# Static Light Scattering Monitoring and Kinetic Modeling of Polyacrylamide Hydrogel Synthesis

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{6}Da) are commonly used in mining, textile, and oil industries (e.g., flocculants, as these materials have the capacity to bind charged particles) [2]. Additionally, polyacrylamide hydrogels (often synthesized with methylene bisacrylamide as crosslinker) are especially important in biomedical and pharmaceutical applications. DNA and protein electrophoresis are probably the most well-known applications of polyacrylamide hydrogels. Also, the use of these materials as controlled release vehicles is being considered in the scientific community.

## 2. Materials and Methods

#### 2.1. Reagents

#### 2.2. Static Light Scattering (SLS) Instrument

^{−1}. Through a flow-to-batch conversion kit, this MALLS instrument was used to perform in-line measurements of scattered light intensity during polyacrylamide homopolymer or hydrogel formation, as below described. The same instrument was used to measure scattered light intensity of the final polyacrylamide products prepared in different reaction conditions, namely with VA-044 initiation at T = 40 °C.

#### 2.3. Polymerization with Ammonium Persulfate/Tetramethylethylenediamine (APS/TEMED) and In-Line SLS Monitoring

#### 2.4. Polymerization with VA-044 at T = 40 °C

#### 2.5. Polymerization Conditions Used in the Experimental Runs

## 3. Theoretical Background

#### 3.1. Kinetic Modeling of Hydrogel Synthesis through Population Balances of Generating Functions

_{1}to A

_{6}, as described in Table 2. Specifically, $n$ is the count of SPR, $m$ is the count of pendant double bonds, $k$ of MCR, $x$ and $y$ of polymerized AAm and MBAm units, respectively, and $l$ of branching points due to backbiting. Considering the kinetic scheme presented in Table 3, the population balance equation for polymer molecules in the generating function domain is described by Equation (2). This equation can be numerically solved using the method of the characteristics [5,6,7,8,9,10,11,12,13,14]. If predictions of moments before gelation are only sought (as below discussed), an initial value problem would result. However, after gelation, a multidimensional boundary value problem (BVP) should be solved [5,6,7,8,9,10,11,12,13,14]. Note that prediction of chain length distributions (not tackled here) always requires a BVP solution in either situation (before or after gelation) [14].

#### 3.2. Analysis of Gels and Gel Formation Processes by SLS

#### 3.2.1. SLS with Diluted Polymer Solutions

^{−1}), with ${I}_{0}$ standing for the intensity of the incident beam, ${I}_{\theta}$ the scattered light intensity at the scattering angle $\theta $, ${V}_{S}$ the volume of the scattering medium, and $r$ the distance between the scattering volume and the detector. On the other hand, $M$ represents the molecular weight of the scatter (monodisperse polymer molecules) and $c$ the respective concentration. When writing Equation (3) in the general form above presented, it is important to note that the parameter $K$ depends on the polarization of incident light. For instance, with vertically polarized light $K=4{\pi}^{2}{n}_{0}^{2}{\left(dn/dc\right)}^{2}/\left({N}_{A}{\lambda}^{4}\right)$, whereas for unpolarized incident light $K=2{\pi}^{2}{n}_{0}^{2}{\left(dn/dc\right)}^{2}\left(1+{\mathrm{cos}}^{2}\theta \right)/\left({N}_{A}{\lambda}^{4}\right)$ (see e.g., [20,21,22]). Here, ${N}_{A}$ is Avogadro’s number, $dn/dc$ the refractive index increment with respect to $c$, ${n}_{0}$ the refractive index of the solvent, and $\lambda $ the wavelength of incident light.

#### 3.2.2. SLS with Semi-Diluted Polymer Solutions and Gels

#### 3.2.3. In-Line SLS Monitoring of Polymers and Polymer Gel Formation

## 4. Results and Discussion

^{−1}·s

^{−1}was estimated for the systems considered in this work, as discussed below. Chain transfer with thiols was here used as reference (thioglycolic acid was considered as CTA), and near to ideal chain transfer constants (${k}_{fs}={k}_{p}$) were reported for these compounds with acrylic monomers. These transfer reactions are accelerated in polar solvents, namely in water (see [47], chapter 6).

^{®}was used to solve the systems of ODEs involved in the simulations.

_{2}S

_{2}O

_{8}data as reference) in order to reproduce the experimental time evolution for monomer conversion reported in [45]. The experimentally observed induction time (around 5 min) was reproduced considering ${k}_{z}={10}^{9}$ L·mol

^{−1}·s

^{−1}and a small concentration of inhibitor/retarder $Z={10}^{-5}$ M.

