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Milchev A.,Bulgarian Academy of Science | Milchev A.,Johannes Gutenberg University Mainz | Klushin L.,American University of Beirut | Skvortsov A.,Chemical Pharmaceutical Academy | Binder K.,Johannes Gutenberg University Mainz
Macromolecules | Year: 2010

We consider the ejection dynamics of a flexible polymer chain out of confined environment. This situation arises in different physical contexts, including a flexible synthetic polymer partially confined in a nanopore and a viral genome partially ejected from its capsid. We describe the chain release from confinement both analytically and by means of dynamic Monte Carlo simulation. We find two distinct regimes of ejection dynamics depending on whether the chain is fully or partially confined. Partially confined chains are ejected from a pore of length L and diameter D after a typical time τ ∝ L2D5/3, regardless of their contour length N. The process is driven by a constant force f ≈ 5kBT/D and follows a "capillary" law. The force value is model-independent as long as the pore diameter exceeds the persistence length of the polymer chain and for pore walls that do not attract the segments of the polymer. In contrast, the ejection of fully confined chains is largely diffusive, the residence time being a nonmonotonic function of N. The drift-dominated ejection of long chains is characterized by narrow distribution of exit times whereas for diffusive-dominated ejection the exit times are described by a broad distribution. One finds good agreement with recent nanofluidic experiments with DNA. © 2010 American Chemical Society.

Fleer G.J.,Wageningen University | Skvortsov A.M.,Chemical Pharmaceutical Academy
Journal of Chemical Physics | Year: 2012

It is well known that lattice and continuum descriptions for polymers at interfaces are, in principle, equivalent. In order to compare the two models quantitatively, one needs a relation between the inverse extrapolation length c as used in continuum theories and the lattice adsorption parameter Δχ s (defined with respect to the critical point). So far, this has been done only for ideal chains with zero segment volume in extremely dilute solutions. The relation Δχ ss(c) is obtained by matching the boundary conditions in the two models. For depletion (positive c and Δχ ss) the result is very simple: Δχ ss = ln(1 + c/5). For adsorption (negative c and Δχ ss) the ideal-chain treatment leads to an unrealistic divergence for strong adsorption: c decreases without bounds and the train volume fraction exceeds unity. This due to the fact that for ideal chains the volume filling cannot be accounted for. We extend the treatment to real chains with finite segment volume at finite concentrations, for both good and theta solvents. For depletion the volume filling is not important and the ideal-chain result Δχ ss = ln(1 + c/5) is generally valid also for non-ideal chains, at any concentration, chain length, or solvency. Depletion profiles can be accurately described in terms of two length scales: Δχ s = tanh2[(z + p)/δ], where the depletion thickness (distal length) δ is a known function of chain length and polymer concentration, and the proximal length p is a known function of c (or Δχ ss) and δ. For strong repulsion p = 1/c (then the proximal length equals the extrapolation length), for weaker repulsion p depends also on chain length and polymer concentration (then p is smaller than 1/c). In very dilute solutions we find quantitative agreement with previous analytical results for ideal chains, for any chain length, down to oligomers. In more concentrated solutions there is excellent agreement with numerical self-consistent depletion profiles, for both weak and strong repulsion, for any chain length, and for any solvency. For adsorption the volume filling dominates. As a result c now reaches a lower limit c ≈ -0.5 (depending slightly on solvency). This limit follows immediately from the condition of a fully occupied train layer. Comparison with numerical SCF calculations corroborates that our analytical result is a good approximation.We suggest some simple methods to determine the interaction parameter (either c or Δχ s) from experiments. The relation Δχ s(c) provides a quantitative connection between continuum and lattice theories, and enables the use of analytical continuum results to describe the adsorption (and stretching) of lattice chains of any chain length. For example, a fully analytical treatment of mechanical desorption of a polymer chain (including the temperature dependence and the phase transitions) is now feasible. © 2012 American Institute of Physics.

