In Situ FBRM Analysis of Additive-Controlled Reactive Crystallization of Lithium Carbonate

Abstract

This work investigates the reactive crystallization of lithium carbonate (Li₂CO₃) by rapidly mixing concentrated aqueous solutions of LiCl (3.0–4.0 M) and Na₂CO₃ (1.5–2.0 M) at 65 °C, using focused beam reflectance measurement (FBRM) for online, in situ monitoring. The effect of low concentrations of poly(acrylic acid) (PAA), sodium hexametaphosphate (SHMP), and sodium tripolyphosphate (STPP) on nucleation and growth dynamics was systematically analyzed. The results show that the process is dominated by an intense initial supersaturation pulse, which governs early nucleation and subsequent population restructuring through growth and aggregation. Additives significantly modify the nucleation-growth coupling: PAA exhibits concentration- and time-dependent behavior, suppressing the detectable fines population and promoting consolidation into coarse fractions under high supersaturation; SHMP acts as a strong kinetic inhibitor, markedly reducing nucleation and, to a greater extent, growth; while STPP exhibits an intermediate, dose-dependent response, maintaining nucleation but limiting effective growth at high concentrations. Scanning electron microscopy observations confirm the formation of spherulitic Li₂CO₃ aggregates in all cases, with compactness and radial organization dependent on the additive. These results demonstrate that targeted additive selection allows for precise control of population dynamics and solid properties in reactive crystallization systems, within the investigated high-supersaturation concentration window, with useful mechanistic guidance for the design and control of Li₂CO₃ precipitation processes.

1. Introduction

Reactive crystallization represents an extreme regime among solid-forming processes, in which supersaturation is generated almost instantaneously as a direct consequence of a chemical reaction. Under these conditions, nucleation, crystal growth, and structural reorganization occur in a strongly coupled manner on very short timescales, resulting in particle populations that evolve far from thermodynamic equilibrium [1,2,3]. As a direct consequence, the final solid properties—crystal size, morphology, and size distribution—are determined by initial kinetic transients rather than by equilibrium conditions [4,5]. Unlike classical crystallization schemes involving cooling or antisolvent addition, reactive systems are characterized by intense kinetic transients, in which the final crystal properties emerge from the dynamic equilibrium among local supersaturation generation, interfacial barriers, and mass-transport limitations. Understanding how these factors govern nucleation stability and population evolution is challenging because nucleation and growth occur on very short timescales, making process control particularly sensitive to chemical and operational variables [6].

Among the different strategies to modulate reactive crystallization, the use of additives has emerged as a particularly effective approach to influence nucleation density, growth rates, agglomeration behavior, and final particle morphology without altering global thermodynamic variables. However, most available studies focus on individual additives or report primarily morphological outcomes, often without systematic in situ kinetic comparison under identical supersaturation conditions. As a result, the relative influence of chemically distinct additive families on measurable population parameters remains insufficiently resolved.

Taborga et al. [7] have shown that the crystallization behavior of lithium carbonate (Li₂CO₃) can be significantly modified by organic additives, thereby affecting both the crystal size distribution and morphology. Surfactant-type additives, such as sodium dodecyl sulfate (SDS), have been shown to reduce the size of Li₂CO₃ crystals. Increasing the concentration of additives produces a pronounced shift in the particle-size distribution toward smaller particles, resulting in growth inhibition and increased nucleation. Conversely, sodium dodecylbenzenesulfonate (SDBS), despite sharing an alkyl chain like that of SDS, promotes anisotropic growth, yielding elongated, acicular crystals due to preferential inhibition of lateral growth. Polymeric additives exert markedly different effects: the presence of polyacrylic acid (PAA) induces the formation of Li₂CO₃ spherulites with more homogeneous, narrower size distributions. This behavior has been attributed to strong interactions between carboxylate functional groups and lithium ions, which delay nucleation and induce non-crystallographic branching during growth, while the underlying crystal structure remains intact.

Recent studies have examined complex aggregation- and precursor-related pathways governing the crystallization and agglomeration of Li₂CO₃, highlighting the roles of non-crystallographic branching and early precursors in the formation of polycrystalline aggregates. Wang et al. [8] showed that, under reactive crystallization, the morphology of Li₂CO₃ depends critically on supersaturation (modulated by temperature, antisolvent addition, and Li⁺ concentration) and additives. Star-shaped or flower-like particles can form without additives, whereas approximately spherical spherulites form upon incorporation of sodium hexametaphosphate (SHMP) and can evolve into core-shell structures under certain conditions. In that same study, SHMP is associated with a pronounced nucleation delay (detected in situ), the induction of non-crystallographic branching, and the promotion of heterogeneous nucleation on crystalline surfaces, thereby reorganizing growth toward radial arrangements and compact architectures. Furthermore, sodium tripolyphosphate (STPP) is reported to exhibit effects like those of SHMP, consistent with high phosphate-group activity in its interaction with Li⁺, whereas a carboxylated polymer (polymaleic acid) can modulate a distinct spherulitic growth mode.

