Pulse Radiolysis Investigations of Solvation Effects on Arylmethyl

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12394

J. Phys. Chem. 1996, 100, 12394-12402

Pulse Radiolysis Investigations of Solvation Effects on Arylmethyl Cation Reactivity in Supercritical Fluids Jianwei Zhang, Karen A. Connery, Joan F. Brennecke,* and John E. Chateauneuf* Department of Chemical Engineering, UniVersity of Notre Dame, Notre Dame, Indiana 46556 ReceiVed: April 5, 1996; In Final Form: May 14, 1996X

Pulse radiolysis has been used to measure the influence of supercritical fluid and cosolvent solvation on arylmethyl cation reactivity in supercritical fluoroform (CHF3) and ethane (C2H6). Ion-neutral reactivity was investigated for the reaction of benzhydryl cation (Ph2C+H) with tetramethylethylene (TME) in CHF3 at 35 and 50 °C, and with triethylamine (TEA) in CHF3 at 35 and 70 °C, and for the reaction of 4,4′-dimethoxybenzhydryl cation ((4-MeOPh)2C+H)) with TEA in CHF3 at 35 and 70 °C, and with TEA in C2H6 at 35 °C. The effect of pressure on the bimolecular rate constants (kbi) for these nucleophilic reactions was investigated over significant fluid density ranges, along the isotherms indicated, and in each case was found to decrease in magnitude with an increase of pressure (solvent density). The reactivity observed was analyzed in terms of the influence of bulk solvent dielectric constant on kbi, the comparison of the pressure effect on kbi with that predicted from transition state theory, and the influence of temperature and solvation on kbi. Evidence for preferential cosolvent solvation was observed for the ionic reactions investigated in supercritical CHF3.

Introduction

Me Me

Currently there is great interest in the development of supercritical fluids as possible alternatives to common organic solvents as reaction media. Development of supercritical fluids for this purpose requires a detailed mechanistic knowledge of the specific factors that influence and control chemical reactivity under a variety of supercritical reaction conditions.1 One important factor in the characterization of chemical reactivity in supercritical fluids is the ability to understand to what degree reaction rate constants are influenced by changes in bulk physical properties of the solvent compared to the influence of the thermodynamic pressure effect on the rate constant, both of which can be substantial in these highly compressible fluids. Time-resolved spectroscopic methods have proven particularly useful in achieving this goal.1 In previous investigations we have used laser flash photolysis and well-defined photochemical probes to investigate the potential influence of solvent and cosolvent solvation on diffusion2,3 and kinetically4-7 controlled reactions in polar and nonpolar supercritical fluids. The previous investigations focused on reactions between nonionic reactants. The current investigation expands the characterization of reactions under supercritical conditions to reactions containing an ionic component. Specifically, pulse radiolysis has been used to generate the arylmethyl cations, benzhydryl cation (Ph2C+H), and 4,4′-dimethoxybenzhydryl cation ((4-MeOPh)2C+H) and measure the influence of pressure and solvent density on bimolecular rate constants of ion-neutral reactivity with tetramethylethylene (TME) and triethylamine (TEA) in polar and nonpolar fluids as described in eqs 1-3. We have previously presented preliminary data8 on reactions 1 and 2. The further investigation of the influence of temperature on these reactions, and the investigation of reaction 3 have resulted in new insights concerning preferential solvation and a more complete characterization of ion-neutral reactivity under supercritical conditions. X

Abstract published in AdVance ACS Abstracts, July 1, 1996.

S0022-3654(96)01033-7 CCC: $12.00

+ Ph2CH + Me2C

kbl

CMe2

CHF3

Ph2CH C

C+

(1)

Me Me + Ph2CH + Et3N

kbl CHF3

+ Ph2CH–NEt3

+ (4–MeOPh)2CH + Et3N

kbl CHF3, ethane

(2) + (4–MeOPh)2CH–NEt3

(3)

Experimental Section Materials. Benzhydrol (Ph2CHOH) (Aldrich, 99%) and 4,4′dimethoxybenzhydrol ((4-MeOPh)2CHOH) (Aldrich, 99%) were recrystallized from absolute ethanol. Tetramethylethylene (2,3dimethyl-2-butene) (Aldrich, 99+%) was purified by bulb-tobulb distillation. Triethylamine (Et3N) (Aldrich, 99%) was distilled from potassium hydroxide prior to use. Fluoroform (CHF3) (DuPont Freon-23, 98% purity) and ethane (C2H6) (Scott Specialty Gases, ultra high purity grade) were each sequentially passed through two high-pressure oxy-traps (Alltech) and two high-pressure charcoal traps (Alltech) to remove oxygen and trace impurities, respectively. Sample Preparation. Sample mixtures were prepared using two Isco Model 260D high-pressure syringe pumps, an injection port for solid solutes, and a Reodyne HPLC injection loop for injection of liquid reactants. Samples were prepared by condensation of CHF3 or ethane into a syringe pump at 0-15 °C. The subcooled liquid (CHF3 or ethane) was then used to fill a preevacuated sample syringe pump through the solid and/ or liquid injection ports containing desired amounts of cation precursor (Ph2CHOH, or (4-MeOPh)2CHOH) and/or liquid reactants (TME or TEA), respectively. The samples were then heated well above the critical temperature (Tc) of the mixtures to facilitate mixing and produce a one-phase homogeneous solution. Cation precursor concentrations were on the order of 10-3 M. Pulse Radiolysis. Pulse radiolysis experiments were performed using a 10-50 ns pulse of 8 MeV electrons from the Notre Dame Radiation Laboratory linear accelerator (LINAC). The Pulse Radiolysis apparatus has previously been described.9 © 1996 American Chemical Society

