Characterization and Intermolecular Interactions of Hydroxypropyl

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Biomacromolecules 2002, 3, 456-461

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Characterization and Intermolecular Interactions of Hydroxypropyl Guar Solutions Yu Cheng,* Kirk M. Brown, and Robert K. Prud’homme Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08544 Received October 14, 2001; Revised Manuscript Received March 6, 2002

Aqueous solutions of guar galactomannan and hydroxypropyl guars (HPG) with different molar substitution (MS) levels were studied using dilute solution viscometry and gel permeation chromatography. When guar is modified to HPG, the added hydroxypropyl groups sterically block the hydrogen bonding sites on the guar backbone and reduce the hydrogen bonding attractions between guar molecules. The effects of molar substitution on the intermolecular interactions are inferred from measurements of the Huggins coefficients, which measure intermolecular interactions in dilute solution, and molecular volumes, which reflect intrachain associations. The behavior can be divided into three regimes: (1) at low MS levels (0 < MS < ∼0.4), there is a sharp decrease in intermolecular interactions as a function of MS; (2) in the intermediate range (∼0.4 < MS < ∼1.0), interactions become independent of MS; (3) at high substitution levels (MS > ∼1.0), the temperature dependence of inter- and intramolecular hydrophobic interactions produces a temperature dependence in the Huggins coefficient and molecular volumes that is not seen at lower substitutions. By acid hydrolysis, HPG samples with a range of molecular weights and consistent polydispersities were obtained. On the basis of these samples, the Mark-Houwink-Sakurada parameters and “characteristic ratio” C∞ were evaluated for HPG (MS ∼ 0.6) and compared to the values for guar. The HPG chain stiffens as the degree of substitution increases. 1. Introduction Guar galactomannan is a water-soluble polysaccharide extracted from the seeds of Cyamopsis tetragonoloba. It consists of a linear backbone of β-1,4 linked mannose units and is solubilized by randomly attached R-1,6 linked galactose units as side chains (Figure 1).1 The ratio of mannose to galactose units ranges from 1.6:1 to 1.8:1 apparently due to climate variation. Guar is widely used in a variety of industrial applications because of its ability to produce a highly viscous solution even at low concentrations. The high viscosity of guar solutions arises due to the high molecular weight of guar (up to 2 million)2 and the presence of extensive intermolecular association (hyperentanglement) through hydrogen bonding.3,4 One important application of guar galactomannan is the hydraulic fracturing process in oil and gas wells.5 Hydraulic fracturing enhances the productivity of wells by increasing the permeability of the formation near the wellbore. Fracturing fluids, which are highly viscous suspensions based on water-soluble polymers (i.e., guar galactomannan), are used extensively in this process. However, guar gums contain as much as 10-14% insoluble residue depending on gum purity and method of isolation.6 This “residue” is not desirable for commercial applications. In addition, guar molecules have a tendency to aggregate during the hydraulic fracturing process, mainly due to intermolecular hydrogen bonding. These aggregates are detrimental to oil recovery because they clog the fractures, restricting the flow of oil. * To whom correspondence should be addressed (fax, 609-258-0211; e-mail, [email protected]).

Figure 1. The structure of guar galactomannan: guar consists of a linear backbone of β-1,4 linked mannose units and is solubilized by randomly attached R-1,6 linked galactose units as side chains. The ratio of mannose to galactose units ranges from 1.6:1 to 1.8:1.

Therefore, low-residue derivatives of guar gum have been developed in attempts to eliminate this problem. Treatment of guar with ethylene oxide, propylene oxide, and chloroacetic acid in an alkaline medium results in the formation of hydroxyethyl guar, hydroxypropyl guar, and carboxymethyl guar, respectively. Substituted guars are more soluble in water than native guar, with less insoluble residues.7 Hydroxypropyl guar (HPG) is the most widely available derivative of natural guar. Stoichiometric control of the propylene oxide substitution results in a significant improvement in guar gum properties and produces guars with a different number of hydroxypropyl groups along the guar backbone. The various degrees of molar substitution (MS) measure the average number of moles of hydroxypropyl

