An Introductory Text
`and Reference for
`Engineers and Chemists
`
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`

`THE ELEMENTS OF
`
`Polymer
`Science and
`Engineering
`
`Second Edition
`
`An Introductory Text and Reference
`for Engineers and Chemists
`
`Alf red Rudin
`University of Waterloo
`
`ACADEMIC PRESS
`An l,11pri11t of Elsevier
`San Diego London Boston
`New York Sydney Tokyo Toronto
`
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`This book is printed on acid-free paper. E)
`
`Copyright © 1999 by Academic Press
`
`All Rights Reserved.
`No part of this publication may he reproduced or
`transmitted in any form or by any means, electronic
`or mechanical, including photocopy, recording, or
`any information storage and retrieval system, without
`permission in writing from the publisher.
`
`Permissions may be so11gh1 directly from Elsevier's Science and lechnology Righls Depar11nent in
`Oxford, UK. Phone: (44) 1865 843830, Fax: (44) 1865 853333. e-mail: permissions@elsevier.co.uk.
`You may also complete your l\.'qucst on-line via the Elsevier homepage: h11p://www.dsevier.com by
`selecting "Cuslomer Support" and lhen "Obtaining Permissions".
`
`ACADEMIC PRESS
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`http://www.apnet.com
`
`ACADEMIC PRESS
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`
`Library of Congress Cataloging-in-Publication Data
`Rudin, Alfred
`The elements of polymer science and engineering /Alfred Rudin.-2nd ed.
`p.
`cm.
`Includes bibliographical references and index.
`ISBN-1 3: 978-0-12-601685-7 ISBN-10: 0-12-601685-2 (acid-free paper)
`I . Polymers.
`2. Polymerization.
`QD381.R8 1998
`547'.7-dc21
`
`98- 11 623
`CIP
`
`ISBN- 13: 978-0- 12-601685-7
`ISBN- 10: 0- 12-601685-2
`Printed in the United States of America
`05 06 MY 9 8 7 6 5 4
`
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`

`Chapter 4
`
`Effects of Polymer Isomerism
`and Conformational Changes
`
`Wirh a name like yours. you mighl be any shape, almost .
`. - Lewis Carroll, Through the Looking Glass
`
`Three types of isomerism are important in macromolecular species. These involve
`constitutional, configurational, and conformational variations. These terms are
`defined and illustrated. Their usage in macromolecular science is very much the
`same as in micromolecular chemistry.
`·
`
`4.1 CONSTITUTIONAL ISOMERISM
`
`The constitution of a molecule specifies which atoms in the molecule are linked
`together and with what types of bonds.
`Isobutane (4-1) and n-butane (4-2) are familiar examples of constitutional
`isomers. Each has the molecular formula C4H 1o butthe C and H atoms are joined
`differently in these two molecules. In polymers the major types of constitutional
`differences involve positional isomerism and branching.
`
`CH3
`CH3 - r - H
`I
`
`CH3
`
`4-1
`
`4-2
`
`121
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`122
`
`4 Effects of Polymer Isomerism and Conformational Changes
`
`4.1.1 Positional Isomerism
`
`Vinyl and vinylidene monomers arc basically unsymmetrical because the two
`ends of the double bond are distinguishable (ethylene and tetrafluorcthylene are
`exceptions). One C of the double bond can he arbitrarily labeled the head and the
`other the tail of the monomer, as shown in the formula for vinyl fluoride (4-3).
`
`head
`
`toil
`
`H
`I
`CH = C
`2
`I
`F
`
`4-3
`
`In principle, the monomer can be enchained by head-to-tail linkages or head(cid:173)
`to-head, tail-to-t,ail enchainments (4-4). Poly(vinyl fluoride) actually has about
`15% of its monomers in the head-to-head, tail-to-tail mode. This is exceptional,
`however. Head-to-tail enchainment appears to he the predominant or exclusive
`constitution of most vinyl polymers because of the influem;e of resonance and
`steric effects.
