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As a sequel to results obtained on the low-temperature behavior of liquids, a similar study is presented for solids. A molecule in a solid interacts with the other molecules of the crystal so that it is subjected to a specific multimolecular potential, kT0. At temperature T < T0, the molecules are localized, and at T > T0, they can participate in processes like self-diffusion and evaporation. As a consequence, the van ’t Hoff equation is disobeyed at a low temperature and properties like vapor pressure, diffusion rate, or reactivity are zero below the specific temperature, T0, which here can be interpreted as a temperature of thermal stability of the solid. To account for this view, the van’t Hoff equation, represented by the green curve in the figure, is extended with a suitable pre-exponential factor, leading to the red curve. Three examples, taken from the literature, are analyzed to demonstrate its applicability. These examples are: the thermal dissociation of calcium carbonate, the sublimation equilibrium pressure of naphthalene, and that of ice. For some other solids, equilibria and dynamic properties, X(T), are examined by means of extrapolations in the X(T) versus T domain, showing the presence of an arrest temperature, which coincides, within experimental accuracy, with the T0 value obtained from the corresponding vapor pressure. As with liquids, kT0 is found to be proportional to the molecular pair potential.

The anomalous behavior of liquid water is apparent from the temperature dependence of many experimental properties. Among these are the abnormal high limiting ionic conductivities λ(0) of protons and hydroxyl ions, which in a previous paper we found to depend linearly on the square root of the absolute temperature T(1/2). Here we describe a further study of these conductivities in both light and heavy water, together with the remarkable transition temperature T(0) [242.7 K in H(2)O and 250.5 K in D(2)O], where the supercooled liquid becomes inert and, for example, restricted water molecule rotation is arrested. From T(0) the rotation barrier heights for the two solvents are determined. The conductivity data enable to obtain experimentally the zero point energies of H(+) and D(+) in liquid water, with results in the right order of magnitude as compared to values estimated along quantum mechanical routes. Contrary to general opinion, the isotope effect λ(0)(H(+))/λ(0)(D(+)) is temperature dependent, its value being close to 2(1/2) only near 20 °C. The isotope effect λ(0)(OH(-))/λ(0)(OD(-)) also takes temperature dependent values, substantially higher than 2(1/2). Still, the linear relationships with T(1/2) sustain a model based on water rotation control for the conductivity mechanism. For a quantitative analysis, the rotation frequency ω is expressed by a simple linear function of T(1/2) in terms of the moment of inertia I and the quantity T(0)(1/2). This "ab initio" calculation is found to be in perfect agreement with theoretical and experimental data in the literature, when ω is identified with the reciprocal of the so-called single molecule relaxation time τ(s). The data analysis eventually leads to the conclusion that the hydrogen ion transfer between water molecules proceeds via two parallel pathways. Next to the rotation controlled hopping mechanism there exists a temperature independent transfer controlled by tunnelling, occurring at all relative orientations of the participating water molecules. The applicability of the excess conductivity concept for hydrogen and hydroxyl ions is critically discussed.

The anomalous behaviour of the Tl+/Tl(Hg) electrode in 1 KNO3 + 0.1 M KCl solution has been studied experimentally applying the theory described in parts IV and VI of this series. It is shown that this anomaly can be explained assuming that the double layer capacity increases on adding thallous ions. The increase Δ C appears to be proportional to the TI+ concentration. The phase angle Φ of the faradaic impedance is equal to π/4.

A comparison is made of studies of the Hg2++/Hg electrode by means of complex plane analysis 1, 2 and double pulse galvanostatic step 4. As a possible explanation for the inconsistent results, interference by the double layer capacity in the latter method is suggested. It is shown that the results obtained for the same electrode by Imai and Delahay3 with faradaic rectification do not satisfy the conditions required for the approximations introduced. The exchange current densities are likely to be larger than reported. Another approximation procedure is proposed, which applies for very fast electrode processes (k0a > 3.10−3√ω.

A new and simple derivation of the diffusion polarization as a function of time is presented for the case wherein a square wave current passes an electrode-solution interface. The moment of zero diffusion polarization, which was already known to be 0.09, is calculated more precisely to be 0.094 of the whole period of the square wave signal. The consequences as regards the cyclic current step method for the determination of rate constants of electrode reactions, are discussed.

The sources of error pertaining to the oscilloscopic determination of rate constants of electrode reactions are studied and the upper and lower limits of the methods are given. The former is mainly determined by the accuracy with which the moment of zero diffusion polarization can be adjusted. It is shown that the extrapolation of cell responses to zero frequency does not eliminate the contribution of the double layer capacitance completely. The remaining contribution is a negative resistance,-2 σ2 Cd, irrespective of waveform.

