The melting points of chain polymers

JOURNAL OF POLYMER SCIENCE VOL. XVI, PAGES 323-343 (1955)

The Melting Points of Chain Polymers

C. W. BUNN, Imperial Chemical Industries, Ltd., Plastics Division, Welwyn Garden City, Herts, England

INTRODUCTION

When a crystalline polymer is heated, the first-order change from a crystalline solid to an amorphous phase (which may be a viscous liquid or a rubber-like solid, depending on the length of the molecules) is undoubtedly the same type of molecular process as the melting of a monomeric substance. It is true that there are two points of difference in the behavior of polymers and monomers: no long-chain polymer is completely crystalline, and melting occurs over an appreciable range of temperature, not sharply as in monomers; nevertheless, the change in the x-ray diffraction pattern from a sharp pattern characteristic of three-dimensional order to a very diffuse pattern similar to that of a monomeric liquid, together with the absorption of a considerable latent heat of melting, indicates essentially similar molecular processes, and in attempting to understand the melting points of polymers in relation to their molecular structures, it is justifiable and indeed highly desirable to include monomeric substances in the discussion and to link up the two classes of substances by tracing the influence of molecular length of the melting point.

The advantages of this approach are empirical rather than theoretical, for it must be admitted that even for monomeric crystals of the simplest substances the process of melting is not a t all well understood from any fundamental theoretical standpoint. At the present time there is little hope of predicting theoretically the relation between chemical constitution and the melting point, even for simple monomeric compounds. Never- theless, i t is now possible, by empirical comparative methods, t o discern in a qualitative manner the main molecular characteristics which determine the melting points of monomeric compounds, and this knowledge is of value in approaching the melting points of the long-chain polymers.

THEORIES OF MELTING

Before proceeding in this way, it is worth while glancing a t the two main theoretical approaches to melting which have been made in recent years. Lindemann' suggested that a crystal melts when the amplitude of vibration of the molecules (which increases with rise of temperature) reaches a critical magnitude related to the distance between neighboring molecules; a t this

323

324 C. W. BUNN

point the crystal, so to speak, shakes itself to pieces. Lennard-Jones and Devonshire,2 on the other hand, focus attention on the increase of lattice defects in crystals as the temperature increases, and show that the lattice eventually becomes unstable with respect to the liquid phase as the proportion of defects grows. The type of lattice defect envisaged-transfer of molecules to interstitial sites-seems very unlikely t o occur; but the particular type of defect is perhaps not so important as the general con- cept of' dcfects; certainly in most crystals, defects such as vacant lattice sites, or molecules in correct sites but wrong orientations, are likely to be much more common. Of coursc, the distortions due t o thermal waves Lhrough the crystal are also defects, and so perhaps the defect theory, considered quite generally, does embrace both approaches; but one should distinguish bctw een distortion waves going through the crystal and isolated displacements and misorientations of molecules. It is worth remarking that, in high polymer crystals, one cannot displace or rotate a chain unit without dragging the rest of the chain (which extends through the entire crystal) with it to some extent; a rigid chain would have to move as a whole; in a more flexible molecule, distortion a t one point would produce waves along the chain. We are therefore inevitably led t o focus attention on thermal wave motions in the crystals. Furthermore, if the melting point depends on the amplitude of the thermal vibrations, then the degree of flexibility of any molecule, monomeric or polymeric, must influence the melting point strongly; in a very flexible molecule small portions of the molecule vibrate semiindependently, so that the melting point would be like that of the small vibrating units-that is, it would be much lower than that of a comparable rigid molecule. Therefore, in considering the melting points of monomeric crystals, it is necessary to distinguish between rigid and flexible molecules, and, for simplicity, t o deal with rigid molecules first.

The melting point, T,, is of course equal to A H / A S , the ratio of latent heat of melting to elitropy of melting; but a t the present time the approach to melting points by way of this expression does not appear profitable. To understand or predict melting points by this approach, it would be necessary to predict, from the chemical constitution, first of all the latent heat of melting, and, quite independenlly, the entropy of melting. The relations between these quantities are a t present even more obscure than the direct relation of melting point to chemical constitution. For this reason, this aspect of the subject is by-passed, and direct correlations between chemical constitution and melting temperatures are sought.

FACTORS CONTROLLING MELTING POINTS OF MONOMERS

In monomeric substances, the melting point for a rigid molecule (one in which no large changes of configuration such as are produced by rotations around single bonds are possible) would be expected to depend on the total forces holding the molecule in place in the lattice, i.e., the cohesion energy,

MELTING POINTS OF CHAIN POLYMERS 325

E, which can be measured experimentally as the molar latent heat of evaporation, L ( E is taken as L - RT, the second term being a small correction for the work done on expansion). If this were all, we should expect a simple relation between melting and boilirlg points, since the boiling point is directly proportional to the molar latent heat of evaporation of the liquid a t the boiling point (Trouton's rule), which in turn is approximately proportional to the latent heat of evaporation of the crystal. In actual fact, the melting points of rigid molecules vary very widely, some being nearly equal to the boiling points while others are less than half the absolute boiling points. The melting points of all rigid molecules for which I have been able to find the necessary data (several hundreds) lie in the broad band ABCD in Figure 1, in which the horizontal axis gives cohesion cnergy

i 300

0 P !i

t '100

I:

y- F L E X I B L E

40.103-- _- 2 0 30

M O L A R C O H E S I O N E N E R G Y ( C A L S )

Fig. 1. Melting points of monomeric substances.

a t the boiling point. (The cohesion energy figures were obtained from the latent heats of boiling, whcre these were available; or from the boiling point and Trouton's rule; or, failing this, from an additive scheme (dc- tails given later) in which each functional chemical group is associated with a definite cohesion energy increment-a scheme which works fairly well for all substances for which it can be tested.) A plot of melting points against boiling points would look very similar to this.

