Advanced Phosphate Removal in Dialysis Employing Lanthanum Impregnated Activated Carbon Fixed-Bed Column

A Thesis Submitted to the Graduate School of the University of Cincinnati

in partial fulfillment of the requirements for the degree of

Master of Science

Chemical Engineering In the Department of Biomedical, Chemical and Environmental Engineering Of the College of Engineering and Applied Sciences

By Reyhaneh Nazarian 2017

Thesis Committee: Stephen W. Thiel, Ph.D. (Chair) Vadim Guliants, Ph.D. Junhang Dong, Ph.D.

Abstract

Incorporating a fixed-bed phosphate adsorption column into a kidney dialysis system for enhanced phosphate removal during regular dialysis treatment may be an effective substitute for current medical strategies used to prevent hyperphosphatemia. In this study lanthanum- impregnated activated carbon was evaluated as a non-toxic and biocompatible candidate to serve as a phosphate adsorbent for use in a packed bed column integrated with the dialysis apparatus.

Lanthanum-impregnated activated carbon (La-AC) was synthesized using chemical impregnation. The morphology and textural properties of the samples were determined using SEM and nitrogen adsorption-desorption and the amount of lanthanum adsorbed on the surface of activated carbon was determined based on the change in liquid-phase concentration using the Arsenazo chemical assay. Preparation parameters (ratio of lanthanum to activated carbon, calcination temperature, and calcination atmosphere) were investigated and optimized to improve phosphate capacity. It was observed that samples with 28 wt% lanthanum on activated carbon calcined at 650 °C under air had the highest phosphate capacity within the range used in this study.

Phosphate loading on La-AC was assessed by determining the batch equilibrium isotherms. Isothermal adsorption studies revealed that phosphate adsorption on the surface of 12 wt% La- AC was well described by the Langmuir model with a maximum phosphate loading of 15.43 mg/g at 37 °C, and 21.14 mg/g at 50 °C. The phosphate adsorption mechanism was further investigated by 1) studying the effects of temperature and solution pH on phosphate adsorption capacity, 2) flow microcalorimetry, and 3) determining the relationship between the phosphate adsorption amount and the change in the pH of the solution. It was concluded that phosphate anions were adsorbed on lanthanum surface active sites mainly via the formation of monodentate and bidentate inner-sphere surface complexes. The enthalpies of formation of the monodenate and bidentate phosphate complexes with lanthanum surface sites were determined to be 21.8 and 44.6 kJ/mol using flow microcalorimetry.

Based on the mechanism suggested by the isotherm studies, a kinetic model was developed based on the assumption of two parallel-pathway surface adsorption reactions to form monodentate and bidentate complexes on the surface of the adsorbent. The model was successfully used to describe the observed kinetics of the adsorption. The proposed parallel- pathway kinetic model is more consistent with thermodynamic assumptions of the adsorption mechanism than is the pseudo-second order kinetic model that is often used to describe phosphate adsorption.

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Acknowledgments I would first like to thank and express by deepest appreciation to my thesis advisor Professor Stephen Thiel at the University of Cincinnati. The door to Professor Thiel’s office was always open and smile was on his face whenever I ran into trouble or had a question about my research or writing. He consistently allowed this paper to be my own work, but steered me in the right direction with his thoughtful guidance and deep knowledge. I cannot express my gratitude enough for all the long hours he shared with me, his generosity, his kindness, and continuous support during my studies.

I would like to acknowledge Professor Vadim Guliants at the University of Cincinnati for his selfless guidance and support. I am gratefully indebted to his unfailing support during my studies and especially in allowing me to complete his course without physically being present in the class. He went above and beyond his duties as a professor and would set up a webcam and email the notes to me. I would also like to thank him for reading my thesis and his valuable remarks.

I want to thank Professor Junhang Dong at the University of Cincinnati for his help during my studies. If it wasn’t for his assistance and support, I would not have been able to start my studies. I would also like to thank him for serving on the committee.

My sincere thanks also goes out to Dr. Rebecca Desch for taking me under her wings upon my entrance to Adsorption and Ion Exchange laboratory and guiding me every step of the way. Aside from being a good friend, she has always showed me continuous support in furthering my education and has taken time out to train and assist me in any way I needed. I would like to thank Shada Salem for training me in the lab as well as my studies and being a supportive friend.

A very special gratitude goes out to my colleagues and friends Dr. Amina Darwish, Dr. Ali Gitipour, and Taylor Robie for our time spent together. I was fortunate enough to work at the Adsorption and Ion Exchange Laboratory with such brilliant scientists and gained lots of valuable knowledge.

I must express my profound gratitude to my parents because they taught me how to think for myself and always encouraged me to work hard to reach my goals. Without their unconditional love and support it would not be possible for me to succeed. I would also like to thank my

v brother, Hamed, for his unfailing support throughout my life and my uncle, Adel, for his continuous encouragement and unlimited help whenever I need.

I would also like to thank my husband, Behrang, who has supported me throughout the entire process. His support, quiet patience and unwavering love were undeniably the base upon which my passion has been built on. I would like to thank my two sons, Taha and Yaseen, for always motivating me to pursue my education. Even though this process has taken more time than I had initially planned on, it has been much more enjoyable with their presence.

I would like to thank all my friends especially Ms. Motahara Basam, Ms. Akram Jourabchi, Dr. Zahra Vashaie, and Dr. Christine Aidala, because without them I would not be as strong as I am today and this accomplishment would not have been possible without them. Thank You.

Finally I would like to thank my mother-in-law and father-in-law for their help and support during my last tough days of finishing this project. Without their help it was not easy to complete this study.

Reyhaneh Nazarian

Table of Contents List of Figures x List of Tables xiii List of Symbols xiv 1. Introduction and Objectives 1

1.1. Phosphate and Its Presence in the Body 2

1.2. Hyperphosphatemia 3

1.3. Phosphate and Waste Water Treatment 5

1.4. Phosphate Adsorbents 6

1.5. Phosphate Adsorption Isotherms 8

1.6. Phosphate Adsorption Mechanism and Reaction at the Oxide 11

Surface

1.7. Kinetics of Phosphate Adsorption 16

1.8. Effect of Environmental Parameters on Phosphate Adsorption 22

1.9. Research Objectives 23

2. Experimental Materials and Methods 25

2.1. Materials 26

2.2. Preparation of the Adsorbent 26

2.3. Adsorbent Characterization 27

2.3.1. Arsenazo Chemical Assay 27

2.3.2. Scanning Electron Microscopy 28

2.3.3. Nitrogen prosimetry 28

2.4. Molybdenum Blue Assay 29

2.5. Adsorption Experiments 31 vii

2.6. Flow Microcalorimetry 32

2.7. Kinetics of Adsorption 32

3. Synthesis, Characterization, and Optimization of Lanthanum- 33

Impregnated Activated Carbon

3.1. Lanthanum Impregnated Activated Carbon (La-AC) 34

3.2. Optimization of La-AC as phosphate Adsorbent 38

3.2.1. Lanthanum to Activated Carbon Mass Percentage 38

3.2.2. Calcination Conditions 39

3.3. Summary 46

4. Thermodynamics of Phosphate Adsorption 47

4.1. Adsorption Isotherm 48

4.2. Influence of Initial pH on Phosphate Capacity 54

4.3. Thermodynamic Studies of Phosphate Adsorption 57

4.4. pH Studies 60

4.5. Influence of Bovine Serum Albumin (BSA) on Phosphate 62

Adsorption

4.6. Summary 64

5. Kinetics of Phosphate Adsorption 66

5.1. Experimental Phosphate Adsorption Kinetics 67

5.2. Application of Previous Models of Phosphate Adsorption 70

5.3. Parallel-Pathway Kinetics 73

5.3.1. Theory 73

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5.3.2. Analysis of Experimental Data and Discussion 76

5.4. Summary 81

6. Summary and Conclusion 82 7. Future Work 86 References 89 Appendix A: R Script Used in Chapter 4 for Regression of Adsorption 98 Isotherms at 37 and 50 °C by Langmuir and Freundlich Equations Appendix B: Mathematica Script to Solve Equations 5.9, 5.13, and 5.14 101 Simultaneously Appendix C: Experimental Data of Chapter 4 104 Appendix D: Experimental Data of Chapter 5 106 Appendix E: BET Adsorption-Desorption Isotherm of AC and La-AC 107

List of Figures Figure 1.1 Phosphate Exchange between different compartments of the body 3 Figure 1.2 a) Phosphate isotherm on ACF-LaFe at room temperature b) obtained data 10 was well fitted by Linear Langmuir adsorption isotherm Figure1.3 illustrations of a) outer-sphere complexes and b) inner-sphere complexes 13 Figure1.4 Possible configurations of phosphate surface complexes 14 Figure 1.5 Interactions in phosphate adsorption onto La-ACF 15 Figure 1.6 -OH possible groups on zirconium hydroxide 17 Figure 1.7 ATR-FTIR spectra of phosphate adsorbed on the surface of goethite at pH 9 19 Figure 2.1 Equilibrium lanthanum adsorption on activated carbon. T: 25 °C, 28 Impregnation time: 24 hours Figure 2.2 Phosphate calibration curves at different pH using molybdenum blue assay in 30 conjugation with UV scan at 640 nm Figure 3.1 SEM images of a) images 1, 2, 3, and 4 shows acid washed activated carbon 35 at different magnifications b) images 5 and 6 shows La-AC before calcination at different magnification. La to AC: 12% wt, T: 25 °C, Impregnation Time: 24 hours Figure 3.2 a) Size distribution of carbon chunks on the surface of acid-washed activated 37 carbon, bin size: 50 nm b) size distribution of needle like structure on the surface of activated carbon after soaking in 12% lanthanum solution, bin size: 50 nm, T: 25 °C, Impregnation Time: 24 hours Figure 3.3 XRD results of AC and 12% wt La-AC, T: 25 °C, Impregnation Time: 24 38 hours, Calcination Temperature: 650 °C Figure 3.4 Lanthanum loading on the activated carbon surface. La: AC weight 39 percentages: 8, 12, and 20% , T: 25 °C, Impregnation Time: 24 hours Figure 3.5 Effect of calcination temperature on phosphate equilibrium loading for 12% 40 wt La-AC calcined under air flow. T: 37 ° C. Initial potassium phosphate (K2HPO4) concentrations: 25-300 mg/L, 48 hour equilibration time. Figure 3.6 a and b) SEM images of La-AC carbon calcined at 650° C under air flow. 42 Image a represents the same agglomeration can be seen in image b, but with higher magnification, La: AC weight percentages: 12%, Impregnation Temperature: 25 °C, Impregnation Time: 24 hours Figure 3.7 Effect of calcination temperature on phosphate equilibrium loading for La- 43 AC calcined under nitrogen. La: AC weight percentages: 12%, T: 37 ° C. Initial potassium phosphate (K2HPO4) concentrations: 25-300 mg/L, 48 hour equilibration time. x

Figure 3.8 SEM images of La-activated carbon calcined at 650° C under nitrogen from 44 two different spots of the same sample. La: AC weight percentages: 12%, Impregnation Temperature: 25 °C, Impregnation Time: 24 hours Figure 3.9 comparison of phosphate loading of La-AC carbon calcined at a) 200° C, b) 45 450° C, c) 650° C under air and nitrogen, T: 37 ° C. Initial potassium phosphate (K2HPO4) concentrations: 25-300 mg/L, 48 hour equilibration time. Figure 4.1 Equilibrium phosphate adsorption isotherms. T: 37 ° and 50 °C. Initial 49 potassium phosphate (K2HPO4) concentrations: 0.143 to 1.722 mmol/L (25-300 mg/L), 48 hour equilibration time. Figure 4.2 a and b) Fitted Langmuir model to the observed adsorption isotherm data. T: 52 37 and 50 °C. Initial potassium phosphate (K2HPO4) concentrations: 0.143 to 1.722 mmol/L (25-300 mg/L), 48 hour equilibration time. Figure 4.3 Effect of solution pH on phosphate adsorption on La-AC. Initial potassium 55 phosphate concentration: 1.148 mmol/L; T = 37°C; incubation time: 48 hours Figure 4.4 FMC thermograms for phosphate adsorption on Ac and La-AC at room 57 temperature. Bed mass: 77.6 mg; mobile phase rate: 1.85 mL/h; sample loop volume: 2.2 mL. Figure 4.5 Thermogram of phosphate adsorption on lanthanum ions on the surface at 58 room temperature. Bed mass: 77.6 mg; mobile phase rate: 1.85 mL/h; sample loop volume: 2.2 ml. Figure 4.6 Possible configurations of phosphate surface complexes [Shin et al, 2004] 59 Figure 4.7 Initial and final phosphate solution as the function of phosphate loading on 60 La-AC. T: 37°C. Initial potassium phosphate concentrations: 0.143 to 1.72 mmol/L; 48 hour equilibration time. Figure 4.8 Plot of released hydroxyl ions vs. phosphate loading. T: 37 °C. Initial 61 potassium phosphate concentrations: 0.143 to 1.72 mmol/L; 48 hour equilibration time. Figure 4.9 Effect of BSA concentrations on phosphate loading on La-AC. Initial 63 potassium phosphate concentration: 0.574 mmol/L; T = 37°C; incubation time: 48 hours. Initial BSA concentrations: 0, 22, 37, and 42 g/L Figure 4.10 Effect of phosphate solution on BSA loading on La-AC. Initial potassium 64 phosphate concentration: 0.574 mmol/L; T = 37°C; incubation time: 48 hours. Initial BSA concentrations: 0, 22, 37, and 42 g/L Figure 5.1 Adsorption kinetics of potassium phosphate solution at 0.574 mmol/L on La- 68 AC and potassium phosphate solution at 1.148 mmol/L on AC and La-AC at 37 °C.

Figure 5.2 Liquid-phase concentrations of potassium phosphate solutions at initial 69 concentrations of 0.574 and 1.148 mmol/Lon La-AC at 37 °C over time xi

Figure 5.3 Predicted and experimental adsorption kinetics of potassium phosphate on 72 La-AC at 37 °C based on pseudo-second-order equation. Dots represent observed kinetics and solid curves represent predicted pseudo-second-order kinetics. Figure 5.4 Modeled and Experimental adsorption kinetics of potassium phosphate on La- 78 AC at 37 °C. Dots show observed kinetics and solid curves show proposed parallel- pathway kinetics. Figure 5.5 Modeled and Experimental liquid-phase concentrations of potassium 79 phosphate on La-AC at 37 °C at initial solution concentrations of 0.574 and 1.148 mmol/L. Dots show observed kinetics and solid curves show proposed parallel-pathway kinetics.

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List of Tables Table 2.1 Summary of purchased materials 26 Table 3.1 Textural properties of lanthanum-impregnated activated carbon 34 Table 3.2 Course of decomposition of lanthanum nitrate toward lanthanum oxide from 41 room temperature to 650 °C Table 4.1 Best-fit Langmuir and Freundlich parameter estimates 51

Table 4.2 Phosphoric acid equilibria. * values are reported dissociation pKa at 40°C, and 56 ** values are reported dissociation pKa at 25°C Table 4.3 Heats of adsorption of phosphate on La-AC 59 Table 5.1 The values of rate constants and maximum adsorption capacities found by 71 linear regression of pseudo-second-order equation to observed kinetic data Table 5.2 The parameter values have been used for parallel-pathway kinetic model 76 Table 5.3 Best-fit kinetic parameters for parallel-pathway kinetic model 77 Table 5.4 Statistic summary of modeled kinetics 80

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List of Symbols A Phosphate ions Ab Measured absorbance AX,AY Surface complexes C Concentration of adsorbing species (mol/cm3)

C0 Molar density of the solution

CA Adsorbate concentration in the liquid phase (mmol/L)

CA0 Initial adsorbate concentration in the liquid phase (mmol/L) ∆G Gibbs free energy (kJ/mol) ∆G0 Standard Gibbs free energy (kJ/mol) ∆H Enthalpy (kJ/mol) K Equilibrium constant

n n-1 kf Freundlich constant (L /µmol ·g) ki Forward rate constant for reaction i k-i Reverse rate constant for reaction i

KL Langmuir adsorption constant (L/mmol) L Path length (cm) m Mass (mg) N Freundlich parameter Q Adsorption capacity (mg/g)

Qmax Maximum adsorption capacity (mg/g)

Qe Equilibrium adsorption capacity (mg/g)

Qi0 Initial number of adsorption sites of type i

Qi Adsorption capacity of component i (mg/g) R Universal gas constant (8.314 J/mol.K) T Temperature (°K) T Time (min) V Liquid volume (mL) xiv

Ε Extinction coefficient constant (1/mol.cm) µ Standard state chemical potential (J/mol)

List of Abbreviation AC Activated carbon ACF Activated carbon fiber ATP Adenosine triphosphate BET Brunauer Emmett Teller BSA Bovine serum albumin DNA Deoxyribonucleic acid FMC Flow microcalorimetry La-AC Lanthanum impregnated activated carbon pka Logarithmic acid dissociation constant RNA Ribonucleic acid SEM Scanning electron microscopy TCA Tricholoroacetic acid Uv-Vis Ultraviolet visible light XRD X-ray diffreaction

Chapter 1: Introduction and Objectives

1.1 Phosphate and its presence in the body

Phosphorus, which is commonly found in the human body as phosphate, plays a critical role in life processes. There is in total around 600 g phosphate available in the human body. About 86% of the phosphorus in the body is present in bones and teeth, and the remainder is present in cells (around 14%), soft tissues, and extracellular fluids (around 0.08%). Phosphorus and calcium work to build and mineralize a strong bones and teeth. Furthermore, phospholipids are the main structural constituent of the cells in the body. As a component of ATP, phosphate has an essential role in how the body stores and uses energy to regulate the metabolism. In addition phosphate is involved in the growth, maintenance, and repair of all tissues and cell process by producing proteins, and is part of the backbone of the genetic building blocks RNA and DNA. Phosphate is also critical to help balance and consume some vitamins and minerals such as vitamin D, iodine, magnesium, and zinc [Takeda et al, 2004].

