Structure Studies of Poly(diallyldimethylammonium chloride-co

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Langmuir 1998, 14, 4350-4358

Articles Structure Studies of Poly(diallyldimethylammonium chloride-co-acrylamide) Gels/Sodium Dodecyl Sulfate Complex Fengji Yeh, Eugene L. Sokolov, Thomas Walter, and Benjamin Chu* Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York 11794-3400 Received September 10, 1997. In Final Form: April 15, 1998 Cationic poly(diallyldimethylammonium chloride) (PDADMACl)-polyacrylamide polyelectrolyte copolymer gels have been synthesized by free radical copolymerization with various degrees of cross-linking over a range of charge densities. The polyelectrolyte gels and an oppositely charged surfactant, sodium dodecyl sulfate (SDS), associate to form complexes even when the SDS concentration in the external solution which is in equilibrium with the polyelectrolyte gel is below the critical micelle concentration (cmc). Small-angle neutron scattering (SANS) and small-angle X-ray scattering (SAXS) have been used to study the structure of the polyelectrolyte gels and the gel/surfactant complex, respectively. SANS results of PDADMACl gels with various degrees of cross-linking suggest that the static concentration fluctuations induced by the cross-links are about 2 orders of magnitude larger than the dynamic solution concentration fluctuations. SAXS results on the spatial arrangements of the PDADMACl-SDS complex suggest a hexagonal supramolecular structure in the gel phase. The intercylinder distance d of the superstructures in the gel phase is estimated from the primary diffraction peak with d ) 37 Å. It is surprising that the degree of cross-linking (up to 12 mol %) of PDADMACl gels has no effect on the structure of the complex, due probably to the compensating effects on the mesh size of the collapsed gel with different degrees of crosslinking and to the large spatial inhomogeneity inside the gels. The ordered supramolecular structure is not observed in the PSC when the initial external SDS concentration is above its cmc.

Introduction Polymer gels have captured the intense interest of polymer scientists in recent decades. The polyelectrolyte gel in which the polymer chains contain charged groups on the backbone or on the side chains represents one of the most important members in the polymer gel family. The charged polymer network is superabsorbent, and able to absorb and hold large amounts of water or fluid and to undergo sharp volume transitions induced, for example, by small changes in pH, solvent quality, temperature, and electric field1-5 or by the presence of low molecular weight salts, such as halides6,7 and surfactants.8,9 These polymeric materials have found extensive commercial applications as sorbents in personal care products such as infant diapers, feminine hygiene products, and incontinence products.10,11 In addition, they have also received * To whom correspondence should be addressed. (1) Tanaka, T. Phys. Rev. Lett. 1978, 40, 820. (2) Siegel, R. A.; Firestone, B. A. Macromolecules 1988, 21, 3254. (3) Tanaka, T.; Fillmore, D. J.; Sun, S. T.; Nishio, L.; Swislov, G.; Shah, S. Phys. Rev. Lett. 1978, 45 (20), 1636. (4) Ohmine, I.; Tanaka, T. J. Chem. Phys. 1982, 77, 5725. (5) Osada, Y.; Kishi, R. J. Chem. Soc., Faraday Trans. 1989, 85, 655. (6) Kudo, S.; Kosaka, N.; Konno, M.; Saito, S. Polymer 1992, 33 (23), 5040. (7) Starodoubtsev S. G.; Khokhlov A. R.; Sokolov E. L.; Chu B.; Macromolecules 1995, 28, 3930. (8) Ibragimova, Z. Kh.; Kasaikin, V. A.; Zezin, A. B.; Kabanov, V. A. Polym. Sci., 1986, 28, 1826. (9) Vasilevskaya, V. V.; Rayabina, V. A.; Starodubtsev, S. G.; Khokhlov, A. R. Polym. Sci. 1989, 31, 784. (10) Gross, J. R. In Absorbent Polymer Technology; Brannon-Peppas, L., Harland, R. S., Eds.; Elsevier Science Publishing Company Inc.: New York, 1990; pp 3-22.

