Polymer Characterization — Molar Masses

Practically, polymers with molar masses between 2 x 104 and 2 x 106 g/mol can be characterized by membrane osmometry, but measurements of Mn <104 g/mol have also been reported with fast instruments and suitable membranes [16]. The lower limit is set by insufficient retention of short polymer chains. Above M 2 x 106 g/mol, the osmotic pressure, which is proportional to Mr1, is too low for a reasonable signal-to-noise ratio. An advantage of the low molar mass cut-off is that impurities with a very low molar mass can permeate through the membrane and, hence, do not contribute to the measured osmotic pressure. Their equilibration time may, however, be different from that of the solute, leading to complex time-dependent signals. 

Non-ionic associative thickeners are usually poly(ethylene oxide) polymers whose molar mass has been extended 1 some linking group and in which hydrophobic blocks have been incorporated, usually by the same linking group. Urethane linking groups are most commonly used, and this type is now commonly called a HEUR (hydrophobe-modified ethylene oxide urethane) thickener. Because they can provide well-characterized model systems, academic research has ccxicentrated on HEUR thickoiers with tominal hydrophobes, but commercial materials may contain either or both tominal and internal hydrophobes. 

Only few data are available on the physical properties of chitin in solution due to the difficulties in dissolving this polymer. Solubilization would be necessary to characterize molar mass but also for processing because chitin cannot be processed in molten state. The cohesion of this polymer is too large due to stabilization by a dense hydrogen bond network and thermal decomposition instead of melting occurs upon heating. 

Characterization of Synthetic Polymers 2 Molar Mass Measurement... 

In many cases distribution functions are determined experimentally the characterization of petroleum fractions by true-boiling-point distillation or gas-chromatographically simulated distillation, and the characterization of polymers by gel-permeation chromatography. In principle, the integrals of continuous thermodynamics may be directly solved based on these experimentally determined distribution functions. However, this approach delicate numerical analyses and the assumption the complete distribution function has been obtained by experiment clearly this is no the case, for example, for some polymers only molar-mass averages are determined. Thus, there are numerous cases where smoothed or analytical distribution function provides more reliable phase equilibrium calculation than those obtained by use of the experimentally determined distribution function. When the integrals of continuous thermodynamics possess analytical solutions considerably numerical simplification is afforded and this is one motive for the desire to have analytical expressions for the distribution function. 

A theoretical prediction of water-soluble polymer solutions is difficult to obtain due to their ability to build up aggregations and associations. A prediction of the viscosity yield is much easier to observe for solutions of synthetic polystyrene due to its simple solution structure. These solutions have been well characterized in other studies [19-23] concerning their chemical composition, molar mass and sample polydispersity. 

Polymerization reactions. Polymers are characterized mainly by the distribution of molar mass about the mean... 

Microgels are distinguished from linear and branched macromolecules by their fixed shape which limits the number of conformations of their network chains like in crosslinked polymers of macroscopic dimensions. The feature of microgels common with linear and branched macromolecules is their ability to form colloidal solutions. This property opens up a number of methods to analyze microgels such as viscometry and determination of molar mass which are not applicable to the characterization of other crosslinked polymers. 

An example can best explain the procedure. A poly(bisphenolA carbonate) sample characterized by a broad-MMD was injected in an SEC apparatus, about 100 fractions were collected, and 24 of them were analyzed by MALDI [7]. Figure 15.2 reports the SEC trace of the PC sample. The trace covers a quite broad range of elution volumes and it is centered at about 30 ml. The polymer starts eluting at about 26 ml and ends at about 38 ml. The MALDI spectra yielded MP values (see above). Using this information, the SEC trace in Fig. 15.2 is calibrated and the average molar masses turn out to be Mw = 55,800, Mn = 23,600. 

GPC calibration curves are established based on the radius of gyration of known-molecular-weight polymers, such as well characterized, narrow-molecular-weight distribution polystyrene. Branched polymers have a lower radius of gyration for their molar mass than the corresponding linear molecule. Thus, as branching increases the GPC numbers become less and less accurate and so should only be used for trends, and not exact calculations as some authors have done. 

Erom Equations 12.46 and 12.47, one sees that ThEEE retention is related to (l/5j), but not specifically to a conventional analyte property, such as molar mass M or particle diameter d. However, since HSj depends on M or d, it also mediates the dependence between R and M or d. At constant Tq conditions, the relationship between X, M, and AT can be experimentally exploited by using standards. Eor instance, in polymers mass characterization, monodisperse or polydisperse standards can be employed for a specific polymer-solvent system. Once the relationship X vs. M, that is, the so-called calibration curve, is obtained, it is universal, that is, valid for any ThFFF instrument [3]. A typical calibration function, which relates the instrumental response to analyte property (in this case M), is... 

Recently, a miniaturized thermal apparatus, [t-ThFFF, was developed and applied to characterize the molar mass distribution of synthetic polymers in organic solvent as well to determine the particle size distribution of nanoparticles (PSs latex) in aqueous carrier. This 4-ThFFF proved to performed well in both macromolecule and particle analysis [48]. 

As explained in Sections 16.3.4, 6.4.1, and 16.4.2, SEC is a nonabsolute method, which needs calibration. The most popular calibration materials are narrow molar mass distribution polystyrenes (PS). Their molar mass averages are determined by the classical absolute methods—or by SEC applying either the absolute detection or the previously calibrated equipment. The latter approach may bring about the transfer and even the augmentation of errors. Therefore, it is recommended to apply exclusively the certified well-characterized materials for calibrations. These are often called PS calibration standards and are readily available from numerous companies in the molar mass range from about 600 to over 30,000,000g moL. Their prices are reasonable and on average (much) lower than the cost of other narrow MMD polymers. Other available homopolymer calibration materials include various poly(acrylate)s and poly(methacrylate)s. They are, similar to PS, synthesized by anionic polymerization. Some calibration materials are prepared by the methods of preparative fractionation, for example, poly(isobutylene)s and poly(vinylchloride)s. 

A useful approach to detection in polymer HPLC presents the on-line hyphenation of different measurement principles. For example, an RI detector combined with a UV photometer produces valuable additional information on the composition of some copolymers. Further progress was brought with the triple detection RI plus LALS plus VISCO [313], which is especially suitable for branched macromolecules and the tetra detection UV plus RI plus LALS plus VISCO, which enables characterization of some complex polymer systems, exhibiting a distribution not only in their molar mass and architecture, but also in their chemical composition such as long chain branched copolymers. 

The architecture of hypeibranched polymers and dendrimers is connected with difficulties in determining molar mass. Many of the common characterization techniques—e.g. size exclusion chromatography (SEC)—used for polymers are relative methods where polymer standards of known molar mass and dispersity are needed for calibration. Highly branched polymers exhibit a different relationship between molar mass and hydrodynamic radius than their linear counterparts. 

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