Rheological Comparison of Organogelators Based on Iron and

Mar 31, 2009 - Organogels were prepared from a 1:3 molar ratio of metal/ligand complexes of iron(III) or aluminum(III) with methyl dodecanephosphonic ...
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Rheological Comparison of Organogelators Based on Iron and Aluminum Complexes of Dodecylmethylphosphinic Acid and Methyl Dodecanephosphonic Acid† Gary P. Funkhouser,* Narongsak Tonmukayakul, and Feng Liang Halliburton Energy Services, 2600 S. 2nd Street, Duncan, OKlahoma 73533 Received December 31, 2008. Revised Manuscript Received February 23, 2009 Organogels were prepared from a 1:3 molar ratio of metal/ligand complexes of iron(III) or aluminum(III) with methyl dodecanephosphonic acid or dodecylmethylphosphinic acid at a concentration of 10 mM in dodecane. Gelation occurs spontaneously upon dissolution of the solid complex. Dynamic oscillatory measurements over the temperature range of 100-150 °C indicate that these materials behave as living polymers. Both reptation and reversible chain scission contribute to stress relaxation. The phosphonate ester complex gels are stronger than the corresponding dialkylphosphinate complex gels. Even at 150 °C, the phosphonate ester complexes maintained significant structure. Zero-shear viscosity activation energies are in the range of 26.5-61.2 kJ/mol, comparable to that for typical polymer melts.

Low-molecular-mass organogelators (LMOGs) are an interesting class of materials that gel organic solvents by self-assembling into 3D networks. Gel formation may result from a variety of interactions, including hydrogen bonding, π-π interaction, London dispersion forces, van der Waals forces, electrostatic interaction, and metal complexation. Many of the organogels are produced by a sol-gel process where the solution is cooled to form a fibrous network resulting in gelation. In some cases, the gel may be formed without the heating and cooling cycle by adding a solution of the gelator in a polar solvent.1,2 Spontaneous gelation may also be achieved by reacting two components in situ to form the required structure. Some examples of two-component gelators are alkylamine and carbon dioxide,3 dihydroxynaphthalene and sodium bis(2-ethylhexyl)sulfosuccinate,4 cholic acid ester and carbohydrate,5 and didodecylphosphoric acid and aluminum isopropoxide.6 Less common are materials that form gel networks upon heating, such as cobalt(II) triazole complexes.7 The rheological properties of organogels vary considerably. Many gels formed from crystalline networks are irreversibly destroyed by shear, resulting in a thin slurry.8 Temperature also has a strong influence on gel rheology. Gels formed from a solgel process generally do not persist to high temperature because of the redissolution of the gelator. Living polymers,9 or inverse rodlike micelles,10 can produce gels that recover from shear degradation. In certain applications, such as hydraulic fracturing † Part of the Gels and Fibrillar Networks: Molecular and Polymer Gels and Materials with Self-Assembled Fibrillar Networks special issue. *Corresponding author. E-mail: [email protected].

(1) Beginn, U.; Tartsch, B. Chem. Commun. 2001, 1924–1925. (2) Bhattacharya, S.; Krishnan-Ghosh, Y. Chem. Commun. 2001, 185–186. (3) George, M.; Weiss, R. G. Langmuir 2003, 19, 1017–1025. (4) Waguespack, Y. Y.; Banerjee, S.; Ramannair, P.; Irvin, G. C.; John, V. T.; McPherson, G. L. Langmuir 2000, 16, 3036–3041. :: (5) Willemen, H. M.; Vermonden, T.; Marcelis, A. T. M.; Sudholter, E. J. R. Langmuir 2002, 18, 7102–7106. (6) Page, M. G.; Warr, G. G. J. Phys. Chem. B 2004, 108, 16983–16989. (7) Kuroiwa, K.; Shibata, T.; Takada, A.; Nemoto, N.; Kimizuka, N. J. Am. Chem. Soc. 2004, 126, 2016–2021. (8) Terech, P.; Pasquier, D.; Bordas, V.; Rossat, C. Langmuir 2000, 16, 4485– 4494. (9) Terech, P.; Schaffhauser, V.; Maldivi, P.; Guenet, J. M. Langmuir 1992, 8, 2104–2106. (10) Shchipunov, Y. A.; Hoffmann, H. Rheol. Acta 2000, 39, 542–553. (11) Howard, G. C.; Fast, C. R. Hydraulic Fracturing; Monograph Series; Society of Petroleum Engineers of AIME: New York, 1970; Vol. 2, Chapter 1.

