The model was used as a guide for a future experimental space that is aiming to produce polymer formulations with improved properties.
The model was then updated with the new experiments and a formal optimization was performed that produced a polymer that met all of the design criteria.
To design a polymer whose properties change with both temperature and light, such that it is a liquid at room temperature, forms a gel upon injection into the eye, and subsequently can be irradiated with UV light to affect the pore size. Specifically, the design goals included:
- Gelation temperature between 25°C and 37°C
- High Mn – to provide rapid gelling after injection but below the kidney clearance limit ~32 kDa
- High photo-responsive material (high incorporation rate of photocrosslinkable functional groups)
- High reaction yield (polymer recovery)
Based on the chemical characteristics of the polymers in this study, there was a trade-off between achieving a high photo-responsive material that has a high Mn and a high polymer recovery.
Prior to working with ProSensus, there had been twelve formulations that failed to meet one or more of the other design goals. The successful formulation was developed in the second iteration of ProSensus’ formal optimization framework. It exhibited a cloud point of 36°C, Mn of ~3 kDa, and a significantly higher recovery than previous formulations that contained the same comonomers.
The ProSensus Approach
ProSensus’ framework facilitates rapid product development in a simple 5-step framework:
- Step 1: Develop and maintain good databases
- Step 2: Build multivariate models using all available data that is relevant to the goal(s) at hand
- Step 3: Design latent-variable DOE’s to augment the existing data
- Step 4: Update the model with the new experiments from step 3
- Step 5: Formulating new products
At the beginning of this project, data was available on 23 failed polymers. Putting this data into a tabular “database” format was easily done in a spreadsheet, with one row for each trial formulation and one column for each ingredient, reaction condition, and polymer property. Choice of units is important because it impacts the interpretability of the models.
|Variables||Units Selected||Reasoning for Choice of Units|
|Reactants||Mol % of total reactants||Batch sizes can vary|
|Solvents||mL/mol of total reactants||Each solvent variable expresses the effect of that solvent and also the concentration of reagents|
The ingredient and reaction variables are not independent (e.g. reaction temperature is limited by the boiling point of the solvent used) but this is handled inherently by multivariate (latent variable) models.
For multivariate model building, ProSensus built a PLS model using the data (formulations, reaction conditions, polymer properties) from the 23 failed polymer experiments. This model brought together four chemistry types together such that they could be analyzed as one comprehensive data set, and the effect of each reactant and process condition could be quantified.
Formulating New Polymers
In the first iteration of model-based formulations (Step 3), four new sets of ingredients and reaction conditions were devised but the polymer formulations produced failed to meet all the objectives. Since the design goals were not yet met, the new data from the four new formulations was added to the “database” (Step 4) and the model was updated. As new data is added, the model becomes “smarter” because it gains “knowledge” of a wider design space or different combinations of ingredients and process conditions.
ProSensus’ formal optimization methods allow the definition of a target value and relative importance for each polymer property. The optimization methods allow bounds on the values of ingredient amounts, reaction conditions, and defined constraints.
Deviations from the model plane are also allowed but extreme extrapolation is penalized. Therefore, new areas can be explored, but within reasonable bounds around the model space. This combination of defined target values, bounds and constraints used in optimization is a very powerful technique for formulating new products quickly.
In the second iteration, ProSensus’ formal optimization methods were used (Step 5) and produced a promising formulation.
Shown at left is a visual indication (score plot) that this formulation was promising: rather than being located near other points of the same chemistry type, it is located near the cluster of NIPAM-only polymers, which naturally have a cloud point in the desired range, a high Mn, and good recovery.
This formulation was synthesized and tested in the lab and it exhibited a cloud point of 36 °C, Mn of nearly 3 kDa, and a significantly higher recovery than previous formulations that contained the same comonomers. In short, a multivariate model-based approach succeeded in formulating a successful polymer formulation that had met all the design goals in two iterations only where 23 trial-and-error experiments based on a literature survey had previously failed.
- M. Tzoc Torres, E. Nichols, J.F. MacGregor, T. Hoare, Designing multi-responsive polymers using latent variable methods“, Polymer, 55, 2014.