Thermal Analysis of Polymeric Materials Part 10 docx

5 Structure and Properties of Materials
___________________________________________________________________
526
Fig. 5.100
Fig. 5.99
By inspection, one can see that the kink is the result of the collision of a transverse
(A), torsional (B), and longitudinal vibration (C) between 0.5 and 1.1 ps (see also
Fig. 1.47). After formation, this particular kink defect had a life time of about 2 ps.
The mechanism of twisting of a single chain is illustrated in Fig. 5.102. One can
see a very gradual twist starts at about 1.5 ps, and is completed after 2.3 ps. After this
5.3 Defects in Polymer Crystals
___________________________________________________________________
527
Fig. 5.101
Fig. 5.102
twist, the whole chain has been rotated by about 90
o
. It remains with minor
fluctuations in this position until 7 ps when the rotation reverses. The twist is so
gradual that no gauche conformations are necessary for its occurrence.
The sequence of Figs. 5.103
105 illustrates the details of the diffusion of a chain
through the crystal. The figures refer to a chain that was driven into the direction of
5 Structure and Properties of Materials
___________________________________________________________________
528
Fig. 5.103
Fig. 5.104
the indicated gradient by application of an external force. Figure 5.103 illustrates the
gauche conformations that appear during the diffusion (compare to Fig. 5.98). There
is no direct involvement of the gauche defects in the motion. At later time, the

increase in gauche bonds is connected with the chain having moved out of the crystal
in the positions above 85.
5.3 Defects in Polymer Crystals
___________________________________________________________________
529
Fig. 5.105
Figure 5.104 shows more details how the chain moves. The almost horizontal,
dotted lines represent the non-moving chains which surround the chain being moved
out of the crystal by the force gradient. One should note the initial pulling of the lower
chain-end into the crystal at 0
2 ps. This is followed by an expulsion of the upper
chain-end out of the crystal between 2 and 4 ps.
The mechanism of the diffusion of the chain is shown even better in the enlarged
plot of the end-to-end distance of the moving chain in Fig. 5.105. The longitudinal
acoustic mode of vibration (LAM) is clearly visible. From the LAM frequency one
can extract a sound velocity in the chain direction which agrees with experiments. On
this LAM vibration a series of spikes is superimposed which occur on motion of the
chain into or out-of the crystal as seen in Fig. 5.104. The sliding diffusion of the chain
through the crystal is, thus, coupled strongly with the skeletal vibrations and does not
involve diffusion of the point defects themselves, but rather seems to be connected
with the twisting motion of the chain which is illustrated in the movie of the chain
dynamics of a single chain in Fig. 5.102.
The change of the rate of diffusion with temperature is illustrated in Fig. 5.106.
Although point defects are not directly involved in the motion, they help in the motion
of the chain. The motion decreases towards zero in the temperature range where the
concentration of gauche bonds reaches zero in Fig. 5.100, i.e., with gauche defects
present, the diffusion is more facile.
Instantaneous projections of segments of C
50
H

100
within a crystal at different
temperatures are shown in Fig. 5.107. The MD simulation represents the hexagonal
polymorph. One can see that the crystal is divided in nanometer-size domains and has
increasingly averaged chain cross-sections at higher temperatures. Both yield on
macroscopic X-ray analysis hexagonal, average symmetry. At higher temperature,
chains start to leave the surface of the crystal, indicating the first stages of fusion.
5 Structure and Properties of Materials
___________________________________________________________________
530
Fig. 5.107
Fig. 5.106
5.3.5 Deformation of Polymers
Turning to the macroscopic deformation of polyethylene, as experienced on drawing
of fibers, one observes frequently the formation of a neck at the yield point, as
illustrated in Fig. 5.108. The stress-strain curve in Fig. 5.108 illustrates a typical
5.3 Defects in Polymer Crystals
___________________________________________________________________
531
Fig. 5.108
Fig. 5.109
drawing of quenched polyethylene. During plastic deformation in the neck, the cross-
section is drastically reduced, so that the true stress and strain are actually increasing
instead of decreasing.
Figure 5.109 illustrates a calculation of the true draw ratio by following the
changes of the cross-section at various positions along the fiber, starting at the point
of initial necking. In Fig. 5.110 the true stress-strain curves are plotted as calculated
5 Structure and Properties of Materials
___________________________________________________________________
532