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Interactions of Hydroxypropyl Guar Solutions

groups substituted per mole of anhydrous sugar units. Therefore, it is a measure of the total number of moles of propylene oxide that have been added to the guar polymer chain along the guar backbone. At low degree of substitution, some of the hydroxyl groups on the guar backbone are substituted, leading to a polymer composed of many different monomers. McNeil and Albersheim have studied the structure of HPG, and an analytical method was presented to identify and quantify the monomer composition of HPG.8 A statistical kinetic model to describe heteropolysaccharide ethers was also proposed and is shown to afford a good description of analytical data on HPG.9 The flow properties of a HPG solution (MS ≈ 1.0) were studied by Lapasin et al.10 The shear-dependent behavior of HPG resembles that of isotropic polymer solutions. However, there is no report in the literature on how hydroxypropyl substitution affects the intermolecular interactions in guar systems. In this study, the dilute solution properties of a series of HPGs with different substitution levels are compared and discussed. HPG samples were produced with different molecular weights but consistent polydispersities using an acid hydrolysis procedure. HPG with a MS about 0.6, which is widely used in industry, was characterized using gel permeation chromatography (GPC) and dilute solution viscometry. The Mark-HouwinkSakurada parameters and “characteristic ratio” C∞ were determined which demonstrate the role of HP substitution on local chain configurations. Intermolecular interactions, reflected in the Huggins coefficients obtained from the second-order term in the solution viscosity versus polymer concentration, show that HP substitution decreases attractive hydrogen bonding interactions. 2. Experimental Section 2.1. Materials. Standard food grade guar gum was supplied by Rhone-Poulenc Inc. (Guar LJX-2, Lot 9504545). HPGs were obtained from Halliburton Services with a series of molar substitutions: MS ) 0.2, 0.6, 1.07, and 1.57. All polymer solutions were prepared by adding the proper amount of polymer to deionized water under vigorous stirring for an hour. Sodium azide (0.01 wt %) (FisherChemical) was added as a preservative. The solution pH was adjusted to 7.0 using HCl (EM Science). Finally, the polymer solution was transferred to a container and then placed on a low shear roller for approximately 20 h to complete hydration. Commercial guars contain several impurities, among which are cell debris, proteins, and water. Bavouzet reported that native guar was composed of 83% (w/w) pure guar.11 HPG has about 95 wt % pure polymer.12 All solutions were centrifuged in a Sovall RC5C centrifuge (DuPout) for 4 h at 16000g and 17-20 °C to remove insolubles. The decrease in actual polymer concentration after centrifugation was adjusted using the 83% and 95% active polymer contents for guar and HPG, respectively. 2.2. Acid Hydrolysis of HPG. A procedure for acid hydrolysis of galactomannan polymers has been developed for the preparation of degraded polymer samples with various molecular weights, while retaining consistent polydispersi-

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ties.13 First, 7.5 g of HPG (MS ≈ 0.6) was dispersed in 14 mL of ethanol in a sealed jar and placed in the oven at 70 °C to allow the system to equilibrate. Then, 0.075 g of hydrochloric acid (HCl) (37 wt % aqueous solution, EM Science) was added, and the solution was stirred for 3-5 min. The jar was sealed to prevent ethanol or HCl from escaping. Then the sample was place in an oven at 70 °C to let the reaction proceed for 1, 2, 5, 10, or 30 h. Finally, the reaction was terminated by adjusting the solution pH to 7, and the sample was dried in a vacuum oven at 70 °C. 2.3. Intrinsic Viscosity Measurement. Intrinsic viscosity [η] is a measure of the inherent ability of a polymer to increase solution viscosity. In the dilute range, solution viscosity can be represented by a power series in polymer concentration cp η ) ηs(1 + [η]cp + kH[η]2cp2 + ...)

