text:
Gas chromatography
From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
Gas chromatography
A gas chromatograph with a headspace sampler
Acronym
GC
Classification
Chromatography
Analytes
Organic
Inorganic
Must be volatile
Other techniques
Related
Thin layer chromatography
High performance liquid chromatography
Hyphenated
Gas chromatography-mass spectrometry
Gas chromatography (GC) is a common type of chromatography used in analytical chemistry for separating and analyzing compounds that can be vaporized without decomposition. Typical uses of GC include testing the purity of a particular substance, or separating the different components of a mixture (the relative amounts of such components can also be determined). In some situations, GC may help in identifying a compound. In preparative chromatography, GC can be used to prepare pure compounds from a mixture.[1][2]
In gas chromatography, the mobile phase (or "moving phase") is a carrier gas, usually an inert gas such as helium or an unreactive gas such as nitrogen. Helium remains the most commonly used carrier gas in about 90% of instruments although hydrogen is preferred for improved separations.[3] The stationary phase is a microscopic layer of liquid or polymer on an inert solid support, inside a piece of glass or metal tubing called a column (a homage to the fractionating column used in distillation). The instrument used to perform gas chromatography is called a gas chromatograph (or "aerograph", "gas separator").
The gaseous compounds being analyzed interact with the walls of the column, which is coated with a stationary phase. This causes each compound to elute at a different time, known as the retention time of the compound. The comparison of retention times is what gives GC its analytical usefulness.
Gas chromatography is in principle similar to column chromatography (as well as other forms of chromatography, such as HPLC, TLC), but has several notable differences. First, the process of separating the compounds in a mixture is carried out between a liquid stationary phase and a gas mobile phase, whereas in column chromatography the stationary phase is a solid and the mobile phase is a liquid. (Hence the full name of the procedure is "Gas–liquid chromatography", referring to the mobile and stationary phases, respectively.) Second, the column through which the gas phase passes is located in an oven where the temperature of the gas can be controlled, whereas column chromatography (typically) has no such temperature control. Finally, the concentration of a compound in the gas phase is solely a function of the vapor pressure of the gas.[1]
Gas chromatography is also similar to fractional distillation, since both processes separate the components of a mixture primarily based on boiling point (or vapor pressure) differences. However, fractional distillation is typically used to separate components of a mixture on a large scale, whereas GC can be used on a much smaller scale (i.e. microscale).[1]
Gas chromatography is also sometimes known as vapor-phase chromatography (VPC), or gas–liquid partition chromatography (GLPC). These alternative names, as well as their respective abbreviations, are frequently used in scientific literature. Strictly speaking, GLPC is the most correct terminology, and is thus preferred by many authors.[1]
Contents
1 History
2 GC analysis
3 Physical components
3.1 Autosamplers
3.2 Inlets
3.3 Detectors
4 Methods
4.1 Carrier gas selection and flow rates
4.2 Stationary compound selection
4.3 Inlet types and flow rates
4.4 Sample size and injection technique
4.4.1 Sample injection
4.5 Column selection
4.6 Column temperature and temperature program
5 Data reduction and analysis
5.1 Qualitative analysis
5.2 Quantitative analysis
6 Applications
7 In popular culture
8 See also
9 References
10 External links
History[edit]
Chromatography dates to 1903 in the work of the Russian scientist, Mikhail Semenovich Tswett. German graduate student Fritz Prior developed solid state gas chromatography in 1947. Archer John Porter Martin, who was awarded the Nobel Prize for his work in developing liquid–liquid (1941) and paper (1944) chromatography, laid the foundation for the development of gas chromatography and he later produced liquid-gas chromatography (1950).
GC analysis[edit]
A gas chromatograph is a chemical analysis instrument for separating chemicals in a complex sample. A gas chromatograph uses a flow-through narrow tube known as the column, through which different chemical constituents of a sample pass in a gas stream (carrier gas, mobile phase) at different rates depending on their various chemical and physical properties and their interaction with a specific column filling, called the stationary phase. As the chemicals exit the end of the column, they are detected and identified electronically. The function of the stationary phase in the column is to separate different components, causing each one to exit the column at a different time (retention time). Other parameters that can be used to alter the order or time of retention are the carrier gas flow rate, column length and the temperature.
In a GC analysis, a known volume of gaseous or liquid analyte is injected into the "entrance" (head) of the column, usually using a microsyringe (or, solid phase microextraction fibers, or a gas source switching system). As the carrier gas sweeps the analyte molecules through the column, this motion is inhibited by the adsorption of the analyte molecules either onto the column walls or onto packing materials in the column. The rate at which the molecules progress along the column depends on the strength of adsorption, which in turn depends on the type of molecule and on the stationary phase materials. Since each type of molecule has a different rate of progression, the various components of the analyte mixture are separated as they progress along the column and reach the end of the column at different times (retention time). A detector is used to monitor the outlet stream from the column; thus, the time at which each component reaches the outlet and the amount of that component can be determined. Generally, substances are identified (qualitatively) by the order in which they emerge (elute) from the column and by the retention time of the analyte in the column.
Physical components[edit]
Diagram of a gas chromatograph.
Autosamplers[edit]
The autosampler provides the means to introduce a sample automatically into the inlets. Manual insertion of the sample is possible but is no longer common. Automatic insertion provides better reproducibility and time-optimization.
Different kinds of autosamplers exist. Autosamplers can be classified in relation to sample capacity (auto-injectors vs. autosamplers, where auto-injectors can work a small number of samples), to robotic technologies (XYZ robot vs. rotating robot – the most common), or to analysis:
Liquid
Static head-space by syringe technology
Dynamic head-space by transfer-line technology
Solid phase microextraction (SPME)
Inlets[edit]
Split/splitless inlet.
The column inlet (or injector) provides the means to introduce a sample into a continuous flow of carrier gas. The inlet is a piece of hardware attached to the column head.
Common inlet types are:
S/SL (split/splitless) injector; a sample is introduced into a heated small chamber via a syringe through a septum – the heat facilitates volatilization of the sample and sample matrix. The carrier gas then either sweeps the entirety (splitless mode) or a portion (split mode) of the sample into the column. In split mode, a part of the sample/carrier gas mixture in the injection chamber is exhausted through the split vent. Split injection is preferred when working with samples with high analyte concentrations (>0.1%) whereas splitless injection is best suited for trace analysis with low amounts of analytes (<0.01%). In splitless mode the split valve opens after a pre-set amount of time to purge heavier elements that would otherwise contaminate the system. This pre-set (splitless) time should be optimized, the shorter time (e.g., 0.2 min) ensures less tailing but loss in response, the longer time (2 min) increases tailing but also signal.
On-column inlet; the sample is here introduced directly into the column in its entirety without heat, or at a temperature below the boiling point of the solvent. The low temperature condenses the sample into a narrow zone. The column and inlet can then be heated, releasing the sample into the gas phase. This ensures the lowest possible temperature for chromatography and keeps samples from decomposing above their boiling point.
PTV injector; Temperature-programmed sample introduction was first described by Vogt in 1979.[citation needed] Originally Vogt developed the technique as a method for the introduction of large sample volumes (up to 250 µL) in capillary GC. Vogt introduced the sample into the liner at a controlled injection rate. The temperature of the liner was chosen slightly below the boiling point of the solvent. The low-boiling solvent was continuously evaporated and vented through the split line. Based on this technique, Poy developed the programmed temperature vaporising injector; PTV. By introducing the sample at a low initial liner temperature many of the disadvantages of the classic hot injection techniques could be circumvented.[citation needed]
Gas source inlet or gas switching valve; gaseous samples in collection bottles are connected to what is most commonly a six-port switching valve. The carrier gas flow is not interrupted while a sample can be expanded into a previously evacuated sample loop. Upon switching, the contents of the sample loop are inserted into the carrier gas stream.
P/T (Purge-and-Trap) system; An inert gas is bubbled through an aqueous sample causing insoluble volatile chemicals to be purged from the matrix. The volatiles are 'trapped' on an absorbent column (known as a trap or concentrator) at ambient temperature. The trap is then heated and the volatiles are directed into the carrier gas stream. Samples requiring preconcentration or purification can be introduced via such a system, usually hooked up to the S/SL port.
The choice of carrier gas (mobile phase) is important. Hydrogen has a range of flow rates that are comparable to helium in efficiency. However, helium may be more efficient and provide the best separation if flow rates are optimized. Helium is non-flammable and works with a greater number of detectors and older instruments. Therefore, helium is the most common carrier gas used. However, the price of helium has gone up considerably over recent years, causing an increasing number of chromatographers to switch to hydrogen gas. Historical use, rather than rational consideration, may contribute to the continued preferential use of helium.
Detectors[edit]
Further information: Chromatography detector
The most commonly used detectors are the flame ionization detector (FID) and the thermal conductivity detector (TCD). Both are sensitive to a wide range of components, and both work over a wide range of concentrations. While TCDs are essentially universal and can be used to detect any component other than the carrier gas (as long as their thermal conductivities are different from that of the carrier gas, at detector temperature), FIDs are sensitive primarily to hydrocarbons, and are more sensitive to them than TCD. However, a FID cannot detect water. Both detectors are also quite robust. Since TCD is non-destructive, it can be operated in-series before a FID (destructive), thus providing complementary detection of the same analytes.[4]
Other detectors are sensitive only to specific types of substances, or work well only in narrower ranges of concentrations. They include:
Thermal Conductivity detector (TCD), this common detector relies on the thermal conductivity of matter passing around a tungsten -rhenium filament with a current traveling through it.[5] In this set up helium or nitrogen serve as the carrier gas because of their relatively high thermal conductivity which keep the filament cool and maintain uniform resistivity and electrical efficiency of the filament.[5][6] However, when analyte molecules elute from the column, mixed with carrier gas, the thermal conductivity decreases and this causes a detector response.[6] The response is due to the decreased thermal conductivity causing an increase in filament temperature and resistivity resulting in fluctuations in voltage.[5] Detector sensitivity is proportional to filament current while it is inversely proportional to the immediate environmental temperature of that detector as well as flow rate of the carrier gas.[5]
