Skip to main content
SpringerLink
Log in

Solute Reaction Dynamics in the Compressible Regime

  • Chapter
Supercritical Fluids

Part of the book series: NATO Science Series ((NSSE,volume 366))

Abstract

Supercritical fluid (SCF) solvents are unique in that their densities can be varied continuously from gas-like to liquid-like values simply by varying the thermodynamic conditions. Because many of a fluid’s solvating properties are strongly dependent on the fluid density, such large changes in density can have dramatic effects on solute reactivity [1,2]. For example, at low pressures supercritical water supports homolytic, free radical reactions, whereas at higher pressures, heterolytic, ionic reactions dominate [3,4]. Thus, thermodynamic control of SCF solvent densities promises to enable us to control reaction outcome and selectively produce desired products.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Savage, P. E., S. Gopalan, T. I. Mizan, C. J. Martino, and E. E. Brock: 1995, ‘Reactions at supercritical conditions — applications and fundamentals’. AIChE J. 41, 1723.

    Article  CAS  Google Scholar 

  2. Eckert, C. A., B. L. Knutson, and P. G. Debenedetti: 1996, ‘Supercritical fluids as solvents for chemical and materials processing’. Nature 383, 313.

    Article  CAS  Google Scholar 

  3. Antal Jr., M. J., A. Brittain, C. DeAleida, S. Ramayya, and J. C. Roy: 1987, “Heterolysis and homolysis In supercritical water”. In: T. G. Squires and M. E. Paelaitis (eds.): Supercritical Fluids, ACS Symposium Series 829. Washington: ACS.

    Google Scholar 

  4. Klein, M. T., Y. G. Mentha, and L. A. Tony: 1992, ‘Decoupling substituent and solvent effects during hydrolysis of substituted anisoles In supercritical water”. Ind. Eng. Chem. Res. 31, 182.

    Article  CAS  Google Scholar 

  5. Brennecke, J. F.: 1993, ‘Spectroscopic investigations of reactions In supercritical fluids: A review’. In: E. Kiran and J. R Breneecke (eds.): Supercritical Fluid Engineering Science; ACS Symposium Series. Washington: ACS.

    Google Scholar 

  6. Hansen, J. P. and I. R. McDonald: 1986, Theory of Simple Liquids. London: Academic Press.

    Google Scholar 

  7. Fisher, M. E.: 1964, ‘Correlation functions and the critical region of simple fluids’. J. Math. Phys. 5, 944.

    Article  Google Scholar 

  8. Rovere, M., D. W. Heermaen, and K. Binder: 1990, ‘The gas-liquid transition of the two-dimensional Lennard-Jones fluid’. J. Phys. Condens. Matter 2, 7009.

    Article  Google Scholar 

  9. Martinez, H. L., R. Ravi, and S. C Tucker: 1996, ‘Characterization of solvent clusters in a supercritical Leonard-Jones fluid’. J. Chem. Phys. 104, 1067.

    Article  CAS  Google Scholar 

  10. Tucker, S. C. and M. W. Maddox: 1998, ‘The effect of solvent density inhomogeneities on solute dynamics in supercritical fluids: A theoretical perspective’. J. Phys. Chem. B 102, 2437.

    Article  CAS  Google Scholar 

  11. Yoshii, N. and S. Okazaki: 1997, ‘A large-scale and long-time molecular dynamics study of supercritical Leonard-Jones fluid. An analysis of high temperature clusters’. J. Chem. Phys. 107, 2020.

    Article  CAS  Google Scholar 

  12. Goodyear, G. and S. C. Tucker: 1999, “What causes the vibrational lifetime plateau in supercritical fluids?’. J. Chem. Phys. 110, 3643.

    Article  CAS  Google Scholar 

  13. Tucker, S. C.: 1999, ‘Solvent density inhomogeneities in supercritical fluids’. Chem. Rev. 99, 391.

    Article  CAS  Google Scholar 

  14. Wu, R.-S., L. L. Lee, and H. D. Cochran: 1990, ‘Structure of dilute supercritical solutions: Clustering of solvent and solute molecules and the thermodynamic effects’. Ind. Eng. Chem. Res. 29, 977.

