A thermodynamic theory of mechanical relaxation due to energy transfer between strain-sensitive and strain-insensitive modes in polymers

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Abstract
A thermodynamic theory has been developed on the relaxation strength of mechanical relaxation due to energy-transfer between strain-sensitive (intermolecular) modes and strain-insensitive (intramolecular) modes. Assuming that the strain-insensitive modes exhibit an overwhelmingly large heat capacity and function as a heat reservoir of constant temperature during the relaxation process, the relaxation strength ΔG, the difference between instantaneous and equilibrium moduli, is given as ΔG = TG2 Tα2 1/Cz1, where T is the absolute temperature, GT is the isothermal elastic modulus, and 1 and Cz1 are the thermal expansion coefficient and the specific heat at constant strain of the strainsensitive modes, respectively. This assumption is reasonable for a polymeric solid in which backbone chains have a lot of vibrational degrees of freedom whose energy is rather insensitive to intermolecular distance and, on the contrary, the potential for localized motion such as motion of side chains is highly sensitive to intermolecular distance. In a special case where the strain-sensitive modes are a set of vibrators with an angular frequency ω, ΔG = γ2Cz1T, where γ is the Grüneisen constant, defined by the strain-derivative of ω, = −∂ In ω∂z. The case where the strainsensitive modes are a set of rotators in an n-fold symmetrical potential can be treated as an extension of the above case. In the case where the strain-sensitive modes involve the transition between two states, ΔG in the present theory is reduced to that of the well-known two-state transition theory. Agreement is obtained between theory and experiment for a-methyl relaxation of poly(methy1 methacrylate).