Function polydispersity index

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. 

The development of mass spectroscopic techniques such as matrix assisted laser desorption (MALDI) and electrospray mass spectrometry has allowed the absolute determination of dendrimer perfection [7,8], For divergent dendrimers such as PAMAM and PPI, single flaws in the chemical structure can be measured as a function of generation to genealogically define an unreacted site of or a side reaction producing a loop at a particular generation level. Mass spectromet-ric results on dendrimers, not only demonstrate the extreme sensitivity of the technique, but also demonstrate the uniformity of the molecular mass. The polydispersity index of Mw/Mn for a G6 PAMAM dendrimer can be 1.0006 which is substantially narrower than that of living polymers of the same molecular mass [7],... 

First Order Stoppage Alone. If stoppage is determined solely by a first order process, such as transfer, the foregoing analysis predicts a nearly exponential distribution function. The polydispersity index must then be very close to 2.00. The same result is obtained for bulk and solution polymerizations dominated by chain transfer. Compartmentalization thus has no major effect on the polydispersity of the polymer produced, as was recognized by Gerrens (11), if the stoppage process is dominated by chain transfer. This contrasts with the significant effects of compartmentalization if bimolecular events dominate termination. 

It can be established by the following reasoning. If n = %, each particle contains at most one free radical. Growing chains in the latex particles can thus either grow or be terminated instantaneously by entrant free radicals. These mutually exclusive kinetic events immediately prescribe the Flory most probable distribution function for the growing chains (12) this is an exponential distribution function with a polydispersity index of 2.00 (13). 

Disproportionation Alone. Figure 2 displays the polydispersity index as a function of n- for termination by disproportionation. Again, these have been calculated by a full analysis ( 1). ... 

Figure 1. Polydispersity index of the polymer produced in Interval II of an emulsion polymerization terminated solely by combination as a function of the average number of free radicals per particle...

A polymerization that provides a transition into a discussion of gelation is the condensation of an excess of A-B with a small amount of an /-functional monomer, R-A/, that contains / equivalent functional groups of Type A, but no functional groups of Type B.[3 Linear chains are obtained when / is 1 or 2, but multichain condensation polymers are produced when/>2. At high conversion the polydispersity index depends only on/. 

Table 4 Polydispersity index as a function of initiator concentration and sonication time, with hexadecane as costahUizer and MMA as monomer ([140])...

In the case of polydisperse polymers, the limiting compliance increases strongly with the broadness of the distribution of molecular weights. The limiting comphance is not, however, a simple function of the polydispersity index, because its value depends on the shape of the distribution itself. There is indeed no simple correlation with any molectilar weight moments (averages), and moleciilar models will be really helpfid to describe the elasticity of the melt. 

Fig. 10.3. Effects of polymer capping ratios on quantum dot properties, (a) Fluorescence quantum yield blue curve) and polydispersity index red curve) of 2.5 nm CdTe quantum dots as a function of molar capping ratio. Polydispersity indices were calculated from gel filtration chromatograms, (b) Photostability data at various capping ratios (MCR = 1.5, 1.0, or 0.5) and in the absence of polymer (MCR = 0)...

Moreover, rotational rheometers can be used in dynamic oscillatory mode, frequency sweep, to assess the elastic G module as well as the viscous G" module and the correlated phase angle 6, as a function of the frequency co. G and G" allow to study the viscoelastic behaviour of HA macromolecules. Fig. (15) shows the frequency sweep curves (G, G", and tg(5) vs. the frequency co) for an HA sample (Mw=1350 kDa, polydispersity index D=1.6, concentration c = 2%) at 20 °C. 

How does this polydispersity index depend on functionality / at a given... 

Although in controlled radical polymerisation, termination reactions cannot be excluded completely, they are limited in their extent and consequently the molecular weight is controlled, the polydispersity index is small and functionalities can be attached to the macromolecules. These features are indicative of the realisation of well-defined polymer architectures such as block copolymers, starshaped and comb-shaped copolymers. 