Flame Ionization detector (FID), in this common detector electrodes are placed adjacent to a flame fueled by hydrogen / air near the exit of the column, and when carbon containing compounds exit the column they are pyrolyzed by the flame.[5][6] This detector works only for organic / hydrocarbon containing compounds due to the ability of the carbons to form cations and electrons upon pyrolysis which generates a current between the electrodes.[5][6] The increase in current is translated and appears as a peak in a chromatogram. FIDs have low detection limits (a few picograms per second) but they are unable to generate ions from carbonyl containing carbons.[5] FID compatible carrier gasses include helium, hydrogen, nitrogen, and argon.[5][6]
Catalytic combustion detector (CCD), which measures combustible hydrocarbons and hydrogen.
Discharge ionization detector (DID), which uses a high-voltage electric discharge to produce ions.
Dry electrolytic conductivity detector (DELCD), which uses an air phase and high temperature (v. Coulsen) to measure chlorinated compounds.
Electron capture detector (ECD), which uses a radioactive beta particle (electron) source to measure the degree of electron capture. ECD are used for the detection of molecules containing electronegative / withdrawing elements and functional groups like halogens, carbonyl, nitriles, nitro groups, and organometalics.[5][6] In this type of detector either nitrogen or 5% methane in argon is used as the mobile phase carrier gas.[5][6] The carrier gas passes between two electrodes placed at the end of the column, and adjacent to the anode (negative electrode) resides a radioactive foil such as 63Ni.[5][6] The radioactive foil emits a beta particle (electron) which collides with and ionizes the carrier gas to generate more ions resulting in a current.[5][6] When analyte molecules with electronegative / withdrawing elements or functional groups electrons are captured which results in a decrease in current generating a detector response.[5][6]
Flame photometric detector (FPD), which uses a photomultiplier tube to detect spectral lines of the compounds as they are burned in a flame. Compounds eluting off the column are carried into a hydrogen fueled flame which excites specific elements in the molecules, and the excited elements (P,S, Halogens, Some Metals) emit light of specific characteristic wavelengths.[6] The emitted light is filtered and detected by a photomultiplier tube.[5][6] In particular, phosphorus emission is around 510–536 nm and sulfur emission is at 394 nm.[5][6]
Atomic Emission Detector (AED), a sample eluting from a column enters a chamber which is energized by microwaves that induce a plasma.[6] The plasma causes the analyte sample to decompose and certain elements generate an atomic emission spectra.[6] The atomic emission spectra is diffracted by a diffraction grating and detected by a series of photomultiplier tubes or photo diodes.[6]
Hall electrolytic conductivity detector (ElCD)
Helium ionization detector (HID)
Nitrogen–phosphorus detector (NPD), a form of thermionic detector where nitrogen and phosphorus alter the work function on a specially coated bead and a resulting current is measured.
Alkali Flame Detector, AFD or Alkali Flame Ionization Detector, AFID. AFD has high sensitivity to nitrogen and phosphorus, similar to NPD. However, the alkaline metal ions are supplied with the hydrogen gas, rather than a bead above the flame. For this reason AFD does not suffer the "fatigue" of he NPD, but provides a constant sensitivity over long period of time. In addition, when alkali ions are not added to the flame, AFD operates like a standard FID.
Infrared detector (IRD)
Mass spectrometer (MS), also called GC-MS; highly effective and sensitive, even in a small quantity of sample.
Photo-ionization detector (PID)
The Polyarc reactor is an add-on to new or existing GC-FID instruments that converts all organic compounds to methane molecules prior to their detection by the FID. This technique can be used to improve the response of the FID and allow for the detection of many more carbon-containing compounds.[7] The complete conversion of compounds to methane and the now equivalent response in the detector also eliminates the need for calibrations and standards because response factors are all equivalent to those of methane. This allows for the rapid analysis of complex mixtures that contain molecules where standards are not available.
Pulsed discharge ionization detector (PDD)
Thermionic ionization detector (TID)
Vacuum Ultraviolet (VUV) represents the most recent development in Gas Chromatography detectors. Most chemical species absorb and have unique gas phase absorption cross sections in the approximately 120–240 nm VUV wavelength range monitored. Where absorption cross sections are known for analytes, the VUV detector is capable of absolute determination (without calibration) of the number of molecules present in the flow cell in the absence of chemical interferences.[8]
Some gas chromatographs are connected to a mass spectrometer which acts as the detector. The combination is known as GC-MS. Some GC-MS are connected to an NMR spectrometer which acts as a backup detector. This combination is known as GC-MS-NMR. Some GC-MS-NMR are connected to an infrared spectrophotometer which acts as a backup detector. This combination is known as GC-MS-NMR-IR. It must, however, be stressed this is very rare as most analyses needed can be concluded via purely GC-MS.[citation needed]
Methods[edit]
This image above shows the interior of a GeoStrata Technologies Eclipse Gas Chromatograph that runs continuously in three-minute cycles. Two valves are used to switch the test gas into the sample loop. After filling the sample loop with test gas, the valves are switched again applying carrier gas pressure to the sample loop and forcing the sample through the column for separation.
The method is the collection of conditions in which the GC operates for a given analysis. Method development is the process of determining what conditions are adequate and/or ideal for the analysis required.
Conditions which can be varied to accommodate a required analysis include inlet temperature, detector temperature, column temperature and temperature program, carrier gas and carrier gas flow rates, the column's stationary phase, diameter and length, inlet type and flow rates, sample size and injection technique. Depending on the detector(s) (see below) installed on the GC, there may be a number of detector conditions that can also be varied. Some GCs also include valves which can change the route of sample and carrier flow. The timing of the opening and closing of these valves can be important to method development.
Carrier gas selection and flow rates[edit]
Typical carrier gases include helium, nitrogen, argon, hydrogen and air. Which gas to use is usually determined by the detector being used, for example, a DID requires helium as the carrier gas. When analyzing gas samples, however, the carrier is sometimes selected based on the sample's matrix, for example, when analyzing a mixture in argon, an argon carrier is preferred, because the argon in the sample does not show up on the chromatogram. Safety and availability can also influence carrier selection, for example, hydrogen is flammable, and high-purity helium can be difficult to obtain in some areas of the world. (See: Helium—occurrence and production.) As a result of helium becoming more scarce, hydrogen is often being substituted for helium as a carrier gas in several applications.
The purity of the carrier gas is also frequently determined by the detector, though the level of sensitivity needed can also play a significant role. Typically, purities of 99.995% or higher are used. The most common purity grades required by modern instruments for the majority of sensitivities are 5.0 grades, or 99.999% pure meaning that there is a total of 100ppm of impurities in the carrier gas that could affect the results. The highest purity grades in common use are 6.0 grades, but the need for detection at very low levels in some forensic and environmental applications has driven the need for carrier gases at 7.0 grade purity and these are now commercially available. Trade names for typical purities include "Zero Grade," "Ultra-High Purity (UHP) Grade," "4.5 Grade" and "5.0 Grade."
The carrier gas linear velocity affects the analysis in the same way that temperature does (see above). The higher the linear velocity the faster the analysis, but the lower the separation between analytes. Selecting the linear velocity is therefore the same compromise between the level of separation and length of analysis as selecting the column temperature. The linear velocity will be implemented by means of the carrier gas flow rate, with regards to the inner diameter of the column.
With GCs made before the 1990s, carrier flow rate was controlled indirectly by controlling the carrier inlet pressure, or "column head pressure." The actual flow rate was measured at the outlet of the column or the detector with an electronic flow meter, or a bubble flow meter, and could be an involved, time consuming, and frustrating process. It was not possible to vary the pressure setting during the run, and thus the flow was essentially constant during the analysis. The relation between flow rate and inlet pressure is calculated with Poiseuille's equation for compressible fluids.
Many modern GCs, however, electronically measure the flow rate, and electronically control the carrier gas pressure to set the flow rate. Consequently, carrier pressures and flow rates can be adjusted during the run, creating pressure/flow programs similar to temperature programs.
Stationary compound selection[edit]
The polarity of the solute is crucial for the choice of stationary compound, which in an optimal case would have a similar polarity as the solute. Common stationary phases in open tubular columns are cyanopropylphenyl dimethyl polysiloxane, carbowax polyethyleneglycol, biscyanopropyl cyanopropylphenyl polysiloxane and diphenyl dimethyl polysiloxane. For packed columns more options are available.[5]
Inlet types and flow rates[edit]
The choice of inlet type and injection technique depends on if the sample is in liquid, gas, adsorbed, or solid form, and on whether a solvent matrix is present that has to be vaporized. Dissolved samples can be introduced directly onto the column via a COC injector, if the conditions are well known; if a solvent matrix has to be vaporized and partially removed, a S/SL injector is used (most common injection technique); gaseous samples (e.g., air cylinders) are usually injected using a gas switching valve system; adsorbed samples (e.g., on adsorbent tubes) are introduced using either an external (on-line or off-line) desorption apparatus such as a purge-and-trap system, or are desorbed in the injector (SPME applications).
Sample size and injection technique[edit]
Sample injection[edit]
The rule of ten in gas chromatography
The real chromatographic analysis starts with the introduction of the sample onto the column. The development of capillary gas chromatography resulted in many practical problems with the injection technique. The technique of on-column injection, often used with packed columns, is usually not possible with capillary columns. The injection system in the capillary gas chromatograph should fulfil the following two requirements:
The amount injected should not overload the column.
The width of the injected plug should be small compared to the spreading due to the chromatographic process. Failure to comply with this requirement will reduce the separation capability of the column. As a general rule, the volume injected, Vinj, and the volume of the detector cell, Vdet, should be about 1/10 of the volume occupied by the portion of sample containing the molecules of interest (analytes) when they exit the column.
Some general requirements which a good injection technique should fulfill are:
It should be possible to obtain the column’s optimum separation efficiency.
It should allow accurate and reproducible injections of small amounts of representative samples.
It should induce no change in sample composition. It should not exhibit discrimination based on differences in boiling point, polarity, concentration or thermal/catalytic stability.
It should be applicable for trace analysis as well as for undiluted samples.
However, there are a number of problems inherent in the use of syringes for injection:
Even the best syringes claim an accuracy of only 3%, and in unskilled hands, errors are much larger
The needle may cut small pieces of rubber from the septum as it injects sample through it. These can block the needle and prevent the syringe filling the next time it is used. It may not be obvious that this has happened.
A fraction of the sample may get trapped in the rubber, to be released during subsequent injections. This can give rise to ghost peaks in the chromatogram.
There may be selective loss of the more volatile components of the sample by evaporation from the tip of the needle.[9]
