A Study of White and Black Phosphorus

 

My interest in phosphorus was aroused by several recent reports of the electronic properties of black phosphorus , in particular the research by Xia , Wang , and Jia (2014) (the references are presented at the end of the text , below . Underlined blue hyperlinks can be clicked when online to retrieve the article cited . The requested document will open in a new window) . I was intrigued by the lamellar morphology of the black allotrope , resembling that of graphite . As is well known , graphite forms many intercalation compounds (GICs) with a wide range of electron donors (eg. Alkali metals) and electron acceptors (electrophiles) .

One such GIC , the graphiteantimony pentafluoride system , has long been of particular interest to me . GraphiteSbF5 compounds were first prepared in 1976 (Lalancette and Lafontaine) ; a year later Vogel discovered that graphite with 75% by weight of intercalated SbF5 had the astonishingly high electrical conductivity of ~ 1,000,000 ohm-1-cm-1 . This far surpasses even that of silver (630,120 ohm-1-cm-1) , which has the highest electrical conductivity of all the metallurgical metals . GraphiteSbF5 thus holds the world record for ambient electrical conductivity , and it remains an extraordinary metallic solid and a benchmark GIC . I wondered if analogous intercalated compounds with similarly high electrical conductivities could be formed by the insertion of suitable electrophiles into the host structure of black phosphorus .

Apparently the same idea occurred to Japanese researchers over thirty years ago :

Intercalation of AsF5 to black phosphorus was tried and several-fold increase in the electrical conductivity was observed (Maruyama and co-workers , 1981, from the abstract of their research paper) .

They also studied the intercalation of lithium , cesium , iodine , ammonia , and pyridine into black phosphorus , as reported in a later research paper in 1986 .

One of the major impediments to investigating the chemistry and physics of black phosphorus is its relative scarcity as a chemical reagent . It was first synthesized from the white allotrope in 1914 by P.W. Bridgman , one of the early pioneers in high pressure chemistry (Nobel Prize for Physics , 1946) . When white phosphorus is heated at 200 C under about 12,000 kg/cm2 (~ 1200 MPa , 1.2 GPa , 12,000 atmospheres) pressure for about 30 minutes it transforms almost quantitatively into the black form , with traces of adhering red phosphorus on the container walls and with small specks of unconverted white phosphorus in the interior . Bridgman claimed , “About 50 g of black phosphorus may be formed at a time” (p. 1348) . In later decades several techniques were devised for preparing black P from white or red P at ambient pressure . For example , crystallization of black P from molten bismuth (Maruyama and co-workers , a later research paper in 1986) ; using mercury as a catalyst in its formation ; and most recently , rearranging red P to black P with SnI4 and AuSn mineralization catalysts (Nilges , Kersting , and Pfeifer , 2008) have all been successful . Despite these research efforts , black P remains non-commercial and inaccessible to all but the few experienced chemists able to synthesize it in-house .

A small ampoule containing several pieces of shiny black phosphorus (somewhat resembling anthracite coal) is shown in a YouTube video (MP4 , 21 seconds runtime , 1563 KB) .

I thus became interested in studying the electronic structures of both white and black phosphorus with the objective of devising a possible new synthesis of the latter from the former allotrope , and to explore how both forms might be converted into new metallic solids with high electrical conductivities .

 

The Electronic Structure of White Phosphorus , P4

 

Long before black phosphorus (in 1914) there was white phosphorus , first isolated around 1669 by the German alchemist Hennig Brand . White phosphorus is highly reactive , and is pyrophoric to a certain extent ; it burns in air , emitting a brilliant light and a dense , white smoke of P4O10 .

An impressive YouTube video of the combustion of a pea-sized chunk of white phosphorus in oxygen has been prepared by chemistry demonstrators at the University of Nottingham , UK (MP4 , 4:15 runtime , 16,399 KB) . See also this related YouTube video : MP4 , 6:28 runtime , 29,452 KB .

White phosphorus slowly oxidizes at room temperature , radiating a pale phosphorescent light ; hence its name . Pure white P rapidly turns a pale yellow colour when exposed to light , even when stored under water in a tightly closed bottle ; this is why the white allotrope is often called yellow phosphorus. The term “white phosphorus” is used exclusively in this web page . It has the appearance of a translucent , light yellow to orange wax . White P melts at 44 C and boils without decomposition at 280.5 C under ambient pressure . P4 vapour begins to dissociate into diatomic P2 molecules (with PP triple bonds) at around 800 C .

White P is a molecular solid at STP , consisting of tetrahedral P4 molecules packed into the crystal lattice . Maxwell , Hendricks , and Mosley (1935) discovered the unusual trigonal pyramid structure of the P4 molecules by studying electron diffraction patterns of phosphorus vapour :

“The combined data show that the molecule has the form of a regular tetrahedron with a P–P distance of 2.21 0.02 ” (p. 708) .

The first definitive determination of the crystal structure of solid white phosphorus was made by Corbridge and Lowe (1952) using an X-ray diffraction technique :

“The X-ray photographs indicated a body-centered cubic lattice with a = 18.51 0.03 ” (p. 629) .

During the mid-1900s theoretical chemists published many versions of the electronic structure of P4 . I think the solution to this long-standing puzzle may actually be quite simple , but before discussing it I'll briefly review two earlier models of chemical bonding in P4 that are fairly representative of the many theories that have been proposed for it .

I'll call the first P4 electronic structure to be considered Pauling's model, as its authors were Pauling and Simonetta (1952) . The 60 PPP bond angles in P4 required some ingenuity in rationalizing :

Pauling and Simonetta proposed after extensive bond energy computations that the phosphorus atoms in the P4 molecule had essentially 3p hybridization , with the 3s2 orbital and electrons remaining native (unhybridized , and therefore having an approximately spherical symmetry) . They calculated that the best fit with the known thermochemical properties of P4 was an spd hybrid orbital on P , having 0.4 % 3s , 2.2% 3d , and 97.4 % 3p character .

Kimball (1940) had theorized that an spd hybrid orbital would have an unsymmetrical planar geometry , so personally I would tend to discount the 3s and especially 3d contributions to the hybrid orbital . He had proposed the trigonal pyramid p3 hybrid orbital , which I think is most suitable for this Valence Bond scenario . Phosphorus is a pre-Transition metal p-block element and has no d orbitals at all ; and the 3d orbitals are at the 4s,p energy level (GIF image , 16 KB) , making them inaccessible for hybridization with 3s,p native orbitals . Apparently an earlier theorist (Moffitt , 1948) had proposed the “pure” p3 hybrid orbital (with no 3s and 3d contributions) for the P4 covalent bonds ; Pauling and Simonetta's model is really a reworking , or refinement , of Moffitt's earlier approach .

Ignoring any small (and to me , dubious) 3s and 3d contributions to the trigonal p3 hybrid orbital , Pauling's model of the electronic structure of the P4 molecule is sketched as follows :

The common perception of the P4 molecule is that its high reactivity is caused by the considerable PP bond strain imposed by the narrow 60 PPP bond angles . Quite to the contrary , Pauling and Simonetta began their dissertation by stating ,

“An interesting problem in chemical bond theory is offered by the relative stability of the P4 molecule.........The strain associated with these small bond angles might be expected to be rather large....... In fact , however , the strain energy is smaller , the difference in enthalpy of ordinary white phosphorus (PIII) and the stable form , black phosphorus , being 10.3 kcal mole-1” (p. 29 , my emphasis in red) .