Fig. 5.110
from the actual cross-section at the moment of stress measurement for experiments on
drawing at different temperatures. Figure 5.110 shows three regions of different
behaviors. Region (1) is the Hookean region. It indicates elastic deformation with a
constant Young’s modulus as defined in Fig. 4.143. In the scale of the stress in the
figure the slope appears almost vertical, i.e., Young’s modulus is rather large. This
region of elastic deformation decreases with increasing temperature parallel to the
increase of gauche defects seen in Fig. 5.100. In the region of the neck of Fig. 5.108,
a catastrophic change occurs, the polymer yields as marked by (2). Rather than
breaking, the modulus increases in parallel with the production of a stronger fiber
morphology in a process called strain hardening (3). At the ultimate break, most
molecules are arranged along the fiber axis in fibrillar crystals and inter-fibrillar,
oriented intermediate-phase material. The oriented, noncrystalline material can often
be described as a mesophase. Its structure was derived in Sect. 5.2 on the example of
poly(ethylene terephthalate) in Figs. 5.68–72. A more detailed deformation
mechanism is schematically given in Fig. 5.111. It was suggested already in 1967 by
Peterlin and coworkers (see also [34]).
The simulations discussed in the previous Section begin to explain some of the
details of the drawing process. In particular, they show the enormous speed that is
possible on a molecular scale for the sliding of the chain within the crystal. The ratio
between macroscopic time scales of about 1.0 s and the molecular time scale of 1.0
ps is 10
12
! The simulations indicated that the initiation of the diffusion seems to come
from a sessile gauche defect or kink. On application of an external force, this can lead
to a moving of the chains, catastrophically deforming the crystal morphology with the
possible creation of a metastable mesophase as an intermediate, as indicated
schematically in Fig. 5.111 and shown sometimes to be able to remain as a third phase
in Fig. 5.69–72. On annealing, part or all of the initial structure may be regained.
5.3 Defects in Polymer Crystals

___________________________________________________________________
533
Fig. 5.111
5.3.6 Ultimate Strength of Polymers
To use flexible linear macromolecules as high-strength materials, themolecular chains
should be arranged parallel to the applied stress and be as much extended as possible.
The resulting modulus is then dependent on the properties of the isolated chain and the
packing of the chains into the macroscopic cross-section. The properties of the chain
can be derived from the same force constants as are used for the molecular dynamics
calculation in Sect. 5.3.4 with Figs. 1.43 and 1.44. The ultimate strength, also called
tenacity or tensile strength, in turn, depends on the defects in form of chain ends and
other defects that produce the slipping mechanism and reduce the ultimate number of
chains available at break to carry the load. The moduli, thus, are close-to structure
insensitive, while the ultimate strengths are structure sensitive as was suggested in the
summary discussion of Fig. 5.80 of Sect. 5.3.1.
Figure 5.112 compares the specific tensile strengths and moduli of a number of
strong materials. The specific quantities are defined as shown in the figure as the
modulus divided by the density. This quantity is chosen to emphasize the materials
of high strength at low weight. For these properties most desirable are the materials
found in the upper right corner of the plot. Many rigid macromolecules as defined in
Fig. 1.6 collect along the drawn diagonal with a rather small ratio of strength-to-
modulus because of the above-mentioned deformation mechanism followedultimately
by a crack development that breaks the crystals by separating a few crystal layers at
a time needing much less stress. In flexible polymers, the covalent backbone bonds
are stronger than metallic or ionic bonds (see Sect. 1.1). High-strength fibers result
when chains of a proper mesophase gradually orient parallel to the stress and the
molecules become fully extended in large numbers over a small deformation limit.
5 Structure and Properties of Materials
___________________________________________________________________
534

