Reaction Kinetics and Subsequent Rheology of Carboxymethyl Guar

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Applied Chemistry

Reaction Kinetics and Subsequent Rheology of Carboxymethyl Guar Gum Produced From Guar Splits Jie Gao, and Brian Patrick Grady Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b00782 • Publication Date (Web): 09 May 2018 Downloaded from http://pubs.acs.org on May 9, 2018

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Industrial & Engineering Chemistry Research

Reaction Kinetics and Subsequent Rheology of Carboxymethyl Guar Gum Produced From Guar Splits Jie Gao and B.P. Grady* School of Chemical, Biological and Materials Engineering, University of Oklahoma, Norman, OK 73019 KEYWORDS: guar gum, carboxymethylation, rheology, kinetics

ABSTRACT: Carboxymethyl guar gum (CMG) has been widely used in various industrial fields, although its use is especially important in hydraulic fracturing operations because of the high viscosity of their aqueous solutions and the ability to reversibly crosslink the material. However, detailed reaction kinetics for production of carboxymethyl guar has not been previously reported.

In this study, we use a two-step environmentally friendly method to

produce carboxymethyl guar gum by chemical modification of guar gum (GG) splits. We quantify conversion by NMR spectroscopy and wet chemistry methods, and establish a structure and property relationship based on the rheological properties of corresponding CMG products. In addition, borate and zirconium crosslinkers are applied to study the rheological effect of crosslinking on GG and CMG aqueous solutions. Furthermore, we investigate, for the first time, reaction kinetics of carboxymethylation of guar splits and report a rate equation to quantify reaction kinetics.

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1. INTRODUCTION Guar gum (GG), a member of the galactomannan family, is a natural polysaccharide extracted from the seeds of Cyamopsis Tetragonaloba. The general structure of guar gum is shown in Figure 1.

It consists of a linear chain of β-1,4-linked D-mannose units (M) as the main

backbone, attached by α-1,6-linked D-galactopyranose residues (G) as the side branches.1 The most common configuration is for the galactose branches to occur in every other mannose unit. The exact ratio of mannose to galactose unit (M/G) may vary with origin and climate, normally ranging from 1.5:1 to 2:1.2-3 The molecular weight of guar is the highest of all known natural polymers produced of industrial gums which enables this water-soluble polysaccharide to produce highly viscous solutions at low polymer concentrations.4

n

Figure 1. Structure of guar gum

Guar gum is widely used in various industries such as oilfield,5 food,6 pharmaceutical industry,7 paper,8 cosmetic9 and textile.10 Depending on the end products, a variety of different techniques are used for processing guar. Generally, guar seeds are dehusked to make guar splits, then often that product is milled and screened to obtain guar gum powder which in turn can be easily dissolved in water.

Though guar gum possesses high molecular weight and can also form extensive intermolecular hydrogen bonding resulting in high solvation and thereby increased viscosity, some limitations exist such as uncontrolled and incomplete hydration at room temperature, poor clarity of the solution, low thermal stability and high susceptibility to microbial degradation, which restrict its


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application in industry.11-12 Chemical modification provides an efficient route for overcoming these limitations with improved swelling, solubility and stability. One significant use of these modified guars has been in petroleum production, specifically, in hydraulic fracturing operations. The purpose of the guar gum or its derivatives being part of the fracturing fluid is twofold. The first purpose is to reduce leak-off, i.e. fluid that leaves the wellbore and penetrates into microscopic fissures within the rock. The second is to enable the fluid to carry solid proppant particles, usually sand, to the fractures, e.g. cracks in the rock, so that the proppant can hold the fracture open when the fracturing pressure is released. In addition, borate or organometallic zirconate or titanate moieties can be used to crosslink the guar in a reversible manner using pH as a control to turn on and off crosslinking. Crosslinked fluids have a larger capacity to suspend and transport proppant particles than the corresponding uncrosslinked fluids with the same polymer dosage.13

