arXiv subjects

A. Johner

Publications and source records attributed to A. Johner.

At least 19 recordsLinked to original sources

arXiv2025

Conformational properties of strictly two-dimensional equilibrium polymers

Two-dimensional monodisperse linear polymer chains are known to adopt for sufficiently large chain lengths $N$ and surface fractions $\phi$ compact configurations with fractal perimeters. We show here by means of Monte Carlo simulations of reversibly connected hard disks (without branching, ring formation and chain intersection) that polydisperse self-assembled equilibrium polymers with a finite scission energy $E$ are characterized by the same universal exponents as their monodisperse peers. Consistently with a Flory-Huggins mean-field approximation, the polydispersity is characterized by a Schulz-Zimm distribution with a susceptibility exponent $\gamma=19/16$ for all not dilute systems and the average chain length $ \propto \exp(\delta E) \phi^{\alpha}$ thus increases with an exponent $\delta = 16/35$. Moreover, it is shown that $\alpha=3/5$ for semidilute solutions and $\alpha \approx 1$ for larger densities. The intermolecular form factor $F(q)$ reveals for sufficiently large $ $ a generalized Porod scattering with $F(q) \propto 1/q^{11/4}$ for intermediate wavenumbers $q$ consistently with a fractal perimeter dimension $d_s=5/4$.

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arXiv2022

Marginally compact hyperbranched polymer trees

Assuming Gaussian chain statistics along the chain contour, we generate by means of a proper fractal generator hyperbranched polymer trees which are marginally compact. Static and dynamical properties, such as the radial intrachain pair density distribution or the shear-stress relaxation modulus, are investigated theoretically and by means of computer simulations. We emphasize that albeit the self-contact density diverges logarithmically with the total mass $N$, this effect becomes rapidly irrelevant with increasing spacer length $S$. In addition to this it is seen that the standard Rouse analysis must necessarily become inappropriate for compact objects for which the relaxation time $τ_p$ of mode $p$ must scale as $τ_p \sim (N/p)^{5/3}$ rather than the usual square power law for linear chains.

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arXiv2011

Interchain monomer contact probability in two-dimensional polymer solutions

Using molecular dynamics simulation of a standard bead-spring model we investigate the density crossover scaling of strictly two-dimensional self-avoiding polymer chains focusing on properties related to the contact exponent set by the intrachain subchain size distribution. Irrespective of the density sufficiently long chains are found to consist of compact packings of blobs of fractal perimeter dimension dp = 5/4.

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arXiv2011

Scale-free static and dynamical correlations in melts of monodisperse and Flory-distributed homopolymers: A review of recent bond-fluctuation model studies

It has been assumed until very recently that all long-range correlations are screened in three-dimensional melts of linear homopolymers on distances beyond the correlation length $ξ$ characterizing the decay of the density fluctuations. Summarizing simulation results obtained by means of a variant of the bond-fluctuation model with finite monomer excluded volume interactions and topology violating local and global Monte Carlo moves, we show that due to an interplay of the chain connectivity and the incompressibility constraint, both static and dynamical correlations arise on distances $r \gg ξ$. These correlations are scale-free and, surprisingly, do not depend explicitly on the compressibility of the solution. Both monodisperse and (essentially) Flory-distributed equilibrium polymers are considered.

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arXiv2010

Static Properties of Polymer Melts in Two Dimensions

Self-avoiding polymers in strictly two-dimensional ($d=2$) melts are investigated by means of molecular dynamics simulation of a standard bead-spring model with chain lengths ranging up to N=2048. % The chains adopt compact configurations of typical size $R(N) \sim N^ν$ with $ν=1/d$. % The precise measurement of various distributions of internal chain distances allows a direct test of the contact exponents $Θ_0=3/8$, $Θ_1=1/2$ and $Θ_2=3/4$ predicted by Duplantier. % Due to the segregation of the chains the ratio of end-to-end distance $\Rend(N)$ and gyration radius $\Rgyr(N)$ becomes $\Rend^2(N)/\Rgyr^2(N) \approx 5.3 < 6$ for $N \gg 100$ and the chains are more spherical than Gaussian phantom chains. % The second Legendre polynomial $P_2(s)$ of the bond vectors decays as $P_2(s) \sim 1/s^{1+νΘ_2}$ measuring thus the return probability of the chain after $s$ steps. % The irregular chain contours are shown to be characterized by a perimeter length $L(N) \sim R(N)^{\dc}$ of fractal line dimension $\dc = d-Θ_2 =5/4$. % % In agreement with the generalized Porod scattering of compact objects with fractal contour the Kratky representation of the intramolecular structure factor $F(q)$ reveals a strong non-monotonous behavior with $q^dF(q) \sim 1/(q R(N))^{Θ_2}$ in the intermediate regime of the wave vector $q$. This may allow to confirm the predicted contour fractality in a real experiment.

