Optical tracking of relaxation dynamics in semi-dilute hydroxypropylcellulose solutions as a precise phase transition probe

Phase separation of thermo-responsive polymers in solution is a complex process, whose understanding is essential to screen and design materials with diverse technological applications. Here we report on a method based on dynamic light scattering (DLS) experiments to investigate the phase separation of thermo-responsive polymer solutions and precisely define the transition temperature (T PS ). Our results are applied on hydroxypropylcellulose (HPC) solutions as an important biosourced green water-soluble polymer. As determined by DLS, the amplitudes of the fast and slow modes of relaxation dynamics evolve as temperature gets closer to the phase transition point eventually leading to phase separation. The evolution of the modes with temperature is markedly different for concentrations below the overlap concentration (𝑐 ∗ ) (dilute regime), above 𝑐 ∗ (semi-dilute regime) and above the entanglement concentration (𝑐 𝑒 ) . In the three cases though, the fast and slow mode amplitudes undergo a sharp transition in a narrow temperature range, defining accurately the phase separation locus. The results agree with turbidimetric analysis for the phase transition determination but with a better precision. Our results also show that the one-phase dynamics and phase separation dynamics in the two-phase region are only in continuity for 𝑐 > 𝑐 𝑒 , revealing mechanistic details about the HPC phase separation process. Above T PS we identify a temperature range where the intensity autocorrelation function has a single-exponential shape. In the latter regime, we monitor the


Introduction
3][4] Critical aspects to designing and screening such systems rely on a better understanding of the phase transition and the determination of well-characterized phase diagrams and phase transition solution temperatures since the latter temperatures are the main experimental data needed to further investigate the fundamentals of phase separation mechanisms and kinetics.Different approaches based on optical measurements (transmittance, scattering intensity at different angles and refractometry) and differential scanning calorimetry are currently utilized to approach and locate the phase boundary (TPS) of thermo-responsive water-soluble polymers in a broad range of concentrations.However, the typical criteria to define such transition are rather arbitrary without a clear physical significance that justifies a particular choice, which represents one of the major sources of diversity (as much as 20 % of TPS) of phase diagrams for several thermoresponsive polymers widely used in applications, such as poly(N-isopropylacrylamide) (PNIPAm) 5 , hydroxypropylcellulose (HPC) 6,7 , methylcellulose [8][9][10] , hydroxypropylmethyl cellulose 8,9 , among others.Taking into account that phase separation mechanisms of thermoresponsive polymers strongly depend on the temperature quench depth 10 the arbitrariness in defining TPS represents a clear limitation to investigating phase separation mechanisms and kinetics in a temperature range close to TPS.
In this article we are interested in exploring another approach to define the phase separation transition of a thermo-responsive water-soluble polymer in a broad range of concentrations based on Dynamic Light Scattering (DLS).DLS is a well suited technique to investigate polymer dynamics over a large concentration range and a large temporal window of relaxation times. 11In the dilute regime, at which polymer concentration is below the overlap concentration ( * ), the intensity autocorrelation function ( 2 ()) reports a single relaxation mode which describes Brownian motion of single coils for monodisperse systems 12 whatever the solvent quality is. 13 At concentrations above  * the system resides in the semi-dilute regime, at which polymer chains overlap and possibly entangle.Li et al. demonstrated that for poly(styrene) in a thermodynamically good solvent (benzene) at   * ⁄ = 30,  2 () is still described by a single diffusive relaxation mode, 14 while a second non-diffusive relaxation mode is evidenced (slow mode) at higher  when the solvent quality gets poorer. 13,14The interpretation of the latter slow mode has been controversial and the subject of extensive research in the last decades for deciphering its origin with respect to blobs relaxations below or above the entanglement concentration ( e ).Pioneering works by Brown et al. 15,16 and more recently Yuan et al. 13 attributed the slow mode relaxation to permanent aggregates in the single-phase region, while more recent experiments 11,17 described the slow relaxation dynamics of aqueous PNIPAm solutions as originating from transient clusters having a non-diffusive nature.In addition, a second slow dynamical mode was identified for shape-persisitent stiff polymers. 18,19Several studies in this area focused on the effect of polymer concentration, polymer architecture, and temperature on the slow mode 17,[20][21][22] in order to explain the origin of this slow relaxation dynamic.Here our goal is different: we address the question of whether it is possible to extract relevant quantitative information about the phase transition of a polymer solution in the semidilute regime by following the fast and slow mode evolution as temperature gets closer to phase separation.For this study we selected HPC aqueous solutions as a thermo-responsive biosourced polymer which was recently designed as an excellent candidate for making porous membranes excluding the use of organic solvents. 3It displays lower critical solution temperature behavior in water at 40℃ (up to 40 %), 23,24 a very convenient feature for many applications, and was first characterized in 1988 to phase separate by spinodal decomposition at  = 10 %. 25 In this article we show that the approach of HPC phase transition significantly impacts the fast and slow mode behaviors.By following the latter modes up to the phase boundary, we demonstrate that it is possible to define the phase transition temperature with a remarkable accuracy.This methodology provides a more precise and physically meaningful approach to determine the phase transition temperature than the commonly used turbidimetric method.
We also show that the evolution of relaxation modes for HPC is strongly concentration dependent and provides clues to describe the phase separation mechanisms by varying the concentration.For instance, a remarkable continuity of modes from the single-phase region to the two-phase region observed for entangled solutions reveals that the non-diffusive transient clusters formed in the single-phase region are precursors of the phase separating objects.
Finally, we show that DLS can be used to resolve the growth kinetics of HPC domains for concentrations as high as 5 % and thermal quenches of an amplitude such as the single exponential nature of  2 () is preserved.

