Atomistic Simulation studies of the Cement Paste Components

Overview of Atomistic Simulation Methods
Thus, the temperature can be modified tuning the velocity, which in his turn can be
modified changing the time step [163, 164]. A new variable which relates the real time of
the system and the new rescaled one is introduced:
∂ t = s(t ′) ∂ t′
(2.4.9)
and the equation of motion then reads:
2
∂ qi
1 ∂s
∂qi
Fi = m⋅ + t
2
∂ ′ s ∂ t ′ ∂ t ′
(2.4.10)
where the second term determines the friction between the system and the heat bath.
Under constant pressure and temperature, in the so-called isobaric-isothermal
ensemble the pressure can be maintained constant at each time step varying the size and
the shape of the simulation box [162, 165]. Then, the atomic coordinates are rescaled for
the new box. As in the previous case, the Langrangian equations of motion are modified
and they yield the following expression:
F
∂ q ∂s 2 ∂V
∂q
⎜
⎟
∂t′ ⎝∂t′ 3V ∂t′ ⎠ ∂t′
2
1/3 i ⎛
⎞ i
i
= m⋅V
⋅ + +
2
(2.4.11)
This formula is deduced for cubic boxes. Anyhow, the method can be extended
similarly to non-cubic systems [157].
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