Molecular Diffusivity of Phenol in Sub- and Supercritical Water

ARTICLE pubs.acs.org/JPCB

Molecular Diffusivity of Phenol in Sub- and Supercritical Water: Application of the Split-Flow Taylor Dispersion Technique Andriy Plugatyr* and Igor M. Svishchev Department of Chemistry, Trent University Peterborough, Ontario, Canada K9J 7B8 ABSTRACT: The binary diffusion coefficient of phenol in aqueous solution was examined from ambient to supercritical water conditions by using the developed split-flow Taylor dispersion technique. The technique significantly simplifies diffusivity measurements in hightemperature and supercritical water, as the sample injection and detection are performed ex situ at ambient conditions. The binary diffusion coefficient of phenol increases from 1.013 10-9 m2 s-1 at 298.7 K and 25 MPa to about 34.71 10-9 m2 s-1 at 672.9 K and 30 MPa and follows Arrhenius behavior with an activation energy of 15.09 kJ/mol. The diffusion coefficient of phenol in infinitely dilute solution was also calculated by means of molecular dynamics (MD) simulations over a wide temperature and density range (298-773 K and from 0.07 to 1.0 g/cm3, respectively). A dramatic increase in the diffusivity was observed upon transition into the low density supercritical region. The obtained experimental data agrees well with available literature values and the MD results. At subcritical conditions the experimentally obtained binary diffusion coefficients generally follow the predictions from the Stokes-Einstein equation, with the estimate for the hydrodynamic radius of the solute taken from MD data.

1. INTRODUCTION Technological applications of high-temperature and supercritical water for power generation, hazardous waste utilization, materials processing, etc. have attracted much attention over the last two decades.1-6 Despite recent progress in the area, still very little is known about mass transfer coefficients of organic and inorganic solutes in aqueous solutions at elevated temperatures and pressures. This is primarily due to experimental difficulties of determining transport coefficients near and above the critical point of water (Tc = 647 K, pc = 22.1 MPa). To date, only a few experimental measurements of diffusion coefficients in sub- and supercritical water have been reported.7-14 The technical difficulties of measuring diffusion coefficients in aqueous solutions at extreme conditions have prompted application of molecular dynamics (MD) simulation methods.15-26 Among different methods,27-29 employed for the diffusion measurements in supercritical fluids, the most commonly used is the Taylor dispersion technique.29-39 The method is based on the dispersion measurement of a narrow pulse of a solute flowing through a long tube of uniform diameter in a fully developed laminar flow. The Taylor dispersion technique (i.e., the capillary peak broadening method) combines experimental simplicity with potentially high achievable accuracy. The fundamentals and practical applications of the Taylor dispersion technique have been described in-detail by Levelt-Sengers et al.,32 Funazukuri,33 Alizadeh et al.,40 and others. Unfortunately, application of the Taylor dispersion method to diffusion coefficient r 2011 American Chemical Society

measurements at extreme experimental conditions in situ is difficult and requires sophisticated analytical equipment, capable of withstanding high temperatures and pressures. To our knowledge, only one experimental investigation of diffusion coefficients in high temperature water using the in situ Taylor dispersion technique has been reported by Goemans et al.10 Recently, we have developed the ex situ flow injection methodology,41 which has been successfully applied to the examination of the hydrodynamic regime of a flow-through tubular reactor under supercritical water conditions. The main advantage of the ex situ method is that the sample injection and detection are performed outside the “hot zone” of the experimental apparatus, which enables one to use standard analytical equipment for tracer detection. In this study, we apply the ex situ flow injection methodology to binary diffusion coefficient measurements at sub- and supercritical water conditions by using the split-flow Taylor dispersion technique. The goal of this study is 2-fold. First, to examine the diffusivity of phenol from ambient to supercritical water conditions by using the developed split-flow Taylor dispersion technique. Second, to calculate the molecular diffusion coefficient of phenol by means of molecular dynamics (MD) simulations over a wide temperature and density range. Phenol is an aromatic compound that Received: November 9, 2010 Revised: January 11, 2011 Published: March 02, 2011 2555

dx.doi.org/10.1021/jp1107075 | J. Phys. Chem. B 2011, 115, 2555–2562

The Journal of Physical Chemistry B

ARTICLE

Figure 1. Schematic diagrams of the (a) traditional (in situ) and (b) split-flow Taylor dispersion techniques (ex situ, this study).

exhibits both hydrophobic and hydrophilic interactions. From this perspective, it is certainly interesting to investigate whether its diffusion coefficient follows simple hydrodynamic behavior (Stokes-Einstein) in the wide temperature range. The remainder of this paper is organized as follows. The employed methods, experimental apparatus and procedures are described in section 2. The results are discussed in section 3. Our conclusions are given in section 4.

