Study of the Crystal Growth Mechanism and Critical Secondary Nucleus Size of Poly(ethylene oxide)/Urea Inclusion Compound

Abstract

This study focuses on the crystal growth mechanism and the critical nucleus size of the inclusion compound formed between poly­(ethylene oxide) and urea (PEO-U-IC) β spherulites crystallized from the melt. The surface nucleation mechanism during the crystal growth process is proposed based on the exponential dependence of the spherulite radial growth rate G on the negative reciprocal of product of the isothermal crystallization temperature multiplied by the degree of supercooling (−1/(T cΔT)). The radial growth rates G of PEO-U-IC β spherulites crystallized from the mixed melt with the gradual addition of the diluting agent N,N′-dimethyl urea (2MeU) were measured under a polarized optical microscope. On the basis of the first nucleation theorem proposed by Kashchiev, the critical secondary nucleus size n* during the surface nucleation is determined from the slope of linear fitting line of ln G versus ln x, where x is the mass fraction of urea in U/2MeU. The critical secondary nucleus consists of 3–9 entities with each entity of the inclusion compound crystal containing 1 urea and 1.5 ethylene oxide repeating units when the crystallization temperature ranges from 65 to 85 °C. The relationship that n* is proportional to 1/(ΔT)2 confirms that the critical secondary nuclei at the solid–melt interface are two-dimensional.

Critical Size of Secondary Nuclei Determined via Nucleation Theorem Reveals Selective Nucleation in Three-Component Co-Crystals

“…The results of samples with the urea mass fractions in urea/thiourea lower than 60% are not shown here because of the large uncertainties of the data. The radial growth rate decreases with the increasing temperature in each sample, and its special tendency supports the surface nucleation mechanism for spherulite growth [4,17]. Figure 5 illustrates the relationship between the spherulite radial growth rates G of IC and the mass fractions x of urea in urea/thiourea.…”

“…Figure 6 shows the plot of lnG and lnx. Deduced from the theory based on the Nucleation Theorem, lnG is proportional to lnx of the crystallizable component in the binary blend system if the other component does not participate in the crystallization, as confirmed by our previous work on the PEO/urea/dimethylurea blend system [17], and Equation (7) dominates the crystallization kinetics of the double-component crystallization system. However, to our surprise, the preferable linear dependence of lnG on lnx still occurs in the PEO/urea/thiourea ternary isomorphic IC system.…”

“…A power-law relationship between the radial growth rate G and the mass fraction x of urea in the total mass of urea and the diluent was observed, and the exponent gave the critical size of the secondary nucleus. Our results revealed that a critical secondary nucleus of the PEO/urea IC β crystal consisted of 4 to 9 entities in the studied temperature range [17].…”

“…A power-law relationship between the radial growth rate G and the mass fraction x of urea in the total mass of urea and the diluent was observed, and the exponent gave the critical size of the secondary nucleus. Our results revealed that a critical secondary nucleus of the PEO/urea IC β crystal consisted of 4 to 9 entities in the studied temperature range [17].In this work, we attempt to extend the Nucleation Theorem to determine the critical size of the secondary nuclei in a three-component co-crystal system poly (ethylene oxide)/urea/thiourea inclusion compound. Thiourea is an analogue molecule of urea, and as a result, the three components co-crystallize.…”

“…As a result, the composition of the critical secondary nuclei is different from that of the bulk inclusion compound crystals. The work is expected to deepen our understanding of the nucleation of multi-component co-crystals.Entropy 2019, 21, 1032 2 of 12 compound (IC) during its crystal growth process [17]. The PEO/urea ICs consist of guest PEO chains residing in the cavities formed by the host urea molecules [18][19][20][21][22][23][24][25][26].…”