5534
J . Phys. Chem. 1994, 98, 5534-5540
Quenching Kinetics of Anthracene Covalently Bound to a Polyelectrolyte. 1. Effects of Ionic Strength M. E. Morrison, R. C. Dorfman, W. D. Clendening, D. J. Kiserow, P. J. Rossky,’ and S. E. Webber’ Department of Chemistry and Biochemistry, The University of Texas at Austin, Austin, Texas 78712-1167 Received: February 1 , 1994; In Final Form: March 31, 1994”
Steady-state and time-resolved fluorescence quenching experiments have been performed for the following polyelectrolytes: (1) 9-ethanol anthracene (9EA) covalently bound to polymethacrylic acid (PMA) in pH 11 water and (2) vinyldiphenylanthracene (DPA) bound to polystyrene sulfonate (PSS) in neutral water, where in each case the chromophores comprise less than 1 mol % ’ of the polymer. The quencher used was T1+ (from T l N 0 3 ) with additional ionic strength provided by KN03. Quenching experiments were performed as a function of quencher concentration and ionic strength. The quencher concentration ranged from 0 to 3 mM, and the ionic strength ranged from 2 to 100 mM. At each ionic strength Stern-Volmer plots for the steady-state and time-resolved data agree, which implies that quenching is almost entirely diffusive. At low ionic strengths, the rates of fluorescence quenching in these polyelectrolyte solutions exceed the diffusion-controlled rate expected for homogeneously distributed reactants by approximately 2 orders of magnitude. A dramatic reduction in the reaction rate is observed for only slight increases in the ionic strength, and a t high salt concentrations the rate asymptotically approaches this diffusion-controlled limit. The Stern-Volmer plots exhibit negative curvature corresponding to that observed if a fraction of the fluorophores are inaccessible to quenchers. This inaccessibility is interpreted in the context of a diffusion/reaction theory. A simple model for the quenching dynamics using a Smoluchowski diffusion equation and a Poisson-Boltzmann potential of mean force for a rod-like polymer is briefly discussed and shown to account for many, but not all, aspects of the observations.
I. Introduction The photophysics and thermodynamicsof polyelectrolytes have been explored for some time.l-Iz A great deal of theoretical and experimental work has been done on the thermodynamics of polyelectrolytes in solution as well as in constraining environments.612 In this work we are interested in how the polyelectrolyte modifies the “environment” for the fluorescence quenching reaction between an optically excited chromophore bound to the polyelectrolyte and charged quenchers in solution. The polyelectrolyte and its immediate vicinity can be regarded as a “restricted reaction space” [RRS] where we define a RRS as a molecular level environment that directly affects the kinetics or course of a reaction. This is in accord with other work in which micelles, starburst dendrimers, DNA, sol gels, and biological receptor sites were also considered as RRS’s.I3-I5 Our general aim is the following: Any reaction space can be characterized geometrically, topologically, chemically, and in terms of the intermolecular forces it produces. We would like to determine which of these features are important and how they influence the dynamics of chemical reactions. The specific aim of the present experiments and dynamical theory is to develop a model with minimal complexity that will reproduce the experimental results. This will help elucidate the diffusive properties of charged species in the electrostatic potential of the polyelectrolyte and will help reveal the important features of this class of RRS. In this work, we present steady-state and time-resolved quenching data for the chromophores 9-ethanol anthracene (9EA) covalently bound to polymethacrylic acid (9EA-PMA) in basic solution and vinyldiphenylanthracene (DPA) covalently bound to polystyrenesulfonate (DPA-PSS). The quenching experiments were performed as a function of quencher concentration (T1+ from TlN03) and ionic strength (from KN03). At each ionic strength a Stern-Volmer analysis was performed on both the steady-state and the time-resolved data. Calculations using a @
Abstract published in Advance ACS Abstracts, May 1, 1994.
