Scientists have long studied how atoms and molecules structure themselves into intricate clusters. Unlocking the design secrets of nature offers lessons in engineering artificial systems that could self-assemble into desired forms.In the Jan. 29 issue of Science, a team from Harvard led by Vinothan Manoharan and Michael Brenner presents additional clues to how and why groups of atoms and molecules may favor less symmetrical and more complex, flexible geometric patterns.The answer relates to a familiar concept in physics called entropy, the ways in which particles are able to arrange themselves. The researchers first caught sight of the link by using magnetic “stick and ball” construction toys that can make varying shapes.Manoharan, associate professor of chemical engineering and physics in Harvard’s School of Engineering and Applied Sciences (SEAS) and the Department of Physics, and his colleagues used colloidal particles, a suspended chemical mixture seen in semi-solid foods such as mayonnaise, to simulate the clustering behavior of atoms and molecules.“To allow clusters to form, we put a few tiny polystyrene spheres in microscopic cylindrical wells filled with water. The particles act as ’sticky’ hard spheres and naturally cluster together just like groups of nearby interacting atoms and molecules do,” said Manoharan.The researchers expected that simple, highly symmetric shapes would arise most often. Instead, two surprising, related, and scalable phenomena arose when the number of particles used in their experiments reached six or rose above nine.Six particles can form into a symmetrical octahedron and into a more complex tri-tetrahedron shape. In terms of chemical structure, each shape results in 12 bonds, and hence, has the same amount of potential energy. With the potential energy being equal, Manoharan and colleagues thought that both shapes would occur in equal proportion. They found, however, that the tri-tetrahedron occurs 20 times more often than the octahedron.“The only possible explanation was entropy,” said Manoharan. “Most people are familiar with entropy as a measure of ‘disorder,’ but the most useful definition of entropy is simply the number of different ways a bunch of particles can arrange themselves.”Natalie Arkus, a former applied mathematics graduate student who worked with Brenner, the Glover Professor of Applied Mathematics and Applied Physics, provided a hint to solving the puzzle, as she discovered a method to calculate all the possible structures that could be formed using geometric magnetic toys made up of magnetic metal rods and silver ball bearings.Since there are more ways for the complicated tri-tetrahedron structure to form (something that can be seen by labeling the toy spheres and counting the ways they can be put together), the shape appears far more frequently than the octahedron. In general, among clusters with the same potential energy, highly symmetric structures are less likely to arise.The researchers also found that when the number of particles reaches nine or higher, entropy plays another important role.Because the number of possible structures with nine or more particles is vast, the team focused on what are called nonrigid, or flexible, structures. Nonrigidity occurs when a cluster is half octahedral and shares at least one vertex, allowing the cluster to twist without breaking or forming another bond (something also easily seen by using the toys).“Because they can move flexibly, the nonrigid clusters have high vibrational entropy,” explained Manoharan. “In cases with nine or more particles, symmetric clusters do not appear as often due to rotational entropy. The ability to rotate is useful, as it allows clusters to have extra bonds.”As a general rule, the team found that for all clusters up to eight particles and a select number of structures with up to 12, the most symmetric structures occurred the least often due to entropy.“Our findings illustrate, in a tangible way, what the concept of entropy means,” said Manohran.Looking ahead, the researchers are interested in using their results to understand the emergence of bulk crystallization, or how particles come together in the early stages of forming a crystal.Manoharan and Brenner’s co-authors included Guangnan Meng, a research associate in the Department of Physics at Harvard University, and Natalie Arkus, a graduate of SEAS and now a postdoctoral fellow at the Rockefeller University. The authors acknowledge support from theNational Science Foundation and the Defense Advanced Research Projects Agency.
The investigation is ongoing. The Ithaca Police Department asks anyone with information regarding this incident to contact them at (607) 272-3245, the Police Tipline at (607) 330-0000, or the Anonymous email tip address: www.cityofithaca.org/ipdtips. ITHACA (WBNG) — Ithaca police responded to a personal injury motor vehicle crash yesterday evening on Fairgrounds Memorial Parkway. According to police, the crash followed a physical dispute. A vehicle leaving the scene hit a female and fled the area. The victim was taken to a regional trauma center and the extent of their injuries is still being determined. Police say the suspect vehicle was described as a dark colored, four door sedan. The driver of the vehicle has not been identified. The Ithaca Fire Department, Bangs Ambulance, and the NY State Police assisted the Ithaca Police at the scene.
A coalition of civil society groups has called on the House of Representatives to repeal problematic articles in the revision to the Constitutional Court (MK) Law, alleging they contain conflicts of interest that can harm the Court’s impartiality.Among the coalition members are West Sumatra’s Andalas University’s Constitution Study Center (PUSaKO), Indonesia Center for Law and Policy Studies (PSHK), Indonesia Corruption Watch (ICW) and judicial watchdog KoDe Inisiatif.”The House and the government must drop the article that increases the minimum age of justices to 60 years and it should not scrap the existing regulation that justices can serve for only five years and must be reelected for another term,” Hemi Lavour of Pusako said in an online press conference on Friday. “The articles would only benefits a few justices.”The coalition said that if passed, most Constitutional Court judges who were currently in office would keep their position until they were 70 years old, 10 years longer than the maximum age for justices set in the existing 2011 Constitutional Court Law. The coalition also noted that only one judge could not continue the term because he has not reached the age of 60 at the end of his service.Read also: Constitutional Court rejects judicial review request on tenure of its own judgesAgil Oktrayal of the PSHK lambasted the government and the House, saying the revisions were a constitutional setback, especially because the House never included the bill in the 2020 priority list (Prolegnas) “The House never came up with the academic rationalization related to the amendments,” Agil said.He also raised suspicions that the bill was being used as a “political swapping” tool as many controversial laws were currently being challenged at the Court, such as the state spending and financial relief law, the mining law, the Corruption Eradication Commission (KPK) Law and the omnibus bill on job creation.Agil further criticized the swift deliberation of the bill, which was conducted behind closed doors between the House and the government during the ongoing COVID-19 pandemic.“The deliberation process was very quick and closed [to the public]. This goes against the spirit of reform; in the Reform era of 1998, people wanted to have a Constitutional Court,” he said.The court was officially established in 2003 following mounting support from the public who demanded an institution that would allow them to challenge laws or election results. The House Commission III overseeing legal affairs began deliberating the bill on Monday. The government then submitted the problem inventory list (DIM) of the bill on and formed a working committee with the House on Tuesday.On Wednesday and Thursday, the government and the House discussed the bill twice in closed-door hearings.Read also: House starts deliberating Constitutional Court Law revisionCommittee member Sarifuddin Sudding said the commission and the government had agreed on several changes in the bill, such as the extension of the minimum age limit to become a Constitutional Court justice, as well as the terms of office for chief justice, deputy chief justice and justices.If the House and the government can agree on all the revisions, the commission will pass the revision into law.“After that, we will bring the revised draft to a plenary session for the second level of deliberations,” the National Mandate Party (PAN) politician said.Constitutional justice Enny Nurbaningsih denied that the Court had any interest in the revision of the MK law.Enny said the justices would always uphold the Bangalore Principles of Judicial Conduct, which identify six core values of the judiciary, namely independence, impartiality, integrity, propriety, equality, competence and diligence.“The Constitutional Court justices will carry out their tasks independently. This is a non-negotiable principle,” she told The Jakarta Post on Friday.Topics :