Experimental Sample preparation
A commercial HPC (Sigma-Aldrich) was employed for this study since the very same polymer proved to be a valuable choice for further applications for membranes. 3The weight average molecular weight ( W ), evaluated by size exclusion chromatography (Shimadzu LC-20AD) using a Shodex OHpak SB-803/SB-804 column and poly(ethylene glycol) molecular weight standards, is 72 kg/mol and PDI3.HPC aqueous solutions in the concentration range 0.5 to 30 % (wt.%) were prepared by fully dispersing HPC powder in preheated Milli-Q water at 60℃ with stirring for 2 h.The samples were then cooled and stored at 4℃ overnight to complete hydration of the polymer.The aqueous solutions were transparent at room temperature.
Samples with  ≤ 10 % were filtered using 0.45 m Millipore filters directly into dust-free PMMA light scattering cuvettes.Solutions with concentration higher than 20 % were prepared from filtered 10 % solution and concentrated under reduced pressure (220 mbar) at 60℃ due to the impossibility to filter such concentrated samples.The overlap concentration  * was determined from the definitions  * = 3/(4 A  g 3 ), /(2 where 0 <  < 1 is a constant related to the coherence of the detection optics.For a polydisperse system, 27  1 () is related to the distribution of the characteristic relaxation time distribution In this study (()) was calculated using the Laplace inversion of  1 () (normalized to 1 at  = 0) on the basis of eqs 1 and 2 by the Maximum Entropy Method. 12,28() usually displays two major relaxation modes (fast and slow).Fast mode correlation time ( fm ) and slow mode correlation time ( sm ) were extracted from the mean peak position of fast and slow relaxation modes, respectively.The contribution of each mode (amplitude) was obtained from the relative peak area of each distribution mode.Additionally, correlation times and amplitudes were also obtained by a similar analysis than that reported by Yamamoto et al. 20 by fitting to a sum of single-exponential functions.The obtained results (data not shown) were in good agreement with those obtained from Maximum Entropy Method.

