Grafting Density Governs the Thermoresponsive Behavior of P(OEGMA-co-RMA) Statistical Copolymers

Thermoresponsive copolymers that exhibit a lower critical solution temperature (LCST) have been exploited to prepare stimuli-responsive materials for a broad range of applications. It is well understood that the LCST of such copolymers can be controlled by tuning molecular weight or through copolymerization of two known thermoresponsive monomers. However, no general methodology has been established to relate polymer properties to their temperature response in solution. Herein, we sought to develop a predictive relationship between polymer hydrophobicity and cloud point temperature (TCP). A series of statistical copolymers were synthesized based on hydrophilic oligoethylene glycol monomethyl ether methacrylate (OEGMA) and hydrophobic alkyl methacrylate monomers and their hydrophobicity was compared using surface area-normalized partition coefficients (log Poct/SA). However, while some insight was gained by comparing TCP and hydrophobicity values, further statistical analysis on both experimental and literature data showed that the molar percentage of comonomer (i.e., grafting density) was the strongest influencer of TCP, regardless of the comonomer used. The lack of dependence of TCP on comonomer chemistry implies that a broad range of functional, thermoresponsive materials can be prepared based on OEGMA by simply tuning grafting density.


Experimental Methods
Copolymerization kinetic studies. Kinetic experiments for one polymer from each series (50% RMA for P(OEGMA500-co-MMA), P(OEGMA500-co-EMA), P(OEGMA500-co-BMA), P(OEGMA500-co-HMA) and 30% RMA for P(OEGMA500-co-LMA) were carried out in order to determine the conversion of each monomer at the same time intervals (i.e., 60, 120, 180, 240, 300, 360, 420 and 480 min). Samples were periodically taken from the polymerization mixtures under nitrogen and then diluted with CDCl3 prior to 1 H NMR analysis. Integrations of monomer signals were compared to those internal standard resonances to determine monomer conversions.
Determination of TCP by UV-Vis spectroscopy. Solutions of P(OEGMA) homopolymer or P(OEGMA500co-RMA) copolymer were prepared at 5 mg mL -1 in nanopure water. The temperature-dependent change in transmittance % was recorded at λ = 550 nm within the temperature range of 20 o C to 93 o C at a heating rate of 1 o C min -1 . Samples were run for two heating/cooling cycles and TCP values taken as the temperature at which the sample transmittance had decreased to 50% on the second heating cycle.
Determination of TCP by µDSC. Solutions of P(OEGMA) homopolymer or P(OEGMA500-co-RMA) copolymer were prepared at 5 mg mL -1 in nanopure water. Samples and reference solvent (nanopure water) were degassed for 15 min prior to measurement by using the degassing unit of the instrument.
Measurements were conducted within the temperature range of 0 o C to 115 o C under a constant pressure of 3 atm. Samples were run two for heating/cooling cycles, with heating and cooling rates for the first and second cycles of 2 o C min -1 and 0.5 o C min -1 , respectively. Data were processed using NanoAnalyze software and TCP values were determined by taking the maximum of the first derivative of the corrected heat rate (µJ s -1 ) vs. temperature ( o C) plots of the second heating trace.
Determination of ΔHmix by µDSC. Data obtained from µDSC as described above were normalized based on their peak maxima. Normalized ΔH values were then calculated via integration of the signal associated with the demixing transition using straight line baseline correction across the collected temperature range from ca. 5-100 o C.

