Polydispersity perturbation

In this section I will outline some apparent sources of polydispersity perturbation. What I mean by the word apparent is that the MWD of the polymer is made to appear different - whether broader or narrower - to what it truly is. Such effects are obviously instramental in origin, although one hesitates to label them as instrumental error, because in most instances it is more a case of workers not fully appreciating exactly what the instrument is delivering. 

In this section I will summarize some real sources of polydispersity perturbation, i.e., factors that alter the tme PDI of a MWD. 

Several colloidal systems, that are of practical importance, contain spherically symmetric particles the size of which changes continuously. Polydisperse fluid mixtures can be described by a continuous probability density of one or more particle attributes, such as particle size. Thus, they may be viewed as containing an infinite number of components. It has been several decades since the introduction of polydispersity as a model for molecular mixtures [73], but only recently has it received widespread attention [74-82]. Initially, work was concentrated on nearly monodisperse mixtures and the polydispersity was accounted for by the construction of perturbation expansions with a pure, monodispersive, component as the reference fluid [77,80]. Subsequently, Kofke and Glandt [79] have obtained the equation of state using a theory based on the distinction of particular species in a polydispersive mixture, not by their intermolecular potentials but by a specific form of the distribution of their chemical potentials. Quite recently, Lado [81,82] has generalized the usual OZ equation to the case of a polydispersive mixture. Recently, the latter theory has been also extended to the case of polydisperse quenched-annealed mixtures [83,84]. As this approach has not been reviewed previously, we shall consider it in some detail. 

The inlet concentration of monomer and initiator were each separately varied in a very slow sinusoidal manner. The Dj, was again predicted to increase in comparison with the non-perturbed case, but they concluded that different results might be observed with regard to the magnitude and direction of the change in the polydispersity under non-isothermal conditions. 

In many perturbative results there naturally occurs the Debye function averaged over polydispersity. We thus introduce... 

It is clear a priori that it does not make sense to choose r > Rg, since then the coil would be smaller than an effective segment. To leading order of bare perturbation theory Rg is given by the expression for a noninteracting chain R 2N (Eq. (3,32) d = 3), where we neglect polydispersity effects. Renormalizing this expression we find... 

The termination process occurs instantaneously via entrant free radicals of (near) zero molecular weight. These radicals do not perturb significantly the distribution of chain lengths in converting growing chains to dead polymer. Indeed, termination in this instance is equivalent to chain transfer, which gives an identical value for the polydispersity index. 

Lorbach and Hatton [56] analyzed the polydispersity and back mixing effects in terms of the advancing reaction front model by assuming pseudosteady-state diffusion within the macrodrop so that the zero order solution to the perturbation expansion could be used. Mok et al. [57] proposed a... 

These formulae have the merit of expressing II, C, and in simple algebraic form as functions of the parameters f, b, and m. However, they have two defects. They describe ensembles whose polydispersion varies in an uncontrolled manner, whereas, to the same order of perturbation, the calculation can be made for a monodisperse ensemble, as was shown in Chapter 10, Section 8.4 [see (10.8.27) and (10.8.28)]. 

In the field of emulsions characterization, it is well known that dilution may create perturbation on the surface properties of the droplets and on interactions between the droplets. To give an example, matter transfers resulting from osmotic shocks may occm causing polydispersity changes as has been shown when such events are required (5,6). In fact, very few techniques avoid dilution, namely, dielectric or hert-zian spectroscopy (7-9), rheology (2), conductimetry (6,7), and more recent ones based on acoustical methods (10), focussed beam reflectance (11,12), or microwave attenuation (13). All these techniques are complementary and new techniques are always wel come. 

Abstract The most promising approach for the calculation of polymer phase equilibria today is the use of equations of state that are based on perturbation theories. These theories consider an appropriate reference system to describe the repulsive interactions of the molecules, whereas van der Waals attractions or the formation of hydrogen bonds are considered as perturbations of that reference system. Moreover, the chain-like structure of polymer molecules is explicitly taken into account. This work presents the basic ideas of these kinds of models. It will be shown that they (in particular SAFT and PC-SAFT) are able to describe and even to predict the phase behavior of polymer systems as functions of pressure, temperature, polymer concentration, polymer molecular weight, and polydispersity as well as - in case of copolymers - copolymer composition. 

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