Fig. 5.112
Fig. 5.113
Figures 5.113–115 illustrates the need to parallelize the chains of poly(ethylene
terephthalate) applying the three-phase structure, identified in Figs. 5.69–72 [25].
Figure 4.113 shows the model for the combination of the three phases [35,36]. The
orientation in the mesophasematrix, measuredbyitsaverageorientationfunction (OF)
obtained from the X-ray diffraction pattern [24], is of most importance for the
modulus and, surprisingly, also for the ultimatestrength,asindicatedbythe left curves
5.3 Defects in Polymer Crystals
___________________________________________________________________
535
Fig. 5.114
Fig. 5.115
of Figs. 4.114 and 4.116. The right curves are computed assuming the fibers consist
only of two phases and, using the total orientation, were summed over all chains.
Only the left curves extrapolate within a factor of two to the known ultimate modulus
of the crystal of poly(ethylene terephthalate). The extrapolated tenacity is, as
expected, smaller than the extrapolated modulus.
5 Structure and Properties of Materials
___________________________________________________________________
536
5.4 Transitions and Prediction of Melting
The discussion in this chapter has dealt in Sects. 5.1 to 5.3 with the description of
structure and properties of crystals, perhaps the best-known branch of material science
of polymers. Complications arise, however, since most crystallizing polymers do not
reach equilibrium. The metastable, multiphase structures will be discussed in Chaps.
6 and 7. They represent the most complex structure and need for their description all
tools of thermal analysis of polymeric materials.
In this section, the upper temperature limit of the crystalline state is explored on
the basis of experimental data on the thermodynamics of melting, extrapolated to

equilibrium. The more common nonequilibrium melting will see its final discussion
in Sects. 6.2 and 7.2. The other condensed states of macromolecules, the mesophases,
glasses, and melts are treated in Sects. 5.5 and 5.6. Much less is known about them
than about the crystals.
5.4.1 Transitions of Macromolecules
The transitions in flexible linear macromolecules are distinguished by their non-
equilibrium nature. Figure 5.116 gives a schematic overview of the possible
transitions, modeled on the thermal analysis of a quenched, amorphous poly(ethylene
terephthalate) presented as a fingerprint DSC in Fig. 4.74. Examples of more
quantitative TMDSC analyses of PET are given in Figs. 3.92, 4.122, and 4.136–139.
A special review of TMDSC of the glass transition of PET is seen in Figs. 4.129–133.
In Fig. 5.116, the glass transition temperature is labeled T
g
and characterized by an
increase in heat capacity (see Sects. 2.3 and 2.5) and marks the change of the brittle,
glassy solid to a supercooled, viscous melt. More details on glass transitions are
discussed in Sects. 5.6, 6.1, and 6.3.
Next is the exothermic crystallization transition at T
c
. Such crystallization on
heating above the glass transition temperature is called cold crystallization [37]. It
contrasts to crystallization on cooling from the melt, see also Figs. 4.122, 4.136, and
4.138. After cold crystallization, the sample is semicrystalline with about 40%
crystallinity, as indicated in Fig. 4.136.
The following melting range is rather broad and indicated by the endotherm,
centered about T
m
. Most of the breadth is produced by the wide range in lamellar
crystal perfection and thickness (see Sects. 5.2 and 5.3), and additional reorganization
occurs during the melting experiment which will be addressed in Sect. 6.2. The

resulting melt is stable up to over 600 K, and finally shows an exothermic peak that
signals decomposition. The appearance of decompositions of other polymers in
thermogravimetry is illustrated in Fig. 3.49.
The main object in the present section is to gain a quantitative understanding of the
equilibrium melting temperature and the changes in enthalpy and entropy during the
transition. The melting transition assigns the upper temperature limit of the solid state
of the crystalline polymers, as pointed out in Fig. 1.6, just as the glass transition alone
limits the solid state of amorphous and mesophase polymers (see Sects. 5.5 and 5.6).
Beyond these temperatures, polymers cannot be used as bulk structural materials,
fibers, or films.
5.4 Transitions and Prediction of Melting
___________________________________________________________________
537
Fig. 5.116
Before an analysis of the more common, nonequilibrium melting is possible in
Sect. 2.4 and Chap. 6, the empirical information that can be extracted from equilib-
rium melting of small and large molecules in crystals needs to be understood. For
such a discussion, equilibrium data have first to be extrapolated from nonequilibrium.
Forthe equilibriumvaluesofthestructure-insensitive,thermodynamic functions, such
as enthalpy, volume, and heat capacity, it is sufficient to extrapolate to 100%
crystallinity, as discussed in Sect. 5.3.2. The equilibrium melting temperature, T
m
o
,
is more difficult to obtain with precision. Equilibrium crystals have been made and
measured only for few macromolecules, such as polyethylene in Fig. 4.18, some
polyoxides, and polytetrafluoroethylene. Extrapolations of melting temperatureswith
increasing perfection as linked to fold lengths or crystallization temperatures are often
chosen as approximation for T
m

