# Electrochemistry of J Ross Macdonald

Because there are more than 250 scientific publications listed in this website, http://jrossmacdonald.com, the present file, written in 05/2009 and updated in 2012 and 2013, is provided to help readers identify the electrochemical ones, and especially those of most importance and/or popularity by subject. Macdonald’s early work in electrochemistry was more theoretical than experimental and all of it involved both the ionics and electrodics aspects of electrochemistry. Much of the early electrochemistry work involved ions in solution and concentrated on ionic motion, double-layer structure and effects, and reaction and adsorption at electrodes. In contrast, most of his publications since about 1987 have been devoted to theoretical and experimental Impedance Spectroscopy (IS) studies of the effects of ionic conduction and dielectric behavior in solids such as single crystals, disordered materials, supercooled liquids, and glasses. Details, keyed to specific publications, are summarized below.

As a help to the reader, a citation activity number, as of 2010, will be listed for appropriate papers discussed below. There are two relevant gatherers of such data: ISI (Web of Science), coverage beginning in 1955, and Google Scholar, less complete. A paper with 100 citations will be designated by either I100 or G100. To provide a possibly appropriate scale measure, the SPIRES database of SLAC states that items that are cited at least 500 times are classified as “renowned,” their highest category; ones from 250-499 as “famous;” and ones from 100 to 249 as “very well known.” Obviously, older papers have had more time to accumulate citations than recent ones.

This website now makes available all of Macdonald’s scientific publications in pdf form for possible downloading. They appear in a both a categorized listing and in a temporally ordered serial one (where they may be downloaded) and will be referred to below by their numbers in the serial listing. A relevant category, Electrolytes/Electrochemistry, involves four subcategories and lists more than four pages of publications. In addition, the category, Conductive-System Response and Dispersion, comprises nearly four pages of relevant publications. Many early papers involved collaboration with Carl Barlow or Donald Franceschetti.

**1953 – 1987**

Macdonald’s work in this time frame began with #**11**, G68, of 1953, “Theory of Space-Charge Polarization Effects in Photoconductors, Semiconductors, and Electrolytes,” the first work in this important area that correctly included Poisson-equation requirements; later extended and illustrated in #’s **100**, I136; **105**, I94: “Binary Electrolyte Small-Signal Frequency Response;” and **183**: “Small-Signal AC Response of an Electrochemical Cell with Completely Blocking Electrodes,” in 1962, 1973, 1974, and 1988, respectively. Further important related work appeared in **122**, I72 and **124**, I56 of 1977 and 1978. Accurate numerical and analytical results of the nonlinear frequency and transient responses of ionic materials subjected to a dc potential difference were presented for the first time in **126**, I26 and **131**, I26 of 1979. Also, probably the first accurate treatments of finite-length Warburg responses appear in **91**, I91, and **92**, I40. Further, the LEVM fitting program includes on pp. 4-9 and 4-10 anomalous-diffusion generalizations of such responses.

A great deal of work since 1953 was concerned with the electrolyte double layer, some of it groundbreaking. See the categories, “Double layer, adsorption” and “Space Charge” in the categorized list in the website. Early work on double layer theory and behavior appears in **18**, I25 and **66**, I114. Especially noteworthy are the 48-page paper on “Equilibrium Double Layer Theory” of 1965, #**77**, and the 200-page double-layer discreteness-of-charge paper, #**87**, in Advances in Electrochemistry and Chemical Engineering, Vol. 6, of 1967. This review organizes and extends discreteness of charge calculations for infinite imaging, **71**, I43; single imaging, **78**, I29; and dielectric-conductive imaging, **84**, I17 of 1964-1966. Later in the 1980’s many detailed new analyses of double layer structure and behavior appeared: e.g, #’s **129, 138, 143, 148, 151, 152, 156, 160, 164, 168, 176**, and **180**.

Note that #**138** is a comprehensive 46-page paper, the invited NAS Whitehead Memorial Lecture of 1980, on “Interface Effects in the Electrical Response of Non-metallic Conducting Solids and Liquids.” Further, #**180**, “Impedance Spectroscopy and the Double Layer in Solids and Liquids,” is an 87-page one resulting from an invitation to speak at the 30th Welch Conference on Chemical Research: Advances in Electrochemistry, 1986*. Particularly interesting are the last 17 pages in #180 containing discussion of this subject by experts in the field.* A 1991 paper entitled, “Interpretation of Finite-Length-Warburg-Type Impedances in Supported and Unsupported Electrochemical Cells with Kinetically Reversible Electrodes,” #