Evaluation of Oligomer Hydrophobicity
LogPoct Analysis. Octanol-water partition coefficients (LogPoct) were calculated for monomers and oligomeric models in Materials Studio 2019, 2 using an atom-based approach (ALogP98 method) 3 for all molecular models containing C, H, N, and O atoms.
Surface Area Analysis. Octanol-water partition coefficients (LogPoct) were normalized by solvent accessible surface area (SA) using Materials Studio 2019. [4][5][6][7] First, single oligomers were subjected to a Geometry Optimization procedure using the Forcite Molecular Dynamics (MD) module with a COMPASS II force field. The force field contains information on important parameters, like preferred bond lengths, bond angles, torsion angles, partial charges, and van der Waals radii that influence the conformation. 8 To minimize energy and determine a preferred conformation, these simulations ran until the energy of the oligomer decreased below predetermined convergence criteria (1 × 10 -4 kcal mol -1 energy convergence, 0.005 kcal mol -1 /Å force convergence, and 5 × 10 -5 Å displacement convergence). Second, these SA values represent the Connolly surface area created by an algorithm that rolls a ball over the surface of the oligomer.
To ensure the SA values are meaningful in the context of octanol-water partition coefficients (LogPoct), the probe had a 1.4 Å radius to match the size of a water molecule. Third, to monitor variations in surface area calculations as the n-mer size increased, oligomers were annealed for 25 cycles using a sinusoidal temperature ramp (300 -700 K) to maximize variability in SA values. After averaging SA values for cycles 23-25, the standard deviation ranged from 0.2-1.2% with an average of 1.0%.

Models.
Oligomeric models contained appropriate ratios of OEGMA and alkyl methacrylate units to mimic experimental conditions. In addition, models were proton terminated and contained OEGMA units

Data Analysis Initial Screening of Descriptors
Correlations between polymer descriptors and TCP were initially screened by visual inspection of the scatter plot matrix shown below in Figure S1. This scatterplot matrix was constructed using the R language environment (v 3.   An asterisk denotes a linear relationship with p < 0.05.

Predictive Model Development
A rigorous elimination/selection stepwise regression analysis was performed to construct a quantitative structure-activity relationship (QSAR) model from the experimental data. The model was trained on the 19 OEGMA copolymers using 4 experimental descriptors (Mol, Wt, MW, and D) and 2 computational descriptors (LP and LPSA) identified as significant in the analysis above. The models were validated via a 5-fold repeated resampling method wherein stratified k-fold datasets were used. This analysis was implemented using the R language environment (v 3.6.3) and the RStudio integrated development environment (v 1.2.5033). Algorithms for model training and cross-validation were implemented using the classification and regression training (CARET) package developed by Dr. Max Kuhn. 9 Table S1 shows the results of the stepwise regression, expressed in terms of the fitness of each model as a function of the number of included descriptors. Based on these data, the optimum model includes 2 descriptors: Mol and Wt. Linear regression statistics for this model are provided in Table S2 and model validation using the training dataset is shown in Figure S3.

Screening of Literature Descriptors
As before, correlations between descriptors and the response variable UV were screened using a scatter plot matrix. These data include a total of 44 unique entries from 10 literature reports (see below for a complete list of raw data and literature references). Data selection was restricted to P(OEGMA-co-R) containing OEGMA units with Mn ~ 500 g mol -1 where the apparent linear relationship between UV and the descriptors was most obvious (see Figure 4 in main text). Scatter plot and correlation matrices for these data are shown in Figures S4 and S5, respectively. As before, Mol and Wt were most strongly correlated to UV.

Model Validation with Literature (Test) Data
The 2-descriptor model was validated using a test dataset consisting of literature Mol, Wt, and UV values.
Whilst the predicted values appear to be linearly correlated with literature UV data, R 2 and RMSE values (R 2 = 0.920, RMSE = 8.42) obtained from this prediction were comparatively worse than for the training dataset (R 2 = 0.976, RMSE = 2.53). This result was diagnostic of "overfitting" of the initial training dataset, likely the result of the strong intercorrelation between the Mol and Wt descriptors that differed between the experimental and literature datasets. Thus, a standard single variable linear regression model was employed in further analysis that related measured or literature UV values to Mol which yielded similar R 2 and RMSE for both the training and test (R 2 = 0.970, RMSE = 4.57) datasets. Linear regression statistics for this model using training (experimental) data are provided in Table S3.               Table S7. TCP of P(OEGMA500-co-RMA) copolymers determined by µDSC.