TECHNICAL REVIEW
Normal Alkane! William R. Turner Research and Engineering Department, Company, BY00 Passyunk Avenue, Phiiaaeipnaa, r a . w i 4 b
WILLIAMR. TURNER is a r e search chemist in the Research and Engineering Department of the ARC0 Chemical Co., Division of the Atlantic Richfield Co., Philadelphia, Pa. He holds a B.S. in chemistry from the University of Pennsylvania and i s coauthor oJ several papers dealing with composition, properties, and behavior oJ petroleum waxes. I n addition to waxes his interests include petrochemicals, polymers, and synthetic nutrients. He is a member of the American Chemical Society, the American Association for the Advancement of Science, and the Franklin Institute and a Fellow of the American Institute of Chemists.
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T h e normal alkanes or normal paraffins are widely distributed in nature in the waxy coatings associated with the leaves, fruits, and nuts of many different plants; in coatings and secretions of various forms of animal life (Douglas and Eglinton, 1966; Gerarde and Gerarde, 1961, 1962; Kolattukudy, 1968; Ora et al., 1965); and in many fractions of petroleum, shale oils, tars, and coals (Ludwig, 1965; Martin e t al., 1963; Raude and Eisen, 1966; Tanaka et al., 1928). The normal alkanes are important constituents of most petroleum waxes and major components of the lower molecular weight waxes commonly known as paraffin (Carpenter, 1926; Dean, 1966; Edwards, 1958; H a t t and Lamberton, 1956; LeMaire, 1957; Ludwig, 1965; Maaee, 1960; Minchin, 1948; Schneider and Heymer, 1963). The term "paraffin" is often applied not only to the normal alkanes hut also to derivatives of these compounds and to many mixtures of normal alkanes with other materials. T o avoid ambiguity in the discussion which follows, the term "normal alkane" will be used exclusively in referring t o the high purity materials. The broad utility of petroleum waxes provided an incentive for much of the study given the normal alkanes over the past 50 years. The simple molecular structure and the complex phase behavior of these compounds made them a desirable medium for investigating organic crystallography. I n addition, a knowledge of alkane physical properties and thermodynamic functions have brought a better understanding of the behavior of polymers such as polyethylene. Considerable information about the normal alkanes has been accumulated over the years through studies made on concentrates separated from petroleum waxes or prepared b y chemical reactions, hut only in the past two decades have purification and analytical techniques been developed to the point where certain characteristics of the longer chain compounds could be established with a good degree of certainty. The syntheses and properties of the normal alkanes reported by Schiessler et al. (1946) and in Properties of Hydrocarbons of High Molecular Weight (1967) represent major contrihutions to knowledge about these materials. General information on synthesis and chemical reactions of the normal alkanes is given by Asinger (1968). Surveys of their physics and physical chemistry have been published by Cines (1950) and Daniel (1953). Certain aspects of the solid phase hehavior of the normal alkanes have been reviewed by Broadhnrst (196210) and Mnynkh (1960, 1963a). This review of the physical behavior of the normal alkanes
The physical behavior of the normal alkanes, particularly those in the petroleum wax molecular weight range, are reviewed. Discussed are molecular ordering in the liquid state, crystalline characteristics, rotational, subcell, and packing transitions, and crystal packing and stacking; effects of carbon atom number in the aliphatic chain, impurities, and pressure; phase behavior of binary systems; conditions for forming solid solutions, eutectics, and mixed systems; and relationships between differences in chain length, molecular packing, and solid state compatibility. The principles outlined should help in predicting binary behavior, There are 437 references including physical properties, thermodynamic functions, and kinetics.
aiid their binary niixtuiw attempts to show d i e r e their behavior rrwnlile.: that of nlo3t other wbstniices and where it shoni: n marked departure €i,om that umxlly observed. T h e di.cu>.ioii aiqiliw geiierally t o all normal alkanes but is directctl paIticulm~ly to tlie alkanes found in petroleum waxeh. Paraffin Series. T h e noriiial alkanes are aliphatic hydroc a ~ h ) nI)cloiiging ~ to a ianiily of compoiiiid~:,t h e paraffin series. i n which all nienilws coiit:iiii c a r l ~ o naiid hydrogen iii the proportioiis given by the foimuln Cn1~Ln I2. C and H re1)iweiit cai,boii aiid Ii>drogen, m p r c ~ i v e l y ,and n is the iiuinlm of caarbo~iatoms i n tlie molecde. The repetitive 1iatui.e of the chemical constitution of the alkane series permits treatinciit of their phy&~l pi,opertie.: as dependent not only on 1 1 i ~ e w iand r ~ ~ temperature b u t a1.o on their serial iiiinibe~~s (Cine., 1950; Goriir et al., 1939; I v a i i o v d y , 1962; Koefocd, 1953; Kiirata and Isida, 1955; Mesliclieryako~,1959; Parks et a l . ) 1930). Pome phy&al prop~rties,such as liquid density ant1 boiliilg pniiit, change fnii,lj. regularly as the molerular w i g l i t - iiici,enGe; others iiivolviiig the solid state, w c 1 i aq melting point>show a n altnilatioii among t'lie lower inembers of t h e swie. accordiiig to whether the number of carbon atoms i i i tlie compound is odd 01' even (Hei,brandson and Sarliotl. 1955; AIiiller, 1929a)b; Tiliclieev et, al., 1951). The iiunibei~ of rai1)on atoms is an im1)ortant factor in determining their comp!w phase behavior, described i n detail later. 111 many ot'her phy3ical properties t.he normal alkanes, all much alike, are typical nonpolar compouiids of low diPlectric coiistant. estremrly low electrical conductivitJ-, and low solubility i n water. The paraffiii series takes it,. iianie from tlir Latin parum affini5, meaiiiiig small affinity, because thesp conipoiind~are not wactive chemically. Some of t'he norma1 alkane. form crystalline adducts with coinpoulids like urea (.Isinger. 1968; I'embrrtoii and Parsonage, 1965, 1966, 1967; Ychies.:lri, and Fletter, 1952; Zimmerschied et al., 1950). -1moirg the many piiblirations dealing with the physical propertiei, the thei~motlyiiarnicfunctions, and the kinetics associated with the normal alkanes are: Altenberg, 1964; .lmbrose and T o ~ v n ~ e i i1968; d, Araiiow et al., 1958; .Itkinson and Ricliartl,wi, 1969; Xveyard, 1967; =iveyard and Haydon, 1965; 13artenrv, 1950; Billnieyer, 1952; Hoelhouaer, 1960; l3roadhurst, 1960, 1962a,h, 1963, 1966; Carniichael, 1953; 1963; Fiiike et, al., Doolittlc, 1964; Iloiigla~et a].: 1954; DOWV', 1954; Floi,y a i d Trij, 1963; Flory et al.. 1961 , 1964; Fox a d Zismaii, 1952; Franks, 1966; Gupta, 1956; Hijmans, 1961; Holdel,, 1965; Huffmaii et al., 1931; Hugel, 1953; Huggins, 1954; 1vanov.szky. 1966; Jasper et al., 1953; Karapet'yants, 1957; E;aixpct'yaiit\ and Yeii, 1963; Kobayashi, 1937; Kwgleiv& and Zwoliwki, 1961 ; Kudchadker and Zwolinski, 1966; Ltv-is>1965; Li et al.. 1956; llaiin, 1967; hIatsukuma aiid l a k i g a n a , 1963; Mazee, 1948; XcClure, 1968; XcCubbin, 1962; 3fcCullough and Messerly, 1961 ; Nelpolder et, al., 1964; X e w r l y et al., 1967; Aleyer aiid van der KykJ 1937;
Xiiyukh, 196313; Kakanishi et al., 1960; Orivoll and Flory, 196i; Osbourne and Ginnings, 1947; Palit, 1963; Parks, 1936; Parks and Huffman, 1931; Parks and Light, 1934; Parks and Rowe, 1946; Parks et al., 1930, 1949; Patt'ersoii and Bardin, 1970; Pechdd et al., 1966; Person and Pimentel, 1953; Phillips and Riddiford, 1966; Pitzer, 1940; Porter and Johnson, 1960; Schaerer et' al., 1955, 1956; Schonhorn, 1966; Shimoiiaev, 1965; Sniitteiiberg and l\Iulder, 1948; Smyth, 1963; Stiel and Tliodos, 1962; Templin, 1956; Thomson, 1954; Varshni, 1953; Varshni aiid Srivastava, 1959; Kiener, 1948; Wiiining, 1959. Compilat~ionsof properties data are available in Doss, 1943; Egloff, 1953; Ferris, 1955; Properties of Hydrocarbons of High Molecular R'eight, 1967; Rossini et al.. 1953. Carbon Chain Structure. In t h e aliphatic chain of crystallized normal alkanes, each carbon atom is bonded t o two others a i d to two hjdrogeii at'oms. The rarbon-to-carbon bond angles are always great'er than the ideal tetrahedral angle, about 112". The intramolecular carbon-to-carbon distance is about l.53A (13uiinJ 1939; Shearer and Vand, 1956). Considerable information on the properties of t,he bonds is available (Lennard-Joiies and Pople, 1951). The polarizabilities along and across the bond have been calculated from measureinelits of density aiid refractive indices of normal alkaiie crystals (Bunn and Daubeiiy, 1954). The dissociatioii energy for carboii bonds a t room temperature is high, of the order of 50-100 kca1,'mol (Daniel, 1953). The vibration frequency characteristics for the stretching of carboii-carbon bonds and for the bending of carbon-hydrogen bonds, as determined from spectroscopic measurements, are similar (Pit,zer, 1940). These facts indicate t,liat t,he carboil-carbon bond lengtlis aiid bond angles are niaiiit,aiiied b y strong forces. O n the other hand, a rotation can occur readily about the single bonds, opposed by yeak forces only, since neither a change of bond lengths nor angles is involved (Ast80n,1951; Daniel, 1953, l'itzer, 1951). As a result of rotation about the single bonds, the carbonhydrogen units of the chaiii caii assume a variety of positions differing in energy (Jernigaii, 1968; lIaii11, 1967; >IcCullough and lIcJ\Zahoii, 1965; Scott, and Scheraga, 1066; Snyder, 1967; Somayajulu aiid Zowolinski 1966; Taylor, 1948). One coiiformation, however, represents minimal potential energy and resuks from the competing forces arising from the tendency of t,he bond angles to assume ideal values and of the nonboiided atoms to be situat'ed a t an equilibrium distance (Kit'aigorodskii, 1960a). In the case of the normal alkanes the arrangement giving miiiimum energy i 4 that in which the chain takes the form of a flat zig-zag of carbon atoms (Daniel, 1953; Woodward and Sauer, 1965). In this low energy arrangement, the methylene group hydrogen at.oms are located in planes passing through t,he carbon atoms and perpendicular t o the cbaiii ases (Vaiiisht'ein and Pinsker, 1950). F h e n a normal alkane molecule is said to have a "straight" chain, the reference is actually being Ind. Eng. Chern. Prod. Res. Develop., Vol. 10,
