i.e. materials with a negative refractive index) which find applications in super lenses or optical cloaking. Tanjeem et al. are constructing such a resonator by self-assembling nanospheres on the surface of the cylinder. The nanospheres are suspended in an SDS solution together with a cylinder of diameter , much larger than the diameter of the nanospheres (). The nanospheres then stick to the surface of the cylinders by a depletion force.

Crystallography

A simple cubic unit cell, with stacks of atoms arranged as if at the eight corners of a cube would form a single cubic hole or void in the center. If these voids are occupied by ions of opposite charge from the parent lattice, the cesium chloride structure is formed.

Crystallography

Drugs receive regulatory approval and are granted patents for only a single polymorph. In a classic patent dispute, the GlaxoSmithKline defended its patent for the Type II polymorph of the active ingredient in Zantac against competitors while that of the Type I polymorph had already expired. Polymorphism in drugs can also have direct medical implications since dissolution rates depend on the polymorph. Polymorphic purity of drug samples can be checked using techniques such as powder X-ray diffraction, IR/Raman spectroscopy, and utilizing the differences in their optical properties in some cases.

Crystallography

Acid–base titrations depend on the neutralization between an acid and a base when mixed in solution. In addition to the sample, an appropriate pH indicator is added to the titration chamber, representing the pH range of the equivalence point. The acid–base indicator indicates the endpoint of the titration by changing color. The endpoint and the equivalence point are not exactly the same because the equivalence point is determined by the stoichiometry of the reaction while the endpoint is just the color change from the indicator. Thus, a careful selection of the indicator will reduce the indicator error. For example, if the equivalence point is at a pH of 8.4, then the phenolphthalein indicator would be used instead of Alizarin Yellow because phenolphthalein would reduce the indicator error. Common indicators, their colors, and the pH range in which they change color are given in the table above. When more precise results are required, or when the reagents are a weak acid and a weak base, a pH meter or a conductance meter are used. For very strong bases, such as organolithium reagent, metal amides, and hydrides, water is generally not a suitable solvent and indicators whose pKa are in the range of aqueous pH changes are of little use. Instead, the titrant and indicator used are much weaker acids, and anhydrous solvents such as THF are used. The approximate pH during titration can be approximated by three kinds of calculations. Before beginning of titration, the concentration of is calculated in an aqueous solution of weak acid before adding any base. When the number of moles of bases added equals the number of moles of initial acid or so called equivalence point, one of hydrolysis and the pH is calculated in the same way that the conjugate bases of the acid titrated was calculated. Between starting and end points, is obtained from the Henderson-Hasselbalch equation and titration mixture is considered as buffer. In Henderson-Hasselbalch equation the and are said to be the molarities that would have been present even with dissociation or hydrolysis. In a buffer, can be calculated exactly but the dissociation of , the hydrolysis of and self-ionization of water must be taken into account. Four independent equations must be used: In the equations, and are the moles of acid () and salt ( where X is the cation), respectively, used in the buffer, and the volume of solution is . The law of mass action is applied to the ionization of water and the dissociation of acid to derived the first and second equations. The mass balance is used in the third equation, where the sum of and must equal to the number of moles of dissolved acid and base, respectively. Charge balance is used in the fourth equation, where the left hand side represents the total charge of the cations and the right hand side represents the total charge of the anions: is the molarity of the cation (e.g. sodium, if sodium salt of the acid or sodium hydroxide is used in making the buffer).

Chromatography + Titration + pH indicators

A mass spectrometer is typically utilized in one of two ways: full scan or selective ion monitoring (SIM). The typical GC–MS instrument is capable of performing both functions either individually or concomitantly, depending on the setup of the particular instrument. The primary goal of instrument analysis is to quantify an amount of substance. This is done by comparing the relative concentrations among the atomic masses in the generated spectrum. Two kinds of analysis are possible, comparative and original. Comparative analysis essentially compares the given spectrum to a spectrum library to see if its characteristics are present for some sample in the library. This is best performed by a computer because there are a myriad of visual distortions that can take place due to variations in scale. Computers can also simultaneously correlate more data (such as the retention times identified by GC), to more accurately relate certain data. Deep learning was shown to lead to promising results in the identification of VOCs from raw GC–MS data. Another method of analysis measures the peaks in relation to one another. In this method, the tallest peak is assigned 100% of the value, and the other peaks being assigned proportionate values. All values above 3% are assigned. The total mass of the unknown compound is normally indicated by the parent peak. The value of this parent peak can be used to fit with a chemical formula containing the various elements which are believed to be in the compound. The isotope pattern in the spectrum, which is unique for elements that have many natural isotopes, can also be used to identify the various elements present. Once a chemical formula has been matched to the spectrum, the molecular structure and bonding can be identified, and must be consistent with the characteristics recorded by GC–MS. Typically, this identification is done automatically by programs which come with the instrument, given a list of the elements which could be present in the sample. A "full spectrum" analysis considers all the "peaks" within a spectrum. Conversely, selective ion monitoring (SIM) only monitors selected ions associated with a specific substance. This is done on the assumption that at a given retention time, a set of ions is characteristic of a certain compound. This is a fast and efficient analysis, especially if the analyst has previous information about a sample or is only looking for a few specific substances. When the amount of information collected about the ions in a given gas chromatographic peak decreases, the sensitivity of the analysis increases. So, SIM analysis allows for a smaller quantity of a compound to be detected and measured, but the degree of certainty about the identity of that compound is reduced.

