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Muscle fatigue
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Muscle fatigue is the decline in ability of a muscle to generate force. It can be a result of vigorous exercise but abnormal fatigue may be caused by barriers to or interference with the different stages of muscle contraction. There are two main causes of muscle fatigue: the limitations of a nerve’s ability to generate a sustained signal (neural fatigue) and the reduced ability of the muscle fiber to contract (metabolic fatigue).
Contents
[hide]
1 Muscle contraction
2 Nervous fatigue
3 Metabolic fatigue
3.1 Substrates
3.2 Metabolites
3.2.1 Chloride
3.2.2 Potassium
3.2.3 Lactic acid
4 Pathology
5 Molecular mechanisms
6 Effect on performance
7 Electromyography
8 See also
9 References
10 External links
Muscle contraction[edit]
Main article: Muscle contraction
Muscle cells work by detecting a flow of electrical impulses from the brain which signals them to contract through the release of calcium by the sarcoplasmic reticulum. Fatigue (reduced ability to generate force) may occur due to the nerve, or within the muscle cells themselves.
Nervous fatigue[edit]
Nerves are responsible for controlling the contraction of muscles, determining the number, sequence and force of muscular contraction. Most movements require a force far below what a muscle could potentially generate, and barring pathological nervous fatigue, is seldom an issue. But in extremely powerful contractions that are close to the upper limit of a muscle's ability to generate force, nervous fatigue (enervation), in which the nerve signal weakens, can be a limiting factor in untrained individuals.
In novice strength trainers, the muscle's ability to generate force is most strongly limited by nerve’s ability to sustain a high-frequency signal. After a period of maximum contraction, the nerve’s signal reduces in frequency and the force generated by the contraction diminishes. There is no sensation of pain or discomfort, the muscle appears to simply ‘stop listening’ and gradually cease to move, often going backwards. As there is insufficient stress on the muscles and tendons, there will often be no delayed onset muscle soreness following the workout.
Part of the process of strength training is increasing the nerve's ability to generate sustained, high frequency signals which allow a muscle to contract with its greatest force. It is this neural training that causes several weeks worth of rapid gains in strength, which level off once the nerve is generating maximum contractions and the muscle reaches its physiological limit. Past this point, training effects increase muscular strength through myofibrilar or sarcoplasmic hypertrophy and metabolic fatigue becomes the factor limiting contractile force.
Metabolic fatigue[edit]
Though not universally used, ‘metabolic fatigue’ is a common term for the reduction in contractile force due to the direct or indirect effects of two main factors:
Shortage of fuel (substrates) within the muscle fiber
Accumulation of substances (metabolites) within the muscle fiber, which interfere either with the release of calcium (Ca2+) or with the ability of calcium to stimulate muscle contraction.
Substrates[edit]
Substrates within the muscle serve to power muscular contractions. They include molecules such as adenosine triphosphate (ATP), glycogen and creatine phosphate. ATP binds to the myosin head and causes the ‘ratchetting’ that results in contraction according to the sliding filament model. Creatine phosphate stores energy so ATP can be rapidly regenerated within the muscle cells from adenosine diphosphate (ADP) and inorganic phosphate ions, allowing for sustained powerful contractions that last between 5–7 seconds. Glycogen is the intramuscular storage form of glucose, used to generate energy quickly once intramuscular creatine stores are exhausted, producing lactic acid as a metabolic byproduct.
Substrate shortage is one of the causes of metabolic fatigue. Substrates are depleted during exercise, resulting in a lack of intracellular energy sources to fuel contractions. In essence, the muscle stops contracting because it lacks the energy to do so.
Metabolites[edit]
Metabolites are the substances (generally waste products) produced as a result of muscular contraction. They include chloride, potassium, lactic acid, ADP, magnesium (Mg2+), reactive oxygen species, and inorganic phosphate. Accumulation of metabolites can directly or indirectly produce metabolic fatigue within muscle fibers through interference with the release of calcium (Ca2+) from the sarcoplasmic reticulum or reduction of the sensitivity of contractile molecules actin and myosin to calcium.
Chloride[edit]
Intracellular chloride partially inhibits the contraction of muscles. Namely, it prevents muscles from contracting due to "false alarms", small stimuli which may cause them to contract (akin to myoclonus). This natural brake helps muscles respond solely to the conscious control or spinal reflexes[citation needed] but also has the effect of reducing the force of conscious contractions.
Potassium[edit]
High concentrations of potassium (K+) also causes the muscle cells to decrease in efficiency, causing cramping and fatigue. Potassium builds up in the t-tubule system and around the muscle fiber as a result of action potentials. The shift in K+ changes the membrane potential around the muscle fiber. The change in membrane potential causes a decrease in the release of calcium (Ca2+) from the sarcoplasmic reticulum.[1]
Lactic acid[edit]
It was once believed that lactic acid build-up was the cause of muscle fatigue.[2] The assumption was lactic acid had a "pickling" effect on muscles, inhibiting their ability to contract. The impact of lactic acid on performance is now uncertain, it may assist or hinder muscle fatigue.
Produced as a by-product of fermentation, lactic acid can increase intracellular acidity of muscles. This can lower the sensitivity of contractile apparatus to Ca2+ but also has the effect of increasing cytoplasmic Ca2+ concentration through an inhibition of the chemical pump that actively transports calcium out of the cell. This counters inhibiting effects of potassium on muscular action potentials. Lactic acid also has a negating effect on the chloride ions in the muscles, reducing their inhibition of contraction and leaving potassium ions as the only restricting influence on muscle contractions, though the effects of potassium are much less than if there were no lactic acid to remove the chloride ions. Ultimately, it is uncertain if lactic acid reduces fatigue through increased intracellular calcium or increases fatigue through reduced sensitivity of contractile proteins to Ca2+.
