Mass distributions

Moment of Inertia. Moment of inertia, I, is a property of the mass distribution of a body around an axis (I = Smr ). Its SI unit is kg-m. ... 

When a distribufion of particle sizes which must be collected is present, the aclual size distribution must be converted to a mass distribution by aerodynamic size. Frequently the distribution can be represented or approximated by a log-normal distribution (a straight line on a log-log plot of cumulative mass percent of particles versus diameter) wmich can be characterized by the mass median particle diameter dp5o and the standard statistical deviation of particles from the median [Pg.1428]

An interesting feature of these polymers is that they have a tetramodal molecular mass distribution which has been deliberately built in and which is claimed to improve processability. This is achieved by the following procedure ... 

When the styrene has been consumed, to give living polymers of narrow molecular mass distribution, more styrene and more catalyst is added. The styrene adds to the existing chains and also forms new polymer molecules initiated by the additional sec-butyl-lithium. 

Polymer. The polymer determines the properties of the hot melt variations are possible in molar mass distribution and in the chemical composition (copolymers). The polymer is the main component and backbone of hot-melt adhesive blend it gives strength, cohesion and mechanical properties (filmability, flexibility). The most common polymers in the woodworking area are EVA and APAO. 

Before we go back to Eq. (14.30), we shall evaluate the mass distribution function for the particles whose size distribution is of the form (14.33), i.e., normal probability size distribution. 

Using the same reasoning as with the particle number distribution above, we observe that if the x- and y-axes are provided with the nonlinear scales, n and tf, defined by Eqs. (14.34) and (14.35), the mass distribution m x)/m t) can be described by a straight line... 

Crystal number, area and mass Mass distributions... 

The mass distribution from the idealized MSMPR crystallizer is thus a Gamma function, as shown in Figure 3.8b. 

Figure 3.8 MSMPR mass distributions a) cumulative, (h) differential...

The ANN model had four neurones in the input layer one for each operating variable and one for the bias. The output was selected to be cumulative mass distribution thirteen neurones were used to represent it. A sigmoid functional... 

Statistical analyses were performed on each of the groups to yield, as data availability permitted, estimates of fragment-range distributions and fragment-mass distributions. The next sections are dedicated to the statistical analysis according to the Baker et al. (1978b) method. 

Figure 6.38. Fragment-mass distribution for event groups 2 and 3 (Baker et al. 1978b).

Figure 6.39. Fragment-mass distribution for event group 6.

FIGURE 2.4 Calibration curve of dextran on Sephacryi S-300 SF. Calibration curves were calculated from one chromatogram of a broad MWD reference sample using data for the molecular mass distribution as obtained by a calibrated gel filtration column ( , upper curve) and on-line MALLS ( ). The calibration curve was found useful for estimating the size of globular proteins. [Reproduced from Hagel et al. (1993), with permission.]... 

The broad pore size distribution of Sepharose makes it well apt for the analysis of broad molecular mass distributions of large molecules. One example is given by the method for determination of MWD of clinical dextran suggested in the Nordic Pharmacopea (Nilsson and Nilsson, 1974). Because Superose 6 has the same type of pore size distributions as Sepharose 6, many analytical applications performed earlier on Sepharose have been transformed to Superose in order to decrease analysis time. However, Sepharose is suitable as a first try out when no information about the composition of the sample, in terms of size, is available. 

Table 9.9 (6) gives some guidelines for proper SEC separation conditions when analyzing polymer standards with narrow molar mass distribution on a single 30-cm column. The conditions have to be adjusted when running industrial polymers (which are normally much wider in molar mass distribution). Depending on the width of the MMD, concentrations can be increased by a factor of 3 to 10 for such samples. As a general rule, it is advisable to keep the concentration of the injected solution lower than c [ j] < 0.2. 

In this stage of the investigation, poly(methyl methacrylates) (PMMAs) were selected as the polymeric probes of intermediate polarity. Polymers of medium broad molar mass distribution and of low tacticity (14) were a gift of Dr. W. Wunderlich of Rohm Co., Darmstadt, Germany. Their molar masses ranged from 1.6 X 10" to 6.13 X 10 g-mol. For some comparative tests, narrow polystyrene standards from Pressure Co. (Pittsburgh, PA) were used. 

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