HUMBLE OIL ti REFINING BAYTOWN TECHNICAL LIBRARY
ISTRISSIC T’ISCOSITI--~TOI,E:C~I~~~~ TYEIGHT R FOR P O I ~ I ’ I S O R ~ - T T I , E S‘~ ’ THOMAS G FOS Goodiirni
.JR
,
.r
$SI)114~1,
I-LORY
T i i r n n d li’iibbrr C‘ompnnii, l h r o n . O h i o RecciLrti .lcrgrisl 18 1948
Iluring tlic p a z t fir e yea1 s the intrinsic viicosit icz from no less than ten polymer series (8) have been she\\ n c\;perimentnllv t o tlcycntl on moleciilar 71 eight ;icmrtling to the *iniple re1:~tionsliip
nherc I< and n ai(>cwistantb tor factorily approvimated by equation I . Hon-ever. the graclunl decreahe in the degree of permeation of the domain of the polymer molecule as the molecular w i g h t increases should manifest itself in 21 decrease in the empirical value of a , provided the molecular weight range covered i q adequately large. Recently we have sought to take into x c o u n t the increase in the r olumc of the randomly kinlied chain iesiilting from the interferences between distantly caonnected segment5 of the polymer chain, iL factor \\-hich is believed to outn-eigh in importance the one mentioned above. _@in the form of the predicted dependence of intriniic viscohity 011 molecular iveight (’anhe approximated by Prcsentedat t h e Tn erity-secoii(1Satioiial Colloid Svmposiuiii, hichwvns held uridci the , i m p i c e s of tlic Division of Colloid Chemistrv of the .4mericnn ChcniicDI Society ‘it ( ‘1111Ilridge, Jlassacliusetts, June 23-25. 1948 Coiitril)ution So 1SF froin t h c Rcsciii r h I,‘thoi:itor\ of t hc Coodvcai T~ic.:inti I < I I ~ I ~ > c ~ I (’ompanr 2 T h e norlc presented i n this p i p r i compriscs ‘I p ~ o g i m n of fund:iincntal icsr:ircll o n I Lit). wr and plastics being carried out undei :L contr:ict hetween t h e Officr of S n v n l Rrsc trc11 rnd t h c Goodvrnr Tirr :ind Ruhlicr Cotnp:inv 107
equation 1 m’er liniited ianges This factoi, hov ei-ei, 3houltl 1t1i1ig 2Lbollt ;in increase in the apparent value of CI with increase in AI. These considerations imderline the importanw of w u i irig experimental data on the dependence of inti insic viscosity on molecular weight orei the Tyidest possible range. -111 unuwally broad range is covered by previoiisly published data on the inti insir viscosities of polyiiobutylenc in tliisohutylene (5). Throughout the niolecului ?I caight range investigat et1 15000 to 1,300,000), equation 1 applies n ithin the cxpcrimental error. In the present InT-estigation these observations ha1-e been extended t o include polyi-obutylenc- of lower molecular n-eight. In addition, the effect5 of solvent type and temperature on the intrinsic riscosity-molecular weight relationship for this ideally iioii-polar polymer h a r e been inyestig:ited.
b;s’r.iI.
I ;x1’Pi(. \.iscwities in r:irbori tetrachloride ;LI 30°C'., 1iiii1;ing u s e of tlie relationship applying to this :;cil~-ent as established he lo^\- (tiible 1). lIolec1ilar weights of the lo\\-c.rfractions \\-crc obtained from cryosropic nieasuwrllrrits in pure cy~lohesrtiic. 1hc cj-caloiiesme \vas prepnrccl hy hyrlrogeiiation of thiophene-fret kienzene over Raney nickel. The prodiict I\-:LS treated for 5ever:il days \\-it11 coiicwitriitetl ,dt'tiri(b acid itt 100°C. and distilled. The obaervetl freezing points of tn-o cj-c'lohesme fractions thus ohtained \vert G.3li"C. and 6.-18"C., a s comp:u.eti with the litemtiire value of Ci.S"C. The c ' r ~ measurements Ti-ere m:dc in a conventional nianncr, employing vigorous , -itleast tn-o und usunlly three freezing-point measurements \\-ere matle on each solution, the reproducibility of the arerage value being rt0.01T. Results of the cryoscopic measurcinents are given in t:ible 2. The molecular weights were calculated from the \-:in't IIoff equation, employing T-:ilues of 12';'~ extrapolated t80zero concentration. This extrapolation v-as niade by drawing parallel lines: through the data for the respective f i w t i o i r s mi plots of Al',!c 1's. c r .
