Дополнение к статье V. Shikin, I. Chikina, and S. Nazin “Relaxation phenomena in cryogenic electrolytes”, Fiz. Nizk. Temp. 39, 712 (2013)
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irk-123456789-1195042017-06-08T03:06:24Z Дополнение к статье V. Shikin, I. Chikina, and S. Nazin “Relaxation phenomena in cryogenic electrolytes”, Fiz. Nizk. Temp. 39, 712 (2013) Шикин, В. Chikina, I. Назин, С. Письма pедактоpу 2014 Article Дополнение к статье V. Shikin, I. Chikina, and S. Nazin “Relaxation phenomena in cryogenic electrolytes”, Fiz. Nizk. Temp. 39, 712 (2013) / В. Шикин, I. Chikina, С. Назин // Физика низких температур. — 2014. — Т. 40, № 5. — С. 608-609. — Бібліогр.: 19 назв. — рос. 0132-6414 PACS 67.10.–j http://dspace.nbuv.gov.ua/handle/123456789/119504 ru Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Письма pедактоpу Письма pедактоpу Шикин, В. Chikina, I. Назин, С. Дополнение к статье V. Shikin, I. Chikina, and S. Nazin “Relaxation phenomena in cryogenic electrolytes”, Fiz. Nizk. Temp. 39, 712 (2013) Физика низких температур |
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Article |
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Шикин, В. Chikina, I. Назин, С. |
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Шикин, В. Chikina, I. Назин, С. |
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Шикин, В. |
| title |
Дополнение к статье V. Shikin, I. Chikina, and S. Nazin “Relaxation phenomena in cryogenic electrolytes”, Fiz. Nizk. Temp. 39, 712 (2013) |
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Дополнение к статье V. Shikin, I. Chikina, and S. Nazin “Relaxation phenomena in cryogenic electrolytes”, Fiz. Nizk. Temp. 39, 712 (2013) |
| title_full |
Дополнение к статье V. Shikin, I. Chikina, and S. Nazin “Relaxation phenomena in cryogenic electrolytes”, Fiz. Nizk. Temp. 39, 712 (2013) |
| title_fullStr |
Дополнение к статье V. Shikin, I. Chikina, and S. Nazin “Relaxation phenomena in cryogenic electrolytes”, Fiz. Nizk. Temp. 39, 712 (2013) |
| title_full_unstemmed |
Дополнение к статье V. Shikin, I. Chikina, and S. Nazin “Relaxation phenomena in cryogenic electrolytes”, Fiz. Nizk. Temp. 39, 712 (2013) |
| title_sort |
дополнение к статье v. shikin, i. chikina, and s. nazin “relaxation phenomena in cryogenic electrolytes”, fiz. nizk. temp. 39, 712 (2013) |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Дополнение к статье V. Shikin, I. Chikina, and S. Nazin “Relaxation phenomena in cryogenic electrolytes”, Fiz. Nizk. Temp. 39, 712 (2013) / В. Шикин, I. Chikina, С. Назин // Физика низких температур. — 2014. — Т. 40, № 5. — С. 608-609. — Бібліогр.: 19 назв. — рос. |
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Low Temperature Physics/Физика низких температур, 2014, т. 40, № 5, c. 608–609
Дополнение к статье V. Shikin, I. Chikina, and S. Nazin
“Relaxation phenomena in cryogenic electrolytes”,
Fiz. Nizk. Temp. 39, 712 (2013)
В. Шикин1, I. Chikina2, С. Назин1
1Институт физики твердого тела РАН, г. Черноголовка, 142432, Россия
E-mail: shikin@issp.ac.ru
2IRAMIS, LIONS, UMR SIS2M 3299 CEA-CNRS, CEA-Saclay, F-91191 Gif-sur-Yvette Cedex, France
Статья поступила в редакцию 6 декабря 2013 г.
PACS: 67.10.–j Квантовые жидкости: основные свойства.