considerable attention for a variety of more specialized applications including matrixes for enzyme immobilization,12 biosorbents in preparative chromatography,12 materials for agricultural mulches,13 and matrixes for controlled release devices.14 The interactions between polyelectrolytes and low molecular weight molecules such as simple inorganic salts4,15 and charged surfactants8,9,16 have been intensively studied during the past few decades. The volume transition of the polyelectrolyte network depends strongly not only on the oppositely charged ions of the salts6 but also on the valency of the ions.4 Electrostatic interactions between the charges and hydrophobic interactions between the polymer backbone and the surfactants are dominant interactions between polyelectrolyte gels and oppositely charged surfactants.17-20 The strong interac(11) Buchholz, F. L. In Absorbent Polymer Technology; BrannonPeppas, L., Harland, R. S., Eds.; Elsevier Science Publishing Company Inc.: New York, 1990; pp 23-44. (12) Samsonov, G. V.;. Kuznetsova, N. P. Adv. Polym. Sci. 1992, 104, 1. (13) Kazanskii, K. S.; Dubrovskii, S. A. Adv. Polym. Sci. 1992, 104, 97. (14) Colombo, P. Adv. Drug Delivery Rev. 1993, 11, 37. (15) Ricka, J.; Tanaka, T. Macromolecules 1985, 18, 83. (16) Goddard, E. D.; Hannan, R. B. J. Colloid Interface Sci. 1976, 55, 73. (17) Thanh, L. M.; Makhaeva, E. E.; Starodubtsev, S. G. Polym. Sci., Ser. A 1993, 35, 476. (18) Okuzaki, H.; Ossda, Y. Macromolecules 1994, 27, 502,. (19) Khandurina, Yu. V.; Rogacheva, V. B.; Zezin, A. B.; Kabanov, V. A. Polym. Sci. 1994, 36, 184. (20) Yeh, F.; Sokolov, E. L.; Khokhlov, A. R.; Chu, B. J. Am. Chem. Soc. 1996, 118, 6615.

S0743-7463(97)01028-7 CCC: $15.00 © 1998 American Chemical Society Published on Web 07/17/1998

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tions induce complex formation at very low surfactant concentrations, commonly known as the critical aggregation concentration (cac),21 which is usually orders of magnitude lower than the critical micelle concentration (cmc) of the free surfactant solution. The aggregation of surfactant in the gel network changes the osmotic pressure inside the network and causes the gel to shrink and finally collapse.8,9 The resulting polymer-surfactant complexes (PSCs) were shown to be a new class of polymer colloids. Ordered supramolecular structures formed in the complexes of the polyelectrolyte gel and the oppositely charged surfactant havd been reported.20,22-26 It is surprising that highly ordered supramolecular structures are formed in the presence of a random polymer network. Furthermore, the crystal structures are not sensitive to the degree of cross-linking in the polyelectrolyte gels; even the size of the crystalline domain is larger than the average mesh size of the polymer network.20 In this work, efforts have been made to examine the effects of the degree of cross-linking in forming the ordered structures in the PSC. The cationic poly(diallyldimethylammonium chloride)/polyacrylamide copolymer gels were studied by small-angle neutron scattering (SANS). In addition, the interaction between the cationic copolymer gels (PDADMACl/PAAm) and the anionic surfactant (sodium dodecyl sulfate), as well as the supramolecular structures of these gel-surfactant complexes, is investigated by small-angle X-ray scattering (SAXS). Theoretical Background of SANS For neutral polymer solutions in the semidilute regime, the elastic scattered intensity is given by a Lorentzian equation (or the Ornstein-Zernike equation)27

I(q) )

I(0) (1 + ξ2q2)

for ξq < 1

(1)

and

I(q) ) (ξq)-1/vF

for ξq > 1

(2)

where ξ is the correlation length and vF is the Flory excluded volume exponent, with vF ) 3/5 for good solvent, vF ) 1/2 for poor solvent. When cross-links are introduced into these polymer solutions, the concentration fluctuations are perturbed due to the cross-link formation. An exact solution for the scattering function from gels has not yet been achieved because of the complexity and the variety of cross-link formation. However, several scattering functions have been proposed. Geissler et al.28 tried to separate the scattering intensity function into two contributions, i.e., the solution-like and the solid-like concentration fluctuations. The solution-like concentration fluctuation was assumed to be the same as the corresponding polymer solution and is of the form of eq 1. The solid-like concentration fluctuation was caused by (21) Chu, D.; Thomas, J. K. J. Am. Chem. Soc. 1986, 108, 6270. (22) Ilavsky, M.; Sedla´kova´, Z.; Bouchal, K.; Pleˇtil, J. Macromolecules 1995, 28, 6835. (23) Khandurina, Yu. V.; Dembo, A. T.; Rogacheva, V. B.; Zezin, A. B.; Kabanov, V. A. Polymer Sci. 1994, 36, 189. (24) Okuzaki, H.; Osada, Y. Macromolecules 1995, 28, 380. (25) Chu, B.; Yeh, F.; Sokolov, E. L.; Starodubtzev, S. G.; Khokhlov, A. R. Macromolecules 1995, 28, 8447. (26) Sokolov, E. L.; Yeh, F.; Khokhlov, A. R.; Chu, B. Langmuir 1997, 12, 6229. (27) de Gennes, P.-G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, 1979. (28) Mallam, S.; Horkay, F.; Hecht, A.-M.; Geissler, E.; Pruvost P. J. Chem. Phys. 1989, 91, 6447.

