J. J. Kiefer., P. Somasundaran~ and K. P. Ananthapadmanabhanb
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1 Polymer Solutions, Blends, and Interfaces t. NOO and D.N. Rubingh 1992 Elsevier Scicocc Publishers B.V. All rights rcservoo. 423 Size of Tetradecyltrimethylammonium Bromide Aggregates on Polyacrylic Acid in Solution by Dynamic Fluorescence J. J. Kiefer., P. Somasundaran~ and K. P. Ananthapadmanabhanb -Langmuir Center for Colloids and Interfaces, Columbia University, New York, New York bunilever Research U.S., 45 River Road, Edgewater, New Jersey Abstract Interaction between tetradecyltrimethylammonium bromide (1T AB+) and polyacrylic acid (PAA) has been studied with dynamic and steady state fluorescence using pyrene as a photophysical probe in conjunction with potentiometric studies using a surfactant sensitive solid-state membrane electrode. Variables studied include charge density, and salt concentration. Steady-state fluorescence experiments combined with potentiometric measurements show the presence of hydrophobic host sites for pyrene when the ratio of bound surfactant to ionized carboxyl groups is of the order of 0.03, and this ratio appears to be independent of charge density for the systems studied. Dynamic fluorescence experiments were used to estimate the aggregate size as a function of the fraction of bound surfactant. The results show thai the aggregate size remains essentially constant along the binding isotherm and is larger at higher degrees of ionization. 1. INTRODUCfION Interactions between polymers and surfactants are of immense commercial and academic interest. Due to their characteristically different properties they are often present together in many commercial and natural systems. Their co-existence in aqueous solutions leads to interactions between them resulting in changes in their physical properties. In recent years, significant progress has been made in developing an understanding of such interactions between them. Early work focused on interactions of anionic surfactants with uncharged water soluble polymers such as polyethylene oxide (PEa) and polyvinylpyrrolidone (PVP). Interactions of anionic surfactants with uncharged polymers were found to be weak and occur below surfactant concentrations almost an order of magnitude less than the cmc of the pure surfactant (1-4). Recently surfactant sensitive membrane electrodes have been used to measure surfactant binding isotherms to polymers (5-10). Surface tension experiments have also been
2 42S considered to arise from hydrophobic interaction among adjacent surfactant molecules which are associated with the polymer. When the polymer and the surfactant bear opposite charge, the surfactant monomers are strongly attracted to the vicinity of the polymer backbone by electrostatic forces. The onset of cooperative interaction is characterized by a marked change in solution properties at a distinct surfactant concentration often referred to as the critical aggregate concentration or CAC. These properties include solution viscosity, turbidity and ability to solubilize organic solutes. The interaction of surfactant with the polymer can be described in terms of a ligand polymer equilibrium extended to include the cooperative interactions among adjacent bound ligands. This statistical model is based on work by Zimm et al. (19,20) which was originally developed to model the helix-coil transition in uncharged and charged polypeptides. Schwarz (21) extended this model to describe the stacking of dye molecules on linear biopolymers. Satake and Yang (22) later derived an equivalent model to that of Schwarz which described the cooperative interaction of sodium dodecyl sulfate to poly(l-ornithine) and poly(d,lornithine). The equations developed by Satake and Yang have been extensively used by Kwak (23;24) to describe binding of ionic surfactants to oppositely charged polymers. According to this model, surfactant binding to the polymer can be represented as (00) + S': (01) K {I} (01)+ S.=:!'" (11) K(u) (2) where "0" and" 1" represent unoccupied and occupied sites respectively. K is the intrinsic affinit)' of the ligand to a site that contains no occupied neighbor and K( u) represent the affinity of a ligand to a site that has an adjacent occupied site. This is equivalent to modeling the polymer as a one-dimensional lattice. AnY given state of the systems is represented as a sequence of "1" and "a". The energy of interaction between two adjacent ligands is contained in the parameter "u" which is generally called a cooperativity parameter. Thus the interaction of ligand with the polymer can be characteriud as cooperative if, u > 1, and non-cooperative if, u = 1, and anti-cooperative if, u < 1. In the general case of polymer-surfactant interactions, values of "u" are found to be much greater than 1 due to the hydrophobic interaction between adjacent surfactant molecules. According to the Zimm-Bragg formalism, the statistical mechanical partition function Q that represents the process governed by equations 3 and 4 can be given by, 0.(1.1) (1 \s/u Q "(~) where N represents the number of binding sites on the polymer, and sand s/u represent the statistical weights of an occupied "11" with an unoccupied "00" nearest neighbor sand occupied nearest neighbor "01" s/u respectively. These parameters can be related to the intrinsic binding constant and the cooperativity parameter by, (~ s = K(u)[S] s/u = K[S] (4) (5)