`
`H
`H H
`H
`H
`I
`I
`I
`I
`I
`2, 2, 2,, 2 2,
`-CH -C-CH -C-CH -C-C-CH -CH -C 'VVV
`
`F
`
`F
`
`F F
`
`F
`
`HEAD - TO -TAIL
`
`HEAD - TO -HEAD
`TAIL - TO -TAIL
`
`4-4
`
`Vinyl monomers polymerize by attack of an active center (4-5) on the double
`bond. Equation (4-1) represents head-to-tail enchainment:
`y
`y
`y
`I
`I
`I
`
`W0 c~ - T •+Cf½= l - W0 c~ - r -Cf½ -1 •
`
`y
`I
`
`( 4-1)
`
`X
`
`X
`
`4-5
`
`X
`
`X
`
`4-6
`
`while Eq. (4-2) shows the sequence of events in head-to-head, tail-to-tail polymer(cid:173)
`ization:
`
`W0 c~ - 1 uc~ = 1-W-/1 Cf½-1-1-cf½•
`
`y
`I
`
`X
`
`y
`I
`
`X
`
`y
`I
`
`y
`I
`
`X X
`
`(4-2)
`
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`4.1 Constitutional Isomerism
`
`123
`
`The active center may he a free-radical, ion, or metal-carbon bond (Chapter 6). In
`any event the propagating species 4-6 will be more stable than its counterpart 4-7
`if the unpaired electron or ionic charge can be delocalized across either or both
`substituents X and Y. When X and/or Y is bulky there will be more steric hindrance
`to approach of the two substituted C atoms than in attack of the active center on
`the methylene C as in reaction (4-1 ). Poly(vinyl nuoride) contains some head(cid:173)
`to-head linkages because the F atoms are relatively small and do not contribute
`signilkanlly lo the resonance stabilization of the growing macroradical.
`Positional isomerism is not generally an important issue in syntheses of poly(cid:173)
`mers with backbones which do not consist exclusively of enchained carbons.
`This is because the monomers which form macromolecules such as poly(ethylcne
`terephthalate) (1-5) or nylon-6,6 (1-6) are chosen so as to produce symmetrical
`polymeric structures which facilitate the crystallization needed for many appli(cid:173)
`cations of these particular polymers. Positional isomerism can be introduced
`into such macromolecules by using unsymmetrical monomers like 1,2-propylcne
`glycol (4-8), for example. This is what is done in the synthesis of some film(cid:173)
`forming polymers like alkyds (Section 5.4.2) in which crystallization is undesir(cid:173)
`able.
`
`H
`I
`CH.3 - C- CH20H
`I
`OH
`4-8
`
`It has been suggested that tail-to-tail linkages in vinyl polymers may constitute
`weak points at which thermal degradation may be initiated more readily than in
`the predominant head-to-tail structures.
`Polymers of dienes (hydrocarbons containing two C-C double bonds) have
`the potential for head-to-tail and head-to-head isomerism and variations in double(cid:173)
`bond position as well. The conjugated diene butadiene can polymerize to produce
`1,4 and 1,2 products:
`
`H H
`I
`I
`CH2 = C - C = CH2
`2
`3
`4
`
`H H
`I
`I
`+ c- c-+.;
`~ I X
`
`H - C = CH2
`1,2- polybutodiene
`
`H
`H
`I
`I
`+ c~ - c = c - c~ +x
`
`1 ;4 -polybutodiene
`
`(4-3)
`
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`124
`
`4 Effects of Polymer Isomerism and Conformational Changes
`
`The C ·atoms in the monomer are numbered in reaction (4-3) and the polymers
`are named according to the particular atoms involved in the enchainment. There
`is no 3,4-polybutadiene because carbons I and 4 are not distinguishable in the
`monomer structure. This is not the case with 2-substituted conjugated butadienes
`like isoprene:
`
`H
`I
`C = CH:z
`
`Cfi:2 = C -
`I
`CHJ
`
`CH 3
`I
`+CH:z- C -t.:
`I X
`H-C = CH:z
`1,2 - polyisoprene
`
`H
`I
`+ CH:z- C -t.:
`I X
`C-CH
`J
`II
`CH:z
`3,4 - polyisoprene
`
`THJ ~
`+ CH:z - C = C - CH:z "'1x
`
`1 ,4 - polyisoprene
`
`(4-4)
`
`Each isomer shown in reaction (4-4) can conceivably also exist in head-to-tail
`or head-to-head, tail-to-tail forms and thus there arc six possible constitutional
`isomers of isoprcne or chloroprene (structure of chloroprcne is given in Fig. 1-4 ).