An attempt to discern empirically what molecular characteristics determine the position of any substance in this broad band showed that there is a convincing correlation between the melting point and the symmetry of general over-all shape; not molecular symmetry in the strict sense-it is general over-all shape that is important. All molecules of approximately spherical shape (ranging from the rare gascs, through SF6 and the like, to cage molecules like camphor derivatives) are a t the top of the band, with melting points nearly equal to their boiling points; most cylindrical mole-

326 C. W. BUNN

cules are in the first subdivision, flat symmetrical molecules in the second, flat unsymmetrical molecules in the third, and asymmetric molecules in the fourth. The tendency for spherical molecules to have high melting points is already recognized3; but it does not appear to be generally realized that the correlation is remarkably good-for there are no exceptions in this group-all the substances fall nearly on a straight line; nor is it realized that the influence of shape extends through the entire shape-spectrum. Another general tendency is that within any one type of shape-symmetry, a skeletal shape with pronounced hollows in the outline depresses the melting point (details will be published elsewhere).

The mechanism whereby low shape-symmetry depresses the melting point is a matter for speculation. Melting is a catastrophic breakdown of a highly organized vibrating system. Vibrating systems are notoriously susceptible to resonance and feedback effects: any €eedback is liable to lead to a great build-up of amplitude until the whole system gets out of control and disintegrates. In crystals composed of nonspherical molecules, rotation of one molecule affects its neighbors (or some of them) by cog-wheel effects. One of the consequences of this is that impulses may work round in circles and thus produce feedback effects; and the lower the shape-symmetry of the molecules, the greater the number of different types of rotation which can lead to such feedback effects ; an asymmetric molecule presents an unsymmetric outline from all points of view and thus may have cog-wheel effects by rotation round any direction. Consequently, the lower the shape-symmetry, the greater the chance of feedback effects and therefore the greater the amplitude of the vibrations a t any temperature and the lower the melting point (for a given cohesion energy). This would account not only for the general effect of shape-symmetry but also for the depressing effect of skeletal shape.

Since molecular shape influences the melting point strongly, it might be supposed that the effect has something to do with the eficiency of packing of the molecules in the crystal. Kitaigorod~ki~ has shown that the proportion of the space occupied by the molecules does vary considerably in different organic crystals; and a low molecular packing efficiency in a crystal might lower the melting point. Some calculations of this quantity show, however, that this factor does not account for the large effects observed. The less symmetrical molecules do not necessarily pack more openly than highly symmetrical ones; packing efiiciency does not depend on symmetry but on highly specific shape characteristics. Possibly the smaller differences between the melting points of substances of the same symmetry type and similar cohesion energy may be influenced by molecular packing eficiency; but the large effects of shape-symmetry do not appear to depend on it.

Flexible chain molecules melt lower than comparable rigid molecules, as we should expect. This is well illustrated by the series of normal paraffin hydrocarbons, also shown in Figure 1 : with increasing molecular

I shall offer one simple suggestion.

One other possible influence should be mentioned.


length, the melting point a t first rises (steadily, cxcept for the well-known alternation of odd and even members in the shorter molecules), but eventually becomes independent of molecular length, approaching the limiting value of 136.5OC.5 for high molecular polynicthylene (which would be far off to the right of the diagram). But the most striking illustration of the effect of molecular flexibility is given by the polyphenyls (also shown in Fig. 1) : when the rings are linked para fashion, so that they are bound to remain in a straight line even though individual rings rotate, the melting point rises rapidly with the number of rings (almost as rapidly as in the fused-ring series, naphthalene-anthracene, etc.), but when the rings are linked mela fashion so that rotation round bonds causes large changes of configuration just as in the parafin hydrocarbons, the melting point rises only very slowly with the number of rings.6 para-Pentaphenyl melts a t 395"C., while the meta compound melts a t 112°C. The para seven-ring compound melts a t 54j°C., while in the meta series even the one with sixteen rings only melts a t 321 "C. The longer flexible molecules lie, in the diagram, far below even the least symmetrical rigid molecules which have similar cohesion energies.

FACTORS CONTROLLING THE MELTING POINTS OF HIGH POLYMERS

The melting point of each chemically different long-chain polymer may be regarded as the limiting melting point of the appropriate series of shorter chained substances. Consequently, if the relation between melting point and molecular length is of the same general nature in the different series, we should expect that high or low melting points in the polymers would be associated with corresponding high or low melting points in the relevant short-chain monomers. This is borne out by the facts, in the few cases

I 10 20 30 4 0 so x 103

M O L A R C O H E S I O N ENERGY (CALS.)

Fig. 2. Melting points of chain series.

328 C. W. BUNN

for which data are available. I'olytetrafluorethylene, (-CF2-)p, melts a t 33OoC., very much higher than polymethylene, (-CH2-)p, and corre- spondingly the shorter fluorocarbons melt higher than the corresponding parafins (see Fig. 2). The aliphatic polyesters like polytetramethylene adipate melt lower than polymethylene ; and corresponding short-chain esters like dibutyl adipate and butyl valerate (Fig. 2 again) also melt lower than normal hydrocarbons of the same cohesion energy (or even of the same chain length).

The conclusions drawn for rigid monomeric molecules lead us to expect that the melting points of high polymer crystals will depend on some function of the cohesion energy of the molecules, on the degree of flexibility of the chains, and on certain shape effects-probably the degree of departure from cylindrical shape. There may of course be other factors, but these three are likely to be the most important. To make further progress along these lines, it is necessary to corisider what molecular characteristics may appropriately be used as indications of the magnitudes of the cohesion energy and flexibility factors.

It is obvious that the cohesioIi energy of the whole molecule, which was used in discussing monomers, is not appropriate for polymers, since for long molecules of any one series the melting point is independent of molecular length. The reason for this independence is not merely that a polymer crystal contains only segments of molecules (any one molecule threads its way through several crystals) ; it is also that even in one crystal different parts of the same molecule vibrate semiindependently-or, rather, they influence each other by wave motions just as do the separate molecules in monomer crystals. The cohesiori energy and flexibility factors are both intimately concerned here, and it would appear that for a simple type of chain like polymethylene, (-CH2-)p, it would be appropriate to refer to the cohesion energy per chain unit (in this case CH2) and to the energy required to rotate round the chain bonds, since this is the chief source of flexibility. (The energies needed for bending or stretching bonds are much higher and need not be considered.) For more complex molecules in which the chain units are not all of the same type, there are inevitable diEculties; where there are two or more different chain units (as in polyesters, with CH2, C=O, and 0 chain units, or polyvinyl compounds generally, with CH2 and CHR) the cohesion energies for the different chain units are likely to be very dissimilar. It may be appropriate to refer to the average cohesion energy per chain unit. Similarly, in all such molecules the energy required for rotation round the chain bonds is not the same a t each bond: the average energy for rotation may not be a significant quantity; in some circumstances the most easily rotating bonds may dominate the situation (see later discussion of chain esters).