the puckering of the network by the cross-links and was assumed to have the form of exp[-Ξsqs].29,30 Thus, the total scattering function for chemically cross-linked gels is given by

I(q) ) IS(0) exp(-Ξsqs) +

IL(0) (1 + ξ2q2)

(3)

where Ξ is the mean size of the solid-like (static) nonuniformity or the mean size of the static concentration fluctuations. The exponent s depends on the network structure. When a Gaussian spatial distribution is assumed to result from the built-in inhomogeneity due to cross-linking formation, i.e., s is equal to 2, then the scattering function has the form

I(q) ) Is(0) exp(-Ξ2q2) +

IL(0) (1 + ξ2q2)

(4)

Equation 4 was found to be an appropriate function to describe the scattering from chemically cross-linked gels.28,29,31-33 However, the exponent, s, has also been reported as 0.7 in poly(vinyl acetate) gels.30,34 Experimental Section Gel Preparation. Polyelectrolyte gels were prepared by freeradical copolymerization of monomers containing diallyldimethylammonium chloride (DADMACl; Fluka Chemika Biochemika Corp.), acrylamide (AAm; Fisher Scientific), and N,N′methylene-bisacrylamide (MBAA; Fisher Scientific) in aqueous solution. A 10 wt % ammonium persulfate (Fisher Scientific) aqueous solution and N,N,N′,N′-tetramethylethylene-diamine (TEMED; Fisher Scientific) were used as the initiator and the accelerator, respectively. The degree of cross-linking was determined by the amount of MBAA added to 100 mol % of total DADMACl and AAm (0.5%, 1%, 2%, 5%, 10% MBAA in molar ratio). The molar ratio of DADMACl and AAm was determined by the desired charge content (100%, 75%, 50%, 20%, 0% of DADMACl in molar ratio). A 100% charge content means that no AAm was added, whereas a 0% charge content means only AAm and MBAA were added. The concentration of the monomers is 40% (w/w). The mixed monomer solution was first heated to 50 °C to dissolve MBAA and then cooled to room temperature and degassed by dry nitrogen. After 5 µL of TEMED and 25 µL of ammonium persulfate solution were added and well mixed, the mixture was injected between glass plates through a 0.22 µm Millipore filter. Gelation was carried out at 22 °C for 24 h between two glass plates (65 mm × 100 mm) separated by two spacers with a thickness 0.63 ( 0.04 mm or in a capillary tube. After gelation, one piece of the gel was quickly cut from the center and weighed on an analytical balance. This first piece of gel is referred to as the control gel. It is used to determine the polymerization ratio. The formed gels were then washed in a large amount of distilled water for three weeks in order to remove the soluble polymer and unreacted monomers. The distilled water was changed every 1-2 days. Gel-Surfactant Complexation. Cylindrical samples of about 2 mm in diameter were prepared by immersing measured amounts of gel (m0, 0.1-0.5 g) in aqueous solutions of sodium dodecyl sulfate. For the measurements of surfactant binding isotherms, the volume of the surfactant solution was kept at such a level that ratio γ, defined by (number of surfactant (29) Mallam, S.; Horkay, F.; Hecht, A.-M.; Rennie, A.; Geissler, E. Macromolecules 1991, 24, 543. (30) Horkay, F.; Hecht, A.-M.; Mallam, S.; Geissler, E.; Rennie, A. Macromolecules 1991, 24, 2869. (31) Shibayama, M.; Ikkai, F.; Nomura, S. Macromol. Symp. 1995, 93, 277. (32) Zrinyi, K.; Rosta, J.; Horkay, F. Macromolecules 1993, 26, 3097. (33) Shibayama, M.; Tanaka, T. J. Chem. Phys. 1992, 97, 6829. (34) Horkay, F.; Burchard, W.; Hecht, A.-M.; Geissler, E. Macromolecules 1993, 26, 4203.