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arXiv2009

Non-extensivity of the chemical potential of polymer melts

Following Flory's ideality hypothesis the chemical potential of a test chain of length $n$ immersed into a dense solution of chemically identical polymers of length distribution P(N) is extensive in $n$. We argue that an additional contribution $δμ_c(n) \sim +1/ρ\sqrt{n}$ arises ($ρ$ being the monomer density) for all $¶(N)$ if $n \ll $ which can be traced back to the overall incompressibility of the solution leading to a long-range repulsion between monomers. Focusing on Flory distributed melts we obtain $δμ_c(n) \approx (1- 2 n/ ) / ρ\sqrt{n}$ for $n \ll ^2$, hence, $δμ_c(n) \approx - 1/ρ\sqrt{n}$ if $n$ is similar to the typical length of the bath $ $. Similar results are obtained for monodisperse solutions. Our perturbation calculations are checked numerically by analyzing the annealed length distribution P(N) of linear equilibrium polymers generated by Monte Carlo simulation of the bond-fluctuation model. As predicted we find, e.g., the non-exponentiality parameter $K_p \equiv 1 - /p! ^p$ to decay as $K_p \approx 1 / \sqrt{ }$ for all moments $p$ of the distribution.

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arXiv2009

Distance dependence of angular correlations in dense polymer solutions

Angular correlations in dense solutions and melts of flexible polymer chains are investigated with respect to the distance $r$ between the bonds by comparing quantitative predictions of perturbation calculations with numerical data obtained by Monte Carlo simulation of the bond-fluctuation model. We consider both monodisperse systems and grand-canonical (Flory-distributed) equilibrium polymers. Density effects are discussed as well as finite chain length corrections. The intrachain bond-bond correlation function $P(r)$ is shown to decay as $P(r) \sim 1/r^3$ for $ξ\ll r \ll \r^*$ with $ξ$ being the screening length of the density fluctuations and $r^* \sim N^{1/3}$ a novel length scale increasing slowly with (mean) chain length $N$.

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arXiv2009

A finite excluded volume bond-fluctuation model: Static properties of dense polymer melts revisited

The classical bond-fluctuation model (BFM) is an efficient lattice Monte Carlo algorithm for coarse-grained polymer chains where each monomer occupies exclusively a certain number of lattice sites. In this paper we propose a generalization of the BFM where we relax this constraint and allow the overlap of monomers subject to a finite energy penalty $\overlap$. This is done to vary systematically the dimensionless compressibility $g$ of the solution in order to investigate the influence of density fluctuations in dense polymer melts on various s tatic properties at constant overall monomer density. The compressibility is obtained directly from the low-wavevector limit of the static structure fa ctor. We consider, e.g., the intrachain bond-bond correlation function, $P(s)$, of two bonds separated by $s$ monomers along the chain. It is shown that the excluded volume interactions are never fully screened for very long chains. If distances smaller than the thermal blob size are probed ($s \ll g$) the chains are swollen acc ording to the classical Fixman expansion where, e.g., $P(s) \sim g^{-1}s^{-1/2}$. More importantly, the polymers behave on larger distances ($s \gg g$) like swollen chains of incompressible blobs with $P(s) \si m g^0s^{-3/2}$.

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arXiv2009

Perimeter Length and Form Factor of Two-Dimensional Polymer Melts

Self-avoiding polymers in two-dimensional ($d=2$) melts are known to adopt compact configurations of typical size $R(N) \sim N^{1/d}$ with $N$ being the chain length. Using molecular dynamics simulations we show that the irregular shapes of these chains are characterized by a perimeter length $L(N) \sim R(N)^{\dpm}$ of fractal dimension $\dpm = d-Θ_2 =5/4$ with $Θ_2=3/4$ being a well-known contact exponent. Due to the self-similar structure of the chains, compactness and perimeter fractality repeat for subchains of all arc-lengths $s$ down to a few monomers. The Kratky representation of the intramolecular form factor $F(q)$ reveals a strong non-monotonous behavior with $q^2F(q) \sim 1/(qN^{1/d})^{Θ_2}$ in the intermediate regime of the wavevector $q$. Measuring the scattering of labeled subchains %($s F(q) \sim L(s)$) the form factor may allow to test our predictions in real experiments.