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in petroleum production,11 the gel must tolerate both shear and elevated temperature. Only a few types of organogels have been used in hydraulic fracturing, including aluminum soaps of fatty acids such as napalm12 and other long-chain fatty acids,13 aluminum and iron(III) phosphate diesters,14,15 and iron(III) alkanephosphonate monoesters.16 A common property of these materials is their ability to gel liquid hydrocarbons spontaneously by dissolving the complex or by forming the complex in situ. Whereas all of these materials form large aggregates resembling large inverse-rodlike micelles, the structure of the aluminum-fatty acid soap gels has some significant differences compared to that of the aluminum phosphate ester or aluminum phosphonate ester gels. The molar ratio of fatty acid to aluminum is 2:1 in the structure responsible for gelation, and water is required for gelation to occur.17,18 The long-range structure to form large aggregates was originally attributed to the linking of aluminum hydroxy di-soaps via bridging hydroxyls,19 and recent work indicates that long-range structure results from the aggregation of colloidal particles.20 In comparison, aluminum phosphate diester and aluminum alkylphosphonate monoester complexes that are useful as gelling agents have a ligand-to-metal molar ratio of 3:1 and do not require water to form the gel structure.6,21,22 All of the small-molecule organogelators used in hydraulic fracturing have two features in common: a large hydrocarbon group for oil solubility and two oxygen atoms for metal (12) Fieser, L. F.; Harris, G. C.; Hershberg, E. B.; Morgana, M.; Novello, F. C.; Putnam, S. T. Ind. Eng. Chem. 1946, 38, 768–773. (13) Clark, J. B. Treatment of Wells. U.S. Patent 2,596,844, 1952. (14) Monroe, R. F. Gelling Hydrocarbon Fluids with Combinations of Aluminum Alkyl Orthophosphates and Amines. U.S. Patent 3,575,859, 1971. (15) McCabe, M. A.; Norman, L. R.; Stanford, J. R. Method of Gelling Hydrocarbons and Fracturing Subterranean Formations. U.S. Patent 5,514,645, 1996. (16) Taylor, R. S.; Funkhouser, G. P. Methods and Compositions for Treating Subterranean Formations with Gelled Hydrocarbon Fluids. U.S. Patent 6,511,944, 2003. (17) McRoberts, T. S.; Schulman, J. H. Proc. R. Soc. London, Ser. A 1950, 200, 136–148. (18) Gilmour, A.; Jobling, A.; Nelson, S. M. J. Chem. Soc. 1956, 1972–1976. (19) Gray, V. R.; Alexander, A. E. J. Phys. Chem. 1949, 53, 23–38. (20) Wang, X.; Rackaitis, M. J. Colloid Interface Sci. 2009, 331, 335–342. (21) George, M.; Funkhouser, G. P.; Weiss, R. G. Langmuir 2008, 24, 3537– 3544. (22) Fukasawa, J.-I.; Tsutsumi, H. J. Colloid Interface Sci. 1991, 143, 69–76.

Published on Web 03/31/2009

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Figure 1. Organogelators used in hydraulic fracturing: (a) fatty acid, (b) orthophosphoric acid diester, and (c) alkanephosphonic acid monoester. R0 is typically smaller than R. (d) Dialkylphosphinic acid, although not used in fracturing, has similar structural features. Scheme 1

Figure 2. Potential bonding configurations between phosphorus ligands and metal, where R = C12H25, X = OCH3 or CH3, and M = Al(III) or Fe(III): (a) pendant monodentate, (b) chelating monodentate, (c) bridging bidentate, and (d) possible segment of a polymeric structure.

