| \chapter{Visualization} |
|
|
| \section{Making pictures using VTK} |
|
|
| VTK is a nice visualization toolkit tailored for scientific purposes. It builds on top of OpenGL and is available |
| for most platforms. One of the most useful features is the ability to define scientific data in e.g.\ |
| grid form ("structured points") and to manipulate that data. Each grid point can contain various data forms: |
| scalars like temperature and pressure, but also vector data like velocity or fields. |
|
|
| There are several ways to visualize frameworks in RASPA using VTK: |
| \begin{itemize} |
| \item{Ball and stick}\\ |
| RASPA will output vtk-files for all the molecules in the system as well as the framework itself. |
| \item{Volume rendered surface area}\\ |
| RASPA will output a "structured point" grid of the adsorption energy. The structure is probed using Widom insertion |
| at random positions and the result is averaged. The lowest and highest values are recorded and then scaled between |
| 0 and 2$^{16}$. |
| \item{Volume rendered density plots of adsorbates}\\ |
| RASPA computes a 3D histogram of the positions of adsobates per component and for the total fluid. |
| This type of plots are very useful to find out where and how the molecules adsorb. |
| \end{itemize} |
|
|
| \section{Ball and stick} |
|
|
| At the start of any run, RASPA outputs the current state in VTK files, located in `VTK/System[int]'. The files |
| are `FrameworkAtoms.vtk', `AdsorbateAtoms.vtk', `CationAtoms.vtk', and `Frame.vtk'. In |
| `Example/Visualization/BallStickRASPA' the example for erionite is shown. |
| \begin{verbatim} |
| SimulationType MC |
| NumberOfCycles 0 |
| |
| Forcefield ExampleZeolitesForceField |
| |
| Framework 0 |
| FrameworkName ERI_mono |
| UnitCells 1 1 1 |
| \end{verbatim} |
|
|
| \begin{figure}[t] |
| \centering |
| \subfloat[]{\includegraphics[width=7.5cm]{./Visualization/ERI_ball_stick_front.jpg}} |
| \subfloat[]{\includegraphics[width=7.5cm]{./Visualization/ERI_ball_stick_side.jpg}} |
| \caption{Ball and stick picture of erionite (ERI): (a) front view, (b) side view. The erionite structure is |
| monoclinic: $a=b=13.27$ \AA\ and $c=15.05$ \AA, $\alpha=\beta=90^\circ$ and $\gamma=120^\circ$.} |
| \label{Fig: ERI ball-and-stick} |
| \end{figure} |
|
|
| After copying the vtk-files to `Examples/Visualization/ERI/VTK' one can run the VTK code. The VTK program |
| will produce a picture `Picture.jpg' and looks like Figure \ref{Fig: ERI ball-and-stick}. |
| The file `Frame.vtk' looks like: |
| \begin{verbatim} |
| # vtk DataFile Version 1.0 |
| Frame |
| ASCII |
| |
| DATASET POLYDATA |
| POINTS 8 float |
| 50.000000 -0.000000 -0.000000 |
| 150.000000 0.000000 0.000000 |
| 100.000000 86.602540 0.000000 |
| 0.000000 86.602540 0.000000 |
| 50.000000 0.000000 113.413715 |
| 150.000000 0.000000 113.413715 |
| 100.000000 86.602540 113.413715 |
| 0.000000 86.602540 113.413715 |
| LINES 6 36 |
| 5 0 1 2 3 0 |
| 5 4 5 6 7 4 |
| 5 0 1 5 4 0 |
| 5 2 3 7 6 2 |
| 5 0 4 7 3 0 |
| 5 1 2 6 5 1 |
| \end{verbatim} |
| It contains 8 points: the corners of the frame, and 6 closed poly-lines that form the ribbons. Using the `vtkTubeFilter' |
| we can use these lines to turn them into bigger tubes and color the tubes white. |
| The coordinate system is chosen as $150\times150\times150$ to be compatible with structure grids (for the density and surface). |
| The information about the framework is listed in `FrameworkAtoms.vtk': |
| \begin{verbatim} |
| # vtk DataFile Version 1.0 |
| Cube |
| ASCII |
| |
| DATASET POLYDATA |
| POINTS 108 float |
| 38.346000 20.221693 11.847197 |
| 38.125000 36.762778 28.353429 |
| 35.205000 30.250267 18.259608 |
| .... |
| .... |
| LINES 232 696 |
| 2 0 2 |
| 2 0 3 |
| 2 0 13 |
| .... |
| .... |
| POINT_DATA 108 |
| SCALARS my_scalars float |
| LOOKUP_TABLE default |
| 2.1 |
| 2.1 |
| 1.52 |
| .... |
| .... |
| VECTORS vectors float |
| 0.125 0 0 |
| 0.125 0 0 |
| 0.03125 0 0 |
| .... |
| .... |
| \end{verbatim} |
| The first points are the 108 framework atoms, next the lines section describes the bonding between them. |
| The last two sections denote the size and color of the atoms (Note that the VECTORS section is a trick to |