Healthy kidneys help regulate and control the phosphate level in the body. Extra blood serum phosphate is removed by the kidneys and passed out of the body in the urine. Depending on kidney function, the amount of phosphate needed daily may vary. On average 800-1000 mg phosphorus are required; a healthy adult may consume approximately 1400 mg per day. Usually around 1300 mg of the phosphate consumed in the diet is absorbed by the small intestine, and only a small amount of phosphate is excreted via feces. The primary route of phosphate excretion is urine. Figure 1.1 shows schematically the exchange of phosphate among different compartments in the body [Rhoades et al, 2008].

Figure 1.1 Phosphate Exchange between different compartments of the body [Rhoades et al, 2008]

1.2 Hyperphosphatemia

Hyperphosphatemia is an abnormally elevated serum phosphate level. The normal range of phosphate concentrations in the blood is 3.5-4.5 mg/dL (1.12-1.45 mmol/L). Hyperphosphatemia can result from increased phosphate intake, decreased phosphate excretion, or disorders that transfer intracellular phosphate to extracellular fluids. Hyperphosphatemia is a critical risk factor for cardiovascular mortality and morbidity in dialysis patients. Despite significant progress to improve dialysis, the prevalence of hyperphosphatemia in kidney dialysis patients is still high [Rhoades et al, 2009; and Kuhlmamm, 2006].

Common treatments to normalize and control the serum phosphate level are based on three principles: improvement of the dialysis prescription for increased phosphate removal, restriction of the phosphate uptake by control of the patient’s diet, and medical strategies to inhibit the gastrointestinal absorption by using phosphate binders [Kuhlmann, 2006]. Frequent dialysis,

3 nocturnal dialysis, and extended dialysis can improve phosphate levels, but, these strategies are expensive and difficult to implement [Spalding et al, 2002; and Kuhlmamm, 2006]. Limiting phosphate intake in the patient’s diet can lead to inadequate protein intake and malnutrition [Kuhlmamm, 2006].

Oral phosphate binders reduce phosphate adsorption in the gastrointestinal tract by reacting with phosphate to form an insoluble compound that cannot be adsorbed. Several classes of phosphate binders have been used to treat hyperphosphatemia, including aluminum compounds, calcium- containing phosphate binders (calcium acetate and calcium carbonate), and Sevelamer compounds (Sevelamer carbonate). Sevelamer carbonate is a polymeric amine, poly (allylamine– co-N,N’-diallyl-1,3-diamino-2-hydroxypropane) carbonate salts. In the intestine the amine groups of the Sevelamer protonate and bind with phosphate through ionic and hydrogen bonds to form an insoluble compound [Perry et al, 2014]. However, phosphate binders have unsafe long- term side effects, such as an increased likelihood of cardiovascular disease. There are also novel approved classes of phosphate binders such as colestilan, iron-containing phosphate binders, magnesium, and niacin/nicotiamde. The potential risk and long-term side effects of some of those novel medications have not yet been investigated thoroughly [Gotoh et al, 2013].

Studies have shown that 8-12% of patients using oral phosphate binders reject the treatment due to digestive symptoms such as nausea, vomiting, constipation, and abdominal distension [Ketteler et al, 2013]. Therefore, they are not recommended for prolonged treatment. Methods are still needed to improve phosphate level management. The investigator’s group has proposed using a fixed-bed adsorption system integrated with hemodialysis as a method to improve phosphate removal. In the proposed process, blood leaving the dialyzer passes through a fixed- bed column packed with an adsorbent to remove additional phosphate and then returns to the patient’s vein.

This strategy is motivated by the observation that adsorption can be an economical and highly effective approach to remove phosphate at low concentrations from wastewater [Zhang et al, 2011]. In the next section the use of adsorption to remove phosphate from wastewater is reviewed.

1.3 Phosphate and Waste Water Treatment

To date, most phosphate adsorption studies have focused on waste water treatment. Phosphorus, which in aquasystems occurs mainly as phosphate, is released by human activities such as mining, industrial and agriculture [Lao et al, 1997; Liu et al, 2013]. Phosphate contamination in water (even at the level of ~ 10 mg/L) can cause algal blooms that can deplete the dissolved oxygen and decrease the water quality, leading to eutrophication. In addition, some algal blooms produce toxins and bacterial growth that can cause human illness through exposure to contaminated water [Carpenter et al, 1998]. Therefore, it is crucial to remove phosphate from wastewater before it is discharged into the environment [Donnert et al, 1999; Lao et al, 1997; and Cooperband et al, 2002]. The most widely applied phosphate removal technologies include chemical and biological phosphorous removal [Geradi et al, 2010].

On average, domestic wastewater contains 6-8 mg/L phosphate, including 3-4 mg/L orthophosphate, 2-3 mg/L condensed phosphorus such as polyphosphates, and 1 mg/L organic phosphorus. Condensed and inorganic phosphorus can be converted to orthophosphate by bacterial degradation. Chemical precipitation can be used to remove orthophosphate from wastewater. Adding multivalent ions such as calcium (Ca2+), aluminum (Al3+), and iron (Fe2+ and Fe3+) in wastewater treatment leads to the formation of insoluble phosphate compounds that can be removed from wastewater and by operations such as sedimentation, flotation, and filtration. Chemical precipitation can be used to reduce the total phosphorus concentration to less than 1 mg/L [Spellman, 2000], but cannot be directly implemented to remove phosphate in dialysis.

Biological phosphorus removal consists of assimilation and adsorption of phosphate, and enhanced biological phosphorus removal (EBPR). Assimilation and adsorption of phosphate depends on incorporation of phosphate into bacterial cells. Bacterial cells need soluble - 2- orthophosphate (H2PO4 , HPO4 ) for energy storage, cellular activity, synthesis of cellular material, and cellular growth. Around 3% of dry weight of bacterial cells consists of phosphate. Insoluble phosphate compounds can be incorporated into bacterial cells, and over the time these insoluble compounds degrade to release orthophosphate. Phosphorus compounds both

5 assimilated and adsorbed by bacterial cells are removed from wastewater; however, bacterial cells containing phosphorus compounds may release phosphorus back to the environment in the recycle process [Wastewater Handbook]. As with chemical precipitation, biotreatment cannot be directly applied to dialysis.

Biotreatment, chemical precipitation, or combinations of both can effectively remove phosphate, but these methods are not recommended at low phosphate concentrations [Geradi et al, 2010]. Many studies have shown that fixed-bed adsorption is the most effective method to remove phosphate at trace concentration levels [Zhang et al, 2011]. Unlike biotreatment and chemical precipitation, fixed-bed adsorption is potentially applicable to phosphate removel during dialysis.

Adsorption is the selective transfer of a component (the adsorbate) from a fluid phase to a solid surface (the adsorbent); desorption is the reverse process. In adsorption, accumulation of a dissolved component in the liquid phase occurs at the solid interface as a result of interactions between the dissolved component and surface boundaries. To design a fixed-bed adsorption column, the first step is identifying an appropriate adsorbent. Many types of natural and synthesized phosphate adsorbents have been proposed and investigated for environmental applications. In the next section the common phosphate adsorbents for environmental applications are reviewed, and from among them a candidate phosphate adsorbent for clinical applications is proposed.

1.4 Phosphate Adsorbents

Many phosphate adsorbents have been proposed for environmental applications, including red mud [Pradhan et al, 1998], polymeric ligand exchangers [Zhao et al, 1998; Blaney et al, 2007], goethite and akaganeite [Chitrakar et al, 2006], gibbsite [Wang et al, 2007], fly ash [Chen, 2007], and hydrous metal oxides [Chitrakar et al, 2005; Tanada et al, 2003; Chitrakar et al, 2006; and Genz et al, 2004]. In addition, phosphate adsorption using hydrous oxides of iron (III), lanthanum, aluminum, zirconium, and manganese have been studied [Kawashima et al, 1986; Yao et al, 1996; Tang et al, 1997; Gao et al, 2003; Juang et al, 2004; Chitrakar et al, 2005; and

Chubar et al, 2005]. However, adsorbents used in clinical applications must be non-toxic, biocompatible, regenerable, and inexpensive.

Aluminum, lanthanum, and zirconium compounds are appropriate candidates for medical and biological purposes; however, studies have shown that aluminum can cause neurological toxicity and bone diseases in dialysis patients. [Mudge et al, 2011]. Lanthanum is non-toxic, its absorption and bioavailability are low, it does not cause neurological toxicity or bone disease, does not pass through the blood-brain barrier, and has no reported hepatotoxic effects [Persy, et al, 2009]. Recent experimental and clinical studies indicate that zirconium compounds are also biocompatible and exhibit low toxicity [Lee et al, 2010].

Due to their low surface area, hydrous oxides of aluminum, lanthanum, and zirconium are often impregnated onto mesoporous supports [Zhu et al, 2005; Ou et al, 2007]. The mesoporous support provides a uniform pore size distribution and high surface area to support the impregnated metal oxides, and to provide easy access for the adsorbate to reach the surface active sites of the metal oxides. Activated carbon fibers loaded with lanthanum (hydr)oxide [Zhang et al, 2011and 2012], hydroxyl-iron-lanthanum doped activated carbon fibers [Liu, 2013], lanthanum loaded granular ceramics [Chen et al, 2012], lanthanum-impregnated silica gel [Ou, 2007], lanthanum doped onto diamino functionalized mesoporous silicates [Zhang et al, 2010], lanthanum impregnated onto zeolite [Ping, 2008], a novel synthesized amorphous zirconium hydroxide [Chitrakar, 2005], and aluminum-impregnated mesoporous silicates [Shin, 2004] are examples of biocompatible phosphate adsorbents.

Zhang et al. [Zhang et al, 2011] synthesized a novel activated carbon fiber (ACF) impregnated with lanthanum to remove phosphate from wastewater. They studied the effect of La/ACF ratio, impregnation time, activation time, and activation temperature on the La-ACF phosphate adsorption capacity to optimize the adsorbent. They reported the highest selectivity at a La/ACF mass ratio of 11.78%, an activation time of 2.5 h, and an activation temperature of 650 °C. An adsorbent synthesized under these conditions had a phosphate removal capacity of 97.6% within 3 h at an initial phosphate concentration of 30 mg/L at room temperature.

Blaney et al [Blaney et al, 2007] noted that inorganic metal oxide particles such as granular activated alumina, zirconium oxide, and iron oxide particles did not have sufficient mechanical strength and attrition resistance be applied long term in a fixed-bed packed column process. To remedy this problem they developed a novel adsorbent by dispersing hydrated ferric oxide nanoparticles within polymeric anion exchangers. They illustrated that sorption capacity was greatly enhanced due to the Donnan effect exerted by the fixed positive charges of the anion exchanger.

Lanthanum oxide supported on activated carbon was selected for the work reported in this thesis due to its non-toxicity and the biocompatibility of lanthanum.

1.5 Phosphate Adsorption Isotherms

Adsorption isotherms describe the equilibrium behavior of adsorbate uptake over a range of concentrations at constant temperature. The equilibrium phosphate adsorption can be measured by mixing a known volume of phosphate solution with a known amount of adsorbent, waiting to reach equilibrium, measuring phosphate concentration in supernatant, and calculating the amount of adsorbed phosphate from a mass balance. There are several models available to describe adsorption isotherms mathematically. [Milonjic, 2007].

Of particular interest are the Langmuir and Freundlich isotherms, which are widely used. The Langmuir isotherm is derived theoretically assuming that a fixed number of identical active sites are available on the surface of the adsorbent, so adsorption is governed by the number of available surface active sites, not the available area for the adsorption. It is further assumed that the adsorbate molecules do not interact with each other. If C denotes the liquid-phase concentration of the adsorbate (mmol/L), Q the adsorbate surface coverage (mg/g), Qmax monolayer surface coverage (mg/g), and KL the Langmuir adsorption coefficient (L/mmol) then the Langmuir adsorption isotherm is expressed as follow [Liu et al, 2006]:

(1.1)

Qmax and KL are often determined from the slope and intercept of the linear plot of C/Q vs. C, using linear regression based on Equation 1.2.

(1.2)

The Langmuir adsorption isotherm has also been described thermodynamically by the change in the standard-state chemical potential of the adsorbate molecule on the adsorbent surface and in the solution [Smith, 2004; Liu, 2005]:

(1.3)

is the standard Gibbs free energy change for the adsorption of the adsorbate molecule onto the adsorbent surface (J/mol), is the standard-state chemical potential of the adsorbate molecule on the surface of the adsorbent (J/mol), is the standard-state chemical potential of the adsorbate molecule in the solution (J/mol), K (dimensionless constant) is equilibrium constant obtained from Langmuir isotherm, R (8.34 J/K.mol) is ideal gas constant, and T (K) is the temperature.

The Freundlich isotherm is an empirical adsorption expression proposed by Freundlich in 1909. In concentration units, the Freundlich equation is expressed as [Liu et al, 2006]:

(1.4)

Or (1.5)

1/n Q is the adsorption capacity (mg/g), Kf (mg/g)(L/mmol) and n are the Freundlich parameters, and C (mmol/L) is the adsorbate concentration in the liquid phase.

For example, a novel hydroxide composite of lanthanum (III) mixed with iron (III) doped onto activated carbon fiber (ACF), ACF-LaFe, was developed for phosphate adsorption by Liu et al [Liu et al, 2013]. Their adsorption isotherms revealed a sharp increase in adsorbed phosphate at low equilibrium concentrations but the isotherm became flat at higher phosphate concentrations (Figure 1.2). Liu and coworkers explained that at low phosphate concentrations the surface active sites were sufficient for phosphate anions to be adsorbed; however the surface active sites became saturated at higher phosphate concentrations. Therefore, at higher phosphate concentrations the phosphate uptake did not increase significantly. The obtained adsorption data were fit with both Langmuir and Freundlich curves, and based on correlation coefficient values the observed adsorption data were well-described by Langmuir isotherm. Liu et al calculated the maximum phosphate adsorption capacity to be 29.44 mg/g and the Langmuir adsorption coefficient to be 8.60 mg/L.

Figure 1.2 a) Phosphate isotherm on ACF-LaFe at room temperature b) obtained data was well fitted by linearized Langmuir adsorption isotherm [Liu et al, 2012]

Zhang et al [Zhang et al, 2012] prepared a novel lanthanum hydroxide-doped activated carbon fiber (ACF-LaOH) using ultrasound-assisted chemical precipitation. The phosphate adsorption isotherms at various concentrations of phosphate (10-70 mg/L) at room temperature were well described by the Langmuir model, indicating homogeneous adsorption on the surface. The maximum adsorption capacity was calculated to be 15.3 mg/g.

Shin et al. [Shin et al, 2004] found that phosphate adsorption onto aluminum-impregnated mesoporous silica was well described by the Langmuir isotherm, and mesoporous silica impregnated with 10% aluminum had a maximum phosphate adsorption capacity of 862 µmol/g (82 mg/g) and Langmuir adsorption coefficient of 0.599 g/µmol.min, and reached equilibrium within 1 hour.

In another work, Ou and coworkers [Ou, 2007] incorporated lanthanum into the mesoporous silica structure using cogellation rather than the more common impregnation method. The phosphate adsorption isotherm was well fit using the Langmuir model, and the maximum adsorption capacity was calculated to be 23.1 mg/g after 10 hr for the sample with the Si/La molar ration of 10 [Ou, 2007].

The Freundlich isotherm can also be used to model phosphate adsorption isotherm. Ping and coworkers [Ping et al, 2008] used zeolite nanoparticles modified with lanthanum oxide as a phosphate adsorbent. At 20 °C, pH 6.0, and 24 hr contact time the adsorption isotherm was well fit using the Freundlich isotherm. The maximum phosphate adsorption capacity was found to be

24.6 mg/g, and the constant value of Kf and 1/n in the Freundlich equation were calculated 16.76 mg/L and 0.2209, respectively. The model La(III) zeolite showed the potential of regenerability [Ping et al, 2008].

