Scattering from ramied polymeric systems (original) (raw)

Scattering from Ramified Polymeric Systems

Condensed Matter Physics, 2004

Here, of great interest to us is a quantitative study of the scattering properties from ramified polymeric systems of arbitrary topology. We consider three types of systems, namely ramified polymers in solution, ramified polymer blends, or ternary mixtures made of two ramified polymers of different chemical nature immersed in a good solvent. To achieve the goal of the study, use is made of the Random Phase Approximation. First we determine the exact expression of the form factor of an ideal ramified polymer of any topology, from which we extract the exact expression of its gyration radius. Using the classical Zimm's formulae and the exact form factor, we determine all scattering properties of these three types of ramified polymeric systems. The main conclusion is that ramification of the chains induces drastic changes of the scattering properties.

Disorder effects on the static scattering function of star branched polymers

Condensed Matter Physics, 2012

We present an analysis of the impact of structural disorder on the static scattering function of farmed star branched polymers in d dimensions. To this end, we consider the model of a star polymer immersed in a good solvent in the presence of structural defects, correlated at large distances r according to a power law ∼ r −a. In particular, we are interested in the ratio g (f) of the radii of gyration of star and linear polymers of the same molecular weight, which is a universal experimentally measurable quantity. We apply a direct polymer renormalization approach and evaluate the results within the double ε = 4 − d, δ = 4 − a-expansion. We find an increase of g (f) with an increasing δ. Therefore, an increase of disorder correlations leads to an increase of the size measure of a star relative to linear polymers of the same molecular weight.

Static partial scattering functions for linear and ring random copolymers

Polymer Journal, 2010

The static partial scattering functions for linear and ring random copolymers of type A-B are investigated. In the case of random distribution of the different kinds of monomers, analytic forms can be derived. Monte Carlo simulations are used to make evaluations on biased distributions of the different kinds of monomers. Results clearly show that the number, fraction and distribution of monomers have significant effect on the scattering intensities at QÂR g 41, where Q is the magnitude of the scattering vector and R g is the radius of gyration of the polymer. The scattering function in molten state is also calculated on the basis of random phase approximation.

Dynamic scattering from solutions of semiflexible polymers

Physical Review E, 1997

The dynamic structure factor of semiflexible polymers in solution is derived from the wormlike chain model. Special attention is paid to the rigid constraint of an inextensible contour and to the hydrodynamic interactions. For the cases of dilute and semidilute solutions exact expressions for the initial slope are obtained. When the hydrodynamic interaction is treated on the level of a renormalized friction coefficient, the decay of the structure factor due to the structural relaxation obeys a stretched exponential law in agreement with experiments on actin. We show how the characteristic parameters of the system (the persistence length ℓp, the lateral diameter a of the molecules, and the mesh size ξm of the network) are readily determined by a single scattering experiment with scattering wavelength λ obeying a ≪ λ ≪ ℓp and λ < ξm. We also find an exact explicit expression for the effective (wave-vector-dependent) dynamic exponent z(k) < 3 for semiflexible polymers and thus an enlightening explanation for a longstanding puzzle in polymer physics.

Interpretation of dynamic scattering experiments on ternary polymer mixtures

Polymer, 1992

The dynamics of a ternary polymer mixture consisting of either homopolymers A and B, or diblock copolymers A-B, in a matrix of homopolymers C, is studied using the random phase approximation and assuming incompressibility. The relaxation frequencies and the amplitudes of the modes in dynamic scattering on such a mixture have been calculated as a function of the wave number q. In addition, the first cumulant of the dynamic scattering function of a labelled component is obtained in all q regions including the high q region where the segmental diffusion dominates the relaxation of the scattering function. The particular mixture consisting of A-B diblock copolymers in a matrix of homopolymers A, studied recently by St/ihn and Rennie, is analysed in detail, by calculating the first cumulant in the entire q region.

Depolarized light scattering from critical polymer blends

Macromolecular Theory and Simulations, 1999

Depolarized light scattering of binary polymer blends in disordered state near the demixing critical point is considered both theoretically and experimentally. It is shown that the depolarized scattering in such systems is predominantly due to double scattering processes induced by composition fluctuations. For long enough polymer chains, this scattering is stronger than the contribution from intrinsic anisotropy fluctuations. The general equation for the static and dynamic double scattering function is obtained in terms of the system structure factor. The scattering functions are calculated both analytically and numerically (dynamic part) for polymer blends. We found that the depolarized intensity depends on the polymerization degree N and the relative distance from the critical point s = 1 -v*/v (where v is the Flory-Huggins interaction parameter and v* its critical value) as I vh l N 2 /s 2 , which is in good agreement with the experimental data. It is also shown that the dynamic scattering function is decaying non-exponentially. We calculate the relaxation rate and the non-exponentiality parameter as functions of the scattering angle and s. These theoretical predictions are compared with experimental data for three chemically different blends.

A scattering function of star polymers including excluded volume effects

This work presents a new model for the form factor of a star polymer consisting of self-avoiding branches. This new model incorporates excluded volume effects and is derived from the two-point correlation function for a star polymer. This model is compared with small-angle neutron scattering measurements from polystyrene stars immersed in a good solvent, tetrahydrofuran. It is shown that this model provides a good description of the scattering signature originating from the excluded volume effect, and it explicitly elucidates the connection between the global conformation of a star polymer and the local stiffness of its constituent branch. research papers J. Appl. Cryst. (2014). 47 Xin Li et al. A scattering function of star polymers 5 of 5

Scattering functions of semidilute solutions of polymers in a good solvent

Journal of Polymer Science Part B: Polymer Physics, 2004

Expressions for analyzing small‐angle scattering data from semidilute solutions of polymers in a good solvent over a broad range of scattering vectors are examined. Three different scattering function expressions are derived from Monte Carlo simulations. The expressions are similar to those of polymer reference interaction site models, with a scattering‐vector‐dependent direct correlation function. In the most advanced model, the screening of excluded‐volume interactions beyond the overlap concentration is taken into account. Two simpler expressions, in which the screening of excluded‐volume interactions is not included, are also applied. The three models are tested against small‐angle neutron scattering (SANS) experiments on polystyrene in deuterated toluene for a broad range of molar masses and concentrations over a wide range of scattering vectors. For each model, simultaneous fits to all the measured scattering data are performed. The most advanced model excellently reproduces t...