Application to Polymer Analysis

This section is concerned with the information that can be obtained by TDFRS about the molar mass and size distribution and the various molar mass averages. 

Once the scaling relation of Eq. (39) is known, the molar mass distribution can, at least in principle, be obtained from a Laplace inversion of the multi-exponential decay function as defined in Eq. (40). At this point, the differences between PCS and TDFRS stem mainly from the different statistical weights and from the uniform noise level in heterodyne TDFRS, which does not suffer from the diverging baseline noise of homodyne PCS caused by the square root in Eq. (38). 

In any case, the rate distribution function P(r), or the discrete pk, must first be determined from t,het(t) or g (t). Since this Laplace inversion is highly unstable, it is necessary to impose additional constraints, and various algorithms have been proposed in the literature [53,54,56,57,58,59]. Thorough discussions of these methods with respect to PCS data can be found in Ref. [60,61,62]. Here we will concentrate on the CONTIN program developed by Provencher [53,54,57]. 

---

Application to polymer analysis Combination of individual pore sizes (columns or gels) to cover required molecular weight range Molecular weight range covered by single pore size... 

As in the case with IR spectrometers, there exists a wide variety of specialty techniques especially applicable to polymer analysis. 

S. Mori, HPLC application to polymer analysis, in Handbook of HPLC, E. Katz, R. Eksteen, P. Schoenmakers, N. Miller, eds., Marcel Dekker, New York, 1998. 

Matrix-Assisted Laser Desorption/Ionization (MALDl) This topic has received much attention since several years ago, especially with regard to its application to polymer analysis. 

Two years after the introduction of GC by James and Martin in 1952, Davison et al. reported the first work on off-line Py-GC of polymers. These workers demonstrated that Py-GC was quite effective for the characterization of polymeric materials. In 1959, on-line Py-GC systems and their applications to polymer analysis were reported independently by three research groups Lehrle and Robb, Radell and Strutz, and Martin. These achievements triggered a boom in Py-GC. 

Mori, S. HPLC application to polymer analysis. In Handbook of HPLC Katz, E., Eksteen, R., Schoenmakers, P, MiUer, N., Eds. Marcel Dekker New York, Basel, 1998. 

Applications of ISS to polymer analysis can provide some extremely useful and unique information that cannot be obtained by other means. This makes it extremely complementary to use ISS with other techniques, such as XPS and static SIMS. Some particularly important applications include the analysis of oxidation or degradation of polymers, adhesive failures, delaminations, silicone contamination, discolorations, and contamination by both organic or inorganic materials within the very outer layers of a sample. XPS and static SIMS are extremely comple-mentar when used in these studies, although these contaminants often are undetected by XPS and too complex because of interferences in SIMS. The concentration, and especially the thickness, of these thin surfiice layers has been found to have profound affects on adhesion. Besides problems in adhesion, ISS has proven very useful in studies related to printing operations, which are extremely sensitive to surface chemistry in the very outer layers. 

Although the OTHdC has several unique applications in polymer analysis, this technique has several limitations. First, it requires the instrumentation of capillary HPLC, especially the injector and detector, which is not as popular as packed column chromatography at this time. Second, as discussed previously, the separation range of a uniform capillary column is rather narrow. Third, it is difficult to couple capillary columns with different sizes together as SEC columns. 

Having said this, it was felt therefore that there is a need for a book addressing analysis and characterisation of polymers from the point of view of what we wish to call the primary analytical question. Many excellent textbooks and reference works exist which address one or more individual analytical techniques, see, for example, references [1-10]. These books form the basis of the knowledge of the technique expert. They also contain many excellent and varied examples on successful applications of analytical techniques to polymer analysis and characterisation. There are also books which address the multitude of analytical techniques applied in polymer analysis, see, for example, references [11-24], However, a synthetic chemist may wish to know the constitution of his/her polymer chain, a material scientist may want to find out the reasons why a fabricated sample had failed. What technique is best or optimal to study chain constitution will depend on the situation. Polymer failure may result from morphological features, which needs to be avoided, a contaminant, a surface property degradation, etc. When a sample has been processed, e.g., a film blown, molecular orientation may be the key parameter to be studied. A formulation scientist may wish to know why an additive from a different supplier performs differently. It is from such points of view that polymer analysis and characterisation is addressed in this book. 

The application of election Microscopy technique to polymer analysis involves sufficient extension beyond the ordinary techniques. Some salient points are discussed here. 

There are two main sources of error propagation in static measurements, errors due to successive dilutions and errors due to initial instrument offset. Other errors which are also applicable to SEC analysis are discussed in (J ). These errors can be propagated using the criteria presented here. If w is the intial mass of polymer and Vj is the amount of solvent added to obtain the desired concentration Ci, the dilution process can be represented by the following set of equations ... 

T. Hatakeyama and F. X. Quinn, Thermal Analysis Fundamentals and Applications to Polymer Science, Chap. 4, Wiley, New York, 1994. 

The Eyring analysis does not explicity take chain structures into account, so its molecular picture is not obviously applicable to polymer systems. It also does not appear to predict normal stress differences in shear flow. Consequently, the mechanism of shear-rate dependence and the physical interpretation of the characteristic time t0 are unclear, as are their relationships to molecular structure and to cooperative configurational relaxation as reflected by the linear viscoelastic behavior. At the present time it is uncertain whether the agreement with experiment is simply fortuitous, or whether it signifies some kind of underlying unity in the shear rate dependence of concentrated systems of identical particles, regardless of their structure and the mechanism of interaction. 

Hatakeyama, T. and FIX. Quinn Thermal Analysis. Fundamentals and Applications to Polymer Science, 2nd Edition, John Wiley, Sons, Inc., New York, NY, 1999. 

The analysis of brittle fracture is the very domain of Linear Elastic Fracture Mechanics (LEFM). A comprehensive introduction to its fundamentals and the validity of its application to polymers has been given by Williams [25] and more recently by Grellmann and Seidler [26]. The fracture criteria and relevant test procedures elaborated by the ESIS technical committee TC4 can be found in [27]. 

Unfortunately, ESI-MS has had limited application in polymer analysis [163,164]. Unlike biopolymers, most synthetic polymers have no acidic or basic functional groups that can be used for ion formation. Moreover, each molecule gives rise to a charge distribution envelope, thus further complicating the spectrum. Therefore, synthetic polymers that can typically contain a distribution of chain lengths and a variety in chemical composition or functionality furnish complicated mass spectra, making interpretation nearly impossible. 

Havriliak, S. Havriliak, S. J. (1997) Dielectric and Mechanical Relaxation in Materials— Analysis, Interpretation and Applications to Polymers, Munich, Hanser. 

D. Briggs. Surface Analysis, in Encycl. Polym. Set Eng., Vol 165 Wiley (1989), 399-442. (Review of XPS and SIMS, principles and application to polymer surfaces.)... 

Knot theoretical techniques are easily applicable to polymer chains that do form actual knots or links, such as some DNA fragments or various catenanes [59-72,204-213]. By appropriate modifications, the knot theoretical polynomials are also applicable to the analysis of chirality properties of general molecules that may not form knots by themselves, but the space around them can be represented by a knot. This approach has led to the concept of chirogenicity, and to a nonvisual, algorithmic, computer-based analysis of molecular chirality [62]. 

---