14358
J. Phys. Chem. C 2007, 111, 14358-14364
Electric Birefringence of Electrolytes near Charged Surfaces, I Sourav Saha and Lynden A. Archer* School of Chemical and Biomolecular Engineering, Cornell UniVersity, Ithaca, New York 14853 ReceiVed: January 2, 2007; In Final Form: April 22, 2007
We investigate electric birefringence of aqueous electrolyte solutions near a negatively charged silica glass surface using evanescent wave laser polarimetry (EWLP). By probing changes in the polarization state of visible light totally internally reflected at the solid-liquid interface, EWLP facilitates unprecedented measurements of electric-field-induced birefringence in a thin electrolyte film, O (150 nm), adsorbed on the glass surface. For aqueous NaCl and MgCl2 solutions (1-100 mM), these measurements reveal Kerr law behavior over a range of pH and solution concentrations. The Kerr coefficients are, however, several orders of magnitude larger than values normally obtained from bulk electric birefringence measurements. We propose that formation of anisotropic, polarizable ionic clusters near the glass surface is the source of these observations. Orientation of the clusters by the electric field is confined in the plane defined by the glass/electrolyte interface and is attributed to rearrangement of the constituent ions. Birefringence relaxation measurements reveal relaxation times, τ, many orders of magnitude larger than typically observed in molecular fluids. These measurements also show that τ is independent of both the electrolyte concentration, c, and pH. We discuss these latter observations in terms of an ion redistribution process, wherein the intrinsic surface adsorptiondesorption rates of ions in the clusters determine the time constant for relaxation of surface birefringence.
I. Introduction Electric-field-induced orientation and relaxation of polarizable, charged macromolecules in electrolyte solutions have been studied extensively using electric birefringence techniques. These measurements are important because they provide unique insight into the molecular origin of polarization and structural transitions in synthetic and naturally occurring polyelectrolytes.1-7 Field-induced orientation of ionized polyelectrolytes is now known to result from multiple processes, including interaction of the applied electric field with permanent dipoles on the molecules and interaction with transient dipoles induced via the covalent (electronic and atomic) polarizability or the polarizability of condensed counterions. Although it is widely believed that polarization of condensed counterions by the electric field is the most dominant molecular phenomenon responsible for macroscopic polarization of polyelectrolyte solutions,1,8-11 little is known about the exact mechanism and time scale of counterion redistribution near a charged molecule. In this article, we employ an evanescent wave laser polarimetry (EWLP) technique described elsewhere12 to study both the polarization mechanism and field-induced orientation effects produced by counterion redistribution near a negatively charged glass surface. In these measurements, a dc electric field is applied parallel to the glass/electrolyte interface, and birefringence induced within a very thin layer (∼140 nm) of electrolyte solution at the glass/electrolyte interface is measured. The phenomenon of electric birefringence produced by electric-field-induced orientation of optically anisotropic and polarizable molecules, known as the Kerr effect, is well-known and widely studied. In the Kerr regime, a square law relationship between the steady-state birefringence, ∆n′ss, and an applied electric field, E, is observed. Kerr behavior has been reported * To whom correspondence should be addressed. E-mail: laa25@ cornell.edu.
not only for water and other organic molecules with permanent dipole moments,13 but also for aqueous ionic14 and polyelectrolyte solutions.1,6 Likewise, polarization of condensed ions at charged surfaces (e.g., the glass walls used in capillary electrophoresis equipment, charged particles undergoing electrophoresis in simple electrolyte buffers, or buffers containing neutral polymer) might be expected to give rise to Kerr law electric birefringence characteristics. In this study, we investigate both the mechanism of polarization and the origin of anisotropic polarizability of condensed counterions near a negatively charged glass surface. II. Experiment Figure 1a is a schematic of the EWLP experimental apparatus. The electrolyte cell consists of a 30 × 10 × 1 mm open channel cut into a polyoxymethylene base with platinum-black-coated electrodes (separation, 30 mm) located at each end of the channel. The electrolyte solutions are sealed in the channel using a silica glass hemisphere (radius ) 20 mm; refractive index, n1 ) 1.52), which carries a net negative charge, the magnitude of which can be manipulated through the pH of the electrolyte solution. The hemisphere’s weight and the fluid’s surface tension are the only forces that restrain the fluid in the channel. Later, we will show that the Kerr coefficient of an electrolyte near a charged substrate is 7-8 orders of magnitude larger than typical of electrolyte solutions in bulk. Moderate dc electric fields (250 V/cm), generated by applying a voltage across the channel using a power supply (Biorad, PowerPac 1000) are therefore used throughout to generate electric birefringence in the electrolytes. Because of their small amplitude, these fields are imposed by manually turning on the power supply at a preset time. The field is removed by manually turning the power supply off at a chosen time. This situation can be contrasted with the much higher fields (∼10 kV/cm) and short permissible pulse duration times (approximately microseconds) normally required
10.1021/jp0700229 CCC: $37.00 © 2007 American Chemical Society Published on Web 09/08/2007
Electric Birefringence of Electrolytes, I
J. Phys. Chem. C, Vol. 111, No. 39, 2007 14359
I(t) ≈
Figure 1. Schematic diagrams of optical arrangements used for (a) evanescent wave laser polarimetry, EWLP; (b) bulk electric birefringence experiments.