o
. The final quantity considered is the entropy of
melting (
S
fusion
= H
fusion
/T
m
o
). The enthalpy of fusion is structure insensitive and
the melting temperatures of polymers are typically in the range of 300 to 600 K, errors
of 5
20 K in T
m
o
are, thus, acceptable for entropy estimates since most thermody-
namic functions are known only with errors of ±3%. The often heard argument that
equilibrium information is not available for polymers is not valid in this range of
precision, and it will be shown in this section that valuable information can be
deduced from a discussion of the equilibrium entropy of fusion.
The discussion of T
m
o
must involve four independent variables, namely the
enthalpies and entropies of both the melt and the crystal. It, however, will be shown
that good estimates of T
m
o
can be made by using empirical rules for S

fusion
,tobe
derived next. For similar macromolecules
H
fusion
is usually also similar and derivable
from the chemical structure. For aliphatic polyesters, for example,
H
fusion

2.3 kJ (mole of backbone atoms)
1
. For a summary of extrapolated equilibrium data
the ATHAS Data Bank, summarized in Appendix 1, should be consulted.
5 Structure and Properties of Materials
___________________________________________________________________
538
Fig. 5.117
5.4.2 Crystals of Spherical Motifs
The melting of crystals of spherical motifs is the easiest to describe. It is assumed that
before melting, the crystal is in perfect order in a cubic or hexagonal close-pack with
long-range order and undergoes only vibrational motion. The melting can then be
broken into three steps: (1) An increase to the usually larger volume of the melt. (2)
The disordering of the crystalline arrangement to the liquid which shows short-range
order only. (3) The introduction of additional defects into the liquid structure which,
at least for spherical motifs, is often a quasi-crystalline structure and can have defects
of the type described for crystals in Sect. 5.3. Of the three types of disorder of
Fig. 2.102 which can be introduced on melting of different molecules, spherical motifs
can gain only positional disorder. If the motifs are not spherical, rotation adds the
orientational disorder. Finally, after fusion, flexible molecules may carry out internal

rotations that lead to conformational disorder.
Figure 5.117 lists as the first four substances the entropy of melting of monatomic
noble gases. Quite clearly, all noble gases have close to the same entropy of fusion.
A simple corollary of this observation is that the value of the melting temperature is
linked mainly to the heat of fusion. This, in turn, suggests that the packing for
different noble gases is not only similar in the crystals, but also in the melts, so that
the increase in interaction energy for atoms with larger number of electrons via the
London dispersion forces is the cause of the higher T
m
o
. To explain the similar
entropies of fusion, one can assume that the entropy of going from positions fixed in
the crystal lattice to full access for the motifs to the liquid volume is R, the gas
constant of 8.31 J K
1
mol
1
, the communal entropy [38]. An additional 0.7 R was
estimated for the two other stages of melting [39]. Assuming that the latter
5.4 Transitions and Prediction of Melting
___________________________________________________________________
539
Fig. 5.118
contributions to the entropy of fusion are approximately proportional to the introduced
disorder, one can include all within the rather wide, empirically derived, limits of the
positional entropy of fusion. Similar proportionalities are assumed for the other types
of disorder included in Fig. 2.103.
The metals in Fig. 5.117 expand the table of entropies of fusion. Perhaps it is not
surprising that the metals have an entropy of melting similar to the noble gases. Their
crystal structures are frequently also hexagonal or cubic and closely packed with a

coordination number of 12 as mentioned in Sect. 1.1.2. A comparison of chromium
and sodium in Fig.5.117 shows that in metals, enormous differences in melting
temperatures can be produced with the same entropy of fusion. The maximum in
variation of entropies of melting is illustrated between tin and sodium. Some
additional metals are shown in Fig. 5.118. In all cases shown, the wide variation of
melting temperatures is based mainly on differences of the intermolecular forces and
demonstrated by the comparison of the metals tungsten and potassium.
Larger changes in entropies of fusion can be discussed in terms of changes in
coordination number between the crystal structure and the quasi-crystalline structure
in the melt. The changes in heat of fusion, in turn, are to be linked to the bond
energies that will change with coordination number, CN, the changing number of
electrons in the conduction band, as well as changes of the character of the bonds from
the metallic CN (usually 12) to the covalent CN (often 4, see Fig. 1.5).
The rule of constant entropy of melting was first observed by Richards [40], and
should be compared to the rule of constant entropy of evaporation of 90 J K
1
mol
1
by simple liquids as proposed by Trouton (see Sects. 1.1 and 2.5.7). Both rules are
helpful in developing an understanding of the differences of transition temperatures
for different materials. A general application of Richards’s rule requires, however,
5 Structure and Properties of Materials
___________________________________________________________________
540
Fig. 5.119
modification whenever other than positional disorder is produced on melting. Before
exploring the melting of such different molecules, Fig. 5.118 shows also some
entropies of melting of larger, but close to spherical motifs (molecules). Surprisingly,
they still seem to follow Richards’s rule. A more detailed investigation, however,
reveals that most of these molecules have one or more additional transitions at lower

