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| This reaction is one in which a molecule of species A interacts with a molecule of species B. The A molecule is converted into a B molecule. The final product consists of the original B molecule plus the B molecule created in the reaction. | | This reaction is one in which a molecule of species A interacts with a molecule of species B. The A molecule is converted into a B molecule. The final product consists of the original B molecule plus the B molecule created in the reaction. |
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− | | + | 这个反应是物种A的分子与物种B的分子相互作用,A分子转化为B分子。最终产物由原始的B分子加上反应中产生的B分子组成。 |
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| A similar example exists for living chemical systems. The sun provides energy to green plants. The green plants are food for other living chemical systems. The energy absorbed by plants and converted into chemical energy generates a system on earth that is orderly and far from chemical equilibrium. Here, the difference from chemical equilibrium is determined by an excess of reactants over the equilibrium amount. Once again, order on earth is generated at the expense of entropy increase of the sun. The total entropy of the earth and the rest of the universe increases, consistent with the Second Law. | | A similar example exists for living chemical systems. The sun provides energy to green plants. The green plants are food for other living chemical systems. The energy absorbed by plants and converted into chemical energy generates a system on earth that is orderly and far from chemical equilibrium. Here, the difference from chemical equilibrium is determined by an excess of reactants over the equilibrium amount. Once again, order on earth is generated at the expense of entropy increase of the sun. The total entropy of the earth and the rest of the universe increases, consistent with the Second Law. |
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| The key feature of these rate equations is that they are [[nonlinear]]; the second term on the right varies as the square of the concentration of B. This feature can lead to multiple fixed points of the system, much like a [[quadratic equation]] can have multiple roots. Multiple fixed points allow for multiple states of the system. A system existing in multiple [[macroscopic]] states is more orderly (has lower entropy) than a system in a single state. | | The key feature of these rate equations is that they are [[nonlinear]]; the second term on the right varies as the square of the concentration of B. This feature can lead to multiple fixed points of the system, much like a [[quadratic equation]] can have multiple roots. Multiple fixed points allow for multiple states of the system. A system existing in multiple [[macroscopic]] states is more orderly (has lower entropy) than a system in a single state. |
− | | + | 这些速率方程的关键特征是它们是[[非线性];右边的第二项随B浓度的平方而变化。这一特性可导致系统的多个不动点,就像[[二次方程]]可以有多个根一样。多个固定点允许系统的多种状态。存在于多个[[宏观]]状态的系统比处于单一状态的系统更有序(熵更低)。 |
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| The graph for these equations is a [[sigmoid function|sigmoid curve]] (specifically a [[logistic function]]), which is typical for autocatalytic reactions: these chemical reactions proceed slowly at the start (the [[induction period]]) because there is little catalyst present, the rate of reaction increases progressively as the reaction proceeds as the amount of catalyst increases and then it again slows down as the reactant concentration decreases. If the concentration of a reactant or product in an experiment follows a sigmoid curve, the reaction may be autocatalytic. | | The graph for these equations is a [[sigmoid function|sigmoid curve]] (specifically a [[logistic function]]), which is typical for autocatalytic reactions: these chemical reactions proceed slowly at the start (the [[induction period]]) because there is little catalyst present, the rate of reaction increases progressively as the reaction proceeds as the amount of catalyst increases and then it again slows down as the reactant concentration decreases. If the concentration of a reactant or product in an experiment follows a sigmoid curve, the reaction may be autocatalytic. |
− | | + | 这些方程的图形是一个[[西格莫函数| S形曲线]](特别是[[逻辑函数]]),这是自催化反应的典型特征:这些化学反应在开始时(诱导期]])进行得很慢,因为催化剂很少,随着催化剂用量的增加,反应速度逐渐增加,然后随着反应物浓度的降低,反应速度再次减慢。如果一个实验中反应物或产物的浓度服从sigmoid曲线,则该反应可能是自催化的。 |
