Numerical Solutions of the Complex Langevin Equations in Polymer Field Theory

The Journal of Chemical Physics

2012

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101

130

Complex coacervation, a liquid-liquid phase separation that occurs when two oppositely charged polyelectrolytes are mixed in a solution, has the potential to be exploited for many emerging applications including wet adhesives and drug delivery vehicles. The ultra-low interfacial tension of coacervate systems against water is critical for such applications, and it would be advantageous if molecular models could be used to characterize how various system properties (e.g., salt concentration) affect the interfacial tension. In this article we use field-theoretic simulations to characterize the interfacial tension between a complex coacervate and its supernatant. After demonstrating that our model is free of ultraviolet divergences (calculated properties converge as the collocation grid is refined), we develop two methods for calculating the interfacial tension from field-theoretic simulations. One method relies on the mechanical interpretation of the interfacial tension as the interfacial pressure, and the second method estimates the change in free energy as the area between the two phases is changed. These are the first calculations of the interfacial tension from full fieldtheoretic simulation of which we are aware, and both the magnitude and scaling behaviors of our calculated interfacial tension agree with recent experiments. Complex coacervation, a liquid-liquid phase separation that occurs when two oppositely charged polyelectrolytes are mixed in a solution, has the potential to be exploited for many emerging applications including wet adhesives and drug delivery vehicles. The ultra-low interfacial tension of coacervate systems against water is critical for such applications, and it would be advantageous if molecular models could be used to characterize how various system properties (e.g., salt concentration) affect the interfacial tension. In this article we use field-theoretic simulations to characterize the interfacial tension between a complex coacervate and its supernatant. After demonstrating that our model is free of ultraviolet divergences (calculated properties converge as the collocation grid is refined), we develop two methods for calculating the interfacial tension from field-theoretic simulations. One method relies on the mechanical interpretation of the interfacial tension as the interfacial pressure, and the second method estimates the change in free energy as the area between the two phases is changed. These are the first calculations of the interfacial tension from full fieldtheoretic simulation of which we are aware, and both the magnitude and scaling behaviors of our calculated interfacial tension agree with recent experiments.

Section: E Numerical Methodsmentioning

confidence: 99%

“…Several recent developments have made "field-theoretic simulations" (FTS) tractable, 20,21 where the full fluctuations of the fields are taken into account. Recently, such an approach has been used to study complex coacervation.…”

Section: Introductionmentioning

confidence: 99%

Investigation of the interfacial tension of complex coacervates using field-theoretic simulations

Riggleman

Kumar

The Journal of Chemical Physics

2012

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101

130

“…In practice, we have found that when used in tandem with appropriate semi-implicit time integration schemes, the discretized CL dynamics schemes presented in the previous section can be made both stable and accurate for arbitrary numbers of species and choices of interaction parameters in the weak and intermediate segregation regime. A number of the algorithms discussed here were presented in the context of two-species simulations by Lennon et al 17 , and all are compared in the context of multi-species simulations in Section IV.…”

Section: A Complex Langevin Time Integratorsmentioning

confidence: 99%

A multi-species exchange model for fully fluctuating polymer field theory simulations

Düchs

Delaney

The Journal of Chemical Physics

2014

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Field-theoretic models have been used extensively to study the phase behavior of inhomogeneous polymer melts and solutions, both in self-consistent mean-field calculations and in numerical simulations of the full theory capturing composition fluctuations. The models commonly used can be grouped into two categories, namely species models and exchange models. Species models involve integrations of functionals that explicitly depend on fields originating both from species density operators and their conjugate chemical potential fields. In contrast, exchange models retain only linear combinations of the chemical potential fields. In the two-component case, development of exchange models has been instrumental in enabling stable complex Langevin (CL) simulations of the full complex-valued theory. No comparable stable CL approach has yet been established for field theories of the species type. Here we introduce an extension of the exchange model to an arbitrary number of components, namely the multi-species exchange (MSE) model, which greatly expands the classes of soft material systems that can accessed by the complex Langevin simulation technique. We demonstrate the stability and accuracy of the MSE-CL sampling approach using numerical simulations of triblock and tetrablock terpolymer melts, and tetrablock quaterpolymer melts. This method should enable studies of a wide range of fluctuation phenomena in multiblock/multi-species polymer blends and composites.

“…Although FTS is computationally more expensive than SCFT, recent numerical advances have made high resolution FTS feasible for a wide variety of polymer systems. 17 Polyelectrolytes have been the subject of extensive theoretical and computational research for decades. [1][2][3][4][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] Statistical field theory models have played a significant role in these theoretical investigations, and both mean-field and nonmean-field approaches have been employed to gain insights into the structure and thermodynamics of a wide variety of polyelectrolyte systems.…”

mentioning

confidence: 99%

“…Recent improvements in stochastic integration algorithms for the CL equations have enabled high-resolution, three-dimensional (3D) field-theoretic simulations. 17 Here we report on the application of CL-FTS to polyelectrolyte complexation phenomena, specifically to the same symmetric binary polycationpolyanion model that was used for the analytical one-loop calculations. A particular focus of our CL-FTS study is the location and size of the two-phase region where coacervation takes place.…”

mentioning

confidence: 99%

Field‐theoretic simulations of polyelectrolyte complexation

Popov

Lee

J Polym Sci B Polym Phys

2007

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This viewpoint article is intended as a brief introduction to the emerging subject of field-theoretic simulations (FTS) of charged polymers. While the direct numerical simulation of field theory models has begun to impact several traditional areas of polymer science, including blends and block copolymers, polyelectrolytes have hitherto not been the subject of field-theoretic simulations.Here we report on a preliminary FTS study of polyelectrolyte complexation that demonstrates the potential of this novel numerical approach.Polyelectrolytes are ubiquitous in nature and in applications ranging from personal care products to paints, coatings, and processed foods. Indeed, practically all biopolymers are polyelectrolytes. In the application context, the introduction of dissociable groups is one of the most powerful ways to confer water solubility on a polymeric material. Scientifically, the polymer bound charges, which are compensated by a sea of oppositely charged counterions, produce a coupling between chain conformations and electrostatics that leads to an incredible richness of polyelectrolyte phenomena. However, this richness comes with a price: charged polymers are among the most difficult polymer systems to study theoretically or to simulate on the computer [1,2,3,4]. The explanation lies in the long range nature of Coulomb interactions -charged segments feel each other at much larger distances than segments in neutral polymer systems.