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Yeh et al.

molecules in solution)/(number of charged groups in the gel derived from initial charge density ), was constant with γ ) 5. It means that the number of surfactant molecules is always in excess of the number of charged groups for complexation. The influence of cross-linking density was studied at a single surfactant concentration of approximately 1/6 (1.5 mM for SDS) of the cmc concentration (9.0 mM for SDS). The gel samples were left in the surfactant solution for one week and then taken out and weighed. Drying was carried out in a vacuum oven at about 60 °C for at least 4 h. Samples of the same gel of known mass were also dried in the same manner to find the concentration of the polymer in the gel. These data were later used in calculating the binding ratio which can be obtained by the weight of dried complex (mc), initial gel weight (m0), polymer concentration in the gel (cg), and the molecular weight of SDS (Ms) and DADMACl (Mg). Small-Angle Neutron Scattering and Small-Angle X-ray Scattering Measurements. SANS experiments were performed by using the biology small-angle neutron scattering spectrometer35 located at H9B in the high-flux beam reactor (HFBR) of Brookhaven National Laboratory. Cold neutrons were derived from a solid-hydrogen cold-neutron source located in the beam thimble of H9B beam line. The wavelength was set at 7.29 Å with a spread in ∆λ/λ of about 10%. The sample-to-detector distance was 1758 mm. The swelling gels with various degrees of cross-linking were first vacuum-dried to remove the hydrogenated water and then reswollen in deuterium water D2O (99.9% D, Cambridge Isotope Laboratories) to full equilibration. Samples were placed in capped quartz cells, and the thickness of the cell was 2 mm. The measurements were performed at room temperature. Measured scattered intensity profiles were corrected for detector nonlinearity, incident neutron intensity variation, sample absorption, and environmental background contributions. The scattering images were first integrated radially to scattering profiles. The analysis of the scattering profiles was performed by using a nonlinear fitting procedure to fit

I(q) ) Is(0) exp(Ξ0.5q0.5) +

IL(0) (1 + ξ2q2)

(4b)

in which IS(0) (Gaussian) and IL(0) (Lorentzian) are linear coefficients and Ξ and ξ were varied iteratively to minimize the variance between the experimental data and eq 4b. Small-angle X-ray scattering (SAXS) was performed at the X3A2 State University of New York (SUNY) Beam Line, National Synchrotron Light Source (NSLS), Brookhaven National Laboratory (BNL), using a laser-aided prealigned pinhole collimator.36 The incident beam wavelength (λ) was tuned at 1.54 Å. A twodimensional detector-image plate (IP) was used in conjunction with an image scanner manufactured by Fuji Co. as the detection system for the SAXS measurements. The sample-to-detector distance was 490 mm. The q range covered was from 0.02 to 0.7 Å-1 for the image plate with q ) 4π/λ(sin (θ/2)) and θ being the scattering angle. The experimental data were corrected for background scattering and sample transmission. The smearing effect was negligible for this setup.

Results and Discussions The prepared gels were characterized by using a gravimetric method and SANS. The polymerization yield (R) increases with increasing molar ratio of neutral monomer (AAm) and is roughly independent of the degree of cross-linking. The conversion of monomers to copolymers was calculated from the control gels by the expression

R)

md 0.4mi

(5)

(35) Shneider, D. K.; Schoenborn, B. P. In Neutrons in Biology; Schoenborn, B. P., Ed.; Plenum: New York, 1984; pp 119. (36) Chu, B.; Harney, P. J.; Li, Y.; Linliu, K.; Yeh, F.; Hsiao, B. S. Rev. Sci. Instrum. 1994, 65, 597.

