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Journal of Physical Chemistry B
Volumn 111, Issue 51, 2007, Pages 14290-14294
Vapor pressure and sublimation rate of molecular crystals: Role of internal degrees of freedom
Author keywords

[No Author keywords available]
Indexed keywords

DESORPTION; SUBLIMATION; VAPOR PRESSURE; VIBRATIONAL SPECTRA;
EID: 38349157528     PISSN: 15206106     EISSN: None     Source Type: Journal    
DOI: 10.1021/jp076038g     Document Type: Article
Times cited : (17)
References (34)
  • 4
    • 84906402014 scopus 로고    scopus 로고
    • Although eq 1 appears to suggest direct desorption from a kink site into the vapor phase, vegg could, in principle, include multistep processes involving detachment from the kink site into the flat surface, re-attachment to the same kink site, or diffusion on the flat surface, followed by either desorption into the vapor phase (from the flat surface) or incorporation into another kink site and so on. No matter how many steps it takes to desorb into the vapor phase, the net desorption energy is still △E. It is also to be noted that εs, the potential energy at the kink site of a crystal surface, is equal to the potential energy per molecule in the bulk crystal phase. Thus, △E is equivalent to the heat of sublimation △H at T, 0, i.e, △E, △HT, 0, excluding zero-point vibrational energy, At finite T, △H is smaller than △E by a few k
    • BT; see eq 8.
  • 6
    • 84906402015 scopus 로고    scopus 로고
    • Burnham, A.; Gee, R.; Maiti, A.; Qiu, R.; Rajasekar, P.; Weeks, B.; Zepeda-Ruiz, L. LLNL Technical Report, UCRL TR 216963, 2005. Experimental results on vapor pressure of PETN documented in this work are from R. Behrens' presentation: Update on the Analysis of Thermally and Chemically Stabilized PETN Powders, JOWOG Focused Exchange Meeting, May 2003, Sandia National Lab, Albuquerque, NM.
    • Burnham, A.; Gee, R.; Maiti, A.; Qiu, R.; Rajasekar, P.; Weeks, B.; Zepeda-Ruiz, L. LLNL Technical Report, UCRL TR 216963, 2005. Experimental results on vapor pressure of PETN documented in this work are from R. Behrens' presentation: "Update on the Analysis of Thermally and Chemically Stabilized PETN Powders," JOWOG Focused Exchange Meeting, May 2003, Sandia National Lab, Albuquerque, NM.
  • 9
    • 84906373209 scopus 로고    scopus 로고
    • 6
    • 6
  • 10
    • 28844503728 scopus 로고    scopus 로고
    • Sticking coefficient k for ice surface has been experimentally determined to be ∼1; see e.g., Batista, E. R.; Ayotte, P.; Bilic, A.; Kay, B. D.; Jonsson, H. Phys. Rev. Lett. 2005, 95, 223201. For most other molecular crystals, experimental values of K do not exist, although it is expected to be of the order of 1.
    • Sticking coefficient k for ice surface has been experimentally determined to be ∼1; see e.g., Batista, E. R.; Ayotte, P.; Bilic, A.; Kay, B. D.; Jonsson, H. Phys. Rev. Lett. 2005, 95, 223201. For most other molecular crystals, experimental values of K do not exist, although it is expected to be of the order of 1.
  • 16
    • 84906373206 scopus 로고    scopus 로고
    • Equation 4 (and later eqs 5, 8) are valid only for NM ≥ 3. For monatomic systems (e.g, Ar, Zrot, 1, and there are no vibrational modes in the vapor phase. Thus, the last two terms on the right-hand-side of eq 4 are zero. Also, the exponent of Z vib(veff) in eqs 5, 7, and 9 (as well as the prefactor of fVib(veff) in eq 8) becomes 3 (rather than 6, while the definition of veff (i.e, eq 6) gets modified as 3 In{Z vib(Veff, f dv gph(v) x ln{Z vib(v, The factor of 3 comes from the 3 lost translational degrees of freedom (and subsequently gained as three additional phonon modes) when an atom moves from a vapor to a solid phase
    • vib(v)}. The factor of 3 comes from the 3 lost translational degrees of freedom (and subsequently gained as three additional phonon modes) when an atom moves from a vapor to a solid phase.
