• Bulletin of the Korean Chemical Society
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• 제34권5호
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• pp.1454-1456
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• 2013

The fluctuations in concentrations of reactants dominate the long-time dynamics of the single (A + A ${\rightarrow}$ 0) and two species (A + B ${\rightarrow}$ 0) diffusion-influenced annihilation reactions. Although hierarchical Smoluchowski approaches can provide a systematic and flexible framework to deal with the fluctuation effects, their results are too complicated to be analytically solved. For the efficient numerical calculation of the complicated fluctuation effect terms, we show that the presented point particle approximation is not only practical but also quite accurate for most conditions in diffusion-influenced reaction systems.

• Bulletin of the Korean Chemical Society
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• 제35권10호
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• pp.3089-3091
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• 2014

• Bulletin of the Korean Chemical Society
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• 제33권3호
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• pp.1015-1019
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• 2012

The direct calculation method is generalized to the excited-state diffusion-influenced reversible reaction of a neutral and a charged particle under an external field with two different lifetimes and quenching in three dimensions. The present method provides an alternative way to calculate the binding probability density functions and the survival probabilities from the corresponding irreversible results. The solutions are obtained as the series solutions by the diagonal approximation due to the anisotropy of the unidirectional external field. The numerical results are found to be in good agreement with those of the previous study [S. Y. Reigh et al. J. Chem. Phys. 132, 164112 (2010)] within a weak field limit. The solutions of two approaches show qualitatively the same overall behavior including the power laws at long times.

• 대한화학회지
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• 제52권3호
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• pp.217-222
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• 2008

본 논문에서는 반응 매질의 부피가 촉매 반응 속도에 미치는 영향을 조사하였다. 단순하지만 정확한 모델에 대한 연구로부터 촉매 반응의 반응 속도 계수는 매질의 부피가 줄어들 수록 증가함을 알게 되었다. 평균 반응속도 상수(average reaction rate constant)는 Collins-Kimball 속도 상수의 일반화 된 형태로 얻어졌는데, 속도 상수는 부피의 효과를 보정해주는 인자를 포함하고 있다. 조사한 모델의 반응물 농도는 전통적 화학 반응론에서 예측되는 지수함수적 감소와는 상당한 차이를 보이는데 이는 기존 화학 반응속도론에서는 무시되는 반응분자 공간 분포의 비평형 확산운동(non-equilibrium diffusive dynamics)의 효과 때문이다. 반응 매질의 부피 가 유한한 점을 고려하면, 반응 시간이 충분히 오래 지났을 때, 기존의 확산지배 반응에서는 예측 되는 않는 지수 함수적 농도 감소가 얻어지는데, 그 속도 상수 역시 반응매질 크기에 의존한다.

• Bulletin of the Korean Chemical Society
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• 제35권4호
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• pp.1209-1211
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• 2014

• Bulletin of the Korean Chemical Society
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• 제21권1호
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• pp.93-96
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• 2000

A diffusion-influenced pseudo-first order reversible reaction A + B ⇔C + B is investigated by the molecular dynamics (MD) simulation method. Theoretical finding that the temporal evolution of reactants [conditional probabilities] in the reversible system can be expressed by the irreversible survival probability with an effective rate parameter is confirmed even in the presence of solvent particles. We carry out molecular dynamics simulations for both the irreversible and the reversible cases to evaluate the survival and the conditional probabilities for each cases. When the resultant irreversible survival probability is inserted into the proposed relation, the conditional probabilities given by the simulation are exactly reproduced.

• Bulletin of the Korean Chemical Society
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• 제13권4호
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• pp.398-404
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• 1992

We have investigated the kinetics of diffusion-influenced bimolecular reactions in which one reactant has an internal mode, called the gating mode, that activates or deactivates its reactivity intermittently. The rate law and an expression for the time-dependent rate coefficient have been obtained from the general formalism based on the hierarchy of kinetic equations involving reactant distribution functions. The analytic expression obtained for the steady-state reaction rate constant coincides with the one obtained by Szabo et al., who derived the expression by employing the conventional concentration-gradient approach. For the time-dependent reaction rate coefficient, we obtained for the first time an exact analytic expression in the Laplace domain which was then inverted numerically to give the time-domain results.

• Bulletin of the Korean Chemical Society
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• 제33권3호
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• pp.971-974
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• 2012

The facilitated diffusion effect on protein-DNA binding is studied. A rigorous theoretical approach is presented to deal with the coupling between one-dimensional and three-dimensional diffusive motions. For a simplified model, the present approach can provide numerically exact results, which are confirmed by the lattice-based Monte Carlo simulations.

• Bulletin of the Korean Chemical Society
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• 제33권3호
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• pp.925-928
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• 2012

The accurate expression for the steady-state velocity of an irreversible enzyme-catalyzed reaction obtained by Shin and co-workers (J. Chem. Phys. 2001, 115, 1455) is generalized to allow for the rebinding of the product. The amplitude of the power-law ($t^{-1/2}$) relaxation of the free- and bound-enzyme concentrations to steady-state values is expressed in terms of the steady-state velocity and the intrinsic (chemical) rate constants. This result is conjectured to be exact, even though our expression for the steady-state velocity in terms of microscopic parameters is only approximate.

• Bulletin of the Korean Chemical Society
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• 제33권3호
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• pp.1020-1028
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• 2012

This work compares various models for geminate reversible diffusion influenced reactions. The commonly utilized contact reactivity model (an extension of the Collins-Kimball radiation boundary condition) is augmented here by a volume reactivity model, which extends the celebrated Feynman-Kac equation for irreversible depletion within a reaction sphere. We obtain the exact analytic solution in Laplace space for an initially bound pair, which can dissociate, diffuse or undergo "sticky" recombination. We show that the same expression for the binding probability holds also for "mixed" reaction products. Two different derivations are pursued, yielding seemingly different expressions, which nevertheless coincide numerically. These binding probabilities and their Laplace transforms are compared graphically with those from the contact reactivity model and a previously suggested coarse grained approximation. Mathematically, all these Laplace transforms conform to a single generic equation, in which different reactionless Green's functions, g(s), are incorporated. In most of parameter space the sensitivity to g(s) is not large, so that the binding probabilities for the volume and contact reactivity models are rather similar.