Chromatography + Titration + pH indicators

The Macromolecular Crystallographic Information File (mmCIF) also known as PDBx/mmCIF is a standard text file format for representing macromolecular structure data, developed by the International Union of Crystallography (IUCr) and the Protein Data Bank It is an extension of the Crystallographic Information File (CIF), specifically for macromolecular data, such as proteins and nucleic acids, incorporating elements from the PDB file format. mmCIF is intended as an alternative to the Protein Data Bank (PDB) format and is now the default format used by the Protein Data Bank. mmCIF was designed to address limitations of the PDB format in terms of capacity and flexibility, especially with the increasing size and complexity of macromolecular structures being determined. The format is part of the larger Crystallographic Information Framework, a system of exchange protocols based on data dictionaries and relational rules expressible in different machine-readable manifestations, including, but not restricted to, the original Crystallographic Information File and XML.

Crystallography

QR has many uses as a fluorescent probe. The use of QR as a probe is relatively safe, inexpensive, and a sensitive method compared with other fluorescence probes like ethidium bromide or dimeric cyanine dyes. QR is also an ideal fluorescent probe because substrates of interest, such as antibodies, can be detected within a 0.3nM detection limit without the use of radiolabeled or fluorescently labeled oligonucleotides, which are the DNA components. In other words, quinaldine red is preferred tag since its binding increases the fluorescence without extra tags being needed. The dye's ability to bind to proteins makes it a great tag. Once bound to a protein, fluorescent signals are emitted which allow the strength of QR binding to the protein to be determined. Using this technique allows for many dynamic interactions to be understood. Another variation to detecting the QR probes is by measuring the fluorescence via a spectrofluorometer. This allows the concentration of the QR-substance (could be a protein or nucleic acids) to be measured. This also indirectly allows the binding ability of QR to the substance to be measured. Using this technique gives an emission wavelength of 520/160 nm. QR's ability to bind to substrates and fluoresce can be further utilized to determine the location of a substrate with the use of Raman spectroscopy and the electronic absorption spectra. For example, when a cell is not energized, a cell will not take up QR. When a cell is energized, aggregations of red substrate can be found within a cell, and this can be detected with Raman spectroscopy In addition to being used as a fluorescent probe, QR can also be used as an agent in bleaching. When exposed to intensive rays such as X-rays, gamma rays, and electron beams, the dye is able to photobleach a substance. In the case of dental bleaching, a laser is the source of intensive rays. QR is dissolved in a mixture of water, ethanol, isopropyl alcohol, glycerol, and other solvents and is placed on the teeth. In the presence of oxygen, the QR and carrier particles solution uses its sensitivity to light energy to ultimately bleach teeth, making them whiter. Quinaldine red is also used as an indicator in experiments. In an assay for inorganic and organic phosphates, QR proved to be a better indicator due to a low blank and its color stability. When being used as an indicator, a color change is involved in order to indicate a change in the pH. For example, in a solution containing inorganic phosphate and ammonium molybdate in sulfuric acid, a reaction could occur where the two substances react forming a phosphomolybdate complex ion, or no reaction could occur. In this case, if pale pink mixture of quinaldine red turns to a colorless solution, this indicates the presence of a free phosphate. If the solution turns a dark red, that indicates the phosphomolybdate complex ion has formed. By using QR as an indicator in this manner, enzymatic activities can be monitored.

Chromatography + Titration + pH indicators

Modern two-dimensional chromatographic techniques are based on the results of the early developments of paper chromatography and thin-layer chromatography (TLC) which involved liquid mobile phases and solid stationary phases. These techniques would later generate modern gas chromatography (GC) and liquid chromatography (LC) analysis. Different combinations of one-dimensional GC and LC produced the analytical chromatographic technique that is known as two-dimensional chromatography. The earliest form of 2D-chromatography came in the form of a multi-step TLC separation in which a thin sheet of cellulose is used first with one solvent in one direction, then, after the paper has been dried, another solvent is run in a direction at right angles to the first. This methodology first appeared in the literature with a 1944 publication by A. J. P. Martin and coworkers detailing an efficient method for separating amino acids – "...but the two-dimensional chromatogram is especially convenient, in that it shows at a glance information that can be gained otherwise only as the result of numerous experiments" (Biochem J., 1944, 38, 224).

