423Polymer Solutions, Blends, and Interfacest. NOOa and D.N. Rubingh (editors)@ 1992 Elsevier Scicocc Publishers B.V. All rights rcservoo.

Size of Tetradecyltrimethylammonium Bromide Aggregates onPolyacrylic 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, NewYork

bUnilever Research U.S., 45 River Road, Edgewater, New Jersey

AbstractInteraction between tetradecyltrimethylammonium bromide (1T AB+) and polyacrylic

acid (PAA) has been studied with dynamic and steady state fluorescence using pyrene as aphotophysical probe in conjunction with potentiometric studies using a surfactant sensitivesolid-state membrane electrode. Variables studied include charge density, and salt concentration.Steady-state fluorescence experiments combined with potentiometric measurements show thepresence of hydrophobic host sites for pyrene when the ratio of bound surfactant to ionizedcarboxyl groups is of the order of 0.03, and this ratio appears to be independent of chargedensity for the systems studied. Dynamic fluorescence experiments were used to estimate theaggregate size as a function of the fraction of bound surfactant. The results show thaI theaggregate size remains essentially constant along the binding isotherm and is larger at higherdegrees of ionization.

1. INTRODUCfION

Interactions between polymers and surfactants are of immense commercial andacademic interest. Due to their characteristically different properties they are often presenttogether in many commercial and natural systems. Their co-existence in aqueous solutions leadsto 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 betweenthem. Early work focused on interactions of anionic surfactants with uncharged water solublepolymers such as polyethylene oxide (PEa) and polyvinylpyrrolidone (PVP). Interactions ofanionic surfactants with uncharged polymers were found to be weak and occur below surfactantconcentrations almost an order of magnitude less than the cmc of the pure surfactant (1-4).

Recently surfactant sensitive membrane electrodes have been used to measuresurfactant binding isotherms to polymers (5-10). Surface tension experiments have also been

42S

considered to arise from hydrophobic interaction among adjacent surfactant molecules whichare 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 byelectrostatic forces. The onset of cooperative interaction is characterized by a marked changein solution properties at a distinct surfactant concentration often referred to as the criticalaggregate concentration or CAC. These properties include solution viscosity, turbidity andability to solubilize organic solutes.

The interaction of surfactant with the polymer can be described in terms of a ligandpolymer equilibrium extended to include the cooperative interactions among adjacent boundligands. This statistical model is based on work by Zimm et al. (19,20) which was originallydeveloped 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 describedthe cooperative interaction of sodium dodecyl sulfate to poly(l-ornithine) and poly(D,L-ornithine). 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 tothis 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 intrinsicaffinit)' of the ligand to a site that contains no occupied neighbor and K( u) represent the affinityof a ligand to a site that has an adjacent occupied site. This is equivalent to modeling thepolymer as a one-dimensional lattice. AnY given state of the systems is represented as asequence of "1" and "a". The energy of interaction between two adjacent ligands is containedin the parameter "u" which is generally called a cooperativity parameter. Thus the interactionof ligand with the polymer can be characteriud as cooperative if, u > 1, and non-cooperativeif, 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 betweenadjacent surfactant molecules. According to the Zimm-Bragg formalism, the statisticalmechanical partition function Q that represents the process governed by equations 3 and 4 canbe given by,

Q "(~)0.(1.1) (1

\s/u(~

where N represents the number of binding sites on the polymer, and sand s/u represent thestatistical weights of an occupied "11" with an unoccupied "00" nearest neighbor sandoccupied nearest neighbor "01" s/u respectively. These parameters can be related to theintrinsic binding constant and the cooperativity parameter by,

s = K(u)[S] (4)

s/u = K[S] (5)

427

2.3 Fluorescence Decay of Pyrene : Measurement of Surfactant Aggregation NumbersFluorescence decay of pyrene monomer and excimer have been extensively studied in

homogeneous and fragmented systems such as micellar solutions (19,20). The formation of anexcimer occurs when pyrene monomer is excited by adsorption of light to give p' which formsan association complex with a pyrene monomer in the ground state P according to thefollowing 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 excimerformation-dissociation rate constant and K. is the excimer decay constant. In the above schemewe assume that other nonradiative decay processes are negligible and do not contribute to theobserved decay rate of the probe in the system.

The extent of excimer formation will depend on a number of factors, namely thenumber of probes in the system and the viscosity of the probes' environment. In a fragmentedmedium such as surfactant micelles, the distribution of the probe molecules throughout thesystem as well as micelle size will affect the observed decay profiles. When no excimer ispresent, the observed fluorescence intensity as a function of time will be characterized by amono-exponential decay (27,28). When sufficient probes are present, such that more than oneprobe is present in a particle, excimer formation can occur. In this case the observedfluorescence intensity will be characterized by a multi-exponential decay.