3 Fluorescence Decay of Pyrene : Measurement of Surfactant Aggregation Numbers Fluorescence decay of pyrene monomer and excimer have been extensively studied in homogeneous and fragmented systems such as micellar solutions (19,20). The formation of an excimer occurs when pyrene monomer is excited by adsorption of light to give p' which forms an association complex with a pyrene monomer in the ground state P according to the following scheme, K., P + hv --+ p' ~ K. p + p'--+- pp' -,.+ P + P + hv where ~ is the rate constant for decay. of~~~ited pyrene monomer, KE is the excimer formation-dissociation rate constant and K. is the excimer decay constant. In the above scheme we assume that other nonradiative decay processes are negligible and do not contribute to the observed decay rate of the probe in the system. The extent of excimer formation will depend on a number of factors, namely the number of probes in the system and the viscosity of the probes' environment. In a fragmented medium such as surfactant micelles, the distribution of the probe molecules throughout the system as well as micelle size will affect the observed decay profiles. When no excimer is present, the observed fluorescence intensity as a function of time will be characterized by a mono-exponential decay (27,28). When sufficient probes are present, such that more than one probe is present in a particle, excimer formation can occur. In this case the observed fluorescence intensity will be characterized by a multi-exponential decay. In micellar media it is generally assumed that the probes are distributed among the micelles according to Poisson statistics. Experimental studies comparing aggregation numbers of surfactant micelles determined from excimer formation and quenching studies to those obtained from techniques such as light scattering have shown that the assumptions regarding probe distributions are valid at ionic strengths less than 0.5 M (27). If the rate constant for excimer dissociation is small compared to the rate excimer fluorescence decay, ~ «K., the monomer fluorescence intensity as a function of time, assuming a Poisson distribution of probes, is given by I(t) = I(O)eXP{-Kot - 0[1 - exp(ket)]} (8) where n is the average number of probes per particle. At long times, the fluorescence decay profiles represent the decay due to monomeric emission in the absence of excimer formation. Thus, equation [10] reduces to Ln[l(t)/I(O)] = -0 - Kot (9) If the assumptions used in the derivation of the kinetic model are correct, then the long time profiles as a function of n should be parallel. Extrapolation to t = 0 gives, n, the average probe occupancy number. Experiments as a function of probe concentration allows one to check the
4 429 electrode was then placed in standard TfAB solutions (1 x 10-6 to 1 X 10-3 M TfAB) for 2 minutes and the mv reading in each standard was recorded and a calibration curve was constructed. In general the electrode calibration is very reproducible. However directional drift in the calibration curve was observed. This caused the C3libration to shift (+2 my) along the potential axis while maintaining a constant slope. The effect of this drift on the experiment was minimized by calibration of the electrode before and after each titration. The m V readings were then averaged and a single calibration curve constructed. A typical surfactant electrode calibration curve is shown in figure 1. As can be seen, the plot is linear over several orders of TfAB concentration indicating Nernstian behavior with a slope of 59.6 my/decade. Binding isotherms were obtained by titrating the polymer solution with a standard Tf AB solution in a glass beaker maintained at ~C.! The potential of the surfactant electrode relative to,a saturated calomel reference (Fisher Scientific) was recorded using a Kyoto Electronics model AT-210 autotitrator equipped with a standard titration preamplifier and model AT-I 18 autopiston buret. The instrument was programmed to deliver either 0.1 or 0.2 ml increments of standard TfAB. The resulting potential was recorded 2 minutes after each incremental addition of titrant. Free surfactant concentrations were calculated by comparison of the recorded mv potential to the calibration curve. 1e-6 1 e-5, [TTASJf Fiszure 1 Calibration of TfAB Electrode T = 25 C.
