Correlations between Tm and

A rough correlation exists between Tg and T for crystal lizable polymers, although the molecular mechanisms that underly both transitions differ. Any structural feature that enhances chain stiffness will raise Tg, since this is the temperature needed for the onset of large-scale segmental motion. Stronger intermolecular forces will also produce higher Tg s. Tliese same factors increase T, as described on page 382, in connection with Eq. (11-1). 

Statistical copolymers of the types described in Chapter 8 tend to have broader glass transition regions than homopolymers. The two comonomers usually do not fit into a common crystal lattice and the melting points of copolymers will be lower and their melting ranges will be broader, if they crystallize at all. Branched and linear polyethylene provide a case in point since the branched polymer can be regarded as a copolymer of ethylene and higher 1-olefins. 

The Tg values quoted in Table 11 -2 are either measured by very slow rate methods or are obtained by extrapolating the data from faster, nonequilibrium techniques to zero rates. This is a fairly common practice, in order that the glass transition temperature can be considered as characteristic only of the polymer and not of measuring method. 

Many relatively slow or static methods have been used to measure Tg. These include techniques for determining the density or specific volume of the polymer as a function of temperature (cf. Fig. 11-1) as well as measurements of refractive index, elastic modulus, and other properties. Differential thermal analysis and differential scanning calorimetry are widely used for this purpose at present, with simple extrapolative eorrections for the effects of heating or cording rates on the observed values of Tg. These two methods reflect the changes in specific heat of the polymer at the glass-to-rubber transition. Dynamic mechanical measurements, which are described in Section 11.5, are also widely employed for locating Tg. 

In addition, there are many related industrial measurements based on softening point, hardness, stiffness, or deflection under load while the temperature is being varied at a stipulated rate. No attempt is usually made to compensate for heating rate in these methods, which yield transition temperatures about 10-20 higher than those from the other procedures mentioned. Some technical literature that is 

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Estimate Tm of the sample by plotting the melting curve. Perform regression analysis to deduce the correlation between Tm and the base composition of DNA by comparing the following data of DNAs from other sources ... 

The fact that both kinetic stages are dependent upon the same power of the oxygen pressure is already reflected in the close correlation between tm and To in the Series I results of Table I. That this correlation also extends through the Series II results is of particular interest. Since RT/a at 20° is 11.7 fig (Section IV-1), the expression for to from Table I and Equation... 

It has been asserted (14) that above their melting points, the structural relaxation times in polymer fluids would be much less than 10" sec. This proved to be true for molten PE. However, for polyethylene oxide (PEO) a temperature of maximum loss was observed at approximately 60°C at a frequency of 6.06 GHz (J5). The melting point of PEO is near 60°C. The temperature of maximum loss for bisphenol-A polycarbonate (16) was 280°C at a frequency of 5.43 GHz. The melting point of bisphenol-A polycarbonate is 240°C. Thus any general correlation between Tm and structural relaxation in fluids seems unwarranted. 

This empirical correlation between Tm and Xm now allows the transformation of the exactly valid heat balance, Equ.(4-153), formulated for the extremum, into a relation which depends on Tm only. 

Figure 4 shows vapor pressure curves of rare-earth metals[24], clearly showing that there is a wide gap between Tm and Dy in the vapor pressure-temperature curves and that the rare-earth elements are classified into two groups according to their volatility (viz.. Sc, Y, La, Ce, Pr, Nd, Gd, Tb, Dy, Ho, Er, and Lu, non-volatile elements, and Sm, Eu, Tm, and Yb, volatile elements). Good correlation between the volatility and the encapsulation of metals was recently... 

Finally, a fourth class of alkaloids has been discovered, apparently specific to the leaves of P. Lyallii (57). It consists of two unseparable products, 37 and 38, in the ratio 2 to 1, which readily give lyaloside (23) on mild methanolysis, along with two esters, namely, methyl ferulate and methyl sinapate (39 and 40, respectively). Elucidation of their structure was essentially based on NMR considerations (57). Graphical correlations between 1H- and 13C-NMR spectra, associated with analysis of the residual constant coupling during a step by step [200 Hz per 200 Hz from 0 (TMS) to 2000 Hz] off-resonance procedure, permitted the precise assignment of all the carbon atoms of the products (58). 