The remarkable thermal stability of P4 as noted above , its molecules remain intact up to ~ 800 C – is physical proof of the actual strength of the PP bonds , which should not be confused with their high chemical reactivity . For example , the organophosphines and phosphites , with unstrained PC and PO bonds respectively , are very sensitive to oxygen ; indeed the alkyl phosphines are notoriously pyrophoric , and must be handled in an inert atmosphere under anerobic conditions . This merely indicates the facile combination of P and O atoms , and of the considerable PO bond strength .

In the above sketch the assumption was made that the PPP bond angles radiating from the apex of the trigonal pyramid were 60 each . Such tight bond angles would permit a direct head-to-head” overlap of the sigma lobes of the p3 hybrid orbital . Pauling and Simonetta , though , calculated their spd pyramid's PPP bond angles as 89 55' , essentially 90 (p. 30) . This suggests that the overlapping of the sigma lobes on adjacent P atoms would have to be bent or curved : these would be the so-called banana bonds”, as postulated for cyclopropane , for example .

Such PP banana bonds feature prominently in a second theory of the chemical bonding in P4 by Hart , Robin , and Kuebler (1965) . Their extensive calculations on the PP bond energetics , supported by a detailed infrared spectral analysis of P4 , led them to propose a model of it somewhat similar to that of Pauling and Simonetta , but with no hybridization of the 3s and 3p orbitals . Their picture of P4 is that of a cubic structure , with P atoms and banana bond overlap zones alternating at the eight cube corners :

Note carefully that only the 3p3 orbitals and electrons are involved in this bonding scheme ; the 3s2 orbital and electrons remain unaffected . Another way of visualizing the overlapping of the 3px,y.z native orbitals in the molecule is shown in this sketch :

The positive symmetry (white) lobes overlap to form the sigma covalent PP bonds ; the negative symmetry (gray) lobes presumably don't overlap at all in the P4 crystalline solid (if they did , they would produce only destabilizing PP antibonds) . Hart and co-workers state (in their article abstract) ,

“Our calculation predicts that strong pi bonds are present in the molecule , and their presence leads to a resonance which , in turn , vitiates [invalidates] the concepts of “bend bonds” and “strain energy” in P4”.

Pi bonds are produced by the side-by-side combination of two native p orbitals . In the model sketched above , however , only end-to-end pp sigma bonds would be present in the molecule .

The HartRobinKuebler picture of P4 is thus of an overall cubic structure (of combined atoms and electric fields) , and a prediction of weak intermolecular bonding (caused by the negative symmetry lobes) . As mentioned above , P4 molecules have a body-centered cubic packing arrangement in the white phosphorus crystalline solid , and white P has a fairly low melting point of 44 C . These physical properties seem to support , or at least be consistent with the theoretical electronic structure of the molecule proposed by Hart , Robin , and Kuebler .

 

The Adamantane Model of the P4 Molecule

 

Consideration of the two P4 bonding models outlined above made me wonder if fully hybridized phosphorus atoms could be involved in the covalent PP bonds ; and if so , how ? I must admit to being both dissatisfied and suspicious of any electronic model in which the 3s2 orbital and electrons remain in a native”, unhybridized state . The obvious fully hybridized orbital for the phosphorus atoms would be tetrahedral sp3, but the PPP bond angles should ideally be 109 28' for such hybridization . How can the huge discrepancy in the tetrahedral angle and the actual 60 PPP bond angles in P4 be reconciled ?

Using my Framework Molecular Model kit (Prentice-Hall , Englewood Cliffs , NJ) to help in visualizing the sigma lobes' overlap , I built a remarkably compact , simple , beautiful structure . Both excited and delighted I checked in my Aldrich Catalog Handbook of Fine Chemicals to confirm its identity : it was indeed the adamantane molecule !

The adamantane model of the covalent bonding in P4 is outlined in the following sketch :

Adamantane molecules pack in a face-centered cubic (fcc , also called cubic close-packed , ccp) crystal structure in the solid state . This very compact packing combined with undoubtedly strong intermolecular hydrogen bonds result in the unusually high melting point (270 C) of adamantane . As mentioned above , crystalline P4 also has a cubic (bcc) molecular packing , but a rather low melting point (44 C) . Obviously there is no hydrogen bonding between the P4 molecules , which probably have just relatively weak Van der Waals intermolecular bonding .

The Wikipedia article comments , It [adamantane] is unique in that it is both rigid and virtually stress-free. Its CCC bond angles are all at , or very close to the tetrahedral ideal of 109. The proposed adamantane model for chemical bonding in P4 can thus rationalize the actual low PP bond strain in it , as noted by Pauling and Simonetta , resulting in its recognized thermal stability . At the same time we can readily understand why it is so chemically reactive , just as the organophosphines and phosphites are .

In the following section we'll see how it might be possible to experimentally distinguish between the Pauling , Hart , and adamantane models of covalent bonding in the white phosphorus P4 molecules .

 

Reaction of White Phosphorus with One-Electron Oxidizers

 

Why is the electronic structure of P4 is so important ? The answer is , white phosphorus might be converted into a phosphorus synthetic metal and possibly even a high temperature superconductor if the Pauling and Hart models are accurate . However , if the adamantane model is applicable (as I think it probably is) , no such metallic solid could be synthesized from it . Also , the tetrahedral sp3 hybridization will carry over into the phosphorus atoms in the black allotrope . Intercalation of various sorts of reagents in black P will result only in a modest enhancement of its electrical conductivity . A study of the reaction of P4 with various one-electron oxidizers might help to distinguish between these models .

Nitrosonium salts , NO+ X, are stable , crystalline solids , whose nitrosonium cation is a powerful one-electron oxidizer :

NO+ + e-  -------------->   NO (g)  ;  E0red  =  1.45 V .

The accompanying X anions in the NO+ X salts are chemically unreactive and non-nucleophilic .

The nitrosonium one-electron oxidation of a white phosphorus molecule , P4** , should convert it into a phosphinium radical cation , P4*+ , and release nitric oxide gas as a by-product :

P4** + NO+ X ---------> P4*+ [X] + NO (g) ; X = BF4 , ClO4 , PF6 , AsF6 , SbF6.

The equation immediately above would be applicable to the various allotropes of phosphorus as well as to organophosphines and phosphites , all of which have phosphous atoms with a lone pair of electrons in either native 3s orbitals or (most likely) sigma lobes of tetrahedral sp3 hybrid orbitals .

Nitrosonium salts are commercially available (Alfa-Aesar , Aldrich) at a moderate cost . They are slightly soluble in acetonitrile . White phosphorus is very soluble in carbon disulfide , and is somewhat soluble in benzene and ethyl ether :

White phosphorus might be sufficiently soluble in acetonitrile to carry out the one-electron oxidation with a nitrosonium salt in a homogeneous solution . A medium polarity solvent such as tetrahydrofuran (THF) might also be investigated as a P4–nitrosonium salt co-solvent . Holleman and Wiberg mention in their textbook Inorganic Chemistry (34th edition , 1st English edition) ,

“......... although it [P4] is easily soluble in carbon disulfide or tetrahydrofuran (p. 680) .

Nitrosonium cation rapidly hydrolyses and decomposes on contact with water , so any solvent used in the reaction should be carefully dried beforehand .

One-electron oxidation of the P4 should occur and might even be quite vigorous . I suspect that in practice the phosphinium radical cation P4*+ would form , but it would promptly unzip and undergo a cationic polymerization to red or black phosphorus . However , let's assume that P4*+ is stable under the reaction conditions used for its synthesis . The chemical nature of the P4*+ X salt would critically depend on the electronic nature of the phosphorus 3s2 orbitals and electrons .