Column selection[edit]
The choice of column depends on the sample and the active measured. The main chemical attribute regarded when choosing a column is the polarity of the mixture, but functional groups can play a large part in column selection. The polarity of the sample must closely match the polarity of the column stationary phase to increase resolution and separation while reducing run time. The separation and run time also depends on the film thickness (of the stationary phase), the column diameter and the column length.
Column temperature and temperature program[edit]
A gas chromatography oven, open to show a capillary column
The column(s) in a GC are contained in an oven, the temperature of which is precisely controlled electronically. (When discussing the "temperature of the column," an analyst is technically referring to the temperature of the column oven. The distinction, however, is not important and will not subsequently be made in this article.)
The rate at which a sample passes through the column is directly proportional to the temperature of the column. The higher the column temperature, the faster the sample moves through the column. However, the faster a sample moves through the column, the less it interacts with the stationary phase, and the less the analytes are separated.
In general, the column temperature is selected to compromise between the length of the analysis and the level of separation.
A method which holds the column at the same temperature for the entire analysis is called "isothermal." Most methods, however, increase the column temperature during the analysis, the initial temperature, rate of temperature increase (the temperature "ramp"), and final temperature are called the "temperature program."
A temperature program allows analytes that elute early in the analysis to separate adequately, while shortening the time it takes for late-eluting analytes to pass through the column.
Data reduction and analysis[edit]
Qualitative analysis[edit]
Generally chromatographic data is presented as a graph of detector response (y-axis) against retention time (x-axis), which is called a chromatogram. This provides a spectrum of peaks for a sample representing the analytes present in a sample eluting from the column at different times. Retention time can be used to identify analytes if the method conditions are constant. Also, the pattern of peaks will be constant for a sample under constant conditions and can identify complex mixtures of analytes. However, in most modern applications, the GC is connected to a mass spectrometer or similar detector that is capable of identifying the analytes represented by the peaks.
Quantitative analysis[edit]
The area under a peak is proportional to the amount of analyte present in the chromatogram. By calculating the area of the peak using the mathematical function of integration, the concentration of an analyte in the original sample can be determined. Concentration can be calculated using a calibration curve created by finding the response for a series of concentrations of analyte, or by determining the relative response factor of an analyte. The relative response factor is the expected ratio of an analyte to an internal standard (or external standard) and is calculated by finding the response of a known amount of analyte and a constant amount of internal standard (a chemical added to the sample at a constant concentration, with a distinct retention time to the analyte).
In most modern GC-MS systems, computer software is used to draw and integrate peaks, and match MS spectra to library spectra.
Applications[edit]
In general, substances that vaporize below 300 °C (and therefore are stable up to that temperature) can be measured quantitatively. The samples are also required to be salt-free; they should not contain ions. Very minute amounts of a substance can be measured, but it is often required that the sample must be measured in comparison to a sample containing the pure, suspected substance known as a reference standard.
Various temperature programs can be used to make the readings more meaningful; for example to differentiate between substances that behave similarly during the GC process.
Professionals working with GC analyze the content of a chemical product, for example in assuring the quality of products in the chemical industry; or measuring toxic substances in soil, air or water. GC is very accurate if used properly and can measure picomoles of a substance in a 1 ml liquid sample, or parts-per-billion concentrations in gaseous samples.
In practical courses at colleges, students sometimes get acquainted to the GC by studying the contents of Lavender oil or measuring the ethylene that is secreted by Nicotiana benthamiana plants after artificially injuring their leaves. These GC analyse hydrocarbons (C2-C40+). In a typical experiment, a packed column is used to separate the light gases, which are then detected with a TCD. The hydrocarbons are separated using a capillary column and detected with a FID. A complication with light gas analyses that include H2 is that He, which is the most common and most sensitive inert carrier (sensitivity is proportional to molecular mass) has an almost identical thermal conductivity to hydrogen (it is the difference in thermal conductivity between two separate filaments in a Wheatstone Bridge type arrangement that shows when a component has been eluted). For this reason, dual TCD instruments used with a separate channel for hydrogen that uses nitrogen as a carrier are common. Argon is often used when analysing gas phase chemistry reactions such as F-T synthesis so that a single carrier gas can be used rather than two separate ones. The sensitivity is reduced, but this is a trade off for simplicity in the gas supply.
Gas Chromatography is used extensively in forensic science. Disciplines as diverse as solid drug dose (pre-consumption form) identification and quantification, arson investigation, paint chip analysis, and toxicology cases, employ GC to identify and quantify various biological specimens and crime-scene evidence.
In popular culture[edit]
Movies, books and TV shows tend to misrepresent the capabilities of gas chromatography and the work done with these instruments.
In the U.S. TV show CSI, for example, GCs are used to rapidly identify unknown samples. For example, an analyst may say fifteen minutes after receiving the sample: "This is gasoline bought at a Chevron station in the past two weeks."
In fact, a typical GC analysis takes much more time; sometimes a single sample must be run more than an hour according to the chosen program; and even more time is needed to "heat out" the column so it is free from the first sample and can be used for the next. Equally, several runs are needed to confirm the results of a study – a GC analysis of a single sample may simply yield a result per chance (see statistical significance).
Also, GC does not positively identify most samples; and not all substances in a sample will necessarily be detected. All a GC truly tells you is at which relative time a component eluted from the column and that the detector was sensitive to it. To make results meaningful, analysts need to know which components at which concentrations are to be expected; and even then a small amount of a substance can hide itself behind a substance having both a higher concentration and the same relative elution time. Last but not least the results of the sample must often be checked against a GC analysis of a reference sample containing only the suspected substance.
A GC-MS can remove much of this ambiguity, since the mass spectrometer will identify the component's molecular weight. But this still takes time and skill to do properly.
Similarly, most GC analyses are not push-button operations. You cannot simply drop a sample vial into an auto-sampler's tray, push a button and have a computer tell you everything you need to know about the sample. The operating program must be carefully chosen according to the expected sample composition.
A push-button operation can exist for running similar samples repeatedly, such as in a chemical production environment or for comparing 20 samples from the same experiment to calculate the mean content of the same substance. However, for the kind of investigative work portrayed in books, movies and TV shows, this is clearly not the case.
See also[edit]
Analytical chemistry
Chromatography
Gas chromatography–mass spectrometry
High-performance liquid chromatography
Inverse gas chromatography
Standard addition
Thin layer chromatography
Unresolved complex mixture
References[edit]
^ Jump up to: a b c d Pavia, L., Gary M. Lampman, George S. Kritz, Randall G. Engel (2006). Introduction to Organic Laboratory Techniques (4th Ed.). Thomson Brooks/Cole. pp. 797–817. ISBN 978-0-495-28069-9. CS1 maint: Multiple names: authors list (link)
Jump up ^ "Gas Chromatography". Linde AG. Archived from the original on 3 March 2012. Retrieved 11 March 2012.
Jump up ^ Grob, Konrad (1997). "Carrier Gases for GC". Restek Advantage, Restek Corporation. Retrieved March 9, 2016.
Jump up ^ "Gas Chromatography". ACRF. Retrieved 11 March 2012.
^ Jump up to: a b c d e f g h i j k l m n o p Harris, Daniel C. (1999). "24. Gas Chromatography". Quantitative chemical analysis (Chapter) (Fifth ed.). W. H. Freeman and Company. pp. 675–712. ISBN 0-7167-2881-8.
^ Jump up to: a b c d e f g h i j k l m n o p Higson, S. (2004). Analytical Chemistry. OXFORD University Press ISBN 978-0-19-850289-0
Jump up ^ Dauenhauer, Paul (January 21, 2015). "Quantitative carbon detector (QCD) for calibration-free, high-resolution characterization of complex mixtures". Lab Chip. 15 (2): 440–7. doi:10.1039/c4lc01180e. PMID 25387003.
Jump up ^ Schug, Kevin A.; Sawicki, Ian; Carlton, Doug D.; Fan, Hui; McNair, Harold M.; Nimmo, John P.; Kroll, Peter; Smuts, Jonathan; Walsh, Phillip; Harrison, Dale (1834). "Vacuum Ultraviolet Detector for Gas Chromatography". Analytical Chemistry. 86 (16): 8329. doi:10.1021/ac5018343. PMID 25079505.
Jump up ^ Grob, Robert L.; Barry, Eugene F. (2004). Modern Practice of Gas Chromatography (4th Ed.). John Wiley & Sons. ISBN 0-471-22983-0.
External links[edit]
Media related to Gas chromatography at Wikimedia Commons
Chromatographic Columns on the UC Davis Wiki
Gas Chromatography at Curlie (based on DMOZ)
hide
v
t
e
Chromatography
Techniques
Affinity chromatography
Column chromatography
Displacement chromatography
Electrochromatography
Gas chromatography
High-performance liquid chromatography
Capillary electrochromatography
Ion chromatography
Micellar electrokinetic chromatography
Normal-phase chromatography
Paper chromatography
Reversed-phase chromatography
Size-exclusion chromatography
Thin-layer chromatography
Two-dimensional chromatography
Hyphenated methods
Gas chromatography–mass spectrometry
Liquid chromatography–mass spectrometry
Pyrolysis–gas chromatography–mass spectrometry
Theory
Distribution constant
Freundlich equation
Kovats retention index
Retention factor
Van Deemter equation
Prominent publications
Biomedical Chromatography
Journal of Chromatography A
Journal of Chromatography B
Category
Commons
Analytical Chemistry
Authority control
GND: 4019330-5
NDL: 00562270
Retrieved from "https://en.wikipedia.org/w/index.php?title=Gas_chromatography&oldid=845872652"
Categories:
Gas chromatography
Laboratory techniques
Hidden categories:
CS1 maint: Multiple names: authors list
All articles with unsourced statements
Articles with unsourced statements from December 2012
Articles with unsourced statements from April 2013
Articles with Curlie links
Wikipedia articles with GND identifiers
Wikipedia articles with NDL identifiers
Navigation menu
Personal tools
Not logged in
Talk
Contributions
Create account
Log in
Namespaces
Article
Talk
Variants
Views
Read
Edit
View history
More
Search
Navigation
Main page
Contents
Featured content
Current events
Random article
Donate to Wikipedia
Wikipedia store
Interaction
Help
About Wikipedia
Community portal
Recent changes
Contact page
Tools
What links here
Related changes
Upload file
Special pages
Permanent link
Page information
Wikidata item
Cite this page
Print/export
Create a book
Download as PDF
Printable version
In other projects
Wikimedia Commons
Languages
العربية
Bosanski
Català
Čeština
Deutsch
Eesti
Español
فارسی
Français
Hrvatski
Bahasa Indonesia
Italiano
ಕನ್ನಡ
Magyar
Bahasa Melayu
Nederlands
日本語
Norsk
Polski
Português
Română
Русский
Simple English
Slovenčina
Српски / srpski
Srpskohrvatski / српскохрватски
Suomi
Svenska
Tagalog
தமிழ்
Türkçe
中文
23 more
Edit links
This page was last edited on 14 June 2018, at 18:38 (UTC).
Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization.
Privacy policy
About Wikipedia
Disclaimers
Contact Wikipedia
Developers
Cookie statement
Mobile view
Enable previews