for reliable electric birefringence measurements in conducting media.13,15 A helium-neon laser with wavelength λ ) 633.2 nm incident at an angle of φ ) 83° to the direction y (see Figure 1a) is employed to generate an evanescent field in the electrolyte solution near the 1-2 (glass-electrolyte solution) interface. The refractive index of the electrolyte solution, n2 = 1.33, implies a critical angle, φc, of asin(n2/n1) close to 61°. Thus, for φ > φc, the laser light is totally reflected at the 1-2 interface, and the evanescent wave carries information about the optical properties of the material in medium 2 located within a characteristic penetration depth, dP, of λ/(2πxn12sin2φ-n22), which is ∼140 nm for our experiment configuration.12,16 Our goal is to quantify the effect of steady electric fields in the channel on transient molecular orientation near the interface. This goal is easily realized using the optical arrangement shown in Figure 1a, which allows the time-dependent birefringence, ∆n′(t), and orientation angle, χ(t), of optically anisotropic molecules near the interface to be simultaneously determined. The laser light is first polarized parallel to the direction of the electric field x using a linear polarizer (P), and subsequently modulated using a photoelastic modulator (PEM) and a quarter wave plate (Q) oriented in the configurations shown. Following total internal reflection at the 1-2 interface, the light beam is analyzed using a circular polarizer (CP) and photodetector (D) and demodulated using lock-in amplifiers. The time-dependent intensity, I(t), measured by the detector is related to the intensity of the incident light, I0; the polarization modulation frequency, ω; the birefringence retardation, δ′ ) 2πdeff∆n′/λ, of the electrolyte medium; and the apparent orientation angle, χ′, by the following expression,12
I0 [1 - 2J1(A) sin(δ′) cos(2χ′) sin(ωt) + 2J2(A) sin 2 (δ′) sin(2χ′) cos(2ωt)] (1)
where deff ≈ 2dP/(cos φ) is the effective optical path length, which is ∼2.3 µm for the optical configuration depicted in Figure 1a. ∆n′ is the induced birefringence of the electrolyte medium near the glass surface. J1(A) and J2(A) are Bessel function coefficients that arise from the modulation;17 both coefficients are determined from separate calibration experiments using materials of known birefringence retardation (e.g., retardation plates) with the PEM tuned to achieve J0(A) ) 0.12,17 For the PEM settings and optical configuration used in this study, the condition J0(A) is achieved for A ≈ 2.3. The calibration experiments yielded J1(A) ≈ 0.51 and J2(A) ≈ 0.42; i.e., close to the expected theoretical values. An alternative form of eq 1, I(t) ≈ Rdc - Rω sin(ωt) + R2ω cos(2ωt), indicates that two lock-in amplifiers tuned to ω and 2ω with appropriate phases and a low pass (dc) filter are sufficient to measure all Fourier amplitudes, Rk, of the optical signal, allowing δ′ (or ∆n′) and χ′ to be determined simultaneously. To compare the electric birefringence arising from the electrolyte layer near the glass surface with that arising from the bulk electrolyte solution, electric birefringence measurements were also attempted using the optical setup described in Figure 1b. The optical train and experimental running conditions are maintained the same as for the EWLP experiment (see Figure 1a), except that the glass hemisphere is replaced by a glass cover slip, and the transmitted light beam from the bulk electrolyte solution is collected through a cylindrical glass window depicted in Figure 1b. Normal incidence ensures that the optical path length and penetration depth , which are several orders of magnitude larger than both deff (∼2.3 µm) and dp (∼140 nm) in the EWLP configuration, are the same for this arrangement, ∼1 mm. Electrolyte solutions were prepared by dissolving appropriate amounts of NaCl and MgCl2 in DI water (∼18 MΩ, pH ∼ 5) to make up solutions with concentrations in the range 1-100 mM. To study the effect of electrolyte pH on birefringence, NaCl solutions were also made up in various buffers that consisted of maleate (pKa ) 2.0), formate (pKa ) 3.75), acetate (pKa ) 4.76), pyridine (pKa ) 5.23), phosphate (pKa ) 7.2), and Tris (pH ) 8.06) buffers. The pH of the resulting solutions was adjusted over a wide range (2, 3, 4, 5, 7, 8, and 9) by titrating with strong base (NaOH) or strong acid (HCl) as required. The glass hemisphere and