Phosphate recovery from water using cellulose enhanced magnesium carbonate pellets: Kinetics, isotherms, and desorption

Abstract

Phosphorus is an essential and limited nutrient that is supplied by a depleting resource, mineral phosphate rock. Eutrophication is occurring in many water bodies which provides an opportunity to recover this nutrient from the water. One method of recovery is through adsorption; this study focused on fabricating a porous and granular adsorptive material for the removal and recovery of phosphate. Magnesium carbonate was combined with cellulose in varying weight ratios (0, 5, 10, 15, 20%) to synthesize pellets, which were then calcined to increase internal surface area. Physiochemical properties such as surface area, surface morphology, elemental composition, and crystal structure of the materials were characterized using Brunauer, Emmett, and Teller (BET) surface area analysis, X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDS). The pellet proved to be uniform in composition and an increase in BET surface area correlated with an increase in cellulose content until pellet stability was lost. Phosphate adsorption using the pellets was studied via batch kinetics and sorption isotherms. The pseudo-second-order kinetics model fits best suggesting that the adsorption occurring was chemisorption. The isotherm model that fit best was the Langmuir isotherm, which showed that the maximum equilibrium adsorption capacity increased with an increase in cellulose content between 10% and 20%. The average adsorption capacity achieved in the triplicate isotherm study was 96.4 mg g⁻¹ for pellets synthesized with 15% cellulose. Overall, using cellulose and subsequent calcination created an additional internal surface area for adsorption of phosphate and suggested that granular materials can be modified for efficient removal and recovery of phosphate from water.

Graphical Abstract

1. Introduction

As the limiting nutrient in most waterways, increased loads of phosphorus (P) can cause eutrophication, which leads to hypoxia and the proliferation of harmful algal blooms [1], [2], [3], [4], [5]. Additionally, while viewed as a pollutant at excessive concentrations (i.e., >20 μg L⁻¹) [6], phosphate (PO₄³⁻), the main species of phosphorus in the environment, is necessary for a range of industrial purposes including the production of agricultural fertilizers, animal feeds, and chemical pesticides [7]. Environmental Protection Agency (EPA) limit for acceptable phosphorus levels is only 0.1 mg/L or lower. Phosphate reserves are quickly declining [8], making a recovery and reuse of PO₄³⁻ an essential component of phosphate remediation. Adsorption is a technique which can both remove and recover PO₄³⁻ from aqueous suspensions and has been extensively studied. Adsorbents ranging from modified iron oxide [9], [10] to calcined waste eggshells [11], to magnesium modified corn biochar [12] have been investigated for phosphate adsorption. However, adsorption suffers from the problem of bottle-necking (i.e., after saturation, the adsorbent will no longer be applicable) [13]. While the use of highly adsorptive fine powders, which can desorb phosphate after remediation, is a growing area of study [14], their removal from the solution after adsorption is difficult. Therefore, the synthesis of highly adsorptive, inexpensive, and granular sized sorbents, which can recycle PO₄³⁻ would be extremely beneficial to the problem of nutrient pollution.

Magnesium (Mg) has been widely used in the medical field as a phosphate binder in dialysis patients as Mg can effectively bind PO₄³⁻ without the adverse health effects demonstrated by aluminum and calcium [15], [16], [17], [18], [19], [20]. Additionally, Mg salts have been used for environmental applications in drinking and wastewater [21], [22]. For example, Mg has effectively been employed in enhanced biological phosphate removal (EBPR) processes, which allow phosphorus accumulating organisms (PAOs) to release P under anaerobic conditions and then excessively uptake P under aerobic conditions. The addition of Mg salts in EBPR processes under anaerobic conditions resulted in the formation of phosphate precipitates including newberyite (MgHPO₄) and struvite (MgNH₄PO₄·6H₂O) [23], [24], [25]. Newberyite and struvite can be used as slow-release fertilizers making their formation during phosphate remediation processes ideal for recycling PO₄³⁻ [21], [26], [27], [28].

For the above PO₄³⁻ remediation processes, powdered, water-soluble Mg salts (e.g., magnesium chloride) were used [21], [27]. Here, magnesium carbonate (MgCO₃) was selected to prepare pellets (i.e., 6 mm × 17 mm) as phosphate adsorbents due to its very low water solubility (i.e., 0.11 g L⁻¹ at 25 °C) [29]. Mechanically stable pellets were prepared by blending different ratios of MgCO₃ and cellulose, which acted as a binder. The cellulose binder was burned off to create porosity in the pellet. After pellet stability in water was ensured, phosphate adsorption was evaluated.

