Illustrating mixing

This screencast shows Molecular Workbench simulations I have made to illustrate mixing.

The first simulation illustrates the mixing of 2 ideal gases, which mix readily.  Since the gas particles don't interact you can think of the mixing as each gas expanding to fill both containers independently of each other.  As I have shown in this simulation, the driving force for this expansion is an increase in entropy.  Therefore, the driving force for mixing two ideal gasses is also purely entropic.

The second set of simulations illustrates the mixing of 2 liquids.  Since they are liquids there must be attractive interactions between the atoms.  If there were no interactions they would be (ideal) gasses.  The strength of the interactions (and the temperature) determine whether they mix or not.

In the first liquid simulation, the attraction between two green atoms (ε_GG), between two blue atoms (ε_BB), and between a green and a blue atom (ε_GB) are the same.

This means that a green atom doesn't care whether it is sitting next to a blue atom or another green atom.  The net effect is that green and red atoms are equally likely to be on the right or left side of the container, and the liquids mix for the same reason as the ideal gasses mix: the driving force is purely entropic. That means the enthalpy of mixing is zero:

This is the definition of an ideal mixture (or ideal solution).  The two liquids will mix at any temperature.

In the second liquid simulation, the attraction between two blue atoms (ε_BB) is stronger than between two green atoms (ε_GG) and between a green and a blue atom (ε_GB).

Note that the ε's are negative: a smaller ε means a stronger attraction.  This means that the blue particles would rather be with other blue particles, i.e. the enthalpy increases if the particles are mixed.

(z is the number of contacts between particles in solution, and x_G is the mole fraction of green atoms).  This is an example of a non-ideal mixture, where the definition for a non-ideal mixture is

Because Δ_mixH > 0 this non-ideal solution mixes spontaneously (i.e. Δ_mixG < 0) only for

Oil and water is a common example of such an non-ideal mixture: the oil-oil interactions are stronger than the oil-water and water-water interactions.

Salt and water is another example of on idea mixture, but here Δ_mixH <  0 so salt and water almost always mixes spontaneously.  The interpretation is that the interactions between the salt ions and water is stronger than the average interaction between salt ions and between water molecules.

Implications and limitations
The definition of Δ_mixH in terms of the ε's suggest that liquids should also mix if

which would be a more general definition of an ideal mixture.

This is tested in the third liquid simulation.  As you can see the liquids mix more than in the second simulation, but not quite as much as in the first simulation.  This is mostly because of the simulation runs only for 100 picoseconds, which is to short to mix fully.  But another reason is that there is less space (on average) between the blue atoms compared to the green atoms, because the blue atoms attract each other more.  The next effect is that the blue particles tend to stay together to lower the enthalpy.  More mathematically,  z (the number of contacts between particles in solution) is not exactly the same for the blue and green particles so the interpretation of Δ_mixH in terms of the ε's breaks down.  The "safest" definition of an ideal mixture thus remains:

i.e. "like dissolves like".

Accessing the simulations
You can play around with the simulations here and here, or you can download the models here and here if you have Molecular Workbench installed on your computer.

The Open Science unjournal

In this post I do something a little different than normal for this blog: I introduce a scientific unjournal called Open Science.  It doesn't exist, but it should.
 
What is an unjournal?
An unjournal is to journals what an unconference is to conferences.  To define what an unjournal is, take the first 2 sentences in the wikipedia entry on unconferences and substitute a few words:  "An unjournal is a facilitated, participant-driven journal centered on a theme or purpose. The term "unjournal" has been applied, or self-applied, to a wide range of publications that try to avoid one or more aspects of a conventional publishing, such as loss of copyright, high fees, [list your favorite pet-publishing-peeve here]."

Here are some frequently asked questions (FAQs) about Open Science:

How do I publish in Open Science?
The usual way is to deposit your manuscript on openscienceunjournal.org.  Once you have completed the submission process the paper is given a time and date stamp and the paper is published and open for review (see next question).  While there is a recommended template available for the paper, there is no fixed format.  It is possible to upload all your raw data or link to the data if it is hosted elsewhere.  Experience has shown that this tends to increase the scores (see below) of your papers significantly.

You can also choose to publish the paper on any of the unjournal sites whose contents are linked to openscienceunjournal.org.  These sites are often run by established publishers and offer more user-friendly interfaces, but may require a fee and may ask you to give up your copyright (though the content is open access by definition).