0022-3654/94/2098-5534%04.50/0
diffusive model for the quenchers are presented briefly and are compared to the data. 11. Experimental Section
Polyelectrolyte solutions present certain experimental difficulties. Polyelectrolytes do not dissolve as readily as simple electrolytes and have a tendency to adsorb onto the container walls. All glassware and quartz cells were soaked in a strong base/alcohol bath followed by extensive washes with deionized water to remove residual polyelectrolytes from the walls. Since polyelectrolyte solutions sometimes represent a growth medium for bacterial life, only fresh solutions were used. A. Sample Preparation. The polyelectrolyte-modified fluorescence quenching reaction experiments involved two types of fluorophore-tagged polymers. These were 9-ethanol anthracene tagged polymethacrylic acid (9EA-PMA) and vinyldiphenylanthracene tagged polystyrenesulfonate (DPA-PSS). The fluorophore loading in both cases was approximately 1 mol % (see Chart 1). The quenching agent used was the thallous ion, T1+ (from TlN03). The contribution to the total ionic strength included several sources. These were the base KOH (only for the case of 9EA-PMA), the quencher, TlNO3, and the excess salt source KNO3. The KN03salt was chosen because the diffusion constants of T1+ and K+ are similar. As expected, K+ alone has a negligible effect on the fluorescence. The stock solution of approximately 1.10 mM 9EA-PMA (concentration expressed in methacrylic acid monomer units) in pH 11 water was prepared in the following way: Distilled, deionized water was passed through a filter of 0.2-pm pore size. Sufficient polymer was added to 15 mL of water to givea monomer unit concentration of approximately 26.7 mM. This concentrated solution was sonicated for 2 h, after which the polymer was completely dissolved. Then it was diluted to its final concentration and pH by addition of ca. 2 mM KOH solution with stirring. The polymer stock solution was prepared and stored under minimum light conditions. A DPA-PSS stock solution of 1.10 mM (concentration in sodium styrenesulfonate monomer units) was prepared by 0 1994 American Chemical Society
Polyelectrolyte-Modified Reaction Dynamics
The Journal of Physical Chemistry, Vol. 98, No. 21, 1994 5535
' 1' A
CHART 1 C b COOH + Y - IC H z H I - c H z k (CH&O-C=O I
SqNa'
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CH3
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7.69~10" 3.39~10" 1.34
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Figure 1. Steady-state fluorescence spectra of 9EA-PMA quenched by TI+with no addition of KNO3. Monomer concentration 1.1 mM, pH =
following a similar procedure as outlined above except for the omission of KOH, since PSS entirely ionizes under neutral water conditions. The quencher stock solution was 0.055 M TlN03. For experiments involving gEA-PMA, stock solutions were in p H 11 water (using KOH). For DPA-PSS, the T l N 0 3 stock solution was prepared from neutral water. The KNO3 salt stock solution was prepared at a concentration of 1.10 M. All stock solutions were degassed with argon prior to sample preparation. Samples were prepared by mixing stock solutions directly in optical cuvettes that had a 1-cm path length, and 5 mL of the polyelectrolyte stock solution was added to a cell. A small aliquot of the concentrated salt solution was added with a microliter pipette to give the desired ionic strength. The contribution to the ionic strength from the KN03 ranged from 0 to 100 mM. Next a small aliquot of the concentrated quencher solution was added to the desired concentration (from 0 to 3 mM for most experiments). The change in concentration of the polymer due to the aliquots was taken into account, although the change in the concentration was never greater than 10%. pH measurements were taken with a Sargent-Welch pH 2050 meter calibrated with standard buffer solutions. (Fisher Scientific: pH 4, potassium biphthalate buffer, 0.05 M; pH 7, potassium phosphate monobasic, 0.05 M adjusted to pH 7 with NaOH; pH 10,potassiumcarbonate potassium borate, potassium hydroxide buffers.) The concentration of the polyelectrolyte was chosen to give an optical density (OD) I0.10 at the fluorophore's maximum absorption wavelength (380 nm and a concentration of 1.1 X 10-5 M for both anthracene derivatives). This low OD minimizes possible fluorophore-fluorophore interactions, energy transfer, and reabsorption, while providing sufficiently intense emission spectra. Optical absorption of all background species such as quencher, salt, base, water, and the quartz cell was negligible above 250 nm. B. QuasielasticLight-ScatteringExperiments. Polyelectrolyte stock solutions were passed through a 0.4-pm pore syringe filter and directly into the light-scattering vials. Proper amounts of quencher and salt stock solutions were similarly passed through 0.2-pm pore filters. The vials of polyelectrolyte solution were then centrifuged to remove adventitious dust. Light-scattering measurements using a Brookhaven BI 2030 apparatus were performed to determine if increasing the ionic strength induces the formation of polymer aggregates. N o evidence of polymer aggregation was found for 9EA-PMA up to 100 mM ionic strength. This suggests that there are neither polymer-polymer interactions nor fluorophore-fluorophore hydrophobic interactions in these systems. C. Steady-State Anisotropy Experiments. The anisotropy measurements were performed by an SPF 500 spectrofluorometer. The anisotropy reflects the fluorophore's relative degree of rotational mobility. Anisotropies were measured for three types
11.
