Study on Influence Law and Mechanism of Rheological Properties of High-Viscosity Fluoroether Oil-Based Ferrofluids

Comments 1: The manuscript presents a solid experimental investigation on high-viscosity fluoroether oil-based ferrofluids. However, the scientific novelty relative to previous PFPE-based ferrofluids (e.g., Chen et al., Nanomaterials, 2021) could be stated more explicitly. Please clarify what new insights this work offers beyond higher concentration ranges.

Response 1: We thank the Reviewer for raising this critical point. The novelty of our work extends significantly beyond merely increasing the particle concentration. It lies in the systematic exploration of the synergistic effects and underlying mechanisms within the previously unreported parameter space of ultra-high particle concentrations (>50 wt.%) coupled with ultra-high viscosity carrier liquids. Our study provides the following new key insights:

We quantitatively reveal that at these ultra-high concentrations, the influence of particle concentration on viscosity begins to dominate over the effect of the magnetic field, which is a crucial guideline for material design in high-stress applications where zero-field viscosity is critical

We elucidate that the carrier liquid's molecular weight not only affects zero-field viscosity but, more importantly, dramatically amplifies the field-induced yield stress. For instance, the 50 wt.%-7480 g/mol sample achieved a yield stress of 589.79 Pa at 500 mT, an order of magnitude greater than the 54.89 Pa for the 50 wt.%-4600 g/mol sample under the same field.

We report, for the first time in such PFPE-based systems, that a sample at 50 wt.% can undergo a field-induced transition from a liquid to a gel-like state, while samples at 60 and 70 wt.% exhibit a gel-like character even in the absence of a field, indicating the formation of a robust, continuous particle network.

These phenomena and their quantitative relationships were not deeply discussed or uncovered in previous studies on PFPE-based ferrofluids, which typically focused on lower concentration regimes.

Comments 2: The rationale for choosing Zn₀.₂Fe₂.₈O₄ nanoparticles instead of pure Fe₃O₄ is briefly mentioned but not deeply justified. A comparison of their magnetic response or rheological sensitivity to field strength would strengthen the motivation.

Response 2: We appreciate the Reviewer's suggestion. The primary motivation for selecting Zn₀.₂Fe₂.₈O₄ nanoparticles is their superior saturation magnetization (M_s) compared to pure Fe₃O₄ nanoparticles of comparable size, which is a key factor for achieving a strong magnetorheological response. This is well-supported by literature: for instance, one study (DOI: 10.1039/c8nj00547h) showed that Zn_xFe_3-xO₄ particles with x=0.2 can achieve an M_s as high as 65 emu/g. Another reference (DOI: 10.1016/j.jmmm.2014.11.076) reported that Zn_0.18Fe_2.82O₄ nanoparticles exhibited an M_s of 59 emu/g at 300 K, significantly higher than the 49 emu/g for Fe₃O₄ under identical measurement conditions. A higher M_s leads to stronger interparticle magnetic dipole interactions, thereby enhancing the field-induced viscosity and yield stress, which is central to the theme of our work.

Comments 3: The methodology section is technically detailed but could better highlight how reproducibility and error control were ensured, especially in the rheological measurements at ultra-high viscosities where wall slip or sedimentation might occur.

Response 3: We thank the Reviewer for this important comment. We have now expanded the Methodology section to explicitly address these points. The measures taken to ensure data reliability are as follows:

1. Mitigating Wall Slip: A parallel-plate geometry made of non-magnetic metal was used with a set gap of 1 mm. This geometry is known to minimize wall slip effects for highly viscous and structured fluids. Consistency of results was verified in preliminary tests

2. Preventing Sedimentation: The FTIR and TGA data (Fig. 2) confirm a successful and robust chemical coating of the nanoparticles, ensuring excellent dispersion stability in the carrier liquid. Furthermore, as demonstrated by the zero-field viscoelastic results (G' > G'' for 60 and 70 wt.% samples), the samples themselves possess gel-like characteristics and ultra-high viscosity, which inherently suppress particle sedimentation over the measurement timeframe.