key: html

type: local

value: div

attrs: id class

values: mw-page-base noprint

values: mw-head-base noprint

value: a

attrs: id class lang

values: firstHeading firstHeading en

values: siteSub noprint

attrs: class href

values: mw-jump-link #mw-head

values: mw-jump-link #p-search

value: caption

value: img

attrs: alt src width height srcset data-file-width data-file-height

attrs: href class

value: td

attrs: colspan style

value: tr

value: th

attrs: href title

values:
/wiki/Thin_layer_chromatography
mw-redirect
Thin layer chromatography

values:
/wiki/Preparative_chromatography
mw-redirect
Preparative chromatography

values: checkbox button toctogglecheckbox toctogglecheckbox display:none

values:
/wiki/Mikhail_Semenovich_Tswett
mw-redirect
Mikhail Semenovich Tswett

values:
/wiki/Archer_John_Porter_Martin
mw-redirect
Archer John Porter Martin

values:
/wiki/Stationary_phase_(chemistry)
mw-redirect
Stationary phase (chemistry)

attrs: alt src width height class srcset data-file-width data-file-height

values:
/wiki/Solid_phase_microextraction
mw-redirect
Solid phase microextraction

values: This claim needs references to reliable sources. (December 2012)

values:
noprint Inline-Template Template-Fact
white-space:nowrap;

values:
/wiki/Mass_spectrometer
mw-redirect
Mass spectrometer

values:
/wiki/Photo-ionization_detector
mw-redirect
Photo-ionization detector

values: seems a bit of a stretch to couple GC-MS to NMR and IR (April 2013)

attrs: alt src width height class data-file-width data-file-height

values: Edit section: Carrier gas selection and flow rates

values: Edit section: Stationary compound selection

values: Edit section: Inlet types and flow rates

values: Edit section: Sample size and injection technique

values:
/wiki/Functional_groups
mw-redirect
Functional groups

values: Edit section: Column temperature and temperature program

values: Edit section: Data reduction and analysis

values:
/wiki/Integration_(calculus)
mw-redirect
Integration (calculus)

values:
/wiki/Reference_standard
mw-redirect
Reference standard

values:
/wiki/Parts_per_notation
mw-redirect
Parts per notation

values: Category:CS1 maint: Multiple names: authors list

values:
nofollow
external text
//doi.org/10.1039/c4lc01180e

values:
/wiki/PubMed_Identifier
mw-redirect
PubMed Identifier

values:
nofollow
external text
//www.ncbi.nlm.nih.gov/pubmed/25387003

values:
nofollow
external text
//doi.org/10.1021/ac5018343

values:
nofollow
external text
//www.ncbi.nlm.nih.gov/pubmed/25079505

values: -moz-column-width: 30em; -webkit-column-width: 30em; column-width: 30em; list-style-type: decimal;

attrs: alt src title width height srcset data-file-width data-file-height

values: nowraplinks hlist collapsible autocollapse navbox-inner mw-collapsible mw-made-collapsible

values: navigation navbox Chromatography padding:3px

attrs: alt src width height style srcset data-file-width data-file-height

values:
nofollow
external text
https://d-nb.info/gnd/4019330-5

values: Category:All articles with unsourced statements

values: Category:Articles with unsourced statements from December 2012

values: Category:Articles with unsourced statements from April 2013

values: Category:Wikipedia articles with GND identifiers

values: Category:Wikipedia articles with NDL identifiers

values: Discussion about edits from this IP address [ctrl-alt-n]

values: A list of edits made from this IP address [ctrl-alt-y]

values: You are encouraged to create an account and log in; however, it is not mandatory

values: You're encouraged to log in; however, it's not mandatory. [ctrl-alt-o]

values:
/wiki/Gas_chromatography
View the content page [ctrl-alt-c]
c

values: Discussion about the content page [ctrl-alt-t]

values: p-namespaces navigation vectorTabs p-namespaces-label

values:
p-variants
navigation
vectorMenu emptyPortlet
p-variants-label

values: Past revisions of this page [ctrl-alt-h]

values: p-views navigation vectorTabs p-views-label

values:
p-cactions
navigation
vectorMenu emptyPortlet
p-cactions-label

values:
mw-wiki-logo
/wiki/Main_Page
Visit the main page

values:
/wiki/Main_Page
Visit the main page [ctrl-alt-z]
z

values: Featured content – the best of Wikipedia

values: Find background information on current events

values:
/wiki/Special:Random
Load a random article [ctrl-alt-x]
x

values: portal navigation p-navigation p-navigation-label

values: Guidance on how to use and edit Wikipedia

values: About the project, what you can do, where to find things

values: A list of recent changes in the wiki [ctrl-alt-r]

values: portal navigation p-interaction p-interaction-label

values: List of all English Wikipedia pages containing links to this page [ctrl-alt-j]

values: Recent changes in pages linked from this page [ctrl-alt-k]

values:
/wiki/Wikipedia:File_Upload_Wizard
Upload files [ctrl-alt-u]
u

values: A list of all special pages [ctrl-alt-q]

values: Permanent link to this revision of the page

values: Link to connected data repository item [ctrl-alt-g]

values: Printable version of this page [ctrl-alt-p]

values: portal navigation p-wikibase-otherprojects p-wikibase-otherprojects-label

values: استشراب غازي – Arabic

values:
interlanguage-link interwiki-bs
display: none;

values:
interlanguage-link interwiki-ca
display: none;

values:
interlanguage-link interwiki-cs
display: none;

values:
interlanguage-link interwiki-et
display: none;

