Scaling laws for the 2d 8-state Potts model with Fixed Boundary Conditions

We study the effects of frozen boundaries in a Monte Carlo simulation near a first order phase transition. Recent theoretical analysis of the dynamics of first order phase transitions has enabled to state the scaling laws governing the critical regime of the transition. We check these new scaling laws performing a Monte Carlo simulation of the 2d, 8-state spin Potts model. In particular, our results support a pseudo-critical beta finite-size scaling of the form beta(infinity) + a/L + b/L^2, instead of beta(infinity) + c/L^d + d/L^{2d}. Moreover, our value for the latent heat is 0.294(11), which does not coincide with the latent heat analytically derived for the same model if periodic boundary conditions are assumed, which is 0.486358...Comment: 10 pages, 3 postscript figure

Gold Glyconanoparticles for Mimics and Measurement of Metal Ion-Mediated Carbohydrate−Carbohydrate Interactions

To mimic and measure calcium ion-mediated carbohydrate-carbohydrate interactions, four lactose derivatives have been synthesized for assembly on gold nanoparticles. The series of lactose derivatives varied by the length of the thiolated ethylene glycol anchor chain [O(CH2CH2O)mCH2CH2SH; where m = 0, 1, 2, and 3] used to self-assemble the carbohydrates to the preformed gold nanoparticles of ca. 16 nm diameter. Upon addition of calcium ions to the lactose-stabilized nanoparticles, rapid carbohydrate-carbohydrate interactions were visualized and subsequently measured using UV-visible spectrometry and transmission electron microscopy (TEM). The nanoparticle aggregates formed via metal-mediated carbohydrate-carbohydrate interactions could be readily redispersed through the addition of EDTA. Multiple reaggregation and redispersion cycles were achieved, confirming that the aggregation process was due to metal ion-mediated carbohydrate interactions rather than calcium chelation by residual citrate ions on the particle surface. The essential involvement of the lactose moiety in Ca2+ complexation was shown by control measurements on related d-glucose-derivatized nanoparticles, where a significantly reduced aggregation response was obtained only at high ion concentrations. Other group 2 metal ions with radii larger than that of calcium, viz., barium and strontium, were also shown to mediate the aggregation of the lactose-stabilized nanoparticles. The induced aggregation of the lactose nanoparticles was determined to be quantitatively dependent upon the calcium ion concentration. Furthermore, the analytical sensitivity of the calcium-induced aggregation and the linear dynamic range were dependent on the length of the ethylene glycol anchor chain. The shortest ethylene glycol chain (m = 0) gave the most sensitive response with the optimum limit of detection (0.8 mM Ca2+), whereas the longest ethylene glycol chain (m = 3) provides a measurement of calcium ion concentration over the largest linear dynamic range (10-35 mM Ca2+). This work has shown that the self-assembled deposition of lactose derivatives on gold nanoparticles provides multivalent carbohydrate surfaces that can be used as mimics for the measurement of biologically relevant carbohydrate-carbohydrate interactions. Additionally, this study has highlighted the importance of the structure and length of the ligand that anchors the carbohydrate sugar to the gold particle surface to facilitate such carbohydrate interactions and for “tuning” the analytical characteristics of bioassays developed using metal nanoparticle technology