Molar-mass distributions

In this figure we have introduced the fact that in a particular sample the measured molar mass is an average. Here we have used a number average defined as 

For a typical condensation polymerisation, the molar mass distribution function is generally in the range 3—20, but is sometimes even greater. On the other hand, in vinyl polymerisation the values typically wiU be in the range 1.05—3.0. The narrowest molar mass distributions are observed with anionic and certain cationic initiated polymerisations. Molar mass effects are observed with aU polymer systems but they are more important in the physical properties of amorphous polymers than in their crystalline analogues. 

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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. 

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. 

Huber, A. (1992). In Analysis of Polymers/Molar-Mass and Molar-Mass Distribution of Polymers, Polyelectrolytes and Latices (W.-M. Kulicke, ed.), Hiithig Wepf Verlag, 61, 248. 

The molar mass distribution of hyperbranched polymers is, therefore, always larger than diat of titeir linear homologues and tends toward infinity when conversion becomes close to 1. The use of a B3, comonomer, acting as a chain limiter and core molecule, helps in reducing polydispersity and controlling the molar mass of the final polymer.197... 

As already discussed (Section 2.2.1.3), interchange reactions are also implicated in the formation of random copolyesters exhibiting the most probable molar mass distribution when polyester blends are melt mixed. They are also involved in the randomization of block copolyesters taking place in the melt upon heating.2,m 211... 

The effect is that the polymer molecules are separated into fractions. These are measured by an appropriate detector located at the end of the column, and the detector records the response as a peak on a chart. The chromatogram thus consists of a series of peaks corresponding to different elution volumes, the shortest elution volume being due to the largest molar mass polymer molecules within the sample. Details of the molar mass distribution can be determined from the size and number of the individual peaks in the chromatogram. An example of a gel permeation chromatogram is shown as Figure 6.4. 

The viscosity level in the range of the Newtonian viscosity r 0 of the flow curve can be determined on the basis of molecular models. For this, just a single point measurement in the zero-shear viscosity range is necessary, when applying the Mark-Houwink relationship. This zero-shear viscosity, q0, depends on the concentration and molar mass of the dissolved polymer for a given solvent, pressure, temperature, molar mass distribution Mw/Mn, i.e. 

The experimental zero-shear viscosities obtained for polystyrene (PS) of different molar masses (with a very narrow molar mass distribution Mw/Mn=1.06-1.30) and different concentrations in toluene and fra s-decalin are plotted as log r sp vs. log (c- [r ]) in Fig. 6. 

Table 1. Characterisation data and viscosities, ri0, of polystyrene (molar mass distribution Mw/Mn<1.3) in toluene at 25 °C. Theoretical viscosities, ri0(theor), were calculated from Eq. (14). In the last column A represents the relative deviation of ri0(theor) from T 0(exp) ...

Polymers in solution or as melts exhibit a shear rate dependent viscosity above a critical shear rate, ycrit. The region in which the viscosity is a decreasing function of shear rate is called the non-Newtonian or power-law region. As the concentration increases, for constant molar mass, the value of ycrit is shifted to lower shear rates. Below ycrit the solution viscosity is independent of shear rate and is called the zero-shear viscosity, q0. Flow curves (plots of log q vs. log y) for a very high molar mass polystyrene in toluene at various concentrations are presented in Fig. 9. The transition from the shear-rate independent to the shear-rate dependent viscosity occurs over a relatively small region due to the narrow molar mass distribution of the PS sample. 

The retention behaviour of oligomers in RPLC/-NPLC-APCI-MS (35 to 1500 Da) has been described [637]. In isocratic chromatography only a limited number n of oligomers can be separated, as the retention usually increases excessively at high n, so that gradient elution is necessary for successful separation of samples with broader molar mass distribution. RPLC-APCI-UV/QITMS was used for the analysis of accelerators (CBS, MBT, MBTS, BT) extracted... 

SEC-GC-FID, according to Figure 7.40, has been used to carry out the simultaneous determination of the polymer average molecular masses and molar mass distribution and the concentration of additives [984]. The effluent was split and adsorbed on PTV packing material before GC analysis. The choice of PTV... 