Figure 1. Conversion rate of copolymerization of poly(diallyldimethylammonium chloride) (PDADMACl)/polyacrylamide (PAAm). R ) md/(0.4 mi) where mi is the mass of control gel right after polymerization and md is the mass of the dry control gel.

where mi is the mass of control gel right after polymerization, and md is the mass of the dry control gel. The polymer concentration at the end of polymerization was assumed to be the same as the initial monomer concentration, i.e., 40% (w/w). Figure 1 shows the dependence of polymerization yield, R, to the charge density, . The charge density, , is defined as the initial feed molar ratio of DADMACl to AAm. The real charge density, r, which is defined as the molar ratio of charged monomer to all monomer units, is lower than  and will be discussed latter. For simplicity, the charge density, , from the initial molar ratio of charged to total monomers will be used throughout this paper except where the real charge density, r, is specified. The polymerization yield, R, is 0.25, for the 100% charged polymer gel (pure PDADMACl), whereas it is 1.00 for the 100% neutral one (PAAm). This substantial difference in the conversion rate came from the different reactivity between the monomers and the cross-linker. The low conversion rate of the 100% PDADMACl polymer gels reflects the reactivity difference between the monomer, DADMACl, and the cross-linker, MBAA. The neutral acrylamide has comparable reactivity with MBAA and a higher reactivity than that of the ionic diallyldimethylammonium chloride from Figure 1. The relative reactivity of two different monomers can be described by the reactivity ratio r1 ≡ k11/k12 and ratio r2 ≡ k21/k22 where kij is the rate constant between polymer i (Pi) and monomer j (Mj). By applying the steady-state assumption, i.e., the concentrations of initiator and monomer remain essentially constant during a short interval of time, the copolymer composition equation can be represented by37

F F2 (f - 1) ) r1 - r2 f f

(6)

where f ) [P1]/[P2] and F ) [M1]/[M2]. A plot of (F/f)(f-1) as ordinate and (F2/f) as abscissa (not shown) is a straight line whose slope is r1 and whose intercept is minus r2. It is obvious that if M1 has much higher reactivity than M2, the chain P1 would be formed much easier than P2. (37) Rosen, S. L. In Fundamental Principles of Polymeric Materials, second edition; John Wiley & Sons: New York, 1993.

Poly(diallyldimethylammonium) Gels

Figure 2. Dependence of charge density to initial feed charged DADMACl monomer.

By assuming that AAm could be completely incorporated in the polymer gels during the copolymerization, the reactivity ratios r1 (DADMACl) and r2 (AAm) were calculated as 0.29 and 2.16, respectively. The r1 and r2 values are relatively low when compared with the literature values, 0.58 and 6.7, respectively, of a linear PDADMACl/PAAm copolymer from Tanaka.38 However, the cross-linker, MBAA, having comparable reactivity to AAm might interfere with the reactivity ratios of AAm and DADMACl in our system. On the basis of the above assumption, we can also calculate the real charge density, r, from the conversion rate of the control gels. The plot of real charge density, r, to the feed monomer molar ratio of DADMACl/AAm is shown in Figure 2 as well as that of a literature curve.38 The swelling capacity is calculated from the increase in mass of the swollen polymer sample from the dry state and is typically reported as a ratio of the grams of fluid absorbed per gram of dry polymer. Thus, the swelling ratio Sr of the control gel in pure water is defined as Sr ) (mw - md)/md where mw is the mass of fully swollen control gel. Figure 3 shows the dependence of the swelling ratio Sr to the degree of cross-linking, F, at various charge densities , of PDADMACl-PAAm copolymer gels. The swelling ratio increases with increasing charge density due to the condition of electroneutrality of the gel. The higher the concentration of charged groups on the polymer chains (or the concentration of noncompensated charges for the case of polyampholyte networks), the higher the concentration of counterions; thus, the higher the osmotic pressure inside the network, the higher the degree of swelling. According to Figure 3, the degree of cross-linking has a strong effect on the swelling ratio. The swelling ratio drops much faster with increasing cross-linking density, F, than with decreasing charge density, r. The crosslinking agent MBAA is a neutral molecule, and its reactivity is comparable to that of the monomer AAm. Thus the same assumption can be applied to the crosslinker as well as to the monomer AAm, i.e., the addition of a cross-linking agent would cause both a reduction in the charge density and an increase in the rigidity of the polymer network. Table 1 lists a summary of the data on conversion rate, R, charge densities,  and r, and degrees of cross-linking, F and Fr. (38) Tanaka, H. J. Polym. Sci., Polym. Chem. Ed. 1986, 24, 29.

