高分子物理I：固態物理.pdf

549 m1040 高分子物理高分子物理i：固態物理：固態物理 童世煌童世煌 高分子科學與工程學研究所高分子科學與工程學研究所 mechanical properties dt d dt dydx dy dtdx dy du xy xy / newtons law : viscosity solid liquid time dependent! mechanical behavior: static methods 應力鬆弛(stress relaxation)：施予一定值的應變，觀測應力 隨時間的變化。 蠕變(creep)：施予一定值的應力，觀測應變隨時間的變化。 maxwell and voigt-kelvin model et exp 0 t e 00 et e exp1 0 0 e maxwell model voigt-kelvin model burgers (four-element) model t e e t e 2 2 2 0 3 0 1 0 exp1 the creep experiment for burgers model, while a few problems in viscoelasticity can be solved with the maxwell or kelvin elements alone, more often they are used together or in other combinations. the burgers model model exhibits some familiar behavior patterns. consider the effects of stretching a rubber band around a book. initially e1stretching takes place. as time passes, e2+ 2+ 3relaxations take place. on removing the rubber band at a later time, the remaining e1recovers. usually the rubber band circle is larger than it was initially. this permanent stretch is due to 3. viscoelasticity and the deborah number mechanical behavior: dynamic methods where the strain is in phase with the stress, i.e. 0, the sample is classed as elastic. an example of an elastic material might be a metal spring. where the strain is 90 out of phase with the stress, i.e. 90, the sample is classed as viscous. viscous materials such as glycerine exhibit large damping properties. most materials are classified as viscoelastic i.e. between 0 and 90. most polymers exhibit this behavior and have an elastic and viscous component. applied or measured or amorphous states: modulus vs temperature glassy region glass transition region rubbery plateau region rubbery flow region liquid flow region comparison mechanical behavior for amorphous, 100% crystalline, semicrystalline and cross-linked polymers. 100% crystal or highly cross-linked semicrystalline cross-linked amorphous tgtm(100% crystal) course roadmap amorphous crystalline polymer chain polymerization molecular weight intra- and inter-molecular forces structure of polymer chain morphology glass transition crystal structures crystallization kinetics liquid crystalline chain orientation lc structures theories of the glass transition the complete theoretical understanding of glass transition phenomenon is not yet available. the current theories can be divided into three groups: the free-volume theory -the wlf equation the kinetic theory thermodynamic theory free-volume theory volume of solid = volume occupied by molecules + unoccupied volume free volume即指unoccupied volume。可將其視為與分子具有 同等級大小的洞，而這種洞的產生是由於imperfection of packing order所產生，而分子運動即是將分子移至此洞，因 此必須有足夠的洞，分子才能動。 free-volume theory 高分子的運動與小分子相同嗎？ 非常類似，但必須進行協同式運動，因此 需要較大的或較多的孔洞。 自由體積是分子運動的門檻。另外一個門 檻是什麼？ 能量 fox and flory found that below tgthe same specific volumetemperature relationships held for all the polystyrenes, independent of molecular weight. they concluded that (a) below tgthe local conformational arrangement of the polymer segments was independent of both molecular weight and temperature. (b) the glass transition temperature was an iso-free-volume state. tgas an iso-free-volume state ttg時，沒有足夠的洞做glass transition 的運動，只能做一些原子的熱運動 (vibration) ， 而 溫 度 的 升 高 ， 只 增 大 vibration的振幅，而造成occupied volume 的膨脹(normal thermal expansion), free volume並沒有改變，hole 的大小及分布 而均被冷凍。 ttg時，hole增加，而足以提供較大規 模的運動，此時體積的增加來自 1. normal thermal expansion的增加 2. free volume的增加 故v-t圖斜率增加。 t v 0tg tgas an iso-free-volume state when t = tg vf the specific free volume below tgtemperature when t tg v0,0k the specific volume at 0k (no free volume) g r kg g kfg t dt dv vt dt dv vvv 0, 00, 0 g r g tt dt dv vv t dt dv vvv g kf 0, 0 when t 1000, tg與之無關 ii & iii間的劃分線可以表示cooperative motions所需參與的主鏈原子數。 