<<< Time Table >>> (吉留氏のタイトルと要旨変更 ９月１８日)
Ryo Akiyama (Kyushu Univ., Japan)
Opening Remarks (13:30~13:40)
1:Masayuki Irisa (Kyushu Inst. Tech., Japan)
Title: Van der Waals picture of solvation based on scaled particle theory (13:40~14:10)
2:Roland Roth (Max-Planck Institut fur Metallforschung and
Institut fur Theoretische und Angewandte Physik, Universitat Stuttgart, Germany )
Title: From the Physics of Confined Fluids to a Mechanism for Gating in Ion Channels(14:10~14:50)
3:Hiroshi Furusawa (Kochi Univ. Tech., Japan)
Title: Lower bound approach to the van der Waals theory of strongly coupled Coulomb fluids.(14:50~15:30)
Poster Preview (15:30~15:50)
Poster Session / Coffee (15:50~16:50)
Poster Presentations.(追加が有ります。)
4:Takashi Yoshidome (Kyoto Univ., Japan)
Title: Entropic effect arising from complex solute-solvent correlations(16:50~17:20)
5:Tsuyosi Yamaguchi (Nagoya Univ., Japan)
Title: How the attractive interaction affects the solute diffusion?(17:20~17:50)
6:Akira Yoshimori (Kyushu Univ., Japan)
Title: Yamaguchi theory and Van der Waals picture(17:50~18:20)
<<< Abstract >>>
Roland Roth (Max-Planck Institut fur Metallforschung and
Institut fur Theoretische und Angewandte Physik, Universitat Stuttgart, Germany )
Title: From the Physics of Confined Fluids to a Mechanism for Gating in Ion Channels
Abstract:
Any van der Waals like fluid, with a strong repulsion at short distance
and attraction at intermediate separation can phase separate into a gas
and liquid phase, if the attraction is sufficiently strong. Under
confinement the system can undergo further phase transitions if it is
close to liquid-gas coexistence: capillary condensation in a hydrophilic
confinement and capillary evaporation in a hydrophobic confinement. These
phase transitions are well studied for various length scales.
In this talk we focus on very narrow, slightly hydrophobic, channels and
show that capillary evaporation can occur at a channel diameter, which is
only a few times the particle diameter [1]. From this observation we
suggest a mechanism for gating in biological ion channels [1,2]. Gating
is the process of regulating the ionic current through the channel by
allowing or stopping it. The suggested gating mechanism is based on the
idea that the hydrophobic gate of the channel can form or break a small
bubble by changing its geometrical conformation. If a bubble forms in the
gate, the ionic current through the channel is stopped.
[1] R. Roth and K.M. Kroll, J. Phys.: Condens. Matter 18, 6517-6530
(2006).
[2] R. Roth, D. Gillespie, W. Nonner, and R.E. Eisenberg, Biophys. Journal
94, 4282-4298 (2008).
Hiroshi Furusawa (Kochi Univ. Tech., Japan)
Title: Lower bound approach to the van der Waals theory of strongly coupled Coulomb fluids.
Abstract:
It has been demonstrated in the literature that the van der Waals picture applies
to strongly coupled (SC) Coulomb fluids ranging from plasmas to counterions dissociated
from a macroion: the density correlations are reproducible by mimic systems with only
a short-ranged part empirically separated from the full Coulomb potential. Moreover,
recent works of the local molecular field theory [1] suggest relevance of the mean-field
approximation for the remaining long-ranged contribution.
In this talk, I present a hybrid formulation of lower bound approach in liquid state theory
and field theoretic treatment, which provides the following [2, 3]: a first principle for
specifying the mimic potential, straightforward rederivation of the lower bound correlation energy,
a mean-field equation for coarse-grained SC counterions, and the reason
why the saddle-point approximation is valid at strong coupling.
References:
[1] Rodgers, J. M., Kaur, C., Chen, Y.-G. & Weeks, J. D. "Attraction Between Like-Charged Walls:
Short-Ranged Simulations Using Local Molecular Field Theory." Phys. Rev. Lett. 97, 097801 (2006).
[2] Frusawa, H. "Functional Integral Approach to Coulomb Fluids in the Strong Coupling Limit."
