Glowing beacons reveal hidden order in dynamical systems: Experimental confirmation of a fundamental physical theorem

 A dynamical system in which repeated measurements on a single particle yield the same mean result as a single measurement of the whole ensemble is said to be ergodic. The ergodic theorem expresses a fundamental physical principle, and its validity for diffusive processes has now been demonstrated.

The so-called ergodic theorem formulates a fundamental physical principle relating to the behavior of dynamical systems. Essentially the theorem states that in a multiparticle system each individual particle behaves just as "chaotically" as does the system as a whole. In other words, one can extrapolate from the behavior of a single element to that of the whole system. Strangely enough, in spite of its wide-ranging implications, the theorem has not been rigorously tested experimentally. A collaborative effort mounted by Professor Christoph Bräuchle's team in the Department of Chemistry at LMU Munich and Professor Jörg Kärger's group at Leipzig University has now confirmed the validity of the theorem by measuring the diffusive behavior of ensembles of particles and the trajectories of single molecules in the same system. Using fluorescent molecules as tracers and high-resolution imaging methods, the LMU investigators were able to track the paths of individual molecules, while the Leipzig group studied the collective behavior of the whole ensemble. "It will be very interesting to take a closer look at systems that do not conform to the tenets of the ergodic theorem and to determine the reasons for their aberrant behavior," says Bräuchle.

The term "diffusion" refers to the random motion of particles, such as atoms and molecules, under the influence of thermal energy. This physical process is an essential component of innumerable phenomena in nature, and also plays a crucial role in many technological procedures. For instance, in virtually all chemical reactions, diffusion is responsible for bringing reactants sufficiently close together to enable them to react at all. It is generally accepted that the ergodic theorem is applicable to the dynamics of diffusive processes. The theory basically states that repeated measurements of a given variable -- such as the distance covered by a particle in a given time interval -- should yield the same average value as a single measurement of the same variable on a collection of particles -- provided the system considered is in a state of equilibrium. However, as Kärger points out, "although diffusive processes have been investigated for the past 150 years, the principle of ergodicity has not yet been experimentally verified."

This is because it has so far been possible to quantify diffusive processes only by means of ensemble measurements -- i.e. measurements of many particles simultaneously. One of the most informative methods for this purpose is pulsed-field gradient nuclear magnetic resonance (PFG-NMR), a technique for which Kärger and his group are well known. The actual trajectory of a single particle, on the other hand, could not be observed directly. "With the development of single-molecule spectroscopy and single-molecule microscopy, we can now follow the trajectories -- and therefore monitor the diffusion behavior -- of single molecules," Bräuchle explains. Optical tracking methods visualize molecules on the basis of their fluorescence, making it possible for their positions to be localized and monitored with a precision of a few nanometers.

This still leaves one problem to be solved -- successful application of the two methods requires very different, indeed apparently conflicting, conditions. NMR measurements need high concentrations of molecules with large diffusion coefficients, while single-molecule spectroscopy works best with extremely dilute solutions of species with small diffusion coefficients. By using particular organic dyes with high fluorescence yields in combination with porous silicate glasses containing networks of nanometer-sized channels in which the dye molecules can diffuse, the researchers were able to create conditions that were compatible with both methods. This experimental set-up allowed them to perform single-molecule and ensemble measurements on the same system.

When the two teams compared their data, they found that the diffusion coefficients (the parameter that describes diffusive motion) obtained by the two techniques agreed with each other -- providing the first experimental confirmation of the ergodic theorem in this context. The next step will be to examine systems in which the theory does not apply. "The diffusion of nanoparticles in cells looks like an interesting example," says Bräuchle, "and for us the important thing is to find out why the ergodic theorem doesn't hold in this case."

The project in Munich was carried out under the support of the Cluster of Excellence "Nanosystems Initiative Munich" (NIM) and DFG Priority Program 749 (Dynamics and Intermediate Molecular Transformations), while the work in Leipzig was supported by the DFG as part of Research Unit 877 (From Local Constraints to Macroscopic Transport).

The above story is reprinted from materials provided by Ludwig-Maximilians-Universitaet Muenchen (LMU).

Note: Materials may be edited for content and length. For further information, please contact the source cited above.

Journal Reference:

Florian Feil, Sergej Naumov, Jens Michaelis, Rustem Valiullin, Dirk Enke, Jörg Kärger, Christoph Bräuchle. Single-Particle and Ensemble Diffusivities-Test of Ergodicity. Angewandte Chemie, 2011; DOI: 10.1002/ange.201105388

New device measures viscosity of ketchup and cosmetics

A device that can measure and predict how liquids flow under different conditions will ensure consumer products -- from make-up to ketchup -- are of the right consistency.

The technology developed at the University of Sheffield enables engineers to monitor, in real time, how the viscous components (rheology) of liquids change during a production process, making it easier, quicker and cheaper to control the properties of the liquid.

