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Here, n

is the number of statistical chain segments be-

tween two successive entanglements and T

is the trapping

factor (0 < T

< 1), characterizing the portion of elastically

active entanglements. The first bracket term of Eq. (36.8)

considers the constraints due to interchain junctions, with an

elastic modulus G

proportional to the density of network

junctions. The second addend is the result of tube con-

straints, whereby G

is proportional to the entanglement

density of the rubber. The parenthetical expression in the

first addend considers the finite chain extensibility of poly-

mer networks by referring to a proposal of Edwards and

Vilgis [23]. For the limiting case n

¼ Sl

 3, a sin-

gularity is obtained for the free energy W

, indicating the

maximum strain of the network, which is reached when the

chains between successive trapped entanglements are fully

stretched out. In the limit n

!1the original Gaussian

formulation of the nonaffine tube model, derived by

Heinrich et al. [24] for infinite long chains, is recovered.

The presence of rigid filler clusters, with bonds in the

virgin, unbroken state of the sample, give rise to hydro-

dynamic reinforcement of the rubber matrix. This is speci-

fied by the strain amplification factor f, which relates the

external strain «

of the sample to the internal strain ratio l

of the rubber matrix (Eq. (36.5)). In the case of a precondi-

tioned sample and for strains smaller than the previous

straining («

< «

m,max

), the strain amplification factor f

is independent of strain and determined by «

m, max

(f ¼

f («

m, max

) ). For the first deformation of virgin samples it

depends on the external strain (f ¼ f («

) ). By applying a

relation derived by Huber and Vilgis [25,26] for the ampli-

fication factor of overlapping fractal clusters, f («

m,max)

f («

) can be evaluated by averaging over the size distribu-

tion of rigid clusters in all space directions. In the case of

preconditioned samples this yields

f («

m, max

) ¼ 1 þ cF

3d

eff

m¼1

m,min

d

f(j

)dj

m,min

f(j

)dj

;

, (36:9)

where c is a constant of order one and F

eff

is the effective

filler volume fraction of the structured filler particles, i.e.,

primary aggregates of carbon black or silica. j

is the cluster

size, d is the particle size, f(j

) is the normalized size

distribution, d

 1:8 is the mass fractal dimension and

 3:1 is the anomalous diffusion exponent on fractal

CCA-clusters [18].

The second addend in Eq. (36.7) considers the energy

stored in the substantially strained fragile filler clusters

(«

) ¼

=@t>0

(«

)

m,min

)«

,«

)f(j

)dj

(36:10)

where G

is the elastic modulus and «

A,m

is the strain of

the fragile filler clusters in spatial direction m. The de-

pendency of these quantities on cluster size j and external

strain «

can be derived from basic micromechanical

considerations about elasticity and fracture mechanics of

tender filler clusters imbedded into a strained rubber matrix.

This also allows for a specification of the strain dependent

integral boundaries j

¼ j

(«

) and j

m, min

¼ j

(«

m,max

A detailed presentation of the morphological and mechanical

properties of filler clusters in elastomers is found in [16].

It is demonstrated in Fig. 36.13 that the quasistatic stress–

strain data (up-cycles) at different prestrains of silica filled

rubbers can be well described in the scope of the above

dynamic flocculation model of stress softening and filler-

induced hysteresis up to large strain. Thereby, the size

distribution f(j

) has been chosen as an isotropic logarith-

mic normal distribution (f(j

) ¼ f(j

))

f(x

) ¼

exp 

ln (x

)



ﬃﬃﬃﬃﬃﬃﬃﬃﬃ

p=2

m ¼ 1,2,3 (36:11)

with the mean cluster size x

 j

=d and distribution width

b. A similar good agreement between experimental data and

simulation as shown in Fig. 36.13 can be obtained for carbon

black filled elastomers and for biaxial tension data [16]. The

obtained microscopic material parameter appear reasonable,

providing information on the mean cluster size j

and dis-

tribution width b, the tensile strength of filler–filler bonds

and the polymer network chain density n

 G

Beside the characteristic stress softening up to large

strains (Mullins effect) as shown in Fig. 36.13, the model

also considers the hysteresis behavior of reinforced rubbers

(Payne effect). Obviously, since the sum in Eq. (36.10) is

taken over stretching directions with @«=@t > 0, only, up-

and down cycles are described differently. An example

considering a fit of the hysteresis cycles of silica filled

EPDM rubber in the medium strain regime up to 50% is

shown in Fig. 36.14. For these adaptations an alternative

form of the cluster size distribution has been assumed,

which allows for an analytical solution of the integrals in

Eqs. (36.9) and (36.10):

f(x

) ¼

exp 



m ¼ 1,2,3: (36:11

)

It must be noted that the topological constraint modulus G

has been considered as a fixed parameter in the simulations

shown in Figs. 36.11 and 36.12 and was not used as a fitting

parameter. The chosen values G

¼ 0:2 MPa and G

¼ 0:6

MPa correspond to the known entanglement densities of the

606 / CHAPTER 36

S-SBR- and EPDM rubber matrix, respectively, which is

about three times larger in the case of EPDM.

