Polymodal distribution

This can result in polymodality of the molecular weight distribution when the exchange between the chain carriers is slow and they lead to the independent growth. Polymodality of the MWD is observed indeed. This phenomenon has been explained by differences in diffusion of the short and long polymer chains, but multiplicity of the chain carriers seems to us to be a more probable explanation. 

Harding, J. P. (1949). The use of probability paper for the graphical analysis of polymodal frequency distributions. Journal of the Marine Biobgical Association, 28, 141-153. 

The function v(D) can be measured experimentally, or in some cases be simulated as normal, lognormal, etc. distribution. It is also possible to obtain polymodal distributions with several max-imums or some special kind of distribution. For example, the distribution of the particles formed by crashing is frequently described by a Rosin-Rammler distribution [51,52] as... 

Polymerizations often afford polymodal product molecular weight distributions,18 with typically a low molecular weight fraction of several hundred daltons (fraction I), an intermediate fraction of about 4,000 (fraction II) and then a high molecular weight fraction of 10s or 106 (fraction III), though the relative proportions of the fractions depend... 

FIGURE 5.1 Cluster model of amylopectin. A and B denote nomenclature of branch chains, 0=reducing end, c.l. = chain length in degree of polymerization. Reprinted from Carbohydrate Research, Vol. 147, Hizukuri (1986), Polymodal distribution of the chain lengths of amylopectin, and its significance, Pages 342-347, with permission from Elsevier. 

Hizukuri, S. (1986). Polymodal distribution of the chain lengths of amylopectin, and its significance. Carbohydr. Res. 147,342-347. 

Figure 6 shows calibration curves for three other two column combinations, each representing 30,000 to 40,000 plates per set. The 10 A° plus 10 A° curve can be interpreted to show a deficiency in relative pore population in the range equivalent to about 50,000 to 600,000 molecular weight. The other two, properly calibrated, can conceivably be used for determination of molecular weight distributions. However, utility for resolution of specific polymodal mixtures is too difficult to assess from calibration curve alone. How much curvature of a calibration curve translates into utility or non-utility Calibration curves indicating pore size populations all have the same shape for given column combinations whether the plate count level is 5000 plates or 20,000 plates or 80,000 plates. 

Broad or Polymodal Distribution of Chain Lengths. A given chain is characterized by its maximum (full) extension ratio ... 

The polymodal distribution of unit chains and their proportions in amylopectin support the cluster model. The cluster model of amylopectin suggests a repeat structure made up of one population of A chains, another of relatively short B chains (Bj), and three populations or more of long B chains (B2, B3, B4, B5). The various populations of chains appear to be separated with a periodicity of 12, so that A chains have been assigned to the group of chains with DPn 6-12, B] chains = DP 13-24, B2 chains = DP 25-36 and (Bn)n>3 to chains > 37.225 The weight-percent... 

Data with a polymodal distribution If we give a series of patients a standard oral dose of the anti-tuberculosis drug isoniazid, obtain a blood sample from each individual 6 h later and determine the isoniazid concentrations of those samples, the results will probably look like Figure 3.1. The data are bimodal, because the metabolism of isoniazid is genetically controlled and we all fall into one of two groups - fast or slow metabolizers. The fast metabolizers form the cluster at the low end of the concentration scale and the slow metabolizers form a distinct group with higher levels. 

Pore structure can markedly affect char reactivity. Coals in general are highly porous with a polymodal pore size distribution. Pores normally are classified into macropores (>500 A in diameter), transitional pores (20-500 A in diameter), and micropores (<20 A in diameter). Upon pyrolysis, the pores in the coal open up, but the, char still contains microporosity. Coal chars in general, and lignitic chars in particular, retain coal s polymodal pore distribution. Surface areas of coal chars are in the range 100-800 m2/g. Most of this surface area and, therefore, most of the active surface reside inside the pores, so accessibility of reactive gases to active sites is very important. 

Most of the catalytic applications of carbon materials deal with their use in processes carried out under dynamic conditions which are very different to those of static systems. In such processes the accessibility to the catalytically active sites or chemical functionalities is especially important because of the short contact times between the reactives and the carbon catalyst and the polymodal distribution of pores that they present [1]. A large proportion of their surface area and chemical surface groups resides in micropores [2] of diameters very close to the molecular dimension of the reactives and/or the products and so the reaction kinetics may be strongly diffusion controlled. 

Genuinely bimodal or polymodal distributions may result from the combination of two or more unlimited distributions, indicating that more than one underlying population is being sampled (Fig. 40.5). An example of a bimodal distribution is the height of adult humans (females and males combined). 

Reddish brown (SYR 3/6 to 5/8) sediments are present almost throughout Level C, mostly in the epiphreatic passage (Fig. 5) but also within the enlarged joint that extends upwards beyond the flat roof. The sediments are highly uniform, and consist of abundant angular silt-sized quartz in a reddish clay matrix. Laser particle size analyses of sediment from Bone Chamber (Fig. 6) show that the grain size distribution is polymodal the coarsest grain size (medium-coarse silt) comprises only a small proportion of the... 

Gel permeation chromatography indicates a polymodal polydispersity with a broad molecular weight distribution. Currently it is not possible to specify the definite values of the average molecular weights due to a lack of comparable standards. 

Bimodal or polymodal distributions have more than one peak and may indicate that the distribution is nonhomogeneous because of the mixing of two or more distributions. If so, the criteria used to select... 

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