2. METHODS AND MATERIALS 2.1. Split-Flow Taylor Dispersion Technique. The conventional and the employed split-flow Taylor dispersion techniques are schematically illustrated in Figure 1. In a traditional Taylor dispersion experiment, the impulse/response curves are recorded in situ at the entrance and the exit of the diffusion coil. In contrast, the developed split-flow Taylor dispersion technique relies on splitting the flow equally between two flow channels, which are identical in all respects except one contains the diffusion coil. The two response curves, obtained ex situ, are then used for the calculation of the binary diffusion coefficients by means of a deconvolution procedure. Briefly, in the Laplace space, the response of a system without the diffusion coil, r1(s), can be written as

r1 ðsÞ ¼ pðsÞ hA ðsÞ hB ðsÞ

ð1Þ

where is p(s) is the Laplace transform of the normalized input pulse function, P0 (t), and transfer functions hA(s) and hB(s) characterize the flow in the fore and after sections of the experimental apparatus, respectively. The fore and after sections of the flow system include injector, preheater, temperature exchanger, back-pressure regulator, detector, various fittings,

etc. The response of the system with the diffusion coil, r2(s), is given in the Laplace domain by r2 ðsÞ ¼ pðsÞ hA ðsÞ hD ðsÞ hB ðsÞ

ð2Þ

where hD(s) is the transfer function of the diffusion coil of the flow system. Thus, under suitable experimental conditions, the transfer function of the diffusion coil, hD(s), can be found from the deconvolution of the two normalized experimental response curves R20 (t) and R10 (t) R¥ 0 R2 ðtÞe-st dt r2 ðsÞ ¼ R0¥ 0 ð3Þ hD ðsÞ ¼ -st dt r1 ðsÞ 0 R1 ðtÞe The proposed split-flow experimental approach simplifies many technical aspects in conducting experimental measurements at extreme conditions as the signal detection is performed at ambient conditions after temperature and pressure let down. 2.2. Experimental Apparatus. The schematics of the experimental apparatus is shown in Figure 2. An HPLC pump (Waters 590), equipped with two pulse dampeners, is used to deliver pure deionized (Milli-Q) deoxygenated water. The internal lowpressure transfer lines are constructed of No-Ox (VICI) or PEEK tubing in order to prevent solvent regassing. A six-port two-position electrically actuated sample injection valve (Valco), equipped with a 250 μL sample loop, was employed to carry out flow injections of a tracer solution. A 1:1 flow splitter was constructed inhouse by using a zero dead volume mixing tee (Valco) and two electroformed nickel microcapillaries (ID = 0.05 mm, L = 0.3 m). The 1:1 split ratio was confirmed to be accurate within 1% by gravimetric analysis. Each flow channel is equipped with a 3.0 m long preheater coil and 0.7 m lead-in and lead-out capillaries. A 9.96 m stainless steel (SS316) diffusion tube was employed in 2556

dx.doi.org/10.1021/jp1107075 |J. Phys. Chem. B 2011, 115, 2555–2562


ARTICLE

Figure 2. Schematic diagram of the experimental apparatus.

this study. The inner diameter of the diffusion tube was determined gravimetrically, in a separate set of experiments, to be 0.79 mm. The preheaters and the diffusion coil were mounted on a custom-made tubing holder with a circular diameter of 15 cm. The resulting coiling ratio, ω = Dc/d0, was calculated to be about 190 to 1. The diffusion coil assembly was placed in a custom-made sand bath which sits inside a muffle furnace (Isotemp 650 Series, Fisher Scientific). The temperature of the furnace was maintained by the built-in PID controller equipped with a K-thermocouple. The temperature uniformity of the sand bath, as monitored by two thermocouples, was determined to be (0.6 at 673 K. A custom-built heat exchanger (L = 2.5 m), coupled to a cold plate (TE Technology), was used to cool down the effluent to ambient temperature. The temperature of the heat exchanger was maintained at 25 C by a temperature controller (TC-24-25, TE Technology). The pressure in the system was controlled by an adjustable back pressure regulator (P-880, Upchurch). Both temperature and pressure in the system were monitored using a data logger (PrTC-210, Omega). Cooled and depressurized effluent was passed through a 10 mm optical path stainless steel flow cell (FIA-Z-SMA, FIA Inc.). Online spectroscopic measurements were performed using an UV-vis spectrometer (USB-2000, Ocean Optics). All parts of the flow-through apparatus were constructed of stainless steel SS316 tubing (OD = 1/1600 , ID = 0.0300 ) and connected using SS316 zero dead volume unions (Valco). 2.3. Experimental Procedure. In this study we have chosen to examine the binary diffusion coefficients of phenol. High thermal stability of phenol at elevated temperatures and pressures has been reported previously.42,43 Standard 1000 ppm aqueous phenol solution (LabChem Inc.) was used to prepare fresh 100 ppm (1.06 mM) working solutions. Both carrier water and phenol solutions, deoxygenated by helium sparging, were kept under argon to prevent regassing. The residual dissolved oxygen concentration, monitored by a NeoFox system (Ocean Optics) equipped with a FOSPOR oxygen probe, did not exceed 300 ppb. Prior to each injection, the system was allowed to stabilize at set operating conditions for about two hours. Subsequently, a solute pulse was injected into the flow system. The beginning of spectra acquisition was synchronized with the injection event. The primary channel of the spectrometer was used to monitor phenol absorbance at a wavelength of 270 nm. The spectrometer acquisition time was set at 1 s. 2.4. Molecular Diffusivity Calculations. In this study we apply transfer function formalism for the evaluation of binary

diffusion coefficients from the experimental response curves. The axially dispersed plug flow model (ADPF)40 was used to describe the dispersion of a solute in the diffusion coil DC D2 C DC ¼ Da 2 - u 0 Dt Dx Dx

