Polydisperse sample

The use of hexafluoroisopropanol (HFIP) as an SEC eluent has become popular for the analysis of polyesters and polyamides. Conventional PS/DVB-based SEC columns have been widely used for HFIP applications, although the relatively high polarity of HFIP has led to some practical difficulties (1) the SEC calibration curve can exhibit excessive curvature, (2) polydisperse samples can exhibit dislocations or shoulders on the peaks, and (3) low molecular weight resolution can be lost, causing additive/system peaks to coelute with the low molecular weight tail of the polymer distribution... 

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. 

Linssen and de Vries [285] have examined 1 % di-f-butyl-p-cresol (DBPC) in low-MW poly(tetrahydro-furan) by means of DOSY (Figure 5.13). DOSY is a powerful tool for the analysis of polydisperse samples and complex mixtures, such as anionic surfactants. It is not to be expected that DOSY will rapidly become a standard tool in polymer/additive analysis. 

If a small polydisperse sample of powder is dissolved under sink conditions, then the dimensions, b, of the particle will decrease linearly with respect to time [33-37] ... 

For polydisperse samples, the weight average intrinsic viscosity [p])w is measured (Equation (8)) and the so-called viscosity averaged molar mass is obtained ... 

In a sedimentation equilibrium run, the stationary radial concentration profile, which is established after a few hours for a 1-mm column, is analyzed according to Equation (72) or, in case of polydisperse samples, Equations (74) or (75). Contrary to the sedimentation velocity experiment, the diffusion coefficient D is not required. 

If one does not use the short gradient pulse (SGP) approximation, the term A has to be substituted with (A 8/3). In the case of a mono-disperse system, the plot of ln(E) versus y2g282A is a straight line having the absolute value of the slope equal to the self-diffusion coefficient. For polydisperse sample, the signal intensity decay can be interpreted in terms of a distribution of diffusing species ... 

Classical Analysis. The classical analytical methods are even applicable for polydisperse samples and rest on the CLD (Sect. 8.5.3) and on Vonk s [189] distance distribution function (DDF) ([189-191] [101] p. 168)... 

For polydisperse sample, situation becomes a bit more complex, but a detailed analysis can yield average Molecular weights with different weightings such as > Mn, Mz which are useful measures of breadth of distribution. 

The spreading factor C is the variance of the chromatograms of the monodisperse polymer species, i.e. of the instrumental spreading fimction G(V,Vr), If O g varies linearly vd.th the retention volume of the monodisperse polymer, then<0 > is numerically equal to the interpolated value 0 (v) of the function (T (Vr) for the polydisperse sample at its mean elution volume. 

In order to determine g as a function of molecular weight, one approach is to use universal calibration with SEC analysis of molecular-weight polydisperse samples (31-33). For a multiarm (MA) branched material, the intrinsic viscosity of polymer eluting in v is ... 

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 ... 

If c and dc/dx are known as a function of x and the measurement is carried out in a theta solvent, the molecular weight M of monodisperse polymers can now be calculated precisely. If the solvent is not a theta solvent, the obtained value of M is an apparent molecular weight from which the true value can be calculated upon plotting 1/M vs. c and extrapolation to c —> 0. For polydisperse samples, one has to insert the average of dc/dx in the above equation, and the thus calculated molecular weight represents a weight-average,... 

Once the and coefficients are experimentally determined, they can be used to characterize an unknown monodisperse or polydisperse sample from the experimental determination of X under given experimental conditions (see Equation 12.48). 

Determining Calibration Curves frcm Polydisperse Samples. In conventional SEC interpretation, narrow molecular weight distribution standards are needed for calibration purposes. Nonlinear regression has enabled polydisperse scimples to be used. A variety of methods... 

If Equation (11) represents the relationship between [77] and M for a monodisperse polymer sample, then the intrinsic viscosity for a polydisperse sample containing weight fraction Wi with a molecular weight Mj will be... 

The synthesis of graft copolymers can be achieved either by "grafting from or by grafting onto processes.— The former method seems more versatile, but it does not allow an adequate structure control, and it often yields rather polydisperse samples. On the contrary "grafting onto" methods allow a precise control of the size and of the nunber of grafts, but it is only applicable to a limited number of systems. 

If intrinsic viscosity is used to evaluate the molecular weight of a polydisperse sample, the molecular weight so obtained is an average value. Equation (1.20) defined the viscosity average, which is the kind of average obtained. We are now in a better position to see how this comes about. 

When a low viscous solvent must be used in combination with a rather low molecular weight of the polymer, measurements are restricted to low /3-values, due to the discussed onset of turbulent flow. As in such a case the extinction angle % does not deviate very much from 45 degrees within the regime of laminar flow, it must be measured with a high absolute accuracy to furnish a reliable value for cos 2% or cot 2% [cf. eq. (3.42) or (3.44a)]. Measurements on a polydisperse sample become more reliable under such conditions due to the fact that cot 2 is increased by the polydispersity factor [eqs. (3.75a) and (3.83a)]. Examples for such a behaviour will be discussed in Section 3.8.3. 

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