The research is a joint project between the University's Department of Chemical and Biological Engineering and the School of Mathematics and Statistics. A paper describing the innovation is published Oct. 24, 2011 in the journal Measurement Science and Technology.

Dr Julia Rees from the University's Department of Applied Mathematics, who co-authored the study, said: "Companies that make liquid products need to know how the liquids will behave in different circumstances because these different behaviours can affect the texture, the taste or even the smell of a product."

The viscosity of most liquids changes under different conditions and designers often use complicated mathematical equations to determine what these changes might be.

The team from Sheffield has now developed a way of predicting these changes using a non-invasive sensor system that the liquid simply flows through. The sensor feeds information back through an electronic device that calculates a range of likely behaviours.

Dr Rees, from the Department of Applied Mathematics, explains: "Measuring the individual components of a liquid's viscosity is called rheometry. We can produce equations to measure a liquid's total viscosity, but the rheology of most liquids is very complicated. Instead, we look at properties in a liquid that we can measure easily, and then apply maths to calculate the viscosity. The sensor device we have developed will be able to make these calculations for companies using a straightforward testing process."

Companies developing new products will be able to incorporate the device into their development process, meaning there will no longer be a need for `grab samples' to be taken away for expensive laboratory testing, providing cost and efficiency savings.

The device can be made to any scale and can even be etched onto a microchip, with channels about the width of a human hair. This will be useful for testing where only small samples of fluid are available, for example in biological samples.

Dr Rees' team have developed a laboratory prototype of the system and are currently working to refine the technology and develop a design prototype.

Will Zimmerman, Professor of Biochemical Dynamical Systems in the Department of Chemical and Biological Engineering at the University of Sheffield, worked on the project alongside Dr Rees. He says: "Because the microrheometer works in real time, materials, time and energy will not be wasted when processing flaws are detected. Conservation is one of the best ways to 'green' industrial processing with greater efficiency. Ben Franklin's maxim, 'waste not, want not' is just as true today."

Story Source:

The above story is reprinted from materials provided by University of Sheffield.

Note: Materials may be edited for content and length. For further information, please contact the source cited above.

Journal Reference:

H C Hemaka Bandulasena, William B Zimmerman, Julia M Rees. An inverse method for rheometry of power-law fluids. Measurement Science and Technology, 2011; 22 (12): 125402 DOI: 10.1088/0957-0233/22/12/125402

Disclaimer: Views expressed in this article do not necessarily reflect those of ScienceDaily or its staff.

New benchtop polymer characterization method developed

 Researchers at UC Santa Barbara have developed a new and highly efficient way to characterize the structure of polymers at the nanoscale -- effectively designing a routine analytical tool that could be used by industries that rely on polymer science to innovate new products, from drug delivery gels to renewable bio-materials.

Professor Omar Saleh and graduate student Andrew Dittmore of the UCSB Materials department have successfully measured the structure and other critical parameters of a long, string-like polymer molecule -- polyethylene glycol, or PEG -- by stretching it with an instrument called magnetic tweezers.

"We attach one end of the PEG molecule to a surface, and the other to a tiny magnetic bead, then pull on the bead by applying a magnetic field," explained Saleh. "The significance is that we're able to perform the elastic measurements -- force vs. length measurement -- to see aspects of polymer structure that are hard to see in any other way, and we can do it within minutes on a benchtop apparatus."

Their research to characterize this particular polymer will lay the groundwork for developing a screening tool that could be used by a number of industries, according to Saleh's research team.

"Our measurements of PEG can be used as a baseline for comparison to other polymers, including biomolecules such as DNA, RNA and proteins, which display more complex physics," said Dittmore. "We chose to study PEG because it is an inert polymer that is biocompatible, soluble in water, and used for many technological purposes. The protocols we developed will be useful for future work with a variety of polymers, greatly expanding the versatility of the magnetic tweezers technique."

PEG is one of the most frequently used polymers in creams, cosmetics, adhesives and medicines, but its application goes beyond everyday household products. As a coating, PEG can shield against an unwanted immune response to give a medicine a stealth-like quality. To this end, it is used to enhance the effectiveness of anticancer drugs by increasing the circulation time in the body. PEG repels other molecules and is often used as a nonfouling coating for biomedical implants and biosensors that detect the presence of drugs or antibodies in blood.

In 1974, Paul Flory won the Nobel Prize in Chemistry for his theories regarding polymer structure in a solvent. Inspired by the work of Flory, and theories put forth decades earlier by UCSB materials and physics professor Philip Pincus, Saleh and Dittmore set out to develop an experiment that would validate their theories.

"Flory and de Gennes taught us that the structure of a polymer in solution depends on both the quality of solvent and also the length of the chain. Pincus extended upon this theory, and brought force into the picture as an important experimental variable," said Dittmore. "Now we have a method to directly test these ideas at the single-molecule level, using a powerful and quantitative technique."

"Until now, the most general method to obtain comparable data is to use neutron or x-ray diffraction which involves expensive national facilities such as nuclear reactors or particle accelerators. Thus, this research opens up a broad area of research that can be carried out at academic and industrial laboratories with modest resources," commented Professor Philip Pincus, Chair of Biomolecular Science and Engineering at UCSB.