Carboxymethyl guar (CMG) is an anionic guar derivative with high viscosity dissolution speed, good transparency, and good stability. The advantage for crude oil fracturing fluids compared to hydroxypropyl guar (HPG), another guar derivative gum, is CMG’s low price. A number of laboratory procedures have been developed to obtain carboxymethyl guar gum. Carboxymethyl guar is synthesized by reacting monochloroacetic acid or its sodium salt with deprotonated guar gum. Strong base, such as sodium hydroxide, is needed to activate hydroxyl group of guar for the nucleophilic substitution. Many previous academic works related to carboxymethyl guar preparation used relatively expensive and high-toxicity organic solvents like acetone, ethanol, isopropanol and butanol as the medium.3, 14-16 In Pal’s17 and Dodi’s18 paper, guar powder was dissolved in water. However, the usage of a larger excess of water (approximately at a 50:1 ratio to guar powder18) leads to significant issues for waste disposal or recycle in any commercial application.

Industrially, guar splits, rather than guar powder, is modified using water at ~1:1 water:guar ratio. Guar splits are the form of guar prior to crushing them to make powders and using guar splits has significant cost advantages as compared with using the powders.

The specific

temperatures and order of addition of ingredients is typically considered a trade secret and varies


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somewhat. The reaction kinetics between guar and the strong base has not been estabilished in any previous publically available venue to our knowledge.

In the present work, we report a new laboratory procedure for chemical modification of guar splits modelled on that used industrially. In addition, we evaluate a variety of different reaction parameters to control the degree of substitution. Rheological testing is used to establish the structure-property relationships between guar modification levels, crosslinker, and rheological properties. Furthermore, for the first time to our knowledge, reaction kinetics for the carboxymethylation of guar splits have been determined.

2. MATERIALS AND METHODS 2.1 Materials Guar gum splits were provided by United Guar LLC. Not all of the guar split is guar gum;18 approximately ~15% of the materials were impurities as measured by dissolving the splits in water followed by centrifugation and measuring the undissolvable fraction.19 Sodium hydroxide (NaOH) and sodium monochloroacetate (SMCA) were purchased from Sigma-Aldrich. Boric acid and sodium zirconium lactate were purchased from City Chemical LLC. All chemicals were used as received without further modification.

2.2 Carboxymethylation of guar splits Carboxymethylation of guar splits was carried out by a two-step reaction strategy shown below. A two-step strategy was necessary in order to minimize the side reaction between NaOH and SMCA also shown below.

Main Reaction: GG-OH + NaOH → GG-ONa (Alkoxy sodium salt of GG, yellow) + H2O GG-ONa + Cl-CH2-COONa (SMCA) → GG-O-CH2-COONa + NaCl

Reaction 1 Reaction 2

Side Reaction: NaOH + ClCH2COONa (SMCA) → HOCH2COONa (sodium gylocate) + NaCl


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First, guar splits were hydrated by a weight equivalent amount of water (or hydrated by aqueous sodium hydroxide solution directly). Then sodium hydroxide was added under a nitrogen atmosphere to deprotonate the hydroxyl groups of guar gum and form alkoxides, thereby increasing their nucleophilicity. Two different deprotonation temperatures were tested, room temperature and 50°C; the deprotonation time was 30 minutes rather than 15 minutes used in Pal’s work17 to give extra time for the reaction to occur because of possible mass transfer limitations with the swollen splits as compared to the powder. A color change from white to pale yellow occurred after reaction with NaOH; this changed color indicates of the presence of the alkoxy sodium salt of the guar gum. In the second reaction step, SMCA was reacted with the alkoxides at 60°C to produce CMG. The color remained throughout the reaction, consistent with the successful production of the sodium form of CMG. On the other hand, a change from yellow to milky is an indication that the acid form is produced. After the reaction, the product was cooled down and dispersed into 70% (V/V) ethanol. The unreacted alkali was neutralized with diluted hydrochloric acid. Final CMG product was washed with 70% ethanol, then followed by acetone, and dried overnight in vacuum. Reactions were performed in a 2CV helicone mixer from Design Integrated Technologies, Inc. This mixer is a twin cone vessel using intersecting dual helical-conical blades that intermesh throughout the conical envelope of the bowl, which allows top loading and bottom discharging. This reactor gives good mixing of the sticky swollen solid splits. All the materials were mixed and stirred in this bowl at 30 rpm. A thermal jacket was used to control temperature.