**188**, I58, has proved to be of perennial interest with, for example, 49 hits on it at the JRM website for the month of March 2009. Other popular papers in the period from 1972 to 1984 are

**91**, I91;

**108**, I217;

**120**, I127;

**132**, I70;

**149**, I218; and

**162**, I84.

Paper #**120**, I127 presents the development of the first complex nonlinear least squares (CNLS) fitting program for accurate fitting of both the real and imaginary parts of frequency-response immittance data simultaneously. It later led to the important LEVM fitting and inversion computer program, one largely developed, supported, and extended in #’s **179**, G73; **196**, I54; **206**, I36; **220**, I34; etc., freely available and widely used in the electrochemistry area. This large program and manual, useful for electrochemical impedance spectroscopy (EIS) and for all other IS areas of application, have been accessed about 100 times a month on average in recent times, frequently downloaded, and several thousand or more copies of it are in use throughout the world.

**1987- to date**

Most of Macdonald’s extensive work on impedance (more generally: immittance) spectroscopy deals with the effects of mobile ions in solution and in solids. Notable is the book, *Impedance Spectroscopy*, Wiley 1987, #**178**, that Macdonald edited and was a major contributor to. It was the first substantial book devoted to IS. In a contemporaneous review of it, it was termed a “classic work” and a “must” have. It and its 2005 second edition, longer, more comprehensive, and more up to date, see #**234**, have been very popular and useful to many workers in the field. As an example, entering JR Macdonald in Google Scholar led, on 5/6/09, to 1811 citations of the 1992 summary paper #**187**, G1811: “Impedance Spectroscopy,” and to 947 for the original IS book, **178**, G947.

In an exploration of citations for publications of electrochemical and condensed-matter physical scientists using Google Scholar, very few papers or books exceeded 500 citations and no papers with citation numbers even close to 1811 were discovered. It is presumably so high here because it involves the concatenation of “Macdonald” and “Impedance Spectroscopy.” Its citation count is still increasing appreciably each month, and its size and continued growth are consistent with the identification of Macdonald as a principal father of the IS and EIS fields.

Other particularly popular IS-related publications, in addition to those mentioned above, are **177**, I111; **181**, I106; **186**, I96; and **188**, I58. Below, other relevant publications are listed by subject.

**>Subject identifications**

*>Distributions of relaxation times (DRT) and inversion of EIS data*>

See #’s**181**,**197, 206, 212, 229, 239, 241**, and**244**. The first accurate determinations of DRTs from temporal or frequency domain data and comparison of inversion methods.*>Discrimination between dielectric-system and conductive-system dispersion*

See #’s**174, 211, 216, 218, 227, 246, 247**,**248**,**249, 252, and 256**. Is it impossible for experimental data? See**256**for discussion of six**ambiguities**in IS model fitting.*>Electrode effects and their modeling*

See #’s**162**(constant-phase element),**227, 237, 243, 245, 246, 248**,**249, 251, 252, and 254**. These effects are often improperly ignored in data fitting analyses, often leading to incorrect fitting- parameter estimates.*>Nearly constant loss behavior and new physical representations for it*>

See #’s**203, 225, 226, 227, 231**,**249**, and**251**.*>Some materials whose IS data sets are analyzed by CNLS and LEVM*- >Beta-PbF
_{2}:**142, 146**. - >Hydrogen-doped, single-crystal Li
_{3}N:**150**. - >Electrochromic thin films:
**154**. - >Single-crystal beta-alumina:
**163, 171**. - >NaCl:
**201**. - >Yttrium-stabilized zirconia:
**205**. - >Water, n-pentanol alcohol, glycerol:
**206**. - >Methanol:
**208**. - >CaTiO
_{3}:30%Al^{3+}:**209** - >Li
_{2}O-Al_{2}O_{2}-2SiO_{2}(LAS) glass:**208, 209, 212, 224, 239**. - >Na
_{2}O-3SiO_{2}:**212, 221, 225.** - >Single-crystal 0.88ZrO
_{2}-0.12Y_{2}O_{3}, xNa_{2}O-(1-x)GeO_{2}:**226, 227, 230.** - >0.5Li-0.5La-TiO
_{3}:**234**,**235**. - >Mixed alkali, 0.5Li-0.5La-TiO
_{3}, xK_{2}O-(1-x)GeO_{2}:**235**. - >Alkali phosphate and metaphosphate glasses:
**237**. - >0.18Li-0.61La-TiO
_{3}:**238**. - >Metal-core orthosilicate shell and iron oxide shell nanocomposites:
**240**,**242**. - >Seven different materials:
**243** - >Supercooled 0.4Ca(NO
_{3})_{2}-0.6KNO_{3}(CKN):**245**,**249**. - >Glass-forming molecular liquids N-methyl-e-caprolactam (NMEC), glycerol:
**246**. - >Fast-ion glass 0.35Li
_{2}S-0.65GeS_{2}:**248**. - >LiPO
_{3}:**251.** - >Hydrogel:
**252**. - CaCu
_{3}Ti_{4}O_{12}:**252, 254, 256.** *n*-octylcyanobiphenol:**256.**_{ }_{ }_{ }