    Article  CAS  Google Scholar 

  15. Cummiegs, P. T., H. D. Cochran, J. M. Simonson, R. E. Mesmer, and S. Karaborni: 1991, “Simulation of supercritical water and of supercritical aqueous solutions’. J. Chem. Phys. 94, 5606.

    Article  Google Scholar 

  16. Petsche, I. B. and P. G. Debenedetti: 1989, ‘Solute-solvent interactions in infinitely dilute supercritical mixtures: A molecular dynamics study’. J. Chem. Phys. 91, 7075.

    Article  CAS  Google Scholar 

  17. Knutson, B. L., D. L. Tomasko, C. A. Eckert, P. G. Debenedetti, and A. A. Chialvo: 1992, “Local density augmentation in supercritical fluid solutions: A comparison between fluoresence spectroscopy and molecular dynamics results’. In: F. V. Bright and M. E. McNally (eds.): Supercritical Fluid Technology, ACS Symposium Series 488. Washington: ACS, p. 60.

    Chapter  Google Scholar 

  18. Flanagin, L. W., P. B. Balbuena, K. P. Johnston, and P. J. Rossky: 1995, Temperature and density effects on an SN2 reaction in supercritical water’. J. Phys. Chem. 93, 5196.

    Article  Google Scholar 

  19. Johnston, K. P. and C. Haynes: 1987, ‘Extreme solvent effects on reaction rate constants at supercritical fluid conditions’. AIChE J. 33, 2017.

    Article  CAS  Google Scholar 

  20. Kim, S. and K. P. Johnston: 1987, ‘Molecular interactions in dilute supercritical fluid solutions’. Ind. Eng. Chem. Res. 26, 1206.

    Article  CAS  Google Scholar 

  21. Kajimoto, O., M. Futakami, T. Kobayashi, and K. Yamasaki: 1988, ‘Chargetransfer-state formation in supercritcal fluid: (N,N-dimethylamino)benzonitrile in CF3H.’ J. Phys. Chem. 92, 1347.

    Article  CAS  Google Scholar 

  22. Sun, Y. P., M. A. Fox, and K. P. Johnston: 1992, ‘Spectroscopic studies of para(N,N-dimethylamino)benzonitrile and ethyl para-(N,N-dimethylamino)benzoate in supercritical trifluoromethaee, carbon dioxide, and ethane”. J. Amer. Chem. Soc. 114, 1187.

    Article  CAS  Google Scholar 

  23. Carlier, C. and T. W. Randolph: 1993, ‘Dense-gas solvent-solute clusters at nearinfinite dilution — EPR spectroscopic evidence’. AIChE J. 39, 876.

    Article  CAS  Google Scholar 

  24. Rice, J. K., E. D. Niemeyer, R. A. Dunbar, and F. V. Bright: 1995, ‘Statedependent solvation of pyrene in supercritical CO2. J. Amer. Chem. Soc. 117, 5830.

    Article  Google Scholar 

  25. Heitz, M. P. and M. Maroncelli: 1997, ‘Rotation of aromatic solutes in supercritical CO2: Are rotation times anomalously slow in the near critical regime?’. J. Phys. Chem. A 101, 5852.

    Article  CAS  Google Scholar 

  26. Zhang, J., D. P. Roek, J. E. Chateauneuf, and J. F. Breneecke: 1997, ‘A steady state and time-resolved fluorescence study of quenching reactions of anthracene and 1,2-benzantracene by carbon tetrabromide in supercritical carbon dioxide’. J. Amer. Chem. Soc. 119, 9980.

    Article  CAS  Google Scholar 

  27. Levelt-Sengers, J. M. H., ‘Supercritical fluids: Their properties and applications’. In: E. Kiran, P. G. Debeeedetti, and C. J. Peters (eds.): Supercritical Fluids II. Dordrecht: Kluwer. this volume.

    Google Scholar 

  28. Levelt-Sengers, J. M. H.: 1991, Thermodynamics of solutions near the solvent’s critical point’. In: T. J. Bruno and J. F. Ely (eds.): Supercritical Fluid Technologies. Boca Raton: CRC Press, p. 1.