Is Open Science peer reviewed?
For a publication in an unjournal such as Open Science the question should be: is my article in Open Science peer reviewed?  That is in large part up to you.  The paper is open for online, non-anonymous, and completely transparent review and you have 2 months in which you can change the content of the article in response to the comments.  After the 2 month period you cannot change the content, but you can of course respond to new comments online.  For very serious criticisms you may want published a new Open Science article to respond.

It is up to you to solicit reviews, though any published author of a peer-reviewed paper (defined below) can review your paper during the 2 months review process.  Based on our experience only well-written and well-presented articles on scientifically interesting questions get reviewed.

An Open Science article is neither rejected nor accepted at the end of the review process.  Instead it receives an initial score (see next FAQ).  Obviously, any paper that does not generate a single review (or is reviewed but gets an initial score of 0) is not considered peer reviewed.

What is the impact factor of Open Science?
For a publication in an unjournal such as Open Science the question should be: what is the impact factor of my article in Open Science?  During the 2 months review process each reviewer gives the paper a score between 5 (good) and 0 (bad).  This score can be adjusted by the reviewers based on the changes you make within the first 2 months, after that it is fixed. The initial score for your paper is the average of all reviewers final scores.  

If the paper is cited it receives an additional score (called the current score).  The score is determined by the number of citations, and if the citing paper is published in Open Science, the score is weighted by the initial and current score of that paper.  The authors of that paper can also choose to indicate how important your paper was to theirs.  If high scoring papers cite your paper in a positive manner, the current score of your paper increases. Self-citations are not included.  

Why should I review for Open Science?
The work you put into reviewing is now documented for all to see.  Have you contributed greatly to science by identifying Open Science papers with high current scores?  Do the reviews you submit carry more weight with the author and other reviewers as a result?  Some sites now list Open Science reviewers with particularly high impact as a kind of editorial board for the journal.

How should I cite an Open Science paper?
One suggestion is: Author(s), Title, Open Science, date of submission, initial/current score.  If you publish in Open Science using the suggested template, the current score is updated automatically. 

Why should I publish in Open Science?
There are many reasons:
(1) You retain the copyright and anyone can see the paper.
(2) Your paper is accessible upon submission. (Don't rush to publish though: you only have 2 months to get a good initial score).
(3) The impact of your paper is evident in the citation, but disconnected from the conventional impact factor of the journal you managed to get it in to.  The initial score of your paper can help the paper off to a good start, but your truly important papers will ultimately be identified by its current score.
(4) You choose the publishing format you like.  What's your pleasure? machine readable? interactive figures? link to raw data?
(5) Your paper is a living document: comments or questions continue to roll in on important papers and you can update links to your papers (related articles, a new data format) as you see fit.
(6) If you write a good paper, you will get more reviews (i.e. more suggestions and input) but the rantings of a single idiot reviewer will not prevent publication.  Isn't this the place to publish daring and ground-breaking work?  

So what brought this on?
The blogosphere: Egon Willighagen's latest post got me thinking about this particular idea, but the general problems it is trying to address was brought to my attention by many other blogs such as Michael Nielsen's The Future of Science and Is Scientific Publishing About to be Disrupted? posts; most posts by Peter Murray-Rust; Henry Rzepa's long fight to include interactive figures in conventional journals; Mat Todd's excitement for an unconference and the discussion it generated at Derek Lowe's blog.  Why can't we have this in a journal?

Is the Open Science unjournal a good idea?
The blogosphere will decide: no comments on, and no re-blogging of, this post will mean this idea dies a quiet death (by receiving an initial and current score of 0).  But if you get enough smart people fired up about an important idea that can be solved by IT, good things can happen.

The molecular basis of differential scanning calorimetry: heat capacity and energy fluctuations

Melting and boiling points are convenient and important measures of stability.  But how do you measure a melting point of, for example, nanoparticles that are too small to see?

This screencast shows two Molecular Workbench simulations (you can find them here and here) I made [see credits at the end of the post] to illustrate the connection between phase transitions, changes in heat capacity, and energy fluctuations, and the slides below takes you through the basic ideas behind them.

Slide 1: In the first simulation heat is added to a nano-particle and the resulting temperature increase is measured. When viewing the simulation notice that the temperature increases less during the melting/evaporation.

Slide 2: To analyze the data we first switch the x and y-axes, so that heat added (i.e. the internal energy, U) is plotted as a function of temperature.