| allow the VTK `glyphs', here spheres, to be scaled by the scalar data, but colored by the magnitude of the |
| VECTOR data. Hopefully this will be easier in future versions of VTK). |
|
|
| The VTK program is also interactive, one can zoom in and out (scroll button) and rotate (click on the canvas, closer |
| to the center rotates less then further away). In computer graphics, a sphere is not a sphere, but a collection |
| of polygons. More polygons means a smoother surface but less responsive in the interactive mode. |
| For final pictures, one should use many polygons and anti-aliasing, which really improve the quality of the |
| picture. |
|
|
| The VTK files are written in `src/movies.c' in the routine `void WriteVTK(int system)'. The top of this file also |
| defines the colors. This same color definition is also used in the VTK `main.c'. |
|
|
| \section{Framework surface} |
|
|
| The ball and stick pictures are useful, but still do not provide information about pore shape and connectivity. |
| A more suitable approach is to visualize the energy landscape for a certain probe atom. |
| For energy landscape pictures, we divide the unit cell |
| into e.g. $150\times150\times150$ voxels (volume-elements). |
| At millions of random positions in the unit cell |
| the free energy of a test-particle (usually a helium or methane unit atom) is calculated |
| and assigned to the appropriate voxel. To visualize this energy landscape |
| the three-dimensional dataset is volume rendered, |
| removing the parts that generate overlap (the structure itself) by making it |
| completely transparent. |
| Low energy values are rendered with medium transparency, allowing the inside of the pores/cages to |
| be viewed as voids. Higher energy values are rendered less and less |
| transparent until the energy approaches |
| a cutoff energy and is regarded as part of the zeolite wall. Also color is assigned according |
| to the energy value (green for the outside view of a cage). |
|
|
| To speed up computation of surface and density pictures it is advisable to use energy-grids. For the upcoming example |
| we need grids for CO$_2$-atoms and helium: |
|
|
| \begin{verbatim} |
| SimulationType MakeGrid |
| |
| Forcefield ExampleZeolitesForceField |
| |
| Framework 0 |
| FrameworkName ERI_mono |
| UnitCells 3 3 2 |
| ExternalTemperature 300.0 |
| |
| NumberOfGrids 3 |
| GridTypes O_co2 C_co2 He |
| SpacingVDWGrid 0.1 |
| SpacingCoulombGrid 0.1 |
| \end{verbatim} |
| We need $3\times3\times2$ unit cells to obey the minimum-image convention. |
|
|
| Next we are going to generate the VTK `FrameworkatomsSurface.vtk' that contains data on the energy-grid for a chosen |
| probe atom. Here, we use helium. |
| An example input to generate the surface-grid is listed here (`Example/Visualization/ERI/SurfaceRASPA') |
| \begin{verbatim} |
| SimulationType Visualization |
| NumberOfCycles 10000000000 |
| PrintEvery 100000 |
| |
| Forcefield ExampleZeolitesForceField |
| ChargeMethod None |
| |
| Framework 0 |
| FrameworkName ERI_mono |
| UnitCells 3 3 2 |
| ExternalTemperature 300.0 |
| |
| NumberOfGrids 1 |
| GridTypes He |
| SpacingVDWGrid 0.1 |
| SpacingCoulombGrid 0.1 |
| UseTabularGrid yes |
| |
| component 0 MoleculeName helium |
| MoleculeDefinition ExampleDefinitions |
| IdealGasRosenbluthWeight 1.0 |
| BlockPockets no |
| BlockPocketsFileName ERI_mono |
| CreateNumberOfMolecules 0 |
| \end{verbatim} |
|
|
| Even though the grid is generated for a single unit, in general one still needs $3\times3\times2$ unit cells because |
| the charge interaction is dependent on the amount of chosen unit cells. |
| The grid file `FrameworkSurface.vtk' is located in `VTK/System[int]'. |
|
|
| To visualize the pore-shape, copy the `FrameworkSurface.vtk' to `Examples/Visualization/ERI/VTK'. Do not copy the other VTK files |
| because they are generated for a $3\times3\times2$ grid, and we need the framework-atoms and frame- VTK files |
| for a $1\times1\times1$ structure. |
| Running the VTK-program now shows the surface inside the structure, as shown in |
| Figure \ref{Fig: ERI density}(a). If we compare Figure \ref{Fig: ERI density}(a) to Figure \ref{Fig: ERI ball-and-stick} |
