Guth-Smallwood equation

In the presence of reinforcing fillers, the elasticity modulus of the elastomers increases in first approximation according to the Guth-Smallwood equation 1111171... 

The theory of reinforcement of polymers and elastomers refers to the Guth-Gold-Smallwood equation (Equation (23.1)) to correlate the composite initial modulus Efi with the filler volume fraction (0) ... 

In Section 23.2 was discussed the theory of reinforcement of polymer and elastomers which refers to the Guth-Gold-Smallwood equation (Equation (23.1)) to correlate the compound initial modulus (E ) with the filler volume fraction ( ). Moreover, it was already commented on the key roles played by the surface area and by the aspect ratio (/). Basic feature of nanofillers, such as clays, CNTs and nanographites, is the nano-dimension of primary particles and thus their high surface area. This allows creating filler networks at low concentrations, much lower than those typical of nanostructured fillers, such as CB and silica, provided that they are evenly distributed and dispersed in the rubber matrix. In this case, low contents of nanofiller particles are required to mutually disturb each other and to get to percolation. Moreover, said nanofillers are characterized by an aspect ratio /that can be remarkably higher than 1. Barrier properties are improved when fillers (such as clays and nanographites) made by... 

The viscosity equation is usually generalized to Young or shear modulus G (Guth and Gold, 1938 Medalia, 1973 Smallwood, 1944) ... 

In the mid-1940 s Guth (1945) and Smallwood (1944) developed a widely employed (Cohan, 1947 Kraus, 1965c, Chapter 4) equation expressing rubber reinforcement directly in terms of filler concentration. An important form of the equation can be written as... 

The increase in modulus may also often be expressed in terms of the slightly different Mooney (1951) or Guth (1944)-Smallwood (1944) equations. For example, with glass-bead-filled epoxy resins, Lewis and Nielsen (1970) found agreement between predicted and observed values of modulus in the rubbery region using the Mooney (1951) equation ... 

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