To fully understand the phosphate adsorption behavior studying the adsorption isotherms will not be sufficient. In addition to investigating the adsorption isotherms, understanding the underlying adsorption process and mechanism on the surface of the adsorbent is necessary. In the following section the possible phosphate adsorption reactions and mechanisms on hydrous metal oxide surfaces are reviewed.

1.6 Phosphate Adsorption Mechanism and Reaction at the Oxide Surfaces

Metal oxide surface groups are usually represented as hydrolyzed species due to acid-base reactions as follows [Ouvrard et al, 2002]:

(1.6)

(1.7)

Ions in the bulk solution can react with hydrolyzed surface oxides to form ion pairs or covalent bonds. Based on the types of interactions between the surface active metal oxides and ions in the electrolyte solution, outer-sphere or inner-sphere complexes are formed. Electrostatic interactions between the solution ions and surface-hydrolyzed metal oxides lead to the formation of outer-sphere complexes, in which water molecules remain between the exchanged sites and the adsorbed ions. For example, if the oxide surface is positively charged the balancing anions located in the double layer at the exact vicinity of the surface can be exchanged with solution anions. The overall exchange interaction between the balancing ions in the double layer in the exact vicinity of the charged surface and same-charged ions in the solution is described as follow [Ouvrard et al, 2002]:

(1.8)

In this equation, and denotes the balancing ions in the system and subscript s denotes the balancing ions in the double layer at the exact vicinity of the charged surface. Figure 1.3(a) schematically shows an example of the formation of outer-sphere complexes on a positively charged solid surface.

Figure 1.3 Illustrations of a) outer-sphere complexes and b) inner-sphere complexes

When specific interactions between anions in the solution and surface oxide result in the direct bonding of the adsorbed species onto an active oxide surface, inner-sphere complexes are formed. If anions in the solution are dominant species and they tend to adsorb onto a solid surface, the mechanism involves anion adsorption as the result of anion exchange with surface hydroxyl groups [Ouvrard et al, 2002]:

(1.9)

(1.10)

In the above equations denotes a hydrolyzed metal oxide on the surface of the adsorbent, denotes an existing anion in the solution, and and denotes the anion bindings to the active metal oxide on the adsorbent surface. As can be seen from Equations 1.9 and 1.10, an anion can be directly bound to metal oxide surface active sites as a result of an exchange with surface hydroxyl groups. Figure 1.3(b) schematically shows an example of the formation of inner-sphere complex on a positively charged solid surface as a direct binding of bulk anion to the active site on the surface.

Generally, phosphate adsorption mechanisms include two types of interactions: formation of inner-sphere surface complexes and surface precipitation. Surface precipitation is the result of

13 interactions between adsorbed phosphate anions and dissolved metal ions from the adsorbents [Li et al, 2013; Arai et al, 2007; and Ler et al, 2003]. However, it is believed that phosphate is usually adsorbed onto the surface of metal oxides by formation of inner-sphere complexes as a result of ligand exchange with reactive surface hydroxyl groups. There are three possible phosphate complexes: monodentate, bidentate, and binucleare complexes (Figure 1.4) [Shin et al, 2004].

Figure 1.4 Possible configurations of phosphate surface complexes [Shin et al, 2004]

As shown in Figure 1.4, in the monodentate configuration the stochiometry between phosphate and surface hydroxyl ions is one-to-one, while in the bidentate configuration the adsorbed phosphate anion reacts with two surface hydroxyl groups of metal oxide, meaning that the stochiometric ratio is one to two. It is often hypothesized that adsorption of anions on metal oxides includes two reaction steps: formation of monodentate surface complexes (step I) followed by the formation of bidentate surface complexes (step II) [Shin et al, 2004].

It is possible that phosphate adsorption includes interactions other than the formation of inner- sphere surface complexes. Zhang and coworkers proposed that phosphate adsorbs onto lanthanum-impregnated activated carbon fibers (La-ACF) based on electrostatic, ion exchange, and Lewis acid-base interactions between the functional groups on the adsorbent and phosphate

14 anions in the solution. They found that initially phosphate adsorption onto ACF-La was the result of ion exchange between phosphate and surface hydroxide groups; the phosphate was chemically bound to lanthanum active sites. Subsequently, coordinated water molecules around the adsorption sites were deporotonated; at this stage phosphate was absorbed by electrostatic interactions. They also proposed that phosphate anions could bond to La active sites via the interactions with oxygen species in the phosphate anions. Oxygen in the phosphate structure could react with La sites to form La-O coordination bonds through Lewis acid-base interactions. Figure 1.5 schematically shows the phosphate adsorption mechanism onto La-ACF.

Figure 1.5 Interactions in phosphate adsorption onto La-ACF [Zhang et al, 2011]

It is also possible that phosphate adsorption onto surface metal active sites includes only the formation of outer-sphere complexes. Due to the easy desorption of adsorbed phosphates Chitrakar et al. [Chitrakar, 2005] assumed that phosphate adsorption onto amorphous zirconium hydroxide did not involve direct bonding of metal ion to the adsorbed anions, but rather involved electrostatic bonding to form outer-sphere complexes:

(1.11)

A thermodynamic description of phosphate adsorption onto La-AC is not adequate to explain completely phosphate adsorption and the underlying adsorption mechanism. Dynamic studies of the adsorption process are needed to better understand the adsorption mechanism. In the following section, the kinetics of phosphate adsorption on metal oxide surfaces is reviewed.

1.7 Kinetics of Phosphate Adsorption

Kinetic studies of adsorption can provide deep insight into reaction pathways and fundamental knowledge concerning the adsorption mechanism. Investigating the rate at which phosphate anions transfer from solution and bind to the solid interface makes it possible to engineer and design the appropriate adsorption devices and processes [Plazinski et al, 2009].

To predict the adsorption rate, an understanding the adsorption steps is important. The adsorption process includes the following steps: i) migration of the adsorbate in the bulk solution, ii) diffusion of the adsorbate across a thin boundary layer surrounding the adsorbent, iii) intraparticle diffusion, which includes the diffusion of the adsorbate toward the pores and along the pore walls of the adsorbate, and iv) adsorption/desorption of adsorbate molecules at the adsorbent surface. Normally the slowest step or steps in the adsorption process controls the adsorption rates. [Ho et al, 1999]

In experimental adsorption studies the effects of step (i) can be minimized by incorporating viscous mechanical mixing in the experimental apparatus. Numerous kinetic models have been created to describe the contributions of the remaining steps. In the most common models it is assumed that step (iv) is the rate controlling step, or at least one of the rate controlling steps. Physical or chemical interactions between active sites on the surface of the adsorbent and adsorbate molecules drive the migration of adsorbate molecules located in the vicinity of the adsorbent to the interface. It is postulated that these physical or chemical interactions govern the overall adsorption rate.[Ho et al, 1999]

Studies using hydrous metal oxides have shown that phosphate adsorption includes two steps: a rapid initial adsorption process that occurs in a few minutes to a few hours followed by a slow

16 adsorption process that may last for days or even weeks. Several explanations have been proposed for this two-step adsorption process. [Luengo, 2006]. Chitrakar et al. [Chitrakar et al, 2005] studied the use of amorphous zirconium hydroxide to remove phosphate from a single electrolyte solution (NaH2PO4), phosphate-enriched seawater, and model wastewater. They found that although the phosphate uptake of their novel adsorbent had a higher capacity than previously reported adsorbents, phosphate uptake was slow, requiring up to 7 days to reach equilibrium. They observed that phosphate removal from 0.3 and 1 mg/L NaH2PO4 solutions and 2 mg/L model wastewater was almost 100% in 4-6 days. They assumed that the phosphate adsorption by surface hydroxyl groups on the adsorbents occurred in a period of minutes to hours; however the slow adsorption process was completed in a period of days. They attributed this slow adsorption to the random structure of amorphous zirconium hydroxide. The adsorbent’s random structure had two types of hydroxyl groups, (i) terminal –OH groups available on the surface, and (ii) bridging –OH groups in the interior of the solid, connected by two Zr atoms as shown in Figure 1.6.

Figure 1.6 Possible -OH groups on zirconium hydroxide [Chitrakar et al, 2005]

As Figure 1.6 indicates, there were more adsorption sites available in the interior metal matrix, but slow phosphate diffusion might have hindered the access of anions to those interior sites.

In another example, it was found phosphate removal using lanthanum-doped mesoporous SiO2 was faster at the initial stage and became slower at the end of the test. Ou et al [Ou et al, 2007]

17 proposed that as the phosphate adsorbed to lanthanum sites, LaPO4 was formed that blocked the pores of the mesoporous SiO2 and hindered access to the interior adsorption sites.

Shin and coworkers [Shin et al, 2004] showed that mesoporous silica impregnated with 10% aluminum had a maximum phosphate adsorption capacity of 862 µmol/g (82 mg/g), and reached equilibrium within 1 hour. They related the high adsorption capacity and fast kinetics to the structure of the pores of the substrate and surface structure of Al oxides. Hexagonal open pores of Al-impregnated SBA-15 improved the access of adsorbate to the adsorption sites, and hence enhanced the kinetics of adsorption. Potentiometric titration and modeling using surface complexation theory showed that Al impregnation onto SBA-15 led to a higher surface hydroxyl density of Al oxide, and therefore to a higher adsorption capacity.

Most kinetic studies on phosphate adsorption have been obtained based on macroscopic adsorption data. However, Luengo et al [Luengo et al, 2006] investigated the phosphate adsorption process onto synthesized goethite obtaining spectroscopic data. Using in situ ATR- FTIR spectroscopy combined with batch experiments the evolution of the adsorbed phosphate anions onto the surface as a function of reaction time was monitored. In the first 5 minutes, adsorption was rapid, but became slower; after 300 minutes, equilibrium was attained. ATR-

FTIR peaks indicated that at pH 4.5 both monoprotonated bidentate ((FeO)2(OH)PO) and nonprotonated bidentate ((FeO)2PO2) surface complexes could be formed at the beginning of the experiment. However, at pH 7.5 and 9 the dominant surface complexes were nonprotonated bidentate complexes ((FeO)2PO2). Figure 1.7 shows ATR-FTIR results at pH 9. The intensity of the ATR-FTIR peaks increased over time due to increasing amounts of adsorbed phosphate. The ATR-FTIR band position did not change during the reaction, indicating that the surface complexes formed remained the same over time. Those results were consistent with a mechanism that included two reaction steps: initial fast adsorption followed by slow surface diffusion into pores. The same peak positions over time indicated that the surfaces complexes first formed transferred slowly into pores by surface diffusion without changing their identity during reaction time.

Figure 1.7 ATR-FTIR spectra of phosphate adsorbed on the surface of goethite at pH 9 [Luengo et al, 2006]

To develop a model to explain interfacial kinetics, many simple and compact equations based on simple principles such as pseudo-first-order and pseudo-second-order equations have been used [Ho et al, 1999]. Equation 1.12 shows the differential form of the pseudo-first-order equation, and Equation 1.13 show the solution of Equation 1.12 with the initial condition Q(t=0)=0.

(1.12)

(1.13)

In the above equations Q(t) is the amount adsorbed at time t (mg/g), Qe is (mg/g), and k1 is the temperature-dependent kinetic constant (1/t).

The pseudo-second-order equation is used when merely the ions exchange reaction at the surface active sites controls the overall adsorption rate. The differential form of pseudo-second-order reaction, and its solution with the initial condition Q(t=0)=0 are written as follows:

(1.14)

(1.15)

Again, Q(t) is the amount adsorbed at time t (mg/g), Qe is the amount adsorbed

and k2 is the temperature-dependent kinetic constant (1/t).

These equations can be used to correlate kinetic data. In the derivation of these formulas it was assumed that the surface kinetic reaction is the controlling step. Several rate equations can be tested in parallel to identify the best fit equation [Ho et al, 1999]. Based on the correlation coefficient values it was shown that pseudo-second order adsorption model given by equation 1.15 better describes the adsorption kinetics of phosphate on lanthanum hydroxide-doped activated carbon fiber (ACF-La) [Zhang et al, 2011], hydroxyl lanthanum-iron doped activated carbon fiber (ACF-LaFe) [Liu et al, 2013], lanthanum (La(III))-loaded granular ceramics [Chen et al, 2012], some novel synthesized inorganic ion exchanger such as ZrO2.XH2O and

Fe2O3.Al2O3.XH2O [Chubaret al, 2004], and aluminum-impregnated mesoporous silicates [Shin et al, 2004]. In addition it was found that the pseudo-first order adsorption equation (Equation 1.13) is appropriate to describe the adsorption kinetics of phosphate on lanthanum-impregnated silica gel [Ou, 2007].

D’Arcy et al introduced a modified pseudo-second order rate equation to describe the adsorption kinetics of phosphate onto a bi-functional TiO2-Fe2O3 bi-composite. In their kinetic model, they assumed adsorption followed two simultaneous, parallel reaction pathways with separate kinetic parameters. D’Arcy et al found their two-pathway rate law model was more accurate than the single pathway formulation to describe phosphate adsorption on the surface of TiO2-Fe2O3 bi- composite. Spectroscopic analysis showed that both monodentate and bidentate inner-sphere surface complexes were formed on the surface of the adsorbent. However, the formation of monodentate and bidentate surface complexes occurred at different rates which could be responsible for the bimodal kinetics. The two surface binding pathways were as follows:

(1.16)

(1.17)

Where Ck is the initial phosphate concentration in the solution, Q1 and Q2 are the monodentate and bidentate complexes formed on the adsorbent surface respectively, and k1 and k2 are the rate constant for each complexation reaction, respectively.

The rate equations for each of the steps were written as:

(1.18)

(1.19)

(1.20)

Where Qe 1/2 are the equilibrium concentrations of phosphate, and t is time. By mass balance, the total amount of the adsorbed phosphate was related to monodentate and bidentate complex concentrations as follows: (1.21)

Solving Equations 1.18 -1.21 yields:

(1.22)

(1.23)

(1.24)

There are two significant problems with D’Arcy’s model. First, the material balance equation does not account for the volume of liquid or the adsorbent mass. Second, the thermodynamic driving force of the adsorption is proportional to ( ). However, Qe should be the phosphate loading in equilibrium with the solution, and so should vary with time. D’Arcy’s model assumes a constant value for Qe throughout the entire course of the adsorption, which is an incorrect assumption.

Phosphate adsorption onto the surface of the adsorbent is also influenced controlled by external parameters including pH, temperature, and the ionic strength of the solution, so an understanding the effect of those external parameters on phosphate adsorption should lead to a better understanding of the adsorption mechanism. In Section 1.8, a brief review on effect of adsorption parameters on phosphate adsorption is presented.

1.8 Effect of Environmental Parameters on the Phosphate Adsorption

The phosphate adsorption capacity is highly dependent on parameters such as pH, temperature, and the ionic strength of the solution. Hydrous metal hydroxides show amphoteric behavior, capable of exchanging anions in acidic conditions and cations in basic conditions. The ionic species of the phosphate and surface chemistry of the adsorbent also strongly affect the adsorption capacity. All of these parameters are functions of the pH of the solution, and will affect the phosphate uptake. Furthermore, ions that compete with phosphate for adsorption sites can impact phosphate uptake. Hence, the adsorption capacity also depends on the ionic strength of the solution.

Temperature is also an important factor in phosphate removal from aqueous solution. Temperature usually increases phosphate uptake by metal oxides [Chen et al, 2012; Liu, 2011]. phosphate adsorption onto metal oxides is endothermic, so increasing the temperature favors higher phosphate adsorption. Higher temperature also increases the mass transport rate by increasing the phosphate driving force onto adsorbent surface and by reducing the energy barrier of the reaction between the phosphate ions and hydrous metal active sites.

For example, the effect of pH, ionic strength, and temperature were investigated on phosphate adsorption capacity of ACF-La. The amount of phosphate adsorbed by ACF-La increased with the increase of pH solution from pH 2 to pH 4, decreased slowly from pH 4 to pH 8, and decreased remarkably with increasing pH above pH 8. This effect was related to the change in the surface charge from positive to negative on the adsorbent by increasing pH. The adsorption capacity of ACF-La decreased with increase of the ionic strength of the solution. Furthermore, increasing the temperature from 20 °C to 50 °C increased phosphate uptake from 8.54 to 9.41 mg/g. Temperature studies also provided information on the enthalpy and entropy of the adsorption. Based on the temperature studies, enthalpy and entropy of the adsorption were reported 21.4 kJ mol-1 and 74.6 J mol-1 K-1, respectively [Liu et al, 2013].

1.9 Research Objectives

Developing a fixed-bed column system to remove phosphate from blood serum requires developing a non-toxic biocompatible material with low cost and high adsorption uptake capability. Understanding the role of external environmental parameters governing phosphate adsorption, such as pH, temperature, interfering ions, and the ionic strength of the solution, are of particular interest. Moreover, to have clear insight into the phosphate uptake behavior it is necessary to understand the adsorption isotherms and kinetics [Liu et al, 2013].