    Google Scholar 

  29. Wood, R. H., J. R. Quint, and J.-R E. Grolier: 1981, ‘Thermodynamics of a charged hard sphere in a compressible dielectric fluid.’, J. Phys. Chem. 85, 3944.

    Article  CAS  Google Scholar 

  30. Luo, H. and S. C. Tucker: 1996, ‘A continuum solvation model including electrostriction: Application to the anisole hydrolysis reaction in supercritical water’. J. Phys, Chem. 100, 11165.

    Article  CAS  Google Scholar 

  31. Wu, R.-S., L. L. Lee, and H. D. Cochran: 1992, ‘Solvent structural changes in repulsive and attractive supercritical mixtures — a molecular distribution study’. J. Supercritical Fluids 5, 192.

    Article  CAS  Google Scholar 

  32. A related viewpoint is that of a Langmuir adsorption analogy in which the solvent response to the solute-solvent interaction potential is characterized by some parameter related to the solvent’s chemical potential, see Refs. [102,103].

    Google Scholar 

  33. Chialvo, A. A. and R T. Cummings: 1994, ‘Solute-induced effects on the structure and thermodynamics of infinitely dilute mixtures’. AIChE J. 40, 1558.

    Article  CAS  Google Scholar 

  34. Mountain, R.: 1999, ‘Voids and clusters in expanded water’. J. Chem. Phys. 110, 2109.

    Article  CAS  Google Scholar 

  35. Goodyear, G., M. Maddox, and S. C. Tucker, ‘Density inhomogeneities ie the compressible regime of a supercritical Leonard-Jones fluid’., submitted.

    Google Scholar 

  36. For anything other than hard-spheres, the size of a particle is not well defined — one could choose anything from the distance of closest approach between two particles at zero energy (σLJ), to the distance of closest approach observed at liquid densities (< σLJ), to the separation at the van der Waals minimum (> σLJ), to the mean volume available to each particle (1/p). In the present work, the radius determining the excluded area of the central particle was taken to be 0.73 σLJ in the case of the smaller local radius pt = 1.78 σLJ and 0.9 σLJ for the larger local radius pi = 3.09 σLJ. [35] We chose the excluded area used in the former case such that at the liquid density of 0.711 σ-2lj the mean local density (pi), see below, is equal to the bulk density. This removes pure structural effects, i. e. the solvent shell structure, from our analysis of the local densities. The exact value chosen is less critical at the larger radius, and here we simply used the value at which the radial distribution function first becomes non-zero in the liquid. A detailed discussion of how the choice local radius and excluded area are interrelated and affect the interpretaion of the local densities is given in Ref. [35].

    Google Scholar 

  37. The critical parameters of Tc = 0.477 and pc = 0.38 σ-2lj for the truncated (at 2.5 σLJ), ueshifted, 2-dimensional Lennard-Jones fluid are taken from Ref. [104]. These are better estimates of the critical parameters than were used in our earlier studies of the same system (Refs. [9], [10] and [13]). Thus, the reduced values Tr = T/Tc and pr = p/pc differ slightly from previously quoted values. For example, the state T = 0.55 and p = 0.30 σ-2LJ was previously given as Tr = 1.17 and pr = 0.86, but becomes Tr = 1.15 and pr = 0.79 with the more accurate critical parameters.

