Methods for Determining Polymer—Polymer Miscibility

Chapter

3 Methods fo r Determinin g Polymer-Polyme r Miscibilit y

3.1

CRITERIA FOR ESTABLISHING MISCIBILITY

Small-angl e neutro n scatterin g n i one-componen t amorphou s polymer s has establishe d tha t th e polyme r chai n n i th e bul k stat e s i essentiall y ran ­ domly place d [1 , 2] . Thi s conclusio n support s th e vas t bod y of othe r evidenc e for rando m statistics . An exampl e fro m thi s evidenc e s i th e hig h dependenc e of viscosit y on molecula r weigh t abov e a critica l molecula r weight , implyin g the presenc e of highl y entangle d chains . The appropriat e pictur e fo r one component , amorphou s polymer ss i tha t of A rathe r tha n Β or C n i Fig . 3.1 . Polymer s dissolve d n i solvent s usuall y ar e "expanded " by th e interactio n of th e solven t wit h th e chai n segments . Expande d mean s simpl y tha t th e averag e end-to-en d distanc e s i increase d ove r tha t of th e bulk . A polyme r dissolve d n i a polyme r solven t migh t be expande d by favorabl e interactions , in whic h cas e a structur e represente d by Fig . 3.1 C woul d result . n I th e extreme , a polymer-polyme r adduc t suc h as DNA migh t form . The situa ­ tio n n i Fig . 3.1 Β implie s some segregatio n on a segmenta l scale , bu t a rando m dispersin g of molecula r centers. Method s wit h hig h resolution , suc h as X-ra y scattering , small-angl e neutro n scattering , nmr relaxation , an d electro n microscopy , sugges t tha t many miscibl e system s fal l betwee n A an d Β or A an d C; i.e. , th e component s ar e no t as randoml y mixe d as th e molecule s in a single-componen t system . A s pointe d ou t by Yu [3] , th e homogeneit y of th e polymer-polyme r solu ­ tion , becaus e of it s hig h viscosity , wil l depen d a grea t dea l on th e method s of preparatio n an d th e tim e an d temperatur e (energy ) o t whic h th e mixtur e is subjected . He fel t tha t concentratio n equilibriu m migh t be approachabl e 117

118

3. Methods for Determining Polymer-Polymer Miscibility

Random segments

Random centers Fig. 3.1. system.

Interacting segments

Variations in the placement of two different polymer molecules in a miscible

onl y as an asymptote . More recen t evidenc e show s that , wit h reasonabl e care , thermodynami c equilibriu m ca n be brackete d fairl y easily . By takin g advantag e of spinoda l decomposition , a one-phas e mixtur e ca n be trans ­ forme d int o a two-phas e mixtur e regardles s of th e diffusiona l barriers . Returnin g o t th e one-phas e regio n involve s a longe r wai t [4 ] or gentl e mixin g in th e melt . Preparatio n of mixe d polyme r system s wit h th e ai d of solvent s can lea d o t spuriou s result s [5 , 6] . Shown schematicall y n i Fig . 3. 2 s i an extrem e case , demonstrate d by Robar d et al. [6] , fo r th e syste m PS-PVMECH 3C1. Remova l of solven t durin g th e preparatio n of polyme r mixture s shoul d be accompanie d by mixing , suc h as wit h a two-rol l mill ,o t ai d n i th e equilibratio n of th e polyme r phases , or by annealin g at a suitabl e tempera ­ tur e [4] . It must be emphasize d tha t an y experiment s on polyme r mixture s per ­ forme d at temperature s othe r tha n th e temperatur e of equilibratio n wil l be subjec t o t unknow n effect s du e o t th e slo w proces s of reequilibratio n at th e s

s

Normal Possible Fig. 3.2. Schematic representation of ternary phase behavior of a system containing two polymers and a solvent.

3.2. Glass Transition Temperature

119

tes t temperature . For example , th e presenc e of tw o 7^' s (o r tw o phase s by microscopy ) fo r a glass y sampl e quenche d o t roo m temperatur e fro m th e melt doe s not mean tha t th e component s wer e immiscibl e n i th e melt . Of course , th e revers e situatio n s i tru e as well . 3.2 GLASS TRANSITION TEMPERATURE

Polymers , as wit h many common liquids , exhibi t certai n characteristic s simila r o t a second-orde r transition , fi indee d on e exists , upo n sufficien t supercoolin g belo w thei r crystallin e meltin g point . The temperatur e an d pressur e derivative s of th e thermodynami c quantitie s of energy ,E, enthalpy , H, entropy , S, an d volume , V, exhibi t a discontinuit y at thi s transition , wherea s E, H, S, an d V, al l first-order derivative s of th e fre e energy , ar e continuou s quantitie s throug h thi s transition . The viscou s liqui d (o r flexible, rubber y materia l n i th e cas e of hig h molecula r weigh t polymers ) s i trans ­ forme d int o a hard , glass y materia l upo n passin g throug h thi s transition . This glas s transitio n s i characteristi c of th e polysilicate s mor e commonl y referre d o t as glasses . However , polyphosphat e glasses , organi c liquids , an d organi c polymer s als o exhibi t th e feature s of thi s glas s transition . A glas s transitio n temperatur e ha s eve n bee n assigne d o t wate r (vi a extrapolatio n techniques ) wit h a valu e of 128° K [7] . Highl y crystallin e material s (e.g. , metals ) may indee d exhibi t glas s transition s bu t th e experimenta l difficult y of supercoolin g o t a glass y stat e prio r o t crystallizatio n limit s investigatio n of th e glass y state . Crystallizabl e polymers , however , do no t achiev e tota l crystallinity , eve n f i supercoolin g o t a trul y amorphou s stat e s i no t possible . The amorphou s structur e lef t betwee n th e crystallin e region s allow s deter ­ minatio n of th e glas s transition . The natur e of th e glass y stat e of liquid s an d polymer s ha s bee n th e subjec t of many investigation s ;thus , variou s theorie s an d interpretation s hav e bee n forwarded . Due o t th e similarit y of th e glas s transitio n o t a second-orde r thermodynami c transition , experimenta l investigation s of th e secon d deriva ­ tive s of th e fre e energy , G, fo r polymer s hav e bee n compare d o t thos e of tru e second-orde r transitions . Rehag e an d Borchar d [8 ] hav e contraste d glas s transitio n behavio r wit h tru e second-orde r thermodynami c transition s (e.g. , rotationa l transition s as wel l as th e liqui d heliu m transitio n at 2.2°K) . For second-orde r transitions , th e secon d derivative s of G (specifi c hea t at con constan t pressure , cp; isotherma l compressibility , k; an d th e coefficien t of therma l expansion , a) hav e lowe r value s abov e th e T% tha n below . Thi s s i in contras t o t th e behavio r observe d wit h th e glas s transition . The glas s transitio n temperatur e shift s o t highe r temperature s wit h increasin g coolin g rates , als o n i genera l contras t o t tru e second-orde r transitions . Thus ,t i was

120

3 . Methods for Determining Polymer-Polymer Miscibility

conclude d tha t th e glas s transitio n canno t be considere d o t be a tru e second orde r thermodynami c transition . Semiempirica l free-volum e treatment s of viscosit y relationship s fo r liquid s and polymer s hav e bee n propose d o t accoun t fo r th e rapi d chang e n i vis ­ cosit y wit h temperatur e [9-11] . Fro m th e sam e basi c approach , Williams , Landel , an d Ferr y [12 ] propose d a universa l relationshi p - 17.44( Γ - Γβ)/[51. 6 + ( Γ- Tg)] (3.1 ) where aT represent s th e temperatur e variatio n of th e segmenta l frictio n co ­ efficien t fo r mechanica l relaxations . Thi s empirica l relationshi p ha s bee n applie d successfull y o t describ e th e relaxatio n or viscosit y variatio n of polymer s n i th e temperatur e rang e of Tg < Τ < (Tg + 100°C) . Elegan t theoretica l treatment s of th e glas s transitio n temperatur e hav e been propose d by Gibb s an d DiMarzi o [13 ] an d Nos e [14 ] usin g lattic e models tha t allo w vacan t sites . The basi c differenc e betwee n thes e tw o approache ss i th e assumptio n of a tru e second-orde r transitio n fo r th e Gibbs DiMarzi o treatment , unlik e tha t of Nose's . In summary , th e glas s transitio n temperatur e ha s bee n viewe d as a second orde r transition , an isoviscou s state , an isoconfigurationa l state , an d an iso-free-volum e state . For a detaile d discussio n of th e natur e of th e glass y state , th e cite d reference s [15-17 ] wil l provid e an excellen t background . The most commonl y use d metho d fo r establishin g miscibilit y n i polymer polyme r blend s or partia l phas e mixin g n i suc h blend ss i throug h determina ­ tio n of th e glas s transitio n (o r transitions ) n i th e blen d versu s thos e of th e unblende d constituents . A miscibl e polyme r blen d wil l exhibi t a singl e glas s transitio n betwee n th e 7^' s of th e component s wit h a sharpnes s of th e transi ­ tio n simila r o t tha t of th e components . n I case s of borderlin e miscibility , broadenin g of th e transitio n wil l occur . Wit h case s of limite d miscibility , two separat e transition s betwee n thos e of th e constituent s may result , depictin g a componen t 1-ric h phas e an d a componen t 2-ric h phase .I n case s where stron g specifi c interaction s occur , th e T% may go throug h a maximu m as a functio n of concentration . The basi c limitatio n of th e utilit y of glas s transitio n determination s n i ascertainin g polymer-polyme r miscibilit y exist s wit h blend s compose d of component s whic h hav e equa l or simila r ( < 20° C difference ) 7^'s , whereb y resolutio n by th e technique so t be discusse d of tw o 7^' ss i no t possible . In th e analysi s of polymer-polyme r miscibilit y vi a th e utilizatio n of macroscopi c technique s o t observ e th e glas s transition , certai n question s have bee n pose d fo r whic h unambiguou s answer s do not presentl y exist . The basi c questio n revolve s aroun d th e leve l of molecula r mixin g require d to yiel d singl e glas s transitio n temperature s fo r miscibl e polyme r mixtures . The leve l of molecula r mixin g o t yiel d a singl e T%n i polyme r mixture ss i no t loga T=

3.2. Glass Transition Temperature

121

clearl y define d presently , an d experimenta l investigation s recentl y reporte d and cite d n i othe r section s of thi s treatis e hav e bee n directe d towar d thi s specifi c question . The questio n rephrase d s i what siz e of a "domain " or "phase " of com­ positio n differen t tha n tha t of th e bul k mixtur e s i require d o t yiel d distinc t macroscopi c propert y characteristic s (i.e. , I n some blends , microscopi c evidenc e of phas e structur e ha s bee n observe d wher e single -Tg behavio r was determined . This , of course , pose d th e questio n of domai n siz e require d for uniqu e Tg behavio r of th e individua l domains . Recen t studie s of th e physica l structur e of th e amorphou s stat e may provid e a clu e o t thi s anomal y [18, 19] . Wit h amorphou s homopolymers , electro n microscop y ha s show n tha t domain s of loca l orde r may exis tn i th e amorphou s stat e [20] . Small angl e neutro n scatterin g experiment s demonstrat e tha t loca l orde r doe s no t exis tn i th e amorphou s stat e [1 , 2] ; th e polymeri c chain s ar e n i a rando m conformation . Whil e much of th e effor ts i presentl y directe d towar d resolvin g the difference s foun d by thes e tw o experimenta l technique s fo r unblende d homopolymers , th e result s wil l hav e direc t bearin g on resolvin g th e questio n of th e leve l of molecula r mixin g n i polyme r blend s a s derive d fro m macro ­ scopi c glas s transitio n determinations . A s th e glas s transitio n valu e s i inheren t n i th e propert y characteristic s (e.g. , viscosity , crystallizatio n kinetics , thermomechanica l properties ) of a material , th e existenc e of a singl e an d sharp , singl e an d broad , shifted , or individua l transitio n fo r a blen d reveal s th e macroscopi c propert y charac ­ teristic s of th e blend . Thus , whil e ther e may exis t debat e concernin g th e leve l of molecula r mixing , th e glas s transitio n behavio r of th e blen d wil l remai n an extremel y importan t characteristic . For th e present , thes e feature s of th e Tg behavio r wil l be assume d o t asses s qualitativel y th e leve l of misci ­ bility . Hopefully , when th e abov e question s on th e effec t of domai n siz e an d leve l of molecula r mixin g on transitio n behavio r ar e answered , a quantitativ e assessmen t of th e leve l of miscibilit y wil l be possible . An interestin g revie w 4 h he ha of th e abov e questio n ha s bee n presente d by Kapla n [21] ,n i whic s assigne d a valu e of 15 0 Β as th e domai n siz e require d o t contai n a'universal' ' segmenta l lengt h associate d wit h th e glas s transition . Furthe r investigation s are necessar y o t determin e f i indee d thi s valu e s i "universal. " 3.2.1

Mechanical Methods

Mechanica l method s fo r determinatio n of th e transitiona l behavio r of polymer s an d polyme r blend s hav e bee n cite d mor e frequentl y tha n th e othe r technique so t be discussed . The elasti c an d viscoelasti c propertie s of polymer s derive d by subjectin g polymer s o t small-amplitud e cycli c deformatio n ca n yiel d importan t informatio n concernin g transition s occurrin g on th e molec -

122

3. Methods for Determining Polymer-Polymer Miscibility

ula r scale . Dat a obtaine d ove r a broa d temperatur e rang e ca n be use d o t ascertai n th e molecula r respons e of a polyme rn i blend s wit h othe r polymers . In a highl y phase-separate d polyme r blend , th e transitiona l behavio r of th e individua l component s wil l be unchanged . Likewise ,n i a miscibl e blend , a singl e an d uniqu e transitio n correspondin g o t th e glas s transitio n wil l appear . Dynamic mechanica l testin g ca n be accomplishe d usin g variou s experimenta l arrangements .I n thi s discussion , bot h fre e an d force d vibrationa l technique s wil l be covered . Free-vibratio n dynami c mechanica l testin g device s includ e the torsio n pendulum , freel y vibratin g reed , an d th e torsiona l brai d analyzer . Force d vibratio n technique s emplo y th e viscoelastomete r or a force d vibrat ­ ing reed . The torsio n pendulu m consist s of an inertia l sourc e (dis k or rod ) connecte d to a polyme r specime n (e.g. , a rectangl e wit h lengt h ρ widt h > thickness ) which s i firmly fixed at th e othe r end . The inertia l sourc e s i angularl y dis ­ place d an d released , allowin g th e specime n o t vibrat e freely . The resultan t damped sinusoida l wave s i the n determine d usin g a suitabl e recordin g devic e such as a rotar y variabl e differentia l transformer , linea r variabl e differentia l transformer , or a mirro r system . The dampe d sinusoida l wave ca n be use d o t calculat e th e shea r modulus , G\ th e los s modulus , G", an d mechanica l loss , tan (5 , define d a s GIG'. Tan δ ca n als o be calculate d mor e directl y as tan δ = n I (Α/Β)/Νπ

(3.2a )

where A an d Β ar e th e magnitude s of individua l cycle s (A > B) an dΝ s i th e number of cycle s betwee n A an d B. The shea r modulus , G' ,s i calculate d fro m 2 2 G' = An If jk (3.2b ) where k s i a geometrica l shap e facto r determine d fro m sampl e dimensions , /i s th e inertia l force , an d /si th e frequenc y of th e sinusoida l wave (cycles/sec) . Generalize d dat a (ta n δ, G', G") fo r polymer-polyme r blend s versu s tem ­ peratur e ar e illustrate d n i Fig . 3. 3 fo r behavio r expecte d of two-phas e blends . In Fig . 3.4 , th e generalize d dat a expecte d of miscible , one-phas e blend s ar e depicted . Actua l experimenta l dat a fo r th e miscibl e polyme r blen d poly(viny l chloride)-(ethylene/ethy l acrylate/carbo n monoxide ) terpolyme r ar e illus ­ trate d n i Fig . 3.5 , whic h clearl y show s an intermediat e glas s transitio n tem ­ peratur e fo r th e blend . The torsiona l brai d analyze r [22] , a variatio n of th e torsio n pendulum , has th e advantag e of bein g capabl e of handlin g ver y brittl e material s a s wel l as ver y fluid materials . A fiberglass brai d or othe r suitabl e suppor t s i im­ pregnate d wit h th e materia l o t be tested . One en d s i firmly fixed whil e th e othe r en d s i attache d o t an inertia l system . Absolut e value s of th e shea r modulus , G' , an d th e los s modulus , G", canno t be determine d usin g thi s

123

3.2. Glass Transition Temperature

A

θ

1 log tan 6

log G

Β

Fig. 3.3. Generalized behavior of the dynamic mechanical properties of a two-phase blend. , mixture. , pure components ;

log tan h

log G

Fig. 3.4. Generalized behavior of the dynamic mechanical properties of a miscible blend. , mixture. , pure components ;

2 technique . However , th e mechanica l los s an d a relativ e modulu s (cycles/sec) can be use d o t ascertai n transition s occurrin g n i th e experimenta l specimens . The vibratin g ree d arrangemen t [23 ] ca n be use d o t measur e polyme r transition s vi a determinatio n of th e tensil e modulu s an d mechanica l los s in eithe r fre e or force d vibration . The experimenta l apparatu s fo r force d vibratio n consist s of a polyme r stri p rigidl y fixed at on e en d an d force d o t vibrat e transversel y vi a an electromagneti c vibrato r drive n by a variabl e frequenc y source . At th e resonanc e frequency , a maximu m n i th e deflectio n of th e fre e en d s i observed . The tensil e modulus i calculate d fro m [23 ] 2 2,E, s Ε=

3S.24dL*fr/D

(3.3 )

where d = density , L = lengt h of polyme r strip , D = thickness , an d fr =

124

3. Methods for Determining Polymer-Polymer Miscibility

-180

-140

-100

-60

-20

20

60

100

T(°C) Fig. 3.5. Mechanical loss and shear modulus versus temperature data for : ethylene/ethylacrylate/carbon monoxide (E/EA/CO) (71.8/10.5/17.7) terpolymer, ; 50/50 blend of terpolymer with poly(vinyl chloride), ; and p o l y v i n y l chloride), · · · · . [ F r o m L . M. Robeson and J. E. McGrath, Polym. Eng. Sci. 17, 300 (1977).]

resonanc e frequenc y (cycles/sec) . The mechanica ss i give n by 3 l los tan δ = Ε'ΙΕ' = F/A0 where

21 F =

[ — 5.478

+

2(7.502 +

6.15M )

(3.4) /

2

]/1.689M

2 (3.5)

and M s i th e rati o of amplitud e of th e fre e en d o t th e clampe d end s of th e plasti c strip .A0 = 1 . 8 7 5 . Dynamic mechanica l testin g of material s subjecte d o t a cycli c tensil e strai n (force d vibration )s i anothe r metho d commonl y employe d o t measur e polymeri c transitions . The instrument , commonl y referre d o t as a viscoelasto meter [ 2 4 , 2 5 ] , operate s on th e principl e tha t an applie d sinusoida l tensil e

125

3.2. Glass Transition Temperature

strai n applie d o t th e specime n generate s a sinusoida l stres s wit h a phas e angl e <5 . The horizonta l specime n s i attache d at on e en d o t a drive r uni t pro ­ vidin g oscillator y motio n whil e th e othe r en d s i connecte d o t a loa d trans ­ ducer . Output s of th e stres s an d strai n transducer s ar e converte d o t provid e direc t ta n 5 < readings . The absolut e valu e of th e comple x tensil e modulu s E* (Ε* = E' + iE") s i give n by \E*\=FI/AIA

(3.6 )

where F = tensil e force , A = cross-sectiona l area , /= lengt h of specimen , and Δ/ = amplitud e of elongation . The n Ε an d E" ca n be calculate d wit h the followin g relationships . Ε = Ε* co sδ

(3.7 )

Ε" = E ta nδ

(3.8 )

A n exampl e of th e us e of viscoelastomete r dat a o t determin e polymer polyme r miscibilit y s i give n n i Fig . 3. 6 fo r th e blen d of poly(vinyliden e fluoride) an d poly(methy l methacrylate ) [26] . 40% PVF 2 60% PMMA E*

T(°C) Fig. 3.6. Dynamic mechanical properties at 110 Hz for an annealed poly(vinylidene fluoride)-poly(methyl methacrylate) (40/60) blend using a Rheovibron Viscoelastometer. [Reprinted with permission from D . R. Paul and J. O. Altamirano, Adv. Chem. Ser. 142, 371 (1975). Copyright by the American Chemical Society.]