In all three P4 models the 3s2 electrons , whether native or hybridized , would be readily susceptible to one-electron oxidation . However , native 3s orbitals , which are spatially voluminous and have an omnidirectional positive symmetry , could overlap throughout the lattice in the solid P4*+ X salt to form a crystal-wide polymerized molecular orbital, which I have referred to throughout my Chemexplore writings as a crystal orbital (abbreviated XO) . In pure P4 the XO would be 100% filled with 3s2 electrons , and accordingly white phosphorus is an insulator . In P4*+ X the XO would be 50% filled with 3s1 electrons . Therefore , in the Pauling and Hart models P4*+ X is predicted to be a phosphorus synthetic metal and an electrical conductor .

Let's go one step further and consider the nature of the P4 dication , (P4)2+ (X)2 . Two of the eight 3s2 electrons have been removed from the four-atom XO , leaving six per P4 molecule . Would these six electrons form an electronically stable aromatic sextet (as in benzene and other aromatic organic molecules , for example) ?

Would these stable aromatic sextets be able to move through the (P4)2+ (X)2 lattice under an applied potential difference , acting as the electrical charge carriers in the solid ? Could the sextets thus be a new form of Cooper pair , making (P4)2+ (X)2 a superconductor ? Would the sextets be stable even at room temperature , making the dication salt an ambient superconductor ? Benzene's electron sextets whirl endlessly around their rings ; they are unable to escape the 2p pi MOs in which they are eternally trapped . But the (P4)2+ sextets would be in a 3s sigma XO which fills the intermolecular voids of the crystalline salt . That's their highway through the lattice , the conduction (and maybe superconduction) band for the now free , mobile 3s valence electrons .

A simple MO diagram of the electronic structure of P4 is presented in the web page , “Introduction to Inorganic Chemistry , Molecular Orbital Theory”. The author has also discussed the existence and electronic structure of the (P4)2+ dication . However , its most likely molecular structure was thought to be a square ring , rather than the intact tetrahedron sketched above . This square ring (P4)2+ dication is also possibly aromatic , with (4n + 2) p electrons resonating in the ring . It is strongly reminiscent of the disulfur dinitride molecule , S2N2 , discussed in another Chemexplore web page .

It's fun to speculate about such marvels , and what a better place to do so than on a web page from a small , obscure chemistry website on the Internet . Of course , the adamantane model of P4 is undoubtedly the correct one , and in this case no 3s sigma XO can be created in P4*+ X, even assuming it can be successfully synthesized . The 3s lone pairs are in highly directional stereochemical sigma lobes of the tetrahedral hybrid orbital in this picture , not in omnidirectional , spherical 3s native orbitals . Such stereochemical lone pairs can't overlap continuously through the lattice like the native orbitals can (and do , in the metallurgical metals) .

They can however be partially oxidized by one-electron oxidizers to form radical cations . The Wurster Blue organic salts , which have aminium radical cations , are excellent examples of the one-electron oxidation of the nitrogen lone pairs in amines :

Many new Wurster Blue compounds with extensive p electron delocalization were proposed in an earlier Chemexplore web page . It was hoped that such materials might be metallic solids and electrical conductors to a certain extent .

Another interesting example of such an aminium radical cation is tris”, the mercifully short abbreviation for tris(4-bromophenyl)aminium hexachloroantimonate , which is a stable , crystalline , dark blue salt :

The Wurster Blue nitrogen compounds shown above all have an extensive pi orbital one-electron resonance which both stabilizes them and results in their intense colours (dark blue and black) .

One-electron oxidizers can also partially oxidize pi bonds in olefins , thereby creating carbocations which can in some cases be isolated as stable salts with inert , non-nucleophilic anions (eg. BF4 , ClO4 , PF6 , AsF6 , SbF6 ) . Tris has been used to catalyse Diels-Alder cyclization reactions in cases where unactivated (ie. relatively non-electrophilic) dienophiles are used . Presumably tris extracts an electron from the olefin's pi bond and thereby makes it a strongly electrophilic one-electron p bond . The dienophile can now successfully cyclize with the diene . This mechanism suggests that tris might similarly react with P4 to form the radical cation salt P4*+ SbF6 + tris(4-bromophenyl)amine . Tris can be readily synthesized , and is commercially available , eg. Aldrich .

The phosphinium radical cation salt P4*+ X might be prepared at a low temperature , eg. in a dry ice–acetone cooling bath , but lacking any one-electron pi resonance like the Wurster Blues it would probably be unstable when warmed to room temperature and would likely polymerize into red or black phosphorus . Such a cationic polymerization of P4 might actually be a synthetically useful method of converting white phosphorus to the red or black forms under ambient pressure .

 

Polymerization of P4 into Black Phosphorus

 

As mentioned above , there are several preparative routes to black phosphorus from both the white and red allotropes . Despite these successes black P remains a costly laboratory curiosity . An efficient , economical process for manufacturing black P as an industrial commodity from its white precursor would be desireable .

White P is produced on a multi-ton scale by the reduction of phosphate rock (calcium phosphate) with carbon (metallurgical grade coke , from coal) and silica in an electric furnace at 14001500 C (the Readman Process , 1890) . P4 vapour is distilled from the reaction mixture and is condensed in a cooled receiver . The calcium silicate slag and CO gas by-products are recovered and used in Portland cement and for heating purposes , respectively .

P4 tetramer might be converted into the black phosphorus polymer using well-known methods of anionic , cationic , and neutral free radical polymerization developed for all the common organic polymers . Bridgman (1916) investigated several catalytic methods to convert white P into black P at lower pressures and temperatures than he had used in earlier experiments in 1914 . Sodium was tried as such a catalyst ; as an electron donor it could be considered an anionic catalyst . However , violet rather than black phosphorus was isolated :

“The violet phosphorus was made by heating white phosphorus under pressure in the presence of sodium . I discovered quite by accident that metallic sodium is a very efficient catalyzer of the transition from white to violet . The white phosphorus , with a trace of sodium , was subjected to a pressure of 4000 kg at room temperature , and then heated at constant volume to 200 ” (p. 610) .

Cationic polymerization was alluded to above . Various Lewis acids such as BF3 , AlCl3 , FeCl3 , ZnCl2 , and SnCl4 could be tried as catalysts with P4 in a suitable solvent (THF might be the best one) . Possibly only a few drops of the catalyst solution added to the white phosphorus solution , mechanically stirred under nitrogen or argon , would be sufficient to initiate the cationic polymerization of the P4 .

Antimony pentafluoride mentioned at the top of this page in connection with its graphite intercalation compound might be a very powerful cationic polymerization catalyst in this context . It is a strong Lewis acid , a medium strength oxidizer [E0red = 0.671 V for Sb(V) -----> Sb(III)] , and a notable one-electron oxidizer , being used in the formation of carbocations via hydride extraction from hydrocarbon substrates . The Atomistry web page reviewing the chemistry of SbF5 mentions that ........“Antimony pentafluoride reacts with phosphorus forming a yellow vapour......”.