Estimation of Intermolecular Forces

The cohesion energies of chain units in polymer molecules may be estimated by an additive system, based on the properties of substances com-


posed of small molecules, in which a definite increment is associated with each functional group of atoms. More than one such scheme has been pro- posed in the past7.8 and figures relevant to some of the well-known polymers

TABLE I COHESION ENERGY AND VOLUME INCREMENTS FOR COMMON GROUPS

Cohesion energy, Volume, cc. per mole Group cal. per mole

-CK- 680 21.8 -CH3 1700 27.8 -CeH4- 3900 83.9 -C& 5400 89.9 -CH=C€f- 1700 32.0 -C(CH,)=CI 1- 2400 53.8 -CII=CH, 2700 37.8 -C-CH 2750 -c€r(cIr,) - 1360 4.2 .8 -C (CH3)z- 1900 65.4 -CH(CsHd 4300 105.7 -CFz- 760 34.0

-

-CFa iaoo 46.1 -CCIz- 3100 53.4 -CHCI- 2360 37.6 -Cl zaoo 21.8 -Br 3100 30.5 -1 4200 40.5 -co- 2660 21.6

-CO-0- (ester) 2900 28.9 -CO-0-CO- (anhydride) 3900 50.5 -OH (alcohol) saoo 14.9 -COOH 5600 36.5 -CHO€I- 5100 30.7 -CH (CO'OCH,) - 3300 72.5 -CH(O.CO.C€I,) - 3500 72.5

-SH 3380 -NHz (amine) 3100 -NH- (amine) 1500 14.6 -CO'NH- 8500 36.2 -CO.NH, 8500 42.2

-0- 1000 7 . 3

- -S- 2200 -

-

-0.CO.NH- a740 43.5

have been given by Mark.g My own system is based on the fact that the cohesion energy ( L - R T ) of a small-molecule liquid a t the boiling point can be represented to a fair approximation as the sum of increments due to the constituent functional groups. (It is best not to attempt to sub- divide as far as atoms.) Table I gives figures for some of the common groups. These figures are appropriate for the molecular volumes a t the boiling point, which, be i t noted, are also (for small molecules) additive functions of the volume increments of the atomic groups, to a similar de-

330 C. W. BUNN

p e e of approximation. To obtain the cohesion energy for any molecule, it is only necessary to add the increments for the constituent groups. There is no reason why these figures should not be used for high polymer molecules, if it is remembered that they are appropriate for a molecular volume equal t o the sum of the corresponding volume incrcmcnts given in Table I. The molecular volumes in actual polymer specimens are smaller than these sums, and the cohesion energies therefore greater. A correction for the smaller molecular volumes can be made: for hydrocarbons, it is found empirically that if EL and Ez are the molar cohesion energies a t molar volumes V1 iind Vz, respectively, then:

vz - v, - 1.73---- ___.~ - EI -

E2 Vl

and this is probably also true for other substances in which iritermolecular forces are of van der Waals’ type. (The expression holds whether there is a change from liquid to solid or not.) For the discussion of melting points, cohesion energies of‘ different substances in some standard state should be compared; it would not be appropriate to compare them a t room temperature-in fact, the only satisfactory basis for comparison is a t the absolute zero of temperature; but since there are not suficient data on heats of va- porization a t low temperatures and the extrapolation from values a t room temperature and above would be a long one, this is scarcely practicable. Probably, as a general indication of the magnitude of intermolecular forces, comparison of the cohesion energies a t the “boilirig point” volumes is suficient. Figures for a number of polymers on this basis are given in Table 11. (Since the zero point volumes of monomers are, according to the limited available information, an approximately constant fraction (0.7) of the boiling point volumes, the zero point cohesion energies would be higher than the “boiling point” cohesion energies by an approximately constant factor (about 1.7).)

Molecular Flexibility. In small rnolecules like ethane, H3C-CH3, and n-butane:

cJr2 CII, / \ /

CH:, CH1

rotation round the central bond is accompanied by energy changes which pass through three minima (at the staggered positions 120” apart) and three maxima. In ethane the potential barriers to rotation (heights of the maxima) are all equal, the heights being about 3000 cal. per mole; in n- butane the energy for the plane zigzag configuration is lower than the other two minima by 800 cal., but the barriers are again about 3000 cal. in height. I n a long unbranched CH, chain the situation is presumably similar to that in n-butane.

The vibrations of such a chain molecule in a crystal are largely made up of rotations round the chain bonds. It is likely that rotations of 120” to


TABLE I1 COHESION ENERGIES OF POLYMERS

No. of chain

E units

680 1 760 1

3040 2 3780 2 2580 2 19380 18 23800 14 26520 18 5800 + 680n n + 2 9880 10 2900 + 680n n + 2 11060 J

9700 + 680n n + 3 14900 5 17620 9 16320 10

18320 10

16960 + 680n n + 8

8740 + 680n n + 3 1000 + 680n n + 1 2200 + 680n n + 1 4400 + 680n n + 2

3760 3

Average E per chain

unit

680 760

1520 1890 1290 1076 1700 1474

988

2212

2980 1958 1632

1832

-

-

-

-

-

-~

-

1250

M.P., OC.

(Ref.)

136.5 ( 5 ) 330 -

200 (10)

149 (11) 265 (12) 215 (12)

52 (13)

264 (12)

346 (12)

0

-

-

-

214 (12) 146 (12)

240 (14)

-

(12,151 (12) (16)

cis 20 trans 60

-

the next energy minimum seldom occur, because owing to the zigzag configuration such large rotations would produce gross distortions, too large to be tolerated in the structure; the rotations which occur most fre- quently are therefore represented by oscillations in the lowest trough of the energy diagram. Since the energy necessary to climb up the sides of the trough is some function of the height of the next maximum (a cosine curve is usually assumed), it is reasonablc to take the magnitude of this energy barrier as an indication of the degree of flexibility of the molecule. Figures for energy barriers in several other types of small molecules have been collected by McCoubrey and UbbelohdeI7; it is significant that they are of the same order of magnitude (1000-5000 cal. per mole) as the cohesion energy figures for chain units; this is the reason why these two factors- intermolecular forces and molecular flexibility-are of equal importance in determining the melting points (and many other properties) of high polymers.