Lactic acid is now used as a measure of endurance training effectiveness and VO2 max.[3]
Pathology[edit]
Muscle weakness may be due to problems with the nerve supply, neuromuscular disease (such as myasthenia gravis) or problems with muscle itself. The latter category includes polymyositis and other muscle disorders.
Molecular mechanisms[edit]
Muscle fatigue may be due to precise molecular changes that occur in vivo with sustained exercise. It has been found that the ryanodine receptor present in skeletal muscle undergoes a conformational change during exercise, resulting in "leaky" channels that are deficient in calcium release. These "leaky" channels may be a contributor to muscle fatigue and decreased exercise capacity.[4]
Effect on performance[edit]
Fatigue has been found to play a big role in limiting performance in just about every individual in every sport. In research studies, participants were found to show reduced voluntary force production in fatigued muscles (measured with concentric, eccentric, and isometric contractions), vertical jump heights, other field tests of lower body power, reduced throwing velocities, reduced kicking power and velocity, less accuracy in throwing and shooting activities, endurance capacity, anaerobic capacity, anaerobic power, mental concentration, and many other performance parameters when sport specific skills are examined.[5][6][7][8][9][10]
Electromyography[edit]
Electromyography is a research technique that allows researchers to look at muscle recruitment in various conditions, by quantifying electrical signals sent to muscle fibers through motor neurons. In general, fatigue protocols have shown increases in EMG data over the course of a fatiguing protocol, but reduced recruitment of muscle fibers in tests of power in fatigued individuals. In most studies, this increase in recruitment during exercise correlated with a decrease in performance (as would be expected in a fatiguing individual).[11][12][13][14]
Median power frequency is often used as a way to track fatigue using EMG. Using the median power frequency, raw EMG data is filtered to reduce noise and then relevant time windows are Fourier Transformed. In the case of fatigue in a 30-second isometric contraction, the first window may be the first second, the second window might be at second 15, and the third window could be the last second of contraction (at second 30). Each window of data is analyzed and the median power frequency is found. Generally, the median power frequency decreases over time, demonstrating fatigue. Some reasons why fatigue is found are due to action potentials of motor units having a similar pattern of repolarization, fast motor units activating and then quickly deactivating while slower motor units remain, and conduction velocities of the nervous system decreasing over time.[15][16][17][18]
See also[edit]
Asthenia
Debility
Fatigue (medical)
Central fatigue
Malaise
Muscle weakness
Paresis
References[edit]
Jump up ^ Silverthorn, Dee Unglaub (2009). Human Physiology: An Integrated Approach. Pearsin Benjamin Cummings. p. 412. ISBN 0321559800.
Jump up ^ Sahlin, K (1986). "Muscle fatigue and lactic acid accumulation". Acta Physiologica Scandinavica. Supplementum. 556: 83–91. PMID 3471061.
Jump up ^ Lundby, C (2015). "Performance Enhancement: What Are the Physiological Limits?". Physiology. 30 (4): 282–292. doi:10.1152/physiol.00052.2014. PMID 26136542.
Jump up ^ Bellinger, A.M., Reiken, S., Dura, M., Murphy, P.W., Deng, S., Landry, D.W., Nieman, D., Lehnart, S.E., Samaru, M., LaCampagne, A., and Marks, A.R. (2008). "Remodeling of ryanodine receptor complex causes "leaky" channels: A molecular mechanism for decreased exercise capacity". Proceedings of the National Academy of Sciences of the United States of America. 105 (6): 2198–202. doi:10.1073/pnas.0711074105. PMC 2538898  . PMID 18268335. CS1 maint: Multiple names: authors list (link)
Jump up ^ Knicker, A. J., Renshaw, I., Oldham, A.R.H., Cairns, S.P. (2011). "Interactive processes link the multiple symptoms of fatigue in sport competition". Sports Medicine. 41 (4): 307–28. doi:10.2165/11586070-000000000-00000. PMID 21425889. CS1 maint: Multiple names: authors list (link)
Jump up ^ Montgomery, P. G., Pyne, D.B., Hopkins, W.G., Dorman, J.C., Cook, K., Minahan, C.L. (2008). "The effect of recovery strategies on physical performance and cumulative fatigue in competitive basketball". Journal of sports sciences. 26 (11): 1135–45. doi:10.1080/02640410802104912. PMID 18608847. CS1 maint: Multiple names: authors list (link)
Jump up ^ Linnamo, V., Hakkinen, K., Komi, P.V. (1998). "Neuromuscular fatigue and recovery in maximal compared to explosive strength loading". European journal of applied physiology and occupational physiology. 77 (1–2): 176–81. doi:10.1007/s004210050317. PMID 9459539. CS1 maint: Multiple names: authors list (link)
Jump up ^ Smilios, I., Hakkinen, K., and Tokmakidis, S. (2010). "Power output and electrographis activity during and after a moderate load muscular endurance session". Journal of strength and conditioning research / National Strength & Conditioning Association. 24 (8): 2122–31. doi:10.1519/JSC.0b013e3181a5bc44. PMID 19834352. CS1 maint: Multiple names: authors list (link)
Jump up ^ Linnamo, V., Hakkinen, K., Komi, P.V. (1998). "Neuromuscular fatigue and recovery in maximal compared to explosive strength loading". European journal of applied physiology and occupational physiology. 77 (1–2): 176–81. doi:10.1007/s004210050317. PMID 9459539. CS1 maint: Multiple names: authors list (link)
Jump up ^ Girard, O., Lattier, G., Micallef, J., and Millet, G. (2006). "Changes in exercise characteristics, maximal voluntary contraction, and explosive strength during prolonged tennis playing". British Journal of Sports Medicine. 40 (6): 521–6. doi:10.1136/bjsm.2005.023754. PMC 2465109  . PMID 16720888. CS1 maint: Multiple names: authors list (link)