(1)

where ηs is the solvent viscosity and kH is the Huggins coefficient. The intrinsic viscosity can be determined by measuring viscosity of solutions at low concentrations and extrapolating to infinite dilution, according to the Huggins or Kraemer relationships, respectively.14 ηsp/cp ) [η] + kH[η]2cp

(2)

ln(ηr)/cp ) [η] + kK[η]2cp

(3)

where ηr is the relative viscosity, defined as the ratio of solution viscosity and solvent viscosity η/ηs, and ηsp is the specific viscosity (ηr - 1). The viscosities of dilute solutions of guar and HPG were determined by using a capillary viscometer (Schott Gerate Ubbelohde Type No. 53110). The temperature of the thermostat was controlled within a range of (0.1 °C. The viscometer was calibrated with standard sucrose aqueous solutions. Intrinsic viscosity [η] is related to the viscosity average molecular weight of the polymer through the MarkHouwink-Sakurada (MHS) relationship: [η] ) KMwR, where K and R are constants, both related to the “stiffness” of the polymer. For flexible polymer coils, R is 0.5 in a θ solvent and 0.8 in a good solvent. The Huggins coefficient is a measure of polymer-polymer interactions in solution. Experimentally, the Huggins coefficient is independent of molecular weight for long chains, with values of roughly 0.30-0.40 in good solvents and 0.50-0.80 in θ solvents. The Huggins coefficient assumes high values when intermolecular association exists.15 2.4. Gel Permeation Chromatography (GPC). GPC was carried out with two columns, a TSK G3000PWXL and a TSK G6000PWXL, in series. For protection, a guard column (TSK GDNA-PW) was used before the two columns. All columns were thermostated at 40 °C to minimize peak broadening. The HPLC system consisted of a pump (Waters M510), a differential refractometer (Waters 410), and an injector (Valco SSA C12P). The mobile phase was 55 mM Na2SO4 and 0.02% NaN3 aqueous solution. Flow rate was 0.6 mL/min. Degraded guar samples were diluted to 0.05 wt % and filtered through a 0.45 µm filter (Whatman Autovial) prior to analysis.

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Cheng et al. Table 1. Intrinsic Viscosity, Huggins Coefficient, and Weight Average Molecular Weight for Natural Guar and Various HPGs [η], dL/g [η], dL/g kH kH (25 °C) (25 °C) (40 °C) (40 °C) natural Guar HPG (MS ∼ 0.2) HPG (MS ∼ 0.6) HPG (MS ∼ 1.07) HPG (MS ∼ 1.53)

16.39 14.65 14.51 15.43 15.92

0.79 0.53 0.32 0.32 0.31

16.07 15.12 14.27 14.62 14.51

0.73 0.43 0.29 0.36 0.37

Mw 1.935 × 106 1.910 × 106 1.928 × 106 1.861 × 106 1.945 × 106

Figure 2. Huggins extrapolation to intrinsic viscosity for native guar and HPGs at 25 °C.

The retention process of GPC is based on the volume of the polymer coil in solution. Flory proposed that the polymer molecular weight is related to its hydrodynamic volume 〈R2〉3/2 through16 [η] ) φ〈R2〉3/2/Mw

(4)

where 〈R2〉 is the mean square end-to-end distance of the polymer and φ is a constant equal to 2.5 × 1023 g-1. The equation is also called the Flory-Fox equation. The hydrodynamic volume of the polymer coil can be estimated using 〈R2〉3/2, which is equal to [η]Mw/φ. Therefore, a plot of [η]Mw/φ versus the elution volume yields a universal curve for a given chromatographic column, irrespective of the chemical composition and architecture of the polymer. This is known as the universal calibration curve, which makes it possible to determine the absolute molecular weight (MW) of macromolecules.17 In this study, two different polymer standards, pullulan and guar, were used to calibrate the columns. Nine fractions of pullulan standards with average molecular weight ranging from 5900 to 1.6 × 106 were purchased from Shodex Corp. (Japan). Two fractionated guar standards, which had been characterized by light scattering, Meyprogat 7 (Mp ) 58 000) and CSAA 200 (Mp ) 2 000 000), were kindly provided by Rhodia Inc. The MHS relationships (i.e., [η] ) KMwR) of guar and pullulan in aqueous solution are K) 3.8 × 10-4 dL/g, R ) 0.723 for guar18 and K ) 1.9 × 10-4 dL/g, R ) 0.67 for pullulan.19 Therefore, a universal calibration curve was plotted for guar and pullulan and all points fall on a single straight line. The molecular weight (MW) and molecular weight distribution (MWD) of degraded guar samples were determined based on the universal calibration curve. 3. Results and Discussion 3.1. Effect of Hydroxypropyl Substitution. Figure 2 shows the Huggins extrapolation to intrinsic viscosity for natural guar and HPGs at 25 °C. The calculated intrinsic viscosity and Huggins coefficient are listed in Table 1. A Kraemer extrapolation to intrinsic viscosity was also conducted, and similar results were obtained. At 25 °C natural