    Google Scholar 

  38. It is worth making a few technical points about the relevant length scales in this system. Traditionally, in the study of critical phenomena, two length scales are identified: first, there is the range of the direct pair correlation function, which, given that this function falls off (to leading order) as does the ieterparticle interaction potential, is a fundamental length scale of the chemical system under study. Second, is the length over which the total correlation function decays, i.e. the correlation length ξ, and it thus measures the spatial extent over which density fluctuations remain correlated (on average), a quantity which is related to the mean domain size. As the critical point is approached, this latter length diverges while the former ‘potential interaction length’ does not. It is therefore traditional to classify phenomena occuring on the correlation length scale as ‘long-range’ and those occurring on the ‘potential interaction length’ as’ short-range’ or ‘local’ When one is interested in speciic chemical phenomena, such as a spectroscopic shift, or, as here, a vibrational relaxation rate, the ‘local’ region of interest will be the range over which the solvent environment affects the solute probe. While this range may often correspond to the ‘potential interaction length’ (here 2.5 σLJ), it need not be exactly this length; thus, we herein reserve the term ‘local’ for the range relevant to a probe molecule, which we denote ri. The local lengths chosen here, ri = 1.78 and 3.09 σLJ, correspond approximately to first and second solvation shell cut-offs, respectively, with the former being the relevant length for the vibrational relaxation rates. Additionally, as one moves away from the critical point, the correlation length becomes shorter and the ‘local’ and long-range” correlation length scales become poorly separated, if separated at all.[105] In the Leneard-Jones system pictured in Fig. 1 (T = 0.55, p = 0.30 σ-2lj), the correlation length is estimated to be ξ = 3.3 σ;LJ, [27] and only the smaller local region (ri = 1.78 σ LJ) can be considered to be of shorter range than the correlation length. However, in such intermediate cases, i.e. where the local and long-range’ length scales are not well separated, it is useful to remember that the correlation length is an exponential decay constant, such that at a distance of ξ the magnitude of the mean correlations will have decayed by only 63%. Additionally, this decay constant reflects only the mean, and distributions in the domain sizes may exist. Indeed, as noted above, the computed distribution of local densities at the state point shown in Fig. 1 suggests that significant ‘local’ inhomogeneities exist on both the length scales ri = 1.78 and 3.09 ξLJ, even though ξ = ri in the latter case.

    Google Scholar 

  39. See Refs. [35] and [12] for an in-depth discusioe about how the choice of the excluded volume (area in 2D) affect the local density enhancements computed.

    Google Scholar 

  40. Note that on the very short, first-solvatioe-shell length scale (ri = 1.78 σ-LJ), the density inhomogeneities persist to bulk densities well below the critical density, such that the mean local density on this short length-scale still exceeds the bulk value at very low densities (Fig. 2a). At these very low densities, short-range local density enhancements arise as a result of the non-idealities of the system, that is, from the intermolecular interactions. As the bulk density approaches the critical value, there is a crossover to a region in which the local density enhancements arise, at least in part, as a result of critical fluctuations and the concomitant long-length-scale density inhomogeeeities, by the preferential sampling mechanism described in the text. Clearly, the larger the local radius, the more important will be the critical fluctuations in causing the local density enhancements, and thus the more localized these enhancements will be to the critical region of the phase diagram. Unfortunately, we have no method of rigorously separating the degree to which either of these two mechanisms, the preferential sampling effect due to long-length-scale density inhomogeneities and the intermolecular interaction effect, contribute to the observed local density enhancement at a given state point.

    Google Scholar 

  41. Since the compressibility enters only as a response function, this view does not imply that the local density inhomogeneities are proportional to or divergent with the compressibility. See Refs. [10] and [30].

    Google Scholar 

  42. Petsche, I. B. and P. G. Debenedetti: 1991, ‘Influence of solute-solvent asymmetry upon the behavior of dilute supercritical mixtures’. J. Phys. Chem. 95, 386.

    Article  CAS  Google Scholar 

  43. Note that very near the critical point, where the local and long-range effects are well separated, it is fundamentally incorrect to ascribe the bulk compressibility, which grows large as a result of long-range fluctuations, on a local scale, that is, to a local volume element. Nevertheless, these models work relatively well.

    Google Scholar 

  44. Kajimoto, O.: 1999, ‘Solvation in supercritical fluids: Its effect on solubility and chemical reactions’. Chem. Rev. 99, 355.

    Article  CAS  Google Scholar 

  45. Brennecke, J. F., D. L. Tomasko, and C. A. Eckert: 1990, ‘Naphthalene triethylamine exciplex and pyrene exclmer formation in supercritical fluid solutions’. J. Phys. Chem. 94, 7692.

    Article  CAS  Google Scholar 

  46. Kim, S. and K. P. Johnston: 1987, ‘Effects of supercritical solvents on rates of homogeneous chemical reactions’. In: T. G. Squires and M. E. Paulaitis (eds,): Supercritical Fluids, ACS Symposium Series 329. Washington: ACS.