Complementarily, Yang et al. [9] rethought the agglomeration of Li₂CO₃ from a perspective different from the classical collision-based model: they propose that agglomeration may originate primarily from the formation and evolution of “precursor aggregates” that then transition to more developed crystalline morphologies, rather than from adhesion between already well-formed crystals. In this context, it is also observed that SHMP modifies subunit morphology, promotes branching, and inhibits secondary nucleation, thereby favoring the formation of more compact spherulites with narrower size distributions, with direct implications for separation properties and product quality.

In a previous study, our group investigated the reactive crystallization of Li₂CO₃ from LiCl and Na₂CO₃ solutions, monitored in situ using Focused Beam Reflectance Measurement (FBRM), and analyzed in detail the effects of polyacrylic acid (PAA) of different molecular weights on particle nucleation, growth, and morphological evolution [10]. This work demonstrated that the process is dominated by an extremely intense initial supersaturation pulse, characterized by very high nucleation and growth rates in the first few seconds after mixing, followed by rapid system reorganization. It was also shown that Li₂CO₃ precipitates systematically as spherulitic aggregates, whose compaction, size, and distribution depend strongly on both the level of supersaturation and the molecular weight of PAA, which simultaneously modulates primary nucleation, inhibits growth, and promotes morphological reorganization without altering the crystalline structure. However, that study focused on a single type of polymeric additive, leaving open whether the observed kinetic and structural behaviors are specific to PAA or reflect more general mechanisms associated with the additive’s chemistry and its interactions with the crystal-solution interface. Based on this, the present work is a direct extension aimed at deepening the mechanistic understanding of the control of reactive Li₂CO₃ crystallization in the presence of different additives, through in situ monitoring to discriminate population dynamics and clarify the factors governing the transitions among nucleation, growth, and spherulite assembly.

In reactive crystallization processes, supersaturation arises abruptly. It evolves on very short timescales, producing intense pulses of nucleation and growth that ex-situ techniques cannot adequately resolve. In this context, FBRM has become a key tool for in situ, real-time monitoring of particle population dynamics in highly transient systems. Pioneering studies demonstrated that FBRM enables high-temporal-resolution capture of initial nucleation events and subsequent crystal growth in rapid precipitation systems, providing direct information on particle number and its temporal evolution [11]. Furthermore, its application to continuous crystallization processes has shown that chord-length distribution (CLD) trends obtained by means of FBRM are statistically proportional to the crystal-size distribution when morphology is relatively regular, enabling estimation of nucleation and growth rates from population balances [12]. More recently, FBRM is particularly well suited to studying reactive crystallization under highly supersaturated and rapidly changing conditions, as it allows discrimination between primary and secondary nucleation and the direct quantification of kinetic parameters from CLD data, even in the absence of sampling and observation [13]. Although FBRM measures chord lengths rather than actual particle diameters, its high temporal resolution and sensitivity to relative population changes make it a central tool for comparative analysis of kinetics and population evolution in reactive crystallization systems, such as the one addressed in this study.

In this context, the selection of PAA, SHMP, and STPP was motivated by their distinct chemical structures and potential interaction modes with Li₂CO₃ crystallization systems. PAA represents a flexible carboxylated polyelectrolyte capable of surface adsorption and growth modulation, whereas SHMP and STPP are polyphosphates with different structural configurations and coordination behavior.

Although previous studies have reported morphological modifications induced by individual additives, a systematic comparison of their effects under identical reactive crystallization conditions—using in situ monitoring to quantify fines and coarse populations, mean chord lengths, chord length distributions (CLD), kinetic parameters, and final particle morphology—remains limited. Therefore, this work aims to comparatively evaluate how chemically distinct additives influence measurable population metrics under highly transient supersaturation conditions.

2. Results

2.1. Effect of Additives on Crystal Populations at Different Supersaturation Levels

Online monitoring using FBRM enabled quantification of the evolution of suspended particle counts during the reactive crystallization of Li₂CO₃, distinguishing among specific size fractions. This subchapter analyzes the effect of additives on the number of crystals classified as fine (<10 µm) and coarse (50–150 µm), as well as on the f/c ratio, defined as the ratio between the number of fines and the number of coarse crystals at any given time during the process.

