Understanding the Grafting of Telechelic Polymers on a Solid Substrate to Form Loops

Recent experimental and theoretical studies have demonstrated that relative to singly tethered chains, the presence of polymer loops at interfaces significantly improves interfacial properties such as adhesion, friction, and wettability. In the present study, a simple system was studied to examine the formation of polymeric loops on a solid surface, where the grafting of carboxylic acid terminated telechelic polystyrene from the melt to an epoxy functionalized silicon is chosen. The impact of telechelic molecular weight, grafting temperature, and surface functionality on the telechelic attachment process is studied. It was found that grafting of the telechelic to the surface at both ends to form loops is the primary product of this grafting process. Moreover, examination of the kinetics of the grafting process indicates that it is reaction controlled. Fluorescence tagging of the dangling ends of singly bound chains provides a mechanism to monitor their time evolution during grafting, and these results indicate that the grafting process is accurately described by recent Monte Carlo simulation work. The results also provide a method to control the extent of loop formation at interfaces and therefore provide an opportunity to further understand the role of the loops in the interfacial properties in multicomponent polymer systems.

Writing in a Mathematics Classroom: A Form of Communication and Reflection

In this action research study, I investigated the use of journaling in my seventh grade mathematics classroom. I discovered that journaling can be a very rewarding and beneficial experience for me and for my students. Through journaling, my students became more adept at using correct mathematical terminology in writing and in speaking. The students also believed that they learned the content more deeply and retained it better. Additionally, implementing mathematical journals caused me to emphasize the use of correct terminology and thorough explanations of mathematical thinking in classroom discussions. As a result of this research, I plan to refine my journaling process and continue to use mathematical journals with my future classes.

Evaluating Measurement Invariance with Censored Ordinal Data: A Monte Carlo Comparison of Alternative Model Estimators and Scales of Measurement

Evaluations of measurement invariance provide essential construct validity evidence. However, the quality of such evidence is partly dependent upon the validity of the resulting statistical conclusions. The presence of Type I or Type II errors can render measurement invariance conclusions meaningless. The purpose of this study was to determine the effects of categorization and censoring on the behavior of the chi-square/likelihood ratio test statistic and two alternative fit indices (CFI and RMSEA) under the context of evaluating measurement invariance. Monte Carlo simulation was used to examine Type I error and power rates for the (a) overall test statistic/fit indices, and (b) change in test statistic/fit indices. Data were generated according to a multiple-group single-factor CFA model across 40 conditions that varied by sample size, strength of item factor loadings, and categorization thresholds. Seven different combinations of model estimators (ML, Yuan-Bentler scaled ML, and WLSMV) and specified measurement scales (continuous, censored, and categorical) were used to analyze each of the simulation conditions. As hypothesized, non-normality increased Type I error rates for the continuous scale of measurement and did not affect error rates for the categorical scale of measurement. Maximum likelihood estimation combined with a categorical scale of measurement resulted in more correct statistical conclusions than the other analysis combinations. For the continuous and censored scales of measurement, the Yuan-Bentler scaled ML resulted in more correct conclusions than normal-theory ML. The censored measurement scale did not offer any advantages over the continuous measurement scale. Comparing across fit statistics and indices, the chi-square-based test statistics were preferred over the alternative fit indices, and ΔRMSEA was preferred over ΔCFI. Results from this study should be used to inform the modeling decisions of applied researchers. However, no single analysis combination can be recommended for all situations. Therefore, it is essential that researchers consider the context and purpose of their analyses.

EC94-852 Cash Flow Planning Form

This extension circular covers the following areas of a cash flow planning form: Beginning Cash Balance, Operating Sales (crop and hay, market livestock, livestock product, custom work); Capital Sales (breeding livestock, machinery and equipment); Personal Income (wages, interest); Operating Expenses (car/truck, chemicals, conservation, custom hire, feed purchased, fertilizers and lime, freight and trucking, gasoline, fuel and oil, insurance, labor hired, rents and leases, repairs and maintenance, seeds and plants, storage, warehousing, supplies, taxes, utilities, veterinary, breeding fees and medicine, feeder livestock); Capital Purchases (breeding livestock, machinery and equipment, family living withdrawals, personal investments, income and social security, term loan payments); Net Cash Available (operating loan borrowings, operating loan payments); and Ending Operating Loan Balance. Along with the Cash Flow Planning Form is a Projected Income Statement Form which covers Projected Business Income (operating sales, breeding livestock, estimated cash income adjustments, estimated gross revenues, estimated value of production); Project Business Expenses (cash operating, esimated operating, prepaid and supplies, cash investment in growing crops, accounts payable); Projected Net Income Summary (estimated net income from operations, estimated net business income, estimated net income after taxes, estimated earned net worth change); and a Physical Inventory Flows Worksheet.

The Evolution of Sonata Form in the Wind Music of W.A. Mozart

Mozart’s wind music occupies a rather small space in the overall scope of his compositional output, numbering a total of ten works. Yet when viewed in the larger context of Mozart’s life, the wind music was written over the span of nine years, encompassing a large period from his youth up to his last decade in Vienna. Ranging from the simple divertimenti (K. 166 and 186) through the Tafelmusik (K. 213, 240, 252, 253 and 270) and finally culminating in the three Serenades (K. 361, 375 and 388), the wind music demonstrates Mozart’s maturation in wind writing, and also serves to illustrate the evolution in his use of sonata forms.