@@ -2766,7 +2766,10 @@ \subsection{Tutorial 5: Reactive silicon dioxide}
27662766\centering
27672767\includegraphics [width=0.55\linewidth ]{SIO}
27682768\caption {A portion of the silicon dioxide structure as simulated during
2769- \hyperref [reactive-silicon-dioxide-label]{Tutorial 5}. Atoms are colored by their charges.}
2769+ \hyperref [reactive-silicon-dioxide-label]{Tutorial 5}. Atoms are colored
2770+ by their charges: the hydrogen atoms appear as small greenish spheres, silicon
2771+ atoms as large orange spheres, and oxygen atoms as blue spheres of intermediate
2772+ size.}
27702773\label {fig:SIO }
27712774\end {figure }
27722775
@@ -3124,9 +3127,8 @@ \subsubsection{Decorate the surface}
31243127\includegraphics [width=\linewidth ]{SIO-decorated}
31253128\caption {Cracked silicon oxide after the addition of hydrogen atoms
31263129during \hyperref [reactive-silicon-dioxide-label]{Tutorial 5}. The atoms
3127- are colored by their charges. Dangling oxygen groups appear in greenish, bulk
3128- Si atoms with a charge of about $ 1.8 ~\text {e}$ appear in red/orange, and bulk
3129- O atoms with a charge of about $ -0.9 ~ \text {e}$ appear in blue.}
3130+ are colored by their charges, with the newly added hydrogen atoms appearing as small
3131+ greenish spheres.}
31303132\label {fig:SIO-decorated }
31313133\end {figure }
31323134
@@ -3135,10 +3137,11 @@ \subsection{Tutorial 6: Water adsorption in silica}
31353137
31363138\begin {figure }
31373139\centering
3138- \includegraphics [width=0.55\linewidth ]{GCMC}
3139- \caption {Water molecules adsorbed in cracked silica (SiO$ _2 $ ) material as simulated
3140- during \hyperref [gcmc-silica-label]{Tutorial 6}. Water molecules are colored in
3141- cyan and white, oxygen (O) atoms from SiO$ _2 $ in red, and silicon (Si) atoms in yellow.}
3140+ \includegraphics [width=0.6\linewidth ]{GCMC}
3141+ \caption {Water molecules (H$ _2 $ O) adsorbed in cracked silica (SiO$ _2 $ ) material as simulated
3142+ during \hyperref [gcmc-silica-label]{Tutorial 6}. The oxygen atoms of the water
3143+ molecules are represented in cyan, the silicon atoms in yellow, and the oxygen
3144+ atoms of the solid in red.}
31423145\label {fig:GCMC }
31433146\end {figure }
31443147
@@ -3208,11 +3211,6 @@ \subsubsection{Generation of the silica block}
32083211thermo_style custom step temp etotal vol density
32093212\end {lstlisting }
32103213
3211- % SG
3212- % FROM . Chem. Phys. 97, 2682–2689 (1992)
3213- % https://doi.org/10.1063/1.463056
3214- % 3 steps only. Say that its too fast to be correct. Show density.
3215- % Show rdf instead of box size?
32163214Finally, let us implement the annealing procedure which
32173215consists of three consecutive runs. This procedure was inspired
32183216by Ref.\, \cite {della1992molecular }. First, to melt the system,
@@ -3255,12 +3253,10 @@ \subsubsection{Generation of the silica block}
32553253\begin {figure }
32563254\centering
32573255\includegraphics [width=\linewidth ]{GCMC-dimension}
3258- \caption {a) Temperature $ T$ as a function of time $ t$
3259- during the annealing of the silica system
3260- from \hyperref [gcmc-silica-label]{Tutorial 6}.
3261- b) System density $ \rho $ during
3262- annealing. The vertical dashed lines mark the transition between the different
3263- phases of the simulation.}
3256+ \caption {a) Temperature $ T$ as a function of time $ t$ during the annealing
3257+ of the silica system from \hyperref [gcmc-silica-label]{Tutorial 6}.
3258+ b) System density $ \rho $ during the annealing process. The vertical dashed lines
3259+ mark the transition between the different phases of the simulation.}
32643260\label {fig:GCMC-dimension }
32653261\end {figure }
32663262
@@ -3269,7 +3265,7 @@ \subsubsection{Generation of the silica block}
32693265\includegraphics [width=0.9\linewidth ]{GCMC-generate}
32703266\caption {Amorphous silica ($ \text {SiO}_2 $ ) simulated
32713267during \hyperref [gcmc-silica-label]{Tutorial 6}. Silicon atoms are
3272- represented in yellow, and the oxygen atoms in red.}
3268+ represented in yellow, and oxygen atoms in red.}
32733269\label {fig:GCMC-snapshot }
32743270\end {figure }
32753271
@@ -3313,16 +3309,17 @@ \subsubsection{Cracking the silica}
33133309\end {lstlisting }
33143310The \lmpcmd {fix nvt} command is employed to control the temperature of the system.
33153311As observed from the generated images, the atoms
3316- progressively adjust to the changing box dimensions. At some point, bonds begin to break,
3317- leading to the appearance of dislocations (Fig.~\ref {fig:GCMC-cracked }).
