Resumes & CVs

28 pages
10 views

A kinetic Ising model study of dynamical correlations in confined fluids: Emergence of both fast and slow time scales

of 28
All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Share
Description
Experiments and computer simulation studies have revealed existence of rich dynamics in the orientational relaxation of molecules in confined systems such as water in reverse micelles, cyclodextrin cavities, and nanotubes. Here we introduce a novel
Transcript
  See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/46146945 A kinetic Ising model study of dynamicalcorrelations in confined fluids: Emergence of both fast and slow time scales  Article   in  The Journal of Chemical Physics · August 2010 DOI: 10.1063/1.3474948 · Source: PubMed CITATIONS 5 READS 55 2 authors: Rajib BiswasUniversity of Chicago 15   PUBLICATIONS   47   CITATIONS   SEE PROFILE Biman BagchiIndian Institute of Science 469   PUBLICATIONS   11,842   CITATIONS   SEE PROFILE All content following this page was uploaded by Biman Bagchi on 14 August 2014. The user has requested enhancement of the downloaded file. All in-text references underlined in blue are added to the srcinal documentand are linked to publications on ResearchGate, letting you access and read them immediately.  1 A kinetic Ising model study of dynamical correlations in confined fluids: Emergence of both fast and slow time scales Rajib Biswas and Biman Bagchi   Solid State and Structural Chemistry Unit Indian Institute of Science Bangalore 560012, India  Email:  bbagchi@sscu.iisc.ernet.in  ABSTRACT Experiments and computer simulation studies have revealed existence of rich dynamics in the orientational relaxation of molecules in confined systems such as water in reverse micelles, cyclodextrin cavities and nano-tubes. Here we introduce a novel finite length one dimensional Ising model to investigate the propagation and the annihilation of dynamical correlations in finite systems and to understand the intriguing  shortening   of the orientational relaxation time that has been reported for small sized reverse micelles. In our finite sized model, the two spins at the two end cells are oriented in the opposite directions , to mimic the effects of surface that in real system fixes water orientation in the opposite directions. This produces opposite polarizations to propagate inside from the surface and to  produce bulk-like condition at the centre. This model can be solved analytically for short chains. For long chains we solve the model numerically with Glauber spin flip dynamics (and also with Metropolis single-spin flip Monte Carlo algorithm). We show that model nicely reproduces many of the features observed in experiments. Due to the destructive interference among correlations that propagate from the surface to the core, one of the rotational relaxation time components decays faster than the bulk. In general, the relaxation of spins is non-exponential due to the interplay between various interactions. In the limit of strong coupling between the spins or in the limit of low temperature, the nature of relaxation of the spins undergoes a qualitative change with the emergence of a homogeneous dynamics  where decay is  predominantly exponential, again in agreement with experiments.  2 I.   INTRODUCTION Dynamical correlations amongst molecules that are confined within small volumes are  perturbed due to the surface and are very difficult to describe quantitatively. This is particularly so for water whose unique features are intimately related to the hydrogen bond network that gets modified by the surface interactions. In reverse micelles (RMs), where one can control the size of the system, one can systematically study the effects of confinement 1-8 . Recent experimental and computer simulation studies have studied water in variety of environments 1-11  such as water around bio-molecules 1-3 , around micelles 4-6 , in reverse micelles 7,8 , in cyclodextrins 9,10 , in Zeolites 11  and nano-tubes. Discussions have often focused on the relative effects of nano-confinement versus surface interactions. However, no purely theoretical study of such problems has been presented. The initial experimental studies employing solvation dynamics 12,13  measurements reported a very slow component which could arise from the motion of water molecules trapped near the charged surfactant group or due to the motion of the solute probe itself. Subsequently a series of detail experimental studies of rotational dynamics of water has been carried out by Fayer and coworkers by using 2D ultrafast IR spectroscopy of O-H and O-D bonds 14-17 . These experiments revealed a wealth of information, particularly in the short timescale window. One of the salient features of the recent experimental results of Fayer and coworkers 16  is the observation of a rotational relaxation time component  faster   than the bulk. While the bulk rotational correlation time of O-D bond is 2.7ps, same near the core is found to be 1.5ps (for  0 10 w   , where 0 w  is the characterization parameter for RMs, defined as water molecules per surfactant molecule). This significant acceleration of the relaxation rate in the core is yet to be explained.  3 Although there does not seem to exist any purely theoretical study of the problem, several computer simulation studies of water relaxation dynamics in RMs have been reported 18,19 . In one of the early pioneering studies, Faeder and Ladanyi 18  simulated and found that the rotational dynamics slow down by a factor of 2 to 3. Subsequently, Senapati and Berkowitz 19  have also reported that the translational and the rotational dynamics of water slow down in confined geometry of RMs with change in inter water hydrogen bonding. They have also observed that the reorientational relaxation of water in the solvation layer may slow down  by three orders of magnitude which is in good agreement with the experimental results 7 . Several studies on dynamics of water in micelles have also been reported 4-6 . It is interesting to contrast the behavior of water in micelles and reverse micelles. In the case of reverse micelles the confinement may induce new effects which could be more important than the surface specific interactions. In a recent study of water structure and dynamics in the grooves of DNA it has been found that confinement can significantly distort the bulk behavior  20 . Recent experimental and theoretical studies on various confined systems have now given enough evidence for the presence of multiple time scales in confined water systems srcinating generally from the presence of two ensembles of water molecules 14-17 . One type is referred to as free or bulk water and the other is called bound or surface water whose motion is restricted. The latter is responsible for slow dynamics. Relative importance of the two relaxation modes depend on size and nature of the system. In order to explain the interplay between these two limits of water, here we propose a one dimensional simple theoretical model. Our model is essentially a modified finite length Ising model. In this finite sized model, the two spins at the two end cells are oriented in the opposite directions , to mimic the effects of surface that in real system fixes water orientation in the  4 opposite directions. Fortunately, this model can be solved analytically for short chains. For long chains we solve the model numerically with Glauber spin flip dynamics (and also with Metropolis single-spin flip Monte Carlo algorithm). Interestingly, this model can reproduce many of the features observed in experiments. Due to the destructive interference among correlations that propagate from the surface to the core, one of the rotational relaxation time components decays faster than the bulk. Another new result is that in the limit of strong coupling between the spins or in the limit of low temperature, the nature of relaxation of the spins undergoes a qualitative change with the emergence of a homogeneous dynamics  where decay is predominantly exponential. II.   THE MODEL The key observation behind the model is that in confined systems, such as reverse micelles, the water molecules that are located diametrically opposite to each other are orientated opposite to each other  . This is because the surface water molecules are strongly hydrogen bonded with the charged surface groups. The opposite correlations induced by spatially opposite surface groups  propagate inside and are expected to annihilate each other at the center. Thus, we may expect a  pool of water molecules at the center where water molecules are as free as or sometimes even freer than the bulk. Of course, for large sized reverse micelles, the center pool is expected to be  bulk like any way. However, the correlations effect should be appreciable at small to intermediate sized micelles. To model the above phenomenon in a simple way, we have taken a one dimensional Ising chain with two terminal spins fixed in opposite directions , one as up (i.e. ‘+1’) and the other at the opposite side as down (i.e. ‘ - 1’) . See Fig. 1.  for a schematic illustration. We assume
Related Documents
View more...
We Need Your Support
Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks
SAVE OUR EARTH

We need your sign to support Project to invent "SMART AND CONTROLLABLE REFLECTIVE BALLOONS" to cover the Sun and Save Our Earth.

More details...

Sign Now!

We are very appreciated for your Prompt Action!

x