values: کروماتوگرافی گازی – Persian

values:
interlanguage-link interwiki-fa
display: none;

values: Chromatographie en phase gazeuse – French

values:
interlanguage-link interwiki-hr
display: none;

values:
interlanguage-link interwiki-it
display: none;

values: ಗ್ಯಾಸ್ ಕ್ರೊಮ್ಯಾಟೋಗ್ರಫಿ (ಅನಿಲ ವರ್ಣರೇಖನ) – Kannada

values:
interlanguage-link interwiki-kn
display: none;

values:
interlanguage-link interwiki-hu
display: none;

values:
interlanguage-link interwiki-nl
display: none;

values: ガスクロマトグラフィー – Japanese

values:
interlanguage-link interwiki-ja
display: none;

values:
interlanguage-link interwiki-no
display: none;

values:
interlanguage-link interwiki-pl
display: none;

values:
interlanguage-link interwiki-ro
display: none;

values: Газовая хроматография – Russian

values:
interlanguage-link interwiki-simple
display: none;

values:
interlanguage-link interwiki-sk
display: none;

values: Гасна хроматографија – Serbian

values:
interlanguage-link interwiki-sr
display: none;

values:
interlanguage-link interwiki-sh
display: none;

values:
interlanguage-link interwiki-fi
display: none;

values:
interlanguage-link interwiki-sv
display: none;

values:
interlanguage-link interwiki-tl
display: none;

values: வளிம வண்ணப்படிவுப் பிரிகை – Tamil

values:
interlanguage-link interwiki-ta
display: none;

values:
interlanguage-link interwiki-tr
display: none;

values: All languages (initial selection from common choices by you and others)

values: mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject page-Gas_chromatography rootpage-Gas_chromatography skin-vector action-view