^{−1}) is presented at different scattering angles ($q=4\pi {n}_{0}\mathrm{sin}\left(\theta /2\right)/\lambda $ in A

^{−1}) for the final products obtained in homopolymer and gel synthesis (the pairs H4/L2, H7/L5, and H8/L6 were here selected for illustration purposes). In Figure 10b, Figure 11b, and Figure 12b the associated excess Rayleigh ratios, ${R}_{ex,q}={R}_{gel,q}-{R}_{sol,q}$ are presented. Note that analysis of the excess scattering of gels, compared to the analogue homopolymers, is often performed using the Rayleigh ratios instead of the direct intensities (see Equation (6)). In Figure 10b, Figure 11b, and Figure 12b, the fitting of the excess Rayleigh ratios to the Debye-Bueche and Guinier models (see Equations (9) and (10)) is also shown, allowing the estimation of the characteristic length scale of the gel $\left(\mathsf{\Xi}\right)$. In Figure 13, similar data for the excess Rayleigh ratios of gels produced with APS/TEMED or VA-044 initiation are presented (see Table 1).

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Depiction of some possible frozen inhomogeneities often found in polymer gels: (

**a**) spatial inhomogeneities, (

**b**) topological inhomogeneities, and (

**c**) connectivity inhomogeneities (scheme adapted from [24] with the publisher’s permission).

**Figure 2.**Depiction of plausible spatial inhomogeneities observed with (

**a**) reversible deactivated radical polymerization (RDRP) polymerization and (

**b**) free radical polymerization (FRP) polymerization (scheme adapted from [34] with the publisher’s permission).

**Figure 4.**Predicted monomer conversion (

**a**) and average molecular weights (

**b**) for aqueous acrylamide polymerization at $T=21$ °C (the remaining simulation conditions are the same described in [45], namely ${Y}_{M}=$ 5% and ${Y}_{I}=$ 0.5%). Main kinetic parameters used in the simulations are those reported in [2,18], and the decomposition rate for APS/TEMED was estimated in order to reproduce the time evolution for monomer conversion reported in [45] (see Table 4). For comparison purposes, the measured value for ${\overline{M}}_{w}$ reported in [45] was also included in plot (

**b**).

**Figure 5.**Predicted time-evolution of monomer conversion, polymer concentration, and average molecular weights for a typical run performed in this work concerning acrylamide polymerization with APS/TEMED initiation. (

**a**) Monomer conversion, ${\overline{M}}_{n}$ and ${\overline{M}}_{w}$. (

**b**) Polymer concentration (g/L) and ${\overline{M}}_{w}$. The detailed experimental conditions correspond to product L2 in Table 1.

**Figure 6.**Predicted time-evolution of polymer concentration (g/L) and in-line measured static light scattering signal (the 90° detector is here considered) for polyacrylamide synthesis at different starting conditions. (

**a**) homopolymer L1, (

**b**) L2, (

**c**) L3, and (

**d**) L4 (see Table 1).

**Figure 7.**Predicted time-evolution of polymer concentration and average molecular weights up to gelation for a typical run performed in this work concerning AAm/MBAm polymerization with APS/TEMED initiation ($T=26\xb0\mathrm{C},{Y}_{M}=$ 9%, ${Y}_{CL}=$ 0.5%, and ${Y}_{I}=$ 0.1%). (

**a**) Polymer concentration (g/L) and ${\overline{M}}_{w}$ considering two different values for the reactivity of the pendant double bonds (${C}_{p}$). (

**b**) ${\overline{M}}_{n}$ and ${\overline{M}}_{w}$ up to gelation considering two values for ${C}_{p}$.

**Figure 8.**Predicted time-evolution of weight-average molecular weight (${\overline{M}}_{w}$) and in-line measured static light scattering signal during AAm/MBAm hydrogel formation. Predictions considering two different values for the reactivity of the pendant double bonds (${C}_{p}$) are here compared. (

**a**) hydrogel H1, (

**b**) H2, (

**c**) H3, (

**d**) H4, (

**e**) H5, and (

**f**) H6 (see Table 1).

**Figure 9.**Typical results concerning the in-line static light scattering monitoring of polyacrylamide homopolymers and hydrogel formation processes. (

