Polythermal Nucleation Kinetics of NaHCO 3 -Na 2 CO 3 -H 2 O in the Presence of Polyectrolyte Additives

The particle size distribution (PSD) of substances is important to their transportation and packaging. The crystal nucleation kinetics measured from the metastable zone width (MSZW) and/or the induction time are vital to the control of the PSD. In this work, the existence of three polyelectrolyte additives (sodium polystyrene sulfonate (SPS), Polyacetic acid (PAA) and sodium carboxymethylcellulose (CMC)) showed varying effects on the MSZW and induction times of NaHCO 3 -Na 2 CO 3 -H 2 O system. SPS lowers the MSZW and induction time while both parameters were increased in the presence of CMC and PAA. The nucleation inhibition effects were observed to be prominent for both PAA and CMC resulting in observed finer PSDs as cooling rate, b increases from 0.5 K/min to 2.65 K/min. The PSD increases with b for both pure and SPS additive, whereas they decrease for both PAA and CMC.


Introduction
Sodium bicarbonate (NaHCO3) is an essential green inorganic chemical widely used in various industries.NaHCO3 is produced by passing CO2 into an aqueous solution to precipitate NaHCO3.Small needle-like NaHCO3 crystals (prone to agglomeration) are obtained [Kang,, 2021, Jiang, 2019].The addition of Na2CO3 to a solution of NaHCO3 promotes its crystal growth, size and nucleation [Jiang, 2019].The particle size distribution (PSD) of substances is important to their transportation and packaging.The crystal nucleation kinetics (measured from the metastable zone width (MSZW) and/or from the induction time) can be obtained from various model adaptations of the CNT and are vital to the control of final crystal properties such as the PSD [Shiau, 2021;Sangwal, 2010;Kashchiev, 2010;Małysiak, 2021].
In the present work, the effect of three polyelectrolyte additives on the nucleation parameters, and PSD of NaHCO3-Na2CO3 system was investigated.The Nyvlt and Sangwal approaches were used to estimate the nucleation kinetics parameters of NaHCO3-Na2CO3 from MSZW and induction time data.

Theories for the MSZW
The MSZW (ΔTm) denotes the temperature difference between the saturation temperature (T0) and the temperature at which nucleation is detected, (Tm) for a given b; i.e., ΔTm = T0 -Tm.The Nyvlt's model and its modification by Sangwal are two of the most important models for studying the nucleation kinetics by fitting MSZW data against the cooling rates based on CNT.While the Nyvlt's model indicates a linear relationship between ln(ΔTm) vs lnb, the Sangwal's modification, called the self-consistent Nyvltlike approach proposes a relationship between ( ∆   0 ) vs b.Both models and can used to fit accurately the additive effects on MSZW data.The nucleation order, m (which is an indication of the nucleation/growth mechanism) can be obtained from the slope of the models.
where the slope in Eq. (1) = 1/m, and m is the apparent nucleation order, K is the nucleation constant.Both m and K are related to the appearance of visible crystals at Tm.
Eq. ( 1) can be expressed in linear form; A plot of ln( ) vs lnb enables the determination of the value of m from the inverse of the slope, 1/ [10,11].

Materials and Methods
Cooling crystallization experiments were conducted in a 300 mL double-jacketed glass vessel using a programmable temperature bath.Pure analytical grade NaHCO3, Na2CO3 and the polyelectrolye additives were purchased from Sinopharm Chemical Reagent Co. Ltd. and Zichuan Yaodong Chemical Co.Ltd, respectively.18g of NaHCO3 + 0.4 mol Na2CO3 were added to a jacketed vessel with 100 g water.The procedure was repeated with water + 10 ppm each of 3 different polyelectrolye additives, sodium polysterene sulfonate (SPS), Polyacetic acid (PAA) and sodium carboxymethylcellulose (CMC).The solutions were heated and stirred at 400 rpm to achieve complete dissolution of all solutes and cooled at varying cooling rates (0.5-2.67 K/min)) from 361.15 K to 308.15 K.The particle size distribution (PSD) was examined by a microscope and ImageJ.

