Page252FIGURE 3Unitcellofordinaryiceato°C.Circlesrepresentoxygenatomsofwatermolecules.Nearest-neighborintemuclearO-odistanceis 2.76 A;0 is 1090substructure is evident from molecule W and its four nearest neighbors, with 1, 2, and 3 being visible, and the fourth lying belowthe plane of the paper directly under molecule W.When Figure 4a is viewed in three dimensions, as in Figure 4b, it is evidentthat two planes of molecules are involved (open and filled circles).These two planes are parallel, very close together, and theymove as a unit during the “slip"or flow of ice under pressure, as in a glacier.Pairs of planes of this type comprise the basalplanes"ofice. By stacking several basal planes, an extended structure of ice is obtained. Three basal planes have beencombined to form the structure shown in Figure 5. Viewed down the c axis, the appearance is exactly the same as that shown inFigure4a,indicatingthatthebasalplanes areperfectlyaligned.Ice is monorefringentinthisdirection,whereasitisbirefringent irall other directions.The c axis is therefore the optical axis of ice.With regard to the location ofhydrogen atoms in ice, it is generally agreed that:1. Each line connecting two nearest neighbor oxygen atoms is occupied by one hydrogen atom located 1 0.01 A from theoxygen to which it is covalently bonded, and 1.76 ± 0.01 A° from the oxygen to which it is hydrogen bonded. This configurationisshowninFigure6A2.If the locations of hydrogen atoms are viewed over a period oftime,a somewhat different picture is obtained.A hydrogenatom on a line connecting two nearest neighbor oxygen atoms, X and Y, can situate itself in one of two possiblepositionseither 1 A from X or 1 A°from Y.The two positions have an equal probability of being occupied. Expressed inanotherway,eachpositionwill,ontheaverage,beoccupiedhalfofthetime.ThisispossiblebecauseHOHmolecules,exceptat extremely low temperatures, can cooperatively rotate,and hydrogen atoms can“jump"be-
Pag e 25 FIGURE 3 Unit cell of ordinary ice at 0°C. Circles represent oxyg en atoms of water molecules. Nearest-neig hbor internuclear O-O distance is 2.76 Å; q is 109°. substructure is evident from molecule W and its four nearest neighbors, with 1, 2, and 3 being visible, and the fourth lying below the plane of the paper directly under molecule W. When Figure 4a is viewed in three dimensions, as in Figure 4b, it is evident that two planes of molecules are involved (open and filled circles). These two planes are parallel, very close together, and they move as a unit during the “slip” or flow of ice under pressure, as in a glacier. Pairs of planes of this type comprise the “basal planes” of ice. By stacking several basal planes, an extended structure of ice is obtained. Three basal planes have been combined to form the structure shown in Figure 5. Viewed down the c axis, the appearance is exactly the same as that shown in Figure 4a, indicating that the basal planes are perfectly aligned. Ice is monorefringent in this direction, whereas it is birefringent in all other directions. The c axis is therefore the optical axis of ice. With regard to the location of hydrogen atoms in ice, it is generally agreed that: 1. Each line connecting two nearest neighbor oxygen atoms is occupied by one hydrogen atom located 1 ± 0.01 Å from the oxygen to which it is covalently bonded, and 1.76 ± 0.01 A° from the oxygen to which it is hydrogen bonded. This configuration is shown in Figure 6A. 2. If the locations of hydrogen atoms are viewed over a period of time, a somewhat different picture is obtained. A hydrogen atom on a line connecting two nearest neighbor oxygen atoms, X and Y, can situate itself in one of two possible positions—either 1 Å from X or 1 A° from Y. The two positions have an equal probability of being occupied. Expressed in another way, each position will, on the average, be occupied half of the time. This is possible because HOH molecules, except at extremely low temperatures, can cooperatively rotate, and hydrogen atoms can “jump” be-
Page 264.52Ao(a)(b)FIGURE4The"basal plane"ofice (combination oftwolayers of slightly different elevation).Each circlerepresents theoxygen atomofa watermolecule.Open and shaded circles,respectively,representoxygenatomsintheupperandlowerlayersofthe basal planes.(a)Hexagonal structureviewed down the c axis.Numberedmoleculesrelatetotheunitcell inFigure3.(b)Three-dimensionalviewofthebasal plane.Thefrontedgeofviewb corresponds to thebottomedge ofviewa.The crystallographic axes have been positionedin accordance with external (point)symmetry.tween adjacent oxygen atoms. The resulting mean structure, known also as the half-hydrogen, Pauling, or statistical structure, isshown in Figure 6B.With respecttocrystal symmetry,ordinary icebelongstothedihexagonal bipyramidal classof thehexagonal system,In addition,icecanexistinnineothercrystallinepolymorphicstructures,andalsoinanamorphousorvitreousstateofratheruncertainbutlargelynoncrystal-
