Yamakawa model

In the case of the refined Yamakawa model, this gives... 

Yamakawa and co-workers have formulated a discrete helical wormlike chain model that is mechanically equivalent to that described above for twisting and bending/79111 117) However, their approach to determining the dynamics is very different. They do not utilize the mean local cylindrical symmetry to factorize the terms in r(t) into products of correlation functions for twisting, bending, and internal motions, as in Eq. (4.24). Instead, they... 

Boldarev AS, Gasilov VA, Faenov AYa, Fukuda Y, Yamakawa K (2006) Gas-cluster targets for femtosecond laser interaction Modelling and optimization. Rev. Sci. Instrum. 77 0831121-08311210... 

Abdallah Jr. J, Csanak G, Fukuda Y, Yamakawa K, Akahane Y, Aoyama M, Inoue N, Ueda H, Faenov AYa, Magunov AI, Pikuz TA, Skobelev IYu (2003) Time-dependent Boltzmann kinetic model of X-rays produced by ultrashort-pulse laser irradiation of argon clusters. Phys. Rev. A 68 0632011-0632018... 

According to perturbation calculations based on the Kirkwood-Riseman model [Kirkwood and Riseman (139) and Yamakawa and... 

A uniform distribution of flexibility describes some molecules such as DNA and PBG a simple model for such molecules is the flexible beam or worm-like chain (Saito 1967 Yamakawa 1971) which has a finite bending rigidity k that is uniform along the chain contour. When we define a contour variable s as the distance along the chain contour from one of the ends and define s) as the curve in space defining the conformation of the worm-like molecule, the bending free energy is... 

A later paper by workers associated with the Takasago process reported on ab initio MO calculations for the catalytic cycle. Their work suggested that steps b and c (Scheme 9.22) involved an intramolecular OA of C-H, followed by a RE in which the hydride ligand attached itself to the terminal carbon of the allyl group. See M. Yamakawa and R. Noyori, Organometallics, 1992, 11, 3167. It is not clear which pathway is correct because the theoretical study used only PH3 and not BINAP to model the Rh-catalyzed isomerization. See also C. Chapuis, M. Barthe, and J.-Y. de Saint Laumer, Helv. Chim. Acta, 2001, 84, 230. 

Yamakawa K et al (2007) FEM model analysis of single-pole-type heads with different coil structures. lElCE Trans Electron E90-C 1555-1560... 

In this chapter, we will review theories of dilute polymer solution viscoelasticity based on a bead-spring model The purposes of this chapter are to introduce these theories to non-specialists and to see how they might be compared with experimental results. Therefore, we will not examine the validity of the model or the statistical mechanical calculations involved in these theories. A review article by Fixman and Stockmayer (4) and a book by Yamakawa (5) include instructive descriptions on these problems. 

Torre D, Zeroli C, Giola M, Ferrario G, Fieri GP, Bonetta G, Tambini R (1994) Serum levels of interleukin-1 alpha, interleukin-1 beta, interleukin-6, and tumor necrosis factor in patients with acute viral hepatitis. Clin Infect Dis 18 194 Tsuji H, Harada A, Mukaida N, Nakanuma Y, Bluethmann H, Kaneko S, Yamakawa K, Nakamura S-1, Kobayashi K-I, Matsushima K (1997) Tumor necrosis factor receptor p55 is essential for intrahepatic granuloma formation and hepatocellular apoptosis in a murine model of bacterium-induced fulminant hepatitis. Infect Immun 65 1892-1898... 

Yamakawa (38) and Imai (83) have published an alternative description based on a random coil model and the Kirkwood-Riseman theory (62) and obtained for theta-solvent conditions an equation equivalent to ... 

Caroline and co-workers have recently reported measurements of translational diffusion coefficients in solutions of PS in two mixed-solvent systems at or near theta conditions. In the solvent CCb-methanol (85), they observed the diffusion theta state, defined when the coefficient y of Equation 41 equals 0.5, to occur at 25°C and a volume fraction of CCI4, (fyCCU = 0.8025. In this system there is strong preferential adsorption of the polymer for CCI4, and it is not possible to define a true theta state such that y = a = V2 and A2 = 0 simultaneously. Under diffusion theta conditions, the concentration dependence of Dt apparently is closely described by the Pyun-Fixman hard-sphere model. In the mixed solvent benzene—2 propanol, polystyrene exhibits a true theta condition at T = 25.5°C and (benzene) = 0.04. Frost and Caroline confirmed that y = 0.5 within experimental error in this system (86) and report that values of the parameter fcf are scattered between the extreme values corresponding to the predictions of Yamakawa (and Imai) and the soft-sphere model of Pyun-Fixman (or the Freed theory). 