2.3 NMR spectroscopy NMR spectroscopy was performed at 500 MHz with a Varian VNMRS-500 spectrometer. Both GG and CMG samples were dissolved in D2O and analyses were performed at a probe temperature of 343K.

2.4 Determination of the degree of substitution The degree of substitution (DS) is defined as the average number of substituent groups attached per anhydroglucose unit (AGU); the latter value is three for guar gum. Theoretically, the degrees


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of substitution may therefore range from zero to three (fully substituted). However, primary hydroxyl groups are much more reactive than secondary hydroxyl groups. If only primary hydroxyl groups react, the maximum DS is 0.67.

The degree of substitution of carboxymethyl guar gum was determined by the back titration method.20 Carboxymethyl guar gum (1 g) was dispersed in 50 mL of 2 M HCl (used 70% ethanol as solvent), and the suspension was under magnetic stirring continuously for 4h. During this process, the sodium form of the carboxymethyl guar gum (Na-CMG) was converted to the hydrogen form (H-CMG). H-CMG was washed with 95% (V/V) ethanol until free of chlorine (tested by 0.1M silver nitrate solution), and then washed with acetone and dried overnight in vacuum. Dried H-CMG (0.5 g) was then dissolved in 50 mL of standardized 0.1 M NaOH solution and stirred for 4h. The excess of NaOH was back titrated with standardized 0.1 M HCl solution using phenolphthalein as the indicator. The DS was determined using the following calculation:

DS =

162 ×

− 58 ×

nCOOH = CNaOH × VNaOH −CHCl × VHCl where 162 g/mol is the molar mass of an anhydroglucose unit (AGU); nCOOH (in mol) is the amount of COOH group calculated from the titration; 58 g/mol is the net increase in the mass of an AGU for each carboxymethyl group substituted, and mds (in g) is the weight of polymer sample. CNaOH and CHCl are the molar concentration of standard NaOH and HCl solutions, respectively; VNaOH is the volume of NaOH, and VHCl is the volume of HCl used for the titration of the excess of NaOH.20

2.5 Rheological studies Rheological properties of carboxymethyl guar gum with different DS values were evaluated via both steady-shear and oscillating experiments. Rheological measurements of uncrosslinked materials were performed by a SR5000 rheometer (Rheometric Scientific) using a cone-and-plate


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fixture having a cone angle of 4° and a diameter of 40 mm. The gap was set at 0.079 mm as recommended by the manufacturer for this particular set of tools. Aqueous CMG solutions were prepared at a series of concentrations from 0.018% to 1% by weight. 0.1% (V/V) of bactericide was added to prevent biodegradation of the CMG samples. The oscillatory measurements were performed for 1% solution of each CMG sample. All the tests were made at a shear strain of 4%, which was in the linear viscoelastic range for all samples as determined by a strain sweep. Frequencies were set between 0.1 to 100 rad/s. The test temperature was maintained at 25°C. Crosslinked samples were prepared for both pristine guar and modified carboxymethyl guar (DS = 0.49) at a concentration of 0.5 wt%, which is within the range recommended and used by the oilfield industry.21 Sodium thiosulfate (0.12%) was added as a gel stabilizer. Sodium carbonate was used to adjust pH above 9.5. Rheological properties was evaluated first with no crosslinker, and then borate and organometallic zirconium crosslinkers were added at concentrations of 20, 50, 100 and 200 parts per million (ppm), respectively. Measurements for crosslinked samples were carried out on TA Instruments Discovery Series Hybrid Rheometer (DHR-2) equipped with a 40 mm parallel-plate geometry with a gap that was approximately 1 mm for all materials. The temperature was maintained at 25°C throughout the experiments. In this case, shear strains varied because of the desire to maximize response while still maintaining the linear viscoelastic region for each sample. 3. RESULTS AND DISCUSSION

3.1 Reaction Conditions Effect on Degree of Substitution Different recipes were used to develop the relationship between reaction conditions and degree of substitution.

