Polydispersivity index

Comonomer is exhausted at relatively low conversion (20), but a random copolymer is nevertheless obtained. This is because a very facile transacetalisation reaction allows for essentially random redistribution of the comonomer units (18) and also results in a polydispersity index near 2.0 (21). 

It may be shown that M > M. The two are equal only for a monodisperse material, in which all molecules are the same sise. The ratio MI /MI is known as the polydispersity index and is a measure of the breadth of the molecular weight distribution. Values range from about 1.02 for carefully fractionated samples or certain polymers produced by anionic polymerization, to 20 or more for some commercial polyethylenes. 

The minimum polydispersity index from a free-radical polymerization is 1.5 if termination is by combination, or 2.0 if chains ate terminated by disproportionation and/or transfer. Changes in concentrations and temperature during the reaction can lead to much greater polydispersities, however. These concepts of polymerization reaction engineering have been introduced in more detail elsewhere (6). 

The MWD is the ratio of Mw Mn and is called the polydispersity index. This largely varies from one grade of polymer to the other, depending on the polymerization conditions and the type of catalyst used. Figure 14 shows different types of MWD for the polymers. 

The dispersity is also commonly called the polydispersity index or the polydispersiiy. 

Assuming that no intramolecular or side reactions take place and that all groups are equireactive, the polydispersity index, 7P, of hyperbranched polymers obtained by step-growth polymerization of ABX monomers is given by Eq. (2.2), where pA is die conversion in A groups.196 Note that the classical Flory relationship DPn = 1/(1 — pa) holds for ABX monomer polymerizations ... 

See also PBT degradation structure and properties of, 44-46 synthesis of, 106, 191 Polycaprolactam (PCA), 530, 541 Poly(e-caprolactone) (CAPA, PCL), 28, 42, 86. See also PCL degradation OH-terminated, 98-99 Polycaprolactones, 213 Poly(carbo[dimethyl]silane)s, 450, 451 Polycarbonate glycols, 207 Polycarbonate-polysulfone block copolymer, 360 Polycarbonates, 213 chemical structure of, 5 Polycarbosilanes, 450-456 Poly(chlorocarbosilanes), 454 Polycondensations, 57, 100 Poly(l,4-cyclohexylenedimethylene terephthalate) (PCT), 25 Polydimethyl siloxanes, 4 Poly(dioxanone) (PDO), 27 Poly (4,4 -dipheny lpheny lpho sphine oxide) (PAPO), 347 Polydispersity, 57 Polydispersity index, 444 Poly(D-lactic acid) (PDLA), 41 Poly(DL-lactic acid) (PDLLA), 42 Polyester amides, 18 Polyester-based networks, 58-60 Polyester carbonates, 18 Polyester-ether block copolymers, 20 Polyester-ethers, 26... 

Molecular weights of polysaccharides in solution can also be measured by osmotic pressure and light scattering. Osmotic pressure yields the number average molecular weight, which can be usefully used with Mw from sedimentation equilibrium as a measure of polydispersity Preston and Wik [28] have done this for example with hyaluronic acid. The ratio Mw/Mn the polydispersity index is often given as a measure of polydispersity, and can be related to the width of a molecular weight distribution via the well-known Herdan [96] relation ... 

To run the residence time distribution experiments under conditions which would simulate the conditions occurring during chemical reaction, solutions of 15 weight percent and 30 percent polystyrene in benzene as well as pure benzene were used as the fluid medium. The polystyrene used in the RTD experiment was prepared in a batch reactor and had a number average degree of polymerization of 320 and a polydispersity index, DI, of 1.17. 

This trend is illustrated by the curves for the micro-mixed reactor in Figures 8 through 14. Also characteristic of the seeded, micro-mixed reactor is the convergence of the polydispersity index to 2 for a high degree of polymerization. This trend is illustrated to some extent in Table VI which presents the calculated degrees of polymerizations. 

