Interdisciplinary Applied Mathematics

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N


Mdip =    qi ri>


i=1


where N is the    number    of    point    charges in the    model,    and    qi    and    ri    are


the charge and position vector of the point charge i, respectively. The magnitude of the dipole moment, p,dip, is the length of the dipole vector fxdip. Experimentally, the dipole moment of a single water molecule in liquid state at 300 K is determined to be 2.95±0.2 Debye (1 Debye = 3.336×10~30 C m) (Gubskaya and Kusalik, 2002). Sometimes, it is advantageous to describe the water molecule simply as a dipole, e.g., when studying the response of the water molecule to an electrical field. In this case, the orientation of the water is usually characterized by the dipole orientation angle 0dip with respect to a certain reference direction (see Figure 11.1). Some of the important properties of water obtained experimentally are summarized in Table 11.1.


A    large    number    of    “hypothetical”    models    for    water have    been    developed in    order to discover    the    structure    of    water,    on    the    basis that if    the


(known) model can successfully predict the physical properties of water, then the (unknown) structure of water can be determined. They involve positioning the electrostatic sites and Lennard-Jones sites, which may or


TABLE 11.1. Important properties of water (H2O) f


Dipole moment


2.95 ±0.2 Debye


Boiling point


100°C at 101.325 kPa


Isothermal compressibility


0.4599 GPa-1


Density


997.05 kg/m3


Dielectric constant


78.4


Diffusion coefficient


2.27 x 10~9m2/s


Enthalpy of Vaporization


40.657 kJ/mol (100°)


Electronic polarizability (liquid)


1.48 A3


Specific heat capacity (Cp)


75.327 J/mol/K


Specific heat capacity (Cv)

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