Experimental Procedures

complexation (Figure 1). In the case of phosphoric acid diesters and alkanephosphonic acid monoesters, one more alkyl group is used to cap the extra acid functionality that would interfere with gelation. This second alkyl group is typically small to avoid steric interference in the metal complexation.23,24 Dialkylphosphinic acids also have the features of hydrocarbon groups for oil solubility and two oxygen atoms available for metal complexation, making them potential candidates for use in hydraulic fracturing. Bis(2,2,4-trimethylpentyl)phosphinic acid in a hydrocarbon solvent is a common metal extractant25 demonstrating two features necessary for gelation: oil solubility and metal complexation. In the case of bis(2,2,4-trimethylpentyl) phosphinic acid, steric bulk likely interferes with its ability to form the large aggregates necessary for gelation. However, many other dialkylphosphinic acids form large aggregates (coordination polymers) with metals through tetrahedral26,27 or octahedral coordination.28 Here, we compare the high-temperature rheological properties of gels prepared from aluminum and iron(III) complexes of methyl dodecanephosphonic acid and dodecylmethylphosphinic acid (Scheme 1) in dodecane. These complexes all formed clear, colorless gels upon dissolution at ambient temperature. By using the same alkyl groups on both ligands, the differences in performance can be attributed to metal-ligand interactions with minimal influence from steric effects. This research expands upon the rheological characterization of metal-phosphorus ligand organogels performed by our group21,24,29,30 and others.6,22,26,27,31 (23) Crawford, D. L.; Earl, R. B.; Monroe, R. F. Friction Reducing and Gelling Agent for Organic Liquids. U.S. Patent 3,757,864, 1973. (24) Funkhouser, G. P.; Taylor, R. S. Tekna 2004 International Oil Field Chemistry Symposium, Geilo, Norway, March 28-31, 2004; paper 22. (25) Danesi, P. R.; Reichley-Yinger, L.; Mason, G.; Kaplan, L.; Horwitz, E. P.; Diamond, H. Solvent Extr. Ion Exch. 1985, 3, 435–452. (26) Rose, S. H.; Block, B. P. J. Am. Chem. Soc. 1965, 87, 2076–2077. (27) Crescenzi, V.; Giancotti, V.; Ripamonti, A. J. Am. Chem. Soc. 1965, 87, 391–392. (28) Saraceno, A. J. Coordination Polymers Involving Doubly Bridged Trivalent Octahedral Metals. U.S. Patent 3,275,574, 1966. (29) George, M.; Funkhouser, G. P.; Terech, P.; Weiss, R. G. Langmuir 2006, 22, 7885–7893. (30) Grady, B. P.; Ghosh, A.; Funkhouser, G. P. Petroleum Society’s 8th Canadian International Petroleum Conference (58th Annual Technical Meeting), Calgary, Alberta, Canada, June 12-14, 2007; paper 2007-013. (31) Kim, V.; Bazhenov, A. V.; Kienskaya, K. I. Colloid J. 1997, 59, 455–460.

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General Methods. NMR spectra were determined on a Bruker Avance 300 MHz spectrometer using tetramethylsilane and orthophosphoric acid (external) references for 1H and 31P, respectively. Infrared spectra were recorded on a Nicolet 6700 FT-IR spectrophotometer fitted with a Thermo Scientific Smart iTR diamond ATR cell. Materials. 2-Propanol (99.5%), aluminum isopropoxide (99.99%), tetrahydrofuran (99.9%), triethylamine (99%), iron (III) chloride (97%), dimethyl phosphite (98%), t-butyl peroxide (98%), hexamethyldisilazane (97%), and iodomethane (99%) were obtained from Aldrich. Acetonitrile (ACS reagent), dichloromethane (HPLC grade), and hexanes (HPLC grade) were obtained from Fisher. Technical grade 1-dodecene was obtained from Chevron Phillips. Technical grade dodecane (Norpar 12) was obtained from Exxon Mobil. Dichloromethane and dodecane were dried over 4 A˚ molecular sieves. All other materials were used as received. Methyl Dodecanephosphonic Acid (1). CAS 388625-44-3 was synthesized in a similar manner to methyl hexadecanephosphonic acid, reported previously,32 with the modification of extending the refluxing time from 3 to 24 h. The product was recrystallized twice from hexanes to remove the side product resulting from dimethyl phosphite free-radical addition to the C-2 position of the R-olefin. 1H NMR (CDCl3, 300 MHz): δ 0.88 (t, 3 H, J = 6.7 Hz), 1.16-1.44 (m, 18 H, CH2), 1.53-1.82 (m, 4 H, CH2), 3.72 (d, 3 H, JH-P = 11.0 Hz, OCH3). 31P NMR (CDCl3, 121 MHz): δ 37.13. Dodecylphosphinic Acid. Sodium dodecylphosphinate was prepared from 1-dodecene and sodium hypophosphite using a procedure reported by Stiles et al.33 The salt was shaken with excess 1 M hydrochloric acid, extracted into hexanes, and dried over anhydrous magnesium sulfate. The solvent was removed on a rotary evaporator to give the product as a white solid (87% yield), which was used without further purification. The product contained approximately 9% dialkylphosphinic acid as indicated by 31P NMR. Dodecylmethylphosphinic Acid (2), [CAS 13176-16-4]. A 500 mL round-bottomed flask (flame-dried) was charged with 11.70 g (0.05 mol) of dodecylphosphinic acid. The flask was fitted with a Claisen head, septum stopper, reflux condenser, and nitrogen purge. Anhydrous dichloromethane (50 mL) was added, and the mixture was cooled in an ice bath and stirred. Hexamethyldisilazane (8.614 g, 0.0535 mol) was added, and the flask was warmed to room temperature. The mixture was heated to reflux for 2 h. Ammonia evolved, and the white solid dissolved. The flask was cooled in an ice bath and 3.33 mL (0.0535 mol) of iodomethane was added. The flask was warmed to ambient temperature and stirred for 3 days. The white precipitate was removed by vacuum filtration. The filtrate was shaken with 250 mL of 1 M hydrochloric acid to liberate dodecylmethylphosphinic acid. The solution was dried over (32) Dickert, J. J., Jr.; Rowe, C. N. Lubricating Compositions Containing Metal Phosphonates. U.S. Patent 3,798,162, 1974. (33) Stiles, A. R.; Harman, D.; Rust, F. F. Preparation of Phosphorus-Containing Organic Compounds. U.S. Patent 2,724,718, 1955.

