1 microscopic properties
1.1 static structure factor
1.2 sound dispersion , structural relaxation
1.3 effects of association
microscopic properties
static structure factor
structure of classical monatomic liquid. atoms have many nearest neighbors in contact, yet no long-range order present.
in liquid, atoms not form crystalline lattice, nor show other form of long-range order. evidenced absence of bragg peaks in x-ray , neutron diffraction. under normal conditions, diffraction pattern has circular symmetry, expressing isotropy of liquid. in radial direction, diffraction intensity smoothly oscillates. described static structure factor s(q), wavenumber q=(4π/λ)sinθ given wavelength λ of probe (photon or neutron) , bragg angle θ. oscillations of s(q) express near order of liquid, i.e. correlations between atom , few shells of nearest, second nearest, ... neighbors.
a more intuitive description of these correlations given radial distribution function g(r), fourier transform of s(q). represents spatial average of temporal snapshot of pair correlations in liquid.
radial distribution function of lennard-jones model fluid.
sound dispersion , structural relaxation
the above expression sound velocity
c
=
k
/
ρ
{\displaystyle c={\sqrt {k/\rho }}}
contains bulk modulus k. if k frequency independent liquid behaves linear medium, sound propagates without dissipation , without mode coupling. in reality, liquid shows dispersion: increasing frequency, k crosses on low-frequency, liquid-like limit
k
0
{\displaystyle k_{0}}
high-frequency, solid-like limit
k
∞
{\displaystyle k_{\infty }}
. in normal liquids, of cross on takes place @ frequencies between ghz , thz, called hypersound.
at sub-ghz frequencies, normal liquid cannot sustain shear waves: zero-frequency limit of shear modulus
g
0
=
0
{\displaystyle g_{0}=0}
. seen defining property of liquid. however, bulk modulus k, shear modulus g frequency dependent, , @ hypersound frequencies shows similar cross on liquid-like limit
g
0
{\displaystyle g_{0}}
solid-like, non-zero limit
g
∞
{\displaystyle g_{\infty }}
.
according kramers-kronig relation, dispersion in sound velocity (given real part of k or g) goes along maximum in sound attenuation (dissipation, given imaginary part of k or g). according linear response theory, fourier transform of k or g describes how system returns equilibrium after external perturbation; reason, dispersion step in ghz..thz region called structural relaxation. according fluctuation-dissipation theorem, relaxation towards equilibrium intimately connected fluctuations in equilibrium. density fluctuations associated sound waves can experimentally observed brillouin scattering.
on supercooling liquid towards glass transition, crossover liquid-like solid-like response moves ghz mhz, khz, hz, ...; equivalently, characteristic time of structural relaxation increases ns μs, ms, s, ... microscopic explanation above-mentioned viscoelastic behaviour of glass-forming liquids.
effects of association
the mechanisms of atomic/molecular diffusion (or particle displacement) in solids closely related mechanisms of viscous flow , solidification in liquid materials. descriptions of viscosity in terms of molecular free space within liquid modified needed in order account liquids molecules known associated in liquid state @ ordinary temperatures. when various molecules combine form associated molecule, enclose within semi-rigid system amount of space before available free space mobile molecules. thus, increase in viscosity upon cooling due tendency of substances become associated on cooling.
similar arguments used describe effects of pressure on viscosity, may assumed viscosity chiefly function of volume liquids finite compressibility. increasing viscosity rise of pressure therefore expected. in addition, if volume expanded heat reduced again pressure, viscosity remains same.
the local tendency orientation of molecules in small groups lends liquid (as referred previously) degree of association. association results in considerable internal pressure within liquid, due entirely molecules which, on account of temporary low velocities (following maxwell distribution) have coalesced other molecules. internal pressure between several such molecules might correspond between group of molecules in solid form.
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