2. Experimental

2.1. Materials

Analytical grade MgCO₃ powder (Fisher Scientific) was made into pellets, 6 mm in diameter and 17 mm in length on average, using the MZL Flat Die Pellet Mill (Xuzhou Orient Industry) as seen in Fig. 1. Varying amounts of a cellulose binder, with average particle size of 20 μm (Sigma Aldrich), was used to optimize the pellet design. Pellets were made with a constant moisture content of 45% water to MgCO₃ weight ratio. Cellulose was added in varying weight ratios from 0 to 20%. Conditions for the use of the pellet mill were kept as consistent as possible, but the instrument did allow for variation as related to the length of pellets made. After synthesis, the pellets were calcined at 300 °C to remove cellulose for additional porosity without complete decomposition of the magnesium carbonate. Five specific pellet conditions were selected for further study with regard to cellulose ratio and calcination time: 0% cellulose calcined for 17 h (0%17), 5% cellulose calcined for 1 h (5%1), 10% cellulose calcined for 2 h (10%2), 15% cellulose calcined for 1 h (15%1) and 20% cellulose calcined for 2 h (20%2). The calcination temperature was varied based upon the stability test conducted after each trial of pellet production. It is hard to control the pellet uniformity such as how much pressure it can experience, water ratio inside and outside the pellet, cellulose distribution, etc. Due to these effects, the pellets were calcined at different temperatures. The phosphate stock solution was created using analytical grade sodium phosphate monobasic dihydrate (NaH₂PO₄·2H₂O) (Fisher Scientific).

Fig. 1.

Pellets were synthesized with magnesium carbonate and cellulose for phosphate adsorption (photo by E. Martin).

2.2. Sample characterization

Pellet composition was examined using SEM-EDS (EDAX JEOL 7401) performing both a line scan and cross-section scan of the pellet from each batch. The uniformity was determined by comparing the percentage of carbon (C), oxygen (O) and Mg present across each scan. The BET surface area was determined using the NOVA 2000e Surface Area & Pore Size Analyzer (Quantachrome). Samples were first purged with nitrogen gas at 150 °C overnight before analysis. The surface morphology of the MgCO₃ pellets was observed using SEM (Philips XL 30 ESEM-FEG), at an accelerating voltage of 30 kV. The crystal structure was determined using XRD (PANalytical X’Pert) with the 2-theta diffractometer under CuK_α radiation, and a wavelength of 1.54 μm and the XRD patterns were analyzed using JADE software (MDI, Inc., Livermore, CA).

2.3. Adsorption studies

2.3.1. Kinetic studies

Kinetic experiments were conducted to understand the adsorption reaction rates between adsorbate and adsorbent phosphate concentration. The initial conditions for the kinetic study were: (i) adsorbent amount: one pellet (∼0.4 g), (ii) temperature: 22.7 °C ± 0.5, (iii) pH: 7.0 ± 0.1, (iv) target phosphate concentration: 160 mg L⁻¹, and (v) mixing speed: 150 rpm. The study was conducted with 125 mL of the sodium phosphate monobasic dihydrate stock solution mixed with the five different MgCO₃ pellet compositions in 125 mL Nalgene polypropylene bottles and placed on a G10 Gyratory shaker (New Brunswick Scientific Co., Inc., USA). Samples were taken at various times (1, 2, 3, 4, 7, 9, 11, 14, 18 and 25 days) to analyze for phosphate concentration remaining in the solution. The samples were filtered using a 0.45 μm nylon syringe filter (Whatman) and analyzed for phosphate using a UV–Vis spectrophotometer (DR 2700, HACH) via the US EPA PhosVer 3® (Ascorbic Acid) method at 880 nm. The experiment was conducted once, and the phosphate samples were analyzed in duplicate and averaged.

2.3.2. Sorption studies

Next, an isotherm experiment was completed with varying sorbent masses, from 1 (∼0.4 g) to 6 (∼2.4 g) pellets, to find the maximum equilibrium adsorption capacity of each material. The phosphate concentration in the stock solution was raised to 330 mg L⁻¹ but, otherwise, the conditions were the same as for the kinetics studies. The various 125 mL Nalgene bottles were left on the shaker for 25 days to reach equilibration and then analyzed for phosphate concentration remaining in solution using the US EPA PhosVer 3® method. The isotherm with all five pellet compositions was conducted once. An additional isotherm experiment for the 15%1 pellet was conducted in triplicate. All of the phosphate analysis was conducted in duplicate and averaged.