In particular it can be shown that the dynamic flocculation

model of stress softening and hysteresis fulfils a ‘‘plausibil-

ity criterion’’, important e.g., for finite element (FE) appli-

cations. Accordingly, any deformation mode can be

predicted based solely on uniaxial stress–strain measure-

ments, which can be carried out relatively easily. From the

simulations of stress–strain cycles at medium and large

strain it can be concluded that the model of cluster break-

down and reaggregation for prestrained samples represents a

fundamental micromechanical basis for the description of

nonlinear viscoelasticity of filler reinforced rubbers.

Thereby, the mechanisms of energy storage and dissipation

are traced back to the elastic response of tender but fragile

filler clusters [16].

36.5 SUMMARY AND CONCLUSIONS

During dynamic-mechanical deformation at certain

(high) frequencies the silica systems are dynamically softer.

This is related to ‘‘dynamically softer’’ hinge-like filler–

filler interactions via the partially immobilized rubbery

interfacial layers between neighboring silica aggregates

within the agglomerates or the (infinite) filler network,

respectively. Figure 36.3 demonstrates the structure of

filler–filler bonds in a bulk rubber matrix. The gap size of

neighboring filler particles with confined glassy polymer

and the bound rubber layer, governing the stiffness and

strength of filler–filler bonds are indicated. In general, the

black discs represent primary carbon black aggregates. The

finding that the silica systems are dynamically softer might

explain an improved (dynamical) interlocking between

0123

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.5

1.0

1.5

2.0

2.5

Strain ξ

Stress s

0.1

[MPa]

2.532

2.933

3.455

4.130

5.400

max

0.13 MPac

= 0.2MPa

=100

Qε

= 24 MPa

/d = 22

b = 0.8

FIGURE 36.13. Uniaxial stress–strain data of S-SBR samples with 60 phr silica at different prestrains «

max

¼ 100, 150,

200, 250, and 300% (symbols) and fittings (lines) with the stress softening model Eqs. (36.7)–(36.11). The fitting parameters

are indicated. The insert shows a magnification of the small strain data.

max

= 10.1

eff

= 0.26

=1.09 MPa

= 0.60 MPa

/ T

= 45

Qε

= 31 Mpa

7.520

5.915

4.733

4.225

3.694

Stress [MPa]

Strain [%]

01 10 20 30 40 50

−0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

EPDM / 60 phr silica

FIGURE 36.14. Uniaxial stress–strain cycles of EPDM sam-

ples with 60 phr silica at different prestrains «

max

¼ 10,

20, 30, 40, and 50% (symbols) and fittings (lines) with the

stress softening model Eqs. (36.7)–(36.10). Here, the cluster

size distribution Eq. (36.11) has been used. The obtained

fitting parameters are listed in the insert.

REINFORCEMENT THEORIES / 607

sliding tire tread rubber materials and rough road surfaces

during ABS-braking on wet road surfaces where the braking

process leads to a high frequency (kHz–MHz range)

dynamic-mechanical deformation of the tread rubber mater-

ial [10]. As a practical result, an improved wet skid per-

formance of passenger car tires is expected with the silica

technology [10].

A deeper understanding of molecular mechanisms of

filler flocculation and reinforcement by active fillers like

carbon black or silica represent a fundamental tool for

problem solving in engineering praxis. In particular, the

implementation of micromechanical models into FE-codes

will open a new way for more precise simulations of the

dynamic deformation and damping behavior of rubber

goods, including stress softening effects and filler induced

hysteresis. Even investigations and simulations of the filler

cluster kinetics are of increasing interest [27,28]. This might

be useful for a better understanding and prediction of com-

plex time-dependent rubber deformations like, for example,

tire tread deformations under combined driving and corner-

ing conditions.

ACKNOWLEDGMENTS

The authors are indebted to Dr J. Meier (DIK) and

Dr J. Schramm (Continental AG) for the fruitful cooperation

and to the DFG (FOR 492) for financial support.

REFERENCES

1. G. Heinrich, M. Klu

ppel, T. A. Vilgis, Curr. Opin. Solid State Mater.

Sci. 6, 195 (2002).

