We extend dynamical self-consistent field theory (dSCFT) to large, nonlinear polymer chains to simulate the evolution of high-generation dendrimers in a solvent. Because the number of beads N within these bead-spring dendrimers is very large, we introduce a numerical technique to efficiently analyze the Rouse modes of the dendrimer through a decomposition of the dendrimer into many smaller subchains, achieving a significant improvement, from O(N-2) to O(N), in the scaling of the simulation time for the Rouse motion of the dendrimer. By adjusting the strength of the interaction between dendrimer and solvent beads, we obtain qualitative and quantitative agreement with the core-chain morphology, 22 nm radius, and high degree of hydration measured experimentally using small-angle neutron scattering for 11-generation, glucose-based phytoglycogen dendrimers in water, validating dSCFT in this context.

We study the spinodal decomposition in a symmetric, binary homopolymer blend using our recently developed dynamical self-consistent field theory. By taking the extremal solution of a dynamical functional integral, the theory reduces the interacting, multi-chain dynamics to a Smoluchowski equation describing the statistical dynamics of a single, unentangled chain in a self-consistent, time-dependent, mean force-field. We numerically solve this equation by evaluating averages over a large ensemble of replica chains, each one of which obeys single-chain Langevin dynamics, subject to the mean field. Following a quench from the disordered state, an early time spinodal instability in the blend composition develops, before even one Rouse time elapses. The dominant, unstable, growing wavelength is on the order of the coil size. The blend then enters a late-time, t, scaling regime with a growing domain size that follows the expected Lifshitz-Slyozov-Wagner t1/3 power law, a characteristic of a diffusion-driven coarsening process. These results provide a satisfying test of this new method, which correctly captures both the early and late time physics in the blend. Our simulation spans five orders-of-magnitude in time as the domains coarsen to 20 times the coil size, while remaining faithful to the dynamics of the microscopic chain model.

We examine nucleation of the stable body-centred-cubic (BCC) phase from the metastable uniform disordered phase in an asymmetric diblock copolymer melt. Our comprehensive, large-scale simulations of the time-dependent, mean-field Landau-Brazovskii model find that spherical droplets of the BCC phase nucleate directly from disorder. Near the order-disorder transition, the critical nucleus is large and has a classical profile, attaining the bulk BCC phase in an interior that is separated from disorder by a sharp interface. At greater undercooling, the amplitude of BCC order in the interior decreases and the nucleus interface broadens, leading to a diffuse critical nucleus. This diffuse nucleus becomes large as the simulation approaches the disordered phase spinodal. We show that our simulation follows the same nucleation pathway that Cahn and Hilliard found for an incompressible two-component fluid, across the entire metastable region. In contrast, a classical nucleation theory calculation based on the free energy of a planar interface between coexisting BCC and disordered phases agrees with simulation only in the limit of very small undercooling; we can expand this region of validity somewhat by accounting for the curvature of the droplet interface. A nucleation pathway involving a classical droplet persists, however, to deep undercooling in our simulation, but this pathway is energetically unfavourable. As a droplet grows in the simulation, its interface moves with a constant speed, and this speed is approximately proportional to the undercooling.

Type IV pili (T4P) are very thin protein filaments that extend from and retract into bacterial cells, allowing them to interact with and colonize a broad array of chemically diverse surfaces. The physical aspects that allow T4P to mediate adherence to many different surfaces remain unclear. Atomic force microscopy (AFM) nanoscale pulling experiments were used to measure the mechanical properties of T4P of a mutant strain of Pseudomonas aeruginosa PAO1 unable to retract its T4P. After adhering bacteria to the end of an AFM cantilever and approaching surfaces of mica, gold, or polystyrene, we observed adhesion of the T4P to all of the surfaces. Pulling of single and multiple T4P on retraction of the cantilever from the surfaces could be described using the worm-like chain (WLC) model. Distinct peaks in the measured distributions of the best-fit values of the persistence length Lp on two different surfaces provide strong evidence for close-packed bundling of very flexible T4P. In addition, we observed force plateaus indicating that adhesion of the T4P to both hydrophilic and hydrophobic surfaces occurs along extended lengths of the T4P. These data shed new light, to our knowledge, on T4P flexibility and support a low-affinity, high-avidity adhesion mechanism that mediates bacteria-surface interactions.

We develop a self-consistent field theory for particle dynamics by extremizing the functional integral representation of a microscopic Langevin equation with respect to the collective fields. Although our approach is general, here we formulate it in the context of polymer dynamics to highlight satisfying formal analogies with equilibrium self-consistent field theory. An exact treatment of the dynamics of a single chain in a mean force field emerges naturally via a functional Smoluchowski equation, while the time-dependent monomer density and mean force field are determined self-consistently. As a simple initial demonstration of the theory, leaving an application to polymer dynamics for future work, we examine the dynamics of trapped interacting Brownian particles. For binary particle mixtures, we observe the kinetics of phase separation.

We examine the dynamical evolution of a stable lamellar phase nucleating from a metastable cylinder phase in a diblock copolymer melt, through large-scale simulations of the time-dependent Landau-Brazovskii model. Ellipsoidal nuclei form, whose minor axis is parallel to the cylinder axis. We use our observation of both shrinking and growing droplets to determine the critical nucleus size as a function of undercooling, and find that the critical size grows as we approach coexistence. The nucleus shape and critical size agree, near coexistence, with the predictions of an approximate theory. This supports the idea that the underlying microstructure produces an anisotropic droplet interfacial tension, and that the interplay between this interfacial tension and a reduction in bulk free-energy is central to the nucleation process. The nucleus interface moves with a time-independent velocity that depends on the interface orientation in a manner that preserves the ellipsoidal droplet shape into the late stages of growth. Near coexistence, the magnitude of the interfacial velocity varies linearly with undercooling, consistent with theoretical predictions and experimental observations.

We study the influence of the surface field on lamellar morphologies that form in a diblock copolymer melt confined in a cylindrical nanopore, using self-consistent mean-field theory. By varying the pore diameter and surface field strength and by introducing a slight composition asymmetry, we systematically explore the stability regions of parallel and perpendicular lamellar phases and accurately compute the phase boundaries. When the surface field is weak, or the natural period of the lamellae is incommensurate with the pore size, lamellae perpendicular to the pore wall are preferred. A strong surface preference and/or a small composition asymmetry can lead to the formation of concentric parallel lamellae. In narrow pores, we find that complex structures can exist as equilibrium phases between regions of parallel and perpendicular lamellae. When we reduce the volume fraction of the block preferred by the pore wall, this composition asymmetry competes with the Surface preference and call lead to the formation of perpendicular lamellae. This suggests a route to produce perpendicular lamellar phases in the common experimental situation where a surface preference is present. This competition also enables us to characterize the strength of the surface field in the theory.

A multiblock model is developed for the study of the phase behavior of gradient copolymers. The model is able to describe gradient copolymer chains with arbitrary composition profiles. The validity of the multiblock model of gradient copolymers is established by good agreement between RPA (random phase approximation) results for a continuous composition distribution and a multiblock model. The phase behavior of gradient copolymers is examined using self-consistent mean-field theory (SCMFT) for multiblock copolymers. Phase diagrams of gradient copolymer melts with different gradient profiles are constructed by solving the SCMFT equations. It is discovered that the phase behavior depends sensitively on the gradient profiles. In particular, new triple points are observed, and the stability region of phases with curved interfaces shrinks as the gradient profile becomes smooth. For linear gradient copolymers, the lamellar phase is predicted to be the only stable ordered phase.