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Effect of solution viscosity on dynamic surface tension detection
Analytica Chimica Acta 534 (2005) 79–87
Effect of solution viscosity on dynamic surface tension detection Bethany A. Staggemeiera , Terry O. Collierb , Bryan J. Prazena , Robert E. Synoveca,∗ a
Center for Process Analytical Chemistry, Department of Chemistry, Box 351700, University of Washington, Seattle, WA 98195, USA b 3M Engineering Systems Technology Center, 3M Center, Building 0518-01, St. Paul, MN 55144, USA Received 16 June 2004; received in revised form 8 November 2004; accepted 8 November 2004 Available online 21 December 2004
Abstract A dynamic surface tension detector (DSTD) was used to examine the molecular diffusion and surface adsorption characteristics of surfaceactive analytes as a function of solution viscosity. Dynamic surface tension is determined by measuring the differential pressure across the air/liquid interface of repeatedly growing and detaching drops. Continuous surface tension measurement throughout the entire drop growth is achieved for each eluting drop (at a rate of 30 drops/min for 2 l drops), providing insight into the kinetic behavior of molecular diffusion and orientation processes at the air/liquid interface. Three-dimensional data are obtained through a calibration procedure previously developed, but extended herein for viscous solutions, with surface tension first converted to surface pressure, which is plotted as a function of elution time axis versus drop time axis. Thus, an analyte that lowers the surface tension results in an increase in surface pressure. The calibration procedure derived for the pressure-based DSTD was successfully extended and implemented in this report to experimentally determine standard surface pressures in solutions of varied viscosity. Analysis of analytes in viscous solution was performed at low analyte concentration, where the observed analyte surface activity indicates that the surface concentration is at or near equilibrium when in a water mobile phase (viscosity of 1.0 Cp). Two surface-active analytes, sodium dodecyl sulfate (SDS) and polyethylene glycol (MW 1470 g/mol, PEG 1470), were analyzed in solutions ranging from 0 to 60% (v/v) glycerol in water, corresponding to a viscosity range of 1.0–15.0 Cp. Finally, the diffusion-limited surface activity of SDS and PEG 1470 were observed in viscous solution, whereby an increase in viscosity resulted in a decreased surface pressure early in drop growth. The dynamic surface pressure results reported for SDS and PEG 1470 are found to correlate with solution viscosity and analyte diffusion coefficient via the Stokes–Einstein equation. © 2004 Published by Elsevier B.V. Keywords: Surface activity; Surface tension; Surface pressure; Surfactant; Polymer; Viscosity; Diffusion coefficient
1. Introduction Surface-active analytes comprise both hydrophobic and hydrophilic structural regions. Thus, in aqueous solution, these species diffuse toward the air/liquid interface and are preferentially adsorbed at the surface, thereby lowering the surface tension of the solution. This ability has caused the surface activity of such water-soluble polymers and surfactants to be an area of wide interest for a variety of applications including water treatment, food and consumer products, cosmetics, agrochemicals, and drug industries [1–6]. A range ∗
Corresponding author. Tel.: +1 2066852327; fax: +1 2066858664. E-mail address: [email protected] (R.E. Synovec).
0003-2670/$ – see front matter © 2004 Published by Elsevier B.V. doi:10.1016/j.aca.2004.11.022
of analytical techniques have been developed for the characterization of these surface-active species including both equilibrium methods such as the DeNouy ring detachment, pendant drop, sessile drop, and Wilhelmy balance (inclined plate) analyses [7,8], and dynamic methods such as maximum bubble pressure, oscillating jet, fast formed drop (FFD) technique, dynamic Wilhelmy plate, and Langmuir trough analyses [7,9–13]. Numerous studies have been performed on the dynamic aspects of surface activity molecules in both non-viscous and viscous aqueous solutions [9–11,14]. Dynamics of surface adsorption have long been known to affect the rate of surface tension lowering [7,14]. Two general mechanisms have been described for the rate-controlled diffusion and adsorption of surface-active analytes at an
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interface, taking into account a subsurface layer defined as a distance of several molecular diameters into the bulk solution from the surface [7,14,15]. The first mechanism is a bulk diffusion-controlled process, where the diffusion of the surface-active molecule from the bulk phase to the subsurface is the rate-limiting step and molecular orientation and adsorption to the air/liquid interface occurs without delay. The second mechanism is a diffusion–adsorption-controlled process, where diffusion of the surface-active molecule from the bulk to the subsurface occurs relatively rapidly, but here the molecule encounters some barrier to adsorption at the interface such as steric hindrance to molecular rearrangement at the surface, or lack of vacant space at the surface [7,14,15]. Dynamic diffusion and adsorption processes to achieve equilibrium surface concentrations have been noted to occur on the timescale of milliseconds to days [14]. Herein is reported the evaluation and application of the dynamic surface tension detector (DSTD), a growing dropbased technique utilizing a pressure sensor [16–18], to the determination of standard surface pressures for calibration and the examination of two surface-active analytes in viscous solution (glycerol:water, over a range of 0:100–60:40 volume ratio) on a drop formation time-scale of 0.2–2 s. Threedimensional data are obtained, with surface tension first converted to surface pressure, which is plotted as a function of elution time axis versus drop time axis. Thus, a surface-active analyte that lowers the surface tension results in an increase in surface pressure. The dynamic nature of the DSTD response allows the study of the adsorption of analytes to the air/liquid interface during a period of drop expansion, where the viscosity of the solution may limit molecular diffusion to the drop surface and molecular orientation for adsorption. Previous DSTD studies and evaluation of the calibration procedure for a variety of surfactants, proteins, and polymers were performed in non-viscous solution (i.e. water or buffers essentially at 1.0 Cp viscosity) [16,18–21]. Building upon this previous work, reported herein is the first application of the DSTD to the examination of analytes in viscous solution, where surface pressures for standards are not typically available in literature. In this work, the calibration equations previously derived for DSTD measurements were successfully redefined and utilized to experimentally determine accurate surface pressures of a standard (5% v/v acetic acid) in solutions of varied viscosity, thus allowing accurate surface pressures of analytes in viscous solution to then be determined. Two surface-active analytes, sodium dodecyl sulfate (SDS) and poly(ethylene) glycol (MW 1470 g/mol, PEG 1470), were chosen for analysis of their behavior in viscous solution, in order to evaluate the performance of the DSTD. In water, SDS is shown to be at equilibrium, or non-kinetically hindered (i.e., diffuses to and adsorbs at the air/liquid interface quickly, thus giving essentially constant surface pressure throughout drop growth), even at concentrations below that chosen for analysis in viscous mobile phase [22]. By contrast, the second analyte chosen, PEG 1470, was evaluated at an equilibrium concentration below which a kinetic hindrance is
observed in water. In this case the kinetic hindrance for PEG 1470 is likely due to a diffusion–adsorption-controlled process where the bulk concentration is insufficient to replenish the surface concentration fast enough during the initial rapid drop expansion. Thus, the impact of solution viscosity on the dynamics and sensitivity of the DSTD response is explored using these two test analytes, further expanding the scope of the DSTD technology for application to viscous solutions.
2. Theory The DSTD is based upon a growing drop technique, implementing a pressure sensor where the pressure signal is dependent upon surface tension properties of a given sample (Fig. 1). Pressure measurement is made throughout drop growth for each drop forming at a capillary tip. The air/liquid surface tension, γ, for a drop of radius r, is related to the pressure signal P, (pressure relative to atmospheric pressure, P0 ), according to Eq. (1), the time dependent Young–Laplace equation [17], P(t)X,M = (2γ(t)X,M /r(t)) + PC,M
(1)
where the P, γ, and r are all functions of time, t, during drop growth. X represents sample, M represents the mobile phase, and PC,M accounts for the viscosity-based pressure drop in the capillary tubing due to the relative position of the sensor from the capillary tip. P(t) is the individual drop profile pressure signal measured by the pressure sensor in the DSTD over the growth of a given drop. The dynamic surface pressure of a given sample in mobile phase, π(t)X,M , is the surface tension of the sample in mobile phase, γ(t)X,M , subtracted from the surface tension of the mobile phase itself, γ(t)M , π(t)X,M = γ(t)M − γ(t)X,M
(2)
Thus, an analyte that lowers the surface tension results in an increase in surface pressure. In cases where the analyte and the standard may both easily be analyzed in the same mobile phase, the calibration equation can be obtained in the following manner, as presented in previous reports [17,18]. The dynamic surface pressure of an analyte (A) in a mobile phase (M) can be expressed as a function of the drop radius and pressure signals of mobile phase and the sample via the combination of Eqs. (1) and (2): π(t)A,M =
r(t) [P(t)M − P(t)A,M ] 2
(3)
The subtraction of the two surface tension values removes the pressure offset (PC,M ) from the surface pressure term. The PC,M is assumed to be constant for a given mobile phase, meaning the analyte itself generally does not significantly affect the mobile phase viscosity [18]. A similar equation can be derived for the calibration standard (S) in the mobile
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Fig. 1. Schematic of the DSTD instrument configuration. The sample is introduced at 60 l/min via a 90 l sample loop connected to the injection valve and detected at the capillary sensing tip. Drops are repeatedly formed at the tip and removed via pneumatic detachment regulated to 2 s, resulting in 2 l drops. The pressure sensor, connected to the tubing with a side arm, is fitted with an internal membrane, which is used to measure the differential pressure across the liquid–air interface with respect to atmospheric pressure, P0 of the forming drops.