126

3 . Methods for Determining Polymer-Polymer Miscibility

Anothe r metho d of mechanicall y determinin g th e glas s transitio n of poly ­ mers s i by simultaneousl y measurin g th e modulu s an d resilience . Thi s metho d involve s th e measuremen t of th e stress-strai n curv e whil e elongatin g th e specime n o t 1 % (o r lower ) strai n an d the n reversin g th e directio n of strai n back o t 0% strai n at th e sam e testin g rat e (e.g. , 0. 1 in./mi n pe r inc h of tes t specime n length) . The strai n require d o t reac h zer o stres s on th e retur n curv e is the n divide d by th e strai n reache d befor e reversa l (i.e. , 1%) o t yiel d a valu e time s 10 0 terme d percen t resilience . Generalize d dat a illustrate d n i Fig . 3. 7 provid e th e basi s fo r definin g percen t resilienc e: 2 percen t resilienc e = (AB/OA) χ 10 (3.9 ) The modulu s ca n be determine d fro m th e slop e of th e stress-strai n curve . The modulu s an d percen t resilienc e dat a plotte d agains t temperatur e ca n be use d o t determin e one-phas e versu s two-phas e behavior , as illustrate d by th e generalize d curve s depicte d n i Figs . 3. 8 an d 3.9 . The modulus-temperatur e dat a obtaine d vi a thi s techniqu e ar e as accurat e , as thos e obtaine d by th e previousl y describe d mechanica l method s ;however

Stress

A Β Strain Fig. 3.7.

Generalized stress-strain data utilized for resilience determination.

\ \

log Ε

50/50 A/B

ο c •J "t o rr

T '9A

gB

•gA

•QB

Fig. 3.8. Generalized modulus and resilience versus temperature data for a two-phase polymer blend.

127

3.2. Glass Transition Temperature

resilienc es i no ta s sensitiv e a s mechanica l loss . Nevertheless , thi s typ e of dat a has bee n use d by severa l investigator s o t characteriz e polyme r blend s [27 , 28], as illustrate d n i Fig . 3.1 0 fo r blend s of tetramethy l bispheno l A poly ­ carbonat e an d polystyrene , whic h wer e foun d o t exhibi t a hig h leve l of miscibilit y [28] . 50/50 A/B

log Ε

te

Τ 9(Α Β)

+

\

9(Α+Β) SB

Fig. 3.9. Generalized modulus and resilience versus temperature data for a single-phase polymer blend.

10 T E T R A M E T H Y L B I S P H E N OL A P O L Y C A R B O N A T E

Ε (psi)

ιο- μ

10

100

150

300

T(°C) Fig. 3.10. Modulus-temperature data for a 50/50 blend of polystyrene with tetramethyl bisphenol A polycarbonate (mixtures prepared at temperatures indicated). [From M. T. Shaw, J. Appl. Polym. Sci. 18, 449 (1974).]

128 3.2.2

3. Methods for Determining Polymer-Polymer Miscibility

Dielectric Methods

The electrica l propertie s of polymer s ar e analogou s o t mechanica l proper ­ tie sn i tha t th e dielectri c constant , ε' ,s i simila r o t compliance , th e dielectri c los s factor , ε" ,s i simila r o t mechanica l loss , an d th e dielectri c strengt h s i analogou s o t tensil e strength . The dielectri c los s facto r an d th e dissipatio n factor , ta n δ (ε"/ε'), ar e of primar y interes t n i thi s discussio n as the y ar e commonly use d o t ascertai n polymeri c transition s suc h as th e glas s transition . The experimenta l advantag e of obtainin g transitio n dat a fro m electrica l measurement s ove r dynami c mechanica l testin g s in i th e eas e of changin g frequency . The majo r disadvantag e s i th e difficult y n i determinin g th e transi ­ tion s of nonpola r polymers . Generall y nonpola r polymer s wil l requir e sligh t modification , suc h as oxidation , o t provid e sufficien t polarit y o t resolv e adequatel y secondar y los s transition s as wel l a s glas s transition s n i blends . For pola r polymers , fi on e represent s th e dipol e by a singl e relaxatio n time , τ , the n th e constituent s of th e comple x dielectri c constant , ε* , ar e define d as (3.10 ) 22 ε' = ε ^ + (ε (3.11 ) 0 - e J 0/ +2 ω 2τ ) (3.12 ) ε" = (ε 0 - ε0)ωτ/( 0 1 + ωτ ) where ε0 an d ε ^ ar e th e limit s of ε ' at zer o frequenc y an d infinit e frequency , respectively . The los s facto r goe s throug h a maximu m when ωτ = 1. The dielectri c constan t increase s a s molecula r motio n n i a polyme r in ­ creases ; thus , larg e secondar y relaxation s an d th e glas s transitio n wil l yiel d increasin g values . The generalize d behavio r fo r th e dielectri c constan t an d the dielectri c los s facto r yield s th e schematic s fo r miscibl e or phase-separate d polyme r blend s illustrate d n i Fig . 3.11 . An experimenta l exampl e of th e dielectri c metho d fo r establishin g th e miscibilit y of polyme r blend s s i illustrate d n i Fig . 3.1 2 fo r poly(2,6-dimethyl-l,4-phenylen e oxide)-poly styren e blend s [29] . A techniqu e n i whic h th e chang e of dielectri c los s s i measure d unde r a definit e temperatur e progra m s i terme d th e thermodielectri c los s measure ­ ment. Thi s recen t techniqu e ha s bee n use d fo r estimatin g th e leve l of poly ­ mer-polyme r miscibilit y [30] . As th e dielectri c los s of a sampl e s i dissipate d in th e for m of heat , a differentia l therma l analyze r ha s bee n utilize d o t measur e ε " n i thi s approach . Thi s ne w techniqu e s i claime d o t be mor e sensitiv e fo r measurin g th e degre e of miscibilit y tha n othe r methods . A brie f outlin e of th e theor y an d dat a analysi s wil l be presented . ιε

129

3.2. Glass Transition Temperature 50/50

T(or frequency) Fig. 3.11. Generalized dielectric loss factor, ε", and dielectric constant, ε', versus tempera­ ture (or frequency) data for single-phase and two-phase polymer blends.

-180

-100

-20

60

220

300

TTC) Fig. 3.12. Dielectric loss of a 50/50 blend of polystyrene and poly(2,6-dimethyl-l,4-phenylene oxide) as functions of temperature and frequency. [Reprinted with permission from W. J. MacKnight, J. Stoelting, and F. E. Karasz, Adv. Chem. Ser. 99, 26 (1971). Copyright by the American Chemical Society.]

130

3. Methods for Determining Polymer-Polymer Miscibility

The apparatu s consist s of an arrangemen t o t measur e th e dielectri c los s of a sampl e n i on e chambe r of a differentia l therma l analyzer . A referenc e sampl es i use d suc h tha t th e dielectri c los ss i determine d fro m th e temperatur e differenc e betwee n th e referenc e an d th e sampl e n i th e electri c field. The di ­ electri c los ss i determine d fro m 2 s" = 4Q/E0f (3.13 ) where Q s i th e hea t generate d pe r uni t volum e pe r second ,fis th e cycli c fre ­ quency , an d E0 s i th e electri c field intensity . The temperatur e difference , AT, betwee n th e sampl e n i th e electri c field an d th e referenc e positio n s i assume d proportiona l o t Q. Therefore , 2 e" = AAT/fV0 (3.14 ) where A s i a constan t dependen t on densit y an d th e specifi c hea t of th e sampl e and V0 s i th e applie d voltage . To simplify , a quantit y ε" * s i define d o t relat e Δ Γo t Ah (heigh t fro m baselin e n i th e DTA data) , yieldin g 2 ε"* = BAh/fV0 (3.15 ) In Fig . 3.13 , ε" * versu s temperatur e s i show n fo r th e miscibl e blen d of poly(viny l nitrate ) an d an ethylene/viny l acetat e copolyme r [30] . Fro m th e same data , contou r surface s of th e dielectri c los s ca n be obtained . I n th e contou r surfaces , th e dielectri c loss , ε"* ,s i take n perpendicula ro t th e surfac e and l o g s / iplotte d agains t l/T. For miscibl e mixtures , a serie s of peak s occur s throug h whic h a singl e lin e ca n be constructed . For immiscibl e blend s for whic h th e constituent s hav e differen t 7g's , tw o serie s of peak s ar e ob -

Fig. 3.13. Temperature dispersion of ε"* at various frequencies for a miscible mixture of p o l y v i n y l nitrate with ethylene/vinyl acetate copolymer (86 wt% vinyl acetate) (30/70 wt ratio). [From S. Akiyama, Y. Komatsu, and R. Kaneko, Polym. J. 7, 172 (1975).]

131

3.2. Glass Transition Temperature

served . Thi s s i illustrate d n i Figs . 3.1 4 an d 3.15 , respectivel y showin g th e miscibl e blen d of polyviny l nitrate)-poly(viny l acetate ) an d th e immiscibl e blen d of polyviny l acetate)-(ethylene/viny l acetate ) copolymer . Thi s graphica l techniqu e yield s a ne w metho d fo r determinatio n of polyme r miscibilit y by evaluatio n of th e characteristi c appearanc e of th e contou r surfaces .

2.5

2.7

2.9

3.1

I000/T(°K"') Fig. 3.14. Contour map of ε"* for the miscible mixture of poly(vinyl nitrate) with poly(vinyl acetate) (30/70). The dashed lines represent crests corresponding to phase transitions. [From S. Akiyama, Y. Komatsu, and R. Kaneko, Polym. J. 7, 172 (1975).]

1000/T(°K) Fig. 3.15. Contour map of ε"* for the immiscible mixture p o l y v i n y l acetate) and ethylene/ vinyl acetate copolymer (86 wt% vinyl acetate) (40/60). [From S. Akiyama, Y. Komatsu, and R. Kaneko, Polym. J. 7, 172 (1975).]

132

3 . Methods for Determining Polymer-Polymer Miscibility

Review s of dielectri c characterizatio n of polymer s ca n be foun d n i th e cite d reference s [31 , 32] . 3.2.3

Dilatometric Methods

Polyme r glas s transition s hav e many characteristic s simila r o t a second orde r thermodynami c transition . Wit h respec t o t volum e change , a discon ­ tinuit y s i observe d n i th e rat e of volum e chang e wit h temperatur e n i th e regio n of th e glas s transition . Dilatometri c method s o t determin e polymeri c glas s transition s wer e on e of th e most common technique s befor e mechanica l method s becam e popular . Dilatometri c technique s an d experimenta l apparatu s hav e bee n adequatel y discusse d elsewher e [33 , 34 ] an d wil l no t be reproduce d here . In a blen d of tw o distinctl y differen t polymers , two-phas e behavio r ca n be determine d by tw o discontinuitie s n i th e derivativ e curv e dV/dT corre ­ spondin g o t th e 7^' s of th e respectiv e phases . Experimenta l dat a exhibitin g one-phas e behavio r fo r a polyme r blen d ar e show n n i Fig . 3.16 , illustratin g the blen d of syndiotacti c poly(methy l methacrylate ) (Tg = 120°C ) an d iso tacti c poly(methy l methacryate ) (Tg = 45°C ) [35] . Not e tha t th e majo r chang e in slop e fo r th e volume-temperatur e dat a occur s at th e Tg (94°C ) of th e blend , wel l betwee n th e componen t 7^s . Dilatometri c technique s ar e les s sensitiv e tha n th e dynami c mechanica l method s previousl y discussed , an d the presenc e of crystallinit y hinder s resolution .

T(°C) Fig. 3.16. Volume-temperature plot of a mixture of 79.4% (by wt) syndiotactic poly(methyl methacrylate with 20.6% (by wt) isotactic poly(methyl methacrylate). [From S. Krause and N. Roman, / . Polym. Sci., Part A 3, 1631 (1965).]

133

3.2. Glass Transition Temperature

3.2.4

Calorimetric Methods

The utilizatio n of calorimetri c method s o t determin e th e glas s transitio n of polymer s an d thei r respectiv e blend s parallel s tha t of dilatometri c method s discusse d n i th e previou s section . The specifi c hea t of polymer s exhibit s a chang e when passin g throug h th e glas s transition , generatin g a maximu m in th e valu e of dCp/dTas generalize d n i Fig . 3.17 . With th e introductio n of sensitiv e calorimeter s withi n th e las t decade , th e calorimetri c techniqu e ha s rapidl y gaine d prominence . The most common instrumen ts i th e differentia l scannin g calorimete r (DSC) . The DSC measure s the amoun t of hea t require d o t increas e th e sampl e temperatur e by a valu e AT ove r tha t require d o t hea t a referenc e materia l by th e sam e AT Throug h sophisticate d instrumentation , controlle d rate s of heatin g or coolin g ar e possibl e wit h hig h accurac y of hea t inpu t (o r output ) o t smal l specimen s (5-5 0 mg) . More detaile d descriptio n of th e utilit y an d desig n parameter s of differentia l scannin g calorimeter s ca n be foun d elsewher e [36 , 37] . This techniqu e ha s successfull y demonstrate d polymer-polyme r miscibil ­ , nitril e rubber-PV C [39] , poly(viny l it y fo r th e system s PPO-polystyren e [38] methyl ether)-polystyren e [40] , poly(vinyliden e fluoride)-poly(methyl meth ­ acrylate ) [41] , an d PVC-(ethylene/viny l acetate/sulfu r dioxide ) terpolyme r [42] . Differentia l scannin g calorimetr y ha s bee n particularl y usefu ln i study ­ ing th e miscibilit y of th e classi c system : nitril e rubber-PVC . Usin g DSC, Zabrzewsk i [39 ] observe d miscibilit y wit h PVC n i al l composition s at level s of 23 o t 45 % acrylonitril e n i th e nitril e rubber ,n i excellen t agreemen t wit h dynami c mechanica l data . Land i [43 ] investigate d simila r blend s an d ob ­ serve d single-phas e behavio r wit h a 34 % acrylonitrile-conten t nitril e rubbe r blende d wit h PVC. He note d tha t th e DSC result s coul d be more clearl y illustrate d by plottin g th e secan t slop e of th e specifi c hea t versu s temperature ,

Τ Fig. 3.17. Generalized behavior of specific heat versus temperature of polymers in the range of the glass transition temperature. Solid line = quenched; dashed line = annealed.

134

3. Methods for Determining Polymer-Polymer Miscibility

-A

0%

PVC

11%

PVC

3 00

LU >

4 6 % PVC

-80

-60

-40 -20

0

20

40

60

80

T(°C) Fig. 3.18. Effect of poly(vinyl chloride) on the single glass transition of nitrile rubber (34% acrylonitrile). Data obtained on a differential scanning calorimeter (DSC). [From V. R. Landi, Appl. Polym. Symp. 25, 223 (1974).]

as show n n i Fig . 3.18 . By usin g thi s dat a reductio n technique , he clearl y demonstrate d tha t variation s n i acrylonitril e conten t as wel la s mixin g tech ­ nique s coul d be mor e clearl y define d tha n by direc t observatio n of th e basi c DS C thermogram . 3.2.5

Thermo-Optical Analysis

A techniqu e terme d thermo-optica l analysi s (TOA) ha s bee n employe d by Shult z et al. [44-47 ] o t investigat e th e miscibilit y of polyme r blends . Thi s techniqu e involve s scribin g scratche s ont o a polyme r or blen d surfac e wit h a stee l stylus . A polarizin g microscop e equippe d wit h a ho t stag e capabl e of temperatur e programmin g s i employed . Ligh t transmitte d throug h th e film place d betwee n crosse d polarize r an d analyze rs i converte d int o voltag e an d plotte d agains t temperature . The scratche d surfac e s i birιfringen t an d thu s ligh t s i onl y transmitte d throug h th e scratches . As th e polyme r (o r con ­ stituent s of th e blend ) pas s throug h th e glas s transitio n temperature , th e orientatio n produce d by scratchin g th e filmdisappear s an d th e reductio n n i birefringenc e lead s o t a decreas e n i transmitte d light . Result s fo r a miscibl e blen d (styrene-/?-chlorostyrene ) copolymer-poly (2,6-dimethyl-l,4-phenylen e oxide ) show n n i Fig . 3.1 9 ar e compare d wit h

135

3.2. Glass Transition Temperature

T(°C) Fig. 3.19. Thermo-optical analysis curves for blends of poly(2,6-dimethyl-l,4-phenylene xoide) (PPO) and styrene-p-chlorostyrene copolymer (0.453 mole fraction styrene). Numbers on the plot represent the weight fraction of PPO in each blend. [Reprinted with permission from A. R. Shultz and Β. M. Brach, Macromolecules 7, 902 (1974). Copyright by the American Chemical Society.]

an immiscibl e blen d of poly (/7-chlorostyrene)-poly(2,6-dimethyl-l,4-phe ene oxide ) show n n i Fig . 3.20 . Singl e transitio n temperature s monotonicall y increasin g wit h th e conten t of th e highe r Tg componen t ar e characteristi c of the miscibl e blen d (Fig . 3.19) , wherea s tw o transition s correspondin g o t th e blen d constituent s ar e observe d fo r th e immiscibl e blen d (Fig . 3.20) . The conclusion s [46 ] reache d usin g thermo-optica l analysi s o t characteriz e mis ­ cibilit y n i polyme r blend s wer e n i excellen t agreemen t wit h mor e common technique s (e.g. , dynami c mechanica l an d calorimetry) . 3.2.6

Radioluminescence Spectroscopy

A uniqu e metho d o t measur e th e glas s transitio n of polyme r blends , terme d radioluminescenc e spectroscopy , ha s bee n successfull y utilize d by Zlatkevic h

136

3. Methods for Determining Polymer-Polymer Miscibility

T(°C) Fig. 3.20. Thermo-optical analysis curves for blends of poly(2,6-dimethyl-l,4-phenylene oxide) (PPO) and poly(/?-chlorostyrene). Numbers on the plot represent the weight fraction of PPO in each blend. [Reprinted with permission from A. R. Shultz and Β. M. Beach, Macro­ molecules 7, 902 (1974). Copyright by the American Chemical Society.]

and Nikolski i [48 ] an d Bτhm et al. [49] . Irradiatio n (electro n or y ray ) of th e polyme r or blen d n i th e glass y stat e result s n i trappe d secondar y electron s which ar e rapidl y released , yieldin g luminescence , onc e th e sampl e tem ­ peratur e reache s th e glas s transition . Maximu m luminescenc e s i observe d at a temperatur e quit e clos e o t Tg value s reporte d by more common tech ­ niques . For two-phas e blends , tw o distinc t peak s ca n be observe d n i lumin ­ escenc e versu s temperature , correspondin g o t th e respectiv e 7^'s . Resolutio n of th e T% of a mino r phas e (a s lo w a s severa l volume s percent )s i quit e good , thus providin g equa l or superio r sensitivit y o t mechanica l or calorimetri c methods . For a descriptio n of specifi c experimenta l procedure s an d equip ­ ment design , se e Zlatkevic h an d Nikolski i [48 ] an d Bτhm [50] .