Pag e 26 FIGURE 4 The “basal plane” of ice (combination of two layers of slig htly different elevation). Each circle represents the oxyg en atom of a water molecule. Open and shaded circles, respectively, represent oxyg en atoms in the upper and lower layers of the basal planes. (a) Hexag onal structure viewed down the c axis. Numbered molecules relate to the unit cell in Fig ure 3. (b) Three-dimensional view of the basal plane. The front edg e of view b corresponds to the bottom edg e of view a. The crystallog raphic axes have been positioned in accordance with external (point) symmetry. tween adjacent oxygen atoms. The resulting mean structure, known also as the half-hydrogen, Pauling, or statistical structure, is shown in Figure 6B. With respect to crystal symmetry, ordinary ice belongs to the dihexagonal bipyramidal class of the hexagonal system. In addition, ice can exist in nine other crystalline polymorphic structures, and also in an amorphous or vitreous state of rather uncertain but largely noncrystal-
Page2704FIGURE5Theextendedstructureofordinaryice.Onlyoxygenatomsareshown.Openandshaded circles,respectively,represent oxygen atoms in upper and lowerlayers ofabasalplane.line structure. Of the eleven total structures, only ordinary hexagonal ice is stable under normal pressure at o°C.The structure of ice is not as simple as has been indicated.First of all, pure ice contains not only ordinary HOHmolecules butalso ionic and isotopic variants of HOH.Fortunately,the isotopic variants occur in such small amounts that they can, in mostinstances, be ignored, leaving for major consideration only HOH, H+ (H:O+), and OH.Second, ice crystals are never perfect, and the defects encountered are usually of the orientational (caused by proton dislocationaccompaniedbyneutralizingorientations)orionictypes(causedbyprotondislocationwithformationofH:O+andOH)(seeFig. 7). The presence of these defects provides a means for explaining the mobility of protons in ice and the small decrease in dcelectrical conductivitythatoccurswhenwaterisfrozenIn addition to the atomic mobilities involved in crystal defects, there are other types of activity in ice. Each HOH molecule in iceis believed to vibrate with a root mean amplitude (assuming each molecule vibrates as a unit) of about 0.4 A at-10°C.Furthermore, HOH molecules that presumably exist in some of the interstitial spaces in ice can apparently diffuse slowly throughthelattice.Ice therefore is far from static or homogeneous, and its characteristics are dependent on temperature. Although the HOHmolecules in ice are four-coordinated at all temperatures, it is necessary to lower the temperature to about -180°C or lower to“fix" the hydrogen atoms in one of the many possible configurations. Therefore, only at temperatures near -180°C or lower will
Pag e 27 FIGURE 5 The extended structure of ordinary ice. Only oxyg en atoms are shown. Open and shaded circles, respectively, represent oxyg en atoms in upper and lower layers of a basal plane. line structure. Of the eleven total structures, only ordinary hexagonal ice is stable under normal pressure at 0°C. The structure of ice is not as simple as has been indicated. First of all, pure ice contains not only ordinary HOH molecules but also ionic and isotopic variants of HOH. Fortunately, the isotopic variants occur in such small amounts that they can, in most instances, be ignored, leaving for major consideration only HOH, H+ (H3O+ ), and OH- . Second, ice crystals are never perfect, and the defects encountered are usually of the orientational (caused by proton dislocation accompanied by neutralizing orientations) or ionic types (caused by proton dislocation with formation of H3O+ and OH- ) (see Fig. 7). The presence of these defects provides a means for explaining the mobility of protons in ice and the small decrease in dc electrical conductivity that occurs when water is frozen. In addition to the atomic mobilities involved in crystal defects, there are other types of activity in ice. Each HOH molecule in ice is believed to vibrate with a root mean amplitude (assuming each molecule vibrates as a unit) of about 0.4 Å at -10°C. Furthermore, HOH molecules that presumably exist in some of the interstitial spaces in ice can apparently diffuse slowly through the lattice. Ice therefore is far from static or homogeneous, and its characteristics are dependent on temperature. Although the HOH molecules in ice are four-coordinated at all temperatures, it is necessary to lower the temperature to about -180°C or lower to “fix” the hydrogen atoms in one of the many possible configurations. Therefore, only at temperatures near -180°C or lower will