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made to a zig-zag arrangement of the carbon atoms in the position of least energy, the form in which the molecule is usually found in the solid state and a t temperatures just above the melting point. Keller and O'Coiinor (1958) have suggested that normal alkanes of sufficiently long chains probably crystallize with chain-folding as has been postulated for certain polymers. Degrees of Molecular Order. A system containing many molecules comprises one or more homogeneous regions known as phases. I n each particular phase the molecules are arranged in a characteristic pattern, which may be quite unorganized as in fluid or glassy phases or may be a repetitive spatial grouping of a small number of molecules, as in a crystalliiie phase (Turnbull, 1956). The condensatioii of molecules into liquid and solid phases is promoted by short-range intcrmolecular attractive forces and is opposed by molecular thermal motion. The molecules in a coiidenscd phase are bound more strongly than in the vapor phase; as the boiidiiig forces increase with lowered temperature, the molecular positions and momentums become more restricted, aiid t,lic entropy is correspondingly reduced. Under varied temperatures and pressures the long chain normal alkanes assume a variety of molecular patt,erirs reflecting gradations of order. This intcimting behavior illustrates that matter does appear iii states other thaii the comnioii vapor, liquid, and solid forms. Cnder ordiiiary pressure, only a t temperatures above the boiling 1)oiiits of the normal alkanes should the molecules be considered in a stat'e of complete disorder, and only a t extremely low tem1)eratures is there a state of complete or nearly complete molecular order. Between t,hese tlwo extremes the molecular arrangemelit becomes more ordered as the temperature decreases (IZernal, 1937).
The change in degree of order with variations in tcmperature does not necessarily occur at a constant rate but often a t specific levels of temperature goes through stages detected b y the appearance of discontinuities in measurements of the physical properties. The transition hctwceii phases caii be either gradual or abrupt depending upor the relative sti'e~igt~lis of the driving and hindering forces involved, The phase equilibrium temperature is reached when heat loss from the system is i n balaiice with heat being developed by such condeiisatioii proccsscs as liquid formatioii, crystallization, and solid phase transformatioii. Phase equilibria arc affected by the areas and curvatures of the iiiterfaccs betweeii phases (Buff, 1951; Herring, 1953; Tolmaii, 1948, 1949). A t,hermodynamic explanation for the stabilit,y of phases has been developed (Guggenheim, 1949; Prigogine and Defay, 1954). For phases t o be in equilibrium, the total free energy must be a minimum a t constant pressure, temperature, and composition (Cines, 1950). The number of variables t h a t must be specified to determine the st'at'e of a system is given by the phase rule. Vapor State
In the vapor state the molecules are thought to be moving about rapidly and quite freely except for collisions with each other and with the walls of the containing vessel. The orientations of the normal alkane molecules should be com1)letely random in the vapor phase since the long chains are frce to change their shapes aiid dimeiisioiis contiiiuall~-as they twist and undergo rotations about' their many atomic bonds. Solid films of normal alkanes coiideiised from the vapor phase sometimes show an amorphous structure which later becomes crystalline (Lampe, 1961, 1962). The initial disordered 240 Ind.
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arrangements seen in the films likely reflect the molecular randomness in the gaseous state from which they are formed. liquid State
The condensatioi>of matter in the vapor state upon cooling usually produces the liquid form of the substance. In the liquid state the molecules have moved much closer together than in the vapor state; therefore, thc liquid density is much greater than that of the vapor. I n the liquid state the molecules are so close that the system is practically jiicompressible; yet, they can move freely enough to offer little resistance to a change in shape of the liquid. The compressibilities of the liquid irormal alkalies have been measured (Golik and Adameiiko, 1965; Staveley and I'arham, 1952). The orieiitatioir of long chain molecules, such as the normal alkalies i i i the liquid state, must be described as raridom except where the coiiditioii of a relatively dense packing rcquiiw that the nearcbt iicighbors about any one long rnolecwle be roughly parallel to it. With declining tcrnper:tture this esce1)tioii applies ever more strongly and finally becomes the rule (Wariwi, 1933). 111the liquid st,atc at highel, teml)rratures aiid in solution, the long chain iiormal alkane molecules are believed to assume more or less coiled and coiitiiiuously variable coiifoi~matioiis as the result of iirteriial rotat,ioiis or toi.sioria1 motioiis about the iiidividual boiids of the chain (Ivaiiov~zky,1062). The average leirgth aird radius of the chain moleculc.; have bee11 calculated by a number of workers (I3rady et al., 1967; Freiikcl, 1946; Suzuki, 194i; Taylor, 1948; 'Yreloai*, 1943; Reidmaiiii et al., 1953; Wliittiiigt,on and C'litipmair, 1966). Because of the grcat indefiiriteness of t,he niolcrular shapes in the liquid state, the values are iieccssai~ily statistical in nature. Liu and I:llman (1968) have suggested that, iiitramolecular c h i l i folding may occur iii solutioirs of the normal alkanes. Wheii cooled sufficiently, n liquid is best described n s a solid form which may be either crystalliiie or gla depeiidiiig 1)artly 011 how the cooliiig is cffccted, but mostly on the ease with which molecular aggregatioii caii t,akc Iilace. The lat,ter is closely related to the degree of geometrical regularity of the molecular struct'ure aiid applieb not' only to substances of low molecular weight but also to high molecular weight polymei~icmat,erials (I3uiii1, 1954; Richardson et al.. 1963). Rit81ipolymers such as h e a r polyethylene, crystallization irequently is incomplete, taking place only in those regioiis where the polymer chains fit most closely toget,lier (Chiang and Flory, 1961). Glass Formation. I n a glass the molecular arrangement is mostly unorganized and similar to that in a liquid at. higher temperatures, but the molecules are close together and ixtertwined, seriously liampering molecular motion. As a result the fluidity of the material is extremely low (Turiibull, 1956). The maberial appears to be a solid although its structure resembles that of a liquid. Aiiy liquid will form a glass a t some temperature above O O K if crystallization does not intervene (Fox and Floi,y, 1950; Turnbull and Coheii, 1958). Whether crystallization will occur or not is determiiied by the size of the iiucleation Erequency and crystal growth constant and by the rat,e a t which the liquid is cooled. Once formed, a glass is stable a loiig tiine because the crystal growth rate within is small. For crystallization to occur, a long range order must develop i i i the material and be accompanied by a substantial loss of eiitrol)y (Turnbull, 1956). As a result' t,lie liquid stat'e frequently exhibits considerable stability. Great degrces of suprcooling
of a liquid can often be developed before crystallization will take place (Frank, 1939: Ifoffman, 1958). Sometimes it does riot occur, and a glass is formed (Tipson, 1956; Turnbull, 1963). llaterial which has molecular shapes t h a t make close aggregation difficult but ivhich can assume random molecular positions in t,he liquid state with an economical use of volume, teiids to form glasses. Some of the branched chain alkanes illustrate this type of behavior (Meshcheryakov, 1959; of High llrolecular Weight, 1967; l’ropert’ies of IIytirocarl)o~~s Smyth, 1946; Sugisaki et al., 1968). If a molecular ordering sufficient to permit tnllizatioii is iiot achieved upon moderate cooliiig, furt cooling is a p t to cause sur11 a large viscwsity inc*rease th:it molecular mobility is seriously Iiami)eredjanti :I stable glasr will result. Theoretical d u e s for the glass trailsition temperatures of the normal alkalies have been calculated (Miller, 1968). However, the higher ~rornialalkanes do not form g1 cooled froin the liquid a t moderate rates (Lewis, 1965; ‘lhriibull a i d (’ormia, 1961). ‘This weak, glass-forming teiidrncy is csplaiiied 011 the basis that crystal nucleation in loiig rhaiii molecules i q u i r e s aggregation, iiot of elitire molecules, h i t oiily of molecular segments (hIandelkern, 1958; I’rice and Perry, 1968; Turiibull and Cohen, 1960). The ttiitleiicy for I)reoi,ieiit:tt,ion of normal alkane molecules just above tlie freezing 1)oiiit is also a contributing factor. Molecular Ordering. A general tendency for ordering in liquids has been noted by a number of observers (13eriia1, 1937; I%rowii and Shawv,1957; Kitaigorodskii and Aliiyukh, 1961 ; LeKous, 1969; lliiller, 1933; Smith, 1967; Stewart, 1928; ’l’inimerma~is~ 1961 ; ITnistiitter aiid H:tiiseii-I)aiiiie~vitz~ 1948). ‘l’heoi,ies 011 the nature aiid viscosity of liquids have heeii tlevclopctl based 011 the 1)~eudo-crystalliiiebehavior of tlic liquid st’ate (Eyriiig, 1936; Frankel, 1946; l l o t t and Gurney, 1939). The proposed concepts are t’hat phase changes call occur within the liquid state (i\iitoiioff et al., 1950) and that solid ~)olyniorpliisni is related t o certain privileged molecular conformations which develop in the fluid phase (Timmernians, 1952). Wheii cwoletl in the liquid state, the normal alkanes show a strong tendelicy toward molecular preorientatioii as the freezing point is ai m c h e d . -1lthough t,he long-range order characteristic of ci talline materials never develops in the n-alkaiie liquid, a short-range order does evolve just above the freezing temperature. ‘This phenomenon, termed “cybotaxis” (Seyer et al., 1944)) is defined as “a transient orientation of molecules in a liquid revealed by X-ray diffraction effects aiialogous to those produced by crystals.” X-ray studieq indicate that just above t’he freezing point, the normal alkane molecules assume arrangement with their long ases parallel and terminal methyl groups staggered, thus not’ falling mnsisteiitly into regular planes (hfiiller, 1932b). Several liquid struct,ureshave been proposed for the normal alkaiics based on discoiitinuities observed in a number of properties \vith variations in temperature (;\loore e t al., 1953). High polymers show aiialogous changes (Fox and Flory, 1950). In the liquid oriented state the zig-zag carbon chains of the normal alkniies are believed to be approsimately straight, hut t,hey are iiot arranged to make their end groups form regular layers. Airotation of the chains about their long ases evidently occurs, and the chains occupy spaces cylindrical in shape. Therefore, the packiiig of the chains, t h a t of cylindrical rods, robab ably is the relatively loose packing of cylinders arraiigetl with cent,ers forming a square patterii rather than the
