Solubility Science: Principles and Practice Prof Steven Abbott Steven Abbott TCNF Ltd, Ipswich, UK and Visiting Professor, University of Leeds, UK [email protected] www.stevenabbott.co.uk Version history: First words written 15 Sep 2015 Version 1.0.0 15 Sep 2017 Version 1.0.1.1 05 Oct 2017 (Some additions on HSP) Version 1.0.1.2 05 Jan 2018 (An update on RDF calculations for large, complex solute molecules such as proteins) Version 1.0.1.3 05 April 2020 (A number of typos fixed thanks to the kind checking by Lee McManus) Version 1.0.2.0 March 2021 (Crystallization chapter added) Version 1.0.2.1 March 2021 (Minor crystallization updates) Version 1.0.2.1a March 2021 (Correction on NOESY) Copyright © 2017-21 Steven Abbott This book is distributed under the Creative Commons BY-ND, Attribution and No-Derivatives license. Contents Preface 6 Abbreviations and Symbols 10 1 Solubility Basics 12 1.1 The core concepts 15 1.1.1 Concentration 15 1.1.2 MVol 16 1.1.3 µ 17 1.1.4 G 17 1.1.5 a and γ 18 1.1.6 And a few other things 19 1.2 KB theory 19 1.2.1 Getting a feeling for Gij and Nij values 25 1.2.2 Measuring Gij values 27 1.2.3 Information from density 30 1.2.4 Pressure 31 1.2.5 A toy KB world 32 1.2.6 Excluded volume 33 1.2.7 Fluctuation theory 34 1.2.8 Scattering 36 1.2.9 What have we achieved with all this effort spent on KB? 36 1.3 Other solubility theories are available 37 1.3.1 Abraham parameters 37 1.3.2 MOSCED and PSP 38 1.3.3 UNIFAC 38 1.3.4 NRTL-SAC 39 1.3.5 The criteria for a successful solubility theory 39 2 Transforming solubility thinking 43 2.1 Hydrotropes - or are they Solubilizers? 43 2.2 Gu2 is good, G22 is bad, G11 is irrelevant 46 2.3 scCO2 entrainment 51 2.4 KB and proteins 55 2.5 The problem with the RDF 56 2.6 KB and Ionic Liquids 58 2.7 KB and the end of stamp collecting 59 3 Hansen Solubility Parameters 61 3.1 Regular Solution Theory and Lattice Theory 61 3.2 Hansen Solubility Parameters 65 3.3 Distance 66 3.4 HSP Values 68 3.5 Two more solubility theories 69 3.5.1 Ideal Solubility 69 3.5.2 Flory-Huggins 71 3.5.3 χ in practice 73 3.5.4 χ and KB 74 3.6 Polymer-Polymer (in)solubility 77 3.7 One more polymer-polymer formula 78 3.8 Solvent blends 79 3.9 HSP and Temperature 82 3.10 The HSP of water 83 3.11 Are HSP meaningful for large particles? 84 3.12 The problem of small solutes 84 3.13 The HSP of nail polish 85 3.14 Working with a new polymer 87 3.15 HSP via IGC 89 3.16 More from the real world 91 3.17 The future for HSP 91 4 COSMO-RS 93 4.1 COSMO-RS and Water 96 4.2 Beyond simple solutes 100 4.3 The future of COSMO-RS 102 5 Dispersions 103 5.1 DLVO 104 5.2 Zeta potential ζ 109 5.3 Depletion flocculation 110 5.4 Too much/little solubility 112 5.5 Controlled non-solubility 114 5.6 Is that it? 115 6 Solubilizers 117 6.1 Surfactant solubilizers 117 6.2 Solubilization: Solvents to pre-ouzo 120 6.2.1 Solvo-surfactants 121 6.2.2 Pre-ouzo systems 122 6.3 Designing the perfect solubilizer 123 6.3.1 Fragrances 123 6.3.2 Pharma APIs 124 6.3.3 Non-correlations 125 6.3.4 No good ideas 127 7 Aqueous solubility 129 7.1 The Yalkowsky GSE 129 7.1.1 Poorly water-soluble drugs 130 7.2 Hofmeister horrors 132 7.2.1 The Potential of Mean Force 135 7.2.2 The KB view of Hofmeister - and more 137 7.2.3 The KB view of biologics (biopharmaceuticals) 140 7.2.4 The KB view of benzene salting out 142 7.2.5 The KB view of Hofmeister and cellulose 143 7.3 Aqueous polymers 145 7.3.1 Neutral polymers 145 7.3.2 Ionic polymers (Ionomers and polyelectrolytes) 146 7.3.3 Smart polymers 147 7.4 Aqueous solubility summary 147 8 Green solubility 149 8.1 Why most green solubility projects will not save the planet 149 8.1.1 Making a significant difference 149 8.1.2 Affordability 150 8.1.3 Trashing the planet in the name of "green" 150 8.1.4 A spare few $ million for safety 151 8.2 The hype of scCO2 152 8.3 The hype of ionic liquids and NADES 153 8.3.1 Natural Deep Eutectic Solvents (NADES) 154 8.4 Being positive about green solvents. 155 8.4.1 Being smart about green solvent options 156 8.4.2 Being smart about green solvent choices 157 8.5 The take-home message about green solubility. 