RESULTS
The int,rinsic viscosities for polyisobutylene fractions covering :L u-ide molecular m i g h t range in a variety of solvents at several temperatures: are given in table 3 (see also table 5). =1 log-log plot of the intrinsic viscosity for a gi;.en solvent and temperature against the nioleciilar weight is linear (dashed lines of figures 1 and 2 ) , in accordance with equation 1 , i\-ithinthe experimentnl error over a Tvide range in -11. The values of I< and (I deduced from the linear plots are given in t,able 4. A%t moleculnr n-eights belon- 2000, hoivever, the observed values of [v] deviate from the above simple relationship. It is well lmon-11 ( - k , 11) that henzene and toluene at room temperature are
!
~
~
~
~
200
THOMAS G FOX, JIL. .LSD ii.iuL J. FLOW
-
-- -
-
T;\BLI< 2 C Iyoscopic datu o n polyisobutylene
ucfLons
ft
-
~
C, CRAUS/100
POLYMER
G OF
Ala
(AT/c)
0. 685
0 24-4 0.231 0.224
890 f 50"
0.3% 0 387 0.386 0.3i7
530 & 25
0.283 0.268 0.268 0.266
765 =t40
0.135 0.132 0.126 0.124 0.115
l i 3 0 f 80
li
SOLIEUT
IXstillatc S o 1
Distillate 10 2
2 80 I 45 0 3 71 1 S6
0 90 0
Distillate S o 3
%.3d 1.51 0.67 0
N o 4 (residue)
5 60 3.22 1.99 0 ct7 0
0.335
l of toluene and methanol. Recently Cragg md Rogers (2). vwl;iiig \I it11 wlutionq of (;R-S in mixtiues of various solventb 11 ith met1i:inol in varying piopoi tiom, founcl thebe piedictions to he essentially correct. Thc present data (table\ 3 id .j),v-lieiein the iolvent poner is altered *impl>-b ~ changiiig d ~ e n i ixtlwr tliuii bl- rhe addition of n lion-solvent, arr in agi eeiiient with theye prcdiction5, asauining that tlie heat of solution of polyiwbutylene in cyclohemne :ind in ( a i hon t etrachlnride is smnll. 'Thus foi a given polyi.sobui ylent' the iiitriii+i~I o .it:; in A poor d m n t ( ~ P I I Z C ~ ?or~ toluene) is roiisideinbljlo\\ er th:m in :\ good wlvent (cycloheunc or carbon tetrachloride) and the tempci,tture tlepentlcnw i b ~iiuclimore pronoiuiced in the forme1 cabe. Inspection of table -1- ieye:d- iiutlicl~that in grner:al the better the solvent the higher the \-:he oi a in eqiution 1 ; exceptions to thiq order u t the n-values in the table are not ~ W , T Y J I Iiiic ~ cxpci imc~nt:ilFiror.
~ h e i c-\- I\ tlic I ~ u I : ~ ! ) I~ oi n~01c~c.iilcs pi I. iibir cwit imeter, I - i.; t h e eti'i'ectil c volunic 01 eiich inolcc ulc. :incl 4 i, ;L 1iydiodyn:iniic iactor ( 3 ) . It 111 is thc molecular \\eight and c i. the cwicentiation in grain< pel 100 w., the intrinGc8 i c+orrcbpondinglya< Tiwi4tv may be cspr -,)
m b
=
coo
3i
1 that loiig-rliciiii, iri egii1:irly coiled p o l p i e r Inolrcule, ould Kuhn 13 i ~ i 1 iiiiSc(1 offer lea,t rr>i\tancc 1 o flo;\ ( i t tlic solution if the encoinpasrecl solvent moved with the po1ynic.i molcculc 'Ilie polymer incleciile \\-auld then act 2~ it giant sphei c many time- 1:ugc.i t h:in tlw ucrii:~l wliime of the polymer inoleculc itself ; h r n c ~J-? 4oiiltl ~ 1 c-pon(1, 2 1.oiighly at least, t o the volume pervaded by the iandomly coileil rIi,iin In p l a c ~of ? 6 ,Kuhn inserted the Einstein factoi 2.5 for :L ,uspcii+ion (,i ~nipciictrahlcsphcr( ReccAntlj- Debye and Rueche ( 3 ) have iiitrocluced u hydroti\ namic f a r ' t u r 4 , hich tlrpendi on the extent to vhich the veloritv field of tlic yolveni pmetr,ite- the r:t~iJ~)iii coil. In the limit of very high molecular weight (rel,itn-cl>-lo\\ pel incation), 0 .ippronches 2.5. I of niolccul:tr pmimctci-s. In thc approximation iisually employed in treating the spatial configuration c f A C.
