Statistical treatment of random

The statistical treatment of random stepwise crosslinking reactions (e.g. polycondensation) neglecting ring formation originates from Stock-mayer and Flory and is explained in Flory s book (55) on a number of examples. Using simple probability statistics, it is possible to calculate the molecular size distribution in the sol and in the gel, fractions of sol and gel, the crosslinking density and the fraction of free functionalities in... 

The groups of Windle (1) and Blackwell (2) have demonstrated that particular sequences of monomers in thermotropic LC random copolyesters lead to very small crystalline regions in the solid state. Based on a statistical treatment of random copolymerization one concludes that the probability of sequences matching in two different chains, and hence the degree of crystallinity, increases as the chain length is lowered (1). 

Thus far the discussion in this chapter has concentrated on the statistical treatment of random errors in calibration data and calibration equations, with only passing mention of the implications of the practicalities involved in the acquisition of these data. For example, no mention has been made of what kind of calibration data are (or can be) acquired in common analytical practice, under which circumstances one approach is used rather than another and (importantly) what are the theoretical equations to which the experimental calibration data should be fitted by least-squares regression for different circumstances. Moreover, it is important to address the question of analytical accuracy to complement the discussion of precision that we have been mainly concerned with thus far the meanings of accuracy and precision in the present context are discussed in Section 8.1. The present section represents an attempt to express in algebra the calibration functions that apply in different circumstances, while exposing the potential sources of systematic uncertainty in each case. 

Statistical treatment of random errors, 971-983 Stator, motor, 53 Stern-Volnier equation, 408,409 Stokes... 

APPENDIX 1 Evaluation of Analytical Data 9(>7 alA Precision and Accuracy 967 alB Statistical Treatment of Random Errors 971 alC Hypothesis Testing 983 alD Method of Least Squares 985 Questions and Problems 988... 

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