3.3

MICROSCOPY

Direc t visua l confirmatio n of th e presenc e of tw o phase s ha s bee n use d more ofte n tha n an y othe r metho d a s a preliminar y indicatio n of th e degre e

3.3. Microscopy

137

of miscibilit y n i a polymer-polyme r system . Many hav e turne d o t microscop y to ai d n i determinin g no t onl y th e presenc e bu t th e connectivitie s of th e phases . Electro n microscopy , wit h 50Β resolution , ha s show n tha t heter ­ ogeneitie s exis t eve n n i miscibl e polyme r systems . Suc h s i th e natur e of solu ­ tion s of 50Β molecules . 3.3.1

Visible, Including Phase Contrast

Both transmitted-ligh t an d phase-contras t microscop y requir e a s a mini ­ mu m a differenc e n i refractiv e inde x betwee n th e phase s fo r contrast . Trans ­ missio n contras ts i bes t obtaine d wit h difference s n i opacit y or color ; how­ ever , wit h phase-contras t optic s goo d contras ts i obtaine d wit h transparen t material s an d s i therefor e th e preferre d metho d fo r polymer-polyme r sys ­ tems. Stainin g s i anothe r metho d of enhancin g contras t an d a limite d stainin g technolog y ha s bee n develope d fo r polymer s ;however ,t i pale sn i compariso n wit h tha t known o t biologists . Typica l phase-contras t technique s ar e summarize d n i th e paper s of Mars h et ai [51] , Inou e et al [52] , Vasil e an d Schneide r [53] , an d Walter s an d Keyt e [54] . Generally , film s of 5 μΐ η or les s ar e microtome d or cas t fo r observations . Enhancemen t of contras tn i mixture s of crystallin e polymer s ca n be obtaine d by us e of polarize d ligh t [55] . Osmiu m tetroxid e staining , wel l known n i electro n microscopy , ha s als o bee n use d o t enhanc e contras t fo r optica l work [52] . Stain s fo r variou s polymer s ar e liste d by Braue r an d Newman [56, 57] . A sampl e of th e effect s possibl e wit h stain ss i give n n i Tabl e 3.1 . Optica l microscop y on two-phas e mixture s ha s reveale d many type s of structures , includin g interpenetratin g phases . The fineness of th e phase s has bee n relate d o t mixin g intensit y an d viscosit y ratio , bu t no t ofte n [58 ] to degre e of solubility . The us e of scatterin g (dark-field ) optic s fo r th e deductio n of tw o phase s is no t common n i polymer-polyme r studie s eve n thoug h hig h intensit y ligh t at righ t angle s o t th e optica l axi s (ultramicroscopy ) ca n revea l th e presenc e of scatterin g bodie s fa r smalle r tha n th e resolvin g powe r of th e microscope . Miyat a an d Hat a [59 ] hav e describe d th e us e of th e ultramicro ­ scop e on th e syste m poly(methy l methacrylate)-poly(viny l acetate) . 3.3.2

Electron Microscope

Transmissio n electro n microscop y (TEM) ha s bee n widel y use d n i polymer-polyme r studies . The necessar y ste p of microtomin g ca n be facili ­ tate d by cryogeni c or chemica l methods . Electro n opacit y difference s ar e ofte n achieve d by selectiv e chemica l reactio n [58 , 60 ] or by annealin g n i th e electro n bea m [58 , 61] . Treatmen t of solubl e polyme r system s wit h an y

138

3. Method s fo r Determinin g Polymer-Polyme r Miscibilit y TABLE 3. 1 Colors Obtaine d wit h th e Smit h Stain , a Mixtur e o f Methylen e Blu e an d Suda n II I Dyes, Applie d t o Variou s Polymers " Material Colors of Hydrophilic

Color Materials Bright blu e

Cellophane Cotton Paper fibers

Blue Very ligh t t o ver y dee p blu e depending o n typ e o f fibe r and degre e o f hydratio n Blue-green wit h lighte r blu e ski n

Rayon (viscose ) Colors of Hydrophobic Acrylate polymer s Butadiene/acrylonitrile copolymer s Butadiene/styrene copolymer s Ethyl cellulos e Natural rubber , unfille d Natural rubber , wit h hydrophili c filler Polyamide resin s Polyethylene Polyisobutylène (Vistanex ) Vinyl chlorid e polymer s Vinyl pyridin e copolymer s (Gentac )

Materials Orange Orange t o brownis h re d Orange t o brownis h re d Dull re d orang e Orange-yellow Greenish yello w Orange-yellow Pale yello w Pale pin k Pale pin k Orange

Colors of Mixed Hydrophilic-Hydrophobic Cellulose acetat e Cellulose nitrate , unplasticize d Cellulose nitrate , plasticize d A n y hydrophobi c polyme r wit h hydrophilic group s i n th e structur e or wit h hydrophili c additive s

Materials

Green Colorless t o ligh t gree n Colorless t o oliv e gree n Greenish orang e

Materials Unaffected by Either

Dye

Dacron Mylar Nylon

a

Fro m S . B . Newman , in "Analytica l Chemistr y o f Polymers " (Ο. M. Kline, ' éd.), Part III, p. 261, Wiley (Interscience), N e w York, 1962.

chemica l agen t shoul d be regarde d wit h cautio n as t i may caus e phas e separa ­ tion . Heatin g or coolin g ca n hav e simila r effects . The productio n of artifact s durin g microtoming , staining , replication , an d exposur e o t th e bea m ar e well known bu t continu e o t caus e difficulties . Severa l polymer-polyme r system s of reporte d miscibilit y hav e bee n show n

3.3. Microscopy

139

to contai n domain s by usin g th e electro n microscope . Smit h an d Andrie s [58] foun d tha t th e syste m SBR-P B was immiscibl e eve n wit h as littl e as 3% styren e n i th e SBR, bu t tha t th e phas e siz e progressivel y decrease d wit h styren e content . Thi s s in i conflic t wit h th e result s of Mars h et al. [51] , who foun d no evidenc e fo r multipl e phase s n i SBR-P B or n i SBR-(ethylene butadiene ) copolymer . Matsu o et al. [60 ] foun d some (40 0 Β) heterogeneit y in th e syste m PVC-NBR containin g 40 % acrylonitrile , althoug h onl y on e glas s transitio n was observed .

Fig. 3.21. Transmission electron micrograph showing contrast between P M M A (light) and S A N (dark) phases developed during exposure to the electron beam [Reproduced with permission from L. P. McMaster, Adv. Chem. Ser. 142, 43 (1975). Copyright by the American Chemical Society.]

140

3. Methods for Determining Polymer-Polymer Miscibility

McMaster [61 ] foun d tha t TEM was usefu l fo r followin g th e phas e de ­ compositio n of th e miscibl e syste m PMMA-SAN . The geometr y of th e phase s correlate d wel l wit h th e expecte d occurrenc e of spinoda l decomposi ­ tio n nea r th e critica l composition . Excellen t contras t was achieve d by pro ­ longe d exposur e of th e sample s o t th e electro n beam , as ca n be see n n i Fig . 3.21 . Thi s techniqu e ha s bee n studie d n i mor e detai l by Thomas an d Talmo n [62] , who hav e attribute d th e contras t developmen t o t differentia l thinning . The techniqu e of scannin g electro n microscop y (SEM) ha s foun d a nich e in phas e studie s [54] . Contras t depend s n i thi s techniqu e on difference s n i surfac e topograph y or textur e an d thi s ca n be emphasize d by breakin g th e specime n n i it s glass y state . Ifvitrificatio n require s cooling , ther e s i agai n the dange r of phas e changes . Differentia l swellin g [63 ] involve s a simila r hazard .

3.4 SCATTERING METHODS

3.4.1

Cloud-Point Method

By definition , a stabl e homogeneou s mixtur e s i transparent , wherea s an unstabl e nonhomogeneou s mixtur e s i turbi d unles s th e component s of th e mixtur e hav e identica l refractiv e indexe s [64] . Give n a stabl e homogeneou s mixture , th e transitio n fro m th e transparen to t th e turbi d stat e ca n be brough t about by variation s of temperature , pressure , or compositio n of th e mixture . The clou d poin t correspond s o t thi s transitio n point—th e poin t of incipien t phas e separation . I ts i no t necessaril y an equilibriu m event , bu t th e fac t tha t the opalescenc e almos t alway s disappear s on reversa l of th e temperature pressure-compositio n variatio n strongl y indicate s tha t th e drivin g force s ar e thermodynami c n i origin . For polyme r mixtures , th e cloud-poin t curve s ar e usuall y measure d usin g a thi n filmmade fro m a thoroughl y mixe d blend . The film s i observe d throug h a microscop e illuminato r fo r low-angl e bac k or forwar d scatterin g relativ e to th e inciden t light . The specime n s i the n heate d at a ver y lo w rat e suc h tha t the temperatur e increase s at an infinitesimall y slo w rate . The first fain t cloudines s appears , denotin g th e clou d point , an d th e temperatur e s i re ­ corded . A fe w degree s abov e thi s clou d point , th e cycl e s i reversed ; th e sampl e s i graduall y cooled . The temperatur e at whic h th e faintes t opales ­ cenc e jus t disappear s s i als o recorded . Thi s s i repeate d fo r a serie s of com­ position s an d a temperature-compositio n plo t s i generated . The resul t s i calle d th e cloud-poin t curv e (CPC) . Generally , th e CPCs foun d on heatin g and on coolin g th e sampl e do not agree . The reason s fo r thi s ar e many; the y ste m mostl y fro m kineti c factor s plu s th e fac t tha t a phas e transitio n poin t

141

3.4. Scatterin g Method s

can be observe d onl y afte r bi g enoug h cluster s hav e forme d o t creat e suffi ­ cien t refractiv e inde x difference s fo r scatterin g an observabl e quantit y of light . Thi s shortcomin g n i th e CPC measuremen ts i ofte n correcte d by pre ­ sentin g an averag e of th e tw o CPCs. A numbe r of investigator s [65-67 ] hav e made CPC measurement s fo r severa l binar y high-polyme r mixtures .I n eac h case , th e CPCs ar e measure d above th e system' s glas s transitio n or meltin g point . System s studie d includ e polystyrene-poly(viny l methy l ether ) [65] ; poly(e-caprolactone)-poly(sty rene-co-acrylonitrile ) [66] ; polycarbonate-poly(e-caprolactone ) [67] ; an d mixture s [67 ] of poly(vinyliden e fluoride) wit h poly(methy l methacrylate) , poly(ethy l methacrylate) , poly(methy l acrylate) , an d poly(ethy l acrylate) . All of thes e system s exhibi t th e lowe r critica l solutio n temperatur e (lest ) behavior . Other CPC measurement s [68-72 ] on oligomeri c an d shor t chai n lengt h system s hav e exhibite d uppe r critica l solutio n temperatur e (ucst ) behavio r

Polyisobutene

•Weight fractio n PS T [Polystyrène

0.2 0. 4 0. 6 0. 8 Fig. 3.22 . Cloud-poin t curve s fo r polyisobutene-polystyren e mixture s o f variou s molecula r weights. [Fro m R . Koningsvel d an d L . A . Kleintjens , J. Polym. Sci., Polym. Symp. 6 1 , 22 1 (1977).]

142

3 . Methods for Determining Polymer-Polymer Miscibility

and the y hav e reveale d unusua l asymmetr y an d bimodalit y of th e phas e diagram . The asymmetr y s i foun d n i th e experimenta l CPCs of Allen , Gee , and Nicholso n [68 ] fo r lo w molecula r weigh t mixture s of polyisobutylen e and poly(dimethy l siloxane) . Thi s asymmetr y manifest s itsel f a s a shif t of the maximu m poin t fro m lo w concentration s of th e hig h molecula r weigh t componen t (wit h silicone ) o t hig h concentration s of tha t component . The bimodalit y ha s bee n demonstrate d fo r a lo w molecula r weigh t mixtur e of polystyren e wit h polyisopren e or polyisobuten e [72] . Thi s behavio r ha s als o been observe d by Power s [70 ] fo r a lo w molecula r weigh t a-methylstyrene viny l toluen e copolyme r mixe d wit h a lo w molecula r weigh t polybutene . Aharon i [71 ] observe d a simila r phenomeno n wit h hig h molecula r weigh t epoxy an d copolyeste r comixe d wit h l,1^2,2'-tetrachloroethane . The genera l observatio n fo r thes e system s was tha t th e phenomeno n was no t relate d o t the polydispersit y of th e polymers .I n fact , th e bimodalit y tende d o t increas e as th e polyme r polydispersit y was reduced . Figur e 3.2 2 illustrate s th e bimoda l cloud-poin t curve s fo r polyisobutene polystyren e mixtures . For thes e measurement s Koningsvel d an d Kleintjen s [72] use d a low-spee d analytica l centrifug e whic h allowe d determinatio n of the CPCs on th e polyme r mel t withi n reasonabl e times . Thi s als o remove d the necessit y of makin g tw o CPC measurements , i.e. , on heatin g an d on cooling .

3.4.2

Conventional Light Scattering Method

Light scatterin g ha d it s humbl e beginnin g wit h Lor d Rayleigh' s mathe ­ matica l result s [73 ] advance d n i answerin g a seemingl y innocen t questio n regardin g why th e sk y s i blue . Later , Smoluchowsk i formulate d [74 ] a fluc­ tuation s theor y whic h extende d Rayleigh' s result so t includ e liqui d solution s; thi s was subsequentl y refine d by Einstei n [75] . Accordin g o t thes e theories , if a ligh t bea m passe s throug h a mediu m whos e volum e element s (containin g the constituen t particles ) ar e smal l compare d o t th e wavelengt h of th e light , the ligh t wil l be scattered . The scattere d ligh t intensit y s i proportiona l o t the mean squar e of th e concentratio n fluctuations n i th e smal l volum e element s and , therefore , inversel y relate d o t th e secon d derivativ e of th e fre e energ y wit h respec to t concentration . For multicomponen t system s [76 ] an d polydispers e polymer s [77] , th e t du e o t densit y an d tha t du e scatterin g s i made up of tw o contribution s :tha to concentratio n fluctuations. At condition s fa r remove d fro m th e spinodal , the forme r ca n be eliminate d merel y by subtractin g th e scatterin g intensit y of th e pur e solven t fro m tha t of th e solution . I n th e regio n of th e spinoda l

143

3.4. Scattering Methods

thi s procedur e break s down. One no w need s o t allo w fo r th e couplin g betwee n th e fluctuations as wel l as th e additiona l energ y require d o t estab ­ lis h th e finite concentratio n gradien t discusse d earlie r n i Sectio n 2.2.4 . Accordin g o t Deby e [78] , thes e furthe r complication s ca n be bypasse d by making severa l measurement s at a serie s of angle s an d extrapolatin g th e scatterin g intensitie s o t zer o angle . Hence ,s o lon g as th e measurement s ar e made prio r o t actua l phas e separation , th e scattere d intensit y depend s on the mean squar e of th e concentratio n fluctuations much th e sam e way as in th e origina l Rayleig h scatterin g [73] . For a multicomponen t system , th e scattere d ligh t extrapolate d o t zer o scatterin g angl eθ s i give n by Zernik e [76 ] a s 22 4π η

v1 Jdndn dcdc y

ij

[IV].« o = kT AV (3.16 ) c where Re, th e Raleig h ratio , denote s th e scattere d intensit y du e o t concen ­ tratio n fluctuation; λ, th e wavelengt h of th e ligh t in vacuo; fe,Boltzmann' s 2e temperature constant ; T, th e absolut ; n, th e refractiv e index ; a deter ­ minant wit h element s ô {AG)/ôCi dcj n i whic h G represent s th e Gibb s fre e energ y of mixin g fo r a volum e elemen t AV; Ci an d cj9 th e concentration s of th e component s i an d j ; an d Bij9 th e cofacto r of th e elemen t ij of th e determinant . In orde r o t determin e th ec element s of it s cofactors , an d henc e an analytica l expressio n fo r [# ]e=o > Scholt e [79 ] mad e us e o f th e Flory e Huggin s [80 , 81 ] fre e energ y functio n which , fo r a binar y mixtur e of poly dispers e polymers , si expresse d n i weigh t fraction s a s [82 ] m 1 1 vv AG pAV (3.17 ) RT j 2,j The Rayleig h ratio , afte r th e necessar y differentiation s an d substitutio n int o Eq. (3.16) , si give n by [79 ] 22 c £-11 4π η 1 /dn 1 [R0]0=o = 2 ΝΑλ p\dw1 w1Mw1 + Τ,1 ( — Λττw1)Mw2 + Sdw1 I (3.18 ) 2 2 s fo Hence, ligh t scatterin g measurement s at a numbe r of concentration r a known binar y polyme r mixtur e enabl e calculatio n of 5Γ/3νν an d th e 1 determination , throug h doubl e integration , of th e polymer-polyme r inter ­ actio n function , Γ. The characte r of Γ yield s informatio n abou t th e leve l of miscibilit y of th e mixture . Alternatively , on e ca n generat e th e spinoda l fi t is i recalle d tha t Gibb' s

144

3. Methods for Determining Polymer-Polymer Miscibility

conditio n fo r th e stabilit y limit , expresse d n i Eq. (2.83 ) of Sectio n 2.4. 3 s i equivalen to t statin g tha t |6| = 0

(3.19 )

c This implie s that , on approachin g th e spinoda l fro m withi n th e stabl e region , th e reciproca l of[Re]e==0 shoul d ten d o t zero . Tha t is , fi on e perform s ligh t scatterin g measurement s at constan t concentratio n bu t cvariou s tem ­ perature s withi n th e homogeneou s stabl e region , a plo t of \/[Re]e=0 versu s temperatur e extrapolate d o t zer o ordinat e yield s th e spinoda l temperatur e for th e give n concentration . Repeate d fo r a serie s of concentrations , on e s i abl e o t describ e th e spinoda l locus . The procedur e ca n be schematicall y represente d a s n i Fig . 3.2 3 wher e th e soli d point s ar e th e scatterin g value s obtaine d fro m measurement s withi n th e stabl e region . Usin g thi s techniqu e for thre e polystyren e sample s wit h M w value s of 51,000,163,000 , an d 520,000 , Scholt e [79 ] successfull y determine d th e spinoda l envelop e fo r polystyrene cyclohexane . Anothe r ligh t scatterin g metho d whic h permit s determinatio n of th e spinoda l curv e s i th e va n Aartse n quenchin g metho d [83] . The metho d relie s on th e fac t tha t a highl y concentrate d solutio n ca n be thrus t directl y int o the unstabl e regio n fi a small , thi n sampl e s i use d n i a quenchin g mediu m of rathe r larg e hea t capacity . Becaus e of th e resultan t rapi d exchang e of heat , phas e separatio n of th e nucleatio n an d growt h typ e doe s no t tak e plac e befor e th e spinoda l mechanis m set s in . Durin g th e quenchin g period , th e scattere d intensit y varie s wit h tim e n i a manne r depicte d n i Fig . 3.24 .n I thi s

TEMPERATURE Fig. 3.23. temperature.

Schematic of scattered light intensity at zero scattering angle as a function of

145

3.4. Scattering Methods

Final

0=0 Initial

TIME Fig. 3.24. Schematic of the time dependence of the scattered light intensity during the quenching period in the van Aartsen method.

t

Spinodal Temperature

QUENCHING Fig. 3.25.

Plot of t ,

1/2

TEMPERATURE

as obtained from Fig. 3.24, against temperature, illustrating the

determination of the spinodal temperature.

figure, t1/2 s i define d as th e tim e necessar y o t reac h hal f th e maximu m in ­ tensity . When measurement s ar e made at a serie s of temperatures , t1!2 plotte d agains t th e quenchin g temperatur e ca n be typicall y represente d by Fig. 3.25 . The spinoda l temperatur e s i take n equa l o t tha t quenchin g temperatur e where t i 2/ increase s o t hig h values . For poly(2,6-dimethyl-l,4-phenylen e oxide ) n i caprolactam , va n Aartse n [84 ] determine d th e spinoda l locu s by

146

3. Methods for Determining Polymer-Polymer Miscibility

takin g t1J2 o t be 1 0 min . He als o studie d th e solutio n of ethylene/viny l acetat e copolyme rn i caprolactam . Kratochvi l et al. [85 , 86 ] hav e interprete d ligh t scatterin g fro m ternary mixture s (polyme r 1-polyme r 2-mutua l solvent ) usin g Stockmayer' s theor y to obtai n a paramete r aki n o t th e interactio n paramete r fo r th e tw o polymers . Thei r result s indicat e wit h fai r certaint y tha t thi s paramete r decrease s as th e calculate d interactio n paramete r increases , an unexplaine d result . The value s of th e paramete r di d no t depen d on solvent—a n importan t finding—but th e number of solvent s employe d was limited . 3.4.3

Pulse-Induced Critical Scattering (PICS)

This elegan t variatio n [87 ] of th e conventiona l ligh t scatterin g metho d was develope d at th e Universit y of Esse x by J . M. G. Cowie , M. Gordon , J . Goldsbrough , an d B. W. Ready . The techniqu e s i essentiall y a hybri d of Scholte' s metho d [79 ] of measurin g scattere d ligh tn i th e stabl e regio n an d van Aartsen' s procedur e [83 , 84 ] of scatterin g measurement s n i th e unstabl e region . In th e origina l design , th e sampl e cel l hold s onl y a fe w microliter s of th e solutio n place d n i a mediu m whic h s i capabl e of deliverin g therma l pulses . The tim e scal e of eac h therma l puls e s i shorte r tha n th e tim e scal e of th e nucleatio n an d growt h mechanism ; consequently , th e scatterin g measure ­ ments ca n be made at temperature s withi n th e metastabl e regio n an d th e

Temperature Trace

1—

k

)

1f

1

1

11 Light Intensity

1 1

I

1 ^

Trace

TIME Fig. 3.26. Schematic representation of the principle behind the pulse-induced critical scattering (PICS) technique.