ð4Þ

where C is the solute concentration, hu0 is the cross section averaged axial velocity of the fluid, and Da is the axial dispersion coefficient. The latter is related to the binary diffusion coefficient of a solute, D12, via30,31 Da = D12 þ

u0 2 d0 2 192D12

ð5Þ

where d0 is the inner diameter of the tube. Note, that eq 5 is subject to certain experimental conditions discussed in detail by Alizadeh et al.40 and Levelt-Sengers et al.32 The transfer function for the ADPF model (eq 4) with small extents of dispersion (PeL > 500) is given by44 PeL ADPF ð1 - jÞ ð6Þ h ðsÞ ¼ exp 2 qffiffiffiffiffiffiffiffiffiffiffiffiffi u0 L where j ¼ 1 þ 4sτ eclet number, hτ Pe and PeL ¼ Da is the axial P is the mean residence time of the fluid in the system and L is the characteristic length of the section of experimental apparatus. From eqs 3 and 6 it follows that R¥ 0 R2 ðtÞe-st dt PeL ð1 - jÞ ¼ R0¥ 0 ð7Þ exp -st dt 2 0 R1 ðtÞe The parameters of the transfer function, namely the mean residence time, hτ, and the Peclet number, PeL, were obtained from the experimental response curves R10 (t) and R20 (t) by using the time domain curve-fitting procedure, described by Fahim.45 Finally, the binary diffusion coefficients were calculated from eq 5 with hu and Da given by L ð8Þ u0 ¼ τ and Da ¼

u0 L PeL

ð9Þ

2.5. Simulation Details. The simple point charge extended (SPC/E) water model of Berendsen et al.46 was used in this 2557



ARTICLE

Table 1. Summary of the Experimental Conditions and Values of the Binary Diffusion Coefficients of Phenol Obtained by Using the Split-Flow Taylor Dispersion Technique N

T, K

4 298.74 ( 0.59

p, kPa

F, g/cm

ηa, μPa 3 s

D12 109, m2/s

102.5 ( 27

0.998

878.7 ( 13.6

1.025 ( 0.020

12 298.65 ( 0.14 25136 ( 48

1.008

876.6 ( 3.12

1.013 ( 0.012

5 323.50 ( 0.33 25006 ( 27

0.999

548.8 ( 3.32

1.802 ( 0.036

9 373.54 ( 0.18 25064 ( 27

0.970

287.5 ( 0.55

3.897 ( 0.070

6 424.11 ( 0.24 25029 ( 16 11 472.73 ( 0.18 25059 ( 31

0.929 0.882

187.3 ( 0.33 140.3 ( 0.16

6.637 ( 0.099 9.795 ( 0.298

6 523.26 ( 0.15 24997 ( 60

0.821

111.6 ( 0.12

12.05 ( 1.05

11 571.87 ( 0.16 25032 ( 18

0.745

92.1 ( 0.12

19.79 ( 1.35

8 622.23 ( 0.12 24986 ( 11

0.628

73.1 ( 0.12

25.76 ( 1.62

5 648.42 ( 0.15 30148 ( 11

0.558

64.5 ( 0.12

28.00 ( 0.90

0.352

43.4 ( 0.23

34.71 ( 2.96

10 672.87 ( 0.09 29995 ( 5 a

Values were obtained from the IAPS Formulation 1985 for the Viscosity of Ordinary Water Substance.59

study. Among the several rigid point charge models for phenol found in literature,47-49 we have used the model of Mooney et al.,49 which is known to work well at ambient and high temperature conditions. Molecular dynamics simulations were carried out in the NVT and the NPT ensembles. Constant density simulations were performed from 0.2 to 1.0 g/cm3 at 298, 373, 473, 573, 673, and 773 K. The constant pressure simulations were carried out over the same temperature range with the pressure set at 18.6 MPa, which corresponds to 25 MPa of the real fluid. Note, that the critical pressure of the SPC/E water was estimated to be 16.3 MPa by Hayward and Svishchev,50 16.0 MPa by Guissani and Guillot51 and 16.4 MPa by Plugatyr and Svishchev.52 The system size was 503 water molecules and 1 phenol molecule. The isokinetic equations of motions were integrated using the forth-order Gear algorithm53 with the time step of 1 fs. Rotational degrees of freedom were represented using quaternions.54 The equilibrated simulation run lengths were 500 ps. The longrange Coulomb forces were evaluated using Ewald summation technique in cubic periodic boundary conditions. The cutoff distance for the LJ interactions was set at the half of the cell length. The translational self-diffusion coefficients were calculated from the velocity autocorrelation function (VACF) accumulated up to 4 ps. The simulations were carried out on a Linuxbased parallel Transport GX28 system with dual 64 bit AMD Opteron processors.

