A. TERAMOTO, R. OKADA, AND H. FUJITA Vol. 67 indicate that equation 4 instead of equation 5 should be used to evaluate the electrophoretic effect. Kay and Dye5 reached the same conclusion in their analysis of data for the alkali halides. These results also indicate that the inclusion of the (1 + FC) term cannot be used to explain the rather lorn d values obtained for the relatively large ions involvedo. For example, if 8 ( J ) for Bu4n'Cl is increased by 1 A. due to the inclusion of this term, A, as calculated from equation 4 would be 0.25 lower than the experimental value obtained from transference numbers. This is a significant difference and indicates that the same values of 8 would not fit both conductance and transference data. This result will cast considerable doubt on the validity of the 1 + FC term for nitromethane solutions if it is shown from viscosity measurements to be large. Since equation 4 rather than equation 5 appears to give the better evaluation of the electrophoretic effect, possibly a better method of handling equation 6 would be t o plot A* given by against C/(1 -~Y C~'~) using an initial value of d to calculate he if transference data are not available. From the slope J' a better value of d could be obtained and convergence should be rapid since he is insensitive to 8.The viscosity of a sample of poly-n-butyl methacrylate (PBMA) in diethyl phthalate (DEP) was measured, using six different kinds of viscometer, over the complete range of composition ( i e . , 0 to 100% in polymer weight fraction) and over the temperature range from 0 to 120'. Plots for the logarithm of viscosity os. weight fraction of polymer a t temperatures above 60' showed a curvature convex downward in the region approaching pure solid. This type of viscosity-concentration relation had not been observed in previous studies on other typical amorphous polymers, but is similar to that found very recently for polyethylene mixed with low molecular weight paraffin. The free volume theory of Fujita and Kishimoto for the viscosity of very concentrated solutions of an amorphous polymer has been modified so that effects of the density of chain entanglements may be taken into account. The assumption that the free volumes of polymer and plasticizer are additive has also been discarded. Instead, it has been assumed that the free volume of a given polymer-plasticizer mixture increases linearly with temperature. The free volume theory SO modified was found to account well for experimental data in the region where the volume fraction of DEP is snialler than about 0.2. Beyond this limit the analysis in terms of the modified theory led to an anomalous conclusion that the dilution of the density of chain entanglements produces an increase of the viscosity of this polymer-plasticizer system. This appears to indicate that the range of concentration in which the free volume theory may be applied may not be as wide as so far supposed.
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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