closer approximately hesagonal packing thought to be characteristic of many of t,he normal alkalies just below the freezing point (Larsson, 1967; Lufcy e t al., 1951; Valid, 1953). Although the distance between adjacent chains is about the same in the liquid as in the solid, the square packing of the liquid molecules requires a larger volume; On freezing, the structure contracts into the smaller volume required by the hesagonal packing (Daniel, 1953). Liquid Crystals. Some materials exhibit mesomorphism, a form of ordering in the liquid state upon cooling that produces what are termed “liquid crystals.” Kitaigorodskii and hliiyukh (1961) have described this condition as basically one of disorder in which there is a concession to those forces striving for order. True liquid crystals are formed when long molecules are closely arrayed in the liquid state, but the crystalh are so rigid in nature that they cannot find enough free space to permit rotation (Timmermaiis, 1961). Because certain orieiitatioiis are privileged, an anisotropy develops which would ordinarily apply only to a solid system (Brown and Shaw, 1957; Fergasoii, 1964). The orientation observed with the normal alkanes just above the freezing point has been described as a liquid crystal format,ion. -4 smectic phase has been reported, for example, for a paraffin was (Zocher and Nachado, 1959). However, the normal alkanes do not appear to form true liquid crystals (I3rown and Shaw, 1957) since the great flesibility of the aliphatic chain encourages molecular rotation even i n a closely packed environmeiit. Also, normal alkanes do not have the entropy characteristics associated with liquid crystals. The usual measurements of refractive index do not’detect anisotropy in the normal alkane liquid (Harrison e t al., 1958; R e s t , 1937), but flow birefringence, electro-optic effects, and other optical anisotropic behavior have been reported (Champion and North, 1968; Champion et al., 1970; Jernigan and. Flory, 1967; Philippoff , 1960). Therefore, the mesomorphic arrangement into which normal alkanes enter just above the freezing point seems similar to but not identical Supercooling of Normal Alkane Liquids. If cooled slowly, a pure liquid may not crystallize a t the freezing point b u t instead may become supercooled or undercooled to some critical limit before crystals spontaneously appear (deNordwall and Staveley, 1954; Reynolds, 1963). Turnbull and Coheii (1968) have observed that a substance is easily supercooled if the ratio of it’s boiling to freezing temperatures equals or esceeds 1.8. For many simple molecular substances, the critical temperature represents about 80% of the absolute freezing temperat,ure (Buckle, 1960; Thomas and Staveley, 1952). However, normal alkanes in the range of C16-C31 (abbreviations for n-C16H34and n-C.;hH;o) have critical limits of about 95% of their freezing points-that’ is, they will spontaneously crystallize when undercooled 10-15OC below their freezing points (Phipps, 1964; Turnbull and Cormia, 1961). Crystallization is less likely to occur with the lower members of the alkane series (deNordwall and Staveley, 1954). This unusual behavior of the normal alkanes is attributed to the ease with which molecular segments of the long chain molecules can form aggregates to serve as nucleation centers (Xandelkern, 1958; Turnbull and Cohen, 1960). Turnbull aiid Cormia (1961) thought that the segments must be at least as long as the unit cell of the crystal to form a nucleus. In actual practice, unless the liquid is dispersed in fine droplets, crystallization will usually occur well above the critical limit because heterogeneous nucleation is operative Ind. Eng. Chem. Prod. Res. Develop., Vol. 10, No. 3, 1971
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ill the system. Thus, the normal alkanes ordinarily require a supbrcooling of only a few degrees below their freezing points to effect crystallization (Turnbull and Cormia, 1961). N a terials showing molecular rotational freedom, like alkanes, usually crystallize from the liquid with little supercooling (Smyth, 1946).
Crystallization
As the temperature of a liquid is lowered, the energy of molecular motion decreases, and the molecules move closer together. I n moving closer together, the molecules tend to acquire a more ordered arrangement with the degree of order being largely determined by the shapes of the molecules and their resulting abilit'y to fit' together in adjacent positions (Ubhelohde, 1950; Warren, 1933). ;It some temperature called the freezing point', the short-range intermolecular attractive forces overcome the energy of molecular motion and bind the molecules int,o a crystal. This biiiding process is not random in nature but occurs between those points of a complex molecule where attractive forces exist,. Thus, the crystal is the result of an orderly fit,t'ing together of molecules, and the visual form of the cryst'al is an outward expression of this arrangement (Vand, 1954). Depending on conditions, more than one orderly arrangemelit may be possible, and several crystalline shapes may develop from the same kind of molecules. The normal alkanes have been reported to crystallize into shapes often described as plate, needle, and malcrystalline in form (Carothers et al., 1930; Clarke, 1951; Hubbard, 1945). Although several crystalline shapes may be seen in a single crystallization, usually one type is predominant under a given set' of conditions (Clarke, 1951; Turner, 1962). If crystallization is est,remely rapid, malcrystalline forms frequently are produced (Clarke, 1951) since an even growth on all faces of a cryst'al is t'hen unlikely to occur. Needle cryst'als have been reported to form only if the normal alkane contains appreciable amounts of impurities (Clarke, 1961; Edwards, 1954, 1957; Graves, 1931). Edwards (1957) re1iort.s that needles may actually be curled plates which form from mistures of the normal alkanes but not from the pure compounds. Another possibility is that' needles appear only when the alkane is i n the high temperature stable cryst'alline form (Fontana, 1953; SlcCrone, 1954; Stenhagen and Tagtstrom 1944). 'this is t'he CYH form which will be discussed lat,er. The role of an impurity in the production of needles, t,hen, might be related either to its effect in curling plates or to its ability to lower the solid transition point of the alkane system, making needles more a p t to form in crystallizations carried out' near room temperature. Thus, if an alkane has a solid transition point, aiid if it is cryst'allized a t a temperature above this point, long, t'ube-like needles will probably form. On the other hand, if crystallization occurs below the solid transition temperature, plates will be obtained. Since crystallizations usually are made at temperatures below the solid transition points of the alkanes, thin rhombic plates are the most common type of alkane cryst'al (Clarke, 1951 ; Daniel, 1953; lIcCrone, 1954). J17hen crystallization is carried out by the slow cooling or slow evaporation of a dilute solution, the crystals usually possess a high degree of geometric regularity. The needles will often be straight and well formed, aiid t'he plates will have nearly perfect rhombic shapes with reproducible interfacial angles (McCrone, 1954). However, crystals from highly concent'rated solutions, the melt, or rapidly chilled dilute 242
Ind. Eng. Chem. Prod. Res. Develop., Vol. 10, No. 3, 1971
solutions will usually tontain many imperfections. Bent and twisted plates, needles attached to plates, and other evidcnces of malcrystallinity are seen. I n crystallizations above the solid t'ransition temperature, lateral growth of the c tal seems random, aiid crystals of extremely irregular outline result. llolecular rot,atioii exists i i i many of the normal alkalies above the transition temperature, and this mot'ioii may interfere with crystalline growth in certain directions (Edward$, 1954; Fontana. 1953). I k l o w this temperaturr where the molecules caiiiiot rotate freely, their positions in the growing crystxl are restricted, and a more regiilar crystalline growth caii occur. Upon rapid cryst,allizatioii, dendrit'ic growth frequently occurs aloiig several diagonals of the sinal1 rhombic Illate3 which form first. This rapid growth produces structures possessing escessive surface energy and tending to rearrange or otherwise be modified so that the dendritic form doe< not persist'. The area between t,he dendriteq gradually fills iu to produce symmetrical rhombs (Dunning, 1963; lIcCroiie, 1954). Two crystal fronts growiiig from oppoyite directions soniet,irnes uiiitc to form a continuous sheet,. X-ray studies suggest that ridges which form in certain crystallographic directioiis on ci,ystals of Iiornial alkalies are related to the shearing whirli occiirs wheii molecular chains undergo tilting (Hassett aiid Kellrr, 1961; Callejit, 1965; Keller, 1961). )lotion Ijicture st'udie. the crystallization of normal oct,adecane show that. a1 growth is qiiit,e a i r irregular process (Thomas and Wehtwater, 1963). Numerous itivestigators have reported the cryst~ullogrnphic liroperties of the normal alkalies (Chicliakli a i d Jessen, 1967; Clarke, 1951; Gol'denberg itlid Zhuze, 1951; Graves, 1931; Hubbard, 1945; Kitaigorodskii, 1961; SIazee, 1948; &IcCroiie, 1954, R%iibyet al., 1960; Shearer and Valid, 1956; Schneider and Heynier, 1963; Stenhagen and 'L'iigtitroni, 1944; Teare, 1959). Mechanism of Crystal Growth. Theoretical explanations are gradually evolving to cover t,he great mass of observations accumulated about crystallizat,ion from bot'li the vapor and liquid states (Avranii, 1939; Duniiiiig, 1963; Frank, 1951, 1952; Kpating, 1964; Reynolds, 1963; Tipsoli, 1956; t'olmer and n'ebber, 1925; Volnier and Schiiltze, 1931 ; Walton, 1965). For this discussion of the normal alkalies where crystallization from the liquid is of greater iiiterea~vvaoii aiid T'and, 1951; Thiiiiiiiig, 1963; R&iby et n l . , 1960; V e m a , 1954). 12ecaiise olily weak forces h i d the chains 1atei.ally in the crystal, the dislocations might be caused by the chains slippiiig past olie anot'her (Verma, 1953). Ot,lier possible causes have been suggested such as the i)resence of impuritie.: or vacaiicies i i i
