Dušek Karel - Protective Coatings Film Formation and Properties

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Distributions are the most typical attributes of macromolecular systems . Distributions of degrees of polymerization and molecular weights are typical for linear polymers, and distributions of molecular weights and composition are typical for copolymers. If a branching unit is present, the distributions are multiplied by the number and positional distributions of branch points. Distributions are always generated by cross-linking ; at the gel point, the distributions of molecular weights get very wide (they diverge). One can say that distributions have turned epitheton constans of the polymeric world. Organic chemists hate distributions, physicists tolerate only those they like, but coating technologists have to live with them. They try to understand them and, possibly, to utilize them to develop more competitive products.

Where are the distributions encountered in practice? Already in raw materials purchased from producerstypical examples are several common polyisocyanates obtained by cyclotrimerization of diisocyanates or by addition of asymmetric diisocyanates to triols. Distributions in molecular weights and numbers of functional groups in telechelic polymers are usually narrower, but they should be accounted for when gelation and network formation are considered. Side reactions are another source of distributionswell-known examples are manifold reaction paths of isocyanate group leading to formation of allophanates, biurets, and isocyanurates, but important as well are transesterifications, transamidations, esteramide interchanges, various types of cleavage, and many other such reactions. Because the starting components are oligofunctional, there exists a variety of combinations in which the side (additional) reaction paths participate. Precursors of polymer networks , intentionally synthesized, are the main sources of distributions. Precursors are prepared in order to adjust group reactivity, processing properties like viscosity buildup, film-forming, and application properties, or specific chemical environment contained within the precursor can be introduced into the coating; not less important is a reduction of health hazards by lowering of volatility and penetration ability of toxic groups.

In this contribution, we will show examples of several ways by which distributions are generated in coatings binders or other thermosetting systems. For deeper understanding, we will refer to literature in which the generation of distributions and their treatment are described. The main aim of this contribution is to show the importance of distributions for cross-linking and for properties of the cross-linked systems , especially those of practical importance. Along with the search for simple model networks to verify or reject theories, the recent decades are characterized by growing interest in understanding and modeling systems of practical importance (for illustration, see examples in Refs. []). Since distributions are the central topic of this contribution, we first outline the ways the distributions can be described and transformed.

The distributions can be described in several ways, for instance, by the number of objects, or their weights. The distribution can also be described by several moments of the distribution. For describing distributions and transforming distributions, we will be using the formalism of the generating functions. In the Appendix, we demonstrate the use of this formalism on the example of distributions of degrees of polymerization or molecular weights and reaction states of simple building units . No special mathematical knowledge is necessary, only the basic knowledge how to differentiate a function which is high-school mathematics. The types of units and bonds are tagged by a respective auxiliary (dummy) variable. The variable serves for the transform and is removed after the respective transformation is done (e.g., transfer of a number distribution into weight distribution). In this way, sometimes troublesome summations can be avoided. The great advantage of the use of the generating function tools is the simplicity of combination of various distributions, e.g., in blends of distributions, or for superimposed distributions like molecular weight and cross-link distributions. For further examples of the use of the probability generating functions (pgf) for description of distribution of complicated macromolecular systems, see Ref. [].

In this contribution, we will show some cases in which the distributions in one or both components of a 2K cross-linking system either exist or are generated unintentionally or intentionally, before they enter the final cross-linking stage. The cross-linking stage is affected by the existence of these distributions; the distributions have an effect on gelation, the fraction of soluble materials, and cross-link density. The description of distributions occurring in real systems and an interpretation of their effects will be explained in the following sections:

The methods used to determine the distributions are very important. The analysis of commercial materials is practically the only source of information on impurities or side products. For distributions in preprepared precursors, certain kinetic or equilibrium parameters are needed as input for theoretical generation of the distribution. Moreover, some of the theoretically generated distributions can be checked experimentally. Molecular ions mass spectrometry is very suitable for this purpose; unfortunately, while precise in molecular mass, the results are not so accurate in quantitative determination of components. Gas, size exclusion, and liquid chromatographies can be very helpful, but they are usually dependent on calibration, which may be not a simple task. Each case should be solved ad hoc by combinations of separation and spectroscopy techniques that help identify the composition of each separated fraction.

In this contribution, the effect of distributions on the cross-linking process, gelation, and network buildup is discussed only qualitatively or semi-quantitatively, but reference is made to work already published and to papers in which modeling of cross-linking is described. A large portion of relevant papers can be found in the references list.