Weak violation of universality for Polyelectrolyte Chains: Variational Theory and Simulations

A variational approach is considered to calculate the free energy and the conformational properties of a polyelectrolyte chain in $d$ dimensions. We consider in detail the case of pure Coulombic interactions between the monomers, when screening is not present, in order to compute the end-to-end distance and the asymptotic properties of the chain as a function of the polymer chain length $N$. We find $R \simeq N^{\nu}(\log N)^{\gamma}$ where $\nu = \frac{3}{\lambda+2}$ and $\lambda$ is the exponent which characterize the long-range interaction $U \propto 1/r^{\lambda}$. The exponent $\gamma$ is shown to be non-universal, depending on the strength of the Coulomb interaction. We check our findings, by a direct numerical minimization of the variational energy for chains of increasing size $2^4<N<2^{15}$. The electrostatic blob picture, expected for small enough values of the interaction strength, is quantitatively described by the variational approach. We perform a Monte Carlo simulation for chains of length $2^4<N<2^{10}$. The non universal behavior of the exponent $\gamma$ previously derived within the variational method, is also confirmed by the simulation results. Non-universal behavior is found for a polyelectrolyte chain in $d=3$ dimension. Particular attention is devoted to the homopolymer chain problem, when short range contact interactions are present.Comment: to appear in European Phys. Journal E (soft matter

Dynamics of polymeric manifolds in melts: Hartree approximation

The Martin-Siggia-Rose functional technique and the self-consistent Hartree approximation is applied to the dynamics of a D-dimensional manifold in a melt of similar manifolds.The generalized Rouse equation is derived and its static and dynamic properties are studied. The static upper critical dimension discriminate between Gaussian and non-Gaussian regimes, whereas its dynamic counterpart discriminates between Rouse- and renormalized-Rouse behavior. The dynamic exponents are calculated explicitly. The special case of linear chains shows agreement with MD- and MC-simulations.Comment: 4 pages,1 figures, accepted by EPJB as a Rapid Not

Dynamics of a polymer test chain in a glass forming matrix: The Hartree Approximation

In this paper the Martin-Siggia-Rose formalism is used to derive a generalized Rouse equation for a test chain in a matrix which can undergo the glass transition. It is shown that the surrounding matrix renormalizes the static properties of the test chain. Furthermore the freezing of the different Rouse modes is investigated. This yields freezing temperatures which depend from the Rouse mode index.Comment: to be published in Journal de Physique I

Detachment of semiflexible polymer chains from a substrate - a Molecular Dynamics investigation

Using Molecular Dynamics simulations, we study the force-induced detachment of a coarse-grained model polymer chain from an adhesive substrate. One of the chain ends is thereby pulled at constant speed off the attractive substrate and the resulting saw-tooth profile of the measured mean force vs height $D$ of the end-segment over the plane is analyzed for a broad variety of parameters. It is shown that the observed characteristic oscillations in the $< f >$-$D$ profile depend on the bending and not on the torsional stiffness of the detached chains. Allowing for the presence of hydrodynamic interactions (HI) in a setup with explicit solvent and DPD-thermostat, rather than the case of Langevin thermostat, one finds that HI have little effect on the -$D$ profile. Also the change of substrate affinity with respect to the solvent from solvophilic to solvophobic is found to play negligible role in the desorption process. In contrast, a changing ratio $\epsilon_s^A / \epsilon_s^B$ of the binding energies of $A$- and $B$-segments in the detachment of an $AB$-copolymer from adhesive surface strongly changes the $$-$D$ profile whereby the $B$-spikes vanish when $\epsilon_s^A / \epsilon_s^B < 0.15$. Eventually, performing an atomistic simulation of a (bio)-polymer {\it polyglycine}, we demonstrate that the simulation results, derived from our coarse-grained model, comply favorably with those from the all-atom simulation.Comment: Latex, 12 pages, 8 figures, to appear in JC