J. Phys. A 38, L121 (2005).
[3] Frusawa, H. "Strong Coulomb Correlations Mimicked by Short-Ranged Interactions:
A Saddle-Point Approximation." preprint.
Masayuki Irisa (Kyushu Inst. Tech., Japan)
Title: Van der Waals picture of solvation based on scaled particle theory
(Scaled Particle Theory からみた溶媒和の van der Waals 描像)
Abstract:
It is well known that thermodynamic quantities including chemical potential
can be derived analytically from van der Waals equation of state (EOS).
Excess thermodynamic quantities of the van der Waals EOS,
which are deviations from those at ideal gas state, are expressed as functions of a packing fraction.
The “van der Waals picture”[1] is taken from the nature of packing fraction in
condensed matters determined from collisions between particles.
The van der Waals picture is valid even for aquerous solutions where solute and
solvent particles have merely repulsive interactions at a short distance, e.g. hydrophobic hydration.
The van der Waals EOS gives quantitative values for real gases but not for liquids.
On the other hand, scaled particle theory (SPT)[2] is a theory giving an analytical
expression of the EOS and solvation free energies for liquids under some simple assumptions.
This theory uses hypothetical scaling of a solute particle with surrounding solvent
particles of fixed radii. In the case of hard spheres, the EOS derived from SPT
reduces to that from the van der Waals when a packing fraction of particles is decreased.
In this talk, the van der Waals picture which is based on the extended scaled particle theory (XSPT)[3],
which has been developed by us in order to apply it to solvation for arbitrary shaped solute molecules,
e.g. biomolecules in aqueous solution. Comparing calculated hydration heat capacities of proteins
with those of experiments, the van der Waals picuter is significant for explanation of temperature
dependence of hydration entropy. In addition, close relations between hydration free energies of
proteins and microscopic surface tensions of them are suggested.
If we have time, we will talk on a fundamental measure theory (FMT)[4], which gives an identical EOT
for hard spheres to that of SPT and also gives the same expression of solvation free energy for
an arbitrary shaped solute as that of XSPT except for one term relating to a third virial coefficient.
1) Chandler, D., Weeks, J. D. and H. C. Andersen, "Van der Waals Picture of Liquids, Solids,
and Phase Transformations", Science 220.4599,787(1983)
2) Reiss, H., Fish, H. L., and Lebowitz, J. L., J.Chem. Phys., 31, 369. (1959)
3) Irisa, M., Ta kahashi, T., Nagayama, K. and Hirata, F., "Solvation free energies of non-polar
and polar solutes reproduced by a combination of extended scaled particle theory and the Poisson
Boltzmann equation", Mol. Phys. 85,1227(1985)
4) Rosenfeld, Y. "Free Energy Model for the Inhomogeneous Hard-Sphere Fluid Mixture and
Density-Functional Theory of Freezing" Phys. Rev. Letters,63,980 (1989)
要旨：
状態方程式の一つであるvan der Waals 方程式から、熱力学関数、特に化学ポテンシャルが
解析的に導出可能であることは、よく知られている。１成分系の場合、理想気体と異なる部分
（excess 項と呼ばれる場合が多い）は粒子の空間充填率（packing fraction）の関数になっている。
液体の van der Waals 描像と呼ばれる概念は、この粒子同士のぶつかりから決まる空間充填に関する
性質を取り上げたものである。例えば水溶液の場合でも、溶質粒子が溶媒粒子（水分子）と近距離的な
斥力相互作用しか持たないと近似できる場合、van der Waals 描像は有効な概念となる。例えば
疎水性分子の水和がそれに当たる。
一般には van der Waals 方程式は実在気体を再現する状態方程式として知られており、液体の場合には
正確な実験値を再現しないと言われている。一方、溶液理論として広く知られている scaled particle
theory (SPT)は、仮想的に大きさをスケールダウンした溶質の溶媒和を考えることにより、ある近似の
もとで溶液の溶媒和自由エネルギーおよび状態方程式を解析的に与える理論である。SPTが剛体球系に
対して与える化学ポテンシャルは、packing fraction が小さいと近似した場合、van der Waals 方程式
