Apparent weight distribution function

The simplest way computationally of obtaining a sedimentation coefficient distribution is from time derivative analysis of the evolving concentration distribution profile across the cell [40,41]. The time derivative at each radial position r is d c r,t)/co /dt)r where cq is the initial loading concentration. Assuming that a sufficiently small time integral of scans are chosen so that Ac r t)/At= dc r t)ldt the apparent weight fraction distribution function g (s) n.b. sometimes written as (s ) can be calculated... 

The short-term, in situ bioavailability of organic matter is a complex function of intrinsic factors, such as the chemical characteristics of the DOM itself, which include of molecular weight distribution, the nutrient contents, and the relative contribution of broad classes of compounds and are determined by the source and the diagenetic state of the matter (Amon et al., 2001). The utilization of DOM and its apparent lability are also affected by extrinsic factors regulating the metabolism of bacteria and, therefore, the utilization of the organic matter by the bacterial community. These factors include temperature, the availability of inorganic and trace nutrients, trophic interactions within microbial food webs, and even the... 

Because the interfering amine functionality was replaced with an imine, it was possible to analyze each fraction for molecular weight distribution by GPC using either polystyrene or specially synthesized polydimethylsiloxane calibration standards. The low molecular weight cyclic content of the early fractions was determined by HPLC and the higher cyclics (Dg, D7, Dg) were identified by GC-MS. The absence of amine functionality in the early fractions, which is indicative of the presence of cyclics, was also confirmed by FT-IR. It is apparent, then, that complete characterization of the fractionated polymer was no small task, especially in light of the fact that even though supercritical fluid fractionation can process initial sample sizes of 20-25 g, some of the fractions were only 0.5-1.0g in size, and therefore the workup required substantial effort and care. 

To deduce the weight distribution of the molecular weight, the chemical composition, and/or the size, Rh, from the distribution function G(T), we have to know the relationship of Rh to M and / as well as the relationship between M and / We need good models for these relations. To solve the At-/relation, the contrast change with different solvents may be helpful. An example of the trials for copolymers is as follows. We assume that the chemical composition is the same for molecules having the same molecular mass, so that we can write the weight fraction, w, and the refractive index increment as a function of M only, that is, w(M) and v(M), respectively. Furthermore, if eqn [99] holds for the copolymer, then we can evaluate the apparent weight fraction, u/app(M), expressed as... 

Apparent Density. This term refers to the weight of a unit volume of loose powder, usually expressed in g/cm (l )- The apparent density of a powder depends on the friction conditions between the powder particles, which are a function of the relative surface area of the particles and the surface conditions. It depends, furthermore, on the packing arrangement of the particles, which depends on the particle size, but mainly on particle size distribution and the shape of the particles. 

Termination of these polymerizations with dichlorodimethylsilane followed by hydrolysis of the protecting group generated polymeric diamines with functionalities of 1.7-1.9 and relatively broad MW distributions (1.49-2.22). The authors considered that the titrimetric method was less reliable for the higher molecular weight polymers and perhaps is a reason for the apparent ineficiency of this amination procedure. A major limitation of this method is the fact that the initiator is insoluble in hydrocarbon solvents and therefore most of the diene polymerizations were carried out in mixtures of hexane and ether which has a deleterious effect on the microstructure of the diene polymers. 

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