the structure, faults in the molecular stacking, and buckling of the embryo crystal (Dunning, 1961 ; Jaccodine, 1960). The introduction of a neighboring homolog into the melt of a pure normal alkane increases the number of dislocation spirals per growth area (Jaccodine, 1960). Through the use of electron microscopy, multiple-beam iiiterferomet,ry, and other optical methods, the steps were determined equal in height t o the lattice constant of the crystal or to small multiples of that. height (Anderson and llawsoii, 1953; Ilawsoii, 1954; Verma, 1954). For example, normal hexatriacontane, C36H74>and normal hectane, C1~H202, both crystallize in growth spirals whose vertical edges are about 43A a i d l25A high, respectively, the lengths of the chain axes in the respective crystal lattices (Dawson, 1952; Daivsoii and Valid, 1951). The dislocation theory of crystal growth (Cabrera and Burton, 1949; Forty, 1954; Frank, 1952) has been reasonably successful in esplaiiiiiig cryst'allizatioii from solutions and vapors having a low degree of supersaturation but is less useful iii predicting result's under other conditions. The growth of ci,ystals from concentrated solutions or from the melt' is oftcii a complex pheiiomenoii upon which diffusion rates, degree of supercooliiig, and multiple dislocations may have aii effect (13m111and Emmett, 1949; Dunning, 1963; Keat,iiig, 1963). Many factors may interfere with the achievemelit of sitiiple spiral structures (Buckley, 1953). Oiicc growth has started, it's rate of coiitiiiuaiice is determiiicd largely by thc rate a t which latent heat of solidification can be i.eniovcd from tlie solid-liquid interface. The phase equilibrium temlierature is reached diel1 the heat loss from t'he system is in halaiice with t,lie heat being developed by the crystallizatioii process. If the growth l~rocesstakes place slowly, tlie faces of the growiiig crystal mill appear more iieai.ly perfect. T h e growiiig crystal always teiids to assume a convex orit,er form-that is, it teiids toward the attainment of a miiiimium surface free eiie (Kitaigorodskii e t al., 1965). Witliiii tlie melt may be a llreferred orielitation for growth; iiuclei forming with tlie favored orientation may generate groivt'h which crowds out that coining from other sites. The more isolated dislocatioii steps may grow faster than those cro\vtlcd together by virtue of the better heat dissipatioii taking place wit,li the former (Chalmers, 1954). Solid State 111 the solid state the molecules have as much kinetic energy of motion at any given temperature as the molecules of a gas at the same temperature; although they are moving, their motioiis are very restricted. The speed of the molecular motion decreases with tempemture as with liquids and gases. Like liquids, solids offer great resist,aiice to compressioii but are much more reluctant to change their shape. Compressibilities of the iiormal alkanes in the solid state have been measured (Eridgman, 1948; Miiller, 1941, Staveley and Parham, 1952). X-Ray studies show t'liat with niaiiy materials the average immediate eiiviroiiment of a molecule is not changed seriously on freeziiig. The interiial energy and density change are small. The gain iii long-raiige order which attends the solidification process is usually accom1)aiiied by a volume decrease amounting to 3-10Y0 (Turnbull, 1956). Xeasurements 011 normal alkalies, however, show that these compounds change about 10-2070 in volume in passiiig from the liquid illto a solid phase (Harrison e t al., 1958; Schaerer et al., 1955; Templiii, 1956, 1963; van Hook and Silver, 1942). The magnitude of the contractioii varies among the iiidividual
Ind. Eng. Chem. Prod. Res. Develop., Vol. 10, No. 3, 1971
243
members of the series and is smaller with alkanes undergoing solid phase transitions. A further contraction of 2-6% takes place during the solid phase changes (Harrison et al., 1958; Templin, 1956, 1963). Thus, in comparison with a great variety of other substances, the normal alkanes exhibit unusual behavior in the magnitude of shrinkage which takes place upon solidification. The normal alkane ci tal is held together by probably coordinate type bonding due to the end methyl groups (Gorin e t al., 1939) and the van der Waals forces between the methylene groups (Ohlberg, 1959; Salem, 1962; Zwanzig, 1963). Calculations of the van der Waals potentials ( ~ I u l l e r j 1936b) show these forces almost esclusively responsible for the bonding of alkanes in the solid state. The additivity of van der Waals forces between methylene groups iii neighboring chains of normal alkanes having an odd number of carbon atoms brings about a decrease in tlie cross sectional area of the chain with an increase in chain length (T'aiid and de Boer, 1947). In alkanes containing an even number of carbon atoms, this additivity result's in a deerease in the angle whicli the chain makes with the basal plane (Ohlberg, 1959). The layer structure of the crystals and their bonding by van der Waals forces determine a number of the macroscopic properties of the normal alkanes. The forces binding individual molecules iiito layers are weak forces, but t,hose forces holding layers together are weaker. Coiisequeiitly, iiornial alkane crystals cleave very easily along layers Xechaiiically, low-molecular-iveight alkane solids are weak materials, and applied forces readily cause gliding along layer planes. The extent of the resulting deformation varies according to tlie type of crystalline structure characteristic of the individual member of the homologous series. High-molecular-weight polymeric alkanes like polymethylene, however, are much stronger mechanically than the lower alkanes. Khere estremely long carbon chains are involved, the many weak attractive forces form a considerable total. 111addition, the strong carbon-to-carbon bonding forces come iiito play as polymer chains interconnect the crystallites makiiig up the bulk material. Solid P h a s e Transitions. M a n y substances exhibit polymorphism-that is, they exist in more than one solid form such that at constant pressure, one form changes iiito another a t a constant temperature. Each form has cliaracterist'ic physical and thermodynamic properties. In general, polymorphic forms of a substance are differentiated eit'her by the arrangement of molecules in a lattice, by the molecular orientation, or by both. Accordiiig to Ileffet (1942), such polymorphism has been detected in more than a thousand organic substances as well as in iiumerous inorganic materials. Thus, phase transformations other than melting aiid boiling are commonly encountered in physical aiid thermodynamic studies of organic substaiices. Two types of polymorphism are normally defined (Findlay, 1951; McCrone, 1965). When each of two polymorphs is thermodynamically stable in a defiiiit,e range of temperature and pressure, the pair is enantiot,ropic. When one is unstable at all temperatures, the pair is monotropic. Theoretical explanations of phase transformations in organic solids frequently are somewhat less than satisfactory, as are many of the att'empts to classify the types of solid transitions (Uuerger, 1951; Domb, 1960; Jaffray, 1948; NcCullough, 1961; hlcCrone, 1965; hIcLaughlin, 1956; Tisza, 1951 ; Ubbelohde, 1957; Westrum and RIcCullough, 1963). The change from the high temperature to the low temperature form takes place with the evolution of latent heat and is 244 Ind. Eng. Chem. Prod. Res. Develop., Vol. 10, No. 3, 1971
accompanied by a sudden entropy decrease and a n abrupt change in volume. This change is called an isothermal or first-order transition (Mayer and St,reeter, 1939; hIcCrone, 1965; St'aveley, 1949) which the normal alkanes undergo. Second-order transitions take place over a range of temperatures even though the major part of the change is often concentrated into a small temperature region. These transitions are acconipaiiied by ail anomaly in the specific heats but. may or may not involve a change iii crystal struct'ure (Staveley, 1949). dlt'hough second-order t,ransitioiis of normal alkanes have received some attentioii iii the literature (Frohlich, 1944; Hoffman, 1952; NcClure, 1968; Zimm et al., 1953), little evidence esists that aiiy pure normal alkane eshibits such a transition. If the change in specific heat is not abrupt, a third-order trailsition is iiidicated. Staveley (1949) suggests that both sharp and gradual transitions are fundameiitally alike and differ oiily in rate of occurrence. Gradual changes occur in some cases, p e r h a l ~by way of a continuous range of mixed structures (.Illen and Eagles, 1960). A substance having a first-order transition invariably has a lower elitropy of fusion than a similar one not polymorphic. Sometime.: the entropy of transition i3 so large relative to that of fusion that the high temperature form must in a sense be already quite like a liquid. This i. uiiderstandable if a t trailsition t,lie molecules gain the orientational freedom ot'her\vi.qeacquired a t melting (dmytli: 1946; Staveley, 1949). Many loiig-chain organic compounds show transitioiis probably relat,ed t o the oiiset of rotation of tlie chain ahout its asis (Uroadhurst, 1960; Crowe a i d Smyth, 1951; Crowe et al., 1952; Daniel and Stark, 1952; Davies aiid Kybett, 1965; Koll) aiid Luttoii, 1951; lleakiiis and Mulley, 1953; Schooii, 1939; Staveley, 1949; Katailabe, 1963; TVilsoii and Ott, 1934). The iiormal alkanes provide iilterest'ing esamples of such behavior. The nature of the rotational pha,?e traiisition iii normal alkane c tal3 has been reviewed by AIcClure (1968). Rotator Phase. J u s t below the freezing point, many of the iiormal alkane3 enter a state sho~vingcharact,eristics both of liquids and of crystalline solids (Staveley, 1949). Kitaigorodskii and IZiiyukh (1961) have described this state as basically one of order but which a t t'he same time represeiits a LLconcessioii to disorder." The tendency to order is satisfied by the esisteiice of a crystalline lattice of the molecular cent,er., aiid the teiideiicy to disorder by the rotmationof the molecules about their chain ases. This rather unusrial crystalline form is variously called t,he alpha phase, the rotational crystalliiie state, or tlie rotator Iihase. I11 a folloiviiig section it is identified a4 the a H phase. Wlieii i i i this form, the normal alkane molecules are in a vertical position with res1)ect to the end group plane.; and are believed t,o have sufficient freedom to rotat,e even though long-range order has been eitablished (Andersoii and Slichter. 