147

3.4. Scattering Methods

solutio n s i stabl e an d homogeneou s durin g th e perio d of th e therma l pulse . A diagrammati c representatio n of th e principl e behin d th e pulse-induce d critica l scatterin g metho d appear s n i Fig . 3.26 . Ligh t scatterin g measure ­ ments ar e performe d at temperature s withi n th e homogeneou s stabl e phas e as n i Scholte' s metho d [79] . However , by coolin g an d heatin g th e sampl e ver y rapidly , th e polyme r mixtur e ca n be maintaine d withi n th e metastabl e regio n and be brough t bac k int o th e stabl e regio n befor e an y phas e separatio n occurs . Figur e 3.2 7 illustrate s th e bloc k diagra m of on e for m of th e apparatu s used fo r pulse-induce d critica l scatterin g measurements . The ligh t sourc e s i a low-powe r helium-neo n lase r an d th e syste m temperatur e s i measure d by a thermistor . The ligh ts i transmitte d by mean s of a ligh t guid e o t th e photo transistor , whic h s i th e light-detectin g system . The sample-cel l chambe r contain s a smal l heate r whic h maintain s th e chamber at a slightl y highe r temperatur e tha n th e surrounding , flowing water . The temperatur e puls e s i produce d by switchin g of f th e smal l heater ; the sampl e cel l an d sampl e coo l down rapidl y (~ 3 sec )o t th e temperatur e of th e flowing water . The scatterin g measuremen ts i made an d th e heate rs i switche d bac k on befor e phas e separatio n eve r begins . Considerabl e versa ­ tilit y s i buil t int o thi s syste m suc h tha t a strea m of temperatur e pulse s ca n be create d fo r shor t period s of tim e at almos t an y bas e temperature . Scholte' s theoretica l developmen t [79 ] is , strictl y speaking , no longe r vali d in thi s region . Accordin g o t Debye' s theor y [78 ] of critica l opalescence , ther e is a conditio n of mathematica l singularit y at th e critica l point . Beyon d th e

Immersion heater

Flow system

Pump

Thermometer Cell

Heater Light guide

\ He-Ne Laser

J

' Refriqeration umt Bath

Heat transfer fluid

Data handling system

Fig. 3.27. Block diagram of one form of the apparatus for pulse-induced critical scattering measurements. [From Κ. E. Derham, J. Goldsbrough, and M. Gordon, Pure Appl. Chem. 38, 97(1974).]

148

3. Methods for Determining Polymer-Polymer Miscibility

immediat e are a of th e singularit y th e theor y predict s th e scattere d intensity , 7, o t obe y th e relatio n 2 / = ΤΡ(θ)/[α(Τ -Tc) + b sinΘ] (3.20 ) where Ρ(θ) s i th e particl e scatterin g factor ; a an d b ar e constants . When th e temperature , T, equal s th e critica l temperature , Tc, th e scattere d intensit y at zer o scatterin g angle , 0, diverges . Onl y at finite angl e woul d th e situatio n 2 be saved . Equatio n (3.20 ) als o indicate s tha t a plo t of 1/ 7 woul d no t be linea r i of th e sam e orde r of magnitud e as b sin0. Thi s agai n limit s if (T — Tc) s how clos e a scatterin g measuremen t ca n be made nea r th e critica l point . 2 Fortunately , however , theoretica l estimatio n indicate s that , fo r θ ~ 30° , b sinθ s i of th e sam e orde r of magnitud e as Τ — Tc < 0.03°C . Tha t is , one coul d stil l go withi n 0.03° C of th e critica l poin t withou t approachin g the nonlinea r region . Thi s ha s bee n essentiall y confirme d by experiment s [87] . The implicatio n of thi s s i clear : Scholte' s extrapolatio n techniqu e [79 ] remain s valid . Moreover , th e spinoda l temperatur e fo r eac h concentratio n is no w locate d by mean s of a much shorte r extrapolation , leadin g o t a mor e accuratel y define d spinoda l locus . A diagrammati c compariso n of th e con ­ ventiona l an d th e pulse-induce d critica l scatterin g s i show n n i Fig . 3.28 . Althoug h th e PIC S metho d ha s bee n applie d o t a serie s of polymer solven t systems , t i ha s onl y recentl y bee n applied , by Koningsvel d an d Kleintjen s [88] ,o t measur e th e spinoda l locu s fo r polyme r mixtures . Figure s 3.2 9 an d 3.3 0 represen t th e spinoda l locu s fo r polyisobutene-polystyrene . They constitut e tw o of th e system s n i Fig . 3.22 , namely , polyisobuten e wit h M w 37 0 an d polystyren e of M w 220 0 an d 2500 . The curve s ar e much bette r Φ

τ

Binodal

C Fig. 3.28. Comparison of the conventional and PICS method, showing points where in­ tensity measurements are made.

3.4. Scattering Methods

149

define d an d the y exhibi t th e now-familia r bimodalit y n i agreemen t wit h th e cloud-poin t curve s of Fig . 3.22 . Recently , Gordo n et al. [89] , at th e Uni ­ versit y of Essex , develope d a centrifuga l homogenize r tha t allow s smal l sample s of high-polyme r system s o t be homogenize d at elevate d tempera ­ ture s fo r pulse-induce d critica l scatterin g measurements . Thi s ne w develop ­ ment promise s o t giv e a boos t o t th e experimenta l studie s n i polymer polyme r miscibility . 3.4.4

Neutron Scattering Methods

While X-ra y scatterin g s i sensitiv e o t densit y fluctuations, an d ligh t scatterin g o t densit y an d concentratio n fluctuations, neutro n scatterin g

1

1 31

—^Wpst

1

10 16 ι

1

1

PIB(370) °' PST(2200) Fig. 3.29. Cloud-point curve ( Δ ), spinodal by PICS (I), and critical point ( O) for a polyisobutene-polystyrene mixture with molecular weights of 370 and 2200, respectively. [From R. Koningsveld and L. A. Kleintjens, Br. Polym. J. 9, 212 (1977).]

150

3. Methods for Determining Polymer-Polymer Miscibility

Fig. 3.30. Cloud-point curve ( • ) and spinodal ( O) as determined by the PICS method for a polyisobutene-polystyrene mixture with molecular weights of 370 and 2500, respectively. [From R. Koningsveld and L. A. Kleintjens, Br. Polym. J. 9, 212 (1977).]

measure s th e differentia l neutro n scatterin g cros s sectio n of smal l concen ­ tration s of protonate d polyme r (tagge d molecules ) disperse d n i a matri x of deuterate d polymer . Thi s allow s a rathe r precis e determinatio n of th e con ­ formatio n of th e tagge d polymer , eve n n i bulk . The thre e diffractio n method s are analyze d n i th e sam e way. If th e Zernik e relatio n [Eq . (3.16) ] s i writte n fo r a binar y mixture , we have [76 ]: 22 2 θ 0=_ 4π η AV 1(dn/dc 2 2)2 (3.21 ) ~ X\kTy (d G/dc2) From

standar d thermodynamic s [90] , 2 2 1 dG N0AV 2 2 2 + 2A2c2 + 3A3c2 + M kT dc2 " c2 w

2

(3.22 )

Substitutin g Eq. (3.22 ) int o (3.21 ) give s Kc2 [Re% = 0

1

2 + 2A2c2 + 3A,c2 +

(3.23 )

3

151

3.4. Scattering Methods

where th e constan t Κ represent s

n A 22 4π η-ζ~

d

- V

K

·

,3 24)

For a larg e particl e suc h as a polyme r chain , a dissymmetr y correctio n P(0) s i introduce d [90 ]: scattere d intensit y fo r larg e particl e scattere d intensit y withou t interferenc e The genera l expressio n fo r P(0 )n i th e limi t of 0 0 s i 2 2 2 * 1 _ 1 16π ™ = + -TÎ2- < ^ g > z sin - + ··· +

^

^

(3.26 )

and Eq. (3.23 ) ca n be writte n as X c2

_

2

1

+ 2 A2c2 + 3 ^3c2 + ··· (3.27 ) c 2 It s io t be note d tha t a plo t of Kc2/[_Re]e=o versu s sin0/ 2 + fcc, origin ­ all y use d by Zimm [90] , give s tw o type s of limitin g result s (k s i an arbitrar y constan t chose n s o as o t provid e a convenien t sprea d of th e data ): (i ) When0-> O K rC 1 2 + 2yl (3.28 ) 2c2 + 3 ^3c2 + ··· [ 1 V L =0 c one obtain s a plo t of Kc/[Re~]e 0=versu s /cc, whic h give s 1/MW as intercep t and 2A2/K as th e limitin g slope , (ii ) When c -0* Kc

1

+

+

sm

(3.29 ) c 2 2 ~\2 2 s sin0/2 one obtain s a plo t of Kc/[R , whic h agai n give s 1/MW e e=0 versu as th e intercep t an d 16π<Λ 0> ζ/3Α as th e limitin g slope . These ar e th e set s of relation s use d by Kirst e an d co-worker s [1 ] fo r analyzin g th e small-angl e neutro n scatterin g of a mixtur e of ~ 1.5 % styrene / % perdeuteropoly(methy l methacrylate ) acrylonitril e copolyme r n i ~98.5 as wel la s th e blen d of 1.5 % poly(a-methylstyrene )n i 98.5 % perdeuteropoly (methy l methacrylate) . The majo r poin t of departur e s in i th e calculatio n of K, which , fo r small-angl e neutro n scattering ,s i give n by ~3X 2-<*g > *

K=(S2

-v2Sl*)/N1

2

(3.30 )

152

3 . Methods for Determining Polymer-Polymer Miscibility

where S2 an d Sx* ar e th e scatterin g lengt h su m fo r polyme r 2 an d th e deu terate d polyme r 1 ;v2 s i th e partia l specifi c volum e of polyme r 2. Figur e 3.3 1 illustrate s th e Zimm plo t fo r th e mixtur e of perdeuteropoly (methy l methacrylate ) an d styrene/acrylonitril e copolymer . Becaus e of th e ­ linearit y exhibite d by th e limitin g curve s an d th e correc t valu e of M w ob taine d fro m th e diagram , t i was conclude d tha t th e polyme r mixtur e s i

153

3.4. Scattering Methods

miscibl e on a molecula r scale . Conversely , th e skewe d natur e of th e Zimm diagra m fo r th e secon d mixture , Fig . 3.32 , indicate s micell e formatio n an d gros s inhomogeneity . Also calculate d ar e th e secon d viria l coefficient s fo r th e homogeneou s mixtur e of SAN-d-PMMA. Thes e appea r n i Tabl e 3.2 . Two attempt s wer e made at calculatin g A2 directl y fro m Flory-Huggin s theor y throug h th e expressio n fo r th e osmoti c secon d viria l coefficien t 2 A2 = v2V1-^-mlX x2) (3.31 ) The first assume s atherma l mixin g (1 χ2 = 0) ; th e secon d assume s a hea t of mixin g represente d by th e Hildebran d solubilit y parameter . Neithe r of th e calculate d result s gav e a satisfactor y descriptio n of th e experimenta l values , as ca n be verifie d fro m Tabl e 3.2 . An alternativ e metho d of testin g th e con ­ sequence s of Eq. (3.31 ) s i o t calculat e th e Flory-Huggin s interactio n paramete r fro m th e experimenta l A2 data . Thi s was don e by Koningsvel d and Kleintjen s [72] , whos e result s appea r n i Tabl e 3. 2 (secon d colum n fro m the right) . Althoug h th e value s ar e seemingl y n i th e righ t direction , compariso n wit h the χ12 value s calculate d directl y fro m th e Flory-Huggin s theor y (las t column of Tabl e 3.2 ) illustrate s tha t th e orde r of magnitud e of th e χί2 s i no t probable . The erroneou s χ12 valu e obtaine d n i th e cas e of th e SAN sampl e wit h 10 % AN s i a confirmatio n of th e failur e of th e theor y n i correctl y

ι

0

ι

ι

ι

1

5

ι

ι

•

ι

I

10

ι

C ι

ι

ι

I

ι

I

4

15 I0

I

I

I 20

2 2

I

I

I

I

I

32 5

· [ x / A " + 0.1 C/ ( g cm" ) ]

Fig. 3.31. Zimm diagram for the system poly(styrene-co-acrylonitrile) (28.7 wt% acrylonitrile) with deuterated poly(methyl methacrylate), both of approximately 200,000 weight average molecular weight (c = concentration of P S A N ) (A = 25°C, Β = 110°C, C = 130°C). [From W. A. Kruse, R. G. Kirste, J. Haas, B. J. Schmitt, and D . J. Stein, Makromol. Chem. 177, 1145 (1976). Copyright by Huthig and Wepf Verlag, Basel.]

154

3. Methods for Determining Polymer-Polymer Miscibility

4 2

2

l0 .[x /A" tO.IC/(g

3 cm" )]

Fig. 3.32. Zimm diagram for poly(a-methylstyrene) mixed with deuterated poly(methyl methacrylate), both of approximately 250,000 weight average molecular weight [c = concentra­ tion of poly(a-methylstyrene)]. [From W. A. Kruse, R. G. Kirste, J. Haas, B. J. Schmitt, and D . J. Stein, Makromol. Chem. Ill, 1145 (1976). Copyright by Hiithig and Wepf Verlag, Basel.]

TABLE 3.2 Values for the Second Viral Coefficients from Neutron Scattering (Exp.) and Calculated a and Solubility Parameters (δ) for Random S A N Assuming Athermal Mixing (Athermal) Copolymers Blended with d - P M M A

3 2

% AN in P S A N 19 19 10 28.7

a

5 M

wχ

10"

2.7 4.4 0.7 2.2

A

2

4

(110°C) ( c m g " mole χ 10 ) Xii

from

Exp.

Athermal

δ

^2exp.(FH)

1.15 1.15 -1.00 0.52

0.02 0.01 0.06 0.02

-1.88 -1.89 -0.08 -5.98

-0.0118 -0.0119 + 0.0110 -0.0052

*i2

c .a( F lH )c 0.0007 0.0005 0.0029 0.0010

The last two columns contain Flory-Huggins interaction parameters calculated from experimental neutron scattering results and directly from Flory-Huggins theory. Table from R. Koningsveld and L. A. Kleintjens, J. Polym. Sci., Polym. Symp. 61, 221 (1977).

3.4. Scattering Methods

155

representin g experimenta l evidence . A furthe r attemp t by Koningsvel d an d Kleintjen s [72 ] n i reconcilin g theor y wit h experimen t involve d th e us e of the ne w theor y of Huggins . Wit h prope r choic e of th e associate d physica l parameters , thi s theor y di d provid e a correc t interpretatio n of th e experi ­ menta l data . Anothe r investigatio n of low-angl e neutro n scatterin g fro m a miscibl e polyme r mixtur e was carrie d ou t by Ballard , Rayner , an d Schelte n [91] .I t involve d poly(deutero-a-methylstyrene ) mixe d wit h polydeuterostyren e and/o r polyprotostyrene . The weigh t percen t composition s of th e polyme r mixture s investigate d wer e 90/10/0 , 90/5/5 , 95/5/0 , an d 95/0/5 , eac h wit h respec to t th e thre e polymers . Gunie r plo t procedur e was use d instea d of th e Zimm plot .I t was foun d tha t th e chai n molecule s ar e statisticall y distributed , indicatin g tha t th e mixture s ar e miscible . From th e above ,t is i clea r tha t th e techniqu e of low-angl e neutro n scatter ­ ing wil l continu e o t findconsiderabl e applicatio n n i th e elucidatio n of th e structur e n i miscibl e polyme r mixtures . Particularly ,t i ca n provid e answer s to suc h question s as o t whethe r th e molecule s n i a mixtur e adop t thei r un ­ perturbe d configuratio n or a differen t dimensio n dictate d by th e neighboring , unlik e interaction , an d whethe r th e molecule s ar e randoml y distribute d or clustered . However , ther es i on e poin t whic h conceivabl y may be a drawbac k of thi s technique . The questio n ha s bee n pose d whethe r a deuterate d matri x is thermodynamicall y differen t fro m a protonate d one . In orde r o t answe r thi s question , Koningsvel d [72 ] use d a slightl y refine d lattic e expressio n n i analyzin g th e chai n lengt h miscibilit y dat a of Kirst e and Lehne n [92] . Kirst e an d Lehne n [92 ] performe d low-angl e neutro n scatterin g experiment s on mixture s of a normal , protonate d poly(dimethy l siloxane ) an d a serie s of deuterate d poly(dimethy l siloxanes ) of varyin g chai n lengths . The calculate d secon d viria l coefficien t plotte d a s a functio n of th e chai n lengt h of th e deuterate d PDMS di d no t agre e wit h what s i expecte d fro m a mixtur e of th e sam e polymer . Indeed , th e experimenta l dat a were satisfactoril y represente d by th e expressio n derive d fo r a binar y mix ­ tur e of tw o differen t polymer s [72] . Thi s finding support s th e contentio n tha t a deuterate d matri x s i thermodynamicall y differen t fro m a protonate d one . Furthe r evidenc e n i suppor t of thi s conclusio n ha s bee n foun d n i th e cloud poin t an d ligh t scatterin g measurement s on protonate d an d deuterate d cyclo hexan e an d polystyren e [93] . 3.4.5

X-Ray Scattering and Other Methods

The physica l structur e of polyme r mixture s ca n be characterize d by th e chai n conformation , th e loca l order , an d th e morphology . Small-angl e neutro n scatterin g elucidate s th e chai n conformatio n [2] ; th e loca l orde r can be studie d by mean s of electro n an d Rayleigh-Brilloui n scatterin g [19] ,

156

3 . Methods for Determining Polymer-Polymer Miscibility

wherea s th e morpholog y ca n be studie d by mean s of ligh t scattering , small angl e X-ra y scattering , magneti c birefringence , an d visible , phase-contrast , and electro n microscop y method s [2] . Small-angl e neutro n scatterin g ha s bee n use d n i th e stud y of polyme r miscibilit y (se e Sectio n 3.4.4) . The us e of electro n scatterin g method s usuall y entail s th e derivatio n of pai r distributio n function s fro m th e electro n scatter ­ ing curve s [2] . No experimen t of thi s natur e ha s s o fa r bee n don e on polyme r mixtures . The Rayleigh-Brilloui n scatterin g techniqu e ha s bee n applie d successfull y by Patterso n an d co-worker sn i th e investigatio n of th e miscibil ­ it y of poly(vinyliden e fluoride)-poly(methyl methacrylate ) mixture s [94] . This involve d measurin g th e polarize d an d depolarize d ligh t scatterin g spectr a an d analyzin g the m n i term s of Rayleigh-Brilloui n equations . Probabl y th e most extensiv e quantitativ e stud y of th e morpholog y of polyme r mixture s was th e wor k of Stei n an d co-worker s [95] , who examine d (i n th e soli d state ) th e blend s of poly(e-caprolactone ) (PCL ) wit h poly(viny l chloride ) (PVC) by low-angl e X-ra y an d small-angl e ligh t scattering . Be­ caus e of th e crystallinit y of PCL, th e author s no t onl y ha d o t describ e th e loca l orde r an d th e molecula r distributio n withi n th e amorphou s modula r structure s bu t als o ha d o t describ e th e spherulit e size , th e repea t perio d of the lamella r substructure , an d th e thicknes s of th e crystallin e n i relatio n o t the amorphou s layers . In th e PVC concentratio n rang e fro m 0o t ~ 60%, low-angl e X-ra y scatter ­ ing measurement s wer e interprete d usin g th e Tsvankin-Buchana n tech ­ niqu e [96 , 97] . Thi s provide d a reasonabl e estimat e of th e repea t perio d of the PCL lamella r substructure , th e thicknes s of th e PCL crystallin e layer , and th e thicknes s of th e amorphou s laye r containin g bot h PCL an d PVC segments . The spherulit e size s wer e measure d by small-angl e ligh t scatter ­ ing and , at ~60 % PVC, no more crystallinit y was observed . I n thi s region , the small-angl e X-ra y scatterin g measuremen t was interprete d n i term s of the Debye-Buech e theor y [98 ] of scatterin g n i heterogeneou s media . The result s wer e consisten t wit h partia l phas e separatio n int o statistica l region s of tw o type s :on e made up of PCL domain s containin g dissolve d PVC an d the othe r made up of PVC domain s containin g dissolve d PCL. The chang e n i the intensit y of scatterin g wit h concentratio n suggest s a transitio n zon e on the orde r of 30 Β betwee n eac h of th e tw o phases . The significanc e of thi s sor t of wor k canno t be overstated . However , t i inherit s a criticis m usuall y levele d at method s use d o t identif y miscibl e polyme r blend s n i th e soli d state . Becaus e change s of stat e too k plac e n i th e preparatio n of th e sample , on e coul d no t make a definit e conclusio n regard ­ ing th e actua l leve l of miscibilit y of th e polymer s involved . Observation s made n i th e nonequilibriu m glass y stat e ar e inadequat e n i rationalizin g th e thermodynami c aspec t of polyme r miscibility .