Jump up ^ Carneiro, J. G., Goncalves, E.M., Camata, T.V., Altimari, J.M., Machado, M.V. (2010). "Influence of gender on the emg signal of the quadriceps femoris muscles and performance in high intensity short term exercise". Electromyography and clinical neurophysiology. 50 (7–8): 326–32. PMID 21284370. CS1 maint: Multiple names: authors list (link)
Jump up ^ Clark, B. C., Manini, T.M., The, D.J., Doldo, N.A., Ploutz-Snyder, L.L. (2003). "Gender differences in skeletal muscle fatigability are related to contraction type and emg spectral compression". Journal of Applied Physiology. 94 (6): 2263–72. doi:10.1152/japplphysiol.00926.2002. PMID 12576411. CS1 maint: Multiple names: authors list (link)
Jump up ^ Beneka, A. G., Malliou, P.K., Missailidou, V., Chatzinikolaou, A., Fatouros, I., Gourgoulis, V., Georgiadis, E. (2013). "Muscle performance following an acute bout of plyometric training combined with low or high intensity weight exercise". Journal of sports sciences. 31 (3): 335–43. doi:10.1080/02640414.2012.733820. PMID 23083331. CS1 maint: Multiple names: authors list (link)
Jump up ^ Pincivero, D. M., Aldworth, C., Dickerson, T., Petry, C., Shultz, T. (2000). "Quadriceps-hamstring emg activity during functional, closed kinetic chain exercise to fatigue". European Journal of Applied Physiology. 81 (6): 504–9. doi:10.1007/s004210050075. PMID 10774875. CS1 maint: Multiple names: authors list (link)
Jump up ^ Jakobsen, M., Sundstrup, E., Andersen, C., Zebis, M., Mortensen, P. (2012). "Evaluation of muscle activity during a standardized shoulder resistance training bout in novice individuals". Journal of strength and conditioning research / National Strength & Conditioning Association. 26 (9): 2515–22. doi:10.1519/JSC.0b013e31823f29d9. PMID 22067242. CS1 maint: Multiple names: authors list (link)
Jump up ^ Sundstrup, E., Jakobsen, M., Andersen, C., Zebis, M., Mortensen, O. (2012). "Muscle activation strategies during strength training with heavy loading vs. repetitions to failure". Journal of strength and conditioning research / National Strength & Conditioning Association. 26 (7): 1897–903. doi:10.1519/JSC.0b013e318239c38e. PMID 21986694. CS1 maint: Multiple names: authors list (link)
Jump up ^ Cardozo, A., Gonçalves, M., & Dolan, P. (2011). "Back extensor muscle fatigue at submaximal workloads assessed using frequency banding of the electromyographic signal". Clinical biomechanics (Bristol, Avon). 26 (10): 971–6. doi:10.1016/j.clinbiomech.2011.06.001. PMID 21696871. CS1 maint: Multiple names: authors list (link)
Jump up ^ Hollman, J., Hohl, J., Kraft, J., Strauss, J., & Traver, K. (2013). "Does the fast fourier transformation window length affect the slope of an electromyogram's median frequency plot during a fatiguing isometric contraction?". Gait & Posture. 38 (1): 161–4. doi:10.1016/j.gaitpost.2012.10.028. PMID 23211923. CS1 maint: Multiple names: authors list (link)
External links[edit]
Muscle Fatigue at the US National Library of Medicine Medical Subject Headings (MeSH)
Retrieved from "https://en.wikipedia.org/w/index.php?title=Muscle_fatigue&oldid=841560038"
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Electronegativity
From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
"Electronegative" redirects here. For the Nightfall EP, see Electronegative (EP).
Electrostatic potential map of a water molecule, where the oxygen atom has a more negative charge (red) than the positive (blue) hydrogen atoms
Electronegativity, symbol χ, is a chemical property that describes the tendency of an atom to attract a shared pair of electrons (or electron density) towards itself.[1] An atom's electronegativity is affected by both its atomic number and the distance at which its valence electrons reside from the charged nucleus. The higher the associated electronegativity number, the more an element or compound attracts electrons towards it.
On the most basic level, electronegativity is determined by factors like the nuclear charge (the more protons an atom has, the more "pull" it will have on electrons) and the number/location of other electrons present in the atomic shells (the more electrons an atom has, the farther from the nucleus the valence electrons will be, and as a result the less positive charge they will experience—both because of their increased distance from the nucleus, and because the other electrons in the lower energy core orbitals will act to shield the valence electrons from the positively charged nucleus).
The opposite of electronegativity is electropositivity: a measure of an element's ability to donate electrons.
The term "electronegativity" was introduced by Jöns Jacob Berzelius in 1811,[2] though the concept was known even before that and was studied by many chemists including Avogadro.[2] In spite of its long history, an accurate scale of electronegativity was not developed until 1932, when Linus Pauling proposed an electronegativity scale, which depends on bond energies, as a development of valence bond theory.[3] It has been shown to correlate with a number of other chemical properties. Electronegativity cannot be directly measured and must be calculated from other atomic or molecular properties. Several methods of calculation have been proposed, and although there may be small differences in the numerical values of the electronegativity, all methods show the same periodic trends between elements.
The most commonly used method of calculation is that originally proposed by Linus Pauling. This gives a dimensionless quantity, commonly referred to as the Pauling scale (χr), on a relative scale running from around 0.7 to 3.98 (hydrogen = 2.20). When other methods of calculation are used, it is conventional (although not obligatory) to quote the results on a scale that covers the same range of numerical values: this is known as an electronegativity in Pauling units.