3. Data Acquisition Protocol: As stated in the original manuscript (Section 2.3), the acquisition time for each data point was set to be ≥ 1/(shear rate). This ensures the measurement captures a steady-state flow, minimizing errors from transient elastic effects, which is particularly crucial for yield-stress fluids.

Comments 4: The interpretation of FTIR and TGA data (Fig. 2) clearly confirms PFPE-acid coating, yet a quantitative estimation of surface coverage or bonding ratio (e.g., using thermogravimetric mass loss) would help verify the coating efficiency and its consistency among samples.

Response 4: We agree with the Reviewer that a quantitative estimation is valuable. Based on the TGA data in Fig. 2(e), the mass loss of approximately 45 wt.% in the temperature range of 280–480 °C is attributed to the decomposition of the coated PFPE-acid. This allows for a quantitative estimate that the PFPE-acid constitutes about 45% of the total mass of the coated composite particles. Since all particle batches were synthesized and coated using an identical procedure (with 10 g of PFPE-acid under consistent reaction conditions), we can reasonably conclude that the surface coverage and bonding efficiency were consistent across all samples. This consistency ensures that the observed differences in rheological properties are primarily due to the controlled variables (particle concentration and carrier liquid molecular weight) rather than variations in surface coating.

Comments 5: The Herschel--Bulkley fitting (Table 1, Table 2) is central to the rheological analysis, but the manuscript could discuss the limitations of this model for viscoplastic ferrofluids perhaps comparing with alternative constitutive models (e.g., Bingham or Casson).

Response 5: This is a valid point. We have now added a discussion on the choice and limitations of the Herschel-Bulkley (H-B) model in the revised manuscript. We acknowledge that the H-B model shows poor agreement at very low shear rates, as noted in our original text. However, it was selected because it effectively captures two key features of our samples: the existence of a yield stress (τ₀) and the pronounced shear-thinning behavior (quantified by the flow index n << 1). In contrast, the Bingham and Casson models, while also featuring a yield stress, are less suitable as they cannot accurately describe the power-law shear-thinning regime that is dominant in our ultra-high concentration ferrofluids. Therefore, the H-B model represents the most appropriate empirical model for characterizing the steady-state flow behavior of our specific systems.

Comments 6: The viscoelastic analysis (Figs. 8--9) is insightful, yet the study could benefit from including frequency sweep tests to complement the strain sweeps. Frequency dependence of G′ and G″ would more clearly distinguish between gel-like and liquid-like states.

Response 6: We fully agree with the Reviewer that frequency sweep tests provide valuable information on the time-dependent viscoelastic behavior and would be an excellent complement to our strain sweep data. In this study, we primarily focused on amplitude sweeps to determine the linear viscoelastic region (LVE) and the critical yield point, which are fundamental for understanding the microstructure's stability under deformation. We acknowledge that frequency sweeps remain an important aspect for a complete rheological characterization and will be a key component of our future investigations to further unravel the dynamics of these complex fluids.

Comments 7: The discussion around the field-induced structure formation (Figs. 4--5) might be expanded using dimensionless parameters (e.g., Mason number or magnetoviscous number) to generalize the findings and enable comparison with prior MR fluid studies.

Response 7: We thank the Reviewer for this excellent suggestion. To address this, we have now incorporated the magnetoviscous parameter (R_H) into the revised manuscript (Section 3.3, Page 8). R_H is defined as the relative increase in viscosity due to the magnetic field, R_H = (η_H-η₀)/η₀. This dimensionless parameter allows us to quantify and generalize the field-induced thickening effect. Analyzing R_H as a function of shear rate and particle concentration provides a more fundamental basis for comparing the magnetoviscous performance of our ferrofluids with other systems reported in the literature.

Comments 8: While the data show clear enhancement of yield stress and storage modulus under magnetic fields, the reversibility or hysteresis of these effects upon field removal was not addressed. Including such information would be valuable for practical sealing or damping applications.