`to say nothing of the potential for mixed structures.
`The constitution of natural rubber is head-to-tail 1,4-polyisoprene. Some meth(cid:173)
`ods for synthesis of such polymers are reviewed in Chapter 9.
`Unconjugated dienes can produce an even more complicated range of macro(cid:173)
`molecular structures. Homopolymers of such monomers are not of current com(cid:173)
`mercial importance but small proportions of monomers like 1,5-cyclooctadicne
`are copolymerized with ethylene and propylene to produce so-called EPDM rub(cid:173)
`bers. Only one of the diene double bonds is enchained when this terpolymeriza(cid:173)
`tion is carried out with Ziegler-Natta catalysts (Section 9.5). The resulting small
`amount of unsaturation permits the use of sulfur vulcanization, as described in
`Section 1.3.3.
`
`4.1.2 Branching
`
`Linear and branched polymer structures were defined in Section 1.6. Branched
`polymers differ from their linear counterparts in several important aspects.
`Branches in crystallizablc polymers limit the size of ordered domains because
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`4.1 Constitutional Isomerism
`
`125
`
`branch points cannot usually fit into the crystal lattice. Thus branched polyethy(cid:173)
`lene is generally less rigid, dense, brittle, and crystalline than linear polyethy(cid:173)
`lene, because the former polymer contains a significant number of relatively short
`branches. The branched, low-density polyethylenes are preferred for packaging
`at present because the smaller crystallized regions which they produce provide
`transparent, tough films. By contrast, the high-density, linear polyethylenes yield
`plastic bottles and containers more economically because their greater rigidity
`enables production of the required wall strengths with less polymer.
`A branched macromolecule forms a more compact coil than a linear polymer
`with the same molecular weight, and the now properties of the two types can differ
`significantly in the melt as well as in solution. Controlled introduction ofrelatively
`long branches into diene rubbers increases the resistance of such materials lo flow
`under low loads without impairing processability at commercial rates in calenders
`orextruders. The high-speed extrusion of linear polyethylene is similarly improved
`by the presence of a few long branches per average molecule.
`Branching may be produced deliberately by copolymerizing the principal
`monomer with a suitable comonomer. Ethylene and I-butene can be copolymer(cid:173)
`ized with a diethylaluminum chloride/titanium chloride (Section 9.5) and other
`catalysts to produce a polyethylene with ethyl branches:
`H
`H
`I
`I
`CH2 = Cf½ + Cf½ = C -W, Cf½ - Cf½ - Cf½- C - Cf½- CH2 W,
`I
`I
`c~
`c~
`I
`I
`CH 3
`CH
`
`( 4-5)
`
`3
`
`The extent to which this polymer can crystallize under given conditions is con(cid:173)
`trolled by the butene concentration.
`Copolymerization of a bifunctional monomer with a polyfunctional co(cid:173)
`monomer produces branches which can continue lo grow by addition of more
`monomer. An example is the use of divinylbenzene (4-9) in the butyl lithium
`initiated polymerization of butadiene (Section 9.2). The diene has a functionality
`of 2 under these conditions whereas the functionality of 4-9 is 4. The resulting
`
`H-rH2
`
`H - C= C~
`
`4-9
`
`elastomeric macromolecule contains segments with structure 4-10. Long branches
`such as these can interconnect and form cross-linked, network structures depend(cid:173)
`ing on the concentration of poly functional comonomer and the fractions of total
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`126
`
`4 Effects of Polymer Isomerism and Conformational Changes
`
`monomers which have been polymerized. The reaction conditions under which
`this undesirable occurrence can be prevented are outlined in Section 7.9.