3. RESULTS AND DISCUSSION The obtained diffusion coefficients along with the summary of the experimental conditions are given in Table 1. Examples of normalized experimental response curves are shown in Figure 3. The reproducibility of the mean residence time (i.e., the first moment of the distribution) for the response curves obtained at identical experimental conditions was determined to be within 1%. In this study, the mean relative error of the fit by using the time-domain curve fitting procedure did not exceed 0.01%. In this work, the average temperature and pressure fluctuations were about 0.3 K and 50 kPa, respectively. At these conditions, the calculated density fluctuations were below 0.4% (mostly 0.05% or better). In order to minimize the effect of diffusion tube curvature, the volumetric flow rate at the pump in

Figure 3. Examples of the experimental response curves obtained at 25 MPa and (a) 298 K and (b) 573 K.

all experiments was kept below 200 μL/min. The calculated Reynolds numbers range from 0.7 to 35.1 with the De2Sc parameter not exceeding 33, where De and Sc are Dean and Schmidt numbers, respectively. According to eq 71 given in ref 40, the deviations from the strait tube behavior at the employed experimental conditions are below 0.3%. The effect of the injected phenol concentrations on the value of the binary diffusion coefficient was examined at 298 K. The results obtained from injecting 25 and 100 ppm solutions were found to be the same, within statistical uncertainty. The effect of the volumetric flow rate at the pump was examined at 298, 373, and 572 K. No statistically significant dependence was found when 100 and 200 μL/min flow rates were used, and the values listed in Table 1 are averages of the two flow rates. In order to ensure correct mass balance during diffusion measurements, the total concentration of phenol was calculated from the obtained response curves and compared with the total concentration of injected tracer. In this study, more than 98% of the injected phenol was detected in each individual experiment. The 1:1 split ratio was also verified by comparing the relative area of the two response curves. The average deviations are within 3%. The traditional Taylor dispersion technique has been previously employed by Castillo,55 Yang and Matthews,56 and 2558



Figure 4. Binary diffusion coefficients of phenol in aqueous solution.

Niesner and Heintz57 for the binary diffusion coefficient measurements of phenol in aqueous solution. These studies were conducted at ambient pressure and provide diffusivity data for phenol over the temperature range from 277.2 to 343.0 K. In order to validate the proposed split-flow methodology we have also performed measurements at ambient conditions. The value of the binary diffusion coefficient of phenol in aqueous solution at 298.7 K and 0.1 MPa obtained in this study is 1.025 ( 0.020 10-9 m2/s. Our result is somewhat higher than that of Castillo et al.55 (0.940 10-9 m2/s at 296.2 K) and Yang and Matthews56 (0.925 10-9 m2/s at 298.15 K) but agrees well with the value of 0.998 10-9 m2/s, reported by Niesner and Heintz57 at 298.2 K. The experimental data along with available literature values are shown in Figure 4. Considering that changes in water density and viscosity with pressure are very small below 373 K, we compare our data obtained at 25 MPa with previously reported values at saturated vapor pressures. Our results of 1.013 ( 0.012 10-9 and 1.802 ( 0.036 10-9 m2/s obtained at 298.6 and 323.5 K, respectively, are in a very good agreement with the values of 0.998 10-9 and 1.788 10-9 m2/s reported by Niesner and Heintz57 at 298.2 and 323.2 K. The value given by Castillo et al.55 at 323 K is 1.62 10-9 m2/s. In Figure 4, we also compare our data with the values of the limiting binary diffusion coefficients of benzene obtained by Tominaga et al.58 along the coexistence curve of water over a wider temperature range. At ambient conditions, the value for benzene of 1.10 ( 0.03 10-9 m2/s, reported by Tominaga et al.,58 is approximately 10% larger than that of phenol and, arguably, reflects the lesser tendency of benzene to form H-bonds with water. The values provided in Figure 4 for benzene were scaled by the relative diffusivities of phenol and benzene at ambient conditions, i.e., using DT(benzene)D298K(phenol)/ D298K(benzene). As can be seen from this figure, our results, obtained by the split-flow Taylor dispersion technique, are in a good agreement with the study of Tominaga et al.58 In Figure 5, we compare our experimental data with the results of our molecular dynamics simulation study. The values for the diffusion coefficients of phenol obtained from MD simulations are shown in Table 2. Due to the fact that the single solute

ARTICLE

Figure 5. Binary diffusion coefficients of phenol in sub- and supercritical water (this study).