As it is usually calculated, electronegativity is not a property of an atom alone, but rather a property of an atom in a molecule.[4] Properties of a free atom include ionization energy and electron affinity. It is to be expected that the electronegativity of an element will vary with its chemical environment,[5] but it is usually considered to be a transferable property, that is to say that similar values will be valid in a variety of situations.
Caesium is the least electronegative element in the periodic table (=0.79), while fluorine is most electronegative (=3.98). Francium and caesium were originally both assigned 0.7; caesium's value was later refined to 0.79, but no experimental data allows a similar refinement for francium. However, francium's ionization energy is known to be slightly higher than caesium's, in accordance with the relativistic stabilization of the 7s orbital, and this in turn implies that francium is in fact more electronegative than caesium.[6]
Contents
1 Electronegativities of the elements
2 Methods of calculation
2.1 Pauling electronegativity
2.2 Mulliken electronegativity
2.3 Allred–Rochow electronegativity
2.4 Sanderson electronegativity equalization
2.5 Allen electronegativity
3 Correlation of electronegativity with other properties
4 Trends in electronegativity
4.1 Periodic trends
4.2 Variation of electronegativity with oxidation number
4.3 Electronegativity and hybridization scheme
5 Group electronegativity
6 Electropositivity
7 See also
8 References
9 Bibliography
10 External links
Electronegativities of the elements[edit]
v
t
e
Periodic table of electronegativity by Pauling scale
→ Atomic radius decreases → Ionization energy increases → Electronegativity increases →
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Group →
↓ Period
1
H
2.20 He
2
Li
0.98 Be
1.57 B
2.04 C
2.55 N
3.04 O
3.44 F
3.98 Ne
3
Na
0.93 Mg
1.31 Al
1.61 Si
1.90 P
2.19 S
2.58 Cl
3.16 Ar
4
K
0.82 Ca
1.00 Sc
1.36 Ti
1.54 V
1.63 Cr
1.66 Mn
1.55 Fe
1.83 Co
1.88 Ni
1.91 Cu
1.90 Zn
1.65 Ga
1.81 Ge
2.01 As
2.18 Se
2.55 Br
2.96 Kr
3.00
5
Rb
0.82 Sr
0.95 Y
1.22 Zr
1.33 Nb
1.6 Mo
2.16 Tc
1.9 Ru
2.2 Rh
2.28 Pd
2.20 Ag
1.93 Cd
1.69 In
1.78 Sn
1.96 Sb
2.05 Te
2.1 I
2.66 Xe
2.60
6
Cs
0.79 Ba
0.89 La
1.1 Hf
1.3 Ta
1.5 W
2.36 Re
1.9 Os
2.2 Ir
2.20 Pt
2.28 Au
2.54 Hg
2.00 Tl
1.62 Pb
1.87 Bi
2.02 Po
2.0 At
2.2 Rn
2.2
7
Fr
>0.79[en 1] Ra
0.9 Ac
1.1 Rf
Db
Sg
Bh
Hs
Mt
Ds
Rg
Cn
Nh
Fl
Mc
Lv
Ts
Og

Ce
1.12 Pr
1.13 Nd
1.14 Pm
1.13 Sm
1.17 Eu
1.2 Gd
1.2 Tb
1.1 Dy
1.22 Ho
1.23 Er
1.24 Tm
1.25 Yb
1.1 Lu
1.27
Th
1.3 Pa
1.5 U
1.38 Np
1.36 Pu
1.28 Am
1.13 Cm
1.28 Bk
1.3 Cf
1.3 Es
1.3 Fm
1.3 Md
1.3 No
1.3 Lr
1.3[en 2]
Values are given for the elements in their most common and stable oxidation states.
See also: Electronegativities of the elements (data page)
Jump up ^ Electronegativity of francium was chosen by Pauling as 0.7, close to that of caesium (also assessed 0.7 at that point). The base value of hydrogen was later increased by 0.10 and caesium's electronegativity was later refined to 0.79; however, no refinements have been made for francium as no experiment has been conducted. However, francium is expected and, to a small extent, observed to be more electronegative than caesium. See francium for details.
Jump up ^ See Brown, Geoffrey (2012). The Inaccessible Earth: An integrated view to its structure and composition. Springer Science & Business Media. p. 88. ISBN 9789401115162.

Methods of calculation[edit]
Pauling electronegativity[edit]
Pauling first proposed[3] the concept of electronegativity in 1932 as an explanation of the fact that the covalent bond between two different atoms (A–B) is stronger than would be expected by taking the average of the strengths of the A–A and B–B bonds. According to valence bond theory, of which Pauling was a notable proponent, this "additional stabilization" of the heteronuclear bond is due to the contribution of ionic canonical forms to the bonding.
The difference in electronegativity between atoms A and B is given by:
| χ A − χ B | = ( e V ) − 1 / 2 E d ( A B ) − [ E d ( A A ) + E d ( B B ) ] / 2 {\displaystyle |\chi _{\rm {A}}-\chi _{\rm {B}}|=({\rm {eV}})^{-1/2}{\sqrt {E_{\rm {d}}({\rm {AB}})-[E_{\rm {d}}({\rm {AA}})+E_{\rm {d}}({\rm {BB}})]/2}}}
where the dissociation energies, Ed, of the A–B, A–A and B–B bonds are expressed in electronvolts, the factor (eV)−1⁄2 being included to ensure a dimensionless result. Hence, the difference in Pauling electronegativity between hydrogen and bromine is 0.73 (dissociation energies: H–Br, 3.79 eV; H–H, 4.52 eV; Br–Br 2.00 eV)
As only differences in electronegativity are defined, it is necessary to choose an arbitrary reference point in order to construct a scale. Hydrogen was chosen as the reference, as it forms covalent bonds with a large variety of elements: its electronegativity was fixed first[3] at 2.1, later revised[7] to 2.20. It is also necessary to decide which of the two elements is the more electronegative (equivalent to choosing one of the two possible signs for the square root). This is usually done using "chemical intuition": in the above example, hydrogen bromide dissolves in water to form H+ and Br− ions, so it may be assumed that bromine is more electronegative than hydrogen. However, in principle, since the same electronegativities should be obtained for any two bonding compounds, the data are in fact overdetermined, and the signs are unique once a reference point is fixed (usually, for H or F).