phase, π(t)S,M =
And for the standard in a water mobile phase, the surface pressure π(t)S,M2 is
r(t) [P(t)M − P(t)S,M ] 2
(4) π(t)S,M2 =
By combining Eqs. (3) and (4), the dynamic surface pressure of the analyte in the mobile phase is given by π(t)A,M = π(t)S,M
P(t)M − P(t)A,M P(t)M − P(t)S,M
(5)
where a standard value for π(t)S,M would need to be obtained from the literature or measured in the laboratory. However in a case where the surface pressure of the standard in the mobile phase, π(t)S,M , is not readily available from literature (i.e., viscous solution mobile phase), it will be shown that a measurement in the laboratory may be performed and an equation similar to Eq. (5) can now be derived and applied to determine the surface pressure of the standard in viscous solution utilizing the standard signal obtained in water, for which a literature value is available. To obtain the surface pressure of the standard in the viscous mobile phase (π(t)S,M1 ), from Eq. (5), the following theory is useful and readily applied, where M1 denotes viscous mobile phase and M2 denotes water mobile phase [19,20]. For the standard in viscous mobile phase, the surface pressure π(t)S,M1 is π(t)S,M1 =
r(t) [P(t)M1 − P(t)S,M1 ] 2
(6)
r(t) [P(t)M2 − P(t)S,M2 ] 2
(7)
Combining Eqs. (6) and (7) and solving for π(t)S,M1 to determine the surface pressure for the standard in viscous solvent, yields, π(t)S,M1 = π(t)S,M2
P(t)M1 − P(t)S,M1 P(t)M2 − P(t)S,M2
(8)
Thus, utilizing Eq. (8) in conjunction with drop profiles for water (P(t)M2 ), viscous mobile phase (P(t)M1 ), standard in water (P(t)S,M2 ), standard in viscous mobile phase (P(t)S,M1 ), and the literature value for the surface pressure of the standard in water (π(t)S,M2 ), which is then readily available from the literature and selected to be independent of time and a constant at a given concentration, the time-dependent surface pressure of the standard in a particular viscous mobile phase, π(t)S,M1 , may be experimentally determined. This surface pressure function π(t)S,M1 for the standard in viscous mobile phase may then be utilized in Eq. (5), above, for the determination of the surface pressure function of an analyte in the viscous mobile phase. Thus, the use of Eq. (8) allows the evaluation of the data of the standard at increased viscosity, and the determination of the standard value, π(t)S,M1 , in a more complex, viscous solvent for use in the determination of the analyte surface pressure via calibration using Eq. (5).
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3. Experimental 3.1. Materials and solutions Acetic acid (glacial, A38S-500) was purchased from Fisher Scientific (Fisher Scientific, Fair Lawn, NJ, USA). The acetic acid was prepared 5% (v/v) in water or viscous mobile phase of various concentrations for standard surface pressure measurements. Poly(ethylene) glycol (PEG 1470, Mw 1470 g/mol, cat. no. 2070-6001) was purchased from Polymer Laboratories (Polymer Laboratories, Amherst, MA, USA). Sodium dodecyl sulfate (98% purity) was obtained from Aldrich (Aldrich Chemical Co., Milwaukee, WI). All chemicals were used as received without further purification. Mobile phase solutions were prepared with nanopure, degassed water (Nanopure Filtration System, Barnstead, Dubuque, IA, USA) or with appropriate volumes of nanopure water and glycerol (99.9% purity, G33-500) purchased from Fisher Scientific (Fisher Scientific, Fair Lawn, NJ, USA). Viscous solutions were prepared with volume ratios of glycerol to water (glycerol:water, volume ratio) (Table 1). The corresponding weight percent glycerol and resulting viscosity for each solution are also shown in Table 1 [23]. Samples were prepared by dissolving analytes in the appropriate viscous solvent or water, identical to the mobile phase for a given analysis.
tus (including pump, tubing, and solvent reservoir) was equilibrated with the working mobile phase prior to performing analysis of samples at a given viscosity prepared in the working mobile phase. Pneumatic drop detachment at a rate of 0.5 Hz, resulted in 2 l drops at a flow rate of 60 l/min, using a solenoid valve (MBD002, Skinner Valve, New Britain, CT, USA). The pressure sensor (Validyne P305D-20-2369, Northridge, CA) was configured with a sensing membrane (Validyne diaphragm 3-34, Northridge, CA) that has an optimum response time for the DSTD measurements of interfacial kinetics. The sensor capillary tip was made from a short piece of PEEK microtight tubing sleeve (0.015 i.d., 0.025 o.d., Upchurch, Oak Harbor, WA). All data were collected at 20 kHz with a personal computer (850 MHz Pentium® , Intel Corporation, Santa Clara, CA) equipped with a data acquisition card (DAC, National Instruments, Austin, TX) and averaged to 50 points/s prior to saving. Data collection, P(t) drop profile pressure signal extraction, and calculation of drop surface pressures were performed via Eqs. (5) and (8) using LABVIEW (Version 6i, National Instruments, Austin, TX) programs written in-house. Data analysis was performed using MATLAB 6.1 (MathWorks, Natick, MA) and Origin (Version 7, Microcal Software, Inc., Northampton, MA).
4. Results and discussion 3.2. Instrumentation 4.1. Calibration procedure in viscous solution A MicroGradient LC pump (Micro Gradient, BrownLee, Santa Clara, CA, USA) was programmed for isocratic elution of the mobile phase to the DSTD. Solutions were introduced for detection via a ten-port injection valve (Rheodyne PR700102-1 Cotati, CA). A poly(etheretherketone) (PEEK) injection loop of 90 l of tubing (Upchurch, Oak Harbor,WA) was used for all experiments. This injection loop is of sufficient volume so that the center of the detected sample plug injected is not diluted by the mobile phase (i.e., at steady-state analyte concentration). A detailed schematic of the DSTD configuration with pneumatic drop detachment is shown in Fig. 1 and has been described in detail in previous reports [16–18]. The apparaTable 1 Volume ratio of glycerol to water in prepared viscous solutions is presented Volume ratio (glycerol:water)
Weight percent glycerol (%)
Viscosity (Cp)
0:100 10:90 20:80 30:70 40:60 45:55 50:50 60:40
0 11.5 22.7 33.5 43.9 48.8 54.0 63.8
1.0 1.5 1.9 2.8 4.2 5.5 7.6 15
This volume ratio results in solutions of the weight percent and viscosity shown in the table.
Drop profiles for mobile phase and analytes are extracted from raw P(t) data collected continuously during a run. Fig. 2(A) shows an overlay of drop pressure profiles, as related to surface tension via Eq. (1), extracted from raw data for water (P(t)M ), 1 mM SDS (P(t)A,M ), and the standard, 5% acetic acid in water (P(t)S,M ), in the upper, middle, and lower profiles, respectively. Fig. 2(B) shows the resulting dynamic surface pressure of the analyte, π(t)A,M , obtained from utilizing these three drop profiles and a literature value for π(t)S,M of 10.3 dyn/cm (5% acetic acid in water) in Eq. (5). The surface pressure for 1 mM SDS is nearly constant throughout drop growth indicating that this is a non-kinetically hindered analyte, which concentrates and orients at the surface of the drop resulting in an equilibrium surface concentration early in drop growth. This constant pressure throughout drop growth is typical of small molecules in non-complex solvents, which are able to diffuse rapidly to the surface of the drop and experience little hindrance when orienting at the air/liquid interface. The initial disturbance seen in the first 0–200 ms of drop growth is due to the loading and unloading of the pressure sensor membrane and is typically not shown, for clarity [24]. The surface pressure at drop detachment averaged over the last 10 points at the end of the 2 s drop (averaged π values from 1.8 to 2.0 s from each surface pressure plot) is defined in Fig. 2(B) and represented by πD .