Figure 3. The Huggins coefficient plotted as a function of the hydroxypropyl molar substitution at 25 and 40 °C.

guar has an intrinsic viscosity of 16.39 dL/g and a Huggins coefficient of 0.79, higher than any of the HPGs. Water is a fairly good solvent for guar. However, the Huggins coefficient of guar in water is much higher than the regular value for a good solvent (0.3-0.4), which indicates the importance of polymer-polymer hydrogen bonding interactions between natural guar molecules. When hydroxypropyl groups are added to guar, the substitution occurs at any of the hydroxyl groups on the chain, either on the backbone or on the galactose side group. This heterogeneous substitution of hydroxypropyl groups sterically blocks the hydrogen bonding sites on the guar backbone and reduces the intermolecular hydrogen bonding between polymer molecules. Osmotic stress studies on guar and HPG systems also show that the attractions between guar chains decrease with the hydroxypropyl substitution.20 Figure 3 is a plot of the Huggins coefficient as a function of the hydroxypropyl substitution at 25 and 40 °C. At 25 °C, the Huggins coefficient first drops with MS, then becomes independent of MS with a value of 0.32. At 40 °C, HPG (MS ) 0.6) has the lowest Huggins coefficient, followed by HPG (MS ) 1.07), HPG (MS ) 1.53), and finally the highest of the substituted guar, HPG (MS ) 0.2). This trend suggests three regimes of behavior: The first regime (0 < MS < ∼0.4) shows a sharp decrease in intermolecular interactions as a function of MS. It is clear that substitution reduces the number of available hydrogen bonding sites on the backbone by sterically hindering backbone-backbone interactions. In the second regime (∼0.4 < MS < ∼1.0), interactions are no longer a function of MS. Additional modification of guar (MS > 0.6) does not decrease the intermolecular association. From a commercial perspective substitution is relatively expensive and substitution levels greater than MS > 0.5 do not perform significantly different than MS

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Table 2. Molecular Weight and Intrinsic Viscosity Data for HPG (MS ∼ 0.6) and Degraded HPG (MS ∼ 0.6) Samples time (h)

Mw

Mn

0 1 5 13.5 31

1.928 × 106 1.01 × 106 5.7 × 105 2.01 × 105 6.8 × 104

9.79 × 105 3.95 × 105 1.71 × 105 6.3 × 104 2.8 × 104

intrinsic polydispersity viscosity (dL/g) 1.97 2.55 3.34 3.17 2.41

14.27 8.53 5.45 2.78 1.03

Figure 4. The effective molecular volume of a polymer coil is plotted as a function of hydroxypropyl molar substitution at 25 and 40 °C.