coverslips were treated with a 50/50 mixture of sulfuric acid and 30 % v/v hydrogen peroxide at 100 °C for 1 h before carrying out the birefringence experiments. This treatment minimizes surface contamination by organics and other adsorbed species. III. Results and Discussion A. Electric Birefringence of Electrolytes Near a Glass Surface. Figure 2a compares the transient birefringence obtained using the arrangements depicted in Figure 1a and b. Both sets of data are for a 10 mM NaCl solution at a fixed electric field, E ) 20 V/cm. It is apparent from the figure that when the electric field is applied, the birefringence of the electrolyte solution near the glass surface rises and approaches a steadystate value. When the electric field is removed, the birefringence slowly decays to its prefield, zero value. These effects are found to be completely reversible irrespective of the number of field applications in a given direction, indicating that no permanent polarization occurs at the fields used in the study. The “true”
14360 J. Phys. Chem. C, Vol. 111, No. 39, 2007
Figure 2. Time evolution of birefringence and raw output data for EWLP and bulk birefringence measurements: (a) ∆n′(t) versus time for (I) 10 mM NaCl solution at E ) 20V/cm, (II) 10 mM NaCl at E ) 20V/cm for bulk electric birefringence experiment, (III) toluene at E ) 333 V/cm in EWLP experiment, and (IV) DI water at E ) 50 V/cm in EWLP experiment. (b) 10 mM NaCl at E ) 50 V/cm in EWLP experiment with progressively increasing electric field duration. The inset shows (∆n′/∆∆n′max)t versus time t for the same conditions as in (b). (c) First and second lock-in signals corresponding to birefringence signal 3 in (b); (inset) χ′ against field application time.
steady-state birefringence value, ∆nss, for any desired electric field, E, is obtained by fitting the time-dependent traces to the formula ∆n′(t) ) ∆n′ss(1 - exp[-t/τ]). Figure 2a shows that no birefringence is observed from the corresponding bulk experiment. The absence of measurable bulk birefringence for the tiny electric fields used in these experiments is indeed expected from the small static Kerr constant, Kλ ≡ ∆n′/λE2 ≈ 3 × 10-14 (m/V2) reported for liquid water,13 and even from the largest optical Kerr constants Kλ ≈ O (10-8) (m/V2) that can be inferred from data for more highly concentrated aqueous electrolyte solutions.14 Conversely, the large birefringence levels obtained in the EWLP experiments are unexpected. EWLP measurements using pure ∼18 MΩ DI water and toluene do not produce measurable birefringence, which simultaneously indicates that the electric birefringence effect observed in the EWLP configuration is a surface phenomenon requiring solvated ions. Significantly, we also find that if the silica glass hemisphere is replaced by one constructed from a heavily leaded glass (Schott Glass, SF57), no birefrin-
Saha and Archer gence is observed, even at an electric field of 100 V/cm. This result indicates that a large surface charge is probably required to produce birefringence near the surface. Figure 2b reports the effect of field application time on the transient birefringence, ∆n′(t). These measurements were all performed using a 10 mM NaCl solution at a fixed electric field of 50 V/cm. The results reported are for sequential (back-toback) measurements when the field is applied in the same direction for progressively longer times with a rest period of 10 min allowed between runs. It can be seen from the figure that the birefringence rise characteristics are the same, irrespective of the time for which the field is applied. A characteristic birefringence relaxation time can be estimated either by fitting the birefringence decay curve to a single-exponential function or by plotting the product of the normalized birefringence decay signal and time (∆n′/∆n′max)t against the time, t, where ∆n′max is the maximum value of the birefringence signal. The time, τ, corresponding to the maximum in (∆n′/∆n′max)t is easily shown to represent the characteristic relaxation time for a Debye-type (single-exponential) relaxation function and the average decay time constant for a relaxation function characterized by multiple, closely spaced Debye-type relaxation processes. From Figure 2b(inset), it can be seen that plots of (∆n′/∆n′max)t versus t corresponding to different field application times coincide. The characteristic time of τ ≈ 20 s