MOTION. The easy stuff; The gaseous state - Translational motion. The crystalline state - Oscillations about a Mean position.

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1 The easy stuff; MOTION The gaseous state - Traslatioal motio The crystallie state - Oscillatios about a Mea positio The hard stuff; The liquid state - Coupled motios

2 MOTION IN POLYMERS LARGE SCALE MOTION PREVENTED BY RANDOM CLOSE PACKING IN THE MELT

3 THE NATURE OF THE GLASS TRANSITION Tg - a thermodyamic Trasitio or a kietic Pheomeo? The observed Tg depeds Upo the rate of heatig Or coolig ~ therefore Kietic. But is there a Uderlyig thermodyamic Trasitio? Reproduced with permissio from A. J. Kovacs, J. Polym. Sci., 30, 131 (1958).

4 THE CONCEPT OF FREE VOLUME Free volume is ot the same as "uoccupied" or empty volume. Molecules have thermal motio. For a material i the glassy state we ca thik of the motio as the balls oscillatig i a cage of their eighbors. These oscillatios create some "free volume" over ad above the empty space characteristic of radom close packig. Ordered Packig of Spheres Radom Close Packig of Spheres "uoccupied volume" Two dimesioal represetatio of the packig of spheres. For polymers, motio of chai segmets, ad ot the etire polymer molecule, is importat.

5 THE CONCEPT OF FREE VOLUME Free volume is ot the same as "uoccupied" or empty volume. Molecules have thermal motio. For a material i the glassy state we ca thik of the motio as the balls oscillatig i a cage of their eighbors. These oscillatios create some "free volume" over ad above the empty space characteristic of radom close packig. Free volume icreases with temperature as the amplitude of the oscillatios icreases. Free volume is ot equally shared betwee all the molecules, but fluctuates. At some istat of time oe molecule might be trapped i a local close-packed cage of its eighbors, while aother has Sufficiet "free volume" available to it that it bouces ito a ew positio. The idea that the Tg correspods to the poit where the free volume falls below a critical value was suggested by Fox ad Flory.

6 THE EFFECT OF MOLECULAR WEIGHT The eds of a chai have more freedom of motio tha the segmets i the ceter of a chai ad, crudely, ca be thought of as havig "more free volume". Low molecular weight chais have more eds per uit volume tha log chais, hece a higher free volume, hece a lower Tg. Fox ad Flory used such simple free volume argumets to obtai the followig equatio: = - K M Glass trasitios of polystyree fractios plotted as a fuctio of molecular weight, M (bottom) ad 1/M (top). From T. G. Fox ad P. J. Flory, J. Appl. Phys., 21, 581 (1950).

7 THE EFFECT OF CHAIN STIFFNESS Chai stiffess affects chai mobility. If there are bulky groups, such as bezee rigs, i the backboe of the polymer chai, there is a high eergy barrier to rotatios, which the oly occur at higher temperatures. Si O O Poly(dimethyl siloxae) C Polyethylee - 80 C Poly(pheylee oxide) C Icreasig Chai Stiffess

8 THE EFFECT OF BULKY SIDE GROUPS The presece of bulky pedat groups attached to the polymer backboe raises the Tg, through steric hidrace to bod rotatios. As the pedat group gets larger, the Tg icreases. However, as at some poit the attached groups o loger get i the way of bod rotatios as they get further ad further away from the chai. The effect of attachig a methyl group to the mai chai of PS, to give poly(_-methyl styree), is greater tha icreasig the size of the aromatic uit, because the close proximity of this group to the polymer backboe itroduces a higher degree of steric hidrace. Polymer Polyethylee Atactic Polypropylee Atactic Polystyree Atactic Poly(α-methyl styree) Atactic Poly(1-viyl aphthalee) Atactic Poly(viyl bipheyl) Chemical Structure - 80 C * CH - 10 C CH CH C CH 100 C 175 C 135 C 145 C Compare PaMS, PVN ad PVBP.