| A chemical reaction cannot oscillate about a position of final equilibrium because the second law of thermodynamics requires that a thermodynamic system approach equilibrium and not recede from it. For a closed system at constant temperature and pressure, the Gibbs free energy must decrease continuously and not oscillate. However it is possible that the concentrations of some reaction intermediates oscillate, and also that the rate of formation of products oscillates. | | A chemical reaction cannot oscillate about a position of final equilibrium because the second law of thermodynamics requires that a thermodynamic system approach equilibrium and not recede from it. For a closed system at constant temperature and pressure, the Gibbs free energy must decrease continuously and not oscillate. However it is possible that the concentrations of some reaction intermediates oscillate, and also that the rate of formation of products oscillates. |
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| These kinetic equations apply for example to the acid-catalyzed hydrolysis of some [[ester]]s to [[carboxylic acid]]s and [[alcohol]]s.<ref name=Moore/> There must be at least some acid present initially to start the catalyzed mechanism; if not the reaction must start by an alternate uncatalyzed path which is usually slower. The above equations for the catalyzed mechanism would imply that the concentration of acid product remains zero forever.<ref name=Moore/> | | These kinetic equations apply for example to the acid-catalyzed hydrolysis of some [[ester]]s to [[carboxylic acid]]s and [[alcohol]]s.<ref name=Moore/> There must be at least some acid present initially to start the catalyzed mechanism; if not the reaction must start by an alternate uncatalyzed path which is usually slower. The above equations for the catalyzed mechanism would imply that the concentration of acid product remains zero forever.<ref name=Moore/> |
− | | + | 例如,这些动力学方程适用于某些[[酯]]到[[羧酸]]和[[醇]]的酸催化水解。最初必须至少存在一些酸来启动催化机制;否则,反应必须通过通常较慢的替代非催化路径开始。上述催化机理的方程式意味着酸产物的浓度永远为零。 |
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| This system of rate equations is known as the [[Lotka–Volterra equation]] and is most closely associated with [[population dynamics]] in predator–prey relationships. This system of equations can yield oscillating concentrations of the reaction intermediates X and Y. The amplitude of the oscillations depends on the concentration of A (which decreases without oscillation). Such oscillations are a form of emergent temporal order that is not present in equilibrium. | | This system of rate equations is known as the [[Lotka–Volterra equation]] and is most closely associated with [[population dynamics]] in predator–prey relationships. This system of equations can yield oscillating concentrations of the reaction intermediates X and Y. The amplitude of the oscillations depends on the concentration of A (which decreases without oscillation). Such oscillations are a form of emergent temporal order that is not present in equilibrium. |
− | | + | 这个速率方程组被称为[[Lotka–Volterra equation]],在捕食者-猎物关系中与[[种群动力学]]联系最为密切。这个方程组可以得到反应中间体X和Y的振荡浓度,振荡的幅度取决于A的浓度(A的浓度减少而不振荡)。这种振荡是一种在平衡状态下不存在的突发时序形式。 |
| The Brusselator in the unstable regime. A=1. B=2.5. X(0)=1. Y(0)=0. The system approaches a [[limit cycle. For B<1+A the system is stable and approaches a fixed point.]] | | The Brusselator in the unstable regime. A=1. B=2.5. X(0)=1. Y(0)=0. The system approaches a [[limit cycle. For B<1+A the system is stable and approaches a fixed point.]] |
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| where, for convenience, the rate constants have been set to 1. | | where, for convenience, the rate constants have been set to 1. |
− | | + | 其中,为了方便起见,速率常数被设置为1。 |
| <math>{d \over dt}[ X_2 ] = [A ] + [ X _2]^2 [Y_2 ] - [B ] [X_2 ] - [X_2 ] + D_x\left( X_1 - X_2 \right)\,</math> | | <math>{d \over dt}[ X_2 ] = [A ] + [ X _2]^2 [Y_2 ] - [B ] [X_2 ] - [X_2 ] + D_x\left( X_1 - X_2 \right)\,</math> |
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| The Brusselator has a fixed point at | | The Brusselator has a fixed point at |
− | | + | 布鲁塞尔振子有一个固定点在 |