Few organic solvents are compatible with antimony pentafluoride . The Merck Index (8th edition , 1968 , p. 90) advises , “[SbF5] Forms solids with sulfur chloride , carbon disulfide , benzene , toluene , petroleum ether (resin formation) , ether , alcohol , acetone , ethyl acetate . Glacial acetic acid gives a clear solution”. The Atomistry web page continues ,

“Many carbonaceous materials are attacked by the pentafluoride , including filter-paper , cork , wood , india-rubber , benzene , ether , alcohol , acetone , glacial acetic acid , ethyl acetate , carbon disulphide , light petroleum and chloroform . With chloroform an easily liquefiable gas (probably CCl3F) is formed”.

Bacon , Dean , and Gillespie (1970) used Freon 114 (“cryofluorane”, ClF2C–CClF2 , b.p. 4 C) as one of several inert solvents in their study of the 19F NMR spectrum of SbF5 and related complex Sb(V) fluorides . They mention , by the way ,

“Structure 2 should give rise to three chemically shifted resonances with the relative areas observed , and it is also in accord with the extremely high viscosity of SbF5 , which suggests a polymer of considerable length” (p. 3414) ; my emphasis in red .

Freon 113 (Cl2FC–CClF2 , b.p. 48 C) might also be a satisfactory inert solvent for both SbF5 and P4 , but with a higher boiling point than Freon 114 it would be more convenient to use in actual practice . Of course , all the Freon CFCs are now politically incorrect because of their destructive effect on the Earth's atmospheric ozone layer , but possibly a small amount of Freon 113 might nevertheless be used in the cationic polymerization experiments , at least where the highly reactive SbF5 is involved .

Two other chlorocarbons might also be satisfactory solvents for the P4–SbF5 polymerization : carbon tetrachloride (b.p. 77 C) and tetrachloroethylene (perchloroethylene , “perc”, a common dry cleaning solvent , b.p. 121 C) . White phosphorus might be only slightly soluble in these latter solvents . The polymerization could be attempted at , say , 50 C , with a vigorous mechanical stirring of the suspended globules of liquid phosphorus (m.p. 44 C) in the solvent . Several drops , or even cc , of SbF5 solution would be added to the stirred mixture to initiate a reaction . Polymerization of the white P to black P not the red or violet allotropes would , of course , be the desired outcome of such a reaction .

In his research with white phosphorus , Bridgman (1916) observed ,

“After pressure has been raised to something over 12,000 kg/cm2 at 200 C the black phosphorus is never produced instantaneously . There is always a period of preparation extending over from 10 to 30 minutes , during which pressure drops slowly , increasing gradually in speed , until it reaches a critical point at which a cataclysmic transformation of the entire mass to black takes place ......... This shows that the change from white to black was practically complete in the first rush .” (p. 611) .

He continues :

“The curve of Fig.1 [above] throws considerable light on the manner of the transition . Direct change from white to black phosphorus does not take place . Some sort of a preliminary change , involving a decrease of volume , must occur before the transition can run . This change takes place at an accelerated pace at 200 C and 12000 kg/cm2 ; it will not take place with practical velocity at much lower pressures or temperatures . When the preliminary change has reached a certain critical stage , at which the change in density necessary to carry white to black is surely not more than 5% accomplished , the entire edifice becomes unstable and topples over into black phosphorus . It is impossible to say just what this preliminary stage consists of . It is most probable , however , that it is some change uniformly distributed throughout the volume . That this preliminary change is necessary is also suggested by an experiment described in the previous paper ; white phosphorus inoculated with black does not transform to black much more easily than when not inoculated” (p. 612) .

Bridgman tried several experiments using red , violet , and black phosphorus as potential catalysts with the white precursor , but no appreciable effect was observed . Only one condition was essential in the white-to-black conversion : a minimum amount of pressure , which turned out to be ~ 12,000 kg/cm2 . Bridgman's “preliminary stage” might have been the formation of a certain concentration throughout the phosphorus of neutral free radicals [*] P42* , from the homolysis of a single P–P bond on the P4 molecule . The critical effect of the pressure was to compress the P4 molecules to the point where the tetrahedrons popped open and flattened out into the P42* free radicals .

Once again I deployed my trusty Framework Molecular Model kit and experimented with various possible structures for the hypothetical P42* free radical . The most realistic of these had two fused hexagonal rings in the boat configuration , which produced a fairly flat molecule . I placed the sterically bulky lone pairs in the equatorial positions , and the less voluminous free radicals in the axial positions on the phosphorus atoms :

A sketch , based on this Framework Model , is presented below :

These P42* free radicals must be electrophilic to a certain extent , and can attack other P–P bonds to produce yet more free radicals . While slow at first , the P42* concentration in the white P must gradually build to the point where the free radical production becomes exponential . A picturesque analogy might be the multiplication of free neutrons in a fissioning mass of uranium 235 or plutonium 239 to the point of detonation . Production of the black P is similarly slow at first , as Bridgman noted while monitoring the pressure–volume changes during his synthesis procedure . Very little occured during its early and middle stages ; only near the end was the black phosphorus formation almost explosively rapid .

Note that throughout this polymerization process the tetrahedral sp3 hybridization on the phosphorus atoms remains intact and unaltered . The P–P bonding of the tetrahedrons is simply rearranged from the compact adamantane-like P4 molecules in the white P to the two-dimensional corrugated sheets in the black P.

One way of testing this free radical model of the P4 polymerization at ambient pressure would be to add a small quantity of a neutral free radical initiator to the white phosphorus and gently warm the two reagents under an inert atmosphere (nitrogen , argon , carbon dioxide) . The initiator would hopefully take the place of the pressure , creating the P42* neutral free radicals which would polymerize into sheets of black phosphorus .

One such initiator is the well-known azobisisobutyronitrile (AIBN) , which is extensively used in the industrial polymerization of many common monomers (styrene , vinyl chloride , acrylonitrile , etc.) , and as a “blowing agent” for plastics (mixing bubbles of nitrogen into them to make foams) :

Using semi-micro quantities of reagents – only a few grams – the intial experiments could involve neat (pure , no solvent) , liquid white phosphorus in which a catalytic quantity (~ several hundred mg) of AIBN is dissolved . A low boiling co-solvent such as carbon tetrachloride (b.p. 77 C) , or higher boiling ones such a o-dichlorobenzene (b.p. 180 C) or diphenyl ether (b.p. 259 C) , could be used to control any appreciable exotherm during the polymerization .

Note that AIBN is the best known of a large family of commercially available azo initiators , many of which are widely used in polymer technology . Most of them are lipophilic (oil-soluble) in nature , (DuPont , Wako) , but water-soluble azo initiators are also offered (DuPont , Wako) . That suggests another interesting variation of the white P-to-black P transformation : suspension polymerization and emulsion polymerization in water , under an inert atmosphere .

Suspension polymerization might be carried out by the rapid mechanical stirring of a warmed (50–80 C) mixture of liquid white phosphorus in water , to which a suitable quantity of a water-soluble azo initiator has been added . Stirring would be fast enough to disperse the phosphorus into very small , finely divided globules (like the preparation of “sodium sand” – well dispersed liquid sodium droplets – in refluxing toluene) . Polymerization of these tiny globules of white phosphorus suspended in the hot water might produce a fine-grained dispersion of black phosphorus in the reaction flask .

Emulsion polymerization would take this process one step further by suspending the white phosphorus in the water as a milky , white , colloidal emulsion , stabilized by a suitable surface active agent (surfactant , detergent) . Literally thousands of prospective surfactants are commercially available for investigation . To start with I would suggest a simple nonionic surfactant such a one of the Brij series , for example Brij 30 , which is a polyethoxylated lauryl alcohol having the formula C12H25(OCH2CH2)4OH . Brij surfactants are readily available , eg. from Aldrich or from the manufacturer (PDF , 721 KB) .

