Prime, B.

Wunderlich, B.

English

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- The Equilibrium M lting of Polymer p-5 G - c d  
Bernhard Wunderlich and Bruce Prime 
densselaer Polytechnic Institute, Troy, N. Y. 
Department of Chemistry. 
For the last few years it has been possible to grow polymer 
crystals which have their molecular chain fully or at least 
largely extendedl. These crystals are, in contrast to the 
metastable folded chain crystals, often close to equilibrium. At . 
present extended chain crystals of polyethylene, polyoxymethylene, 
polycaprolactam, and polytetrafluoroethylene havebeen made2. New 
techniques for growing extended chain crystals are being studied3. 
With this development it becomes possible to discuss the question 
of equilibrium melting of polymers on the basis of exper imentac  
P e S U z t 8 .  
As a starting point the equations described Qy Flory and 
Huggins4 for a pure equilibrium polymer crystal, meZting i n t o  a 
soZut ion will be used. Somewhat reorganized this equation is: 
[. 11 - 1 - - 1 = - R i- 1Ki- ?- (x-l)vi - xui 2 XI 
T: 
T: AH P 
Where Tm is the observed equilibrium melting point of the 
polymer dissolving into a melt of volume fraction up.  
equilibrium melting point of the same polymer into its pure melt. 
AH is the heat of fusion of one mole of polymer. x is the ratio 
of molar volume of polymer to that of the second component i, and 
x is an appropriate interaction parameter defined per mole of the 
second component, which may also be polymeric. On decreasing the 
molecular size of the noncrystallizable component the [X-l)Vi 
term becomes more and more sLgn2ficant leading fhally, for x?lQ, 
and for a system with negligible interaction, to a limiting 
equation for melting point lowering: 
Tg is the 
equation 1 for different values of x .  
pRase diagram calculated using 
The other parameters were chosen to 
fit the case of polyethylene of mo- 405 
X 
4 
20. 
Figure 1 represents an eutectic "K 
1 ,y.. lecular weight 28 500. Tg is 413.1oK, R/AH = 1.23. 10-6, and x is 0.4. x equal 4,20,45, and 85 corresponds 400 approximately to molecular weights 
of 6 000, 1 300, 450, and 250, 
respectively. The melting points 
of these lower molecular weights5. 
Figure 1 are in order 408.50K, 387.40K, 341.8oK and 297.40K. Such low -- 
395~.o 0.5 vp 0 . 
i 
I 
https://ntrs.nasa.gov/search.jsp?R=19680017836 2020-03-12T10:46:18+00:00Z
melting points cause the eutectic point to be very close to the 
zero polymer volume fraction ordinate. Figure 1 represents thus 
the full phase diagram. 
poZymer it is necessary to derive a multicomponent eutectic- 
melting equation. 
that all different molecular weights crystallize in separate 
crystals. The equilibrium melting equation 1 has to be modified 
to accommodate the multicomponent melt. 
‘i is replaced by cui 
x is replaced by 2 
2 zni/xni(x) e CX.U./CU~ 1 1  
The interaction parameter is Cryst. 
assumed to be also an appropri- 
ate average. [A similar treatment 50 
was developed previously by 
Kilian for copolymers without. 
interaction6.) Figure 2 
represents the melting curve of 
a polyethylene calculated using . 
equation’ 1 and 3 assuming the 
lowest molecular weight melts 
into its own pure melt, the next 
fraction melts into a two component 
melt etc. The last trace melting would 
then be the highest molecular weight equilibrium crystal melting 
into a solution of all species given by the molecular weight 
distribution. 
To describe the meZting of a broad moZecuZar weight  homo- 
At ultimate equilibrium it m s t  be assumed 
c31 
- .x  
370 390 410 O K  
a u r e  2 
The marked experimental points are described below, 
To investigate the validity of the above equations two 
sets of experiments  were performed. A linear polyethylene 
was crystallized under elevated pressure so that its morphology 
.showed only extended chain lamallae by electron microscopy. 
Slices of 6 - 8 p  thickness of this polymer cut with a microtom 
were immersed in molten paraffins and sharply fractionated 
samples of polyethylene so that the volume ratio was about 
10. parts melt to 1 part crystals. The specific heat of this 
composite sample was then measured in a Perkin Elmer Scanning 
Calorimeter using previously established  technique^:^ At the 
suspected melting point a halt of 5 hours was scheduled. 
this time heating was resumed to detect any hea‘t *of Eusi.on, 
About 1% of residual crystals could be detected. By repeated 
trials on fresh samples at slightly different temperatures the 
d i s s o z u t i o n  temperature of extended chain polymer crystals in 
paraffins and well characterized fractions could be established 
to an accuracy of 1 O.S°K or better. 
superheating, a difficulty in fast measuring techniques, but 
still allows to work with milligram sized samples. 
After 
This proc‘edure avoids 
The second set of experiments  delt with a linear polyethylene 
,/ 
of known molecular weight distribution. It was crystallized at 
5000K and 4800 atm. hydrostatic pressure. Its density at atmo- 
spheric pressure at 298OK was 0.995 
showed again only extended chain crystals. About 1 g of this 