The objectives of this project were: 1. To prepare, optimize, and characterize a biocompatible, non-toxic, effective, and non- expensive phosphate adsorbent. 2. To obtain adsorption isotherms and kinetic parameters to gain knowledge on phosphate uptake behavior of the adsorbent, including maximum capacity and nature of the adsorption, adsorption nonequilibrium reactions, and adsorption evolution with time. 3. To investigate the effect of solution parameters such as temperature and pH on phosphate loading. 4. To propose and evaluate a mechanism-based model to describe the equilibrium and kinetic data.

The organization of this thesis is as follows:

 Chapter 2 describes the reagents, experimental techniques and characterization tools used in the study.  Chapter 3 contains a description of the synthesis, optimization, and characterization of lanthanum-impregnated activated carbon.  Chapter 4 presents and discusses the results of studies of phosphate adsorption isotherms, adsorption thermodynamics and the mechanism of phosphate adsorption on lanthanum-impregnated activated carbon.  Chapter 5 presents results for the kinetics of phosphate adsorption on lanthanum- impregnated activated carbon, and presents a new model for phosphate adsorption kinetics on the surface of lanthanum impregnated activated carbon.  Chapter 6 summarizes the results and conclusion of the project.  Chapter 7 presents recommendations for future studies based on the results of this study.

Chapter 2: Materials and Methods

2.1 Materials The purchased materials using in this project are listed in Table 2.1. All the chemicals used were of analytical grade.

Table 2.1 Summary of purchased materials Material Supplier

Lanthanum (III) nitrate hexahydrate 98% Acros Organic (NJ, USA)

Arsenazo III Ricca Chemical (R0794000-12A,Arlington, TX, USA)

Activated Carbon Fisher Scientific (AC-1, 05-690A, 50-200 mesh)

Stannous Chloride MP Biomedicals (Solon, OH, USA)

Hydrazine Sulfate Acros Organics (NJ, USA)

Trichloroacetic Acid Fisher Scientific (Pittsburg, PA, USA)

Sulfuric Acid Fisher Scientific (Pittsburg, PA, USA)

Ammonium Molybdate Acros Organics (NJ, USA)

Hydrochloric Acid Fisher Scientific (Pittsburg, PA, USA)

Sodium Hydroxide Fisher Scientific (Pittsburg, PA, USA)

Dbasic Potassium Phosphate Fisher Scientific (Pittsburg, PA, USA)

2.2 Preparation of the Adsorbent

La-impregnated activated carbon was prepared using chemical impregnation as follows [Zhang et all, 2011]. Fisher activated carbon powder was acid washed with 2.45 M HCL at 60 °C, filtered, rinsed with water, and dried at 60 °C in the oven overnight. Then 5 g of acid-washed

26 activated carbon suspended in 50 mL aqueous solution of lanthanum nitrate (La(NO3)3) with an initial lanthanum concentration in the range of 0.05-0.2 M for 24 hours (the impregnation time), rinsed with water, and dried overnight in an oven at 60 °C under air. To convert the surface lanthanum to hydrous lanthanum oxide with high phosphate affinity the lanthanum-impregnated activated carbon was calcined in an oven using a heating rate at 1° C/min and held at the desired activation temperature within the range of 100 to 650 °C under the air or nitrogen flow in the oven for 2.5 hours (the activation time), and then cooled to room temperature at 5° C/min. The effects of lanthanum concentration, calcination temperature, and nitrogen flow on the properties of the adsorbents are described in Chapter 3. The work reported in Chapters 4 and 5 used 12 wt% lanthanum-impregnated activated carbon calcined at 650 °C for 2.5 hours under air flow.

2.3 Adsorbent Characterization

2.3.1 Arsenazo Chemical Assay

To measure the equilibrium amount of lanthanum adsorbed on the activated carbon the Arsenazo III chemical assay was used [Yong et al. 1996]. Four samples of lanthanum nitrate at different lanthanum concentration in the range of 0.05-0.2 mM were prepared, and mixed with 5 g acid- washed activated carbon for 24 hours. For each measurement, 50 µL of lanthanum solution in the supernatant was diluted with 10 ml of water. Then 50 µL of the diluted lanthanum solution was mixed with 1 mL water, 2 ml 0.1 M ammonium acetate buffer (NH4HCO3), and 0.1 mL Arsenazo III. The final solution was stirred, and read using UV-Vis spectrometer at the wavelength of 660 nm. Figure 2.1 shows the lanthanum loading calibration curve at 660 nm at room temperature.

0.5 y = 35.718x - 0.0158 0.4 R² = 0.9592

0.3

0.2 Absorbance 0.1

0 0 0.002 0.004 0.006 0.008 0.01 0.012

Liquid-Phase La Concentration (µmol/L)

Figure 2.1-Lanthanum calibration curve using Arsenazo (III) assay. T: 25 °C, Impregnation time: 24 hours

2.3.2 Scanning Electron Microscopy (SEM)

An SEM (FEI XL-30 FEG Environmental Scanning Electron Microscope) was used for structural and morphological characterization of activated carbon and lanthanum impregnated activated carbon powders. A small quantity of the sample was placed on a SEM sample holder which was covered with carbon tape to improve adhesion of the powders to the sample holder. The sample holder was placed in a gold coating machine and coated with a thin layer of gold to improve charge transfer and to avoid image blurring and charge accumulation.

2.3.3 Nitrogen Porosimetry

The textural properties of activated carbon and lanthanum-impregnated activated carbon (La- AC), pore size and BET surface area, were determined using nitrogen adsorption-desorption (Tristar 3000, Micromeritics, Norcross, GA, USA) at 77 °K with degassing period of 2 hours at 120 °C under dry argon before the measurement. The Brunauer–Emmett–Teller (BET) method was used to determine the surface area and average diameter of pores at a P/P0 range of 0.05 - 0.25 [Brunauer et al, 1938].

2.4 Molybdenum Blue Assay

Dibasic potassium phosphate (K2HPO4) was used to prepare phosphate solutions and stock solutions over a wide range of K2HPO4 concentrations.

Aqueous phosphate solution concentrations were determined using the molybdenum blue assay in conjunction with a UV-Vis spectrometer [Pradhan et al, 2013]. This method is based on the formation of the phosphomolybdate blue complex when molybdate (ammonium molybdate) added to the solution followed by the reduction of the complexes by hydrazine sulfate in trichloroacetic acid medium. The color intensity of the phosphomolybdate blue complexes formed is proportional to the phosphate concentration of the solution, and the phosphate concentration can be read quantitatively using a UV-Vis spectrometer at 640 nm.

Solutions of trichloroacetic acid (TCA) (the solvent), ammonium molybdate (the dye), and hydrazine sulfate (the reducing agent) were prepared as follows. The TCA solution was made from 97 mL water and 3 g trichloroacetic acid. The ammonium molybdate solution was prepared by mixing 95.5 mL water, 3.5 mL concentrated sulfuric acid (H2SO4), and 1 g aluminum molybdate. The hydrazine sulfate solution was prepared by mixing 97 mL water, 2.8 mL concentrated sulfuric acid (H2SO4), 0.2 g hydrozinc sulfate, and 0.02 g stannous chloride.

To quantitatively determine the phosphate concentration, 200 µL of the solution to be assayed was added to 800 µL of the TCA solution, and then mixed with 1 mL of ammonium molybdate and 1 mL of hydrazine sulfate solutions for exactly 10 min in the shaker. A UV-Vis spectrometer (Cary 50 Duo spectrometer, Varian, Santa Clara, CA) was used to read the absorption of the solution at 640 nm.

Following the Beer-Lambert law, the adsorption of the solution is proportional to the concentration of the adsorbing species in the solution and the path length 2.1 [Swinehart, 1996].

(2.1)

29 where Ab is the measured absorbance, L is the path length (cm), c is the concentration of the adsorbing species (mol/cm-3), and is extinction coefficient constant (1/mol.cm).

The calibration curves for phosphate blue assay at different pH of the phosphate solutions are shown in Figure 2.2. For these curves, the phosphate solution pH was adjusted using sodium chloride and hydrochloric acid.

The UV-Vis absorption measurements were done in a cell with path length of 1 cm; the extinction coefficient constant ( was calculated from the slope of the regression line in for adsorption vs. phosphate concentration. For all pH ranges, was found to be 0.1, and independent of pH of the phosphate solutions.

1.6 1.4

1.2

1 0.8

0.6 pH 2-3 Absorbance 0.4 pH 6-7 pH 10-11 0.2 0 0 5 10 15 Phosphate Co (mg/L)

Figure 2.2 Phosphate calibration curves at different pH using molybdenum blue assay in conjugation with UV scan at 640 nm. Using linear regression, ε = 0.10 and R2 =0.99 for all pH ranges tested.

2.5 Adsorption Experiments

In the work reported in Chapter 4, the phosphate adsorption isotherms were obtained for initial phosphate concentrations in the range of 25-300 mg/L. Sample vials containing 1 mL phosphate solution at the desired initial concentration and 10 mg adsorbent were incubated in a shaker (G24, NewBrunswick Scientific, Edison, NJ, USA) for 48 hours to reach equilibrium at either 37 or 50 °C. The phosphate concentration in the supernatant was measured the using molybdenum blue assay described above, and the phosphate loading on the adsorbent was calculated by mass balance. Phosphate adsorption studies were carried out in duplicate or triplicate.

The pH change of phosphate solution at initial concentrations of 100, 150, 200, and 300 mg/L after incubation with activated carbon and La-AC for 48 hours at 37 °C were measured using a pH meter (PH 208, Master Instrument, Sydney, Australia).

To study the effect of pH on phosphate loading, 10 mg adsorbent was suspended in 1 ml of 200 mg/L phosphate solution with pH values in the range of 2.7 to 11. Samples were incubated for 48 hours at 37 °C in a shaker, and phosphate loading on La-AC was measured using the molybdenum blue assay. The initial pH of the solutions was adjusted using sodium chloride and hydrochloric acid and measured using a pH meter.

To study the effect of bovine serum albumin (BSA) on phosphate capacity, BSA was added to 0.574 mmol/L (100 mg/L) phosphate solution to obtain BSA concentrations from 0 to 45 g/L. In the adsorption experiments, each sample vial was prepared with 1 mL phosphate and protein solution at desired protein concentration and incubated with 10 mg adsorbent at 37 °C in a shaker (G24, NewBrunswick Scientific, Edison, NJ, USA) for 48 hours. The phosphate concentration in the supernatant was measured using the molybdenum blue assay followed by UV-Vis spectrometry measurement at 640 nm as described above. Protein loading was determined by UV-Vis spectroscopy measurement at 280 nm.

2.6 Flow Microcalorimetry

A flow microcalorimeter (FMC; Microscal FMC 3vi, Gilson Instrument, Westerville, OH, USA) was used to study the magnitude and dynamics of the enthalpy of phosphate adsorption on La- AC. The FMC bed was packed with 77.6 mg of adsorbent. The flow rate of the mobile phase was 1.85 mL/h, and sample loop volume was 2.2 ml. For each run, the system was equilibrated overnight with the mobile phase (water) to reach to a steady baseline. Then 200 mg/L phosphate solution was injected on to the column through the sample loop. Thermistors in the FMC sensed minute changes in the bed temperature, producing a voltage signal that was recorded by a computer. The voltage signals were recorded for 100 min during the phosphate adsorption on activated carbon and La-AC. A measured calibration factor of 48.60 mV.min/mJ was used to convert the voltage signals to enthalpies. The enthalpy of adsorption was calculated using the following equation [Arai, 2007].

(2.1)

The FMC thermograms were deconvoluted into Gaussian peaks and analyzed using MagicPlot Student 2.3 (MagicPlot Systems, Saint Petersburg, Russia).

2.7 Kinetics of Adsorption

Phosphate adsorption kinetics on La-AC were measured in batch experiments at initial potassium phosphate concentrations of 0.574 and 1.148 mmol/L (100 and 200 mg/L, respectively). For each initial concentration, a set of sample vials was prepared to be measured at a desired time sequentially over 30 hours. For each sample time, there were duplicate or triplicate samples. Each sample vial contained 1 mL phosphate solution at a desired concentration incubated with 10 mg adsorbent in a shaker (G24, New Brunswick Scientific, Edison, NJ, USA) at 37 °C. The phosphate concentration in supernatant of each vial was measured using the molybdenum blue assay described in Section 2.4, and the phosphate loading on the adsorbent was calculated by mass balance.

Chapter 3: Synthesis, Characterization, and Optimization of Lanthanum-Impregnated Activated Carbon

3.1 Lanthanum-Impregnated Activated Carbon (La-AC)

Several aluminum, lanthanum, and zirconium compounds have been developed and investigated for phosphate adsorption. [Kawashima et al, 1986; Yao et al, 1996; Tang et al, 1997; Gao et al, 2003; Juang et al, 2004; Chitrakar et al, 2005; and Chubar et al, 2005]. Among numerous candidate adsorbent materials, lanthanum oxide supported on activated carbon has been selected for use in the current study due to its non-toxicity and biocompatibility [Persy, et al, 2009]. Recent studies have shown that lanthanum oxide has high affinity for phosphate and is relatively inexpensive [Zhang et al, 2011].

Activated carbon has high surface area with small, low-volume pores; it is well-suited for applications involving chemical adsorption [Li et al, 2002]. The high surface area and pore size distribution provide support for the impregnated lanthanum and easy access for phosphate anions to reach to the lanthanum oxide active sites.

Lanthanum-impregnated activated carbon (La-AC) was prepared using an established chemical impregnation protocol described in Section 2.2. The pore size and surface area of the La-AC was determined using nitrogen adsorption-desorption as described in Section 2.3.3; results are shown in Table 3.1; the nitrogen adsorption-desorption data are presented in Appendix E. It was found that loading lanthanum onto AC did not significantly affect the surface area or pore size of the material.

Table 3.1 Textural properties of lanthanum-impregnated activated carbon Material BET BJH Desorption

Surface Area (m2 /g) Pore Diameter (nm)

Activated Carbon Substrate 1043 3.6

La-AC Calcined at 650 °C 1047 3.5

SEM images of acid-washed activated carbon and acid-washed La-AC (before calcination) are shown in Figures 3.1 a) and b). a)

1 2

3 4

b) 5 6

Figure 3.1 SEM images of a) images 1, 2, 3, and 4 shows acid washed activated carbon at different magnifications b) images 5 and 6 shows La-AC before calcination at different magnification. La to AC: 12% wt, T: 25 °C, Impregnation Time: 24 hours

As can be seen in Figure 3.1a), activated carbon has high surface area with graphite-like flat surfaces that run parallel to each other . Although this activated carbon had been acid washed, large chunks of carbon were observed on the surface. Figure 3.2a) shows the size distribution of the large chunks on the surface of activated carbon. Figure 3.1b) shows the surface structure of activated carbon impregnated with lanthanum. Comparison of images 3.1a) 4 and 3.1b) 6 reveals that needle-like structures can be observed on the surface of the La-AC that are not seen on the surface of initial activated carbon. Additional SEM imaging of other samples revealed the same needle-like structures on the surface; these structures appear to be related to lanthanum components on the surface. The appearance of lanthanum structures on the SEM images of lanthanum-impregnated activated carbon fibers has been previously reported [Zhang et al, 2011]. Figure 3.2 b) shows the size distribution of the needle-like structures on the surface of La-AC. To further study the identity of the needle like structures, XRD was run on the samples. As can be seen in Figure 3.3, clear peaks were not obtained, possibly due to the low amount of lanthanum on the amorphous activated carbon background.

36 a)

Distribution(%) 20

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 Carbon Chunk Size (nm)

20 Distribution(%)

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 Needle-Like Structure (nm)

Figure 3.2 a) Size distribution of carbon chunks on the surface of acid-washed activated carbon, bin size: 50 nm b) size distribution of needle like structure on the surface of activated carbon after soaking in 12% lanthanum solution, bin size: 50 nm, T: 25 °C, Impregnation Time: 24 hours

Figure 3.3 XRD results of AC and 12% wt La-AC, T: 25 °C, Impregnation Time: 24 hours Calcination Temperature: 650 °C

3.2 Optimization of La-Activated Carbon as a Phosphate Adsorbent

There are at least four main synthesis parameters that can influence the phosphate adsorption behavior of La-AC: activation time, impregnation time, activation temperature, and the weight percentage of La to activated carbon [Zhang et al, 2011]. Among these four parameters, only the effects of activation temperature and the weight percentage of La to activated carbon were examined in this study.

3.2.1 Lanthanum to Activated Carbon Mass Percentage

To determine the optimum lanthanum to activated carbon mass percentage, three samples of La- activated carbon were prepared at 8 wt%, 12 wt%, and 20 wt% lanthanum to activated carbon as described in Section 2.3.1. Batch experiments showed an increase of La loading with increasing La solution concentration as shown in Figure 3.4. The remainder of the studies reported in this thesis use 12 wt% La-AC.