deduced from these plots is identical to that obtained by fitting the birefringence decay curve to a single-exponential function. Both findings serve to confirm that a single, uncoupled, slow process controls the birefringence relaxation. The fact that the characteristic time is independent of field imposition time is also significant because it indicates that the processes that produce the birefringence are fully reversible and are not accompanied by any permanent, fieldinduced polarization or other changes in physical properties of the electrolyte medium near the glass/electrolyte interface. That a single-exponential function fits the birefringence decay is likewise significant because it indicates that the underlying process responsible for the birefringence is distinct, and its contribution dominates the measured optical response. Santa et al.14 have performed the most thorough investigation of electric birefringence in aqueous electrolytes. These authors have identified an essentially complete list of physical processes that might give rise to electric birefringence in aqueous solutions of symmetric ions. For the relatively low concentrations of NaCl used in the present study, both ions can be assumed to be fully and symmetrically solvated, and the medium properties can be well described by a simple liquid model. It therefore follows that none of the physical processes envisaged by these authors could be the source of the behavior revealed by EWLP. Specifically, in simple liquids, the slowest processes identified by these authors, correlated density fluctuations arising from molecular interactions and strained rotational motion of the solvated ions, occur on typical molecular timescales of, at most, a few nanoseconds, which is clearly much too fast to explain the unusually slow birefringence relaxation times we observe. Further insight about the physical origin of the surface phenomenon reported by the EWLP measurements can be obtained from the orientation angle, χ. To begin, we assume n1, n2, and n3 are the principal values of the refractive index tensor of these molecules in a molecule-fixed coordinate frame (1-2-3), where n1 is in the direction of the optical symmetry axis (principal axis) of the molecule, and n2 and n3 are in the directions perpendicular to the symmetry axis. Thus, for φ f 90°, χ′ ≈ χ, where χ is the orientation angle of the molecules
Electric Birefringence of Electrolytes, I
J. Phys. Chem. C, Vol. 111, No. 39, 2007 14361
Figure 3. Schematic representation and definitions of orientation angles discussed in the text. The coordinate axes are the same as in Figure 1.
in the x-y plane (see Figure 3), and ∆n′ can be expressed as follows:
∆n′ ≈ {(n1 - n2) cos2 χ + (n2 - n3)} cos(2β)
(2)
Here, β is the orientation angle of molecules with respect to the z-axis (see Figure 3). From eq 1, χ′ ) 1/2 tan-1(R2ω/Rω), where Rω and R2ω are first and second lock-in signals, respectively. Figure 2c shows the time evolution of the first and second lock-in signals for a 10 mM NaCl solution obtained at E ) 50 V/cm. The inset in Figure 2c illustrates the corresponding value of χ′ with increasing field duration. It is evident from these figures that R2ω is at least 1 order of magnitude lower than Rω at all times, which makes χ′ close to zero throughout. For the large angle of incidence (φ ≈ 83°) employed in the EWLP experiments, χ ≈ χ′ ≈ 0° and ∆n′ ≈ (n1-n3) cos(2β), implying that the entities in solution responsible for the birefringence are strongly oriented in the x-z plane, that is, essentially parallel to the applied field. Which specific chemical species in the solutions create optical anisotropy near the fluid-glass surface and why these species are so easily aligned by an electric field are clearly central questions for understanding the new phenomena observed. Why the characteristic orientation/relaxation time for these species in a low viscosity electrolyte would be tens of seconds is equally puzzling. To shed light on these and other questions about the fundamental origins of the phenomena, we next study how the electric field, bulk electrolyte concentration, medium pH, and medium viscosity influence the magnitude of the birefringence and its relaxation time. B. Electric Field Dependence. Electric birefringence of optically anisotropic and electrically polarizable molecules generally follows Kerr’s law, except at very high electric fields.