    Google Scholar 

  47. Rhodes, T. A., K. O’Shea, G. Bennett, K. P. Johnston, and M. A. Fox: 1995, ‘Effect of solvent-solute and solute-solute interactions on the rate of a Michael addition in supercritical fleoroform and ethane’. J. Phys. Chem. 99, 9903.

    Article  CAS  Google Scholar 

  48. Zhang, J., K. A. Connery, J. F. Breneecke, and J. E. Chateauneuf: 1996, ‘Pulse radiolysis investigations of solvation effects on arylmethyl cation reactivity in supercritical fluids’. J. Phys. Chem. 100, 12394.

    Article  CAS  Google Scholar 

  49. Kajimoto, O., T. Nayuki, and T. Kobayashi: 1993, ‘Picosecond dynamics of the twisted intramolecular charge-transfer state formation of 4-(N,N-dimethylamino)beezoeitrile (DMABN) in supercritical fluid solvent’. Chem. Phys. Lett. 209, 357.

    Article  CAS  Google Scholar 

  50. Tucker, S. C. and E. M. Gibbons: 1994, ‘Hydrolysis of Anisole in supercritical water: The effect of pressure on reactivity’. In: D. G. Truhlar and C. J. Cramer (eds.): Structure and Reactivity im Aqueous Solution, ACS Symposium Series. Washington: ACS, p. 196.

    Chapter  Google Scholar 

  51. Luo, H. and S. C. Tucker: 1997, ‘A continuum model study of the chloride plus methylchloride reaction in supercritical water’. J. Phys. Chem. B 101, 1063.

    Article  CAS  Google Scholar 

  52. Bennett, G. E., P. J. Rossky, and K. Johnston: 1995, ‘Continuum electrostatics model for an SN2 reaction in supercritical water’. J. Phys. Chem. 99, 16136.

    Article  CAS  Google Scholar 

  53. Maneke, G., J. Schroeder, J. Troe, and F. Voß: 1985, ‘Picosecond-absorbtion study of trans-stilbene in compressed gasses and liquids’. Ber. Bunsenges. Phys. Chem. 89, 896.

    Article  CAS  Google Scholar 

  54. Hara, K., H. Kiyotani, and O. Kajimoto: 1995, ‘High-pressure studies on the excited-state isomerization of 2-vinylanthracene — Experimental investigation of Kramers turnover’. J. Chem. Phys. 103, 5548.

    Article  CAS  Google Scholar 

  55. Schroeder, J. and J. Troe: 1987, ‘Elementary reactions in the gas-liquid transition range’. Ann. Rev. Phys. Chem. 38, 163.

    Article  CAS  Google Scholar 

  56. Honig, B., K. Sharp, and A. Yang: 1993, ‘Macroscopic models of aqueous solutions: Biological and chemical applications’. J. Phys. Chem. 97, 1101.

    Article  CAS  Google Scholar 

  57. Davis, M. E. and J. A. McCammon: 1990, ‘Electrostatics in biomolecular structure and dynamics’. Chem. Rev. 90, 509.

    Article  CAS  Google Scholar 

  58. Cramer, C. J. and D. G. Trahlar: 1995, ‘Continuum solvation models: Classical and quantum mechanical implementations’. In: D. B. Boyd and K. B. Lipkowitz (eds.): Reviews in Computational Chemistry, New York: VCH.

    Google Scholar 

  59. Mohan, V., M. E. Davis, J. A. McCammon, and B. M. Pettit: 1992, ‘Continuum model calculations of solvation free energies: Accurate evaluation of electrostatic contributions’. J. Phys. Chem. 96, 6428.

    Article  CAS  Google Scholar 

  60. An important feature of such compressible continuum models is that they include only direct contributions to the solvent density enhancements, meaning that any predicted density enhancement represents a direct response of the compressible fluid at each location r to the solute-solvent interaction potential at that point r, and does not include indirectly induced enhancements which result because the solvent density enhancement in one volume element induces an enhancement in another volume element as a result of the long range solvent-solvent density correlations. At short ranges (i e. within the range of the solute-solvent interaction potential) it is expected that the direct contribution will dominate the local density enhancements, such that these methods will be useful in the study of local density enhancement effects. Note that it is the neglected indirect density correlations which give rise to divergent partial molar volumes as the critical point is approached, and thus these compressible continuum models are inappropriate for predicting this and other diergent quantities.

