The viscosit ies of solut ions of t hree polysty rene fractions in t hree solve nts of v ar y ing solvent power were m easured at t wo temperat ures. The relat ive vi scosit ies of the syst em s investigated ranged from 1.03 to 43.The appli cability of two empirical expressions for the concen tration depende nce, nam ely t he Martin equation and t he Baker relation, is examined . In addit ion, t he results are represented by m eans of poly nomials of suitable degr ee. The numerical procedures for t he e valuatio n of t he coeffi cien ts are discussed in detail. In t he concent ration r an ge investigated , t he in troduction of a reduced co ncen t rat ion scale S = ['1] c, places t he viscosity-con cen t ration curves for different molec ular weights in t he same solven t on a more nearly common scale. This scale, S, is simply rela ted t o another reduced scale c/co. H ere Co represen ts t he concentration a t which t he equivalent spher es of t he coiling m olec ul es, a s d efin ed at infinite dilu tion, would just begin to o verlap . At c/co « 1, t he con cent ration dependence can be described in terms of hydrody namic in teract ion. This intera ction involves single molecul es and can also involve t he int rinsic v iscosity and interactions of aggregates of low order . An a ttempt is made t o d educe from t he viscosi ty data and on t he basis of cer tain hydrody namic results, t he equilibrium constant s and relative p opulations of s uch aggregates. R easonable values are obt ained . On approaching Co, t he a verage volume a vailable t o a chain molec ule in a good solve nt is redu ced because of t he cage form ed by its nearest neighbors. The effective press ure is just t he internal osmo tic press ure. This leads to an expression for t he concent rat ion depe ndence of t he viscosi ty, in terms of t he vi rial coeffi cie nts of osmotic press ure, luolec ular weight, and size. These equat ions are s hown to be in satisfactory agreemen t wi t h t he experimen tal data. In part icul ar , in t he neighborhood of Co one obtains r easo nabl e values for t he molec ular exte nsio n f actors of t he chain .
Intrinsic viscosities of dextrans of known branching ratio were measured in water formamide, and in a water‐methanol mixture at two temperatures. Weight‐average molecular weights (sedimentation equilibrium) ranged from 1.1 × 104 to 1.7 × 106. A model for the hydrolyzed dextran molecule was assumed. Using the methods of Zimm and Stockmayer, the g factor calculated from this model was compared with the g factor obtained from the intrinsic viscosity‐molecular weight data through the use of the Flory‐Fox theory (g = ratio of squares of radii of gyration of branched to unbranched polymer). The calculated branch lengths required to make consistent the g factors obtained by two different routes were of the same order of magnitude as those found by classical organic chemical methods for other dextran preparations. The intrinsic viscosity‐molecular weight relation at 25°C. in water for linear dextran was predicted from the data. It is suggested that investigations of branched polymers of known constitution be carried out by these methods.
The object of this paper is to present methods for quantitative evaluation of branching in polymers from intrinsic viscosity data. In a previous article: measurements of intrinsic viscosity and molecular weight of B-512 dextrant hydrolyzates were performed under a variety of conditions of solvent and temperature.Simiiar measurements on a dextran produced by another strain of Leuconostoc (NRRL culture B-742) will be presented here. The B-742 dextran difTers from the B-512 dextran in that it is more highly branched. Structural parameters of the two dextrans will be presented and the results compared.To summarize briefly the methods employed to analyze the data, one has from the Flory-Fox theory2 for any chain polymer. Here R is a constant independent of solvent and molecular weight; a is an expansion factor which allows for the effect of the solvent and the volume effect on the volume pervaded by the segments of the chain; and g is the ratio of the squares of the unperturbed radii of gyration' of branched and unbranched molecules having the same chemical constitution.For linear molecules, g 7 1. At the temperature T = 8, where a = 1, and the second virial coefficient is zero, [q] = K M " p (3) as M becomes small, g approaches 1. If we plot [ . M Mi [TI us. -a t T = 8, we obtain A?' ' for an intercept at M = 0. For linear polymers, the slope of this curve is zero, For branched polymers, it is always negative. Then at any value of M, [e g = --Mi (ordinate) (4) Rg -(intercept) Similar methods have been used in studying branched polystyrenes.' The authors are grateful to Florence R. McCann, Louis C. W-illiams, and D. R. Sears for assistance in some rimental work. by Leuconostoc Mesenteroides, B-512 culture (Northern Regional Research Laboratory). 353
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