text:
Dynamo theory
From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
This article is about a proposed theory for the source of the Earth's magnetic field. For an explanation of the operation of a mechanical dynamo, see Dynamo.
Illustration of the dynamo mechanism that creates the Earth's magnetic field: convection currents of fluid metal in the Earth's outer core, driven by heat flow from the inner core, organized into rolls by the Coriolis force, create circulating electric currents, which generate the magnetic field.[1]
In physics, the dynamo theory proposes a mechanism by which a celestial body such as Earth or a star generates a magnetic field. The dynamo theory describes the process through which a rotating, convecting, and electrically conducting fluid can maintain a magnetic field over astronomical time scales. A dynamo is thought to be the source of the Earth's magnetic field, as well as the magnetic fields of other planets.
Contents
1 History of theory
2 Formal definition
2.1 Tidal heating supporting a dynamo
3 Kinematic dynamo theory
3.1 As a spontaneous breakdown of topological supersymmetry
4 Nonlinear dynamo theory
4.1 Energy conversion between magnetic and kinematic energy
4.2 Order of magnitude of the magnetic field created by Earth's dynamo
5 Numerical models
6 See also
7 References
History of theory[edit]
When William Gilbert published de Magnete in 1600, he concluded that the Earth is magnetic and proposed the first hypothesis for the origin of this magnetism: permanent magnetism such as that found in lodestone. In 1919, Joseph Larmor proposed that a dynamo might be generating the field.[2][3] However, even after he advanced his hypothesis, some prominent scientists advanced alternative explanations. Einstein believed that there might be an asymmetry between the charges of the electron and proton so that the Earth's magnetic field would be produced by the entire Earth. The Nobel Prize winner Patrick Blackett did a series of experiments looking for a fundamental relation between angular momentum and magnetic moment, but found none.[4][5]
Walter M. Elsasser, considered a "father" of the presently accepted dynamo theory as an explanation of the Earth's magnetism, proposed that this magnetic field resulted from electric currents induced in the fluid outer core of the Earth. He revealed the history of the Earth's magnetic field through pioneering the study of the magnetic orientation of minerals in rocks.
In order to maintain the magnetic field against ohmic decay (which would occur for the dipole field in 20,000 years), the outer core must be convecting. The convection is likely some combination of thermal and compositional convection. The mantle controls the rate at which heat is extracted from the core. Heat sources include gravitational energy released by the compression of the core, gravitational energy released by the rejection of light elements (probably sulfur, oxygen, or silicon) at the inner core boundary as it grows, latent heat of crystallization at the inner core boundary, and radioactivity of potassium, uranium and thorium.[6]
At the dawn of the 21st century, numerical modeling of the Earth's magnetic field has not been successfully demonstrated, but appears to be in reach. Initial models are focused on field generation by convection in the planet's fluid outer core. It was possible to show the generation of a strong, Earth-like field when the model assumed a uniform core-surface temperature and exceptionally high viscosities for the core fluid. Computations which incorporated more realistic parameter values yielded magnetic fields that were less Earth-like, but also point the way to model refinements which may ultimately lead to an accurate analytic model. Slight variations in the core-surface temperature, in the range of a few millikelvins, result in significant increases in convective flow and produce more realistic magnetic fields.[7][8]
Formal definition[edit]
Dynamo theory describes the process through which a rotating, convecting, and electrically conducting fluid acts to maintain a magnetic field. This theory is used to explain the presence of anomalously long-lived magnetic fields in astrophysical bodies. The conductive fluid in the geodynamo is liquid iron in the outer core, and in the solar dynamo is ionized gas at the tachocline. Dynamo theory of astrophysical bodies uses magnetohydrodynamic equations to investigate how the fluid can continuously regenerate the magnetic field.[9]
It was once believed that the dipole, which comprises much of the Earth's magnetic field and is misaligned along the rotation axis by 11.3 degrees, was caused by permanent magnetization of the materials in the earth. This means that dynamo theory was originally used to explain the Sun's magnetic field in its relationship with that of the Earth. However, this hypothesis, which was initially proposed by Joseph Larmor in 1919, has been modified due to extensive studies of magnetic secular variation, paleomagnetism (including polarity reversals), seismology, and the solar system's abundance of elements. Also, the application of the theories of Carl Friedrich Gauss to magnetic observations showed that Earth's magnetic field had an internal, rather than external, origin.
There are three requisites for a dynamo to operate:
An electrically conductive fluid medium
Kinetic energy provided by planetary rotation
An internal energy source to drive convective motions within the fluid.[10]
In the case of the Earth, the magnetic field is induced and constantly maintained by the convection of liquid iron in the outer core. A requirement for the induction of field is a rotating fluid. Rotation in the outer core is supplied by the Coriolis effect caused by the rotation of the Earth. The Coriolis force tends to organize fluid motions and electric currents into columns (also see Taylor columns) aligned with the rotation axis. Induction or creation of magnetic field is described by the induction equation:
∂ B ∂ t = η ∇ 2 B + ∇ × ( u × B ) {\displaystyle {\frac {\partial \mathbf {B} }{\partial t}}=\eta \nabla ^{2}\mathbf {B} +\nabla \times (\mathbf {u} \times \mathbf {B} )}
where u is velocity, B is magnetic field, t is time, and η = 1 / ( σ μ ) {\displaystyle \eta =1/(\sigma \mu )} is the magnetic diffusivity with σ {\displaystyle \sigma } electrical conductivity and μ {\displaystyle \mu } permeability. The ratio of the second term on the right hand side to the first term gives the Magnetic Reynolds number, a dimensionless ratio of advection of magnetic field to diffusion.
Tidal heating supporting a dynamo[edit]
Tidal forces between celestial orbiting bodies cause friction that heats up their interiors. This is known as tidal heating, and it helps keep the interior liquid. A liquid interior that can conduct electricity is required to produce a dynamo. Saturn's Enceladus and Jupiter's Io have enough tidal heating to liquify their inner cores, but they may not create a dynamo because they cannot conduct electricity.[11][12] Mercury, despite its small size, has a magnetic field, because it has a conductive liquid core created by its iron composition and friction resulting from its highly elliptical orbit.[13] It is theorized that the Moon once had a magnetic field, based on evidence from magnetized lunar rocks, due to its short-lived closer distance to Earth creating tidal heating.[14] An orbit and rotation of a planet helps provide a liquid core, and supplements kinetic energy that supports a dynamo action.
Kinematic dynamo theory[edit]
In kinematic dynamo theory the velocity field is prescribed, instead of being a dynamic variable. This method cannot provide the time variable behavior of a fully nonlinear chaotic dynamo but is useful in studying how magnetic field strength varies with the flow structure and speed.
Using Maxwell's equations simultaneously with the curl of Ohm's law, one can derive what is basically the linear eigenvalue equation for magnetic fields (B) which can be done when assuming that the magnetic field is independent from the velocity field. One arrives at a critical magnetic Reynolds number above which the flow strength is sufficient to amplify the imposed magnetic field, and below which it decays.
The most functional feature of kinematic dynamo theory is that it can be used to test whether a velocity field is or is not capable of dynamo action. By applying a certain velocity field to a small magnetic field, it can be determined through observation whether the magnetic field tends to grow or not in reaction to the applied flow. If the magnetic field does grow, then the system is either capable of dynamo action or is a dynamo, but if the magnetic field does not grow, then it is simply referred to as non-dynamo.
The membrane paradigm is a way of looking at black holes that allows for the material near their surfaces to be expressed in the language of dynamo theory.
As a spontaneous breakdown of topological supersymmetry[edit]
Kinematic dynamo can be also viewed as the phenomenon of the spontaneous breakdown of the topological supersymmetry of the associated stochastic differential equation related to the flow of the background matter.[15] Within supersymmetric theory of stochastics, this supersymmetry is an intrinsic property of all stochastic differential equations, its meaning is the preservation of the continuity of the phase space of the model by continuous time flows, and its spontaneous breakdown is the stochastic generalization of the concept of deterministic chaos.[16] In other words, kinematic dynamo is a manifestation of the chaoticity of the underlying flow of the background matter.
Nonlinear dynamo theory[edit]
The kinematic approximation becomes invalid when the magnetic field becomes strong enough to affect the fluid motions. In that case the velocity field becomes affected by the Lorentz force, and so the induction equation is no longer linear in the magnetic field. In most cases this leads to a quenching of the amplitude of the dynamo. Such dynamos are sometimes also referred to as hydromagnetic dynamos.[17] Virtually all dynamos in astrophysics and geophysics are hydromagnetic dynamos.
The main idea of the theory is that any small magnetic field existing in the outer core, creates currents in the moving fluid there due to Lorenz force. These currents create further magnetic field due to Ampere's law. With the fluid motion, the currents are carried in a way that the magnetic field gets stronger (as long as u ⋅ ( J × B ) {\displaystyle \mathbf {u} \cdot (\mathbf {J} \times \mathbf {B} )} is negative[18]). Thus a "seed" magnetic field can get stronger and stronger until it reaches some value that is related to existing non-magnetic forces.
Numerical models are used to simulate fully nonlinear dynamos. The following equations are used:
The induction equation, presented above.
Maxwell's equations for negligible electric field:
∇ ⋅ B = 0 {\displaystyle \nabla \cdot \mathbf {B} =0}
∇ × B = μ 0 J {\displaystyle \nabla \times \mathbf {B} =\mu _{0}\mathbf {J} }
The continuity equation for conservation of mass, for which the Boussinesq approximation is often used:
∇ ⋅ u = 0 , {\displaystyle \nabla \cdot \mathbf {u} =0,}
The Navier-Stokes equation for conservation of momentum, again in the same approximation, with the magnetic force and gravitation force as the external forces:
D u D t = − 1 ρ 0 ∇ p + ν ∇ 2 u + ρ ′ g + 2 Ω × u + Ω × Ω × R + 1 ρ 0 J × B , {\displaystyle {\frac {D\mathbf {u} }{Dt}}=-{\frac {1}{\rho _{0}}}\nabla p+\nu \nabla ^{2}\mathbf {u} +\rho '\mathbf {g} +2\mathbf {\Omega } \times \mathbf {u} +\mathbf {\Omega } \times \mathbf {\Omega } \times \mathbf {R} +{\frac {1}{\rho _{0}}}\mathbf {J} \times \mathbf {B} ,}
where ν {\displaystyle \nu } is the kinematic viscosity, ρ 0 {\displaystyle \rho _{0}} is the mean density and ρ ′ {\displaystyle \rho '} is the relative density perturbation that provides buoyancy (for thermal convection ρ ′ = α Δ T {\displaystyle \rho '=\alpha \Delta T} where α {\displaystyle \alpha } is coefficient of thermal expansion), Ω {\displaystyle \Omega } is the rotation rate of the Earth, and J {\displaystyle \mathbf {J} } is the electric current density.
A transport equation, usually of heat (sometimes of light element concentration):
∂ T ∂ t = κ ∇ 2 T + ϵ {\displaystyle {\frac {\partial T}{\partial t}}=\kappa \nabla ^{2}T+\epsilon }
where T is temperature, κ = k / ρ c p {\displaystyle \kappa =k/\rho c_{p}} is the thermal diffusivity with k thermal conductivity, c p {\displaystyle c_{p}} heat capacity, and ρ {\displaystyle \rho } density, and ϵ {\displaystyle \epsilon } is an optional heat source. Often the pressure is the dynamic pressure, with the hydrostatic pressure and centripetal potential removed.
These equations are then non-dimensionalized, introducing the non-dimensional parameters,
R a = g α T D 3 ν κ , E = ν Ω D 2 , P r = ν κ , P m = ν η {\displaystyle Ra={\frac {g\alpha TD^{3}}{\nu \kappa }},E={\frac {\nu }{\Omega D^{2}}},Pr={\frac {\nu }{\kappa }},Pm={\frac {\nu }{\eta }}}