    Google Scholar 

  61. Quint, J. R. and R. H. Wood: 1985, ‘Thermodynamics of a charged hard-sphere ion in a compressible dielectric fluid. 2.’. J. Phys. Chem. 89, 380.

    Article  CAS  Google Scholar 

  62. Luo, H. and S. C. Tucker: 1997, ‘A case against anomalously large nonequilibrium solvent effects in supercritical fluids’. Theo. Chem. Acc. 96, 84.

    Article  CAS  Google Scholar 

  63. Re, M. and D. Laria: 1997, ‘Dynamics of solvation in supercritical water’. J. Phys. Chem. B 101, 10494.

    Article  CAS  Google Scholar 

  64. Ryan, E. T., T. Xiang, K. P. Johnston, and M. A. Fox: 1996, ‘Excited-state proton transfer reactions in subcritical and supercritical water’. J. Phys. Chem, 100, 9395.

    Article  CAS  Google Scholar 

  65. More precisely, below the density of maximal compressibility along the isotherm of interest.

    Google Scholar 

  66. Howdle, S. M. and V. N. Bagratashvili: 1993, ‘The effects of fluid density on the rotational Raman spectrum of hydrogen dissolvent in supercritical carbon dioxide’. Chem. Phys. Lett. 214, 215.

    Article  CAS  Google Scholar 

  67. Sun, Y.-P., C. E. Bunker, and N. B. Hamilton: 1993, ‘Py scale in vapor phase and in supercritical carbon dioxide. Evidence in support of a three-density-region model for solvation in supercritical fluids’. Chem. Phys, Lett. 210, 111.

    Article  CAS  Google Scholar 

  68. Urdahl, R. S., D. J. Myers, K. D. Rector, P. H. Davis, B. J. Cherayil, and M. D. Fayer: 1997, ‘Vibrational lifetimes and vibrational line positions in polyatomic supercritical fluids near the critical point’. J. Chem. Phys. 107, 3747.

    Article  CAS  Google Scholar 

  69. Oxtoby, D. W.: 1981, ‘Vibrational population relaxation in liquids’. Adv. Chem. Phys. 47, 487.

    Article  CAS  Google Scholar 

  70. Owrutsky, J. C, D. Raftery, and R. M. Hochstrausser: 1994, ‘Vibrational relaxation dynamics in solution’. Ann. Rev. Phys. Chem. 45, 519.

    Article  CAS  Google Scholar 

  71. Zwanzig, R.: 1959, ‘Contribution to the theory of Brownian Motion’. Phys. of Fluids 2, 12.

    Article  CAS  Google Scholar 

  72. Grote, R. R and J. T. Hynes: 1982, ‘Energy diffusion-controlled reactions in solution’. J. Chem. Phys. 77, 3736.

    Article  CAS  Google Scholar 

  73. Tuckerman, M. E. and B. J. Beme: 1993, ‘Vibrational relaxation in simple fluids comparison of theory and simulation’. J. Chem. Phys. 98, 7301.

    Article  CAS  Google Scholar 

  74. Skinner, J. L.: 1997, ‘Semiclassical approximations to golden rale rate constants’. J. Chem. Phys. 107, 8717.

    Article  CAS  Google Scholar 

  75. Schwarzer, S., J. Troe, and M. Zerezke: 1997, ‘The role of local density in the collisional deactivation of vibrationally highly excited azulene in supercritical fluids’. J. Chem. Phys. 107, 8380.

    Article  CAS  Google Scholar 

  76. Urdahl, R. S., K. D. Rector, D. J. Myers, P. H. Davis, and M. D. Fayer: 1996, ‘Vibrational relaxation of a polyatomic solute in a polyatomic supercritical fluid near the critical point’. J. Chem. Phys. 105, 8973.

    Article  CAS  Google Scholar 

  77. Adams, J. E.: 1998, ‘Solvatochromism in a near-critical solution: Direct correlation with local solution structure”. J. Phys. Chem. B 102, 7455.