Table 2. Binary Diffusion Coefficients of Phenol in Aqueous Infinitely Dilute Solution Obtained by Using MD Simulations

a

F, g/cm3

T, K

1.00

298.15

1.05

1.00

373.15

2.57

1.00

473.16

5.79

1.00 1.00

573.16 673.16

7.12 7.79

1.00

773.16

11.15

0.80

573.16

10.92

0.80

673.16

14.08

0.80

773.16

16.56

0.60

673.16

25.53

0.60

773.16

27.13

0.40 0.40

673.16 773.16

32.45 41.52

0.20

673.16

59.96

0.20

773.16

0.99

323.15

18.6

1.44

0.95

373.15

18.6

2.61

0.91

423.15

18.6

4.72

0.85

473.15

18.6

7.39

0.78 0.68

523.16 573.15

18.6 18.6

10.57 17.83

0.52

623.16

18.6

26.32

0.17

673.16

18.6

68.26

0.09

723.16

18.6

113.29

0.07

773.17

18.6

153.13

Pa, MPa

Dsimul. 109, m2/s

71.22

Corresponds to 25 MPa of real water.

particle dynamics was examined, the statistical uncertainty in the determination of the diffusivity of phenol from MD simulation was calculated to be around 10%. Note, however, that the uncertainty for the water diffusion coefficient does not exceed 1%. As can be seen from Figure 5, a dramatic increase in diffusivity is observed upon transition into low density supercritical states and the effect of water density is far more 2559



ARTICLE

Figure 6. Arrhenius plot for the binary diffusion coefficients of phenol in aqueous solution.

pronounced than that of temperature. Thus, along the 1.0 g/cm3 isochore, the diffusion coefficient of phenol obtained from MD simulations increases from 1.05 10-9 m2/s at 298 K to 11.15 10-9 m2/s at 773 K, whereas at 773 K and 18.6 MPa (F = 0.07 g/cm3), it reaches a value of 153.1 10-9 m2/s. Such behavior can be attributed to the disappearance of the percolating H-bonded network structure of water in low density (F < Fc) supercritical water. Despite the fact that our MD simulations along the 18.6 MPa isobar (which corresponds to 25 MPa for real fluid) somewhat underestimate the experimental values, the overall agreement is rather good. Thus, at 573 and 623 K, the simulated and experimental values were determined to be 17.8 10-9 and 19.8 10-9 m2/s and 26.3 10-9 and 25.8 10-9 m2/s, respectively. The experimental value of 34.7 10-9 m2/s obtained at 673 K and 30 MPa (F = 0.354 g/cm3) is very similar to the MD result of 32.4 10-9 m2/s obtained at the 673 K with density fixed at 0.4 g/cm3. The experimental values obtained at 30 MPa at temperatures above 673 K are associated with a large statistical uncertainty and are not reported. The large uncertainty is due to the combined effect of decreased water density (small mean residence times) and a dramatic increase in phenol diffusivity (small Da) at these conditions. A better accuracy might be obtained with a longer diffusion coil with a larger internal diameter. The analysis of our experimental data shows that over the examined temperature range the binary diffusion coefficient of phenol follows the Arrhenius behavior, as can be seen in Figure 6. The pre-exponential factor and activation energy were determined to be 102.67 and 15.09 kJ/mol, respectively. In Figure 7, we compare available experimental data with the predictions of the commonly used hydrodynamic Stokes-Einstein relation DSE ¼

kT CSE πηR

ð10Þ

where k is the Boltzmann constant, T is the temperature, η is the dynamic viscosity of the solvent, R is the hydrodynamic radius of the solute, and CSE is the Stokes-Einstein coefficient. The limiting values of the CSE are 4 and 6 for the “slip” and “stick” limits, respectively. The “stick” limit result is obtained on the assumption that the fluid “sticks” to the particle surface with frictional coefficient μ = ¥, whereas “slip” condition assumes

Figure 7. Comparison of the experimental results with the predictions of the Stokes-Einstein relation.

zero surface friction (μ = 0). The “stick” limit corresponds to a large (macroscopic) spherical particle diffusing through a solvent of a relatively small size. Considering the size of phenol relative to water molecule, the Stokes-Einstein relation in a “stick” limit (i.e., CSE = 6) was used in this study. The value of the hydrodynamic radius for phenol of 2.5 Å was taken from the analysis of phenol (center of benzene ring) - oxygen (water) radial distribution function at 298 K; it corresponds to the maximum distance at which this g(r) becomes nonzero. The values of the dynamic viscosity of water were obtained from the IAPS Formulation 1985 for the Viscosity of Ordinary Water Substance.59 The results, shown in Figure 7, indicate that the Stokes-Einstein relation holds well up to the critical point of water. Previous studies of Lamb et al.7 and Buttenhoff et al.9 indicate that the hydrodynamic theory provides a good agreement (within 10%) with the experimental data for water densities above 0.5 g/cm3, whereas below Fc the Stokes-Einstein relation appears to be no longer valid.7 Comparison of our experimental and simulation values obtained at 673 K and 30 MPa (F = 0.354 g/cm3) and 673 K and 0.4 g/cm3, respectively, with predictions from the Stokes-Einstein relation indicate that the hydrodynamic theory overestimates the diffusivity of phenol by about 30%. Arguably, such discrepancy cannot be attributed to the “critical slowing-down” effect discussed by Clifford and Coleby.60 In short, the “critical slow-down” of the binary diffusion coefficient can be explained from nonequilibrium thermodynamics considerations, where the diffusion is driven by changes in the chemical potential rather than the concentration gradient. As a consequence, the diffusion coefficient for a concentrated solution approaches zero at the critical point. The effect was experimentally observed in supercritical fluids for concentrated solutions (solute mole fractions being larger than 10-4-10-3) in the vicinity of the critical point.60,61 Note, however, that in the limit of infinite dilution the “critical slowingdown” effect becomes very small and is not observed in the Taylor dispersion experiments, where typical solute concentrations approximate infinite dilution.60 Furthermore, our experimental value obtained at 673 K and 30 MPa (F = 0.354 g/cm3) agrees well with our infinite dilution MD result at 673K and 0.4 g/cm3. 2560