temperatures where the molecules take on a mesophase structure in form of a plastic
crystals as defined in Sect. 2.5. At the melting temperature, or better, the isotropi-
zation temperature, the motifs rotate within the crystal and, thus, average to a sphere,
and satisfy Richards’s rule.
Figure 5.119 extends the list of almost spherical motifs to much larger, organic
molecules with a molecular structure which is still close to spherical. Again, these
molecules are plastic crystals and have gained orientational mobility before ultimate
isotropization. For the discussion of the entropies of fusion these results indicate that
the size of the motif does not significantly influence the entropy of fusion. All data
treated up to now, thus, can be summarized by stating that under the given conditions
the entropy of fusion, or better isotropization, is made up of mainly positional
disordering, and that the entropy of disordering varies little among all these almost
spherical and truly spherical molecules.
Figure 5.120 presents, next, the entropy of melting of 20 alkali halides. All of
these crystals have the F
m
3
m
space group of the NaCl structure which is depicted in
Fig. 5.2. The average entropy of fusion of these 20 salts is 24.43 ±1.7 J K
1
mol
1
.
Since their formula mass refers to two ions, the average positional entropy of fusion
is 12.2 J K
1
mol
1
, in good accord with Richards’s rule. A total of 76 other salts, with

up to four ions per formula, was similarly analyzed [41]. The majority of these salts
follow the same rule of constant entropy of fusion per mole of ions, irrespective of the
5.4 Transitions and Prediction of Melting
___________________________________________________________________
541
Fig. 5.120
charge of the ions. There are, however, a reasonable number of exceptions. Smaller
as well as larger entropies of fusion have been reported. Lower entropies of fusion can
be observed, for example, if the melt is made up of covalently bonded dimers, or if the
crystal is disordered at lower temperatures. Higher entropies of fusion are possible if
the aggregates in the melt attain more orientational freedom than in the crystal with
its correspondingly higher entropy of fusion, as will be discussed next. Excluding 14
such special salts from consideration permitted the analysis of 82 salts and yielded an
average of 10.9 ±2.0 J K
1
mol
1
for the entropy of fusion per mole of ions, in good
accord with Richards’s rule.
5.4.3 Crystals of Non-spherical Motifs
Non-spherical motifs that do not rotate in the crystal before melting, in contrast,
should gain an orientational contribution to
S in addition to the positional disorder.
Figure 5.121 illustrates the rather sizable increase on examples of small molecules.
This observation of a different, but again largely constant entropy of fusion, was made
by Walden [42]. Increasing the size of the motifs, as shown in Fig. 5.122, does not
seem to affect the entropy of melting much, as observed also in Fig. 5.119 for the
rotating large organic motifs. Assuming now that the entropy of fusion is made of two
major contributions, leads to the range for Walden’s rule listed in Fig. 5.122.
Finally, one can derive from Richards’s and Walden’s rules combined that

S
orientational
should be about 10 to 50 J K
1
mol
1
. This uncertainty of the entropy
change is larger than for
S
positional
, but the rotational degrees of freedom have a larger
variation of rotational motion. The rotation may require different amounts of volume,
be coupled between neighboring molecules, and, depending on the symmetry of the
molecules, may have a reduced entropy contribution.
5 Structure and Properties of Materials
___________________________________________________________________
542
Fig. 5.122
Fig. 5.121
5.4.4 Crystals of Linear Hydrocarbons
Flexible molecules have an additional, size-dependent entropy contribution that can
also be derived from the molar entropy of fusion. Figure 5.123 shows the melting
temperatures and entropies of melting of the homologous series of normal paraffins
5.4 Transitions and Prediction of Melting
___________________________________________________________________
543
Fig. 5.123
C
n
H

