Takenao Yoshizaki

Excluded-Volume Effects

This chapter deals with the theory of the excluded-volume effects in dilute solution, such as various kinds of expansion factors and the second and third virial coefficients, developed on the basis of the perturbed HW chain which enables us to take account of both effects of excluded volume and chain stiffness. Necessarily, the derived theory is no longer the two-parameter (TP) theory [1], but it may give an explanation of experimental results [2] obtained in this field since the late 1970s, which all indicate that the TP theory breaks down. There are also some causes other than chain stiffness that lead to its breakdown. On the experimental side, it has for long been a difficult task to determine accurately the expansion factors since it is impossible to determine directly unperturbed chain dimensions in good solvents. However, this has proved possible by extending the measurement range to the oligomer region where the excluded-volume effect disappears. Thus an extensive comparison of the new non-TP theory with experiment is made mainly using such experimental data recently obtained for several flexible polymers. As for semiflexible polymers with small excluded volume, some remarks are made without a detailed analysis.

Dynamics of spheroid‐cylindrical molecules in dilute solution

The dilute solution dynamics of spheroid–cylindrical molecules, i.e., straight cylinders with oblate, spherical, or prolate hemispheroid caps at the ends, is studied in detail. The translational and rotatory diffusion coefficients and the dynamic intrinsic viscosity are evaluated numerically for short cylinders by determining the frictional force by an orthodox method of classical hydrodynamics. For long cylinders, the Oseen–Burgers procedure is shown to be valid, and the results previously obtained by it are still useful. Thus, empirical interpolation formulas for the transport coefficients above are also constructed to be applied to spheroid–cylinders of arbitrary size. The end effects on the translational and rotatory diffusion coefficients are rather small, while the effect on the zero‐frequency intrinsic viscosity is remarkable, depending appreciably on the shape of the ends, though for relatively short cylinders. In general, for a rigid body of revolution having a plane of symmetry perpendicular to its axis, it is shown that the dynamic intrinsic viscosity may be expressed in terms of the zero‐frequency intrinsic viscosity, the rotatory diffusion coefficient about a principal axis in the symmetry plane, and a newly defined factor, which is also associated with the rotational motion about this axis.

Dynamics of helical wormlike chains. I. Dynamic model and diffusion equation

A model, called the discrete helical wormlike chain, is constructed to be suitable for the study of the dynamics of polymer chains, both flexible and stiff. It is a chain of N rigid sub‐bodies such that, apart from its location, its configuration may be specified by N sets of Euler angles, each associated with one sub‐body, and its equilibrium conformational behavior is almost identical with that of the continuous helical wormlike chain. It is shown that the model can simulate rather well several types of elementary motion of real chains, by evaluating the change in the potential energy caused by each motion. The configurational diffusion equation is then formulated. Following the procedure of Fixman, rigid constraints are imposed on the lengths of sub‐bodies (and hence on the total chain length) by setting the components of the flux associated with the constrained coordinates equal to zero through constraining forces, so that the diffusion equation and all configuration‐dependent properties may be writte...

Dynamics of helical worm-like chains. IV. Dielectric relaxation

Dielectric relaxation of both flexible and stiff chain polymers in dilute solution is studied on the basis of the discrete helical worm‐like chain such that an electric dipole moment is attached rigidly or with a rotational degree of freedom to each of the subbodies composing the chain. The complex dielectric constant is formulated with the dipole correlation function, which may be expressed in terms of the L=1 time‐correlation functions derived previously. Then, dielectrically active branches of the eigenvalue spectrum are identified for a given type of dipoles, and a mode analysis of them is made in order to inquire into the interaction between global and local modes. The decay behavior of the dipole correlation function is also examined numerically for various chains. A comparison of theory with experiment is made with respect to the dispersion and loss, and also the dielectric correlation time τD as determined from the loss peak. The theory cannot always well explain the asymmetry of the loss curve, e...

Is a Cloud-Point Curve in Aqueous Poly(N-isopropylacrylamide) Solution Binodal?

Transmittance of light passing through an aqueous solution of a linear poly(N-isopropylacrylamide) (PNIPA) sample synthesized by living anionic polymerization was examined in detail in the vicinity of its cloud point. It is found that the transmittance approaches a constant value between 0 and 100% even at a temperature slightly higher than the cloud point, indicating that macroscopic phase separation does not take place at the cloud point in the solution and therefore the cloud-point curve dose not correspond to the binodal. Static and dynamic light scattering measurements were then carried out for aqueous solutions of the linear sample and also of another one synthesized by radical polymerization, which has random-branched structure, at some temperatures considerably lower than the cloud point. It was found that both the PNIPA samples in aqueous solutions form aggregates even at such temperatures, and the number, size, and density profile of the aggregates depend on the kind of chain end group and also on the primary structure.