Arylmethyl Cation Reactivity in Supercritical Fluids

J. Phys. Chem., Vol. 100, No. 30, 1996 12395

Transient absorption signals were monitored using a pulsed 1000 W xenon lamp source. Transient absorption signals were digitized with a LaCroy 7200A Precision Digital Oscilloscope, and a Gateway 2000 4DX2-66V computer was used for experimental control. Pulse radiolysis of supercritical mixtures was performed using a high-pressure optical cell/flow apparatus that was specifically designed to study pulse-radiolytically induced reactions in supercritical fluids. A detailed description of the high-pressure apparatus, including mechanical drawings of the optical cell components, has recently been reported.10 Briefly, the highpressure optical cell is constructed of stainless steel and fitted with two opposed Suprasil quartz windows that result in an optical path length of 1.75 cm. Perpendicular to the optical path, the cell is fitted with a customized stainless steel port for incidence of the electron beam. The electron beam port is designed to allow free access of the e-beam to a point at which the electrons need only to penetrate a 0.026-0.030 in. stainless steel wall. The honeycomb design of the window allows for even electron distribution across this thin wall while maintaining mechanical strength. Each window component is mechanically sealed with lead and brass packing. All pulse radiolysis experiments were performed under flow conditions. The flow apparatus consists of two 266 mL capacity Isco Model 260D high-pressure syringe pumps, one of which acts as an upstream sample reservoir and the other as a waste reservoir. Prior to an experiment, the temperature and pressure of the sample reservoir were set to desired experimental values. Under flow conditions, the temperature within the high-pressure optical cell was monitored and controlled with a platinum resistance thermometer that made direct contact with the supercritical mixture, and an Omega (Model CN-6070A) temperature controller equipped with a Watlow Firerod cartridge heater. Pressure was monitored at the optical cell using a Heise (Model 901A) pressure gauge (gauge accuracy (0.24 bar). Experiments were typically performed at a constant flow rate of 0.8 mL/min. Under these conditions, the optical cell temperature and pressure were maintained at (0.2 °C and (0.4 bar, respectively. For safety considerations, the optical cell was monitored with a video camera to ensure appropriate temperature, pressure, and flow rate. Additional specifics of the flow system apparatus and operational methodologies are described in detail elsewhere.10

Figure 1. Determination of the bimolecular rate constants (the slopes) from observed pseudo-first-order rate constants at various pressures for the reaction of Ph2C+H with TME at 35 and 50 °C in CHF3.

Results The observed rate constants (kobs) for decay of the arylmethyl cations, Ph2C+H and (4-MeOPh)2C+H, in the presence of either TME or TEA were pseudo first order. Bimolecular rate constants (kbi) for the ion-neutral reactions were obtained from the dependence of kobs on the quenching substrate concentration according to eq 4:

kobs ) ko + kbi[quenching substrate]

(4)

Reaction of Ph2C+H with TME in CHF3. The transient absorption of Ph2C+H was monitored at 435 nm following pulse radiolysis of ca. 10-3 M Ph2CHOH in CHF3. Values of kbi for the reaction of Ph2C+H with TME (reaction 1) at 35 and 50 °C were obtained from plots of kobs vs TME concentration (Figure 1). (It should be noted that the four sets of 35 °C data presented in Figure 1 (top) are only representative of the 10 pressures investigated at 35 °C and were chosen solely on the basis of presentation clarity. Representative pressures were also used in Figures 3 and 5 for the same reason.) The bulk concentration range of [TME] was 9.6-106.0 mM, which corresponds to a

Figure 2. Bimolecular rate constants plotted vs pressure (top) and density (bottom) for the reaction of Ph2C+H with TME at 35 and 50 °C in CHF3.

mole fraction range of 1.0 × 10-3 to 7.6 × 10-3. Values of kbi obtained from Figure 1 decrease from 2.6 × 107 M-1 s-1 at 65.8 bar to 1.2 × 107 M-1 s-1 at 147.9 bar at 35 °C and decrease from 1.6 × 107 M-1 s-1 at 97.6 bar to 0.91 × 107 M-1 s-1 at 173.4 bar at 50 °C. The pressure and density dependence of kbi for the reaction of Ph2C+H with TME at 35 and 50 °C are presented in Figure 2. CHF3 densities were determined from an empirical equation of state for pure CHF3.11 The critical temperature and pressure of pure CHF3 are 26.15 °C and 48.6 bar, respectively (Table 1). Reaction of Ph2C+H with TEA in CHF3. Values of kbi for the reaction of Ph2C+H with TEA (reaction 2) at 35 and 70 °C were obtained from plots of kobs versus TEA concentration (Figure 3). The bulk concentration range of [TEA] was 14.0-

12396 J. Phys. Chem., Vol. 100, No. 30, 1996

Zhang et al.

TABLE 1: Critical Properties Used in the Estimation of Partial Molar Volumes from the Peng-Robinson Equation of State component a

fluoroform ethanea 2.3-dimethyl-2-butene (TME)a triethylamine (TEA)a Ph2C+Hb (4-MeOPh)2C+Hc TS (Ph2C+H/TME)c TS (Ph2C+H/TEA)c TS ((4-MeOPh)2C+H/TEA)c

Tc (K)

Pc (bar)

ω

299.3 305.4 524.0 535.0 770.0 880.8 922.7 922.0 1014.4

48.6 48.8 33.6 30.3 28.6 24.8 18.2 17.1 14.0

0.260 0.099 0.239 0.320 0.442 0.683 0.543 0.675 0.857

a Reference 30. b Properties of Ph2CH2 from ref 30. c Estimated; see text.