where Ra is the Rayleigh number, E the Ekman number, Pr and Pm the Prandtl and magnetic Prandtl number. Magnetic field scaling is often in Elsasser number units B = ( ρ Ω / σ ) 1 / 2 {\displaystyle B=(\rho \Omega /\sigma )^{1/2}} .
Energy conversion between magnetic and kinematic energy[edit]
The scalar product of the above form of Navier-Stokes equation with ρ 0 u {\displaystyle \rho _{0}\mathbf {u} } gives the rate of increase of kinetic energy density, ( 1 / 2 ) ρ 0 u 2 {\displaystyle (1/2)\rho _{0}u^{2}} , on the left-hand side. The last term on the right-hand side is then u ⋅ ( J × B ) {\displaystyle \mathbf {u} \cdot (\mathbf {J} \times \mathbf {B} )} , the local contribution to the kinetic energy due to Lorentz force.
The scalar product of the induction equation with ( 1 / μ 0 ) B {\displaystyle (1/\mu _{0})\mathbf {B} } gives the rate of increase of the magnetic energy density, ( 1 / 2 μ 0 ) B 2 {\displaystyle (1/2\mu _{0})B^{2}} , on the left-hand side. The last term on the right-hand side is then ( 1 / μ 0 ) B ⋅ ( ∇ × ( u × B ) ) {\displaystyle (1/\mu _{0})\mathbf {B} \cdot \left(\nabla \times (\mathbf {u} \times \mathbf {B} )\right)} . Since the equation is volume-integrated, this term is equivalent up to a boundary term (and with the double use of the scalar triple product identity) to − u ⋅ ( ( 1 / μ 0 ) ( ∇ × B ) × B ) ) = − u ⋅ ( J × B ) {\displaystyle -\mathbf {u} \cdot \left((1/\mu _{0})(\nabla \times \mathbf {B} )\times \mathbf {B} )\right)=-\mathbf {u} \cdot (\mathbf {J} \times \mathbf {B} )} (where one of Maxwell's equations was used). This is the local contribution to the magnetic energy due to fluid motion.
Thus the term − u ⋅ ( J × B ) {\displaystyle -\mathbf {u} \cdot (\mathbf {J} \times \mathbf {B} )} is the rate of transformation of kinetic energy to magnetic energy. This has to be non-negative at least in part of the volume, for the dynamo to produce magnetic field.[18]
Order of magnitude of the magnetic field created by Earth's dynamo[edit]
The above formula for the rate of conversion of kinetic energy to magnetic energy, is equivalent to a rate of work done by a force of J × B {\displaystyle \mathbf {J} \times \mathbf {B} } on the outer core matter, whose velocity is u {\displaystyle \mathbf {u} } . This work is the result of non-magnetic forces acting on the fluid.
Of those, the gravitational force and the centrifugal force are conservative and therefore have no overall contribution to fluid moving in closed loops. Ekman number (defined above), which is the ratio between the two remaining forces, namely the viscosity and Coriolis force, is very low inside Earth's outer core, because its viscosity is low (1.2-1.5 x10−2 pascal-second [19]) due to its liquidity.
Thus the main time-averaged contribution to the work is from Coriolis force, whose size is − 2 ρ Ω × u {\displaystyle -2\rho \,\mathbf {\Omega } \times \mathbf {u} } , though this quantity and J × B {\displaystyle \mathbf {J} \times \mathbf {B} } are related only indirectly and are not in general equal locally (thus they affect each other but not in the same place and time).
The current density J is itself the result of the magnetic field according to Ohm's law. Again, due to matter motion and current flow, this is not necessarily the field at the same place and time. However these relations can still be used to deduce orders of magnitude of the quantities in question.
In terms of order of magnitude, J B ∼ ρ Ω u {\displaystyle J\,B\sim \rho \,\Omega \,u} and J ∼ σ u B {\displaystyle J\sim \sigma uB} , giving σ u B 2 ∼ ρ Ω u {\displaystyle \sigma \,u\,B^{2}\sim \rho \,\Omega \,u} , or:
B ∼ ρ Ω σ {\displaystyle B\sim {\sqrt {\frac {\rho \,\Omega }{\sigma }}}}
The exact ratio between both sides is the square root of Elsasser number.
Note that the magnetic field direction cannot be inferred from this approximation (at least not its sign) as it appears squared, and is, indeed, sometimes reversed, though in general it lies on a similar axis to that of Ω {\displaystyle \mathbf {\Omega } } .
For earth outer core, ρ is approximately 104 kg/m3,[19] Ω=2π/day = 7.3x10−5 seconds and σ is approximately 107Ω−1m−1.[20] This gives 2.7x10−4 Tesla.
The magnetic field of a magnetic dipole has an inverse cubic dependence in distance, so its order of magnitude at the earth surface can be approximated by multiplying the above result with (Router core/REarth)3 = (2890/6370)3 = 0.093, giving 2.5x10−5 Tesla, not far from to the measured value of 3x10−5 Tesla at the equator.
Numerical models[edit]
The equations for the geodynamo are enormously difficult to solve, and the realism of the solutions is limited mainly by computer power. For decades, theorists were confined to kinematic dynamo models described above, in which the fluid motion is chosen in advance and the effect on the magnetic field calculated. Kinematic dynamo theory was mainly a matter of trying different flow geometries and seeing whether they could sustain a dynamo.[18]
The first self-consistent dynamo models, ones that determine both the fluid motions and the magnetic field, were developed by two groups in 1995, one in Japan[21] and one in the United States.[22][23] The latter received significant attention because it successfully reproduced some of the characteristics of the Earth's field, including geomagnetic reversals.[18]
See also[edit]
Book: Geomagnetism
Antidynamo theorem
Rotating magnetic field
Secular variation
References[edit]
Jump up ^ "How does the Earth's core generate a magnetic field?". USGS FAQs. United States Geological Survey. Archived from the original on 18 January 2015. Retrieved 21 October 2013.
Jump up ^ Larmor, J. (1919). "How could a rotating body such as the Sun become a magnet?". Reports of the British Association. 87: 159–160.
Jump up ^ Larmor, J. (1919). "Possible rotational origin of magnetic fields of sun and earth". Electrical Review. 85: 412ff. Reprinted in Engineering, vol. 108, pages 461ff (3 October 1919).
Jump up ^ Nye, Mary Jo (1 March 1999). "Temptations of theory, strategies of evidence: P. M. S. Blackett and the earth's magnetism, 1947–52". The British Journal for the History of Science. 32 (1): 69–92. doi:10.1017/S0007087498003495.
Jump up ^ Merrill, McElhinny & McFadden 1996, page 17 claim that in 1905, shortly after composing his special relativity paper, Albert Einstein described the origin of the Earth's magnetic field as being one of the great unsolved problems facing modern physicists. However, they do not provide details on where he made this statement.
Jump up ^ Sanders, Robert (2003-12-10). "Radioactive potassium may be major heat source in Earth's core". UC Berkeley News. Retrieved 2007-02-28.
Jump up ^ Sakuraba, Ataru; Paul H. Roberts (4 October 2009). "Generation of a strong magnetic field using uniform heat flux at the surface of the core". Nature Geoscience. Nature Publishing Group. 2 (11): 802–805. Bibcode:2009NatGe...2..802S. doi:10.1038/ngeo643.
Jump up ^ Buffett, Bruce (2009). "Geodynamo: A matter of boundaries". Nature Geoscience. Nature Publishing Group. 2 (2): 741–742. Bibcode:2009NatGe...2..741B. doi:10.1038/ngeo673.
Jump up ^ Brandenburg, Axel (2007). "Hydromagnetic dynamo theory". Scholarpedia. Retrieved October 7, 2016.
Jump up ^ E. Pallé (2010). The Earth as a Distant Planet: A Rosetta Stone for the Search of Earth-Like Worlds (Astronomy and Astrophysics Library). Berlin: Springer. pp. 316–317. ISBN 1-4419-1683-0. Retrieved 17 July 2010.
Jump up ^ Steigerwald, Bill (October 6, 2010). "Saturn's Icy Moon May Keep Oceans Liquid with Wobble". NASA. Retrieved August 14, 2012.
Jump up ^ Cassis, Nikki (March 19, 2012). "Geologic map of Jupiter's moon Io details an otherworldly volcanic surface". Astrogeology Science Center. Retrieved August 14, 2012. [permanent dead link]
Jump up ^ "Mercury's Surprising Core and Landscape Curiosities". MESSENGER. Carnegie Institution for Science. March 21, 2012. Retrieved August 14, 2012.
Jump up ^ Stevens, Tim (November 9, 2011). "Ancient lunar dynamo may explain magnetized moon rocks". University of California. Retrieved August 14, 2012.
Jump up ^ Ovchinnikov, I.V.; Ensslin, T. A. (April 2016). "Kinematic dynamo, supersymmetry breaking, and chaos". Physical Review D. 93 (8): 085023. arXiv:1512.01651  . Bibcode:2016PhRvD..93h5023O. doi:10.1103/PhysRevD.93.085023.
Jump up ^ Ovchinnikov, I.V. (March 2016). "Introduction to Supersymmetric Theory of Stochastics". Entropy. 18 (4): 108. arXiv:1511.03393  . Bibcode:2016Entrp..18..108O. doi:10.3390/e18040108.
Jump up ^ Parker, Eugene N. (September 1955). "Hydromagnetic Dynamo Models". The Astrophysical Journal. 122: 293–314. Bibcode:1955ApJ...122..293P. doi:10.1086/146087.
^ Jump up to: a b c d Kono, Masaru; Roberts, Paul H. (2002). "Recent geodynamo simulations and observations of the geomagnetic field". Reviews of Geophysics. 40 (4): 1–53. Bibcode:2002RvGeo..40.1013K. doi:10.1029/2000RG000102.
^ Jump up to: a b de Wijs, G. A., Kresse, G., Vočadlo, L., Dobson, D., Alfe, D., Gillan, M. J., & Price, G. D. (1998). The viscosity of liquid iron at the physical conditions of the Earth's core. Nature, 392(6678), 805.
Jump up ^ Ohta, K., Kuwayama, Y., Hirose, K., Shimizu, K., & Ohishi, Y. (2016). Experimental determination of the electrical resistivity of iron at Earth’s core conditions. Nature, 534(7605), 95. Link to a summary
Jump up ^ Kageyama, Akira; Sato, Tetsuya (1 January 1995). "Computer simulation of a magnetohydrodynamic dynamo. II". Physics of Plasmas. 2 (5): 1421–1431. Bibcode:1995PhPl....2.1421K. doi:10.1063/1.871485.
Jump up ^ Glatzmaier, Gary A.; Roberts, Paul H. (1995). "A three-dimensional self-consistent computer simulation of a geomagnetic field reversal". Nature. 377 (6546): 203–209. Bibcode:1995Natur.377..203G. doi:10.1038/377203a0.
Jump up ^ Glatzmaier, G; Roberts, Paul H. (1995). "A three-dimensional convective dynamo solution with rotating and finitely conducting inner core and mantle". Physics of the Earth and Planetary Interiors. 91 (1–3): 63–75. Bibcode:1995PEPI...91...63G. doi:10.1016/0031-9201(95)03049-3.
Demorest, Paul (21 May 2001). "Dynamo Theory and Earth's magnetic Field (term paper)" (PDF). Archived from the original (PDF) on 21 February 2007. Retrieved 14 October 2011.
Fitzpatrick, Richard (18 May 2002). "MHD Dynamo Theory". Plasma Physics. University of Texas at Austin. Retrieved 14 October 2011.
Merrill, Ronald T.; McElhinny, Michael W.; McFadden, Phillip L. (1996). The magnetic field of the earth: Paleomagnetism, the core, and the deep mantle. Academic Press. ISBN 978-0-12-491246-5.
Stern, David P. "Chapter 12: The dynamo process". The Great Magnet, the Earth. Retrieved 14 October 2011.
Stern, David P. "Chapter 13: Dynamo in the Earth's Core". The Great Magnet, the Earth. Retrieved 14 October 2011.
hide
v
t
e
Geophysics
Overview
Outline
Geophysicists
Subfields
Geophysical fluid dynamics
Geodesy
Geodynamics
Geomagnetism
Mathematical geophysics
Mineral physics
Near-surface geophysics
Paleomagnetism
Seismology
Tectonophysics
Physical
phenomena
Chandler wobble
Coriolis effect
Earth's magnetic field
Geodynamo
Geothermal gradient
Gravity of Earth
Mantle convection
Precession of the equinoxes
Seismic wave
Tides
Organizations
American Geophysical Union
American Meteorological Society
Canadian Geophysical Union
Environmental and Engineering Geophysical Society
European Association of Geoscientists and Engineers
European Geosciences Union
International Association of Geomagnetism and Aeronomy
International Union of Geodesy and Geophysics
Royal Astronomical Society
Society of Exploration Geophysicists
Seismological Society of America
Category
Earth science
Commons
Retrieved from "https://en.wikipedia.org/w/index.php?title=Dynamo_theory&oldid=848904584"
Categories:
Geomagnetism
Plasma physics
Magnetohydrodynamics
Structure of the Earth
Computational physics
Unsolved problems in physics
Hidden categories:
All articles with dead external links
Articles with dead external links from September 2017
Articles with permanently dead external links
Navigation menu
Personal tools
Not logged in
Talk
Contributions
Create account
Log in
Namespaces
Article
Talk
Variants
Views
Read
Edit
View history
More
Search
Navigation
Main page
Contents
Featured content
Current events
Random article
Donate to Wikipedia
Wikipedia store
Interaction
Help
About Wikipedia
Community portal
Recent changes
Contact page
Tools
What links here
Related changes
Upload file
Special pages
Permanent link
Page information
Wikidata item
Cite this page
Print/export
Create a book
Download as PDF
Printable version
In other projects
Wikimedia Commons
Languages
العربية
Català
Deutsch
Español
Français
한국어
Bahasa Indonesia
עברית
Nederlands
日本語
Norsk
Polski
Português
Русский
Suomi
ไทย
Türkçe
Українська
Tiếng Việt
中文
11 more
Edit links
This page was last edited on 5 July 2018, at 04:26 (UTC).
Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization.
Privacy policy
About Wikipedia
Disclaimers
Contact Wikipedia
Developers
Cookie statement
Mobile view
Enable previews