3.5. Ternary-Solution Methods

3.5

157

TERNARY-SOLUTION METHODS

3.5.1

Mutual-Solvent Method

Probabl y th e oldes t an d most use d metho d of determinin g polymer polyme r miscibilit y s i th e mutual-solven t approach . I t consist s of dissolvin g T A B L E 3.3 Polymers Used for the Ternary Solution Studies of Table 3.4"

Polymer No.

Material

Osmotic molecular weight Unfractionated

1 2 3 4 5 6 7 7a 7b 8

Methyl cellulose Cellulose acetate Nitrocellulose Ethyl cellulose Benzyl cellulose Polystyrene Polyvinyl acetate Rhodopas H Rhodopas H H Polyvinyl acetal

Intrinsic viscosity

160,000 56,000 92,000 35,000

3.80*c 1.70 c 2.60 c 1.10

225,000

2.15

56,000 112,000 38,000

0.60 c 0.85 e 0.75

d

Methyl methacrylate Rubber

10

Polyvinyl alcohol Fraction 1 Fraction 5 Polystyrene Fraction 1 Fraction 2 Polyvinyl acetal Fraction 1 Fraction 3 Cellulose acetate Fraction 1 Fraction 3

> 2,000,000 Undetermined

24% Methoxyl 55.5% Acetic acid 12.35% Nitrogen 47.6% Ethoxyl 46.5% Benzyl

c

e 9 11

Chemical characteristics

Totally acetylated Copolymer of 10% polyvinyl alcohol, 2% polyvinyl acetate, 88% polyvinyl acetal

3.65

Fractionated 10a 10b 12 12a 12b 13 13a 13b 14 14a 14b

a bFrom A. Dobry e In water. dIn acetone. In chloroform.

60,000

700,000 700,000

1.10* 0.35*

d

4.2' 2.8

e

97,000 39,000

1.10 e 0.58

Same product as for polyvinyl acetal above

56,000 16,000

1.70 e 0.39

Commercial diacetate

e

and F. Boyer-Kawenoki, J. Polym. Sci. 2, 90 (1947).

158

3. Methods for Determining Polymer-Polymer Miscibility

TABLE 3.4

fl

Results of Ternary Solution Studies Using Polymers Described in Table 3.3

Mixture No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Mixture of polymers (see Table 3.3) 1 + 10a 2 + 3 2 + 4 2 + 5 2 + 6 2 + 7a 2 + 8 2 + 9 2 + 10 2+11 3 + 4 3 + 5 3 + 6 3 + 7b

3 + 8

3 + 9 3 + 10 3 + 11 4 + 5 4 4 4 4

+ + + +

6 7b 8 9

Solvent Water Acetone Acetic acid Acetone Acetic acid Ethyl acetate Methyl ethyl ketone Acetone Acetone Acetone N o c o m m o n solvent N o c o m m o n solvent Acetone Acetic acid Mesityl oxide Methyl ethyl ketone Acetone Methyl ethyl ketone Acetic acid Ethyl acetate Amyl acetate Acetone Methyl ethyl ketone Mesityl oxide Acetic acid Methyl acetate Ethyl acetate Propyl acetate Butyl acetate Amyl acetate + 10% absolute alcohol Acetone Ethyl acetate N o c o m m o n solvent N o c o m m o n solvent Chloroform Ethyl acetate Benzene Chloroform Chloroform Acetone

Limit of phase separation, dry content, % 3.2 5.5 Miscible 2.8 5.5 2.0 1.2 5.5 2.1 1.5

3.7 >20 3.2 0.85 Miscible Miscible Miscible Miscible Miscible 1.8 2.0 >5 >20 2.6 1.8 2.2 1.8

Observations

Yield, 2:3 = 2:1*

7 a : 2 = 2:1 2:9 = 3:1

Opaque film

Opaque film Opaque film

2.2 Miscible Miscible

20 4.0 1.2 4.5 4.0 2.2

7 b : 4 = 3:1* 4:9 = 3:1" 4:11 = 5:2*

3.5. Ternary-Solution Methods

T A B L E 3.4

Mixture No. 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78

a

I59

(Continued)

Mixture of polymers (see Table 3.3) 4+10 4+11 5 + 6 5 + 7b 5 + 8 5 + 9 5+10 5 + 11 6 + 7b 6 + 8 6 + 9 6 + 10 6+11 7b + 8

7a + 8

7a + 9

7+10 7b + 11 8 + 9 8 + 10 8+11 9 + 10 9+11 10 + 11 7 + cellulose triacetate

Solvent N o c o m m o n solvent Benzene Chloroform Chloroform Chloroform Dioxane N o c o m m o n solvent N o c o m m o n solvent Chloroform Methyl ethyl ketone Chloroform Benzene N o c o m m o n solvent Benzene Acetone Methyl ethyl ketone Chloroform Acetic acid Mesityl oxide Dioxane Mesityl acetate Ethyl acetate Propyl acetate Butyl acetate Amyl acetate Acetone Ethyl acetate Dioxane Acetic acid N o c o m m o n solvent Benzene Acetone N o c o m m o n solvent Benzene + 5% absolute alcohol N o c o m m o n solvent Benzene N o c o m m o n solvent Chloroform

Limit of phase separation, dry content, %

1.3 Miscible 2.5 10.5 >10

4.0 1.5 3.2 2.6

Observations

5:7b = 1:2' Opaque film

6:9 = 5 : 2 '

2.0 2.0 3.5 6.0 7.2 12.0 7.0 3.8 3.2 3.6 3.9 3.6 4.5 8.5 >10 >10

4:9 = 12:1' 7:9 = 7:1* Opaque film Opaque film

2.8 2.2

7:11 = 5:1* 8:9 = 3:1*

2.0

8:9 = 5 : 2 '

2.0

9:11 = 2 : 3 '

7.5

7: triacetate =

7:8 = 3:1* 7:8 = 2:1*

From A. Dobry and F. Boyer-Kawenoki, J. Polym. Sci. 2, 90 (1947). * Weight ratio of the amount of high polymers for which the limit of separation has been determined. For the other systems this yield is 1:1.

160

3. Methods for Determining Polymer-Polymer Miscibility

and thoroughl y mixin g a 50/5 0 mixtur e of tw o polymer s at lo w o t mediu m concentratio n n i a mutua l solvent . By allowin g th e mixtur e o t stand , usuall y for a fe w days , miscibilit y s i sai d o t prevai l fi phas e separatio n doe s no t occu r; if phas e separatio n doe s occu r th e tw o polymer s ar e sai d o t be immiscibl e wit h eac h other . The metho d was first use d n i th e field of paints , varnishes , and lacquers . A varnis h compositio n whic h on dryin g leave s a turbid , opaque , an d usuall y brittl e films i unacceptable ; th e occurrenc e was als o known o t be due o t th e immiscibilit y of th e constituen t polymers . I t was not , however , unti l 194 6 tha t a thoroug h an d systemati c stud y of polyme r miscibilit y was undertaken . The study , reporte d n i th e classi c pape r by Dobr y an d Boyer Kawenoki [99] , involve d 78 mixture s made up fro m 14 hig h polymer s (cellu ­ lose , vinyl , an d acryli c derivatives ) dissolve d n i 13 solvents . The result s of Dobry an d Boyer-Kawenok i ar e represente d n i Table s 3. 3 an d 3.4 . About a decad e later , Ker n an d Slocomb e [100 ] undertoo k a simila r stud y on 27 othe r mixtures , th e result s of whic h appea r n i Tabl e 3.5 . The si x genera l conclusion s reache d by Dobr y an d Boyer-Kawenok i [99] , confirme d by th e secon d stud y [100 ] stan d o t th e presen t da y almos t withou t contradiction . They deserv e direc t quotatio n n i par t [99 ]: (1) Of th e 35 pair s of hig h polymer s tested , onl y fou r do no t sho w separation . Consequently , compatibilit y (miscibility ) s i th e exception , im­ miscibility is the rule. (2) When tw o hig h polymer s ar e incompatibl e n i on e solvent , the y ar e generall y als o incompatibl e n i al l othe r solvents . Thi s rul e represent s th e normal situation , bu tt is i no t alway s fulfilled . (3) The limi t of phas e separatio n depend s on th e natur e of th e solvent . (4) The molecula r weigh t of th e polymer s s i of grea t importance . The highe r t i is , th e les s compatibl e (miscible ) ar e th e sample s an d th e mor e s i the limi t of phas e separatio n shifte d towar d smalle r (polymer ) concentration . (5) Theoretica l consideration s make t i probabl e tha t no t onl y th e molecu ­ lar weigh t bu t als o th e shap e of th e dissolve d molecule s influence s thei r com­ patibilit y (miscibility) . (6) Ther e s i no obviou s relationshi p betwee n th e compatibilit y (miscibil ­ ity ) of tw o polymer s an d th e chemica l natur e of thei r monomers . The simi ­ larit y of th e principa l chai n s i no t sufficien t o t insur e miscibilit y of tw o polymers . Dobry an d Boyer-Kawenoki' s result s [99 ] wer e als o represente d n i tri ­ angula r diagram s whos e genera l natur e s i simila r o t Fig . 3.2 . Such phas e diagram s suppor t th e spiri t of th e study , namely , tha t at rathe r hig h solven t concentratio n t is i possible , by th e mutual-solven t method , o t tel l tha t Px an d P2 ar e immiscibl e eve n thoug h the y ar e eac h completel y miscibl e wit h th e solvent .

161

3.5. Ternary-Solution Methods

T A B L E 3.5

1

Results of Ternary Solution Studies'

Solvent and solute concentration

System

Volume ratio of upper/lower phase

PMMA/PVAc"

Acetone, 20%

14/5

PMMA/PVAc PMMA/PMA PMA/PVAc PVAc/PMVK PVAc/PMVK PMMA/PS PMMA/PS P M M A / P M A N */ PMMA/PMAN PS/PVAc PpClS/PVAc PpMeS/PVAc PS/PpMeS PS/PVC PS/PpCIS PpMeS/PpCIS PS/PoMeS PS/PmMeS PS/PpMeS PoMeS/PmMeS PoMeS/PpMeS PmMeS/PpMeS PS/PE PS/PMA PEA/PMA PE/PBu

Acetone, 20% Acetone, 20% Acetone, dioxane, benzene Acetone, 20% Ethyl acetate, 20% Chloroform, 20% Methyl ethyl ketone, 15% Acetone, 15% Acetone, 15% Benzene, 20% Benzene, 20% Benzene, 20% Benzene, 20% Tetrahydrofuran, 15% Benzene, 20% Benzene, 20% Chloroform, 20% Chloroform, 20% Chloroform, 20% Chloroform, 20% Chloroform, 20% Chloroform, 20% Xylene, 10% (90°C) Benzene, 20% Acetone, 20% Xylene, 20% (90°C)

14/5 16/9

c

a bFrom R. J. Kern and R. J. Slocombe, c PVAc M ca. 50,000. dP V A c M w c a . 150,000. e N o phasewseparation. / P M A N rç 0.034 0.1% in acetone. sp P M A N rç 0.35 0.1% in acetone. sp

Layer analysis Upper

Lower

56% VAc 60% V A c 71% V A C

12.5% VAc 10.6% VAc 6.3% VAc

14.5% VAc 68% V A c

78% V A c 4.5% VAc

92% M A N 88% M A N

13.7% M A N 1.0% M A N

d

1/1 7/5 2/3 9/13 9/13 9/10 1/1 2/1 15/14 14/15 13/17 2/1 2/1

1.8% CIS

23% V C 0.7% pCIS

96% pCIS

86% V C 99% pCIS

d

5/2 5/2 5/3 3/5 d

25/14 9/7 2/1 4/1

/ . Polym. Sci. 15, 183 (1955).

All thes e experimenta l findings gaine d theoretica l suppor t fro m th e Scott Tompa ternar y solutio n treatmen t of Flory-Huggin s theory . The Scott Tompa developmen t [101 , 102 ] was base d on symmetri c system s (system s where th e Flory-Huggin s polymer-solven t interactio n parameter s ar e equal) , bu tt i was surmise d tha t th e phas e behavio r fo r asymmetri c system s would be similar . The analysi s blame s immiscibilit y on th e unfavorabl e

162

3. Methods for Determining Polymer-Polymer Miscibility

polymer-polyme r interactio n parameter . The solven t effec t was considere d rathe r positive ;t i merel y dilute s th e polymer s s o as o t reduc e th e numbe r of unfavorabl e contact s betwee n th e differen t polymers . Thus ,t i doe s no t reall y matte r what solven t s i used ; fi tw o hig h polymer s ar e immiscibl e n i on e solvent , the y wil l be immiscibl e n i al l solvents . This belie f was hel d fo r a lon g tim e unti l contradictor y experimenta l evi ­ dence bega n o t appear . Hugeli n an d Dondo s [103 ] wer e abl e o t achiev e maximum miscibilit y betwee n polystyren e an d poly(methy l methacrylate ) onl y wit h solvent s havin g comparabl e affinitie s fo r th e polymers ; solvent s of disparat e affinitie s fail , contrar y o t Scott-Tomp a prediction . Ban k et al [40] observe d tha t polystyren e s i miscibl e wit h poly(viny l methy l ether ) n i toluene , benzene , or perchloroethylene , bu t no t n i chloroform , methylen e chloride , an d trichloroethylene , whil e Ker n [104 ] foun d tha t polystyren e s i miscibl e wit h poly(methy l methacrylate ) fi th e mixtur es i prepare d n i benzen e or chlorobenzene , bu t immiscibl e fi th e solven t mediu m s i ethy l acetate . The overridin g conclusio n of thes e experimenta l findings s i tha t solven t effec ts i indee d significan t an d tha t Scott-Tomp a result s must be revised . The first attemp t at reexaminin g th e Scott-Tomp a treatmen t was under ­ take n by Zeman an d Patterso n [5] , who calculate d th e spinodal s fo r a numbe r of ternary , polymer-polymer-solven t systems . Later , Hsu an d Prausnit z [105 ] were abl e o t make th e notoriousl y difficul t calculatio n of th e binodal s vi a numerica l methods . Bot h studie s arrive d at identica l conclusion s: (1)

At lo w polyme r concentratio n th e differenc e betwee n th e tw o poly ­ mer-solven t interactio n parameter s s i directl y responsibl e fo r th e polymer-polyme r immiscibility . (2) At hig h polyme r concentration , th e stat e of miscibilit y s i controlle d by th e magnitud e an d sig n of th e polymer-polyme r interactio n parameter . (3) When th e interactio n betwee n th e polymer s s i lo w or eve n negativ e a close d miscibilit y ga p woul d resul t f i th e tw o polymer-solven t interactio n parameter s ar e different . Even thoug h thes e conclusion s agre e wit h experimenta l observations , the y als o cas t seriou s doub t on th e validit y of th e mutual-solven t metho d n i identifyin g miscibl e polyme r pairs . For instance , asid e fro m th e "normal " diagra m of Fig . 3.2 , thre e othe r type s of ternar y phas e diagram s ar e possible , as show n n i Fig . 3.33 . Based on th e Patterson-Prausnit z [5 , 105 ] ternary-solutio n treatmen t of Flory-Huggin s theory , th e qualitativ e deductio n possibl e fro m mutual solven t experiment s fall s fa r short . For a syste m whos e phas e behavio r s i simila r o t th e "normal " on e n i Fig . 3.2 , th e common solven t metho d say s nothin g abou t th e miscibilit y of polymer s P1 an d P2. As fo r a syste m wit h

3.5. Ternary-Solution Methods

163

s

s

s

Fig. 3.33. Schematics of possible ternary phase diagrams involving two polymers ( P P ) l5 2 and a solvent (S).

a Fig . 3 . 3 3 A phas e diagram , a common solven t experimen t performe d at too hig h a solven t concentratio n woul d conclud e erroneousl y tha tPi s i completel y miscibl e wit h P2. Furthermore , th e metho d migh t indicat e com­ plet e immiscibilit y fi Fig .3.33B s i representativ e of th e ternar y system , wherea s th e tw o polymer s ar e miscibl e at al l proportions . Example s of close d miscibilit y envelope s ar e foun d n i th e phas e diagram s of benzene-buty l rubber-EPD M rubbe r an d of dipheny l ether-atacti c polypropylene-linea r

Diphenyl ether

1 A

// ; / /,

\

/ / 1 / / 1;v // / 1 // lfV 0.1

linear * Polyethylene

J

Rsv V

\

\

\

\

- - - T=I54 °C T=I55 °C

'\ Λ Ν

• phases//

atactic Polypropylene

Fig. 3.34. Ternary phase diagram for the system polyethylene- polypropylene-diphenyl ether showing closed two-phase region. [From R. Koningsveld, L. A. Kleintjens, and Η. M. Schoffeleers, Pure Appl. Chem. 39, 1 (1974).]

164

3. Methods for Determining Polymer-Polymer Miscibility

polyethylen e [82] . Figur e 3.3 4 illustrate s th e phas e diagra m fo r th e latter . The mor e complicate d miscibilit y ga p illustrate d schematicall y n i Fig . 3.33 C is als o foun d n i nature ; Fig . 3.3 5 illustrate s th e solvent-ric h sectio n of th e phas e diagra m fo r dipheny l ether-isotacti c polypropylene-linea r poly ­ ethylen e [82] . The more fruitfu l us e of th e Scott-Tomp a ternar y solutio n treatmen ts in i calculatin g th e polymer-polyme r interactio n parameter . The basi c interpre ­ tativ e concep t her e s i tha t a larg e positiv e valu e indicate s unfavorabl e inter ­ action , a lo w valu e indicate s littl e interaction , an d a negativ e valu e indicate s a rathe r stron g specifi c interaction . The activit y coefficien t of th e solven tn i a ternar y solutio n s i ( - φγ) + (χ12 n I φ1 + 1 φ φ3)(1 - φ,) - χ'^ΦιΦι (3-32 ) 2 + χ13 where th e subscrip t 1 refer s o t th e solven t an d subscript s 2 an d 3 refe r o t th e two polymers ;a,, th e solven t activity ; φ, th e volum e fraction ; χ , th e binar y interactio n parameter ; χ2',3 th e polymer-polyme r interactio n paramete r In a,

=

Diphenyl ether

linear / Polyethylene

isotactic Polypropylene

Fig. 3.35. Illustration of complex phase behavior, using the system polyethylene-isotactic polypropylene-diphenyl ether. [From R. Koningsveld, L. A. Kleintjens, and Η. M. Schoffeleers, Pure. Appl. Chem. 39, 1 (1974).]