The amount of information on potential barriers relevant to the principal types of chain polymers is unfortunately scanty, and the figures are ad-

332 C. W. BUNN

mittedly very roughz3: in some cases, two estimates for the same molecule differ by a factor of 2 or more, so that these are of little value for the discussion of individual polymers. For this reason it is best a t present to proceed by empirical comparative methods, while keeping these general concepts in mind. We shall now discuss some of the well-known polymers against this background. It will be shown that reference to the melting points of monomeric substances often throws light on those of high polymers.

MELTING POINTS OF POLYMER SERIES

Polymethylene and Polytetrafluoroethylene. The cohesion energy of a CF2 group is very nearly the same as that of a CHZ group (see Table I), lierice the very much higher melting point of the fluorocarbon polymer cannot be accounted for by any difference of intermolecular forces. We look, therefore, for a difference of molecular flexibility. The potential barrier for rotation in hexafluoroethane, FZC. CF3, is reported'* to be 4350 cal. per mole-considerably higher than that of ethane, 3000 cal. per mole; the difference is thus in the right direction to explain the high melting point of the fluorocarbon polymer, assuming that similar figures apply to chain molecules. The ratio of the two figures (1.45) is about the same as the ratio of the absolute melting points of the two polymers (603/408 = 1.48) ; but the agreement is probably fortuitous. The absolute melting point would not be expected to be directly proportional t o the potential barrier to rotation, for a chain polymer with zero barrier to rotation would not have a melting point near absolute zero.

It has been pointed out that owing to the fact that fluorine atoms are larger than hydrogen atoms, the surface of the fluorocarbon chain is more filled in, and the chain is in fact more nearly cylindrical, than that of the hydrocarbon chain; and it has been suggested' that this molecular feature is responsible for certain unusual properties of polytetrafluoroethylene (the disorder transition a t 20-30 "C., and the very low coeficient of friction). Is the cylindrical shape also responsible for the very high melting point? It is true that among rigid monomers substances with cylindrical molecules melt higher than those with flat lengthy molecules of compact shape and high symmetry; but this degree of difference of shape is associated with only moderate differences of melting point (50" or less); and since the difference between the shapes of hydrocarbon and fluorocarbon chains is less still, it probably ac- counts for very little of the difference between the melting points of the hydrocarbon and fluorocarbon polymers. The difference must therefore be due chiefly (as suggested above) to the great rigidity of the fluorocarbon chain. To what extent this greater rigidity is due to the greater size of the fluorine atoms (leading to hindered rotation), or to more subtle bond- orientation effects, is not known.

The melting points of many different polyamides are now

Shape effects should be considered.

Polyamides.


known. They are all higher than that of polymethylene, and there is a general rise of melting point with the proportion of amide groups in the chain; this presumably means that there is no great difference of chain flexibility, so that the much higher cohesion energies due to the hydrogen- bonding amide groups have a dominant influence. There is, however, in a plot of melting points against proportion of amide groups (which is equivalent to a plot against cohesion energy per chain unit), a considerable spread in the array of points (for details, see refs. 20,21), and it is a striking fact that polyamides in which there are even numbers of CH, groups between the amide groups melt high, those with odd numbers of CH2 groups melt low, and those with mixed odd and even sequences of CI-I, groups (such as even diamine-odd diacid polymers and vice versa) melt a t intermediate temperatures. It is also interesting that the "even" type polymers fall approximately on a straight line (reproduced, on the present basis of cohesion energy per chain unit, in Fig. 3) : evidently, other things being equal,

POLYESTERS

----I , 0 0 0 1 0 0 0 3 0 0 0

C O H E S I O N ENERqY P E R CHAIN UNIT ( C I L S . )

Fig. 3. Melting points of polymer series.

there is a linear relation between melting point and cohesion energy per chain unit, a t any rate for those polymers in which the amide groups are not too sparsely placed. This straight line, however, does not pass through the point for polymethylene; nor does it pass through the absolute zero of t empera tu re i t cuts the temperature axis a t about -50°C. The fact that the line passes below the point for polymethylene may mean that certain bonds in polyamide molecules are a little more flexible than those in a CH2 chain. There is no independent evidence on the barriers to rotation in such molecules; the CO-NH bonds appear to have some double-bond character, which is usually associated with additional rigidity, and so any

334 C . W. BUNN

additional ease of rotation must be in the adjacent CO-CH2 and NH-CH2 bonds; although estimates of barriers in simple ketones and amines have been made, these niay not be relevant to bonds adjacent to an amide group.

It has been definitely shown2’ that in the crystal structure of one of the ‘ ‘ odd” polyamid es-polycaproamide-all the possible hydrogen bonds are made normally just as in the “even” polymers; it seems likely, therefore, that the low melting points of “odd” members in general are not due to any failure of hydrogen bond formation. This contrast between odd and even polymers recalls the alternation of melting points of odd and even chain monomers (with even members always having the higher melting points) which runs through the whole of organic chemistry; and it is par- ticularly interesting to find that while in the normal parafin series the melting point curves for odd and even members are only a few degrees apart, the difference is very much increased for all chains having heavy or strongly bound groups on both ends; it is about 50°C. for the low-er dicarboxylic acids and diphenyl derivatives, decreasing with increasing number of CH2 groups. The situation is similar in the polyamides-there are CH2 sequences between the amide groups which are strongly bound to neighboring molecules; and here again the difference between odd and even members decreases with increasing length of the CH2 sequences. The quite general occurrence of the phenomenon in such diverse groups of monomers as acids, amides, chlorides, bromides, iodides, and phen yl derivatives rules out any specific influences of crystal structure, and suggests a fundamental cause such as the effect of an odd or even number of units on the pattern of vibrations in the crystals; it appears that the anchoring effect of the heavy groups on the ends of the chain is more effective when the chain is even than when it is odd. It may be remarked that the end bonds con- necting the CH2 chain to the anchoring groups are parallel to each other in an even chain, but are a t an angle of 110” in an odd chain; if melting is due to the uprooting of the anchoring groups by the more freely vibrating CH2 chain, we must ask why this is more easily done when the end bonds are inclined to each other than when they are parallel. The answer to this question is not obvious, but it niay well be connected with other effects referred to below which appear to depend on whether rotatable bonds are parallel or inclined.

