. The Bell System technical journal . s with increase in the number of chain elements andat the high molecular weight viscosity range where the viscosity showsa dispersion in values but the model does not. The sum of the two vis- 1 These results on the mechanical impedance of long chain molecules in sol-vents have been presented at the Xllth International Congress of Pure andApplied Chemistry by W. O. Baker, W. P. Mason and J. H. Heiss, Sept. 13, 1951. MECHANICAL PROrEKTIES OF POLYMERS 143 cosities -qi and 772 assumed as a function of molecular weight is shown byFig. 16. The log of the viscosi
. The Bell System technical journal . s with increase in the number of chain elements andat the high molecular weight viscosity range where the viscosity showsa dispersion in values but the model does not. The sum of the two vis- 1 These results on the mechanical impedance of long chain molecules in sol-vents have been presented at the Xllth International Congress of Pure andApplied Chemistry by W. O. Baker, W. P. Mason and J. H. Heiss, Sept. 13, 1951. MECHANICAL PROrEKTIES OF POLYMERS 143 cosities -qi and 772 assumed as a function of molecular weight is shown byFig. 16. The log of the viscosity starts proportional to the molecularweight but above a molecular weight of 2,400 the increase is very slowand becomes asymptotic to a value of 240 poises. An ecjuation whichfits the increase in viscosity with molecular weight is T 11-8 tanh Z/2370 Vd = Ac \\here Z is the molecular weight. The solid line shows a plot of this curveand the circles are the assumed values to obtain a best fit to the meas- MOLECULAR WEIGHT4000 6000 8000. 40 80 120 160 200 NUMBER OF CHAIN ELEMENTS ^ Fig. 15— values of high frequency shear viscosity and ehisticity for25°C and three fretjuencies plotted against molecular weight. Solid lines are bestfit obtained by a two relaxation mechanism having the element values shown bythe figure. 144 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1952 ured values. This equation indicates that when Z = 2,370 or 43 chainelements the viscosity increases only a small amount more by a chainarticulation effect and hence in this high frequency range we are dealingwith a chain length of about 40 elements or 80 carbon atoms. This ischecked also by a comparison of the static and dynamic viscosity. Thetotal dynamic viscosity due to the two relaxation mechanisms comparedto the static viscosity does not differ markedly until the number ofchain elements is more than 40. Above this value other motions thanthat of the shortest chain segment can take place and can add t
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