∆n′ss ) λKλE2
(3)
Here, λ is the wavelength of the light, and Kλ is the Kerr constant corresponding to wavelength λ. ∆n′ss/E2 is plotted versus electric field, E, in Figure 4a and b for various NaCl and MgCl2 solutions in DI water. An approximate Kerr law square dependence is evident for both salts over the range of electrolyte concentrations (1-100 mM) studied. The corresponding Kerr constants range from 1 × 10-4 m/V2 at low electrolyte concentrations to 4 × 10-3 m/V2 at the highest electrolyte concentrations studied. These values are more than 4 orders of magnitude larger than the largest Kerr coefficients reported for
Figure 4. Kerr law coefficient, ∆n′ss/E2, versus electric field, E. (a) NaCl and (b) MgCl2 solutions in DI water. Legends show the respective electrolyte concentrations. (c) NaCl solutions at variable pH. Closed and open symbols represent 90 mM and 4 mM NaCl concentration.
bulk electrolyte solutions. They are also consistent with the unusually small electric fields E ) 2-30 V/cm (compared with E ≈ kV/cm - MV/cm commonly used for bulk electric birefringence measurements), at which electric birefringence is observed near the glass surface. The unusually long birefringence relaxation times observed also prevents any straightforward explanation of our experimental observations on the basis of the usual Kerr processes reported for molecular fluids or electrolyte solutions. The values of the Kerr constant and the accompanying slow birefringence decay indeed appear to rule out any explanation based on regular polarization or hyperpolarization of small isotropic ions in the bulk electrolytes. Strong electrolytes such as NaCl completely dissociate in water, and the resultant cations (Na+) and anions (Cl-) are solvated by water molecules. These molecules are known to arrange themselves in layers of solvation shells around the ions. The distribution of dipoles in the solvation shell is expected to be symmetric due to the spherical symmetry of the ions and as such cannot produce the large birefringence observed. Computer simulation studies of adsorption of sodium and chloride ions from aqueous electrolyte solutions to charged surfaces show that although water near the surface can assume drastically different structures than observed in bulk, the structure of the solvation complex around these small ions is similar to that
14362 J. Phys. Chem. C, Vol. 111, No. 39, 2007
Saha and Archer
found in the bulk with only modest rearrangement of the water molecules in the coordination shell.18 Hence, small isolated ions adsorbed on the glass surface are not expected to possess a permanent dipole moment. However, if the interionic distances are small enough, the presence of other ions on neighboring adsorption sites could conceivably break the symmetric arrangement of water molecules in the coordination shell, producing hydrated clusters with a net dipole moment. Fast, fieldinduced redistribution of ions in these clusters might further enhance this effect, potentially explaining the large surface birefringence values. C. Dependence of Kerr Constant on Concentration and pH. To understand what role, if any, such surface ionic clusters might play in producing anomalously large Kerr constants in aqueous electrolyte solutions near charged surfaces, it is useful to investigate the effect of pH and electrolyte concentration, c, on ∆n′ss. Figure 4 illustrates the effect of pH and electrolyte concentration on the Kerr constant. It is evident from this plot that although Kλ is a function of c, it is not affected by the solution pH over a rather wide range. In fact, even solution pHs close to the isoelectric point of silica show no measurable effect on the value of Kλ. Any meaningful analysis of this data requires a detailed understanding of how the areal density of surface adsorbed ions is affected by solution pH and c. Surface complexation models provide a good description of adsorption of hydrated ions within the electric layer formed at oxide/ electrolyte interfaces.19-21 The four-layer complexation model has arguably proven the most effective for explaining experimental data on surface charge, as well as the surface potential at oxide surfaces.22-24 The equilibrium equations that describe the reactions occurring at the oxide/electrolyte interface can be expressed as21,25
Ka ) ([A-O-][H+]/[A-OH]) exp(-eΨ0/kT)
(4)
Kb ) ([A-OH2+]/[A-OH][H+]) exp(eΨ0/kT)
(5)
-
-
KC ) ([A-O C]/[A-O ][C]) exp(ZCeΨC/kT)
(6)
KA ) ([A-OH2+A]/[A-OH2+][A]) exp(-ZAeΨA/kT)
(7)
