State of ease

After introduction of cross-links in the strained state, the composite network retracts, upon release, to a stress-free state-of-ease (J9 ) The amount of retraction is determined by the degree of strain during cross-linking and by the ratio >i/v2. The elastic properties relative to the state-of-ease are isotropic for a Gaussian composite network ( 8, 1 9,20). 

Pauline and Cholly, there is intense loneliness for Pauline. There may be less tension in this state of ease, but there does not appear to be more intimacy, because the loneliness prevails. We can infer that back home she was living with her family, not Cholly, and that Pauline would expect her husband to fulfill her need for companionship. 

Figure 1. Entanglement network cross-linked while strained in simple extension showing the unstretched state,X., the state of strain, X, and the equilibrium state of ease, X. ...

Vp for Polymer B. This calculation is an approximation since it ignores an anisotropy that can be predicted from the deviation from neo-Hookean elasticity, but the latter is very small as will be seen below. The sum (v + v ) (for which the term reticulation density has been suggesLea ) can now be compared with the corresponding quantity from stress-strain and state of ease measurements, namely, (2/RT)(C.y determinations of... 

Figure 3. Swelling anisotropy in the state of ease parallel to the stretch direction for samples made from Polymers A, B and C with well defined thermal histories and various radiation doses Polymer A, - 0.53 Polymer B, = 0.63 ...

We now consider the small swelling anisotropy which was ignored in the preceding calculation. The swollen gel may be regarded as a deformed network in which the stretch ratios A, (Q/A), (Q/A) in the x, y, z direction are superimposed on the stretch ratios in the state of ease X, X, X". The free energy of deformation then includes a tirm for dilution with the solvent, but this constant argument exists for a given Q. Substitution of X = AX, ... 

These arbitrarily chosen p values are consistent with the well-known effect of swelling in diminishing the ratio Cp/C. in conventional networks. Although the numerical data are uncertain, the qualitative nature of the anisotropy seems clear. Young s modulus for small extensions of the dry network from the state of ease should correspondingly be smaller in the direction of original stretch than perpendicular to it, but the calculation of this aspect of the anisotropy as well as its experimental measurement is more difficult. 

The cross-linking of 1,2-polybutadiene strained in simple extension has been described in previous papers of this series.When a strained sample with stretch ratio X is crosslinked with y irradiation near the glass-transition temperature (T ), the resulting cross-link network traps the entanglemints originally present after release and warming, the sample seeks a state of ease with stretch ratio Xg in which the forces associated with the cross-links and the trapped entanglements act in opposite directions. 

From X and X, together with stress-strain measurements in extension from the state of ease, or simply from the equilibrium stress at X, the concentration of trapped entanglement strands can be calculated and compared with the entanglement strand density estimated from transient measurements on the uncrosslinked polymer. To obtain consistent results, especially for stress-strain relations in large extensions of the dual network from its state of ease, it is necessary to attribute deviations from neo-Hookean elasticity to the trapped entanglement network, as described by the... 

The stretch ratios X and X after equilibrium retraction to the state of ease were measured with a traveling microscope focussed on fiducial marks. Subsequently, stresses at XI X were measured as a function of time, first nd later at a higher temperature to hasten the... 

Similar very slow molecular processes are revealed in the approach to a state of ease of networks which have been very lightly cross-linked in strained states. ... 

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