Figure 4. Bimolecular rate constants plotted vs pressure (top) and density (bottom) for the reaction of Ph2C+H with TEA at 35 and 70 °C in CHF3.

Figure 3. Determination of the bimolecular rate constants (the slopes) from observed pseudo-first-order rate constants at various pressures for the reaction of Ph2C+H with TEA at 35 and 70 °C in CHF3.

750.0 µM, which corresponds to a mole fraction range of 3.1 × 10-6 to 5.3 × 10-5. Values of kbi obtained from Figure 3 decrease from 1.87 × 1010 at 63.1 bar to 9.29 × 109 M-1 s-1 at 147.9 bar at 35 °C and decrease from 5.32 × 1010 at 76.9 bar to 1.39 × 1010 M-1 s-1 at 146.5 bar at 70 °C. The pressure and density dependence of kbi for the reaction of Ph2C+H with TEA at 35 and 70 °C are presented in Figure 4. Reaction of (4-MeOPh)2C+H with TEA in CHF3 and Ethane. The transient absorption of (4-MeOPh)2C+H was monitored at 496 nm in CHF3 and 508 nm in ethane following pulse radiolysis of ca. 10-3 M (4-MeOPh)2CHOH. Values of kbi for the reaction of (4-MeOPh)2C+H with TEA (reaction 3) at 35 and 70 °C were obtained from plots of kobs vs TEA concentration (Figure 5). The bulk concentration range of [TEA] was 25.1-1433.1 µM, which corresponds to a mole fraction range of 5.5 × 10-6 to 1.02 × 10-4. Values of kbi obtained from Figure 5 decrease from 4.6 × 109 at 61.7 bar to 2.0 × 109 M-1 s-1 at 147.9 bar at 35 °C and decrease from 1.2 × 1010 at 76.9 bar to 2.4 × 109 M-1 s-1 at 180.3 bar at 70 °C. The pressure and density dependence of kbi for the reaction of (4-MeOPh)2C+H with TEA at 35 and 70 °C are presented in Figure 6. Values of kbi for the reaction of (4-MeOPh)2C+H with TEA were also obtained in ethane at 35 °C and decrease from 3.93 × 109 at 75.5 bar to 2.77 × 109 M-1 s-1 at 147.9 bar (not shown); see Discussion section.

Figure 5. Determination of the bimolecular rate constants (the slopes) from observed pseudo-first-order rate constants at various pressures for reaction of (4-MeOPh)2C+H with TEA at 35 and 70 °C in CHF3.

Discussion Carbanions and carbocations play a broad and pervasive role as reactive intermediates in organic reaction chemistry, and an extensive literature on these ionic species has been developed.12-16 However, there is little known of solvent effects on ionic reactions in supercritical fluids, although supercritical fluids have been shown to be superb media for a variety of chemical processes. We also believe that characterization of ionic reactivity in low-temperature supercritical fluids will yield valuable information regarding reaction mechanisms in hydrothermal and supercritical water reduction and oxidation processes.1 Our current investigations have focused on the generation and reactivity of arylmethyl cations with nucleophilic cosolvents as reactants in supercritical CHF3 and ethane.

Arylmethyl Cation Reactivity in Supercritical Fluids

Figure 6. Bimolecular rate constants plotted vs pressure (top) and density (bottom) for the reaction of (4-MeOPh)2C+H with TEA at 35 and 70 °C in CHF3.

(Throughout this paper we refer to the nucleophilic reactants as cosolvents, to be consistent with our previous supercritical fluid investigations of kinetically controlled reactions4-8 of dilute solutes with added reactants having concentrations approaching or surpassing 1 mol %. In the present study the concentrations of TME approach 1 mol %, while the concentrations of TEA are much less. In either case, the concentration of reactant is large in comparison to the concentration of cation, as demonstrated by the observation of pseudo-first-order kinetics. Nevertheless, we believe it would be equally correct to refer to the nucleophilic reactants in the present study as cosolutes. Therefore, even though we believe the terms cosolvent and cosolute may be used interchangeably in context of the present study, we refer to the nucleophilic reactants as cosolvents.) Arylmethyl cations of the general form R3C+ were chosen for our initial studies of ionic reactivity in supercritical fluids since their spectroscopy and reactivity have been well characterized in normal liquids.14-16 Dorfman and co-workers have demonstrated that arylmethyl cations may be generated by pulse radiolysis of organic liquids containing cation precursors (such as, R3CX, where X ) OH, Br, or Cl) by dissociative oxidation of the precursors by solvent (radiolytically) derived cationic species.15,16 We have extended the pulse radiolytic methods of Dorfman’s experiments in normal liquids to supercritical fluids and have demonstrated the ability to generate arylmethyl cations of varying stability (e.g., trityl cation (Ph3C+), 4,4′dimethoxybenzhydryl cation ((4-MeOPh)2C+H), and benzhydryl cation (Ph2C+H)) in supercritical CHF3 and ethane.8,10 In our supercritical fluid experiments, the arylmethyl cations were identified by the demonstration of typical cationic reactivity in the presence of several standard substrates. For example, the above arylmethyl cations demonstrated a characteristic lack of reactivity toward molecular oxygen and, as expected, were found to react rapidly with nucleophiles like MeOH and Et3N. The cations were further identified by their characteristic absorption spectra. However, in each case the cation absorption spectra were consistently found to be blue-shifted from the corresponding solution values. For example, the absorption maximum for Ph2C+H shifted to 435 nm in CHF3 compared to 450 nm in cyclohexane, and absorption maximum for (4-MeOPh)2C+H