This classification enables discrimination between newly nucleated particles (fine) and larger entities (coarse), which may arise from crystal growth, aggregation, or structural consolidation of spherulitic subunits during population evolution. Given that FBRM measures chord length, the coarse fraction represents particles of larger effective size irrespective of whether they originate from single-crystal growth or aggregate formation. The temporal profiles of these fractions are compared under conditions without additives (control) and with the addition of PAA, SHMP, and STPP, at two doses (0.025 and 0.1 g L⁻¹), at both 3 M and 4 M initial LiCl concentrations.

The results enable identification of trends in nucleation intensity, crystal growth rate, and the inhibitory or modifying effects of each additive. The stability of the coarse-crystal population and the persistence of fines over time are also discussed, both of which are relevant to product quality and operational efficiency in solid-liquid separation processes.

Figure 1a–d presents the count results obtained by the FBRM probe at an initial LiCl concentration of 3 M and in the presence of additives at different doses. A kinetic pattern consistent with reactive crystallization under high initial supersaturation is observed: an initial pulse of fines, followed by a progressive attenuation of their counts, while the coarse crystals tend to accumulate over time through growth and/or agglomeration. In Figure 1a, although the PAA condition exhibits a pronounced initial peak during the early supersaturation pulse, the additive-free condition maintains the highest sustained fines counts as the system approaches a quasi-steady regime, suggesting intense initial nucleation followed by fines clearance through supersaturation consumption, aggregate capture, or mass transfer to larger populations. The presence of PAA and STPP moderately reduces fines, showing an early decrease followed by a slight rebound, consistent with a transition from dominant primary nucleation to secondary mechanisms as the population evolves. In contrast, SHMP produces a marked suppression of fines, indicating stronger control over the initial events. In Figure 1b, SHMP and STPP transiently exceed the curve obtained without additives but converge toward similar final values, while PAA is the condition with the lowest coarse count. This is consistent with additives that, depending on their surface affinity and the supersaturation regime, can shift the equilibrium among nucleation, growth, and agglomeration without altering the final large-particle count. As the dose increases (Figure 1d), all curves obtained with additives fall below the curve obtained without additives, and PAA/STPP effectively suppresses the formation of coarse particles. In contrast, the SHMP condition exhibits a progressive decrease in the coarse-particle counts. This behavior may be associated with the strong inhibition of sustained growth observed for this additive, as reflected by the reduced apparent growth rates. Additionally, structural reorganization or consolidation of aggregates may reduce the number of discrete entities detected within the 50–150 mm interval. Since FBRM measures particle counts, a reduction in coarse counts can reflect aggregation dynamics or size redistribution.

Figure 2 shows the fine and coarse particle counts of Li₂CO₃ crystals obtained at 4 M. The curves reveal an initial regime dominated by high supersaturation, in which the fine particle pulse appears in the first few moments and then declines due to supersaturation consumption and population transfer to larger entities. In 2a, the curve without additives remains at the highest level, consistent with intense initial nucleation. In contrast, PAA almost completely inhibits fine particle counts from the outset, whereas SHMP and STPP show an early maximum followed by a decline to levels lower than those without additives. This behavior suggests that at 4 M, the presence of polyelectrolytes strongly modifies the early events: PAA shifts the kinetics toward fewer detectable small entities, while phosphates attenuate the initial generation but do not completely suppress it, consistent with their reported role as kinetic and morphological modifiers for Li₂CO₃. SHMP has been described as strongly inhibiting nucleation and inducing non-crystallographic branching, whereas STPP exhibits similar effects, consistent with the sustained reduction in fines [9]. At the process level, this type of additive- and supersaturation-dependent response is expected in reactive crystallization, where the local creation of supersaturation and mixing scales control the initial pulse, and additives govern the nucleation-growth-agglomeration coupling in the transient [14].

In Figure 2b, all additives increase coarseness above the curve without additives, with PAA showing the most pronounced effect. This apparent reversal of PAA, which suppresses fines but increases coarseness, is consistent with the literature attributing to certain additives a simultaneous modification of face growth and agglomeration/compaction, thereby favoring the rapid conversion of small entities into larger, more stable aggregates or structures. PAA has been reported to affect growth via surface interactions and to exhibit an optimal concentration window, in addition to modulating agglomeration and morphology [15].

2.2. Temporal Evolution of the Fines-to-Coarse Ration (f/c) Under Additive Control

Up to this point, the results obtained at 3 M and 4 M have been compared, allowing us to establish the overall effect of the initial supersaturation on the population evolution of Li₂CO₃ in the presence of additives. From this point forward, the analysis focuses exclusively on the 3 M condition, as this regime provides a more suitable framework for consistently correlating observed kinetic trends with the system’s structural and morphological evolution.

