Transport of Flexible Molecules in Narrow Confinements (original) (raw)
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Polymer chain dynamics under nanoscopic confinements
Magnetic Resonance Imaging, 2005
It is shown that the confinement of polymer melts in nanopores leads to chain dynamics dramatically different from bulk behavior. This so-called corset effect occurs both above and below the critical molecular mass and induces the dynamic features predicted for reptation. A spinodal demixing technique was employed for the preparation of linear poly(ethylene oxide) (PEO) confined to nanoscopic strands that are in turn embedded in a quasi-solid and impenetrable methacrylate matrix. Both the molecular weight of the PEO and the mean diameter of the strands were varied to a certain degree. The chain dynamics of the PEO in the molten state was examined with the aid of field-gradient NMR diffusometry (time scale, 10 À2-10 0 s) and field-cycling NMR relaxometry (time scale, 10 À9-10 À4 s). The dominating mechanism for translational displacements probed in the nanoscopic strands by either technique is shown to be reptation. On the time scale of spin-lattice relaxation time measurements, the frequency dependence signature of reptation (i.e., T 1~m 3/4) showed up in all samples. A btubeQ diameter of only 0.6 nm was concluded to be effective on this time scale even when the strand diameter was larger than the radius of gyration of the PEO random coils. This corset effect is traced back to the lack of the local fluctuation capacity of the free volume in nanoscopic confinements. The confinement dimension is estimated at which the crossover from confined to bulk chain dynamics is expected.
The Journal of Chemical Physics, 2011
Polymer chains, confined to cavities or polymer layers with dimensions less than the chain radius of gyration, appear in many phenomena, such as gel chromatography, rubber elasticity, viscolelasticity of high molar mass polymer melts, the translocation of polymers through nanopores and nanotubes, polymer adsorption, etc. Thus, the description of how the constraints alter polymer thermodynamic properties is a recurrent theoretical problem. A realistic treatment requires the incorporation of impenetrable interacting ͑attractive or repulsive͒ boundaries, a process that introduces significant mathematical complications. The standard approach involves developing the generalized diffusion equation description of the interaction of flexible polymers with impenetrable confining surfaces into a discrete eigenfunction expansion, where the solutions are normally truncated at the first mode ͑the "ground state dominance" approximation͒. This approximation is mathematically well justified under conditions of strong confinement, i.e., a confinement length scale much smaller than the chain radius of gyration, but becomes unreliable when the polymers are confined to dimensions comparable to their typically nanoscale size. We extend a general approach to describe polymers under conditions of weak to moderate confinement and apply this semianalytic method specifically to determine the thermodynamics and static structure factor for a flexible polymer confined between impenetrable interacting parallel plate boundaries. The method is first illustrated by analyzing chain partitioning between a pore and a large external reservoir, a model system with application to chromatography. Improved agreement is found for the partition coefficients of a polymer chain in the pore geometry. An expression is derived for the structure factor S͑k͒ in a slit geometry to assist in more accurately estimating chain dimensions from scattering measurements for thin polymer films.
Entropic attraction: Polymer compaction and expansion induced by nano-particles in confinement
The Journal of chemical physics, 2015
We investigated nanoparticle (NP)-induced coil-to-globule transition of a semi-flexible polymer in a confined suspension of ideal NP using Langevin dynamics. DNA molecules are often found to be highly compact, bound with oppositely charged proteins in a crowded environment within cells and viruses. Recent studies found that high concentration of electrostatically neutral NP also condenses DNA due to entropically induced depletion attraction between DNA segments. Langevin dynamics simulations with a semi-flexible chain under strong confinement were performed to investigate the competition between NP-induced monomer-monomer and monomer-wall attraction under different confinement heights and NP volume fractions. We found that whether NP induce polymer segments to adsorb to the walls and swell or to attract one another and compact strongly depends on the relative strength of the monomer-wall and the NP-wall interactions.
Effect of Nanoconfinement on Polymer Chain Dynamics
Macromolecules, 2020
reported a set of interesting results for the viscosity of unentangled polystyrene of two different molecular weights determined from capillary infiltration into a confining matrix of silica nanoparticles. They found that the viscosity and glass transition temperature (T g) increase as the pore size of the matrix decreases, that is, the confinement effect becomes stronger. They attributed the change in viscosity to a change in segmental relaxation, that is, an increase in T g. However, their interpretation did not consider that a changing T g leads to a change in the monomeric friction coefficient and viscosity-molecular weight relations should be compared at constant friction factor, that is, at a constant distance from the glass transition temperature. We reanalyzed the results at constant friction factor under a framework of changing chain dynamics as confinement strength increases rather than being due only to the changing glass transition temperature. Our reanalysis of the data from Hor et al. as well as data from other literature shows that as unentangled polymers become increasingly confined, the chain dynamics change from Rouse-like to those of an entropic barrier regime. For entangled polymers, the chain dynamics change from those of a reptation-like regime to those of an entropic barrier regime.
