课程名称︰高分子化学 课程性质︰选修 课程教师︰陈文章 开课学院：工学院 开课系所︰化工系 考试日期（年月日）︰102/1/7 考试时限（分钟）：120 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 1. 以热力学观点讨论polymerization-depolymerization of ring type monomer, 试回答下列问题(20 points) (a) △G = △H- T△S (5 points) (1) 若由单体聚合高分子， △S之值为正或负? 其理由为何? (2) 试以此公式，说明逆聚合反应在高温时较易发生之原因。 (b) For the polymerization of cyclic monomer, the following equation can be obtained: RT*ln(1-Φ)=△H-T△S (Φ is the polymer fraction), please contruct a poly by varying Φ with T for the following cases of: (1) △S<0 and △H<0 (2) △S >=0 and △H<0 (3) △S>0 and △H>0 (4) △H=0 and △S>0 (5) △H=0 and △S<0 (10 points) (c) Following (b), if △H = -7.0 kcal/mol and △S=-21 cal/deg-mol, please evaluate the ceiling temperature for the polymerization. (5 points) 2. 针对酯化反应: R-COOH + R-OH ==> R-COO-R+ H2O 而言，其反应可写为 -d[COOH]/dt = k[COOH][OH][acid]。若 [COOH]0 = [OH]0 (起始浓度相等)， 试回答下列问题:(10 points) (a) 试推导出 no acid catalyst added 和 acid catalyzed 两种情形下， P(COOH基反应之比例)与[COOH]0之关系式。(5 points) (b) 试由题目叙述之酯化反应导出DP与P之关系式。(5 points) 3. 对於 amino acid, H2N-R-COOH 而言，若 P为 COOH 基 反应掉之比例，而Nx为 x-mer之数目，试推导出下列二式。(10 points) Mn = Mo/(1-P), Mw= Mo * (1+P)/(1-P) Σx*p^(x-1) = (1-P)^(-2) ，Σx^2*p^(x-1) = (1+P)/(1-P)^3 Hint:由Prob(x)开始，再由Nx表示，并考虑Mn，Mw之定义。 4. 请就 free-radical polymerization kinetics， 推导下列关系式。(30 points) (a) 请由 steady-state approximation 堆导出ri与rt之关系(ri与rt分别为 initial 及 termination rate) (2 points) (b) 若ri = 2fki[I], rt = 2kt[R]^2, rp= kp[M][R]，试推导出 v=(kp^2/2kt)^(1/2)*[M]/ri^(1/2) (3 points) (c) DP= -d[M]/dt / d[P]/dt，试推导出 DP=2v(ktc+ktd)/(ktc+2ktd) (5 points) (注:rp=-d[M]/dt，并尝试将d[P])/dt 表达为combination and disproportionation之rate equation) (d) 若 Xn = d[Pn]/dt / d[P]/dt，且跟根据如下之termination reaction，试推导 出 Xn = (1/v) (1+1/v)^(-n) [(n-1)/v+2(ktd/ktc)]/(1+2(ktd/ktc)) (10 points) (e) 若考虑 chain transfer reaction: Rn + X ----> Pn+X● X●+ M -----> R1 若fn 为 propagating radical 拥有 DP= n之比例， 证明:fn = [Rn]/[R] =( (1+γv)/v)* (1+1/v+γ)^(-n) γ= Cm +Cs [S]/[M]+Cr [r]/[M] 5. For the following free-radical copolymerization shown below, please answer the following question: (10 points) --M1。+ M1 ====> ---M1。 k=kp11 --M1。+ M2 ====> ---M2。 k=kp12 --M2。+ M2 ====> ---M2。 k=kp22 --M2。+ M1 ====> ---M1。 k=kp21 -d[M1]/dt = kp11*[M1。][M1]+kp21[M2。][M1] -d[M2]/dt = kp12*[M1。][M2]+kp22[M2。][M2] (a) please derive the copolymerization composition equation as below: γ= (1+r1([M1]/[M2]))/(1+r2([M2]/[M1])), where r1 = kp11/kp12 , r2 = kp22/kp21 (b) If r1 != r2, please derive the following formula at azeotropic condition: [M1]/[M2] = (1-r2)/(1-r1) (5 points) 6. (i)针对如下 ionic polymerization 考虑 initiator 为 instantaneous conplete dissociation，若kp,[GA]o,[M]o分别为 rate constant, initiator concentration 及单体起始浓度，试证明:(10 points) (1) v = ([M]o/[GA]o) *(1- exp(-kp*[GA]o*t)) (2) Xn=(1/(n-1)!) ([M]o/[GA]o)^(n-1)*exp(-[M]o/[GA]o) (iii) Styrene is added to a solution of sodium naphthalenide in THF so that the initial concentrations of styrene and sodium naphthalenide in the reaction mixure are 0.2M and 1*10^(-3) M respectively. After 5s of the reaction @ 25 degree C, the styrene concentration is determined to be 1.73*10^(-3). Calculate: (a) The rate cinstant for propagation of the polymerization (b) The initial rate of polymerization (c) The rate of polymerization after 10s (d) The number average molecular weight of the polymer after 10s (10 points) -- 莫听穿林打叶声,何妨吟啸且徐行,竹杖芒鞋轻胜马,谁怕,一蓑烟雨任平生 料峭春风吹酒醒,微冷,山头斜照却相迎,回首向来萧瑟处,归去,也无风雨也无晴 --

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