substitutions of 0.5. It is significant that most commercial hydoxyproply guar samples are in the range of MS ) 0.4. The distinguishing feature of the third regime (∼1.0 < MS < 1.53) is the temperature sensitivity of interactions with the highly substituted, somewhat hydrophobic guars. The Huggins coefficient increases with substitution level at elevated temperature, indicating the hydrophobic nature of the hydroxypropyl groups. At room temperature, the Huggins coefficient does not change appreciably over the range 0.4 < MS < 1.5. This temperature-dependent aggregation is observed for other water-soluble polymers21,22 and is the signature of the entropy driven “hydrophobic effect”.23 The average molecular weights of guar and HPG were determined by GPC and listed in Table 1; the molecular weights of the samples are constant (∼1%) over the entire range of hydroxypropyl substitution. Combined with the intrinsic viscosity results, the effective molecular volume of a polymer coil, [η]Mw/φ, is plotted vs substitution levels (Figure 4). Guar has the highest molecular volume. At 25 °C, the molecular volume decreases with molar substitutions to a minimum at MS ) 0.6. When the MS continues to increase, the molecular volume begins to increase again. There are two competing effects as the MS increases: the hydroxypropyl groups reduce the intermolecular attraction, decreasing the effective molecular volume; on the other hand, the introduction of substituting groups increases the chain local rigidity, which, as a result, increases the molecular volume. (The local chain rigidities for guar and HPG is measured and compared later in this paper. The HPG chain is shown to be slightly more rigid than guar.) Therefore, the interplay of the two competing effects gives rise to a minimum molecular volume at MS ) 0.6 and 25 °C. When temperature is increased to 40 °C, the molecular volumes for HPGs below MS ) 0.6 do not appreciably change compared with the values at 25 °C. However, at high substitution levels (MS g 1), the molecular volume decreases as temperature increases, and the reduction increases with MS. This is due to the intramolecular hydrophobic effect, which causes the polymer chain to collapse upon itself, resulting in a reduction of size. During the intrinsic viscosity experiment, HPG solutions were prepared at a low temperature (20 °C) and then heated to a higher temperature (40 °C) for [η] and kH measurements. In dilute solution the segment density within a polymer coil is higher than the average bulk solution segment density. Therefore when temperature is increased and attractive

Figure 5. The relationship between intrinsic viscosity and molecular weight for HPG (MS ∼ 0.6) is shown as a double-logarithmic MarkHouwink-Sakurada plot.

hydrophobic interactions are induced, it is more likely for the HPG coils to collapse through intramolecular hydrophobic attractions, rather than aggregating through intermolecular interactions. At the same time, intermolecular molecular hydrophobic interactions will make the polymer coils more sticky, which leads to an increase of the Huggins coefficient. 3.2. Solution Properties of HPG (MS ≈ 0.6). The MarkHouwink-Sakurada (MHS) Relationship. HPG (MS ≈ 0.6) was degraded using the acid hydrolysis procedure described in the Experimental Section. The number average molecular weight (Mn), weight average molecular weight (Mw), and the polydispersity index (PI ) Mw/Mn) of degraded HPG samples were determined by GPC and are listed in Table 2. If the mixing of HCl is good and the H+ ion is uniformly distributed in the polymer solution, the degradation process produces HPG samples with uniform molecular weight distribution. The PI does not change significantly for different degraded HPG samples, with an averaged value between 2.5 and 3. Four degraded HPG samples (1, 5, 13.5, 31 h) were selected, and their intrinsic viscosities were measured. Figure 5 is a double-logarithmic plot of [η] against Mw. These data give MHS parameters of K ) 1.953 × 10-4 dL/g and R ) 0.775 for HPG (MS ) 0.6). Since the GPC data for the degraded hydroxypropyl guar samples were analyzed using the MHS parameters for natural guar, the HPG molecular weights were recalculated using the experimental MHS values for HPG. The iterative process of calculating molecular weights, determining the MHS parameters, and then resolving for the molecular weights were repeated until identical results, within experimental error, were obtained. This iteration procedure provides a value for R ) 0.785 and a value for K ) 1.72 × 10-4 dL/g for HPG (MS ) 0.6). These values compare to our experimental values for natural

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Cheng et al.

guar of K ) 3.04 × 10-4 dL/g and R ) 0.747. These values compare to those provided by Robinson et al.18 determined by light scattering (K ) 3.8 × 10-4 dL/g, R ) 0.723) for native guar. A flexible coil configuration has an R in the 0.5-0.8 range. If the polymer is a rod, then R approaches 1.8. The increase in R for HPG indicates that the HPG chain is slightly stiffer than natural guar which is consistent with its greater steric hindrance. Intrinsic Chain Flexibility: The Characteristic Ratio (C∞). The simplest model for an ideal chain is the freely jointed segments model, in which the polymer chain is considered as a collection of stiff rods connected by totally flexible, universal joints. The mean squared end-to-end distance for the freely jointed chain, 〈R2〉0, is 〈R2〉0 ) Nlo2