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Figure 3. Storage and loss moduli of dodecane containing 10 mM iron(III)-phosphonate ester complex (5) over the temperature range of 100-150 °C.

Figure 4. Storage and loss moduli of dodecane containing 10 mM aluminum-phosphonate ester complex (3) over the temperature range of 100-150 °C.

anhydrous magnesium sulfate, and the solvent was removed on a rotary evaporator to give the crude product as a waxy yellow solid (95%). The product was distilled in a sublimation apparatus at 180 °C and 0.02 Torr to remove the didodecylphosphinic acid carried over from the dodecylphosphinic acid synthesis. 1H NMR (CDCl3, 300 MHz): δ 0.88 (t, 3 H, J = 6.7 Hz, CH3), 1.20-1.42 (m, 18 H, CH2), 1.46 (d, 3 H, JH-P = 13.9 Hz, PCH3), 1.52-1.78 (m, 4 H, CH2). 1:3 Aluminum/Methyl Dodecanephosphonate Complex (3). A 25 mL round-bottomed flask was charged with 2.644 g (10 mmol) of methyl dodecanephosphonic acid (1), 0.682 g (3.33 mmol) of aluminum isopropoxide, and 20 mL of 2propanol under a nitrogen atmosphere. The flask was fitted with a reflux condenser and a drying tube containing 4 A˚ molecular sieves. The mixture was stirred magnetically and heated to reflux for 1 h, resulting in a large volume of white solid. The alcohol was removed under a stream of dry nitrogen, followed by vacuum. IR ν 2921, 2851, 1466, 1407, 1378, 1350, 1166, 1103, 1050, 824, 772, 720, 599 cm-1. 1:3 Aluminum/Dodecylmethylphosphinate Complex (4). This complex was prepared from 2 using a similar procedure as for complex 3. IR ν 2920, 2852, 1466, 1417, 1378, 1288, 1150, 1084, 890, 806, 757, 721 cm-1. 1:3 Iron(III)/Methyl Dodecanephosphonate Complex (5). A 25 mL round-bottomed flask was charged with 2.644 g (10 mmol) of methyl dodecanephosphonic acid (1), 0.541 g (3.33 mmol) of iron(III) chloride, and 20 mL of tetrahydrofuran. The flask was fitted with a Claisen head with septum, a reflux condenser, and a drying tube containing 4 A˚ molecular sieves. The opaque brown mixture was stirred magnetically, and 1.4 mL (10 mmol) of triethylamine was added dropwise over a 2 h period. White precipitate formed upon addition of triethylamine. The mixture was heated to reflux for 1 h and cooled, resulting in a viscous, opaque, light-yellow liquid. The product was isolated by precipitating in acetonitrile. Triethylamine hydrochloride was removed by dissolving the product in tetrahydrofuran (1 g/100 mL) and precipitating the product by dropwise addition to an equal volume of acetonitrile. The solvent was decanted off and replaced with fresh acetonitrile and stirred overnight. The solid was isolated and dried under vacuum to yield a light-pink rubbery solid. IR ν 2921, 2851, 1466, 1404, 1378, 1189, 1112, 1076, 1040, 822, 768, 720, 585 cm-1.