2n+2
. The first three members of the series with n = 13 illustrate Richards’s rule
with methane, a close to spherical molecule, and Walden’s rule with ethane and
propane, two non-spherical, rigid molecules. The threefold increase in the entropy of
fusion of ethane and propane is caused by the added orientational motion. The linear
increase of mass with the number of C-atoms also increases the interaction-energy
and, thus, keeps T
m
almost constant.
The special change that occurs with the longer molecules (n
 4) is connected with
their flexibility, i.e., the possible rotation about the interior bonds of the molecule. It
becomes first possible in butane with its three conformational isomers, as illustrated
in Fig. 1.37. Figure 5.123 shows that for the paraffins with even n from hexane
(n = 6) to dodecane (n = 12), there is an increase in
S  20 J K
1
mol
1
for each pair
of additional bonds around which rotation is possible. Similar observations can be
made for the paraffins with odd numbers of carbon atoms. The difference in absolute
level of
S between the odd and even series arises from differences in crystal packing
as was analyzed with thermodynamic parameters in Fig. 4.52 for decane. The few
paraffins with exceptionally low
S are, at present, not fully understood. Their low
S may be caused by experimental error caused by incomplete crystallization,
mobility in the crystal through mesophase formation, or by differences in the packing
in the crystal or structure in the melt.

The entropy of melting per carbon atom is given in Fig. 5.123 in parentheses and
approaches the entropy of melting of polyethylene which is 9.91 J K
1
mol
1
.For
polyethyleneandotherflexible polymersthepositionalandorientationalcontributions
to the melting process are negligible because of the many bonds about which rotation
is possible in contrast to a single translational and rotational contribution for the
molecule as a whole. This simplification allows for an easy assessment of the chain
flexibility, as is shown in Section 5.4.5.
5 Structure and Properties of Materials
___________________________________________________________________
544
Fig. 5.124
From entropy data on polymers discussed in the next section and the just presented
small molecules, one can derive that
S
positional
 714 J K
1
mol
1
, S
orientational
 2050
JK
1
mol
1

,andS
conformational
 712 J K
1
mol
1
. Only the last contribution is size-
dependent, i.e., it is proportional to the number of rotatable bonds in the molecule or,
for polymers, the repeating unit. The proportionality of the conformational entropy
of melting to the number of bonds that allow rotation is also the reason for dividing
flexible macromolecules into beads of which each contributes 7
12 J K
1
mol
1
to the
conformational entropy. These empirical limits of entropy gain on disordering can
also be used for the discussion of mesophases, as is shown in Fig. 2.103 (see also
Sects. 2.5 and 5.5).
5.4.5 Crystals of Macromolecules
Turning to macromolecules with Figs. 5.124–126, the positional and orientational
contributions to the entropy of melting can be neglected for the present discussion
since they contribute only little when considering that the total molecule of thousands
of chain atoms can have only one positional and one orientational contribution (see
Fig. 2.103). To discuss the remaining conformational contributions one can divide the
molecules into beads, defined by the bonds causing molecular flexibility. The data in
the tables were calculated per mole of beads, with the number of beads indicated in
parentheses in the column for
S
f

. The tables include also information on packing
fractions in the liquid, k
5
(see Fig. 4.24), and the change of packing fractions on
melting,
, as well as cohesive energy densities, CED. The cohesive energy density
is calculated per mole of interacting groups, i.e., per mole of CH
2
,NH,O,CO,
which maybe different from the number of beads. The CED is derived from the heat
5.4 Transitions and Prediction of Melting
___________________________________________________________________
545
Fig. 5.125
Fig. 5.126
of evaporation of small model compounds or the heat of solution into solvents of
known CED and corrected for volume changes. Out of such tables, omitting the
obvious exceptions, the conformational entropy of melting per bead was derived, as
shown in Figs. 5.124–126 and mentioned already in the discussion of paraffins in
Sect. 5.4.4.
5 Structure and Properties of Materials
___________________________________________________________________
546
Combining the results of all presented data, a number of valuable conclusions can
be drawn about polymers from their melting characteristics. Furthermore, this
experience helps to predictthemelting properties frominformation about the chemical
structure. Adding this information about melting to the predictions possible from the
heat-capacity analysis (see Sect. 2.3 and Appendix 1), a rather complete profile can
be developed for the thermal properties of a given chemical structure.
Some examples of thediscussion ofmelting transitions of flexible macromolecules