In micellar media it is generally assumed that the probes are distributed among themicelles according to Poisson statistics. Experimental studies comparing aggregation numbersof surfactant micelles determined from excimer formation and quenching studies to thoseobtained from techniques such as light scattering have shown that the assumptions regardingprobe distributions are valid at ionic strengths less than 0.5 M (27). If the rate constant forexcimer dissociation is small compared to the rate excimer fluorescence decay, ~ « K., themonomer fluorescence intensity as a function of time, assuming a Poisson distribution ofprobes, 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 decayprofiles 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 timeprofiles as a function of n should be parallel. Extrapolation to t = 0 gives, n, the average probeoccupancy number. Experiments as a function of probe concentration allows one to check the

429

electrode was then placed in standard TfAB solutions (1 x 10-6 to 1 X 10-3 M TfAB) for 2minutes and the mV reading in each standard was recorded and a calibration curve wasconstructed.

In general the electrode calibration is very reproducible. However directional drift inthe calibration curve was observed. This caused the C3libration to shift (+2 mY) along thepotential axis while maintaining a constant slope. The effect of this drift on the experiment wasminimized by calibration of the electrode before and after each titration. The m V readings werethen averaged and a single calibration curve constructed. A typical surfactant electrodecalibration curve is shown in figure 1. As can be seen, the plot is linear over several orders ofTfAB concentration indicating Nernstian behavior with a slope of 59.6 mY/decade.

Binding isotherms were obtained by titrating the polymer solution with a standardTf AB solution in a glass beaker maintained at ~C .!. 0.1. The potential of the surfactantelectrode relative to,a saturated calomel reference (Fisher Scientific) was recorded using aKyoto Electronics model AT-210 autotitrator equipped with a standard titration preamplifierand model AT-I 18 autopiston buret. The instrument was programmed to deliver either 0.1 or0.2 mL increments of standard TfAB. The resulting potential was recorded 2 minutes aftereach incremental addition of titrant. Free surfactant concentrations were calculated bycomparison of the recorded mV potential to the calibration curve.

1e-6 1 e-5 ,.. 1..3[TTASJf

Fiszure 1 Calibration of TfAB Electrode T = 25°C.

431

at the same free TTAB concentration for both i = 1.0 and i = 0.5. The binding result iscontrary to expectation since one would expect the binding isotherm for a polymer with lowercharge density (i = 0.5) to begin at higher free surfactant concentration. These observations canbe 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 condensedcounterions reduces the intrinsic charge density of the polymer to a constant value independentof the degree of ionization. The critical degree of ionization, ie, for PAA is calculated to be0.35 at 25°C in water. Below the critical degree of ionization for PM no counterions arecondensed on the polymer and the charge density is controlled by the degree of ionization andthe 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 fori > ie'

1.2

1

0.2

0 .. -5 -4 -3

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 resultis obtained. Comparison of the curves labeled A on figures 2 and 3, i = 0.25 and 0.10respectively, to those curves labeled B on figure Zand 3, i = 1.0 and 0.5 respectively, we findthat the onset of binding begins at a lower surfactant concentration for charge-density values

433

decrease as i is decreased. This is shown in figure 4 which is a plot of Log(K) as a functionof polymer charge density. As can be seen, the value of Log(K) is constant for values of i from1.0 to about 0.35. Then the curve shows a marked decrease in the value of Log(K) over a verynarrow range of i as would be expected based on condensation theory.

The cooperativity parameter "u" represents the hydrophobic interaction betweenadjacent surfactant molecules associated with the polymer. The magnitude of "u" is seen toincrease markedly as the charge density is reduced. Since the hydrophobic interaction amongbound surfactant molecules would be expected to remain constant, the cooperativity parametermust contain contributions from additional effects other than the hydrophobicinteraction between bound surfactant chains. As the ionic strength is increased a markedincreases in "u" is observed. This behavior is thought to be due to changes in the polymer chainflexibility. Similarly a reduction in the polymer charge density below the critical value of 0.35results in an increased value of "un. In addition, the reduction in charge density will also reducethe repulsion between monomer segments of the polymer leading to a more coiled chain. Thusit seems that "u" contains a significant contribution from polymer conformation. The combinedcontribution from both "K" and "u" is given by 10g[Ku] and is shown in table 1. The value of10g[Ku] is seen to increase as the charge density of the polymer is decreased which is in linewith the observed position of the binding isotherms shown in figures 2 and 3. The surfactantconcentration at the onset of binding is a measure of the strength of the intrinsic interaction ofsurfactant with the polymer. Interestingly, it is the value of (Ku) that reflects the position ofthe 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 whichpennits the cooperative effects to begin at lower surfactant concentrations than expected as wellas hydrophobic interaction between bound surfactant molecules. These additional contributionsmay result from conformational changes in the polymer chain.

Table 1Cooperative Binding Parameters "K" and "u" for PAA-TTAB Systems

Ionization (i) [NaBr]M log[K] Log(Ku)"u~

1.000.251.000.500.250.10

-().