2. A. Medalia, Rubber Chem. Technol. 51, 437 (1978).

3. L. Mullins, N. R. Tobin, Rubber Chem. Technol. 39, 799 (1966).

4. S. Westermann, M. Kreitschmann, W. Pyckhout-Hintzen, D. Richter,

E. Straube, B. Farago, G. Goerigk, Macromolecules 32, 5793 (1999).

5. G. Huber, T. A. Vilgis, Macromolecules 35, 9204 (2002).

6. S. Westermann, W. Pyckhout-Hintzen, M. Kreitschmann, D. Richter,

E. Straube, ‘‘Microscopic Deformations in Filled Polymer Networks’’,

Proceedings Kautschuk-Herbst-Kolloquium 2002, Hannover (FRG),

99–107, 30 October–1 November 2002.

7. S. Vieweg, R. Unger, E. Hempel, E. Donth, J. Non-Cryst. Solids 235/

237, 470 (1998).

8. A. Botti, W. Pyckhout-Hintzen, D. Richter, E. Straube, V. Urban,

J. Kohlbrecher, Physica B 276–278 (2000), 371; A. Botti, W. Pyckh-

out-Hintzen, D. Richter, E. Straube, Physica A 304, 230 (2002);

A. Botti, Microscopic deformations in filled networks. PhD thesis,

University Muenster, Germany, 2001.

9. G. Heinrich, M. Klu

ppel, Adv. Polym. Sci. 160, 1 (2002).

10. G. Heinrich, J. Schramm, A. Mu

ller, M. Klu

ppel, N. Kendziorra,

S. Kelbch, ‘‘Zum Einfluss der Straßenoberfla

chen auf das

Bremsverhalten von Pkw-Reifen beim ABS-nass und ABS-trocken

Bremsvorgang’’, Fortschritt-Berichte VDI, Reihe 12 (Verkehrstechnik/

Fahrzeugtechnik), 69–86, 2002, Nr. 511.

11. M. J. Wang, Rubber Chem. Technol. 71, 520 (1998).

12. H. Montes, F. Lequeux, J. Berriot, Macromolecules 36, 8107 (2003).

13. J. Berriot, F. Lequeux, L. Monnerie, H. Montes, D. Long, P. Sotta,

J. Non-Cryst. Solids 310, 719 (2002).

14. J. Berriot, H. Montes, F. Lequeux, D. Long, P. Sotta, Macromolecules

35, 9756 (2002); ibid. Europhys. Lett. 64, 50 (2003).

15. G. Migliorini, V.G. Rostiashivili, T.A. Vilgis, Eur. Phys. J. B33,61

(2003).

16. M. Klu

ppel, Adv. Polym. Sci. 164, 1–86 (2003).

17. M. Klu

ppel and G. Heinrich, Rubber Chem. Technol. 68, 623 (1995).

18. M. Klu

ppel, R.H. Schuster and G. Heinrich, Rubber Chem. Technol.

70, 243 (1997).

19. Y. Kantor and I. Webman, Phys. Rev. Lett. 52, 1891 (1984).

20. A.R. Payne, J. Appl. Polym. Sci. 8, 2661 (1964).

21. L. Ladouce, Y. Bomal, L. Flandin, D. Labarre, ‘‘Dynamic mechanical

properties of precipitated silica filled rubber: Influence of morphology

and coupling agent’’, Paper No. 33, 157

meeting of the Rubber

Division, American Chemical Society, Dallas, Texas, April 4–6,

2000.

22. M. Klu

ppel and J. Schramm, Macromol. Theory Simul. 9, 742 (2000).

23. S.F. Edwards and T.A. Vilgis, Rep. Prog. Phys. 51, 243 (1988);

Polymer 27, 483 (1986).

24. G. Heinrich, E. Straube, G. Helmis, Adv. Polym. Sci. 85, 33 (1988).

25. G. Huber, PhD-Thesis, University Mainz, Germany (1997).

26. G. Huber and T.A. Vilgis, Euro. Phys. J. B3, 217 (1998); ibid.

Kautschuk Gummi Kunstst. 52, 102 (1999).

27. G. Heinrich, V. Ha

rtel, J. Tschimmel, M. Klu

ppel, ‘‘Kinetics of filler

structures in reinforced polymer networks’’, in Michler, G.H. (Hrsg.):

Polymeric Materials 2004 (Halle/Saale, 29.09. – 01.10.2004), A17.