165

3.5. Ternary-Solution Methods

per segmen t of polyme r 2 [ χ23' = χ2' )χί/χ2, wher eχ s i th e numbe r of 3 (Flory segment sn i th e molecule] . Kwei, Nishi , an d Robert s [106 ] use d vapo r sorptio n measurement s of polystyrene , polyviny l methy l ether) , an d thei r blend s o t successivel y cal ­ culat e th e χ1,2 χ1 ,3 an d correspondin g χ2' a s function s o f temperatur e an d 3 composition . The χ2' s appea r n i Tabl e 3.6 . Base d on th e sig n of χ2' 3 value 3 and it s temperatur e dependence , th e author s conclude d tha t th e mixtur e s i miscibl e (stable ) an d tha tt i exhibit s bot h th e lowe r an d uppe r cloud-poin t curves . Thi s latte r conclusio n s i base d on Patterson' s origina l analysi s [107] , which associate s th e occurrenc e of positiv e temperatur e coefficien t of χ ' 23 wit h th e presenc e of an uppe r critica l solutio n temperatur e behavior , an d a TABLE 3.6 Interaction Parameters from Vapor Sorption Studies for Blends of Polystyrene and Polyvinyl methyl ether)" Τ (°C)

Wt% P V M E in the film

30

35.06

Φι 0.0967 0.1388 0.2006

X23 -0.78 -0.73 -0.73 av - 0 . 7 5

30

45.30

0.0478 0.1104 0.1693

-0.67 -0.69 -0.72 av - 0 . 6 9

30 30 50

55.00 65.00 45.30

0.0389 0.0698 0.0367 0.0438 0.0516

65.00

0.0405 0.0498 0.0918

-0.59 -0.17 -0.59 -0.60 -0.61 av - 0 . 6 0

50

a

-0.47 -0.56 -0.36 av - 0 . 4 6

Reprinted with permission from T. K. Kwei, T. Nishi, and R. F. Roberts, Macromolecules 7, 667 (1974). Copyright by the American Chemical Society.

166

3. Methods for Determining Polymer-Polymer Miscibility

negativ e temperatur e coefficien t of χ2' h th e presenc e of a lowe r critica l 3 wit solutio n temperature . The analysi s may wel l be correct , bu t ther e s i stil l some reservatio n regardin g th e validit y of usin g solutio n measurement s as a basi s fo r derivin g informatio n abou t th e stat e of th e solvent-fre e polyme r mixture . Furthermore ,t is i no w wel l establishe d tha t th e stat e of thermody ­ namic stabilit y of a mixtur e s i no t determine d by th e sig n of th e Gibb s fre e energ y of mixing ; rather ,t is i governe d by th e subtl e detail s of th e composi ­ tio n dependenc e of th e fre e energ y [72] . Consequently , th e negativ e value s calculate d fo r th e PS-PVME blend s sa y nothin g abou t th e stabilit y of th e mixture . 3.5.2

Inverse Gas Chromatography Method

In th e recen t past , gas-liqui d chromatograph y (GLC) ha s receive d genera l recognitio n a s an effective , simpl e techniqu e fo r rapi d measuremen t of poly ­ mer interaction s an d solven t activit y coefficient s n i molte n homopolymer s and thei r mixtures . I t ha s bee n use d n i determinin g suc h propertie s a s th e glas s transitio n temperature , crystallinity , adsorptio n isotherms , heat s of adsorption , surfac e area , interfacia l energy , diffusio n coefficients , comple x equilibri a n i solution , an d curin g processe sn i nonvolatil e thermose t system s [108] . For thes e studies , it s majo r advantage s ar e (i ) th e simplicity , speed , and accurac y wit h whic h a larg e numbe r of system s ca n be investigated , (ii ) th e wid e rang e of easil y controllabl e temperatures , an d (iii ) th e abilit y to wor k at a singl e solutio n concentration . In vie w of thi s unconventiona l usag e of GLC, Guille t [109 ] ha s suggeste d the name "invers e ga s chromatography " becaus e traditiona l GLC deter ­ mines th e propert y of an unknow n sampl en i th e movin g phas e wit h a known stationar y phase , whil e th e invers e metho d determine s th e propert y of th e stationar y phas e wit h th e ai d of a known vaporizabl e solut e n i th e movin g phase . He consider s th e latte r as a molecular-prob e experimen t wher e th e vaporizabl e molecule s ar e designate d prob e molecules . A schemati c diagra m of a ga s chromatograp h appear s n i Fig . 3.36 . I n operation , th e polyme r material , on a preferabl y iner t support ,s i place d n i the colum n maintaine d at a temperatur e whic h s i at leas t 50° C abov e th e syste m Tg fo r glass y materia l an d Tm fo r a crystallizabl e system . A strea m of an iner t carrie r ga s continuousl y passe s throug h th e syste m at a known flow rat e an d unde r a predetermine d pressur e head , whil e th e prob e mole ­ cule s ar e introduce d n i a pulse . The basi c fundamenta l quantit y of ga s chromatograph y s i th e specifi c retentio n volume , define d as th e volum e of carrie r ga s pe r gra m of stationar y phas e require d o t elut e th e prob e molecule . Schematically , th e interactio n of th e mobil e prob e solut e wit h th e stationar y solven t phas e (polymer ) s i illustrate d n i Fig . 3.37 . The enterin g prob e rup -

167

3.5. Ternary-Solution Methods

INJECTION BLOCK

DETECTOR

^—|ΤΠιιιιιιι

SAMPLE MICRO SYRINGE

rlh-

if

GAS SATURATOR Y = ^ j J^ J

PRECISION REGULATOR VALVE BUBBLE FLOW­ METER

CARRIER GAS (Helium)

Fig. 3.36.

CASE I Alkan e solut e int o alkan e solven t Fig. 3.37.

MERCURY MANOMETER

RECORDER

Schematic of a typical gas chromatographic apparatus.

CASE II Alkan e solut e int o pola r solven t

CASE II I Pola r solut e int o pola r solven t

Representation of the interaction of probe (solute) and stationary phase (solvent).

ture s existin g intermolecula r force s an d simultaneousl y form s ne w ones . Considerin g a prob e o fη segment s an d assumin g tha t al l th e segment s ar e randoml y an d completel y absorbe d by th e stationar y phase ,nnp interaction s would b e gaine d b y th e syste m fo r cas e , I2nnp — np fo r cas e II , an d np fo r cas e III . Not e tha t nnp> 2nnp — np; also , nonpola r probe s n i a pola r sta ­ tionar y phas e hav e a smalle r Vg tha n f i th e stationar y phas e wer e nonpolar . It become s apparent , therefore , tha t on e coul d measur e th e polar , nonpolar , and specifi c interaction s of a substrat e by prope r selectio n of th e prob e mole ­ cules . Furthermore , studie s o f tw o homopolymer s an d thei r blend s coul d yiel d vita l informatio n abou t th e polymer-polyme r interaction .

168

3. Methods for Determining Polymer-Polymer Miscibility

The lin k betwee n invers e chromatographi c measuremen t an d th e inter ­ actio n parameter s o f variou s solutio n theorie ss i th e infinite-dilutio n activit y coefficient , which , fro m analysi s o f th e dynamic s o f invers e chromatography , e n i a polymeri c stationar y is obtainabl e directl y fro m V%data . For a prob phase , th e weight-fractio n infinite-dilutio n activit y coefficien t s i [108 , 109] 0 Ρ {B Vt) (3.33 ) -RT " 0 n n i term s o f ί^ , th e specifi c This equatio n coul d alternativel y be writte retentio n volum e correcte d o t 0°C , wher e VIT = K°/273. 2

(3.34 )

Now , n i statistica l thermodynami c theories , th e prob e activity , au s i generall y writte n a s th e su m of tw o term s :a combinatoria l entrop y an d a noncombinatoria l fre e energ y o f mixin g term . Writte n n i th e Flory-Huggin s approximatio n an d combine d wit h th e chromatographi c expression , Eq. (3.33) , th e interactio n paramete r betwee n th e prob e an d th e stationar y phas e s i give n by [108 , 109 ] Xl2 =

nl RTv 2

M2v2

Pi RT

(3.35 )

In th e newe r equation-of-stat e solutio n theory , th e noncombinatoria l ter m s i furthe r broke n down int o tw o terms : th e equation-of-stat e contribu ­ tio n du e o t th e free-volum e dissimilarit y o f th e prob e an d th e polymer , and th e exchang e energ y ter m whic h reflect s th e energ y involve d when i-i orj - j contact s ar e replace d by i-j contacts .I n th e Flor y approximatio n [110 ] th e newl y define d parameter , χ$2, a counterpar t o f χ 12 base d on condition s o f a hypothetica l liqui d a t 0°K , ca n be writte n n i term s o f Vg [108 , 109 ] : 0 nl RTv * Ρ (Bli )V l 2 (3.36 ) 1Xl2 = ~RT ~ M2v2* g The exchang e energ y paramete r X12 ca n be calculate d fro m χ*2 by usin Flory' s expressio n [109 ]: X*2 —

The developmen t s o fa r concern s th e interactio n o f th e prob e wit h a homopolyme r stationar y phase . The extensio n o t th e cas e o f th e mixe d stationar y phas e consistin g o f tw o hig h polymer s ha s take n tw o forms ,

169

3.5. Ternary-Solution Methods

both arisin g fro m th e Scott-Tomp a ternary-solutio n treatment . The activit y of a solven t (a s φ^-* 0) n i tw o polymer s s i give n by In ax = n I φχ + ^1 - ^ + (χιιΦι

φ

2

+

-

^ φ

3

+ Χ13Φ3 ~ ^ ΧιιΦιΦι^

(3-38 )

In applyin g thi s fo r a mixe d stationar y phas e consistin g of tw o hig h polymer s an d a prob e use d essentiall y at zer o concentration , Patterso n et al. [ I ] l lchos e o t us e th e infinite-dilutio n volume-fractio n activit y coeffi ­ cient . Assumin g tha t rjrj = vjvj9 th e resultin g expressio n s i

(3.39 ) Whe n equate d o t th e correspondin g chromatographi c relation , we hav e Vx = n I

RT(w2v2

+

W3U3 )

-Vx)

(3.40 )

where XiJVt s i symmetrica l an d dependen t onl y on th e natur e of ij regard ­ les s of th e chai n length . The ne w interactio n parameter s χ * ar e similarl y describe d fi th e volum e fraction s ar e replace d by th e segmen t fraction s an d the volume s by th e hard-cor e values . Thes e ar e relate d o t th e exchang e energ y parameter s vi a

where Χη/Si si symmetrica l an d dependen t onl y on th e natur e of ij les s of th e chai n length .

regard ­

0

TABLE 3.7 Gas Chromatography Results for the Systems Tetracosane-Dioctyl phthalate and Tetracosane-Poly(dimethyl siloxane) Interaction between solute (component 1) and pure stationary phase (component 3) n-• c

DOP

24

Xl2

8

*i2/*i

Solute

60°C

χ 1 0 -2 J cm 60°C

w-Pentane rt-Hexane «-Heptane «-Octane 2-Methylpentane 3-Methylpentane 2,4-Dimethylpentane Cyclohexane Carbon tetrachloride Benzene Toluene

0.32 0.24 0.20 0.17 0.26 0.23 0.26 0.17 0.26 0.51 0.35

4.5 4.6 4.2 3.4 5.0 4.6 5.0 5.4 10.5 23.4 15.5

a

In

8

75°C

χ 10 2 Jem" 75°C

0.32 0.24 0.20 0.17 0.27 0.24 0.26 0.17 0.26 0.48 0.36

4.4 5.0 4.6 3.8 5.9 5.4 5.4 5.9 10.9 23.0 16.3

Interaction between two components (2 and 3) in the stationary phase PDMS

8

8

75°C

χ 10 2 Jem" 75°C

60°C

X 111Sx χ 10 2 Jem" 60° C

0.76 0.67 0.67 0.68 0.69 0.66 0.70 0.48 0.19 0.16

21.2 19.2 18.8 17.6 20.1 19.7 21.3 19.2 6.3 5.4

0.45 0.43 0.45 0.49 0.42 0.41 0.42 0.44 0.42 0.62

12.5 13.4 13.8 13.4 13.0 13.4 13.4 19.2 20.1 31.4

Zl2

2A D O P S 8 va2iiv2 Xl-$I 2 -3 χ 1 0 -2 n-C -

cm 75°C

J cm 75°C

0.86 0.72 0.77 0.87 0.72 0.74 0.77 0.62 0.48 0.43

33.9 25.5 25.5 26.4 26.8 27.6 28.5 28.5 22.2 19.2

PDMS » - c2-4

Va2*iv2

X /s 8 3 χ2321 0 2

cm 60°C

Jem" 60°C

-

1.01 0.48 0.55 0.64 0.57 0.49 0.49 0.42

34.6 11.7 12.1 12.6 15.9 13.0 13.0 10.9

0.37

14.6

Interaction parameters are listed. Reprinted with permission from D . D . Deshpande, D . Patterson, H. P. Schreiber, and C. S. Su, 7, 530 (1974). Copyright by the American Chemical Society.

Macromolecules

171

3.5. Ternary-Solution Methods

Patterso n et al [111 ] applie d thi s formalis m o t th e treatmen t of tw o mixed stationar y phases , namely , tetracosane-diocty l phthalat e an d tetra cosane-poly(dimethy l siloxane) . Tabl e 3. 7 summarize s some of th e results . Withi n th e alkan e series , ver y littl e variatio n s i observe d fo r th e X23 /S2 and Vlx22> /V2 excep t fo r pentane . Thi s si n i lin e wit h theory . However , th e quantitie s ar e significantl y differen t when pola r probe s ar e used , indicatin g tha t th e interaction s involve d migh t no t be correctl y describabl e by th e presen t theory . Suc h variatio n was no t ascribe d o t experimenta l erro r be ­ caus e th e chec k on dat a consistenc y was reasonabl y successful . For instance , /S2 fo r tetracosane-diocty l phthalat e si simila r o t the magnitud e of X23 tha t fo r th e pur e diocty l phthalat e wit h alkan e probes—s o als o fo r tetra cosane-poly(dimethy l siloxane ) a s compare d o t tha t of pur e poly(dimethy l siloxane) . Patterso n [112 ] als o applie d invers e chromatograph y o t th e stud y of thermodynami c interaction s n i polyviny l chloride ) (PVC) plasticize d by di-n-octy l phthalat e (DnOP) . Tabl e 3. 8 contain s V^i2Z jV2 value s fo r PVCDnO P (82:18 ) as affecte d by temperature . The concentratio n dependenc e of thi s quantit y s i represente d n i Fig . 3.3 8 ; eac h dat a poin t si an averag e of the result s fro m fou r rc-alkane probes . Variatio n of th e interactio n param ­ ete r wit h prob e was much mor e eviden t her e tha n n i th e previou s study , and th e author s ascribe d thi s eithe r o t nonrando m mixin g or o t preferentia l solutio n of th e prob e n i on e of th e component s of th e mixe d stationar y phase . Fro m th e compositio n dependenc e of th e interactio n parameter , th e author s conclude d tha t DnOP at lo w concentratio n (<0.25 ) s i miscibl e wit h PVC, bu t immiscibl e when th e volum e fractio n s i highe r tha n 0.55 . Olabisi' s developmen t [113 ] differ s fro m Patterson' s primaril y n i th e TABLE

3.8

Interaction Parameters for the System P V C - D i o c t y l phthalate by Gas Chromatography"

b

y' Λ 23

Probe

110°C

120°C

130°C

H-Heptane «-Octane «-Nonane rc-Decane Toluene Chlorobenzene

-1.20 -1.17 -1.24 -1.63 -0.72 -0.78

-1.04 -1.07 -0.89 -0.66 -0.66 -0.68

-0.81 -0.94 -0.43 -0.14 -0.60 -0.56

α

From C. S. Su, D . Patterson, and H. P. Schreiber, b Polym. Sci. 20, 1025 (1976). J. Appl. Assumes no crystallinity in PVC.

174

3. Methods for Determining Polymer-Polymer Miscibility

1 -2.001 0.0

»-

1 0.2

' 0.6

0.4

1

1

1

0.8

1

1.0

Φ

PVC Fig. 3.38. The concentration dependence of the interaction parameter for the system PVC-dioctyl phthalate as measured by inverse gas chromatography. [From C. S. Su, D . Patter­ son, and H. P. Schreiber, J. Appl. Polym. Sci. 20, 1025 (1976).]

leve l o f assumption s made . For polymer s wit h rathe r hig h degree s o f poly ­ r asmal l enoug h prob e suc h tha t r ~ 1 [114] , rjr ~ 0 , merizatio n an d fo x 2 and rjr3 ~ 0 2 F ry 1 Ï23 = (*23)Tomp a = ^ ^ ° - ^ O k s Wy (3-42 ) '2 '2 Whe n thes e ar e substitute d int o Eq . (3.36) , th e infinite-dilutio n weight fractio n activit y coefficien t s i [113 ] 1 η Ω ?( )2 3 =\n\yj{w2v2

+ w3i>2)]

+ Xi3 3) - ΧΙ3Φ2Φ3 (3.43 ) ί22 Whe n equate d o t th e correspondin g chromatographi c expression , we have , afte r rearrangemen t [114] , +

(1. 0 +χ φ

1 Χ12Φ2 + Χ13Ψ3 ~Χ23Φ2Φ3 = in ^

ρ^τ/τ^

- ë ( B u - n )

~

(3.44 )

1

173

3.5. Ternary-Solution Methods

χ12 an d χ13 ar e determine d separatel y fro m th e specifi c retentio n volum e of th e prob e wit h th e homopolymer s as prescribe d by Eq. (3.35 ) an d χ23 s i unambiguousl y determine d fro m th e specifi c retentio n volum e of th e prob e a n y phas ea erusin in th e mixe d stationar g Eq. (3.44) .f I th e hard-cor e quantitie s ar e obtained . Th e exchang e energ y paramete r χ^/ s used , χΐ > X*3> d X*3 2 are calculate d fro m an expressio n simila r o t Eq. (3.41 ) an d estimate d value s of th e segmenta l surfac e are a rati o sjsjf By selectin g prob e molecule s base d on th e relativ e magnitud e of thei r dipol e moments , polarizabilities , an d hydrogen-bondin g capabilities . Olabis i [113 ] investigate d fou r type s of polyme r interactions : (i ) proton-accepto r strengt h wit h chlorofor m an d ethano l a s probe s (ii ) proton-dono r strengt h wit h methy l ethy l keton e an d pyridin e as probe s (iii ) pola r strengt h wit h acetonitril e an d fluorobenzene as probe s (iv ) nonpola r strengt h wit h hexan e an d carbo n tetrachlorid e a s probe s Recognizin g tha t no suc h clear-cu t divisio n exist s an d tha t associatio n complexe s stabilize d by electroni c an d electrostati c force s do exis t eve n fo r nonpola r molecules , χ0, χ* , an d X wer e propose d merel y a s relativ e scale s 0 u of interactio n strength s betwee n polymers . The dat a obtaine d fo r poly(e caprolactone) , polyviny l chloride) , an d th e mixtur e appea r n i Tabl e 3.9 . In calculatin g th e exchang e energ y parameter , th e segmenta l surfac e are a rati o sJsj was compute d fro m th e grou p contributio n forma t of Bond i [16] . Based on th e variou s interactio n quantitie s obtaine d wit h chlorofor m a s a prob e an d th e fac t tha t PCL-PVC mixture s ar e known o t be stabl e ove r th e TABLE 3.9 Interaction Parameters for the System P V C - P C L at 120°C Using Gas Chromatography" PCL

X*2 Solute Ethanol Chloroform Methyl ethyl ketone Pyridine Acetonitrile Fluorobenzene Carbon tetrachloride Hexane

a

PVC X

i2

3

X*2

(cal/cm ) 1.15 -0.20 0.533 0.175 1.11 0.127 0.391 1.24

21.4 -4.20 2.75 0.239 19.3 -1.61 1.06 7.89

P C L - P V C (50:50)

3

*12

X23

X23

2.35 1.38 1.00 0.939 1.85 1.25 1.49 1.76

40.6 16.6 4.41 7.34 29.3 8.82 10.2 8.6

Reprinted with permission from Olabisi, Macromolecules American Chemical Society.