Page28(A2工0(B)工FIGURE 6?Locationofhydrogenatoms (in the structure ofice.(A)Instantaneousstructure.(B)Meanstructure [knownalso as thehalf-hydrogen(),Pauling,orstatistical structure]. Open circleis oxygen.LFAULTDFAULTROTATION600OVOFMOLECULEI(A)H30PROTON.-OHJUMPFROMITO2(B)FIGURE7Schematic representation of proton defects in ice.(A)Formation oforientationaldefects.(B)Formationof ionic defects.Open and shaded circlesrepresent oxygen and hydrogen atoms,respectively. Solid and dashed lines representchemical bonds and hydrogen bonds,respectively
Pag e 28 FIGURE 6 Location of hydrog en atoms ( ) in the structure of ice. (A) Instantaneous structure. (B) Mean structure [known also as the half-hydrog en ( ), Pauling , or statistical structure]. Open circle is oxyg en. FIGURE 7 Schematic representation of proton defects in ice. (A) Formation of orientational defects. (B) Formation of ionic defects. Open and shaded circles represent oxyg en and hydrog en atoms, respectively. Solid and dashed lines represent chemical bonds and hydrog en bonds, respectively
Page 29all hydrogenbondsbeintact,andasthetemperatureisraised,themeannumberofintact (fixed)hydrogenbondswilldecreasegradually2.5.2IceinthePresenceof SolutesThe amount and kind of solutes present can influence the quantity, size, structure, location, and orientation of ice crystalsConsiderationherewill begivenonlytotheeffectsof solutesonicestructure.Luyetand co-workers[75,77] studiedthenatureofice crystals formed in the presence ofvarious solutes including sucrose, glycerol, gelatin, albumin, and myosin. They devised aclassification system based on morphology,elements of symmetry, and the cooling velocity required for development of varioustypes of ice structure. Their four major classes are hexagonal forms, irregular dendrites, coarse spherulites, and evanescentspherulites.The hexogonal form, which is most highly ordered, is found exclusively in foods, provided extremely rapid freezing is avoidedandthesoluteisofatypeandconcentrationthatdoesnot interfereundulywiththemobilityof watermolecules.Gelatinat highconcentrations will, for example, result in more disordered forms of ice crystals.2.6 Structure of WaterTo some, it may seem strange to speak of structure in a liquid when fluidity is the essence ofthe liquid state. Yet it is an old andwell-accepted idea [96] that liquid water has structure, obviously not sufficiently established to produce long-range rigidity,butcertainlyfar more organized than thatofmolecules in thevapor state,and ampleto cause theorientation and mobilityofa givenwater moleculeto be influenced by its neighbors.Evidence for this view is compelling.For example, water is an open" liquid, being only 60% as dense as would be expected onthe basis of close packing that can prevail in nonstructured liquids. Partial retention ofthe open, hydrogen-bonded, tetrahedralarrangementof iceeasilyaccountsforwater'slowdensity.Furthermore,theheatoffusionof ice,whileunusuallyhigh,issufficienttobreakonlyabout15%ofthehydrogenbondsbelievedtoexistinice.Althoughthisdoesnotnecessarilyrequirethat85% ofthe hydrogen bonds existing in ice be retained in water (for example, more could be broken, but the change in energycould be masked by a simultaneous increase in van der Waals interactions),results of many studies support the notion that manywater-waterhydrogen bondsdoexist.Elucidationofthestructureof purewater is anextremelycomplexproblem.Manytheories havebeen setforth,butall areincomplete,overly simple,and subjectto weaknessesthat are quickly cited by supporters ofrival theories.That is,ofcourseahealthysituation,whichwilleventuallyresultinanaccuratestructuralpicture(orpictures)ofwater.Inthemeantime,fewstatements can be made with any assurance that they will stand essentially unmodified in years to come. Thus, this subject will bedealt with only briefly.Three general types of models have been proposed: mixture, interstitial, and continuum (also