Entropy, Energy and Dynamics of Coalescing Spherical and 1D Aerosols

Abstract

Aerosol coagulation due to Brownian collision is a non-equilibrium process that generates entropy as the aerosol evolves. While not at equilibrium, a form of steady state arises whereby the aerosol size spectrum achieves a self-preserving distribution (SPD). Although the existence of this SPD is well accepted, the transition to SPD has only been considered from a kinetic perspective. This dissertation primarily investigates the kinetics of aerosol collisions and is the first known work to develop the thermodynamic principles of entropy of an evolving aerosol. The total entropy of an aerosol undergoing collisions and coalescence is defined as the sum of kinetic entropy, surface entropy and configurational entropy. Kinetic entropy is composed of internal energy (1/2 kBT for each degree of freedom) and partition functions (containing translational and rotational contributions). Even though surface entropy and configurational entropy exhibit substantial values, SPD can persist in scenarios characterized by non-coalescing particles (minimal surface entropy change) and homogenous mixing (no configurational entropy change). Thus, they do not play a dominant role in the formation of SPD. A scaled entropy production, σscaled, is introduced and shown to remain constant at SPD. The thermodynamic force, represented as N∞5/6 (where N∞ is the particle number concentration), and the corresponding flux, dN∞−5/6/dt, are derived from the time evolution of particle concentration at SPD. When coagulation begins with a polydisperse aerosol, a linear relationship between flux and force is observed, with σscaled approaching a minimum value at SPD. Conversely, a non-linear relationship is noted for coagulation starting with a monodisperse aerosol, where σscaled reaches a maximum value at SPD. To expand on the work of coalescing aerosols I look at a novel system of 1D materials undergoing collision and “coalescing” processes whereby carbon nanotubes (CNTs) are colliding due to Brownian motion and bundling as a result of van der Waals (vdW) forces. The investigation of the CNT concentration required for aerogel formation during CNT synthesis is critical to tailoring the final properties of CNT-based materials. What’s more, with the increasing replacement of conventional bulk materials by CNT-based materials, the likelihood of exposure to these nanomaterials in daily life has risen, prompting greater concerns regarding CNT safety. It is significant to quantify the adhesion energy of various forms of nanotubes as a fundamental step in assessing their potential for detachment. The current mesoscale model of single-walled carbon nanotubes (SWCNTs) is extended to multi-walled carbon nanotubes (MWCNTs) with a new force field and force constants. The general adhesion energy of all the cylindrical MWCNTs, independent of the layer number, is demonstrated to be 15% higher than the theoretical values of their outermost shells. Length is shown to play a pivotal role in bundling dynamics. What’s more, we employed an analytical model calibrated with the mesoscale simulation results to estimate the bundling time in a timescale close to the collision timescale. Remarkably, we observed excellent agreement between these two models. Thus, we successfully proposed multiscale models that can accurately describe the bundling dynamics across multiple time scales.