Response 8: This is a highly relevant comment regarding practical application. Our current study did not systematically measure the reversibility or hysteresis of the rheological properties over full magnetic field cycles (on/off). Based on the physical mechanism, the field-induced structures are expected to be largely reversible upon field removal due to the randomizing effect of Brownian motion. However, at the ultra-high particle concentrations investigated, non-ideal effects such as slight hysteresis or a finite relaxation time might occur due to strong interparticle van der Waals forces and steric hindrance. A thorough investigation of the reversibility and thixotropic recovery is indeed critical for sealing and damping applications and is planned as a dedicated focus of our subsequent research.

Comments 9: The conclusion section effectively summarizes results but could add a short forward-looking statement on scalability e.g., how the ultra-high-viscosity ferrofluids could be processed or stabilized for industrial use without particle sedimentation.

Response 9: We thank the Reviewer for this constructive suggestion. We have added a forward-looking statement to the Conclusion section as follows:
"Looking forward, translating these ultra-high-viscosity ferrofluids into industrial applications (e.g., high-pressure sealing) requires attention to scalable production and long-term stability. Fortunately, the ultra-high viscosity and gel-like characteristics inherent to the systems studied here provide a favorable condition for suppressing particle sedimentation. Future work will focus on optimizing batch synthesis routes and systematically evaluating the performance evolution under practical service conditions, such as long-term storage, repeated shearing, and thermal cycling, to ensure their reliability in real-world applications."

Comments 10: The overall English quality is strong, but a few long sentences in the results (especially in Sections 3.2--3.4) could be shortened or split for readability. Simplifying the flow without losing precision would make the paper more accessible to a wider audience.

Response 10: We sincerely appreciate this suggestion. We have carefully reviewed the manuscript, particularly Sections 3.2 to 3.4, and have revised several long and complex sentences to improve readability and clarity without compromising scientific accuracy. The changes are highlighted in the revised manuscript.

Comments 1: Throughout the text there are sentences that are missing something and/or don't make sense! E.g., in the abstract "The results indicate that the synthesized ferrite (Fe₃O₄) particles are less than 50 nm and are chemically coated with a fluoroether acid." -> something is missing - this sentence doesn't make sense! Please clarify and check carefully the whole manuscript.

Response 1: We sincerely apologize for this oversight and thank the Reviewer for bringing it to our attention. The sentence in the abstract has been corrected to: "The results indicate that the synthesized zinc-doped ferrite particles are spherical with a size of less than 50 nm and are chemically coated with a fluoroether acid." We have thoroughly checked the entire manuscript to ensure all sentences are complete and clear.

Comments 2: Based on Fig. 2(f) it looks that there is a kind of saturation with increasing %; gap between 50-60wt% is significant larger than between 60-70wt%. I suggest the authors to add two more curves corresponding to 55wt% and 80wt% and comment on this effect/observation.

Comments 3: Figures 3,4, 5, and 8:The gap/difference between 60-70wt% is much larger than between 50-60wt% - Why? Please explain. I believe here the results for two more concentrations 65wt% and even a bigger 80wt% would be very helpful and provide further understanding of the phenomenon, qualitative and quantitative. In particular with respect to the field-induced yield stress variation (Fig. 5) these additional particle concentrations would be beneficial.

Response 2&3: We thank the Reviewer for these insightful observations regarding the non-linear progression of properties with concentration. The primary objective of this study was to systematically reveal the influence laws of particle concentration and carrier liquid molecular weight. The three concentrations selected (50, 60, and 70 wt.%) were strategically chosen to clearly capture the key microstructural transitions: from a state of "loose aggregates" (50 wt.%) to a "percolating network" (60 wt.%), and finally to a "robust, continuous three-dimensional network" (70 wt.%), as discussed in Sections 3.2 and 3.5. This progression effectively demonstrates the complete evolution from liquid-like to gel-like behavior.