1:3 Iron(III)/Dodecylmethylphosphinate Complex (6). This complex was prepared from 2 using a similar procedure as for complex 5. IR ν 2921, 2852, 1466, 1418, 1378, 1287, 1104, 1049, 890, 804, 754, 721 cm-1. Gel Preparation. A 60 mL glass jar was charged with 0.50 mmol of metal complex and 50 mL of dodecane. A magnetic stir bar was added for improved agitation, and the jar was shaken on a wrist-action shaker for 1 to 3 days to produce a clear, colorless gel. Rheological Experiments. Rheological measurements were performed on a Stresstech-HR controlled stress rheometer (Reologica, Inc., Lund, Sweden) fitted with a pressurized cell (sealed-cell) concentric cylinder system, which has an inner cylinder rotating in a stationary outer cylinder. The cup (Ro) and bob (Ri) radii are 13.44 and 12.51 mm, respectively, and the length is 38.1 mm. A thermostatically controlled resistance heating jacket was used to maintain the desired sample temperature. Rheological measurements were carried out at six different temperatures ranging from 100 to 150 °C at intervals of 10 °C. A sealed cell was used to avoid solvent evaporation that would occur over time in an open cell at elevated temperature. Although increased pressure is not necessary to maintain a single-phase sample up to the boiling point of dodecane (approximatey 215 °C), a cell pressure of 2 bars (gauge) was applied with nitrogen for proper operation of the sealed-cell air bearing. The torque map procedure was performed prior to the rheological measurements to check for misalignment of the bob shaft in the sealed-cell air bearing and verify that the inherent contribution of the additional air bearing is low enough to maintain a linear response down to the low-frequency end of the oscillation spectrum. The sample was loaded at ambient temperature and heated to 100 °C without shearing. Heating was continued at this temperature for at least 30 min to ensure that the whole sample reached a state of thermal equilibrium and to eliminate any stress in the sample due to loading. The sample was then subjected to a series of small-amplitude oscillatory sweep (SAOS) tests at various temperatures. With each temperature change, a 10 min equilibration time was employed to attain thermal equilibrium and residual stress relaxation prior to SAOS measurement. Stress sweep experiments were initially performed on the sample at 100 and 150 °C to determine the linear viscoelastic region where the moduli are independent of stress, and SAOS experiments were subsequently carried out within the linear region. It

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Figure 5. Complex viscosity of dodecane containing 10 mM aluminum-phosphonate ester complex (3) over the temperature range of 100-150 °C.

Figure 6. Zero-shear viscosity of the iron-phosphonate ester (b), aluminum-phosphonate ester (9), iron-phosphinate (O), and aluminum-phosphinate (0) gels as a function of temperature. 00

(η*o),

Table 1.0 Zero-Shear Viscosity Entanglement Distance (ξ), 00 G min/G P, and Scission Rate (kbr) for Gels of the 10 mM Metal Complex in Dodecane at 100 °C metal complex

(η*o), Pa 3 s

1:3 aluminum/phosphonate ester (3) 1:3 iron(III)/phosphonate ester (5) 1:3 aluminum/phosphinate (4) 1:3 iron(III)/phosphinate (6)

472 1073 608 34.6

Ea, kJ/mol

00

Gmin / 0 kbr, s-1 ξ, nm GP 54.0 54.0 53.6 54.3

0.030 0.025 0.125 0.134

1.9 2.3 5.6 3.7

was found that the stress of 1.0 Pa is sufficient to cover the frequency region from 0.05 to 50 rad/s over the entire temperature range.

Results and Discussion Gelation Studies. Clear, colorless gels were prepared from approximately 10 mM solutions of a 1:3 molar ratio of metal/ ligand complexes (3-6) in dodecane at ambient temperature. Three possible metal-ligand bonding configurations are shown in Figure 2. Only structure c, where one ligand bridges two metal atoms, has the potential to form a polymeric species large enough to alter the solution rheology significantly. The bidentate bridging structure has been established for an iron(III)/ phosphonate ester complex30 and various metal/phosphinate complexes.26,27 Similar structures have been reported for aluminum/dialkylphosphate complexes22,34,35 and rare earth/dialkylphosphate complexes.36 The gel rheology should depend strongly on the length of the polymer chains, the ratio of bridging to nonbridging ligands, and the strength of the metal-ligand bond. Dynamic Oscillatory Behavior. Dynamic moduli were measured as a function of frequency, and the behavior of the storage (G0 ) and loss (G00 ) moduli of the iron phosphonate ester (34) Florjanczyk, Z.; Wolak, A.; Debowski, M.; Plichta, A.; Ryszkowska, J.; Zachara, J.; Ostrowski, A.; Zawadzak, E.; Jurczyk-Kowalska, M. Chem. Mater. 2007, 19, 5584–5592. (35) Florjanczyk, Z.; Lasota, A.; Wolak, A.; Zachara, J. Chem. Mater. 2006, 18, 1995–2003. (36) Trifonov, Y. I.; Legin, E. K.; Suglobov, D. N. Process Metall. 1992, 7A, 279–284.

