Radical-initiated homo- and copolymerization of cyanomethyl methacrylate

The kinetics of cyanomethyl methacrylate (CyMA) homopolymerization was investigated in acetonitrile with azobisisobutyronitrile as initiator. The rate of polymerization R_p was expressed by R_p = k[AIBN]^0.49[CyMA]^1.2 and the overall activation energy was calculated as 72.3 kJ/mol. Kinetic constants for CyMA polymerization were obtained as follows: k_p/k = 0.10 L^1/2s^?1/2; 2fk_d = 1.57 × 10^?5s^?. The relative reactivity ratios of CyMA(M₂) copolymerization with styrene (r₁ = 0.15, r₂ = 0.29) and methyl methacrylate (r₁ = 0.43, r₂ = 0.75) in acetonitrile were obtained. Applying the Q-e scheme (in styrene copolymerization) led to Q = 1.64 and e = 0.98. The glass transition temperature T_g of poly(CyMA) was observed to be 91°C by thermomechanical analysis. Thermogravimetry of poly(CyMA) showed a 10% weight loss at 265°C in air.     

Composition Operators on the Lipschitz Space of a Tree

The Lipschitz space ${\mathcal{L}}$ of an infinite tree T rooted at o is defined as the space consisting of the functions ${f : T \rightarrow \mathbb{C}}$ such that $$\beta_f = {\rm sup}\{|f(v) - f(v^-)| : v \in T\backslash\{o\}, \,v^- {\rm parent \, of \,} v\}$$ is finite. Under the norm ${\|f\|_\mathcal{L} = |f(o)|+\beta_f,\mathcal{L}}$ is a Banach space. In this article, the functions φ mapping T into itself whose induced composition operator ${C_{\varphi} : f \mapsto f \circ \varphi}$ on the Lipschitz space is bounded, compact, or an isometry, are characterized. Specifically, it is shown that the symbols of the bounded composition operators are the Lipschitz maps of T into itself viewed as a metric space under the edge-counting distance. The symbols inducing compact operators have finite range while those inducing isometries on ${\mathcal{L}}$ are precisely the onto maps fixing the root and whose images of neighboring vertices coincide or are themselves neighboring vertices. Finally, the spectrum of the operators ${C_\varphi}$ that are isometries is studied in detail.     

Measurement of microchannel fluidic resistance with a standard voltage meter

A simplified method for measuring the fluidic resistance (R_fluidic) of microfluidic channels is presented, in which the electrical resistance (R_elec) of a channel filled with a conductivity standard solution can be measured and directly correlated to R_fluidic using a simple equation. Although a slight correction factor could be applied in this system to improve accuracy, results showed that a standard voltage meter could be used without calibration to determine R_fluidic to within 12% error. Results accurate to within 2% were obtained when a geometric correction factor was applied using these particular channels. When compared to standard flow rate measurements, such as meniscus tracking in outlet tubing, this approach provided a more straightforward alternative and resulted in lower measurement error. The method was validated using 9 different fluidic resistance values (from ∼40 to 600 kPa s mm⁻³) and over 30 separately fabricated microfluidic devices. Furthermore, since the method is analogous to resistance measurements with a voltage meter in electrical circuits, dynamic R_fluidic measurements were possible in more complex microfluidic designs. Microchannel R_elec was shown to dynamically mimic pressure waveforms applied to a membrane in a variable microfluidic resistor. The variable resistor was then used to dynamically control aqueous-in-oil droplet sizes and spacing, providing a unique and convenient control system for droplet-generating devices. This conductivity-based method for fluidic resistance measurement is thus a useful tool for static or real-time characterization of microfluidic systems.     

Solvent effects on radical homo- and copolymerizations of methacryloyl fluroride

The effect of solvent in homo- and copolymerizations of methacryloyl fluoride (MAF) was investigated in various aromatic solvents. In these solvents, there is a significant effect on the rate of polymerization, on the tacticity of the resulting poly(methacryloyl fluoride), and on the copolymerization of MAF with methyl methacrylate (MMA). The equilibrium constants between MAF and aromatic solvents were determined from NMR spectroscopic measurements. These results indicated that the solvent effect on the MAF polymerization stems from changes in reactivity of MAF induced by the strong MAF–solvent interaction as well as stabilization of the MAF radical by solvents. Copolymerization of MAF with both p-methoxystyrene (MSt) and p-nitrostyrene (NSt) was also studied.     

Multiplication Operators on the Lipschitz Space of a Tree

In this paper, we study the multiplication operators on the space of complex-valued functions f on the set of vertices of a rooted infinite tree T which are Lipschitz when regarded as maps between metric spaces. The metric structure on T is induced by the distance function that counts the number of edges of the unique path connecting pairs of vertices, while the metric on ℂ is Euclidean. After observing that the space L{\mathcal{L}} of such functions can be endowed with a Banach space structure, we characterize the multiplication operators on L{\mathcal{L}} that are bounded, bounded below, and compact. In addition, we establish estimates on the operator norm and on the essential norm, and determine the spectrum. We then prove that the only isometric multiplication operators on L{\mathcal{L}} are the operators whose symbol is a constant of modulus one. We also study the multiplication operators on a separable subspace of L{\mathcal{L}} we call the little Lipschitz space.     

Glass microfluidic devices with thin membrane voltage junctions for electrospray mass spectrometry

In this study a novel glass membrane was prepared for conducting high voltage (HV) to solution in the channel of a microfabricated device for generation of liquid electrospray. Taylor cone formation and mass spectra obtained from this microdevice confirmed the utility of the glass membrane, but voltage conduction through the membrane could not be successfully explained based solely on the conductivity of the glass itself. This novel method for developing a high-voltage interface for microdevices avoids direct metal/liquid contact eliminating bubble formation in the channel due to water hydrolysis on the surface of the metal. Further, this arrangement produces no dead volume as is often found with traditional liquid junctions. At the same time, preliminary investigations into the outlet design of glass microdevices for interfacing with electrospray mass spectrometry, was explored. Both the exit shape and the use of hydrophobic coatings at the channel exit of the microdevice electrospray interface were evaluated using standard proteins with results indicating the utility of this type of design after further optimization.