Nam-Kyung Lee

Collapse dynamics of a polymer chain: Theory and simulation

We present a scaling theory describing the collapse of a homopolymer chain in poor solvent. At time t after the beginning of the collapse, the original Gaussian chain of length N is streamlined to form N/g segments of length R(t), each containing g ~ t monomers. These segments are statistical quantities representing cylinders of length R ~ t1/2 and diameter but structured out of stretched arrays of spherical globules. This prescription incorporates the capillary instability. We compare the time-dependent structure factor derived for our theory with that obtained from ultra-large-scale molecular-dynamics simulation with explicit solvent. This is the first time such a detailed comparison of theoretical and simulation predictions of collapsing chain structure has been attempted. The favorable agreement between the theoretical and computed structure factors supports the picture of the coarse-graining process during polymer collapse.

Dynamics of collapse of flexible polyampholytes

We provide a theory for the dynamics of collapse of flexible polyampholytes (PAs) using Langevin equation. Metastable pearl-necklace structures form in a time scale proportional to N4/5 (N is the number of monomers). In the late stage of collapse the pearls merge with the largest one growing at the expense of smaller ones (Lifshitz–Slyozov mechanism). The time scale for this process is τcoll∼N. Counterion-mediated collapse of strongly charged polyelectrolytes (PEs) follow a similar route to the globular state. Simulations support the proposed collapse mechanism for PAs and PEs.

Pulling-Speed-Dependent Force-Extension Profiles for Semiflexible Chains

We present theory and simulations to describe nonequilibrium stretching of semiflexible chains that serve as models of DNA molecules. Using a self-consistent dynamical variational approach, we calculate the force-extension curves for worm-like chains as a function of the pulling speed, v(0). Due to nonequilibrium effects the stretching force, which increases with v(0), shows nonmonotonic variations as the persistence length increases. To complement the theoretical calculations we also present Langevin simulation results for extensible worm-like chain models for the dynamics of stretching. The theoretical force-extension predictions compare well with the simulation results. The simulations show that, at high enough pulling speeds, the propagation of tension along the chain conformations transverse to the applied force occurs by the Brochard-Wyarts stem-flower mechanism. The predicted nonequilibrium effects can only be observed in double-stranded DNA at large ( approximately 100 microm/s) pulling speeds.

Modeling collective behavior of molecules in nanoscale direct deposition processes

We present a theoretical model describing the collective behavior of molecules in nanoscale direct deposition processes such as dip-pen nanolithography. We show that strong intermolecular interactions combined with nonuniform substrate-molecule interactions can produce various shapes of molecular patterns including fractal-like structures. Computer simulations reveal circular and starlike patterns at low and intermediate densities of preferentially attractive surface sites, respectively. At large density of such surface sites, the molecules form a two-dimensional invasion percolation cluster. Previous experimental results showing anisotropic patterns of various chemical and biological molecules correspond to the starlike regime [P. Manandhar et al., Phys. Rev. Lett. 90, 115505 (2003); J.-H. Lim and C. A. Mirkin, Adv. Mater. (Weinheim, Ger.) 14, 1474 (2002); D. L. Wilson et al., Proc. Natl. Acad. Sci. U.S.A. 98, 13660 (2001); M. Su et al., Appl. Phys. Lett. 84, 4200 (2004); R. McKendry et al., Nano Lett. 2, 713 (2002); H. Zhou et al., Appl. Surf. Sci. 236, 18 (2004); G. Agarwal et al., J. Am. Chem. Soc. 125, 580 (2003)].

Polyelectrolyte chains in poor solvent. A variational description of necklace formation

Abstract:We study the properties of polyelectrolyte chains under different solvent conditions, using a variational technique. The free energy and the conformational properties of a polyelectrolyte chain are studied by minimizing the free energy FN, depending on N(N - 1)/2 trial probabilities that characterize the conformation of the chain. The Gaussian approximation is considered for a ring of length 24 < N < 28 and for an open chain of length 50 < N < 200 in poor- and theta-solvent conditions, including a Coulomb repulsion between the monomers. In theta-solvent conditions the blob size is measured and found in agreement with scaling theory, including charge depletion effects, expected for the case of an open chain. In poor-solvent conditions, a globule instability, driven by electrostatic repulsion, is observed. We notice also inhomogeneous behavior of the monomer-monomer correlation function, reminiscence of necklace formation in poor-solvent polyelectrolyte solutions. A global phase diagram in terms of solvent quality and inverse Bjerrum length is presented.