Effect of additive and cooling rates on MSZW
The existence of three polyelectrolyte additives showed varying effects on the MSZW of NaHCO3-Na2CO3 system.The MSZW data is listed in Table 1 and fitted to the Sangwal's self-consistent Nyvlt-like model in Figure 1.From Table 1, it can be observed that whilst SPS lowers the MSZW, both CMC and PAA raise it, in the order SPS < Pure < CMC < PAA.Likewise, the trend in MSZW correlates with the nucleation temperatures, To (Figure 2), which can be seen to decrease with increasing cooling rates for all measured systems.
The nucleation kinetics of NaHCO3-Na2CO3 system was studied according to the effects of cooling rate and three polyelectrolyte impurities, and the data is listed in Table 1.At the same To, the MSZW of NaHCO3-Na2CO3 system increases with the cooling rate, attributable to the temperature gradient To-Tm, which widens as cooling rate increases.That is to say, at a constant To, increasing the cooling rate results in decreasing Tm, a factor that lowers the supersaturation and consequently the temperature at which the appearance of the crystal nucleus is detected thereby making the MSZW to widen.The temperature gradient To-Tm =Tm and b are also associated with the duration, tm (referred to as the induction time and calculated as tm = ΔTm/b) at which the crystals are detected, from To (Table 2).The tm is associated with the likely growth of critically sized nuclei to visible entities [Sangwal, 2009].
The tm decreases with increasing b, and is also in the order SPS<Pure<CMC<PAA.

Effect of cooling rate on nucleation behaviour
The introduction of impurities into the crystallizing solution has different effects on the growth mechanism and the interfacial tension of crystals.Table 3 shows the fitting results from Eq. ( 2).The nucleation order, m, values suggest the type of nucleation and growth mechanisms such that 3 < m < 7.5 depicts progressive nucleation, and 2 < m < 3 depicts instantaneous nucleation [13].
By fitting the MSZW values of NaHCO3-Na2CO3 to Eq. ( 2), the m values were; m(Pure) = 6.12, m(SPS) = 5.80, m(PAA) = 5.66, and m(CMC) = 5.46.The observed m values show that the growth and nucleation mechanism of NaHCO3-Na2CO3 was by progressive nucleation.Sangwal associated the dimensionless quantity Φ in Eq. ( 2) to the adsorption of impurity on the crystal nuclei, which affects the diffusion of solute molecules in the solution [Huang, 2009].It can be speculated from Table 3 that the diffusion of solute molecules was also impacted to some extent by the additives.

Effect of cooling rate on nucleation behaviour
NaHCO3 crystals with different morphologies were obtained in water (pure) and in the presence of various additives; needle-like (pure), columnar (SPS), and also flaky (PAA and CMC), at different cooling rates as shown in Figure 3. Varying PSDs were observed as shown in Figure 4; the PSD increases with b for both pure and SPS additive, whereas they decrease with b for both PAA and CMC.The PSD is highest in the presence of SPS additive.In all cases, a higher b corresponds to an observed smaller Tm, leading to varying nucleation inhibition effect, PSDs and MSZWs.The nucleation inhibition effect was prominent for both PAA and CMC resulting in observed finer PSDs as b increases from 0.5 K/min to 2.65 K/min.However, the opposite is true for pure and SPS systems whereby PSDs and crystal sizes increased with increasing cooling rate.That is to say, at a higher b, in both pure and SPS systems, faster nucleation was promoted resulting in larger PSDs with bigger size.The observed PSD and MSZW in the various additives are consistent since the PSD is directly related to MSZW, and a smaller or narrower MSZW is usually associated with an increase in PSD [Huang, 2009].

Figure 2 .
Figure 2. Observed nucleation temperatures indicating the inhibition of nucleation by various additives.

Table 2 .
Induction time of NaHCO3-Na2CO3 system at a constant To = 361.15K