1965; Chapman and Whittiiigton, 1964; Frohlich. 1952; Kakiuchi, 1950, 1951 ; lIalkiii, 1933; AIcClure, 1968; Mullerj 1930, 1932b; Timmerinaiis, 1961 ; Whittingtoii and Chapman, 1965). Crystals in a rotator phase teiid to be traii.;luceiit, plast'ic, and waxy (Smyth, 1963; White arid Bishop, 1940; White e t al.. 1940) aiid show much less resistance t'o deformation (llichils, 1948) than in tlie nonrotat~orphase stable a t lower temperatures. In these re;pects, ~iormalalkalies iii t'he rotator phase resemble the so-called plastic crystals said to show a dielectric behavior and give electron microscopy diagrams resembling liquids rather thaii crystalliiie solids (.\.;ton, 1961, 1963; Duiiiiing, 1961; Smith. 1967; Smyth, 1946; Staveley, 1962; Timmermaiis, 1938, 1953, 1961). However, the normal
alkanes apparently do not form true plastic crystals since, according to a rule of thumb, the entropy of fusion is much too high (Timmermans, 1938). Infrared absorption spect'ra on normal alkanes having a rotator phase show a single band a t about 720 em-' in the liquid st'ate. This baird does not change upon solidification into thc rotator phase (Chapman, 1955; Guseva and Leifman, 1964; Martin e t al., 1958; Nielson and Hathaway, 1963; Tasumi and Shimaiiouchi, 1965) but becomes a doublet below the solid transition point. Two refractive indices are observed in alkanes in the rot'ator phase (Guseva and Leifman, 1964; Ilarrison et al., 1958). The wasiiiess and pia-t'icity of the rotator phase has been attributed to the greater volume occupied b y a somewhat unsymmetrical molecule when rotating (Smyth, 1961). The term "molecular rotmation"in solids does not signify the free molecular rotation of the gaseous state but signifies only t.hat barriers are low enough t,o permit, frequent i,ot,ationalpassage of the molecules. K i t h decreasing temperatmurethe rotational freedom decreases sharply a t a transition point, referred to as rotational (Eucken, 1939; dmyth, 1961). From studies using nuclear resonance and neutron scattering, 5ome degree of rotational freedom persists below the transition temperature but gradually decreases with lowered temperat,ure (Andrewv, 1950; Danner et al., 1964). At the rotational transition the normal alkanes show an abrupt change in many of their physical properties. Nonrotator Phase. Upon cooling through t h e rotational transition temperature, the normal alkanes assume crystalline forms denser than the rot,ator phase. These solid forms vary in structure according to the lengths of the carbon chains. With sonie members of the alkane series, the chains remain in a vertical position with respect to the end group planes; a1though the chains w e closer together bhan in the rotator phase, some degree of rotabion is thought still possible (Chapman, 1955). Other members of t'he series, upon passing through the rotational transition: assume a form in which the carbon chains are tilted with respect to the end group planes slid iii which 110 molecular rotation occurs;. Still other memhers seem to solidify directly itito a tilted structure without going through a rotator phase. Hoffman and Sniyth (1950) suggest that' these lat'ter alkalies do have a rotator phase, but its persistence time is so short that, it, has not been detected. -1 more detailed account of t'he comples cryst8alliiie phase behavior of the normal alkanes will he given in the section dealing with crystalline structure. 13elow the rotational transition temperature, the normal alkanes have an opaque appearance and are denser, harder! and more brittle than above that temperature. Infrared absorption measurements made on the nonrot,at'orphase show a shifting or splitting of the 720 cm-' band observed with the liquid and rotator p h a m of the alkanes. The values of the bands depend upon the lengths of the chains (Krimni et al., 1956; l f a r t i n et al., 1958; Xielson and Hat'haway, 1963; Snyder, 1960, 1961. 1963, 1967; Stein and Sutherland, 1954; Theimer and Theimer, 1962). Either two or three refractive indices cftn be measured in alkanes in the nonrotat,or phase depending on the technique used (Guseva and Leifman, 1964; Harrison et al., 1958; XcCrone, 1954). The values observed again are related to the length of the carbon chain. Mechanism of Solid P h a s e Changes. T h e growth of crystals from fluid phases and of one solid phase in another shows a number of points of similarity. Nucleation occurs when small domains of the phase to be generat,ed first appear
at one or more points in the existing phase. The nuclei propagate at the expense of the initial phase. The total rate of phase change is determined by the rate of nucleation and the rate of growth (Turnbull, 1956). The interface between the phases moves rapidly, in some cases at almost the speed of sound (Fine, 1964). Turnbull (1963) has reviewed the thermodynamics and kinetics of phase changes in solids. In any material a transformation from a high temperature stable form into a low temperature stable form always occurs a t a temperature much lower t'han the phase equilibrium temperature; conversely, a transformation in the opposite direction occurs at a temperature much higher than the equilibrium temperature (Kitaigorodskii e t al., 1965). Since the amount of supercooling or superheating needed to initiate nucleation is usually much greater than that required for nuclei t o grow, the energy barrier opposing nucleation is much greater than that opposing crystal growth. Thus, the rate of nucleation and consequently of growth usually is strongly dependent upon the degree of superheating or supercooling (Turnbull, 1956). The more nearly perfect the crystal undergoing transformation, the greater the amount of supercooling or superheating that must be applied before the phase change will begin (Kitaigorodskii e t al., 1965). According to theory, boundary energy considerations and st,rains in the esist'iiig phase contribut,e to the formation of nuclei. The precursors of the nuclei are clusters of molecules having the st,ructure of the new phase and existing in a st,eady state concentration within the initial phase (Turllbull, 1956). These potential seeds residing within the crystal are responsible for the memory of orientation observed in transformabioiis (Kitaigorodskii et al., 1965). Xucleation is often said to be of two types. When it occurs in the interior of a structurally pure phase, it is called homogeneous or spontaneous nucleation; but if it arises from structural impurities. such as foreign particles or surface imperfections in the crystal, it is called heterogeneous nucleation. Such defects are preferred nucleation sites, and all nucleation basically may be heterogeneous in nat'ure with the cause sometimes undetected. Sucleation occurs a t visible defect sites and is believed to arise from defects too small t'o be seen. To induce transformat'ion in small, highly transluscent,, almost perfectly shaped crystals is often impossible, but if a small defect is created mechanically in the cryst'al, a transformation is induced. Polymorphic transformation may be classified as singly ceiit,ered or mult'icentered according to the number of nuclei groiving within a crystal. Each facet of a growing crystal has its own orientation and rate of growt,h. The rate of traiisformation depends upon t'he composited cryst'allographic orientations. .is in the case of crystal growth from a fluid phase, the advancing crystal front wit'hin a solid phase tends to assume a coiives form, the shape giving minimum surface free energy. The faces of the growing crystal appear more nearly perfect the slower the growth process (Kitaigorodskii e t al., 1965). When crystal trailsformation begins in a supercooled or superheated solid phase, it proceeds rapidly unt,il the equilibrium temperature is attained and then slows to a rate consistent with the rate of heat transfer into or out of the Since the heat of transition is only about'a third of the heat of fusion (Fontana, 1953), solid st'ate phase changes can be relatively fast. Solid P h a s e Behavior of Normal Alkanes. T h e marked changes i n physical properties occurring a t certain temperaInd. Eng. Chem. Prod. Res. Develop., Vol. 10, No. 3, 1971
245
