Star polymers solution properties

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. 

The synthesis of well-defined LCB polymers have progressed considerably beyond the original star polymers prepared by anionic polymerization between 1970 and 1980. Characterization of these new polymers has often been limited to NMR and SEC analysis. The physical properties of these polymers in dilute solution and in the bulk merit attention, especially in the case of completely new architectures such as the dendritic polymers. Many other branched polymers have been prepared, e.g. rigid polymers like nylon [123], polyimide [124] poly(aspartite) [125] and branched poly(thiophene) [126], There seems to be ample room for further development via the use of dendrimers and hyperbran-... 

The synthesis and the properties, both in bulk and in solution, of asymmetric star polymers are reviewed. Asymmetry is introduced when arms of different molecular weight, chemical nature or topology are incorporated into the same molecule. The phase separation, aggregation phenomena, dilute solution properties etc. are examined from a theoretical and experimental point of view. Recent applications of these materials show their importance in modern technologies. 

Asymmetric star polymers are megamolecules [1] emanating from a central core. In contrast to the symmetric stars very little was known, until recently, about the properties of the asymmetric stars. This was due to the difficulties associated with the synthesis of well-defined architectures of this class of polymeric materials. The synthesis, solution and bulk properties, experimental and theoretical, of the following categories of asymmetric stars will be considered in this review ... 

Relatively few theoretical studies have been devoted to the conformational characteristics of asymmetric star polymers in solution. Vlahos et al. [63] studied the conformational properties of AnBm miktoarm copolymers in different solvents. Analytical expressions of various conformational averages were obtained from renormalization group calculations at the critical dimensionality d=4 up to the first order of the interaction parameters uA> uB> and uAB between segments of the same or different kind, among them the radii of gyration of the two homopolymer parts < S > (k=An or Bm) and the whole miktoarm chain < /im > > the mean square distance between the centers of mass of the two homopolymer parts A and B < > and the mean square distance between the center of... 

Hedrick, J.L. Gast, A.P. Impact of core architecture on 70. solution properties of dendrimer-like star polymers. Macromolecules 2003, 36, 5765-5775. 

Comb or densely grafted polymers are defined as polymers that have at least one polymeric chains per monomer unit of the main chain, and Figure 29 shows examples obtained by metal-catalyzed living radical polymerization. Comb polymers possess physical properties similar to those of star polymers in solution. 

Roovers, J. Dilute solution properties of regular star polymers. Plast. Eng. 1999, 53, 285-341. 

The star architecture effects are more important for I q 0) than for Dc because the ratio of the corresponding correction terms, k / k — k, is large when k k. Nevertheless, the experimental Dc c/c reveals a stronger speed-up of Dc with concentration in multiarm stars compared to the semidilute linear polymer solutions. The hard core contribution to the osmotic pressure is essentially hidden in the inhomogeneous density profile and the thermodynamic properties of the star solutions are primarily determined by their polymeric character. 

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]). 

The solution properties of copolymers are much more compHcated. This is due mainly to the fact that the two copolymer components A and B behave differently in different solvents, and only when the two components are soluble in the same solvent will they exhibit similar solution properties. This is the case, for example for a nonpolar copolymer in a nonpolar solvent. It should also be emphasised that the Flory-Huggins theory was developed for ideal Hnear polymers. Indeed, with branched polymers with a high monomer density (e.g. star-branched polymers), the 0-temperature will depend on the length of the arms, and is in general lower than that of a linear polymer with the same molecular weight. 

The synthesis and bulk and solution properties of block copolymers having nonlinear architectures are reviewed. These materials include star-block copolymers, graft copolymers, mik-toarm star copolymers, and complex architectures such as umbrella polymers and certain dendritic macromolecules. Emphasis is placed on the synthesis of well-defined, well-characterized materials. Such polymers serve as model materials for understanding the effects of architecture on block copolymer self-assembly, in bulk and in solution. 

This presentation summarizes results on the synthesis, the dilute solution and bulk properties of dimethylamine and sulfozwitterionic end-functionalized polymers having different architectures (linear homopolymers, diblock and triblock copolymers and star polymers with different number of fimctional groups). 

Polymers are normally classified into four main architectural types linear (which includes rigid rod, flexible coil, cyclic, and polyrotaxane structures) branched (including random, regular comb-like, and star shaped) cross-linked (which includes the interpenetrating networks (IPNs)) and fairly recently the dendritic or hyperbranched polymers. I shall cover in some detail the first three types, but as we went to press very little DM work has been performed yet on the hyperbranched ones, which show some interesting properties. (Compared to linear polymers, solutions show a much lower viscosity and appear to be Newtonian rather than shear thinning [134].) Johansson [135] compares DM properties of some hyperbranched acrylates, alkyds. and unsaturated polyesters and notes that the properties of his cured resins so far are rather similar to conventional polyester systems. 

Discriminating branched and star polymers from linear ones can always be achieved by measuring the properties in dilute solution. In fact, molecules having the same molar mass but different macromolecular architectures exhibit different transport and light scattering properties. More specifically, a branched macromolecule is more compact than a linear molecule having the same molar mass, and therefore it will display less friction and will diffuse more easily in the solvent. Viscometry can be used to detect branched structures, since the Mark-Houwink-Sakurada exponent (Eq. 2.23) for branched and star-shaped polymers is lower tiian that for the corresponding linear chain. Unfortunately, in order to measure the difference, one must have a sample made exclusively... 

Experimental studies of solutions of PE star polymers are rare, because the synthesis of macromolecules with a controlled number and length of branches still presents a significant challenge. A few recent studies report on various properties... 

A quantitative analysis of counterion localization in a salt-free solution of star-like PEs is carried out on the basis of an exact numerical solution of the corresponding Poisson-Boltzmann (PB) problem (Sect. 5). Here, the conformational degrees of freedom of the flexible branches are accounted for within the Scheutjens-Fleer self-consistent field (SF-SCF) framework. The latter is used to prove and to quantify the applicability of the concept of colloidal charge renormalization to PE stars, that exemplify soft charged colloidal objects. The predictions of analytical and numerical SCF-PB theories are complemented by results of Monte Carlo (MC) and molecular dynamics (MD) simulations. The available experimental data on solution properties of PE star polymers are discussed in the light of theoretical predictions (Sect. 6). 

Finally, an analytical theory of conformations of highly branched PE stars is discussed (Sect. 7). The predictions are critically compared to numerical SCF-PB results. Here we focus on the responsive properties of strongly and weakly dissociating PE star polymers, e.g., their ability to change their conformations in response to a varied ionic strength and pH in solution. Inferior solvent quality triggers conformational transitions in PE star polymers (Sect. 8). Relevant theoretical insights are reviewed and compared to MD simulation results. 

We start with a brief review of the theory for conformational and solution properties of neutral (uncharged) star-branched polymers. 

Beyond the overlap concentration threshold, c>c = pN/lP, star polymers form a semidilute solution. Because of the fact that the arms in a star are stretched, the scaling theory [24] predicts that the properties of semidilute solutions of star polymers are distinctively different from those of linear polymers. When the polymer concentration c > c, a semidilute solution is envisioned as a system of closely packed and virtually non-interpenetrating (segregated) polymer stars. A further increase in polymer concentration leads to a progressive contraction of the coronae of the individual stars. This contraction results in an increase in the conformational entropy of the partially stretched star arms. 

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