Polyesters. Aliphatic polyesters melt lower than polymethylene, and there is a general decrease of melting point as the proportion of ester groups in the chain increases, in spite of the increase of intermolecular forces by the polar ester groups. (A detailed diagram has been given elsewhere,20 but the points are reproduced in Fig. 3.) This suggests immediately that in the ester group there is a bond round which rotation is considerably easier than in a CIL chain. Figures for potential barriers to rotation in simple substances (I:CH3)zC0, 1400 cal. per mole; (CH3)20, 2500-3100 cal. per mole) suggest that the CHZ-CO bond is the easily rotating one, but there are several reasons for rejecting this suggestion and attributing espe- cially easy rotation to the 0-CH2 bond: (1) Monomeric chain ketones melt


a little higher than the corresponding normal hydrocarbons; on a molar cohesion energy basis they fall nearly on the same curve as the hydrocarbons, suggesting that CH2-CO and C112-CI-12 bonds rotate equally easily. (9) All chain ethers, monomeric as well as polymeric, melt lower than the corresponding hydrocarbons; this is the clearest indication of easy rotation about the 0-CH2 bond. (3) In the crystal structure of polyethylene terephthalate the ester group

co CIT, / \o/ \

is nearly planar, whereas in polyethylene adipate there is considerable departure from planarity by rotation of 80' about the 0-CH, bond; such a difference, brought about presumably by packing requirements in the two crystals, suggests easy rotation about this bond.22 This conclusion implies either that the estimates of potential barriers in acetone and ether are seriously in error, or that these estimates which apply to the rotation of methyl groups do not apply to chain molecules with groupings

c119 CII,

It should also be mentioned that since chain anhydrides R.CO.0.CO.R melt lower than hydrocarbons, the C0-0 bond may also be easily rotatable.

There is one other generalization which throws an interesting light on the question of flexibility of chain esters. The melting points of monomeric chain esters with one ester group in an unbranched hydrocarbon chain show (Fig. 4,) that for a given chain length the melting point decreases as the ester group moves from the end toward the center of the chain. (There are not enough data to demonstrate this for any one series of isomeric

5 10 IS 20 x 103

MOLAR C O H E S I O N ENERGY (CALS.)

Fig. 4. Melting points of monomeric chain esters.

336 C . W. BUNN

esters, CH,(CH2);C0.O.(CH2),CH3, where m + n = constant, but the assembled data for a variety of esters in Figure 4 show it clearly enough.) This is exactly what one would expect if there is easy flexibility of the molecule a t the ester group: a hinge near the end of the molecule would make little difference to its vibrations, but a hinge a t the center divides the molecule into two half-size units which would vibrate with greater amplitude than a full-length unhinged molecule. The same is true for chains containing two ester groups: the lowest melting point is attained when the ester groups divide the chain into three equal portions. There are indications of similar effects in polymeric esters: the melting point (70-16' C.) of poly(ethy1ene se bacate), (-0(CH2)2O*CO(CH2)&0-),, in which there are alternate long and short segments, is higher than that (56-59" C.) of its isomer poly(hexarnethy1ene adipate), ( - ~ ( ~ ~ ~ ) 6 ~ ~ ~ ~ ( ~ H 2 ) 4 C O - ) ~ , in which the segments are more nearly equal in length.

Polyesters in which there are odd CH2 sequences melt lower than isomers with even sequences.20 The differences are, however, smaller and less consistent than in the polyamides; this may be connected with the fact that the cohesion energy of an ester group is much smaller than that of an amide group, for it will be recalled that in monomeric chain compounds the dif€erences between odd and even melting points show up most clearly for molecules with the most strongly bound end groups. The aliphatic polyesters with the highest proportions of ester groups show extreme diver- gences from the rest20; these might be regarded as strong odd-even effects coming in rather suddenly, or possibly they are special effects due to the very close proximity of the dipolar groups, which by their interaction may stiffen the even molecules (where the dipoles are oppositely directed in a zigzag molecule and therefore give this configuration additional stability) and increase the flexibility of the odd ones in which the dipoles would be parallel and therefore would repel each other, decreasing the stability of the zigzag configuration.

Aromatic polyesters melt very much higher than aliphatic ones; here the flexibility of thc ester group is more than offset by the presence of the rigid benzene ring. In Figure 3 the melting points of several series are plotted on the basis of cohesion energy per chain unit. CEt, 0, CO, and CsH4 are each taken as single chain units, except when a CO group is directly joined to a benzene ring, when the whole group

in the terephthalates, is taken as :I single chain unit which owes its rigidity to resonance effects. On this basis the melting point^'^*'^ of the series -CO~C6H4CO0.(CI-12).0- (tereph thalates), - ~ ~ ~ ~ , ~ 4 ~ ~ ( ~ ~ , ) , ~ ~ ~ , ~ , ~ -

CO.O(C~&).0--, - ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ - ~ ~ ~ ~ ~ ~ ~ ( ~ I I , ) , ~ - (in which the diphenyl unit is taken as a single chain unit), and the single substance -COCH2- c,r-I,.co.o.cH~.c,€r.cH2.o- fit fairly well into a coherent band, and this is taken as some justification of the method of representation and the ideas


on which it is based. Where there are long sequences of CH2 groups, the melting points tend toward that of polymethylene, although it is important to note that there is a minimum in the curve-that is, some of these polyesters melt a little lower than polymethylene. There are again marked odd-even effectsI2-in any series the polymers with even CH2 sequences melt high, those with odd sequences melt low.

These polymers, containing the grouping -0.CO.- NH-, form hydrogen bonds like the polyamides, giving high cohesion energy, but a t the same time they contain O-CH2 bonds like the polyesters, so that the molecular flexibility would be expected to be greater than in the polyamides. The melting points are, as might be expected, intermediate between those of the polyamides and aliphatic polyesters; and again those with even CH2 sequences melt higher than those with odd sequences.20 In Figure 3 they are plotted on the same basis as the other groups of polymers: they fit into the same band as the aromatic polyesters.