2.4. Desorption experiment

The desorption experiments were conducted using 4–6 pellets from the isotherm adsorption experiment in various solutions to analyze the recovery of phosphate. Two solutions varied pH in an attempt to achieve desorption: 0.1 M HCl and 0.1 M NaOH. Pellets were also placed into the deionized water just to measure leaching without changing pH. The spent adsorbents were placed in 125 mL Nalgene bottles with 125 mL of each various solution and left on the shaker at a mixing speed of 150 rpm for 25 days, as with the isotherm experiments. The concentration of phosphate that returned to the solution was measured using the US EPA PhosVer 3® Method mentioned in Section 2.3, and the desorption percentage of phosphate was calculated. This experiment provided insight into the ability of the pellets to release phosphate as a potential slow release fertilizer.

3. Results and discussion

3.1. Sample characterization

3.1.1. Physical characteristics

The first step for pellet characterization was to ensure that the pellets had uniform composition. This was accomplished by investigating two separate batches of a pellet from the same recipe, namely the 15%1 pellet. One pellet from each batch was analyzed using SEM via a line scan as well as a cross-section scan. The elemental composition of these pellets prior to adsorption was determined using EDS for Mg, O, and C. Fig. 2 shows the percentage range of each element across the particular scan of the pellet.

Fig. 2.

Line scan and cross-section scans of two 15% cellulose samples for carbon, oxygen, and magnesium; (a) line scan of sample 1, (b) cross-section scan of sample 1, (c) line scan of sample 2, (d) cross-section scan of sample 2.

The two cross-section scans have the same distance scanned because the diameters of the pellets were limited to the diameter of the die hole on the pelletizer, which was about 6 mm. The line scans show the variety in length of the two pellets. Overall, the range of percentages of each element was consistent for the two pellets in both the line scan and the cross-section scan. The carbon and magnesium percentages ranged from 15 to 35% and the oxygen ranged from 45 to 55%. This showed uniform composition between the two batches and demonstrated the random distribution of each element within the pellet.

Physical properties of the pellets are summarized in Table 1. The BET surface areas for the 0%17, 5%1, 10%2, 15%1, and 20%2 pellets were 27.5, 33.2, 36.9, 43.1, and 37.6 m² g⁻¹, respectively. As the ratio of cellulose increased, the BET surface area increased until the 20%2 sample. At this point, the stability of the pellet began to be lost which could account for the decrease in surface area. The 20%2 sample had more visual char that was clogging the pores and decreasing the surface area. As expected, the addition of cellulose provided additional internal surface area.

Table 1.

Physical characteristics of the 5 various pellet recipes (n = 100).

General Characteristics
Diameter	6.0 mm ± 0.05
Length	17.0 mm ± 2.13
Surface area	377.0 mm2 ± 40.63
Volume	480.8 mm3 ± 61.56
Weight	0.4 g ± 0.05

Pellet specific characteristics	Weight change from calcination (%)	BET Surface Area (m2 g−1)
0%17	−64 ± 2	27.5
5%1	−49 ± 2	33.2
10%2	−46 ± 2	36.9
15%1	−51 ± 2	43.1
20%2	−59 ± 4	37.6

3.1.2. Surface morphology of the pellets

Fig. 3 shows SEM images of the surface of the 0% cellulose baseline pellet and the 10% cellulose pellet before and after phosphate adsorption. Many particulate aggregates were observed on the surface of the MgCO₃ pellets before phosphate exposure. To confirm phosphate adsorption on the surface of the pellet, the elemental composition was checked with EDS. A clear peak was seen for phosphorus on the 10%2 pellet while the 0%17 pellet did not have such a clear peak. This illustrated that increased cellulose content resulted in an increase in phosphate adsorption, as expected.

Fig. 3.

SEM images of (a) 0%17 pellet before adsorption, (b) 0%17 pellet after adsorption, (c) 10%2 pellet before adsorption and (d) 10%2 pellet after adsorption (all scale bars represent 1 μm).

3.1.3. XRD analysis

Various magnesium phosphates can form depending upon the pH and molar concentration and are listed below.

• Monomagnesium phosphate (Mg(H₂PO₄)₂)

• Dimagnesium phosphate (MgHPO₄)

• Magnesium phosphate tribasic (Mg₃(PO₄)₂)

Amorphous magnesium phosphate.

