Monodisperse materials

It may be shown that M > M. The two are equal only for a monodisperse material, in which all molecules are the same sise. The ratio MI /MI is known as the polydispersity index and is a measure of the breadth of the molecular weight distribution. Values range from about 1.02 for carefully fractionated samples or certain polymers produced by anionic polymerization, to 20 or more for some commercial polyethylenes. 

The advantage of iterative strategies is based on the specific preparation of well defined structures and structurally perfect spacers of nanometer scale. This stepwise approach yields monodisperse material in contrast to other statistical routes. The use of the same reactants and the conversion of the same functional groups facilitates the synthetic effort compared with non-iterative methods. 

It has long been reaUsed that the key physics determining the rheology of high molecular weight polymers in the melt state arises from the topological interactions between the molecules [1,2]. This is deduced from observations on many different monodisperse materials that ... 

The monodisperse materials described hereafter were obtained with the Couette type cell designed by Bibette et al. [ 150,159]. It consists of two concentric cylinders (rotor and stator) separated by a very narrow gap (100 pm), allowing application of spatially homogeneous shear rates over a very wide range (from 0 to 14280 s ), with shearing durations of the order of 10 s. 

Polymer Preparation. Poly-para-methylstyrene (P-p-MS) was prepared by anionic polymerization in benzene at 50"C initiated by n-butyllithium (9) or in THF at 25°C initiated by sodium naphthalene (10). Polymerizations in benzene allowed preparation of more monodisperse materials than those prepared in THF since the propagation rate is slower relative to the initiation rate in the nonpolar solvent (11). Two different molecular weight materials were chlorinated (P-p-MS 1 and P-p-MS2). 

The simplest measure of the breadth of a distribution is the ratio of two different types of average molecular weight. Specifically the ratio of Mw to Mn is by far the most widely used for this purpose, and is called the polydispersity index. It has a minimum value of unity (for a monodisperse material in which all the chains have exactly the same length). The extent to which it exceeds unity is a measure of the breadth of the distribution. Typical values are in the range 1.5-2.0, but many polymerizations yield considerably larger values. 

Ungar and Zeng [33] have comprehensively summarized the research on strictly monodisperse materials from their first synthesis in 1985 until 2001. From the earliest studies it became apparent that, due to the monodisper-sity of the materials, the thickness of the lamellar crystals formed is always an integer fraction of the extended chain length (allowing for any chain tilt), such that the polymers always crystallize in the extended chain form or fold exactly in half (once-folded), or in three (twice-folded), etc. This behavior means that, when the alkanes are crystallized at a particular temperature, the entire lamellar population has very closely the same thickness and stability. The use of such an ultra-pure system to study the impact of thickness on lattice parameters removes many of the problems inherent to polymers, whilst maintaining the most important characteristic of chain length. 

Combinations of other molecular weight averages are also possible to give analogous Q and U values. For a monodisperse material Q = 1 and U = 0. 

The molybdenum neopentyUdene complex Mo(CHBu )(NR)(OBu )2 is the active catalyst used in a fascinating development for the synthesis of 11-Vt semiconductor clusters (ZnS, CdS, PbS) and silver and gold nanoclusters of predictable size within microdomains in films of block copolymers prepared by ROMP. Block copolymers of norbomene and a functionalized norbomene that wiU complex with a metal-containing compound were prepared and characterized as monodisperse materials. The functionalized component (amine, alkoxide, or thiolate) then sequestered the metal and the metallated block copolymer was cast into a film which was subsequently treated with H2S to convert the metal into the sulfide. The molybdenum complexes have also featured in the development of the synthesis of side-chain liquid crystal polymers by living ROMP.98 99... 

Monodisperse Materials Prepared Biosynthetically 756 An Analysis of Dispersity and Molecular Weight 757 A Melting Analysis 759... 

For monodisperse materials the interference effects are minimal and the power spectrum of the material is well defined. 

Fig. 10 Apparent distributions of monodisperse material for different sizes of the measuring gap...

In this section we examine many of the methods that have been developed to make monodisperse materials. Whether or not they are ideal for ceramics fabrication, monodisperse particles are certainly important as model systems for testing theories of colloidal stability, light scattering, drying, and sintering. 

From a strictly mechanical perspective, the question arises whether polydis-perse materials yield better materials for industrial use, or whether monodisperse materials are superior. For many properties, it is the polydisperse sample that achieves the best performance. For other properties, a little low molecular weight impurity can seriously degrade properties like the ultimate modulus and the resistance to embrittlement over time. The goal of polymer engineering is to understand these issues well enough to blend the best brew. 

Thus, each point on the viscosity curve rj y) corresponds to a value ofM. Figure 8.1 illustrates this. The continuous lines are viscosity curves for several of the hypothetical monodisperse polymers with molecular weights within the range of the polydisperse material, whose viscosity curve is shown by a dashed line. Each monodisperse material has a characteristic shear rate y M) and a zero-shear viscosity t]q M) that correspond to the molecular weight M. Thus, each shear rate between the Newtonian plateau and power law region of the polydisperse material will be the critical shear rate y M) of one of the monodisperse materials of which it is comprised. 

The relaxation function for monodisperse material F M,t) must be specified. 

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