# Glass and Jamming Rheology in Soft Particles Made of PNIPAM and Polyacrylic Acid

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

_{3}, all from Sigma-Aldrich (St. Louis, MI, USA), and the crosslinker N,N’-methylene-bis-acrylamide (BIS), from Eastman Kodak (Kingsport, TN, USA), were used. NIPAM monomer and BIS, used as crosslinker, were recrystallized from hexane and methanol respectively, dried under reduced pressure (0.01$\phantom{\rule{0.166667em}{0ex}}\mathrm{mmHg}$) at room temperature and stored at 253$\phantom{\rule{0.166667em}{0ex}}\mathrm{K}$. AAc monomer was purified by distillation (40$\phantom{\rule{0.166667em}{0ex}}\mathrm{mmHg}$, 337$\phantom{\rule{0.166667em}{0ex}}\mathrm{K}$) under nitrogen atmosphere in presence of hydroquinone and stored at 253$\phantom{\rule{0.166667em}{0ex}}\mathrm{K}$. SDS, used as surfactant, KPS and APS, used as initiators, TEMED, a reaction accelerator, EDTA, a chelating agent for purifying dialysis membranes, and NaHCO${}_{3}$, were all used as received. All other solvents were RP grade (Carlo Erba, Cornaredo, Milan, Italy) and were used as received. Ulatrapure water (resistivity: 18.2$\phantom{\rule{0.166667em}{0ex}}\mathrm{M}\Omega $/cm at 298$\phantom{\rule{0.166667em}{0ex}}\mathrm{K}$) was obtained with Arium® pro Ultrapure water purification Systems, Sartorius Stedim. A dialysis tubing cellulose membrane, MWCO 14,000 Da, (Sigma-Aldrich) was cleaned before use by washing with running distilled water for 3 h, treated at 343$\phantom{\rule{0.166667em}{0ex}}\mathrm{K}$ for 10$\phantom{\rule{0.166667em}{0ex}}\mathrm{min}$ into a solution containing 3.0% NaHCO${}_{3}$ and 0.4% EDTA weight concentration, rinsed in distilled water at 343$\phantom{\rule{0.166667em}{0ex}}\mathrm{K}$ for 10$\phantom{\rule{0.166667em}{0ex}}\mathrm{min}$ and then in fresh distilled water at room temperature for 2$\phantom{\rule{0.166667em}{0ex}}\mathrm{h}$.

#### 2.2. Microgel Synthesis

^{1}H-NMR analysis as described in reference [54], and it was C${}_{PAAc}$ = 24.6%. IPN microgel polydispersity is around 15–20% and was determined both by DLS and TEM measurements as discussed in reference [55]. Future studies will be devoted to understand the internal strucutre of the IPNs. Samples at low concentrations (lower than C${}_{w}$ = 1.0%) were obtained by dilution with distilled water from the same stock suspension at C${}_{w}$ = 1.0% whereas, samples at higher concentrations were obtained by evaporation from the sample C${}_{w}$ = 1.0% and adjusted at pH = 5.5. At this pH a fraction of COOH groups of PAAc chains are protonated while a fraction, not negligible, are deprotonated in the COO${}^{-}$ groups. This affects the aggregation mechanisms that can be ascribed to both like-charge attraction and to intra-particle and inter-particle H-bonding interactions between the CONH group of PNIPAM and the COOH group of PAAc [56].

#### 2.3. Rheological Measurements

#### 2.4. Steady Shear Measurements

#### 2.4.1. Cross and Carreau-Yasuda Models for Viscous Liquids

_{CY}= τ

_{C}. They can be considered non-Newtonian models since both can be rewritten with the simplified expression $\sigma =\eta \left(\dot{\gamma}\right)\dot{\gamma}$.

#### 2.4.2. Yield Stress Materials: The Herschel-Bulkley Model

#### 2.5. Oscillatory Measurements: Storage and Loss Moduli

#### 2.6. Arrhenius and Vogel-Fulcher-Tamman Models for the Concentration Dependence of Viscosity and Relaxation Time

#### 2.7. Characteristic Stress and Time Scales

#### 2.8. Dynamic Light Scattering Measurements

## 3. Results and Discussion

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Hydrodynamic radius R${}_{h}$ (left axis, circles) for IPN microgel at ${C}_{PAAc}=24.6\%$ as a function of temperature measured in diluite conditions (C${}_{w}$ = 0.01%) compared with the viscosity (right axis, squares) at concentration C${}_{w}$ = 0.3% and shear rate 10 s${}^{-1}$.