Ключевые слова: жидкий водород, внедренные ионы.
1. Формализм работы [1], использованный в описа-
нии нелинейных релаксационных явлений в жидком
гелии с радиоактивным источником ионов, либо в сла-
бом жидком электролите, оказывается весьма полез-
ным для анализа линейных по внешнему полю задач.
Речь идет о частотной дисперсии диэлектрической по-
стоянной ( )ε ω произвольного жидкого диэлектрика с
конечной вероятностью распада его молекул на заря-
женные фрагменты. В случае воды (aqua, 2H O) ионы
возникают по схемам
+ +
2 2 3 2H O H O H O OH , или H O H OH ,− −+ ↔ + ↔ + (1)
где соответственно: H+ — голый протон, OH− — гид-
роксил, +
3H O — гидроксоний [2,3].
Линейная задача о поведении системы нейтральных
молекул в слабом однородном электрическом поле E
выясняет, как ведут себя вектора D и P [4]
1
= 4 , =
4
ε −
+ π
π
D E P P E (2)
в функции от поля E. Для сложных жидкостей форма-
лизм вычисления ( )P E продвинут на молекулярный
уровень, позволяя определить ε
«из первых принципов».
И хотя найденные разными способами равновесные
значения theor
aqε дают величины, систематически мень-
ше наблюдаемых: theor
aq 50ε [5–9] вместо exp
aq 80ε
[10,11] — с вариациями, зависящими от свойств ис-
пользуемой модели отдельной молекулы 2H O, конеч-
ность результата theor
aqε ≠ ∞ не вызывает сомнений.
Наряду с однородным сценарием (2) имеется задача
о диэлектрической постоянной ε
при возмущении
жидкой среды сферически симметричным полем от-
дельного заряда [12–17]. Общие свойства ε
, ε
и ка-
чественные различия между ними в настоящей заметке
не обсуждаются.
Пусть теперь вода имеет конечную плотность ионов
в меру тепловой диссоциации молекул на заряженные
фрагменты (1). В однородном внешнем поле 0E ≠
заряженные кластеры начинают двигаться по своим
траекториям, создавая токи, либо собираясь в аккуму-
ляционные слои вблизи границ, пресекающих развитие
стационарного транспорта. Пример ячейки, исполь-
зуемой для измерений ε
, изображен на рис. 1 из [1].
Утверждение, которое предстоит доказать, заключает-
ся в том, что процесс разделения зарядов и образова-
ние аккумуляционных слоев на границах кюветы с
чистой водой под действием внешнего поля 0E ≠
бу-
дет продолжаться до его полной экранировки в объеме
электролита. Индекс параллельности подчеркивает
однородность поля E
.
Полное уничтожение внешнего поля в толще слоя
собственного полупроводника между обкладками кон-
денсатора можно считать уже доказанным, если обра-
тить внимание на далеко идущую аналогию между
статистическими свойствами жидких электролитов и
твердотельных полупроводников [18]. Роль проводя-
щих дырок в обсуждаемой аналогии с полупроводни-
ками играют кластеры гидроксония +
3H O (протон
вместе с «шубой» из молекул воды), подвижными
электронами оказываются заряженные фрагменты OH−
(гидроксил). Аналогия мотивирует статистическое
толкование термодинамики электролитов. В ее рамках
вода является собственным полупроводником (анало-
гия с собственными широкозонными полупроводника-
© В. Шикин, I. Chikina, С. Назин, 2014
Дополнение к статье «Relaxation phenomena in cryogenic electrolytes»
ми, имеющими щель gE T в своем энергетическом
спектре [18]). Характерная щель для распадного спектра
воды имеет масштаб 4800 К 300 КgE [2] ( 300 КT
отвечает комнатным температурам). Ее величина оп-
ределяет, в конечном итоге, степень диссоциации мо-
лекул воды 7
aq 10−α , использованную при оценке
relaxτ (11) в тексте [1]. Согласно [18,19] образование
в поле E
аккумуляционных слоев на границах устрой-
ства, рис. 1 из [1], заполненного собственным полупро-
водником, должно сопровождаться полной экраниров-
кой возмущающего поля в его толще ([19]).