The theoretical description in terms of spherical harmonics also yields a relation between the size polydispersity index p of the microemulsion droplets and the bending elastic constants [43]. The quantity p is accessible by SANS [51, 52, 59-61]. For polydisperse shells as obtained by using deuterated oil and heavy water for the preparation of the microemulsion (contrast variation), one can account for the droplet polydispersity by applying an appropriate form factor, e.g. containing a Gaussian function to model the size distribution [52, 59, 62]. A possible often-used choice is the following form factor... 

The analysis of the light scattering data using CONTIN also allows for a determination of the size polydispersity of the microemulsion droplets, because all the moments u = / pm G(r)rndr which describe the distribution function G(T) are computed (for details see Ref. [98]). The polydispersity index is obtained from... 

Polydispersity of simple bile salt micelles can only be assessed by modem QLS techniques employing the 2nd cumulant analysis of the time decay of the autocorrelation function [146,161]. These studies have shown, in the cases of the 4 taurine conjugates in 10 g/dl concentrations in both 0.15 M and 0.6 M NaCl, that the distribution in the polydispersity index (V) varies from 20% for small n values to 50% for large n values [6,146]. Others [112] have foimd much smaller V values (2-10%) for the unconjugated bile salts in 5% (w/v) solutions. Recently, the significance of QLS-derived polydispersities have been questioned on the basis of the rapid fluctuation in n of micellar assemblies hence V may not actually represent a micellar size distribution [167-169]. This argument is specious, since a micellar size distribution and fast fluctuations in aggregation number are identical quantities on the QLS time scale (jusec-msec) [94]. 

Fig. 6.32 Comparison of the polydispersity index (DPI) obtained in a multilamination micromixer (open symbols) and in a tube reactor (filled symbols) as a function of the radial Peclet number. (Courtesy of the Royal Society of Chemistry [48].)...

Figure 9. Polydispersity index, PDl, as a function of CLDT exponent a for disproportionation, combination and X = 0.333 ( mixed ), as indicated.

Aldehyde end-functionalized DEH-PPV 1 is obtained easily by Siegrist condensation with low polydispersity index (PDK1.3). It can be convert in hydroxyl end-functionalized PPV 2 after reduction of the aldehyde moiety. PPV 1 is converted into NMRP macro-initiator 3 by reacting the Grignard reagent of the appropriated alkoxyamine. ATRP macro-initiator 4 is obtained by a simple esterification on the hydroxyl end-functionalized PPV 2. 

Figure 7.14. Coordinates of the maximum of the Gross frequency relaxation function, Hq (top) and (bottom), vs., respectively, the polydispersity index, M,/M, and the zero shear viscosity, T , a measure of the molecular weight [Utracki and Schlund, 1987].

Figure 2. Autocorrelation function of the end-to-end vector for a C-78 polymethylene melt (T = 450 , P = 1 atm) from different algorithms. The system has a uniform length distribution with polydispersity index of 1.08. For the MC runs, a common base combination of moves was used that consists of reptations (6%), rotations (6%), flips (6%), concerted rotations (32%), and volume move (0.5%). The rest of the moves were configurational-bias CB (49.5%, long dashed line), end bridge (49.5%, full line), and half CB (25%), half end bridge (24.5%, dotted line). The short dashed line corresponds to a NVM molecular dynamics simulation of the same system. The CPU time refers to an IBM/RS600 3CT machine [63].

FIGURE 10.9 Polydispersity index (PDI) of poly(4-vinylbenzocyclobutene)as a function of conversion with E = 8/cgT. The PDI value decreases with conversion and is close to 1. 

Figure 8.1 The first example of a living cationic polymerization of isobutene using cumyl acetate as initiator and BCI3 as activator in dichloromethane at —30°C. Number-average molar mass, polydispersity index (numbers in the plot), and number of polymer chains (inset) are reported as a function of the mass of PIB obtained. Source Reprinted with permission from Faust R, Kennedy JP. J Polym Sci A Polym Chem 1987 25 1847 [28]. Copyright 1987 John Wiley and Sons, Inc.

One polydispersity index which measures the width of the distribution function is the ratio /. For many addition polymers, this polydispersity index lies in the range 1 5-2 0 but other polymers, especially those prepared by Ziegler-Natta catalysts, may have a polydispersity index that is an order of magnitude greater. The polydispersity index is 1-0 for a monodisperse (>ol3mier. Anionic polymerizations can lead to polydispersity indices close to unity. 

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