159 9 Diffusion and Solubility 160 9.1 Fickian diffusion 161 9.2 Practical implications 164 9.2.1 Flavour scalping 164 9.2.2 Safety clothing 166 9.2.3 Adhesion 167 9.2.4 Controlled release 168 9.2.5 Obtaining the diffusion parameters 169 9.3 Diffusion conclusion 171 10 The new language of solubility 172 10.1 Too many schemes 172 10.2 What does "solubility" mean? 174 10.3 Falsifiability 175 10.4 Hydrophobic 177 10.4.1 Hydrophobic hydration 179 10.4.2 Anomalous temperature effects in water 181 10.5 Impossible 186 10.5.1 Using the impossible 187 10.6 Thermodynamics, enthalpy and entropy 189 10.7 A visual language 193 10.8 The end to Babel 194 11 Crystallization 196 11.1 Step 1: Could I ever crystallize this molecule at scale? 198 11.1.1 The metastable, and other, zones 201 11.2 Step 2: What solvent(s) should I use? 203 11.3 Step 3: Quick checks 206 11.4 Step 4: Some real crystallization experiments 207 11.5 Step 5: Sorting out the mess of polymorphs 210 11.6 Impurities 215 11.7 Why we must abandon Crystal Nucleation Theory 216 11.7.1 The behaviour we'd like 216 11.7.2 The behaviour we get 217 11.7.3 The CNT non-explanation 217 11.7.4 2-Step CNT 219 11.7.5 Oiling out 221 11.8 Crystallization Map and Nucleation 222 11.8.1 Seeding 224 11.8.2 Crystal growth 227 11.8.3 Growth versus dissolution 234 11.9 Crystallization via Clusters 235 11.9.1 How stable is a cluster? 240 11.9.2 Cluster theory problems 241 11.9.3 Clusters? So what? 241 11.10 In summary 243 Preface Those of us who have to formulate solutions for industrial applications can adopt two extreme positions with respect to how we go about it. The first way is to rely on intuition and experience, "how it's always been done". The second is to dig deep into profound theory in the hope that the answers will be found there. My experience with formulators around the world is that the "intuition" strategy is overwhelmingly popular and deeply unsatisfactory. And my own experience with high-powered solubility theory is that it is often a long-winded way of getting nowhere. However much of it I read, I could seldom use it to solve a problem. In writing this book I am doing what I always try to do: finding the minimum amount of theory that gives the maximum amount of benefit. In the case of solubility I have found that five bits of theory give me this mini-max. Four of these bits of theory are well-known. The fifth is little known and yet will feature strongly in this book because it is of huge practical importance. Here is what lies at the heart of this book: • Ideal Solubility theory for a crystalline solid simply tells you (mostly from its melting point) the maximum solubility you are likely to have without special effects. Simple and useful, and amazingly little-known. • Hansen Solubility Parameters (HSP). Many readers will have heard of these. They are a 50-year old way of determining the best match between solutes (polymers, crystalline solids, nanoparticles, pigments ...) and solvents by providing three numbers for each solute or solvent which describe the van der Waals, polar and H-bonding capabilities. HSP are usable by experts and non-experts and cope well with the messy realities of a formulator's life. They have never gone out of fashion but recently they have experienced a boom in popularity, partly due to the HSPiP software of which I am co-author. • COSMO-RS. The COnductor Screening MOdel - Realistic Solvents approach relies on deep thermodynamics and one-off quantum chemical calculations to allow highly accurate solubility (and related) predictions. One of the many reasons for the popularity of COSMO-RS is that even for those who do not fully understand how it works, the key components of COSMO-RS have a strong visual element that helps explain where the numbers are coming from. • DLVO. This is the standard theory for dispersions and along with the idea of zeta potential and steric hindrance it is the only particle-specific tool that I have found to be of any practical benefit.