of systems: (a) anthracene in cyclohexane, (b) gEA-PMA, p H = 11, and (c) gEA-PMA, pH = 11 and 1 mM Mg+z. The results for the latter two cases were similar to the free fluorophore in solution. This suggests that their rotational mobility in polyelectrolyte systems is not restricted. In addition, the presence of the divalent counterion Mg+z, which would presumably induce polymer coiling and/or ionic cross-linking, did not result in a significant restriction of fluorophore motion. This is important in our interpretation of experimental data. D. Fluorescence Quenching Experiments. Experiments were performed immediately after the samples were made. Most steady-state fluorescence measurements were performed with an S P F 500 spectrofluorometer. Samples were excited at 380 nm (A, for both fluorophore types), and the fluorescence was recorded from 390 to 600 nm (see Figure 1). The excitation beam passed through a vertical polarizer, and the fluorescence emission was collected a t a right angle to the excitation beam. The emission was detected through a polarizer oriented at the magic angle (54.7O).I6 This eliminated the effects of rotational depolarization although the emission was attenuated approximately 1 order of magnitude. However, the signal to noise ratio is very favorable because of the high quantum yield of these fluorophores. The spectra were integrated to obtain the total fluorescence intensity since there is no change in spectral shape as a function of quenching. The time-resolved fluorescence decay measurements were performed with a laser excitation single-photon counting detection system.'' The samples were excited at 293 nm and emission detected at 430nm. This was the peak of the fluorescence emission for both fluorophore types. The magic angle polarized fluorescence was collected at right angles to the excitation beam in an arrangement analogous to the steady-state polarizer arrangement. The time response of this system is such that a lifetimecomponent of ca. 50-100 ps can be detected with r e c o n v ~ l u t i o n .The ~ ~ halfwidth of the instrument response function is ca. 80 ps. 111. Results and Discussion
A. Stern-Volmer Analysis of Quenching. Fluorescence quenching did not change the shape of the steady-state spectra, as is illustrated in Figure 1 for T1+ quenching of 9EA-PMA with no excess salt. Similar observations were made for DPA-PSS. Figure 2 presents the time-resolved fluorescence decay data as measured by the single-photon counting system for the same solutions as in Figure 1. The decay rates increase with increasing quencher concentration as expected. At low quencher concentrations the decays exhibit almost single-exponential behavior. Only modest increases in the nonexponentiality of the decay are observed for higher quencher concentrations. This implies that the quenching arises primarily from simple diffusive processes.
5536
Morrison et al.
The Journal of Physical Chemistry, Vol. 98, No. 21, 1994
.o.Steady State
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Figure 2. Time-resolvedfluorescence decays of 9EA-PMA quenched by TI+ with no addition of KN03. Same solutions as in Figure 1.
The single-photon decays were fit using a nonlinear leastsquares algorithm to a convolution of the measured instrument response function (Le., the laser pulse plus electronicamplification distortions) and a triple-exponential fitting function. The convolution was used to ensure that the short lifetime components were recovered as accurately as possible. Although the individual amplitudes and the lifetimes obtained from the triple-exponential fit do not have a well defined physical meaning and are subject to fitting artifacts, the average lifetime derived from them is reliable and has an interpretable meaning. Thus the observed fluorescence decay is given by
where R ( T )is the instrumental response function and Zn(t - 7) is the intrinsic fluorescence decay. In the absence of “static quenching” (Le. fluorescence quenching formed by nonemissive complexes), the integral of In(?) equals the total steady-state fluorescence intensity. The average lifetime is given by N (7)
= JomZfl(t) d t = i= I
where the latter form is appropriate for a multiexponential fit and ai = l.16J7 Fitting Zfl(t) to a multiexponential form is merely an empirically convenient method for purposes of obtaining the integral (7).The ratio of the average lifetime of the excited state in the absence of quencher ( ( T O ) ) to ( T ) with quencher is plotted against the quencher concentration, as is the steady-state ratio Zo/Z. Thesecan be fit to the following empirical equation:’*
Ksv is the normal Stern-Volmer constant, and the second-order quenching rate constant is defined by the relationship Ksv = k,( ro). A I is the coefficient for the higher order term and reflects the deviation from the linear Stern-Volmer behavior. The equality of loll and ( T O ) / ( 7 ) indicates that the quenching is diffusive in nature; i.e. all fluorescence quenching is dynamically resolved. Typically a chemical system with a uniform distribution of reactants which undergo reaction upon simple diffusive collisions displays simple Stern-Volmer behavior (Le. linear in [ Q ] ) .Since our observed quenching deviates from linear SternVolmer behavior, one may infer that the polyelectrolyte solution contains a nonuniform distribution of quenchers and fluorophores. For high ionic strengths or very high quencher concentrations, the deviations between the two data sets become more noticeable and it is found that loll # TO)/(^). This indicates that a small
