nơi N1 và N2 là số mol của dung môi và các đại phân tử, tương ứng. Cần nhấn mạnh rằng biểu hiện của entropy của pha trộn này được áp dụng chỉ cho các hệ thống athermic hoặc để hỗn hợpThay thế trong biểu hiện của Smix số mol cho số lượng các phân tử cung cấp cho | 54 THERMODYNAMICS OF MACROMOLECULAR SYSTEMS and ni 0 leading to Sc kn2 ln X - X 1 In z X - 2 In z - 1 Hence the entropy of mixing ASco for mixtures with low AHmlx is simply expressed as ASmix Sco - Sco 1 Sco 2 ASmK -k n1 n2X n1 ln n2 ln nt nt The same expression can be rewritten as a function of the volume fractions of the two components with 1 being the volume fraction of the solvent and 2 being that of the polymer n1 n2X 1 and 2 nt nt which results in a very simple expression for ASmix ASmix -k n1 ln 1 n2 ln 2 Substituting in this expression of ASmix the number of moles for the number of molecules gives with R kNa R being the gas constant ASmix -R N1 ln 1 N2 ln 2 where N1 and N2 are the number of moles of solvent and macromolecules respectively. It should be emphasized that this expression of the entropy of mixing is applicable only to athermic systems or to mixtures exhibiting only weak interactions between molecules that is solutions with low enthalpy of mixing. Deviations from ideality could arise in particular in the following situations which will be discussed later on When molecules interact strongly the assumption of a random placement of the components in the solution is not realistic. Strong interactions induce a short-range order which leads to a lower entropy of mixing In dilute solutions polymers are subjected to excluded volume. Excluded volume prohibits the access of any other homolog into the vicinity of a chain segment and thus causes a lower entropy of mixing At high temperature the density of a mixture can considerably decrease and the contribution of the free volume to the entropy of mixing cannot be neglected. FLORY-HUGGINS THEORY 55 . Enthalpy and Free Energy of Mixing Macromolecular solutions deviate generally from ideality and are characterized by a nonzero enthalpy of mixing. In the Flory-Huggins theory the calculation of AHI1IK is inspired by that of the enthalpy of mixing of regular solutions. Three types of .