**a**) Homopolymer L4. (

**b**) Hydrogel H6.

**Figure 10.**(

**a**) Experimental data relative to the SLS analysis of a polyacrylamide hydrogel and the analogous polyacrylamide homopolymer (Rayleigh ratios at different scattering angles for H4 and L2). (

**b**) Measured excess Rayleigh ratio for hydrogel H4 and data fitted using the Debye-Bueche and Guinier functions.

**Figure 11.**(

**a**) Experimental data relative to the SLS analysis of a polyacrylamide hydrogel and the analogous polyacrylamide homopolymer (Rayleigh ratios at different scattering angles for H7 and L5). (

**b**) Measured excess Rayleigh ratio for hydrogel H7 and data fitted using the Debye-Bueche and Guinier functions.

**Figure 12.**(

**a**) Experimental data relative to the SLS analysis of a polyacrylamide hydrogel and the analogous polyacrylamide homopolymer (Rayleigh ratios at different scattering angles for H8 and L6). (

**b**) Measured excess Rayleigh ratio for hydrogel H8 and data fitted using the Debye-Bueche and Guinier functions.

**Figure 13.**Measured excess Rayleigh ratio for different polyacrylamide hydrogels and the correspondent data fitting using the Debye-Bueche and Guinier functions. (

**a**) H1, (

**b**) H2, (

**c**) H6, and (

**d**) H9.

**Figure 14.**Simulation of the effect of the initiation system (VA-044 at $T=40\xb0$C or APS/TEMED at $T=26\xb0$C) on the dynamics of polymerization and gelation. (

**a**) AAm polymerization with ${Y}_{M}=$ 9% and ${Y}_{I}=$ 0.2%. (

**b**) AAm/MBAm copolymerization with ${Y}_{M}=$ 9%, ${Y}_{CL}=$ 1.0%, and ${Y}_{I}=$ 0.2%.

**Figure 15.**(

**a**,

**b**) In-line measured SLS signal for polymerization runs involving the use of a CTA and their comparison with experiments without CTA. (

**c**) Predicted time-evolution of monomer conversion and weight-average molecular weights (${\overline{M}}_{n}$ and ${\overline{M}}_{w}$) during PAAm synthesis in the presence of a chain transfer agent ($T=26\xb0$C, APS/TEMED, ${Y}_{M}=$ 9%, ${Y}_{I}=$ 0.2%, and ${Y}_{CTA/M}=$ 0.5%). (

**d**) Predicted polymer concentration and ${\overline{M}}_{w}$ corresponding to AAm/MBAm hydrogel synthesis in the presence of a chain transfer agent. Two different CTA concentrations were considered, ${Y}_{CTA/M}=$ 0.5% and ${Y}_{CTA/M}=$ 2.5%, with ${Y}_{M}=$ 9% and ${Y}_{I}=$ 0.2%.

**Table 1.**Polymerization conditions used in the preparation of polyacrylamide homopolymers and hydrogels.

Product | Monomers | Initiator | T (°C) | CTA | ${\mathit{Y}}_{\mathit{M}}$ | ${\mathit{Y}}_{\mathit{I}}$ | ${\mathit{Y}}_{\mathit{C}\mathit{L}}$ | ${\mathit{Y}}_{\mathit{C}\mathit{T}\mathit{A}/\mathit{M}}$ |
---|---|---|---|---|---|---|---|---|