  • 17
    • 84906373207 scopus 로고    scopus 로고
    • The symmetry factor σ is 1 for β-HMX and 2 for PETN and ice water, Note that for the vibrational partition function we use the full quantum expression, whereas for Zrnt, we employ the classical expression. This is because rotational quanta are typically much lower in energy than vibrational quanta, and the classical expression for Z rot, is valid at temperatures above just a few to a few tens of K. See ref 15
    • rot, is valid at temperatures above just a few to a few tens of K. See ref 15.
  • 18
    • 84906402012 scopus 로고    scopus 로고
    • Note that the power of 6 on Zvib,b in eq 5 (and correspondingly, the factor of 6 on the left hand side of eq 6) stems from the 3 translational, 3 rotational degrees of freedom lost (and are subsequently gained as additional phonon modes) when a molecule migrates from the vapor to the solid phase. Also note that the right hand side of eq 6 is just the logarithm of the ratio between the vibrational partition function of the solid and the vapor phases, i.e, ln{Zvib(solid)/Z vib(vapor, This allows eq 5 to be written as p, kBT/Λ3){Z rotZvib(vapor)/Zvib(solid, exp, εg, εs)/kBT, a form closely related to site-desorption rates derived from reaction rate theory.3, 11
    • 3, 11
  • 29
    • 84906358752 scopus 로고    scopus 로고
    • This assumption is made to simplify the present analysis and to make a first-order comparison between the desorption rate of a PETN in the absence and the presence of TriPEON respectively. In reality, θ is a few tenths of a percent.9 This allows processes in which a TriPEON can detach from a kink site into the flat surface, which would expose a PETN at a kink and allow it to escape. Such details are important to accurate lifetime predictions and are under current investigation
    • 9 This allows processes in which a TriPEON can detach from a kink site into the flat surface, which would expose a PETN at a kink and allow it to escape. Such details are important to accurate lifetime predictions and are under current investigation.
  • 30
    • 84906373208 scopus 로고    scopus 로고
    • For a PETN molecule on a PETN surface, eq 10 follows from all of the foregoing analysis embodied in eqs 3, 7. For a foreign molecule like TriPEON on a PETN surface, one needs to revisit eqs 3 and 4. In fact, one now needs to compute the Gibb's free energy of two systems: one in which the TriPEON is at a kink site and the other in which the TriPEON is in the gas phase. We assume here that all kink sites on the surface are saturated by TriPEON a reasonable assumption, given the large binding energy △E of TriPEON to the PETN kink site and given that we typically put enough TriPEON in our formulation, This takes away an extra configuration entropy term involved in the number of ways in which the kink sites can be occupied by TriPEON. Equations 3 and 4 then need to be re-written in terms of the partition function of the system in which there is TriPEON on the surface versus where the TriPEON has desorbed into vacuum as a molecular species. That would change the formal definition of
    • vibtripeon}. With this definition, eq 10 would equally apply to the desorption rate of TriPEON on PETN surface.
  • 31
    • 84906402013 scopus 로고    scopus 로고
    • 8. From molecular dynamics simulations (COMPASS) using a periodic slab representation of me PETN (110) surface we compute a TriPEON binding energy of △E = 51.5 kcal/mol at a kink site, which is 14.5 kcal/mol higher than that the △E of a PETN (see Table 1).
    • 8. From molecular dynamics simulations (COMPASS) using a periodic slab representation of me PETN (110) surface we compute a TriPEON binding energy of △E = 51.5 kcal/mol at a kink site, which is 14.5 kcal/mol higher than that the △E of a PETN (see Table 1).

* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.