Randomization and blocking

One of the assumptions of one-way (and other) ANOVA calculations is that the uncontrolled variation is truly random. However, in measurements made over a period of time, variation in an uncontrolled factor such as pressure, temperature, deterioration of apparatus, etc., may produce a trend in the results. As a result the errors due to uncontrolled variation are no longer random since the errors in successive measurements are correlated. This can lead to a systematic error in the results. Fortunately this problem is simply overcome by using the technique of randomization. Suppose we wish to compare the effect of a single factor, the concentration of perchloric acid in aqueous solution, at three different levels or treatments (0.1 M, 0.5 M, and 1.0 M) on the fluorescence intensity of quinine (which is widely used as a primary standard in fluorescence spectrometry). Let us suppose that four replicate intensity measurements are made for each treatment, i.e. in each perchloric acid solution. Instead of making the four measurements in 0.1 M acid, followed by the four in 0.5 M acid, then the four in 1 M acid, we make the 12 measurements in a random order, decided by using a table of random numbers. Each treatment is assigned a number for each replication as follows  

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G-5—G-9 Aromatic Modified Aliphatic Petroleum Resins. Compatibihty with base polymers is an essential aspect of hydrocarbon resins in whatever appHcation they are used. As an example, piperylene—2-methyl-2-butene based resins are substantially inadequate in enhancing the tack of 1,3-butadiene—styrene based random and block copolymers in pressure sensitive adhesive appHcations. The copolymerization of a-methylstyrene with piperylenes effectively enhances the tack properties of styrene—butadiene copolymers and styrene—isoprene copolymers in adhesive appHcations (40,41). Introduction of aromaticity into hydrocarbon resins serves to increase the solubiHty parameter of resins, resulting in improved compatibiHty with base polymers. However, the nature of the aromatic monomer also serves as a handle for molecular weight and softening point control. 

Table 11.2 Comparison of random and block copolymers (data based on three grades of Novolen - Targor Gmbh)...

Random and Block Copolymers by Ring-Opening Polymerization... 

The thermostability of siloxane-silazane copolymers of both random and block structure is found to be much higher (i.e. 100-200°C) with respect to polysiloxanes. This effect is brought about by introducing only a few silazane entities into the polymer chain. The reasons for the effect are not clear and the mechanism of thermal degradation of polysilazoxanes will require further experimental studies. 

We commonly copolymerize styrene to produce random and block copolymers. The most common random copolymers are styrene-co-acrylonitrile and styrene-co-butadiene, which is a synthetic rubber. Block copolymerization yields tough or rubbery products. 

Statistical experimental design is characterized by the three basic principles Replication, Randomization and Blocking (block division, planned grouping). Latin square design is especially useful to separate nonrandom variations from random effects which interfere with the former. An example may be the identification of (slightly) different samples, e.g. sorts of wine, by various testers and at several days. To separate the day-to-day and/or tester-to-tester (laboratory-to-laboratory) variations from that of the wine sorts, an m x m Latin square design may be used. In case of m = 3 all three wine samples (a, b, c) are tested be three testers at three days, e.g. in the way represented in Table 5.8 ... 

Kimura M, Fukumoto K, Watanabe J et al (2005) Spontaneously forming hydrogel from water-soluble random- and block-type phospholipid polymers. Biomaterials 26 6853-6862... 

In the absence of polymer the sediment volume of silica depends on the non-solvent fraction of the medium as shown in Figure 6. The sediment volume assessment of steric stabilization behavior of the copolymers is illustrated in Figures 7a to 7c. At low styrene contents, both the random and block copolymers show a steady increase in sediment volume as the non-solvent content is raised up to the phase separation value. With polystyrene and random copolymers of high styrene content, the sediment volume stays largely constant with alteration in the non-solvent fraction until the theta-point is approached and then continues to become larger as the limit of solubility is reached. In Figure 7b only the data points of RC 86 are shown, RC 94 giving almost identical values. 

Poly(methyl methacrylate) provides a level of stabilization even though the solution in CCl is below the 0-temperature. All the copolymers, both random and block, are better stabilizers than PMM, the methacrylate units acting as anchors, with stabilizing sequences of styrene loops, of block copolymers, or mixed loops and tails, of random copolymers, at better than 0-conditions. Higher M.W. polystyrenes give silica dispersions too unstable to measure by our optical method the sediment volumes are between those of poly(methyl methacrylate) solutions and pure solvent. 

They obtained moderately monodispersed (1.2 + 0.1) polymacromonomers with 30% initiator efficiency when short macromonomers (DP = 21 to 75) are polymerized. Higher MW macromonomers polymerized only partially. Evidence for interaction of the PEO ether groups with the catalytic center is given and assumed to be responsible for the shortcomings of the living system. Random and block copolymers of PS and PEO macromonomers, as well as of P(EO-b-S) and P(S-b-EO) macromonomers have also been made [112], The same group successfully prepared PS macromonomers with a norbornene group in the a position [113]. 

In addition, the determination of a polymer s endgroup(s) [125,126] and the analysis of random and block-copolymers [127,128] can be achieved by MALDI. However, care has to be taken when judging the MALDI spectra because of the mass-dependent desorption and detection characteristics of the experiment. In case of higher polydispersity (PD >1.1) high-mass ions are underestimated from MALDI spectra. [93,124] The current practice to deal with such samples is to fractionate them by gel permeation chromatography (GPC) [123] or size-exclusion chromatography (SEC) prior to MALDI analysis. [124,129]... 

Fijten MWM, Kranenburg JM, Thijs HML, Paulus RM, Van Lankvelt BM, D Hullu J, Spring-intveld M, Thielen DJG, Tweedie CA, Hoogenboom R, VanVliet KJ, Schubert US (2007) Synthesis and structure-property relationships of random and block copolymers a direct comparison for copoly(2-oxazoline)s. Macromolecules 40 5879-5886... 

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