28. G. Heinrich, F.R. Costa, M. Abdel-Goad, U.Wagenknecht, B. Lauke,

V. Ha

rtel, J. Tschimmel, M. Klu

ppel, and A.L. Svistkov, Kautschuk,

Gummi, Kunstst. 58, 163 (2005)

608 / CHAPTER 36

CHAPTER 37

Densities of Amorphous and Crystalline Polymers

Vladyslav Kholodovych and William J. Welsh

Department of Pharmacology, University of Medicine & Dentistry of New Jersey (UMDNJ) – Robert Wood Johnson Medical

School (RWJMS) and the UMDNJ Informatics Institute, Piscataway, NJ 08854

37.1 Definitions . . ............................................................. 611

37.2 General Trends ........................................................... 611

37.3 Amorphous and Crystalline Polymers . . . .................................... 612

37.4 Density and Crystallinity . . ................................................ 612

37.5 Experimental Determination of Density . .................................... 613

37.6 Experimental Values of Density ............................................ 613

References . . ............................................................. 617

37.1 DEFINITIONS

The density r (or mass density) of a material isdefined as its

mass m per unit volume V: r ¼ m=V. The specific volume v

is the inverse of r: v ¼ 1=r. The density of polymers is

commonly specified in cgs units of g=cm

, although the

SI unit is kg=m

(1 g=cm

¼ 10

kg=m

) and the British

engineering unit is slugs=ft

(1 g=cm

¼ 1:95slugs=ft

For some applications, it is more convenient to define

a quantity called weight density D (or specific weight)

as the weight w per unit volume V of the material: D ¼

w=V ¼ (mg)=V ¼ rg, where g is the acceleration due to

gravity. The corresponding units for D are lb=ft

in the

British system and N=m

in SI.

The specific gravity (or relative density) r

rel

of a material

is the ratio of its density r to the density r

of pure water

at 4 8C (39.28F): r

rel

¼ r=r

¼ D=D

, where D

is the

weight density of water. From this definition, it is apparent

that specific gravity is a dimensionless quantity. Whereas

the numerical value of density will vary from one system of

units to another, the specific gravity has the same value in all

systems of units. Since the density of water in the cgs system

is 1 g=cm

, densities in that system are numerically equal to

the specific gravity: r(in g=cm

) ¼ r

rel

37.2 GENERAL TRENDS

Starting from the lowest members of a homologous ser-

ies, the density first increases gradually then appears to

approach an asymptotic limit. This behavior is illustrated

in Fig. 37.1 by plots of r versus the number of repeated units

n for the homologous series of alkanes H[CH

]

H and the

cycloalkanes [CH

]

[1]. As n becomes larger, the differ-

ence in density between adjacent members of the series

becomes relatively smaller since the changes in molecular

structure are less marked.

Since synthetic polymers are formed mostly from light

elements (carbon, hydrogen, oxygen, and nitrogen), the

densities of solid polymers lie broadly in the range

0.8–1.8 g=cm

. This range is considerably lower than

that for inorganic materials (2:2---4:0g=cm

) and metals

(2:7---11:5g=cm

). Polymers containing heavier elements

such as fluorine, chlorine, and bromine, exhibit significantly

higher densities: polytetrafluoroethylene (2:28 g=cm

poly(vinylidene fluoride) (1:77 g=cm

), and poly(vinylidene

chloride) (1:65---1:87 g=cm

). Hydrocarbon polymers with

relatively open-packed structures dominate the low end of

the density scale: polypropylene (0:90 g=cm

), ethylene–

propylene copolymer elastomer (0:86 g=cm

), and the

thermoplastic polybutylene (0:60 g=cm

) with the lowest

density of all commercial polymers [2–4].

In general, the density of a polymer varies inversely

with temperature but is much less sensitive to pressure.

The introduction of fillers and plasticizers can alter the

density and cause variations in density across a sample

due to nonuniform distribution. Nevertheless, the

average density is nearly invariant to small amounts of

plasticizers.

611

37.3 AMORPHOUS AND CRYSTALLINE

POLYMERS

Polymers can be divided into two groups morphologic-

ally: amorphous polymers and crystalline polymers.

Amorphous polymers lack sufficient regularity in packing

of the chains to produce the sharp x-ray diffraction pattern

characteristic of highly crystalline polymers. The term crys-

talline polymer is actually a misnomer since no polymer is

100% crystalline, containing both crystalline domains and

amorphous domains. Therefore, a more correct yet seldom

used designation is ‘‘semicrystalline’’ polymer.

The polymer chains are packed together more efficiently

and tightly in the crystalline region than in the amorphous

region, consequently the density of the crystalline region r

will typically be larger than that of the corresponding

amorphous region r

. For this reason, the density of a

polymer increases with its degree of crystallinity x

. The

ratio r

can vary considerably from polymer to polymer

from the average value of 1.13 g/cm [3,5]. In typical cases,

the r

and r

of a polymer will generally differ up to 15%

[4]. Polymers with unsubstituted monomeric units, such as

poly(ethylene) and nylon-6,6, show the largest difference

between r

and r

. These chains crystallize in an all-trans

conformation with particularly tight packing of the chains.

In contrast, helix-forming polymers with large substituents,

such as isotactic poly(styrene), pack less efficiently in the

crystalline state thus r

 r

is correspondingly smaller. For

semicrystalline polymers, van Krevelen [5] gives the ap-

proximate relationship r

¼ 1 þ 0:13x

, where r

the density of the (semi-) crystalline polymer.

