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We study the conformational properties of charged polymers in a solvent in the presence of structural obstacles correlated according to a power law $sim x^{-a}$. We work within the continuous representation of a model of linear chain considered as a random sequence of charges $q_i=pm q_0$. Such a model captures the properties of polyampholytes -- heteropolymers comprising both positively and negatively charged monomers. We apply the direct polymer renormalization scheme and analyze the scaling behavior of charged polymers up to the first order of an $epsilon=6-d$, $delta=4-a$-expansion.
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Freezing in charged porous media can induce significant pressure and cause damage to tissues and functional materials. We formulate a thermodynamically consistent theory to model freezing phenomena inside charged heterogeneous porous space. Two regimes are distinguished: free ions in open pore space lead to negligible effects of freezing point depression and pressure. On the other hand, if nano-fluidic salt trapping happens, subsequent ice formation is suppressed due to the high concentration of ions in the electrolyte. In this case, our theory predicts that freezing starts at a significantly lower temperature compared to pure water. In 1D, as the temperature goes even lower, ice continuously grows, until the salt concentration reaches saturation, all ions precipitate to form salt crystals, and freezing completes. Enormous pressure can be generated if initial salt concentration is high before salt entrapment. We show modifications to the classical nucleation theory, due to the trapped salt ions. Interestingly, although the freezing process is enormously changed by trapped salts, our analysis shows that the Gibbs-Thompson equation on confined melting point shift is not affected by the presence of the electrolyte.
We perform Brownian dynamics simulations of active stiff polymers undergoing run-reverse dynamics, and so mimic bacterial swimming, in porous media. In accord with recent experiments of emph{Escherichia coli}, the polymer dynamics are characterized by trapping phases interrupted by directed hopping motion through the pores. We find that the effective translational diffusivities of run-reverse agents can be enhanced up to two orders in magnitude, compared to their non-reversing counterparts, and exhibit a non-monotonic behavior as a function of the reversal rate, which we rationalize using a coarse-grained model. Furthermore, we discover a geometric criterion for the optimal spreading, which emerges when their run lengths are comparable to the longest straight path available in the porous medium. More significantly, our criterion unifies results for porous media with disparate pore sizes and shapes and thus provides a fundamental principle for optimal transport of microorganisms and cargo-carriers in densely-packed biological and environmental settings.
We report studies of the frequency dependent shear modulus, $G^*(omega)=G(omega)+iG(omega)$, of the liquid crystal octylcyanobiphenyl (8CB) confined in a colloidal aerosil gel. With the onset of smectic order, $G$ grows approximately linearly with decreasing temperature, reaching values that exceed by more than three orders of magnitude the values for pure 8CB. The modulus at low temperatures possesses a power-law component, $G^*(omega) sim omega^alpha$, with exponent $alpha$ that approaches zero with increasing gel density. The amplitude of $G$ and its variation with temperature and gel density indicate that the low temperature response is dominated by a dense population of defects in the smectic. In contrast, when the 8CB is isotropic or nematic, the modulus is controlled by the elastic behavior of the colloidal gel.
The flow and deformation of macromolecules is ubiquitous in nature and industry, and an understanding of this phenomenon at both macroscopic and microscopic length scales is of fundamental and practical importance. Here we present the formulation of a general mathematical framework, which could be used to extract, from scattering experiments, the molecular relaxation of deformed polymers. By combining and modestly extending several key conceptual ingredients in the literature, we show how the anisotropic single-chain structure factor can be decomposed by spherical harmonics and experimentally reconstructed from its cross sections on the scattering planes. The resulting wavenumber-dependent expansion coefficients constitute a characteristic fingerprint of the macromolecular deformation, permitting detailed examinations of polymer dynamics at the microscopic level. We apply this approach to survey a long-standing problem in polymer physics regarding the molecular relaxation in entangled polymers after a large step deformation. The classical tube theory of Doi and Edwards predicts a fast chain retraction process immediately after the deformation, followed by a slow orientation relaxation through the reptation mechanism. This chain retraction hypothesis, which is the keystone of the tube theory for macromolecular flow and deformation, was critically examined by analyzing the fine features of the two-dimensional anisotropic spectra from small-angle neutron scattering by entangled polystyrenes. It is shown that the unique scattering patterns associated with the chain retraction mechanism were not experimentally observed. This result calls for a fundamental revision of the current theoretical picture for nonlinear rheological behavior of entangled polymeric liquids.
Porous media with hierarchical structures are commonly encountered in both natural and synthetic materials, e.g., fractured rock formations, porous electrodes and fibrous materials, which generally consist of two or more distinguishable levels of pore structure with different characteristic lengths. The multiphase flow behaviours in hierarchical porous media have remained elusive. In this study, we investigate the influences of hierarchical structures in porous media on the dynamics of immiscible fingering during fluid-fluid displacement. By conducting a series of numerical simulations, we found that the immiscible fingering can be suppressed due to the existence of secondary porous structures. To characterise the fingering dynamics in hierarchical porous media, a phase diagram is constructed by introducing a scaling parameter, i.e., the ratio of time scales considering the combined effect of characteristic pore sizes and wettability. The findings present in this work provide a basis for further research on the application of hierarchical porous media for controlling immiscible fingerings.
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