Validity of the superposition approximation in an application of the modified Oseen tensor to rigid polymers

The validity of the superposition approximation in the Kirkwood–Riseman formulation of polymer transport problems with the modified Oseen tensor is examined. For rigid polymers composed of spherical beads, the frictional forces exerted by them are obtained as the iterative solutions of coupled integral equations equivalent to the Stokes equation under the nonslip boundary condition. From a comparison with these exact solutions, it is found that the Kirkwood–Riseman formulation with the modified Oseen tensor gives correct results to terms of order σ3 in the case of uniform translation in a fluid at rest, but not for these terms in the case of uniform rotation in linear or vanishing flow, where σ is the ratio of the radius of the bead to the separation between the two.

A Monte Carlo study of effects of chain stiffness and chain ends on dilute solution behavior of polymers. II. Second virial coefficient

A Monte Carlo (MC) study is made of the second virial coefficient A2 for polymers using two freely rotating chains, each of bond angle 109°, with the Lennard-Jones 6-12 intramolecular and intermolecular potentials between beads in a cutoff version for the number of bonds in the chain ranging from 6 to 1000 in the Θ and good-solvent conditions. It is found that effects of chain ends on A2 are appreciable for small molecular weight M, as was expected, and that the second virial coefficient A2,Θ at the Θ temperature, at which the ratio 〈S2〉/M of the mean-square radius of gyration 〈S2〉 to M becomes a constant independent of M for very large M, remains slightly negative even for such large (but finite) M where the effects of chain ends disappear. Such behavior of A2,Θ, which cannot be explained within the framework of the binary cluster theory, is shown to be understandable if possible effects of three-segment interactions are considered. The present MC data for A2 (along with the previous ones for 〈S2〉) may t...

Dynamics of helical wormlike chains. II. Eigenvalue problems

A general solution of the eigenvalue problem for the representation of the diffusion operator of the discrete helical wormlike chain is presented. The problem is first, to a great extent, decoupled by transforming the basis set introduced previously to a standard representation which is formed by the eigenfunctions of the total angular momentum operator of the entire chain. In order to find the analytical solutions, the size of the problem thus reduced is further reduced by making two approximations: subspace approximation and block‐diagonal approximation. The former is equivalent to neglecting the memory term in the projection operator method, and the latter consists of introducing Fourier modes as in the conventional chain. The theory then predicts a number of branches of eigenvalue spectra. In fact, here, eight branches, in general, are derived explicitly. Among these, three are associated with dielectric relaxation, and the remaining five with fluorescence depolarization and nuclear magnetic spin rela...

Dynamics of helical worm‐like chains. VI. Fluorescence depolarization

Fluorescence depolarization of both flexible and stiff chain polymers in dilute solution is studied on the basis of the discrete helical worm‐like chain such that a fluorescent probe is attached rigidly or with a rotational degree of freedom to one of the subbodies composing the chain. The emission anisotropy r(t) and the average anisotropy r are formulated, considering in general the difference between the directions of absorption and emission dipoles. For flexible chains, proper account is also taken of the difference between the subbodies with and without the probe in size, and for stiff chains, e.g., DNA, effects of wobbling of the probe are considered. If the absorption and emission dipole moment vectors are parallel to each other, r(t) is equal to the magnetic autocorrelation function multiplied by a factor with the internuclear vector being regarded as the emission vector. Naturally, therefore, the results of analysis of experimental data for the present and magnetic cases are then consistent with...

Dynamics of helical wormlike chains. III. Eigenvalue spectra and time‐correlation functions

Some preliminary numerical results for the eigenvalue spectra and the time‐correlation functions computed from the formulas derived in the preceding paper (paper II) are presented. First, it is claimed that certain conditions must be imposed on the translational and rotatory friction coefficients ζt and ζr of each of the sub‐bodies comprising the model. The parameter ζt must lie in the range over which the diffusion matrix is positive definite. For the present model, the eigenvalues λ01,k in the lowest branch of the spectrum for the diffusion operator may possibly become negative at small wave numbers k because of the preaveraging approximation used. However, it is possible to make λ01,0 very small in magnitude, and thus to neglect it, by choosing ζr properly. For flexible chains, this enables one to remove the negative eigenvalues completely and recover the Rouse–Zimm values for λ01,k at small k in the coil limit in a very good approximation. Then, after the examination of the accuracy of the block‐diago...