The XRD patterns for each sample before and after an adsorption isotherm showed that cellulose, periclase (MgO) and brucite (MgOH) were present for the pellets before adsorption. As shown in Fig. 4a, the pellets had both variations of magnesium present due to mixing magnesium carbonate with water and then calcining the pellets. After adsorption experiments were conducted, magnesium variations were detected mostly as hydromagnesite (Mg₅(CO₃)₄(OH)₂·4H₂O) with some remaining brucite and magnesium phosphate (as cattiite) as shown in Fig. 4b. The pellet with the most phosphate present was the 15%1 pellet as seen with the highest peak of cattiite. Finding magnesium phosphate after the adsorption experiments further confirmed that adsorption occurred and that the increased surface area from cellulose addition was providing additional adsorption capacity.

Fig. 4.

XRD patterns of the various pellets (a) before and (b) after adsorption isotherms were conducted.

3.1.4. Thermal stability of the pellets

The thermal stability of the pellets was investigated using thermogravimetric analysis to determine the pellets made from different proportions of cellulose-water-magnesium carbonate mixture affects the decomposition temperature. The 0%17 pellet provided a good control group to determine if adding cellulose alone affected the thermal stability. Fig. 5 presents the loss in weight as the sample was exposed to higher temperatures.

Fig. 5.

Fig. 5 presents the loss in weight as the samples were exposed to higher temperatures under oxidative conditions.

The 0%17 pellet had a peak for onset degradation temperature at 319 °C as the baseline. The pellets with cellulose showed improvement in onset decomposition temperature. The onset decomposition temperatures for the 5%1, 10%2, 15%1, and 20%2 pellets were 384, 399, 364 and 403 °C, respectively. Cellulose provided binding and increased the thermal stability up until the 15%1 pellet where porosity took control and slightly decreased the stability. The 15%1 pellet still had a higher temperature than the 0%17 pellet. The 20%2 pellet increase thermal stability again because this pellet had more char present on the surface and in the pores which added to thermal stability.

3.2. Adsorption studies

Table 2 represents various adsorptive materials used for recovering phosphate from water categorized by the main element or base material modified to create the adsorbents. The range of adsorption capacity is from 0.28 to 326.63 mg of phosphate adsorbed per gram of adsorbent.

Table 2.

^# Phosphate adsorption capacity, surface area, pH, and temperature for various adsorbents.

