1. the energy-based Cavity Energetic Sizing Algorithm (CESA)，详见Liquid Structure via CavitySize Distributions,J. Phys. Chem. B2000,104,12028-12034.
The CESA algorithm was appliedto each of the above stable structures. CESA is a Monte Carlo technique, inwhich a cavity is defined as a spherical volume with a well-defined center,which is a local minimum in a repulsive particle energy field. As such, the CESAalgorithm is based on energetic rather than geometric considerations and the definitionof the initial test-particle does not affect the cavity size distribution,which is the advantage of CESA. (Cavity size, sorption and transport characteristics ofthermally rearranged (TR) polymers. Polymer52 (2011) 2244-2254)
CESACavity sizedistributions in high free volume glassy polymers by molecular simulation, Polymer 45 (2004) 3907–3912
具体步骤（Cavity size distributions in high free volume glassypolymers by molecular simulation, Polymer 45 (2004) 3907–3912）:
(i) A polymer structure is generated by MD (or MC) simulation.
(ii) The force field used tocreate the above structure is replaced with a pure repulsive force field. Allatoms remain in fixed locations.
(iii) A trial repulsiveparticle is then randomly inserted into the repulsive polymer structure and alocal energy minimum is located in the repulsive force field.
(iv) After the minimum isdetermined, attractive interactions are turned on and the size of the testparticle is adjusted until its potential interaction with all other atoms becomeszero. This size is taken as the diameter of a spherical cavity.
(v) A check is then made todetermine whether the initial random inserting point is inside the cavity ornot. The cavity is only accepted if the initial point is inside the cavity.This procedure leads to volume distribution rather than a number distributionof cavities.
(vi) Steps (iii)–(v) arerepeated enough times to get a representative distribution of cavity sizes fora given structure.
University of Texasat Austin的Frank T Willmore基于此方法，开发了a suite of tools to analyze free volume andcavity sizing，并在他的一篇会议论文A toolkit for the analysis and visualization of free volume in materials中提到“Pleasecontact the author directly to obtain the software.”
2. V-connect and R_max
详见Free VolumeDistributions in Ultrahigh and Lower Free Volume Polymers: Comparison betweenMolecular Modeling and Positron Lifetime Studies, Macromolecules 2002, 35, 2129-2140
Atomistic packing model and free volume distribution of a polymer with intrinsic microporosity (PIM-1)
A recently developed computer program was applied tovalidated packing models, to estimate the size distributions of FVEs, which maybe explored by a spherical penetrant of a certain radius. This free volume isderived by first superimposing a fine grid over the cubic packing model, andthen (at every point of this grid) testing whether an overlap occurs between ahard sphere test particle (representing the penetrating molecule) and any atomof the polymer (represented also by corresponding hard spheres). The result ofthis particle insertion procedure is a classification of grid points as “occupied”or “free”. Subsequently, the connectivity of the free grid points is checkedand connected free grid points are collected into groups, which representindividual holes. This is done in two ways. In the first approach (namedV_connect), thesimple topological criterion is that every point of a group has at least onenext neighbor that is also a member of this group. This approach identifiesholes, which may be of complex shape and of large volume. In a second approach(namedR_max), forevery grid point, its shortest distance to a polymer atom is determined. Amongthese distances, local maxima are defined by calculating the related gradient. Theneach grid point of a free volume region determined with the first approach(V_connect) is assigned to a specific group or set, according to its nearestlocal maximum. The R_max approach may divide larger free volume regions ofelongated or highly complex shape into smaller, more compact regions. Thesecond approach was introduced to better match the situation in PALS experiments,where the positronium probe can obviously, not completely sample very largeholes of complex topology.(Atomistic Packing Models forExperimentally Investigated Swelling States Induced by CO2 in GlassyPolysulfone and Poly(ether sulfone),Journal of Polymer Science: Part B: PolymerPhysics, Vol. 44, 1874–1897 (2006))
目前为止还没有查到相关软件，因此还不清楚如何实现
3. PSDsolve
aMonte Carlo based approach coupled with nonlinear optimization and seems towork quite well，由一位研究者在博士论文期间开发出来的，并免费拿出来共享，可以在网站http://supriyo.net/research/psd/psd.htm上免费下载
Fast Method for Computing Pore Size Distributions ofModel Materials, Langmuir 2006, 22,7726-7731
具体理论与方法，请参考Fast Method for Computing Pore Size Distributions ofModel Materials, Langmuir 2006, 22,7726-7731