    Article  CAS  Google Scholar 

  78. Landau, L. and E. Teller: 1986, ‘Landau-Teller for vibratioeal relaxation’. Z. Sowjetunion 10, 34.

    Google Scholar 

  79. Voth, G. A. and R. M. Hochstrasser: 1996, ‘Transition state dynamics and relaxation processes in solutions — A frontier of physical chemistry’. J. Phys. Chem. 100, 13034.

    Article  CAS  Google Scholar 

  80. Note that in 2-dimensional systems the correlation length remains long further from the critical point than in 3-dimensional systems,[ 106,27] and this is why compressible regime behavior is already observed on the Tr = 1.15 isotherm of the 2-dimensional Leneard-Jones SCR This is in contrast to the experimental isotherms considered: the near-critical isotherm was at Tr = 1.01, while the high temperature isotherm was at Tr = 1.06.

    Google Scholar 

  81. Delalande, C. and G. M. Gale: 1979, ‘A semiclassical model for vibrational energy relaxation in simple liquids and compressed fluids’. J. Chem. Phys. 71, 4804.

    Article  CAS  Google Scholar 

  82. Harris, C. B., D. E. Smith, and D. J. Russell: 1990, ‘Vibrational relaxation of diatomic molecules in liquids’. Chem. Rev. 90, 481.

    Article  CAS  Google Scholar 

  83. Chesnoy, J. and G. M. Gale: 1988, ‘Vibrational energy relaxation in condensed phases’. Adv. Chem. Phys. 70, 297.

    Article  Google Scholar 

  84. Stratt, R. M. and M. Maroncelli: 1996, ‘Nonreactive dynamics in solution: The emerging molecular view of solvation dynamics and vibratioeal relaxation”. J. Phys. Chem. 100, 12981.

    Article  CAS  Google Scholar 

  85. Cherayil, B. J. and M. D. Fayer: 1997, ‘Vibrational relaxation in supercritical fluids near the critical point”. J. Chem. Phys. 107, 7642.

    Article  CAS  Google Scholar 

  86. Breenecke, J. F., D. L. Tomasko, J. Peshkin, and C. A. Eckert: 1990, ‘Fluorescence spectroscopy studies of dilute supercritical solutions’. Ind. Eng. Chem. Res. 29, 1682.

    Article  Google Scholar 

  87. O’Brien, J. A., T. W. Randolph, C. Carlier, and S. Ganapathy: 1993, ‘Qeasicritical behavior of dense-gas solvent-solute clusters at near-infinite dilution’. AIChE J. 39, 876.

    Article  Google Scholar 

  88. Gaeapathy, S., C. Carlier, T. W. Randolph, and J. A. O’Brien: 1996, ‘Influence of local structural correlations on free-radical reactions in supercritical fluids — a hierarchical approach’. Ind. Eng, Chem. Res. 35, 19.

    Article  Google Scholar 

  89. Maroncelli, M. personal communication.

    Google Scholar 

  90. Explicitly, (A)Pi is where P(rNpN pi) is the conditional probability of finding the phase space configuration (rN,pN) given that the local density around the solute (or tagged particle) is pe. Specifically, where P(rN,pN,pi) is the joint probability of finding the configuration (rN,pN) and the local density pi. In the canonical ensemble this joint probability is where H is the Hamiltonian, Q is the canonical partition function, δ is the Dirac delta function, and evaluates the local density around the solute in the configuration (rN,pN).

    Google Scholar 

  91. The homogeneous result will also be obtained from eq. 9 when the distribution P(pi,o) is narrow, as in homogeneous fluids, regardless of the relative time scales of the dynamic process and the local density fluctuations.

    Google Scholar 

  92. Note that one could also encounter the intermediate case in which the time scale for the force correlation function decay is much shorter than that for the local density fluctuations, while the time scales for vibrational relaxation are longer than that for the local density fluctuations, and that this case is conceptually more difficult.

    Google Scholar 

  93. Narasimhan, L., K. A. Littau, D. W. Pack, Y. S. Bai, A. Elschner, and M. D. Fayer: 1990, ‘Probing organic glasses at low temperature with variable time scale optical dephasing measurements’. Chem, Rev. 90, 439.

    Article  CAS  Google Scholar 

  94. Skinner, J. L. and W. E. Moereer: 1996, ‘Structure and dynamics of solids as probed by optical spectroscopy’. J. Phys. Chem. 100, 13251.