Figure 3 presents two graphs of the fines-to-coarse ratio (f/c) over time for an initial LiCl concentration of 3 M and different additive doses. The progressive decrease in f/c over time (at both doses) is consistent with the typical evolution of reactive crystallization: an initial pulse dominated by the generation of small entities (high effective supersaturation and mixing scales), followed by a population redistribution toward larger sizes through growth and/or agglomeration, which reduces f/c as the reaction progresses. With an additive dose of 0.025 g L⁻¹ (Figure 3a), SHMP maintains the lowest values, and STPP also remains below the no-additive condition, suggesting an early shift of equilibrium toward coarse populations due to agglomeration/compaction and/or the effective suppression of secondary nucleation. This reading is consistent with evidence that SHMP modifies subunit morphology, promotes branching, and inhibits secondary nucleation, thereby increasing agglomeration and accelerating the transition to larger effective-size structures (reducing f/c) [8]. The behavior of PAA is indicative of a time- and dose-dependent mechanism; after the initial transient, PAA can decrease agglomeration and alter face growth, maintaining a higher relative fraction of fines compared to coarse particles, which has been reported as part of the simultaneous control of morphology and agglomeration in Li₂CO₃ [15].

At 0.1 g L⁻¹ (Figure 3b), the collapse of f/c to near-zero values for SHMP and the curve without an additive suggests a condition in which the coarse population dominates early on, consistent with intense agglomeration and/or rapid population consolidation. In contrast, PAA and especially STPP exhibit a pronounced initial peak and then stabilize at high values, implying that, at this dose, both additives support a relatively high fraction of fines (or, equivalently, limit the appearance or stabilization of coarse particles) even as the system progresses.

From a mechanistic point of view, this is consistent with (i) selective adsorption and agglomeration control by carboxylated polyelectrolytes (PAA), whose effect exhibits concentration windows and can reduce agglomeration depending on the regime [7,15], and (ii) and (ii) the high reactivity of phosphate groups with Li⁺ and their ability to stabilize critical nuclei and suppress nucleation in certain regimes [9].

2.3. Evolution of Effective Crystal Size and Population Heterogeneity

Figure 4 presents the chord lengths and the square mean weighted to median unweighted ratios (MSW/MNW) as a function of time for Li₂CO₃ crystals obtained at an initial LiCl concentration of 3 M and in the presence of additives at different doses. It can be observed that the chord length reaches detectable values in the early stages, suggesting that the initial formation of entities is governed by a pulse of supersaturation and mixing, after which population restructuring dominates. In Figure 1a, STPP and SHMP remain above the condition without additives, with STPP reaching greater lengths, which is consistent with phosphate additives that can reconfigure the kinetics and induce spherulitic morphologies and assemblies through interaction with Li⁺ and effects on nucleation and branching. In particular, SHMP has been reported to strongly inhibit precipitation/nucleation, interfere with growth, and promote non-crystallographic branching, and STPP has similar effects, favoring more compact or assembled structures, which can result in larger apparent chords and distinct transient responses in FBRM [12]. In contrast, PAA shows a temporal reversal (initially larger, then smaller), consistent with an additive that selectively modulates growth and agglomeration across concentration windows. For Li₂CO₃, PAA has been observed to reduce agglomeration and alter face growth, simultaneously affecting apparent size and aggregate stability [15].

The MSW/MNW reading reinforces the idea that additives shift not only the mean size but also the population heterogeneity. In Figure 1b, the rapid increase followed by a decrease in MSW/MNW across all curves is consistent with the early appearance of a fraction of large entities, followed by relative homogenization through supersaturation consumption and population reorganization. The STPP stands out with persistently low values, suggesting a relatively narrower/more stable population, whereas the SHMP transitions from high values, consistent with a regime change in assembly/compaction. In Figure 1d, SHMP remains the condition with the highest MSW/MNW, indicating a broader distribution with a tail toward large entities, consistent with agglomeration/branching mechanisms reported under high supersaturation, where precursors and non-crystallographic branching can amplify product heterogeneity [11]. In contrast, PAA exhibits the lowest MSW/MNW values at 0.1 g L⁻¹, consistent with more effective control over agglomeration and growth, consistent with the role of polyelectrolytes in modifying kinetic pathways during reactive crystallization [14].