1.6

1.2

0.8

Lanthanum Loading (mmol/g) 0.4

0 0 0.005 0.01 0.015 0.02 Lanthanum Concentration (mmol/L) Figure 3.4 Lanthanum loading on the activated carbon surface. La: AC weight percentages: 8, 12, and 20% , T: 25 °C, Impregnation Time: 24 hours

3.2.2 Calcination Conditions

To study the effect of calcination temperature four 12% La-AC samples were calcined in a furnace at four different temperatures (100, 200, 450, and 650°C) for 2.5 hours under air flow. An adsorption isotherm for each sample was obtained for initial phosphate concentrations in the range of 25-300 mg/L using a 48 hour incubation time at 37 °C to reach equilibrium. The detailed procedure was described in Section 2.2. Figure 3.5 shows the comparison of average phosphate equilibrium adsorptions onto 12% La-AC samples calcined at different temperatures under air flow.

Figure 3.5 Effect of calcination temperature on phosphate equilibrium loading for 12% wt La-

AC calcined under air flow. T: 37 ° C. Initial potassium phosphate (K2HPO4) concentrations: 25-300 mg/L, 48 hour equilibration time.

As shown in Figure 3.5, phosphate capacity decreased as the calcination temperature increased from 100°C to 450°C, but abruptly increased at a calcination temperature of 650°C. This effect may be attributed to different affinities of various lanthanum oxides for phosphate, since different lanthanum oxides are formed at different calcination temperatures in the furnace. The thermal decomposition of lanthanum nitrate to lanthanum oxide from room temperature to 650 °C includes nine endothermic weight loss steps, shown in Table 3.2, that finally lead to the formation of lanthanum oxide at 650 °C [Mekhemer et al, 2001].

Table 3.2 Course of decomposition of lanthanum nitrate toward lanthanum oxide from room temperature to 650 °C [Mekhemer et al, 2001] Temperature °C Lanthanum Complex Formed

Room temp. La(NO3)3·6H2O

90 La(NO3)3·5H2O

105 La(NO3)3·4H2O

150 La(NO3)3·3H2O

175 La(NO3)3·2H2O

215 La(NO3)3·H2O

410 La(OH)(NO3)2

440 LaO(NO3)

570 LaO1.25(NO3)0.5

640 La2O3

It is speculated that different nitrate monohydrate complexes had different tendencies to adsorb phosphate, and lanthanum oxide had the highest affinity for phosphate uptake.

SEM images of 12 wt% La-AC calcined at 650 °C under air flow are shown in Figure 3.6. The needle-like structures on the activated carbon surface seem to have agglomerated and formed big chunks. However, the morphology and the dimensions of the agglomerated chunks differed from the available chunks of activated carbon on the surface. The average size of these lanthana agglomerations was determined to be 2207 nm using the ImageJ program.

b a

Figure 3.6 a and b) SEM images of La-AC carbon calcined at 650° C under air flow. Image a shows the same agglomeration as in image b, but with higher magnification La: AC weight percentages: 12% wt, Impregnation Temperature: 25 °C, Impregnation Time: 24 hours, Calcination temperature: 650 °C for 2.5 hr

The effect of calcination temperature was also studied at three different temperatures (200, 450, and 650°C) under nitrogen flow. Figure 3.7 shows the phosphate equilibrium loading of 12 wt% La-AC calcined at different temperatures under nitrogen flow. The phosphate capacity of the sample calcined at 200 °C is higher than that of the sample calcined at 450 °C; however, the sample calcined at 650 °C shows the highest phosphate loading capacity. Regardless of the calcination atmosphere, phosphate capacity is highest for samples calcined at 650 °C. However, the phosphate adsorption capacity of La-AC calcined at 650 °C under air is higher than of La-AC calcined at 650 °C under nitrogen. The observed influence of calcination temperature on phosphate adsorption on La-AC is consistent with previously reported results for lanthanum- impregnated activated carbon fibers. [Zhang et la, 2011]

10 Calcined at 200 C under Nitrogen 8 Calcined at 450 C under Nitrogen 6 Calcined at 650 C under 4 Nitrogen

Phosphate Phosphate Loading (mg/gAdsorbent) 2

0 0 50 100 150 200 Liquid-Phase Phosphate Concentration (mg/L)

Figure 3.7 Effect of calcination temperature on phosphate equilibrium loading for La-AC calcined under nitrogen. La: AC weight percentages: 12%, T: 37 ° C. Initial potassium

phosphate (K2HPO4) concentrations: 25-300 mg/L, 48 hour equilibration time.

Figure 3.8 shows SEM images of La-AC calcined at 650° C under nitrogen. Unlike the sample calcined at the same temperature under air, the images exhibit more uniformly distributed needle-like structures. Also, unlike the samples calcined at 650°C under air, there is no significant trace of large agglomerates on the surface of La-AC calcined at 650° C under nitrogen. The average length of the needle-like structures in the SEM images was measured to be 576 nm. The reduced oxygen present during calcination under nitrogen compared to calcination under air seems to prevent the agglomeration of the needle-like structures, and seems to cause incomplete formation of lanthanum oxide on the surface. As a result, the phosphate capacity is lower in samples calcined under nitrogen flow. Figure 3.9 a) and b) compares phosphate loading capacity at given temperatures under air and nitrogen.

Figure 3.8 SEM images of La-activated carbon calcined at 650° C under nitrogen from two different spots of the same sample. La: AC weight percentages: 12%, Impregnation Temperature: 25 °C, Impregnation Time: 24 hours

44 a) b)

6 Cacined at 450 C under 4 Air

Calcined at 450 C under 2 Nitrogen

Phosphate Loading (mg/gAdsorbent) 0 0 50 100 150 200 Liquid-Phase Phosphate Concentration (mg/L)

10 8 Calcined at 650 C under 6 Air 4 Calcined at 650 C under Nitrogen 2 Phosphate Loading (mg/gAdsorbent) 0 0 50 100 150 200 Liquid-Phase Phosphate Concentration (mg/L)

Figure 3.9 comparison of phosphate loading of La-AC carbon calcined at a) 200° C, b) 450° C,

c) 650° C under air and nitrogen, T: 37 ° C. Initial potassium phosphate (K2HPO4) concentrations: 25-300 mg/L, 48 hour equilibration time.

3.3 Summary

La-AC was successfully prepared for phosphate adsorption at trace phosphate concentrations; the lanthanum loading was confirmed by SEM imaging and a lanthanum adsorption study using the Arsenazo assay. Phosphate capacity was optimized by varying the mass ratio of lanthanum to activated carbon, the calcination temperature and the calcination atmosphere (air vs. nitrogen). Increasing the initial mass fraction of lanthanum led to higher lanthanum loading and more lanthanum active sites on the surface. Zhang and coworkers [Zhang et al, 2011] synthesized activated carbon fibers loaded with lanthanum oxide for phosphate removal, and they found the optimum mass ratio of lanthanum to activated carbon fiber was 11.78%. La-AC calcined at 650 °C under air flow had the highest phosphate removal of the samples tested, in agreement with previously reported optimum calcination temperature for activated carbon fiber loaded with lanthanum. Samples of La-AC with 12 % La to AC mass ratio calcined at 650 °C under air flow for 2.5 hours were used in the adsorption and kinetic studies reported in Chapters 4 and 5.

Chapter 4- Thermodynamics of Phosphate Adsorptions

A better understanding of phosphate adsorption on La-AC can be achieved by investigating the adsorption isotherms that describe equilibrium behavior over a range of phosphate concentrations at constant temperature, and by studying the effects of adsorption conditions on phosphate uptake. In addition, engineering the appropriate adsorption device for practical applications is based on the thermodynamics of the adsorption process and the underlying mechanisms. Since blood plasma contains various chemicals and biomolecules that can affect phosphate adsorption capacity, understanding the influence of each blood component on phosphate loading on the surface is important. This chapter is focused on adsorption isotherms, the effects of adsorption conditions, and a thermodynamic study of phosphate adsorption on La- AC. Based on the data obtained, a mechanism is proposed to describe phosphate adsorption on La-AC. This mechanism will be used to help interpret the observed kinetics of phosphate adsorption reported in Chapter 5.

4.1 Adsorption Isotherm

An isotherm study was carried out to determine the equilibrium uptake of phosphate and the properties of the phosphate adsorbed on La-AC. Adsorption isotherms were obtained for initial potassium phosphate (K2HPO4) concentrations in the range of 0.143 to 1.722 mmol/L (25-300 mg/L) using a 48 hour incubation time to reach equilibrium at 37 and 50 °C as described in Section 2.5. Figure 4.1 shows equilibrium phosphate adsorption isotherms at 37 and 50 °C.

Phosphate Loading at 37 C Phosphate Loading at 50 C

Phosphate Loading (mg/g Phosphate Adsorbent) 0 0.0 0.4 0.8 Liquid-Phase Phosphate Concentration, mmol/L

Figure 4.1 Equilibrium phosphate adsorption isotherms. T: 37 ° and 50 °C. Initial potassium

phosphate (K2HPO4) concentrations: 0.143 to 1.722 mmol/L (25-300 mg/L), 48 hour equilibration time.

The phosphate adsorption isotherms at both adsorption temperatures, shown in Figure 4.1, reveal that at lower phosphate equilibrium concentrations, phosphate loading increased sharply with increasing liquid-phase phosphate concentration. The isotherms became flatter at higher phosphate concentrations. Increasing the temperature from 37 ° to 50 °C increased the phosphate adsorption capacity, suggesting that phosphate adsorption onto La-AC is chemisorption rather than physisorption, and that phosphate adsorption onto La-AC is endothermic [Liu et al, 2011].

The observed phosphate adsorption isotherms were fit with both the Langmuir and Freundlich models using nonlinear-regression. The Langmuir isotherm is

(4.1)

49 where Q is the adsorption capacity (mg/g), Q max is the maximum adsorption capacity (mg/g), C is the adsorbate concentration (mmol/L), and KL is the adsorption constant (L/mmol). The Freundlich isotherm is

(4.2)

n n-1 where Kf (L /µmol .g) and n are the Freundlich parameters.

Using the R computing environment (R-3.3.0), best fit parameter estimates of the adsorption parameters were determined (Appendix A); regression results are shown in Table 4.1. To compare the performance of the Langmuir and Freundlich isotherms, an F-test was performed on the residual variance at a 95% level of confidence. At 95% confidence for 5, 7 degrees of freedom, the critical value of F is 3.97. The calculated F value for the residual errors of the

Langmuir and Freundlich models is 5.50, significantly above the critical value of F. F > F Critical indicates a statistically significant difference in the performance of the Langmuir and Freundlich models. Based on the regression results, experimental data are better described using the Langmuir isotherm than using the Freundlich isotherm. The successful use of the Langmuir isotherm for phosphate adsorption suggests that phosphate adsorption is reversible, but could also result from a broad distribution of binding energies for the adsorption sites. Chen and coworkers [Chen et al, 2012] have hypothesized that the phosphate adsorbed as a result of electrostatic and ion-exchange interactions on the surface of lanthanum granular ceramics is reversible. In addition, Chubar [Chubar et al, 2005] and coworkers assumed that phosphate adsorption on the surface of hydrated oxides are reversible. In this work, for simplicity it is assumed that phosphate adsorption on La-AC is reversible; however more work should be done to confirm the reversibility of phosphate adsorption on the surface of La-AC.

Table 4.1 Best-fit Langmuir and Freundlich parameter estimates Langmuir Isotherm 37°C 50°C

Qm, mg/g 15.43 + 0.61 21.14 + 1.07

KL, L/mmol 28 + 4.7 8.6 + 1.3 Residual SSQ, (mg/g)2 2.304 1.710 Degrees of Freedom 4 3 Total Residual SSQ, (mg/g)2 4.014 Total Degrees of Freedom 7 Residual Variance 0.5734

Freundlich Isotherm 37°C 50°C

n n-1 Kf ((L /mol .g)) 495.35 + 117.167 2.87 + 0.22 n 3.72 + 0.79 2.52 + 0.12

Residual SSQ, (mg/g)2 14.809 0.662 Degrees of Freedom 4 3 Total Residual SSQ, (mg/g)2 15.471 Total Degrees of Freedom 7 Residual Variance 2.21

The Langmuir regression curves at 37 and 50 °C are shown in Figure 4.2 a) and b), respectively.

51 a)

18 16 14 12 10 8 6 Experimental Data at 37 C 4 2 Langmuir model

Phosphate Phosphate Loading (mg/gAdsorbent) 0 0 0.5 1 1.5 Liquid-Phase Phosphate Concentration (mmol/L) b)

20 18 16 14 12 10 8 6 Experimental Data at 50 C 4 2 Langmuir Model 0 Phosphate Phosphate Loading (mg/gAdsorbent) 0 0.2 0.4 0.6 0.8 1 1.2 Liquid-Phase Phosphate Concentration (mmol/L)

Figure 4.2 Langmuir model fit to the observed adsorption isotherm data. a) T: 37 °C and b) 50

°C. Initial potassium phosphate (K2HPO4) concentrations: 0.143 to 1.722 mmol/L (25-300 mg/L), 48 hour equilibration time.

Using the Langmuir model, the maximum phosphate adsorption capacity on La-AC was calculated to be 15.43 + 0.61 mg/g over 48 hours to reach equilibrium at 37 °C. The phosphate adsorption capacity has been investigated for other lanthanum-based adsorbents. For example,

11.78% wt lanthanum to activated carbon fiber had a maximum phosphate capacity of 15.3 mg/g

52 within 3 h at room temperature [Zhang et al, 2011]. Lanthanum hydroxide doped activated carbon had a maximum phosphate capacity of 15.3 mg/g at room temperature over 6 hours to reach equilibrium [Zhang et al, 2012]. A phosphate capacity of 0.95 mg/g at 40 °C over 30 hours was reported for lanthanum-loaded granular ceramics [Chen et al, 2012]. The maximum phosphate loading of hydroxyl-iron-lanthanum doped activated carbon fibers was calculated to be 29.44 mg/g over 6 hours to reach equilibrium [Liu, 2013]. Wasay and coworkers [Wasay et al, 2013] reported a maximum phosphate uptake of 10.54 mg/g on lanthanum-impregnated silica gel over 20 hours to reach equilibrium. The maximum phosphate adsorption uptake on lanthanum doped onto diamino functionalized mesoporous silicates was calculated to be 54.3 mg/g over 2 hours [Zhang et al, 2010]. The order of magnitude of the maximum phosphate adsorption capacity on La-AC is in consistent with the values of phosphate adsorption capacities reported in the literature.

The standard Gibbs free energy (KJ/mol) of adsorption, , was calculated using the equation [Smith et al, 2004]

(4.3)

where R is the universal gas constant, and T is the temperature (K). The equilibrium constant K is a dimensionless parameter calculated from the Langmuir equilibrium constant (KL) [Zhou et al, 2014]:

K = C0KL (4.4)

3 where C0 is the molar density of the solution; C0 = 55.5 mol/L (55.510 mmol/L) for a dilute aqueous solution.

Using Equations 4.3 and 4.4, the Gibbs free energy of adsorption at 37 °C is:

The negative value of the Gibbs free energy of adsorption indicates a spontaneous process. Liu and coworkers calculated the Gibbs free energy for phosphate adsorption on lanthanum-doped activated carbon fiber to be -40.101, -42.082, and -44.940 kJ/mol at 20, 30, and 40°C, respectively [Liu et al, 2011]. Similarly, Chen et al reported the Gibbs free energy for phosphate adsorption on lanthanum-loaded granular ceramic to be -28.817, -30.445, and -32.074 kJ/mol at 20, 30, and 40°C, respectively [Chen et al, 2012].

4.2 Influence of Initial pH on Phosphate Capacity

It is well known that some anions, including phosphate, arsenate, and nitrate, adsorb on metal oxides mainly via electrostatic, ion-exchange, and Lewis acid-base interactions. The effects of each possible interaction are governed by the pH of the aqueous solution [Zhang et al, 2012, Zhang et al, 2011], so the pH of the solution is an important influence on phosphate adsorption capacity.

Phosphate adsorption on La-AC was investigated in the pH range of 2.7-11. 1.148 mmol/L (200 mg/L) potassium phosphate solution at different pH values were incubated with La-AC for 48 hours at 37 °C and phosphate loading on La-AC were measured using the molybdenum blue assay as described in Section 2.5. Figure 4.3 shows the phosphate loading versus initial solution pH.

14 pKa of dihydrogen phosphate anions=7.2 at 25 °C 13.5 positive surface 13 Negative Surface 12.5 12 11.5 11 10.5 10 Phosphate Phosphate Loading (mg/gAdsorbent) 1 3 5 7 9 11 13 Initial pH of Phosphate Solution

Figure 4.3 Effect of solution pH on phosphate adsorption on La-AC. Initial potassium phosphate concentration: 1.148 mmol/L; T = 37°C; incubation time: 48 hours

Figure 4.3 illustrates that the phosphate adsorption capacity is highly dependent on the initial pH of the solution. Phosphate loading increased as the pH increased from 2.7 to 7.8, reached a plateau and maximum capacity from pH 7.8 to 9, and then decreased at pH 11.