`
`4-10
`
`Another type of branching occurs in some free-radical polymerizations of
`monomers like ethylene, vinyl chloride, and vinyl acetate in which the macro(cid:173)
`radicals are very reactive. So-called "self-branching" can occur in such polymer(cid:173)
`izations because of atom transfer reactions between such radicals and polymer
`molecules. These reactions, which are inherent in the particular polymerization
`process, are described in Chapter 6.
`Although the occurrence of constitutive isomerism can have a profound effect
`on polymer properties, the quantitiative characterization of such structural varia(cid:173)
`tions has been difficult. Recent research has shown that the 13C chemical shifts of
`polymers are sensitive to the type, length, and distribution of branches as well as
`to positional isomerism and stereochemical isomerism (Section 4.2.2). This tech(cid:173)
`nique has great potential when the bands in the polymer spectra can be assigned
`unequivocally.
`
`4.2 CONFIGURATIONAL ISOMERISM
`
`Configuration specifies the relative spatial arrangement of bonds in a molecule (of
`given constitution) without regard to the changes in molecular shape which can
`arise because of rotations about single bonds. A change in configuration requires
`the breaking and reforming of chemical bonds. There are two types of contigura(cid:173)
`tional isomerism in polymers and these are analogous to geometrical and optical
`isomerism in micromolecular compounds.
`
`4.2.l Geometrical Isomerism
`
`When conjugated dienes polymerize by 1,4-enchainment, the polymer backbone
`contains a carbon-carbon double bond. The two carbon atoms in the double bond
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`4.2 Contigurational Isomerism
`
`127
`
`cannot rotate about this linkage and two nonsuperimposablc configurations arc
`therefore possible if the substituenls on each carbon differ from each other. For
`example, the two monomers malcic acid (4-11 , cis) and fumaric acid (4-12, trans)
`
`H-C-C00H
`II
`H-C-C00H
`
`H -C-C00H
`II
`H00C -C-H
`
`4-11
`
`4-12
`
`are geometrical isomers. Natural rubber is the all-cis isomer of 1,4-polyisoprene
`and has the structure shown in 1-18.
`The molecules in solid trans isomers pack more tightly and crystallize more
`readily than cis isomers. (The melting point of fumaric acid is 160°C higher than
`that of maleic acid.) These corresponding differences in polymers are also major.
`The 1,4-cis-polydicnes are rubbers, whereas the trans isomers arc relatively low
`melting thermoplastics.
`Isomerism in diene polymers can be measured by infrared and nuclear magnetic
`resonance spectroscopy. Some of the polymerization methods described in Chapter
`9 allow the production of polydicnes with known controlled constitutions and
`geometrical configurations.
`Cellulose (1-11) and amylose starch do not contain carbon-carbon double bonds
`but they are also geometrical isomers. Both consist of I ,4-linkcd o-glucopyranose
`rings, and the difference between them is in configuration at carbon I. As a result,
`cellulose is highly crystalline and is widely applied as a structural material while
`the more easily hydrolyzed starch is used primarily as food .
`
`4.2.2 Stereoisomerism
`
`Stercoisomerism occurs in vinyl polymers when one of the carbon atoms of the
`It is formally simi(cid:173)
`monomer double bond carries two different substituents.
`lar to the optical isomerism of organic chemistry in which the presence of an
`asy111111etril; 1:arbu11 atu111 pru<luu:s lwu isu111ers whid, an:: 11ut super irnpusablc.