2.4. Population Architecture Revealed by Chord Length Distribution

Figure 5 shows the population information obtained by means of FBRM using unweighted and square-weighted CLD of Li₂CO₃ crystals obtained at an initial LiCl concentration of 3 M and in the presence of additives at different doses. This allows discrimination between the relative presence of fines and the effective contribution of coarse particles to the total inventory, consistent with the previously analyzed temporal trends. For an additive dose of 0.025 g L⁻¹ (Figure 5a,b), the unweighted CLD reveals persistent bimodality under both additive-free conditions and with PAA and STPP, indicating the coexistence of fine and coarse populations. However, PAA shifts the distribution towards a higher proportion of fines, while STPP reinforces the coarse fraction while maintaining the same mode. In contrast, SHMP collapses the distribution into a unimodal form dominated by coarse particles, with a tail toward smaller sizes. This is consistent with its ability to inhibit secondary nucleation and promote more compact assemblies, thus reducing the persistence of an independent fine population. When weighted squared (5b), the differences diminish, and the curves converge toward a distribution dominated by large particles, demonstrating that, despite variations in fines, the effective mass/volume ratio is controlled by large particles. This behavior is consistent with systems in which initial supersaturation generates transient fines, whereas the final structure is governed by growth and agglomeration, as reported for the reactive crystallization of Li₂CO₃ in the presence of polyelectrolyte and phosphate additives.

At higher doses (Figure 5c,d), the response diversifies, further supporting the mechanism. PAA leads to a unimodal CLD centered on fine particles, consistent with a regime in which agglomeration is limited and a dominant small population is stabilized, while SHMP maintains bimodality, with a weakening of the coarse mode, and STPP generates broad distributions that span a wide range of sizes, suggesting the coexistence of competing mechanisms. The square-weighted CLD exhibits contrasting responses, from broad distributions (PAA), indicative of population heterogeneity, to curves close to the condition without additives (SHMP) or bimodal distributions, with a marked reduction in the contribution of coarse particles (STPP). Taken together, these observations confirm that additives not only alter the mean size but also reconfigure the population architecture (bimodality, width, and relative tail weight), in accordance with previous studies that attribute to PAA an effective, dose-dependent control of growth and agglomeration, and to SHMP/STPP a profound modification of nucleation and spherulitic assembly pathways.

2.5. Additive-Dependent Nucleation and Growth Kinetics and Morphological Validation

The maximum nucleation rate ($B$_max) and maximum growth rate ($G$_max), summarized in

Table 1. Maximum nucleation rate ($B$_max) and maximum growth rate ($G$_max) of Li₂CO₃ at different initial lithium chloride concentrations and additive dosages. Units: $B$_max in counts min⁻¹ and $G$_max in µm min⁻¹.

		3 M Initial LiCl
Additive Dose		$B$max	$G$max
	No additive	$6.73\times {10}^5$	$2.97\times {10}^5$
0.025 g/L	PAA	$7.68\times {10}^5$	$1.04\times {10}^5$
	SHMP	$3.29\times {10}^5$	$6.30\times {10}^4$
	STPP	$5.24\times {10}^5$	$1.54\times {10}^3$
0.1 g/L	PAA	$1.14\times {10}^6$	$2.89\times {10}^5$
	SHMP	$2.85\times {10}^4$	$9.20\times {10}^1$
	STPP	$5.70\times {10}^5$	$2.24\times {10}^2$

, were determined according to the criteria used by Piceros et al. (2025) [10]. The results show that, at 3 M LiCl, the additives differentially modify the equilibrium between nucleation and growth during the initial stages of the process. In the absence of additives, the relatively high and comparable $B$_max and $G$_max values reflect a kinetic regime dominated by high initial supersaturation, in which primary nucleation and growth occur almost simultaneously, consistent with previous reports for LiCl-Li₂CO₃ systems monitored by means of FBRM. The addition of PAA at 0.025 g L⁻¹ increases $B$_max but maintains the same order of magnitude for $G$_max, suggesting an intensification of nucleus generation accompanied by sustained crystal growth. This behavior is consistent with ionic complexation and selective polymer adsorption mechanisms on the active faces of Li₂CO₃, which have been widely discussed in the literature for anionic polyelectrolytes. At the highest dose (0.1 g L⁻¹), PAA leads to an even more pronounced increase in $B$_max, whereas $G$_max remains of the same order of magnitude as in the system without additives, indicating that, under these conditions, the initial supersaturation dominates the growth kinetics despite the presence of the polymer.

In contrast, the phosphates studied show a much more pronounced inhibitory effect, particularly on growth. For both doses, SHMP reduces $B$_max and decreases $G$_max by several orders of magnitude, indicating strong suppression of both effective nucleation and the advance of crystalline surfaces. This result is consistent with previous studies reporting interactions between polyphosphates and Li⁺ ions and carbonate surfaces, which promote the stabilization of precursor species or transient aggregates and limit sustained growth [8,9]. STPP exhibits intermediate behavior: at 0.025 g L⁻¹, it moderately reduces $B$_max and $G$_max by two orders of magnitude, while at 0.1 g L⁻¹ it maintains $B$_max at values comparable to the system without additives, but with extremely low $G$_max, which points to a scenario where nucleation occurs, but growth is restricted.

