Rubber molecular weight from elastic

A number of high molecular weight polyisoprenes occur in nature which differ from natural rubber in that they are essentially non-elastic. As with natural rubber they are obtained from the latex of certain plants but they differ in that they are either frani-l,4-polyisoprenes and/or are associated with large quantities of resinous matter. 

The change of chemical potential due to the elastic retractive forces of the polymer chains can be determined from the theory of rubber elasticity (Flory, 1953 Treloar, 1958). Upon equaling these two contributions an expression for determining the molecular weight between two adjacent crosslinks of a neutral hydrogel prepared in the absence of... 

Figure 1. Stress relaxation curves for three different extension ratios. Uncross-linked high-vinyl polybutadiene with a weight average molecular weight of 2 million and a reference temperature of 283 K. G is the apparent rubber elasticity modulus calculated from classical affine theory. (Solid line is data from Ref. 1).

In 1944, Flory (3) noted that the moduli of cross-linked butyl rubbers generally differ somewhat from values calculated from the crosslink density according to the kinetic theory of rubber elasticity. In many cases, the modulus also depends on the primary (uncross-linked) molecular weight distribution of the polymer. He attributed both observations to three kinds of network defects chain ends, loops, and chain entanglements. The latter are latent in the system prior to cross-linking and become permanent features of the network when cross-links are added. 

Each of the viscoelastic parameters G°, rj0, and Je° has associated with it a characteristic molecular weight which either measures an equivalent spacing of entanglement couples along the chain (Me, deduced from G with the kinetic theory of rubber elasticity), or marks the onset of behavior attributed to the presence of entanglements (Mc and AT, deduced from r/0 and Je° as functions of molecular weight). Table 5.2 lists Me, Mc, and M c for several polymers. Aside from certain difficulties in their evaluation, each is a rather direct and independent reflection of experimental fact. 

Viscoelastic properties of molten polymers conditioning the major regularities of polymer extension are usually explained within the framework of the network concept according to which the interaction of polymer molecules is localized in individual, spaced rather far apart, engagement nodes. The early network theories were developed by Green and Tobolsky 49) and stemmed from successful network theories of rubber elasticity. These theories were elaborated more fully in works by Lodge50) and Yamamoto S1). The major elasticity. These theories is their simplicity. However, they have a serious drawback the absence of molecular weight in the theory. 

Chain entanglements are the cause of rubber-elastic properties in the liquid. Below the "critical" molecular mass (Mc) there are no indications of a rubbery plateau. The length of the latter is strongly dependent on the length of the molecular chains, i.e. on the molar mass of the polymer. From the shear modulus of the pseudo rubber plateau the molecular weight between entanglements may be calculated ... 

FIG. 15.41 Effect of molecular weight on critical shear stress at onset of elastic turbulence in poly(methyl methacrylate). From Brydson (1981, Gen Ref, his Fig. 5.8 as reproduced from Howels and Benbow, 1962). Courtesy The Plastics 8t Rubber Institute. 

The average length (or molecular weight) of network chains in a crosslinked polymer can be experimentally determined from the equilibrium rubbery modulus. This relationship is a direct result of the statistical theory of rubber-like elasticity . In the last decade or so, modem theories of rubber-like elasticity 2127) further refined this relationship but have not altered its basic foundation. In essence, it is... 

Fig. 23. Changes of crosslinking density n,. in netformation from a low-molecular-weight silicone rubber at 20 °C, calculated from the elastic modulus (1) and equilibrium swelling in toluene (2) [46]...

Unfortunately the materials do not have a sufficiently well-developed rubbery modulus for use in calculations. One therefore resorts to the equivalent ultimate Maxwell element from which the maximiun relaxation time was computed, and utilizes the modulus corresponding to that ultimate element for subsequent computations. Now if La" " " ions act as crosslinks, then the values should be directly proportional to their concentration, c, since both and c are inversely proportional to the molecular weight between crosslinks. Mg. The former relationship is due to the kinetic theory of rubber elasticity (E = 03qRTIMc where 0 is the front factor, q is the density, and R the gas constant), and the latter to simple stoichiometry (c = g/2Mj) for tetrafunctional crosslinks. A plot of vs. c was shown in Fig. 9, both for La" " " " and for Ca++ indicating that both ions act as crosslinks, at least at low concentrations and only for the ultimate Maxwell element. 

---