Materials Modelling MPhil

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1 Materials Modelling MPhil COURSE MP5: MESOSCALE AND MULTISCALE MODELLING COMPUTING CLASS 1 31/1/ :00-16:00 Dissipative particle dynamics using Materials Studio Aims and objectives Dissipative Particle Dynamics (DPD) is a technique for simulating complex fluids such as surfactant solutions and copolymer melts. A development of Molecular Dynamics (MD) and lattice gas automata, DPD represents long-range hydrodynamic forces directly in its equations of motion allowing more realistic modelling of the dynamics of phase separation and other processes depending on large length-scale interactions. In this practical, you will use the DPD module in Materials Studio to run some mesoscale simulations of a block copolymer system, and analyse the resulting morphologies as a function of structural and energetic parameters. By the end of the session, you should have a better understanding of the coarse-graining process for polymers, and how this leads to large increases in time and length scales over which simulations can be run. 2 Introduction In the DPD methodology, the fundamental particles are beads that represent small regions of fluid material rather than the atoms and molecules familiar from MD simulations. All degrees of freedom smaller than a bead radius are assumed to have been integrated out, leaving only coarse-grained interactions between beads. There are three types of force between pairs of beads, each of which conserves both bead number and linear momentum: an harmonic conservative interaction, a dissipative force representing the viscous drag between moving beads (i.e. fluid elements), and a random force to maintain energy input into the system in opposition to the dissipation. All forces are short-ranged with a fixed cut-off radius. By a suitable choice of the relative magnitudes of these forces, a system can be shown to evolve to a steady-state that corresponds to the Gibbs Canonical ensemble. Integration of the equations of motion for the beads generates a trajectory through the system s phase space from which all thermodynamic observables (e.g. density fields, order parameters, correlation functions, stress tensor, etc) may be constructed from suitable averages. An immense advantage over - 1 -

2 conventional Molecular Dynamics and Brownian Dynamics simulations is that all forces are soft allowing the use of a much larger time-step and correspondingly shorter simulation times. Polymers may be constructed out of the beads in a DPD simulation allowing the investigation of the morphologies of, for example, surfactants and branched polymers. Just as a bead represents a small fluid element whose interactions with other beads include dissipative and random (thermal) terms, so a DPD polymer represents a segment of a real polymer whose size is of the order of the persistence length. The interactions of a polymer with other polymers occur via the conservative, dissipative and random forces between their component beads. Typically, the beads making up a DPD polymer are bound to each other with harmonic forces. Because the fundamental objects in DPD are coarse-grained beads and polymers, mapping the physical and chemical properties of polymers onto the DPD simulation parameters is non-trivial: there is however a correspondence between the beads in a DPD simulation and the atoms and molecules in a real polymeric system. The mesoscale morphologies resulting from a DPD simulation can be analyzed in Materials Studio by means of a three-dimensional display of the beads and polymers making up the system; or by drawing density slices through the simulation box; or by display of isodensity surfaces. The latter can be compared directly with experimental observations e.g. from electron microscopy. The method allows a materials scientist to assess the effects of changes to the molecular composition of a formulation on the microstructure and hence the expected macroscopic properties. In addition, the dynamical pathway followed by the system in evolving to its equilibrium state may also be visualized using the same tools. 3 Practical 3.1 Getting started Log in to a Windows PC, and make a directory in your home space for this practical. Launch Materials Studio via the shortcut icon on the Desktop. On first run, a number of messages may appear concerning file name associations, location of temporary directory, etc. The default options should be selected by pressing OK on each occasion. Create a new project from the dialogue box which appears, entitled MP5_1 At any time when running Materials Studio, online help is available by clicking on the Help Topics item from the Help menu. Searching for DPD or About DPD may provide useful starting points

3.2 Using DPD module within Materials Studio The DPD module is accessible from either the Modules menu, or the equivalent toolbar via an icon, which look like this: This reveals a submenu consisting