where, Ka, Kb, KC, and KA are the respective equilibrium constants for the specified surface reactions. Ψ0, ΨC, and ΨA are electric potentials at the oxide surface and at the surfaces on which cations and anions are adsorbed, respectively; [A-O-], [A-OH2+], and [A-OH] are surface concentrations (mol/cm2) of negatively charged, positively charged, and neutral absorption sites on the oxide surface on which no counterions are adsorbed; [A-O-C] and [A-OH2+A] are the surface concentrations (mol/cm2) of cations and anions adsorbed on the negative and positive adsorption sites; [H+], [C], and [A] are the activities (in mol/L) of H+ (potential-determining ions), C (cations), and A (anions) in the electrolyte solution; and ZC and ZA are the respective valence of the cations and anions. From eqs 4 and 5, it is evident that both [A-O-C] and [A-OH2+A] are functions of solution pH. This implies that electric birefringence produced by ionic clusters composed of only one type of ion (positive or negative), is unlikely to be pH-independent. On the other hand, if these clusters are formed predominantly by association between adsorbed cations and anions, one would anticipate that the number of such clusters per unit area of the surface, N, will be a function of the joint product of both ionic species’ being present at the surface. At low electrolyte concentrations, the average of the product should
Figure 5. Kerr law coefficient, Kλ, versus N (see text). Open circles represent NaCl solutions in DI water, and squares represent MgCl2 solutions. Closed circles and squares represent 4 mM and 90 mM NaCl, respectively, in buffers with varying pH. Lines are straight line fits of the data points.
provide a reasonable estimate of this joint probability, leading to N ∼ ∼ x[A-O-C][A-OH2+A]; i.e., where we have estimated the average product of the concentration of anions and cations at the surface as the geometric mean concentration of the two species. To estimate N for the systems studied here, the concentration of adsorbed counterions is computed by first solving eqs 4-7 using the numerical procedure described in ref 21. The simulation parameters for the glass (SiO2) surface21 used are δ ) 2 -] + [A-OH +] + [A-OH] 2 xKaKb )-7 × 10-4, Ns ) [A-O + + [A-O C] + [A-OH2 A] ) 5 × 1014 cm-2. Activity coefficients, γi, of the ions are estimated using the following expression,25
log γi ) -
[
xI 1.825 × 106 - 0.3I 3/2 (rT) 1 + xI
]
i ) C, A (10)
where, r is the relative permittivity of the solvent and I is the ionic strength of electrolyte solution in moles per liter. Values for KC and KA are chosen to be equal to 0.1 mol-1 dm3. For Na+and Cl-, these values are normally found to give reasonable agreement to experimental data.25 For simplicity, we also assume KC for Mg2+ to be the same as that of for Na+. Other parameters used for these calculations are the same as in ref 21, Cstern ) 0.2 F/m2, r+ ) Cstern/C+ ) 0.15, and r- ) Cstern/C+ ) 0.15. In Figure 5, Kλ ≡ Ef0 (∆n′ss/E2)/λ is plotted against N )
x[A-O-C][A-OH2+A] for all pH and electrolyte concentra-
tions studied. The Kλ values reported in the figure are estimated from the y-intercept of straight lines fitted to the plots of ∆n′ss/E2 versus E (see Figure 4). It can be seen that Kλ is linearly proportional to N for NaCl solutions for all c and pH values, tentatively supporting the idea that hydrated ion pair clusters adsorbed at the glass surface may be the source of the behavior observed. The insensitivity of Kλ to solution pH and linear dependence of Kλ on c is then expected, because N is insensitive to pH and proportional to c. Kλ for MgCl2 solutions is also proportional to N; however, the proportionality constant is lower than for NaCl solutions. It is, nonetheless, important to point out that at high surface concentrations of either species, the geometric mean of the surface concentration will not provide a good estimate for the joint probability and, hence, of the cluster concentration employed in our simple analysis.
Electric Birefringence of Electrolytes, I
J. Phys. Chem. C, Vol. 111, No. 39, 2007 14363
Figure 6. Birefringence orientation angle χ′ versus field E for NaCl solutions at various electrolyte concentrations and pH.
The above results suggest that at low salt concentrations, the Kerr constant of an electrolyte solution near a charged surface could be written in a more familiar form,20
Kλ ≈ (1/λ)[N(g1 - g2)/ns]R/kT
Figure 7. Characteristic relaxation time, τ, versus electric field, E, and pH (inset) for NaCl solutions at varying salt concentrations.