When dissolved in water , surfactant molecules typically form spherical clusters (micelles) in which the lipophilic (non-polar , hydrocarbon) ends are associated together in the center of the cluster . The hydrophilic (polar , oxygenated) ends extend outward from the cluster , and are hydrogen-bonded to the water molecules . In the Brij–white phosphorus scenario the polar (OCH2CH2)4OH part of the surfactant molecules would dissolve in the water phase , while the non-polar C12H25 (lauryl , dodecyl) parts would hopefully dissolve the non-polar white phosphorus globules , which would be sequestered in the interiors of the micelles . Emulsion polymerization of white phosphorus might produce a microcrystalline grade of black phosphorus suitable for electronic applications .

Suggestion : a non-polar lipophilic azo initiator , which would co-dissolve with the P4 globules in the micelle centers , should be used . Emulsion polymerization is carried out industrially on a vast scale world-wide in the manufacture of synthetic latex (elastomeric polymers) , for example of those used in water-based paints . Polymerization of P4 by this technique might be based on similar methods described in the patent literature for the preparation of various latexes by emulsion polymerization .

Now here's an unpleasant possibility : suppose the azo initiator fails to catalyze the polymerization of the white phosphorus in the emulsion . What to do ? Physically , the phosphorus might be safely recovered by steam distillation , which is sometimes used to refine impure samples of white P .

Chemically , an alternate disposal method would involve adding sufficient hot sodium hydroxide solution to convert the unreacted P4 into sodium hypophosphite :

[Hypophosphorus] acid is prepared industrially via a two step process . Hypophosphite salts of the alkali and alkaline earth metals result from treatment of white phosphorus with hot aqueous solution of the appropriate hydroxide , e.g. Ca(OH)2 :

P4 + 3 OH + 3 H2O -----------> 3 H2PO2 + PH3 .

The free acid may be prepared by the action of a strong acid on these hypophosphite salts :

H2PO2 + H+ -----------> H3PO2 .

Alternatively, H3PO2 arises by the oxidation of phosphine with iodine in water :

PH3 + 2 I2 + 2 H2O -----------> H3PO2 + 4I + 4H+ ”.

from the Wikipedia article , Hypophosphorus Acid .

Following the sodium hydroxide treatment sodium hypochlorite solution (Javelle water) would be added to oxidize the hypophosphite a strong reducing agent and the phosphine to orthophosphate . Addition of aqueous CaCl2 then precipitates calcium phosphate , which can be filtered from solution and disposed of in a solid waste receptacle .

A second , simpler way to dispose of unreacted white P suspension or emulsion might be to pass a stream of chlorine gas into the mixture , saturating the water phase , in effect creating hypochlorous acid in situ and chlorinating the P4 . The resulting PCl3 would be instantly hydrolyzed to phosphorous acid (H3PO3) , which would then be oxidized by the HOCl to the relatively harmless H3PO4 . The chlorinated mixture , now quite acidic , is neutralized by K2CO3 . The end-product salts K2HPO4 and KCl could be safely flushed down the laboratory drain (or maybe used as plant fertilizer on someone's vegetable garden !) .

 

Doping Black Phosphorus with Electrophiles

 

Unlike the insulating white , red , and violet allotropes , black phosphorus is a semiconductor . P.W. Bridgman (1914) investigated the electrical properties of his newly discovered material , and determined its resistivity as 0.711 ohm-cm (conductivity = 1.406 ohm-1-cm-1) at 0 C . Black P clearly had a direct electrical conductivity–temperature relationship :

Keyes (1953) measured the resistivity of black P over a wide range temperature range and found its electrical behaviour similar to Bridgman's material :

I flipped Keyes' original Fig. 1 upside-down and back-to-front to show in a simple manner the electrical conductivity–temperature relationship of black P , which clearly is a direct one . Keyes measured its ambient resistivity as 1.5 ohm-cm (conductivity = 0.67 ohm-1-cm-1, p. 584) . He concluded that black P (at least , the sample he studied) was an intrinsic semiconductor with a band gap of 0.33 eV . These electronic properties are compared with four Family IVA/14 semiconductors in the following Table :

The band gap value of 0.34 eV for black phosphorus was from Maruyama and co-workers (a later research paper in 1986 , p. 1068) .

Black P , while having a lamellar , layered morphology like graphite , unlike it lacks any sort of p bonds that might serve as a nodeless XO (crystal orbital = polymerized molecular orbital = conduction band = metallic bond) . The sp3 tetrahedral phosphorus atoms from the white P tetrahedrons are bonded into two dimensional sheets , which are then corrugated in a crenellated pattern and stacked into layers in the crystalline solid :

My thanks to the author and/or copyright holder of the original image , which I have annotated slightly .

My Framework Molecular Model of black phosphorus shows the stereochemical lone pairs of 3s2 electrons , which protrude into the interlayer spaces of the sheets :

Note that the hexagonal rings of phosphorus atoms in the above model are in the energetically stable chair conformation . The existence of a related structure with similar hexagonal P6 rings , informally named blue phosphorus , has been theorized :

A side view of the Framework Molecular Model of blue phosphorus (below) :

Comparing the models of black and blue P , we see that the lone pairs in black P are smoothed back, thus resulting in a more compact packing of the layers than would be obtained in blue P , with the sterically repulsive lone pairs normal to the planes of the phosphorus atoms . To the best of my knowledge blue phosphorus hasn't actually been synthesized yet (as of August , 2014) .

The origin of the semiconducting behaviour of black phosphorus is probably much the same as that in silicon , germanium , and gray tin (Table of semiconductors above) . The Molecular Orbital theory at least , a simple picture derived from MOT is helpful in visualizing the electronic processes in black phosphorus that make it a semiconductor . The conduction band in it is located in the P–P covalent bonds (s MOs) , and in the corresponding P–P s ABMOs at a higher energy level :

In this picture ambient thermal energy promotes a small population of electrons from the s MOs up into the higher energy s ABMOs ; this is possible because of the relatively small bandgap of ~ 0.34 eV for the MO ---> ABMO transition . In conventional semiconductor theory the promotion of negative electrons into the ABMOs leaves corresponding positively-charged holes in the P–P MOs .

I have always been somewhat uncomfortable – and a little skeptical – of the concept of the positive holes , which is central in semiconductor science and technology . After all , how can a hole , which is empty space , have any sort of charge ? I personally prefer to to consider the positive holes as resonating one-electron bonds in the P–P (and other) MOs . One-electron bonds are a familiar , accepted concept in chemical bonding . Two examples of resonating one-electron pi bonds in organic chemistry are sketched above : the molecules of Wurster Blue perchlorate and of “tris”. Inorganic chemistry also provides numerous examples of resonating one-electron systems , notably those of the Robin-Day Class II and Class IIIB mixed-valent compounds . Promotion of the small thermally-excited electron population from the MOs into the ABMOs simply leaves a correspondingly small population of sigma one-electron P–P bonds . We now have a sort of mixed-valent condition in the MOs , with a blend of ordinary two-electron P**P and one-electron P*P bonds . Since all the s MOs are at an identical energy level , the one-electron bonds can resonate in them throughout the lattice .

