%0 Journal Article %1 Schiessel1995Mesoscopic %A Schiessel, H. %A Blumen, A. %D 1995 %J Macromolecules %K 26a33-fractional-derivatives-and-integrals 28a80-fractals 74a20-theory-of-constitutive-functions 76a10-viscoelastic-fluids 94c05-analytic-circuit-theory %N 11 %P 4013--4019 %R 10.1021/ma00115a038 %T Mesoscopic Pictures of the Sol–Gel Transition: Ladder Models and Fractal Networks %U http://dx.doi.org/10.1021/ma00115a038 %V 28 %X In this work we introduce mechanical networks which highlight the relation between viscoelastic and structural properties of chemical systems at the sol-gel transition. Cross-linking polymers at the gel point show in general a power law behavior of the complex modulus, i.e., \$G*(ømega) (iømega)^(0 < < 1)\$, which is related to the (constitutive) gel equation. We present a mechanical ladder model whose stress-strain relation obeys the gel equation with α = ½ and which consists of an infinite number of springs and dashpots. Furthermore, we investigate terminated ladder arrangements which mimic pre- and postgel behavior. To elucidate the complex dependence of a on structural properties which one observes for systems near to the gel point, we analyze mechanical fractal networks.

@article{Schiessel1995Mesoscopic, abstract = {{In this work we introduce mechanical networks which highlight the relation between viscoelastic and structural properties of chemical systems at the sol-gel transition. Cross-linking polymers at the gel point show in general a power law behavior of the complex modulus, i.e., \$G*(\omega) (i\omega)^\alpha (0 < \alpha < 1)\$, which is related to the (constitutive) gel equation. We present a mechanical ladder model whose stress-strain relation obeys the gel equation with α = ½ and which consists of an infinite number of springs and dashpots. Furthermore, we investigate terminated ladder arrangements which mimic pre- and postgel behavior. To elucidate the complex dependence of a on structural properties which one observes for systems near to the gel point, we analyze mechanical fractal networks.}}, added-at = {2019-03-01T00:11:50.000+0100}, author = {Schiessel, H. and Blumen, A.}, biburl = {https://www.bibsonomy.org/bibtex/275b13cb16bb741a90d6b0501fbc61322/gdmcbain}, citeulike-article-id = {14560881}, citeulike-attachment-1 = {schiessel_96_mesoscopic.pdf; /pdf/user/gdmcbain/article/14560881/1133313/schiessel_96_mesoscopic.pdf; 4c099a55afa33de2c9e2000289431e1c22bb9b19}, citeulike-linkout-0 = {http://dx.doi.org/10.1021/ma00115a038}, citeulike-linkout-1 = {http://pubs.acs.org/doi/abs/10.1021/ma00115a038}, doi = {10.1021/ma00115a038}, file = {schiessel_96_mesoscopic.pdf}, interhash = {674684c0658e4784b807daec9bfc7d03}, intrahash = {75b13cb16bb741a90d6b0501fbc61322}, issn = {0024-9297}, journal = {Macromolecules}, keywords = {26a33-fractional-derivatives-and-integrals 28a80-fractals 74a20-theory-of-constitutive-functions 76a10-viscoelastic-fluids 94c05-analytic-circuit-theory}, month = may, number = 11, pages = {4013--4019}, posted-at = {2018-04-04 01:24:38}, priority = {4}, timestamp = {2019-03-01T00:11:50.000+0100}, title = {{Mesoscopic Pictures of the Sol–Gel Transition: Ladder Models and Fractal Networks}}, url = {http://dx.doi.org/10.1021/ma00115a038}, volume = 28, year = 1995 }