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5 pages, 4 figures; International audience; 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 $\delta(F^{-1}(q)) = q^3/32\rho$ that only depends on the concentration $\rho$ of the solution, but neither on the persistence length or the interaction strength.

National audience; Dans cet article nous essayons de donner une brève introduction à la construction de modèles pour la simulation numérique en physique des polymères ; nous voulons illustrer cette modélisation par quelques exemples issus de notre propre recherche.

International audience; The role of short chain branches (SCBs) (C4H9) on the melt and crystalline properties of monodisperse polyethylene systems (C400H802) is investigated, using molecular dynamics simulations of a coarse-grained united-monomer model that represents a chemical monomer as one particle. A method is introduced, whereby SCBs are grown out of the linear backbone to minimize computational expense. Here, this concept is proven by introducing differing numbers (Nb = 0, 1, 2, 4, 10, and 20) of regularly spaced SCBs along the chain backbones and studying their influence on the melt and crystalline properties. By growing SCBs into the melt phase, it is demonstrated that they marginally perturb the original topology, justifying a relatively short equilibration time after growth. Upon crystallization, however, each system’s behavior differs considerably. Cooling and heating cycles are performed to study crystallization and melting at progressively slower rates. The crystalline morphology is observed to depend strongly on both cooling rate and number of branches along the linear backbone. In particular, the lamella thickness decreases systematically with both faster cooling and increasing SCB content. At the highest branch content, of one per 20 backbone carbons (Nb = 20), crystallization is almost entirely suppressed, whereas a small number of branches allows control over the average lamellar thickness. This observation, combined with a prudent method for equilibrating systems with SCBs, opens up opportunities to study more complex chain architectures and mimic industrial polyethylene morphologies.

For polymer chains, the torsional potential is an important intramolecular energy influencing chain flexibility and segmental dynamics. Through molecular dynamics simulations of an atomistic model for melts of cis– trans-1,4-polybutadiene (PBD), we explore the effect of the torsions on conformational properties (bond vector correlations and mean-square internal distances), fundamental thermodynamic quantities (density, compressibility, internal energy, and specific heat), and glass transition temperature Tg. This is achieved by systematically reducing the strength of the torsional potential, starting from the chemically realistic chain (CRC) model with the full potential toward the freely rotating chain (FRC) model without the torsional potential. For the equilibrium liquid, we find that the effect of the torsions on polymer conformations is very weak. Still weaker is the influence on the monomer density ρ and isothermal compressibility κ T of the polymer liquid, both of which can be considered as independent of the torsional potential. We show that a van der Waals-like model proposed by Long and Lequeux [Eur. Phys. J. E 4, 371 (2001)] allows us to describe very well the temperature ( T) dependence of ρ and κ T. We also find that our data obey the linear relation between [Formula: see text] and 1/ T (with the Boltzmann constant kB) that has recently been predicted and verified on the experiment by Mirigian and Schweizer [J. Chem. Phys. 140, 194507 (2014)]. For the equilibrium liquid, simulations result in a specific heat, at constant pressure and at constant volume, which increases on cooling. This T dependence is opposite to the one found experimentally for many polymer liquids, including PBD. We suggest that this difference between simulation and experiment may be attributed to quantum effects due to hydrogen atoms and backbone vibrations, which, by construction, are not included in the classical united-atom model employed here. Finally, we also determine Tg from the density–temperature curve monitored in a finite-rate cooling process. While the influence of the torsional potential on ρ( T) is vanishingly small in the equilibrium liquid, the effect of the torsions on Tg is large. We find that Tg decreases by about 150 K when going from the CRC to the FRC model.