(11)
where (g1 - g2) is the optical anisotropy of the hydrated ionic clusters; R is their electric polarizability; ns is the refractive index of the solution; and N is the surface concentration of the clusters. By analogy to polarization of free ions in the electric double layer near charged particles,9 we anticipate R to be substantially higher than its molecular equivalent. Likewise, (g1 - g2) can be quite large if water molecules hydrate the ionic clusters in a nonsymmetric fashion or if ions in the clusters precess in the presence of the field to form larger anisotropic domains. More details about these effects, including an estimate of the Kerr constant, clearly require more intrusive scattering studies, computer simulations of the electric field response of electrolytes near charged substrates, or both. We do not pursue these effects in this first study. D. Orientation and Relaxation Time. Figure 6 shows the effect of the electric field on the steady-state apparent orientation angle, χ′ (approximately equal to χ (see Figure 3) for φ ) 83°), for NaCl solutions. The inset shows the dependence of χ′ on pH. It is again apparent from these figures that χ ≈ c′ ≈ 0° for all E, c, and pH values studied. One can also rationalize this result using the ionic cluster model. Specifically, it indicates that the principal axis (symmetry axis) of the clusters always remains parallel to the glass surface, that is, in the x-z plane. This result is perhaps expected because the clusters are formed by the ions adsorbed on the glass surface and, as such, are “pinned” to this plane. The characteristic structural relaxation time, τ, determined from the birefingence decay curve might also be expected to reflect the confining influence of the glass substrate. At least two mechanisms can be proposed to explain the process by which birefringence relaxes near the surface: (i) Redistribution of ions among clusters by diffusion. The time scale for this process should depend upon the concentration (surface separation) of adsorbed ions, but also on the medium viscosity. (ii) Local redistribution of ions by adsorption/ desorption processes at the interface. The characteristic time for this process is determined by the intrinsic rates of the adsorption/desorption processes and should therefore be insensitive to the concentration of adsorbed ions and the surrounding medium viscosity. Figure 7 summarizes the τ-versus-E data at various NaCl concentrations. This figure shows that τ is essentially independent of both E and c. The absence of a field dependence means that if the birefringence measured is indeed a result of polarization of water nonsymmetrically distributed around
Figure 8. Effect of glycerol on τ, ∆n′ss, and Kλ for 50 mM NaCl in water/glycerol mixtures at E ) 30 V/cm. (a) Relaxation time, τ, versus percentage of water in water/glycerol mixtures; inset shows the effect of mixture composition on bulk viscosity. (b) ∆n′ss and Kλ (inset) versus percentage of water in the mixtures.
surface adsorbed ionic clusters, the field has at most a negligible influence on the size/structure of these clusters on time scales accessible to our experiments. This point is consistent with our earlier observation that the field application time has no effect on τ (see Figure 2b, inset). Relaxation by mechanism i can be investigated in more detail by deliberately varying the viscosity of the medium and evaluating its effect on the birefringence relaxation time. Figure 8a summarizes results from a series of experiments conducted on a 50 mM NaCl solution at E ) 30 V/cm in which glycerol, a high-viscosity, water-soluble liquid is employed as a cosolvent. It is evident from this figure that the birefringence relaxation time τ is, within the uncertainty of the measurements, unaffected by the solvent composition (water/glycerol). Indeed, the characteristic time τ ∼ 20 s measured in these experiments is identical to that observed when water alone is used as the solvent (see Figure 7 and Figure 2b, inset). Significantly, over the same composition range, the viscosity of water/glycerol mixtures
14364 J. Phys. Chem. C, Vol. 111, No. 39, 2007 increase by more than 2 orders of magnitude as the water content in the solvent is decreased (see Figure 8a, inset). These results convincingly show that mechanism i cannot explain the relaxation phenomena observed. In Figure 8b, ∆n′ss is plotted as a function of the composition of the water/glycerol mixtures. The figure demonstrates that measurable levels of surface birefringence are observed down to small water concentrations, but that the presence of glycerol significantly reduces the effect. It is also apparent that in the presence of glycerol, ∆n′ss continues to manifest a Kerr law E2 dependence on field; values of the mixture Kerr coefficient Kλ are illustrated in the inset to Figure 8b. The lower Kλ values observed in the presence of glycerol can be rationalized in terms of a reduction in the optical anisotropy of the hydrated clusters produced by glycerol, perhaps due to changes in the shape or arrangement of the water molecules in the clusters. IV. Conclusions We report anomalously large electric birefringence in aqueous electrolytes near charged solid substrates. In this first study, we use an evanescent wave laser optical polarimetry technique to investigate the effect of electric field, E; electrolyte concentration, c; and pH on birefringence in a region of O (150 nm) from the surface. Over a wide range of electrolyte concentrations and solution pHs, we find that the steady-state birefringence ∆n′ss varies with E2. This Kerr-law-like behavior and the observed dependence of the Kerr constant Kλ on c and pH are used in conjunction with an ionic cluster model to rationalize our observations. Consistent with the experimental observations, this model yields large levels of birefringence. The ionic cluster model can also be used to rationalize birefringence orientation angles close to zero, irrespective of salt concentration, pH, and field. Unusually long birefringence relaxation times reported by the EWLP experiments are discussed in terms of local redistribution of ions by adsorption/desorption processes at the charged glass surface.
