03964.com

文档资料库 文档搜索专家

文档资料库 文档搜索专家

Plasmonic Steam Generator

Introduction

In this problem we study an efficient process of steam production that has been demonstrated to work experimentally. An aqueous solution of sp

herical nanometer-sized silver spheres (nanoparticles) with only about particles per liter is illuminated by a focused light beam. A fraction of the light is absorbed by the nanoparticles, which are heated up and generate steam locally around them without heating up the entire water solution. The steam is released from the system in the form of escaping steam bubbles. Not all details of the process are well understood at present, but the core process is known to be absorption of light through the so-called collective electron oscillations of the metallic nanoparticles. The device is known as a plasmonic steam generator.

T2

Figure 2.1 (a) A spherical charge-neutral nanoparticle of radius R placed at the center of the coordinate system. (b) A sphere with a positive homogeneous charge density (red), and containing a smaller spherical charge-neutral region (0, yellow) of radius , with its center displaced by . (c) The sphere with positive charge density of the nanoparticle silver ions is fixed in the center of the coordinate system. The center of the spherical region with negative spherical charge density – (blue) of the electron cloud is displaced by , where . (d) An external homogeneous electric field . For time) dependent , the electron cloud moves with velocity . (e) The rectangular vessel ( containing the aqueous solution of nanoparticles illuminated by monochromatic light propagating along the -axis with angular frequency and intensity .

A single spherical silver nanoparticle

Throughout this problem we consider a spherical silver nanoparticle of radius and with its center fixed at the origin of the coordinate system, see Fig. 2.1(a). All motions, forces and driving fields are parallel to the horizontal -axis (with unit vector ). The nanoparticle contains free (conduction) electrons moving within the whole nanoparticle volume without being bound to any silver atom. Each silver atom is a positive ion that has donated one such free electron. Find the following quantities: The volume and mass of the nanoparticle, the 2.1 number and charge density of silver ions in the particle, and for the free electrons their concentration , their total charge , and their total mass . 0.7

Page 1 of 4

Plasmonic Steam Generator

The electric field in a charge-neutral region inside a charged sphere

For the rest of the problem assume that the relative dielectric permittivity of all materials is . Inside a charged sphere of homogeneous charge density and radius R is created a small spherical charge-neutral region of radius by adding the opposite charge density , with its center displaced by from the center of the R-sphere, see Fig. 2.1(b). 2.2 Show that the electric field inside the charge-neutral region is homogenous of the form ( ) , and determine the pre-factor . 1.2

T2

The restoring force on the displaced electron cloud

In the following, we study the collective motion of the free electrons, and therefore model them as a single negatively charged sphere of homogeneous charge density with a center position , which can move along the x-axis relative to the center of the positively charged sphere (silver ions) fixed at the origin of the coordinate system, see Fig. 2.1(c). Assume that an external force displaces the electron cloud to a new equilibrium position with . Except for tiny net charges at opposite ends of the nanoparticle, most of its interior remains charge-neutral. 2.3 Express in terms of and n the following two quantities: The restoring force exerted on the electron cloud and the work done on the electron cloud during displacement. 1.0

The spherical silver nanoparticle in an external constant electric field

A nanoparticle is placed in vacuum and influenced by an external force due to an applied static homogeneous electric field , which displaces the electron cloud the small distance , where . Find the displacement of the electron cloud in terms of , and determine the 2.4 amount of electron charge displaced through the yz-plane at the center of the 0.6 nanoparticle in terms of .

The equivalent capacitance and inductance of the silver nanoparticle

For both a constant and a time-dependent field , the nanoparticle can be modeled as an equivalent electric circuit. The equivalent capacitance can be found by relating the work , done on the separation of charges , to the energy of a capacitor, carrying charge . The charge separation will cause a certain equivalent voltage across the equivalent capacitor. 2.5a Express the systems equivalent capacitance C in terms of 2.5b and , and find its value. 0.7

For this capacitance, determine in terms of and the equivalent voltage should be connected to the equivalent capacitor in order to accumulate the charge

that 0.4 .