I 0
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,-o,,, Steady State -0.Time Resolved
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[TfI (mM)
Figure 3. (a, Top) Stern-Volmer plots of TI+ quenching of 9EA-PMA at threedifferent averageionic strengths (IS = 2.46,29.1, and 77.4 mM) from steady-state and time-resolvedfluorescencedata. The region of the curye fit to eq 3 of the text is indicated by the heavy line. (b, Bottom)
Stern-Volmer plots of TI+ quenching of 9EA-PMA over a larger range of quencher concentration (no added KNO& fraction of the quenching events occur through static quenching under these conditions. Figure 3a presents Stern-Volmer plots for T1+ quenching of 9EA-PMA. Three pairs of curves are shown. Each pair consists of a curve derived from steady-state and time-resolved measurements for a given addition of KN03. The total ionic strength (IS) for the 9EA-PMA system is given byI9
IS = [KNO,]
+ [TINO,] + [KOH]
(4)
Note that we do not include the contribution of the polyanion to the ionic strength although the polyion counterion concentration is included. For 9EA-PMA the polyacid is neutralized by the addition of KOH such that some of the OH- ions are removed from solution. Thus eq 4 slightly overestimates the ionic strength. In our discussion and in the figure captions, the average ionic strength will be referred to since the TIN03 concentration varies slightly along the quenching curve. The Stern-Volmer curves for 9EA-PMA display significant negative deviation from linear behavior, especially at the lowest ionic strength. This feature is diminished for higher ionic strengths. The negative curvature is often taken to imply that a fraction of fluorophore population is not accessible to quenchers.l* Figure4 presents Stern-Volmer plots of T1+quenching of DPAPSS as measured by steady-state ( l o / l ) and time-resolved ( ( T O ) / (7))fluorescence techniques for three different ionic strengths. The total contribution to the ionic strength for the DPA-PSS system is given by
IS = [KNO,]
+ [TlNO,] + 1/2[Na+]
(5)
where the polyanion counterion is Na+. Once again we ignore the contribution from the polyanion. The time-dependent and
The Journal of Physical Chemistry, Vol. 98, No. 21, 1994 5537
Polyelectrolyte-Modified Reaction Dynamics a.Steady State am------------2.0
e .',,,
.
------ -
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0
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Figure 4. Stern-Volmer plots of T1+ quenching of DPA-PSS at three different average ionic strengths (IS = 1.21, 27.7, and 76.4 mM) from steady-stateand time-resolved fluorescence data. Monomer concentration 1.1 mM. 10
[I-
2nb order 'S.V. fit.1'
DPA-PSS
b 0.0
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[Ti'] (mM)
Figure 5. Stern-Volmer plots comparing the fluorescence quenching of 9EA-PMA and DPA-PSS at the lowest ionic strengths (Is = 2.46 and 1.21 mM, respectively). DPA-PMA and DPA-PAA with ionicstrengths of 2.73 and ca. 3 mM, respectively, are shown for comparison. Data points for these latter two curves have been removed for ease of viewing.
steady-state techniques give similar Stern-Volmer curves except at the highest quencher concentrations for the lowest ionic strength case. This differencesuggests that there is a significant component of static quenching at higher T1+ concentrations. However, in general, diffusive quenching strongly dominates. The quenching curves for the DPA-PSS polyelectrolyte system as a function of IS exhibit the same qualitative features as those shown for the 9EA-PMA system. The magnitude of fluorescence quenching of DPA-PSS is significantly smaller than that of 9EA-PMA. These are compared in Figure 5 under the lowest ionic strength conditions, where quenching reactions achieve maximum efficiency. At the highest quencher concentrations only approximately 50% of the excitedstate DPA-PSS population has been quenched by T1+ whereas nearly 90% of the excited-state 9EA-PMA population has been quenched for the equivalent TI+ concentration. Figure 5 also includes the data for DPA-PMA and DPA-PAA (PAA = polyacrylic acid) for comparable solutions. The minimum ionic strengths for the DPA-PMA (2.73 mM) and DPA-PAA (ca. 3 mM) solutions are slightly higher than that of DPA-PSS (1 -21 mM) because the former required the addition of KOH to achieve a basic medium (pH 11). Data for DPA-PAA were originally taken at a polymer concentration of 2 mM, and therefore, for this