ARTICLE

The breakdown of the hydrodynamic behavior for supercritical fluids at low viscosities have been observed previously.27,28,62,63 It was found that at high fluidity (low viscosity) the correlation between diffusion coefficient and the solvent viscosity is better represented by a power law, D12 η-a.62,63 Although the exact location at which a crossover to the power-law behavior occurs is difficult to predict, Debenedetti and Reid27 have suggested that the lower limit for the hydrodynamic theory is at about η ≈ 40 μPa s. At viscosities below 40 μPa s, the hydrodynamic Stokes-Einstein based equations lead to the overestimation of diffusion coefficients in supercritical fluids.27 Interestingly enough, the value of the dynamic viscosity of 43.4 ( 0.23 μPa s calculated at 673 K and 30 MPa (F = 0.354 g/cm3) is very close to the value of 40 μPa s obtained by Debenedetti and Reid27 based on the analysis of Swaid and Schneider64 data for the diffusivity of benzene in supercritical CO2. Enhanced solvent clustering around solute molecule at supercritical conditions could potentially explain the negative deviations from the Stokes-Einstein relation, as “solvated” particle would diffuse slower than predicted by the hydrodynamic theory. Thus, Butenhoff et al.9 have found that ordinary binary mass diffusion coefficients for concentrated aqueous NaNO3 solution under supercritical conditions agreed well with predictions from the Stokes-Einstein equation, provided the diffusing species were represented by a hydrated contact pair (NaNO3 3 4H2O) with an effective ionic radius being two times larger than that of NaNO3 at ambient conditions. Detailed analysis of our MD simulation results reveal that at 673 K and 0.4 g/cm3 phenol is hydrated by approximately 9.5 water molecules and, on average, maintains close to one H-bond (hydroxyl group) with the surrounding water. Coincidently, the hydrodynamic radius of a hydrated phenol of 3.4 Å, taken at the first maximum of the phenol (center of benzene ring) - oxygen (water) RDF at 673 K and 0.4 g/cm3, yields the Stokes-Einstein value of 33.89 10-9 m2/s at 673 K and 30 MPa, which is within statistical uncertainty of our experimental result of 34.7 10-9 m2/s. In order to test the solvent “clustering” hypothesis we have examined the local water structure enhancement/depletion around phenol molecule from ambient to supercritical conditions. The solvent’s local density augmentation/depletion was calculated according to the definition given by Chialvo and Cummings65 F12 ðRÞ - F11 ðRÞ ¼

3F

RR

¥ 0 2 r0 ½g12 ðrÞ - g11 ðrÞr R 3 - r0 3

dr

ð11Þ

where F11(R) is the average solvent’s density in the solvent’s solvation shell with a radius R, and r0, is the radius at which the difference g12(r) - g11(r) becomes nonzero. In this study, g¥ 12(r) and g011(r) were phenol (center of benzene ring) - oxygen (water) and oxygen (water) - oxygen (water) pair-correlation functions, respectively. The value of R was set at 6 Å and corresponds to the outer boundary of the first solvation shell of phenol. The results indicate that along the 25 MPa isobar the ratio of local to bulk density decreases with increasing temperature from 0.98 at 298 K to 0.88 at 573 K, and further to 0.74 at 673 K and 0.4 g/cm3. These calculations demonstrate that, in case of phenol, the negative deviations from the Stokes-Einstein relation cannot be explained by local solvent clustering as the local water density around phenol molecule at these conditions appears to be depleted by about 25% compared to the bulk. Thus,

the value for the hydrodynamic radius of 3.4 Å can not be justified. These results seem to suggest that deviations from the hydrodynamic prediction at low density supercritical states are probably due to the breakdown in the continuum hydrodynamics assumption used in the derivation of the Stokes-Einstein relation. Further systematic investigations of the behavior of binary diffusion coefficients in low density supercritical states are clearly warranted.

4. CONCLUSIONS The application of the developed split-flow Taylor dispersion technique to binary diffusion coefficient measurements in hightemperature compressed water was presented. The split-flow approach significantly simplifies technical aspects of conducting experimental measurements in high-temperature and supercritical water as the sample injection and detection are performed at ambient conditions. The binary diffusion coefficients of phenol in aqueous solution were measured from ambient to supercritical water conditions. The results obtained in this study are in very good agreement with available experimental and simulation data. We may note that previous experimental diffusion coefficient measurements for phenol were conducted only up to a temperature of 343 K.55 The diffusivity of phenol increases from 1.013 10-9 m2/s at 298 K and 25 MPa to 34.71 10-9 m2/s at 673 K and 30 MPa and follows Arrhenius behavior. At densities above 0.5 g/cm3, the obtained diffusion coefficients agree well with the predictions from the Stokes-Einstein equation, with a single value of the hydrodynamic radius taken from MD results at ambient conditions. The diffusion coefficients of phenol in infinitely dilute solution were also calculated by means of MD simulations. The simulations cover wide temperature and density ranges from 298 to 773 K and from 1.0 to 0.07 g/cm3, respectively. A dramatic increase in the diffusivity was observed upon transition into the low density (F < Fc) supercritical region and is related to the disappearance of the extended H-bond network structure of water. Our MD simulations results are in agreement, within the statistical uncertainty, with the obtained experimental values. Overall, the results indicate that MD simulation is complementary to the Taylor dispersion technique for elucidation of mass transfer coefficients in sub- and supercritical water at infinite dilution. ’ AUTHOR INFORMATION Corresponding Author