Turbidimetric measurements
Phase separation temperatures were determined by optical transmittance method using a quartz cell filled with HPC solutions inserted in a thermostat (0.01℃ precision).For determining TPS, a 5 mm thick cell was used, shined by a laser beam ( = 632.8nm).Two photodiodes were placed before and after the sample to measure the transmission of the light through the sample.
Thermal steps of 0.2℃ followed by 30 min equilibration time were performed to monitor the transmittance versus time.As the temperature approached TPS the transmittance decreased with time asymptotically, and therefore the transmittance at infinite time  ∞ (T∞) at each thermal step was extrapolated by fitting to  =  1 exp (−  1 ⁄ ) + T ∞ .From transmittance vs temperature curves, TPS was determined by two different criteria: i) As the abscissa of the intercept between the horizontal asymptote at low temperatures and the tangent to the transmission decrease (T_); ii) As the middle point on the slope of variation between  ∞ and  0 (T 1 2 ⁄ ).

Confocal laser scanning microscopy
HPC phase separation was monitored using an Olympus Fluoview FV1000 inverted confocal microscope.HPC solution (10 L) was sandwiched between two glass slides separated and sealed by a polydimethylsiloxane ring (200 m thick).Rhodamine 6G Chloride was used as the hydrophilic fluorophore.Micrographs were collected with a 40X objective.A thermal stage (Linkam PE 94) was used to control the temperature.The solutions were equilibrated at 30℃ for 30 min followed by heating to the final quench temperature at a rate of 5℃/min.The working distance of the objective was focused in a plane inside the solution, away (~40 μm) from the cover glass, in order to avoid interface effects.

Results and discussion
The overlap concentration ( * ) was estimated to be 1.2 % as defined in the experimental section.
In the dilute regime the product . g , where q is the scattering vector and  g the radius of gyration of the polymer, was estimated to be 0.592 ( = 0.02633 nm −1 ,  g = 22 nm) satisfying . g ˂1.Under these experimental conditions the correlation function yields information about the whole macromolecular motion and not about internal motions of single coils. 29At  = 0.5 % the system is in the dilute regime and TPS was determined to be 44℃ from turbidimetric measurements.The entanglement concentration  e for aqueous HPC at 30℃ should be close to 10 % based on  * value.At  = 20 % (Figure 2d) the behavior of the fast mode is similar to that observed at  = 5 %, showing a marked shift to higher   0 ⁄ with increasing T.However, the slow mode now displays a remarkable continuity in   0 ⁄ in the entire T range analyzed in this study.
Interestingly, at all concentrations it is observed that above the temperature range at which the fast mode vanishes i.e. in the two-phase region, () turns out to be a single narrow mode related to phase separation under the form of polymer aggregates.Small variations in normalized  at this T range are likely due to the aggregate size dependence on the thermal quench, an effect consistent with previous phase separation studies on HPC 25 and PNIPAm. 31

Fast mode
When the polymer concentration is below  * the single relaxation mode is attributed to Brownian motion of single coils, 12 whereas for concentrations above the overlap concentration ( >  * ) this mode reflects cooperative diffusion of chain segments between each blob. 32gure 3a shows the polymer concentration dependence of fast mode relaxation time at T=29.4 ℃.An approximate plateau region is found at concentrations below 0.5 % whereas  fm decreases more markedly with polymer concentration above 0.5 %.This observation suggests that the solution below 0.5 % is in the dilute regime ( <  * ) while at  > 1 % the system enters the semi-dilute regime, in agreement with  * estimation (1.2 %).The decrease in  fm as the polymer concentration increases above 1 % indicates that the average segment correlation length decreases as concentration increases, following a similar trend as that reported for PNIPAm. 33shows a slight increase with T below 39℃, which becomes more notorious above 39℃, likely due to phase separation (PS) into a polymer rich and a polymer lean phase.However, the latter increment of  fm   0 ⁄ in the two-phase region at  = 5 % is notably less marked than that at  = 0.5 %.On the contrary, at  = 20 % the reduced relaxation time  fm   0 ⁄ steadily increases with T, but no sharp transition is observed within the analyzed temperature range.
The slight increment of  fm   0 ⁄ observed below PS in the entire concentration range is likely due to the gradual decrease in solvent quality as the temperature increases from 30℃ (relatively good solvent condition) to the vicinity of theta condition (40℃) 34 where the interactions between segments and segment-solvent gradually change.Brown et al. showed a similar slight increase of fast relaxation time for polystyrene semi-dilute solutions from good solvent (toluene) to theta solvent (2-butanone) conditions, while the fast mode amplitude remained constant. 29A similar trend was observed by Li et al. 14 by cooling polystyrene solution in cyclohexane.The authors explained these results by considering that when the solvent quality decreases, polymer chains contract, resulting in an increase of  * and therefore a slight shift in fast mode relaxation time to higher values, as shown in Figure 3a.Interestingly, over the entire concentration range studied here the fast mode amplitude remains constant up to a temperature at which it decreases sharply, which is likely due to phase separation transition.Also, our results show that the temperature variation of the reduced fast mode relaxation time has no clear dependence with the concentration ranges delimited by  * or  e .

