課程名稱︰高分子化學
課程性質︰選修
課程教師︰陳文章
開課學院：工學院
開課系所︰化工系
考試日期（年月日）︰102/1/7
考試時限（分鐘）：120
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. 以熱力學觀點討論polymerization-depolymerization of ring type monomer,
試回答下列問題(20 points)
(a) △G = △H- T△S (5 points)
(1) 若由單體聚合高分子， △S之值為正或負? 其理由為何?
(2) 試以此公式，說明逆聚合反應在高溫時較易發生之原因。
(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. 針對酯化反應: R-COOH + R-OH ==> R-COO-R+ H2O 而言，其反應可寫為
-d[COOH]/dt = k[COOH][OH][acid]。若 [COOH]0 = [OH]0 (起始濃度相等)，
試回答下列問題:(10 points)
(a) 試推導出 no acid catalyst added 和 acid catalyzed 兩種情形下，
P(COOH基反應之比例)與[COOH]0之關係式。(5 points)
(b) 試由題目敘述之酯化反應導出DP與P之關係式。(5 points)
3. 對於 amino acid, H2N-R-COOH 而言，若 P為 COOH 基 反應掉之比例，而Nx為
x-mer之數目，試推導出下列二式。(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)開始，再由Nx表示，並考慮Mn，Mw之定義。
4. 請就 free-radical polymerization kinetics， 推導下列關係式。(30 points)
(a) 請由 steady-state approximation 堆導出ri與rt之關係(ri與rt分別為
initial 及 termination rate) (2 points)
(b) 若ri = 2fki[I], rt = 2kt[R]^2, rp= kp[M][R]，試推導出
v=(kp^2/2kt)^(1/2)*[M]/ri^(1/2) (3 points)
(c) DP= -d[M]/dt / d[P]/dt，試推導出 DP=2v(ktc+ktd)/(ktc+2ktd) (5 points)
(註:rp=-d[M]/dt，並嘗試將d[P])/dt 表達為combination and
disproportionation之rate equation)
(d) 若 Xn = d[Pn]/dt / d[P]/dt，且跟根據如下之termination reaction，試推導
出 Xn = (1/v) (1+1/v)^(-n) [(n-1)/v+2(ktd/ktc)]/(1+2(ktd/ktc))
(10 points)
(e) 若考慮 chain transfer reaction: Rn + X ----> Pn+X●
X●+ M -----> R1
若fn 為 propagating radical 擁有 DP= n之比例，
證明: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)針對如下 ionic polymerization 考慮 initiator 為 instantaneous conplete
dissociation，若kp,[GA]o,[M]o分別為 rate constant, initiator
concentration 及單體起始濃度，試證明:(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)
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