Swelling of polymers in porous media

Polymer looping kinetics in active heterogeneous environments

A typical biological environment is usually featured by crowding and heterogeneity, leading to complex reaction kinetics of the immersed macromolecules. In the present work, we adopt Langevin dynamics simulations to systematically investigate polymer looping kinetics in active heterogeneous media crowded with a mixture of mobile active particles and immobile obstacles. For comparison, a parallel study is also performed in the passive heterogeneous media. We explicitly analyze the change of looping time and looping probability with the variation of obstacle ratio, volume fraction and crowder size. We reveal the novel phenomena of inhibition-facilitation transition of the looping rate induced by heterogeneity, crowdedness and activity. In addition, our results demonstrate a very non-trivial crowder size effect on the looping kinetics. The underlying mechanism is rationalized by the interplay of polymer diffusion, conformational change and looping free-energy barrier. The competing effect arising from active particles and obstacles on structural and dynamical properties of the polymer yields a consistent scenario for our observations. Lastly, the non-exponential kinetics of the looping process is also analyzed. We find that both activity and crowding can strengthen the heterogeneity degree of the looping kinetics.

Heterogeneous kinetics of the loop formation of a single polymer chain in crowded and disordered media

The cytoplasmic volume of cells is occupied and crowded by a variety of macromolecules, such as proteins and cytoskeleton structures. Such diverse macromolecules make the cell cytoplasm not only structurally heterogeneous but also dynamically heterogeneous: Some macromolecules may diffuse freely inside cell cytoplasm at certain timescales while others hardly diffuse. Studies on the effects of the dynamic heterogeneity on reaction kinetics have been limited even though the effects of the crowdedness and structural heterogeneity were investigated extensively. In this study, we employ a simple model of mixtures of mobile and immobile matrix particles, tune the degree of dynamic heterogeneity by changing the fraction of immobile matrix particles, and investigate reaction kinetics in such heterogeneous media. We employ the loop formation of a single polymer chain as a model reaction and perform Langevin dynamics simulations. We find that the free-energy barrier of the loop formation is decreased as the systems become more crowded with matrix particles. But the free-energy barrier is not sensitive to the dynamic heterogeneity. As dynamic heterogeneity increases with an increase in the fraction of immobile matrix particles, however, the diffusivity of the system decreases significantly. The decrease in the diffusion (due to the dynamic heterogeneity) and the decrease in the free-energy barrier (due to the crowdedness) lead together to a complicated trend of the loop formation kinetics. As the volume fraction of immobile matrix particles reaches a critical value at the percolation transition, the reaction kinetics becomes significantly heterogeneous and the survival probability distribution of the chain loop formation becomes stretched-exponential. We also illustrate that the heterogeneous reaction rate near the percolation transition relates closely to the structures of local pores in which the polymer is located.

Block Copolymer of Flexible and Semi-Flexible Block Confined in Nanopost Array

Coarse-grained molecular dynamics simulations of a diblock copolymer consisting of a flexible and semi-flexible block in a dense array of parallel nanoposts with a square lattice packing were performed. The mutual interactions between the two blocks of the confined diblock chain were investigated through a comparison of their size, structure, and penetration among nanoposts with the corresponding separate chains. The geometry of a nanopost array was varied at constant post separation or at constant width of the passage between nanoposts. The size of a single interstitial volume was comparable to or smaller than the size of the diblock chain. A comparison of the blocks with their separate analogous chains revealed that the mutual interactions between the blocks were shielded by the nanoposts and, thus, the blocks behaved independently. At constant passage width, competitive effects of the axial chain extension in interstitial volumes and the lateral chain expansion among interstitial volumes led to a nonmonotonic behavior of the axial span. The position of the maximum in the span plotted against the filling fraction for a diblock chain was dictated by the semi-flexible block. The semi-flexible block penetrates among the nanoposts more readily and the expansion of the whole diblock copolymer is governed by the semiflexible block. The main findings were explained using the free energy arguments when an interstitial volume was approximated by a channel geometry and a passage aperture by a slit geometry. Detail knowledge of controlled conformational behavior in a compartmentalized environment can contribute to new processes in the storage and retrieval of information.

Combining Diffusion NMR and Small-Angle Neutron Scattering Enables Precise Measurements of Polymer Chain Compression in a Crowded Environment

The effect of particles on the behavior of polymers in solution is important in a number of important phenomena such as the effect of "crowding" proteins in cells, colloid-polymer mixtures, and nanoparticle "fillers" in polymer solutions and melts. In this Letter, we study the effect of spherical inert nanoparticles (which we refer to as "crowders") on the diffusion coefficient and radius of gyration of polymers in solution using pulsed-field-gradient NMR and small-angle neutron scattering (SANS), respectively. The diffusion coefficients exhibit a plateau below a characteristic polymer concentration, which we identify as the overlap threshold concentration c^{⋆}. Above c^{⋆}, in a crossover region between the dilute and semidilute regimes, the (long-time) self-diffusion coefficients are found, universally, to decrease exponentially with polymer concentration at all crowder packing fractions, consistent with a structural basis for the long-time dynamics. The radius of gyration obtained from SANS in the crossover regime changes linearly with an increase in polymer concentration, and must be extrapolated to c^{⋆} in order to obtain the radius of gyration of an individual polymer chain. When the polymer radius of gyration and crowder size are comparable, the polymer size is very weakly affected by the presence of crowders, consistent with recent computer simulations. There is significant chain compression, however, when the crowder size is much smaller than the polymer radius gyration.