`Thus glyceraldehydc exists as two stereoisomers with configurations shown in
`4-13. (The dotted lines denote bonds below and the wedge signifies bonds above
`the plane of the page.) Similarly, polymerization of a monomer with structure
`
`OHC •. , /H
`
`HO~
`
`'CH:zOH
`
`4-13
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`128
`
`4 Effects of Polymer Isomerism and Conformational Changes
`
`4-14 (where X and Y are any substituenls that are not identical) yields poly(cid:173)
`mers in which every other carbon atom in the chain is a site of steric isomerism.
`
`y
`I
`Cf½ = C
`I
`X
`
`4-14
`
`Such a site, labeled C' in 4-15, is termed a pseudoasymmetric or chiral carbon
`atom.
`
`'f
`T
`y
`W. Cf½ - c•- Cf½ - c•- Cf½ - c•w.
`I
`I
`I
`X
`X
`X
`
`4-15
`
`The two glyceraldehyde isomers of 4-13 arc identical in all physical properties
`except that they rotate the plane of polarized light in opposite directions and form
`enantiomorphous crystals. When more than one asymmetric center is present in a
`low-molecular-weight species, however, stcreoisomers are formed which are not
`mirror images of each other and which may differ in many physical properties. An
`example of a compound with two asymmetric carbons (a diastereomer) is tartaric
`acid, 4-16, which can exist in two optically active forms (D and L, mp 170°C), an
`optically inactive form (meso, mp 140°C), and as an optically inactive mixture
`(DL racemic, mp 206°C).
`
`COOH
`I
`HOC-H
`I
`H-C-OH
`I
`COOH
`
`4-16
`
`Vinyl polymers contain many pseudoasymmetric sites, and their properties
`are related to those of micromolecular compounds which contain more than one
`asymmetric carbon. Most polymers of this type are not optically active. The reason
`for this can be seen from structure 4-15. Any ex has four different substituents:
`X, Y, and two sections of the main polymer chain that differ in length. Optical
`activity is innucnced, however, only by the first few atoms about such a center,
`and these will be identical regardless of the length of the whole polymer chain .
`This is why the carbons marked ex are not true asymmetric centers. Only those
`ex centers near the ends of macromolecules will be truly asymmetric, and there
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`4.2 Conflgurational Isomerism
`
`129
`
`are too few chain ends in a high polymer to confer any significant optical activity
`on the molecule as a whole.
`Each pseudoasymmetric carbon can exist in two distinguishable configura(cid:173)
`tions. To understand this, visualize Maxwell's demon walking along the polymer
`backbone. When the demon comes to a particular carbon C' she will see three
`substituents: the polymer chain, X, and Y. If these occur in a given clockwise order
`(say, chain, X, and Y), CX has a particular configuration. The substituents could
`also lie in the clockwise order: chain, Y, and X, however, and this is a different
`configuration. Thus every ex may have one or another configuration. This con(cid:173)
`figuration is fixed when the polymer molecule is formed and is independent of any
`rotations of the main chain carbons about the single bonds which connect them.
`The configurational nature of a vinyl polymer has profound effects on its phys(cid:173)
`ical properties when the configurations of the pseudoasymmetric carbons are reg(cid:173)
`ular and the polymer is crystallizable. The usual way to picture this phenomenon
`involves consideration of the polymer backbone stretched out so that the bonds
`between the main chain carbons form a planar zigzag pattern. In this case the X
`and Y substituents must lie above and below the plane of the backbone, as shown
`in Fig. 4-1. If the configurations of successive pseudoasymmetric carbons are
`regular, the polymer is said to be stereoregular or tactic. If all the configurations
`are the same, the substituents X (and Y) will all lie either above or below the plane
`when the polymer backbone is in a planar zigzag shape. Such a polymer is termed
`isotactic. This configuration is depicted in Fig. 4- la. Note that it is not possible
`to distinguish between all-o and all-L configurations in polymers because the two
`ends of the polymer chain cannot be identified . The structure in Fig. 4-1 a is thus
`identical to its mirror image in which all the Y substituents are above the plane.