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arXiv2007

Static Rouse Modes and Related Quantities: Corrections to Chain Ideality in Polymer Melts

Following the Flory ideality hypothesis intrachain and interchain excluded volume interactions are supposed to compensate each other in dense polymer systems. Multi-chain effects should thus be neglected and polymer conformations may be understood from simple phantom chain models. Here we provide evidence against this phantom chain, mean-field picture. We analyze numerically and theoretically the static correlation function of the Rouse modes. Our numerical results are obtained from computer simulations of two coarse-grained polymer models for which the strength of the monomer repulsion can be varied, from full excluded volume (`hard monomers') to no excluded volume (`phantom chains'). For nonvanishing excluded volume we find the simulated correlation function of the Rouse modes to deviate markedly from the predictions of phantom chain models. This demonstrates that there are nonnegligible correlations along the chains in a melt. These correlations can be taken into account by perturbation theory. Our simulation results are in good agreement with these new theoretical predictions.

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arXiv2007

Intramolecular long-range correlations in polymer melts: The segmental size distribution and its moments

Presenting theoretical arguments and numerical results we demonstrate long-range intrachain correlations in concentrated solutions and melts of long flexible polymers which cause a systematic swelling of short chain segments. They can be traced back to the incompressibility of the melt leading to an effective repulsion $u(s) \approx s/ρR^3(s) \approx ce/\sqrt{s}$ when connecting two segments together where $s$ denotes the curvilinear length of a segment, $R(s)$ its typical size, $ce \approx 1/ρbe^3$ the ``swelling coefficient", $be$ the effective bond length and $ρ$ the monomer density. The relative deviation of the segmental size distribution from the ideal Gaussian chain behavior is found to be proportional to $u(s)$. The analysis of different moments of this distribution allows for a precise determination of the effective bond length $be$ and the swelling coefficient $ce$ of asymptotically long chains. At striking variance to the short-range decay suggested by Flory's ideality hypothesis the bond-bond correlation function of two bonds separated by $s$ monomers along the chain is found to decay algebraically as $1/s^{3/2}$. Effects of finite chain length are considered briefly.

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arXiv2007

Intramolecular Form Factor in Dense Polymer Systems: Systematic Deviations from the Debye formula

We discuss theoretically and numerically the intramolecular form factor $F(q)$ in dense polymer systems. Following Flory's ideality hypothesis, chains in the melt adopt Gaussian configurations and their form factor is supposed to be given by Debye's formula. At striking variance to this, we obtain noticeable (up to 20%) non-monotonic deviations which can be traced back to the incompressibility of dense polymer solutions beyond a local scale. The Kratky plot ($q^2F(q)$ {\it vs.} wavevector $q$) does not exhibit the plateau expected for Gaussian chains in the intermediate $q$-range. One rather finds a significant decrease according to the correction $δ(F^{-1}(q)) = q^3/32ρ$ that only depends on the concentration $ρ$ of the solution, but neither on the persistence length or the interaction strength.

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arXiv2005

Single chain structure in thin polymer films: Corrections to Flory's and Silberberg's hypotheses

Conformational properties of polymer melts confined between two hard structureless walls are investigated by Monte Carlo simulation of the bond-fluctuation model. Parallel and perpendicular components of chain extension, bond-bond correlation function and structure factor are computed and compared with recent theoretical approaches attempting to go beyond Flory's and Silberberg's hypotheses. We demonstrate that for ultrathin films where the thickness, $H$, is smaller than the excluded volume screening length (blob size), $ξ$, the chain size parallel to the walls diverges logarithmically, $R^2/2N \approx b^2 + c \log(N)$ with $c \sim 1/H$. The corresponding bond-bond correlation function decreases like a power law, $C(s) = d/s^ω$ with $s$ being the curvilinear distance between bonds and $ω=1$. % Upon increasing the film thickness, $H$, we find -- in contrast to Flory's hypothesis -- the bulk exponent $ω=3/2$ and, more importantly, an {\em decreasing} $d(H)$ that gives direct evidence for an {\em enhanced} self-interaction of chain segments reflected at the walls. Systematic deviations from the Kratky plateau as a function of $H$ are found for the single chain form factor parallel to the walls in agreement with the {\em non-monotonous} behaviour predicted by theory. This structure in the Kratky plateau might give rise to an erroneous estimation of the chain extension from scattering experiments. For large $H$ the deviations are linear with the wave vector, $q$, but are very weak. In contrast, for ultrathin films, $H<ξ$, very strong corrections are found (albeit logarithmic in $q$) suggesting a possible experimental verification of our results.