dpc: critical dp between region i & ii effect of copolymerization (blending) on tg 1. one phase system (完全互容完全互容) m1, m2mass fraction of 1 and 2. 適用於polymer-plasticizer, random copolymer, polymer-polymer blends 僅觀察到一個tg: fox equation psppo effect of copolymerization (blending) on tg 2. two phase system 包含大部分polymer blend、graft、 blockpolymers 、 interpenetrating polymer networks (ipn)等產生兩相 者，將可觀察到各相的tg。若產生 的兩相是部分互溶，則可用one phase system的公式計算該相的tg。 sbs triblock copolymer. one tgfor polybutadiene phase and another for ps. storagemodulusdependson which phase is continuous. effect of cross-link density on tg or since cross-linking decreases the conformational entropy, qualitatively it may be concluded that the transition temperature is raised. effect of pressure on tg 壓力上升則tg也上升 : expansion coefficient : compressibility the discussion above has assumed constant pressure at 1 atm (1 bar). since an increased pressure causes a decrease in the total volume, an increase in tgis expected based on the prediction of decreased free volume. it was demonstrated that an increase in pressure can bring about vitrification. this result is important in engineering operations such as molding or extrusion, where operation too close to tg(1 bar) can result in a stiffening of the material. effect of crystallinity on tg 在很高的crystallinity時，很不容易決定tg(例如 pe)。一般而 言，crystallinity的增加將提高tg。 其實crystal對tg的影響是來自晶片對非晶質運動的限制。而並 非是來自結晶度。 左右兩圖結晶度一 樣但右圖中的晶體 對非晶質的限制就 比較大因此tg較高 boyer曾指出半結晶性的高分子有二個tg。較低tg是不受晶體 影響的非晶質部分，較高tg是受結晶體影響的分晶質部分。 effect of crystallinity on tg because of the high degree of crystallinity, molecular motions associated with tgare partly masked, leading to a confusion with other secondary transitions. thus various investigators consider the tgof polyethylene to be in three different regions: -30c, -80c, or -128c. effect of crystallinity on tg region a (the tg/tf1/2) contains most of the polymers which are free from side groups other than h and f (and hence symmetrical) and contain such polymers as polyethylene, poly(oxymethylene), and poly(vinylidene fluoride). region b contains most of the common vinyl, vinylidene, and condensation polymers such as the nylons. about 55% of all measured polymers lie in the band tg/tf= 0.667 0.05. region c contains poly(-olefins) with long alkyl side groups as well as other nontypical polymers such as poly(2,6-dimethylphenylene oxide), which has tg/tfapproximately equal to 0.93. for an unknown polymer, then, the relationship tg/tf = 2/3 is a good way of providing an estimate of one transition if the temperature of the other is known. relationships between tgand tf(fusion or melting point) effect of tgon ploymerization 等溫聚合反應開始時系統內都是小分子，且在液態隨著聚合的 進行，部分分子鏈的分子量增加，黏度跟著增加，而達到tg， 因而分子運動變緩慢，反應聚合逐漸減緩，甚至無法進行，此 時反應可能尚未完全。 example 1：emulsion polymerization of polystyrene，反應開始 只有monomer，此時系統的tg低於反應溫度，因此繼續反應。 monomer逐漸減少，polymer chain逐漸增加，系統的tg逐漸增 加。到某一時候，monomer少到某一種程度，而polymer chain 增加到某一程度，使系統之tg高於反應溫度，此時系統即處 於玻璃態而使反應難以繼續。 effect of tgon polymerization example 2：thermosetting process 反應聚合與crosslink同時進行。 tgo: tgof reactants tg : tgof fully cured system geltg : gel與玻璃化同時發生的溫度 the particular s-shaped curve between tg0and tgresults because the reaction rate is increased with increasing temperature.at a temperature intermediate between geltg and tg, the reacting mass first gels, forming a network. then it vitrifies, and the reaction stops, incomplete. other transitions and relaxations tg以下，大鏈段的運動被凍結，但小鏈段的運動及原子的 振動仍存在。為玻璃轉移運動，即為低於tg以下的運動 (sub-glass relaxation) 。 other transitions and relaxations 聚氯乙烯的 relaxation發生在很寬的頻率(溫度)範圍，可能 是bond stretching, bond bending及-c-c-的rotating。而發生在 低頻部分可視為-c-c-的rotating 。 other transitions and relaxations main chain motions eact1115 kcal/mole eact來自二部分: 1.旋轉時，克服鏈內的旋轉位能差。2.克服鏈之間 的凡得瓦力。 for main-chain motions