# Dynamics of thermally induced phase separation in polyvinyl alcohol aqueous solutions: impact of viscosity asymmetry on scaling

Charaf Eddine Merzougui, Florent Malloggi, Hervé Henry, Abderraouf

Bounjad, Aoran Wu, Cyril Chevarin, Jean-pierre Mericq, Denis Bouyer, Patrick Guenoun

► To cite this version:

Charaf Eddine Merzougui, Florent Malloggi, Hervé Henry, Abderraouf Bounjad, Aoran Wu, et al. Dynamics of thermally induced phase separation in polyvinyl alcohol aqueous solutions: impact of viscosity asymmetry on scaling. Macromolecular Chemistry and Physics, 2025, 226 (15), pp.e00083. 10.1002/macp.202500083. hal-05370309

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# Dynamics of Thermally Induced Phase Separation in Polyvinyl Alcohol Aqueous Solutions: Impact of Viscosity Asymmetry on Scaling

Charaf Eddine Merzougui,* Florent Malloggi, Hervé Henry, Abderraouf Bounjad, Aoran Wu, Cyril Chevarin, Jean-Pierre Mericq, Denis Bouyer, and Patrick Guenoun*

This research presents an experimental analysis of thermally induced phase separation (TIPS) dynamics in a polymer aqueous solution with very different viscosities (a factor of about a thousand) between separated phases but with no elastic character. The study encompasses the determination of the phase diagram for the polymer-water system, and the exploration of phase separation (PS) dynamics in critical and off-critical systems using laser scanning confocal microscopy (LSCM). Thus, domain growth is analyzed through a fast Fourier transform (FFT) from the confocal images, providing insights into the characteristic size and the structure factor scaling. The study focuses on 10 and 12 wt. % polyvinyl alcohol (PVA) solutions, revealing distinct morphologies and growth mechanisms. Despite the huge difference in viscosities between separated phases, PVA₁₀ exhibits characteristics of spinodal decomposition with interconnected structures and linear growth (L_m (t) ~ t¹), indicative of hydrodynamic coarsening. Conversely, PVA₁₂ shows a trend toward discontinuous structures with growth following L_m (t) ~ t¹/³, suggesting a diffusion-driven coalescence mechanism. Notably, both systems demonstrate self-similar growth patterns despite the significant viscosity contrast, as confirmed by scaled structure factor analysis.

## 1. Introduction

Phase separation (PS) is a fundamental process in materials science that plays a crucial role in shaping the microstructure of various materials,[1,2] resulting in dispersed or interconnected structures.[3] This process can be induced by various factors, including temperature changes, solvent composition, and the introduction of non-solvents.[4] Among the diverse applications of PS, the separation of concentrated polymer solutions is of particular interest in the field of membrane fabrication.[5] Particularly, the thermally induced phase separation (TIPS) process stands out as important for preparing porous materials, such as polymeric membranes.[6] In TIPS, a homogeneous polymer solution is cooled or heated to induce PS, resulting in a polymer-rich phase that forms the future material matrix and a solvent-rich phase that creates the pore structure after elimination.[7] This technique has been widely used to

produce membranes for various applications, including water treatment, battery separation, and membrane distillation.[8,9]

However, despite its importance, several challenges remain for fully understanding and controlling the PS process in polymer systems. For instance, the occurrence of slow or arrested PS in polymer systems,[10,11] where macroscopic PS is difficult to achieve. This phenomenon makes it challenging to quantify the volume fractions of phases, estimate final compositions, and characterize morphologies during the growth process. Besides, one of the primary issues is the asymmetry between separating phases, where one phase exhibits fluid-like properties while the other is viscous and potentially elastic.[12] This viscosity contrast can significantly affect the dynamics and morphology of the resulting structures. Several experimental studies on glasses have shown that viscosity asymmetry disrupts system symmetry, leading to original fragmentation mechanisms compared to symmetric mixtures.[13,14] Interestingly, enough the scaling of PS (to be defined below) seems to be preserved as well as the occurrence of hydrodynamic growth for bicontinuous morphologies. The latter growth originally described by Siggia,[15] involves interconnected liquid tubes that promote growth through capillary instabilities. In addition, numerical simulations investigating