Worm-like chain statistics have been used by Eizner and Pti-tsyn ( ) for a bead model, and by Yamakawa and Fuji (11) for a cylinder model to calculate [Tj] as a function of p, L and the chain diameter d. Their results can be put in the form ([1]] in dl/g). 

Yamakawa and co-workers developed the quasi-two-parameter (QTP) theory from the earlier two-parameter (TP) theory, to incorporate chain stiffness into the model. Specifically, the QTP theory computes C o via the helical wormlike coil model (HW),... 

To describe the intrinsic viscosity of wormlike coils in the absence of excluded volume, Yamakawa and co-workers developed theoretical descriptions based, first, on the KP model [Yamakawa and Fujii, 1974] and subsequently on its later adaptation, the HW model [Yoshizaki et al., 1988]. Using the cylindrical wormlike coil model, Yamakawa and Fujii [1974] obtained the following expressions, with L expressed in... 

Yamakawa and co-workers were led to develop the HW model [Yoshizaki et al., 1980] by the observation that for some stiff-chain polymer-solvent systems, the KP model generates physically incorrect values of the characteristic parameters Ip and Ml, The following results were obtained [Yoshizaki et al., 1980, 1988], with L expressed in units of... 

Yoshizaki, T., Nitta, L, and Yamakawa, H., Transport coefficients of helical wormlike coils 4. Intrinsic viscosity of the touched-bead model. Macromolecules, 21, 165-171 (1988). 

We may constrain a freely rotating chain in such a way that the internal rotation of each segment is allowed to occur only over a limited range of rotational angle. If the limiting process leading to the wormlike chain is carried out with this additional constraint taken into account, we obtain a continuous chain model first considered by Miyake and Hoshino [2] and also by Burchard [3]. Yet another continuous chain model called the helical wormlike chain was proposed by Yamakawa and Fuji [4]. This chain is derived from a discrete chain somewhat different from the random flight chain [5]. 

The present chapter aims to describe some typical contributions from recent studies on stiff polymers in dilute solution. We will be mainly interested in (1) applicability of the wormlike chain model to actual polymers, (ii) validity of the hydrodynamic theories [2-4] recently developed for this model, and (iii) the onset of the excluded-volume effect on the dimensions of semi-flexible polymers. Yamakawa [5, 6] has generalized the wormlike chain model to one that he named the helical wormlike chain. In a series of papers he and his collaborators have made a great many efforts to formulate its static and dynamic properties in dilute solution. In fact, the theoretical information obtained is now comparable in both breadth and depth to that of the wotmlike chain (see Ref. [6] for an overview). Unfortunately, however, most of the derived expressions are too complex to be of use for quantitative anal) sis and interpretation of experimental data. Thus, we only have a few to be considered with reference to the practical aspects of the helical wormlike chain, and have to be content with mentioning the definition and some basic features of this novel model. 

The most important of recent theoretical studies on semi-flexible polymers is probably the formulation of Yamakawa and Fuji [2,3] for the steady transport coefficients of the wormlike cylinder. This hydrodynamic model, depicted in Figure 5-2, is a smooth cylinder whose centroid obeys the statistics of wormlike chains. In the figure, r denotes the normal radius vector drawn from a contour... 

To estimate Lc more accurately Yamakawa and Shimada [52] computed (5 ) of polymethylene-like rotational isomeric state models with excluded volume by a Monte Carlo method. They considered that bead-bead interactions higher than ones leading to the pentane effect contribute to excluded-volume effects. They found that the simulated polymer in the unperturbed state can be modeled by a wormlike chain and that (5 )/(4 rtK) of perturbed chains begins to deviate from those of unperturbed ones at uk of 3—5. Thus, the Lc by Yamakawa and... 

The appearance of a maximum in the chain length dependence of the characteristic ratio was first found by Yoon and Flory [60] in the RIS chain computations on atactic and syndiotactic polyfmethyl methacrylate)(PMMA). Yamakawa and Fujii [63] showed that their formula for the HW chain with <7o can be fitted accurately to the computed results of Yoon and Flory over dm almost entire range of chain length if the basic parameters of the HW chain are suitably chosen. A similar agreement in characteristic ratio between the HW (<7o = 0) and RIS chains was obtained for other flexible polymers. The choice of relation between the RIS chain model and the discrete chain whose continuous limit is the HW chain. 

Therefore, only a short summary of some of the most important thermodynamie approaehes and models will be given here. The following explanations are restrieted to eoneentrated polymer solutions only beeause one has to deseribe mainly eoneentrated polymer solutions when solvent aetivities have to be ealeulated. For dilute polymer solutions, with the seeond virial eoeffieient region, Yamakawa s book provides a good survey. 

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