Rushbrooke, Physics of Simple Liquids (NorthHolland, Amsterdam, 1968). The number of configurations of D-set objects in the lattice The number of configurations of objects in the mixture Ω D (101) and (115) to express the sequence Ω The number of cells eligible for joining the e κth element to κ φĬonstant factor taken in eqs. Packing fraction ofthe jth component particles in a standard state and in the mixture, respectively ζĮligible cell chosen for joining the e κth element to κ Φ κe Same as κ for the ith, oth, l th object, respectively η o j η M Κ and the next eth element of k, κ and ζ cell. Mqth order function used to compute the value for A q j κĪ simply connected and properly shaped body, being a formed part of the kth particle, while its e κth element is being placed κe, κζ Probability that an element e i of the ith object occupying the cell ζ is not in conflict with κ (def. Probability that an element e i of the ith object, occupying the cell ζ (chosen for the e κ,th element of κe), is not in conflict with κ and with objects belonging to the set Dk\ i(def. The number of elements (volume) of the kth object Z o The set of elements of the hard part of the kth object x κ The number of hard part elements (volume) of the kth object x κ Volume fraction of the jth component and of the hard part of its particles, respectively, in the mixture x κ The set of surface elements of the kth object v * j, v j The number of elements in a surface layer of the kth object S κ (118)) σ κS DĬomponent of the expression for configurational entropy contributed by inserting of the kth particle into the lattice (eq. (1)) ΔS FĪpproximation to ΔS disregarding differences in the size of particles (def. Radius of a spherical region occupied by the vibrating center of a molecule in liquid state S M, S oĬonffgurational entropy of a mixture and of its components in their standard states, respectively ΔSĬonfigurational entropy of mixing (eq. Thickness of a soft spherical layer in a particle Δr , R o q r kĬurrent value for a radius of the kth particle being located δR Radius of a sphere representing the hard part of the kth object ( R o) q Same as ℙ Dk\ i i\ ξ but with the lack of conflict with κ assumed R k Probability of non-conflict arrangement of the ith object with fixed configuration of Dk\ i objects) provided that its first element is placed in any vacant cell, in ζ cell, respectively >ℙ Dk\ i i\ ξ Superscripts used to indicate an order of products and of factors ℙ Dk\ i i\ f,ℙ Dk\ i i\ ξ Probability that a cell chosen for the e κth element of κe is vacant, providing that the objects of D and κ are arranged in an admissible way (def. The number of vacant cells left by objects belonging to D O qĪ sequence consisting of q indices, each of them representing geometrical parameters of a particle as the argument of functions A q j or G q j O q\ j l) cĬth combination of l identical indices j within the sequence O q( j ε O q) P D eκ The total number of lattice cells (volume of the mixture) n D f The number of the jth component particles n The number of particles in the mixture M j Same as g eκ for the previously formed part κ of the kth object κ B Boltzmann constant M Probability that a cell chosen for an element e κ is eligible with respect to the shape of the kth object, provided that previously arranged elements of k satisfy the same condition g eκ (38)) G PĬonstant factor G p j (for identical particles) g eκ Geometrical factors depending only on the shape and size of particles present in the mixture (defined in eq. ):Ī general function representing effects of the shape and size of particles on coefficients A q j (defined in eq.Index of an element of previously formed part κ of object k F q( Index of an element of the kth, ith object, respectively e κ Same as D, while object i is removed and κ added to lattice eκ, ei Set of objects arranged in lattice prior to that being placed Dk\ i The expected number of configurations of object i (having a fixed configuration of Dk\ i) in which i is adjacent to κ D The expected number of configurations of a single object k, κ, κe, i, respectively, having a fixed (taken at random) configuration of objects belonging to the set D, Dk\ r Dk\ i ik Specific surface area of the oth particle B D κiįactor representing the effect of particles belonging to Dκ (1st and further neighbors of κ on probability ακe D i r (eq. (48)-(50) A qĬoefficient A q j for identical particles a o Coefficients in formulae (47), (54) defined in eqs.