PRINClPLES
`OF POLYMER
`SYSTEMS
`Second Edition
`
`FERDlNAND RODRIGUEZ
`Professorof Chernical Engineering
`Cornell University
`
`O HEMISPHERE PUBLISHING CORPORATION
`
`Washington New York
`
`London
`
`St. Louis San Francisco Auckland
`McGRAW-HILL BOOK COMPANY
`New York
`London Madrid Mexico Montreal New Delhi Panama
`Bogotá Hamburg Johannesburg
`Tokyo
`Toronto
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`
`Page 1 of 7
`SNF Holding Company et al v BASF Corporation, IPR2015-00600
`
`

`
`PRINCIPLESOF POLYMER SYSTEMS
`Second Edition
`
`or
`
`Copyright © 1982, 1970 by Hemisphere Publishing Corporation.
`All rights reserved, Printed in the United States of America. No part
`this pubHeation may be reproduced, stored in a retrieval system,
`of
`in any form or by any means, electronic, mechanical,
`transmitted,
`the prior written
`recording, or otherwise, without
`photocopying,
`the publisher.
`permission of
`34567890 BCBC 89876543
`in Press Roman
`This book was set
`by Hemisphere Publishing Corporation.
`iobro,
`The editors were Julienne V. Brown, Valerie M.
`and Elizabeth Dugger;
`the designer was Sharon Martin DePass;
`the production supervisor was Miriam Gonzalez;
`and the typesetter was Wayne Hutchins.
`Inc., was printer and binder.
`BookCrafters,
`
`2
`
`Library of Congress Cataloging in Publication Data
`
`Rodriguez, Ferdinand, date
`Principles of polymer systems.
`chemical engineering series)
`(McCraw-Hill
`Bibliography:
`p.
`Includes indexes.
`and polymerization.
`1. Polymers
`II. Series.
`TP156.P6R62
`
`1982
`
`668.9
`
`L Title.
`
`81-6641
`AACR2
`
`ISBN 0-07-053382-2
`
`Page 2 of 7
`
`

`
`Viscous Flow
`
`167
`
`So for M = 106, a' = 3.56,
`that
`the individual polymer molecules occupy
`is,
`times the volume in cyclohexane than they do in any theta (Flory) solvent.
`four
`in Sec. 2-5 that polymers in contact with solvents of like
`It was mentioned
`i.e., swelling of
`parameter
`ô should show the
`solvation effects,
`greatest
`solubility
`or viscosity of solutions. Now we can
`identify,this solvating ability with
`networks
`the expansion factor
`in Eq. (7-10).
`
`almost
`
`a,
`
`7-4 EFFECT OF CONCENTRATION
`AND MOLECULARWEIGHT
`Equations (7-13),
`(7-14), and (7-15) hold only in dilute solution. Many other equa-
`tions have been proposed to express the variation of viscosity with concentration even
`that of Lyons
`at moderate concentrations. One empirical approach
`and Tobolsky
`is
`(15), who proposed
`
`ki[g]c
`
`=exp
`
`(7-22a)
`
`In the limit of very dilute solutions, ki/(1 -b)
`should be the same as k'
`in the Hug-
`gins equation [Eq. (7-13)]. Under some conditions this one equation can represent
`the
`of a single polymer
`(Newtonian)
`low shear
`from dilute solution
`viscosity
`to the
`[16]. The
`solvent-free melt
`constant
`be positive or negative. The equation
`b
`can
`theoretical
`resembles
`relationship derived
`by Fujita and Kishimoto based on frac-
`a
`tional
`free volume contributions
`[17, 18]. A simpler
`by polymer and solvent
`form,
`in
`which b is zero, was used by Martin some years earlier:
`
`log
`
`= log [p) +K"[p]c
`
`(7-22b)
`
`is
`
`This equation (see Fig. 7-5)
`involves only two
`popular,
`been very
`because
`has
`it
`fitted constants, yet can correlate data to high concentrations.
`It, together with some
`other empirical equations,
`treated more extensively by Ott and Spurlin [19]. As
`is
`one approaches
`the pure molten polymer,
`that
`c > 50,
`the particular solvent used
`is,
`to have little bearing on the viscosity, and n(solution) = n(polymer)u2, where v2
`seems
`the volume fraction of polymer
`[20].
