# The determination of molecular weights of polymers from critical concentrations of ternary systems polymer-polymer-solvent.

код для вставкиСкачатьDie Angewandte Makromolekulare Chemie 6 (1969) 156-160 (Nr. 65) From the Polymer Institute, Slovak Academy of Sciences, Bratislava, CSSR The Determination of Molecular Weights of Polymers from Critical Concentrations of Ternary Systems Polymer-PolymerSolvent* By DUEANBEREK,BRANISLAV BOHMER and DIETERLATH (Eingegangenam 29. Oktober 1968) SUMMARY: The dependence of the critical concentration of the ternary system polymerpolymer-solvent on the molecular weight can be expressed by the relation CC = AE-213 + ccm where cc is the critical concentration, the appropriate average of the molecular weight of both polymers; A and cCmare constants for the given system. The possibility of determining the molecular weight of one of the polymers from the value cc and the molecular weight of the known polymer with the aid of equation (1) is discussed. ZUSAMMENFASSUNG : Die Abhhgigkeit der kritischen Konzentration des ternaren Systems PolymerPolymer-Losungsmittel vom Molekulargewicht kann mittels der folgenden Gleichung ausgedriickt werden : cC = AE-213 ccm + cc ist die kritische Konzentration, der geeignete Mittelwert der Molekulargewichte der beiden Polymeren; A und ccm sind Konstanten fur das gegebene System. Es wird die Moglichkeit erortert, aus cc und dem Molekulargewicht des bekannten Polymeren - mit Hilfe der Gleichung (1) das Molekulargewicht des zweiten Polymeren zu bestimmen. The idea of assessing molecular weights of polymers from phase relationships of ternary systems polymer-polymer-solvent is as old as the study of the phenomenon of phase separation in the mentioned systems. * Presented at the Conference on Chemical Transformation of Polymers, Bratislava, 1968. 156 Determination of Molecular Weights DOBRYand BOYER-KAWENOKI~ suggested an approximative determination of molecular weights from phase volumes after separation of the ternary system containing incompatible polymers. Their idea was later developed by LIPATOV~. Simplifying assumptions proposed by the mentioned authors lead to the conclusion that the ratio of phase volumes of separated systems would be proportional t o the reciprocal ratio of molecular weights of the polymers in the system. Using a standard polymer as one component, it would be easy t o determine the molecular weight of the other macromolecular substance. Practical utilization of this procedure and its more complicated versions is hindered mainly by the fact that the parameters of the phase equilibrium of the ternary systems polymer-polymer-solvent are, to a great extent, influenced by polydispersity of the macromolecular substances3. That is why it appears to be more convenient to use the values of critical concentrations of the systems polymer-polymer-solvent (cc) for the determination of polymer molecular weights. Recently we founds, 5 that for numerous ternary systems in a wide range of polymer molecular weights it can be stated cC = AM413 + cCm (1) where A and ccooare the constants for the given system and average of the molecular weights of both polymers : - M= represents the a+= (M2 x M3)0.5, or _M =-Mm = Yz M2 + Y3 Ms where M2 and M3 are the molecular weights of the polymers (components 2 and 3) and Yi signifies the relative weight fraction of the polymer component i defined by where wi means the weight fraction of the polymer i in the system and w1 the weight fraction of the solvent. By substituting in relations (1) and (2) the experimentally determined critical concentration of an adequately selected and calibrated ternary system we are able to calculate the value of molecular weight Mi, if Mj is known. The dependence (1) (M = Mm ; Mi = Ii?, (viscosity average molecular weight)) for the system polypropylene polystyrene toluene is shown in Fig. 1. The respective values A and cCmare A = 6.55 x 103; cca, = 0.6 g x d-1,and the corresponding correlation coefficient is 0.9912. It appears that the sensitivity of the method is sufficient for normal routine molecular weight determinations although the results are to a small extent