| we see that we have visualized the pore structure itself. Also note, that small ``pockets'' have shown up that are not a |
| part of the main pore system. These pockets should be blocked (See next section). |
|
|
| The ERI-case by default offers a nice view inside the cage. This is not always the case. Using |
| \begin{verbatim} |
| ShiftUnitCells 0.25 0 0 |
| \end{verbatim} |
| one can change the LTA case to a outside-cage-view to an inside-cage-view. (TODO, check whether grids takes this into account.) |
|
|
| \begin{figure}[t] |
| \centering |
| \subfloat[]{\includegraphics[width=7.5cm]{./Visualization/ERI_surface.jpg}} |
| \subfloat[]{\includegraphics[width=7.5cm]{./Visualization/ERI_CO2_density.jpg}} |
| \caption{Picture of ERI: (a) surface picture, (b) density picture (1 CO$_2$ at 300K).} |
| \label{Fig: ERI density} |
| \end{figure} |
|
|
| The `FrameworkSurface.vtk' is a structured points VTK-file. It is rectangular grid of, in this case, |
| $150\times150\times150$ points (a total of 3375000 points). All these values are listed sequentially, |
| but one can convert between 1D and 3D by using |
| \begin{equation} |
| \text{index}=x+y*\text{SIZEY}+z*\text{SIZEX}*\text{SIZEY} |
| \end{equation} |
| Note that the proper aspect ratios can be used. The VTK file looks like |
| \begin{verbatim} |
| # vtk DataFile Version 1.0 |
| Free energy zeolite: ERI_mono (300.000000 K) |
| ASCII |
| DATASET STRUCTURED_POINTS |
| DIMENSIONS 150 150 150 |
| ASPECT_RATIO 1.000000 0.577350 0.756091 |
| ORIGIN 0.0 0.0 0.0 |
| |
| POINT_DATA 3375000 |
| SCALARS scalars unsigned_short |
| LOOKUP_TABLE default |
| 0 |
| 0 |
| .... |
| .... |
| \end{verbatim} |
| The stored values are `unsigned short', so between 0 and 65536 ($2^{16}$). The value are always clipped to this region |
| using the minimum and maximum values of the simulation data. |
|
|
| \begin{figure}[t] |
| \centering |
| \hskip -0.5cm |
| \subfloat[]{\includegraphics[width=7.5cm]{./Visualization/ERI_picture_all.jpg}} |
| \hskip -0.5cm |
| \subfloat[]{\includegraphics[width=9.75cm]{./Visualization/ERI_snapshot.jpg}} |
| \caption{} |
| \label{Fig: ERI picture all} |
| \end{figure} |
|
|
| \section{Density plots} |
|
|
| During a Monte Carlo simulation a 3-dimensional histogram of the positions |
| of all atoms of the molecules is collected (per component). The unit cell is divided into 150x150x150 "voxels". |
| During the simulation the molecules move around in the box, and every cycle data is collected |
| for the histogram. First a position is mapped back from the full simulation box (3x3x2 unit cells) |
| to the main unit cell, and for every atom the voxel corresponding to the mapped position is incremented. |
| At certain intervals the histogram is written to file so that it can be visualized using VTK. |
| The data is always normalized using the highest occurring voxel value. However, the overall brightness |
| is still influenced by the loading of the specific adsorbate in the mixture. |
|
|
| In VTK the data is "volume rendered", more dense regions are less transparent, less dense regions are |
| more transparent. In addition the color changes, less dense regions are grey, more dense are orange, |
| then yellow, and the highest is rendered light blue. The original framework is placed in the picture as |
| a ball-and-stick model, and every position can be related to the framework. |
| We can therefore e.g. decipher a molecular picture of why selectivity occurs. |
|
|
| An example input for RASPA is |
| \begin{verbatim} |
| SimulationType MC |
| NumberOfCycles 100000000 |
| NumberOfInitializationCycles 100 |
| PrintEvery 100 |
| PrintPropertiesEvery 10000 |
| |
| Forcefield ExampleZeolitesForceField |
| |
| Framework 0 |
| FrameworkName ERI_mono |
| UnitCells 3 3 2 |
| ExternalTemperature 300.0 |
| ComputeDensityProfile3DVTKGrid yes |
| WriteDensityProfile3DVTKGridEvery 10000 |
| DensityProfile3DVTKGridPoints 150 150 150 |
| |
| NumberOfGrids 2 |
| GridTypes C_co2 O_co2 |
| SpacingVDWGrid 0.1 |
| SpacingCoulombGrid 0.1 |
| UseTabularGrid yes |
| |
| component 0 MoleculeName CO2 |
| MoleculeDefinition ExampleDefinitions |
| IdealGasRosenbluthWeight 1.0 |