5 431 at the same free TTAB concentration for both i = 1.0 and i = 0.5. The binding result is contrary to expectation since one would expect the binding isotherm for a polymer with lower charge density (i = 0.5) to begin at higher free surfactant concentration. These observations can be explained within the framework of counterion-condensation theory as developed by Manning (30). According to this theory, above a critical degree of ionization, the fraction of condensed counterions reduces the intrinsic charge density of the polymer to a constant value independent of the degree of ionization. The critical degree of ionization, ie, for PAA is calculated to be 0.35 at 25 C in water. Below the critical degree of ionization for PM no counterions are condensed on the polymer and the charge density is controlled by the degree of ionization and the counterions in the Debye-Huckellayer associated with the polyelectrolyte. In other words, PAA will have the same effective charge density independent of the degree of ionization for i > ie' Log([TTAB]f) Figure 2 Binding Isothenn of TfAB to Polyacrylic Acid, [PAA] = 5 x 10" eq Lot, T = 25-C in 0.01 M NaBr, CulVe A (i = 0.25), CulVe B (i = 1.00). When the charge density is less than the critical value completely unexpected result is obtained. Comparison of the curves labeled A on figures 2 and 3, i = 0.25 and 0.10 respectively, to those curves labeled B on figure Zand 3, i = 1.0 and 0.5 respectively, we find that the onset of binding begins at a lower surfactant concentration for charge-density values
6 433 decrease as i is decreased. This is shown in figure 4 which is a plot of Log(K) as a function of polymer charge density. As can be seen, the value of Log(K) is constant for values of i from 1.0 to about Then the curve shows a marked decrease in the value of Log(K) over a very narrow range of i as would be expected based on condensation theory. The cooperativity parameter "u" represents the hydrophobic interaction between adjacent surfactant molecules associated with the polymer. The magnitude of "u" is seen to increase markedly as the charge density is reduced. Since the hydrophobic interaction among bound surfactant molecules would be expected to remain constant, the cooperativity parameter must contain contributions from additional effects other than the hydrophobic interaction between bound surfactant chains. As the ionic strength is increased a marked increases in "u" is observed. This behavior is thought to be due to changes in the polymer chain flexibility. Similarly a reduction in the polymer charge density below the critical value of 0.35 results in an increased value of "un. In addition, the reduction in charge density will also reduce the repulsion between monomer segments of the polymer leading to a more coiled chain. Thus it seems that "u" contains a significant contribution from polymer conformation. The combined contribution from both "K" and "u" is given by 10g[Ku] and is shown in table 1. The value of 10g[Ku] is seen to increase as the charge density of the polymer is decreased which is in line with the observed position of the binding isotherms shown in figures 2 and 3. The surfactant concentration at the onset of binding is a measure of the strength of the intrinsic interaction of surfactant with the polymer. Interestingly, it is the value of (Ku) that reflects the position of the isotherm and not the value of K. It is apparent that the cooperativity parameter, "u", contains a significant contribution from other factors such as polymer conformation which pennits the cooperative effects to begin at lower surfactant concentrations than expected as well as hydrophobic interaction between bound surfactant molecules. These additional contributions may result from conformational changes in the polymer chain. Table 1 Cooperative Binding Parameters "K" and "u" for PAA-TTAB Systems Ionization (i) [NaBr]M log[k] "u~ Log(Ku) () Steady State Fluorescence: Micropolarity Measurements of PAA-TTAB System Figure 6 shows 13/11 of pyrene in the presence of fully ionized PM i = 1.0 is given in figure 5 as a function of the free surfactant concentration. An increase in 13/11 above that obtained for pyrene in water is interpreted as solubilization of pyrene in a hydrophobic structure. It can be seen for figure 5, that the change in behavior of 13/11 closely resembles that of the binding isotherm. The marked increase in binding and the change in 13/11 of pyrene
