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Register a new userConformations and diffusion of flexibly linked colloidal chains
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For biologically relevant macromolecules such as intrinsically disordered proteins, internal degrees of freedom that allow for shape changes have a large influence on both the motion and function of the compound. A detailed understanding of the effect of flexibility is needed in order to explain their behavior. Here, we study a model system of freely-jointed chains of three to six colloidal spheres, using both simulations and experiments. We find that in spite of their short lengths, their conformational statistics are well described by two-dimensional Flory theory, while their average translational and rotational diffusivity follow the Kirkwood-Riseman scaling. Their maximum flexibility does not depend on the length of the chain, but is determined by the near-wall in-plane translational diffusion coefficient of an individual sphere. Furthermore, we uncover shape-dependent effects in the short-time diffusivity of colloidal tetramer chains, as well as non-zero couplings between the different diffusive modes. Our findings may have implications for understanding both the diffusive behavior and the most likely conformations of macromolecular systems in biology and industry, such as proteins, polymers, single-stranded DNA and other chain-like molecules.
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The motion of an optically trapped sphere constrained by the vicinity of a wall is investigated at times where hydrodynamic memory is significant. First, we quantify, in bulk, the influence of confinement arising from the trapping potential on the spheres velocity autocorrelation function $C(t)$. Next, we study the splitting of $C(t)$ into $C_parallel(t)$ and $C_perp(t)$, when the sphere is approached towards a surface. Thereby, we monitor the crossover from a slow $t^{-3/2}$ long-time tail, away from the wall, to a faster $t^{-5/2}$ decay, due to the subtle interplay between hydrodynamic backflow and wall effects. Finally, we discuss the resulting asymmetric time-dependent diffusion coefficients.
Macromolecular diffusion in dense colloidal suspensions is an intriguing topic of interdisciplinary relevance in Science and Engineering. While significant efforts have been undertaken to establish the impact of crowding on the dynamics of macromolecules, less clear is the role played by long-range ordering. In this work, we perform Dynamic Monte Carlo simulations to assess the importance of ordered crowding on the diffusion of globular macromolecules, here modelled as spherical tracers, in suspensions of colloidal cuboids. We first investigate the diffusion of such guest tracers in very weakly ordered host phases of cuboids and, by increasing density above the isotropic-to-nematic phase boundary, study the influence of long-range orientational ordering imposed by the occurrence of liquid-crystalline phases. To this end, we analyse a spectrum of dynamical properties that clarify the existence of slow and fast tracers and the extent of deviations from Gaussian behaviour. Our results unveil the existence of randomly oriented clusters of cuboids that display a relatively large size in dense isotropic phases, but are basically absent in the nematic phase. We believe that these clusters are responsible for a pronounced non-Gaussian dynamics that is much weaker in the nematic phase, where orientational ordering smooths out such structural heterogeneities.
We report on a comprehensive theory-simulation-experimental study of collective and self-diffusion in suspensions of charge-stabilized colloidal spheres. In simulation and theory, the spheres interact by a hard-core plus screened Coulomb pair potential. Intermediate and self-intermediate scattering functions are calculated by accelerated Stokesian Dynamics simulations where hydrodynamic interactions (HIs) are fully accounted for. The study spans the range from the short-time to the colloidal long-time regime. Additionally, Brownian Dynamics simulation and mode-coupling theory (MCT) results are generated where HIs are neglected. It is shown that HIs enhance collective and self-diffusion at intermediate and long times, whereas at short times self-diffusion, and for certain wavenumbers also collective diffusion, are slowed down. MCT significantly overestimate the slowing influence of dynamic particle caging. The simulated scattering functions are in decent agreement with our dynamic light scattering (DLS) results for suspensions of charged silica spheres. Simulation and theoretical results are indicative of a long-time exponential decay of the intermediate scattering function. The approximate validity of a far-reaching time-wavenumber factorization of the scattering function is shown to be a consequence of HIs. Our study of collective diffusion is amended by simulation and theoretical results for the self-intermediate scattering function and the particle mean squared displacement (MSD). Since self-diffusion is not assessed in DLS measurements, a method to deduce the MSD approximately in DLS is theoretically validated.
We demonstrate that a highly charged polyelectrolyte confined in a spherical cavity undergoes reversible transformations between amorphous conformations to a four-fold symmetry morphology as a function of dielectric mismatch between the media inside and outside the cavity. Surface polarization due to dielectric mismatch exhibits an extra confinement effect, which are most pronounced within a certain range of the cavity radius and the electrostatic strength between the monomers and counterions and multivalent counterions. For cavities with a charged surface, surface polarization leads to an increased amount of counterions adsorbed in the outer side, further compressing the confined polyelectrolyte into a four-fold symmetry morphology. The equilibrium conformation of the chain is dependent upon several key factors including the relative permittivities of the media inside and outside the cavity, multivalent counterion concentration, cavity radius relative to the chain length, and interface charge density. Our findings offer insights into the effects of dielectric mismatch in packaging and delivery of polyelectrolytes across media with different relative permittivities. Moreover, the reversible transformation of the polyelectrolyte conformations in response to environmental permittivity allows for potential applications in biosensing and medical monitoring.
Evolving structure and rheology across Kuhn scale interfaces in entangled polymer fluids under flow play a prominent role in processing of manufactured plastics, and have numerous other applications. Quantitative tracking of chain conformation statistics on the Kuhn scale is essential for developing computational models of such phenomena. For this purpose, we formulate here a two-scale/two-mode model of entangled polymer chains under flow. Each chain is partitioned by successive entanglements into strands that are in one of two modes: entangled or dangling. On the strand scale, conformation statistics of ideal (non-interacting) strands follows a differential evolution equation for the second moment of its end-to-end distance. The latter regulates persistent random walks sampling conformation statistics of ideal entangled strands on the Kuhn scale, as follows from a generalized Green-Kubo relation and the Maximum Entropy Principle. We test it numerically for a range of deformation rates at the start-up of simple elongational and shear flows. A self-consistent potential, representing segmental interactions, modifies strand conformation statistics on the Kuhn scale, as it renormalizes the parameters controlling the persistent random walk. The generalized Green-Kubo relation is then inverted to determine how the second moment of the strand end-to-end distance is changed by the self-consistent potential. This allows us to devise a two-scale propagation scheme for the statistical weights of subchains of the entangled chain. The latter is used to calculate local volume fractions for each chemical type of Kuhn segments in entangled chains, thus determining the self-consistent potential.
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