Skvortsov A.M.,Chemical Pharmaceutical Academy | Klushin L.I.,American University of Beirut | Fleer G.J.,Wageningen University | Leermakers F.A.M.,Wageningen University
Journal of Chemical Physics | Year: 2010

We discuss a unique system that allows exact analytical investigation of first- and second-order transitions with finite-size effects: mechanical desorption of an ideal lattice polymer chain grafted with one end to a solid substrate with a pulling force applied to the other end. We exploit the analogy with a continuum model and use accurate mapping between the parameters in continuum and lattice descriptions, which leads to a fully analytical partition function as a function of chain length, temperature (or adsorption strength), and pulling force. The adsorption-desorption phase diagram, which gives the critical force as a function of temperature, is nonmonotonic and gives rise to re-entrance. We analyze the chain length dependence of several chain properties (bound fraction, chain extension, and heat capacity) for different cross sections of the phase diagram. Close to the transition a single parameter (the product of the chain length N and the deviation from the transition point) describes all thermodynamic properties. We discuss finite-size effects at the second-order transition (adsorption without force) and at the first-order transition (mechanical desorption). The first-order transition has some unusual features: The heat capacity in the transition region increases anomalously with temperature as a power law, metastable states are completely absent, and instead of a bimodal distribution there is a flat region that becomes more pronounced with increasing chain length. The reason for this anomaly is the absence of an excess surface energy for the boundary between adsorbed and stretched coexisting phases (this boundary is one segment only): The two states strongly fluctuate in the transition point. The relation between mechanical desorption and mechanical unzipping of DNA is discussed. © 2010 American Institute of Physics.

Klushin L.I.,American University of Beirut | Skvortsov A.M.,Chemical Pharmaceutical Academy
Journal of Physics A: Mathematical and Theoretical | Year: 2011

Phase transitions were recognized among the most fascinating phenomena in physics. Exactly solved models are especially important in the theory of phase transitions. A number of exactly solved models of phase transitions in a single polymer chain are discussed in this review. These are three models demonstrating the second order phase transitions with some unusual features: two-dimensional model of β-structure formation, the model of coilglobule transition and adsorption of a polymer chain grafted on the solid surface. We also discuss models with first order phase transitions in a single macromolecule which admit not only exact analytical solutions for the partition function with explicit finite-size effects but also the non-equilibrium free energy as a function of the order parameter (Landau function) in closed analytical form. One of them is a model of mechanical desorption of a macromolecule, which demonstrates an unusual first order phase transition with phase coexistence within a single chain. Features of first and second order transitions become mixed here due to phase coexistence which is not accompanied by additional interfacial free energy. Apart from that, there exist several single-chain models belonging to the same class (adsorption of a polymer chain tethered near the solid surface or liquidliquid interface, and escape transition upon compressing a polymer between small pistons) that represent examples of a highly unconventional first order phase transition with several inter-related unusual features: no simultaneous phase coexistence, and hence no phase boundary, non-concave thermodynamic potential and non-equivalence of conjugate ensembles. An analysis of complex zeros of partition functions upon approaching the thermodynamic limit is presented for models with and without phase coexistence. © 2011 IOP Publishing Ltd.

Klushin L.,American University of Beirut | Milchev A.,Bulgarian Academy of Science | Skvortsov A.,Chemical Pharmaceutical Academy
ACS Macro Letters | Year: 2013

On the basis of theoretical considerations and computer experiment, we suggest a new technique for separation of polymer molecules. The method is based on filling an array of nanochannels with macromolecules whereby the subsequent ejection time depends strongly on small differences in the end-to-end distances of elongated configurations inside the nanotubes. In contrast to conventional methods for chromatographic separation, the efficiency of the proposed method increases with growing molecular length of the chains. The method appears promising also for the separation of ring from linear polymer chains. © 2013 American Chemical Society.

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