J. Phys. Chem., Vol. 100, No. 30, 1996 12397 shifted to 508 nm in ethane and 496 nm in CHF3 compared to 515 nm in cyclohexane. The apparent blue shift in absorption bands is consistent with our previous investigations of transient species, e.g., benzyl radical2,3 and triplet anthracene,17 in supercritical fluids and may actually be attributed to bathochromic shifts from gas phase values due to London dispersion forces. Therefore, the spectral characteristics and reactivity observed following pulse radiolysis of appropriate cation precursors under supercritical conditions were consistent with those previously reported for cations generated by pulse radiolysis of organic liquids and from laser photoheterolytic bond cleavage methods.14,18 It is worth noting that repeated attempts to generate these cationic species by the laser flash photolysis photoheterolytic cleavage method18 failed, even with added polar cosolvents, e.g., CH3CN, MeOH, and H2O. Therefore, pulse radiolysis may be the only means available to generate these arylmethyl cations in these relatively low dielectric media. It is also worth noting that the ability to perform detailed kinetic investigations on cation-neutral reactivity was to some extent dependent on the spectral characteristics of the cation; however, it was more highly dependent on the kinetic limitations of cation stability and the magnitude of cation reactivity toward a reactant. Therefore, cation reactant combinations were chosen such that a considerable change in cation lifetime (reactivity) was observed while maintaining a low mole percent of added reactant. Reaction of Ph2C+H with TME in CHF3. There are several factors that may influence reaction rates in compressed fluids. These include changing bulk physical properties such as solvent density and the dielectric constant which can influence reaction rates, the thermodynamic pressure effect on the rate constant, and, potentially, some short-range solvation effects. The reaction of Ph2C+H with TME, reaction 1, in supercritical CHF3 was analyzed by three methods: (1) the experimental results were compared with trends that have been observed for reactions of neutral molecules with ions in normal incompressible liquid solutions;19 (2) the experimentally observed pressure effect on the reaction rate constant was compared to the pressure effect on the rate constant predicted from transition state theory using activation volumes determined from a combination of the electrostriction volume from the Drude-Nernst equation20,21 and the intrinsic volumes from the Peng-Robinson equation;22 and (3) comparison of the expected pressure effect on the rate constant calculated from a model set forth by Wood and coworkers23,24 for the partial molar volume of an ion in a supercritical fluid and the intrinsic volumes from the PengRobinson equation.22 Normal Liquid Models (Method 1). Various expressions have been developed for the influence of the solvent on the reaction rate between a neutral molecule and an ion in liquid solvents.19 They are based on the application of transition state theory to the Gibbs free energy change of inserting ions and dipoles into liquid solvents of zero ionic strength and a given dielectric constant. The various expressions predict that ln(kbi) vs 1/ (the reciprocal of the dielectric constant) should be linear with a positive slope of

(

)

2 2 1 ZA e NA 1 1 4πo 2RT rA rq

where rA and rq are the radius of the ionic reactant and the transition state complex, respectively. Since rq is greater than rA and greater dispersal of charge may occur in the transition state complex, reaction rates should be somewhat greater in media of lower dielectric constant. This was observed experi-

12398 J. Phys. Chem., Vol. 100, No. 30, 1996

Zhang et al. TABLE 2: Activation Volumes Estimated from Peng-Robinson Equation of State, Drude-Nernst Equation, and the Method of Wood et al. for the Reaction of Ph2C+H with TME in CHF3 at 35 °C ∆Vjq (cm3/mol)

Figure 7. Experimental rate constants for the reaction of Ph2C+H with TME at 35 °C in CHF3 as a function of the inverse of the solvent dielectric constant.

mentally in supercritical CHF3. The bulk dielectric constant of CHF325 varies significantly over the range of pressures investigated and a plot of ln(kbi) versus 1/ is presented in Figure 7. The plot is remarkably linear, suggesting that the reaction is being affected by the solvent in a manner similar to that observed in ordinary liquid solvents. However, when the slope of ln(kbi) vs 1/ is calculated using normal liquid models, they were found to overpredict the magnitude of the slope of ln(kbi) vs 1/ by about 10%: the slope from the experimental data in Figure 7 is 8.2 while the normal liquid model-predicted slope is 9.1 when assuming reasonable sizes of Ph2C+H and the ionic transition state as 2.45 Å26 and 7.5 Å, respectively. This slope difference may be partly due to the inaccuracy of liquid models which neglect the compressibility of the solvent. It may also be a manifestation of the enhanced local density and, hence, the enhanced local dielectric constant. Thermodynamic Pressure Effect, Drude-Nernst Equation, and Peng-Robinson Equation (Method 2). In the second method of analysis, the Drude-Nernst and Peng-Robinson equations have been used to estimate the anticipated pressure effect on the rate constant from transition state theory.27 Transition state theory provides a bridge between reaction mechanics and thermodynamics and offers a convenient and powerful formalism for exploring and explaining solvent and pressure effects on reactions. This theory views a chemical reaction as occurring via a transition-state species (or an activated complex) and assumes thermodynamic equilibrium between transition state and reactants. Once the transition-state complex is formed, it proceeds directly to products. According to this model, the thermodynamic pressure effect on a bimolecular rate constant is given by28

A + B T [transition state]q f products RT(∂ ln kbi/∂P)T ) -∆Vjq - RTkT

(5)