14
polymer molecule, each successir-e segnieiit of the chain is conuidered t u be free t o assume an orientation relative to its immediate prrdecessor in the chain irhich is independent of the situation of' all otliei, segments of' tlie cahain. In other 11-ords,the angle of rotation about a given bond is considwed tu tie independent uf the arrangement of till other bonds. The wnfigiiration problcni then reduces t'o the treatment of the path described in spare by L: p:utic!e undergoing :t series of unrelated dispincemeiits, the direction of ezcli displncciil~1~t bei!ig suhject entirely to chance sild independent, of the ilircction of' all other displac+c.ments. In this "random flight" approsinlation, t h e distance 1)etnwii ends of the chain should he proportional to the length o f cncli segment :imi l o tlie s q u n i ~root of their numbei~. Other linear dinienaions :ire similarly proportional t o tliv ,squue root of the chain length. or number of segmcnts. I-Itm*e, shoidtl 1~ proportional to the threc--1inlves poiver of the c h i n longth, or t o .ll'3''.m t l the intrinsic viscosity shniild he given liy
[?jl -= ( 3 0 ! l > t , -I/'
'iQ
i.c,., the intrinsic. i-iscosit?. 5hould l w proport-iund t o the q u a i ' ' iuot oi the moleculai, chain lcngth modified 1))- the fuiictional depcnclencc of the hydrodynamic. factor on the chain length (: LI first :y>prosimation oii i\-hich there is superirnposeci u correction for the influence of 1oi:g-range "interferences" hctn-een two segments of the same molecule. Thiis, the ar-eragc eflective ~.olumcof tlie polymer molecule \rill be proportiuiial to trSA1P',iiliere cy czyiwses t11cs altci.ntion in linear tlimeiisions (hie t o intci,iwcBnce.
+
Yir ('1 I
Kuliii (IS) lias pointed out that the * * \ - d o m efilling effect" of real pctlynier iiioleaules (ab t1i;tinguishetl f ~ ~ hypotheticel ~ i i chains lutving negligible crosssectional dimensions and hence obeying the randoni flight' approsirnaticii) must ead to a n tipparent dependenre of thc. effective r-oliinie Tr(3 on n pon-er of AI :.re:iter than 312. On this basis Kulin pretlictctl that the exponent' a in equation 1 ?hoiiltl be lwt\i-een O.G n n t l 0.9. In t l i ~piwelit tcmiinology, Kiihn'i predication
is equivalent t o :t po3tiil:itccl dependence oi a’ on ‘t poi\ ei of A4 hctv on 0. I and 0.4 Recently one oi the :iuthors (6) (krived from consideration- the relationship - mu =
(*I(
I - 2p1)Z1
(
31
here Z is the number oi equivalent segments in the cham, C1 is a parameter someivhat dependent on the particular polymer and solvent, but which generally should lie in the range from 0.1 to 1, and p1 is the energy of interaction parameter given by =
RT‘It’R7’
where B is the cohesix-eeriei gy density coilstant ior the polymer-solvent pair and Til is the molar volume of the hoh’ent. T h i s , equation 5 takes into account not only the configuri5tiorial interferencc of the polymer chain with itself, hut it also includes the influence of cnergy intciwtion of t h r polymer ivith the wlvent Letting 2fI1-1 I?
=
0
and avoiding specihcatioii 01 the size ot the equivalent aegnient (nhich \vi11 depend on the stiffness of the chain and local steric interaction) hv rcplncinq CZ’ ’ Ivith C’M’ where r’ i.; ‘ 1 nen conit :mt :
‘.