-0-

0.010.010.010.01

4.3113.8642.4662.4912.2822.221

6.1547.5989.21101.14490.39813.00

5.1005.5424.4204.5004.9705.130

4.2 Steady State Fluorescence: Micropolarity Measurements of PAA-TTAB SystemFigure 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 13/1 1 above thatobtained for pyrene in water is interpreted as solubilization of pyrene in a hydrophobicstructure. It can be seen for figure 5, that the change in behavior of 13/11 closely resembles thatof the binding isotherm. The marked increase in binding and the change in 13/11 of pyrene

435

the surfactant levels employed here since the total level of pyrene in the system is very lowresulting in poor signal to noise ratio. Consequently, reliable monomer decay profiles in theabsence of excimer formation are difficult to obtain. To circumvent this difficulty, experimentsat various pyrene levels were carried ouL In all cases the pyrene level was such that excimerformation could be observed. The value of K. was determined from the limiting slope at longdecay times for each sample. The values for K. are then averaged to give a single value. Theexperimental data is then fe-fit to equation [10] with K. fixed at the average value and thevalue 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 addedelectrolyte were also determined for comparison with the aggregate size obtained for lTAB inthe presence of polyacrylic acid. Decay profiles of pyrene monomer are shown in figure 7 asa function of pyrene level in micellar solutions. As can be seen, the decay profiles ofpyrene monomer at long times are parallel indicating that the assumptions invoked in thederivation 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 2along with the relevant kinetic parameters. The value of K. was determined at low probe

437

Table 2Summary of Kinetic Parameters of Pyrene Excimer Formation in TTAB Micelle

0

-0.5

.1

-1.5

.2

-2.50 100 200 300

t (nanoaeconds)

400 500

Fagure 7 Pyrene monomer decay in 1T AB micelles,[TrAB] = 0.01 M, [TrAB]/[PY]: Curve A = 211, Curve B = 109.Curve C = 53.

439

0.

-1

.2

~

.~."

.-4

oS0 100 200 300

t(nanoseconds)

400 500

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 10-6.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 ofthe fraction bound. These experimental results suggest that the interaction oflTAB with PAAis analogous to conventional micelli2Btion. Indeed, the vertical slope of the binding isothermsindicates that the surfactant monomer concentration remains constant during aggregateformation. Thus as more surfactant binds to the polymer, the number of aggregates increasesrather than the aggregate size. Our results are in agreement with the fluorescence resultsobtained 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 risingportion of the adsorption isotherm. Interestingly at the interface, the aggregate size increasesat high coverage unlike that of the P AA-lT AB complex. The last column of table 3 gives theaveraged value of the aggregation number measured at an equivalent value of ~ at each degreeof ioni2Btion. Indeed, there is little difference in "N" as a function of the degree of ioni2Btionsuggesting that the interaction of TrAB is essentially the same and is independent of chargedensity within experimental error. Upon closer examination, the results seem to suggest that

, ;::,'~«"

r~~~:~ "..;'~-

441

To compare the aggregate size determined from fluorescence with those calculatedfrom the cooperative binding model, the values of ilK" and "U" given in table 1, were used tocalculate the average aggregate size as a function of the fraction bound surfactant usingequation [7]. The results of these calculations are summarized in table 4 along with theexperimental values. A comparison of the aggregate size obtained from fluorescence asdiscussed above with those predicted from the cooperative binding model shows that while theexperimental results indicate 8 constant aggregate size along the binding isotherm, the modelpredicts 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 Complexin 0.01 M NaBr

Exp. No. p Tr AB/PY IlK., os IlK., os n NN<ow)

-- -1 0.26 .154 108 208 . 106 0.39 292 0.25 .157 61 208 112 0.63 273 0.26 .150 53 208 116 0.76 21 27 f. 44 0.26 .422 107 301 324 0.65 585 0.26 .425 53 310 324 1.10 48 53 f. 76 0.25 .716 157 293 315 0.33 467 0.25 .730 48 293 315 0.60 25 . 36 f. 15

-- -- - - - --- -- -- - -- -- - - -- -- -- -- - - - --- - -- --8 0.50 .157 211 226 105 0.52 67

. 9 0.50 .162 91 226 105 1.10. 61 64 + 410 0.51 .306 107 226 104 0.65 53 -

11 0.51 .293 107 226 104 1.30 50 52 f. 112 0.51 .594 107 181 159 0.54 4613 0.51 .599 70 181 159 1.20 50 48 f. 314 0.51 .802 53 186 142 1.10 45

--- --- - - -- - -- -- - --- - -- --- -- --- --- --15 1.00 .146 118 152 69 0.63 5316 1.00 .147 117 152 69 0.37 31 42 f. 1617 1.00 .420 128 169 69 0.55 5918 1.00 .675 105 187 72 0.52 4819 1.00 .689 40 130 68 1.30 47 48;t.5

the lower region of the binding isotherm is obtained, the model is unable to predict aggregationbehavior that is in agreement with the experimental results. Representation of the polymer chainas 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 arigid linear lattice. The predicted increase of the aggregate size with decreasing charge densityis due to the large increase in the cooperativity parameter. The latter most likely results fromchanges in the polymer conformation with charge density.

443

Finally, the present study shows that fluorescence techniques combined with potentiometrycan 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.

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