The bulk density r of polymer solids is influenced

strongly by the elemental composition and, to a certain

degree, by the packing arrangement of chains and side

groups. A polymer chain must exhibit an ordered, regular

structure to allow efficient packing into the crystal lattice.

Consequently, a stereoregular polymer is more likely to be

crystalline and possess a higher density than the correspond-

ing stereoirregular polymer [2–4]. Polymer chains possess-

ing bulky, protruding side groups will pack inefficiently and

are rarely crystalline. Accordingly, their densities tend to be

lower than average. On the other hand, polymers capable of

forming strong interchain hydrogen bonds or dipole–dipole

interactions induce crystallinity and typically possess

above-average densities.

Amorphous polymers generally exist as hard, rigid, glassy

plastics below their glass-transition temperature T

and as

soft, flexible, rubbery materials above their T

. Comparison

of the densities of the glassy state (r

) and the rubbery

state (r

) for various amorphous polymers indicates that

> r

[5].

Density is often the single parameter that is most clearly

related to the physical and mechanical properties of poly-

mers. For many polymers, properties dependent on crystal-

linity (e.g., stiffness, tear strength, hardness, chemical

resistance, softening temperature, yield point) tend to in-

crease with increasing density. Other properties (e.g., per-

meability to gases and liquids, toughness, flex life) tend to

decrease with increasing density [6].

37.4 DENSITY AND CRYSTALLINITY

From the preceding discussion, it is apparent that density

is a convenient measure of the degree of crystallinity. Thus

‘‘low density’’ (0:910---0:925 g=cm

) polyethylene is about

60% crystalline, while ‘‘high density’’ (0:94---0:97 g=cm

)

polyethylene is about 95% crystalline. These differences in

density arise primarily from differences in the degree of

branching. The branch points sterically preclude packing

into a crystal lattice in their immediate vicinity and thus

lower the degree of crystallinity x

[2–6].

The relationship between the degree of crystallinity and

the observed polymer density can be derived from two

slightly different perspectives, depending on whether one

assumes additivity of the crystalline and amorphous

regions with respect to volume (V ¼ V

þ V

) or to mass

(M ¼ M

þ M

). For the former case, one obtains the

relation

n ¼ x

þ (1x

, (37:1)

where x

¼ M

=M is the mass crystallinity (i.e., the mass

fraction that is crystalline) and n, n

, and n

are the bulk,

crystalline, and amorphous specific volumes, respectively.

Solving for x

, Eq. (37.1) yields

¼ (n  n

)=(n

n

): (37:2)

02040

60 80 100

0.4

0.5

0.6

0.7

0.8

0.9

Density (g/cm

)

Alkanes H[CH

]

Cycloalkanes [CH

]

( )

FIGURE 37.1. Density as a function of repeat unit n for

the homologous series of alkanes (

) and cycloalkanes (D).

Reproduced from [1].

612 / CHAPTER 37

Assuming instead additivity with respect to mass, one

obtains the relation

r ¼ x

þ (1x

: (37:3)

Analogous to Eq. (37.1), where x

¼ V

=V is the volume

crystallinity (i.e., the volume fraction that is crystalline)

and r, r

, and r

are the bulk, crystalline, and amorphous

densities, respectively. Solving Eq. (37.3) for x

, one obtains

¼ (r  r

)=(r

 r

): (37:4)

The mass crystallinity x

and volume crystallinity x

thus defined are interrelated by the equation

¼ (n=n

¼ (r

=r)x

. Unfortunately, it is easy to inad-

vertently use x

and x

interchangeably even though they

may differ up to a few percent. In Eq. (37.5) below taken

from Tadokoro [8], his ‘‘x

’’ is equivalent to the x

in Eq.

(37.1) and (37.2).

1=r ¼ x

þ (1  x

)=r

: (37:5)

37.5 EXPERIMENTAL DETERMINATION OF

DENSITY

In (semi-)crystalline polymers, the measured density of a

sample provides a simple way to estimate the degree of

crystallinity. For example, the density of polyethylene

shows a strong linear correlation with percent crystallinity

[9]. The density of the crystalline region may be calculated

from the dimensions of the unit cell, while the density of the

amorphous region can be estimated by extrapolations from

the melt density aided with a knowledge of the polymer’s

coefficient of thermal expansion a

For a unit cell of Z monomeric units, the density r

of the

crystalline region is given by

(in g=cm

) ¼ ZM=N

V ¼ 1:66ZM=V(

), (37:6)

where N

is Avogadro’s number (6:022  10

), V is the

volume of the unit cell, and M is the molecular weight of the

monomeric unit [8]. The presence of any foreign matter

(e.g., dirt, catalyst, solvent, additives, fillers) in the polymer

sample will affect the measured density and likely reduce

the degree of crystallinity. The presence of even a small

number of voids can lead to more serious inaccuracies.