L1 | AAm | APS/TEMED | 26 | - | 9 | 0.1 | - | - |

L2 | AAm | APS/TEMED | 26 | - | 9 | 0.2 | - | - |

L3 | AAm | APS/TEMED | 26 | - | 5 | 0.2 | - | - |

L4 | AAm | APS/TEMED | 26 | - | 13 | 0.1 | - | - |

H1 | AAm/MBAm | APS/TEMED | 26 | - | 9 | 0.1 | 0.5 | - |

H2 | AAm/MBAm | APS/TEMED | 26 | - | 9 | 0.1 | 1.0 | - |

H3 | AAm/MBAm | APS/TEMED | 26 | - | 9 | 0.1 | 2.0 | - |

H4 | AAm/MBAm | APS/TEMED | 26 | - | 9 | 0.2 | 1.0 | - |

H5 | AAm/MBAm | APS/TEMED | 26 | - | 13 | 0.1 | 0.1 | |

H6 | AAm/MBAm | APS/TEMED | 26 | - | 13 | 0.1 | 0.5 | - |

L5 | AAm | VA-044 | 40 | - | 9 | 0.2 | - | - |

L6 | AAm | VA-044 | 40 | - | 5 | 0.2 | - | - |

H7 | AAm/MBAm | VA-044 | 40 | - | 9 | 0.2 | 0.5 | - |

H8 | AAm/MBAm | VA-044 | 40 | - | 5 | 0.2 | 1.0 | - |

H9 | AAm/MBAm | VA-044 | 40 | - | 9 | 0.2 | 1.0 | - |

L7 | AAm | APS/TEMED | 26 | TA | 9 | 0.2 | - | 0.5 |

H10 | AAm/MBAm | APS/TEMED | 26 | TA | 9 | 0.2 | 1.0 | 0.5 |

**Table 2.**Set of chemical groups considered in the kinetic modeling of the crosslinking polymerization of acrylamide (AAm) with methylene bisacrylamide (MBAm).

Group Alias | Group Description | ${\mathit{\delta}}_{\mathit{P}}$ | ${\mathit{\delta}}_{\mathit{A}}$ |
---|---|---|---|

A_{1} | Secondary propagation polymer radical (SPR) | 1 | 1 |

A_{2} | Pendant double bond | 1 | 1 |

A_{3} | Mid-chain tertiary polymer radical (MCR) | 1 | 1 |

A_{4} | Polymerized Acrylamide unit | 1 | 0 |

A_{5} | Polymerized methylene bisacrylamide unit | 1 | 0 |

A_{6} | Branching point due to backbiting | 1 | 0 |

A_{7} | Acrylamide monomer | 0 | 1 |

A_{8} | Methylene bisacrylamide monomer | 0 | 1 |

A_{9} | Primary radical | 0 | 1 |

A_{10} | Initiator | 0 | 1 |

A_{11} | Chain transfer agent | 0 | 1 |

A_{12} | Inhibitor/retarder | 0 | 1 |

**Table 3.**Set of chemical reactions considered in kinetic modeling of the crosslinking polymerization of acrylamide (AAm) with methylene bisacrylamide (MBAm).

Chemical Reaction | Chemical Equation |
---|---|

Initiator decomposition | $I\stackrel{{k}_{d}}{\to}2f{R}_{0}$ |

Acrylamide initiation | ${R}_{0}+{M}_{1}\stackrel{{k}_{i1}}{\to}{P}_{1,0,0}^{1,0,0}$ |

Methylene bisacrylamide initiation | ${R}_{0}+{M}_{2}\stackrel{{k}_{i2}}{\to}{P}_{1,1,0}^{0,1,0}$ |

Pendant double bond initiation | ${R}_{0}+{P}_{n,m,k}^{x,y,l}\stackrel{{k}_{i3}}{\to}{P}_{n+1,m-1,k}^{x,y,l}$ |

Acrylamide propagation with SPR | ${P}_{n,m,k}^{x,y,l}+{M}_{1}\stackrel{{k}_{p1}}{\to}{P}_{n,m,k}^{x+1,y,l}$ |

Methylene bisacrylamide propagation with SPR | ${P}_{n,m,k}^{x,y,l}+{M}_{2}\stackrel{{k}_{p2}}{\to}{P}_{n,m+1,k}^{x,y+1,l}$ |

Pendant double bond propagation with SPR | ${P}_{n,m,k}^{x,y,l}+{P}_{{n}^{\prime},{m}^{\prime},{k}^{\prime}}^{{x}^{\prime},{y}^{\prime},{l}^{\prime}}\stackrel{{k}_{p3}}{\to}{P}_{n+{n}^{\prime},m+{m}^{\prime}-1,k+{k}^{\prime}}^{x+{x}^{\prime},y+{y}^{\prime},l+{l}^{\prime}}$ |

Backbiting | ${P}_{n,m,k}^{x,y,l}\stackrel{{k}_{bb}}{\to}{P}_{n-1,m,k+1}^{x,y,l+1}$ |

Acrylamide propagation with MCR | ${P}_{n,m,k}^{x,y,l}+{M}_{1}\stackrel{{k}_{pT1}}{\to}{P}_{n+1,m,k-1}^{x+1,y,l}$ |

Methylene bisacrylamide propagation with MCR | ${P}_{n,m,k}^{x,y,l}+{M}_{2}\stackrel{{k}_{pT2}}{\to}{P}_{n+1,m+1,k-1}^{x,y+1,l}$ |