Конечные цели создания аккумуляционных (инвер-
сионных) слоев в полупроводниках и задачи о согласо-
ванном определении ε
в жидких средах несколько
различны. Никто из авторов широко представленных в
[19] исследований 2D заряженных слоев не интересо-
вался степенью экранирования аккумуляционными
слоями внешнего поля и скоростями их релаксацион-
ного образования. При изучении свойств ε
жидкого
диэлектрика эти вопросы — на первом плане.
2. Диэлектрическая постоянная aq ( )ε ω чистой воды
обладает хорошо известной частотной дисперсией.
Речь идет о взаимодействии ее диполей с осциллиру-
ющими однородным электрическим полем, заставля-
ющим разворачиваться молекулы вслед за периодиче-
скими изменениями направления поля. Для воды ха-
рактерная частота Dω дипольной (дебаевской) релак-
сации находится в окрестности 11 12 1(10 –10 ) cD
−ω
,
разделяя между собой область повышенных значений
aq ( ) 1Dε ω ≤ ω и предел aq ( ) 1Dε ω ω → [2]. Здесь
ω — внешняя частота, на которой производятся стан-
дартные измерения емкости конденсатора рис. 1 из [1],
загруженного водой.
Учитывая сказанное выше, имеется еще один, низ-
кочастотный ( )Dω ω
интервал частот, в котором
aq ( )ε ω заметно возрастает, меняя свое значение от
большого aq ( ) 80 1ε ω в области relax 1ωτ
до
формально бесконечного предела aq ( 0)ε ω → → ∞ на
частотах в области relax 1ωτ
(предполагается выпол-
нение неравенства relax 1Dω τ
). Речь идет о релакса-
ционной экранировке внешнего поля небольшим чис-
лом свободных ионов, возникающих при диссоциации
молекул воды. Полная экранировка внешнего поля
даже малым количеством подвижных ионов и кинети-
ка достижения предела
real
aq ( 0)ε ω → → ∞ (3)
сводится к анализу свойств уравнения (10) из [1]. Ха-
рактерное время relaxτ установления стационара со-
гласно (10) из [1] дается формулой (11) из [1]. Числен-
ные значения этого времени для задачи о свойствах
aq ( )ε ω воды приведены в комментариях к (11) из [1] и
находятся в окрестности 3 4
relax (10 –10 ) c− −τ
, что
действительно отвечает ситуации 1
relaxD
−ω τ
.
Отметим наличие в радиотехнической практике
электролитических конденсаторов, емкость которых
аномально велика (с нашей точки зрения) за счет опи-
санного выше эффекта экранировки в электролите,
заполняющем межэлектродное пространство конден-
сатора. Кстати, из типичных приложений таких уст-
ройств в схемах выпрямителей следует оценка
1
relax > 50 Гц−τ , что согласуется с численными оценками
времени relaxτ с помощью (11) из [1].
Работа частично поддержана фондом РФФИ Грант
12 02 00229 и FP7-IRSES program, grant No. 236947
“SIMTECH”.
1. V. Shikin, I. Chikina, and S. Nazin, Fiz. Nizk. Temp. 39, 712
(2013) [Low Temp. Phys. 39, 552 (2013)].
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Low Temperature Physics/Физика низких температур, 2014, т. 40, № 5 609
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/ENU (Use these settings to create Adobe PDF documents that are to be checked or must conform to PDF/A-1b, an ISO standard for the long-term preservation \(archival\) of electronic documents. For more information on creating PDF/A compliant PDF documents, please refer to the Acrobat User Guide. Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.)
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>> setdistillerparams
<<
/HWResolution [2400 2400]
/PageSize [612.000 792.000]
>> setpagedevice
|