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Register a new userAnomalous structure factor of dense star polymer solutions
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Authors
M. Watzlawek
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The core-core structure factor of dense star polymer solutions in a good solvent is shown theoretically to exhibit an unusual behaviour above the overlap concentration. Unlike usual liquids, these solutions display a structure factor whose first peak decreases by increasing density while the second peak grows. The scenario repeats itself with the subsequent peaks as the density is further enhanced. For low enough arm numbers $f$ ($f leq 32$), various different considerations lead to the conclusion that the system remains fluid at all concentrations.
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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 $xi ll r ll r^*$ with $xi$ being the screening length of the density fluctuations and $r^* sim N^{1/3}$ a novel length scale increasing slowly with (mean) chain length $N$.
The phase diagram of star polymer solutions in a good solvent is obtained over a wide range of densities and arm numbers by Monte Carlo simulations. The effective interaction between the stars is modeled by an ultrasoft pair potential which is logarithmic in the core-core distance. Among the stable phases are a fluid as well as body-centered cubic, face-centered cubic, body-centered orthogonal, and diamond crystals. In a limited range of arm numbers, reentrant melting and reentrant freezing transitions occur for increasing density.
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, $rho$, via Monte Carlo and molecular dynamics simulations. % Surprisingly, the correlations in dense three dimensional solutions are found to decay with a power law $C(s) sim s^{-omega}$ 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 $C(s) approx g^{-omega_0} (s/g)^{-omega}$ with $omega_0=2-2 u=0.824$ ($ u=0.588$ being Florys exponent) is set by the number of monomers $g(rho)$ contained in an excluded volume blob of size $xi$. % 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. %
A comparative simulation study of polymer brushes formed by grafting at a planar surface either flexible linear polymers (chain length $N_L$) or (non-catenated) ring polymers (chain length $N_R=2 N_L$) is presented. Two distinct off-lattice models are studied, one by Monte Carlo methods, the other by Molecular Dynamics, using a fast implementation on graphics processing units (GPUs). It is shown that the monomer density profiles $rho(z)$ in the $z$-direction perpendicular to the surface for rings and linear chains are practically identical, $rho_R(2 N_L, z)=rho_L(N_L, z)$. The same applies to the pressure, exerted on a piston at hight z, as well. While the gyration radii components of rings and chains in $z$-direction coincide, too, and increase linearly with $N_L$, the transverse components differ, even with respect to their scaling properties: $R_{gxy}^{(L)} propto N_L^{1/2}$, $R_{gxy}^{(R)} propto N_L^{0.4}$. These properties are interpreted in terms of the statistical properties known for ring polymers in dense melts.
We discuss theoretically and numerically the intramolecular form factor $F(q)$ in dense polymer systems. Following Florys ideality hypothesis, chains in the melt adopt Gaussian configurations and their form factor is supposed to be given by Debyes 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 $delta(F^{-1}(q)) = q^3/32rho$ that only depends on the concentration $rho$ of the solution, but neither on the persistence length or the interaction strength.
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