In the previous papers
(1) we proposed the methods of determining the extension of high polymer from the intrinsic viscosity [η] of its solution: When we take the volume exclusion effect of the chain elements into account, the assumption of mathematical elements is to be discarded, so that the root mean square end-to-end distance of high polymer is to be written as
γ=αbN
1/2where b means the effective bond length, N the degree of polymerization, and α the factor giving the ratio of the extension of real chain to that of mathematical chain. The distribution of the chain elements is postulated so that the above expression may be deduced from it. Then by making use of the relation connecting [η] with equivalent radius R and shielding ratio φ:
[η]=f(R, φ)
and the assumptions for φ and α (after Flory), we can determine the equivalent radius (R) or the end-to-end distance (γ=αbN
1/2) of the chain.
The assumptions for φ and α have been proved to be valid for some special high polymer solutions, but not for all solutions. The best way to establish a method that can be employed for any sort of high polymer solution, is therefore, to eliminate such arbitrary assumptions or, if necessary, to use only there assumptions which can generally be accepted.
The Eight-scattering method here described is the one which answers this purpose. The result, briefly stated, is that if we rewrite the expression γ=αbN
1/2 in the from
γ
2=C
2N
γ2regarding α as the function of N, we obtain for the angular distribution of the scattered light intensity I(θ):
limC→0I(θ)/C=2KM/N
2∫
N0(N-Z)e-uc
2z
γ2dZ
with u=8π
2/3λ
2sin
2θ/2
where C is the concentration of solution M the molecular weight and K a constant factor. With the aid of this relation we can get C
2 and γ
2 and therefore γ from the measurement of I (θ).
(1) H. Mizutani: Busseiron Kenkyu No. 76 (1954)
H. Mizutani: Busseiron Kenkyu No. 82 (1955)
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