Spherulites: How Do They Emerge at an Onset of Nonequilibrium Kinetic-Thermodynamic and Structural Singularity Addressing Conditions?

Abstract

This communication addresses the question of the far-from-equilibrium growth of spherulites with different growing modes. The growth occurs in defects containing and condensed matter addressing environments of (bio)polymeric and biominerals involving outcomes. It turns out that it is possible to anticipate that, according to our considerations, there is a chance of spherulites' emergence prior to a pure diffusion-controlled (poly)crystal growth. Specifically, we have shown that the emergence factors of the two different evolution types of spherulitic growth modes, namely, diffusion-controlled growth and mass convection-controlled growth, appear. As named by us, the unimodal crystalline Mullins-Sekerka type mode of growth, characteristic of local curvatures' presence, seems to be more entropy-productive in its emerging (structural) nature than the so-named bimodal or Goldenfeld type mode of growth. In the latter, the local curvatures do not play any crucial roles. In turn, a liaison of amorphous and crystalline phases makes the system far better compromised to the thermodynamic-kinetic conditions it actually, and concurrently, follows. The dimensionless character of the modeling suggests that the system does not directly depend upon experimental details, manifesting somehow its quasi-universal, i.e., scaling addressing character.

Keywords: (poly)crystal formation; complex growing phenomenon; entropy production; nonequilibrium thermodynamics; physical kinetics; soft condensed matter; spherulites.

Figure 1

Mullins–Sekerka (M–S) type and Goldenfeld (G) type: (a) M–S, local curvatures are indicated by blue dashed circles; (b) G, mean curvature is signified by blue dashed circle.

Figure 2

The dependence of $r\left(\tau \right)$ on the rescaled kinetic ${\beta }_0$ and thermodynamic $\Delta$ dimensionless parameters. In the chosen time interval, the curves reflect a visible tendency to pass from the diffusion-like $\left({\beta }_0\to 0\right)$ to mass-convective-type mode $\left({\beta }_0\nrightarrow 0\right)$. Other realizations of $r\left(\tau \right)$ are presented in [12].