`Combination of Eq.
`(7-16) with (7-13),
`(7-14),
`(7-15),
`(7-22b)
`or
`the
`gives
`effect of molecular wieght
`on y for solutions. For polymer melts several approaches
`are suggested. Log-log plots of 4 versusM often can be resolved into two straight
`lines.
`Typical behavior of melts over
`a large range of molecular weight
`is shown in Fig. 7-7.
`in Fig. 7-7 has a slope of 3.5 ±0.5, and the lower section has
`The upper section
`a
`to I or 2. For each section we can write
`slope closer
`log y = A log M, + B
`
`(7-23)
`
`The break
`thought
`in the curve is
`to represent
`the molecular weight
`at which polymer
`entanglements become
`serious
`to contribute heavily to
`enough
`the viscosity. Single
`
`Page 3 of 7
`
`

`
`168
`
`Principles of Polymer 3 stems
`
`6.0 Pbly
`
`2.0
`
`3.0
`
`rene fractions
`2|y*)
`
`.?'
`
`3.0
`4 0
`* PMMA fractions
`25% by weighi
`in diethyl
`phthalate (60 )
`7°.
`
`4.0
`
`*
`
`.
`
`.
`
`./
`
`(cid:127)
`
`./
`
`f
`
`2.0
`oecomethylene
`adipote
`(109 )
`
`'
`.
`
`-
`
`(cid:127)'
`
`e-caprolactom
`sebacic acid
`(253 )
`
`3.0
`
`-- 2.0
`
`_ g
`4.o
`
`- 2.0
`
`,/
`
`.*'
`
`4.0 -
`
`2.0 -
`
`6.0 -
`
`4.0 -
`
`2.0 -
`
`Polyisobutylene
`(217 )
`
`fractions
`
`Poly(dimethylsiloxane) (25 )
`(y in stokes)
`
`(cid:127)(cid:127)
`
`(cid:127)
`
`-
`
`2.0
`
`3.0
`
`4.0
`log i
`
`2.0
`
`3.0
`
`4 O
`
`FIGURE 7-7
`Logarithmic plots of viscosity
`[20 ]; 1 poise = 0.1 Pa(cid:127)s.
`
`n vs. weight-average number of chain atoms Zw for six polymers
`
`polymer molecules no longer diffuse
`separately, but drag along neighbors. An analogy
`would be the removal of a piece of string
`from a pile of strings. As the average length
`of strings
`the difficulty of removing the string increases. Some values of this
`increases,
`"entanglement molecular weight"
`limited range of
`in Table 7-7. Over
`are given
`molecular weight, another relationship has some usefulness
`[20):
`
`a
`
`log y = A + BM"*
`
`(7.24)
`
`7-5 EFFECT OF TEMPERATURE AND PRESSURE
`flow can be pictured as
`the movement of molecules or seg-
`Viscous
`taking place by
`ments of molecules in jumps from one place in a
`lattice to a vacant hole. The total
`"hole concentration" can
`as space free of polymer,
`"free volume."