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Fig. 2. The calibration procedure is demonstrated using three drop profiles for a non-kinetically hindered analyte. (A) Drop profiles for water (P(t)M ), 1 mM SDS analyte in water (P(t)A,M ), and 5% acetic acid standard in water (P(t)S,M ), from top to bottom. (B) The resulting dynamic surface pressure plot for 1 mM SDS, a non-kinetically hindered analyte, utilizing Eq. (5). πD represents the surface pressure values averaged for the end of the 2 s drop, in this case 4.6 dyn/cm (averaged π values from 1.8 to 2.0 s from each surface pressure plot).
The πD values are used extensively in the remainder of this report. The surface pressure plots π(t)S,M1 of the standard at elevated viscosity were found to be essentially independent of time, yet with a lower surface pressure as viscosity increased. Fig. 3 shows these results for the standard 5% acetic acid with πD plotted (π(t)S,M1 at drop detachment). These surface pressures were experimentally obtained and calculated utilizing Eq. (8) for each solution viscosity studied, where M1 is the viscous solvent and M2 is water. As the viscosity of solution M1 increases, the surface pressure of the standard, π(t)S,M1 , is seen to decrease from 10.3 dyn/cm in water to 1.7 dyn/cm at 15.0 Cp, since acetic acid has less effect on lowering the surface tension of the drops of the more viscous solvent. Therefore, for experiments performed in viscous solvents, these experimentally determined standard surface pressure values presented in Fig. 3 are utilized as π(t)S,M in Eq. (5) for accurate calibration of analytes in solutions of their respective viscosity.
Fig. 3. Standard (5% acetic acid, 10.3 dyn/cm in water) value in varied viscosity mobile phase at the point of drop detachment (πD as defined in Fig. 2(B)) obtained from Eq. (8). The plot above shows the degree to which the surface activity of acetic acid decreases with increasing viscosity. The standard surface pressure obtained for a given solution viscosity is then used for the calibration of analyte surface pressure at that same viscosity.
4.2. Evaluation of surface-active analytes The dynamic surface pressure plots and surface pressure values determined at drop detachment, πD , for SDS in water are reported in Fig. 4(A) and (B). Experimental uncertainty in the surface pressure is approximately the size of the data points (standard deviation of 0.15 dyn/cm) for calibration obtained in water. For the concentration range studied (0.1–5 mM SDS), the surface pressure plots shown in Fig. 4(A) are nearly constant indicating equilibrium surface concentration throughout drop growth. The concentration of SDS that is indicated with a circle in Fig. 4(B), 1 mM, presents a particularly level surface pressure plot in Fig. 4(A) (third from bottom), and was chosen for experiments performed on SDS in solutions of varied viscosity. The surface pressure plots for 1 mM SDS in solutions of varied viscosity (1.0–15.0 Cp), and the corresponding surface pressure values at drop detachment, πD , for this data are revealed in Fig. 5(A) and (B), respectively. As discussed above, the analyte surface pressure was calculated from Eq. (5), utilizing π(t)S,M1 as the surface pressure of the standard for a given viscosity (plotted in Fig. 3, via Eq. (8)). As seen in Fig. 5(A) and (B), the surface pressure is lower for the analyte (as it was for the standard) as viscosity increases, particularly at short drop time (in Fig. 5(A)). The dynamic surface pressure plots for SDS in Fig. 5(A) differ from those shown in Fig. 4(A), where in relatively non-viscous solvent (water, 1.0 Cp) a decrease in surface concentration of SDS observed below 1 mM is still accompanied by an equilibrium surface pressure throughout drop growth. The decrease in surface pressure with increasing viscosity observed for 1 mM SDS early in drop growth in Fig. 5(A), as well as at 2 s (drop detachment) in Fig. 5(B), is indicative of the decrease in the diffusion coefficient, D, of SDS corresponding to the increase in solution viscosity, which is expected at constant temperature according to the Stokes–Einstein equation, D=
kB T 6πηRH
(9)
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Fig. 4. (A) Surface pressure plots for the calibration of SDS at concentrations of 0.1, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 4.0, and 5.0 mM. At all SDS concentrations studied, there is little kinetic effect as the surface pressure is nearly constant throughout drop growth. (B) Maximum surface pressure shown as the surface pressure value at drop detachment, πD , vs. concentration of SDS. The 1 mM concentration chosen for study in varied viscosity is indicated by the circle.
where kB is Boltzmann’s constant, T the temperature in K, η the viscosity, and RH the hydrodynamic radius of the analyte [25]. Thus, in increasingly viscous solutions more time is required for the analyte to initially diffuse to and concentrate at the drop surface, thereby lowering the surface tension and raising the surface pressure. Indeed, recently reported results indicate a relationship between this dynamic surface pressure information and the molecular mass of denatured proteins (indicative of a correlation to their hydrodynamic radius), for example, Ref. [19]. To better understand the appearance of this change in the dynamic surface pressure of SDS presented in Fig. 5(A) and the surface pressure value at detachment in Fig. 5(B) in increasingly viscous solution, a discussion of drop formation and diffusion is helpful. For the growing-drop, the surface area of the drop expands rapidly early in drop formation, depleting the analyte concentration at the surface. While this occurs, the surface concentration is being replenished by the bulk analyte concentration in the solution, as discussed previously as a bulk diffusion-controlled process [7,14,15,18]. When diffusion and arrangement of the analyte at the surface is fast (such as SDS in water), this replenishment is
sufficiently rapid that the surface pressure of the analyte remains essentially constant at equilibrium surface concentration throughout drop growth [18]. By contrast, in a viscous solution the early drop growth is rapid enough that the rate of depletion of the analytes from the drop surface exceeds the rate of diffusion of the analytes from the bulk solvent for replenishment at the surface; thus, the surface pressure of the analyte begins to increase only after the rate of expansion of the drop surface abates. In other words, the increased viscosity may sufficiently lower the diffusion coefficient of the analyte such that the rapid initial expansion of the drop surface area exceeds the rate of the diffusion of the bulk analyte to the drop surface early in drop growth. Recalling that the DSTD data acquisition in these experiments has been regulated to 2 s for each drop, it can be reasonably assumed that the analytes in viscous solvent are still approaching equilibrium when the drop is pneumatically detached. This would result in the decreased surface pressure values with increasing viscosity obtained in Fig. 5(B) at drop detachment (i.e., 2 s). Given a longer drop time, the equilibrium surface pressure seen for SDS in water at 1 mM, 4.6 dyn/cm, should eventually be achieved in viscous solution as well.
Fig. 5. (A) Surface pressure plots for 1 mM SDS in solutions of varied viscosity. As the solution viscosity increases at constant analyte concentration, the dynamic surface pressure corresponding to the concentration and rearrangement of the surfactant at the surface of the drop becomes more pronounced. (B) Surface pressure value at drop detachment, πD , for 1 mM SDS in solutions of varied viscosity, obtained from data in Fig. 5(A). As the solution viscosity increases at constant analyte concentration, the surface pressure of the surfactant decreases. Dotted line indicates reference for zero dyn/cm.
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Fig. 6. (A) Surface pressure plots for the calibration of PEG 1470 at concentrations of 10, 20, 30, 50, 70, 100, 200, 300, and 500 ppm. At higher concentrations, there is little kinetic effect as the surface pressure is nearly constant throughout drop growth. However, at concentrations of 70 ppm and lower, the dynamic surface pressure plots indicate that increased time is required for the analyte to concentrate and rearrange at the drop surface. (B) Maximum surface pressure is shown as the surface pressure value at drop detachment vs. concentration of PEG 1470. The 100 ppm concentration, chosen for study in varied viscosity, is indicated by the circle.