are given next. For polyethylene and a number of all-carbon-and-hydrogen vinyl
polymers in Fig. 5.124 one observes that the short side-groups do not contribute to
S.
Next, one can see that going from polyethylene to polypropylene adds one more
interacting unit, i.e., it increases the heat of fusion. As a result, the melting
temperature increases, yielding a material useable to higher temperature. For poly(1-
butene) and poly(1-pentene), the added CH
2
-groups in the side chain do not seem to
be able to increase the interaction in the crystal as derivable from Figs. 5.25 and 5.26,
so that the melting temperature decreases again. Of special interest is the poly(4-
methyl-1-pentene). The second methyl group at the end of the side chain interacts in
this case sufficiently to increase the heat of fusion and melting temperature. Also, it
can be derived from Fig. 5.124 that all these polymers have the same packing density
in the melt, k
5
, and that the helical polymers pack less-well in the crystal, as was
already found in Sect. 5.1.8 when analyzing their crystal structure.
The top three polymers in Fig. 5.124 show a large variation in properties.
Polytetrafluoroethylene, PTFE, has a much higher T
m
due to the low S. A more
detailed analysis shows that at lower temperature PTFE becomes a conformationally
mobile mesophase, as is discussed in Sects. 2.5 and 5.5 and illustrated in Fig. 2.63.
Adding the entropy of disordering of PTFE of 2.85 J K
1
mol
1
at the lower transitions
at 292 and 303 K, leads to a similar total

S as for polyethylene. The somewhat
higher
S of Se is linked to the chemical depolymerization equilibrium in the melt,
analyzed with Fig. 2.69. The much higher CED of Se, listed in the last column of
Fig. 5.124 is largely compensated by the higher entropy, so that the densely packed
Se, whose crystal structure is shown in Fig. 5.20, melts at only 494 K.
Figure 5.124 shows also the similarity between polyethylene and cis-1,4-
polybutadiene when representing the chains by their bead structure. The C=C-group
is a rigid single bead. The reason of the low melting point of the cis-1,4-
polybutadiene is, however, not obvious. The solution of this puzzle lies with the large
intramolecular contribution on melting of polyethylene from the change of the trans
to gauche conformations, not present in cis-1,4-polybutadiene.
The series of five polymers with particularly low entropies of melting in Fig. 5.124
show crystals that are disordered, most likely to condis crystals (see Sect. 2.5), as
shown above for PTFE. Of special interest is the difference between cis- and trans-
1,4-polybutadiene. Their entropies are shown in Fig. 2.113.
Figure 5.125 illustrates the changes in the homologous series of polyoxides. As
always in such series, the first member can have a more suitable packing for the
chemically different groups. In this case, the higher melting temperature is due to the
higher CED. A similar effect can be seen in the polyesters in Fig. 5.125. Note how
the two added methyl groups in poly(dimethyl propiolactone) increase the melting
point because of better packing in the crystal.
5.5 Mesophases and Their Transitions
___________________________________________________________________
547
The three polyesters in Fig. 5.126 show that the reason for the low melting of the
aliphatic poly(ethylene suberate) is the larger number of beads. The two aromatic
polyesters contain one and two phenylene groupsofsixcarbonslinked into rigid rings,
losing considerable entropy relative to the all flexible aliphatic chain. The aliphatic
nylons, finally, have higher melting temperatures than the corresponding esters

because of the higher CED.
Once these empirical rules have been established, it is possible to link the melting
temperatures of polymers to chain flexibility, interactions (cohesive energy densities),
internal heats of fusion, and the possible presence of mesophases (see Fig. 2.103).
Such analyses are of importance for the design of new polymers and of changes in
existing polymers when there is a need to alter thermal stability.
5.5 Mesophases and Their Transitions
Mesophases are intermediate phases between rigid, fully ordered crystals and the
mobile melt, as explained in the introductory discussion of phases in Sect. 2.5, and
summarized in Figs. 2.103 and 2.107. The quantitative analysis of melting in Sect. 5.4
shows that with a suitable molecular structure, three types of disorder and motion can
be introduced on fusion: (1) positional disorder and translational motion, (2) orienta-
tional disorder and motion, and (3) conformational disorder and motion [43]. In case
not all the possible disorders and motions for a given molecule are achieved, an
intermediate phase, a mesophase results. These mesophases are the topic of this
section. Both structure and motion must be characterized for a full description of
mesophases.
5.5.1 Multiple Transitions
First experimental evidence for mesophases is often the presence of more than one
first-order transitions in DSC curves on heating from the crystal to the melt. The
disordering of a crystal to its mesophase causes a substantial endotherm. Much
smaller endotherms may indicate solid-solid transitions which only involve changes
in crystal structure without introduction of large-amplitude motion. Figure 5.127
illustrates the behavior of poly(oxy-2,2'-dimethylazoxybenzene-4,4'-dioxydo-
decanoyl), DDA-12, a mesophase-forming macromolecule. Before analysis, the
sample was quenched to a LC glass, i.e., a solid with liquid-crystalline order, but
without large-amplitude motion (see Fig. 2.103). On cold crystallization above the
glass transition temperature at about 345 K, metastable condis crystals grow with an
exotherm to a partial crystallinity. At about 395 K, the CD crystals again disorder
with an endotherm to the liquid crystal. The second endotherm in Fig. 5.127 is the

