Characteristic dimensions of random coil polymers

The dimensions of different polymer chains depend strongly on the type of environment and temperature. A good solvent expands the coil. A poor solvent, on the other hand, causes shrinkage. Between these two extremes, so-called theta solvents are found (illustrated in Fig. 2.7 see Chapter 4). Typical of these is that intermolecular and intramolecular interactions are similar in magnitude. All polymers dissolved in theta solvents adapt to the following equation  

The expansion factor (a) is also affected by temperature and type of solvent. It has been shown both theoretically and experimentally that a is a function of the molar mass in good solvents  

The temperature expansion of the unperturbed chain dimensions d(ln r o)/dT is preferably determined by measuring the force in a sample of a lightly crosslinked network polymer as a function of elongation at different temperatures. The fundamental theoretical aspects are explored further in Chapter 4. Table 2.2 presents data collected by Mark (1976). 

Equation 2.12 is valid for any polymer chain regardless of structure. We have to consider an ensemble of N chains each comprising n segments. The average of the squared end-to-end distance, is equal to  

The molar mass dependence of the end-to-end distance follows a square-root law. 

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