Figure 6 shows SEM images of Li₂CO₃ obtained at an initial LiCl concentration of 3 M, in the presence of additives at a dose of 0.025 g L⁻¹. Regardless of the additive, the product consists of spherulites formed by flat plates with radial growth, predominantly <30 μm in size, although there are systematic morphological differences attributable to additive chemistry. Under the additive-free condition, the spherulites exhibit radial growth, with apparent size variability and surface crystallites, features consistent with the population heterogeneity indicated by the corresponding CLD analysis. In contrast, PAA produces more compact and better-defined spherulites without secondary crystallites, consistent with more uniform growth and modulation of new subunit generation (e.g., by passivation/adsorption and surface stabilization), in line with the reduced population skewness (MSW/MNW) and inhibition of consolidation toward extreme populations observed by FBRM. With SHMP, radial growth becomes markedly disordered, with thin, pointed plates and a high abundance of crystallites, suggesting more intense kinetic interference (altered branching mode and greater propensity for thin/precursor subunits), consistent with the significant changes in the fine/coarse metrics and the CLD modality. Finally, STPP retains an overall morphology similar to that of the system without additives, but with a higher abundance of crystallites, indicating less effective control of secondary nucleation. This reading is consistent with intermediate responses in CLD and with transient dynamics in MSW/MNW.

3. Discussion

The results confirm that the reactive crystallization of Li₂CO₃ is governed by an intense initial supersaturation pulse that determines the system’s early dynamics and conditions the subsequent evolution of the crystal population. Unlike conventional crystallization processes that rely on cooling or evaporation, supersaturation is generated gradually; rapid mixing of concentrated solutions induces a highly transient state in which primary nucleation occurs within an extremely short time window. This behavior is consistent with burst nucleation models described in the literature for highly supersaturated systems, in which the massive generation of initial nuclei is followed by a population redistribution dominated by growth, aggregation, and possible secondary nucleation. In this context, the high temporal resolution of FBRM monitoring enabled the capture of dynamics that are often invisible in ex situ techniques, demonstrating that the population architecture is defined in the earliest moments of the process.

From an interpretative standpoint, the evaluated additives exhibit distinct effects on nucleation and growth indicators under transient supersaturation conditions. Although the present study does not directly resolve molecular-scale mechanisms, the observed kinetic trends can be discussed in light of previously reported interaction modes for similar additive systems. Poly(acrylic acid) (PAA) exhibits concentration- and time-dependent behavior, suggesting behavior consistent with selective adsorption onto active growth sites and electrostatic interactions with ionic species in solution, as previously reported for carboxylated polyelectrolytes in Li₂CO₃ systems. Under certain conditions, the suppression of detectable fines and consolidation into coarser populations indicate rapid structural reconfiguration, possibly driven by a combination of partial inhibition of anisotropic growth and promotion of compact aggregation. This type of response is consistent with previous studies in saline systems, in which anionic polymers modify surface kinetics without significantly altering precipitation thermodynamics [7,10,15].

Sodium hexametaphosphate (SHMP), by contrast, acts as a stronger kinetic inhibitor. From a structural standpoint, SHMP is a cyclic polyphosphate bearing multiple negatively charged phosphate groups, which confer high charge density and multidentate coordination capability. This structure enables electrostatic interaction with Li⁺ ions in solution and potential adsorption onto positively polarized growth sites of carbonate surfaces. Such interactions can partially complex Li⁺ in the near-surface region and/or selectively adsorb onto active incorporation sites, thereby increasing the interfacial kinetic barrier to ion attachment.

As a consequence, two coupled effects may arise: (i) a reduction in sustained crystal growth due to surface passivation and decreased incorporation frequency, and (ii) inhibition of secondary nucleation on existing crystal surfaces, since adsorption blocks high-energy defect sites typically responsible for surface re-nucleation. At the same time, differential adsorption across crystallographic orientations may induce anisotropic growth and non-crystallographic branching, favoring the radial assembly of thin subunits into spherulitic aggregates.

The combined suppression of steady growth and reorganization of subunit assembly is consistent with the marked decrease in apparent growth rates ($G$_max), the modification of CLD architecture, and the SEM evidence of disordered yet compact radial structures. These interpretations align with previous reports on phosphate-mediated morphology control and aggregation-mediated growth mechanisms pathways in lithium carbonate crystallization systems [8,9].

Sodium tripolyphosphate (STPP) exhibits an intermediate, dose-dependent response. The coexistence of sustained nucleation with limited growth, especially at higher concentrations, suggests a competitive equilibrium between complexation in solution and surface adsorption. This apparent decoupling between nucleation and growth highlights that small variations in additive chemistry are associated with measurable differences in kinetic indicators under transient supersaturation conditions.