C. E. Merzougui, F. Malloggi, P. Guenoun

CEA Saclay

NIMBE

UMR 3685, LIONS, Gif-Sur-Yvette, Cedex91191, France

E-mail: charaf.merzougui@cea.fr; patrick.guenoun@cea.fr

H. Henry, A. Bounjad

Laboratoire de Physique de la Matière Condensée

CNRS

Ecole Polytechnique

Institut Polytechnique de Paris

Palaiseau91120, France

A. Wu, C. Chevarin, J.-P. Mericq, D. Bouyer

IEM (Institut Européen des Membranes)

Université Montpellier

UMR5635, CNRS, ENSCM, Montpellier 34090, France

<figure><img src="image_2.png" /></figure>

The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/macp.202500083

© 2025 The Author(s). Macromolecular Chemistry and Physics published by Wiley-VCH GmbH. This is an open access article under the terms of the [Creative Commons Attribution-NonCommercial-NoDerivs](https://creativecommons.org/licenses/by-nc-nd/4.0/) License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

DOI: 10.1002/macp.202500083
iments were conducted using a 10 mm quartz cell on a high-performance double-beam Cary 100 Bio UV-vis spectrophotometer, and data were collected at a wavelength of 500 nm. The instrument features a temperature-controlled multicell sample holder, enabling temperature changes of the PVA solutions during analysis. Hence, the transmittance of PVA solutions was monitored as a function of temperature, which was ramped up at a rate of 0.5 C°min⁻¹ from 25 to 70 °C. The cloud point (CP) was then determined from the sharp decrease of the transmittance versus temperature. Typically, CP was defined as the temperature at which the transmittance drops to a specific value, often 50% which was adopted in this study, or 90% of the initial transmittance.[25,26]

The binodal curves were determined by measuring the PVA concentration in both polymer-poor and polymer-rich phases after macroscopic PS of the PVA solution at a definite temperature. The macroscopic separation of 10 mL PVA solution was performed in the oven at the chosen temperature, which allows the polymer-poor phase to be recovered as a supernatant, while the polymer-rich phase settles to the bottom of the sample. The measurement was based then on a calibration curve of PVA concentrations that was first established using UV-vis spectroscopy. To induce the PS, the system was subjected to different quench depths for various PVA concentrations. Specifically, the quench depth refers to the difference between the final temperature applied to the system and the cloud point temperature of the PVA solution.

## 2.4. Rheology Measurements

The rheological properties of both polymer-poor and polymer-rich phases were investigated. Measurements were carried out on an Anton Paar MCR 302 Rheometer at Laboratoire Léon Brillouin (CEA Saclay, IRAMIS), which was equipped with a 50 mm diameter cone-plate geometry (2° angle). The experiments were conducted at a controlled temperature of 22 °C, maintained through the lower plate using a Peltier device. To prevent sample evaporation and drying, the setup was enclosed within a protective hood.

To carry out these experiments, the two phases resulting from PS, i.e., the polymer-lean phase and the polymer-rich phase were first recovered. Afterward, the shear viscosity of each phase was measured separately over a shear rate range varying from 0.01 to 100 s⁻¹, and data were processed with Rheocompass software.

Moreover, the storage modulus (G') and loss modulus (G") were measured for the polymer-rich phase over a frequency range 0.01 < ω < 1000 rad.s⁻¹.

## 2.5. Fast Fourier Transform (FFT) for Confocal Images Processing

FFT was a powerful technique used in image processing for confocal microscopy images. It was used to convert spatial information in the image to frequency domain information, which can help to reveal periodic patterns or the presence of characteristic lengths. More specifically, FFT of confocal images was performed using the Plugin EasyPower spectrum by Gluender, implemented in ImageJ.[27] This plugin makes use of a power-of-two sized domain (which was optimal for FFT calculations) and applies a Hanning window to reduce spectral leakage. This combination helps to minimize artifacts and improve the quality of the

frequency domain representation of the image. This processing allows them to obtain the radially averaged power spectrum image representing the squared modulus of the Fourier transform of concentration fluctuations, the latter being assumed to be directly proportional to the grey level in direct space. These spectra enable to determination of the wave vector $q_m$ corresponding to the maximum peak intensity in the frequency domain, which was used then to calculate the characteristic length $L_m$ (t) of structures within the image. All pictures were shown to exhibit a spinodal ring in Fourier space. This characteristic length measured by the radius of the spinodal ring $q_m$ represents a measure of the typical domain spacing in reciprocal space and increases with time in real space (structure coarsening). In fact, this spacing was inversely proportional to the dominant frequency identified in the FFT,[28] and it can be calculated using the formula:

$$L_m(t) = \frac{2\pi}{q_m} \qquad (1)$$

where $q_m$ is the wave vector at the maximum intensity. In the scaling regime, $L_m(t)$ is usually found to follow a power-law growth of the characteristic domain size:

$$L_m(t) \sim t^{\alpha} \qquad (2)$$

The exponent $\alpha$, known as the growth exponent, depends on the physical mechanism governing the coarsening dynamics.

The structure factor, obtained as the previously described power spectrum, was moreover used to characterize more precisely the form of the phase-separating structure. This approach, initially introduced through numerical simulations,[29,30] was based on the scaling hypothesis that $L_m(t)$ and its dynamics were enough in describing the PS evolution.

In other words, the scaling hypothesis assumes that physical quantities should depend on time solely through this characteristic length scale. Therefore, under the scaling hypothesis, the structure factor should be written as follows:[31]

$$S(q, t) = L_m(t)^d F(qL_m(t)) \qquad (3)$$

where S(q,t) is the structure factor at a given time, F is a time-independent scaling universal function, and d is the dimensionality of the system.

Here, as dealing with 2D images, the 2D scaling hypothesis was explored by forming the following equation:[32]

$$F(x) = \hat{S}(q, t) \cdot q_m^2 \qquad (4)$$

where x is the dimensionless reduced wave number ($x = q/q_m(t)$), and $\hat{S}(q,t)$ the normalized structure factor that can be estimated from the following formula:[32]

$$S(q, t) = \frac{S(q, t)}{\int_{q_1}^{q_2} q S(q, t) dq} \qquad (5)$$

The integration range extends from $q_1 = 0.3$ to $q_2 = 3$ in accordance with previous studies.[33] Scaling was verified if, at each time, all F(x(t)) curves collapse on a single one, meaning that correlations within growing domains were the same at all times provided that the spatial scale was renormalized by $L_m(t)$.
<figure><img src="image_3.png" /><figcaption>**Figure 2.** Experimental binary phase diagram of aqueous PVA solution displaying the cloud point curve, and the binodals for each concentration.</figcaption></figure>

The aforementioned mathematical relationships and scaling principles were applied to analyze the confocal microscopy images obtained from experiments. Specifically, these equations were used to calculate the characteristic length of the observed structures and to examine the scaling behavior of the structure factor.

## 2.6. Ethics Approval

No experiments on animal or human subjects were used for the preparation of the submitted manuscript.

# 3. Results and Discussion

## 3.1. Phase Diagram

The PVA-water binary system (Figure 2) exhibits a complex phase behavior because of polymer polydispersity.[34] It includes a cloud point curve (red curve), defined as the temperature of two phases appearing at a given PVA mass fraction, and binodal curves defining the compositions of coexisting phases at equilibrium that are dependent on each PVA total concentration.[34]

The phase diagram exposed in Figure 2 typically shows a lower critical solution temperature (LCST) behavior, where PVA solution separates upon heating into polymer-rich and polymer-poor phases due to the breaking of hydrogen bonds between polymer and solvent. Remarkably, the cloud point rises steadily with increasing concentration for this particular PVA with this definite degree of hydrolysis. Note that the phase diagram could be notably different for other DHs.

Analysis of the volume fractions of these separated phases, resulting from the macroscopic PS at various PVA concentrations yielded an interesting observation. Specifically, the ratio of these volume fractions $\phi^-$ / $\phi^+$ has been calculated for different quench depths (where $\phi^-$ and $\phi^+$ are the volume fractions of the polymer-poor and polymer-rich phases respectively), and the results are summarized in Table 1. For a PVA$_{10}$ solution, the volumes of the two separated phases were found to be approximately equal for the different quench depths applied to the system. This observation suggests that 10 wt. % PVA concentration represents the critical point for the PVA-water system as already shown in a previous study.[20] In addition to the volume ratio, it is noteworthy