The markedly larger property gap between 60 and 70 wt.% compared to that between 50 and 60 wt.% is precisely a key finding of our work. This non-linearity is rooted in the underlying microstructural evolution. The transition from 50 to 60 wt.% involves the "formation" of a sample-spanning network, while the transition from 60 to 70 wt.% represents the "strengthening and densification" of this pre-existing network. At these ultra-high concentrations, the interparticle spacing becomes drastically reduced, leading to an exponential enhancement of magnetic dipole-dipole interactions (as governed by Equation (2) in the manuscript). This results in the observed "jump" in properties like yield stress and modulus. We are confident that the existing three data points robustly support this interpretation of the microstructural evolution.

Regarding the suggestion to prepare samples at 80 wt.%, we face significant practical challenges. Achieving a homogeneous dispersion at such an extreme concentration is exceedingly difficult due to the immense viscosity and the fundamental limit of particle packing in a liquid medium. The focus of this work was on stable, homogeneous ferrofluids, and venturing to 80 wt.% would push the system into a paste-like regime, which is beyond the scope of this study.

Comments 4: I suggest to add additional points in Fig 5 for different magnetic fields (at least two) as the gap between 100 and 500 mT is quite big.

Comments 5: Based on the latter (Fig. 5) I would suggest a new figure illustration Delta tau vs particle concentrations wt% for two fixed magnetic fields (e.g., 100 and 500 mT). This should very nice illustrate the nonlinear dependence with wt%.

Response 4&5: We sincerely appreciate these excellent suggestions. In direct response, we have conducted a thorough re-analysis of our data and have created a new figure, Figure 5(b), which is now included in the revised manuscript. This new panel plots the field-induced yield stress (Δτ) as a function of particle concentration for three magnetic field strengths: 40 mT, 100 mT, and 500 mT.

This new representation clearly illustrates the nonlinear and synergistic enhancement of Δτ with both increasing particle concentration and magnetic field strength. The data show a clear progression, with the Δτ values for 40 mT consistently below those for 100 mT and 500 mT. The significantly steeper slope of the curves at higher concentrations (from 60 to 70 wt.%) visually confirms the formation of a much more rigid magnetic-field-induced network. The substantial and progressive gaps between the 40 mT, 100 mT, and 500 mT curves across all concentrations underscore the strong field-dependence of the yield stress. We believe this new figure greatly strengthens our discussion and directly addresses the Reviewer's valuable suggestion. The corresponding description has been added to the figure caption and the main text (Page 8).

Comments 6: In this study the authors consider carrier oils of molecular weights 4600 and 7480 g/mol. Why exactly these two options? What is the motivation for this? And did the authors also tested other carrier oils and how would this effect their results? I even believe that below a "critical"/low molecular weight, such a transition may disappear.

Response 6: This is a highly relevant question regarding our material selection. Our choice of PFPE oils with molecular weights of 4600 and 7480 g/mol was based on two key factors:

1. Practical Availability and Relevance: These are standard, commercially available grades of PFPE oil, which facilitates reproducibility and aligns with potential industrial application contexts.

2. Scientific Rationale: These two molecular weights provide a significant contrast in zero-field viscosity and, crucially, in the degree of polymer chain entanglement. This clear dichotomy allows us to decisively demonstrate the profound influence of the carrier liquid's rheological properties on the macroscopic performance of the ferrofluid, particularly the dramatic amplification of the field-induced yield stress, as shown in Figures 8 and Table 2.

We did not test other molecular weights in this study. However, we fully agree with the Reviewer's insightful hypothesis that a critical molecular weight (or critical chain entanglement density) likely exists, below which the pronounced liquid-to-gel transition and the strong enhancement of field-induced yield stress might be diminished or absent, due to insufficient network stabilization. Furthermore, in our preliminary experiments, we found that using very low molecular weight PFPE oils led to significant sedimentation stability issues in high-concentration ferrofluids, making reliable rheological measurements challenging. Systematically exploring the role of carrier molecular weight, including identifying this potential critical value, is a compelling direction for our future research.