何曼君第三版高分子物理答案(新版答案)(7)

解：蠕变曲线如图所示：

4.204.184.164.144.12l/cm4.104.084.064.044.020200040006000t/min800010000

10000 min时

l?4.185cm，?(10000)?9900 min时

4.185?4?0.04625 44.184?4?0.04600 4根据Bolzmann叠加原理，总应变

l?4.184cm， ?(10000)???t???0?t???1?t?100? 因两次加的负荷一样

??t???0?t???0?t?100? ??0?10000???0?9900? ?0.04625?0.04600?0.09225 ∴ l?10000??l0?1????4??1.09225? ?4.369cm

第九章 作业

1、解:C?QSU??C0??e0d

?Q??eUS0d

E?Ud；则Q??e0ES，Q0?e0ES

Q?QP?Q'Q?Q0?e0ES?e0ES0?Q'?S?S?S?(??1)e0E

2、解：假定对介质施加静电场 P?e0(?s?1)E 取向极化强度增大 P?e0(?s???)Et??r

若t?0时，施加静电场E时： Pr?P(1?e?t/?)?e0(??s???)E(1?e?t/)

t??r 加交变电场E?Eiwt0e Pd?e0(???1)E?e0(???1)eiwt Piwtr与Pr,0的关系是：Pr?Pr,0e 其中，Pr,0?11?iw?e0(?s???)E0 总极化强度P?P1d?Pr?e0(???1)E?1?iw?e0(?s???)E ???1?(P/e????0E)?1?(???1)?s1?iw?

????s????1?iw? 复数介电常数????'?i?''

由①式可知 ?'???s?????1?w2?2 ?''?(?s???)w?1?w2?2

当w?0，?''?0 w??，?''?0

将?''对w求导，d?''/dw?0?w??1 ①

?''max?

?s???2

??，2、试推导Debye色散方程式，并求出复介电常数的实部??和虚部???以及?max（对） tan?max 等特征值表达式。

解：已知

????11???K????????1??????????21?i???????s?1 ??K?????????????????2?

??2?s????1?K????????????????3??????24? 式中K??NA

3M联立以上三个方程式。 将（2）式减（3）式，得

?s?1???1??K??————（4） ?s?2???2将（3）、（4）式带入（1）式得：

???1???2?K??K????11?i???

??1?1s?? ????????2???2??2?1?i?????s???1???1??1????2??1?i????????1????2?????1????2???ss??s ??????2???s?2??1?i?????s??i?????i????2?i????2i??????s????2???s?2??1?i?????s??2???s?

从而 ???1??????2???s?2??1?i?????????2?????si???????

????i???????i????2???i????2??i?????????2????????2???ss?s?s??2??i????2?i????4?i????4i????2???4??2??4?ss?s?s???????2????2????4???????i????2???i????2???i????4??i????ss??ss?????2??2??4???i????2?i????2?i????4i???s?s??ss?3????6???3???i????6??i????3??i????6?i????3???6??s?s?s?s??2?i???????2?s???＝s??2i??????2s???2?s令?????2???2?即??????2s则

???????????????2???i????s????2????i????s1?i????????2?i?????????2??????i???????s1?i?????

?????s? ————（5） ?1?i?????这就是Debye色散方程式。

将（5）式右边通分，并上下同乘?1?i???

??????1?i????1?i??????s?????1?i???

?1?i????1?i??? ????1??2?2???s??????i?????i??1???22

?s????2?2?s????????i ?22221???1????s?????s?????????i ????1??2?21??2?2∴ ???????s???————（6）

1??2?2??????s??????————（7）

1??2?2?????s??????tg???————（8）

???s??2?2????，应当令求?maxd????0 d??????????d?s??221???d???? ??d?d? ???s??????1??2?2????s????????2?2??1????222?0

∴ 1??2?2?2?2?2?0

?2?2?1 舍去负根

???∴ ?max???1 代入（7）式

?s???2

同样，要求tg?max，令

dtg??0 d???????????d?s2?s???2???dtg??? ?d?d????s???????s??2?2??????s???????????2?2???s??????222?0

∴ ?s??2?2???2???2?2?0 ?2?2??s?s ??? ?????s???s??代入（8）式

??s????? tg?max???s??????2?s??s?s?????

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