To calculate Pauling electronegativity for an element, it is necessary to have data on the dissociation energies of at least two types of covalent bond formed by that element. A. L. Allred updated Pauling's original values in 1961 to take account of the greater availability of thermodynamic data,[7] and it is these "revised Pauling" values of the electronegativity that are most often used.
The essential point of Pauling electronegativity is that there is an underlying, quite accurate, semi-empirical formula for dissociation energies, namely:
E d ( A B ) = [ E d ( A A ) + E d ( B B ) ] / 2 + ( χ A − χ B ) 2 e V {\displaystyle E_{\rm {d}}({\rm {AB}})=[E_{\rm {d}}({\rm {AA}})+E_{\rm {d}}({\rm {BB}})]/2+(\chi _{\rm {A}}-\chi _{\rm {B}})^{2}{\rm {eV}}}
or sometimes, a more accurate fit
E d ( A B ) = E d ( A A ) E d ( B B ) + 1.3 ( χ A − χ B ) 2 e V {\displaystyle E_{\rm {d}}({\rm {AB}})={\sqrt {E_{\rm {d}}({\rm {AA}})E_{\rm {d}}({\rm {BB}})}}+1.3(\chi _{\rm {A}}-\chi _{\rm {B}})^{2}{\rm {eV}}}
This is an approximate equation, but holds with good accuracy. Pauling obtained it by noting that a bond can be approximately represented as a quantum mechanical superposition of a covalent bond and two ionic bond-states. The covalent energy of a bond is approximately, by quantum mechanical calculations, the geometric mean of the two energies of covalent bonds of the same molecules, and there is an additional energy that comes from ionic factors, i.e. polar character of the bond.
The geometric mean is approximately equal to the arithmetic mean - which is applied in the first formula above - when the energies are of the similar value, e.g., except for the highly electropositive elements, where there is a larger difference of two dissociation energies; the geometric mean is more accurate and almost always gives a positive excess energy, due to ionic bonding. The square root of this excess energy, Pauling notes, is approximately additive, and hence one can introduce the electronegativity. Thus, it is this semi-empirical formula for bond energy that underlies Pauling electronegativity concept.
The formulas are approximate, but this rough approximation is in fact relatively good and gives the right intuition, with the notion of polarity of the bond and some theoretical grounding in quantum mechanics. The electronegativities are then determined to best fit the data.
In more complex compounds, there is additional error since electronegativity depends on the molecular environment of an atom. Also, the energy estimate can be only used for single, not for multiple bonds. The energy of formation of a molecule containing only single bonds then can be approximated from an electronegativity table, and depends on the constituents and sum of squares of differences of electronegativities of all pairs of bonded atoms. Such a formula for estimating energy typically has relative error of order of 10%, but can be used to get a rough qualitative idea and understanding of a molecule.
Mulliken electronegativity[edit]
The correlation between Mulliken electronegativities (x-axis, in kJ/mol) and Pauling electronegativities (y-axis).
Robert S. Mulliken proposed that the arithmetic mean of the first ionization energy (Ei) and the electron affinity (Eea) should be a measure of the tendency of an atom to attract electrons.[8][9] As this definition is not dependent on an arbitrary relative scale, it has also been termed absolute electronegativity,[10] with the units of kilojoules per mole or electronvolts.
χ = ( E i + E e a ) / 2 {\displaystyle \chi =(E_{\rm {i}}+E_{\rm {ea}})/2\,}
However, it is more usual to use a linear transformation to transform these absolute values into values that resemble the more familiar Pauling values. For ionization energies and electron affinities in electronvolts,[11]
χ = 0.187 ( E i + E e a ) + 0.17 {\displaystyle \chi =0.187(E_{\rm {i}}+E_{\rm {ea}})+0.17\,}
and for energies in kilojoules per mole,[12]
χ = ( 1.97 × 10 − 3 ) ( E i + E e a ) + 0.19. {\displaystyle \chi =(1.97\times 10^{-3})(E_{\rm {i}}+E_{\rm {ea}})+0.19.}
The Mulliken electronegativity can only be calculated for an element for which the electron affinity is known, fifty-seven elements as of 2006. The Mulliken electronegativity of an atom is sometimes said to be the negative of the chemical potential. By inserting the energetic definitions of the ionization potential and electron affinity into the Mulliken electronegativity, it is possible to show that the Mulliken chemical potential is a finite difference approximation of the electronic energy with respect to the number of electrons., i.e.,
μ ( M u l l i k e n ) = − χ ( M u l l i k e n ) = − ( E i + E e a ) / 2 {\displaystyle \mu ({\rm {Mulliken)=-\chi ({\rm {Mulliken)=-(E_{\rm {i}}+E_{\rm {ea}})/2\,}}}}}
Allred–Rochow electronegativity[edit]
The correlation between Allred–Rochow electronegativities (x-axis, in Å−2) and Pauling electronegativities (y-axis).