Therefore, the thermodynamic pressure effect is simply the difference in the partial molar volumes of the transition state and the two reactants, ∆Vjq ) VjTS - VjA - VjB, minus a compressibility term (see Glossary for definition of terms). The compressibility term in the equation accounts for the reactant concentrations changing with pressure. The pressure effect can be significant since partial molar volumes of even nonpolar solutes in supercritical fluids as large as -15 000 cm3/mol have been reported in the literature.29 Two factors contribute to the partial molar volume of an ionic species.19 One comes from the electrostriction of the dielectric solvent around the ion and is given by the Drude-Nernst equation20,21 and the other is the volume contribution that comes from simple nonionic forces and can be roughly predicted from an equation of state like the Peng-Robinson equation.22 To calculate partial molar volumes and the isothermal compressibility from the Peng-Robinson

press. (bar)

PR eq of state

Drude-Nernst eq

eq of Wood et al.

170.0 160.0 150.0 140.0 130.0 120.0 110.0 100.0 95.0 90.0 85.0 80.0 75.0 70.0 65.0 60.0

20.5 17.0 12.6 7.1 -0.1 -9.7 -23.2 -43.6 -58.1 -77.3 -103.8 -142.8 -205.0 -318.6 -580.6 -1477.2

30.3 37.1 50.2 63.6 74.0 82.8 93.5 117.7 141.5 176.3 230.0 312.0 440.0 644.0 997.0 1676.0

111.0 117.3 124.6 138.0 148.8 161.5 180.5 200.8 212.9 226.0 242.0 258.3 281.5 351.2 512.8 838.8

equation of state requires properties of the components, such as critical temperature, critical pressure, and the acentric factor. Unfortunately, these properties are not known for Ph2C+H and the transition state. Therefore, Joback’s modification of Lyderson’s method for Tc and Pc and the standard method for the acentric factor were used to estimate the properties of the transition state.30 The transition state was considered to be a Ph2C+H/TME complex. The critical properties of Ph2CH2 were used to estimate those of Ph2C+H. Experimental values of the critical properties of Ph2CH2, TME and CHF3 were available30 and are listed in Table 1. The estimated activation volumes from the Peng-Robinson equation, which range from 20.5 cm3/ mol at 170 bar to -1477.2 cm3/mol at 60 bar, are presented in Table 2. In the calculations all binary interaction parameters were set to the default value of zero in the Peng-Robinson equation of state since no experimental values are available. The Drude-Nernst equation,20,21 given by eq 6, is used to

Vje ) -

NAZ2e2 ∂ 2r ∂P

(6)

calculate the electrostriction contribution to the partial molar volume. In eq 6, NA is the Avogadro number. Assuming that the solvent is a continuum of dielectric constant () and the ion is a hard sphere of radius r with charge Ze, the Drude-Nernst equation states that the partial molar volume from electrostriction should be proportional to the square of charge on the ions and inversely proportional to the ionic radii, and should increase in proportion to the value of (1/)(∂/∂P), which depends on the nature of the solvent. In the derivation of eq 6, the dependence of compressibility on the density of the solvent was neglected. To calculate partial molar volumes from electrostriction for Ph2C+H and the ionic transition state, the radii of the two ionic species were taken as 2.4526 and 7.5 Å, respectively. The choice of the size of the ionic transition state is based on the estimated Bondi radius31 and referenced to the literature values of radii of other cations.32 The partial molar volumes of cations are negative and are estimated to be as large as -1480.0 cm3/mol for Ph2C+H at 65 bar and 35 °C in CHF3. The estimated activation volumes from electrostriction at 35 °C in CHF3 by the Drude-Nernst equation are listed in Table 2. The activation volume resulting from ionic electrostriction is positive simply because the size of the transition state is larger than that of the reactant cation Ph2C+H. It should be noted that, with the exception of the high-pressure data, the sign of the activation

Arylmethyl Cation Reactivity in Supercritical Fluids

J. Phys. Chem., Vol. 100, No. 30, 1996 12399

volume from ionic electrostriction is opposite to that from the Peng-Robinson equation of state. The nonionic contribution from Peng-Robinson activation volume plus isothermal compressibility predicts that the rate constants should actually increase very slightly with increasing pressure, in contrast to observations. However, the ionic contribution, which is based on the pressure derivative of the dielectric constant,25 decidedly predicts that the rates should decrease with increasing pressure and the combined effect of electrostriction and the activation volume plus the compressibility term, calculated from the Peng-Robinson equation of state, is well in line with the measured values, as shown in Figure 8. Thermodynamic Pressure Effect, Model of Wood et al., and Peng-Robinson Equation (Method 3). The third method of analysis is quite similar to the second except that the partial molar volumes of the ions due to electrostriction were calculated by the method developed by Wood and co-workers,23,24 which explicitly includes the compressibility of the dielectric fluid. Wood et al. proposed that the electrostatic field around the ion compresses the solvent, the solvent density increases, and this, in turn, increases the dielectric constant and changes the thermodynamic properties of the ions. An equation was derived to give the distance r from the ion as a function of the local density:

Figure 8. Comparison of the pressure effect on the experimental rate constants to estimated values (see text) for the reaction of Ph2C+H with TME at 35 °C in CHF3.

(7)

Figure 9. Experimental rate constants for the reaction of Ph2C+H with TEA at 35 and 70 °C in CHF3 as a function of the inverse of the dielectric constant.

