Transition state theory approach to polymer escape from a one dimensional potential well

Mökkönen, Harri; Ikonen, Timo; Ala-Nissilä, Tapio; Jónsson, Hannes

doi:10.1063/1.4921959

Cited by 7 publications

(13 citation statements)

References 35 publications

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“…The transition state theory approach followed by explicit dynamical corrections is then preferable over Kramers' approach. Similar at barrier issues arise in polymer escape problems where HTST followed by recrossing corrections has been shown to be a useful approach for estimating the transition rate. 13 At low enough temperature, quantum tunneling through the energy barrier becomes the dominant transition mechanism and the rate can eventually become temperature independent. It is important to have a way to estimate the crossover temperature for tunneling when assessing the stability of a magnetic state.…”

Section: Introductionmentioning

confidence: 99%

Classical to quantum mechanical tunneling mechanism crossover in thermal transitions between magnetic states

et al. 2016

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Transitions between states of a magnetic system can occur by jumps over an energy barrier or by quantum mechanical tunneling through the energy barrier. The rate of such transitions is an important consideration when the stability of magnetic states is assessed for example for nanoscale candidates for data storage devices. The shift in transition mechanism from jumps to tunneling as the temperature is lowered is analyzed and a general expression derived for the crossover temperature. The jump rate is evaluated using a harmonic approximation to transition state theory. First, the minimum energy path for the transition is found with the geodesic nudged elastic band method. The activation energy for the jumps is obtained from the maximum along the path, a saddle point on the energy surface, and the eigenvalues of the Hessian matrix at that point as well as at the initial state minimum used to estimate the entropic pre-exponential factor. The crossover temperature for quantum mechanical tunneling is evaluated from the second derivatives of the energy with respect to orientation of the spin vector at the saddle point. The resulting expression is applied to test problems where analytical results have previously been derived, namely uniaxial and biaxial spin systems with two-fold anisotropy. The effect of adding four-fold anisotropy on the crossover temperature is demonstrated. Calculations of the jump rate and crossover temperature for tunneling are also made for a molecular magnet containing an Mn group. The results are in excellent agreement with previously reported experimental measurements on this system.

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Section: Introductionmentioning

confidence: 99%

Classical to quantum mechanical tunneling mechanism crossover in thermal transitions between magnetic states

et al. 2016

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“…A detailed analysis of the eigenmodes, the barrier height, the barrier shape, and the removal of the peak has been presented in our previous publication. 36 The HTST estimate of the rate saturates to a constant value in the region N > 32. This is because the height of the effective energy barrier, the maximum along the MEP, saturates as the barrier starts to flatten out as shown in Fig.…”

Section: Resultsmentioning

confidence: 99%

“…(9). Anharmonic corrections 36,25 are computed for this mode but they do not completely remove the peak. A detailed analysis of the eigenmodes, the barrier height, the barrier shape, and the removal of the peak has been presented in our previous publication.…”

Section: Resultsmentioning

confidence: 99%

“…The escape rate of polymers has previously been studied 36 using HTST followed by recrossing corrections evaluated using the method of Voter and Doll. …”

Section: Htst and Recrossing Correctionsmentioning

confidence: 99%

“…34 In a recent study of a model polymer escape problem, the application of HTST followed by dynamical corrections was shown to give accurate results as compared to direct dynamical simulations, while the Kramers-Langer approach gave a significant underestimate of the transition rate for the longer polymers. 35,36 Flat energy barriers are also common in magnetic transitions involving the temporary domain wall mechanism. 37,38 The evaluation of the recrossing correction in the WKE procedure can involve large computational effort for extended, flat energy barriers.…”

Section: Introductionmentioning

confidence: 99%

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Efficient dynamical correction of the transition state theory rate estimate for a flat energy barrier

Mökkönen

Ala-Nissilä

Jónsson

2016

The Journal of Chemical Physics

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The recrossing correction to the transition state theory estimate of a thermal rate can be difficult to calculate when the energy barrier is flat. This problem arises, for example, in polymer escape if the polymer is long enough to stretch between the initial and final state energy wells while the polymer beads undergo diffusive motion back and forth over the barrier. We present an efficient method for evaluating the correction factor by constructing a sequence of hyperplanes starting at the transition state and calculating the probability that the system advances from one hyperplane to another towards the product. This is analogous to what is done in forward flux sampling except that there

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Role of Aspartic Acid in the Synthesis of Spherical Vaterite by the Ca(OH)₂–CO₂ Reaction

Luo

Kong

2015

Crystal Growth & Design

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Vaterite crystals with a spherical shape were successfully obtained by the addition of aspartic acid (Asp) in the calcium hydroxide (Ca(OH) 2 )−carbon dioxide reaction system. Crystalline products were characterized by X-ray diffraction, field emission scanning electron microscopy, Fourier transform infrared spectroscopy, Raman spectroscopy, thermogravimetric analysis, and differential scanning calorimetry (TG-DSC). The experimental results indicate that the addition of Asp can inhibit the growth of calcite but promote the formation of vaterite, and the spherical vaterite CaCO 3 is gradually dominant along with the increase of Asp. Meanwhile the content of the vaterite phase is prominently influenced by the reaction temperature, and the optimal temperature for vaterite is at 40 °C. It is proposed that vaterite is induced through the intermediate chelated by Asp and Ca(OH) 2 , and then Asp is adsorbed on the surface of vaterite by chelation, preventing the metastable vaterite from transforming to calcite via a dissolution−recrystallization process. Further, the decrease of pH in the solution could reduce the chelation between Asp and Ca 2+ , leading to the transformation from vaterite to calcite. Hence, the study on the formation and transformation of vaterite will provide additional insight into biomineralization mechanism and industrial production.

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Transition state theory approach to polymer escape from a one dimensional potential well

Cited by 7 publications

References 35 publications

Classical to quantum mechanical tunneling mechanism crossover in thermal transitions between magnetic states

Classical to quantum mechanical tunneling mechanism crossover in thermal transitions between magnetic states

Efficient dynamical correction of the transition state theory rate estimate for a flat energy barrier

Role of Aspartic Acid in the Synthesis of Spherical Vaterite by the Ca(OH)₂–CO₂ Reaction

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Transition state theory approach to polymer escape from a one dimensional potential well

Cited by 7 publications

References 35 publications

Classical to quantum mechanical tunneling mechanism crossover in thermal transitions between magnetic states

Classical to quantum mechanical tunneling mechanism crossover in thermal transitions between magnetic states

Efficient dynamical correction of the transition state theory rate estimate for a flat energy barrier

Role of Aspartic Acid in the Synthesis of Spherical Vaterite by the Ca(OH)2–CO2 Reaction

Contact Info

Product

Resources

About

Role of Aspartic Acid in the Synthesis of Spherical Vaterite by the Ca(OH)₂–CO₂ Reaction