A. Louis Allred and Eugene G. Rochow considered[13] that electronegativity should be related to the charge experienced by an electron on the "surface" of an atom: The higher the charge per unit area of atomic surface the greater the tendency of that atom to attract electrons. The effective nuclear charge, Zeff, experienced by valence electrons can be estimated using Slater's rules, while the surface area of an atom in a molecule can be taken to be proportional to the square of the covalent radius, rcov. When rcov is expressed in picometres,[14]
χ = 3590 Z e f f r c o v 2 + 0.744 {\displaystyle \chi =3590{{Z_{\rm {eff}}} \over {r_{\rm {cov}}^{2}}}+0.744}
Sanderson electronegativity equalization[edit]
The correlation between Sanderson electronegativities (x-axis, arbitrary units) and Pauling electronegativities (y-axis).
R.T. Sanderson has also noted the relationship between Mulliken electronegativity and atomic size, and has proposed a method of calculation based on the reciprocal of the atomic volume.[15] With a knowledge of bond lengths, Sanderson's model allows the estimation of bond energies in a wide range of compounds.[16] Sanderson's model has also been used to calculate molecular geometry, s-electrons energy, NMR spin-spin constants and other parameters for organic compounds.[17][18] This work underlies the concept of electronegativity equalization, which suggests that electrons distribute themselves around a molecule to minimize or to equalize the Mulliken electronegativity.[19] This behavior is analogous to the equalization of chemical potential in macroscopic thermodynamics.[20]
Allen electronegativity[edit]
The correlation between Allen electronegativities (x-axis, in kJ/mol) and Pauling electronegativities (y-axis).
Perhaps the simplest definition of electronegativity is that of Leland C. Allen, who has proposed that it is related to the average energy of the valence electrons in a free atom,[21] [22] [23]
χ = n s ε s + n p ε p n s + n p {\displaystyle \chi ={n_{\rm {s}}\varepsilon _{\rm {s}}+n_{\rm {p}}\varepsilon _{\rm {p}} \over n_{\rm {s}}+n_{\rm {p}}}}
where εs,p are the one-electron energies of s- and p-electrons in the free atom and ns,p are the number of s- and p-electrons in the valence shell. It is usual to apply a scaling factor, 1.75×10−3 for energies expressed in kilojoules per mole or 0.169 for energies measured in electronvolts, to give values that are numerically similar to Pauling electronegativities.
The one-electron energies can be determined directly from spectroscopic data, and so electronegativities calculated by this method are sometimes referred to as spectroscopic electronegativities. The necessary data are available for almost all elements, and this method allows the estimation of electronegativities for elements that cannot be treated by the other methods, e.g. francium, which has an Allen electronegativity of 0.67.[24] However, it is not clear what should be considered to be valence electrons for the d- and f-block elements, which leads to an ambiguity for their electronegativities calculated by the Allen method.
In this scale neon has the highest electronegativity of all elements, followed by fluorine, helium, and oxygen.
v
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e
Electronegativity using the Allen scale
Group →
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
↓ Period
1
H
2.300 He
4.160
2
Li
0.912 Be
1.576 B
2.051 C
2.544 N
3.066 O
3.610 F
4.193 Ne
4.787
3
Na
0.869 Mg
1.293 Al
1.613 Si
1.916 P
2.253 S
2.589 Cl
2.869 Ar
3.242
4
K
0.734 Ca
1.034 Sc
1.19 Ti
1.38 V
1.53 Cr
1.65 Mn
1.75 Fe
1.80 Co
1.84 Ni
1.88 Cu
1.85 Zn
1.59 Ga
1.756 Ge
1.994 As
2.211 Se
2.424 Br
2.685 Kr
2.966
5
Rb
0.706 Sr
0.963 Y
1.12 Zr
1.32 Nb
1.41 Mo
1.47 Tc
1.51 Ru
1.54 Rh
1.56 Pd
1.58 Ag
1.87 Cd
1.52 In
1.656 Sn
1.824 Sb
1.984 Te
2.158 I
2.359 Xe
2.582
6
Cs
0.659 Ba
0.881 Lu
1.09 Hf
1.16 Ta
1.34 W
1.47 Re
1.60 Os
1.65 Ir
1.68 Pt
1.72 Au
1.92 Hg
1.76 Tl
1.789 Pb
1.854 Bi
2.01 Po
2.19 At
2.39 Rn
2.60
7
Fr
0.67 Ra
0.89
See also: Electronegativities of the elements (data page)
Correlation of electronegativity with other properties[edit]
The variation of the isomer shift (y-axis, in mm/s) of [SnX6]2− anions, as measured by 119Sn Mössbauer spectroscopy, against the sum of the Pauling electronegativities of the halide substituents (x-axis).
The wide variety of methods of calculation of electronegativities, which all give results that correlate well with one another, is one indication of the number of chemical properties which might be affected by electronegativity. The most obvious application of electronegativities is in the discussion of bond polarity, for which the concept was introduced by Pauling. In general, the greater the difference in electronegativity between two atoms the more polar the bond that will be formed between them, with the atom having the higher electronegativity being at the negative end of the dipole. Pauling proposed an equation to relate "ionic character" of a bond to the difference in electronegativity of the two atoms,[4] although this has fallen somewhat into disuse.
Several correlations have been shown between infrared stretching frequencies of certain bonds and the electronegativities of the atoms involved:[25] however, this is not surprising as such stretching frequencies depend in part on bond strength, which enters into the calculation of Pauling electronegativities. More convincing are the correlations between electronegativity and chemical shifts in NMR spectroscopy[26] or isomer shifts in Mössbauer spectroscopy[27] (see figure). Both these measurements depend on the s-electron density at the nucleus, and so are a good indication that the different measures of electronegativity really are describing "the ability of an atom in a molecule to attract electrons to itself".[1][4]
Trends in electronegativity[edit]
Periodic trends[edit]
The variation of Pauling electronegativity (y-axis) as one descends the main groups of the periodic table from the second period to the sixth period
In general, electronegativity increases on passing from left to right along a period, and decreases on descending a group. Hence, fluorine is the most electronegative of the elements (not counting noble gases), whereas caesium is the least electronegative, at least of those elements for which substantial data is available.[24] This would lead one to believe that caesium fluoride is the compound whose bonding features the most ionic character.