The dynamic surface pressure plots and surface pressures obtained at drop detachment for the calibration of PEG 1470 in water are reported in Fig. 6(A) and (B). At concentrations greater than ∼70 ppm (parts per million by mass), there is little kinetic hindrance observed in Fig. 6(A) as the PEG 1470 surface pressure plot is nearly constant throughout drop growth. This is in contrast to the surface pressure of PEG 1470 at concentrations below 70 ppm, where the surface pressure is clearly not maximized until later in drop growth, as the bulk analyte concentration is insufficient to replenish the surface concentration until the rate of increase in drop surface area slows. On the resulting calibration plot showing surface pressure values at drop detachment (πD ) versus concentration in Fig. 6(B), 100 ppm is indicated as the concentration to be examined in solutions of varied viscosity. At this concentration, the surface pressure plot in water for the PEG 1470 is essentially constant throughout drop growth, as the bulk solvent concentration of PEG 1470 is just sufficient to replenish the surface concentration of the polymer even during rapid drop surface area expansion early in drop growth.
The dynamic surface pressure plots and the surface pressure at drop detachment for 100 ppm PEG 1470 in solutions of varied viscosity are reported in Fig. 7(A) and (B). These data were determined similarly to those for SDS, via Eq. (5), utilizing the standard π(t)S,M1 as calculated from Eq. (8) for solvents of varied viscosity. As revealed in Fig. 7(A), the diffusion to and arrangement of the PEG 1470 at the surface of the drop is increasingly hindered at short drop time as the solvent viscosity is increased. In addition, as viscosity increases, attenuation of the surface pressure value at drop detachment is observed (Fig. 7(B)), as the PEG 1470 requires more time to reach an equilibrium concentration at the drop surface. As discussed in the case of SDS for Fig. 5(A) and (B), it can again be reasonably assumed that PEG 1470 in viscous solution is still approaching equilibrium at the end of the regulated 2 s drop. Thus, given adequate drop time, the equilibrium surface pressure obtained for 100 ppm PEG 1470 in water should eventually be achieved in viscous solution as well. The Stokes–Einstein equation (Eq. (9)) was utilized to calculate the diffusion coefficient, D, of SDS and PEG 1470 in
Fig. 7. (A) Surface pressure plots for 100 ppm PEG 1470 in solutions of varied viscosity. As the solution viscosity increases at constant analyte concentration, the time required for an increase in surface pressure, corresponding to the concentration and rearrangement of the polymer at the surface of the drop, increases. Dotted line indicates reference for 0 dyn/cm. (B) Surface pressure values at drop detachment for 100 ppm PEG 1470 in solutions of varied viscosity obtained from data in (A). As the solution viscosity increases at constant analyte concentration, the surface pressure of the polymer at the surface of the drop decreases.
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solutions of increasing viscosity. The diffusion coefficients in water (at 1 Cp) are readily available in the literature. These diffusion coefficients were substituted into Eq. (9) (along with the appropriate temperature and required constants) and the hydrodynamic radius RH was calculated for each analyte. The RH was then held constant for each analyte as the viscosity was changed to estimate D at different solution viscosity. For the purposes of this study it is assumed that the RH of these relatively small analytes does not change as significantly as the viscosity was changed. These calculated D values were related to solution viscosity, and an overlay of the curves for the two analytes are shown in Fig. 8(A). According to Eq. (9), the values of D for both analytes are inversely proportional to solution viscosity. It was shown earlier in Figs. 5(B) and 7(B) that the surface pressure at drop detachment is inversely proportional to viscosity as well, due to the decreased ability of the analyte to diffuse to and rearrange at the drop surface in the 2 s time allowed for drop growth. However, even at drop times of 2 s, particularly in the lower solution viscosities studied, the analytes have clearly begun to approach equilibrium surface concentrations where the observed surface pressure is no longer due primarily to the diffusion of analytes to the drop surface. A stronger correlation of surface pressure to diffusion coefficient might be expected earlier in drop growth,
where drop expansion is still occurring rapidly. With this thought in mind, the comparison of the correlation of D, surface pressure, and viscosity both early in drop growth and at drop detachment can be seen in Fig. 8(B) and (C). In these figures, the dependence of surface pressure with increasing solution viscosity obtained at 2.0 s (πD , drop detachment) and π at 0.5 s (early in drop growth) on the calculated diffusion coefficient can be seen for SDS and PEG 1470, respectively. Early in drop growth, at 0.5 s, where the surface concentration is essentially diffusion limited, the surface pressure of both analytes decreases as the solution viscosity increases at a rate that is similar to the decrease of D with increasing viscosity, thus, the relationship is observed to be nearly linear. However, later in drop growth (at drop detachment), the relationship between D and surface pressure deviates from linearity as the analytes begin to approach an equilibrium surface concentration. Note that the methodology used herein is empirical, i.e., plotting surface pressure as a function of analyte diffusion coefficient. The ∼four-fold difference in the slope of the SDS and PEG 1470 plots in Fig. 8(B) and (C) is due to differences in the concentration and surface activity of the molecular species. More study is warranted in order to determine if additional physical meaning can be attributed to the magnitude of the slopes.
Fig. 8. (A) Dependence of the calculated diffusion coefficient, D, to viscosity for SDS (dotted line) and PEG 1470 (solid line). (B) Correlation of calculated diffusion coefficient, D, to the surface pressure π of SDS obtained at 0.5 s (filled squares) and πD at 2.0 s (open circles) into drop growth in increasingly viscous solutions. (C) Correlation of calculated diffusion coefficient, D, to the surface pressure π of PEG 1470 obtained at 0.5 s (filled squares) and πD at 2.0 s (open circles) into drop growth in increasingly viscous solutions.
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5. Conclusion The effect of solution viscosity on the dynamic surface pressure of a common surfactant and a polymer has been evaluated via the DSTD. The calibration equations previously derived for pressure-based measurements by the DSTD were successfully redefined and utilized to experimentally determine surface pressures of a standard (5% v/v acetic acid in water) in solutions of varied viscosity, thus allowing the determination of dynamic surface pressures of analytes in viscous solution. The surface pressure values of SDS and PEG 1470 in increasingly viscous solutions were compared to the calculated diffusion coefficients of the analytes as a function of solution viscosity. A bulk phase diffusion-limited regime of the dynamic surface tensions of SDS and PEG 1470 was observed in viscous solution via the DSTD. An important area of future study follows from the data presented in this work, that expansion of the linear dynamic range of the DSTD may be achieved by increasing the mobile phase viscosity for analysis of highly surface-active species, thereby lowering their attainable surface pressure within the regulated response time.
Acknowledgment We thank the Center for Process Analytical Chemistry (CPAC), a National Science Foundation University/Industry Cooperative Research Center at the University of Washington, for financial support. References [1] Z. Amjad (Ed.), Water Soluble Polymers: Solution Properties and Applications„ Plenum Publishing, New York, 1998. [2] J.E. Glass (Ed.), Hydrophilic Polymers: Performance with Environmental Acceptance, American Chemical Society, Washington, DC, 1996.