(5)

where N and lo stand for the number and length of the monomeric unit, respectively. For a real polymer chain, the end-to-end distance 〈R2〉 is always greater than 〈R2〉0 due to conformational restrictions as well as long-range interactions between different segments (excluded volume effect). The characteristic ratio was introduced by Flory16 and is defined as C∞ ) 〈R2〉/Nlo2

(6)

The characteristic ratio indicates the increase in size of the chain over the random-walk size caused by local conformational constraints. When long-range excluded volume effects can be neglected, the intrinsic viscosity is related to molecular weight through the Flory-Fox equation (eq 4). Combining eqs 4, 5, and 6, we obtain [η] ) φlo3(C∞/mo)3/2Mw1/2 ) KθMw1/2

(7)

where mo is the molecular weight of a monomeric unit (N ) Mw/mo). In good solvents, excluded volume causes polymer coils to expand. An expansion factor Rη is added to eq 7 [η] ) KθMw1/2Rη3

(8)

Estimation of the expansion factor dependence on Mw by Stockmayer and Fixman leads to the simple equation [η] ) KθMw1/2 + 0.51φBMw

(9)

B is related to Flory’s interaction parameter χ1 by B ) V2(1 - 2χ1)/V1Nav

(10)

with V ) specific volume of polymer and V1 ) molar volume of solvent. Rearranging eq 9 gives [η]/Mw1/2) Kθ + 0.51φBMw1/2

(11)

Therefore, by plotting [η]/Mw1/2 against M1/2, long-range and short-range interactions can be separated from each other:24 the intercept Kθ is proportional to the characteristic ratio C∞, representing local conformational constraints; the slope

Figure 6. The Stockmayer-Fixman plot (eq 11) for HPG (MS ∼ 0.6) samples to determine the characteristic ratio. The intercept represents local conformational constraints of the polymer. The slope is a measure of the long-range interactions.

0.51φB is a measure of the long-range interactions. This plot is called the Stockmayer-Fixman plot25 and is done for the MS 0.6 HPG samples in Figure 6. The intercept (Kθ ) 3.19 × 10-4 m3/kg) gives a characteristic ratio of 13.02, assuming lo ) 0.54 nm and mo ) 322.6. This value is higher than our previous experimental result for natural guar (C∞ ) 11.87).13 Robinson et al. also reported a value of C∞ ) 12.6 for guar determined from light scattering and viscosity measurement.18 Compared to guar, the HPG chain is stiffer as the steric hindrance from the substituted groups will restrict the rotation of the polymer backbone bonds, resulting in a greater chain rigidity. This is also consistent with the intrinsic viscosity results that at high substitution level, the molecular volume of the HPG chain increases with degree of substitution. 4. Conclusions In this study, we explored the effect of hydroxypropyl substitution on the intermolecular interactions of guar galactomannan polymers by using dilute solution viscometry and GPC. Natural guar has a higher intrinsic viscosity and Huggins coefficient than the substituted guars. There are several competing forces in the guar and HPG systems. First, intermolecular hydrogen bonding provides an attractive force, tending to cause the chains to aggregate. The second opposing phenomenon is the steric effect from the hydroxypropyl side groups, which blocks hydrogen bonding of the mannose backbone units. The hydroxypropyl substitution increases the local chain rigidity and persistence length of the polymer. Finally, there is a hydrophobic effect between the substituted groups themselves, which is not important at room temperature but manifests itself at elevated temperatures and higher degrees of substitution. The experiments demonstrate three regimes: the first regime (0 < MS < ∼0.4) shows a sharp decrease in intermolecular interactions as a function of MS. In the second regime (∼0.4 < MS < ∼1.0), interactions are no longer a function of MS. In the third regime (MS > ∼ 1.0), inter- and intrahydrophobic effects can play a role at high temperatures (>40 °C). This is the first study to provide quantitative molecular data on the role of hydroxypropyl substitution and hydrogen bonding on dilute solution properties of guar gums. These interactions manifest themselves at higher concentration in