The numerical integration of eq 7 is performed by Simpson’s rule, starting at the density for zero electric field, F0, and choosing a suitably small increment in F. The calculation proceeds until a radius is reached which is equal to the radius of the cation being studied. The result is a series of values of r, for which F is known. The partial molar volume of the cation due to electrostriction is then calculated from local densities corresponding to different distances from the ion over a typical distance of 40-50 Å. The Wood equation required dielectric constants at higher densities than are available in the literature so they were extrapolated from existing data; details of the above numeric procedure for this system are presented elsewhere.33 This compressible continuum model predicts a dramatic local density enhancement close to the ion and negative partial molar volumes that are much larger in magnitude than predicted by the Drude-Nernst equation for the same molecular radii. For example, the partial molar volume of Ph2C+H with a radius of 2.45 Å was estimated to be -3691.6 cm3/mol at 65 bar and 35 °C in CHF3, compared to -1480.0 cm3/mol estimated from the Drude-Nernst equation. Again, in the calculation the radii of the cation Ph2C+H and the transition state were taken as 2.45 and 7.5 Å, respectively. The activation volumes at 35 °C estimated from the method of Wood et al. are listed in Table 2. This method also predicts a decrease in the rate constant with increasing pressure but suggests that the change should be somewhat less dramatic in the low pressure region. These estimates are presented in Figure 8, which compares the experimental and estimated pressure derivatives of the rate constants. Thus, the trend of the measured rates for the reaction of Ph2C+H with TME in supercritical CHF3 can be modeled reasonably well by any of the above methods. Even the simple liquid model (method 1) gives quite good agreement. Method 2 is more detailed and correctly includes the electrostriction of the solvent around the ion, which is important in these reactions. Method 3 is the most detailed of the models, including the compressibility of the solvent; however, it does not match the

data any better than method 2. We attribute this to uncertainty in the parameters needed for both models. As a result, we only present methods 1 and 2 for the reactions that follow. The various models have been used to analyze the data and, at this point, are not intended solely as tools to predict rate constants. From the above analysis of the 35 °C data there would appear to be no indication of preferential solvation, which can play a significant role in kinetically controlled reactions of some neutral species,4-7 influencing this reaction. However, it is apparent from the above analysis that the electrostriction term determines the trend of the pressure effect on the reaction rates investigated, and it is possible that components that may be contributing to preferential ion solvation by TME may be hidden by the uncertainty in the estimates of the electrostriction. In fact, this appears to be the case when one considers the absolute magnitude of rate constants measured for the reaction of Ph2C+H with TME along a higher temperature isotherm, 50 °C. There appears to be little or no difference in the absolute values of kbi for the two temperatures when the data is presented as a function of pressure (Figure 2); however, when the data is presented as a function of solvent density it is readily noticed that the values of kbi for the 50 °C experiments are significantly below the kbi values for the 35 °C isotherm. This result is, of course, inconsistent with a reaction possessing a bimolecular rate constant of this magnitude ∼1 × 107 M-1 s-1 that should require an activation process. We will reserve discussion of this phenomenon until the presentation of the temperature effect observed for the reaction of Ph2C+H with TEA (reaction 2) and (4-MeOPh)2C+H with TEA (reaction 3). Reaction of Ph2C+H with TEA in CHF3. Normal Liquid Models (Method 1) and Temperature Effect. For the reaction of Ph2C+H with TEA, reaction 2, a plot of ln(kbi) vs 1/ is shown in Figure 9 for the experimental rate constants at 35 and 70 °C. The dielectric constants for 70 °C were obtained from linear extrapolation of literature dielectric constant data25 and have been verified to be in very good agreement with least-squares fitting of modified Clausius-Mossotti equations,34,35 using the

r ) q /{(4πo) 4

2

2

∫F [2/(okTF (∂/∂F)T)] dF} F

2

o

12400 J. Phys. Chem., Vol. 100, No. 30, 1996

Zhang et al.

Figure 10. Comparison of the pressure effect on the experimental rate constants with estimated values from method 2 (see text) for the reaction of Ph2C+H with TEA at 35 and 70 °C in CHF3.

same experimental data.25 The dielectric continuum model predicts that the ln(kbi) varies linearly with 1/. The experimental data show remarkable linearity over the pressure range studied at 70 °C. ln(kbi) at high pressure at 35 °C also shows linearity with 1/; however, an upward deviation from the general linear trend occurs at low pressures for this temperature, as shown in Figure 9. Both the temperature effect and the solvent (dielectric constant) effect can possibly contribute to this observed deviation from linearity. The Arrhenius equation predicts that the bimolecular rate constant should increase with an increase in temperature and the magnitude of the increase of the rate constant depends on the value of the activation energy. To separate the temperature effect from a solvent effect, Amis’ derivation36,37 of the dielectric constant dependence of ln(kbi) was used, which uses a Coulomb energy approach for the iondipole interaction and is given in eq 8, where ln(kbi)∞ is the

ln(kbi) ) ln(kbi)∞ +

1 ZAeµBNA 1 4πo RTr 2 

(8)

