Relaxation and Deformation in Glassy Polymers

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e utilized in the discussion of the salient features of plastic yield and nonlinear stress-strain behavior of glassy polymers. GLASSY STATE RELAXATION

The dynamics of the holes (free volumes) and bond rotations during vitrification and physical aging are analyzed on the basis of nonequilibrium statistical mechanics. We have reported that the conformational activation energy controlling the rotational relaxation of bonds is between 1 and 2 orders of magnitude lower than the hole activation energy [3]. As a result, the conformer relaxes much faster than the hole. Since the mechanical properties of glasses vary slowly in time, the dominant contribution to the structural relaxation and physical aging is from the holes. Consider a lattice consisting of n holes and nx polymer molecules of x monomer segments each. The total number of lattice sites (N) and volume (V) are written as: N(t) =n(t)+xnx, and V=vN where t is time, and v is the volume of a single lattice cell. The hole number n(t) consists of both equilibrium and nonequilibrium contributions in the glassy state. The nonequilibrium part of n goes to zero above the glass transition temperature (Tg). The change below Tg defines the glassy state. Minimizing the excess Gibbs free energy due to hole introduction with respect to the hole number, the equilibrium hole fraction, f=i•i/F, is given by 161

Mat. Res. Soc. Symp. Proc. Vol. 321. @1994 Materials Research Society

TY= frex'p

[

-

-E(

)1(1)

r

where c is the mean energy of hole formation, R is the gas constant, and the subscript r refers to the reference condition at T=Tr, which is a fixed quantity near Tg. The e characterizes the intermolecular interaction which affects the bonding between chain segments. We have analyzed the hole dynamics and fluctuations on a fractal lattice [5], and have obtained the solution of nonequilibrium hole fraction, 8(t) =f(t)-f, for a system started from equilibrium qT (t- tdt' R TOT

(2)

2

where q=dT/dt