`If the configurations of successive pseudoasymmetric carbons differ, a given
`substituent will appear alternatively above and below the reference plane in this
`planar zigzag conformation (Fig. 4-1 b). Such polymers are called syndiotactic.
`
`X HX HX HX HX HX HX
`
`Y HY HY YH HY HY HY
`
`X HY HX HY HX HY HX H
`
`(o)
`
`(b)
`
`Y HX HY HX HY HX HY H
`(a) lsotactic polymer in a planar zigzag conformation. (b) Syndiotactic polymer in a
`Fig. 4-1.
`planar zigzag confonnation.
`·
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`130
`4 Effects of Polymer Isomerism and Conformational Changes
`When the configurations at the ex centers are more or less random. the polymer
`is not stereoregular and is said to be atactic. Polymerizations which yield lactic
`polymers are called stereospec(fic. Some of the more important slereospecilic
`polymerizations of vinyl polymers are described briefly in Chapter 9.
`The reader should note that stereoisomerism does not exist if the substiluenls
`X and Y in the monomer 4-14 are identical. Thus there are no conligurational
`isomers of polyethylene, polyisobutene, or poly(vinylidene chloride). IL should
`also be clear that 1,2-poly-butadiene (reaction 4-3) and the 1,2- and 3,4-isomers
`of polyisoprene can exist as isotactic, syndiotactic, and atactic contigurational
`isomers. The number of possible structures of polymers of conjugated dienes can
`be seen to be quite large when the possibility of head-to-head and head-to-tail
`isomerism is also taken into account.
`It may also be useful at this point to reiterate that the stereoisomerism which is
`the topic of this section is confined to polymers of substituted ethylenic monomers.
`Polymers with structures like 1-5 or 1-6 do not have pseudoasymmetric carbons
`in their backbones.
`The importance of stereoregularity in vinyl polymers lies in its effects on the
`crystallizability of the material. The polymer chains must be able to pack together
`in a regular array if they are to crystallize. The macromolecules must have fairly
`regular structures forth is to occur. Irregularities like inversions in monomer place(cid:173)
`ments (head-to-head instead of head-to-tail), branches, and changes in configura(cid:173)
`tion generally inhibit crystallization. Crystalline polymers will be high melting,
`rigid, and difficultly soluble compared to amorphous species with the same con(cid:173)
`stitution. A spectacular difference is observed between isotactic polypropylene,
`which has a crystal melting point of I 76°C, and the atactic polymer which is a rub(cid:173)
`bery amorphous material. Isotactic polypropylene is widely used in fiber, cordage,
`and automotive and appliance applications and is one of the world's major plastics.
`Atactic polypropylene is used mainly to improve the low-temperature properties
`of asphalt.
`lsotactic and syndiotactic polymers will not have the same mechanical proper(cid:173)
`ties, because the different configurations affect the crystal structures of the poly(cid:173)
`mers. Most highly stereoregular polymers of current importance are isotactic.
`[There are a few exceptions to the general rule that atactic polymers do not
`crystallize. Poly(vinyl alcohol) (1-8) and poly(vinyl fluoride) arc examples. Some
`monomers with identical I, 1-substituents like ethylene, vinylidene fluoride, and
`vinylidene chloride crystallize quite readily, and others like polyisobutene do not.
`The concepts of configuralional isomerism do not apply in these cases for reasons
`given above.]
`Stereoregularity has relatively little effect on the mechanical properties of
`amorphous vinyl polymers in which the chiral carbons are trisubslituted. Some
`differences are noted, however, with polymers in which X and Yin 4-14 differ and
`neither is hydrogen. Poly(methyl methacrylate) (Fig. 1-4) is an example of the
`
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`4.2 Configurntional Isomerism
`
`131
`
`latter polymer type. The atactic form, which is the commercially available product,
`remains rigid at higher temperatures than the amorphous isotactic polymer.