Recipes and corresponding DS measured by titration are listed in Table 1.

Subscript 1 refers to the deprotonation step (Reaction 1) while CMG formation is indicated by Subscript 2. Table 1. Guar split reaction recipes and corresponding DS GG

40%

40% SMCA in

splits

Water

NaOH in

Batch

(g)

(g)

Water (g)

T1 (°C)

t1 (min)

Water (g)

T2(°C)

t2(min)

DS

CMG-1

48.6

48.6

30

RT

30

70

60

120

0.31


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CMG-2

48.6

48.6

30

50

30

70

60

120

0.39

CMG-3

48.6

0

30

50

30

70

60

120

0.36

CMG-4

48.6

0

60

RT

30

70

60

120

0.23

CMG-5

48.6

48.6

30

50

30

105

60

120

0.49

CMG-6

48.6

48.6

30

50

30

105

60

240

0.48

Higher temperatures used for the deprotonation step accelerated the activation of hydroxyl groups, which resulted in higher DS. Meanwhile, the color of guar splits changed from white to yellow more obviously when the reaction was conducted at 50°C compared to room temperature, indicating that more hydroxyl groups from guar splits became alkoxy sodium salt. Using the concentrated alkaline solution to hydrate and deprotonate guar splits in one step led to a lower DS as opposed to splitting the water and using part of the water to hydrate the guar splits and part of the water to dissolve the NaOH.

We also evaluated the impact of different reaction time for substitution. 2h and 4h gave similar degree of substitutions when guar splits reacted with the same amount of SMCA (see CMG-5 and CMG-6). The highest DS in our study was 0.49; assuming 15% of the split was not guar gum; the maximum conversion expected if only the primary hydroxyls react was DS=0.57.

3.2 NMR Figure 2 shows 1H NMR spectra for guar splits and carboxymethylated guar sample CMG-5. The solvent peak (D2O-d) was locked at 4.67 ppm, and the peaks at δ = 5.36 ppm and 5.09 ppm were attributed to the anomeric protons of galactosyl and mannosyl residues, respectively. The other sugar protons were located at the range of δ = 3.6 - 4.6 ppm. After carboxymethylation, the peaks at 4.46 ppm, 4.25 ppm and 4.23 ppm became overlapped by the overall sugar peak signals with new peaks at 4.29 ppm and 4.31 ppm. However, this 1H NMR cannot be used for quantification because the signals did not show enough splitting with the added CH2 group.


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Figure 2. 1H NMR spectra recorded in D2O of GG (top) and CMG (bottom)

In order to further confirm the reaction, 2D NMR spectroscopy using the Heteronuclear SingleQuantum Correlation (HSQC) method was performed for both GG and CMG samples. HSQC allowed a 2D heteronuclear chemical shift correlation map between directly-bonded 1H and 13C. The peak signals on HSQC spectrum could be presented by a positive phase and a negative phase in two different colors. The CH and CH3 signals should be phased to be positive and CH2 groups are phased to be negative. Figure 3 showed the HSQC spectrum before and after carboxymethylation reaction. Positive phase was colored in red for GG and yellow for CMG, while negative phase was colored in blue for GG and cyan for CMG.