The change in phosphate adsorption over the wide range of initial pH solution can be explained as follows. At pH 2.7-8 the surface should be positive [Zhang et al, 2012]. Based on the literature, the point of zero charge of activated carbon is between 6 and 9 [Kusmulski et al, 2009]. The positive surface attracts phosphate anions via electrostatic forces, and facilitates ligand exchange [Zhang et al, 2012].

Table 4.2 Phosphoric acid equilibria. * values are reported dissociation pKa at 40°C, and **

values are reported dissociation pKa at 25°C [Delaney, 2011, Nims,1933, and Bates, 1951]

Equilibrium Dissociation pKa

Phosphoric acid can dissociate into monovalent dihydrogen phosphate ( ), divalent hydrogen phosphate ( ), and trivalent phosphate ( ) anions with separate acid dissociation constants. Table 4.2 shows phosphoric acid equilibria at different pH at room temperature. As it is shown in Table 4.2 at pH 2.7-7.2 the predominant species of phosphorus were monovalent ions of . Lanthanum ions on the surface have greater affinity to adsorb

than [Chen, 2012]. As the pH increases from 2.7 to 7.2 the concentration of monovalent phosphate anions decreases and the concentration of divalent phosphate anions increases. Consequently, phosphate uptake increases with pH in this range, reaching a maximum around pH 7.8-9 when the predominant species is divalent .

At pH 9-11 the predominant species was but the surface was negatively charged. The strong electrostatic repulsion between negatively charged groups on the surface, and divalent phosphate anions prevents divalent phosphate anions from approaching the surface of the adsorbent, and ligand exchange becomes less important. Consequently, the adsorption capacity decreases at higher pH. However, Lewis acid-base interactions between phosphate and the lanthanum active sites adsorption can still occur, suggesting that Lewis acid-base interactions between lanthanum active sites and oxygen anions in phosphate govern phosphate adsorption in this pH range [Zhang et al, 2012].

The trend of phosphate loading with different initial pH solutions confirms that the main interactions in phosphate loading on surface of La-AC include electrostatic, ion-exchange, and

Lewis acid-base interactions. At lower initial pH solution between 2 to 9 ligand exchange and electrostatic interactions are dominant, while Lewis acid-base interactions are the principal interaction at higher initial pH solution at 9 to 11.

4.3 Thermodynamic Studies of Phosphate Adsorption

Flow microcalorimetry (FMC) was used to study the nature of phosphate adsorption on activated carbon and on La-AC as described in section 2.5. For each run, the system was equilibrated overnight with mobile phase of pure water flowing through the sample bed to reach to a steady baseline. Then 1.148 mmol/L (200 mg/L) potassium phosphate solution was injected on to the column through the sample loop. Phosphate adsorption caused a change in the temperature of the bed which was recorded as a voltage signal using a computer. The voltage signals were recorded for 100 minutes during the FMC measurement. The thermograms for phosphate adsorption on activated carbon and La-AC are shown in Figure 4.4.

120 AC in contact with 100 200mg/L P 80 La-AC in contact with 200 mg/L P 60

Heat Signal Signal (mv)Heat 0 0 20 40 60 80 100 120 -20

-40

-60 Time (min)

Figure 4.4 FMC thermograms for phosphate adsorption on Ac and La-AC at room temperature. Bed mass: 77.6 mg; mobile phase rate: 1.85 mL/h; sample loop volume: 2.2 mL.

To understand phosphate interaction with the lanthanum active sites on the surface, the effect of interactions with the activated carbon support should be removed from the thermogram for phosphate adsorption on La-AC. The solid blue curve in Figure 4.5 shows the calculated thermogram for phosphate adsorption on lanthanum ions on the surface. At each time the voltage signal was calculated by subtracting the recorded voltage for phosphate adsorption on activated carbon from the recorded voltage value for phosphate adsorption on La-AC.

Figure 4.5 Thermogram of phosphate adsorption on lanthanum ions on the surface at room temperature. Bed mass: 77.6 mg; mobile phase rate: 1.85 mL/h; sample loop volume: 2.2 ml.

In the calculated thermogram of phosphate adsorption on the lanthanum active sites, Figure 4.5, an endotherm began around 20 minutes after sample injection began, reflecting the dead time between the sample loop and the FMC bed, and continued until around 70 minutes when fresh mobile phase began to replace the phosphate solution.

To better interpret the thermogram, it was deconvoluted into three endotherms, attributed to phosphate adsorption on lanthanum active sites. The enthalpy of adsorption for each peak was calculated from the peak area, the calibration factor converting voltage to heat (48.60 mV min / mJ), the bed mass, and the phosphate adsorption. Heats of adsorption are given in Table 4.3.

Table 4.3 Heats of adsorption of phosphate on La-AC ΔHI (kJ/mol) ΔHII (kJ/mol) ΔHIII (kJ/mol)

21.75 44.06 12.46

Previously published NMR and ATR-FTIR studies of phosphate adsorption on metal oxides revealed that uptake of phosphate occurred by formation of several types of surface complexes as a result of ligand exchange with a reactive surface hydroxyl groups [Kang et al, 2011 and Carabante et al, 2009]. The three possible phosphate complexes are monodentate, bidentate, and binuclear complexes as shown in Figure 4.6 [Shin et al, 2004]. Moreover, phosphate adsorption on metal oxides is believed to include two reaction steps: Formation of monodentate surface complexes followed by formation of bidentate / binuclear surface complexes [Shin et al, 2004, Rajan 1974].

Figure 4.6 Possible configurations of phosphate surface complexes [Shin et al, 2004]

The first and second endothermic peaks in Figure 4.5, with adsorption enthalpies of 21.75 and 44.06 kJ/mol, are assigned to the formation of monodentate and bidentate surface complexes, respectively. The large amount of absorbed heat indicates chemisorption and the formation of surface complexes rather than electrostatic attraction and physisorption. In addition, the heat of adsorption for the second peak was approximately twice the heat of adsorption for the first peak, suggesting the phosphate reacted with lanthanum surface active sites to form monodentate

59 complexes for the first peak and phosphate reacted with a different type of lanthanum active surface sites to form bidentate complexes for the second peak.

The low value of the heat adsorption of the third peak (around 12 kJ/mol) suggests adsorption due to electrostatic interactions. The FMC findings are consistent with previous spectroscopic studies on the phosphate surface complexes [Zhang et al, 2012]. The FMC data reveal that phosphate was adsorbed on La-AC due to the formation of monodentate and bidentate inner- sphere complexes, and electrostatic interactions which led to the formation of outer-sphere complexes.

4.4 pH Studies

One feature of phosphate adsorption on La-AC is the release of hydroxyl ions into the solution. Figure 4.7 shows the final pH of the phosphate solution as the function of phosphate loading on La-AC.

11.5 11 10.5

pH 9.5 Final pH Solution 9 Initial pH Solution 8.5 8 7.5 0 5 10 15 20 Phosphate Loading (mg/g Adsorbent)

Figure 4.7 Initial and final phosphate solution as the function of phosphate loading on La-AC. T: 37°C. Initial potassium phosphate concentrations: 0.143 to 1.72 mmol/L; 48 hour equilibration time.

The increase of solution pH with increasing phosphate loading suggests that phosphate adsorption onto La-AC was primarily the result of ion exchange between the phosphate anions and the hydroxyl groups on the surface of the adsorbent.

Rajan [Rajan. 1974] proposed a mechanism for phosphate adsorption on aluminum oxide based on a quantitative relationship between divalent phosphate adsorbed on and hydroxyl ions released from the adsorbent surface at different initial phosphate concentrations. Three adsorption mechanisms were proposed:

Based on these mechanisms, a plot of released hydroxyl ions against phosphate adsorbed will yield straight lines with a slope that indicates the mechanism of the adsorption. The slope of the plot, R, is the ratio of hydroxyl ions released to phosphate adsorbed. For the first reaction, R = 0, for the second reaction, R =1, and for the combined second and third reactions, R=2.

Figure 4.8 shows released hydroxyl ions as the function of phosphate loading on La-AC.

140 120 100 80 60 40 20 0

Rleased Hydroxyl Rleased Hydroxyl Ions (µmol/g) 40 50 60 70 80 90 100 Phosphate Loading (µmol/g)

Figure 4.8 Plot of released hydroxyl ions vs. phosphate loading. T: 37 °C. Initial potassium phosphate concentrations: 0.143 to 1.72 mmol/L; 48 hour equilibration time.

In this study R was found to be 1.64 for phosphate adsorption on La-AC, indicating more than one hydroxyl ion is released for each phosphate ion adsorbed.

Extending Rajan’s approach suggests two ligand exchange reaction for phosphate adsorption on La-AC. For the reaction of phosphate anions with neutral surface sites, R=1; for the reaction of phosphate anions with positive sites, R=0. However, neither of the proposed ligand exchange reactions accounts for R > 1.

Another possible reaction is the formation of bidentate lanthanum phosphate complexes as below:

The R value for the formation of bidentate complex of above reaction is equal to 2. Consequently, the observed value R=1.64 is consistent with a combination of monodentate and bidentate lanthanum phosphate formation.

4.5 Influence of Bovine Serum Albumin (BSA) on Phosphate Adsorption

The phosphate capacity of La-AC may be influence by biomolecules in blood plasma. As a first step to understanding these influences, the effect of bovine serum albumin (BSA) on the phosphate capacity of the adsorbent was investigated. Phosphate adsorption was measured at a potassium phosphate initial concentration of 0.574 mmol/L (100 mg/L) and BSA initial concentrations from 0 to 45 g/L. Samples were incubated for 48 hours at 37 °C before BSA and phosphate uptakes were measured as described in Section 2.5. Figure 4.9 shows phosphate loading at different initial BSA concentrations.

9 8 7 6 5 4 3 2 Phosphate Phosphate loading (mg/g) 1 0 0 22 37 42 BSA concentration (g/L)

Figure 4.9 Effect of BSA concentrations on phosphate loading on La-AC. Initial potassium phosphate concentration: 0.574 mmol/L; T = 37°C; incubation time: 48 hours. Initial BSA concentrations: 0, 22, 37, and 42 g/L

Low BSA concentrations (0-37 g/L) did not significantly affect phosphate adsorption onto La- AC; at a higher initial BSA concentration of 42 g/L (close to the phosphate concentration of blood) phosphate loading decreased by around 20%.

Figure 4.10 shows BSA loading on La-AC in the presence and absence of phosphate with initial concentration of 0.574 mmol/L (100 mg/L). In addition to phosphate, BSA adsorbed on the surface; at higher BSA concentrations, the BSA loading decreased significantly in the presence of phosphate. There appears to be competition between phosphate and BSA for adsorption sites on La-AC. The fact that low BSA concentrations did not interference the phosphate loading confirms this competition.

0.7

0.6

0.5

0.4 BSA loading in the absence 0.3 of phosphate BSA loading in the presence

BSA loading loading BSA (mg/g) 0.2 of phosphate

0.1

0 22 37 42 BSA concentration (g/L)

Figure 4.10 Effect of phosphate solution on BSA loading on La-AC. Initial potassium phosphate concentration: 0.574 mmol/L; T = 37°C; incubation time: 48 hours. Initial BSA concentrations: 0, 22, 37, and 42 g/L

4.6 Summary

In this chapter batch adsorption isotherms for La-AC were reported for phosphate equilibrium concentrations in the range of 0-1.033 mmol/L (0-180 mg/L) at 37 and 50 °C. The adsorption isotherms were well fit using the Langmuir model. The maximum phosphate uptake on La-AC was calculated to be 15.43 mg/g at 37 °C and 21.14 mg/g at 50 °C. Using the Langmuir constant, the Gibbs free energy of adsorption at 37 °C was estimated to be -37.0 kJ/mol, confirming adsorption driven by spontaneous chemical interaction.

A study of phosphate loading at different initial pH conditions revealed different governing interactions in different solution pH ranges. At low pH (2-9), ligand exchange and electrostatic interactions were dominant while at high pH (9-11) Lewis acid-base interaction became more important.

The enthalpy of phosphate adsorption on La-AC at an initial pH of 7 on La-AC at room temperature was determined using flow microcalorimetry. The observed adsorption thermogram showed shoulders close to the peak of the thermogram, suggesting multiple types of interactions with the surface of the adsorbent during adsorption. The thermogram was deconvoluted into three endothermic peaks, which were assigned to the formation of monodentate and bidentate phosphate surface complexes and electrostatic interactions between lanthanum active sites and phosphate anions. Formation of monodenate and bidentate phosphate surface complexes were confirmed based on the number of moles of released surface hydroxyl anions per 1 mole phosphate adsorption on the surface of La-AC. The enthalpy of the formation of monodentate and bidentate phosphate surface complexes were calculated to be 21.75 and 44.06 kJ/mol, respectively. The heat adsorption as the result of electrostatic interactions was calculated 12.46 kJ/mol.

The effect of BSA on phosphate adsorption on La-AC was studied. There was a competition between phosphate and BSA for adsorption sites on La-AC, and the presence of BSA at concentrations close to concentrations found in blood decreased phosphate capacity by around 20%.

Chapter 5: Kinetics of Phosphate Adsorption

In the proposed application, blood containing a high level of phosphate will be brought into contact with the solid adsorbent for a short period of time; the phosphate adsorption system will be far from equilibrium. Consequently, understanding the phosphate adsorption reactions and the evolution of phosphate adsorption with time is crucial for the design and operation of a clinical device. In this chapter, experimental kinetics for phosphate adsorption onto La-AC is reported, and a simple kinetic model based on two-pathway adsorption reactions, described in Chapter 4, is proposed to describe the observed adsorption kinetics.

5.1 Experimental Phosphate Adsorption Kinetics

Phosphate adsorption kinetics on La-AC were measured in batch experiments at initial potassium phosphate concentrations of 0.574 mmol/L (100 mg/L) and 1.148 mmol/L (200 mg/L) and samples were analyzed periodically over 30 hours as described in Section 2.5. There were three replicates for each time point.

Figure 5.1 shows the kinetics of phosphate adsorption onto the La-AC at 0.574 and 1.148 mmol/L at 37 °C and at 1.148 mmol/L at 37°C. Because timing was difficult to control during kinetic experiments, the observed data are more scattered at earlier times.

18 0.574 mmol/L on La-AC 1.148 mmol/L on La-AC 1.148 mmol/L on AC

6 PhosphateLoading (mg/g Adsorbent) 0 0 30 60 90 Time (hours) Figure 5.1 Adsorption kinetics of potassium phosphate solution at 0.574 mmol/L on La-AC and potassium phosphate solution at 1.148 mmol/L on AC and La-AC at 37 °C.

For an initial phosphate concentration of 0.574 mmol/L (100 mg/L), phosphate adsorbed rapidly during the first hour; around 43% of the total adsorption occurred in the first hour. After the first hour, phosphate adsorption proceeded more slowly, with 92% of the total phosphate adsorption occurring within 9 hours. After 30 hours, phosphate adsorption reached an equilibrium uptake of 8.80 ± 0.30 mg/g. In the adsorption isotherm of Figure 4.1 the phosphate loading was reported 9.03 mg/g at initial phosphate concentration of 0.574 mmol/L at 37 °C which is consistent with the measured phosphate loading after 30 hours.

For an initial phosphate concentration of 1.148 mmol/L (200 mg/L), phosphate adsorption was again rapid during the first hour; approximately, 32% of the total phosphate adsorption occurred within the first hour. After the first hour, adsorption proceeded more slowly, with 92% of the total phosphate adsorption again occurring within 9 hours. After 30 hours, phosphate adsorption

68 reached an equilibrium uptake of 13.03 ± 0.51 mg/g. In the adsorption isotherm of Figure 4.1 the phosphate loading was reported 13.45 mg/g at initial phosphate concentration of 1.148 mmol/L at 37 °C, which is in consistent with the measured phosphate loading after 30 hours. Figure 5.2 shows the corresponding liquid-phase phosphate concentrations.

To determine if significant amounts of phosphate adsorbed on the activated carbon support, the kinetics of phosphate adsorption onto activated carbon were also measured; the kinetics of phosphate adsorption onto AC at 37°C and initial phosphate concentration of 1.148 mmol/L (200 mg/L) are shown in Figure 5.1. As can be seen from Figure 5.1, the activated carbon support is not a good phosphate adsorbent. Phosphate loading on AC was quickly reached approximately 2 mg/g and was constant after the first few hours. Phosphate adsorption on the AC substrate is only 13% of the total amount of phosphate uptake on La-AC at an initial phosphate concentration of 1.148 mmol/L.

0.9 0.574 mmol/L on La-AC 1.148 mmol/L on La-AC

0.6

0.3

0.0

Liquid-PhasePhosphate Concentration (mmol/L) 0 30 60 Time (hr)

Figure 5.2 Liquid-phase concentrations of potassium phosphate solutions at initial concentrations of 0.574 and 1.148 mmol/Lon La-AC at 37 °C over time.

