Correlation between β-Relaxation and α-Relaxation in the Family of Poly(n-butyl methacrylate-stat-styrene) Random Copolymers

Previously a rough correlation between the logarithm of the most probable secondary β-relaxation time at the glass temperature T g, log[ τ β ( T g )], and the Kohlrausch−Williams−Watts (KWW) exponent, (1 − n ), of the primary α - relaxation correlation function exp[−( t / τ α ) 1- n ] was found when examining a whole host of chemically different glass-forming materials including amorphous homopolymers, small molecule van der Waal liquids, plastic crystals, and inorganic compounds. This rough correlation is expected from the exact correlation between the logarithm of the primitive relaxation time of the coupling model at the glass temperature T g, log[ τ o ( T g )], and (1 − n ) and from the similarity between the β - relaxation and the primitive relaxation, both being free from intermolecular cooperativity. This correlation holds only when n in the KWW exponent (1 − n ) can be identified with the coupling parameter n α of the α -relaxation in the coupling model. Now, this correlation is examined on a series of poly( n -butyl methacrylate- stat -styrene) copolymers with styrene contents ranging from 0 to 66 mol % utilizing the dielectric relaxation data of Kahle et al. [ Macromolecules 1997, 30, 7214]. For the present extension, the KWW function fails to fit the dielectric data due to the presence of concentration fluctuations in the random copolymer. Instead, the most probable coupling parameter n̂ α of the n -butyl methacrylate component in the copolymers is obtained indirectly through the steepness of the temperature dependences of the most probable α -relaxation time. A good correlation between log[ τ β ( T g )] and n̂ α is found to hold in this series of copolymers as well as in the poly( n -alkyl methacrylates). Moreover, the orders of magnitude of τ β ( T g ) and τ o ( T g ) are not far apart, supporting the similarity between the β - relaxation and the primitive relaxation.