Chemistry Article Summary

Chemistry Article Summary
‘Correlations in the Motion of Atoms in Liquid Argon’ is a seven-page journal article that is authored by A. Rahman, which discusses molecular dynamics. In fact, the article presents the summary of a study that incorporated the use of digital computes to experiment on the time and space (distance) dependence of two-body correlations that characterize the slow inelastic scattering of neutrons in liquid argon at specified temperature and density conditions. Overall, the author notes that the available theories on molecular dynamics have failed to explain the inelastic scattering of neutrons noted in liquid argon, suggesting that a delayed-convolution approximation was necessary to address that need (Rahman, 1964). As such, the article contributes to molecular dynamics studies by testing the prevailing theories and proposing a more appropriate theory that match the results noted for inelastic scattering of neutrons in liquid argon.
The author introduces the article’s intentions by noting the available molecular dynamics theories for the two-body dynamical correlation accounting for the observations made in liquid argon. This is followed by a description of the computational method applied in the paper, noting that an argon atom had a specific mass with the atoms paired to facilitate interactions. The paired atoms were then excited to move, and the movements subjected to calculations that noted the oscillations with the predictor-corrector applied to improve the results accuracy.

Next, the distance of closest approach for the atoms was calculated. This was followed by the mean velocity in oK while undergoing the potential minimum. Finally, the period of oscillations was noted. The results from the computations were evaluated for time-dependent and time-independent correlations. The results presented in the article revealed that there were differences noted each time there was a pass, to imply that approximations involved in the theories and their equations affected motion. An example of this is seen in Figure 1 where fluctuations are noted for temperature in two runs. The results note that five factors influence molecular dynamics and motion, to include the number of particles, range, the computer used, that manner of writing the program, and the number of predictor-corrector cycles (Rahman, 1964).

Figure SEQ Figure * ARABIC 1. Fluctuations in temperature noted for two passes with the temperatures for the two runs noted in part (a) while the velocity is noted in part (b)
The results noted that the test parameters fluctuated, while deviating from what was expected. An example of this is seen in the distribution of the velocities and widths where the reported values vary slightly from the values calculated by Maxwellian distribution. The same trend is noted for the peer distribution function where x-ray results for g(r) calculated at 91.8 oK and 1.8 atm presents transformation peaks at kσ = 6.8, 12.5, 18.5 and 24.5, while the transformation peaks for x-ray scattering occurred at kσ = 6.8, 12.3, 18.4 and 24.4. The results clearly indicate that Rahman’s study produced results that varied from what the other theories had produced. The same differences are noted the use of the velocity autocorrelation function where the correlation appears dissimilar when compared to the velocity for Langevin type autocorrelation, with the difference even greater when compared to Fourier transformation of the correlation. Overall, the results make it clear that while it may be true that persistence of short range correlations is relevant over time if used to describe the behavior of quasi-crystalline such as liquids, the same does not hold true when the distance between the atom participles increases over time since it then starts behaving as a solid rather than a liquid. This is because the increase in distance between particles causes a transformation that approaches the maximum as set in the solids spectrum. Besides that, it was noted that the argon atoms have a short order arrangement with some semblance of permanence that is comparable to the permanent correlation found existing in solids (Rahman, 1964).
In its discussion, the article describes the motion of atoms as following a non-Gaussian behavior. In this case, it is noted that the probability, distance and time are all positive values. For that matter, the probability will approach zero even as displacement increases over a long period of time, with displacement occurring at a much slower pace than what is described in Gaussian model. In fact, plotting the curve for displacement and time follows the Maxwellian distribution for velocities. The non-Gaussian behavior only disappears as time approaches infinity. As such, the article notes that the motion of argon atoms follow a non-Gaussian behavior model since the parameters involved in describing the probability of the particle achieving a set displacement within a given time all present positive values. The atoms only follow the Gaussian model when the time is near zero or it approaches infinity (Rahman, 1964).
The paper then goes on to review convolution approximation as presented by Vineyard whereby the time dependence of the probability of a particle displacement within a set time is best described using an approximation of the probability as a convolution of the probability for distance and probability for distance within a given time. The article notes that Vineyard’s approximation theory has a shortcoming regarding how it handles time whereby the functional relationship between time is ignored. Overall, the article claims that a delayed convolution (as it proposes) would eliminate the errors noted in Vineyard’s approximation theory, particularly the error concerning the presentation of a too rapid decay of probability of particle displacement with time. In addition, the model should include a delay function for distance (Rahman, 1964). In this respect, the article presents the result of a study to evaluate the motion of argon atoms in liquid form with the intention of proposing a novel model to address the shortcomings noted in Vineyard’s approximation theory.

Reference
Rahman, A. (1964). Correlations in the Motion of Atoms in Liquid Argon. Physical Review, 136(2A), A 405-A 411.