- >Beta-PbF
*>Modeling results: old and new analysis models developed and compared*

**>Critiques of various fitting/interpretation models**

The universal dielectric (or dynamic) power-law model and stretched-exponential derived ones: **171**, **211**, **221, 230**, **243.**

Effective medium and distributed transition rate ones: **202**,** 249**.

Errors in the electric modulus formalism model and discussion of correct alternatives: **208, 212, 224, 226, 229, 230, 232, 235, 248**.

The Ngai coupling model and the more appropriate cutoff one: **217, 234, 238, 247.**

The Funke mismatch-and-relaxation and MIGRATION models: **219**, **249.**

Discussion of random-barrier, random-walk data analysis models:** 249.**

The Poisson-Nernst-Planck (PNP/PNPA) ordinary- and anomalous-diffusion conductive-system models: **252-256. **The full PNP/PNPA model, available in Circuit-H of LEVMW, is of exceptional importance because when it is used to fit unsupported IS data it can yield estimates of the values of more physically relevant model parameters than can any other available one: e.g., usual bulk quantities such as resistivity and dielectric constant, and especially a neutral-species concentration, equal concentrations of possibly mobile positive and negative charges dissociated from the neutral species, mobilities and diffusion constants of these species, their dissociation and recombination parameters, and three electrode-reaction and specific-adsorption parameters for each species of mobile charge.

**>Appropriate old and new dispersive models**

DCD, DC0, DC1 Davidson-Cole models; KD dielectric-system and K0 conductive-system stretched-exponential models; the microscopic CTRW Scher-Lax model and its isomorphic macroscopic and microscopic stretched-exponential-derived conductive system CK1 and CUN models: **208, 212, 226, 229, 233, 235, 239, 247, 248, 249**. The CUN model (the CK1 with a beta1 shape parameter value of 1/3) is quasi-universal with beta1 independent of such exogenous variables as temperature and ionic concentration. The CK0, CK1, and CUN models were first derived by Macdonald and were made available for accurate fitting using LEVM. They generally fit conductive-system-dispersive data with charges of a single type mobile appreciably better than do other models. Recently, in **251** much work on the analysis of data from ion-conducting solids is reviewed, and some new evaluations are presented of the applicability of the Barton-Nakajima-Namikawa (BNN) relation for various fitting models. Papers **252-256** present substantial discussions and analyses of the utility and generality of continuum-diffusion fitting models of PNP and PNPA type, starting from the work of paper **11** of 1953.

**>Statistical measures of activity and interest**

In addition to the remarkably high citation numbers for the 1987/2005 IS book and for the #**187** Impedance Spectroscopy review paper, comprehensive measures of the current interest in Macdonald’s work are provided by the statistical results of activity on his webpage for the month of April 2009, a month where only at its end did all of his publications finally became available for downloading. The comparable February 2012 figures are listed in parentheses after the earlier April 2009 ones: 576 (522) unique visitors participated in 755 (784) visits, ones involving 2041(1566) pages and 5206 (8989) hits.

The April 2009 statistical summary involved a listing of 247 identified different pages, showing a maximum of 481 viewings per page down to a minimum of one per page. For example, 165 different viewings were listed for one page. Most of the rest of the other 246 pages also involved multiple viewing of EIS paper listings, such as 21 (32) for paper #**162 **on parameterization of the constant-phase admittance element. Further, of the 64 papers published after 1987, there were 39 electrochemically oriented ones involving two or more individual viewings, with an average of nearly seven per day for this group.

For February 2012, there were download hits for 240 separate items in the scientific and miscellaneous writing lists, ranging from 1506 hits for #**187**, 160 for the LEVM manual, 99 for the LEVM/LEVMW program, and ranging down to 1 hit apiece for the last 15 items of the list.

Finally, for 61 listed countries, there were 1995 hits from USA addresses, 428 from Europe, 387 from Romania (!), 15 for Hungary, etc. These numbers were all smaller for February 2012.