`Completely tactic and completely atactic polymers represent extremes of
`stereoisomerism which are rarely encountered in practice. Many polymers exhibit
`intermediate degrees of tacticity, and their characterization requires specification
`of the overall type an·d extent of stereoregularity as well as the lengths of the tac(cid:173)
`tic chain sections. The most powerful method for analyzing the stereochemical
`nature of polymers employs nuclear magnetic resonance (NMR) spectroscopy for
`which reference should he made to a specialized text [I]. Readers who delve into
`the NMR literature will he aided hy the following hrief summary of some of the
`terminology that is used [2]. It is useful to refer to sequences of two, three, four,
`or five monomer residues along a polymer chain as a dyad, triad, tctrad, or pentad,
`respectively. A dyad is said to be racemic (r) if the two neighboring monomer
`units have opposite configurations and mesa if the configurations are the same. To
`illustrate, consider a methylene group in a vinyl polymer. In an isotactic molecule
`the methylene lies in a plane of symmetry. This is a meso structure.
`
`--H+
`
`m
`
`In a syndiotactic region, the methylene group is in a racemic structure
`
`r
`
`In a triad, the focus is on the central methine between two neighboring monomer
`residues. An isotactic triad (mm) is produced by two successive meso placements:
`
`+H-H-
`
`m
`
`m
`
`A syndiotactic triad (rr) results from two successive racemic additions:
`
`r
`
`r
`
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`4 Effects of Polymer Isomerism and Conformational Changes
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`Similarly, an atactic triad is produced by opposite monomer placements, i.e., (mr)
`or (rm). The two atactic triads arc indistinguishable in an NMR analysis.
`The dyads in commercial poly( viny I chloride) (PVC) are about 0.55% racemic,
`indicating short runs of syndiotactic monomer placements. The absence of a
`completely atactic configuration is reflected in the low levels of crystallinity in
`this polymer, which have a particular influence on the processes used to shape it
`into useful articles.
`
`4.3 POLYMER CONFORMATION
`
`The conformation of a macromolecule of given constitution and configuration
`specifies the spatial arrangements of the various atoms in the molecule that may
`occur because of rotations about single bonds. Molecules with different confor(cid:173)
`mations are called conformational isomers, rotamers, or conformers.
`Macromolecules in solution, melt, or amorphous solid states do not have regu(cid:173)
`lar conformations, except for certain very rigid polymers described in Section 4.6
`and certain polyolefin melts mentioned on page 139. The rate and ease of change
`of conformation in amorphous zones are important in determining solution and
`melt viscosities, mechanical properties, rates of crystallization, and the effect of
`temperature on mechanical properties.
`Polymers in crystalline regions have preferred conformations which repre(cid:173)
`sent the lowest free-energy balance resulting from the interplay of intramolecular
`and intermolecular space requirements. The configuration of a macromolecular
`species affects the intramolecular steric requirements. A regular configuration is
`required ir'the polymer is to crystallize at all, and the nature of the configuration de(cid:173)
`termines the lowest energy conformation and hence the structure of the crystal unit
`cell.
`Considerations of minimum overlap of radii of nonhonded substituents on
`the polymer chain are useful in understanding the preferred conformations of
`macromolecules in crystallites. The simplest example for our purposes is the
`polyethylene (1-3) chain in whi.ch the energy barriers to rotation can be ex(cid:173)
`pected to be similar to those in n-hutane. Figure 4-2 shows sawhorse projections
`of the conformational isomers of two adjacent carbon atoms in the polyethy(cid:173)
`lene chain and the corresponding rotational energy harriers (not to scale). The
`angle of rotation is that between the polymer chain suhstitutents and is taken
`here to be zero when the two chain segments are as far as possible from each
`other.
`When the two chain segments would be visually one behind the other if
`viewed along the polymer backbone, the conformations arc said to be eclipsed.