Interactions of Hydroxypropyl Guar Solutions

several ways. Cross-linking reactions are faster in guar than HPG solution, presumably due to increased interchain association for guar.26 Upon cooling, guar solutions become cloudy as hydrogen bonding causes microphase separation, whereas HPG solutions remain clear. Finally dissolution from the dry state should be more rapid for HPG than guar; however we are not aware of any carefully controlled experiments which demonstrate this effect. Acid hydrolysis of HPG (MS ∼ 0.6) provides HPG samples with a range of molecular weights from 68 000 to 1 900 000 and similar molecular weight distributions. The combination of intrinsic viscosity measurement and GPC allows for characterizing these samples and evaluating the MHS parameters for HPG (MS ∼ 0.6). The characteristic ratio C∞ of HPG was also estimated using the StockmayerFixman plot and compared with that of guar. The HPG molecule stiffens with increasing hydroxypropyl substitution. Acknowledgment. Support of this work by the National Science Foundation (NSFBES9711781) is gratefully acknowledged. References and Notes (1) McCleary, B. V.; Clark, A. H.; Dea, I. C. M.; et al. Carbohydr. Res. 1985, 139, 237. (2) Vijayendran, B. R.; Bone, T. Carbohydr. Polym. 1984, 4, 299. (3) Morris, E. R.; Cutler, A. N.; Ross-Murphy, S. B.; et al., Carbohydr. Polym. 1981, 1, 5. (4) Goycoolea, F. M.; Morris, E. R.; Gidley, M. J. Carbohydr. Polym. 1995, 27, 69. (5) Gidley, J. L.; Holditch, S. A.; Nierode, D. E.; et al. Recent AdVances in Hydraulic Fracturing; Society of Petroleum Engineers, Inc.: Richardson, TX, 1989.

Biomacromolecules, Vol. 3, No. 3, 2002 461 (6) Chatterji, J.; Borchardt, J. K. J. Pet. Technol. 1981, 33, 2042. (7) Gulbis, J. In ReserVoir Stimulation; Economides, M. J., Nolte, K. G., Eds.; Schlumberger Educational Services: Houston, TX, 1987. (8) McNeil, M.; Albersheim, P. Carbohydr. Res. 1984, 131, 131. (9) Reuben, J. Macromolecules 1985, 18, 2035. (10) Lapasin, R.; DeLorenzi, L.; Pricl, S.; et al. Carbohydr. Polym. 1995, 28, 195. (11) Bavouzet, B. Personal communication, 1994. (12) Gulbis, J.; Hodge, R. M. In ReserVoir Stimulation; Economides, M. J., Nolte, K. G., Eds.; John Wiley & Sons LTD: Chichester, England, 2000. (13) Cheng, Y.; Brown, K. M.; Prud’homme, R. K. Submitted to Int. J. Biol. Macromol. 2002. (14) Young, R. J.; Lovell, P. A. Introduction to Polymers; Chapman and Hall: New York, 1991. (15) Bohdanecky, M.; Kovar, J. Viscosity of Polymer Solutions; Elsevier Scientific Publishing Company: Amsterdam, 1982. (16) Flory, P. J. Principles of polymer chemistry; Cornell University Press: Ithaca, NY, 1953. (17) Grubisic, Z.; Rempp, P.; Benoit, H. Polym. Lett. 1967, 3, 753. (18) Robinson, G.; Ross-Murphy, S. B.; Morris, E. R. Carbohydr. Res. 1982, 107, 17. (19) Kato, T.; Okamoto, T.; Tokuya, T.; et al. Biopolymers 1982, 21, 1623. (20) Cheng, Y.; Rau, D. C.; Chik, J.; et al. Submitted to Macromolecules. (21) Winnik, F. M. Macromolecules 1987, 20, 2745. (22) Prudhomme, R. K.; Wu, G. W.; Schneider, D. K. Langmuir 1996, 12, 4651. (23) Tanford, C. The hydrophobic effect: formation of micelles and biological membranes; Wiley-Interscience: New York, 1973. (24) Elias, H.-G. Macromolecules; Plenum Press: New York, 1977. (25) Stockmayer, W. H.; Fixman, M. J. Polym. Sci., Part C: Polym. Symp. 1963, 1, 137. (26) Kramer, J. Ph.D. Thesis, Chemical Engineering, Princeton University, Princeton, NJ, 1987.

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