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[3] S.W. Shalaby, C.L. McCormick, G.B. Butler (Eds.), Water-Soluble Polymers: Synthesis, Solution Properties, and Applications, American Chemical Society, Washington, DC, 1991. [4] M. El-Nokaly, D. Cornell (Eds.), Microemulsions and Emulsions in Foods, American Chemical Society, Washington, DC, 1991. [5] T.F. Tadros, Surfactants in Agrochemicals, Marcel Dekker, New York, 1997. [6] M.M. Reiger, L.D. Rhein (Eds.), Surfactants in Cosmetics, Marcel Dekker, New York, 1997. [7] S.S. Dukhin, G. Kretschmar, R. Miller, Dynamics of Adsorption at Liquid Interfaces: Theory, Experiment, Application, Elsevier, New York, 1995. [8] A.W. Adamson, A.P. Gast, Physical Chemistry of Surfaces, Wiley, New York, 1997. [9] R.M. Manglik, V.M. Wasekar, J.T. Zhang, Exp. Thermal Fluid Sci. 25 (2001) 55. [10] K.E. Miller, R.E. Synovec, Talanta 51 (2000) 921. [11] V.B. Fainerman, V.D. Mys, A.V. Makievski, R. Miller, Langmuir 20 (2004) 1721. [12] T. Horozov, L. Arnaudov, J. Colloid Interf. Sci. 22 (2000) 146. [13] N. Wu, J. Dai, F.J. Micale, J. Colloid Interf. Sci. 215 (1999) 258. [14] J. Eastoe, J.S. Dalton, Adv. Colloid Interf. Sci. 85 (2000) 103. [15] J. Eastoe, A. Rankin, R. Wat, C.D. Bain, Int. Rev. Phys. Chem. 20 (2001) 357. [16] W.W. Quigley, A. Nabi, P.B.J.N. Lenghor, K. Grudpan, R.E. Synovec, Talanta 55 (2001) 551. [17] K.E. Miller, K.J. Skogerboe, R.E. Synovec, Talanta 50 (1999) 1045. [18] K.E. Miller, R.E. Synovec, Anal. Chim. Acta 412 (2000) 149. [19] W.W.C. Quigley, E. Bramanti, B.A. Staggemeier, K.E. Miller, A. Nabi, K.J. Skogerboe, R.E. Synovec, Anal. Bioanal. Chem. 378 (2004) 134. [20] E. Bramanti, W.W.C. Quigley, C. Sortino, F. Beni, M. Onor, G. Raspi, R.E. Synovec, J. Chromatogr. A 1023 (2004) 79. [21] N. Lenghor, K. Grudpan, J. Jakmunee, B.A. Staggemeier, W.W.C. Quigley, B.J. Prazen, G.D. Christian, J. Ruzicka, R.E. Synovec, Talanta 59 (2003) 1153. [22] W.W.C. Quigley, A. Nabi, B.J. Prazen, N. Lenghor, K. Grudpan, R.E. Synovec, Talanta 55 (2001) 551. [23] P. Huibers, Thesis in Department of Chemical Engineering, University of Florida, Gainesville, FL, 1996. [24] W.W.C. Quigley, Thesis in Department of Chemistry, University of Washington, Seattle, 2002, p. 151. [25] G.K. Batchelor, J. Fluid Mech. 74 (1976) 1.
Effect of solution viscosity on dynamic surface tension detection Bethany A. Staggemeiera , Terry O. Collierb , Bryan J. Prazena , Robert E. Synoveca,∗ a
Center for Process Analytical Chemistry, Department of Chemistry, Box 351700, University of Washington, Seattle, WA 98195, USA b 3M Engineering Systems Technology Center, 3M Center, Building 0518-01, St. Paul, MN 55144, USA Received 16 June 2004; received in revised form 8 November 2004; accepted 8 November 2004 Available online 21 December 2004
Abstract A dynamic surface tension detector (DSTD) was used to examine the molecular diffusion and surface adsorption characteristics of surfaceactive analytes as a function of solution viscosity. Dynamic surface tension is determined by measuring the differential pressure across the air/liquid interface of repeatedly growing and detaching drops. Continuous surface tension measurement throughout the entire drop growth is achieved for each eluting drop (at a rate of 30 drops/min for 2 l drops), providing insight into the kinetic behavior of molecular diffusion and orientation processes at the air/liquid interface. Three-dimensional data are obtained through a calibration procedure previously developed, but extended herein for viscous solutions, with surface tension first converted to surface pressure, which is plotted as a function of elution time axis versus drop time axis. Thus, an analyte that lowers the surface tension results in an increase in surface pressure. The calibration procedure derived for the pressure-based DSTD was successfully extended and implemented in this report to experimentally determine standard surface pressures in solutions of varied viscosity. Analysis of analytes in viscous solution was performed at low analyte concentration, where the observed analyte surface activity indicates that the surface concentration is at or near equilibrium when in a water mobile phase (viscosity of 1.0 Cp). Two surface-active analytes, sodium dodecyl sulfate (SDS) and polyethylene glycol (MW 1470 g/mol, PEG 1470), were analyzed in solutions ranging from 0 to 60% (v/v) glycerol in water, corresponding to a viscosity range of 1.0–15.0 Cp. Finally, the diffusion-limited surface activity of SDS and PEG 1470 were observed in viscous solution, whereby an increase in viscosity resulted in a decreased surface pressure early in drop growth. The dynamic surface pressure results reported for SDS and PEG 1470 are found to correlate with solution viscosity and analyte diffusion coefficient via the Stokes–Einstein equation. © 2004 Published by Elsevier B.V. Keywords: Surface activity; Surface tension; Surface pressure; Surfactant; Polymer; Viscosity; Diffusion coefficient
1. Introduction Surface-active analytes comprise both hydrophobic and hydrophilic structural regions. Thus, in aqueous solution, these species diffuse toward the air/liquid interface and are preferentially adsorbed at the surface, thereby lowering the surface tension of the solution. This ability has caused the surface activity of such water-soluble polymers and surfactants to be an area of wide interest for a variety of applications including water treatment, food and consumer products, cosmetics, agrochemicals, and drug industries [1–6]. A range ∗
Corresponding author. Tel.: +1 2066852327; fax: +1 2066858664. E-mail address: [email protected] (R.E. Synovec).
0003-2670/$ – see front matter © 2004 Published by Elsevier B.V. doi:10.1016/j.aca.2004.11.022
of analytical techniques have been developed for the characterization of these surface-active species including both equilibrium methods such as the DeNouy ring detachment, pendant drop, sessile drop, and Wilhelmy balance (inclined plate) analyses [7,8], and dynamic methods such as maximum bubble pressure, oscillating jet, fast formed drop (FFD) technique, dynamic Wilhelmy plate, and Langmuir trough analyses [7,9–13]. Numerous studies have been performed on the dynamic aspects of surface activity molecules in both non-viscous and viscous aqueous solutions [9–11,14]. Dynamics of surface adsorption have long been known to affect the rate of surface tension lowering [7,14]. Two general mechanisms have been described for the rate-controlled diffusion and adsorption of surface-active analytes at an
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interface, taking into account a subsurface layer defined as a distance of several molecular diameters into the bulk solution from the surface [7,14,15]. The first mechanism is a bulk diffusion-controlled process, where the diffusion of the surface-active molecule from the bulk phase to the subsurface is the rate-limiting step and molecular orientation and adsorption to the air/liquid interface occurs without delay. The second mechanism is a diffusion–adsorption-controlled process, where diffusion of the surface-active molecule from the bulk to the subsurface occurs relatively rapidly, but here the molecule encounters some barrier to adsorption at the interface such as steric hindrance to molecular rearrangement at the surface, or lack of vacant space at the surface [7,14,15]. Dynamic diffusion and adsorption processes to achieve equilibrium surface concentrations have been noted to occur on the timescale of milliseconds to days [14]. Herein is reported the evaluation and application of the dynamic surface tension detector (DSTD), a growing dropbased technique utilizing a pressure sensor [16–18], to the determination of standard surface pressures for calibration and the examination of two surface-active analytes in viscous solution (glycerol:water, over a range of 0:100–60:40 volume ratio) on a drop formation time-scale of 0.2–2 s. Threedimensional data are obtained, with surface tension first converted to surface pressure, which is plotted as a function of elution time axis versus drop time axis. Thus, a surface-active analyte that lowers the surface tension results in an increase in surface pressure. The dynamic nature of the DSTD response allows the study of the adsorption of analytes to the air/liquid interface during a period of drop expansion, where the viscosity of the solution may limit molecular diffusion to the drop surface and molecular orientation for adsorption. Previous DSTD studies and evaluation of the calibration procedure for a variety of surfactants, proteins, and polymers were performed in non-viscous solution (i.e. water or buffers essentially at 1.0 Cp viscosity) [16,18–21]. Building upon this previous work, reported herein is the first application of the DSTD to the examination of analytes in viscous solution, where surface pressures for standards are not typically available in literature. In this work, the calibration equations previously derived for DSTD measurements were successfully redefined and utilized to experimentally determine accurate surface pressures of a standard (5% v/v acetic acid) in solutions of varied viscosity, thus allowing accurate surface pressures of analytes in viscous solution to then be determined. Two surface-active analytes, sodium dodecyl sulfate (SDS) and poly(ethylene) glycol (MW 1470 g/mol, PEG 1470), were chosen for analysis of their behavior in viscous solution, in order to evaluate the performance of the DSTD. In water, SDS is shown to be at equilibrium, or non-kinetically hindered (i.e., diffuses to and adsorbs at the air/liquid interface quickly, thus giving essentially constant surface pressure throughout drop growth), even at concentrations below that chosen for analysis in viscous mobile phase [22]. By contrast, the second analyte chosen, PEG 1470, was evaluated at an equilibrium concentration below which a kinetic hindrance is
observed in water. In this case the kinetic hindrance for PEG 1470 is likely due to a diffusion–adsorption-controlled process where the bulk concentration is insufficient to replenish the surface concentration fast enough during the initial rapid drop expansion. Thus, the impact of solution viscosity on the dynamics and sensitivity of the DSTD response is explored using these two test analytes, further expanding the scope of the DSTD technology for application to viscous solutions.