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Figure 3. Plot of swelling ratio Sr of PDADMACl gel versus degree of cross-linking (F) at different charge density (). Sr ) (ws - wd)/wd where ws is the mass of fully swollen control gel in pure water. Table 1. Characteristic Parameters of PDADMACl Gels charge initial conversion swelling cross-linking real charge density MBAA rate ratio density density  (%)1 F (%)a R (%)b Sr Fr (%)a r(%)a 100 100 100 100 100 90 90 90 75 50 50 50 25 0 a

0.5 1 2 5 10 0.2 0.5 2 0.5 0.2 0.5 2 0.5 0.5

25.9 24.0 26.0 42.3 34.9 23.4 39.5 37.0 46.4 62.0 62.5 60.5 75.1 100

944 423 143 27 13 1470 433 80 292 430 161 32 59 5

1.9 4.2 7.7 12 30 0.7 1.2 4.9 1.0 0.3 0.7 2.8 0.6 0.5

98 96 92 88 70 63 75 67 51 31 31 27 13 0

Mol %. b Wt %.

Figure 4. SANS profiles of PDADMACl gels at different crosslinking density (Fr). Symbols are the experimental data while the solid lines are the best fits of eq 4b.

The SANS results for the pure PDADMACl gels with different degrees of cross-linking, Fr, are shown in Figure 4. The scattered intensity increases rapidly with increasing cross-linking density in the low q region. This strong upturn also shifts to higher q values at higher cross-linking

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Yeh et al. Table 2. Structure Parameters of PDADMACl Gels Fr (%)

IS(0)a(CVb)

Ξ/Å

IL(0)a(CVb)

ξ/Å

1.9 7.7 12 30

84600(8.7) 27100(7.6) 87000(2.9) 249000(12)

6270(21) 2330(2.9) 2900(1.0) 2910(6.7)

7.5(5.9) 31.6(2.0) 86.8(7.7) 15200(150)

20.4(5.8) 14.7(2.0) 24.5(5.9) 835(78)

a I (0) and I (0) are expressed in arbitrary units with I(q ) 0) S L ) IS(0) + IL(0). It is the ratio of IS(0)/IL(0) which signifies the magnitude of the two terms in eq 4b. With the experimental low q limit of ∼0.01 Å, the magnitude of Ξ is qualitative at best. b Unit for coefficients of variation is expressed in %. It should be noted that the fitting for Fr ) 30% is inadequate. See text for details.

Figure 5. Ornstein-Zernike plot of PDADMACl gel at Fr ) 7.7%. The straight line denotes the best fit of eq 1.

densities. This phenomenon represents a typical crosslinked polymer gel pattern showing that the cross-linking agent induces a strong inhomogeneity and that the size of inhomogeneity reduces with increasing cross-linking density. A physical value to characterize the inhomogeneity size in a gel network is the correlation length, ξ, which represents the spatial correlation range of local concentration fluctuations in the system. The Lorentzian function (eq 1) provides the relationship between the scattered intensity and the mesh size in semidilute polymer solution. Figure 5 shows the shape of a typical spectrum from the cross-linked gel (PDADMACl gel with Fr )7.7%), in a plot of 1/I(q) vs q2. The asymptotic region at large q values yields a straight line, corresponding to eq 1. In the small q region of Figure 5, I(q)-1 deviates increasingly from the asymptotic Lorentzian function. The deviation increases with increasing degree of cross-linking. In cross-linked gels, the presence of random mechanical constraints generates permanent spatial concentration fluctuations in addition to the thermodynamic temporal concentration fluctuations.39-42 Such a deviation from uniformity is found in all gels investigated so far . The severity and the distribution of the permanent concentration waves depend on the condition under which crosslinking occurs. The Lorentzian function describes only the contribution from the solution-like (dynamic) concentration fluctuations. Thus the contribution from the permanent spatial concentration fluctuations cannot be described by the Lorentzian equation and produces the observed deviation. Geissler et al.40 first tried to introduce the contribution from finite thickness of polymer chains. The corrected scattering function then takes on the form

I(q) )

I(0) (1 + ξ2q2)

exp

(

)

-r02q2 2

(7)

where r0 is the radius of the polymer chain. It had been shown that both the ξ and r0 increase with increasing cross-linking density for polyacrylamide gels. Later (39) Dusek, K.; Prins, W. Adv. Polym. Sci. 1969, 6, 1. (40) Hecht, A.-M.; Duplessix, R.; Geissler, E. Macromolecules 1985, 18, 2167. (41) Bastide, J.; Leibler, L. Macromolecules, 1988, 21, 2647. (42) Matsuo, E. S.; Orkisz, M.; Sun, S.-T.; Li, Y.; Tanaka, T. Macromolecules 1994, 27, 6791.