**Figure 2.**Shear stress $\sigma $ versus shear rate $\dot{\gamma}$ for IPN microgel with PAAc content 24.6% at different weight concentrations in the range (0.05–7.2)% at (

**a**) T = 298$\phantom{\rule{0.166667em}{0ex}}\mathrm{K}$, below the VPT, and (

**b**) T = 311$\phantom{\rule{0.166667em}{0ex}}\mathrm{K}$, above the VPT. Lines are fits with the Cross model for low concentrations and with the Herschel-Bulkley model for concentrations showing a yield stress.

**Figure 3.**Normalized parameters ${\eta}_{0}$, ${\eta}_{\infty}$ and ${\tau}_{C}$ from the Cross fits to the flow curves of Figure 2a, compared with the structural relaxation time ${\tau}_{\alpha}$ measured trough DLS for IPN microgel with PAAc content 24.6% at T = 311$\phantom{\rule{0.166667em}{0ex}}\mathrm{K}$, above the VPT. Lines are fits with the Arrhenius-like model for ${\eta}_{\infty}$ and with the VFT model for ${\eta}_{0}$, ${\tau}_{\alpha}$ and ${\tau}_{C}$.

**Figure 4.**(

**a**) Normalized stress versus Peclet number. Lines are fits following the Herschel-Bulkley model. (

**b**) Apparent yield stress (pink stars), obtained from the Herschel-Bulkley fit to data in (

**a**), versus weight concentration for IPN with ${C}_{PAAc}=24.6\%$ at T = 311$\phantom{\rule{0.166667em}{0ex}}\mathrm{K}$. The black dashed lines represent the value ${\sigma}_{y}$R${}^{3}$/(k${}_{B}$T) = 12.5 it is considered the value that nearly marks the border between glass and jammed state as described in the text.

**Figure 5.**Yield stress for microgel with ${C}_{PAAc}=24.6\%$ at T = 311$\phantom{\rule{0.166667em}{0ex}}\mathrm{K}$ (pink stars) obtained from the Herschel-Bulkley fit to data of Figure 2b compared with data on PNIPAM microgel (black circles) by Ghosh and coworkers [25], on soft polyelectrolyte microgel suspensions (blue traingles) by Pellet and Cloitre [23] and on ultralow crosslinked PNIPAM microgel (grey squares) by Scotti and coworkers [24].

**Figure 6.**Scaled plot of normalized shear stress against reduced shear stress for IPN microgels at C${}_{PAAc}$ = 24.6%, T = 311$\phantom{\rule{0.166667em}{0ex}}\mathrm{K}$ and at different weight concentrations. All data follow two mastercurves indicating the existence of glass and jammed states. Lines are fits to data according to Equation (6).

**Figure 7.**Storage G’ (filled symbols) and Loss G” (open symbols) moduli as a function of frequency for IPN microgels with C${}_{PAAc}$ = 24.6% at concentration C${}_{w}$ = 0.4% in the liquid, C${}_{w}$ = 1.0% in the glass and C${}_{w}$ = 3.6% in the jammed state and at T = 311$\phantom{\rule{0.166667em}{0ex}}\mathrm{K}$ above the VPT.

**Figure 8.**Storage G’ (filled symbols) and Loss G” (open symbols) moduli versus strain $\gamma $ for IPN microgels at C${}_{PAAc}$ = 24.6%, T = 311$\phantom{\rule{0.166667em}{0ex}}\mathrm{K}$ and at different weight concentrations in the glass and jammed states. The arrows indicate the different breaking points.

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**MDPI and ACS Style**

Franco, S.; Buratti, E.; Nigro, V.; Zaccarelli, E.; Ruzicka, B.; Angelini, R.
Glass and Jamming Rheology in Soft Particles Made of PNIPAM and Polyacrylic Acid. *Int. J. Mol. Sci.* **2021**, *22*, 4032.
https://doi.org/10.3390/ijms22084032

**AMA Style**

Franco S, Buratti E, Nigro V, Zaccarelli E, Ruzicka B, Angelini R.
Glass and Jamming Rheology in Soft Particles Made of PNIPAM and Polyacrylic Acid. *International Journal of Molecular Sciences*. 2021; 22(8):4032.
https://doi.org/10.3390/ijms22084032

**Chicago/Turabian Style**

Franco, Silvia, Elena Buratti, Valentina Nigro, Emanuela Zaccarelli, Barbara Ruzicka, and Roberta Angelini.
2021. "Glass and Jamming Rheology in Soft Particles Made of PNIPAM and Polyacrylic Acid" *International Journal of Molecular Sciences* 22, no. 8: 4032.
https://doi.org/10.3390/ijms22084032