| TranslationProbability 1.0 |
| RegrowProbability 1.0 |
| SwapProbability 0.0 |
| CreateNumberOfMolecules 1 |
| \end{verbatim} |
|
|
| Copy the `VTK/System[int]/DensityProfile\_methane.vtk' to `Examples/Visualization/ERI/VTK' as `Density.vtk', |
| rename the surface VTK-file, |
| and run the vtk-code. It will now produce a picture like Figure \ref{Fig: ERI density}(b). |
| If you did not rename the file (or rename it again to `FrameworkatomsSurface.vtk'), a picture with the frameworks atoms, |
| the pore surface and the density of CO$_2$ is produced. It is now easy to show that CO$_2$ preferentially adsorbs |
| in the 8-ring windows separating the erionite cages (in contrast to an alkane which prefers the cages). |
|
|
| Of course, one is not restricted to a unit cell and it is possible to make pictures of bigger volumes. |
| The first way is to use $3\times3\times2$ unit cells, and use the file `Movies/System[int]/Framework\_initial.cssr'. |
| Copy this file as `structure\_name\_3x3x2.cssr' and from then on use $1\times1\times1$ using this new enlarged unit cell. |
| The second method is to use $3\times3\times2$ unit cell but copy the surface and density in the $x$, $y$, $z$ directions |
| in the picture. You have to edit the `main.c' file of the VTK directory and recompile. The relevant settings are: |
| \begin{verbatim} |
| // the resolution of spheres and tubes, the higher the more smooth |
| // use 10, but 50 for the final picture |
| const int Resolution=10; |
| |
| // anti-aliasing, use 1, but 16 for final picture |
| const int AA=1; |
| |
| // control the transparancy of framework, adsorbates, and cations |
| const double FrameworkOpacity=1.0; |
| const double AdsorbateOpacity=1.0; |
| const double CationOpacity=1.0; |
| |
| // zoom in or out by increasing/decreasing the zoom-factor |
| const double ZoomFactor=2.0; |
| |
| // scale the size of the atoms and bonds |
| const double ScaleFactor=1.0; |
| |
| // control the view-point of the oject (input in degrees) |
| const double Azimuth=0.0; |
| const double Elevation=0.0; |
| const double Roll=0.0; |
| |
| // the size of the image in pixels |
| const int ImageSizeX=800; |
| const int ImageSizeY=500; |
| |
| // the number of duplicates in x,y,z (same as the number of unit cells) |
| const int NrDuplicatesX=3; |
| const int NrDuplicatesY=3; |
| const int NrDuplicatesZ=2; |
| |
| // the lengths of the edge-vectors |
| const double A=13.27; |
| const double B=13.27; |
| const double C=15.05; |
| |
| // the angles of the unit cell |
| const double AlphaAngle=90*M_PI/180.0; |
| const double BetaAngle=90*M_PI/180.0; |
| const double GammaAngle=120*M_PI/180.0; |
| \end{verbatim} |
| This can then be used to make a `snapshot' of molecules. For the $3\times3\times2$ structure we need the file |
| `VTK/System[int]/AdsorbateAtoms.vtk' from a simulation. This file is generated at the start of a simulation. |
| After a sufficiently long run to equilibrate the molecules, one |
| could copy the `Restart' to `RestartInitial', put the amount of created molecules at zero and restart from the |
| restart-files using zero cycles to generate the new `AdsorbateAtoms.vtk' file. |
| The picture of a snapshot of 64 CO$_2$ in the $3\times3\times2$ ERI-structure is shown in |
| Figure \ref{Fig: ERI picture all}(b). Note the many CO$_2$ molecules that occupy the barrier. Conclusions |
| are hard to draw based on snapshots. The `density'-plots give average information and therefore the same for |
| each unit cell (because each unit cell is the same [using a rigid structure]). The density plots are based on |
| atoms, and one can clearly see the orientation of CO$_2$ on the barrier. The 3 `blobs' corresponds to the oxygen, carbon, |
| and oxygen of CO$_2$. |
|
|
| \begin{figure}[t] |
| \centering |
| \subfloat[]{\includegraphics[width=5.0cm]{./Visualization/DDR_picture_1.jpg}} |
| \subfloat[]{\includegraphics[width=5.0cm]{./Visualization/DDR_picture_2.jpg}} |
| \subfloat[]{\includegraphics[width=5.0cm]{./Visualization/DDR_picture_3.jpg}} |
| \caption{Blocking pockets in DDR. The DDR structure is converted to a orthorhombic unit cell of |
| $a=24.006,b=13.86$, and $c=40.892$ \AA. In (a) we show the ball-and-stick structure, in (b) the structure |