Figure 6. Log-log plot of SANS profile of PDADMACl gel at Fr ) 7.7%. The solid line is the calculated curve according to eq 4b, while the dashed line is the contribution from solutionlike fluctuations and the dotted line is from solid-like fluctuations.

neutron scattering observations on poly(dimethylsiloxane) networks have shown that the fine-scale polymer distribution involves at least two characteristic lengths.28 The shorter correlation length (ξ) was assumed to describe the more rapid fluctuations of polymer chains undergoing thermal motions, while a longer distance (Ξ) could account for the static accumulation of polymer chains pinned down by junction points or clusters of such cross-linking points. Based on the two-term model, a scattering function of a neutral polymer gel can thus be described as a combination of scattering from a liquid-like part (Lorentzian) and a solid-like part.

I(q) ) Is(0) exp(-Ξsqs) +

IL(0) (1 + ξ2q2)

(3)

As seen in Figure 4, the scattering profiles show different tendencies from two lower cross-linked gels to two higher ones. Satisfactory fits to the shape of two higher crosslinking density gels could be obtained only in the vicinity of s ) 0.5, i.e., considerably lower than the value of a Gaussian spatial distribution (s ) 2). Figure 4 shows both the fits and the experimental results. The fitting curves agree with the experimental data very well for all cross-link densities. Table 2 lists the structure parameters of PDADMACl gels obtained from the nonlinear leastsquares fitting of experimental curves. Figure 6 shows the total scattering and contributions from both the static and dynamic fluctuations. It is apparent that the small angle upturn comes from the static fluctuations, i.e., the inhomogeneity produced by the cross-links, while the dynamic fluctuations from the solution part contribute to

Poly(diallyldimethylammonium) Gels

Figure 7. Concentration dependence of the relative mass ratio of collapsed PDADMACl-SDS complexes to original PDADMACl gels.

the scattered intensity at higher q values of the scattering profile. However, one should also note that, with the Ξ values in the range of hundreds of nm and our lowest q value on the order of 0.1 nm-1, the most we can state is the existence of the solid-like part but not its quantitative magnitude. For the two curves at lower cross-linking densities (1.9% and 7.7%), the fitting results are not sensitive to the exponent s at all. Moreover, the ξ from eq 3 is close to the value from the Ornstein-Zernike equation (eq 1) for Fr ) 1.9% and 7.7%. Thus, in low cross-link density gels, the dynamic fluctuations show similar behavior to that in polymer solution. It is noted that the static correlation length, Ξ, which is much greater than the dynamic correlation length ξ, is in the range of thousands of Å. This result suggests that the polymer network is very loose and flexible at low cross-linking density. In addition, it also accounts for the high swelling ratio of such lightly cross-linked polymer gels. The scattering behavior starts to deviate from the Ornstein-Zernike equation as the cross-linking density is further increased. By fitting the experimental data with eq 3 and s ) 0.5, we found the correlation lengths for both Ξ and ξ which behave differently from the values in the low cross-linking gels. At high cross-linking densities, the Ξ value is almost constant while the ξ value increases with increasing Fr. However, it is unreasonable to accept a ξ value of 800 Å in a polymer gel with a high cross-linking density of 30%. It seems that eq 4b cannot really represent the scattering function at high cross-linked gels, though the fitting curves match the experimental data very well. With such a high cross-linking density as evidenced by a low swelling ratio, water may not be a good solvent, and phase separation could occur. The totally opaque appearance confirms the macrophase separation. Complexation of Gel-Surfactant. Figure 7 shows the ratio of (mass of the collapsed gel sample)/(mass of the original sample) for a gel with Fr ) 4.2% placed in a solution of SDS. The batches shown in Figure 7 represented the gel samples synthesized at different time. For the purposes of this analysis, it is possible to split the whole concentration range into four regions (as seen in Figure 7): (A) very low concentration 0 to 10-4 mol/L (M); (B) low concentration, 10-4 to 3 × 10-3 M; (C) high concentration, 3 × 10-3 to 10-2 M (cmc ) 9 × 10-3 M); and (D) very high concentration, above 10-2 M. In region A the gel starts to shrink, and this shrinking

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can be attributed to the equilibration of osmotic pressure inside and outside of the gel phase. One of the interesting features of region A is that the gel expands slightly in the surfactant solution of very low concentration (around 2 × 10-5 M) when compared with gels in pure water. This phenomenon is reproducible and had been seen in a system of poly(acrylic acid)-polyacrylamide copolymer gels interacting with Cu(II) ion.43 In this region (