3312+ progressively adjust to the changing box dimensions. At some point,
3313+ bonds begin to break, leading to the appearance of
3314+ dislocations (Fig.~\ref {fig:GCMC-cracked }).
33183315
33193316\begin {figure }
33203317\centering
33213318\includegraphics [width=\linewidth ]{GCMC-cracked}
33223319\caption {Block of silica from \hyperref [gcmc-silica-label]{Tutorial 6}
33233320after deformation. Silicon atoms are represented in yellow,
3324- and the oxygen atoms in red. The crack was induced by the
3325- imposed deformation of the box along the $ x$ -axis.}
3321+ and oxygen atoms in red. The crack was induced by the
3322+ imposed deformation of the box along the $ x$ -axis (i.e.,~the horizontal axis) .}
33263323\label {fig:GCMC-cracked }
33273324\end {figure }
33283325
@@ -3332,7 +3329,7 @@ \subsubsection{Adding water}
33323329the Monte Carlo method in the grand canonical ensemble (GCMC). In short, the
33333330system is placed into contact with a virtual reservoir of a given chemical potential
33343331$ \mu $ , and multiple attempts to insert water molecules at random positions are
3335- made. Each attempt is either accepted or rejected based on energy considerations.
3332+ made. Each attempt is either accepted or rejected based on energy considerations.
33363333For further details, please refer to classical textbooks like Ref.~\citenum {frenkel2023understanding}.
33373334
33383335\paragraph {Using hydrid potentials }
@@ -3539,7 +3536,7 @@ \subsubsection{Adding water}
35393536\begin {figure }
35403537\centering
35413538\includegraphics [width=\linewidth ]{GCMC-number}
3542- \caption {Number of water molecules $ N_\text {H2O}$ as a function of the time $ t$
3539+ \caption {Number of water molecules, $ N_\text {H2O}$ , as a function of time, $ t$ ,
35433540as extracted from \hyperref [gcmc-silica-label]{Tutorial 6}.}
35443541\label {fig:GCMC-number }
35453542\end {figure }
@@ -3568,10 +3565,10 @@ \subsection{Tutorial 7: Free energy calculation}
35683565
35693566\begin {figure }
35703567\centering
3571- \includegraphics [width=0.55 \linewidth ]{US}
3572- \caption {Atoms as simulated during \hyperref [umbrella-sampling-label]{Tutorial 7}.
3573- Only the atom colored in pink feels the additional force used for the umbrella
3574- sampling method .}
3568+ \includegraphics [width=0.7 \linewidth ]{US}
3569+ \caption {System simulated during \hyperref [umbrella-sampling-label]{Tutorial 7}.
3570+ The pink atom explores the energetically unfavorable central area of the simulation
3571+ box thanks to the additional potential imposed during umbrella sampling .}
35753572\label {fig:US }
35763573\end {figure }
35773574
@@ -3747,8 +3744,8 @@ \subsubsection{Method 1: Free sampling}
37473744\includegraphics [width=\linewidth ]{US-density-evolution}
37483745\caption {Evolution of the number of atoms $ n_\text {center}$ in the central
37493746region \lmpcmd {mymes} as a function of time $ t$ during equilibration. The dark line
3750- is $ n_\text {center} = 22 \exp (-t/160 )+5 $ and serves as a guide for the eyes. Here, $ U_ 0 = 0.36 ~ \text {kcal/mol} $ ,
3751- $ \ delta = 0.5 ~\text {\AA {}}$ , and $ x_0 = 5 ~\text {\AA {}}$ .}
3747+ is $ n_\text {center} = 22 \exp (-t/160 )+5 $ and serves as a guide for the eyes.
3748+ Here, $ U_ 0 = 0.36 ~ \text {kcal/mol} $ , $ \ delta = 1.0 ~\text {\AA {}}$ , and $ x_0 = 10 ~\text {\AA {}}$ .}
37523749\label {fig:US-density-evolution }
37533750\end {figure }
37543751
@@ -3962,9 +3959,10 @@ \subsubsection{Method 2: Umbrella sampling}
39623959\begin {figure }
39633960\centering
39643961\includegraphics [width=\linewidth ]{US-free-energy}
3965- \caption {The potential $ U$ as a function of $ x$ , measured using umbrella sampling
3966- (blue disks), is compared to the imposed potential given in Eq.~\eqref {eq:U }
3967- (dark line). Parameters are $ U_0 = 2.38 ~\text {kcal/mol}$ , $ \delta = 1.0 ~\text {\AA {}}$ ,
3962+ \caption {The potential $ U$ as a function of $ x$ , measured using umbrella
3963+ sampling during \hyperref [umbrella-sampling-label]{Tutorial 7} (blue disks),
3964+ is compared to the imposed potential given in Eq.~\eqref {eq:U }
3965+ (dark line). Parameters are $ U_0 = 2.38 ~\text {kcal/mol}$ , $ \delta = 1.0 ~\text {\AA {}}$ ,
39683966and $ x_0 = 10 ~\text {\AA {}}$ .}
39693967\label {fig:US-freenergy }
39703968\end {figure }
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