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`—PBINCIPLES
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`POLYMER
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`CHEMISTRY
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`ETHICON EXHIBIT 1016
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`ETHICON EXHIBIT 1016
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`THE GEORGE FISHER BAKER
`NON.RESIDENT LECTURBSHIP IN CHEMISTRY
`AT CORNELL UNIVBRSITY
`
`PRINCIPLES OF POLYMER CHEMISTRY
`BY PAUL J. FLORY
`
`

`
`PRII\CIPLES OF
`
`POLYJ\{TR CHEMISTRY
`
`By Paul J. Flory
`Prolessor ol Chemistry, Stanlord (Jníaersity
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`Cornell {Jniversiry press
`ITHACA AND LONDON
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`Preface
`
`11' WAS the author's privilege to hold the George Fisher Baker Non-
`resident Lectureship in CireÃistry at Cornell University during the
`spring of 1948. This book had its inception at that time' The un-
`completed manuscript was laid aside shortly thereafter, and the work
`wasïot resumed ,rttiil fg¡f . During the intervening years much new
`mâterial became available from the eve¡-increasing literature, and
`major levision of manuscript and outlines consequently was necessary.
`Thå momentum of extensive investigations on the kinetics of addition
`polymerization, undertaken in various laboratories at the close of the
`*u.; curri"d this phase of the subject to an advanced stage of develop-
`ment. The material on dilute polymer solutions, appearing in the later
`
`COPYRIGHT 1953 BY CORNELL UNIVERSITY
`f:Ï:-iïJ.',îil1Ρ"iiî,1:,ïii:!pr,åi:ï'i:"î'å,*r'åî'iå".7
`Hr :ilfl ä;Ï'r*:la'i:#::' Ëì:": ilå jlji ;ru" r + ss o
`pubrished*5Ti::."f ü:..Jå:lffJnerl"universitvPressLtd''
`First þublished' 19Ð by Cotnel'I^(JniuersiÚ1 Press
`Ninth Pinting 1975
`
`International Standard Book Number
`'O 9^O-11^OtUn-t
`'^"'^'^irìïi.¿ in the united states of Amenca
`
`research effort carried on by many investigators over
`years, and especially during the last decade, certain
`well-defined generalizations have emerged. It was felt
`time had come when these should be brought together in a
`:accordance with this objective, experimental results have
`uced primarily for illustrative purposes and to develop the
`these principles Descriptions of the properties of specific
`a.nd extensive cataloging of accumulated data, except as
`ééîve'the foregoing objective, lie outside the intended scope
`v
`
`

`
`PRINCIPLES OF POL.YMER CHEMISTRY
`[XIII-3A
`580
`pared with the former. To a similar approximation the higher terms
`i; il" series expansion of the left-hand member of Eq. (39) mav be
`r.gl".t"¿. Thà swelling equilibrium equation may then be solved
`fol ur*:l/q* wilh the following resultlT
`qul = (Vo/r.)(l/2 - x)/v,
`
`(40)
`
`(3e)
`
`'
`
`(40')
`
`or, from Eq. (39')
`ql" = @x[")(t - 2n't"/M)-r(r/2 - xL)/vL
`Thesesimplifiedrelationshipsofferaclearerinsightintothedependence
`of the .quilib.ir- srvellini ral\o q^ on the quality of the solvent as
`.*p...."d by x1, and on the extent of cross-linking' Because of the na-
`ture of the approximations introduced to obtain Eqs' (a0) and (40')'
`theirttseasquantitativeexpressionsmrrstlrelimitedtonetworksof.