| and the pore surface probed with helium, and (c) the structure with proper blocking of the small disconnected pockets.} |
| \label{Fig: DDR blocking} |
| \end{figure} |
|
|
| \section{Determining blocking pockets} |
|
|
| Some structures have inaccessible parts, i.e. areas that are not reachable from the main pore system. Examples |
| are the sodalite cages in FAU- and LTA-type zeolites. The surface pictures allow us to visualize these pockets, |
| locate the position, and construct a `blocking-file'. |
|
|
| The unit cell of the DDR structure has edge lengths of a=24.006 Angstrom, b=13.86 Angstrom, 40.892 Angstrom |
| with cell angles of 90 degrees. The atomic structure is shown in Figure \ref{Fig: DDR blocking}(a). It is difficult to envision |
| the details of the pore structure from this picture. One can obtain more insight from energy-landscapes. |
| In Figure \ref{Fig: DDR blocking}(b) we show the same structure with the energy landscape a helium atom would feel. In practice, |
| the simulation cell is divided into 150x150x150 bins and during a Monte-Carlo simulation one keeps track of |
| the average energy a molecule feels inside that bin. Here we volume-rendered the resulting energy grid |
| making very high energies transparent, i.e. the part that overlaps with the framework, as well as very |
| favorable energies, i.e. the positions inside the cage. The resulting surface layer can be viewed as the |
| "wall" of the pores. Alternatively, one can make a isocontour (a surface representing a constant, |
| high value of the energy). In Figure \ref{Fig: DDR blocking}(b) the main pore structure is apparent, |
| but also some disconnect pockets show up. It is |
| very important to artificially block these pockets for Monte-Carlo simulations. Also, in |
| Molecular Dynamic simulations, initial positions should be chosen in the main channel system. The blocking |
| procedure can be a simple distance-check from the center of the small pockets and a rejection of all |
| Monte-Carlo trial moves that would place a molecule inside a certain radius. This radius should not be |
| chosen to small or too big, because otherwise one would block not enough, or block parts of the |
| main channel system. In Figure \ref{Fig: DDR blocking}(c) we show the structure with the appropriate blocking centers and radii; |
| all small pockets have disappeared but the main channel system is unchanged. |
|
|
| The blocking procedure is dependent on the type of probe atom. Helium is a good procedure to find small pockets |
| and therefore to obtain the proper unit cell pore volume. This accessible pore volume is in simulation |
| usually obtained via a helium-probe procedure. Helium can also be used to find pockets that |
| could be occupied by other small molecule like CO2, N2, H2, methane, etc. |
| The adsorption results can be dramatically different with or without blocking. Whether the selectivity of |
| mixtures changes to higher or lower depends on the match of the molecule with the small pockets. |
| The small pockets are very favorable for the small molecules because they tend to have a very surface high |
| curvature, i.e.. a very favorable interaction energy). |
|
|
| \section{Making movies} |
|
|
| \subsection{Using VMD} |
|
|
| \subsection{Combining pictures into a movie} |
|
|
| Using ``ffmpeg'', from png-files to a mov-file with h264-encoding |
| \begin{verbatim} |
| ffmpeg -i %03d.png -s:v 1280x720 -acodec aac -ac 2 -strict experimental -ab 160k |
| -vcodec libx264 -preset slow -profile:v baseline -level 30 -maxrate 10000000 |
| -bufsize 10000000 -b 1200k -f mp4 -threads 0 -crf 23 -pix_fmt yuv420p -r 30 Movie.mov |
| \end{verbatim} |
| or using ``mencoder'' with settings |
| \begin{footnotesize} |
| \begin{verbatim} |
| export opt="vbitrate=1280000:mbd=2:keyint=132:vqblur=1.0:cmp=2:subcmp=2:dia=2:mv0:last_pred=3" |
| mencoder -ovc lavc -lavcopts vcodec=msmpeg4v2:vpass=1:$opt -mf type=jpg:fps=25 -nosound -o /dev/null mf://\*.jpg |
| mencoder -ovc lavc -lavcopts vcodec=msmpeg4v2:vpass=2:$opt -mf type=jpg:fps=25 -nosound -o output.avi mf://\*.jpg |
| \end{verbatim} |
| \end{footnotesize} |
|
|
|
|