* 2 3

3

(cal/cm )

(cal/cm ) 0.21 0.33 -0.10 -0.17 -0.40 0.24 1.07 1.16

-0.13 -0.09 -0.61 -0.47 -0.98 -0.15 0.63 0.60

-2.8 -2.4 -6.4 -5.4 -9.3 -2.9 3.0 2.8

8, 316 (1975). Copyright by the

174

3. Methods for Determining Polymer-Polymer Miscibility

whole concentratio n range ,t i was note d tha t χ* d χ23 presen t a clea r 23 an pictur e of PCL-PVC miscibilit y an d tha t complementar y dissimilarit y s i responsibl e fo r th e observe d miscibility . Als o observe d s i th e fac t tha t pola r probe s yiel d positiv e interactio n indice s representativ e of noncomplexin g contributions , wherea s specificall y interactin g probe s sometime s giv e lo w or negativ e values . The variatio n of th e polymer-polyme r interactio n wit h the prob e molecule s was ascribe d o t nonrando m absorptio n of th e prob e n i the mixe d stationar y phas e as wel l a s o t preferentia l solutio n of th e probe s in on e of th e constituent s of th e blen d [113] . The foregoin g chromatographi c metho d ha s succeeded , by an d large ,n i describin g th e miscibilit y stat e of solvent-fre e polyme r mixture s by usin g the solven t at essentiall y zer o concentration . I ts i capabl e of providin g th e interactio n paramete r at an y give n conditio n an d may be abl e o t provid e some subtl e detail s of th e compositio n dependenc e of th e fre e energ y s o paramoun t n i definin g th e complet e stat e of thermodynami c stabilit y of polyme r mixtures . The majo r uncertaint y n i th e accurac y of thi s metho d can be foun d n i th e way chromatographi c column s ar e prepared . Becaus e th e polyme r mixtur e must first be dissolve d n i a mutua l solven t prio r o t deposi ­ tio n on th e iner t support , th e metho d woul d fai l wher e th e mutual-solven t method fails . The preparatio n of column s fo r system s wit h th e sor t of close d miscibilit y loo p discusse d earlie r woul d introduc e severa l uncertaintie s n i the result . Furthermore , recen t development s [88 ]n i th e field of polymer polyme r miscibilit y sho w tha t rathe r hig h accurac y s i neede d fo r prope r definitio n of th e stat e of thermodynami c stability , an d t is i doubtfu l tha t the invers e GLC ca n provid e tha t leve l of significance. And, fro m a practica l standpoint , th e column s ar e extremel y tim e consumin g o t prepar e [114] . Nonetheless , th e invers e GLC metho d ha s bee n applie d successfull y o t the descriptio n of polyme r miscibilit y n i th e liqui d state . I t ha s als o bee n used n i studyin g th e concentratio n dependenc e of th e glas s transitio n tem ­ peratur e of polyme r blend s [108] . Becaus e change s of stat e do occu r durin g sampl e preparation , th e applicabilit y of thi s metho d may be limite d o t sys ­ tems whos e miscibilit y ga p s i known beforehand .

3.6

3.6.1

MISCELLANEOUS

Rheological Properties

a. Binary Studies. The determinatio n of polymer-polyme r miscibilit y by rheologica l measurement s on binar y system s s i rar e an d indee d may be difficul t o t justify . But becaus e th e morpholog y of a two-phas e syste m ca n

3.6. Miscellaneous

175

chang e wit h shearin g rate , wherea s th e structur e of a solubl e syste m cannot , it s i expecte d tha t th e shea r viscosit y functio n of solubl e system s wil l chang e monotonicall y wit h composition . Deviatio n fro m monoton y ca n be take n as positiv e evidenc e of tw o phases . Some example s of th e us e of mel t viscosit y as an indicato r of miscibilit y are available . Kongaro v an d Bartene v [115 ] foun d a monotoni e chang e of the viscosit y functio n wit h compositio n fo r th e syste m rβ-l,4-polyisoprenenatura l rubber , bu t completel y unpredictabl e behavio r fo r natura l rubber nitril e rubber . The syste m natura l rubber-polybutadien e responde d n i an intermediat e fashion . Similar , bu t incomplete , result s wer e obtaine d by Giniyatulli n et al. [116 ] for poly(tetrahydrofuran)-base d urethane s mixe d wit h PVC. Linea r poly urethan e wit h PVC yielde d mel t viscositie s whic h varie d n i a mor e regula r fashio n wit h concentratio n tha n thos e of branche d polyurethane s wit h PVC. In no cas e was th e variatio n completel y monotonie , indicatin g limite d solu ­ . bilit y [117] The viscoelasti c propertie s of th e PPO-P S syste m hav e bee n use d o t demonstrat e it s miscibilit y at a leve l correspondin g o t entanglemen t spacin g [118] . Dynami c measurement s at temperature s abov e th e glas s transitio n and extendin g int o th e flowregio n wer e foun d o t chang e more smoothl y wit h compositio n tha n th e sam e measurement s usin g a mixtur e of tw o PS sample s of differen t molecula r weight s [119] . Viscositie s of th e forme r mix ­ tures , correcte d o t th e sam e fre e volum e o t accoun t fo r th e stead y increas e of Tg fo r th e mixtures , wer e foun d o t chang e smoothl y wit h composition . Thi s behavio r was n i accor d wit h tha t predicted , base d on an averagin g of bot h the weigh t averag e molecula r weight s an d entanglemen t molecula r weights . Simila r conclusion s concernin g smoot h change s wit h compositio n wer e reache d by Schmid t [120 ] usin g blend s of PPO wit h high-impac t PS (HIPS) . By measurin g dynami c viscoelasti c propertie s an d steady-shea r propertie s over a wid e rang e of temperature s an d frequencie s fo r HIPS , PPO, an d a 65/3 5 HIPS-PP O blend , t i was conclude d tha t th e blen d was intimatel y mixed on a segmenta l level . A nove l rheologica l techniqu e fo r th e detectio n of tw o phase s n i polyme r . Thi s mixture s ha s recentl y bee n suggeste d by Hubbe l an d Coope r [121] method presume s tha t th e segmenta l orientatio n of th e component s n i a miscibl e syste m wil l be th e same , wherea s th e segmenta l orientatio n of th e component s n i two-phas e mixture s wil l diffe r significantly . Whil e applie d onl y o t solid s by Hubbe l an d Cooper , th e techniqu e shoul d be equall y ap ­ plicabl e n i an y viscoelasti c region . Result s wit h th e miscibl e system s nitro ­ cellulose-PC L an d PVC-PCL confirme d th e presumption s of th e metho d in tha t th e orientatio n function s fo r bot h component s wer e similarl y relate d to th e strai n applie d o t th e sample .

176

3. Methods for Determining Polymer-Polymer Miscibility

b. Ternary Studies {Polymer-Polymer-Solvent). The dependenc e of in ­ r weigh t ca n be use d o t estimat e th e interac ­ trinsi c viscosit y [η] on molecula a th e Stockmayer-Fixma n relationshi p [122 ] tio n paramete r vi 2 2 [if] = K& M^ + 0.036Φ[(1 - 2 x1 )2M ^ ] M 2/ p2 (3.45 )

2 4k constan s i th e Mark-Houwin t fo r a Θ-solvent , Φs i a universa l where constan t o f abou t 3. 1 χ 1 0 ,M2 s i th e molecula r weigh t o f th e polymer , χ12 s i th e interactio n paramete r fo r solven t 1 wit h polyme r 2, Vx s i th e mola r volume o f solvent , p2 s i th e densit y o f th e polymer , an dΝ s i Avagadro' s number . Thus ,t is i expecte d tha t viscosity , reflectin g th e siz e o f polyme r coil , wil l be influence d by th e thermodynamic s o f thes e systems . Favorabl e inter ­ action s lea d o t highe r intrinsi c viscositie s du e o t expansio n o f th e polyme r coi l wit h solvent . For ternar y systems , t is i no t expecte d tha t [η] wil l chang e much wit h change s n i interaction s betwee n th e tw o polymer s becaus e o f th e hig h dilu ­ tion , bu t thi s doe s no t alway s appea r o t be th e case . Williamso n an d Wrigh t [123 ] foun d larg e positiv e deviation s fro m an y averag e o f th e components ' intrinsi c viscositie s fo r system s o f highl y interactin g polymer s suc h a s PEO-poly(viny l alcohol ) an d poly(acryli c acid)-poly(viny l alcohol) . The behavio r o f th e latte r s i show n n i Fig . 3.39 . Apparentl y thes e system s con ­ sis t o f aggregate s o f severa l molecules . The discrepancie s betwee n averag e and observe d intrinsi c viscosit y fo r most system s ar e ver y smal l [124 , 125] , and th e metho d s i no t recommende d fo r determinin g polymer-polyme r miscibility . A secon d typ e o f experiment , lendin g itsel f o t analysi s b y Eq. (3.45) , ha s been performe d [103] .n I thi s th e intrinsi c viscosit y of polyme r 2s i determine d

1 Οι 0

I 0.2

I

1

1

0.4

0.6

0.8

1.0

1.2

Concentration, g/IOOml Fig. 3.39. Correlations of dilute solution viscosities of poly(vinyl alcohol) (PVA), poly(acrylic acid) ( P A A ) , and their mixture ( χ χ ), showing large deviation of the latter result from an average behavior (---). [From G. R. Williamson and B. Wright, J. Polym. Sci., Part A 3, 3885 (1965).]

1

3.6. Miscellaneous

177

in a solven t containin g aconstant concentratio n of polyme r 3. The valu e thus obtaine d s i relate d o t 23 miscibility . To obtai n χ23 , th e intrinsi c viscosit y of polyme r 2 coul d be determine d n i thi s manne r usin g severa l polyme r 3 solution s of differen t concentrations . Extrapolatio n o t a polyme r 3 concentratio n of 1, followe d by a Stockmayer-Fixma n plot , woul d yiel d χ2.3 Unfortunately , thi s woul d no t be an accurat e metho d becaus e th e secon d ter m of th e Stockmayer-Fixma n relationshi p woul d be small , du e o t th e larg e valu e of Vx a s modifie d by th e presenc e of polyme r 3. Al l of thes e tech ­ nique s depen d heavil y on th e validit y of th e Stockmayer-Fixma n relation ­ ship , whic h s in i conflic t wit h othe r theorie s [122] . A thir d typ e of solutio n viscosit y experimen t ha s bee n more widel y used . In thi s experimen t th e Huggin s constan t Κ as define d by Eq. (3.46 ) belo w 2 Vsjc = [η] + Kc[n] (3.46 ) 2 is examine d [125] . Alternatively , th e grou p b = Κ[η] ca n be use d [124] . Morawet z [122 ] ha s show n tha t interactin g polyme r system s n i thi s experi ­ ment may sho w ver y hig h value s of b compare d wit h th e averag e fo r eac h polymer . Bτhmer et al. [124 ] hav e correlate d directl y th e deviatio n of b fro m the averag e valu e wit h th e polymer-polyme r interactio n parameter . The y conside r thi s more promisin g tha n deviation s n i K, whic h varie s little , fo r determinin g polymer-polyme r interactions . Thi s method , an d othe r adapta ­ tion s [63 , 103 , 123 , 125-129 ] of th e Krigbau m an d Wall treatmen t [130 ] ar e empirica ln i natur e an d shoul d be use d wit h caution . As n i an y ternar y experiment ,t i shoul d be born en i min d tha t a dependenc e on solvent s i likel y an d ther e s i no certai n metho d of eliminatin g thi s de ­ pendence , eve n at hig h solut e concentration . As a minimu m precaution , th e experimen t shoul d be repeate d n i a wid e variet y of solvents . 3.6.2

Volume of Mixing

Blend s of immiscibl e polymer s an d phase-separate d bloc k copolymer s ar e generall y expecte d o t exhibi t no volumetri c deviatio n ove r tha t calculate d utilizin g an additivit y relationshi p [131-133] . Wit h miscibl e polyme r blends , many experimenta l case s exis t showin g tha t th e specifi c volume s ar e no t additiv e [26 , 106 , 134 , 135] . Generally , miscible-blen d densitie s ar e highe r tha n thos e calculate d fro m volumetri c additivit y relationships , especiall y where specifi c interaction s exist . To make vali d comparison s fo r th e actua l stat e n i whic h th e blen d exist s (i.e. , glas s or rubber) , th e calculate d specifi c volum e fo r th e blen d must employ pure-componen t volume s fo r th e sam e state .I n many experimenta l cases , suc h as a rubber y polyme r blende d wit h a glass y polymer , thi s wil l requir e extrapolate d values , as show n n i Fig . 3.40 . Thus , th e specifi c volum e

178

3. Methods for Determining Polymer-Polymer Miscibility

Temperature Fig. 3.40. Generalized volume-temperature response for polymers with different glass transition temperatures, showing extrapolation procedure for blends.

for th e rubber y polyme r A shoul d be th e extrapolate d valu e of th e volume temperatur e dat a fro m th e glass y stat e fi th e blen d s in i th e glass y state . Con­ versely , fi th e blen d Tg s i belo w th e testin g temperature , extrapolatio n of th e specifi c volum e of th e glass y polyme r Β fro m th e rubber y stat e o t th e tes t temperatur e s i require d fo r determinatio n of th e specifi c volum e o t be em­ ploye d n i th e calculations . Miscibl e blend s of a rubber y an d a glass y polyme r would be expecte d o t exhibi t nonadditiv e specifi c volume s n i th e regio n betwee n th e Tg value s of th e respectiv e components . Obviously , volum e chang e (i.e. , densification ) shoul d no t be presente d as evidenc e of polymer polyme r miscibilit y or interactio n betwee n th e component s unles s thi s extrapolatio n s i performed . Studie s by Kwei et al. [106 ] wit h polystyrene-poly(viny l methy l ether ) blend s reveale d significan t densification , a s show n n i Tabl e 3.10 . Thes e result s wer e interprete d as bein g additiona l evidenc e fo r extensiv e mixin g of the components . Poly(vinyliden e fluoride)-poly(methy l methacrylate ) blend s exhibite d negativ e volum e change s at hig h PVF2 contents , bu t positiv e value s fo r PMMA-rich blend s [26] . However , extrapolatio n of th e pure-componen t densitie s o t th e actua l stat e of th e blen d was no t attempted , whic h may explai n thes e results . Some wor k ha s bee n directe d towar d applicatio n of th e free-volum e con ­ cept o t immiscibl e polyme r mixtures . Whil e no t directl y relate d o t miscibl e polyme r systems , thes e studie s do indee d relat e o t volum e chang e n i polyme r

3.6. Miscellaneous

179

TABLE 3.10

a

Densities of Mixtures of Polystyrene and Poly(vinyl methyl ether) ρ (calcd)

τ* Wt% P V M E

a

0 10.00 35.06 45.30 70.00 100

Pj22

1.0505 1.0562 1.0661 1.0615 1.0525 1.0404

(°Q 102 80 18 -18 -23 -29

PS and PVME densities at 23°

1.0495 1.0470 1.0459 1.0434

Extrapolated PVME density

Extrapolated PS density

1.0508 1.0654 1.0614 1.0520

Reprinted with permission from T. K. Kwei, T. Nishi, and R. F. Roberts, Macro­ molecules 7, 667 (1974). Copyright by the American Chemical Society.

mixture s an d may be of importanc e n i understandin g system s of partia l miscibility . Lipato v an d co-worker s [136-139 ] hav e bee n primar y con ­ tributor sn i thi s area . Startin g wit h th e Simha-Boye r relationshi p (AocTg = k) [140] , a verificatio n of th e followin g modificatio n Δα27^2 = k2$2 (3.47 ) was experimentall y attempted . Usin g blend s whic h exhibite d 7^' s of th e respectiv e component s (thu s indicatin g negligibl e phas e mixing) , dynami c dilatometr y an d isotherma l compressio n dat a wer e obtained . Whil e th e pure-componen t Δα Tg dat a agree d reasonabl y wel l wit h th e universa l con ­ stan t of th e Simha-Boye r relationshi p (k = 0.113) , value s of th e expressio n Αοί^/φι wer e consistentl y highe r tha n th e predicte d values . Lipato v an d Vilenski i [138 ] conclude d tha t thi s positiv e deviatio n implie d tha t th e densit y of molecula r packin g n i th e phase-separate d mixtur e was lowe r tha n n i th e pure state , indicatin g highe r molecula r mobilit y or fre e volume . Thi s exces s fre e volum e was propose d o t be associate d wit h th e interphas e region . Simila r investigation s may be of interes t fo r system s exhibitin g partia l miscibility . Δ « ι ^ι = ^ ι 0,ι

3.6.3

Heat of Mixing by Calorimetry

Calorimetr y s i on e of th e most direc t method s of determinin g thermody ­ namic parameters . At constan t pressure , th e hea t release d by a mixin g proces s is proportiona lo t th e enthalp y of mixin g (AH) whil e th e variatio n of enthalp y

180

3. Methods for Determining Polymer-Polymer Miscibility

wit h temperatur e yield s th e fre e energ y (AG) of mixing . The relevan t rela ­ tionshi p s i d(AH/T) d(i/T)

= AG

(3.48 )

|P,JV

For rathe r obviou s reasons , no on e ha s reporte d a calorimetri c experi ­ ment involvin g th e direc t mixin g of tw o polymeri c components , althoug h liqui d oligomer s hav e bee n successfull y employe d [68] . Al l determination s have use d a solven t o t ai d th e mixin g process . The thermodynami c cycl e used o t calculat e AH s i polyme r 1 + polyme r 2

12 mixtur e

AH 2

solutio n 1 + solutio n 2

M

(3.49 )

solutio n 12

AH = AH, + AH2 + AH3 -

AH4

A n equivalent , simplifie d cycl e s i polyme r 1 + polyme r 2 ΔΗ

1 2

12 mixtur e /

(3.50 )

* solutio n 12 AH = AH12 Δ Η4 where AH12 s i determine d usin g a dr y blen d of th e appropriat e rati o of polyme r 1o t polyme r 2. This cycl e was use d as earl y as 195 8 by Struminski i an d Slonimski i [141] , who foun d a genera l agreemen t betwee n ternary-phas e behavio r an d hea t of mixing . The y wer e als o th e first o t recogniz e th e difficultie s involve d wit h calorimetri c measurement s on glass y polymers . Becaus e th e glas s s i no t a thermodynami c state , th e measure d heat s depen d on ho w th e glas s s i prepared . Ichiar a an d co-worker s [142 , 143 ] use d simila r calorimetri c technique s an d reporte d simila r problem s wit h variatio n du e o t preparatio n of glass y samples . Thei r recommendatio n was tha t calorimetri c technique s be con ­ finedo t rubber y samples . Zvere v et al. [144 ] experience d difficultie s wit h crystallinit y difference s betwee n component s an d mixtures . I t s i eviden t tha t crystallinit y change s coul d lea d o t sever e error s n i th e calculate d hea t of mixing . Heat of mixin g of selecte d pola r polymer sn i th e regio n of phas e separatio n

3.6. Miscellaneous

181

can sho w unusua l behavio r wit h concentration , accordin g o t th e result s of Tager an d co-worker s [145 , 146] .I n th e compositio n regio n correspondin g to tw o phases , th e hea t of mixin g was foun d o t chang e signs , a behavio r als o cite d by Patterso n [147 ] fo r hydrocarbons . Novakov et al. [148 ] hav e attempte d o t correlat e "compatibility " wit h th e heat effec t of ste p 4n i Eq. (3.49) . Thi s migh t be possibl e fi extrapolatio n o t 100% solid s wer e performed , bu t otherwis e t i appear s o t be an inadequat e assumptio n becaus e of th e influenc e of solven t on th e process . N o recor d ha s bee n foun d of an attemp t o t measur e th e temperatur e dependenc e of th e hea t of mixin g o t deriv e th e fre e energ y of mixing . Thi ss i not to o surprisin g n i vie w of th e difficult y of th e measurement s an d th e com­ poundin g of erro r on takin g derivatives . However , th e fre e energ y of mixin g and, o t some extent , it s component s hav e bee n determine d wit h th e ai d of absorptio n studies . Tage r an d co-worker s [145 , 146 ] an d Kwei et al. [106 , 149] hav e use d thi s technique . Kweiet al. di d not attemp to t solv e fo r th e component s of th e fre e energy , the y simpl y solve d fo r th e interactio n paramete r fo r th e tw o polymer s (com ­ ponent s 2 an d 3) usin g th e traditiona l equation s of regula r solutio n theory . The sequenc e of relationship s s i 0 a, = PJP, (3.51 ) Αμ1=ΚΤ\ηα1

