The topotactic insertion reaction of lithium ions with X-Mn02 was investigated in LiCl + LiOH solutions. The insertion of lithium ions involved a consumption of a nearly equivalent amount of hydroxyl ions in the aqueous phase, as well as an evolution of about a 90% equivalent amount of oxygen gas. Chemical analyses of the Li+-inserted samples showed that this insertion involved a reduction of Mn(IV) to Mn(III). The major reaction of Li+ insertion could be represented from these results not by an ion exchange but by a new type of redox mechanism: Mn02 + xLiOH -* LiIMn02 + (x/2)H20 + (x/4)02, where x is the number of moles of inserted lithium per mole of manganese. An X-ray diffraction analysis showed that the insertion of lithium ions proceeded topotactically, involving an increase in the lattice constant (o0) of a spinel structure. A new phase, having a slightly larger o0 value than that of X-Mn02, was observed for samples with Li/Mn ratios between 0.08 and 0.2. The a0 value of the new phase increased monotonously with an increase in the Li/Mn ratio in the range Li/Mn > 0.2. The electrode potential vs log CLi plot for the Li+-inserted sample (Li/Mn = 0.32) gave a straight line with a near-Nernstian slope (0.060 V/log CL¡) at pH 8.3; the electrode potentials were nearly constant, independent of the metal ion concentration in the case of sodium or potassium ions. The electrode potential in a 0.1 M LiCl (1 = 1 mol dm"3) solution decreased with an increase in the Li/Mn ratio of the sample. The potential response to the Li/Mn ratio could be well correlated with the change in the crystal phase of the sample.

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A sample of copolymer of styrene and l,4-divinyl-2,3,5,6-tetrachlorobenzene was prepared and fractionated. Using the fractionated copolymers, effects of chain branching on the intrinsic viscosity and sedimentation coefficient were studied experimentally. It was found that in both theta and good solvents, the intrinsic viscosity of the branched polymers obeyed a new semiempirical relationship, [1/]b=g0 · 6 [17]i. Here [1/h is the intrinsic viscosity of a linear polymer having the same molecular weight as the branched one and g is the contraction factor which is defined as the ratio of the mean-square radii of gyration between the branched and linear polymers, i.e., g=(S 2 )b/(S 2 )1. It was also found that the sedimentation coefficient in theta solvent agreed with the theoretical value obtained by Kurata and Fukatsu. The degree of branching estimated from the intrinsic viscosity or sedimentation coefficient was in close agreement with the value estimated from consideration of the copolymerization kinetics.KEY WORDS Branched Polymer / Polystyrene / Degree of Chain Branching / Intrinsic Viscosity / Sedimentation Coefficient / MeanSquare Radius of Gyration / Theta Solvent / Zimm-Stockmayer Theory / Kurata-Fukatsu Theory / In this series of papers, we report the results of a systematic study which has been performed to develop a quick and simple method of estimating the degree of long-chain branching in a polymer molecule.According to Zimm and Stockmayer, 1 the effect of chain branching on the molecular dimension in solution is expressed aswhere

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