*Phone: 1-705-748-1011 ext. 7163. Fax: 1-705-748-1625. E-mail: [email protected].

’ ACKNOWLEDGMENT The authors are grateful for the financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC). ’ REFERENCES (1) (2) (3) (4) 2561

Bermejo, M. D.; Cocero, M. J. AIChE J. 2006, 52, 3933–3951. Kruse, A.; Dinjus, E. J. Supercrit. Fluids 2007, 39, 362–380. Kruse, A.; Dinjus, E. J. Supercrit. Fluids 2007, 41, 361–379. Kruse, A.; Vogel, H. Chem. Eng. Technol. 2008, 31, 1241–1245. dx.doi.org/10.1021/jp1107075 |J. Phys. Chem. B 2011, 115, 2555–2562

The Journal of Physical Chemistry B (5) MacDonald, P.; Buongiorno, J.; Sterbentz, J. W.; Davis, C.; Witt, R. Nuclear Energy Research Initiative Project; 2001-001, INEEL/EXT, 0402530. (6) Kronholm, J.; Hartonen, K.; Riekkola, M. Trac.-Trends Anal. Chem. 2007, 26, 396–412. (7) Lamb, W. J.; Hoffman, G. A.; Jonas, J. J. Chem. Phys. 1981, 74, 6875–6880. (8) Flarsheim, W. M.; Tsou, Y. M.; Trachtenberg, I.; Johnston, K. P.; Bard, A. J. J. Phys. Chem. 1986, 90, 3857–3862. (9) Butenhoff, T. J.; Goemans, M. G. E.; Buelow, S. J. J. Phys. Chem. 1996, 100, 5982–5992. (10) Goemans, M. G. E. Mass Transfer in SCWO Process: Molecular Diffusion and Mass Transfer Coefficients of Inorganic Nitrate Species in Suband Supercritical Water; Proceedings of the Second International Symposium on Environmental Applications of Advanced Oxidation Technologies, 1996. (11) Liu, C. Y.; Snyder, S. R.; Bard, A. J. J. Phys. Chem. B 1997, 101, 1180–1185. (12) Trevani, L. N.; Calvo, E.; Corti, H. R. J. Chem. Soc., Faraday Trans. 1997, 93, 4319–4326. (13) Yoshida, K.; Wakai, C.; Matubayasi, N.; Nakahara, M. J. Chem. Phys. 2005, 123, 164506. (14) Yoshida, K.; Matubayasi, N.; Nakahara, M. J. Chem. Phys. 2006, 125, 074307. (15) Balbuena, P. B.; Johnston, K. P.; Rossky, P. J.; Hyun, J. K. J. Phys. Chem. B 1998, 102, 3806–3814. (16) Goo, G. H.; Sung, G. H.; Lee, S. H. Mol. Simul. 2004, 30, 37–44. (17) Hyun, J. K.; Johnston, K. P.; Rossky, P. J. J. Phys. Chem. B 2001, 105, 9302–9307. (18) Kubo, M.; Levy, R. M.; Rossky, P. J.; Matubayasi, N.; Nakahara, M. J. Phys. Chem. B 2002, 106, 3979–3986. (19) Lee, S. H. Mol. Simul. 2004, 30, 669–678. (20) Lee, S. H.; Cummings, P. T. J. Chem. Phys. 2000, 112, 864– 869. (21) Nieto-Draghi, C.; Avalos, J. B.; Contreras, O.; Ungerer, P.; Ridard, J. J. Chem. Phys. 2004, 121, 10566–10576. (22) Noworyta, J. P.; Koneshan, S.; Rasaiah, J. C. J. Am. Chem. Soc. 2000, 122, 11194–11202. (23) Ohmori, T.; Kimura, Y. J. Chem. Phys. 2003, 119, 7328–7334. (24) Plugatyr, A.; Nahtigal, I.; Svishchev, I. M. J. Chem. Phys. 2006, 124, 024507. (25) Svishchev, I. M.; Plugatyr, A.; Nahtigal, I. G. J. Chem. Phys. 2008, 128, 124515. (26) Svishchev, I. M.; Plugatyr, A. Y. J. Phys. Chem. B 2005, 109, 4123–4128. (27) Debenedetti, P. G.; Reid, R. C. AIChE J. 1986, 32, 2034–2046. (28) Liong, K. K.; Wells, P. A.; Foster, N. R. J. Supercrit. Fluids 1991, 4, 91–108. (29) Funazukuri, T.; Kong, C. Y.; Kagei, S. J. Supercrit. Fluids 2008, 46, 280–284. (30) Aris, R. Proc. R. Soc. London 1956, A235, 67. (31) Taylor, G. I. Proc. R. Soc. London 1953, A219, 186. (32) Sengers, J. M. H. L.; Deiters, U. K.; Klask, U.; Swidersky, P.; Schneider, G. M. Int. J. Thermophys. 1993, 14, 893–922. (33) Funazukuri, T.; Kong, C. Y.; Kagei, S. J. Chromatogr. A 2004, 1037, 411–429. (34) Weingartner, H.; Klask, U.; Schneider, G. M. Z. Phys. Chem.-Int. J. Res. Phys. Chem. Chem. Phys. 2005, 219, 1261–1271. (35) Funazukuri, T.; Kong, C. Y.; Kagei, S. J. Supercrit. Fluids 2006, 38, 201–210. (36) Kong, C. Y.; Funazukuri, T.; Kagei, S. J. Supercrit. Fluids 2006, 37, 359–366. (37) Suarez-Iglesias, O.; Medina, I.; Pizarro, C.; Bueno, J. L. Fluid Phase Equilib. 2007, 260, 279–286. (38) Pizarro, C.; Suarez-Iglesias, O.; Medina, I.; Bueno, J. L. Ind. Eng. Chem. Res. 2008, 47, 6783–6789. (39) Suarez-Glesias, O.; Medina, I.; Pizarro, C.; Bueno, J. L. J. Chem. Eng. Data 2008, 53, 779–784.