tures i n petroleum waxes have often been associated with the polymorphism of the individual chemical compounds making up the waxy mixture (Birdwell and Jessen, 1966; Cines, 1950; Edwards, 1954, 1957, 1958; Minchin, 1948). As t8he major constituent of most waxes, the normal alkanes have received much study, but a great deal of confusion has ariseu over their complex phase behavior. Some of this confusion has resulted from the observation of crystalline st,ruct,ures which are metastable or appear because of the presence of impurities (Smith, 1953). The incomplete picture given b y studies made over a limited temperature range has added t,o the uncertainty. In addition, the nomeiiclat.ure applied to the normal alkane phases b y different observers has varied so much as to cause considerable confusion in itself. I n this discussion, minor deviations from the usual behavior for the most part will be disregarded and the emphasis placed upoii the presentation of a unified picture of the phase relationships of the normal alkanes. The various crystal forms will be identified according to a scheme adopted by 13roadhurst (1962b) for reasons of simplicity and uniformity. This notation combines historical precedeiice with a descriptive symbolism by using the traditional symbols (Y aiid to designate, respectively, the high and low temperature phases of the normal alkanes and by using the subscripts H, 0, T, and 31 to indicate the type of crystalline structure. The symbols aH,PO, PT, and p31 designate, respectively, the hexagonal, orthorhombic, triclinic, and monoclinic crystal structures. These four solid forms are sufficient to characterize the structures of all normal alkanes above C g (abbreviation for n-C9Hno)cont,aining an odd number of carbon atoms in the molecule and the structures of all alkalies above Cq containing an even number of carbon atoms. The remaining estremely short-chain normal paraffins form solid structures which do not fit into the general patt'erii of the longer paraffiiis and will not be discussed here. Esperimeiits by Larsson (1967) and by Takagi and Suzuki (1954) suggest t'hat the structure in the aE phase is not esact'ly hesagonal. Crystalline Structure of Normal Alkanes
Crystals of the normal alkanes separate from a melt or solution in four characteristic geometric forms described iti detail later. Each form can be classified into one of the sis systems used in optical methods of analysis in which each system has a definite arrangement of three or four ases about' which the crystal planes are symmetrically placed. The forms can be classified also by X-ray and other diff raction techiiiques.
[b'o
P
v
-
LAYER
4 ,p Y
Figure 1. Schematic representation of arrangement of normal alkane molecules in layers and of layer stacking (a) (b!
246
Rectangulor layers, CYH and Po structures Oblique layers, and PT structures
Ind. Eng. Chem. Prod. Res. Develop., Vol. 10, No. 3, 1971
From the nature of the reflections obtained from the various faces of the crystals, the arrangement of the molecules j i i the crystal and their distances from each other can be determined. The crystalline structures of t,he normal alkanes have been investigated by a number of workers (At,kiiison and Richardson, 1969; Chernozhukov et al., 1962; Clarke, 1961; King and Garner, 1936; Mazee, 1948; XIiiller, 1932a, 1936a; Miiller and Lonsdale, 1948; Schaerer et al., 1955; Smith, 1953). The shape of the normal alkane molecules is similar in all crystals. The carbon atonis of the methylene groups are believed t'o lie ill one plane forming the fully esteiided zig-zag configuration described earlier. The long ases of the chains are pardlel to each other and are arranged in regular fashion so that the elid groups of the molecules form two parallel planes (Jeiisen, 1970; Xiiller, 1928; Smith, 1953). The chain axes are perpendicular to the elid group planes in the a= and Po structures and are tilted with respect to the eud group planes in the PT and PII forms (Figure 1). Thus, the thickness of a molecular layer depeiids on t'he molecular chain length and on the angle formed by the chaiii ases aiid the end group planes. The density of the solid layer also depends on these factors it] that it reflects the arrangement of the molecules within the layer or t'he molecular side packing. Like other organic compounds, the normal alkalies form crystals constructed in such a way t'hat the projections on one molecule enter the hollows in those surrounding it. The packing arrangement assumed is that giving the closest possible fittiug together of these molecular irregularities under a particular set of coiiditions. This closest liacked arrangement gives the minimum free energy. Although pro1)erties of the molecule other than its geometry niay esert effects, these seem of secondary importance to molecular shape (Kitaigorodskii, 1957b,c, 1961 ; Kitaigorodskii and N n y u k h , 1958, 1959a; Mnyukh, 1960). The molecular side packing or packing within a layer and the end group packing or layer stacking both play a part in determining crystal struct,ure. The energy of the cryst'al probably is made u p of two compoiieiits, one dependelit on the lat'eral interaction of the chaiiis and the other on the ititeractions of the ends. The relative values of these forces will vary with chain length and cause differences iii the st'ability of the cryst,al structures. The structure oht'aiiied is a resultant of two tendeiicies: to form the densest packing and to preserve the highest possible molcciilar symmetry in the crystal ( l l n y u k h , 1960). The mode of side packing in a layer can be analyzed by assumiiig that the aliphatic chain is infinitely long so that eiid group effects can he neglected. The closest packiiig for two adjaceiit zig-zag chains can occur only if a hydrogeii atom from one molecule enters the depression formed by three hydrogeii atoms attached to different carbon atoms i n a n adjaceiit molecule (Figures 2 and 3), 'Three types of closest packing can be described iii this way, differing iii the traiislatioii of a chaiii normal to the asis of t,he adjaceiit molecules and iii t,he orientation of methyleiie plaiies of alternate molecules. The uiiit cells for iiifiiiite length chaiiis can i11 this way be described as beiiig orthorhombic, motiocliliic, and triclinic (Kitaigorodskii and IInyukh, 1958). Cell dimensions are reported iii the literature (SIcCroiie, 1954). In layers built from chains of finite length, however, aiiother parameter, the incliiiation of the chains with respect to the eiid group \)lanes, must be considered. The angle here niay be 90' or another angle, but the methylene group packiiig remailis the same in all cases provided the displacement along the chain of identical molecules is done in multiples of 011eC-C uiiit (Kitaigorodskii, 1961; lIliyukh, 1960). Layers
of molecules of finite length show only a two-dimeiisional periodicity, aiid the cells found in layers have iio significance as crystal cells. However, these layer cells, termed subcells (Vand, 1951), show the characteristics of methylene group packing i i i the various cases ( B u m , 1939; Kitaigorodskii and Xiiyukh, 1959a; Xullerl 1928; lliiller aiid Lonsdale, 1948; Smith, 1953; Vaiii$htein aiid Piiisker, 1950). Figure 4 diagrams the molecular arrangements iii the subcell of: (a) the Po and PSI st,ructures, (b) the PT structure, and ( e ) the CYHstructure. Cross sections perpendicular to the chaiii axes are shown. Hexagonal Crystal Structure. Crystals belonging t o t h e hexagonal system have three equal axes in the same plane intersectilly at an angle of 60” aiid a fourth axis, longer or shorter than the ot’hers and perpendicular to them. This aN structural form, upon cooliiig from the liquid form, is the one which many of the iiormal alkanes in the paraffin was range assume as their first molecular arrangement in the solid state. This form i i closely related t,o the ordered st,ructure which the molecules had already attained in the liquid just above the fi,eeziiig point (Daniel, 1953; Lufcy et. al., 1951; J’aiid! 1953) aiid forms a iiatural sequel to the ordered structure when further cooliiig requiws the molecules t’o enter a lower energy state. X study of the aEiform of iiormal 1101:adecane by Larssoii (1967) indicates that the symmetry actually is not hexagonal. 111the licsagoiial €oi,m the molecular chains are arraiiged perpeiidiculai, to the eiid group planes aiid rotate about their long axes (IIoffmaii, 1952; Nalkin>1933; Niillei,, 1930, 1932b; l’auliiig, 1930: Timmermaiis, 1961). This high degree of molecular rotational freedom is an importaiit characteristic of the CY^ phase and is uot an uiiusual pheiiomeiioii amoiig substaiices i$-hich form talliiie lattices (Kitaigorodskii, 1959; lltiller, 193i, 1940). The structural details of the CYH phase of iiormal alkalies have been reported (Muller~ 1928, 1930, 1932b; Smith, 1953). The subcell is hexagoiial. The hesagoiial structure, symbolized here as CYH,has lieen variously dcsigiiated iii the 1iteratui.e as: the a-form (Garner et al., 1931; GraJ-, 1943), the S, modification (Schaerer et al., 1956), the A-form (Templiii, 1956), aiid the H-form (Kitaigorodskii, et al., 1958). It also has been called the crystalline gas structurc, (Euckeli, 1939; Kitaigorodskii, 1959; Xiiyukh, 1960) the n a s y rotat’ioiially melted or rotator 1)hase (Hoffman and Smyth, 1949; Hoffman, 1952), and the transparent vertical rotating fo1.m (lIiiichiii, 19-18). Although crystalline in nature, it is cliaracteristically plastic, waxy, aiid traiislucent aiid resembles the liquid state in several ways (Miiyukh, 1959b; Staveley, 1949). The CYH form is st,able just below the freezing point iii the
Figure 3. molecules (a)
Various cell arrangements of normal alkane Monoclinic
(b) Triclinic (c) Orthorhombic The chain axes are perpendicular to plane of paper
“odd” alkanes from C9-C43aiid iii the “eveiis” from C22-C12. Some observatioiis iiidicat,e that it ca11 aijpe:ii’ i n t,hc “ ~ v e i i > ” below possibly as a meta-table form (Carey aiid Smith, 1933; Kieras et al., 1964; Scliaei,ei. et al.. 3356; 8mitl1, 1932) t s so briefly that it is not always detected (Hoffman and Ymyth, 1950). Orthorhombic Crystal Structure. Crystals beloiigiiig to the rhombic iystem arc cliaract’erized IIJ- haviiig three ases of unequal length a t right angles to each other. Sometimes called orthorhombic., this structural form, Bo: i-; one of the hard form. assuinctl hy many of the 1)ure normal alkaiies and other long-chili molecule. u p from either the liquid state 01’ the aH form. 111thi. structure the chains are perpeiitlicular to the eild group plniir, so that, a transformation into the structure fi,om either the ordered liquid or the cyIi p1ia.c can take place caiilj- n-hell, upon cooling, chaiii rotatioii ctases 01’ i)ecomc,s greatly re.;tricted. The cyE t o Bo traii;itioii has liemi itleiitified a. a rotational, order-disorder traiiqitioii (Hoffman, 1952) ~v1iic.h might also involve t,orsioiial effects (Olf aiid I’cterliii, 1970; Szigeti. 1952, 1953).