3 3.2 Using DPD module within Materials Studio The DPD module is accessible from either the Modules menu, or the equivalent toolbar via an icon, which look like this: This reveals a submenu consisting Calculation and Analysis. Select Calculation to begin with. A test system, consisting of a diblock copolymer with architecture (A 4 B 4), is already defined and ready to run. You can inspect the mesoscale molecule types from the Species tab. Remember that A and B are beads representing a coarse-grained assembly of many atoms. The interactions between A and B beads can be inspected from the Interactions tab. Note that the interaction matrix for the repulsive forces is symmetric, and the A-B interactions are set to 40.0, and A-A/B-B interactions are both set to 25.0 (in units of k B T). Do not change the values of the dissipation or spring constants yet. The system conditions can be specified from the System tab. Since there is only one species in the simulation, the fraction of diblock copolymer is set to 1.0. Do not change the system extent or density yet. The simulation run length and time step can be specified via the Setup tab. The default value of 20,000 time steps would take too long to run, so change the number of steps to 500. Notice that the total simulation time (in dimensionless units) updates as you do this. Do not change the time step length yet. Change the output periods to 1 frame every 20 steps, and saving restart file every 20 steps. You are now ready to begin the short test DPD calculation. Click Run from the Setup tag, and the job will start. You can monitor the progress of the job from the Job Explorer panel at the bottom of the Materials Studio window

When the test job has completed, you should receive a pop-up window announcing this, and shortly afterwards the output files will appear in the Project Explorer panel on the left-hand side of the

4 When the test job has completed, you should receive a pop-up window announcing this, and shortly afterwards the output files will appear in the Project Explorer panel on the left-hand side of the Materials Studio window. Dismiss the pop-up, and you are now ready to begin analysis of the results. 3.2 Analysing results from DPD run Your output should look something like this: First, start by double-clicking on some of the graphical outputs in the Project Explorer panel on the left-hand side of the Materials Studio window. Particularly interesting things to look at are the temperature and pressure as a function of timestep (they should just about have equilibrated over even this short run) and the diblock densities of A and B beads (note: what do these imply has happened to your structure is this consistent with the visual output?) You can visualise the output more clearly using the Volume Visualization toolbar. This is not visible by default you should enable it from the View -> Toolbars -> Volume Visualization menu option. Double-click on the trajectory file output (called Diblock.mtd ) in the Project panel and then you should see the icons on the Volume Visualization toolbar become activated. You must have the trajectory file active when using the Volume Visualization toolbar. Select the Create Slice icon from the Volume Visualisation. Choose either the A Density or B Density fields to slice through using the Best Fit default option. What do you deduce from the resulting output? Is this consistent with the density profiles inspected above? - 4 -

5 You can manipulate the properties of the slice using the Properties Explorer panel. This is not visible by default, so you will need to enable it from the View -> Explorer -> Properties Explorer menu option. You will see it appear towards the bottom left of the Materials Studio window. Use the Filter drop-down menu to select Slice, and then you will see a list of properties relating to the slice appear in the Property Explorer panel. To edit a property, double-click on its Value. For example, to make the slice invisible, doubleclick on the IsVisible property Yes and change to No. You can also change the SlicePosition coordinates and SliceNormal direction. Once you have generated your slice at the desired position and angle, it is instructive to show the time evolution of the density profile. You can animate your trajectory using the Animation toolbar. This is not visible by default, so you will need to enable it from the View -> Toolbars -> Animation menu option. You should then see a toolbar appear next to the Volume Visualization toolbar with some arrows on it. Remember that the trajectory file must be currently active for the icons to be enabled and visible. You can use the arrows to step through the trajectory frames, either as a continuous movie or frame-byframe. How does the density profile shown on your slice evolve as the simulation progresses? You can also generate isosurfaces using the Volume Visualization toolbar. Make your slice invisible, and generate an isosurface for the B particle density at a threshold level of 1.0 (hint: use the Property panel). You may find it easier to view the isosurface with the Mesoscale Molecules hidden from view. Again, use the Filter menu on the Property panel to select the various attributes of the model to modify. 3.3 Exploration Once you have become familiar with running and analysing DPD jobs, try some experiments of your own. For example, in diblock copolymers, the strength of the segregation of the blocks is governed by the product χn of the Flory interaction parameter and the total chain length. The critical value is about 10.5, below which there is no phase separation. The larger χn, the stronger the separation, and for χn = 100 one expects a sharp interface. Try out DPD for a symmetric diblock copolymer melt, i.e. no solvent, with chain architecture A 8 B 8, and three values of χn, say (10, 12, 100), and look for evidence of phase separation. Look in your lecture notes for how to relate χ to repulsion parameters. How does this compare to a homopolymer in different solvents? For a more quantitative comparison, you can use the Analyze option from the DPD module to calculate the end-to-end length distributions for the block copolymers. How does this vary as a function of χn? (hint: plot mean-square end-to-end distance versus χn on a log-log plot to test for power-law)

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Tutorial 8. Non-Newtonian Transitional Flow in an Eccentric Annulus Introduction The purpose of this tutorial is to illustrate the setup and solution of a 3D, turbulent flow of a non-newtonian fluid. Turbulent