2. Theory The DSTD is based upon a growing drop technique, implementing a pressure sensor where the pressure signal is dependent upon surface tension properties of a given sample (Fig. 1). Pressure measurement is made throughout drop growth for each drop forming at a capillary tip. The air/liquid surface tension, γ, for a drop of radius r, is related to the pressure signal P, (pressure relative to atmospheric pressure, P0 ), according to Eq. (1), the time dependent Young–Laplace equation [17], P(t)X,M = (2γ(t)X,M /r(t)) + PC,M
(1)
where the P, γ, and r are all functions of time, t, during drop growth. X represents sample, M represents the mobile phase, and PC,M accounts for the viscosity-based pressure drop in the capillary tubing due to the relative position of the sensor from the capillary tip. P(t) is the individual drop profile pressure signal measured by the pressure sensor in the DSTD over the growth of a given drop. The dynamic surface pressure of a given sample in mobile phase, π(t)X,M , is the surface tension of the sample in mobile phase, γ(t)X,M , subtracted from the surface tension of the mobile phase itself, γ(t)M , π(t)X,M = γ(t)M − γ(t)X,M
(2)
Thus, an analyte that lowers the surface tension results in an increase in surface pressure. In cases where the analyte and the standard may both easily be analyzed in the same mobile phase, the calibration equation can be obtained in the following manner, as presented in previous reports [17,18]. The dynamic surface pressure of an analyte (A) in a mobile phase (M) can be expressed as a function of the drop radius and pressure signals of mobile phase and the sample via the combination of Eqs. (1) and (2): π(t)A,M =
r(t) [P(t)M − P(t)A,M ] 2
(3)
The subtraction of the two surface tension values removes the pressure offset (PC,M ) from the surface pressure term. The PC,M is assumed to be constant for a given mobile phase, meaning the analyte itself generally does not significantly affect the mobile phase viscosity [18]. A similar equation can be derived for the calibration standard (S) in the mobile
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Fig. 1. Schematic of the DSTD instrument configuration. The sample is introduced at 60 l/min via a 90 l sample loop connected to the injection valve and detected at the capillary sensing tip. Drops are repeatedly formed at the tip and removed via pneumatic detachment regulated to 2 s, resulting in 2 l drops. The pressure sensor, connected to the tubing with a side arm, is fitted with an internal membrane, which is used to measure the differential pressure across the liquid–air interface with respect to atmospheric pressure, P0 of the forming drops.
phase, π(t)S,M =
And for the standard in a water mobile phase, the surface pressure π(t)S,M2 is
r(t) [P(t)M − P(t)S,M ] 2
(4) π(t)S,M2 =
By combining Eqs. (3) and (4), the dynamic surface pressure of the analyte in the mobile phase is given by π(t)A,M = π(t)S,M
P(t)M − P(t)A,M P(t)M − P(t)S,M
(5)
where a standard value for π(t)S,M would need to be obtained from the literature or measured in the laboratory. However in a case where the surface pressure of the standard in the mobile phase, π(t)S,M , is not readily available from literature (i.e., viscous solution mobile phase), it will be shown that a measurement in the laboratory may be performed and an equation similar to Eq. (5) can now be derived and applied to determine the surface pressure of the standard in viscous solution utilizing the standard signal obtained in water, for which a literature value is available. To obtain the surface pressure of the standard in the viscous mobile phase (π(t)S,M1 ), from Eq. (5), the following theory is useful and readily applied, where M1 denotes viscous mobile phase and M2 denotes water mobile phase [19,20]. For the standard in viscous mobile phase, the surface pressure π(t)S,M1 is π(t)S,M1 =
r(t) [P(t)M1 − P(t)S,M1 ] 2
(6)
r(t) [P(t)M2 − P(t)S,M2 ] 2
(7)
Combining Eqs. (6) and (7) and solving for π(t)S,M1 to determine the surface pressure for the standard in viscous solvent, yields, π(t)S,M1 = π(t)S,M2
P(t)M1 − P(t)S,M1 P(t)M2 − P(t)S,M2
(8)
Thus, utilizing Eq. (8) in conjunction with drop profiles for water (P(t)M2 ), viscous mobile phase (P(t)M1 ), standard in water (P(t)S,M2 ), standard in viscous mobile phase (P(t)S,M1 ), and the literature value for the surface pressure of the standard in water (π(t)S,M2 ), which is then readily available from the literature and selected to be independent of time and a constant at a given concentration, the time-dependent surface pressure of the standard in a particular viscous mobile phase, π(t)S,M1 , may be experimentally determined. This surface pressure function π(t)S,M1 for the standard in viscous mobile phase may then be utilized in Eq. (5), above, for the determination of the surface pressure function of an analyte in the viscous mobile phase. Thus, the use of Eq. (8) allows the evaluation of the data of the standard at increased viscosity, and the determination of the standard value, π(t)S,M1 , in a more complex, viscous solvent for use in the determination of the analyte surface pressure via calibration using Eq. (5).
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3. Experimental 3.1. Materials and solutions Acetic acid (glacial, A38S-500) was purchased from Fisher Scientific (Fisher Scientific, Fair Lawn, NJ, USA). The acetic acid was prepared 5% (v/v) in water or viscous mobile phase of various concentrations for standard surface pressure measurements. Poly(ethylene) glycol (PEG 1470, Mw 1470 g/mol, cat. no. 2070-6001) was purchased from Polymer Laboratories (Polymer Laboratories, Amherst, MA, USA). Sodium dodecyl sulfate (98% purity) was obtained from Aldrich (Aldrich Chemical Co., Milwaukee, WI). All chemicals were used as received without further purification. Mobile phase solutions were prepared with nanopure, degassed water (Nanopure Filtration System, Barnstead, Dubuque, IA, USA) or with appropriate volumes of nanopure water and glycerol (99.9% purity, G33-500) purchased from Fisher Scientific (Fisher Scientific, Fair Lawn, NJ, USA). Viscous solutions were prepared with volume ratios of glycerol to water (glycerol:water, volume ratio) (Table 1). The corresponding weight percent glycerol and resulting viscosity for each solution are also shown in Table 1 [23]. Samples were prepared by dissolving analytes in the appropriate viscous solvent or water, identical to the mobile phase for a given analysis.
tus (including pump, tubing, and solvent reservoir) was equilibrated with the working mobile phase prior to performing analysis of samples at a given viscosity prepared in the working mobile phase. Pneumatic drop detachment at a rate of 0.5 Hz, resulted in 2 l drops at a flow rate of 60 l/min, using a solenoid valve (MBD002, Skinner Valve, New Britain, CT, USA). The pressure sensor (Validyne P305D-20-2369, Northridge, CA) was configured with a sensing membrane (Validyne diaphragm 3-34, Northridge, CA) that has an optimum response time for the DSTD measurements of interfacial kinetics. The sensor capillary tip was made from a short piece of PEEK microtight tubing sleeve (0.015 i.d., 0.025 o.d., Upchurch, Oak Harbor, WA). All data were collected at 20 kHz with a personal computer (850 MHz Pentium® , Intel Corporation, Santa Clara, CA) equipped with a data acquisition card (DAC, National Instruments, Austin, TX) and averaged to 50 points/s prior to saving. Data collection, P(t) drop profile pressure signal extraction, and calculation of drop surface pressures were performed via Eqs. (5) and (8) using LABVIEW (Version 6i, National Instruments, Austin, TX) programs written in-house. Data analysis was performed using MATLAB 6.1 (MathWorks, Natick, MA) and Origin (Version 7, Microcal Software, Inc., Northampton, MA).
