Chemistry in noninteger dimensions between two and three. I. Fractal theory of heterogeneous surfaces

单层 分形维数 曲面(拓扑) 吸附 半径 分形 维数(图论) 相似性(几何) 系列(地层学) 化学 数学 材料科学 几何学 纳米技术 组合数学 物理化学 数学分析 图像(数学) 计算机科学 古生物学 计算机安全 人工智能 生物
作者
Peter Pfeifer,David Avnir
出处
期刊:Journal of Chemical Physics [American Institute of Physics]
卷期号:79 (7): 3558-3565 被引量:1102
标识
DOI:10.1063/1.446210
摘要

In this, the first of a series of papers, we lay the foundations for appreciation of chemical surfaces as D-dimensional objects where 2≤D<3. Being a global measure of surface irregularity, this dimension labels an extremely heterogeneous surface by a value far from two. It implies, e.g., that any monolayer on such a surface resembles three-dimensional bulk rather than a two-dimensional film because the number of adsorption sites within distance l from any fixed site, grows as lD. Generally, a particular value of D means that any typical piece of the surface unfolds into mD similar pieces upon m-fold magnification (self-similarity). The underlying concept of fractal dimension D is reviewed and illustrated in a form adapted to surface-chemical problems. From this, we derive three major methods to determine D of a given solid surface which establish powerful connections between several surface properties: (1) The surface area A depends on the cross-section area σ of different molecules used for monolayer coverage, according to A∝σ(2−D)/2. (2) The surface area of a fixed amount of powdered adsorbent, as measured from monolayer coverage by a fixed adsorbate, relates to the radius of adsorbent particles according to A∝RD−3. (3) If surface heterogeneity comes from pores, then −dV/dρ∝ρ2−D where V is the cumulative volume of pores with radius ≥ρ. Also statistical mechanical implications are discussed.
最长约 10秒,即可获得该文献文件

科研通智能强力驱动
Strongly Powered by AbleSci AI
更新
PDF的下载单位、IP信息已删除 (2025-6-4)

科研通是完全免费的文献互助平台,具备全网最快的应助速度,最高的求助完成率。 对每一个文献求助,科研通都将尽心尽力,给求助人一个满意的交代。
实时播报
苏y完成签到,获得积分10
1秒前
华仔应助嘻哈采纳,获得10
1秒前
科研通AI5应助优秀的绿蕊采纳,获得10
4秒前
健忘的初翠完成签到,获得积分10
4秒前
6秒前
lwm不想看文献完成签到 ,获得积分10
6秒前
8秒前
拼搏一曲发布了新的文献求助10
9秒前
CAOHOU应助科研通管家采纳,获得10
10秒前
共享精神应助科研通管家采纳,获得10
10秒前
CAOHOU应助科研通管家采纳,获得10
10秒前
SYLH应助科研通管家采纳,获得20
10秒前
乐乐应助科研通管家采纳,获得10
10秒前
汉堡包应助科研通管家采纳,获得10
10秒前
FashionBoy应助科研通管家采纳,获得10
10秒前
桐桐应助科研通管家采纳,获得10
10秒前
10秒前
深情安青应助科研通管家采纳,获得10
10秒前
CAOHOU应助科研通管家采纳,获得10
10秒前
SYLH应助科研通管家采纳,获得10
10秒前
CAOHOU应助科研通管家采纳,获得10
10秒前
Owen应助科研通管家采纳,获得10
11秒前
SYLH应助科研通管家采纳,获得10
11秒前
SYLH应助科研通管家采纳,获得10
11秒前
11秒前
酷波er应助科研通管家采纳,获得10
11秒前
wushuwen发布了新的文献求助10
11秒前
12秒前
xuan完成签到,获得积分10
13秒前
完美世界应助段一帆采纳,获得10
15秒前
少敏敏完成签到,获得积分10
17秒前
may发布了新的文献求助10
17秒前
22秒前
24秒前
兜兜关注了科研通微信公众号
24秒前
wbh完成签到,获得积分10
25秒前
太牛的GGB发布了新的文献求助10
25秒前
wbh发布了新的文献求助10
27秒前
乐乐应助may采纳,获得10
27秒前
顺利的梦菲完成签到 ,获得积分10
28秒前
高分求助中
A new approach to the extrapolation of accelerated life test data 1000
ACSM’s Guidelines for Exercise Testing and Prescription, 12th edition 500
‘Unruly’ Children: Historical Fieldnotes and Learning Morality in a Taiwan Village (New Departures in Anthropology) 400
Indomethacinのヒトにおける経皮吸収 400
Phylogenetic study of the order Polydesmida (Myriapoda: Diplopoda) 370
基于可调谐半导体激光吸收光谱技术泄漏气体检测系统的研究 350
Robot-supported joining of reinforcement textiles with one-sided sewing heads 320
热门求助领域 (近24小时)
化学 材料科学 医学 生物 工程类 有机化学 生物化学 物理 内科学 纳米技术 计算机科学 化学工程 复合材料 遗传学 基因 物理化学 催化作用 冶金 细胞生物学 免疫学
热门帖子
关注 科研通微信公众号,转发送积分 3989378
求助须知:如何正确求助?哪些是违规求助? 3531442
关于积分的说明 11254002
捐赠科研通 3270126
什么是DOI,文献DOI怎么找? 1804887
邀请新用户注册赠送积分活动 882087
科研通“疑难数据库(出版商)”最低求助积分说明 809173