In morphological terms, the widespread formation of spherulitic aggregates confirms that the system operates in a highly supersaturated regime, where rapid radial growth favors the aggregation of crystalline subunits. The observed differences in compactness and radial organization can be interpreted as a direct consequence of the additives’ kinetic modification. In particular, the greater compaction observed in certain PAA-containing regimes and the greater irregularity in the presence of SHMP may be consistent with differences in aggregation dynamics and surface growth behavior reported in previous studies on additive-mediated lithium carbonate crystallization [8,9].

From an industrial perspective, these findings are relevant to lithium carbonate production, where particle size distribution directly influences filterability, settleability, and behavior in subsequent processing stages. Kinetic control using low-dose additives offers a potentially more flexible strategy than modifying global thermodynamic variables. Furthermore, the system’s sensitivity to mixing conditions underscores the importance of accounting for hydrodynamics in scale-up processes.

It should be emphasized that the conclusions of this work are intended as mechanistic and comparative trends under high-supersaturation reactive crystallization. While the two LiCl concentrations were selected to represent two contrasted supersaturation pulses under otherwise identical conditions, a broader operational mapping would be required to fully parameterize industrial variability. Additionally, the mechanistic interpretations discussed above are framed in the context of previously reported studies on additive-mediated Li₂CO₃ crystallization. The present work provides population-level kinetic and morphological evidence but does not directly resolve molecular-scale interaction pathways. Therefore, the mechanistic considerations presented here are intended as literature-supported interpretations.

4. Materials and Methods

4.1. Materials

All reagents used were commercially available and of analytical grade: lithium chloride (≥99%, Winkler Ltda., Santiago, Chile), sodium carbonate (≥99%, Loba Chemie PVT Ltd., Bombay, India), polyacrylic acid (PAA) with a molecular weight of 230,000, sodium hexametaphosphate (SHMP), and sodium tripolyphosphate (STPP) (all from Aldrich, Taufkirchen, Germany). All solutions were prepared using deionized water.

4.2. Solution Preparation and Precipitation Test

The precipitation of Li₂CO₃ was carried out in a 300 mL batch reactor at 65 °C, a temperature representative of industrial conditions. Mechanical stirring was maintained at 300 rpm to ensure rapid homogenization after reactant addition and to avoid excessive shear that could induce agglomerate breakage or mechanically driven secondary nucleation. Preliminary tests confirmed that at this speed, complete suspension of solids was achieved, no visible dead zones were observed, and FBRM counts remained stable without evidence of artificial fines generation attributable to fragmentation. This setup enabled more precise observation of crystal growth dynamics using FBRM, without significant interference from mechanical disturbances.

In each test, 100 mL of LiCl solution at an initial concentration of 3.0 or 4.0 M was added to the reactor, followed by the corresponding additive dose (see

Table 2. Reactant concentrations and additive dosage (the additive dosage is defined on a volume basis relative to the lithium chloride solution).

[LiCl]0 (mol L−1)	[Na2CO3]0 (mol L−1)	Additives	Additive Dosis (g L−1)
2.0, 3.0	1.5, 2.0	No additive, PAA, SHMP, STPP	0, 0.025, 0.1

). Once the mixture temperature had stabilized, 100 mL of 1.5 M or 2.0 M sodium carbonate solution was rapidly added (within 5 s). This addition caused a temporary drop in the mixture temperature to approximately 45 °C, which returned to 65 °C in about 2 min due to the reactor’s thermostatic control. A rapid addition was chosen to generate a high supersaturation peak and thus capture the initial massive nucleation event.

Crystallization was carried out for 1 h under controlled stirring and temperature conditions, with real-time FBRM monitoring to record system evolution. Crystals were recovered by vacuum filtration, dried at 60 °C, and characterized. Each test was performed in duplicate, revealing consistent trends. For presentation purposes, the graphs include a representative experiment; however, a 5-period moving average was applied to smooth experimental noise and highlight the overall trend.

4.3. Data Analysis

Online monitoring was performed using a Particle Track S400A FBRM^® (Mettler Toledo, Giessen, Germany) equipped with focused beam reflectance technology. The probe was inserted directly into the reactor 2 cm from the bottom, thus avoiding interference from the stirrer. Chord length distribution (CLD) data were recorded at 2-s intervals. The FBRM probe operated at the factory default scan speed of 2 m s⁻¹. Optical and acquisition parameters were kept constant throughout all experiments to ensure direct comparability between conditions.

For analysis, particles with chord lengths less than 10 µm were classified as fine (f), and those between 50 and 150 µm as coarse (c). From these counts, f/c ratios were calculated to indicate the population distribution over time.

