There are a few tentative discussions available regarding the microscopic mechanical properties of functional materials [14,15]. The microscopic world of materials and their motion keep within bounds of the Schrödinger equation
. (1)
To decode the proposed intelligent catalyst, the key relies on the polymeric interactions involved in the networks, i.e, the hydrogen bonds and the complexing interactions. Run with the confinement from energy barriers, the motion of one simple polymeric chain relative to the others can not go beyond the energy barriers. This natural law dictates these polymeric chains the microscopic motion subject to the potential barriers
. (2)
Here, d is the maximal distance borne among these polymeric chains (the further distance would incite a phase transition of the polymeric networks). This outline floats resulting from the effective interactions among these polymeric chains which fundamentally rely on the distance [16]. One polymeric chain excessively close to the others (r ≤ 0) would press the polymeric blocks and thus leads to a dramatically-increasing potential. One polymeric chain excessively faraway from the others (r ≥ d) would incite a phase transition of the polymeric networks, for which U0 must be surmounted. In conjunction with Eq. (2), solving Eq. (1) will show
. (3)
Here, µ and η are individually an integrated variable and a constant. Eq. (3) presents the physically- acceptable energy for the "bound" motion of these polymeric chains and which can be obtained from plotting cot µ against –[(η/µ)2-1]1/2. This will give the maximal value µm ≈ mπ →κ that shows
. (4)
Hence, the "bound" polymeric networks in the catalyst only become possible with Em ≤ U0. The higher energy will incite a phase transition of the polymeric networks which needs the extra energy
. (5)
Once the extra energy is compensated from a heat source (such as the catalytic solution), a phase transition of the polymeric networks would take place:
(6)
Here, Tc and T0 are individually the critical temperature for the phase transition and the ambient temperature, and ms and qs are the mass of the aqueous solution and the specific heat. Owing to the discrepant κ and m between hydrogen bonds and the complexing interactions in this catalyst, the increasing temperatures would result in a hierarchical disruption of the two interactions and stepwise disaggregation of the polymeric networks and as a result leads to the substrate-sieving catalytic ability. This catalyst wouldn't present effective catalysis at low temperatures because of the two interactions which blocked the polymeric networks. With the increasing temperatures, this catalyst would first present catalysis towards small molecules of substrate and then further towards bigger molecules of substrate, by virtue of the hierarchical disruption of the relatively weaker hydrogen bonds and the stronger complexing interactions. In this way, the catalyst assumed the substrate-sieving catalytic ability.