Elementary swelling and gelling theories

It has been experimentally illustrated that it is possible to form an n-phase thermodynamic system where n≥2 and has a value which is limited by the properties of the system. For example, to attain limited chemical reversibility of a mineral matrix such as vermiculite using specific butyl ammonium vermiculite, it is necessary to reform chemical bonds using an additive and a particular ion. In other words, to obtain a similar thin film using exfoliated vermiculite as that obtained with natural vermiculite, hydrophobic or binding electrostatic bonds must be formed or reformed. It has also been observed that complementary structural compounds can be formed from other silicates, such as glycerine/sodium silicate. These compounds can also encase the vermiculite matrices. (Film Formation) is proportional to (A/Temp). (Pressure).(Ionic Content). Hence F=L(A/T)PE, where F=film formation, L=functional constant for the matrix compound, T=temperature, A=temperature constant, P=pressure, E=electrostatic force and P=force/area. Thus, F=LTE2 for unit area. ∑F=pf(L). TE2/∑Pefl=F1, where P=the probability for film formation and ∑Pef(L) is the partition function for the film formation. This concept can be extended to a response geometric algorithm. This means that for every mineral matrix there is an algorithm to describe its formation or its response to an applied field. Thus δ sec2(E) tan(E1) is the response for (F1). V---, V1…Vn, F1…Fn1,…, Fp,…Fnp.