`very low d.egrees of cross-linking in good solvents'
`Ii fras beãn shown in Chapter XI that the force of retraction in a
`stretched netrvork structur.e dlpends also on the degree of crossJinking'
`ii is po..iUle therefore to eliminate the structure parameter (v"/Vo)
`Uy .orrrnir.irrg the elasticity and the swelling equations' and thus to
`arrirre at a re'iationship between the equilibrium swelling ratio and the
`force of retraction at án extension * (nàt to be confused with the srvell-
`ing iu.to. ""). In this manner wè'obtain from Eq' (XI-44)* and Eq'
`ro : - RT(a - | /a'z)lln (l - ur*) * uz^ *'\fi22^]/vr(u'rß - uz^/2) (41)
`where ? refers to the temperature of the stress measurement' If
`the equilibriurn .ru"liing is^very large (uz^111), we may introduce
`approximation. .o.r.rpoîding to thosã which yielded Eq' (40)' Then
`t": RT(a - r/a')(r/2 - xr)/vrq?lt
`(42)
`This equation calÌs attention to the well-established inverse relation-
`ship between the degree of equilibrium swelling of a series of rubber
`vulcanizates in a given solventând the forces of retraction, or "moduli,lf
`which they exhibit on stretching. The indicated approximate d9-
`pendence ãf g- o., the inverse three-fifths porMer of the "modulus" has
`been confirmed.2e 30
`In using Eq. (XI-a ) to derive Eq. (41), we have, in effect, accepted
`the forme-r as a valid representation of the dependence of the force of
`retraction on the extensión. Experiments cited in Chapter XI shoived
`* The total volume I/ 0ccurring in Eq. (xI-44) is to be identified s¡ith the l
`present I¡o inasmuch as the volume was B,ssumed to remain constant during ,,
`elaetic defo¡mation.
`
`XIII-3b]
`
`PH¿.SE EoUIIJIBRIA
`581
`this theoretical relationship to be disturbingly inaccurate. The ¡esult-
`ing quantitative limitations of Eqs. (a1) and (42) must not be over-
`looked. Better agreement rvith experiment could be expected through
`the use of the semiempirical stress-strain relation, Eq. (XI-50), instead
`of Eq. (XI-44) in ihe derivation of Eq. (a1).
`3b. Experimental Results on the Swelling of Nonionic Network
`Systems.-The degree of srveliing observed at equilibrium in a good
`solvent invariably decreases with increasing degrees of cross-link-
`ing.2e'30,3r,32 It also decreases with increase in the primary molecular
`weight M as should be expected according to Eqs. (3g,) and (40,);
`as a matter of fact, quantitative proportionality between gf3 and the
`network imperfection facto¡ (L-2M"/M) has been verifred.2s The
`dependence of the equilibrium swelling ratio on the netrvork structure
`need not be pursued further. Instead, we shail focus the discussion on
`the connection betr,veen q^ and the force of retraction r. The relation-
`ship of the latter quantiúy to the network structure, as embodied in
`v"f V¡ or in M" and M, was discussed in detail in Chapter XI. Hence
`the relationship between q^ and the structure is implicit in the diseus-
`q* a,od r, and its separate
`,sion of the quantitative connection between
`:treatment would represent an unnècessary
`duplication.
`The results shown in Fig. 135 for a series of multilinked polyamidess3
`te the relationship between the equilibrium swelling ratio and
`equilibrium force of retraction ro for the stretched unswollen
`. Swelling measurements were made in z¿-cresol at B0.C;
`orces of retraction were measured on the unsrvollen polymers
`at the several extension ratios a :1.4,2.0, and 3.0 as indicated.
`t 241"C
`range in the degree of crossJinking (r,,) covered by these data is
`sixfold. The logJog plot
`IS suggested by the approximate
`(42). Although the points describe straight lines within experi-
`error in accordance with this relation, the negative slopes are
`greater than the value 5/3 it prescribes. The lines drawn
`are slightly curved, for they have been calculated from the
`accurate relationship given by Eq. (a1) rather than from Eq
`
`Because of the previously mentioned inadequacy of the function
`-l/o', a different value for the parameter xr is required for the set
`points (Fig. 135) at each elongation a. These values are -0.90,
`=0.73, and -0.56 for cY: 1.4,2.0, and 3.0, respectively. If the func-
`tion cu - I f a2 were replaced by an empirical representatìon of the shape
`of the stress-strain curve, a single value of Xr would suffice to represent
`all of the data within experimental er¡or. This limitation of Eq.
`(41) relales to an unexplained feature of the stress-strain curve and is
`
`

`
`582
`
`PRINCIPI,ES OF POI'YMER CHEMISTRY
`
`lxlrr-3b
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`c\
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`4.4
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`3.6
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`FIc. 13õ.-The lclationshiP
`between the equilibrium re-
`io.tiu" force ro (in lbs'/in''?) at
`i;; ;"ri-ous nultilinked
`;';ö
`i:ilJ::*,::"ïi1i:Li"'.i"JJ;
`lll:iilr*t*::,n ""å"J:Ë:
`Ë;
`i.t"iii"i."a PolYmers; O' octa-
`ilïtãä-- oolv*ét'' The lines
`i.iiã ¡.J*.älculated according
`iT'È..-i¿rl' with aPproPriate
`i!"i.iå*"'i*' the o ctaf u n ctional
`;.;^ôt;k;" Iines), an arbi-
`iü.v'ï"it" utite assigned
`iï-ín" ott"^eter Xr for each
`ä""ärtrã".- (Schaefgen and
`FlorY.a3)
`
`o.B
`
`r.o
`
`Log Qn
`
`t.2
`
`1.4
`
`nol peculiar to the swelling behavior, which is of PrimarY concern here.