<table><caption>**Table 1.** Volume fraction ratios of polymer-poor to polymer-rich phases across various quench depths and PVA concentrations.</caption><thead><tr><th>ΔT (quench depth)</th><th></th><th>2</th><th>5</th><th>7</th><th>10</th><th>15</th></tr></thead><tbody><tr><td rowspan="3">ratio of volume fractions<br>(φ⁻/φ⁺)</td><td>PVA<sub>8</sub></td><td>5</td><td>3.2</td><td>2.5</td><td>2.3</td><td>1.4</td></tr><tr><td>PVA<sub>10</sub></td><td>0.93</td><td>0.95</td><td>0.99</td><td>1.02</td><td>1.05</td></tr><tr><td>PVA<sub>12</sub></td><td>0.46</td><td>0.71</td><td>0.82</td><td>0.87</td><td>0.91</td></tr></tbody></table>

that the final concentrations in the polymer-rich and polymer-poor phases are quite symmetric with respect to the initial 10 wt. % value (Figure 2), further supporting the identification of this concentration as the critical point.[35]

It must be stressed that the lowest cloud point temperature observed at 2 wt. % PVA does not correspond to the critical point (10 wt. %) like for monodisperse polymers.[34,36] This discrepancy is due to the polymer's polydispersity.[34,36]

## 3.2. Rheological Behavior of the Separated-Phases

Beyond the concentration disparity between the two phases, the rheological analysis shown in Figure 3 has revealed a striking contrast in their viscosities measured at 22 °C. This significant difference in flow behavior could alter the PS whenever hydrodynamics is relevant to the growth of domains (instabilities, coalescences).

Results presented in Figure 3 disclose that the viscosity of polymer-rich phases is ≈1000 times greater than that of polymer-poor phases resulting from the PS of both PVA$_{10}$ and PVA$_{12}$ solutions. This difference in viscosities can significantly influence the PS dynamics of the system, potentially affecting aspects such as phase mobility, interfacial dynamics, and material processing characteristics.[12,37] Indeed, previous studies reported that the asymmetry in viscosity could break the symmetry of the system.[38] It has been stated in the aforementioned studies that this viscosity contrast can change the dynamics during the separation process leading to different behaviors compared to symmetric mixtures. One could expect these effects to be different between interconnected patterns and disconnected patterns of growth.

It is noteworthy that the measurement temperature was selected to ensure stable and reproducible rheological data. Viscosi-

<figure><img src="image_4.png" /><figcaption>**Figure 3.** Shear viscosity measured at 22 °C of polymer-poor and polymer-rich phases resulting from the phase separation of PVA$_{10}$ and PVA$_{12}$ solutions operated at 55 °C.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>**Figure 4.** Confocal images of the morphology growth over the time within the PVA₁₀ solution during the PS process; temperature increased from 44 to 46 °C (ΔT = 2 °C); images captured using a 10X lens.</figcaption></figure>

ties at the separation temperature are expected lower but in a ratio of the same order of magnitude as can be shown by applying an Arrhenius formula taking into account temperature and concentration in a polymer.[³⁹]

### 3.3. PS Dynamics at Critical and Off-Critical Point

PS dynamics were first explored in a critical mixture, specifically using a PVA₁₀ solution. This study has been conducted using LSCM in conjunction with the temperature-controlled experimental setup described in the experimental section. The temperature was increased from 44 °C, which is the cloud point temperature of the PVA₁₀ solution to 46 °C, resulting in a quench of 2 °C depth. Results are shown in **Figure 4** as a series of 2D optical slices at three different depths, z, of the PVA₁₀ solution undergoing phase separation at 46 °C for 15 min. This approach allowed visualizing the spatial and temporal evolution of the PS process by capturing images over a thickness of ≈180 µm within the sample volume. To avoid surface effects, the lowermost section was acquired ≈10 µm above the microscope coverslip surface, and the uppermost section was acquired ≈10 µm below the microscope slide. The images displayed in Figure 4 illustrate the growth of biphasic domains in the PVA₁₀ solution during the PS, as a 2 °C quench was applied to the system. LSCM images at 0 min refer to the initial system before the PS takes place.