case the quencher concentration has been scaled down by a factor of 2 in order to maintain the same ratio of quencher to charged monomer for all polyelectrolyte-chromophore systems compared. It has been shown previously that quenching curves at low ionic strengths are superimposable when plotted as a function of the ratio [quencher]/[monomer].2 A related concept will bediscussed in section D later. The magnitude of fluorescence quenching for the DPA-labeled polyelectrolytes differs significantly from 9EAPMA. Comparing the DPA-labeled polyelectrolytes, we note the important fact that the different polymer backbones produce only modest changes in the degree of quenching. Their initial slopes differ, but as will be discussed in the next section, the initial Stern-Volmer slopes depend strongly on ionic association. There are at least two mechanisms that might give rise to negative curvature. The change in ionic strength could cause a structural change in the polyelectrolyte such that the polymer is coiled around thechromophore. This would act as a steric barrier to quenchers. Since the coiling of a polymer is statistical, there would be some chromophores that would be "protected" from quenching as well as a fraction that is available to the quenchers. However, the similarity of the DPA-PSS, DPA-PMA, and DPAPAA quenching curves argues against this explanation. Another mechanism for negative curvature is dynamic inaccessibility. In this case the quenchers are unable to contact the chromophores in time to quench them before they fluoresce. This can arise from a nonhomogeneous distribution of quenchers, as has been observed in other systems of different geometry.I3 Independent of mechanism, it is possible to extract numbers for the reaction rate and the hypothetical fraction of chromophores accessible to quenchers using a two-state model, as is done in section C. B. Analysis of the Initial Slope: 4 = & / ( T O ) . The SternVolmer plots exhibit a wide variation in the initial slopes for different ionic strengths. Since the slopes are proportional to the rates of quenching, the differences in the slopes reflect the influence of ionic strength on the reaction rate. The quenching C U N ~ S are fit to thesecond-order Stern-Volmer equation (eq 3). The SternVolmer constant, K,,,obtained from this fitting yields the apparent quenching rate constant, k,, which is the quantity of interest for diffusion-reaction theory. We note that the ( T O ) values of DPAPSS (6.4 ns) and 9EA-PMA (12.0 ns) do not change significantly with ionic strength. This procedure for extracting k, is completely empirical and is appropriate for quenching data for physical systems of any complexity or geometry. This will be discussed more completely in part 11.20 Figure 6 presents plots of the quenching rate constant versus the ionic strength as derived from both time-resolved and steadystate fluorescence measurements of T1+ quenching of 9EA-PMA and DPA-PSS. The effect of ionic strength on the reaction rates is very dramatic, especially in the low ionic strength region (0-25 mM). Within this region the rate drops nearly 1 full order of magnitude. In the intermediate to higher ionic strength regions (25-100 mM), the rates decrease to a lesser extent. On the basis of the similarity in the k, values, it is evident that the reaction rate for low quencher concentrations is not sensitive to the shortrange interactions between T1+ and the carboxylate or styrenesulfonate anions of the two different polyelectrolyte environments. It is useful to compare these experimental rates with the diffusion-controlled bimolecular rate constant on the basis of the classic Smoluchowski model in its simplest form. In this model the rate of a diffusion-controlled reaction depends only on the rate of diffusion between the reactant molecules and their size:
kdin= 4aRD where R and D are the sum of the molecular radii and diffusion coefficients for the reactants, respectively. This model is appropriate for a system in which reactants are distributed homogeneously and experience no electrostatic interactions. In addition, the reaction is assumed to occur with 100% efficiency
Morrison et al.
5538 The Journal of Physical Chemistry, Vol. 98, No. 21, 1994 1 OF
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Figure 7. Fraction of accessibilityJ., plotted as a functionof ionic strength for both polyelectrolyte-fluorophore systems.
Ionic Strength [mM] 14
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a linear Stern-Volmer plot are often taken to imply that some fluorophores are not accessible to quenchers and a two-state model has been developed to address the issue of fluorophore accessibility.I8 In this model it is assumed that one population (A) is accessible to quenchers, whereas the other (B) is not. In the absence of quencher the total fluorescence ( l o ) is given by 0'
Ionic Strength [mMl
With added quencher the fluorescence intensity of population A decreases according to the linear Stern-Volmer equation, whereas for population B the intensity does not change. This leads to the following relation:*8
Figure 6. Second-orderquenching rate constant versus ionic strength for TI+quenchingof (a, top) 9EA-PMA and (b, bottom) DPA-PSS as derived from steady-state and time-resolved fluorescence measurements.