`Dashed curves shown in Fig' 135 for the octafun ctional network
`polymers (filled circles) were calculated from the suitably modifred
`form of Eq (41) which appiies in this caset* using the same value of Xr'
`The exPerimental Points in Fig' 135 for each elongation are seen to
`be in good agreement with the theoreticallY Predicted correlation be-
`tween q* and ro. These results, which are suPPorted bY similar com'
`parlsons on vulcanized rubbers, 2e,30,34 show that the elastic reaction to
`the isotroPic dilation acconpanymg sweliing and to that induced bY
`stretching without (aPPreciable) dilation are umquely related, and
`hence that theY are of common orlgrn' That is to saY, the same
`work is resPonsible for both. The often-Postulated
`bonds" between neighboring chains, which might have been
`to contribuþ to the elastic retractive force, must surelY be inoPerative
`junctions in the Presence of the swelling agent
`AS permanent
`that such bonds like-
`vlew
`correlation betrveen g- and ro conûrms the
`wise do not contribute to rubberlike elasticity, at equiiib.rium at anY
`rate.
`According to these results' swelling measurements on a serl
`'See p. 578, footnote
`
`ttassociation
`assumed
`
`.es of
`
`PHASE EQUILIBRIÂ
`583
`XIII-3b]
`chemically related network structures in the same solvent may be used
`to ascertain the degrees of cross-linking, at least in a relative rvay, iu
`the difierent structures. The same information may, of course'
`be obtained from elasticity measurements. Equilibrium sweliing
`often is easier to measure' however, and for this reason it may be pre-
`ferred.
`Thedegreeofswellingofthesamenetworkstructureindifierent
`solvents frovides a convenient index of the solvent power of each
`solvent for polymers of the given chemical type. The structure factor
`v"fV¡ (see Eq. 39) is fixed throughout such a series of measurements'
`und tfr" swelling q*:!/ur^ depends only on the known molar volume
`vr of the solvenilttd ott the unknown parameter x1' If a value can be
`assigned to xr for one solvent, possibly on the basis of thermodynamic
`*uu".rr."-"rrts on solutions of the linear polymer analog, then an ap-
`farent value of vefVo cl'rt be calculated and xr may be deduced from
`o^¡'o,anyothersolvent.Thismethodhasfoundv¡ideuse.30,32'35
`wiritu tt " absolute values of the parameters thus obtained may be
`open to question, there is little doubt that the method should classify
`..,rãrioo. sãlvents in proper order with respect to polyme's of the given
`type.
`In the application of the swelling method for determining solvent-
`poiymer interactions it is obviously desirable to eliminate the necessity
`of the calibration mentioned in the preceding paragraph and involving
`reliance on an interaction parameter x1 deduced from thermodYnamic
`measurements on a linear PoIYmer anal.og in a selected solvent. In-
`dependent determination of. v"f Vsís to be preferred. IJse of the literal
`value of v"f 'Øo established through quantitative synthesis rvould be
`to lead to error on account of contributions to the elastic response
`of the network arising from imperfections such as the network entangle-
`'ments discussed in ChaPter XI. There it was shown that the observed
`orces of retraction tend alwaYs to be somewhat greater than those
`from the number of actual effective chains v" in the struc-
`interaction parameter,
`tions is needed. Lack-
`a method for introducing this correction in any other way, one may
`from which an aPParent
`to elasticitY measurements3o of ro,
`.value of. v"fVo maY be calculated according to Eq' (XI-44)' This ap-
`parent value of v"f Vsis still subj ect to ambiguity arising from devia-
`l.e' t the result obtained will dePend
`tions from the a-1/42 function;
`, to torrt" extent on the value of a at which the force of retraction is
`measured. Gee36 has shown that the stress-strain behavior of swollen
`networks is in much closer accord with this function; hence an apparent