The findings of Dittmore et al. were published in the journal Physical Review Letters in September. The paper establishes a framework for comparing biomolecules and synthetic polymers based on chain structure that could be further refined and translated into a laboratory tool for industry.

"Many companies are looking to replace the petroleum-based polymers they use in consumer products with polymers made from biomass, such as sugar cane or cellulose," said Professor Glenn Fredrickson, Chair of Functional Materials and Founding Director of the Mitsubishi Chemical Center for Advanced Materials at UCSB. "If their methods could be made into a compact and inexpensive screening tool for polymer properties in an industrial setting, it could be important in affecting industry transformation to producing polymers from renewable resources.

Their research was made possible by support from the National Science Foundation and was carried out at the Materials Research Laboratory: an NSF MRSEC facility at UC Santa Barbara.

"This is an excellent example of high-risk, transformative research that breaks down conventional wisdom," said Craig Hawker, Director of the Materials Research Laboratory at UCSB. "The MRL is proud to have contributed to the success of this project through a Seed program designed to fund research that will revolutionize existing fields. By establishing this technique as a powerful, new strategy for characterizing synthetic polymers, countless future studies are now possible."

Story Source:

The above story is reprinted from materials provided by University of California - Santa Barbara.

Note: Materials may be edited for content and length. For further information, please contact the source cited above.

Journal Reference:

Andrew Dittmore, Dustin McIntosh, Sam Halliday, Omar Saleh. Single-Molecule Elasticity Measurements of the Onset of Excluded Volume in Poly(Ethylene Glycol). Physical Review Letters, 2011; 107 (14) DOI: 10.1103/PhysRevLett.107.148301

Using new technique, scientists uncover a delicate magnetic balance for superconductivity

 A new imaging technology is giving scientists unprecedented views of the processes that affect the flow of electrons through materials.

By modifying a familiar tool in nanoscience -- the scanning tunneling microscope -- a team at Cornell University's Laboratory for Atomic and Solid State Physics have been able to visualize what happens when they change the electronic structure of a "heavy fermion" compound made of uranium, ruthenium and silicon. What they found sheds light on superconductivity -- the movement of electrons without resistance -which typically occurs at extremely low temperatures and that researchers hope one day to achieve at something close to room temperature, which would revolutionize electronics.

What they found was that, while at higher-temperatures magnetism is detrimental to superconductivity, at low temperatures in heavy fermion materials, magnetic atoms are a necessity. "We found that removing the magnetic atoms proved detrimental to the flow [of electrons]," said researcher Mohammad Hamidian. This is important, Hamidian explains, because "if we can resolve how superconductivity can co-exist with magnetism, then we have a whole new understanding of superconductivity, which could be applied toward creating high-temperature superconductors. In fact, magnetism at the atomic scale could become a new tuning parameter of how you can change the behavior of new superconducting materials that we make."

To make things finding, the researchers modified a scanning microscope that lets you pull or push electrons into a material. With the modification, the microscope could also measure how hard it was to push and pull -- a development that Hamidian explains is also significant. "By doing this, we actually learn a lot about the material's electronic structure. Then by mapping that structure out over a wide area, we can start seeing variations in those electronic states, which come about for quantum-mechanical reasons. Our newest advance, crucial to this paper, was the ability to see at each atom the strength of the interactions that make the electrons 'heavy.'"

The Cornell experiment and its results are presented this week by the Proceedings of the National Academy of Sciences. The research team included J.C. Séamus Davis, a member of the Kavli Institute at Cornell for Nanoscale Science and developer of the SI-STM technique. Working with synthesized samples created by Graeme Luke from McMaster University (Canada), the experiment was designed by Hamidian, a post-doctoral fellow in Davis' research group, along with Andrew R. Schmidt, a former student of Davis at Cornell and now a post-doctoral fellow in physics at UC Berkeley. This research was supported by the DOE's Office of Science, the Natural Sciences and Engineering Research Council of Canada, and the Canadian Institute for Advanced Research. Additional collaborators included Ines Firmo of Brookhaven Lab and Cornell, and Andy Schmidt now at the University of California, Berkeley.

For the complete interview with Hamidian, visit: http://www.kavlifoundation.org/science-spotlights/Cornell-disturbing-nanosphere-superconductivity

Story Source:

The above story is reprinted from materials provided by The Kavli Foundation.

Note: Materials may be edited for content and length. For further information, please contact the source cited above.

Journal Reference:

M. H. Hamidian, A. R. Schmidt, I. A. Firmo, M. P. Allan, P. Bradley, J. D. Garrett, T. J. Williams, G. M. Luke, Y. Dubi, A. V. Balatsky, J. C. Davis. How Kondo-holes create intense nanoscale heavy-fermion hybridization disorder. Proceedings of the National Academy of Sciences, 2011; DOI: 10.1073/pnas.1115027108