Sigma ABMOs are nodal in nature ; their regions of higher electron probability density are periodically disected by regions of near-zero electron density , the nodes :

There are also nodes surrounding the atoms in the sigma MOs of covalent bonds . When a potential difference (voltage) is applied to the ends of a semiconductor crystal , the singlet electrons in the MOs are pulled downfield and begin to drift through the lattice . However , they need a certain amount of energy to tunnel through (or “hop across”) the nodes . This energy must be supplied by thermal energy in the crystal's environment . The greater the thermal energy provided to the crystal , the larger the promoted electron population in the ABMOs and the greater the number of one-electron bonds in the MOs ; and also the greater the number of singlet electrons tunneling through the MO nodes .

Thus , semiconductors with nodal MOs always have a direct electrical conductivity–temperature relationship (as does black phosphorus , which was quickly discovered by Bridgman and later confirmed by Keyes) . On the other hand , the metallurgical metals all have s,p conduction bands with nodeless XOs . Their electrical conductivities are mainly governed by the backscattering of their free electrons as they drift through the crystal lattice , which increases with increasing temperature and results in a decreased conductivity . As a result the True Metals (as I call them , GIF image , 41 KB) always have an inverse electrical conductivity–temperature relationship .

Doping of graphite with both electron donors (reducing agents such as K , Rb , and Ca) and with electron acceptors (electrophiles such as AsF5 and SbF5) dramatically increases its electrical conductivity many times that of the virgin , undoped substrate (which is ~ 25,000 ohm-1-cm-1 at room temperature) . All of these dopants seem to function in the GICs by adding or removing electrons from the 2p pi XO , which is the metallic bond in graphite . Is this GIC methodology transferrable to black phosphorus ?

As mentioned near the top of the web page , this question apparently has been considered by Japanese researchers (Maruyama and co-workers , 1981 , a later research paper in 1986) , who studied the intercalation in single crystals of black phosphorus of AsF5 , Cs , Li , iodine , pyridine , and ammonia . They claimed in all cases to have observed significant increases in the electrical conductivity of the resulting adducts :

“About 20% decreases in the resistances were observed in these cases [of iodine , pyridine , and ammonia] (a later research paper in 1986 , p. 1071) .

Any sort of intercalation of a reagent into a substrate should be designed to affect the latter's metallic bond (conduction band) in a predictable manner , based on its perceived electronic structure . That is , a satisfactory electronic structure must be understood first , then the doping reagent is selected to interact with that structure in the desired manner . The electronic structure of the phosphorus atoms in black P is quite simple : they are sp3 tetrahedral , with three P–P covalent bonds and a stereochemical , highly directional lone pair of electrons per P atom . Unlike graphite there are no pi bonds in black P , and the metallic bond is in skeletal framework of the P–P sigma MOs .

Electron doping by strong reducers like the Alkali metals and Ca might conceivably increase the free electron density of the P–P s* ABMOs . However , they will still be nodal in nature , and the doped material will still be a semiconductor . Lewis bases (that can donate their lone pairs of electrons to electrophiles) such as ammonia , pyridine , and other amines are probably futile as electron donors for black P . If anything , the P atoms are themselves nucleophilic , not electrophilic , and the positive symmetry sigma lobes of the donor lone pairs have the wrong shape and symmetry for overlapping with the ABMOs .

Greater success might be achieved by doping black P with various electrophiles . As mentioned , Maruyama and co-workers noted a significant increase in the electrical conductivity of black P doped with AsF5 . As with the Wurster Blue radical cation aminium perchlorate sketched above , the mildly oxidizing As(V) might be creating radical cation P*+ atoms , in effect creating the resonating one-electron P–P bonds chemically hole doping rather than by thermal excitation .

Antimony pentafluoride is the most effective Lewis acid electrophile with graphite (in terms of its electrical conductivity enhancement) discovered to date . The stoichiometry for a quantitative conversion of the P** atoms into P*+ radical cations would be :

2 P** + 3 SbF5 ----------> 2 [P*+ SbF6] + SbF3 .

In practice , though , black P could be doped with varying mole ratios of SbF5 as was discussed for white P . Very likely a non-integral doping level for P**[SbF5]x (x = a mole ratio taken experimentally between 0 and 1) would be required to obtain the optimum electrical conductivity in the partially oxidized black P. The SbF5 could be added neat to the black P in the same way Lalancette and Lafontaine prepared their graphiteSbF5 adducts back in 1976 .

Nitrosonium salts (discussed above as applied to the one-electron oxidation of white P) could also be examined for hole doping black P :

P** + x NO+ X -------- [acetonitrile] ---------> P*+ (X)x + x NO (g) ;

X = BF4 , ClO4 , PF6 , AsF6 , SbF6 ; x = 0 to 1 .

Anhydrous acetonitrile might be a useful solvent in these latter experiments .

Hole-doping of black P by SbF5 and NO+ X should considerably enhance the electrical conductivity of the phosphorus . However , the metallic bond (conduction band) would remain in the nodal P–P sigma MOs , so all of the doped composites would still be semiconductors , with a direct conductivity–temperature relationship . Their conductivities , while enhanced , would remain a small fraction of those of the graphite GICs and of the metallurgical metals .

 

Zerovalent Phosphorus Atoms in Host Lattices

 

The 3s2 3p3 valence electron native state of the P atoms , rather than the hybridized tetrahedral sp3 configuration , might be retained by them if they were inserted into a chemically unreactive host substrate . These valence electrons could form a 3s,p conduction band throughout the host's lattice , making it an excellent phosphorus synthetic metal . The following “thought experiment” will illustrate this concept .

Suppose white P was heated with rhenium trioxide , ReO3 , under some pressure (possibly in an “anvil” type of press , HP–HT) , so that the P4 was dissociated into P0 atoms , which diffuse into the host's lattice . Rhenium trioxide has a simple cubic structure with large central voids :

I have written about ReO3 in several other Chemexplore web pages in connection with superconductivity studies . Rhenium trioxide is a reddish-purple , crystalline solid (JPEG image , 16 KB) , melting at ~ 400 C with decomposition . It is a covalent–metallic solid with an extraordinarily high electrical conductivity , 149,300 ohm-1cm1 , comparable to that of most common metals . ReO3 is considered to be a type of bronze , like the tungsten bronzes for example . As with elementary rhenium and all of its compounds , rhenium trioxide is a costly chemical reagent .

If P0 atoms can be successfully inserted into the central void spaces of ReO3 in an equimolar ratio , a perovskite-like compound , P0ReO3 , would be produced . The tolerance factor “t of this hypothetical material can be calculated from Goldschmidt's equation , assuming the crystal ionic radii , per Shannon and Prewitt , of r = 0.55 for Re(VI) , CN = 6 (octahedral coordination) , and r = 1.21 for the oxygen linking atoms , which have a CN = 2 (linear coordination) . The P0 radius could be 1.11 (half of the P–P bond length in P4 , 2.21 , sketch above) ; or the covalent radius of phosphorus , r = 1.06 ; or its “atomic radius”, said to be r = 1.28 :


For r = 1.11 , t = 0.93 , in the “cubic symmetry range” for perovskites ; for r = 1.06 , t = 0.91 , cubic symmetry ; for r = 1.28 , t = 1.00 , cubic symmetry . These simple calculations suggest that the P0 atoms could fit comfortably into the rhenium trioxide void spaces without disturbing its cubic symmetry or otherwise causing any distortion in its lattice .
A quick glance at the sketch of the ReO3 crystal structure above shows that the P0 atom has about the same radius as the oxygen linking atoms (1.21 ) , and so could readily enter the central voids .