AB

rate constant in a medium with dielectric constant of infinite magnitude and rAB is the reacting distance between an ion A of charge ZAe and a dipole B of dipole moment µB. The second term in eq 8 indicates the solvent effect on the reaction. ln(kbi)∞, depending on temperature only, is the intercept in Figure 9. The experimental data shown in Figure 9 indicate that the difference between ln(kbi)∞ for 35 and 70 °C is very small. Thus, the temperature effect on this reaction is relatively small, as expected for a reaction with this magnitude of rate constant. Thus, the solvent effect is responsible for the upward deviation occurring at low pressures at 35 °C and it may indicate preferential solvation of the cation (Ph2C+H) by the polar quenching substrate (TEA) at lower temperature. This conclusion can be further supported when considering local density enhancement, which has been shown to be greater at lower pressures.38-40 The corresponding local dielectric constant enhancement would be expected to make the rate constant smaller at lower pressures, instead of larger as is shown by the experimental data. A reasonable explanation for the upward deviation is the preferential solvation of the cation by TEA. This would also be consistent with previously observed results for the reactivity of nonionic reactants in supercritical fluids.4-7 There is no indication of preferential solvation from this analysis at 70 °C, where preferential solvation is expected to be diminished by stronger thermal movement of molecules. Thermodynamic Pressure Effect (Method 2). The pressure derivatives of the experimental rate constants at both temperatures are shown in Figure 10 and compared with the predicted values from the second method in which the partial molar volumes were calculated from the Peng-Robinson equation of

state and the electrostriction term was calculated from the Drude-Nernst equation. The same radii (2.45 Å for Ph2C+H and 7.5 Å for the transition state complex of Ph2C+H/TEA) were used in this calculation as in the previous reaction since the sizes of the involved ionic species are similar. Tc, Pc, and ω of the transition state were also estimated as in the above reaction30 and are listed in Table 1. The partial molar volume contributions from dipole-solvent interactions have previously been shown to not contribute significantly to the total partial molar volume unless dipole moments are very large.41 Therefore, it has not been included here since the substrate dipole moment is relatively small. As shown in Figure 10, the predicted pressure derivatives of the rate constants match the pressure derivatives of the experimental rate constants very well at 70 °C. There is some deviation between the prediction and the experimental values at low pressures at 35 °C. While the thermodynamic pressure effect on this kinetically controlled ionic reaction can be predicted fairly well by simple models, the discrepancy between the model prediction and the experimental values at 35 °C again suggests that the cationic species (Ph2C+H) is preferentially solvated by TEA, a strong nucleophile, at lower solvent densities along the lower isotherm investigated. Reaction of (4-MeOPh)2C+H with TEA in CHF3 and Ethane. Normal Liquid Models (Method 1) and Temperature Effect. The reactivity of (4-MeOPh)2C+H with TEA, reaction 3, was also investigated in supercritical CHF3. The greater stability of the bis(4-methoxyphenyl)-substituted cation compared to unsubstituted Ph2C+H results in a lower absolute reactivity of the cation toward TEA, which is primarily due to a larger energy of activation for the reaction. Therefore, the rate constants for the reaction of (4-MeOPh)2C+H with TEA were found to be smaller in magnitude than those for the reaction of Ph2C+H with the same quenching substrate (TEA) in the same solvent (CHF3). These findings are consistent with the characterization of the reactivity of these ions in normal liquids.14 This difference in cation stability allows for a unique opportunity to further investigate the contributions of solvent and temperature effects on the reaction rate constant. Therefore, more complete sets of data where obtained for this reaction along both isotherms and were analyzed by the Coulombic energy approach of Amis, eq 8. As briefly mentioned above, the temperature analysis of kbi vs density observed for the previous reactions of Ph2C+H with TME and TEA were inconsistent with expected Arrhenius activation. Again, a similar and significant deviation from Arrhenius behavior was observed for the reaction of (4MeOPh)2C+H with TEA in CHF3, where the bimolecular rate constants (kbi) at 70 °C were found to be smaller than those at 35 °C when compared at the same density. A reasonable explanation of this phenomenon is presented in the following discussion. A plot of ln(kbi) vs 1/ for reaction 3 is shown in Figure 11 for both temperatures (35 and 70 °C). As for the above reactions 1 and 2, ln(kbi) increases with the inverse of the dielectric constant at both temperatures. To analyze the temperature effect on this reaction, eq 8 is used to obtain ln(kbi)∞ by extending the experimental trend to infinite dielectric constant and reading the intercept. ln(kbi)∞ at 70 °C is found to be slightly larger than that at 35 °C, as is expected from the Arrhenius equation. In addition to the temperature effect, the reaction is also affected by solvent dielectric constant and, possibly, the local composition of reactant. The dielectric constant at 35 °C is greater than that at 70 °C and, thus, it is expected that this would lead to a smaller bimolecular rate constant according to the normal liquid

Arylmethyl Cation Reactivity in Supercritical Fluids

J. Phys. Chem., Vol. 100, No. 30, 1996 12401

Figure 11. Experimental rate constants for the reaction of (4MeOPh)2C+H with TEA at 35 and 70 °C in CHF3 as a function of the inverse of the solvent dielectric constant.

Figure 13. Experimental bimolecular rate constants plotted (top) vs pressure and (bottom) as a function of the inverse of dielectric constant for the reaction of (4-MeOPh)2C+H with TEA in C2H6 at 35 °C. Figure 12. Comparison of the pressure effect on the experimental rate constants with estimated values from method 2 (see text) for the reaction of (4-MeOPh)2C+H with TEA at 35 and 70 °C in CHF3.