Slow mode
Figure 4a shows the concentration dependence of the reduced slow mode relaxation time ( sm   0 ⁄ ) at 29.4℃ in the single phase region and the corresponding amplitude.As the concentration increases,  sm   0 ⁄ is larger and the slow mode amplitude increases.These observations indicate that the slow dynamic process is closely related to chain clustering/entanglement effects. 17 evidencing the non-diffusive nature of the slow mode as previously observed for different polymer solutions. 13The plots of the slow mode amplitude vs T shown in Figure 4b-f reveal that at some temperature the amplitude undergoes a sharp transition to higher values in the entire concentration range between 1 and 30 %.Moreover, the temperature of this transition decreases with polymer concentration and coincides with the fast mode amplitude transition.
Therefore, we can now rationalize the fast and slow amplitude shifts with increasing temperature as coinciding with the HPC phase separation transition, where polymer chains collapse into polymer aggregates.%.Dotted lines correspond to sigmoidal fittings for amplitude vs T plots.
Note that at  ≤ 10 % there is a narrow T range at which  sm   0 ⁄ shifts to larger correlation times, as presented in Figure 4b-d.This temperature range coincides with the temperature at which the slow mode amplitude increases sharply and is the evidence of HPC demixing process.
This behavior is consistent with results by Yamamoto et al. 20 for semi-dilute aqueous PNIPAm solutions showing a sharp transition in slow mode relaxation time at TTPS.However, it is worth highlighting that the slow mode behavior with increasing temperature observed for HPC is in marked contrast to that reported by Yuan et al. for aqueous PNIPAm in semi-dilute regime, where the slow mode reduced  was observed to become faster by increasing T below TPS. 13 This suggests that the slow mode reduced  variations with temperature could be dependent on the nature of the thermo-responsive polymer.Remarkably, this behavior is no longer observed for HPC solutions above  = 15 % as the reduced  sm shows a clear continuity before and after phase separation, as presented in Figures 4e,f.In this regard, we suggest that the different T dependence of  sm   0 ⁄ at  ≤ 10 % and at  ≥ 15 % is related with the transition between the overlap and entanglement regimes ( e is roughly 10 %).In the non-entangled range ( * <  ≤  e ), at which polymer chains overlap to some extent without entanglement formation, the shift of  sm   0 ⁄ to higher values by increasing T at TPS reflects chain and clustering association at the phase separation condition.By contrast, in the entangled range ( ˃  e ) the fact that  sm   0 ⁄ is constant below and above TPS would imply that no additional or further chain/cluster association occurs during phase separation in this concentration range.This presumably reflects that the transient clusters present in the single-phase region are precursors of polymer aggregates formed in the two-phase region.This picture of phase separation of HPC aqueous solutions at  ˃  e raises the question of the nature of the molecular organization occurring at the phase separation transition.While the observation that the fast mode amplitude decreases abruptly at TPS reflects the formation of HPC-HPC contacts/interaction, the almost identical relaxation dynamics found between the slow mode below TPS and the single mode above TPS suggest that preformed aggregates in the two-phase region may retain considerable amount of hydrogen bonded water molecules, as recently described by Patra et al. 35