Assuming the hypothetical perovskite P0ReO3 was chemically stable , the P0 valence electrons (3s2 3p3) could form a metallic bond XO in the solid by the continuous overlapping throughout the lattice of the spherical , voluminous 3s orbitals . As with the ns2 metallurgical metals (for example , magnesium , 3s2) , electron density could leak from the 3s orbitals into the partially occupied 3p orbitals , thus permitting the 3s sigma XO to function as a metallic bond ; that is , as the 3s,p conduction band in the solid .

Given the great strength of the P–O covalent bond , however , I suspect that if white P was combined with rhenium trioxide the P0 would extract one of the ReO3 oxygens to form P2O5 , leaving the less reactive ReO2 (a refractory , ceramic-like material with the rutile crystal structure) as a by-product . Unfortunately a P0ReO3 perovskite probably wouldn't be formed in the reaction . Nevertheless , as an intriguing “thought experiment” it demonstrates the potential of this atom insertion approach for the design and synthesis of remarkable new electronically active materials .

Many reagents have been inserted into the layered dichalcogenides in attempts (mostly futile) to produce new superconducting materials (see the Chemexplore web page , “Exploring Some New Chemistry of Layered Compounds”, for a fuller discussion of this topic) . Here's another “thought experiment” : combine , under HP–HT conditions (anvil press) , varying molar ratios of P0 (as P4) and a graphite-like Transition metal disulfide , MS2 (M = Ti , Nb , Ta , Mo , W ; also Sn) :

x P4 + MS2 -------- [HP–HT] --------> (P0)xMS2 , where x = 0 to 1 .

Such (P0)xMS2 adducts might be metallic solids and possibly even superconducting at low temperatures .

P0 should be chemically stable and inert in the lattices of low-valent metal halides (the higher-valent ones are usually oxidizers and halogenating agents : eg. SbF5) . Such halides might include the low melting chlorides and fluorides of antimony(III) , bismuth(III) , and tin(II) : SbCl3 , m.p. 73 C ; SbF3 , m.p. 287 C ; BiCl3 , m.p. 234 C ; BiF3 , m.p. 727 C ; SnCl2 , m.p. 247 C ; SnF2 , m.p. 215 C .

Some of the MS2 sulfides mentioned above have the layered cadmium iodide structure (GIF image , 24 KB) . Thus , CdI2 (m.p. 388 C) itself might also serve as a host lattice for P0 atoms .

The low melting points of these compounds suggest they are bonded by covalent , and not by ionic bonds (BiF3 might be an exception) . The covalent P4 molecules might therefore dissolve (and hopefully dissociate) in them more readily than in ionic salts .

These examples provide a glimpse into an approach to phosphorus(0) intercalation compounds , which could provide researchers with an entirely new chemistry vista to explore . I hope this web page has given readers a increased appreciation for the wide potential of white and black phosphorus in the continuing search for extraordinary new metallic solids and electronically active materials .

 

References and Notes

 

Xia , Wang , and Jia : F. Xia , H. Wang , and Y. Jia , “Rediscovering Black Phosphorus as an Anisotropic Layered Material for Optoelectronics and Electronics”, Nature Commun. 5 , no. 5458 , July 21st, 2014 (ArXiv.org , February 11th, 2014 , PDF , 667 KB . Note : this PDF file can be opened only with Adobe Acrobat Reader v. 6 or later . If desired , a suitable version of this application can be downloaded for free from Oldversion.com) .

Lalancette and Lafontaine : J.-M. Lalancette and J. Lafontaine , “Intercalation of Antimony Pentafluoride in the Lattice of Graphite”, J.C.S. Chem. Commun. 1973 , p. 815 ; J.-M. Lalancette , “Graphite Intercalated Antimony Pentafluoride”, U.S. Patent 3950262 , April 13 , 1976 .

Vogel : F.L. Vogel , “The Electrical Conductivity of Graphite Intercalated with Superacid Fluorides : Experiments with Antimony Pentafluoride”, J. Mater. Sci. 12 (5) , pp. 982-986 (1977) ; idem , “Process for Conducting Electricity Utilizing a Specifically Defined Graphite Intercalation Compound ”, U.S. Patent 4293450 , October 6 , 1981 . See the Doping of graphite below . Vogel also studied graphiteAsF5 , concluding that its conductivity was ~ 630,000 ohm-1-cm-1 , approximately that of silver : G.M.T. Foley , C. Zeller , E.R. Falardeau , and F.L. Vogel , “Room Temperature Electrical Conductivity of a Highly Two Dimensional Synthetic Metal : AsF5–Graphite”, Solid State Commun. 24 (5) , pp. 391-375 (1977) .

Maruyama and co-workers : Y. Maruyama , S. Suzuki , K. Kobayashi , and S. Tanuma , “Synthesis and Some Properties of Black Phosphorus Single Crystals”, Physica B 105 (1) , pp. 99-102 (1981) .

a later research paper in 1986 : Y. Maruyama et al. , “Electronic Properties of Black Phosphorus Single Crystals and Intercalation Compounds”, Bull. Chem. Soc. Jpn. 59 (4) , pp. 1067-1071 (1986) [PDF , 725 KB] .

P.W. Bridgman : P.W. Bridgman , “Two New Modifications of Phosphorus”, J. Amer. Chem. Soc. 36 (7) , pp. 1344-1363 (1914) .

Nilges , Kersting , and Pfeifer : T. Nilges , M. Kersting , and T. Pfeifer, “A Fast Low-Pressure Transport Route to Large Black Phosphorus Single Crystals”, J. Solid State Chem. 181 (8) , pp. 1707-1711 (2008) [free download from Sciencemadness.org , PDF , 517 KB] .

Maxwell , Hendricks , and Mosley : L.R. Maxwell , S.B. Hendricks , and V.M. Mosley , “Electron Diffraction by Gases”, J. Chem. Phys. 3 (11) , pp. 699-709 (1935) .

Corbridge and Lowe : D.E.C. Corbridge and E.J. Lowe , “Structure of White Phosphorus : Single Crystal X-Ray Examination”, Nature 170 (4328) , p. 629 (October 11 , 1952) .

Pauling and Simonetta : L. Pauling and M. Simonetta , “Bond Orbitals and Bond Energy in Elementary Phosphorus”, J. Chem. Phys. 20 (1) , pp. 29-34 (1952) . A similar approach to the electronic structure of P4 , also postulating spd hybrid orbitals on the P atoms , was made at about the same time by : M. Mashima , “Directed Valence in As4 and P4, J. Chem. Phys. 19 (9) , p. 1216 (1951) ; idem. , “Directed Valence in As4 and P4, J. Chem. Phys. 20 (5) , pp. 801-803 (1952) .

Kimball : G.E. Kimball , “Directed Valence”, J. Chem. Phys. 8 (2) , pp. 188-198 (1940) .

