MICRO AND NANOSCALE SYSTEMS - Foundations of Nanotechnology: Pore Size in Carbon-Based Nano-Adsorbents - page 177

Continuum hypothesis leads to the concept of fluid particles. In contrast to the
ideal of a point particle in ordinary mechanics, in fluid mechanics, particle in the
fluid has a finite size.
At the atomic scale there are large fluctuations due to the molecular struc-
ture of fluids, but if we the increase the sample size, we reach a level where it
is possible to obtain stable measurements. This volume of probe must contain a
sufficiently large number of molecules to obtain reliable reproducible signal with
small statistical fluctuations. For example, if we determine the required volume
as a cube with sides of 10 nm, this volume contains some of the molecules and
determines the level of fluctuations of the order of 0.5%.
The applicability of the hypothesis is based on comparison of free path length
of a particle lin a liquid with a characteristic geometric size d . The ratio of these
lengths called the Knudsen number: Kn = l/ d .
(a) When Kn < 10 -3 justifies hypothesis of a continuous medium, and (b) when
Kn < 10 -1 allows the use of adhesion of particles to the solid walls of the channel.
Theoretical condition can also be varied: both in form U = 0and in a more
complex for m, ass ociated with shear stresses. The calculation of lcan be carried
out as

,

−

3

l≈ V / Na

where, V - molar volume; Na - Avogadro's number.
Under certain geometrical approxima ti ons of the particles of substance, free
path length can be calculated as

2

l= π , (ifused instead r s Stokes radi-
us, as a consequence of the spherical approximation of the particle). On the other
hand, for a rigid model of the molecule r s should be replaced by the cha ra cteristic
size of the particles R g (the radius of inertia), calculated as

1/( 2

r Na

)

R =d , where,
d l - the length of a fragment of the chain (link); n i - the number of links.
Of course, the continuum hypothesis is not acceptable when the system under
consideration is close to the molecular scale. This happens in nanoliquid, such as
liquid transport through nano- pores in cell membranes or artificially made nano-
channels.

. /6

g i l

2.4 THE MOLECULAR DYNAMICS METHOD
In contrast to the continuum hypothesis, the essence of modeling the molecular
dynamics method is as follows. We consider a large ensemble of particles which
simulate atoms or molecules, that is, all atoms are material points. It is believed
that the particles interact with each other and, moreover, may be subject to ex-
ternal influence. Inter-atomic forces are represented in the form of the classical
potential force (the gradient of the potential energy of the system).
The interaction between atoms is described by means of van der Waals forces
(intermolecular forces), mathematically expressed by the Lennard-Jones poten-
tial: