Analysis of intrinsic viscosity data

Abstract

In order to interpret quantitatively intrinsic viscosity data for polymer solutions, especially for chains of poor flexibility, the partially free draining effect discussed in the theories of Kirkwood and Riseman and Debye and Bueche must be also taken into account, as well as the excluded volume effect considered in the theory of Flory and Fox. Although the Flory‐Fox theory is widely used at present for analysis of intrinsic viscosity data, it appears that in most actual cases the draining effect may also play an important part and the two effects may overlap each other to some extent. A new method has been presented in this paper, through which the separation of these tow contributions becomes possible. The exponent a in the Mark‐Houwink equation, [η] = KmM̄va, is divided into two parts: a1, related to the volume effect, and Δ, related to the draining effect. Making use of the theoretical relationship between Km and a, which was derived in the preceding paper, we can calculate the value of Δ, if the Mark‐Houwink constants have been established for a given series of polymer homologues in two solvents. In this way, we can discuss the volume effect and the draining effect separately, and interpret completely intrinsic viscosity data in terms of the parameters appearing in the Flory‐Fox and Kirkwood‐Riseman theories. Furthermore, a new method has been proposed for estimating the Mark‐Houwink constants from the measurements of intrinsic viscosity and molecular weight for a single sample. Only one sample need be used, and thus recourse to the usual more laborious methods is unnecessary. General applicability of our methods has been shown by several examples cited from published data.

On the partially free draining effect in the intrinsic viscosity and sedimentation coefficient of cellulose nitrate solution

“…11 &Ma (1) where K, and a are parameters characteristic for the polymer-solvent system a t a given temperature. yields the following equation between K, and a ; -log Km + log [l + 2((u -0.5)-l -2}-1] = -log K + (a -0.5) log Mo (4) with where [r] 0 is the intrinsic viscosity in a theta solvent, f 2 and F : represent the mean-square end to end distance of the chain in non-ideal and theta (ideal) solvents, respectively, 00 the FLORY viscosity constant in theta solvents, B the long range interaction parameter, Mo a parameter depending on the molecular weight range, Ml-Mz, to which Eq.…”

The draining effect in viscosity and sedimentation for cellulose trinitrate solutions

“…Molecular weight M dependence of intrinsic viscosity can be expressed i. 11 &Ma (1) where K, and a are parameters characteristic for the polymer-solvent system a t a given temperature. yields the following equation between K, and a ; -log Km + log [l + 2((u -0.5)-l -2}-1] = -log K + (a -0.5) log Mo (4) with where [r] 0 is the intrinsic viscosity in a theta solvent, f 2 and F : represent the mean-square end to end distance of the chain in non-ideal and theta (ideal) solvents, respectively, 00 the FLORY viscosity constant in theta solvents, B the long range interaction parameter, Mo a parameter depending on the molecular weight range, Ml-Mz, to which Eq.…”

Single sample methods for estimating the parameters of the Mark-Houwink equation

“…If values of A and / are known values of a and Km can be obtained by use of eqs. [9] and [7] respectively. With this method it can usually be assumed that _~ = Mo, implying that M o is representative of a certain molecular weight range the midpoint of which is the measured molecular weight.…”

“…The term (a -1/2) (log _M~ -log 3/o) in eqs. [8] and [9] then vanishes and the calculation is considerably simplified.…”

“…It is assumed that the draining effect (i. e. A and f) is independent of the solvent. This may not be strictly true but this assumption should not lead to serious errors (9). (f) In applying the three methods it has been assumed that homogeneous fractions are used so that ~n=~w=_M,,.…”