پدیده جالب مذکور صدها سال قبل شناخته شده بود اما توسط یک دانش آموز تانزانیایی به نام Mpemba درسال 1969 به جهان علم امروزی معرفی شد. ظاهراً تا کنون با وجود چندین تئوری، پاسخ قاطعی برای توجیه این پدیده یافت نشده است. آنچه در یک نگاه گذرا نظر فرد را بخود جلب می کند رفتار متفاوت مولکول آب ناشی از پیوند هیدروژنی که این مایع را از بسیاری موارد با دیگر مواد مایع متمایز می کند، می باشد. دو ظرف آب با دمای اولیه 70 و 30 درجه رادرنظر بگیرید. آب 70 درجه برای منجمد شدن باید ضمن سرد شدن از دمای 30 درجه عبور کند واین مستلزم صرف زمان است. وجود همین زمان سبب ظهور پاردوکس مورد اشاره می شود. منحنی زمانی تغییرات دمای آب اکسپونانسیل بوده و این دو منحنی به دلیل پیوند هیدروژنی آب دردودمای اولیه متفاوت یکسان نخواهد بود. یعنی آرایش مولکولی و رفتار آماری مولکولهای آب وقتی بطور گذرا از دمای 30 درجه عبور می کنند با رفتار آماری همین مولکولها وقتی مدتی در دمای تعادل 30 درجه باقیمانده اند متفاوت است. البته این عرایض بنده بیان دلیل وقوع این پدیده نیست بلکه بیانی از مسئله موجود است و چرایی وقوع آن را روشن نمی کند.
در مقاله معرفی شده زیر که بخشی از آن نیز در قالب متن اصلی آمده با جزئیات بیشتر و با اتکا به دانش مولکولی امروزی موضوع مورد بررسی قرار گرفته است.
O:H-O Bond Anomalous Relaxation Resolving Mpemba Paradox
Xi Zhang1,2 Yongli Huang3, Zengsheng Ma3, Chang Q Sun1,2,3*
1. NOVITAS, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798
2. Center for Coordination Bond and Electronic Engineering, College of Materials Science and Engineering, China Jiliang University, Hangzhou 310018, China
3. Key Laboratory of Low-Dimensional Materials and Application Technologies (Ministry of Education) and Faculty of Materials, Optoelectronics and Physics, Xiangtan University, Hunan 411105, China
We demonstrate that the Mpemba paradox arises intrinsically from the release rate of energy initially stored in the covalent H-O part of the O:H-O bond in water albeit experimental conditions. Generally, heating raises the energy of a substance by lengthening and softening all bonds involved. However, the O:H nonbond in water follows actively the general rule of thermal expansion and drives the H-O covalent bond to relax oppositely in length and energy because of the inter-electron-electron pair coupling [J Phys Chem Lett 4, 2565 (2013); ibid 4, 3238 (2013)>. Heating stores energy into the H-O bond by shortening and stiffening it. Cooling the water as the source in a refrigerator as a drain, the H-O bond releases its energy at a rate that depends exponentially on the initially storage of energy, and therefore, Mpemba effect happens. This effect is formulated in terms of the relaxation time τ to represent all possible processes of energy loss. Consistency between predictions and measurements revealed that the τ drops exponentially intrinsically with the initial temperature of the water being cooled.
Keywords: Thermodynamics, Mpemba paradox, hydrogen bond, relaxation, phonon
The Mpemba effect [1>, named after Tanzanian student Erasto Mpemba, is the assertion that warmer water freezes faster than colder water, even though it must pass the lower temperature on the way to freezing. There have been reports of similar phenomena since ancient times, although with insufficient detail for the claims to be replicated. As indicated by Aristotle [2>: "The fact that the water has previously been warmed contributes to its freezing quickly: for so it cools sooner”. Hence many people, when they want to cool water quickly, begin by putting it in the sun. Although there is anecdotal support for this paradox [3>, there is no agreement on exactly what the effect is and under what circumstances it occurs.