The micro-mixed reactor with dead-polymer model was developed to account for the large values of the polydispersity index observed experimentally. The effect of increasing the fraction of dead-polymer in the reactor feed while maintaining the same monomer conversion is to broaden the product polymer distribution and therefore to increase the polydispersity index. As illustrated in Table V, this model, with its adjustable parameter, can exactly match experiment average molecular weights and easily account for values of the polydispersity index significantly greater than 2. 

A micro-mixed, seeded reactor will produce a broad polymer distribution with a high molecular weight tail and polydispersity index that approaches 2 at large degrees of polymerization. 

The effect of dead-polymer and by-passing on the micro-mixed reactor for the same degree of monomer conversion is to broaden the product polymer distribution and thus allow values of the polydispersity index much larger than 2. 

Silane radical atom transfer (SRAA) was demonstrated as an efficient, metal-free method to generate polystyrene of controllable molecular weight and low polydispersity index values. (TMSlsSi radicals were generated in situ by reaction of (TMSlsSiH with thermally generated f-BuO radicals as depicted in Scheme 14. (TMSlsSi radicals in the presence of polystyrene bromide (PS -Br), effectively abstract the bromine from the chain terminus and generate macroradicals that undergo coupling reactions (Reaction 70). 

Our theoretical studies [38] showed that the hyperbranched polymers generated from an SCVP possess a very wide MWD which depends on the reactivity ratio of propagating and initiating groups, r=kjk. For r=l, the polydispersity index where P is the number-average degree of polymerization. 

A way to narrow the MWD and to approach the structure of dendrimers is the addition of a small fraction of a/-functional initiator, to inimers [40,71]. In this process the obtainable degree of polymerization is limited by the ratio of inimer to initiator. It can be conducted in two ways (i) inimer molecules can be added so slowly to the initiator solution that they can only react with the initiator molecules or with the already formed macromolecules, but not with each other (semi-batch process). Thus, each macromolecule generated in such a process will contain one initiator core but no vinyl group. Then, the polydispersity index is quite low and decreases with / M /Mn l-i-l//. (ii) Alternatively, initiator and monomer molecules can be mixed instantaneously (batch process). Here, the normal SCVP process and the process shown above compete and both kinds of macromolecules will be formed. For this process the polydispersity index also decreases with/,but is higher than for the semi-batch process, M /Mn=Pn//. ... 

For SCVCP, the PDI is decreased in proportion to the comonomer ratio, y=[M]o/[I]o M, /Mn=l-I- /(/+ ) for y l [73]. The addition of a multifunctional initiator again affects the polydispersity index [72]. In the batch process it decreases with initiator functionality as M /Mn Pn/(y+l)/, similar to homo-SCVP. The effect is even more pronounced for the semi-batch process where the concentration of the inimer and the comonomer is kept infinitesimally low and M, /Mn=l-i-l//. This result is identical to the value obtained in homo-SCVP,that is, addition of comonomer does not decrease polydispersity any further. 

Table II shows that for SRM 706 good agreementis obtained between SEC/LALLS and conventional SEC sample My, and Rp values when the band-spreading correction was used. However, the NBS 706 polydispersity index (Ry/Rp) given by the supplier (ca. 2.1) does not agree with that 1.°) found here using the SEC/LALLS and conventional SEC techniques. Insensitivity of the LALLS detector to a small amount of low molecular weight material may account for a larger sample R however, this is not supported by the conventional SEC data. The reason for the discrepancy remains unclear.

Dynamical quantities do behave differently, however. This is shown for the diffusion constant in Fig. 5.18, to demonstrate that there is a systematic trend that can be clearly observed in the simulations the greater the polydispersity index p (or the parameter d) the larger the spread in the diffusion constant. 

A measure of the breadth of the molecular mass distribution is given by the ratios of molecular mass averages. The most commonly used ratio Mw/Mn — H, is called the polydispersity index. Wiegand and Kohler discuss the determination of molecular masses (weights) and their distributions in Chapter 6. 

The polydispersity index, M /M, values of comparable samples 78-C24 (V, plus ETCA) and 78-Elln(V0CL, no ETCA) in Figure 7C were 3.95 and 4.79, respectively. Another set of comparable... 

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