Hart , Robin , and Kuebler : R.R. Hart , M.B. Robin , and N.A. Kuebler , “3p Orbitals , Bent Bonds , and the Electronic Spectrum of the P4 Molecule”, J. Chem. Phys. 42 (10) , pp. 3631-3638 (1965) .

nitrosonium cation : The standard reduction potential of NO+ cited was from W.J. Plieth , Nitrogen, Ch. 5 , pp. 321-479 in Encyclopedia of Electrochemistry of the Elements , Vol. 8 , A.J. Bard (ed.) , Marcel Dekker , New York , 1978 ; p. 325 . Use of nitrosonium cation in the preparation of stable carbocation salts : G.A. Olah , G. Salem , J.S. Staral , and T.-L. Ho , “Preparative Carbocation Chemistry . 13 . Preparation of Carbocations from Hydrocarbons via Hydrogen Abstraction with Nitrosonium Hexafluorophosphate and Sodium Nitrite – Trifluoromethanesulfonic Acid”, J. Org. Chem. 43 (1) , pp. 173-175 (1978) .

very soluble in carbon disulfide : J.R. Van Wazer , “Phosphorus and the Phosphides”, pp. 473-490 in the Kirk-Othmer Encyclopedia of Chemical Technology , 3rd edition , vol. 17 , M. Grayson and D. Eckroth (eds.) , John Wiley , New York , 1982 ; see Figure 1 , p. 474 (organic solvents for white phosphorus) .

Holleman and Wiberg : A.F. Holleman and E. Wiberg (Engl. ed. N. Wiberg) , Inorganic Chemistry , 34th edition (1st Engl. ed.) , Academic Press , San Diego (CA) , 2001 ; “Phosphorus (element)”, pp. 677-685 , esp. pp. 680-682 (properties of white and black P) ; white phosphorus dissolves in THF , p. 680 .

crystal orbital : I use the term crystal orbital to mean a polymerized molecular orbital, which spans the entire crystal dimensions (in a macroscopic sample of metal there is only one single metallic bond) . Thus , crystal orbital is synonymous with the terms metallic bond (chemistry) and conduction band (physics) . I abbreviate crystal orbital as XO , since Xal is sometimes used as shorthand for crystal (and I don't want to use CO , which stands for carbon monoxide !) . The term crystal orbital has been used in two excellent solid state chemistry textbooks : P.A. Cox , The Electronic Structure and Chemistry of Solids , Oxford University Press , Oxford , UK , 1987 ; Ch. 4 , pp. 79-133 ; R. Hoffmann , Solids and Surfaces , A Chemist’s View of Bonding in Extended Structures , VCH Publishers , New York , 1988 .

catalyse Diels-Alder cyclization reactions : D.J. Bellville , D.D. Wirth , and N.L. Bauld , “The Cation-Radical Catalyzed Diels-Alder Reaction”, J. Amer. Chem. Soc. 103 (3) , pp. 718-720 (1981) ; D.J. Bellville and N.L. Bauld , “Selectivity Profile of the Cation Radical Diels-Alder Reaction”, J. Amer. Chem. Soc. 104 (9) , pp. 2665-2667 (1982) .

Tris can be readily synthesized : F.A. Bell , A. Ledwith , and D.C. Sherrington , “Cation-radicals : Tris-(p-bromophenyl)amminium Perchlorate and Hexachloroantimonate”, J. Chem. Soc. C 1969 (19) , pp. 2719-2720 ; see also G.W. Cowell , A. Ledwith , A.C. White , and H.J. Woods , “Electron-Transfer Oxidation of Organic Compounds with Hexachloroantimonate [SbCl6] Ion”, J. Chem. Soc. B 1970 (2) , pp. 227-231 .

Readman Process : A.D.F. Toy , “Phosphorus”, Ch. 20 , pp. 389-545 in Comprehensive Inorganic Chemistry , vol. 2 , J.C. Bailar et al. (eds.) , Pergamon Press , Oxford (UK) , 1973 ; black phosphorus is reviewed on pp. 396-399 ; the Readman Process (1890) for the commercial production of white phosphorus is described on p. 390 .

Bridgman (1916) : P.W. Bridgman , “Further Note on Black Phosphorus”, J. Amer. Chem. Soc. 38 (3) , pp. 609-612 (1916) .

violet : violet phosphorus is described in Holleman and Wiberg , p. 682 .

Bacon , Dean , and Gillespie : J. Bacon , P.A.W. Dean , and R.J. Gillespie , “The 19F Nuclear Magnetic Resonance Spectra of Antimony Pentafluoride , cis-Sb3F16 , and Higher Polyanions SbnF5n+1, Can. J. Chem. 48 (21) , pp. 3413-3424 (1970) [PDF , 582 KB , requires Acrobat Reader v. 6 or later] .

azobisisobutyronitrile : A practical synthesis of AIBN from acetone , hydrazine sulfate , and sodium cyanide , and a demonstration of its use as a neutral free radical initiator in the polymerization of styrene and butadiene , are described by : C.G. Overberger , M.T. O'Shaughnessy , and H. Shalit , “The Preparation of Some Aliphatic Azo Nitriles and Their Decomposition in Solution”, J. Amer. Chem. Soc. 71 (8) , pp. 2661-2666 (1949) .

thousands of prospective surfactants : as listed in McCutcheon's Emulsifiers and Detergents , a comprehensive encyclopedia of surfactants , available from goMC.com .

steam distillation : R. Klement , Phosphorus, pp. 518-519 [purification of white phosphorus by steam distillation ; also the preparation of fine particles of white phosphorus in water suspension] in the Handbook of Preparative Inorganic Chemistry , vol. 1 , 2nd edition , G. Brauer (ed.) , Academic Press , New York , 1963 . This valuable compendium of preparative inorganic chemistry (Vols. 1 & 2 combined) can be downloaded for free from the Sciencemadness.org library resources web page [PDF , 19,090 KB ; requires Acrobat Reader v. 6 or later] .

Keyes : R.W. Keyes , “The Electrical Properties of Black Phosphorus”, Phys. Rev. 92 (3) , pp. 580-584 (1953) .

blue phosphorus : Z. Zhu and D. Tomnek , Semiconducting Layered Blue Phosphorus : A Computational Study, Phys. Rev. Lett. 112 (17) , 176802 , 5 pp. (2014) ; ArXiv.org , March 6th, 2014 [PDF , 553 KB] .

one-electron bonds : L. Pauling , The Nature of the Chemical Bond and the Structure of Molecules and Crystals , 3rd ed. , Cornell University Press , Ithaca (NY) , 1960 ; p. 340 ; A. Holden , The Nature of Solids , Dover Publications , New York , 1992 [reprint of the Columbia University Press textbook , 1965] ; p. 91 . The example of the relatively stable hydrogen molecule radical cation , (H2)+, with a one-electron sigma H–H bond , is cited by both Pauling and Holden .

Doping of graphite : F.L. Vogel , “Intercalation Compounds of Graphite”, pp. 261-279 in W.E. Hatfield (ed.) , Molecular Metals , Plenum Press , New York , 1979 ; see especially Table III , “Acceptor Intercalated Compounds of Graphite”, p. 269 . Table III is reproduced below :

bronze : P.G. Dickens and M.S. Whittingham , “The Tungsten Bronzes and Related Compounds”, Quart. Rev. 22 (1) , pp. 30-44 (1968) ; see also : H.R. Shanks , P.H. Sidles , and G.C. Danielson , “Electrical Properties of the Tungsten Bronzes”, Ch. 22 , pp. 237-245 in Nonstoichiometric Compounds , R. Ward (ed.) , Adv. Chem. Series 39 , American Chemical Society , Washington , D.C. 1963 ; M.J. Sienko , “Electric and Magnetic Properties of the Tungsten and Vanadium Bronzes”, Ch. 21 , pp. 224-236 in Nonstoichiometric Compounds ; C.T. Hauck , A. Wold , and E. Banks , “Sodium Tungsten Bronzes”, pp. 153-158 in Inorg. Synth. 12 , R.W. Parry (ed.) , McGraw-Hill , New York , 1970 [reprinted by R.E. Krieger , Huntington , NY] .

 

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