When CH2 groups in a chain are replaced by oxygen or sulfur atoms, the melting point is a t first reduced, in spite of the increase of cohesion energy (see Table 111); this applies to monomeric and polymeric substances alike, and suggests that the S-CH, bond, like the 0-CH2 bond, is easily rotatable. The barrier to rotation in (CH&S, 2000 cal. per mole,17 is consistent with this conclusion (if the estimate can be trusted), for it is lower than that in (CH&CH2. For higher proportions of sulfur there is an increase of melting point. Disulfide polymers containing two linked sulfur atoms in the chain reach a lower minimum than the thioethers, indicating that the S-S link is still more flexible; this appears to be consistent with the fact that "plastic sulfur," a chain polymer which crystallizes a t room temperature only on stretching, evidently has a melting point (if indeed it crystallizes a t all on cooling without stretching) below room temperature, in spite of its high cohesion energy (2000 cal. per S atom). There is, however, a problem here: the melting points in the series (CH!JIzS2, after going through a minimum, rise again to 113' C. in (CI12)2S2; iP plastic sulfur is regarded as the end member of this series, there is again a fall.

Polyurethans.

Polyethers and Polythioethers.

No explanation can be offered for this.

TABLE 111 MELTING POINTS OF SULFIDE POLYMERS

n = 6 5 4 3 2

68 65 67" 61" 145" - 44 39 O 67" 113"

Unsaturated Polymers. The natural isoprene polymers rubber and gutta-percha, (-CH2--C(CH,)=CHCH2-),, as well as polychloroprene, (-CH2-CCl=CH-CH2-),, and 1,bpolybutadiene itself (-CH2-

338 C. W. BUNN

CH=CH-CH2-), all melt much lower than polymethylene; this is consistent with the fact that monomeric chain compounds containing (non- conjugated) double bonds melt lower than the corresponding saturated compounds, and suggests strongly that the lowering of the melting point is due to a properi,y of the bond structure rather than to specific stereochemical or shape effects. The double-bonded group itself is, of course, very rigid, but in several small molecules such as propene, CH3CH=CH2, and isobutene, (CH3)2C=CH2, the estimated potential barriers t o rotation of the methyl groups are lower than in saturated hydrocarbon^.'^ Al- though all such estimates are rough, the fact that low values (450-2100 cal. per mole) have been consistently obtained for several unsaturated hydrocarbons suggests that in this case, even if individual figures are very approximate, we may accept as established the generalization that in such molecules rotation round a (nominally) single carbon-carbon bond is easier when there is an adjacent double bond than in a saturated compound. If this applies to chain molecules, it provides an explanation of the low melting points in question. (I suggested this in 1942,26 but the evidence is now stronger.) There are, of course, conflicting factors-the rigidity of the double-bonded group itself, opposed by the easy rotation about adjacent single bonds. In some situations i t seems likely that the latter effect would be dominant; for instance, in a monomeric paraffin molecule with one double bond at the center of the chain, the presence of one rigid link would make little difference to the vibrations of the whole semistitl' molecule, but the adjacent easily rotating bonds would have the effect of hinging the molecule a t the center and thus allowing much greater vibrations of the two halves (as in the case of chain esters). In the polymers in which every fourth bond is a double bond, the outcome is less certain, although i t may be remarked that for every chain bond which is stiffened, there are

+L

Fig. 5. Rotation of a given number of degrees round bonds a and c distorts a cis molecule more than a trans molecule.


iwo adjacent bonds round which rotation is easier; and in any case local distortions of the molecule, which are perhaps dominant for melting, can be greater when easily rotating bonds are present, so that in a sense the flexibility of a molecule is that of its most easily rotating bonds.

cis-Polyisoprene (rubber) melts lower than the frans isomer, gutta- percha. Although it has been suggestedz6 that this may be due to a specific stereochemical difference which may make rotations round certain bonds easier in the cis isomer, the considerations brought forward in the present paper suggest other possibilities. One is a shape effect: the cis isomer is flatter (further removed from cylindrical in cross section) and less smooth in outline than the trans isomer. The other is that in the cis isomer the rotatable chain bonds adjacent to the double bond are inclined to each other a t an angle of 70°, whereas in the trans isomer they are parallel; even if the barriers to rotation were identical in the two isomers, the net flexibility of the cis molecule would be greater than that of the trans molecule, for a geometrical reason illustrated in Figure 5. Rotation round bonds a and c of a given number of degrees distorts the cis molecule (right)-i.e., shortens the distance mn to m’n’-more than the trans molecule (left), simply because the rotatable bonds are inclined in the cis and parallel in the trans. The fact that cis chain compounds in general melt lower than the trans isomers (in a great variety of monomers as well as in polymers) suggests that this geometrically enhanced flexibility due to inclined rotating bonds, rather than any specific stereochemical or shape effects, is the explanation.

The differences between cis and trans compounds are related to the striking differences noted earlier between the meta and para polyphenols : the para-linked molecules remain linear even when rotation occurs round all the links, while similar rotations in the meta-linked molecules cause gross distortions. This is an extreme case because in para-linked molecules the rotating links are in a straight line. The trans double-bonded molecules are intermediate because the rotating links, although parallel, are not in a straight line.

CONCLUDING REMARKS

The conclusion just reached leads on to the suspicion that the odd-even effects in the polyamides and other series may be due to similar causes; for a t the ends of an odd CH2 sequence, the bonds to the amide or ester groups are inclined a t an angle of 1 1 2 O , whereas at the ends of an even sequence they are parallel, the odd and even sequences being analogous to cis and trans double-bonded groups. If melting depends on uprooting the strongly bound groups, we have to ask why an odd CH2 sequence does this more effectively than an even sequence. The wave motions along a chain molecule are made up of rotations round the successive chain bonds; suppose that at a given temperature a certain maximum rotation round each bond is possible; when an impulse travels along a chain, its amplitude is due to the resultant of individual amplitudes of rotation. A heavy or

340 C. W. BUNN

strongly bound group will of course damp down the motions a t the end of a CH2 sequence, but the forces tending to displace the heavy group must depend on the motions in the CH2 chain. The relative displacement of the groups held by the end bonds will be greater for an odd than for an even sequence for the same geometrical reason as in the case of cis and trans compounds (Fig. 5 ) . The fact that the odd-even effects die out as the CI12 sequence lengthens is also to be expected on this geometrical theory. This seems a reasonable interpretation of the odd-even effects not only i n polymers but in monomeric chain compounds generally.

