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Effect of prenucleation clusters arising from liquid-liquid phase transition on nucleation in a one-component charged colloidal suspension

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Abstract

It is generally thought that liquid-liquid phase transition (LLPT) in a one-component suspension never or only very rarely happens. If this were true, it would contradict the two nonclassical nucleation models building on either liquid droplets or prenucleation clusters (PNCs). One way out of this paradox is to suppose that LLPT occurs in pathway to nucleation. This study specifies the physical parameters of charged colloids which can bring out LLPT according to the consistent prediction of the DLVO (Derjaguin-Landau-Verwey-Overbeek) potential and the Sogami potential about long-range attraction, and reveals that surface charge is not the only factor to affect attraction, size also plays an essential role. For the first time, we follow exactly the evolution from LLPT to nucleation in which PNCs participate, and characterize pre-ordered liquid-like property of the PNCs and their particle-like and template effect by optical microscopy and light scattering. Furthermore, it is found that when the configuration of the PNCs is changed by a little salt, the pathway to nucleation is altered significantly. Our results demystify LLPT in a one-component suspension and dissolve the paradox, thus extending the range of applicability of the nonclassical nucleation models.

Introduction

Nucleation is ubiquitous in nature, but it is still one of the most secretive processes [1]. Principally, there are two ways to understand nucleation. According to classical nucleation theory (CNT), nucleation and crystal growth arise from addition of single atoms or molecules [2]. By contrast, in the context of nonclassical theory, nucleation follows one of the two dominant models, either via highly disordered liquid droplets [3], within which crystalline nuclei grow, or via prenucleation clusters (PNCs) [4], by whose aggregation rather than growth nucleation proceeds. While the former emphasizes coexistence of a dilute liquid phase and a dense liquid phase, the latter takes metastable liquid-liquid phase separation (LLPS) to be a central event [5]. In both cases, liquid–liquid phase transition (LLPT) is an inevitable step in pathway to nucleation. However, it is widely believed that LLPT usually occurs in a binary or multicomponent system, but in a one-component system it is generally thought of as counterintuitive, never or only very rarely happens [6], [7]. As such, this leads to an apparent paradox. If LLPT does not exist in one-component nucleation, then the nonclassical models are invalid, one can resort only to CNT. Yet, as is well known, CNT often fails to make fine-grained predictions of some nucleation phenomena due to its oversimplification. Therefore, if the nonclassical models are expected to hold true, one way to resolve this paradox is to suppose that LLPT also exists in nucleation pathway of a one-component system [8].

But, even though LLPT does exist, it is also quite difficult to experimentally trace its kinetics. There are at least two obstacles. The first is practical difficulty of measuring kinetics of LLPT. Several important approaches, which are developed in atomic liquid, require some extreme conditions, such as high temperature or high pressure [7], [9]. Other accounts in molecular liquid are often constrained to special quench depth or quench rate [10], [11], [12]. The second involves observational indistinguishability of metastable LLPT with liquid-crystal phase transition. Since both occur in the supercooled liquid state, it is hard to disentangle them. A debate about whether LLPT exists in water typically reflects such a situation [13], [14], [15].

Naturally, a way to trace LLPT accurately and to understand correlation between LLPT and nucleation physically is to go beyond atomic and molecular system and into more accessible model system with an appropriate kinetic behavior at room temperature and ambient pressure. A well-developed model system is charged colloid. In comparison with sterically stabilized colloid, its most fundamental feature is that range and strength of particle-particle interaction are heavily dependent on charge, size, particle number density and electrolyte concentration, any change in each of which dramatically changes the interparticle interaction potential [16]. Despite this, it is also not easy to find which charged colloids under what conditions can bring out LLPT. In the past thirty years, only a very few experimental instances have been found [17], [18]. Although there are many discussions about phase behaviors of one-component charged colloidal suspensions, they are mainly grounded in the framework of CNT, without apparent concern for LLPT [19], [20]. The problem with these instances is that there is indeed a lack of an account of how LLPT correlates with nucleation.

From this perspective, this article is devoted to investigating LLPT and nucleation associated with PNCs in a one-component highly charged colloidal suspension. We first specify physical parameters of charged colloids for LLPT, by virtue of showing how tendencies of two pair potentials predict range and strength of attraction. Then, we give a direct experimental evidence of LLPT from which the PNCs arise and characterize structural features of the PNCs and their fundamental roles in the evolution from LLPT to nucleation by means of optical microscopy and light scattering. Further on, corresponding to fully deionized condition, the effects of low salt concentration on LLPT, LLPS and nucleation in which PNCs participated are also examined.

Section snippets

Material

The highly charged carboxyl-modified polystyrene soft spherical particles (PS100) suspended in de-ionized water were purchased from Bangs labs, USA, lot no. PC02N/11787. Their average diameter σ ≈ 100 nm and the size polydispersity determined by light scattering experiment [21] is 3.5%. The effective surface charge per particle Z* =530 ± 25, derived from conductivity experiments [22], [23]. By this way, Z* is very close to the theoretically calculated renormalized charges [19].

Sample preparation

All experiments

Specifying particle charge and size by two potentials

It is by now well accepted that range and strength of attraction between colloids play distinct roles in determining phase behavior of a system. If the attraction is short-range, liquid phase coexists with solid phase. If there is long-range attraction with adequate strength, the system will be nudged into complex phases – two or all three of dilute liquid, dense liquid and solid phase [8], [26]. Generally, the theoretical treatment of interactions between charged colloids is modeled typically

Conclusion

To sum up, the obtained results sufficiently demystify LLPT occurring in the one-component highly charged colloidal suspension and dissolve the paradox, thus extending the range of applicability of the nonclassical nucleation models. Contrary to the received view of the DLVO theory as a repulsion-only assumption [80], both the DLVO potential, despite being totally repulsive at all distances between charged colloids (Fig. 1), and the Sogami potential yield similar pictures reflecting the

Author contributions

The manuscript was contributed and approved by all authors.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11174075) and Nanjing University of Information Science & Technology (Grant No. S8113127001).

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