Date of Award

Spring 1994

Degree Type

Thesis - Restricted

Degree Name

Master of Science (MS)



First Advisor

Day, Art

Second Advisor

Karkheck, John

Third Advisor

Mendelson, Kenneth S.


Percolation theory has been used successfully to model the diverging viscosity at the sol-gel transition. However, percolation theory requires an unphysical dependence on angular forces for rigidity in gels. Dihedral angle forces in weakly bound materials such as gels are too weak to provide rigidity, and Born forces are unphysical since they are not rotationally invariant. We have developed a model consisting of a two-dimensional triangular network of central-force springs containing a liquid. The liquid creates internal stresses on the network which stretch the network even at equilibrium and introduce Born type forces. However, we have found that the Born forces introduced by the liquid can combine with other forces to allow the model to be rotationally invariant. Our springs and liquid model was used to study the elastic properties of a two-dimensional Sierpinski· gasket. Scaling results on the gasket are found to be the same as for a purely centralforce network. The consequence of this result is that the scalar term introduced by the Born forces can be neglected in scaling arguments.