Chromatography + Titration + pH indicators

In materials science, Ostwalds rule or Ostwalds step rule, conceived by Wilhelm Ostwald, describes the formation of polymorphs. The rule states that usually the less stable polymorph crystallizes first. Ostwald's rule is not a universal law but a common tendency observed in nature. This can be explained on the basis of irreversible thermodynamics, structural relationships, or a combined consideration of statistical thermodynamics and structural variation with temperature. Unstable polymorphs more closely resemble the state in solution, and thus are kinetically advantaged. For example, out of hot water, metastable, fibrous crystals of benzamide appear first, only later to spontaneously convert to the more stable rhombic polymorph. Another example is magnesium carbonate, which more readily forms dolomite. A dramatic example is phosphorus, which upon sublimation first forms the less stable white phosphorus, which only slowly polymerizes to the red allotrope. This is notably the case for the anatase polymorph of titanium dioxide, which having a lower surface energy is commonly the first phase to form by crystallisation from amorphous precursors or solutions despite being metastable, with rutile being the equilibrium phase at all temperatures and pressures.

Crystallography

Le Bail analysis is a whole diffraction pattern profile fitting technique used to characterize the properties of crystalline materials, such as structure. It was invented by Armel Le Bail around 1988.

Crystallography

We thus have two new kinds of isometry subgroups: all translations, and rotations sharing a fixed point. Both are subgroups of the even subgroup, within which translations are normal. Because translations are a normal subgroup, we can factor them out leaving the subgroup of isometries with a fixed point, the orthogonal group.

Crystallography

A transversely isotropic material is one with physical properties that are symmetric about an axis that is normal to a plane of isotropy. This transverse plane has infinite planes of symmetry and thus, within this plane, the material properties are the same in all directions. Hence, such materials are also known as "polar anisotropic" materials. In geophysics, vertically transverse isotropy (VTI) is also known as radial anisotropy. This type of material exhibits hexagonal symmetry (though technically this ceases to be true for tensors of rank 6 and higher), so the number of independent constants in the (fourth-rank) elasticity tensor are reduced to 5 (from a total of 21 independent constants in the case of a fully anisotropic solid). The (second-rank) tensors of electrical resistivity, permeability, etc. have two independent constants.

Crystallography

4-nitro phenol is a slightly yellow, crystalline material, moderately toxic. It shows two polymorphs in the crystalline state. The alpha-form is colorless pillars, unstable at room temperature, and stable toward sunlight. The beta-form is yellow pillars, stable at room temperature, and gradually turns red upon irradiation of sunlight. Usually 4-nitrophenol exists as a mixture of these two forms. In solution, 4-nitrophenol has a dissociation constant (pK) of 7.15 at 25 °C.

Chromatography + Titration + pH indicators

The dynamically, or inelastically, scattered electrons provide several types of information about the sample as well. The brightness or intensity at a point on the detector depends on dynamic scattering, so all analysis involving the intensity must account for dynamic scattering. Some inelastically scattered electrons penetrate the bulk crystal and fulfill Bragg diffraction conditions. These inelastically scattered electrons can reach the detector to yield Kikuchi diffraction patterns, which are useful for calculating diffraction conditions. Kikuchi patterns are characterized by lines connecting the intense diffraction points on a RHEED pattern. Figure 6 shows a RHEED pattern with visible Kikuchi lines.

Crystallography

In the 1940s Craig invented the first apparatus to conduct countercurrent partitioning; he called this the countercurrent distribution Craig apparatus. The apparatus consists of a series of glass tubes that are designed and arranged such that the lighter liquid phase is transferred from one tube to the next. The next major milestone was droplet countercurrent chromatography (DCCC). It uses only gravity to move the mobile phase through the stationary phase which is held in long vertical tubes connected in series. The modern era of CCC began with the development of the planetary centrifuge by Ito which was first introduced in 1966 as a closed helical tube which was rotated on a "planetary" axis as is turned on a "sun" axis. Centrifugal partition chromatography was introduced in Japan in 1982; the first instrument was built at Sanki Eng. Ltd. in Kyoto. The first instrument consisted of twelve cartridges arranged around the rotor of a centrifuge; the inner volume of each cartridge was about 15 mL for 50 channels. In 1999 Kromaton developed the first FCPC with radial cells. During cell development, the Z cell was completed in 2005 and the twin cell in 2009. In 2017 RotaChrom designed its top performing CPC cells through computed fluid dynamic simulation software. After thousands of simulations, this tool revealed the drawbacks of conventional CPC cell designs and highlighted the unparallel load capacity and scalable cell design of RotaChrom.

Chromatography + Titration + pH indicators

The instantaneous motion of a rigid body may be the combination of rotation about an axis (the screw axis) and a translation along that axis. This screw move is characterized by the velocity vector for the translation and the angular velocity vector in the same or opposite direction. If these two vectors are constant and along one of the principal axes of the body, no external forces are needed for this motion (moving and spinning]]). As an example, if gravity and drag are ignored, this is the motion of a bullet fired from a rifled gun.

Crystallography