referred to as homogeneous oruniformist models) [5].Mixture models embody the concept of intermolecular hydrogen bonds being momentarily concentratedin bulky clusters of water molecules that exist in dynamic equilibrium with other more dense speciesmomentarily meaning~101l sec [73]Continuum models involve the idea that intermolecular hydrogen bonds are distributed uniformly throughout the sample, and thatmanyofthebondsexistinginicesimplybecomedistortedratherthanbrokenwheniceismelted.Ithasbeensuggestedthatthispermits a continuous network ofwater moleculesto exist that is, ofcourse,dynamic in nature[107,120].The interstitial model involves the concept of water retaining an ice-like or clathrate-type
Pag e 29 all hydrogen bonds be intact, and as the temperature is raised, the mean number of intact (fixed) hydrogen bonds will decrease gradually. 2.5.2 Ice in the Presence of Solutes The amount and kind of solutes present can influence the quantity, size, structure, location, and orientation of ice crystals. Consideration here will be given only to the effects of solutes on ice structure. Luyet and co-workers [75,77] studied the nature of ice crystals formed in the presence of various solutes including sucrose, glycerol, gelatin, albumin, and myosin. They devised a classification system based on morphology, elements of symmetry, and the cooling velocity required for development of various types of ice structure. Their four major classes are hexagonal forms, irregular dendrites; coarse spherulites, and evanescent spherulites. The hexogonal form, which is most highly ordered, is found exclusively in foods, provided extremely rapid freezing is avoided and the solute is of a type and concentration that does not interfere unduly with the mobility of water molecules. Gelatin at high concentrations will, for example, result in more disordered forms of ice crystals. 2.6 Structure of Water To some, it may seem strange to speak of structure in a liquid when fluidity is the essence of the liquid state. Yet it is an old and well-accepted idea [96] that liquid water has structure, obviously not sufficiently established to produce long-range rigidity, but certainly far more organized than that of molecules in the vapor state, and ample to cause the orientation and mobility of a given water molecule to be influenced by its neighbors. Evidence for this view is compelling. For example, water is an “open” liquid, being only 60% as dense as would be expected on the basis of close packing that can prevail in nonstructured liquids. Partial retention of the open, hydrogen-bonded, tetrahedral arrangement of ice easily accounts for water's low density. Furthermore, the heat of fusion of ice, while unusually high, is sufficient to break only about 15% of the hydrogen bonds believed to exist in ice. Although this does not necessarily require that 85% of the hydrogen bonds existing in ice be retained in water (for example, more could be broken, but the change in energy could be masked by a simultaneous increase in van der Waals interactions), results of many studies support the notion that many water-water hydrogen bonds do exist. Elucidation of the structure of pure water is an extremely complex problem. Many theories have been set forth, but all are incomplete, overly simple, and subject to weaknesses that are quickly cited by supporters of rival theories. That is, of course, a healthy situation, which will eventually result in an accurate structural picture (or pictures) of water. In the meantime, few statements can be made with any assurance that they will stand essentially unmodified in years to come. Thus, this subject will be dealt with only briefly. Three general types of models have been proposed: mixture, interstitial, and continuum (also referred to as homogeneous or uniformist models) [5]. Mixture models embody the concept of intermolecular hydrogen bonds being momentarily concentrated in bulky clusters of water molecules that exist in dynamic equilibrium with other more dense species—momentarily meaning ~10- 11 sec [73]. Continuum models involve the idea that intermolecular hydrogen bonds are distributed uniformly throughout the sample, and that many of the bonds existing in ice simply become distorted rather than broken when ice is melted. It has been suggested that this permits a continuous network of water molecules to exist that is, of course, dynamic in nature [107,120]. The interstitial model involves the concept of water retaining an ice-like or clathrate-type