The effect of degree of polymerization on glass‐transition temperatures

Macromolecules, 1980

A model of one-phase mixtures as regular solutions provides the basis of an entropic theory for the prediction of their glass-transition temperatures from pure-component glass-transition temperatures and associated heat-capacity increments. First-order approximations to an initial equation are derived and related to previous equations proposed to describe the composition-dependent glass transition. The phenomenological theory is then applied to the calculation of glass-transition temperatures for one-phase solutions in which the pure components are of arbitrary molecular mass, to give a predictive equation in terms of pure-component chain end and high-polymer glass-transition temperatures and heat-capacity increments. Calculated values of Tg are found to be in satisfactory accord with experimental glass-transition temperatures for an appropriate binary mixture of polymers. Additionally, the experimental dependence of the Wood parameter on degree of polymerization is accounted for.

Macromolecules, 1982

A thermodynamic theory for the compositional variation of glass-transition temperatures is generalized to include copolymers, providing an equation with no adjustable parameters. Properties required for this relation are glass-transition temperatures and glass-transition incrementa of heat capacity for the two associated homopolymers and the fully alternating copolymer, and the monomer reactivity ratios. Formal conditions are obtained for the occurrence, nature, and values of absolute extrema in copolymer glass-transition temperatures and glass-transition incrementa of heat capacity. Previous expressions for the composition dependence of copolymer glass-transition temperatures are derived as secondary approximations to a central equation.

Journal of Polymer Science Part C: Polymer …, 1970

An equation is proposed relating the glass transition temperature (TG) of copolymers to their molecular structure in terms of the mole fractions of the various diad sequences of monomer units combined in the copolymer chain, and temperature parameters (Ti$ characteristic of each type of sequence. ij. The equation, an extension of the Gibbs and DiMarzio copolymer TG theory, accounts for the effect on TG of the different types of bonds between repeating units in different diad sequences, and is in its general form: TG = c n ' j i Tif In a binary copolymer of structure [(a) x (b),,] n, corresponding to the sequences -aa-, -ba-, -ub-, and -bb-. The term nIii is the mole fraction of weighted according to the number of rotatable bonds per sequence, aii, and n'ii = nila ij/ (nqaii). The variation in the distribution of sequences with overall composition is obtained from the copolymerization reactivity ratios. The theory, which quantitatively describes the sometimes observed maximum or minimum in TGcomposition plots, gives good agreement with published data for 11 copolymer systems. Application of the theory to give homopolymer TG'S by extrapolation is demonstrated. Inter-relations are found with other published theories of copolymer TG.

Journal of Polymer Science Part B: …, 2009

Knowledge of the glass transition temperatures (T g s) as function of composition reflects miscibility (or lack of it) and is decisive for virtually all properties of polymer-based materials. In this article, we analyze single blend-average and effective T g s of miscible polymer blends in full concentration ranges. Shortcomings of the extant equations are discussed to support the need for an alternative. Focusing on the deviation from a linear relationship, defined as DT g ¼ T g À u 1 T g,1 À u 2 T g,2 (where u i and T g,i are, respectively, the weight fraction and the T g of the i-th component), a recently proposed equation for the blend T g as a function of composition is tested extensively. This equation is simple; a quadratic polynomial centered around 2u 1 À 1 ¼ 0 is defined to represent deviations from linearity, and up to three parameters are used. The number of parameters needed to describe the experimental data, along with their magnitude and sign, provide a measure of the system complexity.

Polymer, 2007

A semi-empirical method based on the mass-per-flexible-bond (M/f ) principle was used to quantitatively explain the large range of glass transition temperatures (T g ) observed in a library of 132 L-tyrosine derived homo, co-and terpolymers containing different functional groups. Polymer class specific behavior was observed in T g vs. M/f plots, and explained in terms of different densities, steric hindrances and intermolecular interactions of chemically distinct polymers. The method was found to be useful in the prediction of polymer T g . The predictive accuracy was found to range from 6.4 to 3.7 K, depending on polymer class. This level of accuracy compares favorably with (more complicated) methods used in the literature. The proposed method can also be used for structure prediction of polymers to match a target T g value, by keeping the thermal behavior of a terpolymer constant while independently choosing its chemistry. Both applications of the method are likely to have broad applications in polymer and (bio)material science.

Macromolecular Chemistry and Physics, 2002

Materials Letters, 2008

Glass transition temperature Tg values characterize pure polymers, polymer blends, copolymers, as well as matrices in polymer-based composites. Tgs as function of composition reflect miscibility (or lack of it) and determine all properties. We present a new equation for the dependence of Tg on composition in blends as well as in copolymers. We compare results obtained from earlier equations (Fox,

2014

The physical properties of polymers are very much dictated by where the operating temperature lies with respect to the transition temperature between glassy and rubbery states. The precise identification of this glass transition temperature, Tg, is critical in assessing the feasibility of a polymer for a given application. In this book, the behavior of polymers near their Tg and the capability of predicting Tg using theoretical and empirical models is assessed. While all polymers undergo structural relaxation at various temperatures both nearly above and below Tg, practical assessment of a single consistent Tg is successfully performed through consideration of only immediate thermal history and thermodynamic properties. The determination of Tg for a wide variety of polymers of theoretically infinite chain length has been found to be accurately performed through the use of novel quantitative structure-property relationship (QSPR) models. The supplementation of such values to configur...

Journal of Chemical Information and Modeling, 1996

A novel approach to the prediction of the physical properties of polymers is presented. A QSPR study, involving the use of a newly developed statistical package, CODESSA, is described for the T g of a set of 22 low molecular weight polymers which gave a four-parameter equation with R 2 ) 0.928. The physical significance of the descriptors selected is discussed.

The Journal of Physical Chemistry B, 2005

We develop an analytic theory to estimate the glass transition temperature T g of polymer melts as a function of the relative rigidities of the chain backbone and side groups, the monomer structure, pressure, and polymer mass. Our computations are based on an extension of the semiempirical Lindemann criterion of melting to locate T g and on the use of the advanced mean field lattice cluster theory (LCT) for treating the themodynamics of systems containing structured monomer, semiflexible polymer chains. The Lindemann criterion is translated into a condition for T g by expressing this relation in terms of the specific volume, and this free volume condition is used to calculate T g from our thermodynamic theory. The mass dependence of T g is compared to that of other characteristic temperatures of glass-formation. These additional characteristic temperatures are determined from the temperature variation of the LCT configurational entropy, in conjunction with the Adam-Gibbs model for long wavelength structural relaxation. Our theory explains generally observed trends in the variation of T g with polymer microstructure, and we find that T g can be tuned either upward or downward by increasing the length of the side chains, depending on the relative rigidities of the side groups and the chain backbone. The elucidation of the molecular origins of T g in polymer liquids should be useful in designing and processing new synthetic materials and for understanding the dynamics and controlling the preservation of biological substances.