Non-ideality of polymer melts confined to nanotubes

Corrections to chain ideality have been demonstrated recently for polymer melts in the bulk and in ultrathin films. It has been shown that the effect of incomplete screening is stronger in the latter. We show here that the deviation from ideality is even stronger in thin capillaries. Describing the crossover from the free bulk to the confined regime as the radius of the capillary decreases below the typical coil radius we make connection to the so far disconnected work by Brochard and de Gennes (J. Phys. (Paris), Lett., 40 (1979) 399) predicting chain segregation in very thin capillaries. Due to the generalized Porod scattering of the segregated chains, the Kratky representation of the intrachain structure factor reveals a plateau for all regimes although the chains become swollen with increasing confinement.

Semiflexible Chains at Surfaces: Worm-Like Chains and beyond

We give an extended review of recent numerical and analytical studies on semiflexible chains near surfaces undertaken at Institut Charles Sadron (sometimes in collaboration) with a focus on static properties. The statistical physics of thin confined layers, strict two-dimensional (2D) layers and adsorption layers (both at equilibrium with the dilute bath and from irreversible chemisorption) are discussed for the well-known worm-like-chain (WLC) model. There is mounting evidence that biofilaments (except stable d-DNA) are not fully described by the WLC model. A number of augmented models, like the (super) helical WLC model, the polymorphic model of microtubules (MT) and a model with (strongly) nonlinear flexural elasticity are presented, and some aspects of their surface behavior are analyzed. In many cases, we use approaches different from those in our previous work, give additional results and try to adopt a more general point of view with the hope to shed some light on this complex field.

Biofilaments as annealed semi-flexible copolymers

In many in vivo or in vitro situations, biofilaments manifest some annealed heterogeneity and should be considered as annealed random copolymers. The building blocks of the filaments differ from each other, for example, by the internal structure of the monomer, by the presence of some adsorbed species or by the curvature. Based on the copolymer concept, we embed the description of these systems in a common formalism. We demonstrate how the annealed heterogeneous nature of the filament is reflected by statistical correlations like the tangent-tangent correlation function or the cyclization probability. Our results show that annealed filaments adapt cooperatively to external constraints. This could contribute to explain anomalous elasticity manifested by biofilaments.

Stretching DNA: Role of electrostatic interactions

Abstract:The effect of electrostatic interactions on the stretching of DNA is investigated using a simple worm like chain model. In the limit of small force there are large conformational fluctuations which are treated using a self-consistent variational approach. For small values of the external force f, we find the extension scales as where is the Debye screening length. In the limit of large force the electrostatic effects can be accounted for within the semiflexible chain model of DNA by assuming that only small excursions from rod-like conformations are possible. In this regime the extension approaches the contour length as where f is the magnitude of the external force. The theory is used to analyze experiments that have measured the extension of double-stranded DNA subject to tension at various salt concentrations. The theory reproduces nearly quantitatively the elastic response of DNA at small and large values of f and for all concentration of the monovalent counterions. The limitations of the theory are also pointed out.

Reptation of a semiflexible polymer through porous media

We study the motion of a single stiff semiflexible filament of length S through an array of topological obstacles. By means of scaling arguments and two-dimensional computer simulations, we show that the stiff chain kinetics follows the reptation picture, albeit with kinetic exponents (for the central monomer) different from those for flexible chain reptation. At early times when topological constraints are irrelevant, the chain kinetics is the anisotropic dynamics of a free filament. After the entanglement time tau(e) transverse modes are equilibrated under the topological constraints, but the chain is not yet correlated over its whole length. During the relaxation of longitudinal modes, both the longitudinal fluctuation of the central monomer and the longitudinal correlation length grow as approximately sqrt t. After time tau(r) approximately S(2) chain ends are correlated, the chain then diffuses globally along the tube and tube renewal takes place. In the reptation regime, the longitudinal fluctuation of the central monomer grows like approximately t(1). The opening of the intermediate approximately sqrt t regime, absent for a free filament, is a signature of the reptation process. Although the underlying physics is quite different, the intermediate regime is reminiscent of the internal Rouse mode relaxation found for reptating flexible chains. In most cases asymptotic power laws from scaling could be complemented by prefactors calculated analytically. Our results are supported by two-dimensional Langevin simulations with fixed obstacles via evaluation of the mean squared displacement of the central monomer. The scaling theory can be extended to long semiflexible polymers adopting random-walk equilibrium configurations and should also apply in three dimensions for porous media with pore diameter smaller than the persistence length of the filament.