5.2 Application of Previous Models of Phosphate Adsorption

In previous studies, pseudo-first-order (Equation 5.1 and its linear form Equation 5.2) and mainly pseudo-second-order models were used in combination to describe the phosphate adsorption on the metal oxide surfaces. The pseudo-first-order model and its linearized form are

(5.1)

(5.2)

The pseudo-second-order model and its linearized form are (5.3)

(5.4)

Where Q(t) is the amount adsorbed at time t (mg/g), Qe is the amount adsorbed

and k1 and k2 are temperature-dependent constants. These empirical equations have previously been used to correlate measured kinetic data in previous studies of phosphate adsorption. In the derivation of the pseudo-first and pseudo-second order equations it was assumed that the surface kinetic reaction is the controlling step [D’Arcy et al, 2011].

Based on the correlation coefficient, it was shown that pseudo-second order adsorption model, Equation 5.4, is better than the first-order model, Equation 5.2, in describing the adsorption kinetics of phosphate on lanthanum hydroxide doped activated carbon fiber (ACF-La) [Zhang et al, 2011], hydroxyl lanthanum-iron doped activated carbon fiber (ACF-LaFe) [Liu et al, 2013], lanthanum (La(III)) loaded granular ceramics [Chen et al, 2012], some novel synthesized inorganic ion exchanger such as ZrO2.XH2O and Fe2O3.Al2O3.XH2O [Chubar al, 2005], and aluminum impregnated mesoporous silicates [Shin et al, 2004]. However, the pseudo-first order

70 adsorption equation (Equation 5.2) is appropriate to describe the adsorption kinetics of phosphate on lanthanum-impregnated silica gel [Ou, 2007].

The observed phosphate adsorption kinetic data at initial concentrations of 0.574 and 1.148 mmol/L at 37 °C were fit using the linearized form of the pseudo-second-order equation using Mathematica function LinearModelFit (Mathematica, Wolfram Research 9.0, Champaign, IL, USA). The regression results and best-fit values of rate constants (k) and maximum adsorption capacities (Qmax) at initial concentrations of 0.574 and 1.148 mmol/L have been shown in Table 5.1.

Table 5.1 The values of rate constants and maximum adsorption capacities found by linear regression of pseudo-second-order equation to observed kinetic data Initial Best-Fit k Best-Fit Qmax Degrees of Phosphate Co. SSQ (g/mg min) (mg/g) Freedom (mmol/L) 0.574 0.023±0.001 9.34±0.18 1.23 7 1.148 0.019±0.001 14.3±1.7 3.52 7 TOTAL = 4.75 14

The pseudo-second-order model regressions produce rate constants that depend on the initial phosphate concentration. The predicted adsorption rate constant for an initial phosphate concentration of 0.574 mmol/L was about 20% higher than the predicted adsorption rate constant for an initial concentration of 1.148 mmol/L. However, this dependence of the rate constant on solution concentration is in contrast with the surface adsorption mechanism.

Zhang and coworkers [Zhang et al, 2011] modeled phosphate adsorption kinetics on lanthanum(III)-coordinated diamino-functionalized 3D hybrid mesoporous silicate using the pseudo-second-order equation. They found that the rate constant of the adsorption reaction at an initial phosphate concentration of 30 mg/L was around 1.3 times smaller than the rate constant of the adsorption reaction at an initial phosphate concentration of 100 mg/L. In addition the kinetics of phosphate adsorption on lanthanum activated carbon was modeled using the pseudo-

71 second-order equation; the rate constants were calculated to be 0.011, 0.0051, and 0.0037 mg/g min at phosphate initial concentrations of 0.001, 0.01, and 0.1 mol/L, respectively [Liu et al, 2011].

Figure 5.3 shows observed and calculated adsorption kinetics at initial phosphate concentrations of 0.574 and 1.148 mmol/L at 37 °C using the pseudo-second-order kinetic model. The red dots and solid curve represents the experimental and modeled kinetics at 1.148 mmol/L and the black dots and solid curve represents the experimental and modeled kinetics at 0.574 mmol/L.

Adsorbent

mg 8

Loading 6

Phosphate 4 Observed Kinetics at 1.148 mmol/L Predicted Kinetics at 1.148 mmol/L 2 Observed Kinetics at 0.574 mmol/L Predicted Kinetics at 0.574 mmol/L 0 Observed Kinetics at 1.148 mmol/L 0 10 20 30 40 50 60 70

PredictedTime hour Kinetics at 1.148 mmol/L

Observed Kinetics at 0.574 mmol/L Figure 5.3 Predicted and experimental adsorption kinetics of potassium phosphate on La-AC at Predicted Kinetics at 0.574 mmol/L 37 °C based on pseudo-second-order equation. Dots represent observed kinetics and solid curves

represent predicted pseudo-second-order kinetics.

5.3 Parallel-Pathway Kinetic Model

5.3.1 Theory

Consistent with the discussion presented in Chapter 4, previously-published spectroscopic studies revealed the formation of monodentate and bidentate oxy-anions complexation on the surface of metal oxide adsorbent [D’Arcy et al, 2011]. D’Arcy et al hypothesized that the phosphate adsorbed on the surface of metal oxide adsorbent through two simultaneous, parallel pseudo-second order reaction pathways with separate kinetic parameters. Monodentate and bidentate surface complexation are simultaneously formed on the surface of metal oxide adsorbent with separate kinetics, uptake curves, and formation rates. The observed adsorption rate is the total from both parallel adsorption pathways and at each point in time will be dominated by whichever complex is changing most rapidly [D’Arcy et al, 2011].

FMC results obtained during the first hour of phosphate adsorption on La-AC, reported in Chapter 4, confirmed the initial adsorption and formation of monodentate phosphate surface complexation followed by formation of bidentate surface complexation on the La-AC surface. To model the adsorption kinetics, it is hypothesized here that phosphate is adsorbed on the La- AC surface via two Langmuir-type adsorption reaction pathways with separate kinetic parameters as below:

(5.5)

(5.6)

A represents the phosphate ions, X and Y represent distinct types of surface sites, and AX and AY are the surface complexes.

It is important to note that Equation 5.5 and 5.6 are not proposed as elementary reactions involved in phosphate adsorption on La-AC; rather Equation 5.5 and 5.6 simply show assumed adsorption pathways to motivate the form of adsorption rate equations.

Assuming that the adsorption proceeds through a Langmuir mechanism, the adsorption rate equations are:

(5.7)

(5.8)

Qi is the solid phase concentration of component i (mmol/mg), kj and k-j are the forward and reverse rate constants for reaction j, and t is the time (s).

The overall rate equation for the surface adsorption reactions is the sum of the rate equations for each type of adsorption sites as follow:

(5.9)

QA is the total amount of phosphate adsorbed on both monodentate and bidentate active surface sites. Assuming that Qi0 is the initial number of adsorption sites of type i, a mass balance on the adsorption sites yields:

(5.10)

(5.11)

A mass balance for the adsorbate yields:

(5.12)

CA is the adsorbate concentration in the liquid phase (mol/L), CA0 is initial adsorbate concentration in the liquid phase (mol/L), V is the liquid volume in the adsorption experiment (ml), and m is the adsorbent mass in the adsorption experiment (mg).

Substituting the mass balance Equations 5.10 - 5.12 into the rate Equations 5.7 - 5.9 lead to:

(5.13)

(5.14)

Where

(5.15)

Equations 5.13 and 5.14 are subject to the following initial conditions:

(5.16)

At equilibrium the amount of adsorbed monodentate and bidentate phosphate complexation are:

(5.17)

However, only the total amount of phosphate can be directly measured:

(5.18)

To simplify the equation 5.18 as the first approximation it is assumed that:

(5.19)

The adsorption isotherm can then be expressed as:

(5.20)

5.3.2 Analysis of Experimental Data and Discussion

The model developed above was applied to analyze of phosphate adsorption kinetics onto La- AC. Based on the proposed model to predict the adsorption behavior equations 5.9, 5.13, and 5.14 were solved simultaneously using the NDSolve function in Mathematica (Mathematica, Wolfram Research 9.0, Champaign, IL, USA) with appropriate initial conditions. Table 5.2 shows the parameter values used in parallel-pathway kinetic model. The value of Langmuir constant was taken from chapter 4, and the mass of adsorbent and phosphate solution amount were fixed based on experimental conditions.

Table 5.2 Parameter values for the parallel-pathway kinetic model

CA0 CA0 KL Qmax V m (mmol/L) (mg/L) (L/mg) (mg/g) (ml) (mg) 0.574 100 0.16 15.43 1 10 1.148 200 0.16 15.43 1 10

Constant rates of reactions and maximum loading capacities of monodentate and bidentate phosphate complexes were adjusted manually to find the best-fit values. Best-fit values were determined by minimizing the sum-of-squares residual error calculated in the same Mathematica script. Table 5.3 shows the best-fit values obtained by regression the observed kinetic data with parallel-pathway kinetic model. The kinetic model parameter values do not depend on the initial concentration.

Table 5.3 Best-fit kinetic parameters for parallel-pathway kinetic model

k1 (L/mg.hr) k2 (L/mg.hr) Qx0 (mg/g) 0.0108 0.0059 2.91

Figure 5.4 shows the experimental and predicted parallel-pathway adsorption kinetics at initial potassium phosphate concentration of 0.574 mmol/L (100 mg/L) and 1.148 mmol/L (200 mg/L). The black dots and solid curve represent the adsorption kinetics at 0.574 mmol/L, and the red dots and solid curve represent the adsorption kinetics at 1.148 mmol/L.

Adsorbent g

mg 8

Loading 6

Phosphate 4 Observed Kinetics at 1.148 mmol/L

Predicted Kinetics at 1.148 mmol/L

2 Observed Kinetics at 0.574 mmol/L

Predicted Kinetics at 0.574 mmol/L

0 0 10 20 30 40 50 60 70

Time hour

Figure 5.4 Modeled and Experimental adsorption kinetics of potassium phosphate on La-AC at 37 °C. dots show observed kinetics and solid curves show proposed parallel-pathway kinetics

The proposed model was successfully used to correlate the adsorption data, especially at longer times, but underestimated the phosphate loading at initial times. This underestimate may be due to the greater measurement uncertainty at the earlier times, but more work is required to understand the deviation at early times.

Figure 5.5 shows the experimental and predicted parallel-pathway liquid-phase phosphate concentration kinetics at initial potassium phosphate concentration of 0.574 mmol/L (100 mg/L) and 1.148 mmol/L (200 mg/L). The black dots and solid curve represent the adsorption kinetics at 0.574 mmol/L, and the red dots and solid curve represent the adsorption kinetics at 1.148 mmol/L.

1.4 Observed Kinetics at 1.148 mmol/L Predicted Kinetics at 1.148 mmol/L

1.2 Observed Kinetics at 0.574 mmol/L L Predicted Kinetics at 0.574 mmol/L

mmol 1.0

0.8

Concentration Phase

0.6 Liquid

0.4 Phosphate

0.2

0.0 0 10 20 30 40 50 60 70 Time hour Figure 5.5 Modeled and Experimental liquid-phase concentrations of potassium phosphate on La-AC at 37 °C at initial solution concentrations of 0.574 and 1.148 mmol/L. Dots show observed kinetics and solid curves show proposed parallel-pathway kinetics.

To compare the pseudo-second-order and parallel-pathway kinetic model performance, and F- test was performed on the residual errors at a 95% level of confidence. Table 5.4 shows a statistical summary of the two models. Table 5.4 Statistic summary of modeled kinetics Pseudo-Second-Order Kinetic Model

Initial Phosphate Co. Initial Phosphate Co. Parameters 0.574 mmol/L 1.148 mmol/L

k 0.023 0.019

Qmax(mg/g) 9.34 14.30

Residual SSQ (mg/g)2 1.23 3.52

Total Residuals SSQ (mg/g)2 4.75

Total Degrees of Freedom 14

Residual Variance 0.339

Parallel-Pathway Kinetic Model

k1 (L/mg.hr) 0.0108 0.0108

k2 (L/mg.hr) 0.0059 0.0059

Qx0(mg/g) 2.91 2.91

Residual SSQ (mg/g)2 1.11 1.81

Total Residuals (mg/g)2 2.92

Total Degrees of Freedom 15

Residual Variance 0.195

At a 90% confidence level for 14, 15 degrees of freedom, the critical value of F is 1.99. The calculated F value for comparing the pseudo-second-order and parallel-pathway models is 1.73,

80 not above the F critical value. F < F Critical indicates that there is not a statistically significant difference in the performance of the kinetic models; however, the parameters of the parallel- pathway model are independent of the initial phosphate solution concentration, which is more consistent with thermodynamic adsorption mechanism. In addition, unlike the D’Arcy model, the material balance equation (Equation 5.12) accounts for the volume of liquid and adsorbent mass. Also, the thermodynamic driving force for adsorption is expressed more realistically, accounting for the variation of equilibrium loading with the instantaneous liquid-phase concentrations; D’Arcy’s model assumes a constant value for Qe throughout the entire course of the adsorption, which is an incorrect assumption.

5.4 Summary

Experimental and theoretical phosphate adsorption kinetics onto La-AC is studied in this chapter. Observed data of phosphate adsorption kinetics at initial potassium phosphate solution concentrations of 0.574 and 1.148 mmol/L (100 and 200 mg/L) onto La-AC 37 °C were investigated. Phosphate adsorption kinetics onto La-AC were described using a two-pathway simultaneous kinetic model based on a Langmuir adsorption model. It was hypothesized that phosphate adsorption progressed through two surface reaction pathways: the formation of monodenate complexes following by the formation of bidentate complexes on the surface of La- AC with separate kinetic parameters. The model described well the trend of adsorption over time. The statistical performance of the parallel-pathway model was compared with the pseudo- second-order reaction model. An F-test did not show a statistically significant difference between the two models. However, the parallel-pathway model is more consistent with thermodynamic assumptions for phosphate adsorption on La-AC and does not include the questionable assumptions used in the pseudo-second-order model.

Chapter 6: Summary and Conclusions

30 million Americans are living with kidney disease at different stages. In 2009, 398,861 kidney patients received end-stage renal disease (ESRD) treatments including dialysis or a kidney transplant to survive [American Kidney Fund]. In 2012, the number of ESRD patients increased to 616,000 [United States Renal Data System] and it is expected that the number of ESRD patients will continue to increase in future years. In 2013, 88.2% of kidney disease patients began renal replacement therapy with hemodialysis [NIH, National Institute of Diabetes and Digestive and Kidney Diseases].

Unfortunately, the rate of cardiovascular mortality is high in dialysis patients, and accounts for 43% of all-cause mortality in dialysis patients. In 2015, death due to cardiovascular disease accounted for approximately 41% of all the deaths among the kidney patients who were using hemodialysis [United States Renal Data System]. Hyperphosphatemia, elevated serum phosphate level, is identified as the major factor in the progression of renal failure and the further development of the cardiovascular diseases and increased vascular calcification in ESRD patients. Adequate control of serum phosphate and appropriate treatment and prevention of hyperphosphatemia in dialysis patients can significantly reduce the risk of vascular calcification and cardiovascular mortality. Improvement of current dialysis prescription for increased phosphate removal, restriction of phosphate uptake by control of the patient’s diet, and medical strategies to inhibit gastrointestinal phosphate absorption by using phosphate binders are common treatments to manage hyperphosphatemia. However, these general treatments have high expenses and numerous long-term side effects. The current study is part of a broader study to consider the use of a fixed-bed adsorption system integrated with hemodialysis to improve phosphate removal.

The primary goals of this project were to synthesize, characterize, and optimize lanthanum- impregnated activated carbon for phosphate removal at low phosphate concentrations, study the equilibrium adsorption isotherm and adsorption evolution with time, understand the thermodynamics and nature of phosphate adsorption on lanthanum-impregnated activated carbon, and investigate the effect of pH, temperature, and interfering biomolecules on phosphate adsorption.

Lanthanum-impregnated activated carbon (La-AC) was prepared using chemical impregnation method followed by calcination; the effect of calcination temperature, calcination atmosphere (air vs. nitrogen) and the weight percentage of lanthanum were studied. La-AC calcined under air at 650 °C had highest phosphate adsorption capacity, and increasing the weight percentage of lanthanum to activated carbon to prepare phosphate adsorbents led to higher phosphate adsorption capacity. For the work reported here, samples of La-AC with 12 % La to AC mass ratio calcined at 650 °C under air flow for 2.5 hours were used in thermodynamic and kinetic studies.

Phosphate adsorption isotherms for 12 wt% La-AC were obtained at 37 °C and 50° C for initial potassium phosphate (K2HPO4) concentrations in the range of 0.143 to 1.722 mmol/L (25-300 mg/L) using a 48 hour incubation time to reach equilibrium. It was shown that the Langmuir isotherm was better than the Freundlich isotherm to describe phosphate adsorption equilibrium at low phosphate concentrations. The maximum potassium phosphate loading capacities were 15.43±0.61 and 21.14±1.07 mg/g at 37 °C and 50° C, respectively.