models and the general trend from experimental measurements presented above. However, in Figure 11, the measured ln(kbi) for 35 °C is greater than ln(kbi) for 70 °C and the difference becomes larger at lower pressures, which is opposite to the prediction based on the temperature effect and the local density (dielectric constant) enhancement effect. This suggests that preferential solvation of the reactant cation by the nucleophilic quenching substrate (TEA) occurs for this reaction in CHF3 at the lower temperature and would explain why kbi is somewhat smaller at 70 °C than at 35 °C at the same density. Again this appears to be a manifestation of the increased local concentration of TEA around (4-MeOPh)2C+H and partially explains the apparently unexpected results of the temperature analysis of kbi vs density observed for the previous reactions 1 and 2, of Ph2C+H with TME and TEA. Thermodynamic Pressure Effect (Method 2). The thermodynamic pressure effect analysis was also performed for this reaction by method 2. The partial molar volumes were calculated from the Peng-Robinson equation of state and the Drude-Nernst equation. There is no reported value available of the (4-MeOPh)2C+H radius so a radius of 2.70 Å for (4MeOPh)2C+H and 10.0 Å for the transition state complex of (4-MeOPh)2C+H/TEA were chosen, based on their estimated Bondi radii.31 Tc, Pc, and ω of (4-MeOPh)2C+H and the transition state were estimated from the Joback’s modification of Lyderson’s method for Tc and Pc and the standard method for the acentric factor30 and are listed in Table 1. The pressure derivatives of the measured rate constants at both temperatures are shown in Figure 12, compared with the predicted values. The nonionic contribution from the Peng-Robinson equation (PR activation volume and isothermal compressibility), although not presented in Figure 12, predicted an opposite trend to the experimental observations. Once again, the ionic contribution is the key factor and the overall prediction matches the pressure derivatives of the experimental data well for 70 °C. Some deviation at 35 °C may be an indication of preferential solvation

of TEA around the reactant cation. There is no clear indication of preferential solvation for 70 °C in CHF3. Reaction of (4-MeOPh)2C+H with TEA in Ethane. The strong absorption signal of (4-MeOPh)2C+H did allow for an initial investigation of a cation-neutral reaction in supercritical ethane; however, this was limited to a restricted pressure range along the more dense 35 °C isotherm. The cation absorption signal was found to dramatically decrease at lower pressures approaching the critical point of ethane, presumably due to a rapid loss of cation precursor solubility. There was no observable signal below 75.5 bar. Bimolecular rate constants were measured, however, at higher pressures and are plotted vs pressure and the inverse of dielectric constant of ethane34 in Figure 13. The dielectric constant of ethane is considerably lower than that of CHF3, and the range of 1/ was limited to ca. 0.04, compared to a range of ca. 0.35 in CHF3. Nevertheless, the measured kbi in ethane do show similar behavior to that in CHF3, decreasing with an increase in pressure, density, or dielectric constant. Thus, the reaction of this cation with TEA behaves as expected even over the narrow range of dielectric constant available for investigation of this reaction in ethane. No further analysis of this reaction seemed appropriate; however, we do believe this result is important in the demonstration of the ability of very low dielectric media to support ionic reactivity. This may have important implications in high-temperature supercritical water investigation where comparable values of the dielectric constant are observed. Conclusions Pulse radiolysis and time-resolved absorption have been used to generate and characterize the influence of supercritical fluid solvation on the ion-neutral reactivity of benzhydryl and 4,4′dimethoxybenzhydryl cations in supercritical CHF3 and ethane. The effects of pressure and solvent density on the bimolecular rate constants for the reaction of Ph2C+H with TME and TEA in CHF3 and for the reaction of (4-MeOPh)2C+H with TEA in CHF3 and C2H6 were investigated. The results were analyzed by (1) a correlation from solution theory that predicts that ln(kbi) should increase linearly with the inverse of the bulk

12402 J. Phys. Chem., Vol. 100, No. 30, 1996 dielectric constant, (2) the thermodynamic pressure effect on the rate constant predicted from the Drude-Nernst equation, and (3) the thermodynamic pressure effect on the rate constant predicted from the compressible fluid model developed by Wood and co-workers. Analysis of each reaction demonstrated that the electrostriction term was the key factor in determining the thermodynamic pressure effect. Also, comparison of the experimental results with the predictive methods indicated that preferential ion solvation by the cosolvent noticeably influenced one of the reactions studied. Deviation from dielectric continuum theory suggested evidence for enhanced local composition of TEA about Ph2C+H observed at the lower solvent densities along the isotherm closer to the critical temperature of the two isotherms investigated. An analysis of the influence of temperature and solvent density on reactions 1, 2, and 3 also yielded evidence for preferential cation solvation by cosolvent for these ion/neutral reactions. Acknowledgment. Acknowledgment is made to the Donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research (J.Z., K.C., J.F.B.). The work described herein was also supported by the National Science Foundation (J.Z., K.C., J.F.B.) and the Office of Basic Energy Sciences of the U.S. Department of Energy (J.E.C.). We also acknowledge the Notre Dame Radiation Laboratory for the use of their facilities and thank DuPont for the generous donation of the CHF3. Nomenclature e ) charge of an electron kbi ) bimolecular rate constant k0 ) the rate constants in absence of quencher kobs ) the observed pseudo-first-order rate constant kT ) isothermal compressibility NA ) Avogadro’s number P ) pressure r ) distance from a charge center rAB ) the reacting distance between an ion A and a dipole B ri ) radius of molecules or ions rq ) radius of the transition state complex R ) gas constant q ) the charge on the ion [Q] ) molar concentration of quenching substrate T ) absolute temperature, K Vj ) partial molar volume Z ) number of charges Greek Symbols  ) dielectric constant 0 ) permitivity of vacuum F ) density µ ) dipole moment ∆Vjq ) VjTS - VjA - VjB ) reaction activation volume ω ) acentric factor Subscripts c ) critical property e ) electrostriction i ) species i 0 ) bulk property ∞ ) a medium with dielectric constant of infinite magnitude References and Notes (1) Savage, P. E.; Gopalan, S.; Mizan, T. I.; Martino, C. J.; Brock, E. E. AIChE J. 1995, 41, 1723.

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