Phase diagram
From the analysis of fast and slow correlation times and amplitudes it was evidenced that PS temperatures at different concentrations cannot be obtained by following the evolution of the reduced relaxation times only, in particular at  ˃  e .Although this approach could be useful in the dilute regime, 9 the lack of sharpness in temperature dependence when the concentration is above 5 % precludes a precise definition of the phase separation transitions.
By contrast, the observed transitions in the fast and slow mode amplitudes could be employed to precisely map phase separation diagram of HPC in a broad concentration range and this approach compares favorably to TPS determination obtained by other methods.For comparison, Figure 5a shows that the phase separation temperatures determined by the fast and slow mode amplitude evolution with T are identical.The advantage of this approach is that this DLS analysis conducts to sharp transitions that can be used to accurately define TPS as the temperature at which the fast and slow mode amplitude diverges (experimental error ± 0.3℃).
On the other hand, the typical method employed to map phase separation diagrams of HPC, based on following the drop in transmittance as the polymer phase separates with increasing temperature, provides a transmittance signal that decreases slowly with T (Figure 5a).The latter approach prevents a well-defined TPS determination because the transition lacks sufficient sharpness, reducing the accuracy of the method. 6In fact, this drawback is one of the main factors contributing to diversity of phase separation diagrams since different criterions can be selected to determine TPS, as outlined in a recent work of Halperin et al. 5 In this regard, a significant discrepancy (see Figure 3 in Marsano et al. 7 ) was found by comparing previously reported phase diagrams of aqueous HPC based on turbidity measurements from HPC with similar molecular weight and structure for which no discrepancy is expected. 6,36Figure 5b displays the phase separation diagrams for aqueous HPC solutions in the concentration range  = (0.5 − 30)% obtained by DLS from sigmoidal fittings of fast and slow mode amplitude transitions (red) and turbidimetric analysis taken as the midpoint of the transition (T 1 2 ⁄ ) (green) and by the tangent method (T_) (blue).We found that TPS obtained by DLS are in very good agreement with optical transmittance results T_ but with much smaller error bars for the DLS determination.By contrast, the T 1 2 ⁄ method appears to exceed TPS obtained by DLS at equivalent polymer concentration by an average of 2.0℃ (experimental error ±0.3℃), which becomes even larger at the lowest concentration (T 1/2 − T PS = 4.5 ℃).However, the general trend of the diagrams is very similar with a pronounced decrease of TPS at 0.5 % <  < 1 % and a gradual decrease at 1 % <  < 30 %, in agreement with some previous theoretical and experimental HPC phase diagrams reported by Lárez-V et al. 37 This approach thanks to DLS fully clarifies why the so far rather empirical choice of T_ as the PS temperature is probably justified but much less precise.
Additional experiments performed on aqueous poly(vinyl)alcohol solutions (10 wt.%) with a degree of hydrolysis of 72 % also showed good agreement between the TPS obtained by DLS (36℃, data not shown) and the onset of phase separation previously reported by turbidimetric analysis, 2 suggesting that the method to track the TPS presented here is probably relevant for many thermo-responsive water-soluble polymer solutions in the semi-dilute regime.

