The Effect of Polydispersity

One of the most fundamental questions still open regarding the structure/property relationships of SCLCPs is the effect of polydispersity. In some cases, the temperature and nature of the mesophase(s) depend not 

III Molecular Engineering of Side Chain Liquid Crystalline Polymers 

In contrast, the transitions of most well-defined SCLCPs prepared by controlled polymerizations are relatively narrow. The effect of polydispersity was therefore investigated by blending well-defined (pdi 1.28) poly 5- [6 -[4 -(4 -methoxy-phenyl)phenoxy]alkyl]carbonyl bicy-clo[2.2.1]hept-2-ene)s of varying molecular weights (DP =5, 10, 15, 20, 50, 100) to create poly disperse samples (pdi = 2.50-4.78) [22]. In this case, both monodisperse samples and multimodal blends underwent the nematic-isotropic transition over a narrow temperature range. Polydispersity also had no effect on the temperatures of transi- 

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Muthukumar [44] further investigated the effects of polydispersity, which are important for crosslinking systems. He used a hyperscaling relation from percolation theory to obtain his results. If the excluded volume is not screened, n is related to df by... 

There are two important issues concerning the factor that gives the excluded volume 1 /shear rate (ii) what is the effect of polydispersity ... 

As a result of polydispersity effects, the composition of the incipient 13-phase segregated at the cloud point is located on a shadow curve, outside the cloud-point curve (point (3 in Fig. 8.4). The effects of polydispersity on phase diagrams and phase compositions may be found in specialized reviews (Tompa, 1956 Kamide, 1990 Williams et al., 1997). Because < )Mo < ( M,crit(xcp), the incipient (3-phase, which is richer in the modifier, will be dispersed in the a-phase, which is richer in the growing thermosetting polymer. The opposite occurs when < )M0 > M,crit(xcp)- It has been shown both theoretically (Riccardi et al., 1994 and 1996 Williams et al., 1997), and experimentally (Bonnet et al., 1999) that... 

A.W. Chow, and G.G. Fuller, The rheo-optical response of rod-like chains subject to transient shear flow. Part I Model calculations on the effects of polydispersity, Macromolecules 18, 786 (1985) A.W. Chow, G.G. Fuller, D.G. Wallace and J.A. Madri, The rheo-optical response of rod-like chains subject to transient shear flow. Part II. Two-color flow birefringence measurements, Macromolecules 18,793 (1985) A.W. Chow, G.G. Fuller, D.G. Wallace and J.A. Madri, The rheo-optical response of rod-like shortened collagen protein to transient shear flow, Macromolecules, 18, 805 (1985). 

G. Murrucci and N. Grizzuti, The effect of polydispersity on rotational diffusivity and shear viscosity of rodlike polymer in concentrated solutions, J. Polym. Sci., Polym. Lett. Ed., 21, 83 (1983). 

Recently, Chu et al. [41,42] and Chu and Wasan [43] have made simulation and MSA studies of the structure and forces in thin films and colloidal dispersions. They include the effect of polydispersity. They also find oscillatory forces. 

To study charging mechanisms theoretically for either diffusion charging or field charging, it is necessary to make several assumptions regarding the aerosol. First, the particles are assumed to be spherical. This assumption is reasonable for isometric particles. Second, it is also assumed that the particles are monodisperse. The effect of polydispersity complicates but does not invalidate theory. Third, there are no interactions between individual particles. Finally, the ion concentration and electric field near each particle are assumed to be uniform. These last two assumptions are essentially true for all natural and industrial aerosols. Thus except in the most extreme cases, theoiy should be adequate without other modification. 

Bushell, G., Amal, R., and Raper, J., The effect of polydispersity in primary particle size on measurement of the fractal dimension of aggregates. Part. Syst. Charact., 15, 3, 1998. 

Our purpose in this section is to derive a set of useful expressions for the chemical potentials starting with the principles of statistical mechanics. The expressions we shall obtain take the form of virial expansions similar to those of the Edmond and Ogston (6) but having a very different theoretical basis. Our model parameters are isobaric-isothermal virial coefficients which are about an order of magnitude smaller than the osmotic virial coefficients in the Edmond and Ogston model. We shall develop the theory neglecting the effect of polydispersity because we empirically did not find this to be very important at the level of accuracy commonly attainable in experimental phase diagrams for these systems. 

We hope to extend this approach to other polymer systems and to include the effect of polydispersity in a forthcoming paper (Cabezas, H., Jr. Evans, J.D. Szlag, D.C. Huid Phase Equilibria, in press). 

In Reference 36 we have found the sharp cutoffs all imply C = 1.0 0.1. Equation 14.44 is consistent with the form first proposed by Dobbins and Megaridis. However, Eqnation 14.44 is not to be used to fit real data because they neglect the effects of polydispersity, which we consider below. 

More emphasis on multicomponent systems including both mixed solvents, blend-solvent systems, as well as the effect of polydispersity... 

An accurate determination of molecular weight can be done by matrix-assisted laser desorption/ionization time of flight (MALDI-TOF) analysis. Fig. 2.7 demonstrates the effect of polydispersity on the MALDI-TOF analysis of mPEG 5-kDa MAL CV-N. Each peak is separated by 44 mass units associated with the ethyleneoxy units of the polymer. The polydispersity increases with an increase in the size of the PEG. The PEG-conjugate is also polydis-perse and the resolution of the peaks decreases as the molecular weight of either the PEG or the protein increases. The pro-... 

It would be interesting to study the effect of polydispersion on the structure function and to compare them with those which show up in the osmotic pressure fl, but the calculation of these effects has not yet been made. 

Since a reduction in the bubble spectrum is connected to additional difficulties and polydispersity of bubbles in electroflotation and air-dissolved flotation cannot be therefore avoided, it is important to know the effect of polydispersity. This effect should not be too high since the process of particle capture should be ahead of the process of coalescence. It should also not be too low so large bubbles can capture small bubbles in a moderate time. Unfortunately, such a scheme which appears convincing at a first glance means a slow rate of coalescence of small bubbles. The coalescence can proceed faster than particle capture, so that the intensification of capture becomes very important. Hence it is necessary to combine introduction of small bubbles with aggregation of particles. 

The effect of polydispersity of primary chains on experimental gel points was also studied by using activators regenerated by electron transfer (ARGET) ° ATRP for the copolymerization of MA and EGDA. Decreasing the copper concentration from tens of ppm to a few ppm increased the polydispersity of primary chains from M /Mn = 1.1 to 2.0, which accelerated the experimental gel point during the copolymerization of monomer and crosslinker. 

In Section 8.5, the effects of polydispersity on integrated spectra of polydisperse solutions were discussed. It was shown, for instance, that weight-average molecular weights... 

We shall now consider the effects of polydispersity on the interpretation of light scattering measurements on solutions of large molecules. If a solution contains particles having differing weights and shapes, but all scattering independently, then the observed intensity is simply the sum of all the individual intensities ... 

The effect of polydispersity can be seen directly when considering first a system of homogeneous spheres having a Gaussian size distribution [46]. Here the scattering curves are fully determined by the form amplitude BQ(q) as defined... 

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