A cross-linking copolymerization model based on species and sequences balance was developed and applied to styrene-based resins with 1–25% divinylbenzene (DVB). The swelling indices of these resins were estimated using a modified Flory–Rehner equation. The chain density was calculated as a function of the radius of gyration of sequences between cross-links, employing the Flory exponent as an adjustable parameter. The mathematical model was successfully validated against morphology data, yielding an average R2 of 0.936. The model provided the fraction of linear chains and the distribution of sequences between cross-links. This distribution facilitated the calculation of swelling index distribution along the resin, following a logarithmic function of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">${M}_{C}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>M</mi> <mi>C</mi> </msub> </math></EquationSource> </InlineEquation> with an R2 of approximately 0.920. The results suggest that the radius of gyration equation <InlineEquation ID="IEq2"> <EquationSource Format="TEX">${R}_{\text{g}}=0.03{{M}_{c}}_{r}^{\alpha }$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>R</mi> <mtext>g</mtext> </msub> <mo>=</mo> <mn>0.03</mn> <msubsup> <mrow> <msub> <mi>M</mi> <mi>c</mi> </msub> </mrow> <mrow> <mi>r</mi> </mrow> <mi>α</mi> </msubsup> </mrow> </math></EquationSource> </InlineEquation> is applicable for chain segments between cross-links (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">${{L}_{E}}_{r}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mrow> <msub> <mi>L</mi> <mi>E</mi> </msub> </mrow> <mi>r</mi> </msub> </math></EquationSource> </InlineEquation>) in sulfonated styrene–DVB resins. For lightly cross-linked sulfonated resins (1.5–2.5% DVB), water could be considered a theta solvent based on the coiling factors identified (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\alpha \approx 0.5$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>≈</mo> <mn>0.5</mn> </mrow> </math></EquationSource> </InlineEquation>). At higher DVB percentages, the coiling behavior resembled that of polystyrene in apolar media (<InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\alpha \approx 0.6$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>≈</mo> <mn>0.6</mn> </mrow> </math></EquationSource> </InlineEquation>), aligning with literature reports.

Kinetic modeling of the synthesis of styrene–DVB resins for estimating chain density distribution

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2025年9月19日

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Leandro G. Aguiar,
Maria L. T. Reis,
William M. Godoy

摘要

A cross-linking copolymerization model based on species and sequences balance was developed and applied to styrene-based resins with 1–25% divinylbenzene (DVB). The swelling indices of these resins were estimated using a modified Flory–Rehner equation. The chain density was calculated as a function of the radius of gyration of sequences between cross-links, employing the Flory exponent as an adjustable parameter. The mathematical model was successfully validated against morphology data, yielding an average R² of 0.936. The model provided the fraction of linear chains and the distribution of sequences between cross-links. This distribution facilitated the calculation of swelling index distribution along the resin, following a logarithmic function of ${M}_{C}$ $M_{C}$ with an R² of approximately 0.920. The results suggest that the radius of gyration equation ${R}_{\text{g}}=0.03{{M}_{c}}_{r}^{\alpha }$ $R_{g} = 0.03 {M_{c}}_{r}^{α}$ is applicable for chain segments between cross-links ( ${{L}_{E}}_{r}$ ${L_{E}}_{r}$ ) in sulfonated styrene–DVB resins. For lightly cross-linked sulfonated resins (1.5–2.5% DVB), water could be considered a theta solvent based on the coiling factors identified ( $\alpha \approx 0.5$ $α \approx 0.5$ ). At higher DVB percentages, the coiling behavior resembled that of polystyrene in apolar media ( $\alpha \approx 0.6$ $α \approx 0.6$ ), aligning with literature reports.