per collisional event. For theTl+ and 9EA-PMAreactants, where it is estimated that R = 8.52 X 10-8 cm (based on CPK models for anthracene) and D = $00 X 10-5 cm2 s-I for the T1+ 23 (we neglect the fluorophore diffusion), the diffusion-controlled rate is 1.29 X 1010 M-1 s-1. As can be seen from Figure 6 , this estimate falls approximately 2 orders of magnitude below the observed values at low ionic strength. We will discuss elsewhere20 the comparison of the Smoluchowski model in a cylindrical geometry to the more commonly considered spherical geometry. It is reasonable to expect that the experimental rate constant will always exceed this diffusion-controlled limit because one would expect a highly accelerated reaction rate for reactants experiencing a strong attractive potential. At high ionicstrengths the potential is screened. Correspondingly, the kqvaluefor 9EAPMA at the highest observed ionic strength (102 mM) is 4.5 X 1010 M-' s-l, which is only slightly larger than computed above. The remarkably high reaction rate observed at low ionic strengths is a result of the equilibrium accumulation of quencher ions in the immediate vicinity of the polyion, a result expected for polyelectrolytes.21 The sharp variation of rate with ionic strength can be expected to be affected by two types of influences. The first is simply statistical, with quencher ions randomly replaced in this near region by added salt. The second is dynamical, as the diffusion dynamics will experience a decreasingly steep electrostatic potential near the polyion with increasing salt concentration. In addition, polyion conformational changes may play a role although, as we have argued earlier (section A), this does not appear to be an important factor. The analysis presented below indicates that the statistical effect dominates but is insufficient to describe the data quantitatively. C. Inaccessible Fluorophores: The Two-State Model. The initial slope analysis does not extend to the characteristic features observed in the Stern-Volmer curves for higher quencher concentrations. As mentioned earlier, negative deviations from
(7)
= 'OA + O' B
--0' - - 1+ '0-1
where
fa
1 'q?$a[QI
, (9)
fa
represents the fraction of the excited-state fluorophore population that can be quenched at an infinite quencher concentration. fa can be extracted from the data via eq 8 by plotting Zo/(Zo - Z) against l/[Q], and fa is calculated from the intercept. This data analysis was applied to all quenching data for the higher [TP] values (>0.15 mM) for which the extrapolation was most reliable (fits not shown). The inaccessibility of a fluorophore does not necessarily imply that it is immobilized in a region free of quenchers. A theoretical study by Yekta et al. introduced another system which displays "two-state" behavior.13 Their model considered the fluorophores diffusing within a spherical region with quenchers condensed on the outer surface, such that excited-state fluorophores are quenched after diffusion to the surface. It was shown that the accessible fraction depended on the parameter a = D70/R2 ( D is thefluorophorediffusionconstant, R i s theradiusofthespherical region, and 70 is the excited-state lifetime). In this case, the accessibility is defined from a dynamical perspective and we suspect that this is analogous to the situation encountered here. In support of this we recall that fluorescence depolarization measurements did not indicate any diminution of the pendent anthracene mobility even with the addition of a divalent ion (see section C). The plots of fa versus ionic strength are shown in Figure 7. The DPA-PSS and 9EA-PMA systems exhibit a striking difference in the fraction of accessible excited-state fluorophores, withfa = 0.55 and 0.95 for DPA-PSS and 9EA-PMA, respectively. It is worth mentioning that, unlike k,, fa does not exclude any bias due to the excited-state lifetime, 70. The difference in TO)S of the fluorophores might therefore account for the observed difference in accessibility fractions. The accessible fraction,
Polyelectrolyte-Modified Reaction Dynamics I E,
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The Journal of Physical Chemistry, Vol. 98, No. 21. 1994 5539 I
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Figure 8. Scaled Stern-Volmer plot as a function of [Tl+]/IS. Same data as used in Figures 3 and 4.
