Scattering from solutions of star polymers

Marques, Carlos M.; Izzo, Dora; Charitat, Thierry; Mendes, Eduardo

doi:10.1007/s100510050322

Cited by 56 publications

(52 citation statements)

References 22 publications

(29 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the effective stars alone, the colloidal approach is still relevant, but a prior correct subtraction of the other terms is needed. This has been demonstrated for semidilute solutions of neutral stars and applied to data obtained from PS star solutions, by neglecting the cross term [43]. In this case, there is no drastic change in the scattering at c * , because the scattering function of the sea of blobs is only a decreasing function (Lorentzian decay at small q values) [44].…”

Section: Discussionmentioning

confidence: 88%

Small-angle X-ray scattering from salt-free solutions of star-branched polyelectrolytes

Heinrich

Rawiso

Zilliox

et al. 2001

The European Physical Journal E

View full text Add to dashboard Cite

The dispersion state of sodium-sulphonated polystyrene (NaPSS) star-branched polyelectrolytes was investigated in salt-free aqueous solutions, by use of the small-angle X-ray scattering technique. With respect to polystyrene (PS) star-branched polymers of identical functionality, the ordering phenomenon occurring in the neighborhood of the overlap concentration c * is reinforced and observed in a larger range of concentrations. Moreover, the degree of order is no longer maximum at c * and is improved as the concentration decreases. The dispersion state is then mainly controlled by the electrostatic interaction. A crystalline order should therefore be achieved with stars of lower functionality, provided the electrostatic interaction is added to the osmotic repulsion. On the other hand, unusual scattering patterns are measured for aqueous solutions of NaPSS star polyelectrolytes. Indeed, a diffuse scattering is revealed at high angles, in addition to the regular diffraction rings related to preferred interstar distances. It is similar to the broad scattering peak produced by semidilute solutions of NaPSS linear polyelectrolytes and associated to the electrostatic correlation hole within the isotropic model. In the dilute regime (c < c * ), it is just an intramolecular characteristic and represents the electrostatic repulsion between arms belonging to the same star. In the semidilute regime (c > c * ), it also reflects the electrostatic repulsion between arms of distinct stars. So, as the concentration increases, it is mainly caused by the interpenetration of NaPSS stars. Such an observation is in agreement with the composite structure earlier proposed by Daoud and Cotton for star semidilute solutions. For c > c * , NaPSS star aqueous solutions can therefore be pictured as effective stars immersed in a matrix formed by the overlap of the arm ends. With respect to the dilute regime, the effective stars are smaller; the higher the concentration the smaller the size. PACS. 61.25.Hq Macromolecular and polymer solutions -82.70.-y Disperse systems

show abstract

Section: Discussionmentioning

confidence: 88%

Small-angle X-ray scattering from salt-free solutions of star-branched polyelectrolytes

Heinrich

Rawiso

Zilliox

et al. 2001

The European Physical Journal E

View full text Add to dashboard Cite

show abstract

“…1 shows the Guinier representation of the data to show the concentration dependent radii of gyration. The high-q part is dominated by the polymer-solvent fluctuations (blob term) G. This leads to the representation of the SANS intensity by two independent contributions [19][20][21][22] and was justified by Marques et al [23] using the Daoud-Cotton model [24].…”

Section: Resultsmentioning

confidence: 99%

Osmotic shrinkage in star/linear polymer mixtures

et al. 2010

View full text Add to dashboard Cite

Multiarm star polymers were used as model grafted colloidal particles with long hairs, to study their size variation due to osmotic forces arising from added linear homopolymers of smaller size. This is the origin of the depletion phenomenon that has been exploited in the past as a means to melt soft colloidal glasses by adding linear chains and analyzed using dynamic light scattering experiments and an effective interactions analysis yielding the depletion potential. Shrinkage is a generic phenomenon for hairy particles, which affects macroscopic properties and state transitions at high concentrations. In this work we present a small angle neutron scattering study of star/linear polymer mixtures with different size ratios (varying the linear polymer molar mass) and confirm the depletion picture, i.e., osmotic star shrinkage. Moreover, we find that as the linear/star polymer size ratio increases for the same effective linear volume fraction (c/c * with c * the overlapping concentration), the star shrinkage is reduced whereas the onset of shrinkage appears to take place at higher linear polymer volume fractions. A theoretical description of the force balance on a star polymer in solution, accounting for the classic Flory contributions, i.e. elastic and excluded volume, as well as the osmotic force due to the linear chains, accurately predicts the experimental findings of reduced star size as function of linear polymer concentration. This is done in a parameter-free fashion, in which the size of the cavity created by the star, and from which the chains are excluded, is related to the radius of the former from first principles.

show abstract

“…The scattering in such a mixture is shown in Figure 2 for the 251/52 copolymer in the dilute regime (the polymer concentration c is below c * ). At high scattering vectors (above q ∼ 0.5 nm −1 ), the signal is mainly due to fluctuations of the monomer profile, thus revealing the statistics of individual chains [25][26][27]. This signal, concentration independent, is found to be close to q −1 , which indicates a local statistics of nearly rod-like monomers.…”

Section: Structure Of the Charged Coronamentioning

confidence: 97%

Ordering of urchin-like charged copolymer micelles: Electrostatic, packing and polyelectrolyte correlations

Muller

Delsanti

Auvray

et al. 2000

The European Physical Journal E

View full text Add to dashboard Cite

We report the results of small-angle neutron scattering (SANS) studies on aqueous solutions of spherical polyelectrolyte micelles formed by association of charged-neutral diblock copolymers. The neutral moieties are found to self-assemble into small dense spheres (cores of the micelles) whose sizes are independent of the polymer concentration c. In the dilute regime, c < c * , where c * is the overlap concentration of the micelles, the conformation of the charged groups, which form the corona of the micelles, is found to be extended. A liquid-like order is observed over a wide concentration range spanning from the dilute regime to the concentrated regime. For c > c * , polyelectrolyte correlations appear at smaller spatial scales and coexist with the liquid-like order. These results suggest that for dense brushes, above c * , the rod-like statistics of the charged chains begin to disappear due to contraction of corona arms or by interpenetration of coronae. For less dense brushes, the charged chains are found to be extended up to concentrations far above c * , before the progressive development of polyelectrolyte correlations.

show abstract

Scattering from solutions of star polymers

Abstract: We calculate the scattering intensity of dilute and semi-dilute solutions of star polymers. The star conformation is described by a model introduced

Cited by 56 publications

References 22 publications

Small-angle X-ray scattering from salt-free solutions of star-branched polyelectrolytes

Small-angle X-ray scattering from salt-free solutions of star-branched polyelectrolytes

Osmotic shrinkage in star/linear polymer mixtures

Ordering of urchin-like charged copolymer micelles: Electrostatic, packing and polyelectrolyte correlations

Contact Info

Product

Resources

About