7 435 the surfactant levels employed here since the total level of pyrene in the system is very low resulting in poor signal to noise ratio. Consequently, reliable monomer decay profiles in the absence of excimer formation are difficult to obtain. To circumvent this difficulty, experiments at various pyrene levels were carried oul In all cases the pyrene level was such that excimer formation could be observed. The value of K. was determined from the limiting slope at long decay times for each sample. The values for K. are then averaged to give a single value. The experimental data is then fe-fit to equation [10] with K. fixed at the average value and the value of K. and tin" are calculated. ~ Figure 5 MicroJX}larity of PM.1TAB complex. [PM] = 5.0 x 1~ eq L-1. (i = 1.0). in 0.01 M NaBr. The aggregation numbers of IT AB micelles in water and in the presence of added electrolyte were also determined for comparison with the aggregate size obtained for ltab in the presence of polyacrylic acid. Decay profiles of pyrene monomer are shown in figure 7 as a function of pyrene level in micellar solutions. As can be seen, the decay profiles of pyrene monomer at long times are parallel indicating that the assumptions invoked in the derivation of the kinetic model for fragmented media are valid for the present system. The aggregate size of IT AB micelles in water and 0.01 om. NaBr are given in table 2 along with the relevant kinetic parameters. The value of K. was determined at low probe
8 437 Table 2 Summary of Kinetic Parameters of Pyrene Excimer Formation in TTAB Micelle t (nanoaeconds) Fagure 7 Pyrene monomer decay in 1T AB micelles, [TrAB] = 0.01 M, [TrAB]/[PY]: Curve A = 211, Curve B = 109. Curve C = 53.
9 " -4. ~.~ os t(nanoseconds) FIgure 8 Pyrene monomer decay in PAA-TTAB aggregates, [PAA] = 5 x 10" eq. LoJ, i = 1.0, in 0.01 M NaBr, (TTAB}/(PY]: Curve A = 118, Curve B = 30. concentrations of pyrene employed. In general the pyrene level is from 5 x 10.7 to 5 X PAA-7TAB aggregation numbers. 11 can be seen from table 3, that the average aggregate size, "N", remains essentially constant, within experimental error, as a function of the fraction bound. These experimental results suggest that the interaction ofltab with PAA is analogous to conventional micelli2btion. Indeed, the vertical slope of the binding isotherms indicates that the surfactant monomer concentration remains constant during aggregate formation. Thus as more surfactant binds to the polymer, the number of aggregates increases rather than the aggregate size. Our results are in agreement with the fluorescence results obtained for SOS hemi-micelles at the alumina/water interface reported by Chandar et al. (33) which show that the SOS hemi-micelle size remains essentially constant in Ihe steeply rising portion of the adsorption isotherm. Interestingly at the interface, the aggregate size increases at high coverage unlike that of the P AA-lT AB complex. The last column of table 3 gives the averaged value of the aggregation number measured at an equivalent value of ~ at each degree of ioni2btion. Indeed, there is little difference in "N" as a function of the degree of ioni2btion suggesting that the interaction of TrAB is essentially the same and is independent of charge density within experimental error. Upon closer examination, the results seem to suggest that, ;::,'~«" r~~~:~ "..;'~-
10 441 To compare the aggregate size determined from fluorescence with those calculated from the cooperative binding model, the values of ilk" and "U" given in table 1, were used to calculate the average aggregate size as a function of the fraction bound surfactant using equation [7]. The results of these calculations are summarized in table 4 along with the experimental values. A comparison of the aggregate size obtained from fluorescence as discussed above with those predicted from the cooperative binding model shows that while the experimental results indicate 8 constant aggregate size along the binding isotherm, the model predicts that the aggregate size increases with increasing binding. Even though a good fit to Table 3. Summary of Kinetic Analysis of Pyrene Excimer Formation; PAA- TT AB Complex in 0.01 M NaBr Exp. No. p Tr AB/PY IlK., os IlK., os n N N<ow) f f f f f f ;t.5 the lower region of the binding isotherm is obtained, the model is unable to predict aggregation behavior that is in agreement with the experimental results. Representation of the polymer chain as a linear array of binding sites is an over-simplification. The model predictions that the average aggregate size increases with binding is a direct result of modeling the polymer as a rigid linear lattice. The predicted increase of the aggregate size with decreasing charge density is due to the large increase in the cooperativity parameter. The latter most likely results from changes in the polymer conformation with charge density.