`
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`4.3 Polymer Conformation
`
`133
`
`cis
`
`skew+
`
`t
`>-
`0
`0,:
`uJ z
`-L-- w--,l _ _._ _ _.__,...__.__..,____,11;-,-6C
`0
`60 120 180 240 300
`ROTATIONAL ANGLE {O)
`
`~
`
`~
`
`trans
`trans
`Fi~. '1-2. Torsional po1en1ials aboul adjace nt carbon aloms in the polyelhylene chain. The while
`circles represcnl H atoms and the black circles represent segments of the pol ymer chain.
`
`The other extreme conformations shown are ones in which the chain substituenls
`are staggered. The latter are lower energy conformations than eclipsed forms be(cid:173)
`cause the substituents on adjacent main chain carbons are further removed from
`each other. The lowest energy form in polyethylene is the staggered trans confor(cid:173)
`mation . This corresponds lo th~ planar zigzag form shown in another projection
`in Fig. 4-1. It is also called an all -trans conformation. This is the shape of the
`macromolecule in crystalline regions of polyethylene.
`The conformation of a polymer in its crystals will generally be that with the
`lowest energy consistent with a regular placement of structural units in the unit cell.
`It can be predicted from a knowledge of the polymer configuration and the van der
`Waal s radii of the chain substitucnts. (These radii are deduced from the distances
`observed between different molecules in crystal lattices.) Thus, the radius of
`fluorine atoms is slightly greater than that of hydrogen, and the all-trans crystal
`conformation of polyethylene is loo crowded for poly(tetra!luoroethylene) which
`crystallizes instead in a very extended 13 1 helix form . Helices are characterized
`by a number of /j, where f is the number of monomer units per j complete
`turns of the helix. Polyethylene could be characterized as a 11 helix in its unit
`cell.
`Helical conformations occur frequently in macromolecular crystals. lsotactic
`polypropylene crystallizes as a 3 1 helix because the bulky methyl substiluenls on
`every second carbon atom in the polymer backbone force the molecule from a
`trans/trans/trans .. . conformation into a tra11s/gauche/tra11s/gauche ... sequence
`with angles of rotation of0° (trans) followed by a I 20° (gauche) twist.
`
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`4 Effects of Polymer Isomerism and Conformational Changes
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`In syndiotactic polymers, the substituents arc further apart because the configu(cid:173)
`rations of successive chiral carbons alternate (cf.Fig. 4-1 ). The trans/trans/trans . . .
`planar zigzag conformation is generally the lowest energy form and is observed in
`crystals ofsyndiotactic 1,2-poly(buta<liene) and poly(vinyl chloride). Syndiotactic
`polypropylene can also crystallize in this conformation but a trans/trans/gauche/
`gauche .. . sequence is slightly favored energetically.
`Polyamides are an important example of polymers which do not contain pseu(cid:173)
`doasymmetric atoms in their main chains. The chain conformation and crystal
`structure of such polymers is influenced by the hydrogen bonds between the car(cid:173)
`bonyls and NH groups of neighboring chains. Polyamides crystallize in the form
`of sheets, with the macromolecules themselves packed in planar zigzag conforma(cid:173)
`tions.
`The difference between the energy minima in the trans and gauche staggered
`conformations is labeled flE in Fig. 4-2. When this energy is less than the ther(cid:173)
`mal energy RT/ L provided by collisions of segments, none of the three possible
`staggered forms will be preferred. If this occurs, the overall conformation of an
`isolated macromolecule will be a random coil. When flE >RT/ L, there will be
`a preference for the trans stale. We have seen that this is the only form in the
`polyethylene crystallite.
`The time required for the transition between trans and gauche states will depend
`on the height of the energy barrier fl£ in Fig. 4-2. If fl£ < RT/ L, the barrier
`height is not significant and trans/gauche isomerizations will take place in times
`of the order of I 0- 11 sec. When a macromolecule with small /1 E is stretched into
`an extended form, the majority of successive carbon-carbon links will be trans,
`but gauche conformations will be formed rapidly when the molecule is permilled
`to relax again. As a result, the overall molecular shape will change rapidly from an
`extended fo