BLBS102-c05 BLBS102-Simpson March 21, 2012 12:2 Trim: 276mm X 219mm Printer Name: Yet to Come
90 Part 1: Principles/Food Analysisgive rise to the disorder of the H atoms. These rapid exchanges
are in a dynamic equilibrium.
In the structure of Ih, six O atoms form a ring; some of them
have a chair form, and some have a boat form. Two configu-
rations of the rings are marked by spheres representing the O
atoms in Figure 5.5. Formation of the hydrogen bond in ice
lengthens the O H bond distance slightly from that in a sin-
gle isolated water molecule. All O atoms in Ih are completely
hydrogen bonded, except for the molecules at the surface. Max-
imizing the number of hydrogen bonds is fundamental to the
formation of solid water phases. Pauling (1960) pointed out that
formation of hydrogen bonds is partly an electrostatic attraction.
Thus, the bending of O H O is expected. Neutron diffraction
studies indicated bent hydrogen bonds.
Since only four hydrogen bonds are around each O atom, the
structure of Ih has rather large channels at the atomic scale.
Under pressure, many other types of structures are formed. In
liquid water, the many tetrahedral hydrogen bonds are formed
with immediate neighbors. Since water molecules constantly
exchange hydrogen-bonding partners, the average number of
nearest neighbors is usually more than four. Therefore, water is
denser than Ih.Other Phases of IceUnder high pressures, water forms many fascinating H 2 O solids.
They are designated by Roman numerals (e.g., ice XII; Klug
2002, Petrenko and Whitworth 1999). Some of these solids were
known as early as 1900. Phase transitions were studied at certain
temperatures and pressures, but metastable phases were also
observed.
At 72 K, the disordered H atoms in Ih transform into an
ordered solid called ice XI. The oxygen atoms of Ih and ice XI
arrange in the same way, and both ices have a similar density,
0.917 Mg m−^3.
Under high pressure, various denser ices are formed. Ice II was
prepared at a pressure about 1 GPa (1 GPa= 109 Pa) in 1900,
and others with densities ranging from 1.17 to 2.79 Mg m−^3
have been prepared during the twentieth century. These denser
ices consist of hydrogen bond frameworks different from Ih
and XI, but each O atom is hydrogen-bonded to four other O
atoms.
Cubicice,Ic, has been produced by cooling vapor or droplets
below 200 K (Mayer and Hallbrucker 1987, Kohl et al. 2000).
More studies showed the formation of Ic between 130 K and
150 K. Amorphous (glassy) water is formed below 130 K, but
above 150 K Ih is formed. The hydrogen bonding and inter-
molecular relationships in Ih and Ic are the same, but the packing
of layers and symmetry differ (see Fig. 5.5). The arrangement of
O atoms in Ic is the same as that of the C atoms in the diamond
structure. Properties of Ih and Ic are very similar. Crystals of Ic
have cubic or octahedral shapes, resembling those of salt or dia-
mond. The conditions for their formation suggest their existence
in the upper atmosphere and in the Antarctic.
As in all phase transitions, energy drives the transformation
between Ih and Ic. Several forms of amorphous ice having var-
ious densities have been observed under different temperaturesand pressures. Unlike crystals, in which molecules are packed in
an orderly manner, following the symmetry and periodic rules
of the crystal system, the molecules inamorphous iceare im-
mobilized from their positions in liquid. Thus, amorphous ice is
often called frozen water or glassy water.
When small amounts of water freeze suddenly, it forms amor-
phous ice or glass. Under various temperatures and pressures, it
can transform into high-density (1.17 mg/m^3 ) amorphous water,
and very high-density amorphous water. Amorphous water also
transforms into various forms of ice (Johari and Anderson 2004).
The transformations are accompanied by energies of transition.
A complicated phase diagram for ice transitions can be found in
Physics of Ice(Petrenko and Whitworth 1999).
High pressures and low temperatures are required for the ex-
istence of other forms of ice, and currently these conditions are
seldom involved in food processing or biochemistry. However,
their existence is significant for the nature of water. For example,
their structures illustrate the deformation of the ideal tetrahedral
arrangement of hydrogen bonding presented in Ih and Ic. This
feature implies flexibility when water molecules interact with
foodstuffs and with biomolecules.Vapor Pressure of Ice IhThe equilibrium vapor pressure is a measure of the ability or
potential of the water molecules to escape from the condensed
phases to form a gas. This potential increases as the temperature
increases. Thus, vapor pressures of ice, water, and solutions are
important quantities. The ratio of equilibrium vapor pressures of
foods divided by those of pure water is called thewater activity,
which is an important parameter for food drying, preservation,
and storage.
Ice sublimes at any temperature until the system reaches equi-
librium. When the vapor pressure is high, molecules deposit on
the ice to reach equilibrium. Solid ice and water vapor form an
equilibrium in a closed system. The amount of ice in this equi-
librium and the free volume enclosing the ice are irrelevant, but
the water vapor pressure or partial pressure matters. The equi-
librium pressure is a function of temperature, and detailed data
can be found in handbooks, for example, theCRC Handbook of
Chemistry and Physics(Lide 2003). This handbook has a new
edition every year. More recent values between 193 K and 273
K can also be found inPhysics of Ice(Petrenko and Whitworth
1999).
The equilibrium vapor pressure of ice Ih plotted against tem-
perature(T)is shown in Figure 5.6. The line indicates equilib-
rium conditions, and it separates the pressure–temperature(P–T)
graph into two domains: vapor tends to deposit on ice in one,
and ice sublimes in the other. This is the ice Ih—vapor portion
of the phase diagram of water.
Plot of lnPversus 1/Tshows a straight line, and this agrees
well with the Clausius-Clapeyron equation. The negative slope
gives the enthalpy of the phase transition,H, divided by the
gas constant R (=8.3145 J/K/mol).(d(lnP))
(d(1/T))=−H
R