Rheological properties of poly(vinyl chloride)/plasticizer systems—relation between sol–gel transition and elongational viscosity

Poly(vinyl chloride) (PVC)/di-isononyl phthalate systems with PVC content of 45.5 (PVC8) and 70.4 wt% (PVC6) were prepared by a hot roller at 150 °C and press molded at 180 °C. The dynamic viscoelasticity and elongational viscosity of PVC8 and PVC6 were measured in the temperature range from 150 to 220 °C. We have found that the storage and loss shear moduli, G′ and G″, of PVC8 and PVC6 exhibited the power-law dependence on the angular frequency ω at 190 and 210 °C, respectively. Correspondingly, the tan δ values did not depend on ω. These temperatures indicate the critical gel temperature T _gel of each system. The critical relaxation exponent n obtained from these data was 0.75 irrespective of PVC content, which was in agreement with the n values reported previously for the low PVC concentration samples. These results suggest that the PVC gels of different plasticizer content have a similar fractal structure. Below T _gel, the gradual melting of the PVC crystallites takes place with elevating temperature, and above T _gel, a densely connected network throughout the whole system disappears. Correspondingly, the elongational viscosity behavior of PVC8 and PVC6 exhibited strong strain hardening below T _gel, although it did not show any strain hardening above T _gel. These changes in rheological behavior are attributed to the gradual melting of the PVC crystallites worked as the cross-linking domains in this physical gel, thereby inapplicability of the of time–temperature superposition for PVC/plasticizer systems.     

Boson fock representations of stochastic processes

A classification theory of quantum stationary processes similar to the corresponding theory for classical stationary processes is presented. Our main result is the classification of those pairs of classical stationary processes that admit a joint boson Fock canonical representation. Translated fromMatematicheskie Zametki, Vol. 67, No. 1, pp. 3–14, January, 2000.     

Synthesis and characterization of 6‐ and 12‐arm star polymers by nitroxide‐mediated radical polymerization of St and MA from dendritic TIPNO‐based hexafunctional and dodecafunctional macroinitiators

Dendritic multifunctional macroinitiators having six and 12 TIPNO‐based alkoxyamines, TIPNO‐6 and TIPNO‐12 , were synthesized and used in the living radical polymerization of styrene (St), methyl acrylate (MA), N,N‐dimethylacrylamide (DMAAm), and isoprene (IP). The polymerizations of St initiated with TIPNO‐6 gave 6‐arm star polymers with narrow polydispersities of 1.14–1.18. In the polymerizations of MA initiated with TIPNO‐6 and TIPNO‐12 , the influences of added TIPNO on the polydispersity indexes (PDIs) of the resulting star polymers were first investigated, and this led to the successful formation of poly(MA) star polymers with narrow polydispersities (1.10–1.18). Moreover, the polymerizations of DMAAm and IP from TIPNO‐6 in the presence or absence of TIPNO were briefly investigated. The benzyl ether bonds of the poly(St) and poly(MA) star polymers were cleaved by treating with Me₃SiI or Pd/C, and the resulting arm's parts were analyzed with SEC. The PDIs of the resulting arm parts were low (1.19–1.23), and the M_ns agreed with the M_n,theor, indicating that the poly(St) and poly(MA) star polymers had well‐controlled arms. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4364–4376, 2007     

Syntheses and characterization of 16‐arm star and star diblock copolymer and AB8 9‐miktoarm star copolymer via NMRP and ROP from dendritic multifunctional macroinitiators

A dendritic macroinitiator having 16 TEMPO‐based alkoxyamines, Star‐16 , was prepared by the reaction of a dendritic macroinitiator having eight TEMPO‐based alkoxyamines, [G‐3]‐OH , with 4,4′‐bis(chlorocarbonyl)biphenyl. The nitroxide‐mediated radical polymerization (NMRP) of styrene (St) from Star‐16 gave 16‐arm star polymers with PDI of 1.19–1.47, and NMPR of 4‐vinylpyridine from the 16‐arm star polymer gave 16‐arm star diblock copolymers with PDI of 1.30–1.43. The ring‐opening polymerization of ε‐caprolactone from [G‐3]‐OH and the subsequent NMRP of St gave AB₈ 9‐miktoarm star copolymers with PDI of 1.30–1.38. The benzyl ether linkages of the 16‐arm star polymers and the AB₈ 9‐miktoarm star copolymers were cleaved by treating with Me₃SiI, and the resultant poly(St) arms were investigated by size exclusion chromatography (SEC). The SEC results showed PDIs of 1.23–1.28 and 1.18–1.22 for the star polymers and miktoarm stars copolymers, respectively, showing that they have well‐controlled poly(St) arms. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1159–1169, 2007.     

Fast and Accurate Floating Point Summation with Application to Computational Geometry

We present several simple algorithms for accurately computing the sum of n floating point numbers using a wider accumulator. Let f and F be the number of significant bits in the summands and the accumulator, respectively. Then assuming gradual underflow, no overflow, and round-to-nearest arithmetic, up to ?2 ^F?f /(1?2^?f )?+1 numbers can be accurately added by just summing the terms in decreasing order of exponents, yielding a sum correct to within about 1.5 units in the last place. In particular, if the sum is zero, it is computed exactly. We apply this result to the floating point formats in the IEEE floating point standard, and investigate its performance. Our results show that in the absence of massive cancellation (the most common case) the cost of guaranteed accuracy is about 30–40% more than the straightforward summation. If massive cancellation does occur, the cost of computing the accurate sum is about a factor of ten. Finally, we apply our algorithm in computing a robust geometric predicate (used in computational geometry), where our accurate summation algorithm improves the existing algorithm by a factor of two on a nearly coplanar set of points.