The bulk density r of even small samples may be readily

determined using a density-gradient tube or by immersion in

salt solutions of known density. The latter method is well

adapted for rapid work in routine analyses. The density-

gradient method is currently the standard method employed

by numerous workers [10]. A density-gradient column con-

tains a liquid whose density increases continuously from the

meniscus down to the base [11]. Such liquids can consist, for

example, of mixtures of organic solvents or of salt solutions

selected to wet but not swell or dissolve the polymer sample.

With the appropriate mechanical apparatus, it is possible to

form density gradients in which the variation of the density

with column height is linear, concave, convex, etc. The

polymer sample then remains suspended at a particular

height of the gradient column whose density matches the

sample’s density. Another, presumably more accurate,

technique for measuring density is with a dilatometer [11].

Other methods for measuring density are discussed else-

where [12].

The bulk density r can also be determined from straight-

forward measurements of the polymer’s mass and volume

[13]. The mass of the sample is determined by weighing it

on a suitable balance. If the weighing is done in air, this

apparent density should be adjusted for the buoyant effect of

the air on the sample to obtain the true polymer density. The

density of air under normal ambient conditions is about

0:0012 g=cm

(0:075 lb=ft

). The volume of the sample

can be determined accurately using a procedure known as

hydrostatic weighing based on Archimedes’ Principle. The

sample is weighed both in air and while submerged in a

liquid of known density. The volume of the sample is then

equal to its loss of weight in the liquid divided by the density

of the liquid. All density measurements of solids are subject

to error due to the presence of inhomogeneities such as

surface imperfections, trapped air bubbles, presence of

monomer, etc.

Finally, the appreciable variation in published density

measurements from different workers is due in part to dif-

ferences in the thermal, mechanical, and chemical history of

the individual polymer samples, to differences in the labora-

tory skills and techniques of the worker, and to variations in

the types and quality of methods employed to measure the

density.

37.6 EXPERIMENTAL VALUES OF DENSITY

Tables 37.1 and 37.2 provide a compilation of represen-

tative values of macroscopic (bulk) density r for many of

the more common polymers. For easy reference, the data are

listed alphabetically by the name of the polymer. Table 37.1

contains polymers designated by their familiar or trade

names (e.g., nylon, rubber), while Table 37.2 lists polymers

designated by their chemical names using the prefix ‘‘poly.’’

These are alphabetized by the letter following this prefix.

For example, poly(ethylene) and poly(vinylacetate) are

listed under ‘‘e’’ and ‘‘v’’, respectively. In many cases, the

density of a given polymer is represented by a range of

values (e.g., 0:87---0:93 g=cm

) to reflect variations obtained

from different sources of the data.

DENSITIES OF AMORPHOUS AND CRYSTALLINE POLYMERS / 613

TABLE 37.1. Values of density for some polymers designated by their common or trade name.

Common or trade name r(g=cm

) Reference

Acetate rayon 1.32 [6]

Acrylic 1.16 [6]

Acrylonitrile–styrene copolymer 1.075–1.10 [11a]

Acrylonitrile–styrene–butadiene copolymer (ABS) 1.04–1.07 [3]

Aniline-formaldehyde 1.22–1.25 [11a]

Ardel D-100, Arylef, U-100 1.21 [17]

Arnitel 1.17–1.27 [17]

Aramides (nomex, durette, conex, kevlar, twerlon) 1.34–1.47 [17]

Benzylcellulose 1.22 [11a]

Bisphenol-A polycarbonate (BPAPC) 1.2 [11a]

Butyl rubber 0.92 [11a]

Cellulose I 1.582–1.630 [1,14]

Cellulose II 1.583–1.62 [1,14]

Cellulose III 1.61 [14]

Cellulose IV 1.61 [1,14]

Cellulose acetate 1.28–1.32 [11a]

Cellulose acetate-butyrate 1.14–1.22 [11a]

Cellulose formate fiber 1.45 [11a]

Cellulose nitrate 1.35–1.40 [11a]

Cellulose propionate 1.18–1.24 [11a]

Cellulose triacetate 1.28–1.33 [11a,14]

Cellulose tributyrate 1.16 [14]

Chlorinated polyether 1.4 [11a]

Cotton 1.50–1.54 [1,6,11a]

Cotton, acetylated 1.43 [11a]

CXA and plexar resins (ethylene copolymers) 0.935–1.00 [17]

Durel, D-400 1.20 [17]

Ethylcellulose 1.09–1.17 [11a]

Ethylene–propylene copolymer (EPM) 0.86 [3]

Glass 3.54 [11a]

Glass and asbestos 2.5 [11a]