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arXiv2004

Long Range Bond-Bond Correlations in Dense Polymer Solutions

The scaling of the bond-bond correlation function $C(s)$ along linear polymer chains is investigated with respect to the curvilinear distance, $s$, along the flexible chain and the monomer density, $ρ$, via Monte Carlo and molecular dynamics simulations. % Surprisingly, the correlations in dense three dimensional solutions are found to decay with a power law $C(s) \sim s^{-ω}$ with $ω=3/2$ and the exponential behavior commonly assumed is clearly ruled out for long chains. % In semidilute solutions, the density dependent scaling of $C(s) \approx g^{-ω_0} (s/g)^{-ω}$ with $ω_0=2-2ν=0.824$ ($ν=0.588$ being Flory's exponent) is set by the number of monomers $g(ρ)$ contained in an excluded volume blob of size $ξ$. % Our computational findings compare well with simple scaling arguments and perturbation calculation. The power-law behavior is due to self-interactions of chains on distances $s \gg g$ caused by the connectivity of chains and the incompressibility of the melt. %

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arXiv2000

Slow plasmon modes in polymeric salt solutions

The dynamics of polymeric salt solutions are presented. The salt consists of chains $\rm A$ and $\rm B$, which are chemically different and interact with a Flory-interaction parameter $χ$, the $\rm A$ chain ends carry a positive charge whereas the $\rm B$ chain ends are modified by negative charges. The static structure factor shows a peak corresponding to a micro phase separation. At low momentum transfer, the interdiffusion mode is driven by electrostatics and is of the plasmon-type, but with an unusually low frequency, easily accessible by experiments. This is due to the polymer connectivity that introduces high friction and amplifies the charge scattering thus allowing for low charge densities. The interdiffusion mode shows a minimum (critical slowing down) at finite $k$ when the interaction parameter increases we find then a low $k$ frequency quasi-plateau.

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arXiv2000

Polyelectrolyte gels in poor solvent: Equilibrium and non equilibrium elasticity

We study theoretically using scaling arguments the behavior of polyelectrolyte gels in poor solvents. Following the classical picture of Katchalsky, our approach is based on single chain elasticity but it accounts for the recently proposed pearl-necklace structure of polyelectrolytes in poor solvents. The elasticity both of gels at swelling equilibrium and of partially swollen, non equilibrium, gels is studied when parameters such as the ionic strength or the fraction of charged monomers are varied. Our theory could be useful to interpret recent experiments performed in Strasbourg that show that if identical gel samples are swollen to the same extent at different pH the sample with the highest charge has the lowest shear modulus.

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arXiv2000

Stretching necklaces

Polyelectrolytes in poor solvents show a necklace structure where collapsed polymer pearls are linked to stretched strings. In the present paper the elasticity of such chains is studied in detail. Different deformation regimes are addressed. The first is the continuous regime, where many pearls are present. A continuous force extension relation ship is calculated. The main contribution comes from the tension balance and the electrostatic repulsion of consecutive pearls. The main correction term stems from the finite size of the pearls, which monitors their surface energy. For a finite amount of pearls discontinuous stretching is predicted. Finally counterion effects are discussed qualitatively.

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arXiv1998

Compression of finite size polymer brushes

We consider edge effects in grafted polymer layers under compression. For a semi-infinite brush, the penetration depth of edge effects $ξ\propto h_0(h_0/h)^{1/2}$ is larger than the natural height $h_0$ and the actual height $h$. For a brush of finite lateral size $S$ (width of a stripe or radius of a disk), the lateral extension $u_S$ of the border chains follows the scaling law $u_S = ξϕ(S/ξ)$. The scaling function $ϕ(x)$ is estimated within the framework of a local Flory theory for stripe-shaped grafting surfaces. For small $x$, $ϕ(x)$ decays as a power law in agreement with simple arguments. The effective line tension and the variation with compression height of the force applied on the brush are also calculated.

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