J. G. E. M. Fraaije

In this article, we present a new LINear Constraint Solver (LINCS) for molecular simulations with bond constraints. The algorithm is inherently stable, as the constraints themselves are reset instead of derivatives of the constraints, thereby eliminating drift. Although the derivation of the algorithm is presented in terms of matrices, no matrix matrix multiplications are needed and only the nonzero matrix elements have to be stored, making the method useful for very large molecules. At the same accuracy, the LINCS algorithm is three to four times faster than the SHAKE algorithm. Parallelization of the algorithm is straightforward. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 1463–1472, 1997

In this article, we present a new LINear Constraint Solver (LINCS) for molecular simulations with bond constraints. The algorithm is inherently stable, as the constraints themselves are reset instead of derivatives of the constraints, thereby eliminating drift. Although the derivation of the algorithm is presented in terms of matrices, no matrix matrix multiplications are needed and only the nonzero matrix elements have to be stored, making the method useful for very large molecules. At the same accuracy, the LINCS algorithm is three to four times faster than the SHAKE algorithm. Parallelization of the algorithm is straightforward. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 1463–1472, 1997

In this paper we discuss a new generalized time-dependent Ginzburg-Landau theory for the numerical calculation of polymer phase separation kinetics in 3D. The thermodynamic forces are obtained by a mean-field density functional method, using a Gaussian chain as a molecular model. The method is especially aimed at describing the formation kinetics of the irregular morphologies which are typical for many industrial systems. As proof of concept we present the formation of irregular morphologies in quenched symmetric and asymmetric block copolymer melts.

In this paper, we describe a numerical method for the calculation of collective diffusion relaxation mechanisms in quenched block copolymer melts. The method entails the repeated calculation of two opposing fields—an external potential field U, conjugate to the density field ρ, and an energetic interaction field E. The external field is calculated by numerical inversion of the density functionals and the energetic interaction field is calculated directly by integration over the density field. When the two fields are balanced U=E, we recover the self-consistent field solutions; when the two fields are off balance, the spatial gradient of E–U is the thermodynamic force which drives the collective diffusion. We introduce a simple local coupling approximation for the Onsager kinetic coefficients of short freely jointed chains in weakly ordered systems. Fluctuations are added by incorporation of a random Langevin force in the diffusion equation. Numerical results of decomposition in symmetric and asymmetric diblock copolymer melts indicate that the method is capable of describing extremely slow defect annihilation relaxation modes. We find that in the nonlinear regime, the density patterns evolve to metastable states, in which isolated defects separate relatively well-ordered crystalline microdomains. These final states are typical for many industrial applications of incompletely relaxed copolymer melts.

We simulate the microphase separation dynamics of aqueous solutions of the triblock polymer surfactants (ethylene oxide)13(propylene oxide)30(ethylene oxide)13 and (propylene oxide)19(ethylene oxide)33(propylene oxide)19 by a dynamic variant of mean-field density functional theory for Gaussian chains. This is the first 3D mesoscale model for the dynamic behavior of specific complex polymer solutions. Different mesoscale structures (micellar, hexagonal, bicontinuous, and lamellar and dispersed coexisting phases) are formed depending on composition. The numerical results are in good agreement with experiment. The intermediate hexagonal and bicontinuous phases of (ethylene oxide)13(propylene oxide)30(ethylene oxide)13 solution retain a rich defect structure. Concentrated solution (60%) of (propylene oxide)19(ethylene oxide)33(propylene oxide)19 shows the onset of macrophase separation, with small water droplets dispersed throughout the system. We confirm the experimental observation that the lamellar phase formation does not depend on the block sequence. Quenched from homogeneous state, the kinetics of each system consists of a fast local aggregation stage and subsequent slow rearrangement by defect annihilation. We conclude that the simulation method is a valuable tool for description of 3D morphology formation in a wide variety of complex polymer liquids.