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| Noting that photo-polymerization rate is proportional to intensity and that refractive index is proportional to molecular weight, the positive feedback between intensity and photo-polymerization establishes the auto-catalytic behavior. Optical auto-catalysis has been shown to result on spontaneous pattern formation in photopolymers. Hosein and co-workers discovered that optical autocatalysis can also occur in photoreactive polymer blends, and that the process can induce binary phase morphologies with the same pattern as the light profile. Glycolysis consists of the degradation of one molecule of glucose and the overall production of two molecules of ATP. The process is therefore of great importance to the energetics of living cells. The global glycolysis reaction involves glucose, ADP, NAD, pyruvate, ATP, and NADH. | | Noting that photo-polymerization rate is proportional to intensity and that refractive index is proportional to molecular weight, the positive feedback between intensity and photo-polymerization establishes the auto-catalytic behavior. Optical auto-catalysis has been shown to result on spontaneous pattern formation in photopolymers. Hosein and co-workers discovered that optical autocatalysis can also occur in photoreactive polymer blends, and that the process can induce binary phase morphologies with the same pattern as the light profile. Glycolysis consists of the degradation of one molecule of glucose and the overall production of two molecules of ATP. The process is therefore of great importance to the energetics of living cells. The global glycolysis reaction involves glucose, ADP, NAD, pyruvate, ATP, and NADH. |
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− | 注意到光聚合速率与强度成正比,折射率与分子量成正比,强度与光聚合之间的正反馈建立了自催化行为。光学自催化已被证明是光聚合物自发形成图案的原因。Hosein 和他的合作者发现,光学自催化也可以发生在光反应聚合物共混物中,这一过程可以诱导形成与光型相同的二元相形态。糖酵解是由一个葡萄糖分子的降解和两个 ATP 分子的全部产生组成。因此,这个过程对活细胞的能量学来说是非常重要的。糖酵解反应包括葡萄糖、 ADP、 NAD、丙酮酸、 ATP 和 NADH。
| + | 注意到光聚合速率与强度成正比,折射率与分子量成正比,强度与光聚合之间的正反馈建立了自催化行为。光学自催化已被证明是光聚合物自发形成图案的原因。Hosein和他的合作者发现,光学自催化也可以发生在光反应聚合物共混物中,这一过程可以诱导形成与光型相同的二元相形态。糖酵解是由一个葡萄糖分子的降解和两个 ATP 分子的全部产生组成。因此,这个过程对活细胞的能量学来说是非常重要的。糖酵解反应包括葡萄糖、 ADP、 NAD、丙酮酸、 ATP 和 NADH。 |
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| }} Dynamics of the Brusselator | | }} Dynamics of the Brusselator |
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| The initial amounts of reactants determine the distance from a chemical equilibrium of the system. The greater the initial concentrations the further the system is from equilibrium. As the initial concentration increases, an abrupt change in order occurs. This abrupt change is known as phase transition. At the phase transition, fluctuations in macroscopic quantities, such as chemical concentrations, increase as the system oscillates between the more ordered state (lower entropy, such as ice) and the more disordered state (higher entropy, such as liquid water). Also, at the phase transition, macroscopic equations, such as the rate equations, fail. Rate equations can be derived from microscopic considerations. The derivations typically rely on a mean field theory approximation to microscopic dynamical equations. Mean field theory breaks down in the presence of large fluctuations (see Mean field theory article for a discussion). Therefore, since large fluctuations occur in the neighborhood of a phase transition, macroscopic equations, such as rate equations, fail. As the initial concentration increases further, the system settles into an ordered state in which fluctuations are again small. (see Prigogine reference) | | The initial amounts of reactants determine the distance from a chemical equilibrium of the system. The greater the initial concentrations the further the system is from equilibrium. As the initial concentration increases, an abrupt change in order occurs. This abrupt change is known as phase transition. At the phase transition, fluctuations in macroscopic quantities, such as chemical concentrations, increase as the system oscillates between the more ordered state (lower entropy, such as ice) and the more disordered state (higher entropy, such as liquid water). Also, at the phase transition, macroscopic equations, such as the rate equations, fail. Rate equations can be derived from microscopic considerations. The derivations typically rely on a mean field theory approximation to microscopic dynamical equations. Mean field theory breaks down in the presence of large fluctuations (see Mean field theory article for a discussion). Therefore, since large fluctuations occur in the neighborhood of a phase transition, macroscopic equations, such as rate equations, fail. As the initial concentration increases further, the system settles into an ordered state in which fluctuations are again small. (see Prigogine reference) |