Phosphate loading at different initial pH solutions was examined. These studies confirmed that the possible main interactions in phosphate adsorption on surface of La-AC include electrostatic, ion-exchange, and Lewis acid-base interactions. At lower initial pH, phosphate loading increased with increasing pH, and ligand exchange and electrostatic interactions were dominant. The Lewis acid-base interaction was the principal interaction at higher pH, where phosphate loading decreased with increasing initial solution pH.

The enthalpy of phosphate adsorption on 12% wt La-AC was determined using flow microcalorimetry. The observed adsorption thermogram showed shoulders close to the peak of the thermogram, indicating more than one surface reaction during adsorption. The thermogram was deconvoluted into three endothermic peaks, which assigned to the formation of monodentate and bidentate phosphate surface complexation, and electrostatic interactions between lanthanum active sites and phosphate anions. The formation of monodenate and bidentate phosphate surface complexes were confirmed based on the number of moles of surface hydroxyl anions released per mole of phosphate adsorbed. The enthalpies of formation of monodentate and

84 bidentate phosphate surface complexes were calculated to be 21.75 and 44.06 kJ/mol, respectively. The enthalpy of adsorption due to electrostatic interactions was calculated 12.46 kJ/mol.

The phosphate capacity of La-AC may be influenced by biomolecules present in blood plasma. It was shown in this study that bovine serum albumin (BSA) competes with phosphate anions for surface active sites. The presence of BSA proteins at BSA concentrations close to those in blood in the phosphate solution at concentration of 1.148 mmol/L resulted in 20% reduction in the amount of phosphate adsorbed on the surface of 12% wt La-AC at 37 °C.

In the proposed application, blood containing a high level of phosphate will be brought into contact with La-AC for a short period of time. Understanding the phosphate adsorption reactions and phosphate adsorption kinetics will be crucial for the design and operation of a clinical device. Consequently, phosphate adsorption kinetics at initial potassium phosphate concentrations of 100 and 200 mg/L (0.574 and 1.148 mmol/L, respectively) onto 12% wt La to activated carbon at 37 °C were investigated. Phosphate adsorption kinetics onto La-AC are well- described using a two-pathway kinetic model using the Langmuir isotherm to describe adsorption kinetics. It was hypothesized that phosphate adsorption progressed through two parallel surface Langmuir-like reaction pathways resulting in the formation of monodenate and bidentate complexes on the surface of La-AC with separate kinetic parameters.

Chapter 7: Future Work

This study has explored some of the fundamental phenomena involved in phosphate adsorption on La-AC. To design and engineer an appropriate phosphate adsorption device to be incorporated in to current dialysis apparatus for extra phosphate removal in a 4-hour-dialysis session, further studies are recommended. Enhancing the phosphate adsorption capacity on the surface of La-AC by modifying the adsorbent, improving our understanding of mass transfer and kinetics of phosphate adsorption, investigating the effect of all blood components on phosphate adsorption and kinetics, and designing a suitable packed-bed column of La-AC are the next recommended steps.

The first recommended step is improving the phosphate capacity of the adsorbent. A higher weight percentage of lanthanum on the surface of activated carbon resulted in higher phosphate loading. However, this study used samples with 12 wt% lanthanum on activated carbon were used for simplicity. Samples with higher mass percentage of lanthanum should be synthesized and their phosphate adsorption capacity and kinetics should be investigated. In addition, investigating the effects of textural (surface area and pore structure) and surface properties of La- AC on phosphate capacity are recommended. Modifying the surface chemistry may also enhance the phosphate capacity of the adsorbent. Functionalized activated carbon may boost phosphate uptake and prevent competition of other blood biomolecules to be adsorbed on the lanthanum surface active sites. Covering the surface with hydrophilic PEG-groups or big chains of polymers may prevent the bigger protein to reach the surface of the adsorbent, and allows only the small phosphate anions to reach the surface. The synthesis process can also be altered. Specifically, the use of ultrasonic-assisted chemical precipitation to prepare lanthanum impregnated activated carbon rather than chemical impregnation method is recommended to study. It was found that ultrasonic-assisted chemical precipitation to prepare lanthanum hydroxide doped activated carbon fiber was preferred method to control the size and size distribution of lanthanum hydroxide components on the activated carbon surface. In addition, the shock-wave in the liquid as a result of ultrasound transmission produces more uniform distribution of lanthanum hydroxide particles into the supported activated carbon framework. [Zhang,et al, 2012].

Another recommended step is to develop a deeper understanding of phosphate adsorption kinetics and thermodynamics. Understanding more about the adsorption rate and kinetics will enable better design of a fixed-bed column device for more effective phosphate removal. An improved kinetic and mass transfer model improves our insight into phosphate adsorption kinetics. The parallel-path adsorption model presented in this thesis can be improved by adding more rigorous assumptions to the model. For example, phosphate adsorption as the result of electrostatic interactions has been neglected, and the transition between the types of phosphate complexes on the surface has been ignored. Considering the consequences of these phenomena would make the model more precise. In addition, in the proposed parallel-path adsorption model it was hypothesized that the phosphate adsorption reaction on the surface of La-AC is reversible. This assumption should be tested experimentally. If phosphate adsorption is not reversible, the parallel-path adsorption model should be modified based on irreversible surface adsorption reactions.

A third area of future work is to study the influence of other blood plasma components. Blood plasma contains many other biomolecules and anions including sodium, potassium, calcium, magnesium, chloride, carbonate, sulfate, urea, creatinine, cholesterol, lipids, amino acids, sugars, albumins, globulins, and other proteins [Ethier et al, 2007]. These coexisting biomolecules may influence phosphate adsorption. It is expected that some biomolecules and anions in the blood would enhance the electrostatic interactions and some would compete for lanthanum active sites on the surface. Investigating the effect of other biomolecules on phosphate adsorption using the strategy employed in Chapter 4 is recommended.

Finally, a fixed-bed column study of phosphate adsorption is recommended. Batch adsorption experimental findings give basic knowledge on phosphate adsorption onto La-AC but do not provide the complete scale-up information for practical fixed-bed design. A dynamic study of fixed-bed phosphate adsorption is of particular interest to investigate the effect of phosphate concentrations, flow rates, and interfering blood components on the dynamic phosphate adsorption.

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Appendix A: R Script Used in Chapter 4 for Regression of Adsorption Isotherms at 37 and 50 °C by Langmuir and Freundlich Equations Developed by: Professor S. Thiel

# Analysis of Nazarian Isotherm data -- 37C # i37 <- read.csv("Nazarian Isotherm 37C.csv") i37 # CLdata <- i37$CL # Qdata <- i37$Q isotherm37 <- data.frame(i37$CL,i37$Q) # # # Langmuir fit # Lang.iso <- function(x,a,b) { a*b*x/(1+b*x) # a = qmax, b = K } Qm = 10 KL = 2 LangFit <- nls(i37.Q ~ Lang.iso(i37.CL,Qm,KL), data=isotherm37, start=list(Qm=Qm,KL=KL)) summary(LangFit) confint(LangFit) resid.Lang <- residuals(LangFit) resid.Lang ssq.Lang <- sum(resid.Lang*resid.Lang) ssq.Lang # # Plot Langmuir data and fit # plot(i37$CL,i37$Q, xlab="CL", xlim = c(0,200), ylab="Q", ylim = c(0,20)) xtoplot <- data.frame(i37.CL = seq(0,max(isotherm37$i37.CL),len=201)) lines(xtoplot$i37.CL,predict(LangFit,newdata=xtoplot))

# # Freundlich fit # Kf <- 30 n <- 2 FreundFit <- nls(i37.Q ~ Kf*i37.CL^(1/n), data = isotherm37, start=list(Kf=Kf,n=n))

98 summary(FreundFit) confint(FreundFit) resid.Freund <- residuals(FreundFit) resid.Freund ssq.Freund <- sum(resid.Freund*resid.Freund) ssq.Freund # # Add Freundlich curve # lines(xtoplot$i37.CL,predict(FreundFit,newdata=xtoplot),col="red") # # Compare residual variances. Set alternative = "g" to get one-sided # test for resid.Freund > resid.Lang # var.test(resid.Freund,resid.Lang,alternative = "g")

------# # Analysis of Nazarian Isotherm data -- 50C # i50 <- read.csv("Nazarian Isotherm 50C.csv") i50 isotherm50 <- data.frame(i50$CL,i50$Q) # # # Langmuir fit # Lang.iso <- function(x,a,b) { a*b*x/(1+b*x) # a = qmax, b = K } Qm = 10 KL = 2 LangFit <- nls(i50.Q ~ Lang.iso(i50.CL,Qm,KL), data=isotherm50, start=list(Qm=Qm,KL=KL)) summary(LangFit) confint(LangFit) resid.Lang <- residuals(LangFit) resid.Lang ssq.Lang <- sum(resid.Lang*resid.Lang) ssq.Lang # # Plot Langmuir data and fit # plot(i50$CL,i50$Q, xlab="CL", xlim = c(0,200), ylab="Q", ylim = c(0,20)) xtoplot <- data.frame(i50.CL = seq(0,max(isotherm50$i50.CL),len=201))

99 lines(xtoplot$i50.CL,predict(LangFit,newdata=xtoplot))

# # Freundlich fit # Kf <- 30 n <- 2 FreundFit <- nls(i50.Q ~ Kf*i50.CL^(1/n), data = isotherm50, start=list(Kf=Kf,n=n)) summary(FreundFit) confint(FreundFit) resid.Freund <- residuals(FreundFit) resid.Freund ssq.Freund <- sum(resid.Freund*resid.Freund) ssq.Freund # # Add Freundlich curve # lines(xtoplot$i50.CL,predict(FreundFit,newdata=xtoplot),col="red") # # Compare residual variances. Set alternative = "g" to get one-sided # test for resid.Freund > resid.Lang # var.test(resid.Freund,resid.Lang,alternative = "g") var.test(resid.Lang,resid.Freund,alternative = "g")

100

Appendix B : Mathematica Script to Solve Equations 5.9, 5.13, and 5.14 Simultaneously (Figure 5.3 and 5.4)

Remove ["Global`*"]

k1f= 0.0108;k1r=k1f/KX; m=10;v=1;qX0=2.91;qY0=15.43- qX0;KX=0.16;KY=0.16;cp0=200;k2f=0.00059; k2r=k2f/KY; deq1= D[qAX[t],t]- deq2= D[qAY[t],t]- deq3=cp[t]- deq4= qX[t]- deq5= qY[t]- deq6= qA[t]-qAX[t]-

solution=NDSolve[{deq1,deq2,deq3,deq4, deq5,deq6, deq7, deq8,deq9},{qAX,qAY,qX,qY,cp}, {t,0,1000}]

Plot[Evaluate[1000*(qAX[t]+qAY[t])/.solution],{t,0,100

Show[ListPlot[{{1,4.28},{2,5.34},{3,5.65},{4,6.84},{6,8.31},{9,8.67},{17,11.23},{24,11.88},{75,13.03} },PlotRange- Loading

PointSize[0.02]}],Plot[Evaluate[(qAX[t]+qAY[t])/.solution],{t,0,100 },PlotRange- Black,Thick}],Plot[Evaluate[(qAX[t])/.solution ],{t,0,100 },PlotRange-

{t,0,100 },PlotRange->{0,1

- -(5.34))^2+ -(5.65 - - - - - (11.88))^2+(((qAX[t]+qAY[t])/.sol -(13.03))^2

101

qX0s=2.91;qY0s=15.43-qX0;KX=0.16;KY=0.16;cp0s=100; deq1= D[qAXs[t],t]- deq2= D[qAYs[t],t]- deq3=cps[t]- deq4= qXs[t]- deq5= qYs[t]- deq6= qAs[t]-qAXs[t]-

solutions=NDSolve[{deq1,deq2,deq3,deq4, deq5,deq6, deq7, deq8,deq9},{qAXs,qAYs,qXs,qYs,cps}, {t,0,1000}]

Show[ListPlot[{{1,2.41},{2,3.05},{3,3.31},{4,3.84},{6,5.34},{9,5.64},{17,7.27},{24,7.86},{75,8.80}},Pl otRange- [(qAXs[t] +qAYs[t])/.solutions],{t,0,100 },PlotRange-

-(2.41))^2+(((qAXs[t]+qAYs[t])/.s - - - - - )- 24)- -(8.80))^2

Show[ListPlot[{{1,2.41},{2,3.05},{3,3.31},{4,3.84},{6,5.34},{9,5.64},{17,7.27},{24,7.86},{75,8.80}},Pl otRange- our)","Phosphate Loading

+qAYs[t])/.solutions],{t,0,100 },PlotRange- ns],{t,0,100 },PlotRange- s],{t,0,100 },PlotRange-

102

Show[ListPlot[{{1,2.41},{2,3.05},{3,3.31},{4,3.84},{6,5.34},{9,5.64},{17,7.27},{24,7.86},{75,8.80}},Pl otRange->{0,

+qAYs[t])/.solutions],{t,0,100 },PlotRange-

5},{4,6.84},{6,8.31},{9,8.67},{17,11.23},{24,11.88},{75,13.03}},PlotRange-

PointSize[0.02]}],Plot[Evaluate[(qAX[t]+qAY[t])/.solution],{t,0,100 },PlotRange-

103

Appendix C: Experimental Data for Chapter 4 Numerical values for Figure 4.1 Equilibrium phosphate adsorption isotherms at 37 °C

Potassium Phosphate Equilibrium Concentration Phosphate Loading (mmol/L) (mg/g)

0.008 2.30

0.015 4.63

0.04 9.08

0.153 12.21

0.396 13.46

0.872 15.53

Numerical values for Figure 4.1 Equilibrium phosphate adsorption isotherms at 50 °C

Potassium Phosphate Equilibrium Concentration Phosphate Loading (mmol/L) (mg/g)

0.029 5.22

0.053 7.26

0.085 8.52

0.34 15.01

0.671 18.66

Numerical values for Figure 4.3 Effect of solution pH on phosphate adsorption by La-AC at initial phosphate concentration 200 mg/L (0.574 mmol/L)

Initial pH Solution Phosphate Loading (mg/g)

2.73 12.37

5.13 13.21

7.88 13.45

8.51 13.45

11.03 10.21

104

Numerical values for Figure 4.4 Initial and final phosphate solution pH vs. initial phosphate concentration

Initial Potassium Phosphate pH Solution after pH Solution after Initial pH of the Solution Concentration (mmol/L) Exposed to AC Exposed to La-AC

0.574 7.80 7.22 10.69

0.861 7.84 7.23 10.90

1.148 7.88 7.23 10.93

1.722 7.88 7.24 11.10

Numerical values for Figure 4.9 Initial and final phosphate solution as the function of phosphate loading

Phosphate Loading (mg/g) Initial pH of the Solution pH Solution after Exposed to La-AC

7.95 7.80 10.69

12.21 7.84 10.90

13.45 7.88 10.93

15.52 7.88 11.10

Numerical values for Figure 4.10 Plot of released hydroxyl ions vs. phosphate loading

Phosphate Loading Released Hydroxyl Groups (µmol/g of the adsorbent) (µmol/g of the adsorbent)

48.96 45.64

79.41 70.10

85.09 77.26

125.87 89.14

105

Appendix D: Experimental Data for Chapter 5 Numerical values for Figure 5.1 and 5.2 : Adsorption kinetics of potassium phosphate solution at 100 mg/L (0.574 mmol/L) onto La-AC over 30 hr

Phosphate Loading Liquid-Phase Phosphate Time (hour) Concentration (mmol/L) (mg/g)

1 2.41±0.66 0.43±0.05

2 3.05±0.89 0.39±0.07

3 3.31±0.76 0.38±0.06

4 3.84±0.54 0.35±0.04

6 5.34±0.24 0.26±0.01

9 5.64±0.37 0.24±0.03

17 7.27±0.34 0.15±0.03

24 7.86±0.31 0.11±0.02

75 8.80±0.30 0.06±0.02

Numerical values for Figure 5.2 and 5.3: Adsorption kinetics of potassium phosphate solution at 200 mg/L (1.148 mmol/L) onto La-AC over 30 hr

Phosphate Loading Liquid-Phase Phosphate Time (hour) Concentration (mmol/L) (mg/g)

1 4.28±0.58 0.89±0.04

2 5.34±0.1.09 0.83±0.08

3 5.65±0.76 0.82±0.06

4 6.84±0.57 0.75±0.04

6 8.31±0.68 0.66±0.05

9 8.67±0.43 0.64±0.03

17 11.23±0.60 0.49±0.04

24 11.88±0.50 0.45±0.04

75 13.03±0.51 0.39±0.04

106

Appendix E: BET Adsorption-Desorption Isotherms of AC and La-AC Data was obtained by Rebecca Desch.

a) BET isotherm of acid-washed activated carbon

107

b) BET isotherm of lanthanum impregnated carbon calcined at 650 °C

108