## Crystallization Map

### Quick Start

The classic Crystal Nucleation Theory has proven to be disappointing in terms of understanding the multiple phenomena in reality. By thinking in terms of maps of different landscapes we start to see the possibilities of tight clusters (classic CNT), loose clusters, clusters leading to oiling out and clusters developing inside clusters - the 2-step mechanism. With such mapping, crystallization starts to make more sense.

### Credits

The app is inspired by a paper1 by Prof Peter Poole and colleagues at St Francis Xavier U in Nova Scotia that considers crystallization as a landscape for which a map is very helpful.

### Crystallization Map

//One universal basic required here to get things going once loaded
Main();
};
//Any global variables go here

//Main is hard wired as THE place to start calculating when input changes
//It does no calculations itself, it merely sets them up, sends off variables, gets results and, if necessary, plots them.
function Main() {
saveSettings();

//Send all the inputs as a structured object
//If you need to convert to, say, SI units, do it here!
const inputs = {
Mode: document.getElementById('Mode').value,
}

//Send inputs off to CalcIt where the names are instantly available
//Get all the resonses as an object, result
const result = CalcIt(inputs)

//Set all the text box outputs
document.getElementById('Step1').value = result.Step1
document.getElementById('Step2').value = result.Step2
document.getElementById('Step3').value = result.Step3
document.getElementById('Step4').value = result.Step4
//You might have some other stuff to do here, but for most apps that's it for CalcIt!
}

//Here's the app calculation
//The inputs are just the names provided - their order in the curly brackets is unimportant!
//By convention the input values are provided with the correct units within Main
function CalcIt({Mode}) {
getSVG(Mode)
let Step1="1: Supersatured molecules in solution",Step2="",Step3="",Step4="4: Crystals"
if (Mode=="Classic CNT"){
Step2="2: Small, rigid, pre-nucleus"
Step3="3: Larger, rigid, nucleus"
}
if (Mode=="Loose CNT"){
Step2="2: Small loose clusters"
Step3="3: Larger loose clusters"
}
if (Mode=="Oiling Out"){
Step2="2: Small loose clusters"
Step3="3: Larger loose clusters"
Step4="4: Phase separation of oil clusters"
}
if (Mode=="2-Step"){
Step2="2: Small loose clusters"
Step3="3: 2nd phase crystallizing"
Step4="4: 2nd phase crystallized"
}

return {
Step1:Step1,
Step2:Step2,
Step3:Step3,
Step4:Step4,
};

}

function getSVG(theSVG){
const theFile="img/"+theSVG+".svg"
fetch(theFile)
.then(r => r.blob())
.then(svg =>  document.getElementById("svgObj").data = URL.createObjectURL(svg))
}                        

The standard story of crystallization has been acknowledged for decades to be faulty - but there is much confusion about what the alternatives are. My view is that the confusion arises from a lack of understanding of crystallization landscapes. We need to imagine that landscape as being full of mountains, passes, saddlebacks, ridges, and the equivalents of watersheds leading to different final resting places.

Although there are an infinity of possible landscapes, here we look at just 4.

1. Classic CNT. It is clearly the case that some journeys from supersaturated molecules to macro crystals proceeds via a straight path through a simple pass in the mountains to the crystal pastures beyond. Classic CNT describes this well.
2. Loose CNT. It is equally clear that the molecules can assemble not only into sub-crystalline nuclei but into loose, mobile clusters, common in other solubility situations such as near-immiscible liquids. Such large clusters can be found by scattering experiments. At some point, they are sufficiently assembled that the molecules inside can start to crystallize (without the large penalty of crystallizing in a pure solvent environment) and the whole system tips over to a crystal form. So this journey is a long, slowly rising side valley that finds itself near the top of a ridge and can cross over to the crystal pastures.
3. Oiling Out. This is the loose cluster valley that didn't rise enough to reach the ridge over to the crystal form and, instead, kept going till it found a sudden drop down (spinodal) to a stable end point with an oil containing plenty of solvent.
4. 2-Step. We get the loose clusters of the Loose CNT route, but a twist in the landscape allows a different crystal habit to start forming inside the clusters, tipping over a ridge down into a 3rd stable zone.

What do we mean by "large clusters"? In protein crystallization it is common to see "oil" drops in the microscope, with crystallization taking place inside. If you call this 2-step then it is easy to say that 2-step doesn't happen for small molecules because we rarely see such drops. Others believe that clusters are "colloids" and can start to have colloidal interactions with themselves (argued to be not so important) or with seed crystals (argued to be significant). These ideas are not mutually exclusive - they are focussing on different variants of the mountainous landscape.

You will notice that there are no external seeds shown in these maps. That's because I find the ideas of nucleation by primary, secondary or junk seeds to be confused and confusing. However they work, I believe they work via interactions with different clusters in different parts of crystallization space. Maybe a future version will include some seed ideas.

### Landscape Simulations

My own instincts, coming with a Kirkwood-Buff approach to solubility issues, are at ease with this landscape idea. Another phrase for KB is "fluctuation theory" and I was delighted to find a paper1 by Prof Peter Poole and colleagues at St Francis Xavier U in Nova Scotia that uses fluctuation theory to create the sort of landscapes I'd imagined. Their Fig 3 and its landscape equivalent in Fig 8 b (reproduced here with kind permission of the author) exactly capture the 2-Step path shown, far more crudely, here. The x-axis is the cluster size, the y-axis is the ratio of the second type (gold in my image) to the first type (blue). The white line is the path through the landscape - large blue clusters build up till there's room for the gold clusters to be created and the mountain ridge is overcome.

A core insight in the paper (and from the references therein) is that unlike standard CNT where there is just one (negative) free energy for cluster formation and one (positive) barrier from surface energy, there are multiple possibilities. For example, in the 2-Step shown, the surface energy of the golden form within the solution might be impossibly high, while that of the blue form isn't too bad, especially in the loose mode. However, the surface energy of the golden form within the blue cluster is not a problem, so it's relatively easy to crystallize from the blue clusters into the thermodynamically more stable golden form.

My view is that a combination of that sort of theoretical mapping with experiments open to the wider notions of clusters within landscapes will bring fresh vitality to the world of crystallization.

### You might well disagree

It is obvious, I hope, that I'm not an expert on crystallization. I very much welcome disagreement and correction. I can either remove this app if it's hopelessly wrong or create better guides to a wider or different range of landscapes.

1Daniella James, Seamus Beairsto, Carmen Hartt, Oleksandr Zavalov, Ivan Saika-Voivod, Richard K. Bowles, and Peter H. Poole, Phase transitions in fluctuations and their role in two-step nucleation, J. Chem. Phys. 150, 074501 (2019);