Pendant double bond propagation with MCR | ${P}_{n,m,k}^{x,y,l}+{P}_{{n}^{\prime},{m}^{\prime},{k}^{\prime}}^{{x}^{\prime},{y}^{\prime},{l}^{\prime}}\stackrel{{k}_{pT3}}{\to}{P}_{n+{n}^{\prime}+1,m+{m}^{\prime}-1,k+{k}^{\prime}-1}^{x+{x}^{\prime},y+{y}^{\prime},l+{l}^{\prime}}$ |

Transfer to monomer | ${P}_{n,m,k}^{x,y,l}+{M}_{1}\stackrel{{k}_{fm}}{\to}{P}_{n-1,m,k}^{x,y,l}+{P}_{1,0,0}^{1,0,0}$ |

Transfer to chain transfer agent | ${P}_{n,m,k}^{x,y,l}+S\stackrel{{k}_{fs}}{\to}{P}_{n-1,m,k}^{x,y,l}+{R}_{0}$ |

Inhibition of primary radicals | ${R}_{0}+Z\stackrel{{k}_{z}}{\to}Deadproducts$ |

Inhibition of SPR radicals | ${P}_{n,m,k}^{x,y,l}+Z\stackrel{{k}_{z}}{\to}{P}_{n-1,m,k}^{x,y,l}$ |

Inhibition of MRC radicals | ${P}_{n,m,k}^{x,y,l}+Z\stackrel{{k}_{z}}{\to}{P}_{n,m,k-1}^{x,y,l}$ |

Termination by combination SPR/SPR | ${P}_{n,m,k}^{x,y,l}+{P}_{{n}^{\prime},{m}^{\prime},{k}^{\prime}}^{{x}^{\prime},{y}^{\prime},{l}^{\prime}}\stackrel{{k}_{tcss}}{\to}{P}_{n+{n}^{\prime}-2,m+{m}^{\prime},k+{k}^{\prime}}^{x+{x}^{\prime},y+{y}^{\prime},l+{l}^{\prime}}$ |

Termination by disproportionation SPR/SPR | ${P}_{n,m,k}^{x,y,l}+{P}_{{n}^{\prime},{m}^{\prime},{k}^{\prime}}^{{x}^{\prime},{y}^{\prime},{l}^{\prime}}\stackrel{{k}_{tdss}}{\to}{P}_{n-1,m,k}^{x,y,l}+{P}_{{n}^{\prime}-1,{m}^{\prime},{k}^{\prime}}^{{x}^{\prime},{y}^{\prime},{l}^{\prime}}$ |

Termination by combination SPR/MCR | ${P}_{n,m,k}^{x,y,l}+{P}_{{n}^{\prime},{m}^{\prime},{k}^{\prime}}^{{x}^{\prime},{y}^{\prime},{l}^{\prime}}\stackrel{{k}_{tcst}}{\to}{P}_{n+{n}^{\prime}-1,m+{m}^{\prime},k+{k}^{\prime}-1}^{x+{x}^{\prime},y+{y}^{\prime},l+{l}^{\prime}}$ |

Termination by disproportionation of SPR/MCR | ${P}_{n,m,k}^{x,y,l}+{P}_{{n}^{\prime},{m}^{\prime},{k}^{\prime}}^{{x}^{\prime},{y}^{\prime},{l}^{\prime}}\stackrel{{k}_{tdst}}{\to}{P}_{n-1,m,k}^{x,y,l}+{P}_{{n}^{\prime},{m}^{\prime},{k}^{\prime}-1}^{{x}^{\prime},{y}^{\prime},{l}^{\prime}}$ |

Termination by combination MCR/MCR | ${P}_{n,m,k}^{x,y,l}+{P}_{{n}^{\prime},{m}^{\prime},{k}^{\prime}}^{{x}^{\prime},{y}^{\prime},{l}^{\prime}}\stackrel{{k}_{tctt}}{\to}{P}_{n+{n}^{\prime},m+{m}^{\prime},k+{k}^{\prime}-2}^{x+{x}^{\prime},y+{y}^{\prime},l+{l}^{\prime}}$ |

Termination by disproportionation of MCR/MCR | ${P}_{n,m,k}^{x,y,l}+{P}_{{n}^{\prime},{m}^{\prime},{k}^{\prime}}^{{x}^{\prime},{y}^{\prime},{l}^{\prime}}\stackrel{{k}_{tdtt}}{\to}{P}_{n,m,k-1}^{x,y,l}+{P}_{{n}^{\prime},{m}^{\prime},{k}^{\prime}-1}^{{x}^{\prime},{y}^{\prime},{l}^{\prime}}$ |

**Table 4.**Reference set of rate parameters considered in the kinetic modeling of the crosslinking polymerization of acrylamide (AAm) with methylene bisacrylamide (MBAm).