2

(3.52 )

= n I φι + φ2 + Χί2φ2 polyme r 2-solven t 1 = n I φί + φ3 + χί3φ3 polyme r 3-solven t 1 = n I φΧ + 1 ( - φ,) + (χ12 φ2 + χί3 φ3)(\ - Φ,) — Ίίι^ΦιΦζ polyme r 2-polyme r 3-solven t 1 where a, s i th e activity , P, s i th e partia l pressur e of th e solvent , P,° s i th e ful l vapo r pressur e of th e solvent , Αμι s i th e partia l mola r fre e energ y (chemica l potential ) of th e solvent ,χί2 an d χ13 ar e th e interactio n parameter s for polyme r wit h solven t (base d on solven t volume) , an d χ23 s i th e interactio n M o base paramete r fo r th e tw o polymer s (als d on solven t volume) . The resul t might be use d o t approximat e AH throug h th e relationshi p M 3 AM /V = ΡΤχ23 φ2φ3/νι (cal/cm ) (3.53 ) where v, s i th e mola r volum e of th e solvent . The approac h of Tage r an d co-worker s [145 ]o t th e analysi s of absorptio n dat a fo r mixe d polyme r system s follow s th e mor e genera l thermodynami c route . The thermodynami c quantitie s ar e give n on a convenien t weigh t basis ,

182

3. Methods for Determining Polymer-Polymer Miscibility

the subscrip t 2 referrin g o t eithe r a polymeri c componen t or th e polyme r mixture . The serie s of equation s use d s i Αμ1 =

(i/M1)RTln(Pl/P1°)

(cal/ g o f solvent )

(3.54 )

(wjw2) ά{Αμγ) — ΟΟ M Ag = vv Αμ1 + w2 Δμ2 xΜ M AG = Δ#/νν 2

(cal/ g o f polymer )

(3.55 )

(cal/ g o f solution )

(3.56 )

(cal/ g o f polymer )

(3.57 )

where Mx s i th e molecula r weigh t of M th e solvent , w1 an d w2 ar e weigh t frac ­ M tion s of solven t an d polymer , an d Ag s i th e averag e fre e energ y of mixing . The limi t ofAg /w2 a sw2 goe so t zer o s i th e fre e energ y of mixin g th e polyme r (or polyme r mixture ) wit h a n infinit e amoun t of solvent . Becaus e th e absorp ­ tio n experimen t canno t easil y approac h thi s limit ,M th e resul ts i ver y dependen t on th e assumptio n concernin g th e shap e oM f th e Ag (w2) relationshi p a t hig h solven t content . The limitin g value s fo rAG , equa lo t AG, fo r bot h polymeri c component s an d aW1\W2 mixtur e of th e component s may be combine d usin g th e relationshi p AG = WXAGY + W2AG2 - AG4 (3.58 ) where th e subscript s refe r o t th e step s of th e thermodynami c cycl e n i Eq. (3.49) . The valu e ofAG3 s i zer o becaus e of th e infinit e dilutio n of th e solutes . The enthalp y of mixin g may be calculate d fro m th e temperatur e variatio n of AG, usin g th e analo g of Eq. (3.48) . Qualitatively , th e absorptio n isotherm s fo r mixture s of lo w miscibilit y fal l n i a regula r fashio n betwee n th e isotherm s fo r th e pur e components , whil e th e isotherm s fo r highl y miscibl e system s fal l belo w thos e of th e com­ ponents . Thus , a n examinatio n of th e isotherm s ca n provid e a qualitativ e evaluatio n of th e fre e energ y functio n fo r th e tw o components . 3.6.4

Melting Point Depression

The additio n of lo w molecula r weigh t solubl e compound s o t crystallin e polymer s result sn i a meltin g poin t depression . The meltin g poin t depressio n in thi s cas e ca n be determine d by th e expressio n 1 2 l K - Φ2) ~ X i (l ~ Φ2) } (3.59 ) 2 m m AM V 2 Y where χί2 s i th e interactio n parameter , Tm th e experimenta l meltin g point , Tm° th e equilibriu m meltin g point ,AH2 th e hea t o f fusio n o f 100 % crystallin e polyme r pe r mol e o f repea t unit , Vx th e mola r volum e o f diluent , V2 th e Τl

-

= ^fV

183

3.6. Miscellaneous

molar volum e of polyme r repea t unit , an d φ2 th e volum e fractio n of crystal ­ lin e polymer . Meltin g poin t depressio n dat a fo r solute-polyme r blend s si an accepte d metho d fo r th e determinatio n of th e hea t of fusio n fo r th e crystal ­ lin e portio n of semicrystallin e polymers . Calorimetri c dat a of th e polyme r yiel d AHf; thus , wit h th e AH2 dat a of th e solute-polyme r blen d fro m Eq. (3.59) , th e degre e of crystallinit y ca n be determined . In polymer-polyme r blend s n i whic h on e componen t s i crystalline , melt ­ ing poin t depression s ar e als o observed . Example s includ e poly(e-capro lactone)-poly(viny l chloride ) [150] , isotacti c polystyrene-PP O [151] , an d poly(vinyliden e fluoride)-poly(methyl methacrylate ) [152 , 153] . The utilit y of th e meltin g poin t depressio n o t calculat e th e interactio n paramete r was demonstrate d by Nish i et al. [152 , 153] . Thi s method , whic h provide s fo r calculatio n of χ1,2 ha s definit e importanc e an d wil l be sum­ marize d here . The genera l equatio n fo r meltin g poin t depressio n s i 1 1Π 2 1 1 RV7 Φΐ , ( i l , / . . .. , ,2 m m m ^ - - - ( -1 < / > 2 ) + Χ ΐ 2 ( 1- < / > 2 ) Tm Tm° ΑΗ2νγ \ 2 \ m2 (3.60 ) For polyme r mixtures , mr an d m2 (th e degre e of polymerizatio n fo r constit ­ uent s 1 an d 2 ) ar e ver y large , thu s l Ψ m

~ Ψ*

l

= ~

m

6)1 -

^

·

AH

2 Vl Equatio n (3.61 ) indicate s tha t a negativ e χ12 wil l yiel d a meltin g poin t depressio n a s observe d fo r experimenta l system s previousl y cited . Wit h a positiv e interactio n parameter , th e theor y predict s tha t a meltin g poin t elevatio n woul d result ,a s pointe d ou t by Nish i an d Wang [152] . Not e tha t a positiv e χ12 wil l most probabl y resul t n i phas e separatio n du e o t th e un ­ favorabl e thermodynami c situatio n fo r hig h molecula r weigh t polyme r mixtures . In Eq. (3.61) , χ12 an d AH2, presen t as a ratio , canno t be determine d simultaneousl y fro m calorimetri c measurements . n I orde r o t alleviat e thi s experimenta l problem , Nish i an d Wang suggeste d th e followin g approach : The interactio n paramete r χί2 was assume d o t be of th e for m χ12 = BVJRT (3.62 ) where Β si th e polymer-polyme r interactio n energ y density . Equatio n (3.61 ) the n reduce s o t 1 Γ1 Φι \Tm

1 Tm °\

Βν2φ1 ~ AH2Tm

)

184

3. Methods for Determining Polymer-Polymer Miscibility

Recastin g th e dat a n i th e for m of variable s equa l o t (1/T d m - 1/Τ„°)/φ1 an JTm allow sΒ o t be calculate d fro m th e slop e of a plo t of thes e variables ; the n χί2 ca n be determined . Thi s procedur e allow s on e o t averag e experi ­ menta l dat a graphically . Not e tha t calculatio n of χί2 fro m dat a on a singl e blen d s i possibl e (wit h Tm° an d AH2 predetermined) , bu t no t a s accurate . This analysi s indicate s tha t a meltin g poin t depressio n of a crystallin e polyme rn i a polyme r blen d implie s miscibilit y an d allow s fo r th e calculatio n of th e interactio n parameter . Some value s cite d ar e χ12 = —0.29 5 (160°C) for poly(vinyliden e fluoride)-poly(methyl methacrylate ) mixture s [152 ] an d Χα = —0.3 4 (160°C ) fo r poly(vinyliden e fluoride)-poly(ethyl methacrylate ) mixture s [153] .I n usin g th e analysi s fo r meltin g poin t depressio n o t predic t χ1,2 t i must be recognize d tha t a miscibl e polymeri c diluen tn i a crystallin e polyme r ca n alte r th e spherulit e dimensions . As th e meltin g poin t s i in ­ fluenced by th e spherulit e size , correction s fo r thi s variabl e wil l be necessar y to obtai n more accurat e χί2 values . 3.6.5

Nuclear Magnetic Resonance

Proto n nmr experiment s on polymer s ar e generall y confine d o t studyin g the spin-spi n an d spin-lattic e relaxatio n processe s as a functio n of tem ­ peratur e an d compositio n [154] . By convention , th e latte r s i characterize d by a relaxatio n tim e 7i whil e th e spin-spi n relaxatio n tim e s i calle d T2. As wit h mechanica l measurements , simple r result s ar e expecte d wit h one-phas e tha n wit h two-phas e mixtures . But nmr ha s an advantag e ove r mechanica l measurement sn i tha t th e signa l shoul d be independen t of th e shap e an d inter connectivit y (bu t no t th e size ) of th e phase s n i a two-phas e mixture . Thi s allow s on e o t decompos e a multi-tim e relaxatio n proces s an d analyz e th e phase s thereby . The magnitude s of Tx an d T2 ar e influence d by molecula r motions , an d the change s wit h temperatur e ca n be analyze d n i term s of th e onse t of suc h motions . The resultin g Tx versu s temperatur e curv e look s much lik e inverte d mechanica l los s response , whil e th e T2 versu s temperatur e curv e s i quit e reminiscen t of an inverte d modulu s response . Althoug h th e origin s of th e changes wit h temperatur e of bot h mechanica l an d nmr response s ar e th e same, th e strength s or intensit y of th e change s may be quit e differen t wit h 45Also the tw o methods . , th e equivalen t8frequenc y of th e nmr experimen ts i quit e high : ~ 10· Hz fo r T2 an d - 1 0 Hz fo r Τγ. When bot h mechanica l and nmr method s do giv e informatio n on a molecula r motion , th e agree ­ ment s i quit e good . Nuclea r magneti c resonance , as ha s bee n mentioned , ha s a particula r advantag e n i two-phas e systems . Her e tw o time s ar e ofte n resolvable , on e for eac h phase . Thi s techniqu e ha s bee n applie d successfull y o t crystallin e

185

3.6. Miscellaneous

Log

φ'amorphous ζ Time

Fig. 3.41. Schematic of the decay of signal strength after a 90° pulse, showing the extraction of spin-spin relaxation times (7^) for the rigid, crystalline phase and the flexible, amorphous phase.

system s wher e T2 fo r th e proton s n i th e amorphou s phas e s i much greate r tha n tha t fo r th e proton sn i th e crystallin e phase . A doubl e exponentia l deca y of inductio n signal , illustrate d n i Fig . 3.41 ,s i ideall y observed . The relativ e signa l strengt h correspondin g o t thes e tw o processe s reveal s th e crystallinit y of th e sample . The sam e effec t occur s n i glass-rubbe r phas e mixture s fi th e 7^' s ar e sufficientl y fa r apart . The r 2's of a glass-crystallin e mixtur e ar e to o clos e o t be resolved . In quasi-binar y polyme r mixture s th e T2 relaxatio n ha s bee n analyze d in term s of th e tota l proto n conten t of eac h phase . One s i abl e o t determin e the relativ e amount s of eac h phas e f i th e component s hav e abou t th e sam e volume concentratio n of protons . Analyzin g fo r th e compositio n of th e phase s canno t be don e withou t an assumptio n abou t th e additivit y of th e pure components ' relaxatio n times ; however , thi s proble m ha s bee n ap ­ . Figur e 3.4 2 show s th e decompositio n process , usin g linea r proache d [106] additivit y of relaxatio n time s fo r illustration . Perhap s th e most complet e applicatio n of th e nmr metho d o t blend s in ­ volve s th e PS-poly(viny l methy l ether ) (PVME) system . Usin g a 50:5 0 ratio , Kwei et al. [106 ] foun d multipl e Γ/ s aroun d 150°C , th e temperatur e at whic h th e syste m become s opaque , bu t detecte d multipl e T2s at tempera ­ ture s as lo w as 25°C . Thi ss in i accordanc e wit h th e freedo m of T2 fro m spi n diffusion , whic h tend s o t merg e Γ/ s of closel y associate d regions . Thus , T2 detect s region s of relativel y smal l siz e containin g nearl y pur e material . The author s propose d tha t thes e region s ar e th e natura l resul t of geometrica l

186

3 . Methods for Determining Polymer-Polymer Miscibility

Time Fig. 3.42. Illustration of an analysis of the two phases in a binary blend using linear additivity of the r's for each component. The pure components must have different r's, as illus­ 2 2 trated by the dashed lines. The relative amounts of each phase can be deduced from the jy-intercept of straight-line fit to the long-time decay.

constraint sn i polyme r systems . The reaso n fo r th e disappearanc e of multipl e ^ 's belo w 25° C was no t explained . Using Τγ o t follo w phas e separatio n upo n annealin g th e sam e system , Nishiet al. [149 ] foun d tha t th e volum e portio n of eac h phas e remaine d nearl y constan t whil e th e compositio n change d graduall y wit h time , approachin g tha t of th e pur e components . Thi s behavior , expecte d fo r spinoda l decom ­ positio n (se e Sectio n 2.2.3) ,s i show n n i Fig . 3.43 . Becaus e of th e sensitivit y of T2 o t compositiona l variations , to o much , usin g th e syste m PVCinformatio n may be obtained . Nish i et al. [155] Hytrel , foun d singl e 7\' s fo r eac h mixtur e bu t an unanalyzabl e T2 signal . (Pur e PVC itsel f ha s at leas t tw o T2 component s abov e th e Tg, th e shorte r T2 bein g associate d wit h crystallin e regions. ) A singl e 7\ s i an indicatio n of th e absenc e of aggregate s greate r tha n abou t 30 Β, accordin g o t thes e authors . Usin g th e les s miscibl e syste m PVC-PVAC, Elmqvis t [156 ] detecte d a numbe r of component s of Τγ, th e value s an d intensitie s of whic h depende d upon preparatio n an d annealin g procedures . Nuclea r magneti c resonanc e experiment s othe r tha n relaxatio n ar e pos ­ sibl e on soli d polymer s an d polyme r melts . Elmqvis t an d Svanso n [157 ] showed tha t broad line nmr s i a sensitiv e too l fo r th e detectio n of smal l amount s of a sof t phas e imbedde d n i a har d matrix . The reaso n s i tha t th e resonanc e of proton s n i th e sof t phas e s i relativel y shar p compare d wit h th e resonanc e ban d of th e matri x protons . The intensit y of th e ban d du e o t th e

187

3.6. Miscellaneous

τ,

msec

Fig. 3.43. Spin-lattice relaxation as measured from the signal decay following a 180°-τ-90° pulse sequence. The relative constancy of the intensity due to each phase demonstrates that the system P V M E - P S is decomposing by the spinodal mechanism. [Reprinted with permission from T. Nishi, T. T. Wang, and T. K. Kwei, Macromolecules 8, 227 (1975). Copyright by the American Chemical Society.]

sof t segmen ts i accordingl y ver y hig h an d plainl y evident , eve n at concen ­ tration s as lo w as 1%. High-resolutio n nmr s i possibl e n i polymer-polyme r system s afte r sligh t swellin g wit h a lo w viscosit y solvent . Deuterate d solvent s avoi d unnecessar y complicatio n of th e spectrum . Thi s techniqu e prove d usefu l n i th e stud y of alternatin g bloc k copolymer s of polycarbonat e an d poly(dimethy l siloxane ) [158] . The introductio n of a thir d componen t ca n influenc e th e phas e be ­ havior , however , an d cautio n must be exercise d n i th e interpretatio n of suc h experiments . 3.6.6

Other Spectroscopic Techniques

In th e previou s section , nmr spectroscop y was discusse d as a too l fo r analyzin g th e composition , amounts , an d o t some exten t th e size s of th e phase sn i a polyme r mixture . But spectroscop y ca n als o be use d o t investigat e the solvatio n of molecule s [159] , i.e. , th e interactio n of th e molecul e wit h it s environment . Spectroscop y ha s prove d particularl y valuabl e n i th e inter ­ pretatio n of hydroge n bondin g [160 , 161] , an d t is i natura l o t appl y t i o t polymer-polyme r systems . The reasonin g generall y followe d n i th e applicatio n of spectroscop y s i

188

3. Methods for Determining Polymer-Polymer Miscibility

tha t system s of hig h miscibilit y wil l produc e spectr a showin g stron g devia ­ tion s fro m an averag e of th e spectr a of th e tw o components . The degre e of deviatio n as a functio n of miscibilit y canno t be satisfactoril y predicte d beforehand , however . Thi s technique , therefore , ca n onl y substantiat e th e findings fro m othe r method s fo r demonstratin g miscibility . I t doe s provid e valuabl e insigh t int o th e natur e of th e specifi c interaction s betwee n th e macromolecule s an d ca n ofte n provid e clue s fo r th e improvemen t of miscibil ­ it y (Sectio n 4.5) . Infrare d spectroscop y ha s most ofte n bee n use d n i th e analysi s of polyme r mixtures . Thus , th e solubilit y of har d segment s of aromati c polyurethan e n i sof t segment s of variou s polyester s an d polyether s ha s bee n investigate d by frequenc y shift s du e o t hydroge n bondin g of th e urethan e NH grou p [162 , 163] . Specifi c interaction s n i th e system s poly(acryli c acid)-poly (ethylen e imine ) an d poly(methacryli c acid)-poly(ethylen e imine ) wer e demonstrate d vi a infrare d spectroscop y by Zezi n et al [164] . The syste m PMMA-poly(vinyliden e fluoride) exhibit s specifi c interaction s involvin g the carbony l group , accordin g o t infrare d spectroscop y performe d by Coleman an d co-worker s [165] . Infrare d an d ultraviole t spectroscop y on th e well-know n blen d PS-PP O by Wellinghof f an d co-worker s [166 ] provide d evidenc e fo r th e followin g conclusion s :PPO s i loosel y packe d n i th e glass y stat e an d th e additio n of PS reduce s th e fre e volumes . The chain s of th e tw o component s interpene ­ trat e significantly . The reaso n fo r th e hig h miscibilit y s i a stron g interactio n betwee n th e pheny l grou p of th e PS an d th e phenylen e grou p of th e PPO. Ultraviole t emissio n intensit y ha s bee n suggeste d as a too l fo r quantifyin g the degre e of miscibilit y of tw o polymeri c component s [167 , 168] . To emplo y thi s techniqu e th e component s of th e blen d must contai n chromophori c structure s activ e n i th e ultraviolet , or the y must be modifie d wit h appro ­ priat e group s (e.g. , naphthyl , anthryl) . Thi s s i a possibl e disadvantag e be ­ caus e an y modificatio n of structur e ca n chang e phas e relationship s n i th e regio n of th e modification . In th e techniqu e propose d by Morawet z [167] , tw o different chromophore s are incorporated , on e on eac h polymeri c componen t at a leve l of abou t 1%. These group s ar e selecte d s o tha t a radiationles s transfe r ca n occu r betwee n the two . Thi s transfe r s i assume d o t be mor e efficien t a s th e miscibilit y in ­ crease s becaus e clos e proximit y (e.g. , 4 Β) of th e group s s i critica l o t th e transfe r process . The measure d emissio n reflect s thi s efficiency ; tha t is , les s radiatio n s i emitte d by th e transfe r dono r a s th e probabilit y of a radiationles s transfe r increases . I n on e stud y usin g thi s method , naphthyl - an d anthryl tagge d PMM A an d pol y (methy l methacr y late-co-buty l methacrylate ) wer e foun d o t sho w steadil y decreasin g miscibilit y as th e buty l conten t of th e copolyme r was increase d fro m 0o t 40%.

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3. Methods for Determining Polymer-Polymer Miscibility

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