however, can only be sensitive to the excited-state lifetime if the time scale for any diffusive quenching is a t least comparable to TO, The average lifetimes for 9EA and DPA are 12.0 and 6.4 ns, respectively. To estimate the relevant diffusive time scale for quenching, we first note that the fluorophores are present at ca. 1% loading, so that their average spacing along the polymer contour isroughly 250A. Weassumefor thesakeofthisestimate that the most rapid diffusion occurs along the polymer contour where the electrostatic potential is constant.22 If one then evaluates the average initial distance between a quencher ion near the polyion and the nearest polymer-bound fluorophore, the result is roughly I = 60 A. Taking the diffusion constant of the quencher as 2.0 X le5cmZ/s, one obtains a characteristic time of T 12/2Dof 9 ns. Therefore the shorter lifetimeof the excitedstate DPA may dramatically curtail the magnitude of quenching. The polyelectrolyte systems display a very similar decrease in the accessibility fraction as a function of ionic strength. This steady decrease in the fraction of accessible fluorophore tends todiscount the possibility of large-scale perturbations of the fluorophore environment induced by a polyelectrolyte conformational change. It is further consistent with thisview that, at higher ionicstrengths, the K+ counterions displace T1+ from the condensation region of the polyelectrolyte and increase the average separation between the quencher and fluorophore. Exploration of this effect using simple models to evaluate this effect quantitatively will be considered elsewhere.2o D. Scaled Stern-Volmer Plots. The Stern-Volmer plots shown in the previous figures can be plotted with the quencher concentration divided by the total ionic strength. The ratio of the concentration of quencher to the total ionic strength can be interpreted as the fraction of "active" counterions. The idea behind plotting the curves in this way was to see if the Stern-Volmer plots were simply scaled by the mole fraction of the quencher ions to all ions. It is also expected that in the condensation zone around the polyelectrolyte the ratio of quencher to inert salt should be equivalent to the bulk ratio because of the similarity of T1+ and K+. The plots of the scaled Stern-Volmer curves for both the PSS and PMA systems are presented in Figure 8. The lines in Figure 8 (data points not shown for clarity) represent constant ionic strength a t different quencher concentrations. For each polyelectrolyte system, the curves a t different ionic strengths are clustered together. The lowest ionic strength is on the bottom right of each set of curves, and the ionic strength increases to the left. Further, the two sets of curves appear to scale according to the excited-state lifetime. This kind of scaling is also found for theoretical simulations.20 Thus, we can say a t least to a first approximation that all thedata measured for thedifferent polymer systems and a t different ionic strengths all scale simply with the mole fraction of quencher with respect to the total ionic strength and the fluorescence lifetime. However, if statistical dilution were the only effect present, then all the scaled data would coincide
-
Figure 9. Comparison ofk, from theory and experiment. The arameters used were a = 5.0 A (radius of polymer + TI+), b = 2.5 (contour monomer length), D = 200 AZ/ns, sink length = 10.2 A, sink radius = 8.43 A, and [monomer] = 1 mM. The zero potential rate = 1.7 X 1010 M-I s-l.
for each of the polyion systems. As is evident from Figure 8, the statistical effect is a major component, but there are also differences in the dynamics of quenching in the spread for identical polyions. In fact, the increasing slope in the Zo/Zplot when plotted against the scaled quencher concentration is consistent with more rapid radial exchange of quencher and inactive ions a t higher ionic strength. E. Comparison to Theory. The data here can be compared to the Smoluchowski model (in cylindrical geometry) using a Poisson-Boltzmann potential. The model and calculations are discussed in greater detail elsewhere.20 However, we briefly describe our model and some results here. The PMA polymer is taken to be an infinitecylinder with a finite radius (theexcluded volume contact distance between polyelectrolyte and ion is taken to be 5 A). The monomer charges are taken into account by using a charge density equal to the unit charge per monomer contour length (2.5 Alcharge). The chromophore is treated as a cylindrical reaction zone of finite length (radius 8.43 A and length 10.4 A, based on CPK models). The T1+ quenchers (diffusion constant 2.0 X le5cm2/sZ3)diffuse in the solution under the influence of the polyelectrolyte-quencher intermolecular potential, which is affected by the other ions in solution. This ionic atmosphere shields the charges and gives rise to a rapidly decreasing intermolecular potential as a function of the radial distance from the polymer. The Poisson-Boltzmann equation is used to approximate the screened intermolecular potentia1.24Js The polyelectrolyte has the opposite charge of our quenchers, which yields an equilibrium condensation of quencher ions around the p~lyelectrolyte.