“Life is branched” was the motto of a special issue of Macromolecular Chemistry and Physics1 on “Branched Polymers”, indicating that branching is of similar importance in the world of synthetic macromolecules as it is in nature. The significance of branched macromolecules has evolved over the last 30 years from just being considered as a side reaction in polymerization or as a precursor step in the formation of networks. Important to this change in perception of branching was the concept of “polymer architectures”, which formed on new starand graft-branched structures in the 1980s and then in the early 1990s on dendrimers and dendritic polymers. Today, clearly, controlled branching is considered to be a major aspect in the design of macromolecules and functional material. Hyperbranched (hb) polymers are a special type of dendritic polymers and have as a common feature a very high branching density with the potential of branching in each repeating unit. They are usually prepared in a one-pot synthesis, which limits the control on molar mass and branching accuracy and leads to “heterogeneous” products with a distribution in molar mass and branching. This distinguishes hyperbranched polymers from perfectly branched and monodisperse dendrimers. In the last 20 years, both classes of dendritic polymers, dendrimers as well as hb polymers, have attracted major attention because of their interesting properties resulting from the branched architecture as well as the high number of functional groups.2 The challenging synthesis of the dendrimers attracted especially scientists with a strong organic chemistry background and led to beautifully designed macromolecules, which allowed a deeper insight into the effect of branching and functionality. Dendrimers have been considered as perfect “nano-objects” where one can control perfectly size and functionality, which is of high interest in nanotechnology and biomedicine. hb polymers, however, were considered from the beginning as products suitable for larger-scale application in typical polymer fields like coatings and resins, where a perfect structure is sacrificed for an easy and affordable synthetic route. Thus, the first structures that were reported paralleled the chemistry used for linear polymers like typical polycondensation for polyester synthesis. More recently, unconventional synthetic methods have been adopted also for hb polymers and related structures. Presently, a vast variety of highly branched structures have been realized and studied regarding their properties and potential application fields. Excellent reviews appeared covering synthesis strategies, properties, and applications, like the very recent tutorial by Carlmark et al.,3 the comprehensive book on hyperbranched polymers covering extensively synthesis and application * E-mail: voit@ipfdd.de; lederer@ipfdd.de. Chem. Rev. 2009, 109, 5924–5973 5924

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Hyperbranched and highly branched polymer architectures--synthetic strategies and major characterization aspects.

To account for spherulitic crystallization from the melt, one must explain the origins (i) of fibrous crystal habits in the absence of appreciable temperature gradients and (ii) of profuse noncrystallographic branching. Attention is drawn to properties held in common by spherulite‐forming melts of various types and, in particular, to the facts that (a) they are multicomponent systems, (b) they exhibit small coefficients of self‐diffusion, and (c) they crystallize slowly. It is shown that a consequence of these properties is that a plane crystal face cannot grow without suffering an instability of profile. Analagous instabilities lead in metal crystals to a cellular interface but, because of unusual growth kinetics, instability in spherulite‐forming melts gives rise to a drastic modification of crystal habit. Bundles of discrete fibers are formed whose widths are determined by δ = D/G, D being the coefficient of self‐diffusion and G being the growth rate. δ is generally small in these systems and commensurate with the scale of crystalline disorder in the fibers. It is this circumstance that allows noncrystallographic branching to occur.

A Phenomenological Theory of Spherulitic Crystallization

Dilute and semi-dilute solution properties of several classes of branched macromolecules are outlined and discussed. The dilute solution properties are needed for a control of the chemical synthesis. The molecular parameters also determine the overlap concentration which is an essential quantity for description of the semi-dilute state. This state is represented by a multi-particle, highly entangled ensemble that exhibits certain similarities to the corresponding bulk systems. Because of the rich versatility in branching the present contribution made a selection and deals specifically with the two extremes of regularly branched polymers, on the one hand, and the randomly branched macromolecules on the other. Some properties of hyperbranched chains are included, whereas the many examples of slight deviations from regularity are mentioned only in passing. The treatment of the two extremes demonstrates the complexity to be expected in the general case of less organized but non-randomly branched systems. However, it also discloses certain common features.

Solution Properties of Branched Macromolecules

The viscosity of polymers and their concentrated solutions

Branched polyesters: recent advances in synthesis and performance

Theoretical formulas for the intrinsic viscosity and viscoelastic properties of some model branched molecules in dilute solution are calculated by means of the normal coordinate method of Rouse modified to include hydrodynamic interactions. The calculations are exact except for the usual approximation of the hydrodynamic interaction by the Kirkwood-Riseman formula. The ratio of the intrinsic viscosity of a branched molecule to that of a linear molecule of the same weight is found to vary almost as the square root of the ratio of the mean square radii, instead of as the latter ratio to three-halves power, as has been postulated before. It is proposed that this square root relation is applicable in general to branched molecules of all types. Several sets of experimental data in the literature are shown to agree well with this hypothesis.

Dynamics of branched polymer molecules in dilute solution

The development of spherulites in thin films has been observed. At low supercoolings they develop scalloped edges, with each scallop sector having a branched structure reminiscent of a fern frond. At high supercoolings they develop smooth circular boundaries. An x-ray diffraction study has been made both of the fronded structures and of the more perfect spherulites formed at higher supercoolings. Only one of the latter types of spherulites was examined. Here it appears that the crystallites have a rotation axis perpendicular to the spherulite radius. This axis is the 4, 0, 1 direction in the crystal which has a monoclinic unit cell. The fronded spherulites, when examined along the radial frond spine, have the same rotation axis of the crystallites, both ±45° to the radius. This double orientation of rotation axis also occurs in material crystallized in a fine capillary, where the spherulite radial direction is presumably along the capillary axis. Low-angle x-ray diffraction shows spacings of about 200 A. (sometimes to sixth order) parallel to the spherulite radius for both fronded and perfect spherulites.

The morphology and internal structure of poly(ethylene oxide) spherulites

https://www.onlinelibrary.wiley.com/doi/pdf/10.1002/polb.1996.913

Methods are presented for the determination of degree of branching in a randomly branched polymer with tetrafunctional branch units. Typical examples of such polymers are irradiated linear polymers and copolymers of divinyl and monovinyl monomers. The most practicable method is found to be the comparison of the intrinsic viscosity of the branched polymer to the intrinsic viscosity of the corresponding linear polymer of the same weight-average molecular weight. Agreement is found with previously published experimental data on polymers of known degrees of branching. It is also found that the ratio of the mean square radius to the weight-average molecular weight for the polydisperse branched polymer is completely independent of degree of branching. Consequently, light-scattering data alone on the polydisperse polymer is not sufficient to determine branching.

Determination of branching in a randomly branched polydisperse polymer

The lattice model is used to predict the solution properties of graft and block polymers. It is found that the solubility of a graft polymer is critically dependent on the heat of interaction of the various components of the polymers with the solvent. Furthermore, the precipitates from fractionations of graft polymer solutions are no longer simple functions of the over-all molecular weight.

Ralph W. Kilb

Papers

Dynamics of branched polymer molecules in dilute solution

The morphology and internal structure of poly(ethylene oxide) spherulites

Dynamics of branched polymer molecules in dilute solution

Determination of branching in a randomly branched polydisperse polymer

Solution and fractionation properties of graft polymers