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

Yamakawa, Hiromi; Yoshizaki, Takenao

doi:10.1063/1.1579682

Cited by 27 publications

(40 citation statements)

References 32 publications

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“…On the other hand, A 2 can be formulated also by the cluster expansion theory for the helical wormlike beads model. 3,22,23 Retaining the first order terms of the binary and ternary cluster integrals, we can write…”

Section: Theoriesmentioning

confidence: 99%

“…The function IðNÞ of the reduced contour length N (¼ M=M L ) was recently calculated by Yamakawa and Yoshizaki. 23 In eq 16, the B 2 term is the single-contact one, and the B 3 term represents the three-segment interaction between two chains which involves two segments of one chain and one segment of the other chain interacting at a point (a special case of double-contact interactions). The double-contact term with B 3 is not included in eq 14.…”

Section: Theoriesmentioning

confidence: 99%

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Repulsive and Attractive Interactions between Polystyrene Chains in a Poor Solvent

Oribe

Sato

2004

Polym J

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ABSTRACT:The osmotic compressibility up to high concentrations as well as the second virial coefficient were measured for low molecular weight polystyrenes dissolved in a poor solvent cyclohexane at 35, 25, and 15 C, by sedimentation equilibrium. The results of the osmotic compressibility over wide concentration ranges were favorably compared with a recently developed thermodynamic perturbation theory based on the spherocylinder model bearing a square-well potential, and from the comparison, the hard-core diameter d and the depth " of the attractive square-well potential including in the theory were determined for polystyrene in cyclohexane. Compared with the previous results of d and " for the same polymer in 15 C toluene (a good solvent), it turned out that " increases and d decreases with reducing the solvent quality. [DOI 10.1295/polymj.36.747] KEY WORDS Polystyrene / Osmotic Compressibility / Second Virial Coefficient / Sedimentation Equilibrium / Thermodynamic Perturbation Theory / The distribution function theories for polymer solutions 1-3 express the polymer intermolecular interaction in terms of the potential U 12 ð1; 2Þ of mean force, where the arguments 1 and 2 represent all coordinates specifying the position, orientation, and conformation of polymer chains 1 and 2, respectively. If the polymer chain is divided into N 0 identical (spherical) segments, U 12 ð1; 2Þ may be given bywhere uðR i 1 i 2 Þ is the pair potential of mean force between segments i 1 and i 2 belonging to polymer chains 1 and 2, respectively, which is a function of the distance R i 1 i 2 of the two segments. For neutral polymers, the potential uðR i 1 i 2 Þ consists of short-ranged repulsive and long-ranged attractive interaction parts. The two-parameter theory 1-3 and also the renormalization-group theory 4-7 assume that the intermolecular excluded volume effect on the virial coefficients and the osmotic pressure can be expressed as a function of the binary cluster integral 2 defined by 2 4(k B : the Boltzmann constant; T: the absolute temperature) instead of the full function of uðRÞ. However, this assumption does not necessarily hold. Near the theta condition where 2 vanishes, the ternary cluster integral or the three-segment interaction becomes important in virial coefficients against the two-parameter theory. 8 When the polymer concentration is beyond the semidilute regime, the osmotic pressure or the osmotic compressibility cannot be described by the renormalization-group theory. Alternatively, the thermodynamic perturbation theory chooses a system of particles interacting by the hard-core potential as a reference system, and treats the long-ranged attractive interaction in a perturbative way. For example, Barker and Henderson proposed a perturbation theory for the system of spherical particles with a square-well potential. Their theory includes all perturbation terms using the Padé approximation. Recently, Koyama and Sato 10 extended the Barker-Henderson theory to the wormlike spherocylinder system. In the theory, the i...

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Section: Theoriesmentioning

confidence: 99%

Section: Theoriesmentioning

confidence: 99%

Repulsive and Attractive Interactions between Polystyrene Chains in a Poor Solvent

Oribe

Sato

2004

Polym J

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“…The conventional TP theory [10] of A 2 predicts the interpenetration function C appearing in A 2 to be a function only of z, as in the cases of the expansion factors. On the other hand, the theory [1,27,28] of A 2 based on the HW chain model predicts that C is not a function only of z norz because of chain stiffness, and also that the dependence of A 2 on M is remarkably affected, especially for small M, by a chemical difference of the chain ends from the inner parts of the chain. The main purpose of this subsection is to confirm the validity of the HW theory of A 2 for a-PaMS and a-PS.…”

