title: [Network form of the Kedem-Katchalsky equations for ternary non-electrolyte solutions. 5. Evaluation of Nij Peusner's coefficients for polymeric membrane].
abstract: BACKGROUND
  Peusner Network Thermodynamics (PNT) enables symmetrical and/or hybrid transformation of classical Kedem-Katchalsky (K-K) equations to network forms. For homogenous nonelectrolyte solutions that consist of solvent and two dissolved substances, two symmetrical and six hybrid forms of network K-K equations can be obtained that contain symmetrical (Rij or Lij) or hybrid (Hij, Wij, Nij, Kij, Sij or Pij) Peusner's coefficients.
  
  
  OBJECTIVE
  The aim of this paper is to derive network form of K-K equations for homogenous ternary nonelectrolyte solutions that contains Peusner's coefficients Nij (i, j ∈ {1, 2, 3}). These coefficients form a third degree matrix of Peusner's coefficients [N]. We also aim to calculate dependences of Nij coefficients on average concentration of one component of solution in a membrane (C1) when value of the second one (C2) is fixed and to compare these dependences with appropriate dependences for coefficients Rij, Lij, Hij and Wij presented in 1-4 parts of the paper.
  
  
  METHODS
  A cellulose hemodialysis membrane (Nephrophan) of known transport parameters for aqueous glucose and ethanol solutions was a research material. The PNT formalism and classical form of K-K equations for ternary non-electrolyte solutions was a research tool in this paper.
  
  
  RESULTS
  The network form of K-K equations was presented using the hybrid transformation of Peusner's thermodynamic networks for ternary solutions that contain solvent and two dissolved substances. For homogenous solutions, we calculated dependences of Peusner's coefficients Nij (i, j = 1, 2, 3) on average concentration of one component (C1) of the solution in a membrane when value of the second one is fixed (C2). Moreover, we calculated dependences of quotients Nij/Rij, Nij/Lij, Nij/Hij and Nij/Wij on average concentration of one component (C1) of the solution in a membrane when value of the second one is fixed (C2).
  
  
  CONCLUSIONS
  The network form of K-K equations that contain Peusner's coefficients Nij (i, j ∈ {1, 2, 3}) is a novel tool to study membrane transport. Obtained results of calculations showed that coefficients N12, N21, N22 and N32 are sensitive for composition and concentration of solutions separated by a polymer membrane.
authors.affiliation: Katedra Informatyki ekonomicznej, Uniwersytet ekonomiczny, Katowice, Polska.
authors.forename: Kornelia M
authors.initials: KM
authors.lastname: Batko
authors.affiliation: Instytut Marketingu, Politechnika Częstochowska, Gliwice, Polska.
authors.forename: Izabella
authors.initials: I
authors.lastname: Slęzak-Prochazka
authors.affiliation: Katedra Zdrowia Publicznego, Politechnika Częstochowska, Częstochowa, Polska.
authors.forename: Andrzej
authors.initials: A
authors.lastname: Slęzak
mesh_terms: D002482:Cellulose / Q000737:chemistry; D000431:Ethanol; D008567:Membranes, Artificial; D008956:Models, Chemical; D010539:Permeability; D011108:Polymers; D006435:Renal Dialysis / Q000295:instrumentation*; D012996:Solutions / Q000737:chemistry*; D013816:Thermodynamics
chemical_list: D008567:Membranes, Artificial; D011108:Polymers; D012996:Solutions; D000431:Ethanol; D002482:Cellulose