Length distributions

If we consider the chord length distribution, we can express the alternating chords and I2 as ... 

Analysis of tlie global statistics of protein sequences has recently allowed light to be shed on anotlier puzzle, tliat of tlie origin of extant sequences [170]. One proposition is tliat proteins evolved from random amino acid chains, which predict tliat tlieir length distribution is a combination of the exponentially distributed random variable giving tlie intervals between start and stop codons, and tlie probability tliat a given sequence can fold up to fonii a compact... 

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). 

Palm oil[8002-75-3] is derived from the fleshy fmit of the palm tree rather than the nut as with palm kernel oil. Palm oil has a longer chain length distribution than palm kernel oil and provides properties and compositions more similar to tallow than to other vegetable oils (see Table 1). 

Fig. 6. Fiber length distribution for (a) a long sample (group 4) and (b) a short sample (group 7) of chrysotile successive length classes separated by 50 p.m.

Standard Test Method for Length and Length Distribution of Cotton Fibers (Array Method)," ASTM D1440-90, Annual Book ofASTM Standards, Vol 07.01., ASTM, Philadelphia, Pa., 1991, pp. 390—395. 

In the Lasentec instruments a chord-length distribution is generated, from a rotating infrared beam, and this is converted to a size distribution. Since highly concentrated systems can be interrogated this system can be used for on-hne size analysis. 

L. Schafer. Chain length distribution in a model of equlilibrium polymerization. Phys Rev B 46 6061-6070,1992. 

M. S. Turner, M. E. Cates. The relaxation spectrum of polymer length distributions. J Physique 57 307-316, 1990. 

Therefore the a(1 6) branching linkages were hydrolized selectively. The resulting constituting chain-length distribution was determined on a semipreparative Sephacryl S-200/S-400/S-500/S-1000 (12 -I- 55 -I- 66 -I- 135 X 1.6 cm)... 

It is basically a fractionation process that depends not only on molecular size, but also on chemical composition, stereo-configuration, branching, and crosslinking. For multicomponent systems, fractionation with different ion polymolecularity, chemical heterogeneity and sequence length distribution, solubility or elution fractionation is of primary importance. Therefore, gel permeation chromatography or size exclusion chromatography is used as an important tool for the characterization of PBAs. 

The fiber length distribution is determined by the following three stages in processing ... 

A discontinuous fiber composite is one that contains a relatively short length of fibers dispersed within the matrix. When an external load is applied to the composite, the fibers are loaded as a result of stress transfer from the matrix to the fiber across the fiber-matrix interface. The degree of reinforcement that may be attained is a function of fiber fraction (V/), the fiber orientation distribution, the fiber length distribution, and efficiency of... 

It is also useful to define the moments of the chain length distribution. The yth... 

A given chain will undergo i-1 propagation steps (each with probability 0) before terminating (with probability 1-0). Thus, if termination is wholly by chain transfer or disproportionation, the chain length distribution is given by cq. 17 (Figure 5.1) ... 

In conventional radical polymerization, the chain length distribution of propagating species is broad and new short chains are formed continually by initiation. As has been stated above, the population balance means that, termination, most frequently, involves the reaction of a shorter, more mobile, chain with a longer, less mobile, chain. In living radical polymerizations, the chain lengths of most propagating species are similar (i.e. i j) and increase with conversion. Ideally, in ATRP and NMP no new chains are fonned. In practice,... 

It has been shown that equivalent information can be obtained by analysis of logfnumbcr chain length distribution) plots (the log CLD method)."4" 7 For the case where termination is wholly by disproportionation or chain transfer, it is possible to show that (eq. 6) applies ... 

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