Daichi Ida

Mean-Square Radius of Gyration and Scattering Function of Semiflexible Ring Polymers of the Trefoil Knot

A Monte Carlo study of the mean-square radius of gyration Rg2 and scattering function P(k) with k the magnitude of the scattering vector for semiflexible ring polymers of the trefoil knot was conducted by the use of the discrete version of the Kratky–Porod (KP) wormlike ring model. The behavior of Rg2 and P(k) as functions of the reduced contour length λL, defined as the total contour length L divided by the stiffness parameter λ−1, is clarified. A comparison is made of the results for the KP ring of the trefoil knot with those for the KP ring of the trivial knot and for the phantom KP ring without the topological constraints.

Difference in dilute aqueous solution behavior between poly(ethylene glycol) and poly(ethylene oxide)

AbstractStatic light scattering behavior was examined for poly(ethylene glycol) (PEG) and poly(ethylene oxide) (PEO) of small weight-average molecular weight Mw (3 × 103−2 × 104), in methanol and water at 25.0 °C, the former polymer having hydroxy groups at both ends and the latter having a methoxy group at one end and a hydroxy group at the other. It was found that some aggregates of large size are formed in aqueous solutions of the PEO samples with Mw = 3.81 × 103 and 7.00 × 103, while all PEG and PEO samples are isolated in methanol solutions, and the PEG samples and the PEO sample of the largest Mw (=1.60 × 104) are also isolated even in the aqueous solutions. From the results of dynamic light scattering measurements for the aqueous solution of the PEO sample with Mw = 3.81 × 103 at 25.0 °C, there were detected two classes of scatterers having different sizes, i.e., the isolated chains and aggregates, the apparent hydrodynamic radius of the latter being ca. twenty times as large as that of the former.Static light scattering measurements are carried out for poly(ethylene glycol) and poly(ethylene oxide) (PEO) of the weight-average molecular weight Mw ranging from 3×103 to 2×104 in methanol and water at 25.0 °C. Some aggregates of large size are found to be formed only in the cases of PEO of Mw∼O(103) in aqueous solutions, although for other cases polymer chains are isolated in solutions.

A picture of dilute solution behavior of polymers through polyelectrolyte simulation

A Monte Carlo (MC) study is made of the persistence length q and the binary cluster integral β (or the excluded-volume strength B) for polyelectrolytes by the use of the discrete Kratky-Porod wormlike chain with hard-core-effective Debye-Hückel electrostatic pair potentials. The quantity q is determined from the initial decay rate of the bond correlation function after preliminary confirmation of the validity of this procedure using the chain with Lennard-Jones pair potentials. The quantity B is determined from the mean-square radius of gyration along with q by the use of the quasi-two-parameter (QTP) excluded-volume theory. They are evaluated for two model cases of polyelectrolytes, sodium hyaluronate as an example of semiflexible polymers and poly(sodium 4-styrenesulfonate) as a typical example of flexible polymers, both in aqueous sodium chloride. The behavior of MC data so obtained for q and B as functions of added salt concentration c is examined in detail, comparing them with the Odijk-Skolnick-Fixman theory of q and the Fixman-Skolnick (FS) theory of B and also with literature experimental data. In particular, the MC values of B are in almost complete agreement with the FS theory for large c, although the latter still overestimates B somewhat for small c. The values of B themselves and also the validity of the QTP theory in general are discussed in comparison with the case of nonionic polymers.

Some comments on the second virial coefficient of semiflexible polymers

A Monte Carlo study is made of the mean-square radius of gyration S(2) and second virial coefficient A(2) for the two freely rotating chains with the Lennard-Jones (LJ) 6-12 potential and the hard-sphere (HS) one in the range of the bond angle theta from 109 degrees (typical flexible chain) to 175 degrees (typical semiflexible or stiff chain) and in the range of the number n of bonds from 6 to 1000. It is shown that a value may be properly assigned to the collision diameter of the HS potential so that S(2) of the chain with the HS potential agrees well with that of the chain with the LJ one whose parameter values correspond to a good-solvent condition irrespective of the chain stiffness. It is then found that A(2) of the latter chain becomes remarkably smaller than that of the former as the chain stiffness is increased. The result implies that the binary-cluster approximation does not seem to work well for typical semiflexible and stiff polymers.