The domains formed during PS exhibit hallmark characteristics of spinodal decomposition (Figure 4). The resulting morphology apparently features an interconnected, bicontinuous structure of PVA-rich (white) and water-rich (black) regions, spanning uniformly throughout the entire sample volume rather than at discrete nucleation points. This finding agrees with the behavior reported in previous studies on the PS of critical systems such as low molecular weight binary mixtures,[³²] polymer blends,[⁴⁰,⁴¹] or colloid-polymer mixtures.[²⁸] The Cahn-Hilliard theory provides a theoretical framework for this process,[⁴²] describing an initial stage with a characteristic length scale initially constant with time (Cahn's regime),[⁴³] which then grows linearly due to hydrodynamics as explained by Siggia.[¹⁵]

Subsequently, the PS dynamics were also investigated out of the critical concentration with the same experimental setup, using this time an off-critical PVA₁₂ mixture. The temperature was increased from 48 °C, the cloud point temperature of the PVA₁₂ solution, to 53 °C resulting in a quench with 5 °C depth. The obtained results, showing the PS of the PVA₁₂ solution during 30 min at 53 °C, are presented in **Figure 5**.

In contrast to the interconnected structures, characteristic of spinodal decomposition, observed in the PS of the PVA₁₀ solution, the results for the PVA₁₂ solution (Figure 5) reveal a distinctly different morphology. As the PS proceeds, the resulting domains exhibit a trend toward discontinuity rather than interconnectedness, where monodisperse droplets of the poor phase appear like inclusions during time. This evolution suggests a departure from the typical interconnected morphology. This shift in morphological development suggests a different mechanism of PS at play in the PVA₁₂ solution, possibly a diffusion-driven coalescence mechanism for discontinuous structures.[⁴⁴]

### 3.4. Characteristic Size Determination from Confocal Images
Processing

To elucidate the theoretical framework of our experimental observations and confirm the mechanism governing the coarsening dynamics, the FFT processing method described in the experimental section was applied to the images captured at different depths. Hence, the characteristic length L_m (t) was calculated using Equation (1) where q_m is determined as the radius of the spinodal ring, and then its evolution was plotted over time. The power-law growth was tested, as described by Equation (2), which in turn enabled to definition of the growth exponent α, and so to infer the physical mechanism controlling the coarsening dynamics in the concerned system.

**Figure 6** illustrates the time evolution of L_m (t) at different z on a double-logarithmic scale for both PVA₁₀ and PVA₁₂ mixtures. The red dashed line represents a growth power law with the coarsening exponent α = 1, and it appears to closely match with L_m (t) derived from the experimental data. Thus, Figure 6A
<figure><img src="image_6.png" /><figcaption>**Figure 5.** Confocal images of the morphology growth over the time within the PVA₁₂ solution during the PS process; temperature increased from 48 to 53 °C (ΔT = 5 °C); images captured using a 20X lens.</figcaption></figure>

clearly indicates that the characteristic length for the PVA₁₀ solution increases directly from the onset of the measurements, following a power law behavior L_m (t) ~ t¹ consistently across all sampled depths within the volume. This linear response sustains the theory suggesting that the bicontinuous PS is governed by the hydrodynamic coarsening (α = 1). Indeed, this mechanism is characterized by a linear growth of domain sizes with time and is driven by the interfacial tension and the flow from a narrower part of the network tube to nearby thicker parts.[45]

Results presented in Figure 6B demonstrate that the characteristic length for the PVA₁₂ solution increases following a power law behavior L_m (t) ~ t¹/³. Indeed, the red dashed line representing a growth power law with an exponent α = 1/3, fits very well L_m (t) obtained from the experimental data. This exponent value is in agreement with the diffusive nature of the process governing the PS in the PVA₁₂ mixture.[3,45] This mechanism describes the formation of a heterogeneous structure from an initially homogeneous mixture, leading to a discontinuous morphology. Thus, the mechanism outcomes are consistent with the experimental observations from the 2D confocal images (Figure 5), which show the development of discontinuous structures over time. The agreement between the theoretical model and the experimental results provides strong evidence for the diffusion-driven coalescence mechanism in the PVA₁₂ system.

The time evolution of L_m (t) indicates also that the growth of both bicontinuous and discontinuous structures for PVA₁₀ and PVA₁₂ mixtures respectively, is not significantly affected by the confinement in the depth direction and is not at all dependent on height. Throughout the sample volume, a consistent morphological evolution is observed, and it is characterized by comparable characteristic sizes at different depths (z). This uniformity in growth patterns suggests that the PS proceeds similarly throughout the entire sample, regardless of the specific depth examined. These quantitative findings align well with the qualitative observations from the confocal microscopy images.