For a free-radical polymerization and a condensation polymerization process, explain why the molar mass distribution of the polymer product will be different depending on whether a mixed-flow or a plug-flow reactor is used. What will be the difference in the distribution of molar mass ... 

Due to the fact that different end groups can be formed during the polycondensation, the reaction products may exhibit a functionality-type distribution in addition to the molar mass distribution. Although SEC is suitable to analyze the molar mass distribution, it does not yield information on different end groups. For the determination of the functionality-type distribution, other types of liquid chromatography must be used. 

A major challenge in using interactive chromatography for polyamides is to find a suitable mobile phase (Mengerink et al., 2001, 2002 Weidner et al., 2004). Polyamides form semicrystalline morphologies that limit the solubility in organic solvents. Besides hot phenol, formic acid, and trifluoroethanol (TFE) (Mori and Barth, 1999), 1,1,1,3,3,3-hexafluoroisopropanol (HFIP) represents a suitable solvent for polyamides (Chen et al., 2002). These solvents are mainly used to analyze the molar mass distribution of polyamides by SEC. 

Reaction mechanisms and molar mass distributions The molar mass distribution of a synthetic polymer strongly depends on the polymerization mechanism, and sole knowledge of some average molar mass may be of little help if the distribution function, or at least its second moment, is not known. To illustrate this, we will discuss two prominent distribution functions, as examples the Poisson distribution and the Schulz-Flory distribution, and refer the reader to the literature [7] for a more detailed discussion. 

SEC or gel permeation chromatography (GPC) is one of the widely used chromatographic techniques [56,57]. In contrast to the already discussed colligative and scattering methods it is not an absolute method and requires proper calibration with some known polymer standards. One obtains not only the average molar masses (M , Mw, Mz) but the complete molar mass distributions. 

In addition to the determination of molar mass distributions and various molar mass averages there are many experiments, requiring sometimes sophisticated data evaluation, that can be carried out with an analytical ultracentrifuge. Examples are the analysis of association, the analysis of heterogeneity, the observation of chemical reactions, and protein characterization, to mention only a few. A detailed discussion is beyond the scope of this article, but there is excellent literature available [77-79,81,87-89]... 

Figure 16 SEC molar mass distribution of poly(p-phenylene) P3 in THF after universal calibration based on Equations (31) (dashed) and (36) (dotted) and with polystyrene calibration (solid line). 

Many polymer properties can be expressed as power laws of the molar mass. Some examples for such scaling laws that have already been discussed are the scaling law of the diffusion coefficient (Equation (57)) and the Mark-Houwink-Sakurada equation for the intrinsic viscosity (Equation (36)). Under certain circumstances scaling laws can be employed advantageously for the determination of molar mass distributions, as shown by the following two examples. 

In Ref. [107] it has been demonstrated how, based on the scaling law for the diffusion coefficient, molar mass distributions can be calculated from time correlation functions obtained from scattering experiments. 

In order to calculate the molar mass distribution, the scaling law (Equation (52))... 

In Ref. [107] the procedure above has been employed for the measurement of the molar mass distribution of a broad molecular weight polystyrene, obtained by radical polymerization with ethylacetate as solvent. The scaling parameters for this polystyrene in this marginal solvent have been determined to be a 2.8 x 10-4 cm2/s and b 0.52 [107]. The upper curve in Figure 17 shows the resulting molar mass distribution in comparison with the one obtained by SEC. 

Figure 17 Molar mass distributions of polystyrene in ethyl acetate obtained by dynamic light scattering (photon correlation spectroscopy, PCS) and TDFRS with short and long exposure time tp. The dashed curves represent the distribution as determined by SEC. Reproduced with permission from Rossmanith and Kohler [107]. Copyright 1996 American Chemical Society.

Table 4 Molar mass averages (in kg/mol) calculated from the molar mass distributions obtained by SEC, short and long exposure TDFRS, and DLS...

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