ARTICLE

(40) Alizadeh, A.; Nieto de Castro, C. A.; Wakeham, W. A. Int. J. Thermophys. 1980, 1, 243–284. (41) Plugatyr, A.; Svishchev, I. M. J. Supercrit. Fluids 2008, 44, 31–39. (42) Thornton, T. D. Doctoral Thesis; University of Michigan: Ann Arbor, MI, 1991. (43) Koo, M.; Lee, W. K.; Lee, C. H. Chem. Eng. Sci. 1997, 52, 1201–1214. (44) Torres, A. P.; Oliveira, F. A. R. J. Food Eng. 1998, 36, 1–30. (45) Fahim, M. A.; Wakao, N. Chem. Eng. J. 1982, 25, 1–8. (46) Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. J. Phys. Chem. 1987, 91, 6269–6271. (47) Sagarik, K.; Asawakun, P. Chem. Phys. 1997, 219, 173–191. (48) McDonald, N. A.; Carlson, H. A.; Jorgensen, W. L. J. Phys. Org. Chem. 1997, 10, 563–576. (49) Mooney, D. A.; Muller-Plathe, F.; Kremer, K. Chem. Phys. Lett. 1998, 294, 135–142. (50) Hayward, T. M.; Svishchev, I. M. Fluid Phase Equilib. 2001, 182, 65–73. (51) Guissani, Y.; Guillot, B. J. Chem. Phys. 1993, 98, 8221–8235. (52) Plugatyr, A.; Svishchev, I. M. Fluid Phase Equilib. 2009, 277, 145–151. (53) Evans, D. J.; Morriss, O. P. Comput. Phys. Rep. 1984, 1, 297–343. (54) Evans, D. J. Mol. Phys. 1977, 34, 317. (55) Castillo, R.; Garza, C.; Orozco, J. J. Phys. Chem. 1992, 96, 1475–1478. (56) Yang, X. N.; Matthews, M. A. J. Colloid Interface Sci. 2000, 229, 53–61. (57) Niesner, R.; Heintz, A. J. Chem. Eng. Data 2000, 45, 1121–1124. (58) Tominaga, T.; Matsumoto, S.; Ishii, T. J. Phys. Chem. 1986, 90, 139–143. (59) White, H. J., Jr., Sengers, J. V., Neumann, D. B., Bellows, J. C., Eds.; Physical Chemistry of Aqueous Systems: Meeting the Needs of Industry, Proceedings of the 12th International Conference on the Properties of Water and Steam, 1995. (60) Clifford, A. A.; Coleby, S. E. Proc. R. Soc. London, Ser. A: Math. Phys. Sci. 1991, 433, 63–79. (61) Bartle, K. D.; Baulch, D. L.; Clifford, A. A.; Coleby, S. E. J. Chromatogr. 1991, 557, 69–83. (62) Hayduk, W.; Cheng, S. C. Chem. Eng. Sci. 1971, 26, 635–. (63) Feist, R.; Schneider, G. M. Sep. Sci. Technol. 1982, 17, 261–270. (64) Swaid, I.; Schneider, G. M. Ber. Bunsen-Ges. Phys. Chem. Chem. Phys. 1979, 83, 969–974. (65) Chialvo, A. A.; Cummings, P. T. AIChE J. 1994, 40, 1558–1573.

2562


Molecular Diffusivity of Phenol in Sub- and Supercritical Water

Recommend Documents