**3.5. Assessment of the Structure Factor Scaling**

Having examined the evolution of the characteristic size in phase separation dynamics, the scaling of the structure factor was then assessed. As introduced in the experimental section, this aspect provides deeper insights into the spatial correlations and self-similarity of the separating phases over time. In the context of dynamic scaling, the structure factor is related to the characteristic size by Equation (3), and it implies that the time dependence of S (q,t) is entirely contained in L_m (t). This means that as the system evolves, its structural properties change in a self-similar manner.

<figure><img src="image_7.png" /><figcaption>**Figure 6.** Characteristic length evolution over time during the phase separation as determined using the FFT processing method from 2D confocal images of: A/ PVA₁₀ solution and B/ PVA₁₂ solution.</figcaption></figure>
proximately 0.01.[32] Thus, we assume the coarsening speed can be expressed as:

$$v \approx 0.01 \frac{\sigma}{\sqrt{\eta_1 \eta_2}} \qquad (8)$$

For a PVA₁₀ mixture, where $η_1 \approx 4$ Pa·s and $η_2 \approx 4 \times 10^{-3}$ Pa·s (as shown in Figure 3), and with a coarsening velocity of $v = 7.5 \times 10^{-7}$ m·s⁻¹ (determined from the slope of the characteristic length evolution in Figure 6A), the surface tension was estimated to be $σ = 5.0 \times 10^{-7}$ N·m⁻¹. This low value is consistent with expectations near a critical point. Similarly, for the PVA₁₂ mixture, using the same method, the surface tension was found to be approximately: $σ = 6.0 \times 10^{-7}$ N·m⁻¹ (where the correction in temperature for the viscosities has been taken into account).

<figure><img src="image_8.png" /><figcaption>Figure 8. Storage and loss modulus measured at 22 °C of PVA-rich phases (PRP) resulting from the phase separation of PVA₁₀ and PVA₁₂ solutions, with corresponding loss tangent plots (tan δ).</figcaption></figure>

## 3.6. Viscosity Asymmetry Impact on the PS Dynamics

Despite a significant viscosity difference between phases (three orders of magnitude), the PS of the PVA₁₀ solution exhibits a bi-continuous morphology for equal volume separating phases, associated with linear hydrodynamic growth. This seems to be in disagreement with theoretical predictions,[49] and experimental results from polymer blend studies,[50] but agrees with recent results obtained on glasses.[12] As for the PS of the PVA₁₂ solution, a dispersed minority lean-polymer phase is observed, whose typical size is growing as a power law with $α = 1/3$. This is in striking agreement with the behavior of low molecular weight binary mixtures,[3,51] and glasses systems with high viscosity difference in critical cases.[13,14]

Remarkably, structure factor scaling holds in both critical (with hydrodynamic growth) and off-critical (diffusion-driven growth) cases, as shown in Figure 7. This behavior was demonstrated for the critical case of binary mixtures of equal viscosity,[28,29] but predicted also for systems with viscosity contrast through numerical simulations.[19] A scaling of the size distribution of domains was also observed for glasses.[13]

Yet, several numerical studies have suggested that a large difference in viscosity can alter both the PS kinetics and the morphology of the separated phases.[16,17] For instance, the phase with the lower viscosity was predicted to form more elongated, interconnected structures, while the higher viscosity phase forms more compact, isolated domains. Furthermore, these studies indicate a departure from the standard dynamical scaling laws typically observed in symmetric PS, with slower coarsening rates and potential fragmentation in the more viscous phase as separation progresses. More recent studies by phase-field approaches have however found that when phases had roughly equal volume fractions (≈50%),[18,19] the self-similar structure could remain robust, even with viscosity contrasts up to 100.[19] However, significant asymmetry in phase volume fractions (40/60 or 30/70) combined with viscosity differences could lead to remarkable changes in microstructure resulting sometimes in disrupted self-similar growth.[18]

The fragmentation process suggested in numerical studies,[17] was also discussed experimentally by X-ray tomographic study of silicate melts.[13] Instead of simple dynamical scaling, the study

revealed a more complex behavior causing a deviation from the expected dynamical scaling laws typically associated with coarsening phenomena.