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Table 2. Zero-Shear Viscosity (η*o), Entanglement Distance (ξ), Gmin/ 0 GP, and Scission Rate (kbr) Activation Energies for Gels of the 10 mM Metal Complex in Dodecane 00

0

metal complex

η*o

ξ

Gmin/GP

kbr

1:3 aluminum/phosphonate ester (3) 1:3 iron(III)/phosphonate ester (5) 1:3 aluminum/phosphinate (4) 1:3 iron(III)/phosphinate (6)

46.3 39.3 61.2 26.5

3.6 1.7 4.2 4.3

27.2 21.0 23.8 24.8

15.0 11.4 6.6 17.4

complex (5) gel at 100, 130, and 150 °C is shown in Figure 3. The experimental results show two distinct trends in the moduli with respect to frequency. Solution-like behavior (G00 > G’) is observed in the lower-frequency range, but at higher frequencies, G0 is greater than G00 , which is consistent with gel-like behavior. Although not true gels as defined by Winter and Chambon,37 this type of material is commonly referred to as a gel.0 6 At high frequencies, G0 displays a characteristic plateau loss modulus (GP) region, and as the frequency is increased, the 00 decreases0 0 noticeably 0from a local maximum (Gmax) to a minimum (Gmin). The GP behavior is typical of a “strong gel” material that is observed when the characteristic relaxation time of the material is longer than the process time, that is, the time 0 per cycle of oscillation. The magnitude of GP shifts slightly to lower values with increasing temperature, indicating that the number of intermolecular association sites decreases as temperature increases. Because the polymer concentration is constant, temperature-induced chain scission is expected to be 0 00 responsible for the decrease in GP. Gmax decreases only slightly with increasing temperature over the range of temperature 00 tested, whereas the magnitude of Gmin increases rapidly with increasing temperature. The minimum loss modulus is more pronounced at 100 °C, and as the temperature increases, the depth of the minimum decreases. At high frequencies, the loss modulus shows a characteristic upturn from its minimum value that is attributed to a change in the dominant relaxation mechanism from reptation to chain scission at shorter time scales. Similar dynamic oscillatory behavior as a function of (37) Winter, H. H.; Chambon, F. J. Rheol. 1986, 30, 367–382.

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Figure 7. Effect of temperature on the average distance between the chain-chain entanglement (ξ) for gels of iron-phosphonate ester (b), aluminum-phosphonate ester (9), iron-phosphinate (O), and aluminum-phosphinate (0).

00

0

Figure 8. Effect of temperature on the ratio of Gmin/GP for gels of the iron-phosphonate ester (b), aluminum-phosphonate ester (9), iron-phosphinate (O), and aluminum-phosphinate (0).

temperature was also observed for gels of the aluminumphosphonate ester complex (3), aluminum-phosphinate complex (4), and iron(III)-phosphinate complex (6). The crossover frequency (ωc) of the storage and loss moduli increases with increasing temperature, which is a consequence of a decreasing relaxation time of the material with increasing temperature. The observed dynamic behavior of these metal complex gels is very (38) Goldstein, A. M.; Alter, E. N. In Industrial Gums; Whistler, R. L, Ed.; Academic Press: New York, 1979; Chapter 14. (39) Shay, G. D. In Polymers in Aqueous Media: Performance Through Association; Glass, J., Ed.; Advances in Chemistry Series No. 223; American Chemical Society: Washington, DC, 1989; Chapter 25, p 223.

