Complex Polymers Multiple Distributions

The important feature of many polymers is simultaneous presence of distributions in two and several molecular characteristics. Polymers exhibiting multiple distributions are called the complex polymers or complex polymer systems. A detailed discussion of molecular characteristics of polymers and their average values and distributions can be found in numerous monographs and reviews, for example [34,35]. For the present purpose, it is important to repeat that all synthetic polymers and also polysaccharides are polydisperse in their nature. Only mother nature is able to produce macromolecules, for example many proteins, with uniform molar mass. The latter are often improperly called monodisperse(d) polymers. 

Recent development in liquid chromatography analysis of complex polymers shows a clear trend to combine more than one LC separation mechanism/tech-nique together with multiple detection techniques. It is a quite natural direction for the analysis of complex polymers with multivariate distributions in molecular characteristics. The coupled LC techniques have gained wide attention recently in the characterization of complex polymers and there are a number of monographs and reviews on this topic [4,8-13]. In this chapter, recent advances in LC separation of polymers are reviewed. References are generally restricted to the works published after 1995 since most of the works prior to the mid-1990s have been well summarized cdready [8,10,11,13]. 

Controlled-release polymer implants are useful for delivering drugs directly to the brain interstitium. This approach may improve the therapy of brain tumors or other neurologieal disorders. The mathematical models described in this section—which are based on methods of analysis developed in earlier chapters—provide a useful framework for analyzing mechanisms of drug distribution after delivery. These models describe the behavior of chemotherapy compounds very well and allow prediction of the effect of changing properties of the implant or the drug. More complex models are needed to describe the behavior of macromolecules, which encounter multiple modes of elimination and metabolism and are subject to the effects of fluid flow. 

DLS is a technique used in conjunction with -potential measurements to analyze polyplex size (average hydrodynamic diameter) distribution. Because the formation of polyplexes can result in a polydisperse mixture of nanoparticles of different size and shape (induding uncomplexed components), multiple peaks can result. Thus, typical reported data include average hydrodynamic diameter and polydispersity. Most software associated with DLS instmmentation permits assessment of a multimodal size distribution, but such data are often unreported or underreported. The default assumption of a single Gaussian distribution may not be appropriate for the majority of polymer-nucleic add complex formulations that are analyzed by DLS. Also, the analysis of the particle sizes assumes a uniform sphere, which again is not necessarily... 

Because of the complexity of the fractionation mechanism, not many mathematical models have been proposed to describe separation with Tref. Soares and Hamielec [47] used Stockmayer s distribution (Eq. 7) to simiflate the CCD of Hnear binary copolymers synthesized with miflti-site-type catalysts. Under the assumption that the fractionation process of Tref was controlled only by comonomer composition, the CCD was directly converted into the Tref profile using a calibration curve. For the case of ethylene/1-olefin copolymers made with multiple-site catalysts, the CCD of the whole polymer is described as the weighted summation of the CCDs of the copolymers produced by each active site ... 

Continuous thermodynamics has also been applied to derive equations for spinodal, critical point and multiple critical points. To do so with continuous thermodynamics is much easier than in usual thermodynamics. Spinodal and critical points may be calculated for very complex systems or for cases in which the segment-molar excess Gibbs energy and depends on some moments of the distribution function. In simple cases (for example, a solution of a polymer in a solvent, where the segment-molar excess Gibbs energy is independent of the distribution function) the equations of the spinodal and the critical point are known from the usual thermodynamic treatment. However, for more complex systems continuous thermodynamics has achieved real progress, for example, for polydisperse copolymer blends, the polydispersity is described by bivariant distribution functions. ... 

Since most recent polymers are complex mixtures, in which the composition and molar mass depend in multiple ways on the polymerization kinetics, the polymerization technique, and the process conditions, the polymer processing parameters must be carefully controlled and monitored to obtain polymeric materials with the desired properties. It is essential to understand the influence of molecular parameters on polymer properties and end-use performance. Molar mass distribution and average chemical composition may no longer provide sufficient information for process and quality control nor define stmcture-property relationships. Modern characterization methods now require multidimensional analytical approaches rather than average properties of the whole sample [5]. 

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