Diffusion of a Rouse chain in porous media: A mode-coupling-theory study

We use a kinetic mode-coupling theory (MCT) combining with generalized Langevin equation (GLE) to study the diffusion and conformational dynamics of a bead-spring Rouse chain (RC) dissolved in porous media. The media contains fluid particles and immobile matrix ones wherein the latter leads to the lack of translational invariance. The friction kernel ζ(t) used in the GLE can be obtained directly by adopting a simple density-functional approach in which the density correlators calculated by MCT equations of porous media serve as inputs. Due to cage effects generated by surrounding particles, ζ(t) shows a very long tail memory in the high volume fraction of fluid and matrix. It is found that the long-time center-of-mass diffusion constant D_{CM} of the RC decreases with the increment of volume fraction, influencing more strongly by the matrix particles than by the fluid ones. The auto-correlation function (ACF) of the end-to-end distance fluctuation can also be calculated theoretically based on GLE. Of particular interest is that the power-law region of ACF has a nearly fixed length in logarithmic scale when it shifts to longer time range, with increasing the volume fraction of media particles. Moreover, the effect of lack of translational invariance has been investigated by comparing the results between fluid-matrix and pure fluid cases under identical total volume fraction.

Interplay between polymer chain conformation and nanoparticle assembly in model industrial silica/rubber nanocomposites

The question of the influence of nanoparticles (NPs) on chain dimensions in polymer nanocomposites (PNCs) has been treated mainly through the fundamental way using theoretical or simulation tools and experiments on well-defined model PNCs. Here we present the first experimental study on the influence of NPs on the polymer chain conformation for PNCs designed to be as close as possible to industrial systems employed in the tire industry. PNCs are silica nanoparticles dispersed in a styrene-butadiene-rubber (SBR) matrix whose NP dispersion can be managed by NP loading with interfacial coatings or coupling additives usually employed in the manufacturing mixing process. We associated specific chain (d) labeling, and the so-called zero average contrast (ZAC) method, with SANS, in situ SANS and SAXS/TEM experiments to extract the polymer chain scattering signal at rest for non-cross linked and under stretching for cross-linked PNCs. NP loading, individual clusters or connected networks, as well as the influence of the type, the quantity of interfacial agent and the influence of the elongation rate have been evaluated on the chain conformation and on its related deformation. We clearly distinguish the situations where the silica is perfectly matched from those with unperfected matching by direct comparison of SANS and SAXS structure factors. Whatever the silica matching situation, the additive type and quantity and the filler content, there is no significant change in the polymer dimension for NP loading up to 15% v/v within a range of 5%. One can see an extra scattering contribution at low Q, as often encountered, enhanced for non-perfect silica matching but also visible for perfect filler matching. This contribution can be qualitatively attributed to specific h or d chain adsorption on the NP surface inside the NP cluster that modifies the average scattering neutron contrast of the silica cluster. Under elongation, NPs act as additional cross-linking junctions preventing chain relaxation and giving a deformation of the chain with the NP closer to a theoretical phantom network prediction than a pure matrix.

Confinement and partitioning of a single polymer chain in a dense array of nanoposts

We present a Brownian dynamics simulation study on the confinement and partitioning of a single, flexible polymer chain in a dense array of nanoposts with different sizes and separations, especially, when the volume of an interstitial space formed among four nanoposts is less than the volume of the polymer chain. As the interstitial volume decreases by either increasing the nanopost diameter or decreasing the separation between nanoposts, the chain conformation becomes elongated in the direction parallel to the nanoposts. Interestingly, however, the degree of chain elongation varies in a non-monotonic fashion as the interstitial volume decreases while keeping the passage width between two nanoposts constant at a small value. We calculate the free energy of chain partitioning over several interstitial spaces from the partitioning probability, and find that the non-monotonic dependence of the chain elongation results from an interplay between the confinement-driven chain elongation along the direction parallel to the nanoposts and the chain spreading perpendicular to the nanoposts by partitioning chain segments over several interstitial spaces. These results present the possibility of utilizing a dense array of nanoposts as a template to control polymer conformations.

Density fluctuations of polymers in disordered media

We study self-avoiding random walks in an environment where sites are excluded randomly, in two and three dimensions. For a single polymer chain, we study the statistics of the time averaged monomer density and show that these are well described by multifractal statistics. This is true even far from the percolation transition of the disordered medium. We investigate solutions of chains in a disordered environment and show that the statistics cease to be multifractal beyond the screening length of the solution.