    Article  CAS  Google Scholar 

  95. Clouter, M. J., H. Kiefte, and C. G. Deacon: 1986, ‘Vibrational Raman spectra of N2 in the critical region’. Phys. Rev. A 33, 2749.

    Article  CAS  Google Scholar 

  96. We do not give decay lifetimes because the decay of Cp(t) at p = 0.30&#X03C3;-2LZ can not be fit to a single exponential.

    Google Scholar 

  97. Specifically, we refer to fluctuations which are significant relative to the width of the distribution V(pi).

    Google Scholar 

  98. The correlation functions were averaged over groups of Initial local densities, rather than being averaged per single initial local density, In order to Improve the simulation statistics.

    Google Scholar 

  99. Rhodes, T. A. and M. A. Fox: 1996, ‘Photophysics of pheeanthrene In supercritical carbon dioxide. Solvent-solute and solute-solute Interactions revealed by lifetime distribution analysis’. J. Phys. Chem. 100, 17931.

    Article  CAS  Google Scholar 

  100. Betts, T. A., J. Zagrobelny, and F. V. Bright: 1992, ‘Investigation of solutefluid Interactions in supercritical CF3H: A multlfrequeecy phase and modulation fluoresence study’. J. Supercritical Fluids 5, 48.

    Article  CAS  Google Scholar 

  101. Betts, T. A., J. Zagrobelny, and F. V. Bright: 1992, ‘Elucidation of solute-fluid interactions In supercritical CF3H by steady-state and time-resolved fluorescence spectroscopy’. In: F. V. Bright and M. E. P. McNally (eds.): Supercritical Fluid Technology, ACS Symposium Series 488. Wasington: ACS.

    Google Scholar 

  102. Monta, A. and O. Kajimoto: 1990, ‘Solute-solvent Interaction In nonpolar supercritical fluid: A clustering model and size distribution”. J. Phys. Chem. 94, 6420.

    Article  Google Scholar 

  103. Flanagln, L. W., P. B. Balbuena, K. P. Johnston, and P. J. Rossky: 1997, ‘Ion solvation In supercritical water based on an adsorption analogy’. J. Phys. Chem. B 101, 7998.

    Article  Google Scholar 

  104. Panagiotopoulos, A. Z.: 1994, ‘Molecular simulation of coexistence: Finite-size effects and determination of critical parameters for two-and three-dimensional Lennard-Jones Fluids’. Int. J. Thermophys, 15, 1057.

    Article  CAS  Google Scholar 

  105. For a thenaodynamlc description of this Intermediate, crossover regime, see Refs. [107] and [108].

    Google Scholar 

  106. Yeomans, J. M.: 1992, Statistical Mechanics of Phase Transitions. Oxford: Oxford University Press.

    Google Scholar 

  107. Wyczalkowska, A. K., M. A. Anislmov, and J. V. Sengers, ‘Global crossover equation of state of a van der Waals fluid’. In: E. Kiran, P. G. Debenedetti, and C. J. Peters (eds.): Supercritical Fluids II. Dordrecth: Kluwer. this volume.

    Google Scholar 

  108. Anisimov, M. A., S. B. Kiselev, J. V. Seegers, and S. Tang: 1992, ‘Crossover approach to global critical phenomena In fluids’. Physica A188, 487.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Chemistry, University of California, Davis, CA, 95616, USA

    S. C. Tucker & G. Goodyear

Authors
  1. S. C. Tucker
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Goodyear
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Chemical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, USA

    Erdogan Kiran

  2. Department of Chemical Engineering, Princeton University, Princeton, New Jersey, USA

    Pablo G. Debenedetti

  3. Department of Chemical Technology, Delft University of Technology, Delft, The Netherlands

    Cor J. Peters

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Tucker, S.C., Goodyear, G. (2000). Solute Reaction Dynamics in the Compressible Regime. In: Kiran, E., Debenedetti, P.G., Peters, C.J. (eds) Supercritical Fluids. NATO Science Series, vol 366. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3929-8_16

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-3929-8_16

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-6236-4

  • Online ISBN: 978-94-011-3929-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation