ABSTRACT
I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
II. The Scaling Theories and Interfacial Interactions . . . . . . . . . . . . . . . . . . . . . . . . . 133
III. Transitions and Self-Consistent Fields Philosophy . . . . . . . . . . . . . . . . . . . . . . . . . 136
IV. Hyperelasticity Phenomenology and Reinforcement . . . . . . . . . . . . . . . . . . . . . . . 138
V. Theories of Rubber Reinforcement — A Brief Review of the Previous Work . . . . . 140
VI. The Unsolved Problems and Some Paradoxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
VII. The Theory of Rubber Reinforcement — A Novel Approach . . . . . . . . . . . . . . . . . 144
A. General Phenomenological Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
1. Qualitative Description of the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
2. Fractal Geometry, Thermodynamics, and Conformational Statistics . . . . . 148
3. Quantum Mechanics and the Basic Statements of Conclusions . . . . . . . . . 149
B. Definition of the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
1. Definition of the System and its Transitions . . . . . . . . . . . . . . . . . . . . . . . 150
2. Probability Current and Network Response . . . . . . . . . . . . . . . . . . . . . . . 152
3. An Engineering Approach and Scaling Transitions . . . . . . . . . . . . . . . . . . 153
C. Particular Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
VIII. Experimental Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
IX. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
Polymer networks, in general sense, are of the unique molecular type, extending in size (and structure)
from micro-to macroworld [1-8]. In very simplified terms, characteristic dimensions of a polymer
network, following the same constitutive relations, can be extended, from nano-to kilometers, that
is, for a dozen of magnitudes in space scale. In principle, one can expect that using such properties
can bridge over, and connect in synergetic way, properties of some entities from nano-to macro-
scale. But, in the common approach to polymers (and polymer-type carbon networks) this way of
thinking is still very rare. On the other side, some issues obviously related to structure parameters
on both, nano-and macroscale, stay unsolved in spite of the great efforts and investments, extensive
research, and large pool of accumulated data, for a very long time. Such a problem is the reinforce-
ment of rubbers with active fillers. Although based on some obvious phenomena, following from
the fundamental principles (as the interactions due to uncompensated forces at a surface of nano-
particles, making the architecture of active fillers), quantification of that influence on properties of
materials, on macroscale, is not yet possible [2-4].
