Reports: G7

47740-G7 Solvent-Temperature Superposition Rules for Predicting the Rheology of Wormlike Micellar Fluids

Rajesh S. Khare, Texas Tech University

The goal of this project is to use a combination of atomistic and mesoscale simulations to decipher the relationship between the unique rheological properties of wormlike micelles[1] and the molecular scale structure and interactions in these systems.  A description of these modeling efforts is presented below: 

(A) Atomistic simulation: 

The structure and dynamics in the micellar system consisting of EHAC [erucyl bis(hydroxyethyl) methylammonium chloride] surfactant molecule was studied using atomistic simulations.  The molecular dynamics (MD) simulations were carried out using the GROMACS package.[2] The simulated system consisted of 100 EHAC molecules and 54773 water molecules, with 100 chloride ions added to maintain charge neutrality.  The initial structure was energy minimized using the steepest descent method, followed by a constant NPT (number of particles, pressure and temperature) MD simulation run for 40 ns. 

Fig. 1.  Configuration of the EHAC molecules after 40 ns of MD NPT simulation (water molecules have been removed for clarity).  Inset shows an EHAC molecule.

As seen from Fig. 1, the EHAC molecules were observed to form aggregates of different sizes.  The Gromos clustering algorithm[3] in GROMACS was utilized to quantify this aggregation behavior of the EHAC molecules in solution, the results are shown in Fig. 2. 

(a)                                                                       (b)

Fig. 2:  Aggregation of EHAC molecules as shown by (a) Time dependence of the number of clusters and (b) Time dependence of the average number of molecules per cluster.    

(B) Mesoscale simulation: 

In order to capture the rheological properties of the wormlike micelles as measured in experiments, we need to simulate the systems on much longer length and time scales than possible using atomistic simulations. 

In this project, we have decided to use the multi-particle collision dynamics (MPCD) method[4] for this purpose.  The coarse grained models used in these mesoscale simulations will be developed from the atomistic simulations as described above.  As a first step, we are currently developing a simulation code for implementing the MPCD method.  A brief description of this simulation method and the results from our calculations are presented below. 

MPCD Method:

In the MPCD method, the solvent is described as a collection of N point particles.  These particles are assumed to interact at discrete time intervals by collision events and are assumed to undergo free streaming motion in between these collisions.  The dynamics of the solvent particles is thus implemented in two steps:[5]

(1) Streaming step:

               

where  and  denote the position and velocity of particle i at time t

Fig. 3: Schematic illustrating the partitioning of the box into cells containing the solvent particles and one bead-spring polymer chain in MPCD simulation.  Inset shows the rotation of the relative velocity of every solvent particle in a MPCD cell. 

(2) Collision step: The particles are first sorted into cells (see Fig. 3).  The relative velocity (with respect to the center of mass velocity in that cell) of each of the particles in a cell is then rotated by a chosen angle: 

where  is the center of mass velocity and  is the rotation matrix.  The rotation is done by a fixed angle α about a randomly oriented rotation axis.  Same rotation is applied to all particles in one cell but the rotations in different cells are independent of each other.  To ensure Galilean invariance for the simulation, a random lattice shift for the cells is applied before each collision step, to change the neighborhood of the particles.[6] 

A hybrid approach is used for simulating the dynamics of a solution containing a solute that is dissolved in the mesoscopic solvent as described above.  In this case, the free streaming step is replaced by usual MD simulation for the solvent and solute particles to account for the specific interactions between the solute and the solvent whereas the solvent-solvent interactions are captured via the collision step as described above. 

The initial simulation system studied contained 326769 solvent particles in a box of dimensions 32x32x32 and at a temperature of 1/3.  The angle of rotation was π/2 for all cells.  Furthermore, the system contained one colloidal molecule (radius = 3σ, mass = 250) that interacted with the solvent molecules via the Lennard-Jones (LJ) potential (all values are in reduced LJ units).  In the simulation, 50 MD steps were carried out between successive collision steps and the system was equilibrated for 20,000 MD steps.  In order to validate our code, the normalized velocity autocorrelation function (VACF) of the solute particle was calculated.  

Fig. 4:  Normalized VACF of the colloidal particle averaged over 10 blocks

The VACF shown in Fig. 4 is qualitatively similar with that in the literature but differs from it quantitatively.[7]  Currently this issue is being investigated.  Once this issue is resolved and the code is validated, a similar test will be performed for the MPCD code for a polymer solution; the validated code will then be used for studying the rheology of the wormlike micellar systems. 

Impact of the research on the PI and the graduate student

The PI (Khare) has a strong track record of atomistic level simulations of polymeric systems as well as nanoscale transport phenomena.  The ongoing work on this project in the area of MPCD simulations will allow the PI to expand his research portfolio to mesoscopic modeling techniques.  The graduate student (Govind Hegde) working on this project is receiving multidisciplinary training in the areas of chemical engineering, mesoscale and atomistic simulation methods and rheology of complex fluids. 

References:


[1] Siriwatwechakul,W.; LaFleur, T.; Prud'homme, R.K.; Sullivan, P.; Langmuir, 20, 8970-8974 (2004). 

[2] 2. Hess, B.; Kutzner, C.; van der Spoel, D.; Lindahl, E.; J. Chem. Theory Comput. 4, 435-447, (2008). 

[3] Daura, X.; Gademann, K.; Jaun, B.; Seebach, D.; van Gunsteren, W. F.; Mark, A. E.; Angew. Chem. Int. Ed. 38, 236-240, (1999). 

[4] Kapral, R.; Adv. Chem. Phys.; 140, 89 (2008). 

[5] Malevanets, A.; Kapral, R.; J. Chem. Phys. 110, 17, 8605-8613, (1999). 

[6] Ihle, T.; Kroll, D. M.; Phys. Rev. E., 63, 020201, (2001). 

[7] Malevanets, A.; Kapral, R.; J. Chem. Phys. 112, 17, 7260-7269 (2000).