As for the other partition processes discussed above, empirical relations have been sought to relate the vapor pressure (P) to simple molecular parameters. Correlation between P and the boiling point (Tb) and melting point (Tm) has resulted in the proposal of the following equation (Mackay and Yuen 1980) which holds for a wide range of neutral compounds ... 

The VICAT softening temperature is defined as the temperature at which a circular probe of 1.0 mm2 cross section, under a load of 1000 g, penetrates 1.0 mm into a sample 12.7 mm thick (33). Using the same samples as were used for the DTUL tests, the correlation between TM A and VICAT softening temperatures are given in Table 11.5 (32). 

A series of non-equilibrium Tm-values were measured on samples recrystallised from the melt under standard conditions (the so-called Tm2-values, see 1.1.4) and a number of nonequilibrium literature values were used to look for an improved correlation between Tm/Tg relations. We tried to improve the results of such a relation by distinguishing different groups of polymers instead of looking for one relation for all types of polymers. Three groups of polymers offering the best fitting correlations, were selected finally ... 

The correlation between Tm(exp.) and Tm(calc.) and thus the average difference between Tm(exp.) and Tm(calc.) are indeed improved. The average difference is however nearly twice the average [Tg(exp.)-Tg(calc.)] value, see 7.2.2. 

Best TM, CoUins A, et al. Achilles tendon healing a correlation between functional and mechanical performance in the rat. J Orthop Res 1993 ll(6) 897-906. 

Log k appears to correlate with log P for standards between log P —0.5 to 5.0. One limitation of this method is that solutes must be electrically neutral at the pH of the buffer solution because electrophoretic mobility of the charged solute leads to migration times outside the range of Tm and TEof- Basic samples are therefore run at pH 10, and acidic samples at pH 3, thus ensuring that most weak acids and bases will be in their neutral form. This method has been used in a preclinical discovery environment with a throughput of 100 samples per week [24]. 

Data correlation results for single-salt, single-solvent binary systems are shown in Table 1 to Table 6 and Figure 3 to Figure 6. There is an obvious trend between Tm,ca an standard deviation of calculated lny versus measured lny. ... 

However, the TMS-system PC/dodecane/p-xylene has still some severe limitations. Via ICP-investigations a strong rhodium leaching of 47% of the rhodium catalyst was detected. Furthermore, we observed a correlation between the amount of the mediator p-xylene and the amoimt of leaching. The more p-xylene used, the more rhodium is transferred into the non-polar do-decane phase. Therefore, catalyst recycling in these systems is impossible at the moment. 

Table 6.1. Correlation between the entropy of fusion (extrapolated to Tm = 0) and the Lindemaim constant (C/,) for various crystal structures (from Achar and Miodownik 1974)...

Figure 6.3. Correlation between NMR shifts (ppm from TMS) of sp carbon atoms and net charges from Eq. (5.10) using optimized STO-3G charges with p = 30.12 me. The charges are expressed in terms of c/9c. that is, in relative units, for n = —4.4122. This figure now includes the points of Fig. 5.2 plus that of methane and the quaternary carbon of neopentane. (Reproduced with permission from Ref. 44.)...

An analysis of the correlation between the magnetic and geometrical structures of AunTM+ clusters, and a detailed study of the local magnetic moment of the TM impurity will be published elsewhere ... 

A serious difficulty now appears. The quantum master equation (3.14), obtained by eliminating the bath, does not have the required form (5.6) and therefore results in a violation of the positivity of ps(/). Only by the additional approximation rc Tm was it possible to arrive at (3.19), which does have that form (see the Exercise). The origin of the difficulty is that (3.14) is based on our assumed initial state (3.4), which expresses that system and bath are initially uncorrelated. This cannot be true at later times because the interaction inevitably builds up correlations between them. Hence it is unjustified to use the same derivation for arriving at a differential equation in time without invoking a repeated randomness assumption, such as embodied in tc rm. ) At any rate it is physically absurd to think that the study of the behavior of a Brownian particle requires the knowledge of an initial state. 

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