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Figure 9. Effect of temperature on the micellar breaking rate (kbr) for gels of the iron-phosphonate ester (b), aluminum-phosphonate ester (9), iron-phosphinate (O), and aluminum-phosphinate (0).

similar to that of cross-linked water-swellable polymer (aqueous gel) systems38-40 and that of both aqueous and nonaqueous selfassembled surfactant systems.41-43 Dynamic oscillatory results obtained with the aluminumphosphonate ester complex (3) at 100, 130, and 150 °C are shown in Figure 4. This gel has similar dynamic oscillatory behavior to that of the iron-phosphonate ester complex (5) gel. At 100 °C, 0 the results reveal that values of the GP modulus of the aluminum and iron(III) phosphonate ester gels are similar at 55 Pa, which indicates that the intrinsic network structure of both gels is the same. However, at higher0 temperatures, a comparison of the 00 results reveals that the GP, ωc, and Gmin of the aluminumphosphonate ester gel are more sensitive to temperature than are those of the iron-phosphonate ester gel. The complex viscosities (η*) of all four metal complex gels (e.g., the aluminum-phosphonate ester, Figure 5) exhibit a frequency-independent complex viscosity at lower frequencies and a shear-thinning complex viscosity at higher frequencies, consistent with the behavior often observed with polymeric solutions, polymer melts, and self-assembled surfactant systems. Furthermore, these materials display a broader Newtonian range as temperature increases. Increasing temperature is expected to both reduce the time scale of the interactions between the polymer chains and decrease the number of intermolecular association sites, causing the entangled network to relax faster at high temperatures. Faster relaxation extends the frequency-independent viscosity range to higher frequency. The dynamic oscillatory behavior cannot be fitted to a model simply on the basis of reptation. However, it may be explained using the structural kinetics of the reversible micelles approach developed by Cates,41,44,45 which has been successfully (40) Kesavan, S.; Prud’homme, R. K. Macromolecules 1992, 25, 2026–2032. (41) Cates, M. E.; Candau, S. J. J. Phys.: Condens. Matter 1990, 2, 6869–6892. (42) Shikata, T.; Hirata, H.; Kotaka, T. Langmuir 1987, 3, 1081–1086. (43) Koehler, R. D.; Raghavan, S. R.; Kaler, E. W. J. Phys. Chem. B 2000, 104, 11035–11044. (44) Cates, M. E. Macromolecules 1987, 20, 2289–2296. (45) Cates, M. E. J. Phys.: Condens. Matter 1996, 8, 9167–9176.

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employed for rod-like micellar surfactant systems.41,43,45,46 This model postulates that the change in the dynamic oscillatory properties is associated with scission and recombination processes of micelles in the surfactant systems in addition to 0 reptation. The magnitude of GP corresponds to the intrinsic mesh size, or the average distance between the chain-chain entanglement (ξ).47 The relationship can be expressed as ξ3 ≈ 0 kBT/GP, where kB is the Boltzmann constant and T is the sample temperature in Kelvin. The frequency (ω) at which the loss 00 modulus shows an upturn from its minimum value (Gmin) is related to the micellar breaking rate (kbr).41,48 The entanglement length (le) and contour length (Lh) are related by the equation 00 0 Gmin/GP ≈ le/Lh.43 The entanglement length is a function of ξ and the persistence length of the micelles (lp). The persistence length is related to the flexibility of the micelles and is typically determined using either small-angle neutron scattering (SANS) or light scattering, depending on the nature of the measured system.43 However, the lack of a constant lp in these materials complicates the calculation of the polymer contour length (Lh). Therefore, only qualitative trends in Lh can be identified by assuming that the polymer contour length is inversely propor00 0 00 0 tional to Gmin/GP. Values of ξ, Gmin/GP, and kbr at 100 °C for the metal complex gels are displayed in Table 1. Data reported for a 1.5% aqueous wormlike micellar solution at 25 °C43 00 0 was used to calculate ξ, Gmin/GP, and kbr and compare to the values for the metal complex gels at 100 °C. Entanglement lengths (∼90 nm) were higher in the aqueous fluid than in the 00 0 metal complex gels. Gmin/GP for the aqueous system (∼0.06) was between the corresponding values for the metal-phosphonate ester complexes and the metal-phosphinate complexes. However, the breaking rates for the metal complex gels are approximately 10 times higher than for the aqueous system. A complete 0 00 00 list of GP, Gmax, Gmin, their corresponding frequencies, and crossover frequencies as a function of temperature for the metal complex gels are reported in Supporting Information Tables I-IV. The structure of the metal complexes should all be similar, with both aluminum(III) and iron(III) capable of octahedral coordination, and both dodecylmethylphosphinate and methyl dodecanephosphonate can be bidentate ligands. Differences among the metal complexes may arise when the ratio of0 0bridging 0 to nonbridging ligands is different. For example, Gmin/GP is substantially higher for the phosphinate complexes than for 00 0 the phosphonate ester complexes. Higher Gmin/GP is consistent with a longer le or shorter Lh. A higher fraction of nonbridging ligands will make the chain more flexible (decreased lp) with a looser mesh (le > ξ), compared to a chain with all bridging ligands. A high fraction of nonbridging ligands may also decrease the degree of polymerization, therefore shortening Lh. Zero-shear viscosity (η*o) of these gels decreases dramatically with increasing temperature. Figure 6 shows the zero-shear viscosity of all four organogels plotted as a function of reciprocal temperature. The lower strength of the metal-phosphinate complex gels limited the rheology measurements to a narrower temperature range. The experimental results for each organogel can be satisfactorily fitted by an Arrhenius-type equation, log η*o= Ae(Ea/RT), where η*o is the zero-shear complex viscosity, T is (46) Koehler, R. D.; Kaler, E. W. In Structure and Flow in Surfactant Solutions; Herb, C. A., Prud’homme, R. K., Eds.; ACS Symposium Series 578; American Chemical Society: Washington, DC, 1994; pp 2-31. (47) Doi, M.; Edwards, S. F. The Theory of Polymer Dynamics; Oxford University Press: New York, 1986. (48) Granek, R.; Cates, M. E. J. Chem. Phys. 1992, 96, 4758–4767.

