Evaluation of Flory－ Huggins interaction parameter from
cloud points of polymer blends

Cheng Baojia,Zhou Chixing and Yu Wei
(Department of Polymer Science and Engineering,Shanghai Jiaotong University)

利用聚合物共混物的浊点数据计算Flory－Huggins相互作用参数程宝家周持兴俞炜(上海交通大学高分子科学与工程系，200240)通过构造Flory－Huggins相互作用参数与温度、组成的函数关系式，结合Flory－Huggins方程与浊点的判断条件，推导出了由实验浊点数据计算χ的解析式。理论计算与实验结果吻合较好。关键词：聚合物共混物；浊点；相互作用参数

　　Due to the simple form of Flory－ Huggins lattice theory,it is widely used in the study of phase diagram for polymer blends.However,because of neglecting volume changes during mixing,it can not explain the lower critical solubility temperature behavior of most polymer blends.Different solutions,such as equation of state,taking the dependence of Flory－ Huggins interaction parameter (χ ) on temperature (T) and volume fraction (φ ) into consideration,were then utilized for correction.The first method included too many parameters and was rather inconvenient,while the second usually failed to describe the phase behavior of polymer blends due to unsuitable dependence of χ on T and φ .In this work,we put forward a new technique to evaluate χ from experimental cloud points.

Flory－ Huggins equation can be written as:

　(1)

where Δ G is Gibbs free energy of mixing,VS is the volume of segment,V is the volume of blends,R is gas constant,r1 and r2 are the segment numbers of polymer 1 and 2 respectively.
　　The mathematical expression for cloud points is

　(2)

It is suggested that χ can be expressed as^[1]

　(3)

where χ_H is the enthalpic contribution and χ_S is the entropic contribution.To take the effect of concentration into account,χ_H and χ_S can be expressed as linear function of φ separately.However,we introduced a different function to describe the dependence of χ on T and φ:

　(4)

where Ci(i=1,2,3,4,5)are undetermined coefficients respectively.Substituting Eq.(1) and (4)into Eq.(2)gives

　(5)

Substituting φ =0.5 into Eq.(5) gives

　（6）

i.e.C5 can be derived from C3 and C4.Substituting C5 into Eq.(5)gives

　（7）

Then, experimental cloud points can be used to fitEq.(7) by multiple linear regression so as to get the dependences of χ on T and φ .This method was used to fit published[2] cloud points of polybutadiene(PBD)/polyisoprene(PIP) and good agreement was found(Fig 1).Other polymer blends,such as polystyrene/polyvinyl methyl ether,polymethyl methacrylate/styrene－ acrylonitrile copolymer etc,were also studied and theoretical calculation fit well with experimental data.

　　This provides an easier but reliable method to evaluate χ from cloud point.It can be used to get analytic expression of the first and second derivative of Δ G,as well as to calulate phase diagram and interfacial tension etc.

Biography:Cheng Jiabao,Ph.D.student.Published 8 papers.

References

［1］Bates F S,Schultz M F,Rosedale J H.Macromolecules,1992,25(20):5 547
［2］Narh K A.Advances in Polymer Technology,1996,15(3):245

Received:1999－11－28.