11 443 Finally, the present study shows that fluorescence techniques combined with potentiometry can provide a powerful tool to investigate the fonnation and structure of polymer-surfactant aggregates. Acknowledgement The authors thank Unilever Research, U. S. for financial support during this work. 6. References 1. I.D. Robb, in "Anionic Surfactants in Physical Chemistry of Surfactant Action", ed. by E.H. Lucassen-ReyndeB, Marcel Dekker Inc., New York, NY, 1991, p Goddard, E.D.; Colloids and Surfaces, 19, 1986, Goddard, E.D.; Colloids and Surfaces, 19, 1986, "Cationic Surfactants Physical Chemistry" ed. by D.N. Rubingh and P.M. Holland Surfactant Science Series, vol. 37, Marcell Dekker Inc., New York, NY, Hayakawa, K.; Kwak, J.C.T; J. Phys. Chern., 87, 1983, Shimizu, T; Seki,M.; Kwak, J.C.T.; Colloids and Surfaces, 20, 1986, Hayakawa, K.; Santerre, J.P., Kwak, J.C.T.; Macromolecules, 16, 1983, Malikova, A.; Hayakawa,K.; Kwak, J.C.T.; J. Phys. Chern., 88, 1984, Shirahama, K.; Yuasa, H.; Sugimoto, S.; Bull. Chern. Soc. Jpn., 54, 1981, Santerre, J.P.; Hayakawa, K.; Kwak, J.C.T.; Colloids and Surfaces, 13, 1985, Anathapadmanabhan, K.P.; Leung, P.S., Goddard, E.D.; Colloids and Surfaces, 13, 1985, Hayakawa, K; Satake, I; Kwak, J.C.T.; Gao, Z; Colloids and Surfaces, 50, 1990, Hayakawa, K; Ohta, J; Maeda, T.; Satake, I; Kwak, J.C.T; Langmuir, 3, 1987, Zana, R; Lianos, P; Lang, J; J. Phys. Chern., 1985,89, Turro, NJ.; Baretz, B.H.; Kuo, P.L; Macromolecules, Vol. 17, No.7, 1984, Clu, D. Y.; Thomas, J.K.; J. Am. Chern. Soc., 108, 1986, Abuin, E.B.; Scaiano, J.C.; J. Am. Chern. Soc., 106, 1984, Clu, D. Y.; Thomas, J.K; ACS Symposium Series, 358(Photophys. Polym.), 1987, Zimm, B.H.; Bragg, J.K.; J. Chern. Phys., vol. 31, No.3., 1959, Zimm, B.H.; Rice, S.A; Molecular Physics, vol 3, No.4., 1960, Schwarz, G.; Eur. J. Biochem., 12, 1970, Satake, I.; Yang, J.T.; biopolymeb, vol. 15, 1976, Kwak, J.C.T.; J. Phys. Chern.; 1984,88, Hayakawa, K.; Kwak, J.C. T.; in "Cationic Surfactants Physical Chemistry" ed. by D. N. Rubingh and P.M. Holland, Surfactant Science Series, vol 37, Marcell Dekker, lnc. New York, NY, 1990, p Kalyanasundaram, K.; Thomas, J.K; J. Am. Chern. Soc., 99, 1977, Ananthapadmanabhan, K.P.; Goddard, E.D.; Turro, NJ.; Kuo, P.L.; Langmuir, vol 1, No.3, 1985, 352.
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