A. Johner

Long range bond-bond correlations in dense polymer solutions

The scaling of the bond-bond correlation function P1(s) along linear polymer chains is investigated with respect to the curvilinear distance s along the flexible chain and the monomer density rho via Monte Carlo and molecular dynamics simulations. Surprisingly, the correlations in dense three-dimensional solutions are found to decay with a power law P1(s) approximately s(-omega) with omega=3/2 and the exponential behavior commonly assumed is clearly ruled out for long chains. In semidilute solutions, the density dependent scaling of P1(s) approximately g(-omega(0))(s/g)(-omega) with omega(0)=2-2nu=0.824 (nu=0.588 being Florys exponent) is set by the number of monomers g(rho) in an excluded volume blob. Our computational findings compare well with simple scaling arguments and perturbation calculation. The power-law behavior is due to self-interactions of chains caused by the chain connectivity and the incompressibility of the melt.

Chain desorption from a semidilute polymer brush: A Monte Carlo simulation

We discuss the dynamic properties of a semidilute grafted polymer layer exposed to pure solvent. When the grafting energy of the head groups of the chains is finite, the chains desorb and are expelled from the layer. We combine Monte Carlo simulations using the bond fluctuation model to self‐consistent mean field calculations and a scaling analysis. Chain desorption can be seen as a two step process. For strongly grafted polymers the limiting step is the desorption of the head group. The chain is then expelled by the osmotic pressure gradient. A chain cut off the wall is expelled at a constant velocity of its center of mass. The velocity decreases as the inverse of the molecular weight and increases with the grafting density. In the early stages of the expulsion the tension of the monomers close to the wall relaxes and the chain retracts. The retraction is independent of the molecular weight. Our most important result is that the desorption of the head group is a local process with a characteristic time i...

Random and Alternating Polyampholytes

We discuss theoretically the influence of the distribution of the charged monomers on the conformational properties of polyampholyte chains using the random phase approximation. If the distribution is quenched with random positions of the positive and negative charges, the polyampholyte collapses and locally has the same structure as a salt solution. It can be described by the Debye-Huckel theory. If the charges are alternating, the collapsed chain is a dielectric medium that can be characterized by a finite negative virial coefficient. Alternating polyampholytes are more soluble than random polyampholytes. We also study intermediate distributions and the annealed problem where the charges are due to the dissociation of acidic and basic monomers.

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)∼Nν with ν=1/d. The precise measurement of various distributions of internal chain distances allows a direct test of the contact exponents Θ0=3/8, Θ1=1/2, and Θ2=3/4 predicted by Duplantier. Due to the segregation of the chains the ratio of end-to-end distance Re(N) and gyration radius Rg(N) becomes Re2(N)/Rg2(N)≈5.3<6 for N⪢100 and the chains are more spherical than Gaussian phantom chains. The second Legendre polynomial P2(s) of the bond vectors decays as P2(s)∼1/s1+νΘ2, thus measuring the return probability of the chain after s steps. The irregular chain contours are shown to be characterized by a perimeter length L(N)∼R(N)dp of fractal line dimension dp=d−Θ2=5/4. In agreement with the generalized Porod scattering of compact objects with fractal contou...

Diffusive growth of a polymer layer by in situ polymerization

We consider the growth of a polymer layer on a flat surface in a good solvent by in situ polymerization. This is viewed as a modified form of diffusion-limited aggregation without branching. We predict theoretically the formation of a pseudo-brush with density (z) z−2/3 and characteristic height H t3. These results are found by combining a mean-field treatment of the diffusive growth (marginally valid in three dimensions) with a scaling theory (Flory exponent ν = 3/5) of the growing polymers. We confirm their validity by Monte Carlo simulations.

Melt of polymer rings: The decorated loop model

Melts of unconcatenated and unknotted polymer rings are a paradigm for soft matter ruled by topological interactions. We propose a description of a system of rings of length N as a collection of smaller polydisperse Gaussian loops, ranging from the entanglement length to the skeleton ring length , assembled in random trees. Individual rings in the melt are predicted to be marginally compact with a mean square radius of gyration . As a rule, simple power laws for asymptotically long rings come with sluggish crossovers. Experiments and computer simulations merely deal with crossover regimes typically extending to . The estimated crossover functions allow for a satisfactory fit of simulation data.

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.

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 epsilon. 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 static properties at constant overall monomer density. The compressibility is obtained directly from the low-wave vector limit of the static structure factor. 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<<g) the chains are swollen according to the classical Fixman expansion where, e.g., P(s) approximately g(-1)s(-1/2). More importantly, the polymers behave on larger distances (s>>g) like swollen chains of incompressible blobs with P(s) approximately g(0)s(-3/2).

End adsorption of polymer brushes

We study the adsorption of a polymer brush on a solid plate parallel to the plate where the chains are grafted in the limit where only the free-end monomers of the grafted chains adsorb. In the vicinity of the adsorbing plate, there exists a dead zone where no free chain ends are found; the monomer concentration is constant in this region and parabolic close to the grafting plate. In the absence of external force, the equilibrium distance between the two plates is smaller than the natural brush size. The fraction of chains forming bridges increases linearly with the adsorption energy at small adsorption energy and reaches one for a finite adsorption energy. The effect of an external force is also briefly discussed.

Interchain Monomer Contact Probability in Two-Dimensional Polymer Solutions

Using molecular dynamics simulations of a standard bead–spring model, we investigate the density crossover scaling of strictly two-dimensional (d = 2) self-avoiding polymer chains without chain cro...