lbl
I
I
Figure 2. Schematic representation of possible dense packing of cross sections of normal alkane molecules in orthorhombic cell
Figure 4. alkanes:
Molecular arrangements in subcells of normal
( a ) in Bo and p.11 structures (b) in structure (c) in CLH structure Cross sections perpendicular to chain axes a r e shown
PT
Ind. Eng. Chem. Prod. Res. Develop., Val. 10, No. 3, 1971
247
The orthorhombic structure of the normal alkanes, labeled here as Po, has been designated by various investigators as the p-form (Gray, 1943), the pl-form (Hoffman and Decker, 1953), the S P modification (Schaerer e t al., 1956)) the A-phase (Xiiller, 1930; Ohlberg, 1959), the A 2 form (Templin, 1956), and the R form (Kitaigorodskii et al., 1958). This structure has also been termed the vertical, opaque, nonrotating form (llinchin, 1948) and along with /3T and P l I has been described as a rotationally frozen or prerotator phase (Hoffman, 1952). Structural details of the orthorhombic phase have been reported (Bunn, 1939; Heiigstenberg, 1928; King and Garner, 1936; Kitaigorodskii and l l n y u k h , 1958; Sluller, 1928, 1929a, 1930; lliiller aiid Saville, 1925; Smith, 1932, 1953; Teare, 1959; Vainshtein and Pinsker, 1951; Vand, 1953; Wyckoff, 1960). The subcell is orthorhombic. The orthorhombic structure is the stable, low temperature phase of the “odd” normal alkanes Cg and above and is a high temperature lihase of C30 and perhaps af all “evens” above C32. This structure is also the single crystalline pliase of C; (Westrum and JIcCullough, 1963) and, in addition, is the low temperature form assunied by mixtures of iiormal alkanes and, therefore, the usual form observed with normal alkanes of questionable purity. Because of chain end irregularities, the Po structures developed iii normal alkane mixtures are not exactly the same as those assumed by the pure normal alkanes. Monoclinic Crystal Structure. Crystals classified as being monoclinic have three axes of unequal length, two a t right angles! and the third pciyendicular to oiie of these but not to the other. The pArstructural form is assunied by the “even” alkalies above and possibly including C2.! (AIazee, 1960) and CY6 (Broadhurst, 196213) upon cooling from the CYH or 00 phases and perhaps also from the melt in the case of the “even” alkanes above Cl0. 130th monoclinic and triclinic forms have been rellorted for Cp6(Ohlberg, 1959). 13ecause the transition into this pliase is a more complex operation than into the aAror Po phases, the latter are usually preferred among the alkanes as iiitermediate steps. The chains make an angle of about 61” with the end group planes (Gray, 1943), representing a displacement of adjacent chains aloiig their axes of about two carbon-t’o-carbon units so that considerable slippage of chains must occur for this low energy phase to form. Rotatioii of the tilted chains is very restricted. Structural details of the OAIphase in normal alkanes are given in the literature (King and Garner, 1936; Mnyukh, 1969a, 1960; SIuller, 1936a; Shearer and Vand, 1956). The subcell is orthorhombic. The frequent occurrence of the PO structure in the “even” form would be normal alkanes above about Go, where expected to prevail, probably results from impurities not removed in preparation. Impurities of homologues become more difficult to remove from higher-molecular-weight range mixtures. Even though the PJr phase represents a lower energy state than Po, and, therefore, should be preferred, the energy difference between the two forms is small and provides little driving force to bring about a transition, thus contributing to the likelihood of a PO structure. The monoclinic structure, PI[, has been variously designated as the @-form (Gray, 1943), 0-form (Garner et al., 1931), S p modification (Schaerer et al., 1956): P2-B form (Hoffman and Decker, 1953), &form (Templin, 1956), C-phase (A‘ILiller, 1930; Ohlberg, 1959), and R-form (Kitaigorodskii et al., 1958). This structure has shared with the PT structure the designation as the opaque, nonrotating tilted form (Minchin, 1948). Triclinic Crystal Structure. Triclinic crystals have three axes of unequal length, no tn-o intersecting at right angles. 248
Ind. Eng. Chem. Prod. Res. Develop., Vol. 10, No. 3, 1971
The PT or triclinic structure represents t,he lowest energy state into which the shorter “even” carbon number alkanes enter upon cooling either from the melt or aHform. The transition into this form is complex because the chain axes are tilted a t an angle of about 73’ with the end group planes (Gray, 1943), meaning that adjacent chains are displaced in the direction of the chain axes by a distance equal to ahout one C-C unit. Rotation of the chains is very restricted. Structural details of the triclinic phase are giveii in the literature: (King and Garner, 1936; Kitaigorodskii and Xnyukh, 1958, 1959a; Mathisen et al., 1967; Mazee, 1948; Xiiller and Saville, 1925; lliiller and Lonsdale, 1948; Schaerer et al., 1955; Smith, 1953). The subcell is triclinic. f f i t h ( 2 2 2 , C21,and Gee, transition from the liquid into PTocCurs via CYH, b u t with C20 and below, no stable aH phase is observed, and PT persists even down t,o CSaiid C6 (Xorniaii and Mathisen, 1960, 1961) and possibly to C4. Hoffman and Smyth (1950) have suggested that the a Hphase is present in the alkanes Cnoand below but persists such a short time that it is not easily detected. Other workers have confirmed it,s presence by measurement of a metastable melting point (Carey and Smith, 1933; Schaerer et al., 1956; Smith 1932). Transitioiis have been reported several times for (Kieras et al., 1964; Miiller, 1930; Sechitailo et al., 1960; Schaerer et al., 1956; Templin, 1963), but it never has been firmly established that these were not the result of impurities. S o r m a l c26 has been observed to have both PT aiid PII forms as its low t,emperature stable form, and its proper classification has caused considerable discussion (I3roadhurst, 196213; Olilberg, 1939). The PT phase seems to be the long term equilibrium form of CY6. Triclinic modifications have been found in polyethylenes (Kitaigorodkii and Mnyukh, 1958; Teare and Holmes, 1957). The triclinic structure, symbolized here as PT, has been designated also in the literature as the y-form (Gray, 1943), the p-form (Garner e t al., 1931), the S P modification (Schaerer et al., 1956), the &-A form (Hoffman and Decker, 1953), the 1% form (lliiller, 1930; Ohlberg, 1969; Templin, 1966), and the T form (Kitaigorodskii et al., 1958). This structure, along with the monoclinic structure, has also been called the opaque, nonrotating tilted form (Minchjn, 1948). Crystal Packing and Effect of End Groups. T h e crystal structure of a solid represents a solution of the problem of how the bonding forces of atoms or molecules of particular shapes and force fields can be satisfied. Under a given set of conditions, one solution of this problem is usually much better than alternative ones with the result that a certain crystal structure remains stable oT;er a wide range of temperature. Xormal alkane crystals of ten find several alternative structures which have similar stabilities and differ in such minor points as molecular packing arrangements and the restraints imposed upon twisting and turning motions of the long chains. The geometrical packing of the four crystalline forms described above has received considerable attention in the literatue (Kitaigorodskii, 1957b,c, 1961, 1965; Kitaigorodskii and Mnyukh, 1959a; Schoon, 1938). These structures do represent the molecular arrangements which on a theoretical basis could be expected to give the densest packing. If the molecules are pictured as being made up of overlapping spheres of R size aiid distance from each other consistent with the atomic radii and the molecular bond lengths, then arrangements providing the greatest density of packing are in agreement with observed structures. Crystallographic measurements show that the packing of the CH2groups is roughly the same for all three P structures, the main differences in the relative displacements of adjacent