`be regarded
`or
`Doolittle proposed (21Jthat
`should vary with the free Vyin the following
`the viscosity
`way:
`
`log y = A +
`
`le
`
`I
`
`(7-25)
`
`Page 4 of 7
`
`s
`

`
`Ykcous Flow
`to V- Vo, Vis the specific
`the free volume equal
`where A and B are constants, Vy is
`volume (per unit weight), and Vo is
`the specific volume extrapolated from the melt
`to
`free volume f' = Vy/Vis expected to vary
`OK without change of phase. The fractional
`with temperature as follows:
`f' -fg'=
`a is
`
`a AT
`
`169
`
`(7-26)
`
`where
`
`for melt and glass,
`the difference between
`the expansion coefficients
`AT= T- Tg, andf, is
`free volume at T,. For many polymers a is about
`the fractional
`10¯*
`K-1. Also, Williams, Landel, and Ferry [22]
`found empirically
`that
`-17.44(T-T)
`-l7.44AT
`4 =
`51.6+(T-Tg) SI.6+AT
`
`4.8 X
`
`log
`
`=
`
`)
`
`(7-27)
`
`TABLE 7-7
`Applicability of the Empirical Law log y = 3.4 log Z, + K to Long Polymer
`Chains (20]
`
`Range of applicability
`
`Polymer solvent pair
`
`[Polymer],
`wt fraction
`
`y2Zeat
`break*
`
`Highest
`Z studied
`
`Temperature
`ran8e
`studied, °C
`
`Polymers
`andmol
`wt detm'nÍ
`
`Linear nonpolar polymers
`
`i
`
`Polyisobutylene
`Polyisobutylene-xylene
`Polyisobutylene-decalin
`Polystyrene
`Polystyrene-diethyl
`benzene
`Poly(dimethylsiloxane)
`
`1.0
`0.0Sto0.20
`0.05 to 0.20
`1.0
`0.14 to 0.44
`1.0
`
`610
`~1400
`
`-
`
`730
`~1000
`
`-950
`
`53,000
`140,000
`140,000
`7,300
`22,500
`34,000
`
`-9
`
`to 217
`25
`25
`130 to 217
`30 to 100
`25
`
`f:(n)
`W&f:(n)
`W & f:(n)
`f:(n)
`f:(n)
`W:n, L.S.
`
`Linear polar polymers
`
`(cid:127)
`
`Poly(methylmethacrylate)-
`diethylphthalate
`Decamethylene sebacate
`Decamethylene adipate
`Decamethylene succinate
`Diethylene adipate
`w-Hydroxy undecanoate
`
`0.25
`1.0
`1.0
`1.0
`1.0
`1.0
`
`208
`290
`280
`290
`290
`<326
`
`24,000
`960
`1,320
`990
`1,190
`1,443
`
`60
`80 to 200
`80 to 200
`80 to 200
`0 to 200
`90
`
`Poly(e-caprolactam):
`Linear
`Tetrachain
`Octachain
`
`Effect
`
`of branching
`
`1.0
`1.0
`1.0
`
`324
`390
`550
`
`2,300
`1,560
`2,000
`
`253
`253
`253
`
`f:(n)
`W:E
`W:E
`W:E
`W:E
`W:E
`
`W:E
`W:E
`W:E
`
`'Ze is
`the lowest chain length for which equation is valid for
`the solution wherein u,
`volume fraction of polymer.
`Íf = fraction,
`W = whole polymer. Chain lengths determined from n = intrinsic viscosity, w =
`osmotic pressure,
`L.S. = light scattering data, E = end group analysis.
`
`the
`
`is
`
`Page 5 of 7
`
`

`
`170
`
`Principles of Polymer Systems
`
`(7-26), and (7-27) if we
`(7-25),
`the viscosity at Tg. We can combine Eqs.
`where og is
`a change, since, unlike Vy, V does
`too great
`Vo in Eq. (7-25) by V. This is not
`replace
`the difference of
`not change rapidly with temperature. First we write Eq. (7-25)
`as
`two conditions to eliminate the constant A.
`
`g
`
`log -
`
`= -
`
`B(f'
`
`-f')
`
`,
`
`(7-28)
`
`p
`
`log --
`
`(7-29)
`
`Equation (7-26) is used to eliminate f':
`(-Ba AT)
`(-B/fj) AT
`= fj(f) + g á T)
`(f |a) + AT
`that f = 51.6a or 0.025. The
`Identification of Eq.
`(7-29) with Eq.
`shows
`(7-27)
`for all materials (polymers and
`transition occurs
`that
`conclusion is drawn
`the glass
`a temperature where the frac-
`compounds) at
`low-molecular-weight
`inorganic glasses,
`free volume is 2.5% of the total, since the empirical
`relationships used have been
`fional
`found to apply for all
`these materials.
`When T-Tg >100°C, Eq.
`(7-27)
`one [201:
`
`does not work as well
`
`the more general
`
`as
`
`log
`
`= B'
`
`exp
`
`-
`
`(7-30)
`
`temperature Ta for molecular weight M and a
`the viscosity at a reference
`where og is
`integer, while B' and ß are fitted constants. Some typical
`results
`are
`usually is
`an
`seen in Fig.7-8.