Page 2 of 4

Plasmonic Steam Generator

For a time-dependent field , the electron cloud moves with velocity , Fig. 2.1(d). It has the kinetic energy and forms an electric current flowing through the fixed yz-plane. The kinetic energy of the electron cloud can be attributed to the energy of an equivalent inductor of inductance carrying the current . 2.6a Express both 2.6b and in terms of the velocity . 0.7 0.5

T2

Express the equivalent inductance in terms of particle radius , the electron charge and mass , the electron concentration , and calculate its value.

The plasmon resonance of the silver nanoparticle

From the above analysis it follows that the motion, arising from displacing the electron cloud from its equilibrium position and then releasing it, can be modeled by an ideal LC-circuit oscillating at resonance. This dynamical mode of the electron cloud is known as the plasmon resonance, which oscillates at the so-called angular plasmon frequency . 2.7a 2.7b Find an expression for the angular plasmon frequency of the electron cloud in terms 0.5 of the electron charge and mass , the electron density , and the permittivity . Calculate frequency in rad/s and the wavelength . in nm of light in vacuum having angular 0.4

The silver nanoparticle illuminated with light at the plasmon frequency

In the rest of the problem, the nanoparticle is illuminated by monochromatic light at the angular plasmon frequency with the incident intensity . As the wavelength is large, , the nanoparticle can be considered as being placed in a homogeneous harmonically oscillating field ( ) . Driven by , the center ( ) of the electron cloud oscillates at the same frequency with velocity and constant amplitude . This oscillating electron motion leads to absorption of light. The energy captured by the particle is either converted into Joule heating inside the particle or re-emitted by the particle as scattered light. Joule heating is caused by random inelastic collisions, where any given free electron once in a while hits a silver ion and loses its total kinetic energy, which is converted into vibrations of the silver ions (heat). The average time between the collisions is , where for silver nanoparticle we use . Find an expression for the time-averaged Joule heating power in the nanoparticle 2.8a as well as the time-averaged current squared ? ?, which includes explicitly the time- 1.0 averaged velocity squared ? ? of the electron cloud. Find an expression for the equivalent ohmic resistance 2.8b model of the nanoparticle having the Joule heating power current I. Calculate the numerical value of . in an equivalent resistordue to the electron cloud 1.0

Page 3 of 4

Plasmonic Steam Generator

The incident light beam loses some time-averaged power by scattering on the oscillating electron cloud (re-emission). depends on the scattering source amplitude , charge , angular frequency and properties of the light (the speed of light and permittivity in vacuum). In terms of these four variables, By use of logy with is given by . (in ana-

T2

2.9

, find an expression of the equivalent scattering resistance ) in an equivalent resistor-model, and calculate its value.

1.0

The above equivalent circuit elements are combined into an LCR series circuit model of the silver nanoparticle, which is driven by a harmonically oscillating equivalent voltage ( ) determined by the electric field of the incident light. Derive expressions for the time-averaged power losses and involving the of the electric field in the incident light at the plasmon resonance 1.2 2.10a amplitude . 2.10b Calculate the numerical value of , , and . 0.3

Steam generation by light

An aqueous solution of silver nanoparticles is prepared with a concentration . It is placed inside a rectangular transparent vessel of size and illuminated by light at the plasmon frequency with the same intensity at normal incidence as above, see Fig. 2.1(e). The temperature of the water is and we assume, in fair agreement with observations, that in steady state all Joule heating of the nanoparticle goes to the production of steam of temperature , without raising the temperature of the water. The thermodynamic efficiency of the plasmonic steam generator is defined by the power ratio , where is the power going into the production of steam in the entire vessel, while is the total power of the incoming light that enters the vessel. Most of the time any given nanoparticle is surrounded by steam instead of water, and it can thus be described as being in vacuum. 2.11a 2.11b Calculate the total mass per second of steam produced by the plasmonic steam ge0.6 nerator during illumination by light at the plasmon frequency and intensity . Calculate the numerical value of the thermodynamic efficiency steam generator. of the plasmonic 0.2

Page 4 of 4

相关文章:

- 2013年全俄物理奥林匹克理论部分答案
*2013*年全俄*物理奥林匹克理论*部分答案_韩语学习_外语学习_教育专区。*2013*年全俄*物理奥林匹克理论*部分答案 5v2sin4?39-1. ??arctan,L??500m,v0?5vsin2??48m/...