values: mw-page-base noprint

values: mw-head-base noprint

values: firstHeading firstHeading en

values: siteSub noprint

values: mw-jump-link #mw-head

values: mw-jump-link #p-search

attrs: role class

values:
note
hatnote navigation-not-searchable

attrs: href class title

value: sup

attrs: class style

value: b

values: checkbox button toctogglecheckbox toctogglecheckbox display:none

values:
/wiki/Coriolis_effect
mw-redirect
Coriolis effect

values: vertical-align: -2.005ex; width:28.867ex; height:5.509ex;

values: \frac{\partial \mathbf{B}}{\partial t} = \eta \nabla^2 \mathbf{B} + \nabla \times (\mathbf{u} \times \mathbf{B})

values: vertical-align: -0.838ex; width:11.133ex; height:2.843ex;

values: vertical-align: -0.338ex; width:1.33ex; height:1.676ex;

values: vertical-align: -0.838ex; width:1.402ex; height:2.176ex;

values: Edit section: Tidal heating supporting a dynamo

values: Edit section: As a spontaneous breakdown of topological supersymmetry

values: Supersymmetric theory of stochastic dynamics

values:
/wiki/Ampere%27s_law
mw-redirect
Ampere's law

values: vertical-align: -0.838ex; width:11.096ex; height:2.843ex;

values: {\displaystyle \nabla \cdot \mathbf {B} =0}

values: vertical-align: -0.338ex; width:9.777ex; height:2.176ex;

values: vertical-align: -0.838ex; width:13.612ex; height:2.676ex;

values: {\displaystyle \nabla \cdot \mathbf {u} =0,}

values: vertical-align: -0.671ex; width:10.008ex; height:2.509ex;

values: vertical-align: -2.338ex; width:67.31ex; height:5.676ex;

values: vertical-align: -0.338ex; width:1.232ex; height:1.676ex;

values: vertical-align: -0.838ex; width:2.256ex; height:2.176ex;

values: vertical-align: -0.838ex; width:1.887ex; height:3.009ex;

values: vertical-align: -0.838ex; width:10.045ex; height:3.009ex;

values: vertical-align: -0.338ex; width:1.488ex; height:1.676ex;

values:
/wiki/Coefficient_of_thermal_expansion
mw-redirect
Coefficient of thermal expansion

values: vertical-align: -0.338ex; width:1.678ex; height:2.176ex;

values: vertical-align: -0.338ex; width:1.381ex; height:2.176ex;

values: vertical-align: -2.005ex; width:16.639ex; height:5.509ex;

values: \frac{\partial T}{\partial t} = \kappa \nabla^2 T +\epsilon

values: vertical-align: -1.005ex; width:10.079ex; height:3.009ex;

values: vertical-align: -1.005ex; width:2.066ex; height:2.343ex;

values: vertical-align: -0.838ex; width:1.202ex; height:2.176ex;

values: vertical-align: -0.338ex; width:0.944ex; height:1.676ex;

values: vertical-align: -2.338ex; width:44.636ex; height:6.176ex;

values: Ra=\frac{g\alpha T D^3}{\nu \kappa} , E=\frac{\nu}{\Omega D^2} , Pr=\frac{\nu}{\kappa} , Pm=\frac{\nu}{\eta}

values: {\displaystyle B=(\rho \Omega /\sigma )^{1/2}}

values: vertical-align: -0.838ex; width:14.742ex; height:3.343ex;

values: Edit section: Energy conversion between magnetic and kinematic energy

values: vertical-align: -0.838ex; width:3.741ex; height:2.176ex;

values: vertical-align: -0.838ex; width:9.937ex; height:3.176ex;

values: {\displaystyle (1/\mu _{0})\mathbf {B} }

values: vertical-align: -0.838ex; width:8.491ex; height:2.843ex;

values: vertical-align: -0.838ex; width:10.571ex; height:3.176ex;

values: vertical-align: -0.838ex; width:24.792ex; height:2.843ex;

values: vertical-align: -0.838ex; width:43.507ex; height:2.843ex;

values: vertical-align: -0.838ex; width:12.904ex; height:2.843ex;

values: Edit section: Order of magnitude of the magnetic field created by Earth's dynamo

values: {\displaystyle \mathbf {J} \times \mathbf {B} }

values: vertical-align: -0.338ex; width:6.122ex; height:2.176ex;

values: vertical-align: -0.338ex; width:1.485ex; height:1.676ex;

values: vertical-align: -0.838ex; width:10.817ex; height:2.676ex;

values: {\displaystyle J\,B\sim \rho \,\Omega \,u}

values: vertical-align: -0.838ex; width:11.705ex; height:2.676ex;

values: vertical-align: -0.338ex; width:8.993ex; height:2.176ex;

values: {\displaystyle \sigma \,u\,B^{2}\sim \rho \,\Omega \,u}

values: vertical-align: -0.838ex; width:14.334ex; height:3.176ex;

values: vertical-align: -2.171ex; width:11.289ex; height:6.176ex;

values: vertical-align: -0.338ex; width:1.931ex; height:2.176ex;

values:
nofollow
external text
//doi.org/10.1038/ngeo643

values:
nofollow
external text
//doi.org/10.1038/ngeo673

values:
nofollow
external text
https://clas.asu.edu/node/12161

values:
nofollow
external text
//arxiv.org/abs/1512.01651

values:
nofollow
external text
//doi.org/10.1103/PhysRevD.93.085023

values:
nofollow
external text
//arxiv.org/abs/1511.03393

values:
nofollow
external text
//doi.org/10.3390/e18040108

values:
nofollow
external text
//doi.org/10.1086/146087

values:
nofollow
external text
//doi.org/10.1029/2000RG000102

values:
nofollow
external text
//doi.org/10.1063/1.871485

values:
nofollow
external text
//doi.org/10.1038/377203a0

values: -moz-column-width: 30em; -webkit-column-width: 30em; column-width: 30em; list-style-type: decimal;

values:
/wiki/Precession_of_the_equinoxes
mw-redirect
Precession of the equinoxes

values: Environmental and Engineering Geophysical Society

values: European Association of Geoscientists and Engineers

values: International Association of Geomagnetism and Aeronomy

values: International Union of Geodesy and Geophysics

values:
/wiki/Portal:Earth_science
mw-redirect
Portal:Earth science

values: nowraplinks hlist collapsible autocollapse navbox-inner mw-collapsible mw-made-collapsible

values: navigation navbox Geophysics padding:3px

values: Category:All articles with dead external links

values: Category:Articles with dead external links from September 2017

values: Category:Articles with permanently dead external links

values: Discussion about edits from this IP address [ctrl-alt-n]

values: A list of edits made from this IP address [ctrl-alt-y]

values: You are encouraged to create an account and log in; however, it is not mandatory

values: You're encouraged to log in; however, it's not mandatory. [ctrl-alt-o]

values:
/wiki/Dynamo_theory
View the content page [ctrl-alt-c]
c

values: Discussion about the content page [ctrl-alt-t]

values: p-namespaces navigation vectorTabs p-namespaces-label

values:
p-variants
navigation
vectorMenu emptyPortlet
p-variants-label

values: Past revisions of this page [ctrl-alt-h]

values: p-views navigation vectorTabs p-views-label

values:
p-cactions
navigation
vectorMenu emptyPortlet
p-cactions-label

values:
mw-wiki-logo
/wiki/Main_Page
Visit the main page

values:
/wiki/Main_Page
Visit the main page [ctrl-alt-z]
z

values: Featured content – the best of Wikipedia

values: Find background information on current events

values:
/wiki/Special:Random
Load a random article [ctrl-alt-x]
x

values: portal navigation p-navigation p-navigation-label

values: Guidance on how to use and edit Wikipedia

values: About the project, what you can do, where to find things

values: A list of recent changes in the wiki [ctrl-alt-r]

values: portal navigation p-interaction p-interaction-label

values: List of all English Wikipedia pages containing links to this page [ctrl-alt-j]

values: Recent changes in pages linked from this page [ctrl-alt-k]

values:
/wiki/Wikipedia:File_Upload_Wizard
Upload files [ctrl-alt-u]
u

values: A list of all special pages [ctrl-alt-q]

values: Permanent link to this revision of the page

values: Link to connected data repository item [ctrl-alt-g]

values: Printable version of this page [ctrl-alt-p]

values: portal navigation p-wikibase-otherprojects p-wikibase-otherprojects-label

values: نظرية الدينامو – Arabic

values:
interlanguage-link interwiki-ca
display: none;

values: 다이너모 이론 – Korean

values:
interlanguage-link interwiki-ko
display: none;

values: תאוריית הדינמו – Hebrew

values:
interlanguage-link interwiki-he
display: none;

values: Магнитное динамо – Russian

values: ทฤษฎีไดนาโม – Thai

values:
interlanguage-link interwiki-th
display: none;

values: Магнітне динамо – Ukrainian

values:
interlanguage-link interwiki-uk
display: none;

values:
interlanguage-link interwiki-vi
display: none;

values: /static/images/wikimedia-button-1.5x.png 1.5x, /static/images/wikimedia-button-2x.png 2x

values: /static/images/poweredby_mediawiki_132x47.png 1.5x, /static/images/poweredby_mediawiki_176x62.png 2x

values:
suggestions
display: none; font-size: 13px;

values: mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject page-Dynamo_theory rootpage-Dynamo_theory skin-vector action-view