9 Poly(methyl methacrylate) C C O 105 C C C O O O Poly(ethyl methacrylate) 65 C Poly(propyl methacrylate) THE EFFECT OF FLEXIBLE SIDE GROUPS Tg decreases with icreasig side-chai legth. Substituets closest to the chai, the methyl ad ester group, provide the bulk of the steric hidrace. The rest of the attached side chai ca "get out of the way" of motios of the mai chai through rotatios aroud side-chai bods. Because these side chais icrease the free volume through their effect o the packig of the chais, the Tg is lowered. Icreasig Legth of Flexible Side Group Poly(butyl methacrylate) Poly(octyl methacrylate) Poly(dodecyl methacrylate) C C O O C C O O C C O O C C O O ( ) 3 ( ) 7 ( ) C - 2 C - 42 C - 62 C

10 THE EFFECT OF INTERMOLECULAR ATTRACTIONS AND CROSSLINKING Strog itermolecular attractios also act so as to raise the Tg. Atactic Polypropylee Atactic Poly(viyl chloride) CH Cl CH -10 C 87 C The chlorie atom ad methyl group have approximately the same effect o bod rotatios. The polar character of the Cl atom leads to stroger forces of attractio betwee chais, however, so that o average these groups are closer. The free volume is less ad the Tg is higher (reality is probably a bit more complicated tha this Similarly, cross-likig decreases free volume, because parts of the chai Are tied more closely together, hece Tg icreases.

11 THE EFFECT OF DILUENTS AND COPOLYMERIZATION Schematic diagram depictig the itermediate Tg observed i a miscible mixture, relative to oe that is phase separated Q: what would you expect for a radom copolymer vs. a block copolymer? 2 Edotherm 1 Mixture Two Phase Oe Phase The Tg of a mixture ca be simply ratioalized o the basis of free volume argumets to give the Fox equatio Temperature 1 = W W 2 2

12 CHARACTERISTICS OF THE CRYSTALLINE MELTING POINT Whe we use the word "meltig" we will mea the trasitio from a ordered crystallie phase to a disordered liquid phase, usually at a well-defied temperature. Edotherm Hysteresis peak C p T m Temperature A DSC plot showig a chage i the specific heat ( Cp) at the glass trasitio temperature (Tg) ad a edothermic peak at the meltig temperature (Tm).

13 MELTING - EQUILIBRIUM CONSIDERATIONS G f = H f - T S f AT EQUILIBRIUM G f = 0 HENCE Tm = H f S f THE TRICK IS TO RELATE THESE QUANTITIES TO MOLECULAR PROPERTIES. WE SHALL SIMPLY USE QUALITATIVE ARGUMENTS

14 THE EFFECT OF CHEMICAL STRUCTURE ENTHALPY CONSIDERATIONS Assumptio: ethalpy is simply related to the force of attractio betwee the chais. H m must be related to the differece i the forces of attractio betwee polymers packed i a regular array i the crystallie domais ad the forces betwee those same chais whe radomly itertwied i the melt. T m Polyethylee O C N 135 C 265 C T m = H f S f Nylo 6 H The forces of attractio betwee the simple hydrocarbo segmets foud i polyethylee are weak dispersio forces ( 0.2 kcal/mole). I cotrast, ylo 6 cotais the amide group, which forms hydroge bods that are a order of magitude stroger ( 5 kcal/mole).

15 THE EFFECT OF CHEMICAL STRUCTURE ENTROPY CONSIDERATIONS I the crystallie state a polymer chai is i a sigle ordered coformatio. Upo meltig the chai escapes the cage of the crystallie lattice ad ow has the freedom to sample all the coformatios available to it. Melt S f = k (l Ω melt - l Ω cryst )

16 ENTROPY CONSIDERATIOS - CHAIN STIFFNESS (SIMILAR INTERACTIONS) T m O Poly(ethylee oxide) 65 C Polyethylee 135 C T m = H f S f 400 C Poly(p-xylee) Polyethylee CH Isotactic Polypropylee T m 135 C 170 C Bod rotatios are ihibited by steric hidrace ad the umber of cofiguratios available to the chai becomes limited. CH Isotactic Polystyree 225 C