Number chain length distribution

N NCLD NMWD n na electrochemical reaction Molar flow rate, molar flux Number chain length distribution Number molecular weight distribution Number of stages in a CSTR battery, reaction order, number of electrons in electrochemical reaction, number of experiments Number of moles of A present kg - mol lb-mol... 

The weight chain-length distribution (WCLD) of the total free PS is obtained through multiplying each molecular species of the number chain-length distribution (in turn derived from the mass balance of Table 4.1) by its molar mass (mv ), yielding [30] ... 

Anionic polymerization. If one assumes rapid initiation, and no termination or chain transfer, the steady state number chain length distribution follows the Flory or Most Probable Distribution [7]. 

These are identical for the limiting values for the batch reactor, except that they require only the assumption of perfect mixing. Thus, while polydispersi-ties of 2.0 and 1.5 for termination by disproportionation and combination respectively represent unattainable minima for batch polymerization, these same values represent feasible operation in a well-mixed CSTR. Thus, the CSTR will give a narrower dead polymer number chain length distribution since it is possible to maintain a constant reaction environment at steady state. The effect of residence time distribution on the polydispersity is negligible since the lifetime of a single radical is far less than the average residence time. Likewise, for a copolymerization in a CSTR at steady state, the constancy of... 

Although the extent of BB could be determined with a variety of methods, a newly developed approach based on the use of samples with Poisson distribution was employed. Poisson (number chain length) distributions are characterized by one quantity, namely the location of the peak maximum, Lmax, which is easily accessible from experiment. Furthermore, it was shown by Chang and coworker that anionically prepared polystyrenes approach Poisson distributions. 

Number chain length distribution, n(L), calculated for homogeneous pulsed laser polymerization and Lo = 100. An ideal Poisson distribution centred at the same Lmax value Is included and the positions of the points of inflection are presented by circles and triangles. 

From several number chain length distributions simulated for pulsed laser polymerization for a great variety of experimental parametersl l which were converted to chromatographic dimensions and subsequently submitted to the infiuence of BB by applying the Tung equationl l correction functions were deduced. The comparison of the input values for the point of infiection and the maximum lead to the following correction functions ... 

Because two free radicals are leading to one dead polymer, J][P2p] = p/2 must hold true. With this in mind and insertion of equations 113, 114, and 117 and subsequent rearrangement gives the number chain length distribution for a single pulse experiment with termination by combination. 

According to the different termination modes the overall number chain length distribution can be calculated via... 

Definition of Moments Following the nomenclature given in the preceding and that of Ray [7], the A th moment of the number chain length distribution (NCLD) can be defined as ... 

This is a Hory distribution or most probable distribution and much broader (D>1) than the Poisson distribution (D=l) resulting from batch polymerization. The increase in molecular weight polydispersity is due to the fact that the chains are living, and so are directly impacted by the RTD. Recall that the polydispersity of the RTD for a CSTR is 2. For long residence time, approaches 1 and D becomes 2. Thus, the number chain length distribution (NCLD) takes on the breadth characteristics of the RTD, due to the living nature of the polymer chains. For comparison, one should recall that the lifetime of a free radical is 1-10 s. This is insignificant in comparison with the RTD and so that RTD has little to no effect on D in free radical polymerization. 

In the synthesis of block copolymers one is often in the situation for AB-diblock copolymers that M IM is known for the entire block copolymer and for the block synthesized first. The question arises what the value is for the B-block. Under some reasonable assumptions one can calculate this number. If the number chain length distributions for the two blocks are described by the continuous probability distributions Pi(x) and Piiy) where Pi(x) gives... 

The relation between a number chain length distribution, P(x), and the parameters normally used to describe molar mass distributions are given by ... 

Because the higher alcohols are made by a number of processes and from different raw materials, analytical procedures are designed to yield three kinds of information the carbon chain length distribution, or combining weight, of the alcohols present the purity of the material and the presence of minor impurities and contaminants that would interfere with subsequent use of the product. Analytical methods and characterization of alcohols have been summarized (13). 

Two different instrumental measurements were used to test the oxidation hypothesis GC and atomic absorption (AA). GC was used to determine the chain length distribution of the EO. From the GC results, an average chain length number was calculated. The gas chromatogram is shown in Fig. 21.1. In addition, headspace GC measurement of the gaseous compounds dissolved in the liquid ethoxylate was made and compared to typical or good product. Atomic absorption spectroscopy was used to determine the levels of several trace metals known to catalyze oxidation of fatty chemicals. 

SEC-MALLS and SEC-LALLS Coupled chromatography and light-scattering photometry that allows the determination of a number of important values along with chain length distribution, sedimentation equilibrium experiment Ultracentrifugation technique that allows chain length information to be determined. 

From these considerations an important conclusion follows immediately. The structure of a network is insufficiently described if only the number of networks chains and their length distribution is specified. In addition, knowledge of the topography of the chain length distribution or the spatial distribution of the chain length distribution is required. That means that in networks of the same chain length distribution the chains may still be quite differently distributed in space (Fig. 12). 

In general a solution will contain a distribution of chain lengths, characterized by the reduced chain length distribution p(y) (Eq, (5.36)) and the number averaged chain length N. As pointed out in Sect. 11.6, p(y) is invariant under the renormalization group. The other physical variables characterizing the solution can be expressed in terms of N. From Eqs. (11.38), (11.83) we recall the definitions... 

In a polymerization process the chain length distribution or molar mass distribution (MMD) is influenced by a large number of factors and conditions the kinetics of the reaction plays a very important role. The calculation of the resulting MMD is thus very complicated. For one of the simplest cases, a step reaction with polycondensation, a first-order approach is given here. As an example we take a hydroxy acid HO-R-COOH, which, upon condensation, forms the chain -[-O-R-CO-]n. 

The A plus Bj chains dominate the chain length distributions in amylopectins both by weight (58-74%) and by number (85-93%), compared with the sum of the long B chains (see Table 10.8). The A and Bj chains are believed to occur within one cluster, while the B2 and B3 chains transverse two and three clusters, respectively. The B4 chains and beyond are small in number and were not detected by the end group labeling protocol. However, the weight-percent of B4 chains with DPn above —50 (DPW —80) is measurable.217,224,225... 

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