There are some exceptions to this general rule. Gallium and germanium have higher electronegativities than aluminium and silicon, respectively, because of the d-block contraction. Elements of the fourth period immediately after the first row of the transition metals have unusually small atomic radii because the 3d-electrons are not effective at shielding the increased nuclear charge, and smaller atomic size correlates with higher electronegativity (see Allred-Rochow electronegativity, Sanderson electronegativity above). The anomalously high electronegativity of lead, in particular when compared to thallium and bismuth, appears to be an artifact of data selection (and data availability)—methods of calculation other than the Pauling method show the normal periodic trends for these elements.
Variation of electronegativity with oxidation number[edit]
In inorganic chemistry it is common to consider a single value of the electronegativity to be valid for most "normal" situations. While this approach has the advantage of simplicity, it is clear that the electronegativity of an element is not an invariable atomic property and, in particular, increases with the oxidation state of the element.
Allred used the Pauling method to calculate separate electronegativities for different oxidation states of the handful of elements (including tin and lead) for which sufficient data was available.[7] However, for most elements, there are not enough different covalent compounds for which bond dissociation energies are known to make this approach feasible. This is particularly true of the transition elements, where quoted electronegativity values are usually, of necessity, averages over several different oxidation states and where trends in electronegativity are harder to see as a result.
Acid
Formula
Chlorine
oxidation
state
pKa
Hypochlorous acid HClO +1 +7.5
Chlorous acid HClO2 +3 +2.0
Chloric acid HClO3 +5 –1.0
Perchloric acid HClO4 +7 –10
The chemical effects of this increase in electronegativity can be seen both in the structures of oxides and halides and in the acidity of oxides and oxoacids. Hence CrO3 and Mn2O7 are acidic oxides with low melting points, while Cr2O3 is amphoteric and Mn2O3 is a completely basic oxide.
The effect can also be clearly seen in the dissociation constants of the oxoacids of chlorine. The effect is much larger than could be explained by the negative charge being shared among a larger number of oxygen atoms, which would lead to a difference in pKa of log10(1⁄4) = –0.6 between hypochlorous acid and perchloric acid. As the oxidation state of the central chlorine atom increases, more electron density is drawn from the oxygen atoms onto the chlorine, reducing the partial negative charge on the oxygen atoms and increasing the acidity.
Electronegativity and hybridization scheme[edit]
The electronegativity of an atom changes depending on the hybridization of the orbital employed in bonding. Electrons in s orbitals are held more tightly than electrons in p orbitals. Hence, a bond to an atom that employs an spx hybrid orbital for bonding will be more heavily polarized to that atom when the hybrid orbital has more s character. That is, when electronegativities are compared for different hybridization schemes of a given element, the order χ(sp3) < χ(sp2) < χ(sp) holds (the trend should apply to non-integer hybridization indices as well). While this holds true in principle for any main-group element, values for the hybridization-specific electronegativity are most frequently cited for carbon. In organic chemistry, these electronegativities are frequently invoked to predict or rationalize bond polarities in organic compounds containing double and triple bonds to carbon.
Hybridization
χ (Pauling)[28]
C(sp3) 2.3
C(sp2) 2.6
C(sp) 3.1
'generic' C 2.5
Group electronegativity[edit]
In organic chemistry, electronegativity is associated more with different functional groups than with individual atoms. The terms group electronegativity and substituent electronegativity are used synonymously. However, it is common to distinguish between the inductive effect and the resonance effect, which might be described as σ- and π-electronegativities, respectively. There are a number of linear free-energy relationships that have been used to quantify these effects, of which the Hammett equation is the best known. Kabachnik parameters are group electronegativities for use in organophosphorus chemistry.
Electropositivity[edit]
Electropositivity is a measure of an element's ability to donate electrons, and therefore form positive ions; thus, it is opposed to electronegativity.
Mainly, this is an attribute of metals, meaning that, in general, the greater the metallic character of an element the greater the electropositivity. Therefore, the alkali metals are most electropositive of all. This is because they have a single electron in their outer shell and, as this is relatively far from the nucleus of the atom, it is easily lost; in other words, these metals have low ionization energies.[29]
While electronegativity increases along periods in the periodic table, and decreases down groups, electropositivity decreases along periods (from left to right) and increases down groups.
See also[edit]
Electronegativities of the elements (data page)
Chemical polarity
References[edit]
^ Jump up to: a b IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Electronegativity".
^ Jump up to: a b Jensen, W.B. (1996). "Electronegativity from Avogadro to Pauling: Part 1: Origins of the Electronegativity Concept". Journal of Chemical Education. 73 (1): 11–20. Bibcode:1996JChEd..73...11J. doi:10.1021/ed073p11.
^ Jump up to: a b c Pauling, L. (1932). "The Nature of the Chemical Bond. IV. The Energy of Single Bonds and the Relative Electronegativity of Atoms". Journal of the American Chemical Society. 54 (9): 3570–3582. Bibcode:1932JAChS..54.2610C. doi:10.1021/ja01348a011.
^ Jump up to: a b c Pauling, Linus (1960). Nature of the Chemical Bond. Cornell University Press. pp. 88–107. ISBN 978-0-8014-0333-0.
Jump up ^ Greenwood, N. N.; Earnshaw, A. (1984). Chemistry of the Elements. Pergamon. p. 30. ISBN 978-0-08-022057-4.
Jump up ^ More details and sources for this point can be found in the article on francium.