~'~~ It is useful to compare the measured and theoretical initial rates (k,) as a function of ionic strength. In Figure 9 the theoretical rate vs ionic strength is shown and compared to the PMA data. As can be seen, both display the same initial decrease of k, followed by a leveling off at high ionic strength. The magnitudes are also quite similar (within a factor of approximately 2). The experimental data asymptotically approach the zero potential theoretical value, computed to be 1.7 X 1O1O M-1 s-l, which is virtually identical to the spherical Smoluchowski result discussed earlier (see eq 6 ) . However, for the full Stern-Volmer plots, the theoretical and experimental curves have positive and negative curvatures, respectively. Thus, the simplest model can reproduce some aspects of the experiment but does not reproduce the negative curvature in the Stern-Volmer plot. The modifications of a simple cylindrical model that are required to provide a better agreement between experiment and theory will be presented elsewhere.20 IV. Concluding Remarks The results for the T1+fluorescence quenching studies on both 9EA-PMA and DPA-PSS suggest that a t low concentrations of
5540 The Journal of Physical Chemistry, Vol. 98, No. 21, 1994
T1+ quenching is almost entirely diffusive, although at high quencher and salt concentration some static quenching is observed. At low ionic strength the rates of fluorescence quenching in polyelectrolyte solutions exceed the homogeneous solution diffusion-controlled rate by approximately 2 orders of magnitude. Electrostatic screening results in dramatic reduction in the polyelectrolyte-enhanced reaction rate for only slight increases in the ionic strength, and the rate asymptotically approaches the diffusion-controlled limit at higher ionic strengths. Lastly, the results indicate that a significant fraction of the fluorophore population for DPA-PSS remains inaccessible to TI+quenching. The analysis suggests that this is a dynamical effect rather than classical steric hindrance. Future work will address the influences of different types of counterions as well as different modes of chromophore attachments to the polyelectrolyte on the rates of fluorescence quenching. Part 220 will discuss the theoretical aspects of this problem and present more detailed calculations. Acknowledgment. This research has been sponsored by the Officeof Naval Research, Grant No.NOOO14-91-5-1667, whose financial support is gratefully acknowledged. S.E.W. would also like to acknowledge the support of the Robert A. Welch Foundation (Grant F-356).The computational support of the Center for High Performance Computing of the University of Texas System is also gratefully acknowledged. The DPA-PAA data recorded by Dr. Ti Cao and the synthesis of DPA-PMA by Qiang Cao are both gratefully acknowledged. References and Notes (1) Rabani, J. In Photoinduced Electron Transfer, Part B; Fox, M. A., Chanon, M., Eds.; Elsevier Science: Amsterdam, 1989; pp 642-699. (2) (a) Webber, S. E. Macromolecules 1986,19,1658. (b) Delaire, J. A,; Rodgers, M. A. J.; Webber, S.E. J. Phys. Chem. 1984,88,6219.
Morrison et al. (3) Stramel, R. D.; Webber, S. E.; Rodgers, M. A. J. J. Phys. Chem. 1989,93, 1928. (4) Soutar, I.; Swanson, L. Eur. Polym. J . 1993,29,371. (5) Morishima, Y.; Ohki, H.; Kamachi, M. Macromolecules 1993,26, 4293. (6) Drifford, M.; Dalbiez, J. P. Biopolymers 1985,24, 1501. (7) Ander, P.; Kardan, M. Macromolecules 1984, 17, 2436. (8) Katchalsky, A.; Spitnik, P. J. Polym. Sci. 1947,2, 432, 487. (9) Oosawa, F. Polyelecfrolytes; Marcel-Dekker: New York, 1971. (10) Manning, G. S. In Annual Review of Physical Chemistry, Vol. 23; Eyring, H., Christensen, C. J., Johnston, H. S., Eds.; Annual Reviews: Palo Alto, CA, 1972; pp 117-140. ( I 1) Onsager, L. Ann. N. Y.Acad. Sci. 1949,51, 627. (12) Strauss, U. P. In Charged and Reactive Polymers, Vol. I: Polyelectrolytes; Selegny, E., Mandel, M., Strauss, U. p., Eds.; D. Reidel: Dordrecht, 1975; pp 79-86. (13) Yekta, A.; Duhamel, J.; Winnik, M. A. J. Chem. Phys. 1990, 97, 1554. (14) Turro, N. J.; Barton, J. K.; Tomalia, D. A. Acc. Chem. Res. 1991, 21, 332. (15) Johansson, L.; Elvingson, C.; Lofroth, J. Macromolecules 1991,24, 6024. (16) Lakowicz, J. R. Principles of Fluorescence Spectroscopy; Plenum Press: New York, 1983; p 131. (17) Prochazka, K.; Kiserow, D. J.; Ramireddy, C.; Tuzar, Z.; Munk, P.; Webber, S. E. Macromolecules 1992,25, 461. (18) See ref 16, Chapter 9. (19) Atkins, R. W. Physical Chemistry, 4th ed.; W. H. Freeman and Co.: New York, 1990; p 251, eq 6a. (20) Manuscript in preparation. (21) Manning, G. S. In Charged and Reactive Polymers, Vol. 1: Polyelectrolytes; Selegny, E., Mandel, M., Strauss, U. P., Eds.; D. Reidel: Dordrecht, 1975; pp 9-37. (22) Rami Reddy, M.; Rossky, P. J.; Murthy, C. S. J. Phys. Chem. 1987, 91,4923. (23) CRC Handbook of Chemistry and Physics, 66th ed.;Weast, R. C., Ed.; CRC Press: Boca Raton, FL, 1985; p D-167. (24) Bacquet, R. J.; Rossky, P. J. J. Phys. Chem. 1988,92, 3604. (25) Gutron, M.; Weisbuch, G. Biopolymers 1980,19,353. (26) Manning, G. S. J. Chem. Phys. 1969,51, 924. (27) Manning, G. S. J. Chem. Phys. 1969,51, 934.