Langmuir 2009, 25(15), 8672–8677

Article

the absolute temperature, Ea is the activation energy, A is a preexponential factor, and R is the universal gas constant. Zeroshear viscosity activation energies of the metal complex gels (Table 2) are in the range of typical polymer melts.49 Unlike conventional polymers, the metal complex polymers are a living system and do not have a constant degree of polymerization with temperature. Previous work with an iron-phosphonate ester complex showed that the bridging ligand (Figure 2c) was more stable than the nonbridging chelating form (Figure 2b).30 Under equilibrium conditions, the fraction of nonbridging ligands will increase with increasing temperature. Increasing the fraction of nonbridging ligand in the complex lowers the degree of polymerization, resulting in even faster relaxation and a decrease in 0 GP. The “energy of activation” of the zero-shear viscosity is likely a composite of the temperature dependence of reptation, degree of polymerization, chain flexibility, and rate of chain scission. Arrhenius-type behavior is shown for the0 average distance 00 between the entanglement points (ξ), Gmin/GP, and the rate of chain scission (kbr) (Figures 7-9, Table 2). The degree0 0 of polymerization affects Lh, which influences both ξ0 and Gmin/ 0 00 GP. The temperature dependence of ξ and Gmin/GP is due, in part, to changes in the degree of polymerization as a function of temperature, resulting from changes in the relative fractions of bridging and nonbridging ligands. The temperature dependence of kbr should be more like conventional Arrhenius behavior, with Ea related simply to the transition-state energy of the metal-bridging ligand bond breaking.

Conclusions High-temperature dynamic oscillatory measurements show that the metal complex organogels exhibit frequencydependent solution-like and gel-like characteristics consistent with a living polymer. The rheological properties of these samples depend on temperature and the particular metal-ligand combination. On the basis of the Cates model, we found that both the distance between entanglement points (ξ) and the rate of chain scission (kbr) increased with increasing temperature while the polymer contour length (Lh) decreased. These findings are particularly important because ξ, Lh, and kbr control the intrinsic physical properties of the samples, especially the relaxation time and the strength of the network structure. Consequently, the material relaxes more easily, and its network strength decreases as temperature increases. Finally, the measurements show that the phosphonate ester complex gels are stronger than the corresponding dialkylphosphinate complex gels. Even at 150 °C, the phosphonate ester complexes maintained significant structure. The differences in rheological properties among the various metal complexes appear to be a function of the equilibrium concentrations of bridging and nonbridging ligands and the rates of interconversion between bridging and nonbridging. Acknowledgment. We thank Halliburton Energy Services for permission to publish this work. 0

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Supporting Information Available: GP, Gmax, and Gmin, their corresponding frequencies, and the crossover frequency as a function of temperature. This material is available free of charge via the Internet at http://pubs.acs.org. (49) Arnett, R. L.; Thomas, C. P. J. Phys. Chem. 1980, 84, 649–652.

DOI: 10.1021/la8043329

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