Adsorbent	Capacity (mg/g)	Surface area (m2/g)	pH	Temperature (°C)
Kaolinite in Iran	0.32	3.66	2–10	25
Bentonite in Iran	0.28	84.98	2–10	25
Tunisian kaolinite	38.46	68.5	3–9	25
Tunisian smectite	42.19	106.2	3–9	25
Kanuma clay with corn starch and CaO tablet	4.39	15.401	2–12	288.15, 298.15, 308.15 K
Kanuma clay with corn starch, Fe powder, white cement and CaO tablet	3.61	15.59	2–12	288.15, 298.15, 308.15 K
Electrochemically modified Kanuma clay tablet	5.36	16.12	2–12	288.15, 298.15, 308.15 K
La modified bentonite	0.93	N/A	3–11	25
LaAl/Al pillared montmorillonite	13.022/10.307	N/A	3–8	25,30,35
Phoslock®	10.54	39.3	5–9	10,23,35,40
Zenith/Fe bentonite	11.15	N/A	5–9	15,25,35
Calcined Mg-Al-CO3 LDHs	187.1*	82.5–143	3–11	25
Calcined hydrotalcite at 500C	244.58	250–300	9	25,45,65
Calcined hydrotalcite at 400C	192.9	250–300	9	25,45,65
Calcined Zn-Al LDH	41.26	81.2	N/A	25
Calcined MgMn LDH in seawater	7.5	68	3–10	10,25,40
Mg LDH	61	202	3–12	25
Dolomite LDH	36	80	3–12	25
Synthetic hydrotalcite	47.3	N/A	7.8	25
Mg-Al LDH	26.4*	64.4	7	10,25,50
Hydrotalcite	60	44	9	25,45,65
Zeolite in Iran	0.37	13.83	2–10	25
Hydrated aluminum oxide modified natural zeolite	7	17.8	2–11	21
Zeolite/lanthanum hydroxide	71.94	55.69	2.5–10.5	25
Synthetic zeolite	52.91	74.5–174.4	3–9	25
La/Al modified zeolite	2.429	N/A	2–12	10,20,30
HUD synthetic zeolite	79.4	500	2.5–10	298 K
Al modified HUD zeolite	75.8	642	2.5–10	298 K
Zeolites from fly ash	11.79–47.17	29–91.49	1.58–12.11	25
Lanthanum hydroxide-doped carbon fiber	16.1	N/A	2–12	25
Commercial/synthesized lanthanum hydroxide	55.56/107.53	31.1/153.3	1.5–13	25
La doped silicate	26.7	763.2	2–12	25,35,45
La doped vesuvianite	6.7	N/A	3–13	5–35
La(OH)3 modified vermiculites	79.6	39.1	3–11	25,30,35,45
La loaded granular ceramic	0.9015	26.83	2–12	20,30,40
Monohydrocalcite	1.67–3.63*	16.4	8–9	15,25,35
Calcite in Iran	1.82	0.98	2–10	25
Calcined waste eggshell	23.02	19.32	2–10	25,35,45
Freshwater mussel shells	6.95	N/A	1.5–9.5	25
Wasted scallop shell	23	N/A	2–10	15,25,35,45
Recycled crab shells	108.9	N/A	2–10	15–45
Calcite/aragonite in seawater	0.4/1*	N/A	7.2–9	5–45
Gas concrete	17.32	22	2,5,11.5	20,55
MgOH in situ from diatomite	52.08	72.53	5–10	288, 298, 308, 318 K
MgO microspheres made in water	3.17	1.82	5	30
MgO microspheres made in PSS	75.13	72.10	5	30
Natural palygorskite	3.73	206	4–9	25
Acid treated palygorskite	6.64	342	4–9	25
Acid/thermal treated palygorskite	8.31	287	4–9	25
Thermally treated palygorskite	42	47	3–9	25
Magnesium modified corn biochar	200–239	382–494	6–10	288,303,318 K
Magnesium amorphous calcium carbonate	199.44*	70.45	6–10	25
Ca-Mg loaded biochar made at 600C	326.63	487.49	4–10	288, 303, 318 K
Natural calcium-rich attapulgite	3.32	N/A	4,7,10	25
Half-burned dolomite	10	N/A	7.5–8.5	25
Dolomite	48	0.14	1–11	20,40,60
E33	37.74	140.4	7	21
E33 coated with Mn	30.96	102.8	7	21
E33 coated with Ag I/II	25.52/38.80	124.6/142.0	7	21
FeO tailings	8.21	47.9	3–10	5,20,35
FeO anion exchange resin	48	N/A	7.2–7.6	24
Goethite	144	316	5,6.7	25,45,65
Zr coated magnetite nanoparticles	42.19	152.46	3–10	N/A
Magnetic Fe-Zr binary oxide	13.65	106.2	3–11	25
Iron sludge	18.7	113	7.6	N/A
Mesoporous ZrO2	29.71	232	3–11	25
Calcite and Fe-rich calcareous soils	26	0.6	5–8	25
LaO on Fe3O4@SiO2 magnetic nanoparticles	27.8	47.73	2–12	25
2 sedimentary apatites	0.31/1.09	0.72/0.57	8	22
3 igneous apatites	0.41/0.37/0.28	0.53/0.48/0.58	8	22
Aluminumoxid S	34.57	200	6	25,45,65
Activated alumina/2 Al-impregnated silicates	53.7/81.9/58.8*	155/343/328	6.4–7.2	25
Dewatered alum sludge	3.5	N/A	4.3–9	20
Hydrothermally synthesized silicate nanoparticles	93.46	N/A	7	303–323 K
Alkaline residue (AR)	134.8	28.7	10.83	25
AR treated with NaOH	211.9	14.1	11.58	25
AR treated with HCl	2.2	100.6	3.96	25
AR calcined at 800C	139	29.31	2.5–11.5	25
Chitosan modified with zirconium ions	61.7	7.39	2–10	4,15,23
Drinking water treatment residuals	4.17–8.20	21–74	5,7,9	N/A
Calcined paper sludge	∼113.96*	N/A	2–12	10,40,60
Fly ash	32	1.42	3,5,7,9,11	25,40,50,60
Slag	60	1.29	3,5,7,9,11	25,40,50,60
Portland cement	83	1.38	3,5,7,9,11	25,40,50,60

^*Converted from original units.

^#http://rave.ohiolink.edu/etdc/view?acc_num=ucin1490351099058308.

3.2.1. Optimum surface area

To study the best dimensions for the physical size of the pellet, pellets were studied with the varying surface area of 380 mm³, 430 mm³, and 550 mm³ via cutting the pellets. Although the pellets were cut, the overall mass used was kept consistent. The adsorption experiment was run over just four days to investigate the change in adsorption capacity of the three conditions, including the full pellet as a reference baseline. Fig. 6 shows the change in adsorption capacity over the four days for each surface area condition for the four pellet recipes.

Fig. 6.

