Polymers in Solution
Polymers, especially when compared with the monomers from which they are built, have a number of special properties. For example, polymers such as starch and polypropylene oxide are much less soluble in water than their monomers, glucose and propylene oxi
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Polymers in Solution 2.1
Chain Models – 18
2.2
Chain Stiffness – 23
2.3
Entropy Elasticity – 25
2.4
Thermodynamics of Polymer Solutions – 26 Ideal and Real Solutions – 26
2.4.1
References – 37
© Springer-Verlag Berlin Heidelberg 2017 S. Koltzenburg et al., Polymer Chemistry, DOI 10.1007/978-3-662-49279-6_2
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Chapter 2 · Polymers in Solution
Polymers, especially when compared with the monomers from which they are built, have a number of special properties. For example, polymers such as starch and polypropylene oxide are much less soluble in water than their monomers, glucose and propylene oxide. Another observation is that many polymers absorb solvents or water without themselves dissolving. Thus, cotton socks, for instance, absorb water without disintegrating when they are washed in a washing machine. To explain and to be able to describe such properties, this chapter is devoted to a description of the polymeric chain structure and the consequences thereof for polymers in solution. Furthermore, the thermodynamics of polymer solutions are discussed and compared with those of small molecules to develop an understanding of the differences in solubility mentioned above. 2.1
Chain Models
The structure of a polymer and the characteristics that can be derived from it can best be visualized by using a chain model. In this model the repeating units are the chain links, which are (in the simplest linear case) connected together to form a chain. In the case of a polymer chain in which all elements are connected in a trans-conformation, the simplified image in . Fig. 2.1 emerges. The “contour length,” lcont—the complete length of a chain with n links of length l, including all chain elements— is lcont = n l
(2.1)
If one considers solely the three most probable conformational possibilities of every –CH2– entity relative to its direct neighbors, two gauche- and one trans-conformations, this already gives 3n−1 different conformations for the complete polymer chain. Only one of these is the all-trans-conformation; thus its actual occurrence is highly improbable. Despite this, statistical methods are used to describe the dimensions of polymer chains as realistically as possible and thereby predict their behavior. The so-called Gaussian chain is a random arrangement of the segments following the erratic flight or random walk model and assuming free and unimpeded rotation. Every repeat unit is thus connected to the next by an arbitrary angle. . Figure 2.2 shows schematically the basic features of this model. A statistical treatment is based on the size of the mean end-to-end distance R.1 It follows from this that n R = ∑li i =1
(2.2)
..Fig. 2.1 Model of a polyethylene chain in which the –CH2– units are symbolized by kinks. The basis of this representation is an all-trans-conformation (bond angle = 109.47°)
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For reasons of consistency with the most popularly used nomenclature, the symbol R is used for this variable; needless to say, it should not be confused with the universal gas constant
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