Physical Processes

Influence of Ionic-Liquid-Tethered Al2O3 Nanoparticle on the Nonisothermal Cold Crystallization in Ionic-Liquid-Based Nanofluids

“…To characterize the nonisothermal cold crystallization kinetics of the pure-IL and different nanofluids from their supercooled state determination of the effective activation energy ( E X ), the energy required to transport molecular segments to the crystallization surface is very essential. In this regard, the reaction model independent isoconversional methods are advantageous as compared to the other methods . The isoconversional methods also enable us to evaluate the dependence of the E X on conversion and temperature, which is quite helpful in detecting and elucidating complex kinetics and crystal growth mechanism in any system .…”

“…Cold crystallization normally occurs below a certain temperature T max up to which the nucleation rate increases with increasing temperature. Above T max , as the process is solely diffusion controlled, a dramatic decrease of the nucleation rate occurs . On the basis of the energetics involved in the nucleation process, the maximum rate of nucleation can be expressed according to the Fisher and Turnbull model as where Δ G * and E D are considered as the free energy barrier to nucleation and the activation energy for diffusion across the phase boundary, respectively.…”

“…The free energy barrier is infinity near the glass transition temperature, but quickly decreases with heating as where σ is the surface energy, Δ T = T 0 – T ( T 0 is the temperature where nucleation is zero), Δ H f is the heat of fusion, and A is a constant. Equations and can be used to predict a variation in the effective activation energy with temperature . By definition, the effective activation energy is determined by the logarithmic derivative of the rate constant with respect to the reciprocal temperature: …”

“…As the crystallization occurs on heating Δ T < 0, the value in the parentheses of eq is negative and increases asymptotically to zero with increasing temperature. Thus, for cold crystallization the value of E X should be positive and expected to decrease monotonically throughout the process …”

“…Furthermore, the diffusion controlled region, i.e., the region where E X varies inversely, gradually increases. Such a strong X t ( T ) dependence of E X clearly indicates that the consideration of constant activation energy for diffusion ( E D ) in eq is inadequate to demonstrate the complete crystallization process and should be replaced by a conversion dependent function as , where ε are the activation energies of diffusion after complete conversion ( X t = 1) and n determines the strength of the contribution of diffusion in the crystallization process . Replacing E D with ε­( X t ) in eq the expression for the activation energy with contribution of both nucleation and diffusion becomes …”