Journal of Physical Studies 28(1), Article 1602 [7 pages] (2024)
DOI: https://doi.org/10.30970/jps.28.1602

CLUSTERIZATION IN SOLUTIONS AS A PROCESS OF MESOPHASE FORMATION

Yu. F. Zabashta , V. I. Kovalchuk , O. S. Svechnikova , M. M. Lazarenko , O. M. Alekseev , A. V. Brytan , L. Yu. Vergun , L. A. Bulavin 

Taras Shevchenko National University of Kyiv,
64/13, Volodymyrs'ka St., Kyiv, UA–01601, Ukraine

Received 30 October 2023; in final form 23 January 2024; accepted 25 January 2024; published online 12 February 2024

The article examines the mechanism responsible for cluster formation in polymer solutions, a phenomenon observed in both high- and low-molecular solutions. In a two-component “solvent-solute” system, four phases can exist: pure solvent, pure solute, and two phases for the solution (sol phase and mesophase) In the sol phase, the particles (or molecules) of the solute are separated from each other, while in the mesophase, these particles (molecules) combine to form a framework. The chain serves as the structural unit of this framework. In high molecular weight solutions, the structural units are polymer chains. In low molecular weight solutions, a chain represents a linear sequence of solute particles connected to each other.

A phase diagram is proposed for high molecular weight solutions, wherein the gel acts as a mesophase. The mesophase is an intermediate phase between the sol phase and the pure solute phase. In a specific range of concentrations and temperatures, the sol phase and mesophase coexist, resulting in a sol-phase matrix containing clusters of the mesophase. It is generally accepted that the aforementioned phase diagram is also applicable to low molecular weight solutions.

Accordingly, the formation of clusters in solutions, known as clustering, is regarded as a first-order phase transition accompanied by the emergence of a mesophase. The existence of this transition was experimentally verified through light scattering by an aqueous solution of hydroxypropyl methylcellulose.

A model of an ideal mesophase is proposed, characterized by the presence of two types of thermal oscillations in its framework. These are small-scale bending oscillations of chains and large-scale oscillations that propagate in the form of transverse waves.

Based on the principles of statistical physics and elasticity theory, a formula for the free vibrational energy $f$ is derived for the proposed model. Numerical evaluation of $f$ leads to the conclusion that clustering (the formation of clusters in both high and low molecular weight solutions) is a first-order phase transition, i.e., a transition from the sol phase to the mesophase. This type of phase transition falls into the category of weak first-order phase transitions.

Key words: polymer solution, clustering, mesophase, first-order phase transition.

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