Adsorptive capacity for the three different surface area conditions for (a) 5%1, (b) 10%2, (c) 15%1 and (d) 20%2.

Overall, each pellet recipe had a higher adsorption capacity with the decrease in pellet length. This is expected since cutting the pellet exposed another surface for adsorption and illustrated that adsorption is occurring on the surface of the pellets. Fig. 7 illustrates that each variation in the surface area still has the same overall trend in adsorption capacity, namely that the capacity increases with the increase in cellulose content.

Fig. 7.

Adsorptive capacity for the three different surface area conditions for (a) 380 mm³, (b) 430 mm³, (c) 550 mm³.

3.2.2. Kinetic studies

An adsorption experiment was conducted to determine the equilibrium time for the phosphate concentration remaining in the solution after pellets had reached adsorption capacity. Fig. 8 shows how the phosphate concentration in solution changed with respect to time and suggested an apparent equilibrium time of 600 h or 25 days. Each recipe removed a different overall percentage of phosphate; 0%17 removed 34%, 5%1 removed 80%, 10%2 removed 72%, 15%1 removed 95% and 20%2 removed 81%.

Fig. 8.

Phosphate concentration remaining in solution over time as the various pellet recipes reached adsorption capacity.

Batch experiments, with one pellet in 125 mL of a solution with target phosphate concentration of 160 mg L⁻¹, were conducted to determine the rate of phosphate adsorption, specifically to find the order of the rate constant. The kinetics of each of the five pellet recipes were studied and compared with the pseudo-first-order (Fig. 9a) and pseudo-second-order (Fig. 9b) kinetics models to find the best fit using linear regression analysis.

Fig. 9.

Linearized (a) pseudo first-order kinetics model and (b) pseudo-second-order model applied to the four various pellet recipes.

The pseudo-first-order model and pseudo-second-order model are, respectively, as follows:

$$\log \left(q_e-q_t\right)=\log \left(q_e\right)-k_{1}t/2.303$$ (1)

$$t/q_t=1/k_2{q}_e^2+t/q_e$$ (2)

where q_e is the amount of adsorbate adsorbed per unit mass of adsorbent (mg g⁻¹) at equilibrium, q_t is the amount of adsorbate adsorbed per unit mass of adsorbent (mg g⁻¹) at time t, k₁ (h⁻¹) and k₂ (g mg⁻¹ h⁻¹) are the rate constants for the pseudo-first-order model and pseudo-second-order model, respectively. The linear forms of the models, the parameters, and how the parameters correlate with each model (R²) are listed in Table 3. The pellet recipe without cellulose is not included since it is the baseline.

Table 3.

Adsolotion kinetic models, the corresponding linear forms and parameters of MgC₀₃ pellets with various amounts of cellulose for 4 different synthesis conditions (percent cellulose and calcination time) with initial pH 7 at 23 °C.

Sorbent	Pseudo-first-order			Pseudo-second-order
	$\log \left(q_6-q_t\right)=\log \left(q_e\right)-k_{1}t/2.303$			$t/q_t=1/k_2{q}_e^2+t/q_e$
	qe(mg g1)	k1(h−1)	R2	qe(mg g1)	k2(g mg−1h−1)	R2
5%1	33.34	0.0095	0.9824	36.22	0.0004	0.9880
10%2	36.91	0.0084	0.9497	40.50	0.0003	0.9979
15%1	56.49	0.0118	0.9959	52.25	0.0003	0.9959
20%2	27.48	0.0071	0.9312	43.54	0.0005	0.9988

Overall the best fit model was the pseudo-second-order model with R² > 0.98 for all pellet recipes, but the pseudo-first-order model fit all recipes with R² > 0.93, so both models had a strong correlation, which has been found in other phosphate adsorption experiments [12], [30], [31], [32], [33], [34], [35], [36]. The pseudo-second-order model indicates that the adsorption that occurred was chemisorption, which assumes monolayer adsorption. The highest model adsorption capacity for both models occurred for the 15%1 pellet; q_e was 56.49 mg g⁻¹ for pseudo-first-order and 52.25 mg g⁻¹ for pseudo-second-order. In the pseudo-second-order model, k₂q_e² represents the initial adsorption rate. The rate for the 5%1, 10%2, 15%1 and 20%2 pellets were as follows: 0.492, 0.449, 0.823 and 1.021 mg g⁻¹ h⁻¹, respectively. This means that although the 15%1 pellet has the highest adsorption capacity, the 20%2 recipes had the fastest initial adsorption rate of 15%1 as a close second.

