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Equations of state by K. R. Hall (J. Chem. Phys. 1972, 57, 2252): fluid phase, eq 11; solid phase, eq 13.
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The surface of tension is the surface at which the surface tension acts. It is the surface for which the generalized Laplace equation, Δp c ) 2γ /R + ∂γ /∂R reduces to the original one, that is, ∂γ /∂R 0. Here, Δp c is the capillary pressure.
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The surface of tension is the surface at which the surface tension acts. It is the surface for which the generalized Laplace equation, Δp c ) 2γ /R + ∂γ /∂R reduces to the original one, that is, ∂γ /∂R ) 0. Here, Δp c is the capillary pressure.
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Tolmans original definition ( Tolman, R. C. J. Chem. Phys. 1949, 17, 333). A different definition is applied by several authors: δ T ) limR f R e- R p. In our terminology, the latter corresponds to the equilibrium Tolman length, δ T,eq.
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Defined by the position of a step function that has the same spatial integral and amplitude as the interfacial density profile
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Defined by the position of a step function that has the same spatial integral and amplitude as the interfacial density profile.
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Field theoretic models of the vapor-liquid interface predict a strongly size dependent Tolman length that has a positive value for small droplets and tends to a negative value in the large particle limit. See, for example, Fisher, M. P. A.; Wortis, M. Phys. Rev. B 1984, 29, 625. Iwamatsu, M. J. Phys.: Condens. Matter 1994, 6, L173. Hadjiagapiou, I. J. Phys.: Condens. Matter 1994, 6, 5303. Talanquer, V.; Oxtoby, D. W. J. Phys. Chem. 1995, 99, 2865. van Giessen, A. E.; Blokhuis, E. M.; Bukman, D. J. J. Chem. Phys. 1998, 108, 1148. Gránásy, L. J. Chem. Phys. 1998, 109, 9660. Barrett, J. J. Chem. Phys. 1999, 111, 5938. Barrett, J. C. J. Chem. Phys. 2006, 127, 144705. Hruby, J.; Labetski, D. G.; van Dongen, M. E. H. J. Chem. Phys. 2007, 127, 164720.
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Nucleation theories predict the expression J, J 0 exp{-W */kT, for the steady-state nucleation rate,2a where J 0 is the pre-exponential factor depending on the molecular mobility and the size of the critical fluctuation, while W * is the free energy of the critical fluctuation (nucleus, Experimental studies imply that J 0 from the kinetic approach of the CNT describes properly the temperature dependence of the nucleation rate.2a,b Langer 's first principles approach offers an independent way to estimate J 0 [Langer, J. S. Ann. Phys, N.Y, 1967, 41, 108; 1969, 54, 258, In the few cases where J 0 has been evaluated following this route e.g, for vapor condensation: Langer, J. S, Turski, L. A. Phys. Rev. A 1973, 8, 3230, it leads to results very close to those from the classical kinetic approach. For crystal nucleation, Langer 's approach has only been
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Nucleation theories predict the expression J ) J 0 exp{-W */kT } for the steady-state nucleation rate,2a where J 0 is the pre-exponential factor depending on the molecular mobility and the size of the critical fluctuation, while W * is the free energy of the critical fluctuation (nucleus). Experimental studies imply that J 0 from the kinetic approach of the CNT describes properly the temperature dependence of the nucleation rate.2a,b Langer 's first principles approach offers an independent way to estimate J 0 [Langer, J. S. Ann. Phys. (N.Y.) 1967, 41, 108; 1969, 54, 258]. In the few cases where J 0 has been evaluated following this route (e.g., for vapor condensation: Langer, J. S.; Turski, L. A. Phys. Rev. A 1973, 8, 3230), it leads to results very close to those from the classical kinetic approach. For crystal nucleation, Langer 's approach has only been used to evaluate J 0 under the assumption that thermal transport is the rate determining factor (Grant, M.; Gunton, J. D. Phys. Rev. B 1985, 32, 7300). However, usually this is not the case, as normally molecular mobility determines the time scale of nucleation.2a Atomistic simulations imply that for the Lennard-Jones system J 0 from the classical kinetic approach might be too low by about 2 orders of magnitude.2c This indicates that some uncertainty has to be associated with the nucleation barrier if evaluated from the measured nucleation rates using the classical J 0.2a A further difficulty is that often steady state nucleation is assumed when evaluating the experiments without testing whether this assumption is valid. An even more essential source of error can be the presence of heterogeneous nucleation induced by foreign particles distributed in the volume. It cannot be easily distinguished from homogeneous nucleation, and the interpretation of heterogeneous nucleation as homogeneous might lead to a serious underestimation of the free energy of nuclei.2a Apparently, the experimental nucleation rates for various colloidal approximants of the HS system scatter substantially (see, e.g., Figure 5 inGong, T. Y.; Shen, J. G.; Hu, Z. B.; Marquez, M.; Cheng, Z. D. Langmuir 2007, 23, 2919), casting doubts to their relevance to the true HS system.
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