(A)

(B) Figure 3. 1H-13C HSQC spectrum of (A) GG and (B) CMG


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Figure 4. 1H-13C HSQC spectrum overlapped by GG and CMG

GG and CMG spectra were then overlapped and compared yielding several important outcomes as shown in Figure 4. Firstly, in the sugar signal area of GG, we could identify the C6 signals (see Figure 1 for meaning of C6 etc.), which belonged to CH2 group for galactose (61.7 ppm) (GC6) and mannose (67.2 ppm) (M-C6) at high field. The resonance of two H6 signals of mannose (M-H6) was well separated. However, proton signals at H-6 of galactose (G-H6) were found to overlap as indicated by the single HSQC cross peak. These G-H6 and M-H6 peak signals were also found in CMG spectrum, although one of M-H6 proton was shifted from 4.31 ppm to 4.24 ppm. Besides the chemical shift of one M-H6 protons, another difference between GG and CMG is the more methylene group signals in cyan color observed in CMG spectrum, which denoted carboxymethyl substitution. The further information was, besides the exact overlapped original anomeric G1 (5.4 ppm, 99.4 ppm) and M1 (5.1 ppm, 100.8 ppm) signals of guar gum, CMG showed two new signals (5.5 ppm, 106.8 ppm and 5.4 ppm, 108.3 ppm) for anomeric peaks shift, which could be attributed to the carboxymethylation as well.

3.3 Rheology of Uncrosslinked GG and CMG Steady-state viscosities of solutions prepared at different CMG concentrations were measured at different shear rates and results are shown in Figures 5A, 6A and 7A for CMG with DS values from 0.3-0.5. The viscosity curves showed a typical non-Newtonian behavior at low shear rates and a shear-thinning region at higher shear rates. Solution viscosity increased with an increase in


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sample concentration. The transition from the Newtonian plateau to the shear thinning region moved to lower shear rates as the sample concentration was increased. At the same concentration, higher DS samples displayed lower zero shear viscosity. A zero shear viscosity decrease is often caused by molecular weight degradation. However, we don’t believe that temperature or shearing conditions were extreme enough to cause significant molecular weight degradation of the polysaccharide chain. The shear-thickening effect at high shear rates for low viscosity samples is artifact from instrument inertia. Zero shear viscosity was plotted as a function of CMG concentration in Figures 5B, 6B and 7B. The crossover concentration of a polymer, c*, represents the concentration at which polymer chains begin to entangle with one another. The critical concentration values obtained in our measurements are comparable to those presented elsewhere in the literature.22-23CMG with higher DS had a lower crossover concentration. Introduction of carboxymethyl groups makes the polymer more water-soluble, i.e. the chain is more solvated. Hence, the conformation of the chain is expected to be larger for highly substituted CMG, i.e. the root mean square end-to-end distance should be larger (or, alternatively, the persistence length is larger). We believe that this increased solubility is responsible for the lower c*. A reduction in crossover concentration with DS argues against substantial molecular weight degradation at higher DS.

(A)

(B)

Figure 5. (A) Viscosity vs. shear rate curves for different CMG (DS=0.31) concentrations; (B) Zero shear viscosities at different CMG concentrations


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(A)

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(B)


(A)

(B)


Figure 8 shows storage modulus G’ and loss modulus G” curves of CMG samples with three DS levels at 1% concentration (well above the crossover concentration). A crossover point between G’ and G” was measured. For DS = 0.31 and 0.39 CMG samples, we observed this crossover point at 32 rad/s and 63 rad/s, respectively. For DS = 0.49 CMG, there was no crossover of G’ and G” within the measured frequencies, but this value was determined via extrapolation to be ~100 rad/s.


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(A)

(B)

(C)

Figure 8. G’, G” and Tan Delta curves of 1.0 wt% CMG solutions with different DS: (A) 0.31; (B) 0.39; (C) 0.49 The crossover frequency (in s-1) where G’ and G” are equal is the reciprocal relaxation time. This crossover is due to the failure of the entanglements present in solution to relax within the time frame of the oscillation.

These results show that the relaxation time decreases with

increasing DS. The tangent of the loss angle (ratio G''/G'), termed tan delta, is a measure of the internal friction of the material in that condition. Below the crossover point, where G'' is higher than G' (tan delta > 1), the sample is more viscous than elastic, and vice versa when G' is higher (tan delta < 1). At a frequency above the crossover point, the entanglements begin to act as temporary crosslink junctions within the time frame of this experiment. The decrease in relaxation time with increasing carboxyl-substitution could be explained by an effect of a decrease of the friction coefficient. The extra rigidity due to more substituted carboxyl group results in intermolecular repulsion, which in turn weakens molecular entanglements and junctions of CMG in water. For a typical fluid, the double logarithmic plot of G' (ω) and G'' (ω) gives limiting slopes of 2 and 1 respectively in the terminal region of relaxation. The slopes of G' (ω) and G'' (ω) for CMG samples determined at lowest frequency regions are slightly lower than those values indicating that the frequencies were not low enough to reach the terminal region for these samples. Our expectation is that the terminal region should exist for these materials since the polymers are linear.


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Figure 9. Comparison of the complex viscosity (η*) (open symbols) and the shear viscosity (η) (full symbols) for 1.0 wt% CMG solutions with different DS: (diamonds) 0.31; (triangles) 0.39; (circles) 0.49

The complex viscosity calculated from oscillatory measurement was compared in Figure 9 to the steady shear viscosity for 1.0 wt% CMG solutions. The Cox-Merz rule states that the complex viscosity is equal to the steady shear viscosity when the angular velocity is equal to the shear rate.24 As can be observed, CMG samples showed significant quantitative and qualitative deviation of the complex viscosity from the steady shear viscosity. This departure from the CoxMerz rule is likely a result of hydrogen bond association in the molecules. Deviations from the Cox-Merz rule have also been reported for solutions of hydroxyethyl guar gum.25

3.4 Rheology of Crosslinked GG and CMG Borate crosslinkers are widely used for fracturing fluids because of its characteristics as a pH sensitive reversible crosslinks for hydroxyl groups.26 At pH values between 8.5 to 12 the material is crosslinked27 while at low pH the material is not crosslinked. Boric acid may be used as the source of borate ions for crosslinking. In aqueous environment, an acid-base equilibrium is established between boric acid and borate ions as illustrated below: H3BO3 + H2O

KA

B(OH)4 - + H+

The borate ion B(OH)4- is the effective species in crosslinking with guar through cis-hydroxyls, and its concentration is related to the pH. The pKa for the equilibrium reaction is 9.0-9.2.28 Increased pH contribute to shift the boric acid equilibrium toward the borate ions.


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The most common metal crosslinkers are based on the zirconium (IV) and titanium (IV) compounds with certain organic ligands or chelators. The cross linking between guar and polyvalent metallic complexes is usually thought to occur via covalent bonding. Unlike borate crosslinker, these crosslinking bonds attached to Zr and Ti are not reversible. The stability can be maintained in relatively broad pH range, normally from 3.5 to 11.27

Figure 10. Storage and loss modulus at (25°C) of 0.5 % uncrosslinked GG solution.

Figure 11. Storage and loss modulus (at 25°C) of 0.5 % GG solutions with (A) 20 ppm; (B) 50 ppm; (C)100 ppm; (D) 200 ppm of borate crosslinkers at pH = 10

Figure 12. Storage and loss modulus (at 25°C) of 0.5 % GG solutions with (A) 20 ppm; (B) 50 ppm; (C)100 ppm; (D) 200 ppm of zirconium crosslinker


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Crosslinking changes the weakly viscoelastic fluid into strongly viscoelastic gels. Figures 10 and Figure 11 show the behavior of the storage (G’) and loss (G”) modulus as a function of the angular frequency for non-crosslinked GG solution and GG gels with 20 - 200 ppm of borate crosslinker added. GG solution with 20 ppm borate displayed nearly no apparent change in both G’ and G” compared to the solution without crosslinker. Borate crosslinker at 50 ppm and above led to increase of both G’ and G”. Higher G’ value than G” in the entire frequency range clearly indicated an increase in gel-like behavior. Figure 12 showed G’ and G” of crosslinked guar with different concentrations of zirconium crosslinking agent. Crosslinking was observed at even lower concentration of zirconium chelate added (20 ppm) and the effectiveness of zirconium as a crosslinker over borate was also clear at higher concentrations. For example, at 200 ppm crosslinker added, G’ was about a factor of 3 higher for the zirconium crosslinked samples vs. the borate crosslinked samples. In particular for the zirconium crosslinked materials, G’ and G” exhibited nearly independent characteristic curves on the frequency over a wide range, which indicated a three-dimensional network structure in the gels, consistent with the large difference between G’ and G” in this sample.

Figure 13. Storage and loss modulus (at 25°C) of (A) 0.5 % uncrosslinked CMG solution; and CMG solutions with (B) 200 ppm borate crosslinker; (C) 20 ppm zirconium crosslinker; (D) 50 ppm zirconium crosslinker; (E)100 ppm zirconium crosslinker; (F) 200 ppm zirconium crosslinker


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CMG solution w/ and w/o crosslinking agents displayed the performances in Figure 13. CMG solution with 200 ppm boric acid showed similar rheological properties to that of noncrosslinked CMG solution, which indicated the crosslinked gel was not well formed. Borate crosslinking is much less effective with CMG than GG, which may be caused by the fact that CMG molecules are charged species in solution, and the negatively charged carboxymethyl groups attached at various points on the polymer tend to repel each other.

In other words,

carboxymethyl groups partly blocks the freedom of movement of polymer chains and get clustered as well as crosslinked by borate.29

Zirconium crosslinker provided better effectiveness of crosslinking for CMG than borate crosslinker, although below 50 ppm concentration of Zr(VI) only a slight increase of G’ was observed for CMG. When the concentration was at 200 ppm, the samples showed higher G' than G" values indicating that the gel characteristics are more important in determining the elastic response behavior.

3.5 Kinetics of carboxymethylation of guar splits The reaction has two elementary steps. The deprotonation step is generally fast, and the carboxymethylation (Reaction 2) is the rate-determining step. Several ways have been used to determine the rate law for a particular reaction, one of the most often used is the method of pseudo-first order conditions.30 This method is sometimes also referred to as the method of isolation. The procedure is designed to measure the concentration change of one reactant independently while keeping the concentrations of other species constant.

The rate law form for the carboxymethylation reaction is assumed to be: r = k[GG-ONa]m[SCMA]n

Where m is the order of reaction with respect to guar, and n is the reaction order with respect to SMCA. The rate constant k is a function of temperature.

To determine the rate law, we

performed the reaction at 60 °C with the reactants in a mole ratio of GG splits (AGU):NaOH: SMCA=1:1:5.


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Because the change in SMCA concentration was less than 10% under the conditions of the experiment, we assumed that the concentration of SMCA was constant. We combined the actual rate constant for the reaction (k) with the constant concentration of SMCA ([SMCA]0) to form a new constant that we called kexp, which was the rate constant determined by our experimental data. kexp = k[SMCA] 0n Then the rate law equation was expressed as: r = k[GG-ONa]m[SCMA]n = (k[SMCA]0n) [GG-ONa]m = kexp [GG-ONa]m In the equation, the reaction rate is only related to concentration of GG.

Titration was used to monitor the reaction progress by determining DS value at different time. DS determination was repeated for three times with small variation, which was shown in Figure 14 as a function of reaction time. The reaction reached completion within one hour and three reaction orders (m=0, 1 or 2) were used to fit the data.

Figure 14. DS measured by titration at different reaction time For each set of reaction conditions, substitution reaches an equilibrium state with a maximum DS level (DSmax). The simplest assumption is to assume only a fraction of GG hydroxyl sites are available for reaction, which is given by DSmax, According to our experiments, the highest DS


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achieved was 0.49. Hence, we assumed DSmax to be 0.5, which translates to about 85% of the primary hydroxyl sites being available for reaction assuming 15% impurities in the guar splits. Because the GG concentration is proportional to (DSmax -DS): [GG-ONa] = [GG-ONa]0 (DSmax -DS) The data points of (DSmax -DS) before equilibrium were used to plot the graphs verse reaction time according for each reaction order. Specifically, we chose all the 11 data points within the first 50 mins to evaluate the reaction rate. Including more data points after 50 mins worsened the fit, presumably caused by the small separation between the conversion and DSmax. A second order reaction gave the best linear fit with expression shown in Figure 15 and R2 = 0.9977.

Figure 15. Second order fit to data To determine rate order for SMCA, theoretically a similar procedure with excess amount of GG splits could be performed. However, considering that the titration method may not provide high resolution for low DS determination, another reaction in a mole ratio of GG splits (AGU):NaOH:SMCA = 1:1:1.2 was done to monitor the concentration of reactants during the original 10 min.

Three different trials were conducted and DS at 5 and 10 minutes were

determined for each trial. The average degree of substitutions were 0.24 and 0.29 respectively. The concentration of reactants at three time points (0,0 was also included) were input into the equation below:

−

ΔGG-ONa = r = k[GG-ONa]m[SCMA]n Δ


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Two equations were generated

−

GG-ONat2 − GG-ONat1 = rt1 = k[GG-ONa]t1m[SCMA]t1n t2 − t1

−

GG-ONat3 − GG-ONat2 = rt2 = k[GG-ONa]t2m[SCMA]t2n t3 − t2

With the previous fitting results for m these two equations with two unknown variables, rate constant k and reaction order n for SMCA, were solved. The integrated rate law is as follows (with concentration in moles/liter): r = d(CMG)/dt = 2.51×10-2 [GG-ONa]2[SCMA]

Although the leading constant could change on a larger scale because of mass transfer limitations, the rate limiting mass transfer step is likely diffusion of the ingredients into the swollen gel which is entirely independent of scale.

Hence, we believe the reaction rate law

should be 100% transferable to the industrial scale.

4. CONCLUSIONS A method of carboxymethyl modification of guar splits with NaOH and SMCA was reported under organic solvent-free conditions using only a small amount of water to hydrate the splits. Samples with various grades of substitution were synthesized by varying the reaction parameters to obtain maximal DS of 0.49. The success of this low cost and ecofriendly procedure was supported by NMR spectroscopy. All modified guar samples exhibit a clearly shear-thinning pseudoplastic feature. We also established a structure-property relationship between rheological behavior and degree of substitution. Both a decrease in zero shear viscosity and relaxation time were accompanied with an increase in DS. In addition, we investigated GG and CMG crosslinked with boric acid and zirconium chelate respectively. Zirconium crosslinker proved to produce stronger gels at a given crosslinker concentration. CMG was substantially less crosslinked than GG because the carboxymethyl group interfered with binding between hydroxyl


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groups and the ionic species. Finally, we developed a rate law for the abovementioned chemical modification and a kinetic model was proposed. We believed this rate law would provide a potential basis for an engineering design to modify guar splits. AUTHOR INFORMATION Corresponding Author *Tel.: (+1)-405-325-4369. E-mail: [email protected] ACKNOWLEDGMENT This work was financially supported by United Guar and the Oklahoma Center for the Advancement of Science and Technology, Grant AR15-057. The authors gratefully thank Dr. Lewis Norman and Dr. Lynn Norman for providing samples and technical discussion. They also acknowledge Dr. Susan Nimmo for helpful suggestions about NMR.

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TOC Graphic


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Reaction Kinetics and Subsequent Rheology of Carboxymethyl Guar

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