Length-dependent translocation of polymers through nanochannels
2011
We consider the flow-driven translocation of single polymer chains through nanochannels. Using analytical calculations based on the de Gennes blob model and mesoscopic numerical simulations, we estimate the threshold flux for the translocation of chains of different number of monomers. The translocation of the chains is controlled by the competition between entropic and hydrodynamic effects, which set a critical penetration length for the chain before it can translocate through the channel. We demonstrate that the polymers show two different translocation regimes depending on how their length under confinement compares to the critical penetration length. For polymer chains longer than the threshold, the translocation process is insensitive to the number of monomers in the chain as predicted in Sakaue {\it et al.}, {\it Euro. Phys. Lett.}, {\bf 72} 83 (2005). However, for chains shorter than the critical length we show that the translocation process is strongly dependent on the length of the chain. We discuss the possible relevance of our results to biological transport.
Single-polymer dynamics under constraints: scaling theory and computer experiment
Journal of Physics: Condensed Matter, 2011
The relaxation, diffusion and translocation dynamics of single linear polymer chains in confinement is briefly reviewed with emphasis on the comparison between theoretical scaling predictions and observations from experiment or, most frequently, from computer simulations. Besides cylindrical, spherical and slit-like constraints, related problems such as the chain dynamics in a random medium and the translocation dynamics through a nanopore are also considered. Another particular kind of confinement is imposed by polymer adsorption on attractive surfaces or selective interfaces-a short overview of single-chain dynamics is also contained in this survey. While both theory and numerical experiments consider predominantly coarse-grained models of self-avoiding linear chain molecules with typically Rouse dynamics, we also note some recent studies which examine the impact of hydrodynamic interactions on polymer dynamics in confinement. In all of the aforementioned cases we focus mainly on the consequences of imposed geometric restrictions on single-chain dynamics and try to check our degree of understanding by assessing the agreement between theoretical predictions and observations.
Soft Matter, 2012
Using analytical techniques and Langevin dynamics simulations, we investigate the dynamics of polymer translocation through a nanochannel embedded in two dimensions under an applied external field. We examine the translocation time for various ratio of the channel length L to the polymer length N. For short channels L ≪ N , the translocation time τ ∼ N 1+ν under weak driving force F , while τ ∼ F −1 L for long channels L ≫ N , independent of the chain length N. Moreover, we observe a minimum of translocation time as a function of L/N for different driving forces and channel widths. These results are interpreted by the waiting time of a single segment.
Scaling Theory of Polymer Translocation into Confined Regions
Biophysical Journal, 2008
We examine the voltage-driven polymer translocation from a spacious region into a confined region imposed by two parallel planes, so that the entry is impeded by the entropic confinement but aided by the electric field inside the confined region. Two modes of entry are examined: linear translocation where a chain enters the confined region with chain ends, and hairpin translocation where a chain enters the confined region by forming a hairpin. Our calculation shows that translocation time increases with polymer length for linear entries but decreases with polymer length for hairpin entries. Applying to electrophoresis of DNA molecules through periodic spacious and confined regions, our theory shows that the dominance of hairpin translocations leads to the experimentally observed faster migration of longer DNA molecules. Our theory predicts experimental conditions for the validity of this law in terms of polymer length, size of the confined region, and solution conditions.
The effects of slit-like confinement on flow-induced polymer deformation
The Journal of Chemical Physics, 2017
This paper is broadly concerned with the dynamics of a polymer confined to a rectangular slit of width D and deformed by a planar elongational flow of strengthγ. It is interested, more specifically, in the nature of the coil-stretch transition that such polymers undergo when the flow strengthγ is varied, and in the degree to which this transition is affected by the presence of restrictive boundaries. These issues are explored within the framework of a finitely extensible Rouse model that includes pre-averaged surface-mediated hydrodynamic interactions. Calculations of the chain's steady-state fractional extension x using this model suggest that different modes of relaxation (which are characterized by an integer p) exert different levels of control on the coil-stretch transition. In particular, the location of the transition (as identified from the graph of x versus the Weissenberg number Wi, a dimensionless parameter defined by the product ofγ and the time constant τ p of a relaxation mode p) is found to vary with the choice of τ p. In particular, when τ 1 is used in the definition of Wi, the x vs. Wi data for different D lie on a single curve, but when τ 3 is used instead (with τ 3 > τ 1) the corresponding data lie on distinct curves. These findings are in close qualitative agreement with a number of experimental results on confinement effects on DNA stretching in electric fields. Similar D-dependent trends are seen in our calculated force vs. Wi data, but force vs. x data are essentially D-independent and lie on a single curve.