The views developed in parts III and IV of this series are applied to alternating current polarography in the impedance plane. It is shown that from such polarograms a quantity q can be determined which is inversely proportional to concentration. The method covers a concentration range of 5.10−9/n2

From impedance measurements it is shown that the hydrogen ion reduction on mercury behaves as a case of pure activation polarization between -1.1 and -1.3 V vs S.C.E. with 1-α = 0.56 and ksh = 10−15 cm · sec−1. The value of the double layer capacity in that potential range is reported. No influence of hydrogen on the double layer capacity could be observed.

The values of the double layer capacity of the mercury-1 M HCIO4 solution interface at potentials where the dissolution of Hg contributes to the cell impedance, have been determined by the method previously described in parts VI1 and VII2.

The theory developed in part IV1 and part VI2 of this series has been verified by experiments. The results are

The accuracy of the double layer capacity measurements at high potentials described in part IX 1 is critically examined, especially with a view to the correct determination of the ohmic resistance of the cell. A limit for the exchange current density of the redox couple, which can be detected by the method of frequency variation, is determined. The systematic error in the calculated double layer capacity values, if this limit is just reached, is estimated. From impedance measurements in 0.1 M-HClO4 solution it appears that the capacity-potential curve is identical with that in 1 M-HClO4 solution.

The literature values of the limiting ionic conductivities of H(+), OH(-), K(+), Cl(-), Ag(+), and Na(+) in water between 0 and 156 degrees C are analyzed as for the two possible mechanisms of conduction, i.e., controlled by an activation process or by the rotation of the water molecules. Plots of the data versus T(1/2) give straight lines for H(+) and OH(-), which supports the rotation control mechanism for these ions. The other ions give curved plots and therefore are investigated in terms of the activation control mechanism. A remarkable phenomenon is discovered, namely, that except for H(+), the graphs for the other ions on extrapolation to lower temperatures have a common intersection point, T(0)(1/2), with the abscissa corresponding to T(0) = 243.4 K, i.e., -30 degrees C. This seems to indicate the presence of a virtual phase transition at about -30 degrees C, foreboding itself at higher temperatures. Below this temperature the supercooled water does not allow ions to migrate. Also, diffusion of solutes is found to cease, and dissociation constants drop to zero. The values of many physical properties of water appear also to approach zero at -30 degrees C, viz. the self-diffusion coefficient, reciprocal dielectric relaxation time, and solubilities of sparingly soluble salts. From data on the fluidity (reciprocal viscosity) and self-ionization constant it follows that the transition temperature of supercooled D(2)O is 9 degrees higher than of H(2)O. From the nearly quadratic shape of the several temperature dependencies it is inferred that the phase transition in question possibly is of some higher order. Implications for the transport number of protons to be expected in supercooled water are finally discussed.

Second harmonic polarograms in which, as predicted by theory, every reversible redox system gives rise to two peaks have been described in the literature1, 2, 3. In this paper the π radians phase difference between these two peaks is demonstrated, making use of the second harmonic content of the output of the oscillator driving the polarographic circuit. Anomalies in the case of the Tl(Hg)/Tl⊕- and the In(Hg)/In⊕⊕⊕-electrode are discussed.

A simple procedure is described by which the double layer capacity of mercury can be determined at potentials where the Hg/Hg2++ redox couple interferes with the direct mode of double layer capacity measurements. The results agree with those obtained recently with a different method1 .

The theory described in part I of this series 1 is applied to alternating current polarography by treating the complex cell impedance and cell admittance as functions of d.c. voltage. It is proposed to plot a.c. polarograms in the complex impedance or admittance plane. By this method it is possible to reduce the uncertainty in the height of the peak caused by the base current. An exactly linear relationship between the quantity measured and concentration can be obtained over a large range of concentrations by means of a simple construction. The measurements can be performed over a wide range of frequencies. Consequently, in some cases, a higher sensitivity can be obtained, because the most favourable frequency can be chosen. The method is not only suitable for analytical purposes, but also for the determination of the fundamental constants of electrode processes (rate constants, diffusion constants and double layer capacities).

As a more rapid method for the determination of values of the electrode coverage it is proposed to measure the differential capacity as a function of time at an initially clean electrode. This method appears to be applicable if the concentration of the surface-active substance is lower than a certain value. A theoretical expression for the rate of adsorption on a spherical electrode is derived and good agreement with experiment is obtained for 1-hexanol. Electrode coverage against √t curves are measured for 1-hexanol, thymol, sodium dodecyl sulfate and polyoxyethylene lauryl ether.

From double layer capacity measurements the fractional surface coverage of 1-hexanol, thymol, polyoxethylene lauryl ether and sodium dodecyl sulfate is determined at different potentials. It appears that the fractional surface coverage, defined in terms of the integral capacity, does not change with potential within the range -0.20 to -1.00 V against the S.C.E.

It is shown both by calculation and experimentally that in a galvanic cell with two plane electrodes, through which an alternating current flows, the concentration waves interfere if the distance of the electrodes is of the order of a wave length.