- 第16届国际物理奥林匹克竞赛试题及答案
*(理论*部分*)**(*1985 南斯拉夫 波尔托罗日) 题 1 一位年青的业余无线电爱好者用...第二种方案是使飞第 3 页共 6 页 第十六届*国际*中学生*物理奥林匹克竞赛试题*...

- 2009-2013年全俄物理奥林匹克理论部分附答案
- 2009-
*2013*年全俄*物理奥林匹克理论*部分附答案_学科*竞赛*_高中教育_教育专区。这是2009-*2013*年(43-47届)全俄*物理奥林匹克*的*理论*部分的*试题*与答案。2009...

- 第2届国际物理奥林匹克竞赛试题与解答
- 第
*2*届*国际物理奥林匹克竞赛试题*与解答(1968 年于匈牙利的布达佩斯) 【题1】 在倾角为 30 的斜面上,质量为 m2=4 kg 的木块经细绳与质量为 m1=8 kg 、 半...

- 历届国际物理奥林匹克竞赛试题与解答
- 历届
*国际物理奥林匹克竞赛试题*与解答 第2届 (1968 年于匈牙利的布达佩斯) 0 【...按照教科书中通常的*理论*推导,半径 PO=R 的凹面镜的焦点位于距离 R 的中点 F...

- 第31届国际物理奥林匹克竞赛试题理论试题
- 北京英才苑网站 http://www.ycy.com.cn 版权所有盗版必究 第 31 届
*国际物理奥林匹克竞赛*试题*理论试题*题1 A 某蹦迪运动员系在一根长弹性绳子的一端, 绳的另 ...

- 2013年第30届全国中学生物理竞赛预赛试卷及答案(word版)
*2013*年第30届全国中学生*物理竞赛*预赛*试卷*及答案(word...4m2 m1 由玻尔*理论*可知,当氢原子中的核外电子由...(8 分*)国际*上已规定 133 Cs 原子的频率 f=...

- 02历届国际物理奥林匹克竞赛试题与解答
- 北京英才苑网站 http://www.ycy.com.cn 版权所有盗版必究 历届
*国际物理奥林匹克竞赛试题*与解答第2届 (1968 年于匈牙利的布达佩斯) 【题1】 在倾角为 300 的...

- 第8届国际物理奥林匹克竞赛试题及解答
- 世纪金榜 圆您梦想 www.jb1000.com 第 8 届
*国际物理奥林匹克竞赛试题*与解答(1975 年于德意志民主共和国的居斯特罗) 【题 1】一根杆以恒定的角速度 ω 绕竖直...

- 2015年全俄物理奥林匹克(理论部分)竞赛试题及答案
- 2015年全俄物理奥林匹克
*(理论*部分)*竞赛试题*及答案_学科*竞赛*_初中教育_教育专区。...第27届*国际物理奥林匹克*... 20页 2下载券 2009-*2013*年全俄物理奥林... 43...

更多相关标签:

- 奥林匹克数学竞赛 | 国际奥林匹克数学竞赛 | 国际化学奥林匹克竞赛 | 奥林匹克数学竞赛试题 | 国际物理奥林匹克竞赛 | 国际地理奥林匹克竞赛 | 世界奥林匹克竞赛 | 小学奥林匹克数学竞赛 |

- 2013国际物理奥林匹克竞赛理论试卷(3)
- 2013国际物理奥林匹克竞赛理论试卷(1)
- 2013国际物理奥林匹克理论试卷数据表
- 2013初三暑假物理奥赛17(奥赛实战二)
- 2013年高一物理奥赛选拔测试2 2013
- 2013舒幼生暑假物理奥赛培训班联谊赛试卷(杭州富阳)
- 扬州市江都区国际学校2012-2013学年度第二学期八年级物理期中试卷及答案
- 河南省安阳一中2012-2013学年高一第二次阶段考试物理试题(奥赛班)
- 河南大学物理与电子学院2012—2013学年第二学期期末考试《通信原理》试卷A答案
- 2013初三暑假物理奥赛2(质量和密度)
- 2013国际物理奥林匹克竞赛理论试卷(3)
- 2013国际物理奥林匹克竞赛理论试卷(1)
- 32届国际物理奥林匹克竞赛试题及答案(中文)
- 2013年第54届国际数学奥林匹克竞赛真题中文版(官方)
- 第31届国际物理奥林匹克竞赛试题