Supplementary Information: Phase Behavior and Molecular Thermodynamics of Coacervation

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1 1 Supplementary Information: Phase Behavior and Molecular Thermodynamics of Coacervation in Oppositely Charged Polyelectrolyte/Surfactant System: Cationic Polymer JR 400 and Anionic Surfactant SDS Mixture by Dongcui Li, Manish S. Kelkar & Norman J. Wagner S.1 SDS micellization in water (ITC calibration measurement) Figure S.1 presents the determination of the CMC * for pure SDS in water at 35± 0.2 C. This demicellization is also evident in all the ITC phase behavior studies. The enthalpy of micellization was measured as a calibration step by initially loading the sample cell with deionized water and inecting a titrant of c = 100mM of SDS (above CMC). The titration is SDS carried out using 6µ Linections lasting a period of 20 seconds, with 10 minutes between each inection and a total of 45 inections per run. tot tot The quantities q( t ), Q ( T, P, c s, ) and Qtot ( T, P, cs, ) are plotted in Figure S.1 for inection of 100mM SDS into deionized water. As the titrant is above CMC, whereas the sample cell initially is not. There are several thermodynamic processes that contribute to Q : (1) the dilution of micelles, (2) the demicellization of surfactant aggregates into monomers, and (3) the dilution of monomers to the cell concentration. Q ( T, P, c ) = H ( T, P) H ( T, P) + H ( T, P) tot n m s, dil mic dil (1) There is no demicellization enthalpy when the sample cell is above the CMC * : Q ( T, P, c ) = H ( T, P) + H ( T, P) tot n m s, dil dil (2) tot The CMC is defined as the inflection point of the Q ( T, P, cs, ) curve, and Hmic is the difference in Q ( T, P, c ) before and after the determined value of CMC *. The CMC * can be also obtained by the tot s, tot total cumulative plot of Qtot ( T, Pc, s, ). By assuming small V, the low-concentration of SDS and high-

2 concentration of SDS can be fitted with linear relationships, where the CMC * is defined as

c VQ ( T, P, c ) = c V ( H ( T, P) + H ( T, P) + H ( T, P)) tot tot n n m in tot, s, s, dil mic

(a) Molar heat of inection, and (b) total cumulative molar heat for demicellization of 100mM

2 2 concentration of SDS can be fitted with linear relationships, where the CMC * is defined as the intersection point of those two fit lines. c VQ ( T, P, c ) = c V ( H ( T, P) + H ( T, P) + H ( T, P)) tot tot n n m in tot, s, s, dil mic dil (3) Figure S.1. (a) Molar heat of inection, and (b) total cumulative molar heat for demicellization of 100mM SDS in H 2 O at 35± 0.2 C S.2 Visual phase behavior comparison Figure S.2 shows the specific points investigated in our visual phase behavior study. Figure S.2. Visual phase behavior study for JR 400/SDS mixture at 25.0± 0.1 C

3 3 S.3 Path dependence study Figure S.3 presents the path dependence study: two samples with different phase stabilities were prepared and were diluted with either SDS stock solution or JR 400 stock solution to the region of discrepancy. Sample 1 (red star: 0.40mM JR400/0.6mM SDS 0.28mM JR400/1.8mM SDS) was initially at low SDS concentrations and then SDS stock solution was added to drive the sample fall in the higher SDS concentrations. Sample 2 (black star: 0.08mM JR400/5mM SDS 0.16mM JR400/1.8mM SDS) started at high SDS concentrations and then was diluted by JR 400 stock solution to lower SDS concentrations. (Compositions are given in units of charge equivalence) Figure S.3 Path dependence study: the arrows indicate two opposite dilution paths (red star: sample 1, black star: sample 2) S.4 Temperature dependence Figure S.4 is a plot of the molar heat per inection ITC isotherms at different temperatures. The phase boundary is shown to be independent of temperature over the temperature range studied ( C ).

4 Figure S.4 ITC molar heat per inection for titration of SDS into 0.1 mm JR 400 solution at different temperatures S.5 Satake-Yang fitting protocol Figure S.

4 4 Figure S.4 ITC molar heat per inection for titration of SDS into 0.1 mm JR 400 solution at different temperatures S.5 Satake-Yang fitting protocol Figure S.5 is a schematic comparison of the least-square-error fitting protocol by Lapistky et al. 40 and the cumulative fitting method in this study. Figure S.5 ITC least-square-error fitting protocols based on the Satake-Yang model