Insights into the two-phase region
A correct interpretation of  2 () in the two-phase region may give access to monitoring the phase separation kinetics and measuring characteristic size of polymer aggregates which may form and grow with time.However, DLS theory can only be applied to interpret  2 () signal provided multiple-scattering effects are absent.As HPC aqueous solution enters into the twophase region, the system gets turbid (near TPS) and by further heating the sample well above TPS (T − T PS ≥ 10 o C), it turns into a cloudy phase separated system.Despite this apparent multiple-scattering character above TPS, the correct interpretation of  2 () actually depends on the T quench depth.To illustrate this effect,  2 () was collected at different temperatures using a heating rate of 3 °C min ⁄ to allow for a fast quenching experiment (less than 1 or 4 min heating in the two-phase region for the lower and higher T quench, respectively).Figure 6a shows that  2 () signal is mostly a single exponential in the two-phase region near TPS (T − T PS ≤ 4 o C).By contrast, for a higher T quench (T − T PS ≥ 10 o C),  2 () deviates from the single exponential behavior, as represented in Figure 6a at the same concentration.This is likely due to the formation of denser polymer aggregates that act as efficient scatterers bringing multiple-scattering effects.Indeed, in the multiple-scattering regime, in the back-scattering geometry,  2 () can be fitted to Eq. 3 according to diffusing-wave spectroscopy theory (DWS) assuming spherical scatterers. 38The data are described satisfactorily by Eq. 3 ( = 0.5) at  = 10 % and 20 %, while a slight deviation to a higher a value is encountered for  = 5 %.
These results give evidence of the existence of two regimes within the 2-phase region:   1.However, the large differences observed for concentrated solutions ( = 10 %) manifest that the diffusion coefficient of the aggregates cannot be interpreted as originating from non-interacting objects and that the diffusion coefficient deviates from the dilute limit (Stokes-Einstein value).Figure 8a shows the evolution of  DLS with time at  = 5 % (single-scattering regime, 43℃).
In the earlier stage of the experiment ( ≤ 10 min),  DLS satisfies a scaling law  DLS ()~√ 3 , suggesting that HPC domain growth may follow a classical coarsening behavior. 25,40Note that for  > 10 min,  DLS reaches a plateau indicating that further coarsening of polymer domains is impeded.Such arrested phase separation behavior is consistent with the absence of macroscopic phase separation in the entire concentration range considered in this study (even after 5 days at 43℃).DLS results compare favorably well with the growth kinetics captured by confocal microscopy (Figure 8).The arrested-like phase separation behavior observed for other LCST noninonic water-soluble polymers has been regarded as originating from gelation (methylcellulose, 8,10 hydroxypropylmethylcellulose 8 ) or from the effect of electrostatic charges at the interface of polymer aggregates inducing colloidal stability (PNIPAm 31 ).However, our results show that HPC phase separation is fundamentally different from those systems since phase separation does not induce gelation, and the arrested-like behavior after the growing stage persists by increasing the ionic strength (Figure 8b), which rules out a pure electrostatic effect as for the case of PNIPAm.In addition, confocal microscopy analysis revealed that the arrested phase separation behavior is also observed for higher T quenches (50℃, data not shown) where the multiple-scattering regime is relevant.A potential explanation to the observed HPC arrestedlike phase separation mechanism could be the formation of polymer aggregates concentrated enough (glassy) to prevent colloidal coalescence.However, validation of this hypothesis would require direct measuring of the aggregate composition, and is left for a future work.

Conclusions
The thermo-responsive phase separation of commercial hydroxypropylcellulose was investigated in a broad concentration range covering the dilute and semi-dilute regime by dynamic light scattering.Our results show that the fast and slow mode amplitudes undergo a sharp transition by increasing the temperature near the phase separation temperature.
Accordingly, we propose that by following those transitions, it is possible to define the phase separation boundary with a remarkable accuracy.Solutions with concentrations in the range We suggest that the method described here to map the phase separation diagram and kinetically resolve domain growth in the two-phase region is general and applies to other polymers displaying lower (or upper) critical solution temperature, provided the single scattering regime is correctly determined.