4. Results and discussion 3.2. Instrumentation 4.1. Calibration procedure in viscous solution A MicroGradient LC pump (Micro Gradient, BrownLee, Santa Clara, CA, USA) was programmed for isocratic elution of the mobile phase to the DSTD. Solutions were introduced for detection via a ten-port injection valve (Rheodyne PR700102-1 Cotati, CA). A poly(etheretherketone) (PEEK) injection loop of 90 l of tubing (Upchurch, Oak Harbor,WA) was used for all experiments. This injection loop is of sufficient volume so that the center of the detected sample plug injected is not diluted by the mobile phase (i.e., at steady-state analyte concentration). A detailed schematic of the DSTD configuration with pneumatic drop detachment is shown in Fig. 1 and has been described in detail in previous reports [16–18]. The apparaTable 1 Volume ratio of glycerol to water in prepared viscous solutions is presented Volume ratio (glycerol:water)
Weight percent glycerol (%)
Viscosity (Cp)
0:100 10:90 20:80 30:70 40:60 45:55 50:50 60:40
0 11.5 22.7 33.5 43.9 48.8 54.0 63.8
1.0 1.5 1.9 2.8 4.2 5.5 7.6 15
This volume ratio results in solutions of the weight percent and viscosity shown in the table.
Drop profiles for mobile phase and analytes are extracted from raw P(t) data collected continuously during a run. Fig. 2(A) shows an overlay of drop pressure profiles, as related to surface tension via Eq. (1), extracted from raw data for water (P(t)M ), 1 mM SDS (P(t)A,M ), and the standard, 5% acetic acid in water (P(t)S,M ), in the upper, middle, and lower profiles, respectively. Fig. 2(B) shows the resulting dynamic surface pressure of the analyte, π(t)A,M , obtained from utilizing these three drop profiles and a literature value for π(t)S,M of 10.3 dyn/cm (5% acetic acid in water) in Eq. (5). The surface pressure for 1 mM SDS is nearly constant throughout drop growth indicating that this is a non-kinetically hindered analyte, which concentrates and orients at the surface of the drop resulting in an equilibrium surface concentration early in drop growth. This constant pressure throughout drop growth is typical of small molecules in non-complex solvents, which are able to diffuse rapidly to the surface of the drop and experience little hindrance when orienting at the air/liquid interface. The initial disturbance seen in the first 0–200 ms of drop growth is due to the loading and unloading of the pressure sensor membrane and is typically not shown, for clarity [24]. The surface pressure at drop detachment averaged over the last 10 points at the end of the 2 s drop (averaged π values from 1.8 to 2.0 s from each surface pressure plot) is defined in Fig. 2(B) and represented by πD .
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Fig. 2. The calibration procedure is demonstrated using three drop profiles for a non-kinetically hindered analyte. (A) Drop profiles for water (P(t)M ), 1 mM SDS analyte in water (P(t)A,M ), and 5% acetic acid standard in water (P(t)S,M ), from top to bottom. (B) The resulting dynamic surface pressure plot for 1 mM SDS, a non-kinetically hindered analyte, utilizing Eq. (5). πD represents the surface pressure values averaged for the end of the 2 s drop, in this case 4.6 dyn/cm (averaged π values from 1.8 to 2.0 s from each surface pressure plot).
The πD values are used extensively in the remainder of this report. The surface pressure plots π(t)S,M1 of the standard at elevated viscosity were found to be essentially independent of time, yet with a lower surface pressure as viscosity increased. Fig. 3 shows these results for the standard 5% acetic acid with πD plotted (π(t)S,M1 at drop detachment). These surface pressures were experimentally obtained and calculated utilizing Eq. (8) for each solution viscosity studied, where M1 is the viscous solvent and M2 is water. As the viscosity of solution M1 increases, the surface pressure of the standard, π(t)S,M1 , is seen to decrease from 10.3 dyn/cm in water to 1.7 dyn/cm at 15.0 Cp, since acetic acid has less effect on lowering the surface tension of the drops of the more viscous solvent. Therefore, for experiments performed in viscous solvents, these experimentally determined standard surface pressure values presented in Fig. 3 are utilized as π(t)S,M in Eq. (5) for accurate calibration of analytes in solutions of their respective viscosity.
Fig. 3. Standard (5% acetic acid, 10.3 dyn/cm in water) value in varied viscosity mobile phase at the point of drop detachment (πD as defined in Fig. 2(B)) obtained from Eq. (8). The plot above shows the degree to which the surface activity of acetic acid decreases with increasing viscosity. The standard surface pressure obtained for a given solution viscosity is then used for the calibration of analyte surface pressure at that same viscosity.
4.2. Evaluation of surface-active analytes The dynamic surface pressure plots and surface pressure values determined at drop detachment, πD , for SDS in water are reported in Fig. 4(A) and (B). Experimental uncertainty in the surface pressure is approximately the size of the data points (standard deviation of 0.15 dyn/cm) for calibration obtained in water. For the concentration range studied (0.1–5 mM SDS), the surface pressure plots shown in Fig. 4(A) are nearly constant indicating equilibrium surface concentration throughout drop growth. The concentration of SDS that is indicated with a circle in Fig. 4(B), 1 mM, presents a particularly level surface pressure plot in Fig. 4(A) (third from bottom), and was chosen for experiments performed on SDS in solutions of varied viscosity. The surface pressure plots for 1 mM SDS in solutions of varied viscosity (1.0–15.0 Cp), and the corresponding surface pressure values at drop detachment, πD , for this data are revealed in Fig. 5(A) and (B), respectively. As discussed above, the analyte surface pressure was calculated from Eq. (5), utilizing π(t)S,M1 as the surface pressure of the standard for a given viscosity (plotted in Fig. 3, via Eq. (8)). As seen in Fig. 5(A) and (B), the surface pressure is lower for the analyte (as it was for the standard) as viscosity increases, particularly at short drop time (in Fig. 5(A)). The dynamic surface pressure plots for SDS in Fig. 5(A) differ from those shown in Fig. 4(A), where in relatively non-viscous solvent (water, 1.0 Cp) a decrease in surface concentration of SDS observed below 1 mM is still accompanied by an equilibrium surface pressure throughout drop growth. The decrease in surface pressure with increasing viscosity observed for 1 mM SDS early in drop growth in Fig. 5(A), as well as at 2 s (drop detachment) in Fig. 5(B), is indicative of the decrease in the diffusion coefficient, D, of SDS corresponding to the increase in solution viscosity, which is expected at constant temperature according to the Stokes–Einstein equation, D=
kB T 6πηRH
(9)
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Fig. 4. (A) Surface pressure plots for the calibration of SDS at concentrations of 0.1, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 4.0, and 5.0 mM. At all SDS concentrations studied, there is little kinetic effect as the surface pressure is nearly constant throughout drop growth. (B) Maximum surface pressure shown as the surface pressure value at drop detachment, πD , vs. concentration of SDS. The 1 mM concentration chosen for study in varied viscosity is indicated by the circle.
where kB is Boltzmann’s constant, T the temperature in K, η the viscosity, and RH the hydrodynamic radius of the analyte [25]. Thus, in increasingly viscous solutions more time is required for the analyte to initially diffuse to and concentrate at the drop surface, thereby lowering the surface tension and raising the surface pressure. Indeed, recently reported results indicate a relationship between this dynamic surface pressure information and the molecular mass of denatured proteins (indicative of a correlation to their hydrodynamic radius), for example, Ref. [19]. To better understand the appearance of this change in the dynamic surface pressure of SDS presented in Fig. 5(A) and the surface pressure value at detachment in Fig. 5(B) in increasingly viscous solution, a discussion of drop formation and diffusion is helpful. For the growing-drop, the surface area of the drop expands rapidly early in drop formation, depleting the analyte concentration at the surface. While this occurs, the surface concentration is being replenished by the bulk analyte concentration in the solution, as discussed previously as a bulk diffusion-controlled process [7,14,15,18]. When diffusion and arrangement of the analyte at the surface is fast (such as SDS in water), this replenishment is
sufficiently rapid that the surface pressure of the analyte remains essentially constant at equilibrium surface concentration throughout drop growth [18]. By contrast, in a viscous solution the early drop growth is rapid enough that the rate of depletion of the analytes from the drop surface exceeds the rate of diffusion of the analytes from the bulk solvent for replenishment at the surface; thus, the surface pressure of the analyte begins to increase only after the rate of expansion of the drop surface abates. In other words, the increased viscosity may sufficiently lower the diffusion coefficient of the analyte such that the rapid initial expansion of the drop surface area exceeds the rate of the diffusion of the bulk analyte to the drop surface early in drop growth. Recalling that the DSTD data acquisition in these experiments has been regulated to 2 s for each drop, it can be reasonably assumed that the analytes in viscous solvent are still approaching equilibrium when the drop is pneumatically detached. This would result in the decreased surface pressure values with increasing viscosity obtained in Fig. 5(B) at drop detachment (i.e., 2 s). Given a longer drop time, the equilibrium surface pressure seen for SDS in water at 1 mM, 4.6 dyn/cm, should eventually be achieved in viscous solution as well.