- a’
(”(1
-
0/ T)JL1’
(61
Correspondence inclic.atec1 bet\\ ecn 8 .md the absoliit E tenipcratuic at n hich precipitation sets in for ;t solvent hich niises enclothermally with the polvmer , for a iolvent n.hicli mixes exotherinally 8 ]vi11 be negatirc Equation 6 can be replaccd by where According t o equation ti, u’ (and the constant of proportionality in eywtion 7 as well) will exhibit a comparatively small variation over fairly vide ranges in molecular weight. The \ d u e of a’ to be eniployed will depend of course on the mean value of the quantity on the right side of equation ti. In a good solvent for Tvhich C’(1 - O / T ) is large, a’ nil1 approach 0.3 a t large values of X ;in :L poor solvent, medium for nhich i - O/1‘ is near zero, a’ should approach zero. Thub, aside from the contribution of the dependence of 4 on 111,the value of the exponent a in equation 1 should lie in the range from 0.8 t o 0.3, the former value being approached in gooc! solvents a t suficientlj- high molecular reights. Experimentally ohserved d u e s of a generally occur in this range i indeed, valid csreptions are d i n o w n among polymer ieries for n-hich the intrinsic ~isc.ositT--molerular weight correlation has been extended t o include highmoleciilar-n-eight polymerb. This fact iuggests that Tarintion of thc hydro-
205
I S T R I K S I C VISCOSITY O F POLYIBOBUTYLEIUE
+
dynamic factor with molecular weight may be relatively unimportant throughout the high-molecular-weight range; presumably is near its asymptotic limiting value. The data of this paper have been treated on the basis of the postulate that may be treated as a constant over the molecular Tveight range covered. It is to be noted nevertheless that the combined variations of a3and of with Jf are such as to compensate to some extent for the deviations from equation 1 Jvhich n-ould ensue if either factor alone 1ver.e to r-ary with ,If while the other remained strictly constant. ,Isthe molecular weight decreases, d In a3/d In M decreases. At sufficiently lo^ molecular. Tveights, however, d In $,/d In III must increase appreciably lvith further reduction in M (3). Hence, these tn-o factors mag mutually preserve the empirical relationship given by equation 1 over a ivider molecular Treight i m g e than would be observed if either one alone were present.
+
+
+
2 C'oitipnt~isonof e.tprimrtital datu with theory
The 1 esulty of the :hove treatment w e cxpreised by equationh -1- and ti. Choosing a for the vdriahle t o be eliminated fiom these tn-o equations, the dependence of the intrinsic. viscosity on molecular \reight and temperature is specihed in terms of iour parameters, 4 , K,,, ( I t , and 0 If the hydrodpamic factor 4 IS constant (a3 postulated above), the product +KOmay be handled as a single parameter, thus reducing the number to three. + K O should be independent of molecular weight, solvent type, and temperature. The value of 6 i d 1 depend on the interartion forces characteristic of the given polymer-solvent pair. The third parameter C" contains all of the uncertaintiri inherent in the statistical treatment of the thermodynamic properties of high-polymer solutions in terms of the lattice model. It may be expected t o vary some\vliut 11-ith solvent type but it should be independent of molecular weight and of temperature. -1pplying intrinsic viscosity-molecular weight data for a given solvent a t a fixed temperature to the simultaneous solution of equations 4 and G, the yiiantity +KO may be evaluated. In this way +I-.
+
purpose of rompens:xting thc c!i'cct of ;til asstimed intwase in V \\-auld :Lccentu:Ltc the clific.ulty of ~ i ( , ( . ( ~ m r n o t~tic.l ~('0n~'O~li~:liiT ~ti~i~ drci,eni;e in 0 irit'li T in :Lpool. soh-c~iit. 1he present reslilts provide good e\-idence f u r tlic npprosiniate constancy of the hydrociyni~iriicfact or throughout the great cr part of the iiiolecular m i g h t range. The dependence of the intrinsic viscosity on solvent type, temperature, and molecular \\-eight (apart from the 11''' factor) is largely embodied in the expansion factor a3. The present results do not, howeyer, preclude the existence of a significant variation of 4 u-ith moleciilar wciglit :it' molec.ulai, weights below 50,000. r .
