%0 Book Section %1 statphys23_0673 %A Das, Subir K. %A Kim, Young C. %A Fisher, E. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K charge-charge criticality electrolytes grandcanonical model montecarlo primitive restricted rules simulation statphys23 sum topic-2 %T Near-Critical Electrolytes: Are the charge-charge sum rules obeyed? %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=673 %X ~~~~~In an electrolyte solution the charge-charge structure factor obeys $S_ZZ(k;T,\rho)$ $=0+\xi_Z,1^2k^2-\xi_Z,2^4k^4+...$ , where $\xi_Z,1$ and $\xi_Z,2$ are the second- and fourth-moment charge-charge correlation lengths depending on $T$ and the overall ion density $\rho$. The vanishing of the leading term, the first Stillinger-Lovett (SL) sum rule 1, simply reflects bulk electroneutrality. The second SL rule 1, or second-moment condition, dictates that $\xi_Z,1=\xi_D$, where the Debye screening length $\xi_D$ is proportional to $k_BT/q_0^2\rho$~, $q_0$ being the elementary charge. ~~~~~Our grandcanonical Monte Carlo simulations of a fully size and charge symmetric 1:1 (finely-discretized) hard-sphere electrolyte, or restricted primitive model 2, impose electroneutrality, so satisfying the first sum rule automatically. However, careful finite-size scaling analysis of extensive histogram reweighted data indicates that the second-moment condition is violated at criticality by approximately 10\%, $\xi_Z,1^c$ exceeding $\xi_D^c$. It is also found that $\xi_Z,2^4$ diverges to $+ınfty$ as $TT_c$, closely mirroring $S_NN(0)$, the density-density fluctuations. These findings contradict Generalized Debye-H$\mboxu$ckel theory 3 and the exactly soluble charge-symmetric spherical models 4, both of which support the second-moment condition at criticality and the finiteness of the fourth-moment. Nevertheless, the observed behavior is strikingly similar to that of the charge-asymmetric spherical models 4.\\ 1) F.H. Stillinger and R. Lovett, J. Chem. Phys. 48, 3858 (1968).\\ 2) Y.C. Kim and M.E. Fisher, Phys. Rev. Lett. 92, 185703 (2004).\\ 3) B.P. Lee and M.E. Fisher, Europhys. Lett. 39, 611 (1997).\\ 4) J.-N. Aqua and M.E. Fisher, Phys. Rev. Lett. 92, 135702 (2004).

@incollection{statphys23_0673, abstract = {~~~~~In an electrolyte solution the charge-charge structure factor obeys $S_{ZZ}(k;T,\rho)$ $=0+\xi_{Z,1}^2k^2-\xi_{Z,2}^4k^4+...$ , where $\xi_{Z,1}$ and $\xi_{Z,2}$ are the second- and fourth-moment charge-charge correlation lengths depending on $T$ and the overall ion density $\rho$. The vanishing of the leading term, the first Stillinger-Lovett (SL) sum rule [1], simply reflects bulk electroneutrality. The second SL rule [1], or {\it second-moment condition}, dictates that $\xi_{Z,1}=\xi_D$, where the Debye screening length $\xi_D$ is proportional to $\sqrt{k_BT/q_0^2\rho}$~, $q_0$ being the elementary charge. ~~~~~Our grandcanonical Monte Carlo simulations of a fully {\it size} and {\it charge} {\it symmetric} 1:1 (finely-discretized) hard-sphere electrolyte, or {\it restricted primitive model} [2], impose electroneutrality, so satisfying the first sum rule automatically. However, careful finite-size scaling analysis of extensive histogram reweighted data indicates that the second-moment condition is violated {\it at} criticality by approximately 10\%, $\xi_{Z,1}^c$ exceeding $\xi_D^c$. It is also found that $\xi_{Z,2}^4$ diverges to $+\infty$ as $T\rightarrow T_c$, closely mirroring $S_{NN}(0)$, the density-density fluctuations. These findings contradict Generalized Debye-H$\ddot{\mbox{u}}$ckel theory [3] and the exactly soluble charge-{\it symmetric} spherical models [4], both of which support the second-moment condition {\it at} criticality and the finiteness of the fourth-moment. Nevertheless, the observed behavior is strikingly similar to that of the charge-{\it asymmetric} spherical models [4].\\ 1) F.H. Stillinger and R. Lovett, J. Chem. Phys. \textbf{48}, 3858 (1968).\\ 2) Y.C. Kim and M.E. Fisher, Phys. Rev. Lett. \textbf{92}, 185703 (2004).\\ 3) B.P. Lee and M.E. Fisher, Europhys. Lett. \textbf{39}, 611 (1997).\\ 4) J.-N. Aqua and M.E. Fisher, Phys. Rev. Lett. \textbf{92}, 135702 (2004).}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Das, Subir K. and Kim, Young C. and Fisher, E.}, biburl = {https://www.bibsonomy.org/bibtex/28e2db50b689ef389371670c84f5a3897/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {1f04102f0ee34b0d54484bd1e1c3f56b}, intrahash = {8e2db50b689ef389371670c84f5a3897}, keywords = {charge-charge criticality electrolytes grandcanonical model montecarlo primitive restricted rules simulation statphys23 sum topic-2}, month = {9-13 July}, timestamp = {2007-06-20T10:16:26.000+0200}, title = {Near-Critical Electrolytes: Are the charge-charge sum rules obeyed?}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=673}, year = 2007 }