`the compression of a melt
`to decrease the free volume and
`One would expect
`It can be seen that the viscosity of highly compres-
`consequently increase the viscosity.
`that of the less compressible
`'affected more by pressure
`sible polystyrene
`than
`is
`that polystyrene
`polyethylene (Fig. 7-91It will be remembered (Sec. 7-2, Table 7-2)
`had a higher value of ro /n than polyethylene. Because increasing pressure will
`increase
`it
`to use Eq.
`(7-27) with a pressure-
`temperature,
`transition
`is possible
`the glass
`the form of the dependence (24,
`if one knows
`dependent T, to correlate viscosity
`25]. For several polymers, d(Tg)/dP is reported to be in the range of 0.16 to 0.43°C/
`a value of 03°C/MPa [24].
`It
`for example,
`is harder
`to
`MPa. Polystyrene,
`has
`the temperature and pressure dependence of polymer solutions. Also,
`generalize about
`plots of viscosity vs. concentration
`linear, especially in concen-
`are not
`logarithmic
`trated solutions (Fig.7-10).
`
`7-6 MODELS FOR NON-NEWTONIANFLOW
`is a constant for any polymer with a
`It has been assumed until now that
`the viscosity
`temperature, and pressure. Two more
`given molecular weight, solvent, concentration,
`deformation takes place and the length of time at a
`are the rage at which
`variables
`given rate of shear. For even if we hold the rate of deformation constant,
`the viscosity
`
`Page 6 of 7
`
`

`
`Viscous Flow
`
`171
`
`-
`
`T2
`6.0
`5.0
`i
`I
`Decamethylene
`Ñ,=4,5IO
`
`x 106
`
`7.0
`adipote
`
`e
`
`x 10"
`
`-
`
`72
`
`2.0
`
`i
`
`4.0
`
`:
`
`6.0
`
`I
`
`8.
`
`- 10.0
`
`acetate
`Polyvinyl
`Ñ,=170,000
`
`-8.0
`
`-6.0
`
`4.0
`
`- 2.0
`
`n-poroffins
`
`odipote
`Diethylene
`Ma = 900
`
`1.5·
`
`1.0-
`
`0.5
`
`Ë
`L
`
`OC
`
`8.0
`
`12.0
`Tl "
`
`-
`
`16.0
`
`x 10
`
`20.0
`
`14.0
`
`18.0
`
`6.0
`
`10.0
`-Ex 10
`T
`
`"
`
`-
`
`FIGURE 7-8
`[20].
`(7-30)
`Viscosity-temperature
`curves according to Eq.
`or decrease with time. If the effect is temporary and viscosity goes back
`may increase
`long enough with no deforming
`(after the system has
`to its original
`relaxed
`value
`increases with time of
`(viscosity
`rheopery
`the behavior
`imposed), we call
`forces
`(Fig. 7-11).
`thixotropy (viscosity decreases with time of deformation)
`deformation)
`or
`structures
`is partially due to intermolecular
`this behavior when viscosity
`One expects
`Ionic polymers in water
`tend to
`that take some time to be established or destroyed.
`relaxed but disperse
`thixotropic, because the polymers probably aggregate when
`be
`individually when sheared.
`and act
`The variation of viscosity with rate of deformation can be shown by a combina-
`7, 9, or 4, since p can be defined as a variable by Eq. (7-3).
`tion of any two variables
`(viscosity increases with i or r) or pseudoplastic (viscosity
`Behavior can be dilatant
`decreases with i or 7) (Fig. 7-12). Most examples of dilatant behavior are particulate
`In slurries and con-
`latexes, slurries, and concentrated suspensions.
`dispersion such as
`there may be almost no flow, 9 = 0, until 7 reaches some "yield
`centrated suspensions
`this "Bingham plastic" behavior.
`(Fig. 7-12). Ordinary toothpaste approaches
`value"
`The typical behavior of polymer
`solutions and melts is pseudoplastic. The de-
`to express the behavior of all such materials
`velopment of a single mathematical model
`has not been successful. One of the simplest approaches
`[26]
`to approximate sec-
`is
`tions of log 7-log i plots by straight
`lines-the "power-law" model (Fig. 7-12):
`7 = Kj"
`
`(7-31)
`
`Page 7 of 7