Monodisperse sample

Plate count should always be tested with a monodisperse sample of low molecular weight. Polymers can also be used, but they show much lower plate counts because their diffusion coefficients are much smaller than those of low molecular weight compounds. 

The function C(r/r0) can be determined experimentally from the degradation yield curve of a truly monodisperse sample since the function C(r2/ro) is simply... 

Anionic pol5Tnerizations make the molecular weight standards that are used to calibrate size-exclusion chromatographs. Equation (13.38) predicts PD = 1.001 at In = 1000. Actual measurements give about 1.05. The difference is attributed to impurities in the feed that cause terminations and thus short chains. Also, the chromatograph has internal dispersion so that a truly monodisperse sample would show some spread. Even so, a PD of E05 is extremely narrow by pol5Tner standards. This does not mean it is narrow in an... 

Calibration refers to characterizing the residence time in the GPC as a function of molecular weight. Axial dispersion refers to the chromatogram being a spread curve even for a monodisperse sample. A polydisperse sample then is the result of a series of overlapping, unseen, spread curves. 

One possibility is that although averages for polystyrene standards require correction, those for PMMA would not According to symmetrical axial dispersion theory (5) the correction depends upon both the slope of the calibration curve (different for each polymer type) and the variance of the chromatogram of a truly monodisperse sample. Furthermore, the calibration curve to be utilized can be obtained from a broad standard as well as from monodisperse samples. The broad standard method may itself incorporate some axial dispersion correction depending upon how the standard was characterized. 

Resolution factor (= l./(2 x variance of chromatogram of truly monodisperse sample))... 

The size of a spherical particle is readily expressed in terms of its diameter. With asymmetrical particles, an equivalent spherical diameter is used to relate the size of the particle to the diameter of a perfect sphere having the same surface area (surface diameter, ds), the same volume (volume diameter, dv), or the same observed area in its most stable plane (projected diameter, dp) [46], The size may also be expressed using the Stokes diameter, dst, which describes an equivalent sphere undergoing sedimentation at the same rate as the sample particle. Obviously, the type of diameter reflects the method and equipment employed in determining the particle size. Since any collection of particles is usually polydisperse (as opposed to a monodisperse sample in which particles are fairly uniform in size), it is necessary to know not only the mean size of the particles, but also the particle size distribution. 

The scaling exponent a can be related to the particle shape. One finds a = 2,0, 0.5, and 0.8 for a thin rod, solid sphere, ideal chain, and swollen chain, respectively. For most polymers K and a have been tabulated [23]. For a monodisperse sample Equation (36) can be used for a crude determination of the molar mass ... 

Strictly speaking, monodisperse samples would be required for the determination of the Mark-Houwink coefficients. Since, however, the poly-dispersities of the nine individual fractions are only moderate (Mw/Mn 2) and since both Mw and [tj] are measured as weight averages with the same statistical weights, the error introduced by the incorrect treatment of the polydispersity could be neglected. 

The core first method has been applied to prepare four-arm star PMMA. In this case selective degradation of the core allowed unambiguous proof of the star structure. However, the MWD is a little too large to claim that only four-arm star polymers are present [81], Comb PMMAs with randomly placed branches have been prepared by anionic copolymerization of MMA and monodisperse PMMA macromonomers [82], A thorough dilute solution characterization revealed monodisperse samples with 2 to 13 branches. A certain polydispersity of the number of branches has to be expected. This was not detected because the branch length was very short relative to the length of the backbone [83]. Recently, PMMA stars (with 6 and 12 arms) have been prepared from dendritic... 

However, the choice of c as reference is not advisable, because R is a z-average while is a weight average. Even for monodisperse samples the various definitions are not equivalent. Therefore c is a quantity that strictly de-... 

Figure 37. The effect of change in molecular weight at constant dispersity on the e-beam sensitivity of poly(p-chlorostyrene). The very high contrast was achieved by fractionating to obtain nearly monodispersed samples.

Identity is only given for monodisperse samples, i.e., polymers whose macromolecules have all the same molar mass. Moreover, might be equal to if the exponent a in the [q] to M relation is equal to 1. 

The above considerations are valid only for monodisperse samples of rather low molecular weight. When characterizing polydisperse samples, all components i having different molecular weights M, and concentrations c, scatter independently from each other. Thus one obtains the following equation ... 

The above ideas have been applied to several different sizes of M0S2 nanoparticles. Specifically, relatively monodisperse samples of 3.5-, 4.5-, and 8-nm particles are easily accessible. The absorption spectra of these sizes of M0S2 nanoparticles are collected in Fig. 5. 

It is well known that all elution curves, obtained by diverse chromatographic techniques, show the following common feature They cannot be reduced to a vertical straight line1 even if a strictly monodisperse sample is injected into the column, but always show a bell-shaped curve with a finite width, evidently not originating in the MWD of the injected sample. This experimental result can be explained by an axial acceleration of the injected species by the stream of the column liquid, leading... 

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