In various series of polymers which may be regarded as CIIZ chains in which CII2 groups are replaced a t varying regular intervals by other groups, the graph of melting point against cohesion energy per chain unit shows a minimum : the polymers with sparsely placed strongly bound groups actually melt lower than polymethylene. This has been discussed by Izard,14 who connects this depression with Flory’s treatment27 of the depression of the melting point by copolymerization. This does not seem justified; Flory’s treatment is based on the assumption that in a copolymer, orily the homogeneous stretches of the main component crystallize ; the proportions of homogeneous stretches which can form crystals are determined sta- tistically, assuming a random succession of units in the copolymer. The effect is somewhat similar to the depression of the melting point of a monomer by an impurity which does not enter into the crystals. But in the homopolymers considered here, the different chain units are all in- cluded in the crystals, and it is not justifiable to regard them as copolymers and apply Flory’s treatment. Indeed, one series which shows no minimum (copolymers of hexamethylene sebacamide and sebacate) is explained quite reasonably by Izard as due to mixed crystal formation; it is therefore not consistent to expect homopolymer series to show minima. The explanation of the minima which some liomopolymer series do show is not to be found in a copolymer theory. The explanation suggested by the prescrit treatment is that the depression of the melting point is due to the introduction of easily rotating bonds. The insertion of ester groups sparsely a t regular intervals in a polyniethylene chain does increase the average cohesion energy per chain unit, but only a little; and it is entirely reasonable that the additional flexibility effect due to the introduction of easily rotating bonds should a have much greater depressing effect on the melting point than the elevating effect of a slightly increased cohesion energy. However, for a fuller understanding of this phenomenon, and indeed of the whole subject of polymer melting points, a theory expressing the quantitative interaction of cohesion energy and molecular flexibility factors is required. Any attempt to develop such a tfieory might well be focused on the fact that the minimum for aliphatic polyesters is much deeper than for aromatic polyesters and polyurethans ; indeed the fact that aliphatic and aromatic polyesters do not fit on the same curve, in the treatment adopted here, certainly calls for comment. The clue is presumably that if

One other general effect deservcs additional cornrnent.


we compare an aliphatic with an aromatic polyester of the same cohesion energy per chain unit, the aliphatic chain contains a much higher proportion of easily rotating 0-C bonds, so that the over-all flexibility of the molecule is greater.

Shape effects do not appear to be very important in the series of polymers considered here, probably because most of them consist of slender molecules which are roughly cylindrical in shape. Shape effects like those which are prominent in monomers must be expected for polymer molecules having large side groups; a shape having large projections and depressions would be expected to depress the melting point, not necessarily owing to bad packing but more probably to vibration interaction of interlocking molecules.

References

1. F. A. Lindemann, Physik. Z., 11, 609 (1910). 2. J. E. Lennard-Jones and A. F. Devonshire, Proc. Roy. Soc., A169, 317 (1939);

3. W. 0. Baker and C. P. Smyth, Ann. N. Y. Acad. Sci., 40, 447 (1940). 4. A. Kitaigorodski, Acta Physicochim. U. R. S. S., 22, 309 (1947). 5. L. Mandelkern, M. Hellmann, D. W. Brown, D. E. Roberts, and F. A. Quinn,

6. G. Egloff, Properties of Hydrocarbons. 7. M. Dunkel, 2. physik. Chem., A138, 42 (1928). 8. P. A. Small, J. Applied Chem., 3,71 (1953). 9. H. Mark, Physical Chemistry of High Polymeric Systems, Interscience.

A170, 464 (1939).

J. Am. Chem. SOC., 75,4093 (1953).

10. R. C. Reinhardt, Ind. Eng. Chem., 35,422 (1943). 11. D. D. Coffmann, N. L. Cox, E. L. Martin, W. E. Mochel, and F. J . van Natta,

12. R. Hill and E. E. Walker, J. Polymer Sci., 3, 609 (1948). 13. C. S. Fuller and C. L. ISrickson, J . Am. Chem. Soc., 59, 344 (1937). 14. E. F. hard , J . Polymer Sci., 8, 503 (1952). 15. R. Thiebault, Compt. rend. journ. intern. plastiques, 1949, 75. 16. C. S. Marvel and R. R. Chambers, J . Am. Chem. Soc., 70,993 (1948). 17. J. C. McCouhrey and A. R. Uhbelohde, Quart. Revs. Chem. Soc., 5,364 (1951). 18. E. L. Pace and J. G. Aston, J . Am. Chem. Soc., 70,566 (1948). 19. C. W. Bunn and E. R. Howclls, Nature, 174,549 (1954). 20. C. W. B u m , Chapter 12 of Fibres from Synthetic Polymers, ed. R. Hill, Elsevier,

21. D. R. Holmes, C. W. Runn, and D. J. Smith, J. Polymer Sci., in press. 22. R. d e P . Daubeny, C. W. Bunn, and C. J. Brown, Proc. Roy. Soc., A226, 531

23. E. Blade and G. 13. Kimhall, J . Chem. Phys., 18, 630 (1950). 24. L. S. Rayner, private communication. 25. C. S. Marvel and R. R. Chambers, J. Am. Chem. SOC., 70,993 (1948). 26. C. W. Bunn, Proc. Roy. Soc., A180,67, 82. 27. P. J. Flory, J. Chem. Phys.. 17,223 (1949).

J. Polymer Sci., 3, 85 (1948).

1953.

(1954).

Synopsis

The molecular characteristics which determine the melting points of high polymer crystals are considered, and it is shown that the properties of monomeric crystals often throw light on those of the polymers. The principal factors controlling melting points

342 C. W. BUNN

appear to be molar cohesion energy (of the whole niolecule for monomers, or per chain unit for polymers), molecular flexibility (due to rotation round bonds), and molecular shape effects. Figures for the cohesion energy increments of a number of chain units and substituent groups are given, and melting points of polymer series are correlated with cohesion energy per chain unit. The flexibility factor is less easy to assess; barriers to rotation in appropriate monomer molecules are relevant, but available data are very rough. The approach therefore is mainly by empirical and comparative methods. When plotted against cohesion energy per chain unit, the melting points of various series of aromatic polyesters and polyurethans fall within the same band, while those of the polyamides lie on the whole higher and those of the aliphatic polyesters, polyethers, pol ythioethers and polydisulfides much lower. The differences are attributed t o difference of molecular flexibility arising from the presence of easily rotating 0-C, S-C and S-S bonds. The low melting points of rubber and other unsaturated polymers are attributed to the fact (which can now be regarded as definitely established by independent evidence) that rotation round single bonds which are adjacent to double C=C bonds is easier than in saturated chains. Easily rotating bonds which are inclined to each other, as in cis isomers, confer greater chain flexibility than the parallel bonds in trans isomers, and thus lead to lower melting points. The marked odd-even effects in saturated molecules which run through the whole of organic chemistry (the even members always melting higher than the odd) are attributed to similar effects arising from the fact that the end bonds of an odd CII, sequence are inclined to eacb other while those a t the ends of an even sequence are parallel.

