Monodisperse polymer, definition

In the derivation of eqn. (7) it was assumed that n (number of equivalent random links) is the same for all chains. For our samples (B2 system, Mw/Mn=1.45), this assumption is definitely not correct. Therefore, it is desirable to obtain birefringence results on networks prepared from monodisperse polymer (in that n is constant), before the validity of n itself is questioned. 

The ratio Mw/ Mn must by definition be greater than unity for a polydisperse polymer and is known as the polydispersity or heterogeneity index. Its value often is used as a measure of the breadth of the molar mass distribution, though it is a poor substitute for knowledge of the complete distribution curve. Typically Mw/ Mn is in the range 1.5-2, though there are many polymers which have smaller or very much larger values of polydispersity index. A perfectly monodisperse polymer would have Mw/ Mn = 1.00. 

Eq. (18.17) is simply the definition of the Doi-Edwards damping function with the independent-alignment approximation (Chapters 8 and 12). The damping functions of Doi and Edwards with and without the independent-alignment approximation both explain well the experimental results of a well-entangled nearly monodisperse polymer system (Fig. 9.2). Note that here the unit vector u° represents the orientation of a Fraenkel segment as opposed to the orientation associated with an entanglement strand or primitive step in the Doi-Edwards theory. 

In synthesizing polymers in vivo and in vitro, molecular homogenous ( monodisperse ) polymers (i.e., those in which every macromolecule has the same molar mass or molecular weight ) occur only under quite specific conditions. The overwhelming majority of polymer syntheses proceed more or less randomly, and the resulting macromolecular substances have more or less broad molar mass distributions. The kind of molar mass distribution obtained depends on the nature of the polymerization, which may be either thermodynamically or kinetically controlled. Each kind of distribution is characterized by a definite relationship between the mole fraction x and the degree of polymerization X. Consequently, it is possible in many cases to deduce the kind of polymerization involved from the type of distribution function obtained. 

When only a single value is allowed, i.e ko = k =k, we call the model the fixed multiplicity model. Thus, for k = 2, the fixed multiplicity model reduces to the pairwise association. The normalization relation (7.98) for the fixed multiplicity model of monodisperse polymers (/ and n definite) is given by... 

We take the Mark-Houwink-Sakurada equation (Eq. 3-44) as given. We assume also that the same values of K and a will apply to all species in a polymer mixture dissolved in a given solvent. Consider a whole polymer to be made up of a series of I monodisperse macromolecules each with concentration (weight/volume) c, and molecular weight A/,. From the definition of [r ] in Eq. (3-37),... 

Although it is simple to understand what a dendrimer is just by looking at the beautiful chemical structures drawn in the literature, there is at present no rigorous definition of the term dendrimer . It is generally agreed that monodispersity is an essential characteristic of dendrimers, which are thus sets of molecules all having the same identical constitution (and thus the same molecular weight), differently from hyperbranched polymers [1], which are a mixture of different, even if chemically similar, macromolecules. 

Consider a monodispersed latex, where water-phase termination is negligible and termination is instantaneous when a radical enters a polymer particle containing one radical. By definition, IV2 = IV3 = — = 0 and the total radical entry rate per liter of latex equals p. Application of the stationary-state hypothesis gives... 

The light scattering methods provide statistically averaged quantities when applied to polydisperse samples (e.g., micellar or polymer solutions). The case of independent scatterers can be rigorously treated 2 by using the mass distribution function of the particles, f M). By definition, dm =f(M)dM is the mass of particles in the range between M and (M + dM), scaled by the total particle mass. As shown by Zimm, the scattering law in such a system can be presented similarly to the case of monodisperse particles (see Equation 5.405) ... 

Another of SEC s serious imperfections is that it relies on calibration. However there are really only a handful of polymers for which monodisperse standards are available, and all of these are common polymers. A way around this is to use universal calibration, but this firstly relies on Mark-Houwink-Kuhn-Sakurada (MHKS) parameters being known, and secondly it requires that workers are aware of the need for this procedure - many evidently are not. Further, given that the aim of much research in polymer synthesis is to make new polymers for which, by definition, MHKS parameters will not be available, it follows that in many cases universal calibration will not be possible anyway. 

Klein (1980 1982) has performed the most definitive experiments to date on the distance dependence of the steric interactions of polymer coated macroscopic surfaces. Monodisperse polystyrene, of molecular weight 1 x 10 or 6 X 10 , was adsorbed onto the mica plates by incubation of the plates with a very dilute solution (ca 7 x 10 g dm ) of the polymer in cyclohexane at 24 C. The polymer solution (save for ca 1 cm between the plates) was then replaced by pure cyclohexane. 

A modified technique to produce emulsion droplets is the so-called activated swelling method starting from polymer particles (41). Note, as per the definition given above, a polymer solution is also considered to form an emulsion. This procedure implies that the first seed particles, which may be composed of any polymer, are swollen with the highly water-insoluble compound-2 in a volume ratio between 1 1 and 5 1. These seed particles can be very monodisperse if prepared by the... 

Macromolecules that are almost, but not exactly, monodisperse are formed by time-controlled processes. If an initiator solution is added very suddenly to a monomer solution in such a way that all the initiator molecules are distributed homogeneously, then, with a suitable initiator, all the chains can be started simultaneously. Every chain has an equal chance of propagation. The degree of polymerization is proportional to the yield, and shows a linear increase with time. The molecular weight distributions are exceptionally narrow (see Chapter 18). Since, by definition, no deactivation reactions take place in these processes, the chain ends remain active when the monomer has been exhausted. On addition of fresh monomer, the polymerization continues. For this reason, these polymers are also referred... 

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