A high-quality contemporary animal care and use program (ACUP) is a multifaceted dynamic system with three distinct organizational entities--the institutional official (IO), attending veterinarian (AV), and institutional animal care and use committee (IACUC)--each of whose authorities and responsibilities are mandated by a complex set of laws, regulations, policies, and guidelines. The 3-legged stool is presented here as a metaphor for the properly constituted and functioning ACUP, with the legs of the stool representing the IO, AV, and IACUC: when one component is weakened, the stool remains standing but tilts--the ACUP remains in compliance with animal welfare standards but is at risk of failure. Mechanisms for assessing an ACUP's strengths and weaknesses include both external evaluators, such as the US Department of Agriculture, Office of Laboratory Animal Welfare, and Association for Assessment and Accreditation of Laboratory Animal Care, and internal evaluators, such as the IACUC, AV, and IO. However, each of these evaluators primarily assesses whether aspects of the ACUP are in compliance with current standards; they do not necessarily cite weaknesses in a compliant program. This article stresses the need for ACUPs to undertake a self-assessment of risk and outlines a number of ways programs can recognize their risks, with examples for each of the three components, which are characterized as either "weak" or "overzealous" in meeting their mandates. I caution against the use of a legacy of compliance as the sole means for evaluating an ACUP's strength, and instead promote the value of rigorous risk assessment/mitigation to ensure that a program is both strong and resilient.

Combining the results of three techniques the rate constant kF of Cd(II) reduction from aqueous 0.5 M Na2SO4 is obtained in a wide potential range. Just as has been found earlier with other base electrolytes the In kf vs. potential plot is strongly curved, indicating the mechanism of the electrode reaction to consist of several steps. Mathematical analysis of this curve compels us to the conclusion that the mechanism is CEeC. An attempt is made to reconcile the different values of the standard rate constant ks and transfer coefficient α published over many years, taking into account that experimental data were obtained in different regimes of the electrode potential and often unduly extrapolated to the standard potential.

An earlier study on the properties of supercooled water and some solutes obtained by simple graphical extrapolation of data available in the literature, determined above the freezing point, led to the hypothesis that water could have a temperature of structural arrest at t0 =-30 °C for H2 O and -22 °C for D2 O. From the present investigation of many more properties of a widely varied nature, this discovery is confirmed throughout. The method is compared with the classical logarithmic Arrhenius and van't Hoff methods that predict t0 always to occur at 0 K, and with the more recently used power law dependence method. With the latter, extrapolated plots intersect the temperature axis at or near to a value of ts =-45 °C, that is, systematically more negative than t0 . It is argued that this ts value, which is the so-called singularity temperature, is likely to be an artefact. It is suggested that, instead of using modified van 't Hoff or Arrhenius relationships to describe temperature dependences in the full temperature range, polynomials in (t-t0 ) should be used.

The reduction of Zn(II) from aqueous l M NaClO 4 solution in the presence of 1 mM HClO 4 was studied at dropping gallium and mercury electrodes. The dropping microelectrode technique was succesfully extended to the use of gallium as the electrode material. Net Zn(II)/Zn(Ga) waves were obtained after subtracting the H 3 O + reduction current recorded in the absence of the Zn(II)/Zn(Ga) couple from the experimental voltammograms. The waves obtained at the conventional dropping gallium electrode proved to be reversible and occurred around E f 0 (Zn(II)/Zn(Ga)) = ∮.989 V vs. SSCE. On the short timescale of the dropping gallium and mercury microelectrodes the Zn(II) reduction appeared quasi-reversible, which made it possible to determine the kinetic parameters of the reaction. The Zn(II) reduction at liquid gallium was found to proceed via the same two-step electron transfer mechanism as that established earlier at mercury. Within the entire accessible potential range the reduction rate constant at gallium was found to be about four times higher than that at mercury.

The faradaic admittance for a consecutive E-C-E mechanism with two stable intermediates is derived with the assumption that the chemical reaction is unidirectional. Both cases where this reaction is homogeneous or heterogeneous are treated. The admittance derived assuming that the chemical step is slow in comparison with the frequency of the a.c. perturbation has the same frequency dependence as that derived by Armstrong and Firman for a consecutive E-E mechanism with a stable intermediate. The presence of the chemical step in the E-C-E mechanism appears in the altered potential dependence of the admittance data. Four cases are distinguished in which the general admittance expression reduces to the simpler Randles expression (pseudo-Randles cases). The theory is applied to the reduction of nitromethane in aqueous 1 M NaCl solutions of pH 2.4. Several methods of analysis are proposed. It is found that a simultaneous analysis of the frequency and potential dependence of the admittance data is to be preferred compared with the habitual procedure of frequency analysis at successive fixed potentials. The final reaction parameters obtained from the analysis are discussed in comparison with previous data obtained in basic media, which conform well to an E-Ce mechanism with only one stable intermediate.