The selection of these thresholds was based on the characteristic CLD structure observed in all experiments. A dominant mode below 10 μm appeared consistently during the initial supersaturation pulse, associated with newly generated entities. A second, clearly separated mode emerged above about 50 μm, corresponding to growing crystals and/or spherulitic aggregates. The intermediate region (10–50 μm) exhibited transition populations and was therefore excluded from the classification of fine/coarse to ensure kinetic discrimination between regimes dominated by nucleation and those dominated by growth.

The FBRM probe recorded particles larger than 150 μm; however, its contribution to total counts was lower and occurred mainly in later stages due to occasional aggregation events. The inclusion of these particles in the coarse fraction does not modify the temporal trends or the evolution of the f/c ratio. Therefore, the 50–150 μm window was selected as a statistically robust and kinetically representative interval for comparative analysis.

Median unweighted chord length (MNW) and squared mean weighted chord length (MSW) were determined directly from the CLD. While MSW represents the average size when all particles are weighted equally, it assigns greater weight to larger particles. The MSW/MNW ratio was used to characterize the relative trend of the sample with respect to the population: higher values indicate a population enriched in large crystals, whereas values close to unity indicate a more uniform size.

The modal (mean) MSW value has been shown to be comparable to conventional size-analysis methods in the 50–400 µm range, as reported by Heath et al. [16]. Based on this, the population balance approach can be applied, using the j-th moments $j$ (${\mu }_j$) obtained directly from the CLD to estimate kinetic parameters [17]. In particular, the FBRM probe reports ${\mu }_0$ and ${\mu }_1$, in real time, which can be used to calculate the nucleation rate $B\left(t\right)$ and the growth rate $G\left(t\right)$ throughout the experiment.

The instantaneous nucleation rate $B\left(t\right)$ was estimated as the time derivative of the zero-order momentum (${\mu }_0$), according to the following expression [18]:

$${\displaystyle \frac{d{\mu }_0}{dt}}=B$$

(1)

The growth rate $G\left(t\right)$ was obtained from the zeroth and first order moments, using the relation:

$${\displaystyle \frac{1}{{\mu }_0}}\left({\displaystyle \frac{d{\mu }_1}{dt}}\right)=G$$

(2)

These expressions allow us to derive $B\left(t\right)$ and $G\left(t\right)$ as functions of time, representing, respectively, the rate of appearance of new particles and the average rate of length increase. The maximum velocities $B$_max and $G$_max were determined as the peak values of the derivatives $d{\mu }_0/dt$ and $d{\mu }_1/dt$, calculated from the smoothed CLD data. It is important to note that these velocities represent apparent magnitudes based on the count and chord length, and do not necessarily reflect the absolute number of crystals or the linear growth rate on specific crystal faces. Nevertheless, they constitute valid indicators for kinetic comparison between conditions with different additives.

It should be noted that the CLD obtained by means of FBRM does not correspond precisely to the particle size distribution (PSD), since it measures optical chord lengths affected by the shape and orientation of the particles. However, since all particles in this study exhibited similar spherulitic morphologies, CLD accurately reflected size changes. This was supported by SEM imaging, which confirmed the agreement in fine/coarse particle ratios. Therefore, FBRM data provided reliable information on kinetic and morphological trends.

4.4. Characterization

The crystals obtained from Li₂CO₃ were separated by filtration under reduced pressure and dried for 24 h in a desiccator. They were then observed using optical microscopy and characterized by means of scanning electron microscopy (SEM) on a JEOL JSM-6360 LV instrument (JEOL Ltd., Tokyo, Japan). All measurements were performed at room temperature.

5. Conclusions

This study demonstrates that the reactive crystallization of Li₂CO₃ is governed by an initial supersaturation pulse that controls primary nucleation and conditions the subsequent evolution of growth, aggregation, and population redistribution. The use of online FBRM enabled the resolution of these early dynamics and the clear differentiation of the mechanistic effects of various phosphate and polymeric additives under the investigated high-supersaturation reactive crystallization conditions (3–4 M LiCl).

In the absence of additives, the system exhibits comparable nucleation and growth, resulting in populations with broad size dispersion and evidence of secondary nucleation. The addition of PAA significantly modifies the nucleation-growth coupling: depending on concentration and the supersaturation regime, it can suppress the fines population early on and favor consolidation toward more stable, coarse fractions, thereby reducing population heterogeneity. SHMP acts as a strong kinetic inhibitor, markedly decreasing maximum nucleation and, to a greater extent, growth, leading to distributions dominated by coarse particles or irregular structures associated with interference in crystal growth. STPP exhibits intermediate, dose-dependent behavior, capable of sustaining nucleation without effective growth at high concentrations, or of promoting partial consolidation at low doses.

SEM observations confirm that, under all conditions, Li₂CO₃ precipitates mainly as spherulites, whose compactness and radial order depend on the additive, consistent with the observed kinetic trends.