Polydispersity index

A criterion for selecting a right pore size to separate a given polydisperse polymer is provided here. To quantify how much the MW distribution narrows for the initial fraction, an exponent a is introduced (2). The exponent is defined by [PDI(0)] = PDI(l), where PDI(O) and PDI(l) are the polydispersity indices of the original sample and the initial fraction, respectively. A smaller a denotes a better resolution. If a = 0, the separation would produce a perfectly monodisperse fraction. Figure 23.7 shows a plot of a as a function of 2RJd (2). Results... 

Anionic polymerizations carried out in aprotic solvents with an efficient initiator may lead to molecular weight control (Mn is determined by the monomer to initiator mole ratio) and low polydispersity indices. The chains are linear and the monomer units are placed head-to-tail. Such polymers are commonly used as calibration samples and for investigation of structure-properties relationships. 

A carbazole-functionalized norbornene derivative, 5-CN-carbazoyl methy-lene)-2-norbornene, CbzNB, was polymerized via ROMP using the ruthenium catalyst Cl2Ru(CHPh)[P(C6Hii)3]2 [100]. The polymerization was conducted in CH2C12 at room temperature, to afford products with polydispersity indices close to 1.3. Subsequent addition of 5-[(trimethylsiloxy)methylene]-2-norbornene showed a clear shift of the SEC trace of the initial polymer, indicating that a diblock copolymer was efficiently prepared in high yield. 

The effects of composition distribution on the morphology of PS-fc-P2VP diblock copolymers were investigated by Matsushita et al. [160]. They produced PS- -P2VP samples with various composition distributions but with constant average composition by blending. If the polydispersity indices of each block were lower than 1.7, the expected lamellar domains were detected (Fig. 49). 

Characteristic initiation behavior of rare earth metals was also found in the polymerization of polar and nonpolar monomers. In spite of the accelarated development of living isotactic [15] and syndiotactic [16] polymerizations of methyl methacrylate (MMA), the lowest polydispersity indices obtained remain in the region of Mw/Mn = 1.08 for an Mn of only 21 200. Thus, the synthesis of high molecular weight polymers (Mn > 100 x 103) with Mw/Mn < 1.05 is still an important target in both polar and nonpolar polymer chemistry. Undoubtedly, the availability of compositionally pure materials is a must for the accurate physical and chemical characterization of polymeric materials. 

For the superior performance design with consecutive, multiply furcated capillaries using conventional manifolds, flow distribution quality was determined. Polydispersity indices for eight capillaries ranged from 1.66 to 1.71, i.e., it showed a low spread, demonstrating that flow distribution was reasonably achieved. The molecular number average was... 

Table 12 Theoretical number average molar masses (M ) and polydispersity indices for the for ...

For the evaluation of the SEC measurements, a second plot can be created where the obtained values o M (left coordinate, should increase linearly with conversion) and the polydispersity indices (PDI, right coordinate, should be lower than 1.3) are plotted vs. the conversion.This plot again can be used to discuss the degree of control, and the time period where control was achieved during the chain growth process.This time is in general approx. 2 h. 

All base polyesters have been characterized with SEC (Table 4). The polydisper-sity indices indicate a narrow distribution of hydrodynamic radius. Three differently end-capped polyesters, H4, H9, and HIO, were analyzed in THE and acetone. The results were extremely sensitive to the change in polarity of the solvent even though the polydispersity indices agreed quite well. 

Morphological structures and properties of a series of poly(ethyl acrylate)/clay nanocomposites prepared by the two distinctively different techniques of in situ ATRP and solution blending were studied by Datta et al. [79]. Tailor-made PNCs with predictable molecular weights and narrow polydispersity indices were prepared at different clay loadings. WAXD and studies revealed that the in situ approach is the better option because it provided an exfoliated morphology. By contrast, conventional solution blending led only to interlayer expansion of the clay gallery. 

Figure 1.6 Effect of molecular weight on the strength-melt flow index interrelationship of polystyrene for three polydispersity indices.

Block length polydispersity indices"for blends were calculated on the assumption that the block polymers, as prepared, were composed of monodisperse blocks. This is, of course, an approximation justified only by the narrowness of the molecular weight distribution in polymerizations of the present type. The block heterogeneity indices given here should, therefore, be regarded as relative measures of breadth of distribution. 

Fitting the experimental distribution to distributions calculated as described above leads to the conclusion that the efficiency of reactions for the synthesis of the sample must be between 97 and 98% for each step [169]. Polydispersity indices derived from the calculated distributions include the trace low molecular weight species that would be present but undetectable at the experimental signal to noise ratio, giving a more realistic measure of polydispersity. Thus, this statistical treatment would place the polydispersity of the sample between 1.005 and 1.003. 

Fig. 46. Tensile strength of highly oriented polyethylene at Young s modulus = 50 GPa versus weight average molecular weight for various polydispersities (indicated in graph). With permission of the publishers John Wiley Sons. Inc. (C)...

H(x) is a continuous distribution of the logarithms of relaxation times and is called the "relaxation spectnun" by rheologists, whilst the "true" distribution of relaxation times is xH(x). We have reported on Figure 1 the normalized distribution of relaxation times for 4 polystyrene samples with polydispersity indices ranging from 1.05 to 4.2 [2]. It is clear that the distribution of relaxation times broadens with the distribution of molecular weights these features will be anal3 d in terms of molecular models in sections 3 to 6. 

The PD MS chains used were hydroxyl terminated and were obtained from Petrarch Systems, Inc. (Bristol, PA). Their number-average molecular weights (MJ were 660 and 880 g/mol for the short chains and 21.3 X 10 g/mol for the long chains (7). Their polydispersity indices would be expected to be 2. 

Finally, the polydispersity index is higher for the sheared reaction system as compared to the quiescent reaction system. This is in agreement with experimental data (Table 3), however, the difference in the computed polydispersity indices for flow and no flow is small compared to the experimental values since the computations are carried out for relatively low conversions. The simple model thus gives a good qualitative account of all the experimental observations. 

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