Polydispersity, effect

The phase behaviour of mixtures of monodisperse hard spheres and polydisperse ideal polymers has been investigated using original FVT [67]. At fixed mean 

Computer simulations show that crystallization of hard spheres does not occur above a polydispersity of 11.8% in diameter [69]. Pusey [70] provided a simple argument suggesting that the maximum polydispersity ff ix depends on the close packing and melting volume fractions (t and respectively. 

For hard spheres with (j) = 0.74 and f = 0.545, (4.40) provides g , = 0.11, so 11%. In dispersions with large q, small colloids are needed in practice because it is difficult to synthesize model polymer chains with sizes 200 nm in solution. Small colloids ( 100nm) are often quite polydisperse. Therefore, systems studied with large q in general tend to be relatively polydisperse in colloidal sphere size. This implies that in experimental systems with large q, crystallisation is suppressed or absent. 

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The apparent difference between viscosity average (M ) and number average molecular weight (M ) for unfractionated triacetate samples and high molecular weight fractions may be attributed to the presence of hemicellulose and polydispersity effect in these materials as shown in the table in question and in Figure 3. 

If the scattered amplitude f. is a function of K, then /2K is K dependent through the polydispersity effect, even though Dg s are independent on K. Such an effect has been investigated in detail... 

A ternary system consisting of two polymer species of the same kind having different molecular weights and a solvent is the simplest case of polydisperse polymer solutions. Therefore, it is a prototype for investigating polydispersity effects on polymer solution properties. In 1978, Abe and Flory [74] studied theoretically the phase behavior in ternary solutions of rodlike polymers using the Flory lattice theory [3], Subsequently, ternary phase diagrams have been measured for several stiff-chain polymer solution systems, and work [6,17] has been done to improve the Abe-Flory theory. 

These results make it clear that the forms of t]0 — rjs and Je° are completely independent of model details. Only the numerical coefficient of Je° contains information on the properties of the model, and even then the result depends on both molecular asymmetry and flexibility. Furthermore, polydispersity effects are the same in all such free-draining models. The forms from the Rouse theory cany over directly, so that t]0 - t]s, translated to macroscopic terms, is proportional to Mw and Je° is proportional to the factor A/2M2+, /A/w. Unfortunately, no such general analysis has been made for models with intramolecular hydrodynamic interaction, and of course these results apply in principle only to cases where intermolecular interactions are negligible. 

Not all the results of scaling theory are equally well supported by the more fundamental renormalization approach. In Sect. 9,3 we discuss which features should not be taken too literally. We furthermore should note that scaling theory in general ignores such complications as polydispersity effects. Ln the sequel we therefore explicitly consider a monodisperse system. 

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... 

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... 

Monodisperse polymer blocks have been assumed all along. Polydispersity effects could be introduced in an ad-hoc fashion by assuming a molecular weight distribution (such as the Zimm-Schultz) ... 

V. Polydispersity effects over the entire range in binary mixtures (linear-linear, star-star and linear-star). 

The polydisperse effect had very little influence on mass transfer behavior (see Fig. 4.3). 

My, oo). This new phase boundary for the cloud point of the rubber is shown as the upper curve in Figure 1.34 and will correspond to an extent of conversion pcvphase dispersed in the thermoset (a-)phase and, as shown in Figure 1.34, the theoretical composition of the P-phase will be given by the position on the cloud-point boundary as shown. (It has been noted that this is not strictly correct due to polydispersity effects and the actual composition lies outside this line (Pascault et al, 2002)). 

However, in real systems the decay is more complex due to polydispersity effects and different types of motions which can contribute. A different way to formulate the above function is based on the fluctuation of Z given by 8Z(t) = Z(t) — (Z). Using this expression leads... 

There has been some controversy concerning whether these two equations are sufficient to describe the molecular weight dependence of r o completely, or whether polydispersity effects also need to be taken into account. A review of this issue [5] shows that (unlike the definite effect of polydispersity on the viscosity at high shear rates) there is no consistent effect of polydispersity on r)o, and that some of the apparent evidence to the contrary may have been an artifact of the large uncertainties in the measured values of Mw. We will, hence, use equations 13.4 and 13.5 and not incorporate any corrections related to polydispersity in calculating qo-... 

The polydispersion effects concerning the behaviour of the function Kp/Il(q) associated with a Brownian chain, are as follows ... 

In practice, this formula coincides with (10.6.32), but (10.6.32) corresponds to a monodisperse ensemble. Thus, to that order, polydispersion effects are not felt. 

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