isotropization to the melt. The isotropization is reversible, the disordering is not, as
can be tested with TMDSC. Low-molar-mass analogs behave similarly. For example,
p-butyl-p'-methoxyazoxybenzenes can be quenched to a semicrystalline LC glass and
shows then a DSC-trace, as displayed in Fig. 5.128, which can be compared to
Fig. 5.127. The difference is that the cold crystallization of the small molecules yields
close to equilibrium crystallinity instead of the polymeric semicrystalline sample.
5 Structure and Properties of Materials
___________________________________________________________________
548
Fig. 5.127
Fig. 5.128
Another example of mesophase calorimetry is shown in Fig. 5.129. On the left,
DSC traces are given for poly(dimethyl siloxane), PDMS, which does not exhibit a
mesophase, on the right, for poly(diethyl siloxane), PDES, with a stable mesophase.
The samples A were quenched with liquid N
2
to the amorphous state, samples B,
cooled at 10 K min
1
, and samples C, slowly cooled or annealed. The quickly cooled
5.5 Mesophases and Their Transitions
___________________________________________________________________
549
Fig. 5.129
samples, A, show cold crystallization at T
c
(see Sect. 3.5.5). The samples C show only
weak glass transitions, and PDMS displays one, PDES two relatively sharp
endotherms. On cold crystallization, A, PDES forms only the condis phase with
partial crystallinity. The semicrystalline PDES of samples B and C disorder to the

condis phase at about 200 K. The condis phase was shown to be able to be annealed
to extended-chain crystals.
In Sect. 2.5 a similar two-step melting was discussed for the condis state of trans-
1,4-polybutadiene. The cis-isomer shows in Fig. 2.113 complete gain of the entropy
of fusion at a single melting temperature, while the trans isomer loses about 2/3 of its
entropy of transition at the disordering transition. The structure of the trans isomer
is close to linear, so that conformational motion about its backbone bonds can support
a condis crystal structure with little increase in volume of the unit cell.
The existence-range of the condis crystal of poly(tetrafluoroethylene), PTFE, can
be seen from the phase diagram of Fig. 5.130. The calorimetric heat capacity analysis
of PTFE is described as an example of the ATHAS applications in Fig. 2.63, and the
entropies of transition, which lead tothehighisotropization temperature, arediscussed
in Sect. 5.4.3.
A TMDSC analysis at different frequencies and amplitudes reveals in Fig. 5.131
that the solid-solid transition which changes the 1*13/6 helix to the 1*15/7 helix is
irreversible, while the transition to the condis state is reversible [44]. The
conformational disorder consists mainly of a mobility of the 1*15/7 helix from left-
to right-handed, averaging the structure of the backbone chain so that it fits into the
trigonal symmetry. The low-temperature crystals are triclinic with a fixed left- or
right-handed 1*13/6 helix (see Sects. 5.1 and 5.2). Crystal form III is a high-pressure
phase with a close-to-planar chain conformation, and form IV, located between the
two endotherms of Fig. 5.131, is made up of rigid 1*15/7 helices.
5 Structure and Properties of Materials
___________________________________________________________________
550
Fig. 5.130
Fig. 5.131
Figure 5.132 illustrates that mesophases can also be identified by rheological
properties. The crystals of PTFE show a highly anisotropic flow parallel to the
molecular axes, a property often found in smectic liquid crystals. As soon as the

molecules start to melt, however, the shear-stress increases abruptly because of the
chain-entanglement that occurs during melting. On a microscopic basis, PTFE