The Hartree approximation in dynamics of polymeric manifolds in the melt

The Martin-Siggia-Rose (MSR) functional integral technique is applied to the dynamics of a D - dimensional manifold in a melt of similar manifolds. The integration over the collective variables of the melt can be simply implemented in the framework of the dynamical random phase approximation (RPA). The resulting effective action functional of the test manifold is treated by making use of the selfconsistent Hartree approximation. As an outcome the generalized Rouse equation (GRE) of the test manifold is derived and its static and dynamic properties are studied. It was found that the static upper critical dimension, $d_{\rm uc}=2D/(2-D)$, discriminates between Gaussian (or screened) and non-Gaussian regimes, whereas its dynamical counterpart, ${\tilde d}_{uc}=2d_{\rm uc}$, distinguishes between the simple Rouse and the renormalized Rouse behavior. We have argued that the Rouse mode correlation function has a stretched exponential form. The subdiffusional exponents for this regime are calculated explicitly. The special case of linear chains, D=1, shows good agreement with MD- and MC-simulations.Comment: 35 pages,3 figures, accepted by J.Chem.Phy

Polymer chain scission at constant tension - an example of force-induced collective behaviour

The breakage of a polymer chain of segments, coupled by anharmonic bonds with applied constant external tensile force is studied by means of Molecular Dynamics simulation. We show that the mean life time of the chain becomes progressively independent of the number of bonds as the pulling force grows. The latter affects also the rupture rates of individual bonds along the polymer backbone manifesting the essential role of inertial effects in the fragmentation process. The role of local defects, temperature and friction in the scission kinetics is also examined.Comment: 6 pages, 7 page

Field - Driven Translocation of Regular Block Copolymers through a Selective Liquid - Liquid Interface

We propose a simple scaling theory describing the variation of the mean first passage time (MFPT) $\tau(N,M)$ of a regular block copolymer of chain length $N$ and block size $M$ which is dragged through a selective liquid-liquid interface by an external field $B$. The theory predicts a non-Arrhenian $\tau$ vs. $B$ relationship which depends strongly on the size of the blocks, $M$, and rather weakly on the total polymer length, $N$. The overall behavior is strongly influenced by the degree of selectivity between the two solvents $\chi$. The variation of $\tau(N,M)$ with $N$ and $M$ in the regimes of weak and strong selectivity of the interface is also studied by means of computer simulations using a dynamic Monte Carlo coarse-grained model. Good qualitative agreement with theoretical predictions is found. The MFPT distribution is found to be well described by a $\Gamma$ - distribution. Transition dynamics of ring- and telechelic polymers is also examined and compared to that of the linear chains. The strong sensitivity of the ``capture'' time $\tau(N,M)$ with respect to block length $M$ suggests a possible application as a new type of chromatography designed to separate and purify complex mixtures with different block sizes of the individual macromolecules.Comment: 20 pages, 10 figure

Pulling an adsorbed polymer chain off a solid surface

The thermally assisted detachment of a self-avoiding polymer chain from an adhesive surface by an external force applied to one of the chain ends is investigated. We perform our study in the "fixed height" statistical ensemble where one measures the fluctuating force, exerted by the chain on the last monomer when a chain end is kept fixed at height $h$ over the solid plane at different adsorption strength $\epsilon$. The phase diagram in the $h - \epsilon$ plane is calculated both analytically and by Monte Carlo simulations. We demonstrate that in the vicinity of the polymer desorption transition a number of properties like fluctuations and probability distribution of various quantities behave differently, if $h$ rather than $f$ is used as an independent control parameter.Comment: 17 pages, 9 picture

Thermal Breakage and Self-Healing of a Polymer Chain under Tensile Stress

We consider the thermal breakage of a tethered polymer chain of discrete segments coupled by Morse potentials under constant tensile stress. The chain dynamics at the onset of fracture is studied analytically by Kramers-Langer multidimensional theory and by extensive Molecular Dynamics simulations in 1D- and 3D-space. Comparison with simulation data in one- and three dimensions demonstrates that the Kramers-Langer theory provides good qualitative description of the process of bond-scission as caused by a {\em collective} unstable mode. We derive distributions of the probability for scission over the successive bonds along the chain which reveal the influence of chain ends on rupture in good agreement with theory. The breakage time distribution of an individual bond is found to follow an exponential law as predicted by theory. Special attention is focused on the recombination (self-healing) of broken bonds. Theoretically derived expressions for the recombination time and distance distributions comply with MD observations and indicate that the energy barrier position crossing is not a good criterion for true rupture. It is shown that the fraction of self-healing bonds increases with rising temperature and friction.Comment: 25 pages, 13 picture