Saha and Archer Acknowledgment. We are grateful to Abraham Stroock for many helpful discussions. The study was supported by the National Science Foundation (Grants DMR0551185 and DMR 0404278). References and Notes (1) Lachenmayer, K.; Oppermann, W. J. Chem. Phys. 2002, 116, 392. (2) Yamaoka, K; Matsuda, K. J. Phys. Chem. 1985, 89, 2779. (3) Hagerman, P. J. Curr. Opin. Struct. Biol. 1996, 6, 643. (4) Zacharias, M.; Hagerman, P. J. J. Mol. Biol. 1995, 247, 486. (5) Stellwagen, N. C. Biophys. Chem. 1996, 58, 117. (6) Stellwagen, N. C. Colloids Surf. 2002, 209, 107. (7) Hong, M. K.; Narayan, O.; Goldstein, R. E.; Shyamsunder, E.; Austin, R. H.; Fisher, D. S.; Hogan, M. Phys. ReV. lett. 1992, 68, 1430. (8) Mandel, M. Mol. Phys. 1961, 4, 489. (9) Fixman, M.; Jagannathan, S. J. Chem. Phys. 1981, 75, 4048. (10) Antosiewicz, J.; Porschke, D. J. Chem. Phys. 1991, 95, 5983. (11) Manning, G. S. J. Chem. Phys. 1993, 99, 477. (12) Dao, T. T.; Archer, L. A. Langmuir 2001, 17, 4042. (13) Khanna, R. K.; Dempsey, E.; Jones, G. P. J. Phys. E: Sci. Instrum. 1978, 11, 1210. (14) Santa, I.; Foggi, P.; Righini, R.; Williams, J. H. J. Phys. Chem. 1994, 98, 7692. (15) Chen Y-J; Orttung, W. H. J. Phys. Chem. 1972, 76, 216. (16) Harrick, N. J. Internal Reflection Spectroscopy; Harrick Scientific Corp.: Ossining, NY, 1987; Chapter 2. (17) Fuller, G. G. Optical Rheometry of Complex Fluids; Oxford University Press: New York, 1995; Chapter 3. (18) Rose D. A.; Benjamin, I. J. Chem. Phys. 1993, 98, 2283. (19) Yates, D. E.; Levine, S.; Healy, T. W. J. Chem. Soc., Faraday Trans. 1 1974, 70, 1807. Chan, D.; Perram, J. W.; White, R. L.; Healy, T. W. J. Chem. Soc. Faraday Trans. 1 1974, 71, 1046. (20) Davis, J. A.; James, R. O.; Leckie, J. O. J. Colloid Interface Sci. 1978, 63, 480. Davis J. A.; Leckie, L. O. J. Colloid Interface Sci. 1978, 67, 90. (21) Barrow N. J.; Bowden, J. W. J. Colloid Interface Sci. 1987, 119, 236. (22) Charmas, R.; Piasecki, W.; Rudzinski, W. Langmuir 1995, 11, 3199. (23) Bousse, L.; de Rooij, N. F.; Bergveld, P. Surf. Sci. 1983, 135, 479. (24) Barrow, N. J. AdV. Agron. 1985, 38, 183. (25) Charmas, R.; Piasecki, W.; Rudzinski, W. Langmuir 1995, 11, 3199.