Figure 2 .
Figure 2. Relaxation time distribution () at different temperatures for concentrations (a)

Figure 5 .
Figure 5. (a) Transmittance, fast and slow mode amplitude temperature dependence for  =

3 ,
where 2/3 is an empirical fitting parameter,  * is the transport mean free path and 〈  〉 is the average penetration depth into the sample (2 mm in the experiments),  0 is the characteristic relaxation time and the exponent  is 0.5 in DWS theory.The  2 () signal was measured as a function of time at 50℃ for concentrations 5, 10 and 20 % and fitted to Eq 3. At 30 min, the best-fitted values of  are 0.65, 0.51 and 0.49 (± 0.03) at 5, 10 and 20 %, respectively.Figure 6b displays the logarithm of the normalized autocorrelation function at  = 5 %, 10 % and 20 % plotted as a function of (   0 ⁄ )  using the best values of .

( 1 )
Single-scattering regime, in the T range close to TPS (T − T PS ≤ 4 o C), where the singleexponential nature of  2 () is preserved for at least 6 h; (2) Multiple-scattering regime, in the T range well above TPS (T − T PS ≥ 10 o C), presumably by the formation of denser polymer aggregates.Confocal microscopy images taken at  = 5 % in both regimes reveal that deeper T (T − T PS ≥ 10 o C) quenches lead to denser structures, as presented in Figure 7, supporting the picture of multiple-scattering regime produced by denser particles.

Figure 8 .
Figure 8. Evolution of characteristic dimension  DLS and  Confocal as a function of time during phase separation of HPC solutions at  = 5 % in (a) pure water and (b) NaCl 0.01 M.

(
* <  ≤  e ≈ 10 * ) undergo phase separation with a marked shift of  sm   0 ⁄ to higher values, reflecting clustering association at the phase separation condition.On the contrary, solutions in the range  >   phase separate with a remarkable continuity of normalized relaxation times between the slow mode (below TPS) and the single mode characteristic of the two-phase region.This behavior suggests that transient clusters formed in the single phase entangled region may act as precursors of polymer aggregates in the two-phase region, at temperatures close to TPS.The resulting phase separation diagram was compared to studies conducted by turbidimetric analysis using different criteria to define the phase boundary, showing that DLS transition temperatures reflect the onset of phase separation.Within the two-phase region two temperature dependent regimes were identified.A singlescattering regime in the temperature range close to TPS (T − T PS ≤ 4 o C), characterized by slightly turbid samples.In this regime, monitoring growth kinetics of HPC solutions at  ≤ 5 % it is possible by means of tracking the relaxation time of  2 ().Characteristic domain size growth at  = 5 % follows the power law  DLS ()~√ 3 in the earlier stage of phase separation( ≤ 10 min), suggesting a diffusive or coalescence/aggregation coarsening behavior.After the initial growing stage, the characteristic domain size levels off, suggesting an arrested-like phase separation mechanism, which inhibits macroscopic phase separation regardless of the ionic strength and quench temperature.A multiple-scattering regime was found at higher temperature quenches (T − T PS ≥ 10 o C) at which the samples adopt a turbid and milky appearance.In this regime the system cannot be regarded as originating from non-interacting particles and therefore domain sizing and kinetic studies require a correct determination of  values for a DWS model to be applied in the back-scattering geometry.
3/2 A  g 3 ), and [] −1 , where ,  g ,  A and [] are the molar mass, the radius of gyration of polymer chains, the Avogadro constant and the intrinsic viscosity, respectively.In this work we use the  * value obtained from[] −1 , since the other two definitions are less precise due to the uncertainty in  g as PDI is high.The entanglement concentration  e , representing the concentration above which the polymer chains form an entangled network, was estimated as  e ≈ 10 * , as reported byColby 26

Table 1 .
Characteristic HPC domain size in the two-phase region obtained in the concentration  values as low as 0.1 for strongly interacting systems.By fitting  2 () to Eq. 3, assuming that  DWS =  Confocal as obtained in the multiple-scattering regime, one gets a  value of the order of 0.3 at  = 5 % and 0.1 at  = 10 %.Although this is consistent with expectations, a precise determination of  for HPC at different compositions is clearly out of the scope of this report.
polymer aggregates cannot be neglected in the concentration range considered here.It is worth noting that Sanyal et al.39showed that  decreases with the repulsive interactions between  (%)