Hytrel 1.17–1.22 [17]

Keldax 1.67–1.83 [17]

Keltan 0.89 [17]

Kevlar 1.44 [6]

KL 1–9300/1–9310 (Bayer) 1.21–1.44 [17]

Lignocellulose 1.45 [11a]

Levasint 0.97 [17]

Levaflex 0.89–1.04 [17]

Maleic anhydride–styrene copolymer 1.286 [11a]

Melamine-formaldehyde 1.16 [11a]

Methyl polyvinyl ketone 1.12 [11a]

Methylcellulose 1.362 [11a]

Nomex 1.38 [6]

Noryl 1.06–1.2 [17]

Nylon 6 1.12–1.24 [1,3]

Nylon 66 1.13–1.15, 1.22–1.25 [1,3]

Nylon-610 1.156 [1]

Nylon-12 1.02–1.034 [1,3]

Rubber, butyl 0.92 [3]

Rubber (unvulcanized) 0.91 [1,3]

Rubber (hard) (Ebonite) 1.11–1.17 [1,11a]

Rubber, chlorinated (Neoprene) (CR), unvulcanized 1.23 [1,11a]

Rubber, chlorinated (Neoprene) (CR), vulcanized 1.32–1.42 [1]

Rubber, fluorinated silicone 1 [11a]

Rubber, silicone 0.8 [11a]

Rubber, silicone (vulcanized) 1.3–2.3 [11a]

614 / CHAPTER 37

TABLE 37.1. Continued.

Common or trade name r(g=cm

) Reference

Rubber, styrene–butadiene (SBR), (unvulcanized) 0.93–0.94 [3,11a]

Rubber, styrene–butadiene (SBR), (vulcanized) 0.961 [11a]

Silk 1.25–1.35 [6,11a]

Santoprene 0.95–0.98 [17]

Tafmer 0.88 [17]

Toluene-sulfonamide-formaldehyde 1.21 –1.35 [11a]

Urea-formaldehyde 1.16 [11a]

Urea-thiourea-formaldehyde 1. 477 [11a]

Viscose Rayon 1.5 [6]

Vestopren 0.90–1.10 [17]

Wool 1.28–1.33 [6,11a]

TABLE 37.2. Values of density for some polymers designated by their chemical name.

Chemical name r(g=cm

) Reference

Poly-

acetylaldehyde 1.07 [5]

acrolein 1.322 [11a]

acrylic acid 1.22 [11a]

acrylonitrile (PAN) 1.01–1.17, 1.20 [3,11a]

acrylonitrile-vinyl acetate 1.14 [11a]

amide-6 (PA-6) 1.12–1.24 [1.3]

amide-66 (PA-66) 1.13–1.15, 1.22–1.25 [1,3]

amide-610(PA-610) 1.156 [1]

amide-12(PA-12) 1.02–1.034 [1.3]

aryl ether ketone (PEEK) 1.2, 1.3 [16,17]

arylate 1.21 [3]

benzimidazole (PBI) 1.43 [17]

bisphenol carbonate (BPAPC) 1.2 [5]

butadiene-1,2, isotactic 0.96 [1,11a]

butadiene-1,2, syndiotactic 0.96 [1,11a]

butadiene-1,4-cis 1.01 [1]

butadiene-1,4-trans 0.93– 0.97,1.01 [1,11a]

1-butene 0.85 [5]

butene 0.91–0.92 [3]

butyl acrylate 1.08 [5]

sec.-butyl acrylate 1.05 [5]

butylene 0.6 [3]

tert.-butyl methacrylate 1.03 [5]

-n-butyl methacrylate 1.055 [11a]

sec.-butyl methacrylate 1.04 [5]

tert.-butylstyrene 0.957 [16]

caprolactam, nylon 0.985 [16]

carbonate (PC) 1.14–1.2 [3,16]

chlorobutadiene 1.25 [11a]

chloroprene (Neoprene rubber) (CR), unvulcanized 1.23 [1,3]

chloroprene (Neoprene rubber) (CR), vulcanized 1.32–1.42 [1]

chlorotrifluoroethylene 2.03 [5]

dichlorostyrene 1.38 [11a]

2,2-dimethylpropyl acrylate 1.04 [5]

dimethylsiloxane 0.97 [16]

dodecyl methacrylate 0.93 [5]

1-ethylpropyl acrylate 1.04 [5]

etheretherketone (PEEK) 1.27 [3]

DENSITIES OF AMORPHOUS AND CRYSTALLINE POLYMERS / 615

TABLE 37.2. Continued.

