(367c) Non-Linear Modeling of the Formation of Activated Carbons: Stochastic Approach

Activated carbons (ACs) constitute a type of carbon adsorbents, which have long been known to be inordinately effective for the purification of gases and liquids and the separation of mixtures of gases or liquids. The formation of ACs entails the modification of the original internal surfaces of carbonaceous substrates, e.g., coal or biomass, which can be carried out by a variety of chemical and/or physical methods, thereby augmenting the carbonaceous substrates' adsorbing capacities. The formation of ACs tends to proceed randomly or stochastically because of the discrete and mesoscopic nature of the carbonaceous substrates; the random encounters between the activation agent and the carbon on the carbonaceous substrates' internal surfaces; the intricate morphology, or structure, of the carbonaceous substrates' internal surfaces; and the incessant variation of the process with time. Thus, it is highly desirable that the formation of ACs from carbonaceous substrates be analyzed, modeled, and simulated in light of a stochastic paradigm. Herein, the formation of ACs is modeled as a stochastic process, specifically, as a pure-birth process whose intensity of transition is non-linear. This non-linear intensity of transition aims at incorporating the effects of morphological, i.e., structural, characteristics of the carbonaceous substrates' internal surfaces on the formation of ACs. The resultant model gives rise to the process' master equation whose solution renders it possible to compute the mean and higher moments about this mean. These higher moments, of which the variance is of special importance, are collectively a manifestation of the process' inherent fluctuations. Moreover, the master equation is simulated via the Monte Carlo method at the initial stage of the formation of ACs. The results of modeling are validated by comparing them with the available experimental data.