3.2.3. Sorption isotherms

Sorption isotherms describe the relationship between the equilibrium adsorbate concentration in the solution and the amount of phosphate adsorbed on the adsorbent. Batch experiments, with one to six pellets in 125 mL of a solution with target phosphate concentration of 330 mg L⁻¹, were conducted to determine the maximum adsorption capacity of the pellets.

The two studies were compared for overall adsorption capacity of phosphate concentration from solution as the adsorbent mass was increased. Fig. 10a and 10b represent the two isotherms for overall adsorption capacity on a number of pellets basis.

Fig. 10.

Adsorption capacity comparison with 5 pellet recipes in two isotherm experiments with initial concentration (a) 160 mg L⁻¹ and (b) 330 mg L⁻.

The lower concentration was more easily removed using multiple pellets than the higher concentration but the adsorption capacities were higher overall in the solution with higher phosphate concentration originally. Since the only option with the pellets was to increase the mass used for the isotherm, the original concentration used in kinetics for one pellet was not high enough to show a removal trend for multiple pellets.

Isotherm data was fitted to both the Langmuir and Freundlich models (see Figs. S1 and S2) to determine the best fit using regression analysis as shown in Fig. 11a and b, respectively.

Fig. 11.

Linearized (a) Langmuir model and (b) Freundlich model applied to the four various pellet recipes.

The linearized Langmuir equation is as follows:

$$C_e/q_e=1/q_{\max }{C}_e+1/K_L{q}_{\max }$$ (3)

where q_e is the amount of adsorbate adsorbed per unit mass of adsorbent (mg g⁻¹), C_e is the amount of unadsorbed adsorbate concentration in solution at equilibrium (mg L⁻¹), q_max is the maximum amount of adsorbate per unit mass of adsorbent to form a complete monolayer on the surface (mg g⁻¹), and K_L is a constant related to the affinity of the binding sites (L mg⁻¹). Similarly, the linearized Freundlich equation is as follows:

$$\log \left(q_e\right)=\log K_F+1/n\log C_e$$ (4)

where K_F is the adsorption capacity of the adsorbent (mg g⁻¹ (L mg⁻¹)^1/n) and n indicates sorption favorability. The parameters found via plotting these linearized equations are shown in Table 4, excluding the 0% cellulose baseline pellet.

Table 4.

Adsorption isotherm models, the corresponding linear forms and parameters of MgCO₃ pellets with various amounts of cellulose for 4 different synthesis conditions with initial pH 7 at 23 °C.

Sorbent	Langmuir isotherm			Freundlich isotherm
	$C_e/q_{\text{e}}=1/q_{\mathit{max}}{C}_e+1/K_L{q}_{\mathit{max}}$			$\log q_e=\log K_F+1/n\log C_e$
	qmax (mg g−1)	KL (L mg−1)	R2	KF (mg g−1 (L mg−1)1/n)	n−1	R2
5%1	18.69	−0.1264	0.9761	17.47	0.0683	0.8257
10%2	14.47	−0.1247	0.9381	20.61	0.1900	0.9513
15%1	28.17	−0.4517	0.9917	19.57	0.2126	0.7094
20%2	44.25	0.9741	0.9995	16.06	0.4031	0.9124

Based on this analysis, the best fit for the isotherm studies was the Langmuir model revealing that the adsorption occurred in a monolayer fashion. This confirms the findings that the pseudo-second-order kinetics model fits best, which also assumes monolayer adsorption. The maximum theoretical adsorption capacities found using the Langmuir model were: 18.7, 14.5, 28.2, and 44.3 mg g⁻¹ for 5%1, 10%2, 15%1 and 20%1 pellets, respectively. Here the 20%2 pellet had the highest capacity, but this is the least stable pellet.

The final isotherm conducted was completed for the 15%1 pellet in triplicate with the 330 mg L⁻¹ solution to find the reproducibility of the adsorption capacity. The results were modeled with the linearized Langmuir and Freundlich models as shown in Fig. 12a and b, respectively. The parameters determined from these models are listed in Table 5 (See Fig S3 for SEM and EDS data).

Fig. 12.

Linearized (a) Langmuir model and (b) Freundlich model applied on the triplicate isotherm experiment with 15%1 pellets.

Table 5.

Adsorption isotherm models, the corresponding linear forms and parameters of MgCO₃ pellets with 15% cellulose with initial pH 7 at 23 °C. Data from triplicate experimental runs.