material was sealed in a dilatometer and its mel t ing  oharac$er i s -  
tios 
volume was converted tq crystallinity using known X-ray and melt 
specific volumes as a function of temperature. 
of the dissolution 
shown in Fig. 3 ,  4.b 
while those of the OK 
dilatometry are 
indicated by the 405 
filled circles in 
Fig. 2 .  
out curve in Fig. 
3 represents the 
experimental data 395 
well. It has been 
calculated using 
equation_$, insert390 
ing the following 
independently log Molecular Weight determined exper imenta l  
parameters .  TS for infinite 
molecular weight is 414.6OK as founron up to 1 0 ~  extended chain 
single crystals melting into a 1.4 lo7 M.w., melt8. For lower mole 
cular weights the interpolation formula derived by Broadhurst5 wa 
modified with this experimental value to: 
where n is the number of carbon atoms. Equation 4 has .been shown5 
to work well for paraffins above 44 carbon atoms with a value of 
414.3. The change to 414.6 makes it also, fit the polymer experiments 
cited here. AH as a function of temperature was calculated using 
p value of 929 cal/rnole CH2 at 414.60K as determined by calorimetry: 
The variation with temperature was calculated using the thermodynamic 
relationship, 
Experimental values for the heat capacity of completely amorphous 
and completely crystalline polymer were taken from references 
7,9, and 10. Molar volumes and densities of paraffins are also 
availablell. x and TS for the extended chain crystals used in 
the measurements can be calculated for the best fit of-equation 1. 
A constant value of 0.4 for x and 412.1°K for Tfl was obtained. 
412.1°K corresponds according to equation 4 to a molecular weight 
Of 15 000. The experimental number average molecular weight in 
the crystals used was 8 200, about 40% by weight of the sample 
has a molecular weight above 15 000. Electron microscopy can 
g/ml. Electron microscopy 
was determined by standard dilatometry, \The measured specific 
The Pe8UZt8 415 
experiments are * T *~.-*-.-@- 
? 
The drawn 400 \ 
Figpure 3 
T: = 414.6 (n-1.5) / (n+S.O) r41 
dAH/dT = ACp 151 
- 3- 
detect lamellar thicknesses up:to 20 000 8. 
in the 1-3 000 R range. 
412.1°K. 
experiments carried out with paraffins and folded chain crystals. l 2  
The analysis of the diZatomster  d a t a  Fig. 2 shows 
agreement of the calculated curve and experimental data for the 
first 50% melting. At higher temperatures the experimental melt- 
ing curve is sharper  than the calculated one. The maximum 
melting point finally is about 2.50K lower than the calculated 
one. This means the last 40% by weight of the extended chain 
crystals behave as if their chain length corresponds to about 
15 000 molecular weight. The only change being the increase 
of molecular weight of the melt. This experimental observation 
parallels the dissolution experiments described above. It could 
be interpreted such that about 153300 molecular weight little 
separation into different molecular weights on crystallization 
took place under the chosen crystallization conditions. 
Most lamellae were 
This agrees reasonable well with TB of 
A constant value of x seems contradictory to similar 
Summariaing it can be said that if crystals which are close 
to equilibrium are molten, keeping equilibrium throughout 
the experiments, previously derived equilibrium melting equations 
can be used for the description. A self consistent set of homo- 
polymers crystallized with a largely extended chain conformation 
seems to be caused by a diluent effect of the.%Gwer molecular 
weight. The chosen pressure crystallization conditions seemed 
to be able to achieve separation into different molecular weight 
cpystals up to about 15000 molecular. 
AoknowZedgements: This work was supported by the Office of 
Naval Research and the National Aeronautics and Space 
Administration. The fractions of polyethylene were prepared 
and characterized by R. H. HorowZtz of W, Gyace C o .  Some 
calorimetry was carried out by C. M. Cormler of our laboratory. 
1, 
2 .. 
3 .  
4 .  
5. 
6. 
7 .  
8 ,  
9. 
10 
11. 
12. 
Re Ee r e nc e s 
E!. Wunderlich and T. Arakawa, J .  PoZymer Sei., 2A 3697 (19641 
B. Wunderlich , E. Hellrnuth, M. Jaffe, F. Liberrnand 
J. Rankin, KoZZoid q ; ,  and 2.. PoZymere,' '204, - 125 (1965). 
B,-Wunderlich and F, Liberti, BuZZetin A m .  P h g s ,  S O Q , ~  
11, 248 (19662 
S e  for example M. L. Huggins, PhysicaZ Chemistry of High 
PoZymers, J. Wiley, N. Y. p. 73 1958 
M. G. Broadhurst J. Chem. Phys.,"36, 2578 (1962) 
H. G. Kilian XoZZoid-Z and 2 .  PoZCere' '202, 97 (1965). 
B. Wunderlich , J. Phys. Chem.,"69, 20781965) 
T. Arakawa, and B. Wunderlich, JTPoZymer S e i .  to be 
published,.GUPAC Preprint 42 Prague 1965. 
B. Wunderlich, and M. Dole, J .  PoZymer Sci., 24 ,  201 (1957) 
B. Wunderlich, J .  Chem. P h y s . ,  3 7 ,  1203 (19623 
G. Egloff, Physical Constants o37Hydrocarbons, Vol V., 
Reinhold Publ. Co. New York (1953) 
See for example A. Nakajima and F. Hamada, KoZZoid-Z and 
2 .  PoZymere, - 2 0 5 ,  5 5  (1965) 
-'f - 


The equilibrium melting of polymers

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