Diffusion and Viscosity of Low Polymers in Solution

Rossi, C.; Bianchi, Umberto; Bianchi, E.

doi:10.1002/macp.1960.020410104

Cited by 56 publications

(4 citation statements)

References 14 publications

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“…This conclusion is substantially the same as t h a t recently reached by ROSSI and associates14) from diffusion and viscosity studies on low polystyrene samples. This result suggests t h a t the molecular dimensions of polystyrenes with very low molecular weight a t infinite dilution are almost independent of the kind of solvent and equal those in the theta solvent.…”

supporting

confidence: 88%

Viscometric test of the theory of KURATA, STOCKMAYER and ROIG for the expansion of a polymer molecule

1963

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Test of the KURATA-STOCKMAYER-ROIG (KSR) equation for the linear expansion factor, tc, of a linear polymer molecule as a function of the molecular weight M was made by evaluating OL from the familiar FLORY-FOX relation tc3 = [q]/[q'J0. The systems chosen are eleven polystyrene fractions in toluene and in methyl ethyl ketone at 34.5OC. and in cyclohexane a t 34.5; 45.0: and 55.0"C. It is shown that the KSR equation is well obeyed by the data for the toluene system over a very wide range of molecular weight, while it is valid only for relatively high molecular weights in methyl ethyl ketone and in cyclohexane. I n all cases studied, the expansion of the polymer coil due to long-range interferences between chain elements tends to vanish below a certain chain length which depends on solvent and temperature. Such a critical chain length is abnormally large in the methyl ethyl ketone system, amounting to about 300 monomer units. The reason for this result is not clear to us. Application of the well-known FLORY equation a5-a3 = CN1rz to the present data demonstrates its serious limitations. ZUSAMMENFASSUNG: m Mit Hilfe der bekannten FLoRY-Fox-Beziehung tc3 = [q],"ql0 wurde die Giiltigkeit der KURATA-STOCKMAYER-ROIG-Gleichung (KSR) fiir a, den linearen Ausdehnungsfaktor einer Polymerkette, als Funktion des Molekulargewichtes gepriift. Als Systeme wurden 11 Polystyrolfraktionen gewalt, die in Toluol und Methylathylketon bei 34,5 "C sowie in Cyclohexan bei 34,5, 45,O und 55,O"C viskosimetriert wurden. Es wird gezeigt, daR das Toluolsystem die KSR-Gleichung iiber einen weiten Moleknlargewichtsbereich gut erfiillt. FiirMethylathylketon und Cyclohexan gilt die Gleichung nur bei relativ hohen Mlolekulargewichten. Unterhalb einer bestimmten Kettenlange zeigt die auf weitrawnige Wechselwirkung der Kettenglieder zuriickzufiihrende Ausdehnung des Polymerknauels eine Neigung zum Verschwinden. Diese kritische Kettenlange ist in allen hier untersuchten F a e n vorhanden; sie hangt von Losungsmittel und Temperatur ab und ist mit ca. 300 Monomereinheiten beim Methylathylketon besonders groR. Eine Erklarung fiir dieses letzte Ergebnis wird nicht gegeben.Die Anwendung der bekannten FLoRY-Beziehung tc5-a3 = CN"2 auf die MeBergebnisse dieser Arbeit zeigt den beschrankten Giiltigkeitsbereich der Gleichung.

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supporting

confidence: 88%

Viscometric test of the theory of KURATA, STOCKMAYER and ROIG for the expansion of a polymer molecule

1963

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“…The analogous behaviors of MHS plot in the low molecular weight region have been reported for many polymer-solvent systems. [35][36][37][38][39][40] The existent distribution of molecular weights in the polymer samples has to be taken into account in quantitative discussions of dilute solution properties. We are here ultimately interested in a fair estimate of the unperturbed chain dimensions of PET by use of the expression, (29) where l/J 0 and < r 2 > 0 are the viscosity constant and the mean square end to end distance in an ideal state, respectively.…”

Section: On the Sedimentation Datamentioning

confidence: 99%

Ultracentrifugal Characterization of Poly(ethylene terephthalate) in Dilute Solutions

Ohoya

Hasegawa

Tsubakiyama

et al. 2001

Polym J

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ABSTRACT:The well-fractionated poly(ethylene terephthalate) (PET) samples ranging in weight average molecular weight Mw from 0.9 to 16 X 10 4 have been studied by sedimentation velocity and equilibrium, and viscometry in hexafluoroisopropanol (HFIP) and m-cresol at 30°C. The second virial coefficient A2 determined in HFIP by the sedimentation equilibrium method is found to have high dependence on Mw expected for the helical wormlike chains in very good solvents. The constant l/J 113 P-1 in the Mandelkern-Flory equation is 2.54X10 6 for PET in HFIP and 2.57X10 6 in mcresol, being in excellent agreement with that reported for several polymer-solvent systems. In spite of an important polymer that has been widely used for a variety of industrial purposes, poly(ethylene terephthalate) (PET) is not still completely disclosed about its molecular characteristics and solution properties. I-s For example, there is significant disagreement among the constants of K' and a of the Mark-HouwinkSakurada (MHS) relationship, eq 1, compiled for several PET-solvent systems in "Polymer Handbook"; 9where [7]] is the intrinsic viscosity and M is the molecular weight. The reasons for this are that PET is soluble only in a limitted number of rather peculiar and dangerous solvents, such as trifluoroacetic acid (TFA) and achlorophenol (o-CP), and that the establishments of most MHS equations are based on the number average molecular weight Mn using the unfractionated samples. The reliable unperturbed chain dimensions, therefore, have not been determined in terms of the MHS relation proposed.The molecular weight and its distribution for several commercial PET samples have recently been measured in hexafluoroisopropanol (HFIP) by Naoki et al. 10 with light scattering and gel permeation chromatography (GPC). On the other hand, a series of preliminary experiments11·12 revealed that HFIP is an easy handling and very good solvent for PET. In this work, we direct our efforts toward the establishment of rigorous MHS relations for PET in HFIP and m-cresol. For this purpose, the polymer was first fractionated by a column elution method 13 and then the fractions obtained were characterized by sedimentation experiments and viscometry. The results for m-cresol solutions were compared with tTo whom all correspondence should be addressed. those obtained in m-cresol by Meyerhoff and Shimotsuma.2 Sedimentation equilibrium offers the weight average molecular weight Mw and requires least correction for polydispersity. HFIP is available with high refractive index increment dn/dc allowing a measurement at low polymer concentraion and providing good precision in Mw. The viscosity-molecular weight relations thus determined are available for the reliable evaluation of unperturbed chain dimensions ( < r 2 >ofM ) 112 from which the chain conformational parameter CJ is derived by the Stockmayer-Fixman method. 14 According to rather old-fashioned theory of the polymer solutions, 15 the dependences of a part of the molecular parameters obtained on molecular weight ar...

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“…We are, therefore, led to conclude that the drainage parameter of the Kirkwood-Riseman theory must be taken at least ten times larger than would be expected from the physical dimensions of the polymer chain, in order to avoid conflict with the experimental results for polystyrene. This conclusion is not restricted to the data of one investigator, for recently RossI, BIANCHI and BIANCHI (221) have found that [~/]oM -v, remains constant down to a molecular weight of 700 for polystyrene in toluenemethanol theta-solvent mixture. An entirely similar conclusion may be reached for other flexible chain polymers, including poly(ethylene oxide), I The function XF o (X) as tabulated in the original paper of KIRKWOOD and I~ISEMAN (139) is somewhat too large numerically.…”

Section: Intrinsic Viscositymentioning

confidence: 99%