Eventually, the results from this experimental study indicate that the viscosity contrast did not significantly alter the dynamics of the PS compared to symmetrical mixtures and that the resulting morphology of the separated phases is always self-similar.

Another concept to be considered is viscoelastic PS,[12,52] where the dissymmetry in elasticity between phases is able to alter both growth laws or scaling regimes. Network-like structures were notably predicted to occur in this case.[53]

To assess the potential relevance of these theories in the PVA system, the storage modulus (G') and loss modulus (G") were measured for the polymer-rich phase resulting from the macroscopic PS of both PVA₁₀ and PVA₁₂ mixtures. Results shown in Figure 8 indicate however that if G' and G" increase with increasing frequency for both solutions, the phases exhibited a liquid-like behavior, with G" consistently exceeding G' across the entire studied frequency range. Elastic effects are then evaluated to be rather weak in our system, ruling out a significant influence of viscoelastic contrast on phase separation. Indeed, these measurements clearly demonstrate that the polymer chains are not entangled in this system. The experimental data confirms we are operating in a concentration regime below the entanglement threshold for this particular PVA.

This is confirmed by plotting the tangent of the loss angle (tan δ) against frequency, which provides crucial information for understanding phase changes under shear conditions. In fact, tan δ serves as a quantitative measure of whether a system behaves more like a solid-like elastic body or a liquid-like viscous fluid. Generally, when tan δ > 1, fluid character dominates, while solid character prevails when tan δ < 1.[54] The results show that the PVA-rich phases resulting from the PS of both PVA₁₀ and PVA₁₂ mixtures exhibited liquid-like viscous fluid behavior. This observation is consistent with the findings obtained from the measurements of storage modulus (G') and loss modulus (G"). The observed results corroborate existing literature reports regarding the rheological characteristics of high-concentration PVA aqueous solutions.[55] Therefore, the concentrated phase cannot be considered as elastic, and theories of viscoelastic PS are not relevant in this case.
4. Conclusion

This study provides a comprehensive experimental investiga-
tion into the PS behavior of PVA aqueous solutions using the
TIPS method. The study exhibits the underlying mechanisms
of growth of the resulting morphologies of PS in both critical
and off-critical PVA systems, proving in both cases their temporal
self-similarity.

The critical PVA₁₀ mixture exhibits a characteristic spinodal
decomposition mechanism, as evidenced by interconnected, bi-
continuous structures observed through LSCM. FFT analysis of
these images revealed growth dynamics following a power law
with an exponent α = 1, indicative of hydrodynamic coarsen-
ing. In contrast, the off-critical PVA₁₂ mixture displays a discon-
tinuous morphology with a growth exponent α = 1/3, suggest-
ing a diffusion-driven coalescence mechanism. As already ob-
served for pure fluids and low-molecular-weight binary mixtures,
a minute change in the phase volume ratio is sufficient to switch
from a bicontinuous interconnected pattern to a disconnected
one.

Notably, despite the significant viscosity contrast between the separated phases, both systems demonstrate self-similar growth, as evidenced by the collapse of scaled structure factors onto master curves. This observation challenges previous numerical and experimental studies that predicted unconventional patterns in systems with viscosity asymmetry, with deviation from the standard dynamical scaling laws observed in symmetric PS.

Furthermore, rheological characterization of the separated phases revealed predominantly fluid-like behavior, ruling out viscoelastic effects in our case.

These results suggest that viscosity asymmetry is not a key fac-
tor of PS and that complex structures observed in the formation
of membranes arise from additional parameters. This work paves
the way for further experimental investigations with other poly-
mer systems to investigate whether these findings are universal.

Acknowledgements

The authors gratefully acknowledge the Agence Nationale de la Recherche (SIMUMEM Project: ANR-21-CE06-0043) for financial support. The authors also thank Laboratoire Léon Brillouin (CEA Saclay, IRAMIS) for granting access to their double-beam Cary 100 Bio UV-vis spectrophotometer and Anton Paar MCR 302 Rheometer for conducting experiments.

Conflict of Interest

The authors declare no conflict of interest.

Data Availability Statement

The data that support the findings of this study are available from the cor-
responding author upon reasonable request.

Keywords

characteristic size, PVA polymer, structure factor scaling, TIPS process, viscosity asymmetry

Received: February 16, 2025
Revised: May 1, 2025
Published online: May 28, 2025

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