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− | 反应物的初始量决定了与体系化学平衡的距离。初始浓度越大,系统离平衡越远。随着初始浓度的增加,顺序发生突变。这种突变被称为相变。在相变阶段,宏观量的波动,如化学浓度,随着系统在更有序的状态(低熵,如冰)和更无序的状态(更高的熵,如液态水)之间振荡而增加。同样,在相变过程中,宏观方程,如速率方程,会失效。速率方程可以从微观角度推导出来。推导通常依赖于对微观动力学方程的平均场理论近似。平均场理论在大波动的存在下会崩溃(见平均场理论文章的讨论)。因此,由于大的波动发生在相变附近,宏观方程,如速率方程,失败了。随着初始浓度的进一步增加,系统进入有序状态,在这种状态下波动又很小(见 Prigogine 参考文献)
| + | 反应物的初始量决定了与体系化学平衡的距离。初始浓度越大,系统离平衡越远。随着初始浓度的增加,顺序发生突变。这种突变被称为相变。在相变阶段,宏观量的波动,如化学浓度,随着系统在更有序的状态(低熵,如冰)和更无序的状态(更高的熵,如液态水)之间振荡而增加。同样,在相变过程中,宏观方程,如速率方程,会失效。速率方程可以从微观角度推导出来。推导通常依赖于对微观动力学方程的平均场理论近似。平均场理论在大波动的存在下会崩溃(见平均场理论文章的讨论)。因此,由于大的波动发生在相变附近,例如速率方程等的宏观方程便失灵了。随着初始浓度的进一步增加,系统进入有序状态,在这种状态下波动又很小(见 Prigogine 参考文献) |
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| :<math>{d \over dt}[ Y_2 ] = [B ] [X_2 ] - [ X_2 ]^2 [Y_2 ] + D_y\left( Y_1 - Y_2\right) \,</math> | | :<math>{d \over dt}[ Y_2 ] = [B ] [X_2 ] - [ X_2 ]^2 [Y_2 ] + D_y\left( Y_1 - Y_2\right) \,</math> |
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| Here, the numerical subscripts indicate which box the material is in. There are additional terms proportional to the diffusion coefficient D that account for the exchange of material between boxes. | | Here, the numerical subscripts indicate which box the material is in. There are additional terms proportional to the diffusion coefficient D that account for the exchange of material between boxes. |
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− | | + | 在这里,数字下标表示材料在哪个盒子里。还有一些与扩散系数D成比例的附加项,它们解释了盒子之间的物质交换。 |
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| Asymmetric autocatalysis occurs when the reaction product is chiral and thus acts as a chiral catalyst for its own production. Reactions of this type, such as the Soai reaction, have the property that they can amplify a very small enantiomeric excess into a large one. This has been proposed as an important step in the origin of biological homochirality. | | Asymmetric autocatalysis occurs when the reaction product is chiral and thus acts as a chiral catalyst for its own production. Reactions of this type, such as the Soai reaction, have the property that they can amplify a very small enantiomeric excess into a large one. This has been proposed as an important step in the origin of biological homochirality. |
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| If the system is initiated with the same conditions in each box, then a small fluctuation will lead to separation of materials between the two boxes. One box will have a predominance of X, and the other will have a predominance of Y. | | If the system is initiated with the same conditions in each box, then a small fluctuation will lead to separation of materials between the two boxes. One box will have a predominance of X, and the other will have a predominance of Y. |
− | | + | 如果系统在每个箱子的相同条件下启动,那么小的波动将导致两个箱子之间的物料分离。一个方框的优势是X,另一个方框的优势是Y。 |
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| Real examples of [[clock reaction]]s are the [[Belousov–Zhabotinsky reaction]] (BZ reaction), the [[Briggs–Rauscher reaction]], the [[Bray–Liebhafsky reaction]] and the [[iodine clock reaction]]. These are oscillatory reactions, and the concentration of products and reactants can be approximated in terms of [[damping|damped]] [[oscillation]]s. | | Real examples of [[clock reaction]]s are the [[Belousov–Zhabotinsky reaction]] (BZ reaction), the [[Briggs–Rauscher reaction]], the [[Bray–Liebhafsky reaction]] and the [[iodine clock reaction]]. These are oscillatory reactions, and the concentration of products and reactants can be approximated in terms of [[damping|damped]] [[oscillation]]s. |
− | | + | 时钟反应]]的真正例子是[[Belousov–Zhabotinsky reaction]](BZ反应)、[[Briggs–Rauscher 反应]]、[[Bray–Liebhafsky 反应]]和[[碘钟反应]]。这些都是振荡反应,产物和反应物的浓度可以用阻尼,振荡来近似。 |
| In 1995 Stuart Kauffman proposed that life initially arose as autocatalytic chemical networks. | | In 1995 Stuart Kauffman proposed that life initially arose as autocatalytic chemical networks. |
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