21 1
ISTRIA-SIC V I S C O S I T Y OF POLYISOBUTYLENE
I
I
I
1
M =1,260,000
TOLUENE
-
M = 463,000
0
s U
0
MEIl0,OOO
n
rr
v
-
u
M*48,000
v
0
0
0
Ms 10,200
0
I
I
I
I
0
30
60
90
-
TOG. FIG.5 . The intrinsic viscosity us. tenipcrature for toluene solutions of several polyiso butvlene f'inctioiis
1.260,000 -163.000 110.000 92.700 48,000 10.200 9.550
:i.Sl 3.04
2.1s 1.92
1.50
Thc solid lines arc drnn-n :recording t o t h e o r v .
3.07
3.44 2.76 2.06 2 .00 1.T7 1.42 1.41
3.W
1.55 1.3;
"0s 1.71
L2i
1.15 1.08 1.0;
1 .IO
1.13 1.0;
1.42 1.2s i.16
2.2; 1.57
1.42
2,-k3 1.9() 1.5s
1.31 1.17 1.17
1.42 1.23 1.22
1.05
1.10
1.85
1.02
1.05
1.20
1.50
212
THOMAS G FOX, J R . , AND l’.lYL J. FLORY YUblMdRY
Intrinsic viscosities oi polyisohutylene fractions cuvering ;L I\ ide molecular weight range have been measured in cyclohexane, carbon tetrachloride, diisobutylene, toluene, and benzene at various temperatures from - 10°C. to 90°C. The intrinsic viscosity for a given polymer in different solvents a t the same temperature decreases regularly from the best to the poorest solvent for the polymer, the order in which they are given above. The intrinsic viscosity in the poorest solvents, benzene and toluene, increases rapidly with temperature; in the other solvents a low temperature coefficient is observed. Log-log plots of the intrinsic viscosity us. the molecular weight in a given solvent at a particular temperature are approximately linear over a wide molecular weight range; the slope of the line increases with increasing solvent power from 0.53 for benzene at 25°C. t o about 0.70 for the best solvents. The results have been compared TI ith recent theuretical interpretations of intrinsic viscosities of high polymers. They are in agreement with the postulate that the intrinsic viscosity reflects directly the effective volume of the molecule in dilute solution, the hydrodynamic factor expressing the interaction of the equivalent sphere with the solvent remaining very nearly constant except , perhaps, at low molecular iveight5. The dependence of the intrinsic viscosity on the molecular weight, solvcnt poi\ w, find temperat tire i$ in agreement with theoretical prediction*. The authors wish to ac.linu\\-ledge the in carrying out thc csperimentd u-orh.
istutic-c’ of MY.Robert
E. Marshall
IIEE’F: RE S C E S (1) (2) (3) (4)
(5) (6) (7) (8j
(9) (10) (11) (12) (13)
;II.FWEY. T., J K . ,U a R ~ ~ o r ~h.. c s.\su . ~ I A R €1.: K , .J. A n i . C‘lieni. S o c . 64, 15.57 (1042). CRAW,1,.H., . 4 m ROGERS, T. SI.: Can. ,J. Research B26, 230 (1938). I~FJBY l’., EAXD , B r r ~ c mA, . A[,: ,J, Chcni. P h y s . 16, 573 (1948). E : ~ A N S , € ~ . ~ , , ~ \ S D ~ - OD~ .St V( :. :, 1iid.Eiiy. C(htm.34,-+61(1942). FLORY. 1’. J . : J. .\m. Chem. Soc. 65, 3 i 2 (lW3‘1. FLORY, 1’. J . : .J. Cheni. l’liys.. i i i p r r w . Fox, T. G , Jrt., .4NU E’LORY,1’. -1. : .I. A i n . C ’ t i c l n . Sicic. 70, 2384 (1Y58). TEIS, t V . l’., ASU ~ I A H . : .I.R Polymer KSc4. , 2 , 503 (1947) GOLDBERG, A . I . ,H H~-GGISS, >I. I,.: J . ed t’hys. 10, TOO (1939). HITGGIXS, 11.I..: J . .\pplied l’hys. 14,246 (1943). K E u r , A4.R., A N D l ’ m E R s , ET.: Ind. 1,:ng. Chtm. 34, 1192 (1942). KIRKWOOD, J. G., ASD RISELIS. ,J.: -1. (ilieni. Phys. 16, 565 (1948). KL-HS.W . : Kolloid-%.68, 2 (1034). I
