Star polymer dynamics

Single Chain Structure Factor for Star-Polymer Dynamics.221... 

Star Polymer Dynamics and Rheological Properties 6.03.2.4.1 Behavior in soiution... 

Vlassopoulos, D., Fytas, G., Pakula, T., and Roovers, J. (2001) Multiarm star polymers dynamics. Journal of Physics-Condensed Matter, 13, R855-R876. 

Vesicles and droplets encompass fluid which is not exchanged with the surrounding. In contrast, for star-like molecules fluid is free to penetrate into the molecule and internal fluid is exchanged with the surrounding in the course of time. This intimate coupling of the star-polymer dynamics and the fluid flow leads to a strong modification of the flow behavior at and next to the ultrasoft coUoid particularly in non-equilibrium systems. 

The paper is organized in the following way In Section 2, the principles of quasi-elastic neutron scattering are introduced, and the method of NSE is shortly outlined. Section 3 deals with the polymer dynamics in dense environments, addressing in particular the influence and origin of entanglements. In Section 4, polymer networks are treated. Section 5 reports on the dynamics of linear homo- and block copolymers, of cyclic and star-shaped polymers in dilute and semi-dilute solutions, respectively. Finally, Section 6 summarizes the conclusions and gives an outlook. 

The dynamics of highly diluted star polymers on the scale of segmental diffusion was first calculated by Zimm and Kilb [143] who presented the spectrum of eigenmodes as it is known for linear homopolymers in dilute solutions [see Eq. (77)]. This spectrum was used to calculate macroscopic transport properties, e.g. the intrinsic viscosity [145], However, explicit theoretical calculations of the dynamic structure factor [S(Q, t)] are still missing at present. Instead of this the method of first cumulant was applied to analyze the dynamic properties of such diluted star systems on microscopic scales. 

As we conjectured in the introduction, the fundamental role of topology in this approach to entangled polymer dynamics would indicate that changes to the topology of the molecules themselves would radically affect the dynamic response of the melts. In fact rheological data on monodisperse star-branched polymers, in which a number of anionically-polymerised arms are coupled by a multifunctional core molecule, pre-dated the first application of tube theory in the presence of branching [22]. Just the addition of one branch point per molecule has a remarkable effect, as may be seen by comparing the dissipative moduli of comparable linear and star polymer melts in Fig. 5. 

Fig. 6. Proposed mechanism of entangled dynamics of a star polymer in a melt. Retractions as shown partially renew the tube, beginning with rapid retractions near the free end and much more rarely renewing deeper parts of the molecule...

Fig. 7. The effective free-energy potentials for retraction of the free end of arms in a mon-odisperse star polymer melt. The upper curve assumes no constraint-release, the lower two curves take the dynamic dilution approximation with the assumptions (Ball-...

The mathematical treatment that arises from the dynamic dilution hypothesis is remarkably simple - and very effective in the cases of star polymers and of path length fluctuation contributions to constraint release in Hnear polymers. The physics is equally appealing all relaxed segments on a timescale rare treated in just the same way they do not contribute to the entanglement network as far as the unrelaxed material is concerned. If the volume fraction of unrelaxed chain material is 0, then on this timescale the entanglement molecular weight is renormalised to Mg/0 or, equivalently, the tube diameter to However, such a... 

Using the Rouse result, the left hand side of Eq. (30) is just l/2t. In the case of star polymers, using the approximate result for t(x) from Eq. (21) and the corresponding dynamic dilution result 0(x)=(l-x) the criterion becomes... 

So the criterion that the effective constraint-release must be fast enough to allow local pieces of umelaxed chain to explore any dilated tube fully confirms the assumption of dynamic dilution for nearly the whole range of relaxation timescales exhibited by star polymers. 

The recognition of the two fundamental mechanisms of reptation and arm fluctuation for linear and branched entangled polymers respectively allows theoretical treatment of the hnear rheology and dynamics of more complex polymers. The essential tool is the renormahsation of the dynamics on a hierarchy of timescales, as for the case of star polymers. It is important to stress that experimental checks on well-controlled architectures of higher complexity are still very few due to the difficulty of synthesis, but the case of comb-polymers is an example where good data exists [7]. 

A feature of theories for tree-like polymers is the disentanglement transition , which occurs when the tube dilation becomes faster than the arm-retraction within it. In fact this will happen even for simple star polymers, but very close to the terminal time itself when very little orientation remains in the polymers. In tree-like polymers, it is possible that several levels of molecule near the core are not effectively entangled, and instead relax via renormalised Rouse dynamics (in other words the criterion for dynamic dilution of Sect. 3.2.5 occurs before the topology of the tree becomes trivial). In extreme cases the cores may relax by Zimm dynamics, when the surroundings fail to screen even the hydro-dynamic interactions between the slowest sections of the molecules. 

A strong test of this theory is presented by a blend of two dynamically different components (but of identical local chemistry) such that the volume fraction of both is large. Two cases of especial interest suggest themselves blends of linear with star polymers [42,55] and blends of star polymers with widely separated molecular weights [56]. Recent work on both these systems has shed further light on the nature of co-operative constraint release and the remarkable power of the theoretical tools we now have at hand. 

Much experimental work has appeared in the literature concerning the microphase separation of miktoarm star polymers. The issue of interest is the influence of the branched architectures on the microdomain morphology and on the static and dynamic characteristics of the order-disorder transition, the ultimate goal being the understanding of the structure-properties relation for these complex materials in order to design polymers for special applications. 

All the discussions of entangled polymer dynamics above were limited to linear chains. The molecular architecture of the chain (star vs. linear vs. 

Multiarm star polymers have recently emerged as ideal model polymer-colloids, with properties interpolating between those of polymers and hard spheres [62-64]. They are representatives of a large class of soft colloids encompassing grafted particles and block copolymer micelles. Star polymers consist of f polymer chains attached to a solid core, which plays the role of a topological constraint (Fig. Ic). When fire functionality f is large, stars are virtually spherical objects, and for f = oo the hard sphere limit is recovered. A considerable literature describes the synthesis, structure, and dynamics of star polymers both in melt and in solution (for a review see [2]). 

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