Section: Second Virial Coefficientmentioning

confidence: 99%

Fine characterization of oligomers and polymers in dilute solution

Osa

2006

Science and Technology of Advanced Materials

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A fine characterization was made of atactic poly(a-methylstyrene) and atactic polystyrene on the basis of the helical wormlike chain model. It is found that there is a remarkable difference in chain stiffness and local chain conformation between the two polymers. Such a difference is shown to be reflected clearly in behavior of equilibrium, transport, and dynamical properties and also in the excludedvolume effects. r

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“…2 Â 10 À16 for 0 R < c , where T Ã is the reduced temperature defined by T Ã ¼ k B T= . Further, we put ¼ 1 for simplicity, as previously 13,14 done.…”

Section: Modelmentioning

confidence: 99%

“…The regular three-arm star chain model used in this study is essentially the same as that used in previous MC studies 13,14 of hS 2 i and the second virial coefficient of linear chains with intra-and intermolecular excluded volume, i.e., the freely rotating chain 3,11 with a cutoff version of the Lennard-Jones (LJ) 6-12 potential 15 between beads. On the basis of sets of sample configurations generated by the use of the Metropolis method 16 with the pivot algorithm [17][18][19] for the regular three-arm star and linear chains, both having the same total chain length, the values of ½ for the two kinds of chains and then the ratio g of the former ½ value to the latter may be evaluated.…”

mentioning

confidence: 99%

A Monte Carlo Study of the Intrinsic Viscosity of Semiflexible Regular Three-Arm Star Polymers

Ida

Yoshizaki

2007

Polym J

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ABSTRACT:A Monte Carlo (MC) study is made of the intrinsic viscosity ½ and also of the mean-square radius of gyration hS 2 i for regular three-arm star freely rotating chains of bond angles ¼ 109 , 165 , and 175 and with the Lennard-Jones 6-12 potentials between beads having the parameter values corresponding to the Â temperature, in the range of the total number n of bonds in the chain from 60 to 300. Three kinds of approximate values of ½ are calculated by the use of the Kirkwood-Riseman (KR) approximation, the Zimm rigid-body ensemble approximation which gives an upper bound ½ (U) to ½ , and by the Fixman method which gives a lower bound ½ (L) , the KR value of ½ being designated ½ (KR) . On the basis of the three kinds of MC values of ½ so obtained, the behavior of the ratio g of ½ for the star chain to that for the linear one, both having the same n, is examined as a function of the reduced contour length L as defined as the total contour length L of the corresponding Kratky-Porod (KP) wormlike chain divided by its stiffness parameter À1 , the values of L having been determined from an analysis of the present and previous MC data for hS 2 i on the basis of the KP chain. It is found that the KR value g (KR) of g as defined by ½ (KR) (star)= ½ (KR) (linear) lies between the values of an upper bound g (U) and a lower one g (L) , which are defined by The mean-square radius of gyration hS 2 i and/or the intrinsic viscosity ½ as measures of the average chain dimension of polymers in dilute solution depend largely on their molecular structure, e.g., linear or branched. It has therefore been of great interest to investigate the difference in hS 2 i or ½ between linear and branched polymer chains, and many theoretical and experimental studies 1-9 have already been made. However, almost all of those studies were of flexible polymers except for the theoretical one by Mansfield and Stockmayer, 4 the Monte Carlo (MC) one by Zimm, 5 and the experimental one by Goodson and Novak. 9 Mansfield and Stockmayer calculated hS 2 i of the Kratky-Porod (KP) wormlike 10,11 star chain (without excluded volume) and examined the behavior of its ratio g S to hS 2 i of the corresponding linear one having the same total length of the chain contour (molecular weight). Zimm evaluated ½ of ''wormlike'' four-and six-arm stars by the use of his rigidbody ensemble approximation. 12 Unfortunately, however, his calculation is rather limited, as mentioned by himself that it was a preliminary survey. Goodson and Novak synthesized three-arm star poly(n-hexyl isocyanate) by living titanium-catalized coordination polymerization, 9 and then investigated the behavior of hS 2 i, ½ , and g S as functions of molecular weight.In this paper, we make an extensive MC study of ½ for semiflexible regular three-arm star polymers in the Â state, which has not yet been made.The regular three-arm star chain model used in this study is essentially the same as that used in previous MC studies 13,14 of hS 2 i and the second virial coefficient of linear chains with in...

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

Cited by 27 publications

References 32 publications

Repulsive and Attractive Interactions between Polystyrene Chains in a Poor Solvent

Repulsive and Attractive Interactions between Polystyrene Chains in a Poor Solvent

Fine characterization of oligomers and polymers in dilute solution

A Monte Carlo Study of the Intrinsic Viscosity of Semiflexible Regular Three-Arm Star Polymers

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