Chemical name r(g=cm

) Reference

ethersulfone 1.4 [17]

ethyl acrylate 1.095, 1.12 [5,11a]

ethyl methacrylate 1.11, 1.12 [5,11a]

ethylbutadiene 0.891 [10c,16]

ethylene 0.870, 0.910–0.965 [1,6,10c,11a]

ethylene (amorphous) 0.85 [1,11a,14]

ethylene (crystalline) 0.99 [1,11a]

ethylene (high density:HDPE) 0.941–0.965 [1,3,6,15,17]

ethylene (linear low density: LLDPE) 0.918–0.935 [3,6,17]

ethylene (low density: LDPE) 0.910–0.925 [1,3,6,15,17]

ethylene (medium density: MDPE/IDPE) 0.926–0.940 [1,3,17]

ethylene (very low density: VLDPE) 0.900 [17]

ethylene glycol 1.0951 [11a]

ethylene glycol fumarate 1.385 [11a]

ethylene glycol isophthalate, cryst. 1.358 [11a]

ethylene glycol phthalate 1.352 [11a]

ethylene glycol waxes 1.15–1.20 [11a]

ethylene isophthalate 1.34 [5]

ethylene phthalate 1.34 [5]

ethylene terephthalate (PET) 1.33–1.42 [1,3,5,6]

formaldehyde 1.425 [11a]

-n-hexyl methacrylate 1.01 [11a]

imide 1.43 [3,6]

isobutene 0.917 [14]

isobutyl methacrylate 1.02–1.04 [5,11a]

isobutylene 0.87–0.93 [5,11a,16]

isoprene (1,4-) 0.900–0.913 [16]

-N-isopropylacrylamide 1.070–1.118 [11a]

isopropyl acrylate 1.08 [5]

isopropyl methacrylate 1.04 [5]

methacrylonitrile 1.1 [11a]

methyl acrylate 1.07–1.223 [5,11a,16]

methyl methacrylate (PMMA) 1.16–1.20 [1,5,11a,14]

-p-methylstyrene (PMA) 1.01 [17]

4-methyl-1-pentene 0.84 [5]

myrcene 0.895 [10c]

trans-octenamer (TOR) 0.91 [17]

olefin-co-vinyl alcohol (GL/EVAL) 0.97–1.52 [17]

oxymethylene (POM) 1.41–1.435 [1,3]

-p-phenylene (H resins) 1.145–1.35 [17]

phenylene oxide 1.00–1.06 [3,16]

phenylene-1,3,4-oxadiazole (POD) 1.40 [17]

polysulfide (Thiokol A) 1.6 [11a]

polysulfide (Thiokol B) 1.65 [11a]

propyl methacrylate 1.06–1.08 [5,11a]

propylene (PP) 0.85–0.92 [3,6,5,10c]

propylene, amorphous 0.87 [11a]

propylene, head-to-head 0.878 [10c]

propylene, isotactic 0.90–0.92 [1,11a]

propylene, isotactic (crystalline) 0.92–0.939 [1,11a]

propylene, syndiotactic (crystalline) 0.93 [1]

propylene oxide 1 [16]

styrene (PS) 1.04–1.09 [1,3,5,6,11a,14,17]

styrene, crystalline 1.08–1.111 [1,11a]

styrene–butadiene thermoplastic elastomer 0.93–1.10 [6]

sulfone 1.20–1.24 [3,6,17]

616 / CHAPTER 37

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p.508.

TABLE 37.2. Continued.

Chemical name r(g=cm

) Reference

tetrafluoroethylene (PTFE) 2.28–2.344,2.17 [1], [17]

thiodiethanol 1.35 [17]

trifluorochloroethylene 2.11–2.13 [11a]

vinyl acetate (PVAC) 1.08–1.25 [1,3,5,11a]

vinyl alcohol (PVA) 1.21–1.31 [11a]

vinyl butyral 1.07–1.20 [11a]

vinylcarbazole 1.2 [11a]

vinyl chloride (PVC) 1.37–1.44 [1,3,5,11a,17]

vinyl chloride-co-methyl acrylate 1.34 [11a]

vinyl chloride, flexible 1.25–1.35 [11a]

vinyl chloride, rigid 1.35–1.55 [11a]

vinyl chloride acrylonitrile (60/40) 1.28 [11a]

vinylidene chloride (PVDC) 1.65–1.875 [3,5,6,11a]

vinylethylene 0.889 [10c,16]

vinyl formal 1.2–1.4 [11a]

-p-vinylphenol 1.2 [17]

-p-vinylphenol, brominated 1.9 [17]

vinyl pyrrolidone (PVP) 1.25 [11a]

vinyl-vinylidene chloride 1.7 [1,11a]

vinylidene fluoride (PVDF) 1.75–1.78 [1]

vinylisobutyl ether 0.91–0.92 [11a]

-m-xylene adipamide 1.22 [11a]

DENSITIES OF AMORPHOUS AND CRYSTALLINE POLYMERS / 617