Slide 3: The data is a bit noisy (mainly because the simulation heats the particle too fast: from 0 to almost 3000 K in about 200 picoseconds!), so I smooth it by fitting a curve to it.

Slide 4: From the smoothed data I can calculate how fast the energy changes with temperature.  This is the heat capacity (C_v), which peaks at a temperature around 1350 K - the melting temperature of the particle.

Slide 5: This observation forms the basis of differential scanning calorimetry, which measures the temperature as a function of the flow of energy to a system, and determines the melting point by finding the temperature where the heat capacity peaks.

Slide 6: One way to explain why the heat capacity peaks at a phase transition such as melting is through its relation to energy fluctuations: the system changes most during a phase transition ("bonds" between particles are broken and formed), so the energy fluctuates more, meaning that the heat capacity is largest.

Slides 7, 8, and 9: In the second set of simulations the energy is plotted a function of time at 3 temperatures: before the particle melts (500 K), when the particle melts/evaporates (1350 K), and after the particle has evaporated (3000 K).

Slide 10: Results from the 3 simulations are compared.  Clearly the fluctuations are largest when the temperature is 1350 K.  The fluctuations at 3000 K are larger than at 500 K, even though the heat capacities are similar.  This is because the heat capacity is proportional to the average energy fluctuation divided by the temperature squared (slide 6).

Calorimetry

View more presentations from molmodbasics.

You may wonder why we don't see two heat capacity peaks: one for melting and one for evaporation.  This is because of the particle is so small (i.e. composed of relative few particles).  For a macroscopic systems (like water) the phase transitions are well defined.  Water is ice at 272 K, melts at 273 K, and is a liquid at 274 K (at 1 atmosphere of pressure); and the heat capacity has a very narrow peak at 273 K. As particles become smaller their phase transitions become less well defined, the heat capacity peak becomes broad, and in some cases (like this one) you get a single heat capacity peak for melting and evaporation.  This means that the phase transition cannot really be classified as melting or evaporation and that is occurs over a relatively large temperature range.  Li and Truhlar have an interesting article on this subject. If you would like to play around with or modify the simulations they can be downloaded here and here, but you need to download Molecular Workbench first. Credits: The simulations are based on models and scripts by Arie Aziman and Carlos Gardena, who based their work on a model by Dan Damelin, i.e. they are made possible, like Molecular Workbench itself, by open source science.

Nobel reactions

You may have heard this already: this years Nobel prize in chemistry went to Richard F. Heck, Ei-ichi Negishi, and Akira Suzuki "for palladium-catalyzed cross couplings in organic synthesis".  Like last year, molecular modeling and animation is here to bring the science behind the prize to life.  This time, through the very excellent Chemtube3D (a Molecular Modeling Basics favorite) and its page on on organopalladium chemistry.

Illustrating energy states

Here is a screencast showing 2 simulations I made to illustrate energy states (often also called microstates).  Open any book on statistical mechanics and you'll see a formula like this (for the Boltzmann distribution),

and, perhaps, a figure much like this.

But what are these "energy states" and ε's exactly? Hopefully the screencast and associated simulations, which you can find here and here, will help make this clearer.

About the simulations
If you want to play around with the HCl simulation, note that you have to reload the page if you want to change the translational motion.  This simulation is made with Jmol.  The molecular dynamics simulation of butane is made with Molecular Workbench.

iPad: even 3-D molecules that can be viewed from any angle

I recently came across this report on inkling.com, a new company aimed at bringing interactive textbooks to the iPad.  Interactive molecular models was mentioned two times and clearly left an impression on the author (italics are mine):

"Inkling’s software turns textbooks into interactive content, with video, hyperlinks between text and images, notes that can be shared between students and teachers, and even 3-D molecules that can be viewed from any angle."

"MacInnis – who worked at Apple for eight years, including a stint in the company’s educational division — says that the iPad is the perfect device for the kind of interactivity that Inkling provides because it has the ability to produce high-end graphics, such as the 3-D spinning molecule that is a feature of the company’s biology textbook."

This feature is also shown in inklings promotion video, excerpt below:
Update: MacInChemBlog keeps a list of science related iPhone/iPad apps.

Molecular Modeling Basics reviewed in Chemistry World

A very nice review of the book (and blog!) by fellow blogger Henry Rzepa in Chemistry World.  Much appreciated.