^ Jump up to: a b c Allred, A. L. (1961). "Electronegativity values from thermochemical data". Journal of Inorganic and Nuclear Chemistry. 17 (3–4): 215–221. doi:10.1016/0022-1902(61)80142-5.
Jump up ^ Mulliken, R. S. (1934). "A New Electroaffinity Scale; Together with Data on Valence States and on Valence Ionization Potentials and Electron Affinities". Journal of Chemical Physics. 2 (11): 782–793. Bibcode:1934JChPh...2..782M. doi:10.1063/1.1749394.
Jump up ^ Mulliken, R. S. (1935). "Electronic Structures of Molecules XI. Electroaffinity, Molecular Orbitals and Dipole Moments". J. Chem. Phys. 3 (9): 573–585. Bibcode:1935JChPh...3..573M. doi:10.1063/1.1749731.
Jump up ^ Pearson, R. G. (1985). "Absolute electronegativity and absolute hardness of Lewis acids and bases". J. Am. Chem. Soc. 107 (24): 6801–6806. doi:10.1021/ja00310a009.
Jump up ^ Huheey, J. E. (1978). Inorganic Chemistry (2nd Edn.). New York: Harper & Row. p. 167.
Jump up ^ This second relation has been recalculated using the best values of the first ionization energies and electron affinities available in 2006.
Jump up ^ Allred, A. L.; Rochow, E. G. (1958). "A scale of electronegativity based on electrostatic force". Journal of Inorganic and Nuclear Chemistry. 5 (4): 264–268. doi:10.1016/0022-1902(58)80003-2.
Jump up ^ Housecroft C.E. and Sharpe A.G. Inorganic Chemistry (2nd ed., Pearson Prentice-Hall 2005) p.38
Jump up ^ Sanderson, R. T. (1983). "Electronegativity and bond energy". Journal of the American Chemical Society. 105 (8): 2259–2261. doi:10.1021/ja00346a026.
Jump up ^ Sanderson, R. T. (1983). Polar Covalence. New York: Academic Press. ISBN 978-0-12-618080-0.
Jump up ^ Zefirov, N. S.; Kirpichenok, M. A.; Izmailov, F. F.; Trofimov, M. I. (1987). "Calculation schemes for atomic electronegativities in molecular graphs within the framework of Sanderson principle". Doklady Akademii Nauk SSSR. 296: 883–887.
Jump up ^ Trofimov, M. I.; Smolenskii, E. A. (2005). "Application of the electronegativity indices of organic molecules to tasks of chemical informatics". Russian Chemical Bulletin. 54 (9): 2235–2246. doi:10.1007/s11172-006-0105-6.
Jump up ^ SW Rick; SJ Stuart (2002). "Electronegativity equalization models". In Kenny B. Lipkowitz; Donald B. Boyd. Reviews in computational chemistry. Wiley. p. 106. ISBN 978-0-471-21576-9.
Jump up ^ Robert G. Parr; Weitao Yang (1994). Density-functional theory of atoms and molecules. Oxford University Press. p. 91. ISBN 978-0-19-509276-9.
Jump up ^ Allen, Leland C. (1989). "Electronegativity is the average one-electron energy of the valence-shell electrons in ground-state free atoms". Journal of the American Chemical Society. 111 (25): 9003–9014. doi:10.1021/ja00207a003.
Jump up ^ Mann, Joseph B.; Meek, Terry L.; Allen, Leland C. (2000). "Configuration Energies of the Main Group Elements". Journal of the American Chemical Society. 122 (12): 2780–2783. doi:10.1021/ja992866e.
Jump up ^ Mann, Joseph B.; Meek, Terry L.; Knight, Eugene T.; Capitani, Joseph F.; Allen, Leland C. (2000). "Configuration energies of the d-block elements". Journal of the American Chemical Society. 122 (21): 5132–5137. doi:10.1021/ja9928677.
^ Jump up to: a b The widely quoted Pauling electronegativity of 0.7 for francium is an extrapolated value of uncertain provenance. The Allen electronegativity of caesium is 0.66.
Jump up ^ See, e.g., Bellamy, L. J. (1958). The Infra-Red Spectra of Complex Molecules. New York: Wiley. p. 392. ISBN 978-0-412-13850-8.
Jump up ^ Spieseke, H.; Schneider, W. G. (1961). "Effect of Electronegativity and Magnetic Anisotropy of Substituents on C13 and H1 Chemical Shifts in CH3X and CH3CH2X Compounds". Journal of Chemical Physics. 35 (2): 722. Bibcode:1961JChPh..35..722S. doi:10.1063/1.1731992.
Jump up ^ Clasen, C. A.; Good, M. L. (1970). "Interpretation of the Moessbauer spectra of mixed-hexahalo complexes of tin(IV)". Inorganic Chemistry. 9 (4): 817–820. doi:10.1021/ic50086a025.
Jump up ^ Fleming, Ian (2009). Molecular orbitals and organic chemical reactions (Student ed.). Chichester, West Sussex, U.K.: Wiley. ISBN 978-0-4707-4660-8. OCLC 424555669.
Jump up ^ "Electropositivity," Microsoft Encarta Online Encyclopedia 2009. (Archived 2009-10-31).
Bibliography[edit]
Jolly, William L. (1991). Modern Inorganic Chemistry (2nd ed.). New York: McGraw-Hill. pp. 71–76. ISBN 978-0-07-112651-9.
Mullay, J. (1987). Estimation of atomic and group electronegativities. Structure and Bonding. 66. pp. 1–25. doi:10.1007/BFb0029834. ISBN 978-3-540-17740-1.
External links[edit]
Wikimedia Commons has media related to Electronegativity.
WebElements, lists values of electronegativities by a number of different methods of calculation
Video explaining electronegativity
Electronegativity Chart, a summary listing of each elements electronegativity along with an interactive periodic table
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