Observations [1, 4> in Figure 1, show the following facts: a) hot water freezes faster than the cold water under the same conditions; b) the temperature θ drops exponentially with cooling time (t) and duration (Δt) for water transiting into ice varies with experimental conditions (volume, exposure surface, etc. For example, freezing 35 °C water takes about 90 min in (a) but 35 min in (b)); c) the skin is warmer than sites near the bottom in a beaker of water being cooled. Besides, blocking heat transfer from the skin with a film of oil drastically slowed cooling. The fact that the temperature of the skin remains higher than the in the bulk of the water throughout the process of cooling is in accordance with findings that the heat capacity of the supersolid skin is higher than the body as the H-O bond there is shorter and stronger [5>.
Figure 1 Mpemba effect. (a) Initial temperature (θi) dependence of the cooling duration (t) for ice formation; (b) Numerical fitting of the cooling profiles (scattered data) of 30 ml water at θi = 35 °C and 25 °C without cover or mixing [4 >; (c) time dependent skin-bottom temperature change [1 >.
This phenomenon forms thermodynamics paradox, but a number of possible explanations have been proposed in terms of evaporation, convection, frost, supercooling, latent heat of condensation, solutes, thermoconductivity, supercooling, etc [6-11>. Nikola Bregovićs [4>, the winner of the a competition held in 2012 by the Royal Society of Chemistry calling for papers offering explanations to the Mpemba effect, explained that the effect of convection that enhances the probability of warmer water freezing first should be emphasized in order to express a more complete explanation of the effect. Even if the Mpemba effect is real, it is not clear whether the explanation would be trivial or illuminating [12>. Investigations of the phenomenon need to control a large number of initial parameters (including type and initial temperature of the water, dissolved gas and other impurities, and size, shape and material of the container, and temperature of the refrigerator) and need to settle on a particular method of establishing the time of freezing, all of which might affect the presence or absence of the Mpemba effect. The required vast multidimensional array of experiments appeared to prevent the effect from being understood. However, little attention [13> has been paid to the nature and the initial states of the water source. Why this effect happens only to water other than to other usual materials? Focusing on the relaxation dynamics of the O:H-O bond in water is necessary.
Figure 2 O:H-O bond in water ice. The O:H-O bond is composed of the weak O:H van der Waals (vdW) bond in the left-hand side with vdW interaction (~0.1 eV) and the strong H-O covalent bond in the right with exchange interaction (~4.0 eV). H atom is the coordination origin. Inter-electron-pair (small paring dots on oxygen) Coulomb repulsion couples the two parts to relax in the same direction by different amounts under applied stimuli such as heating (blue spheres) or cooling (red spheres) associated with energy change along the respective potential curve. The O:H follows actively the general rule of thermal expansion in liquid water [14>. At cooling, the contraction of the O:H bond ejects the O atom in the H-O bond up to release energy, which differentiates water from other materials in cooling.
Let us look at the hydrogen bond (O:H-O) of water and ice first [15>. The O:H-O bond forms a pair of asymmetric, coupled, H-bridged oscillators with ultra-short-range interactions, see Figure 2 [16>. The cooperative relaxation in length and energy of the O:H-O bond and the associated energy entrapment and polarization differentiate water ice from other usual materials in the structure order and physical properties under varies stimuli [5, 14, 17>. Heating lengthens and softens of the O:H bond with energy of 10-2 eV level, which contributes insignificantly to the system energy. Thermal expansion of the O:H bond shortens and stiffens the H-O bond [14> because of the coupling by the repulsion between electron pairs on oxygen. This event results in the blue shift of the H-O stretching vibration frequency [18> and the entrapment of the O 1s binding energy [19>, as given in Table 1.The heating-cooling reverses oxygen coordinates along the potential curves. The red spheres correspond to oxygen atoms in the cold state and the blue one to the hot. Being opposite to other usual materials, heating stores energy ΔE into the H-O bond, as the energy variation of the O:H bond is negligible.