RCsum6

Les caractkristiques molCculaires qui dCterminent les points de fusion de hauts polymbres cristallisCs ont C t C CtudiCes; on montre que les propriCtCs du cristal monomCrique offre fr6quemment un kdaircissement concernant les propri6tCs correspondantes du p l y - mkre. Les facteurs principaux controlant les points de fusion sont 1’Cnergie de cohksion molCculaire (de la molkcule entibre dans le cas des monombres, de I’unitC periodique dans le cas des polymbres), la flexibilitg moleculaire (due h la rotation autour des liaisons exis- tantes), e t les effets dus Q la forme moMculaire. Des valeurs sont indiquCes pour les increments d’knergie de cohCsion pour un certain nombre d’unitCs periodiques et pour certains substituants; les points de fusion de plusieurs polymbres ont C t C reliCs B cette Energie de cohEsion par unit6 pikiodique. Le facteur de flexibilitC est plus delicat; les empbchements & la rotation dans des mol6cules de monombres appropriks sont Cvidents; les resultats obtenus jusqu’ici sont trks approximatifs, e t proviennent de mCthodes purement empiriques et comparatives. Si on porte en diagramme les points de fusion en regard de 1’6nergie de cohesion de I’unitC phriodique, on constate que de nombreuses sCries de polyesters e t polyurCthanes aromatiques tombent dans un mGme domaine, tandis que les points figuratifs des polyamides se situent tous B une rCgion plus C1evC.e; ceux des polyesters, pol yCthers, polythioCthers e t polydisulfures aliphatiques se situent beaucoup plus bas. Les differences sont attribudes h des diffbrences de flexibilith molCculaire resultant de la prCsence de liaisons mobiles 0-C, S-C e t S-S. Les points de fusion bas des caoutchoucs et d’autres polymbres non-saturCs sont h attribuer au fait (qui peut, Gtre considCr6 maintenant comme dbfinitivement Ctabli pour des motifs totalement indCpendant 3) que la rotation autour des liaisons simples qui sont adjacentes aux doubles liaisons est plus facile que dans une chaine saturCe ordinaire. Des liens aisement mobiles et inclinCs les uns par rapport aux autres, ainsi qu’il en est le cas pour les isombres-cis, confbrent une plus grande flexibilitC des chaines que les liens parallkles entre eux, qni sont prCsens dans les isornbres-trans, dont les points de fusion sont plus BevCs. Les effets d’altwnance pair-impair bien connus dans les molCcules saturCes et quise retrouvent dans toute la chimie organique (les membres B nombre pair fondent toujours plus haut que ceux h nombre impair) doivent Gtre attribues B des effets sembl- ables; Ies liaisons t~rminales dans une sequence impaire de groupes CH, sont inclinfet


les unes par rapport aux autres, tandis qu’elles sont parallbles dans le cas d’un nombre pair de m&mes groupes.

Zusammenfassung

Die Molekulareigenschaften, die den Schmelzpunkt von Ilochpolymerkristallen bes- timmeii, werden betrachtet, und es wird gezeigt, dass die Eigenschaften monomerer Kristalle oft Erklirungen iiber die IGgenschaften der Polymere geben. Die Hauptfak- toren, die den Schrnelzpunkt kontrolliereu, simd molare KohBsionsenergie (des ganzen Molekuls fur Monomere, oder pro Ketteneiriheit fur Polymere), molekulare Biegsarn- keit (durch Rotation um Bindungen herum bedingt) und molekulare Form-Effekte. Es werden Zahlen fur die Irikremente der Koliasionsenergie einer Anzahl von Ketten- einheiten und substituierenden Gruppen gegeben, und Schmelzpunkte von Polymerreihen werden mit der Kohasionsenergie pro Ketteneinheit in Beziehung gebracht. Der Biegs- amkeitsfaktor ist weniger leicht zu bestimmen; Schranken der Rotation sind in geeigne- ten Monomermolekulen bezeichnend, aber die erhaltbaren Daten sind sehr ungenau. Die Annaherung wird deshalb hauptsachlich durch empirische und vergleichende Meth- oden vorgenommen. Bei graphischer Darstellung gegen die KohAsionsenergie pro Ketteneinheit fallen die Schmelzpunkte der verschiedenen Reihen aromatischer Poly- ester und Polyurethane irinerhalb des gleichen Bandes, wahrend die der Polyamide im allgemeinen hoher uud die der aliphatischen Polyester, PoIyather, Polythioather und Polydisulfide vie1 tiefer liegen. Die Unterschiede werden den Unterschieden der mole- kularen Biegsamkeit zugeschrieben, die aus der Gegenwart von leicht rotierenden 0-S, S-C und S-S Bindungen eritstehen. Die niedrigen Schmelzpunkte von Kaut- schuk und anderen ungesattigten Polymeren werden der Tatsache zugeschrieben (welche jetzt als endgiiltig und durch unabhangige Beweise festgestellt betrachtet werden kann), dass Rotation um einfache Bindungen herum, welche benachbart zu doppelten C=C Bindungen stehen, einfacher als in gesattigten Ketten ist. Leicht rotierende Bindungen, welche gegeneinander geneigt sind, wie in &-Isomeren, verleihen grossere Ketten- biegsamkeit als die parallelen Bindungen in trans-Isomeren, und fuhren so zu niedrigeren Schmelzpunkten. Die starken ungerade-gerade Effekte in gesattigten Molekulen, die in der gesamten organischen Chemie bestehen (die geraden Glieder schmelzen immer hiiher als die ungeraden) werden ahnlichen Effekten zugeschrieben, die von der Tatsache herruhren, dass die Endbindungen einer ungeraden CHz-Sequenz gegeneinander geneigt sind, wahrend die am Ende einer geraden Sequenz parallel sind.

Received December 1, 1954

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The melting points of chain polymers