chains aloiig the chain axes; the displacement is iioiie for P I ! . The phases (Shearer and Valid, 1956). Thus, the relative stabilities of these latter two crystalline structures must he attributed t o differelices iii t,he eiicl group packiiigs. Tlie differelices in free energies between the two forms is then necessarily quite small which partially explains why the higher-molecular-weight “eveii” normal alkanes so frequently appear iii the Po phase rather than /33r which would be the expected form. The eiid groul) 1)acking effects must alqo be important iii esplaiiiiiig ivliy the /3T form doe$ not appear above C26, and the plr form does not appear below. The shift a t C26 probably occurs because of the diiiiiiiishiiig ratio of eiid groups t o chaiii groups (Uroadhurst, 196211: llriller, 1930) aiid the effects upon the free energy of the resulting subcells (hliiyukh, 1960). Both structural forin. have been observed with Cy6. Why this particular niolecu1:ir size should form such a sharp divisioii mark iii the structural scheme has not yet been explaiiied on a Triclinic packiiigs have been found in samples of polyethyene (Teare aiid Holmes, 1957), normally orthorhombic. The effects of end groups in packing caii be seeii also iii the well-kiion-n odd-even altematioii (Hoffman and Decker, 1953) in iiieltinp temperatures of the normal alkalies below C23 and in .solid phase traiisitioii teniperatures of the norinnl alkanes between C20 a i d approximately C‘,$ (lICiller, 1929a). Tliese alteriiatioiis occur oiily if a tilt’ed chain structure is involved. \Then the nietliylcne chains are packed vertically as in the 0iH niitl Po l)haies, the riid group p a c k i n g probaI.11~are the same for both odd- and eveii-iiunibered cliaiiis. \Tlicii the chains are tilted. only those chains liaviiig aii even iiuiiiber of carboii a t o m will have tlie symriietry required for equivaleiit low eiieigy packing of the g1’oLiI)j a t both ends of the molewles. However, as has been pointed out iii the case of loiig-chaiii esters (Xalkiii, 1933), if aii odd-numbered chain is tilted, and one eiid as.wmes the p r e f e r i d Ion- energy position, the otlier elid is forced into a differelit and alq)ai’eiitly higher energy positioii. Thus, the tilted structures reprrseiit low energy molecular arrangeinelits for the “eveii” alkanes but not for the “ o d d ’ oiies. \\-here no tilting is involved, as iii tlie liquid, Iiesngoiinl, or ortliorhombic phases, the “even” and “odd” iiormal alkalies are equivalent. S o alteixation is in nieltiiig points above Clo, but below C20,alteriiatioii does occur becnu>e of the /3T structure which tlie eveii-iiumbered chains assume. The alteriiatioii in transit,ioii point betweeii C20and perhaps C4, doe> occur because tilted phases :ire involved. The arraiigenieiit .;lio~vii i i i Figure 5 illustrates how oddiiumhered carlmi chains would be unable to achieve high deiisity 1)ackiiig in a tilt,ed structu1.e readily accommodating the “even” chains (Hroadliurst, 1962b; Xalkiii, 1931, 1933). dside from the effects of tilting chains noted above, t,he crystalliiie density of the normal alkanes is also affected by the number of carboii atoms in the chaiii. The effect can occur in two ways. Tlie vaii der TVaals forces between adjacent’ chains increase with each methylene unit added. The total of attractire forces 1)etn.eeii two cliaiiis becomes greater as the chains iiicrense in length, remlting in a decrease i i i cross sect,ioiial area of tlie cell a i the chaiii leiigth increases (Ohlberg, 1959; Valid aiid de 13oer, 1947). hi additioii, alkane crj-stals consist of layer3 of molecules villose thickness depends oii the number of calboii atoms in tlie cliniii. *is this number increases there arc fewer but thivker layers, aiid, therefore, fewer iiiterlayer spaces. 130th of these factors tend t o produce a corresponding illcrease iii the forces operating within tlie crystal with a coiisequent deiisit’y increase (13uckiiigham, 1934; Xazee, 1948 ;
pot oiie C-C unit for &, and two C-C units for CH2 packiiig is nearly identical in the 60 aiid
’ODD‘
pM-7 7 Figure 5. Schematic illustration of effect on packing density of “even” vs. “odd” normal alkanes Small circles represent methylene groups; large represent methyl groups phase, “evens” allow more closely fitting which mark layer planes. In layers than “odds” and thus give higher density pocking
Bx
lIcCroiie, 1954; l111yukI1, 1963a; Vaii Hook and Silver, 1942). Along n-it11 the iiiereased tleiisity of the longer chain crystals is a n increase iii melting point, reflecting tlie stronger iiiteriiiolecular forces which oppose the liberation of the niolecular cliaiiis from the highly ordered meiit. The melting points of tlie iioriiial alkalies increase with chain length and approach a limiting value representing the iiieltiiig teiuperature of ai1 infinitely long alkane chaiii (13roadhurst, 1962a, 1966; Etessam aiid Sawyer, 1939; Flory and Vrij, 1963; Garner et al., 1931; Herbrandson and Sachod, 1955; Iiravchenko, 1947; Quiiiii and Maiidelkerii, 1958; Richardsoii, 1965; vaii Xes aiid vaii TTesten, 1951 ; STunderlich and Dole, 1957). This value is in the range of 135-145’C and has been approached very closely by the synthesis of high molecular weight, substantidly linear polyethylenes and polymethylenes (Kaiitor and Ostoff, 1953; JIaiidelkwi et a]., 1953). Certain physical !)roperties of the alkanes i n the solid s t a t e reflect aiiisot’ropism. The traiisiiiissioii of light through the cryst’al in orthoscopic observatioiis (Clarke, 1951) measurements of refractive iiidices (Ilnrrisoii et, al., 1958; Johnson, 1954), and measuremeiits of iiifi,ured absorptioii shows differences due to crystal oiientatioii. The mecliaiiical compressibility of t,lie crystals of certain iioriual alkanes near the nieltiiig point is also anisotropic, with the crystals being about 35 times as compressible in directions across the chain as aloiig tlie cliaiii asis itself ( l I d l e r , 1941). I n the fornier case only weak intermolecular forces are beiiig opposed, whereas ill the latter case tlie deformation of strong carboii hoiids iii iiivolvcd. Significance of Carbon Chain Length. Useful information about the crystalline structures of tlie normal alkanes has been obtained through measurements of the length of their carboii chaiiis in the solid state. X-Ray trcliiiiques are used t o obtain “long spaciiig” d a t a , which for a particular phase are virtually iiisensit’ive to temperature variations. .imong the many workers who have made such measurements are: Uarbezat-Debreuil, 1958; Francis et al., 1937; Hoffmaii and ~
Ind. Eng. Chem. Prod. Res. Develop., Vol. 10, No. 3, 1971
249
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3 0 4 0 SO 60 70 8 0 NUMBER OF CARBON ATOMS
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90 100
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' 4 '8
24' ' '32 NUMBER OF CARBON ATOMS
'
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64
Figure 6. Relationship between X-ray long spacing and phase type among normal alkanes
Figure 8. alkanes
Decker, 1953; NcCrone, 1954; Miiller, 1928, 1930; Norman and IIatliiseii, 1960, 1961; Ohlberg, 1959; Piper and Malkiii, 1926; Piper et al., 1925, 1930, 1931; Ranby et al., 1960; Robertson, 1953; Schmidt, 1942; Shearer and Vand, 1956; Smith, 1953; Stiil1bei.g et al., 1952; aiid Stenhagen aiid Tagtstrom, 1944. The data show that the individual members of tlie series fall into different classes according to the position which the fully extended chain occupies i n the crystal. Uroadhurst, (1962b) has selected from published data, values for the long spacings of t'he normal alkanes. These data, suitably processed and plotted against carboii number, fall 011 three straight lines
correspondiiig to the vertical lilia>es 0 1 ~and so and t o the aiid P T spacings tilted phases 6.11 and PT (Figure 6). 130th have been reported for Cy6.The "odd" normal alkalies below CI1fall uiider the line representing the vertical pliaqes. iiidicating that these shortest odd-nuiiiliercd alkalies differ from the longer members i n having cliaiii; tilt,ed i n what likely is some form of triclinic structurr. The data for aiid CS4sugge5t that tlic low temperature Where the spacstable form of pure long-chain alkanes is ing value indicates a vertical chain p ~ e \ e i i tthe ~ I)o.*ibility exists that this form ma>-arise from the lireseiice of iniiiurities. Phase Transition Temperatures. Many values have been reported in tlie literature for the phase changes which t'ake place ill the iioi,mal alkanes (;lustill, 1930; ,Itkinson and Richardsoii, 1969; Uuiin, 1955; Cines, 1950; Clarke, 1951; Etessani and Sawyer, 1939; Fiiike et al., 1954; Francis et al., 1937; Ganlei, et al., 1931; Gray, 1943; Hildebrandt and It'achter, 1929; Isiliara, 1948; Johiimi, 1954; Joliet: 1953; Iiarapet'yaiits, 1957; Iiolvoort, 1938; I