Fig. 5. (A) Surface pressure plots for 1 mM SDS in solutions of varied viscosity. As the solution viscosity increases at constant analyte concentration, the dynamic surface pressure corresponding to the concentration and rearrangement of the surfactant at the surface of the drop becomes more pronounced. (B) Surface pressure value at drop detachment, πD , for 1 mM SDS in solutions of varied viscosity, obtained from data in Fig. 5(A). As the solution viscosity increases at constant analyte concentration, the surface pressure of the surfactant decreases. Dotted line indicates reference for zero dyn/cm.
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Fig. 6. (A) Surface pressure plots for the calibration of PEG 1470 at concentrations of 10, 20, 30, 50, 70, 100, 200, 300, and 500 ppm. At higher concentrations, there is little kinetic effect as the surface pressure is nearly constant throughout drop growth. However, at concentrations of 70 ppm and lower, the dynamic surface pressure plots indicate that increased time is required for the analyte to concentrate and rearrange at the drop surface. (B) Maximum surface pressure is shown as the surface pressure value at drop detachment vs. concentration of PEG 1470. The 100 ppm concentration, chosen for study in varied viscosity, is indicated by the circle.
The dynamic surface pressure plots and surface pressures obtained at drop detachment for the calibration of PEG 1470 in water are reported in Fig. 6(A) and (B). At concentrations greater than ∼70 ppm (parts per million by mass), there is little kinetic hindrance observed in Fig. 6(A) as the PEG 1470 surface pressure plot is nearly constant throughout drop growth. This is in contrast to the surface pressure of PEG 1470 at concentrations below 70 ppm, where the surface pressure is clearly not maximized until later in drop growth, as the bulk analyte concentration is insufficient to replenish the surface concentration until the rate of increase in drop surface area slows. On the resulting calibration plot showing surface pressure values at drop detachment (πD ) versus concentration in Fig. 6(B), 100 ppm is indicated as the concentration to be examined in solutions of varied viscosity. At this concentration, the surface pressure plot in water for the PEG 1470 is essentially constant throughout drop growth, as the bulk solvent concentration of PEG 1470 is just sufficient to replenish the surface concentration of the polymer even during rapid drop surface area expansion early in drop growth.
The dynamic surface pressure plots and the surface pressure at drop detachment for 100 ppm PEG 1470 in solutions of varied viscosity are reported in Fig. 7(A) and (B). These data were determined similarly to those for SDS, via Eq. (5), utilizing the standard π(t)S,M1 as calculated from Eq. (8) for solvents of varied viscosity. As revealed in Fig. 7(A), the diffusion to and arrangement of the PEG 1470 at the surface of the drop is increasingly hindered at short drop time as the solvent viscosity is increased. In addition, as viscosity increases, attenuation of the surface pressure value at drop detachment is observed (Fig. 7(B)), as the PEG 1470 requires more time to reach an equilibrium concentration at the drop surface. As discussed in the case of SDS for Fig. 5(A) and (B), it can again be reasonably assumed that PEG 1470 in viscous solution is still approaching equilibrium at the end of the regulated 2 s drop. Thus, given adequate drop time, the equilibrium surface pressure obtained for 100 ppm PEG 1470 in water should eventually be achieved in viscous solution as well. The Stokes–Einstein equation (Eq. (9)) was utilized to calculate the diffusion coefficient, D, of SDS and PEG 1470 in
Fig. 7. (A) Surface pressure plots for 100 ppm PEG 1470 in solutions of varied viscosity. As the solution viscosity increases at constant analyte concentration, the time required for an increase in surface pressure, corresponding to the concentration and rearrangement of the polymer at the surface of the drop, increases. Dotted line indicates reference for 0 dyn/cm. (B) Surface pressure values at drop detachment for 100 ppm PEG 1470 in solutions of varied viscosity obtained from data in (A). As the solution viscosity increases at constant analyte concentration, the surface pressure of the polymer at the surface of the drop decreases.
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solutions of increasing viscosity. The diffusion coefficients in water (at 1 Cp) are readily available in the literature. These diffusion coefficients were substituted into Eq. (9) (along with the appropriate temperature and required constants) and the hydrodynamic radius RH was calculated for each analyte. The RH was then held constant for each analyte as the viscosity was changed to estimate D at different solution viscosity. For the purposes of this study it is assumed that the RH of these relatively small analytes does not change as significantly as the viscosity was changed. These calculated D values were related to solution viscosity, and an overlay of the curves for the two analytes are shown in Fig. 8(A). According to Eq. (9), the values of D for both analytes are inversely proportional to solution viscosity. It was shown earlier in Figs. 5(B) and 7(B) that the surface pressure at drop detachment is inversely proportional to viscosity as well, due to the decreased ability of the analyte to diffuse to and rearrange at the drop surface in the 2 s time allowed for drop growth. However, even at drop times of 2 s, particularly in the lower solution viscosities studied, the analytes have clearly begun to approach equilibrium surface concentrations where the observed surface pressure is no longer due primarily to the diffusion of analytes to the drop surface. A stronger correlation of surface pressure to diffusion coefficient might be expected earlier in drop growth,
where drop expansion is still occurring rapidly. With this thought in mind, the comparison of the correlation of D, surface pressure, and viscosity both early in drop growth and at drop detachment can be seen in Fig. 8(B) and (C). In these figures, the dependence of surface pressure with increasing solution viscosity obtained at 2.0 s (πD , drop detachment) and π at 0.5 s (early in drop growth) on the calculated diffusion coefficient can be seen for SDS and PEG 1470, respectively. Early in drop growth, at 0.5 s, where the surface concentration is essentially diffusion limited, the surface pressure of both analytes decreases as the solution viscosity increases at a rate that is similar to the decrease of D with increasing viscosity, thus, the relationship is observed to be nearly linear. However, later in drop growth (at drop detachment), the relationship between D and surface pressure deviates from linearity as the analytes begin to approach an equilibrium surface concentration. Note that the methodology used herein is empirical, i.e., plotting surface pressure as a function of analyte diffusion coefficient. The ∼four-fold difference in the slope of the SDS and PEG 1470 plots in Fig. 8(B) and (C) is due to differences in the concentration and surface activity of the molecular species. More study is warranted in order to determine if additional physical meaning can be attributed to the magnitude of the slopes.
Fig. 8. (A) Dependence of the calculated diffusion coefficient, D, to viscosity for SDS (dotted line) and PEG 1470 (solid line). (B) Correlation of calculated diffusion coefficient, D, to the surface pressure π of SDS obtained at 0.5 s (filled squares) and πD at 2.0 s (open circles) into drop growth in increasingly viscous solutions. (C) Correlation of calculated diffusion coefficient, D, to the surface pressure π of PEG 1470 obtained at 0.5 s (filled squares) and πD at 2.0 s (open circles) into drop growth in increasingly viscous solutions.
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5. Conclusion The effect of solution viscosity on the dynamic surface pressure of a common surfactant and a polymer has been evaluated via the DSTD. The calibration equations previously derived for pressure-based measurements by the DSTD were successfully redefined and utilized to experimentally determine surface pressures of a standard (5% v/v acetic acid in water) in solutions of varied viscosity, thus allowing the determination of dynamic surface pressures of analytes in viscous solution. The surface pressure values of SDS and PEG 1470 in increasingly viscous solutions were compared to the calculated diffusion coefficients of the analytes as a function of solution viscosity. A bulk phase diffusion-limited regime of the dynamic surface tensions of SDS and PEG 1470 was observed in viscous solution via the DSTD. An important area of future study follows from the data presented in this work, that expansion of the linear dynamic range of the DSTD may be achieved by increasing the mobile phase viscosity for analysis of highly surface-active species, thereby lowering their attainable surface pressure within the regulated response time.
Acknowledgment We thank the Center for Process Analytical Chemistry (CPAC), a National Science Foundation University/Industry Cooperative Research Center at the University of Washington, for financial support. References [1] Z. Amjad (Ed.), Water Soluble Polymers: Solution Properties and Applications„ Plenum Publishing, New York, 1998. [2] J.E. Glass (Ed.), Hydrophilic Polymers: Performance with Environmental Acceptance, American Chemical Society, Washington, DC, 1996.
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