influenced by the polydispersity of the respective polymers. The values Mi can be substituted + + 157 D. BEREK, B. BOHMER and D. LATH I I I I 0 5 10 15 I - -21 I 20 'Ym'3 7c4 Fig. 1. The dependence of the critical concentration of the ternary systems polypropylene-polystyrene-toluene (atactic polymers) on weight average molecular weights of polymers. The values Mw/Mn = R for systems marked by numbers are aa follows : Point 1: 2: 3: 4: 5: Rpp 1.41, 1.41, 1.41, 1.41, 1.37, RPS 2.67; 2.11; 1.80; 1.67; 1.61 ; 6: , 7: 8: 9: 10: Rpp 1.41, 3.65, 3.41, 3.65, 2.85, RPS 1.44; 1.61; 2.27; 2.27; 1.46. by number or weight etc. averages of the molecular weights of polymers using different values of A and cCm for any kind of molecular weight average. When applying the proposed simple method of determination of values of critical concentration5 we proceed from molar volumes of polymers (Vi): from equation (3), resulting from SCOTT'Sconsiderations6 we can calculate the ratio of the theoretical critical volume fractions (vie) of polymers in the system. The optically determined limiting miscible concentration of ternary systems containing the polymers in the theoretical critical representation can be considered in good approximation with the proper critical concentration of the systems. 168 Determination of Molecular Weights I n our case one of the Vi values is unknown. Therefore, we must first estimate the molecular weight of the polymer examined and then - based on the obtained results - carry out one or more re-determinations. Under such conditions the accuracy of the determined molecular weight will be better than & 15% depending on the molecular weight range and calibration accuracy. For purposes of more approximate but speedy molecular weight determinations, however, the determination of limiting miscible concentrations of ternary systems containing equal weight portions of both polymers (Yi = 0.5) is sufficient. Such procedure is particularly suitable for polydisperse polymers, where values of limiting miscible concentrations are often less changing with relative concentration of the polymers in the system335. For in equation (1) it then seems to be better to use the geometric mean value a (a+). The proposed method of the polymer molecular weight determination is unpretentious with respect to time, experimental equipment and sample consumption (0.1g). It could be applied particularly in routine series analyses preferably in the range of lower molecular weights (104- 3 . 104) and for the determination of molecular weights of copolymers. (In this case, increased attention is to be given to the selection of the solvent and reference polymer because of the influence of chemical composition of the copolymer on critical concentration of the ternary system.) The method can also be of use for direct analysis of polymer mixtures, production of which is a t present steadily growing. Experimental Experimental data on purification, on fractionation, and on viscosity molecular weight determination of polymers as well aa on determination of limiting miscible concentrations have been described395. The values of were calculated from the relation [q] = K-a calibrated by light scattering (polypropylenepoints 5,107, polystyrene points 1, 2, 3, 4, 5, 6, 7, lo*), those of P,, were calculated from fractionation data (polypropylenepoints 1, 2,3, 4, 5, 6, 7, 8, 9,polystyrene points 8,9). The other values of H, were determined osmometrically (static osmometers with Ultracella “allerfeinst” membranes Sartorius Membranfilter, Gottingen) in toluene at 30°C. zw 1 2 3 4 A. DOBRY and F. BOYER-KAWENOKI, J. Polymer Sci. 2 (1947)90. S.M.LIPATOV, Kolloid-J. 22 (1960)639. D.BEREK,D. LATHand V. ~ ~ U R ~ O VJ.I Polymer ~ , Sci. C 16 (1967)659. F.BURKHARDT, H. MAJERand W. KUHN,Helv. chim. Acta 43 (1960)1192. 159 D. BEREK,B. BOHMER and D. LATH 5 6 7 8 D. BEREK,B. BOHMER and D. LATH,Plaste und Kautschuk 14 (1967) 556. R. L. Scow, J. chem. Physics 17 (1949) 279. 8. FLORI~N, Polymer Institute SAV, unpublished results. M. I ~ R A Tand A W. H. STOCKMAYER, Fortschr. Hochpolymeren-Forsch.3 (1963) 196. 160

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