5 5 S.6 Binding and free SDS concentration profile by ITC The number of SDS molecules per single PSC, NAgg, p ( ITC ), is estimated by the total bounded SDS molecules after two binding steps (eqn. (4)). bound bound N, ( ITC) = N + N = ( c (I)+ c (II))/N Agg p I II s s p (4) The first binding step (Satake-Yang model) deals with the charge neutralizing of PSCs, where the number of bounded surfactant molecules is calculated based the binding isotherm (Fig. S.6 (a)-(b)) from the best fitting parameters (Ku,u ) at a given solution composition (c p ) (eqn. (5)). 1 tot bound Kucs ( I) 1 cs ( I) = cs ( I ) + cs ( I) = cs ( I) + c p Kucs ( I ) (1 Kucs ( I)) + u (5) The second step considers the excess adsorbed surfactant molecules during the formation of polymerbound micelles. Above the global PSCs neutralization, the excess of surfactant is assumed to be distributed evenly in the PSCs phase and the supernatant phase, therefore the bound surfactant for forming polymer-bound micelles can be estimated (eqn. (6)). Note that the aggregation number calculated in this manner is only a first approximation. A more precise value of the association number can be obtain by other experimental methods, such as scattering methods (SAXS or SANS), or molecular-level measurements (i.e. time-resolved fluorescence quenching or NMR).. c tot tot (c (redissolution)-c (I)) (II)= 2 bound s s s (6)

6 6 Figure S.6 (a) Free and binding SDS as a function of total SDS in the solution (predicted by Satake- Yang model with the best fitting parameters) showing 0.5 mm JR 400 solution as an example (b) Estimated bound and free surfactant. The open circle in (a) indicates the binding state of Cp=0.5 mm in charge equivalence S.7 Disorder-Order PSCs transition Figure S.7 (a) shows the disorder-order cluster transition by dynamic light scattering experiment, figure S.7 (b) is the average cluster hydrodynamic radius from 10 consecutive measurements for each sample and the zeta potential as a function of anionic/cationic charge ratio (Z -1 ).

Z -1 (S/P) S.8 Mapping the ITC isotherm on to the visual phase diagram Figure S.

The spinodal boundary in the ITC differential plot was connected to the transition from the Satake- Yang binding peak and the

This composition might represent the transition composition, where the polymer charges are all saturated and an excess of

7 7 Figure S.7 (a) Order-disorder PSCs: Particle size distribution from DLS (b) Particle size and zeta potential as a function of charge ratio Z -1 (S/P) S.8 Mapping the ITC isotherm on to the visual phase diagram Figure S.8 shows how to determine the ITC phase boundary and map the compositions to the visual phase map (figure 5). The spinodal boundary in the ITC differential plot was connected to the transition from the Satake- Yang binding peak and the followed linear region with a small, but finite slope (non-zero net enthalpy indicates the excess adsorption). This composition might represent the transition composition, where the polymer charges are all saturated and an excess of surfactant binding, due to the hydrophobic JR400 backbone, begins. Owing to the distinct surfactant binding mechanisms, the differential ITC plot shows the characteristic Satake-Yang peak before the spinodal boundary, and a finite small slope in the spinodal regime, and eventually, a second significant redissolving peak upon approaching the true

8 redissolution binodal boundary. Correspondingly, these phase transitions can be identified on the cumulative ITC isotherm.

fit. Note that this crossover point matches the total SDS concentration where the binding degree approaches 0.9-0.95.

The uncertainty of the ITC boundary in figure 5 is from three replications of ITC measurements independently.

8 8 redissolution binodal boundary. Correspondingly, these phase transitions can be identified on the cumulative ITC isotherm. To assign the actual composition of such spinodal-binodal line in ITC measurement for each single binding isotherm, we ve calculated the S-Y binding isotherm (as given in figure S.8 and also given by figure 7) and assigned the spinodal boundary as the crossover point between the binding isotherm and the followed linear fit. Note that this crossover point matches the total SDS concentration where the binding degree approaches The binodal redissolution boundary is assigned by the transition point to the second peak. The uncertainty of the ITC boundary in figure 5 is from three replications of ITC measurements independently. Similarly, in the cumulative plot, the spinodal position is identified by the transition from Satake-Yang isotherm to a linear regime with a finite slope before the true binodal boundary. The crossover point of the two linear regimes with before and after redissolving is assigned as the binodal boundary (the slope transition could be very clearly found in figure 11).

9 9 Figure S.8 ITC phase boundary determination Although there is no direct theoretical proof that the ITC isotherms can identify the spinodal phase boundary, we have shown the correspondence experimentally. ITC can only signal such transitions if these transitions have an obvious and measurable enthalpy change. With appropriate subtraction and interpretation, the intrinsic enthalpy transitions are typically explained by the change of phases (or structure), reactions, binding (adsorption) mechanisms or other possible changes that could occur in the system.

PCCP PAPER. 1. Introduction. Renu Sharma, Ajar Kamal, Tejwant Singh Kang* and Rakesh Kumar Mahajan* View Article Online View Journal View Issue

PCCP PAPER. 1. Introduction. Renu Sharma, Ajar Kamal, Tejwant Singh Kang* and Rakesh Kumar Mahajan* View Article Online View Journal View Issue PAPER View Article Online View Journal View Issue Cite this: Phys. Chem. Chem. Phys., 2015, 17, 23582 Received 7th May 2015, Accepted 6th August 2015 DOI: 10.1039/c5cp02642c www.rsc.org/pccp 1. Introduction