Kinetic Step | Rate Parameters | Reference |
---|---|---|

Initiator decomposition | With VA0-44 | [46] |

${k}_{d}=1.29\times {10}^{13}\mathrm{exp}\left(-\frac{108.2\times {10}^{3}}{RT}\right)$ | ||

$f=0.7$ | ||

With K_{2}S_{2}O_{8} in 0.1 M NaOH solution | [47] | |

${k}_{d}=709\times {10}^{15}\mathrm{exp}\left(-\frac{148\times {10}^{3}}{RT}\right)$ | ||

$f=0.5$ | ||

A multiplication factor of 2000 on the ${k}_{d}$ value for K_{2}S_{2}O_{8} was estimated in this work with APS/TEMED | This work | |

Chain propagation | ${k}_{p}={k}_{pmax}\mathrm{exp}\left(-{W}_{M}\left(1.015+0.0016T\right)\right)$ | [2,18] |

${k}_{pmax}=9.5\times {10}^{7}\mathrm{exp}\left(-\frac{2189}{T}\right)$ | ||

Transfer to monomer | ${C}_{trm}={k}_{fm}/{k}_{p}=0.00118\mathrm{exp}\left(-\frac{1002}{T}\right)$ | [2,18] |

Termination SPR-SPR | ${k}_{tss}=2\times {10}^{10}\mathrm{exp}\left(-\frac{1991+1477{W}_{M0}}{T}\right)$ | [2,18] |

${\alpha}_{ss}={k}_{tdss}/{k}_{tss}=0.1$ | ||

Backbiting | ${k}_{bb}=3.7\times {10}^{9}\mathrm{exp}\left(-\frac{5874}{T}\right)$ | [2,18] |

Addition to MCR | ${k}_{pT}=0.0155\mathrm{exp}\left(-\frac{1412}{T}\right)$ | [2,18] |

Cross termination SPR-MCR | ${k}_{tst}=0.27{k}_{tss}$${\alpha}_{st}={k}_{tdst}/{k}_{tst}=0.7$ | [2,18] |

Termination MCR-MCR | ${k}_{ttt}=0.01{k}_{tss}$${\alpha}_{tt}={k}_{tdtt}/{k}_{ttt}=0.9$ | [2,18] |

Inhibition | ${k}_{z}={10}^{9}$ | This work |

Chain transfer to agent | ${k}_{fs}={k}_{p}$ | This work |

^{−1}for the unimolecular steps and in L·mol

^{−1}·s

^{−1}for the bimolecular steps. Temperature ($T)$ expressed in K in the rate parameter expressions and the ideal gas constant was $R$ = 8.314 J/(mol·K).

**Table 5.**Correlation length ($\mathsf{\Xi}$ in nm) for different kinds of products estimated through static light scattering measurements and using different models for data analysis, namely the Debye-Bueche (DB) and the Guinier (GU) functions.

Product | H1 | H2 | H3 | H4 | H5 | H6 | H7 | H8 | H9 | |
---|---|---|---|---|---|---|---|---|---|---|

$\mathsf{\Xi}\left(\mathrm{nm}\right)$ | DB | 24 | 27 | - | 20 | - | 36 | 64 | 48 | 24 |

GU | 31 | 35 | - | 27 | - | 42 | 65 | 54 | 31 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Gomes, C.; Dias, R.C.S.; Costa, M.R.P.F.N.
Static Light Scattering Monitoring and Kinetic Modeling of Polyacrylamide Hydrogel Synthesis. *Processes* **2019**, *7*, 237.
https://doi.org/10.3390/pr7040237

**AMA Style**

Gomes C, Dias RCS, Costa MRPFN.
Static Light Scattering Monitoring and Kinetic Modeling of Polyacrylamide Hydrogel Synthesis. *Processes*. 2019; 7(4):237.
https://doi.org/10.3390/pr7040237

**Chicago/Turabian Style**

Gomes, Catarina, Rolando C.S. Dias, and Mário Rui P.F.N. Costa.
2019. "Static Light Scattering Monitoring and Kinetic Modeling of Polyacrylamide Hydrogel Synthesis" *Processes* 7, no. 4: 237.
https://doi.org/10.3390/pr7040237