ABSTRACT:The effect of the excluded volume on the dynamics of a polymer chain is studied, using a stochastic jump model introduced by Orwoll and Stockmayer. The relaxation time of the normal mode of the averaged position vectors is obtained as 'tp-1=1:p101-1(1-Cpz) where 1:p1o1 is the relaxation time in the absence of the excluded volume effect, z is the usual excluded volume parameter, and Cp is a constant depending on the mode number p. The slowing down is not so large as in the computer simulation by Verdier. Further, the autocorrelation function of the normal mode of the averaged position vectors is shown to be a simple exponential function, in contrast to the nonexponential form used by Verdier. These differences are due partly to the particularity of the lattice model used by Verdier and partly to the approximations we have used.KEY WORDS Excluded Volume Effect/ Relaxation Time / Slowing Down / Freely Jointed Chain Model / Lattice Model / A polymer molecule in solution suffers frictional as well as random forces from surrounding solvent molecules and moves irregularly. To investigate the effect of such Brownian motion on the dynamics of a polymer molecule, a bead-and-spring model was proposed by Rouse 1 in 1953 and independently by Bueche 2 in 1954. This model was improved so as to take account of the hydrodynamic interaction 3 -7 and of the excluded volume effect. 5 -7 In regard to the excluded volume effect, however, the theory is still not satisfactory, as will be mentioned later. On the other hand, Verdier and Stockmayer 8 presented a stochastic jump model on a cubic lattice to study the dynamics of a polymer in solution by computer simulation. Later Verdier 9 investigated this model precisely and found that in the absence of the excluded volume effect the relaxation curve of the autocorrelation function of the end-to-end distance is quite similar to that of the Rouse model. Verdier 10 confirmed this agreement by calculating numerically the autocorrelation function of the square of the normal mode of the position vectors. This agreement was also explained analytically by Iwata and Kurata 11 for the lattice model and by Orwoll and Stockmayer 12 and by Verdier 13 for the freely jointed chain. The latter model will be explained in the next section.The effect of the excluded volume on the dynamics of a polymer is not as well understood as is the effect of the excluded volume on the equilibrium polymer configurations. The excluded volume effect on the polymer dynamics was investigated by Tschoegl 4 in the Rouse model only indirectly, through the introduction of a nongaussian distribution of the lengths between consective beads. Verdier and his coworkers8-10 · 14 made a computer simulation of the dynamics of a lattice polymer by taking account of the excluded volume effect in such a way that a bead cannot make a jump into a position which is already occupied by another bead. The purpose of this paper is to investigate analytically the effect of the excluded volume on the dynamics of a polymer in solu-601

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Semidilute poor solvent polymer solution is investigated by the method of Ursell-Mayer cluster expansion. Series and ring-form diagrams are considered for polymers to calculate the osmotic equation of state of the solution, and this equation is shown to be the same as obtained by Edwards by a different method. The static structure factor, which is the Fourier transform of the correlation function of the system, is also calculated in the same approximation; the first term of this factor corresponds to the Jannink-de Gennes result by the random phase approximation. The osmotic compressibility equation, which connects the osmotic pressure and the correlation function, is considered to check the consistency of our results and confirm the validity of the present approximation. Effects of the excluded volume on the equation of state and on the structure factor are investigated up to the first order of the excluded volume parameter z. It is shown that the excluded volume does not affect the osmotic equation of state as well as the structure factor in this approximation.

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