が与えるものと同等になる。このように、定性的な van der Waals 方程式に SPT が理論的な説明を与
える関係になっている。
発表では演者が蛋白質分子の水和を考察するために拡張した、拡張 scaled particle theory (XSPT)
をもとに SPT からみた液体の van der Waals 描像について説明する。XSPT は、粒子の形状を球に
限定していた SPT を、任意の形状の分子（蛋白質分子など）に適応できるように拡張したものである。
蛋白質の水和熱容量をXSPTで計算し実験と比較した結果、van der Waals 描像が重要であることが
わかった。また、溶質分子と溶媒分子の境界面をミクロな界面と考えると、水和熱容量と表面張力との
関係が示唆される。SPTの枠組みが元々仮想的なスケーリングを用いており、マクロな極限とミクロな
極限（分子サイズ）での溶質の溶媒和の双方を同時に議論できることに起因している。
また、密度汎関数法の一つに fundamental measure theory (FMT) があり、この理論は幾何学的な
考察により空間内の数密度分布の関数として剛体ポテンシャル系の熱力学量を議論する。このFMTは
剛体球系に対してSPTと全く同じ状態方程式を与える。滑らかな凸体の場合もXSPTとほとんど同じ
状態方程式を与え、異なる部分は３次のビリアル係数の近似方法の違いに起因する。滑らかな凸体の
場合の３次のビリアル係数の数値計算の文献値によると、正確な３次のビリアル係数の値を挟む形で
FMTとXSPTは近似をそれぞれ行っていることに相当することがわかる。時間が許せば、このFMTと
XSPTの関係についても説明したい。
Tsuyosi Yamaguchi (Nagoya Univ., Japan)
Title: How the attractive interaction affects the solute diffusion?
Abstract:
The effects of the solute-solvent attractive interaction on the diffusion coefficient of
the solute are analyzed by the memory function formalism. The attractive and repulsive
parts of the memory function (generalized friction coefficient) are defined as the response
of the attractive and repulsive forces, respectively, to the external impulsive force,
and they are evaluated from the force-force time correlation functions obtained by MD
simulations. The systems we studied are the Lennard-Jones fluid near the triple point and
those in the supercritical region. The physical picture that the theoretical analysis shows
will be discussed in views of the van der Waals picture.
Reference:
"Effects of the solute-solvent and solvent-solvent attractive interactions on solute diffusion"
T. Yamaguchi and Y. Kimura, Molecular Physics, 98, 1553-1563 (2000)
Akira Yoshimori (Kyushu Univ., Japan)
Title: Yamaguchi theory and Van der Waals picture
Abstract:
To study diffusion of a large particle,
we have developed a theory,
applying a perturbative method to the theory
introduced by Yamaguchi et al.
If R is the diameter of a diffusion particle,
we have expanded the basic equations of the Yamaguchi theory
in terms of 1/R,
neglecting the terms higher than 1/ R2.
Using the theory,
we can easily calculate the diffusion coefficient
from the pair distribution function
for the diffusion and solvent particles.
The pair distribution function is primarily determined
by short-ranged repulsive interaction
according to the van der Waals picture.
Thus, the present theory shows that the diffusion coefficient
is influenced in a minor way by attractive interaction.
Reference:
T. Yamaguchi, T. Matsuoka, and S. Koda, J. Chem. Phys.,
123, 034504 (2005)
A.Yoshimori, Condensed Matter Physics, 2007, vol. 10, No. 4(52), p. 563
Takashi Yoshidome (Kyoto Univ., Japan)
Title: Entropic effect arising from complex solute-solvent correlations
Abstract: In the van der Waals picture, the structure and properties of fluids are
determined primarily by the repulsive part of the potential. Therefore,
studies on the hard-sphere system are of fundamental importance. It is known
that when a large hard-sphere solute is immersed in small hard spheres
forming the solvent, the small hard spheres are enriched near the solute and
this enrichment becomes greater as the solvent density increases, despite
the absence of an attractive part in the solute-solvent potential. In this
talk, I argue the physical origin of the enrichment using the integral
equation theory combined with the morphometric approach. Interestingly
enough, the enrichment and the pressure denaturation of proteins can be
understood within a same framework.