(268g) Equilibrium and Non-Equilibrium Dissipative Particle Dynamics Simulations of Pluronic/Water Mixtures

Structured fluids, characterized by complex rheology, appear in many chemical processes of the pharmaceutical, personal-care and household cleaner industries. They are produced by mixing different ingredients and mathematical models capable of describing the resulting microstructures and emerging rheologies are extremely useful. In this work simple structured fluids constituted by two copolymers, Pluronic L64 and P104, in water are simulated by using the coarse-grained technique called Dissipative Particle Dynamics (DPD).

Model description and computational details

DPD was firstly introduced by Hoogerbrugge and Koelman [1] and then modified and improved by Groot, Warren, Español and Pagonabarraga (among the most important contributors [2]). This technique consists in describing the interactions between beads, namely clusters of molecules, according to the Langevin’s equation and as dictated by two types of interactions: bonded (e.g. between two beads belonging to the same polymeric chain) and non-bonded. Non-bonded interactions are obtained by summing three terms: conservative, dissipative and stochastic. The dissipative and stochastic terms are reconciled by using the fluctuation-dissipation theorem in order to conserve momentum. Model parameters are identified by tuning the properties of the DPD fluid in order to match the properties of the simulated systems. Targeted properties are for example the isothermal compressibility and the solubility of one component into another. Different models can be used to describe bonded interactions. The ones used in this study are the harmonic potential and the FENE potential, this latter being used since it avoids over-elongations of the chains, due to shear effects.

DPD simulations are run with periodic simulation boxes at equilibrium and under non-equilibrium conditions (i.e. under shear). Non-equilibrium simulations are performed in order to investigate shear effects by using the well-known Lees-Edward boundary conditions [3]. Simulations are performed with the code LAMMPS [4] and the interaction parameters used to describe Pluronic L64 and P104 chains are taken from the literature [5]. A cluster analysis is also performed in order to identify the shape of the microstructures observed, with particular attention to their gyration radius and aggregation number (e.g. number of Pluronic molecules into a micelle/cluster).

Results and discussion

Simulation results show that DPD is capable of reproducing the entire phase diagrams of both Pluronic L64/water and Pluronic P104/water with the same model parameters. By increasing the Pluronic concentration in water different microstructures are observed: spherical micelles, loosely packed or ordered in a cubic lattice, rod-like micelles ordered in an hexagonal lattice, entangled networks, lamellar phases and inverse micelles. The phase diagrams are validated against experimental ones [5,6].

The cluster analysis, mainly limited to spherical and rod-like micelles, allows to extract from simulation data the cluster mass distribution (CMD). This is in turn used to: (1) quantify the actual geometrical shape of the micelles and (2) investigate the relationship between standard chemical potential of the micelles and aggregation number. This analysis demonstrates that at low Pluronic concentrations the micelles are spherical, as the exponent relating aggregation number and radius of gyration is approximately 1/3, whereas at higher concentrations micelles become rod-like, with an exponent equal to approximately 1/2. As expected, the standard chemical potential of the micelles decreases with the aggregation number until a plateau is reached. From this trend geometrical parameters, consistent with the previous ones are obtained, as well as estimates of the critical micellar concentrations for both Pluronic L64 and P106, which are found to be in line with the experimental values.

Non-equilibrium simulations are performed to detect phase transitions and eventually variations in the relative viscosity when shear is applied. Different shear rates are tested on the equilibrium structures and interesting morphological changes are detected. When shear is applied at low concentrations, spherical micelles tend to coalesce into bigger micelles, interconnected networks align themselves into ordered hexagonal structures and lamellae clearly are broken up into separated sheets. These morphological changes are quantified by measuring the effect that shear has on the CMD. The CMD expresses the probability of finding one micelle composed by a number of N Pluronic molecules (i.e. aggregation number). Simulation results show that for spherical and rod-like micelles the CMD is shifted to new, bigger structures under non-equilibrium conditions, meaning that micelles are coalescing together. This result is extremely interesting as it suggests that a way to describe these changes can be the use of the Smoluchowski coagulation equation similarly to what done with coagulating colloidal particles.

DPD results also prove that at higher concentrations, shear effects cause a non-Newtonian behaviour in the Pluronic/water mixture. This is not observed in the micellar region, in which the fluid still behaves as a Newtonian fluid. On the contrary in the area of the phase diagram in which interconnected, gel, disordered structures are observed, the application of shear causes a drop in the viscosity, due to the reorganization of the molecules into much ordered aggregates.

Conclusions

In this work, we have verified that DPD is a powerful tool to simulate structured fluids characterized by complex rheologies. Equilibrium simulations with the same model parameters well describe the phase diagrams of both Pluronic L64/water and Pluronic P104/water. The observed microstructures are qualitatively and quantitatively in agreement with experimental observations. This is confirmed by a detailed cluster analysis and the corresponding trends for the standard chemical potential. When shear is applied in non-equilibrium DPD simulations morphological changes are quantified, resulting in the coalescence of spherical and rod-like micelles and breakup and deformation of the other microstructures. The resulting rheology is in line with experiments, as the mixtures exhibit Newtonian behaviors at low concentrations (i.e. when spherical micelles are formed) and non-Newtonian shear-thinning behaviors at higher concentrations.

References

[1] Hoogerbrugge P.J., Koelman J. M. V. A, (1992), EPL, 19, 155-160.

[2] Groot R.D., Warren P.B., (1997), J. Chem. Phys., 107, 4423-4435

[3] Lees A.W., Edwards S.F., (1972), Journal of Physics C: Solid State Physics, 5, 1921-1928.

[4] Plimpton S., (1995), J. Comput. Phys., 117, 1-19.

[5] Prhashanna A., Khan S. A., Chen S.B., (2016), Colloids Surf. A Physicochem. Eng. Asp., 506, 457-466

[6] Wanka G., Hoffmann H., Ulbricht W., (1994) Macromolecules, 27, 4145–4159.