A multiscale approach is used to model and analyze the ablation of porous materials. Models are developed for the oxidation of a carbon preform and of the char layer of two phenolic impregnated carbon ablators with the same chemical composition but with different structures. Oxygen diffusion through the pores of the materials and in depth oxidation and mass loss are first modeled at the microscopic scale. The microscopic model is then averaged to yield a set of partial differential equations describing the macroscopic behavior of the material. Microscopic and macroscopic approaches are applied with progressive degrees of complexity to gain a comprehensive understanding of the ablation process. Porous medium ablation is found to occur in a zone of the char layer that we call the ablation zone. The thickness of the ablation zone is a decreasing function of the Thiele number. The studied materials are shown to display different ablation behaviors, a fact not captured by current models that are based on chemical composition only. Applied to Stardust's phenolic impregnated carbon ablator, the models explain and reproduce the unexpected drop in density measured in the char layer during Stardust postflight analyses [Stackpoole, M., Sepka, S., Cozmuta, I., and Kontinos, D., "Post-Flight Evaluation of Stardust Sample Return Capsule Forebody Heat-Shield Material," AIAA Paper 2008-1202, Jan. 2008]. Nomenclature C = oxygen concentration, mol=m 3 D = diffusion coefficient, m 2 =s D dis = dispersion coefficient, m 2 =s d p = mean pore diameter, m f = rarefaction function J = molar ablation rate, mol=m 2 =s Kn = Knudsen number k = reactivity, m=s L D = diffusion length, m L R = reaction length, m L 0 = sample initial length, or thickness, m M = molar mass, kg=mol n = vector normal to the surface P = pressure, Pa Pe = Péclet number P f = local fiber perimeter, m q = local molar flux density, mol=m 2 =s R = ideal gas constant, 8:314 J=mol=K Sx; y; z; t = surface function S p = local horizontal section of a pore, m 2 s = volume surface, m 2 =m 3 T = temperature, K V = averaging volume, m 3 v = velocity, m=s v = molecular agitation mean velocity, m=s x, y, z, t = space (m) and time (s) coordinates = exponential coefficient for tortuosity law of the pore-filling matrix ERSA = effective reactive surface-area coefficient " = porosity = tortuosity = mean free path, m h 2 j i = mean square displacement in direction j, m = density, kg=m 3 = Thiele number = solid molar volume, m 3 =mol Subscripts B = bulk e, eff = effective ERSA = effective reactive surface area f = fiber g = pyrolysis gases i = indicator or index-number K = Knudsen m = matrix ref = reference w = wall

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The molecular dynamics technique with the ab initio based classical reactive force field ReaxFF is used to study the adsorption dynamics of O(2) on Pt(111) for both normal and oblique impacts. Overall, good quantitative agreement with the experimental data is found at low incident energies. Specifically, our simulations reproduce the characteristic minimum of the trapping probability at kinetic incident energies around 0.1 eV. This feature is determined by the presence of a physisorption well in the ReaxFF potential energy surface (PES) and the progressive suppression of a steering mechanism when increasing the translational kinetic energy (or the molecule's rotational energy) because of steric hindrance. In the energy range between 0.1 and 0.4 eV, the sticking probability increases, similar to molecular beam sticking data. For very energetic impacts (above 0.4 eV), ReaxFF predicts sticking probabilities lower than experimental sticking data by almost a factor of 3 due to an overall less attractive ReaxFF PES compared to experiments and density functional theory. For oblique impacts, the trapping probability is reduced by the nonzero parallel momentum because of the PES corrugation and does not scale with the total incident kinetic energy. Furthermore, our simulations predict quasispecular (slightly supraspecular) distributions of angles of reflection, in accordance with molecular beam experiments. Increasing the beam energy (between 1.2 and 1.7 eV) causes the angular distributions to broaden and to exhibit a tail toward the surface normal because molecules have enough momentum to get very near the surface and thus probe more corrugated repulsive regions of the PES.

This section summarizes the Rotational Isomeric State (RIS) tables and the charges on the five polymer samples (PET, PP, PCTFE, PVDC and PVOH) selected for the present solubility study. The RIS table contains information on the conditional probability of key dihedral angles in the polymer chain determined by separately minimizing the energy of the representative torsions, with coupling where applicable. The charges on the polymers are calculated from electrostatic potential fits (ESP) to Hartree Fock (6-31G ** basis set) quantum charges using the Jaguar program (Schrödinger LLC). The atomic charges for the monomer structures are calculated first after replacing the head and tail atoms (hydrogens) by methyl groups (CH 3) to avoid terminal edge effects on the charges. A macro is then used to assign the Jaguar calculated quantum charges back to the monomer after first replacing the terminal methyl groups with hydrogen atoms. The residual charge is redistributed over the entire monomer, except for the terminal hydrogen atoms that remained uncharged. The terminal hydrogens are used as dummy atoms for the monomer as they are deleted when a polymer chain is generated. The monomer configuration with ESP charges is used to build a trimer and to determine the main representative torsions of the PET polymer.