Nature of Branching in Disordered Materials

The phenomenon of structural branching is ubiquitous in a wide array of materials such as polymers, ceramic aggregates, networks and gels. These materials with structural branching are a unique class of disordered materials and often display complex architectures. Branching has a strong influence over the structure-property relationships of these materials. Despite the generic importance across a wide spectrum of materials, our physical understanding of the scientific nature of branching and the analytic description and quantification of branching is at an early stage, though many decades of effort have been made. For polymers, branching is conventionally characterized by hydrodynamic radius (size exclusion chromatography, SEC, rheology) or by counting branch sites (nuclear magnetic resonance spectroscopy, NMR). SEC and rheology are, at best, qualitative; and quantitative characterization techniques like NMR and transmission electron microscopy (TEM) (for ceramic nanoparticulate aggregates) have limitations in providing routine quantification. Effective structure characterization, though an important step in understanding these materials, remains elusive. For ceramic aggregates, theoretical work has dominated and only a few publications on analytic studies exist to support theory.

A new generic scaling model is proposed in Chapter I, which encompasses the critical structural features associated with these complex architectures. The central theme of this work is the application of this model to describe a variety of disordered structures like aggregated nano-particulates, long chain branched polymers like polyethylene, hyperbranched polymers, multi-arm star polymers, and cyclic macromolecules. The application of the proposed model to these materials results in a number of fundamental structural parameters, like the mass-fractal dimension, d_f, the minimum path dimension, d_min, connectivity dimension, c, and the mole fraction branch content, φ_br. These dimensions reflect different features of the global structure, and it is categorically shown that this dimensional analysis results in effective structure characterization of these materials. Small-angle scattering of x-rays and neutrons can be used to quantify branch content and characterize the structure, through application of concepts native to fractal geometry.

The application of the scaling model to nano-particulate aggregates yields quantitative information regarding the structure of these materials. In-situ small and ultra small angle x-ray scattering data collected on fumed silica and soot particles is presented in Chapter II. These measurements were performed at Advanced Photon Source, Argonne National Laboratory, UNICAT beam-line and the European Synchrotron Radiation Facility, Grenoble, France, ID2 beam-line. The dimensional analysis is successful in not only giving an average snap-shot of the nano-particulate aggregates, but also yields information regarding the growth processes involved in the complex pyrolysis technique of synthesizing these materials.

In case of macromolecular systems, the minimum path dimension, d_min, is shown to reflect the thermodynamics of the system. This is categorically established in Chapter III on hyperbranched polymers, where the scaling model accurately predicts the good-solvent to θ-condition transition in these highly branched polymers with increasing molar mass.

The scaling model is applied to the long standing problem of quantifying long chain branching in polyethylene in Chapter IV. Small angle neutron scattering data on dilute solutions of polyethylene were obtained at the Intense Pulsed Neutron Source (SAND beam-line); NIST center for Neutron Scattering (NG3 beam-line); and Los Alamos Neutron Scattering Center (LQD beam-line). This work, for the first time in literature, reports the length of a long chain branch in polyethylene in terms of the average molar mass of the branches, and the average number of carbon atoms in the long chain branch.

Cyclic polymers are examined in the Chapter V. The scaling model presents a new pathway to describe small angle scattering data to characterize cyclic structures. The Casassa form factor from literature is also critiqued in the framework of the scaling approach to describe small angle neutron scattering from cyclic macromolecules like polydimethylsiloxane.

In the Appendix section, results from phase separation kinetics study of segmented polyurea are presented. Using small angle x-ray scattering, the mechanism of phase separation between the hard and soft segments in polyurea is shown to occur by spinodal decomposition like mechanism.

This dissertation provides a universal tool, to quantify branch content and obtain the specifics of the structural features needed to describe complex architectures in disordered materials, irrespective of the family of materials to which they belong. This tool enables an understanding of the underlying branching phenomena, and prediction of structure property relationships such as rheology of long chain branched polymers.