Sorbent	Langmuir isotherm			Freundlich isotherm
	$C_e/q_{\text{e}}=1/q_{\mathit{max}}{C}_e+1/K_L{q}_{\mathit{max}}$			$\log q_e=\log K_F+1/n\log C_e$
	qmax (mg g−1)	KL (L mg−1)	R2	KF (mg g−1 (L mg−1)1/n)	n−1	R2
15%1	91.74	0.3586	0.9657	28.95	0.2825	0.9457
15%1	116.28	0.5478	0.9785	36.46	0.4531	0.7824
15%1	81.30	0.4786	0.9944	29.89	0.2333	0.7358
Average	96.44±18.0	0.46±0.1		31.76±4.1	0.32±0.1

The triplicate analysis of the 15%1 pellet resulted in an average q_max of 96.4 mg g⁻¹ with a standard deviation of 18 mg g⁻¹ and relative standard deviation of 18.6% for the experiments. The variation in predicted adsorption capacity from the kinetics and isotherm experiments can be explained by the variation in diffusion and surface area of pellets exposed to the solution. The bottles in the kinetics experiment were moved from the shaker for each sample throughout the experiment whereas the bottles in the isotherm experiment were kept on the table until the full 25 days had passed. During the movement for the kinetics experiment, the pellet may have shifted in the solution and exposed the additional surface area for adsorption.

3.3. Desorption experiment

Since the adsorption of phosphate was proven reasonably successful, pellets from the isotherm were studied for the ability to recover phosphate through desorption. Three different solutions were used to try to achieve this: deionized water (pH ∼ 6.6), 0.1 M HCl (pH < 2) and 0.1 M NaOH (pH ∼ 12.4). Table 6 shows the percentage of desorption seen after 25 days. This desorbability parameter is defined by the ratio of phosphate desorbed over phosphate adsorbed and provides an indicator for phosphate recovery potential.

Table 6.

Desorption of adsorbed phosphate using three different solutions.

Sorbent	0.1 M HCl			0.1 M NaOH			DI Water
	Adsorbed PO43− (mg g−1)	Desorbed PO43− (mg g−1)	Desorption Percentage	Adsorbed PO43− (mg g−1)	Desorbed PO43− (mg g−1)	Desorption Percentage	Adsorbed PO43− (mg g−1)	Desorbed PO43− (mg g−1)	Desorption Percentage
5%1	7.29	0.26	3.6%	10.69	0.14	1.3%	8.93	0.01	0.1%
10%2	7.65	0.06	0.7%	11.98	0.23	1.9%	9.43	0.01	0.1%
15%1	8.32	0.08	1.0%	12.69	0.56	4.4%	10.44	0.01	0.1%
20%2	9.25	0.07	0.8%	13.91	0.35	2.5%	11.07	0.01	0.1%

Based on the results, leaching into the water without a desorption aid was negligible. Even with the change in pH, only as much as 4% of phosphate was desorbing. To further investigate what was occurring on the surface of the pellet, XRD analysis was conducted on each pellet after desorption in the acidic and basic solutions (Fig. 13a and b, respectively).

Fig. 13.

XRD patterns of the various pellets after (a) 0.1 M HCl solution and (b) 0.1 M NaOH solution desorption experiments were conducted.

From the figure, magnesium phosphate was no longer detected on the pellets after the desorption period (25 days). On closer inspection of the experiment with the acidic solution, phosphorus was detected via EDS but may have been amorphous and not detectable by XRD. For the basic solution desorption experiment, the XRD pattern was shifted slightly such that the phosphate compound and hydromagnesite peaks were not differentiable.

4. Conclusions

MgCO₃ pellets prepared with varying amounts of cellulose were found to be effective adsorbents for removing phosphate from aqueous suspensions. The calcination of the pellets with higher cellulose ratios proved to result in increased BET surface area until the pellet with 20% cellulose. The highest surface area achieved was 43.1 m² g⁻¹ for the 15%1 pellet. The increased surface area corresponded to an increased adsorption capacity as seen through the Langmuir models. Although the highest theoretical adsorption capacity was 44.3 mg g⁻¹ for the 20%2 pellet from the isotherm, the 15%1 pellet showed the most promise from kinetics experiments and surface area analysis. The 20%2 pellet was the least stable after calcination so the 15%1 pellet would provide adsorption without the stability being lost. From the isotherm experiments conducted for the 15%1 pellet, the adsorption capacity had an average of 96.4 mg g⁻¹. The surface of the pellets changed as phosphate was adsorbed as shown by the SEM and XRD analysis. While enhanced P availability might occur when exposed to the real world, the simple dissolution/desorption experiment suggested quite a minimal release. It, of course, says nothing about the very slow release.