Gordon-Taylor Equations Research Articles

State diagram of whole milk for freeze-drying application

The state diagram is a key parameter when optimizing a freeze-drying cycle, as it allows us to set the optimum processing temperature for a specific product. The purpose of this work is to provide some thermodynamic and physicochemical data for optimizing the freeze-drying cycle of whole milk. Freezing point measurements were determined using differential scanning calorimetry and cryoscopy methods, and glass transitions were evaluated by DSC. The endothermic peak was used as the equilibrium freezing point, a variation from 273.93 K to 264.92 K was detected when the dry matter content varied from 0 to 75%. Tg midpoint temperature was used as glass transition of dry mater. Furthermore, Fox and Gordon-Taylor equations were used to predict the glass transition curve to determine Tg', this temperature was used as an approximation of the critical temperature Tc. Collapse temperature was determined using the freeze-drying microscopy setup.

Modeling Strategy for Enhanced Recovery Strength and a Tailorable Shape Transition Behavior in Shape Memory Copolymers

By integrating the Fox–Flory equation and the rubber elasticity principle, a phenomenologically constitutive model was proposed in this study to describe high mechanical recovery strength and a tailorable shape transition behavior of shape memory polymer (SMP) copolymers. The thermodynamics of different monomers in the copolymers were formulated by considering their influences on glass-transition temperatures (Tg) and elastic moduli based on the Fox–Flory and Gordon–Taylor equations. Effects of the Tg, weight fraction, molecular weight, storage modulus, and rubbery modulus of various monomers on thermomechanical and shape recovery behaviors of the SMP copolymers were theoretically investigated and discussed. Working principles of enhanced mechanical strength and a tailorable shape transition behavior of the SMP copolymers have been well-described using this newly proposed model, which offers an effective strategy for designing SMPs with high mechanical strength and a desirable shape memory behavior. Furthermore, molecular dynamics simulations were used to predict the glass-transition temperature from a molecular scale and the experimental results fit well with our modeling results.

State diagrams of candied orange peel obtained using different hypertonic solutions

State diagrams were established for the candied orange peel obtained by saturation with sucrose or glucose-fructose syrup. Differential scanning calorimetry was used to determine the freezing points and glass transition temperatures in order to generate freezing curve and glass transition curve. Curves were modelled by the Chen and Gordon-Taylor equations. Maximal freeze concentration parameters (Xw’, Tm’ and Tg’) were determined from state diagrams in the 0.185–0.218 kg water/kg sample; −36.9 to −34.8 °C; and – 54.6 to −53.3 °C range. All values depended on the glucose, fructose, sucrose, and maltose content. Orange peel candied with 100% sucrose syrup showed that the glass transition curve can predict sugar crystallization when the product moisture content increases. The dependence between the Tg value and moisture content can be used to control the transformations occurring during storage of products containing amorphous sugars. The glucose-fructose syrup applied during candying prevented sucrose recrystallization.

094 Application of the Kwei equation for predicting the Tg of stabilizing formulations containing sugars and salts

Sugars such as trehalose and sucrose have been used in numerous formulations to improve the shelf-life of products ranging from foods to pharmaceuticals and more recently they have also been used as a key protectant for preserving cell-based products. Disaccharides are known to have high glass transition temperatures and thus can immobilize molecules at high storage temperatures. Frequently these sugars are used in combination with salts for the purpose of buffering, oncotic control, or to maintain membrane potentials. The effect of salts on the glass-forming sugars has not been comprehensively studied. To better understand the effect of salts on the potential for the storage of glassy compositions we investigated various predictive models for sugar/salt formulations using data from the literature as well as new data generated on binary mixtures of trehalose and choline dihydrogen phosphate (CDHP). CDHP has recently been shown to have promise as a stabilizing agent for proteins and DNA, and thus may have utility in preserving certain biospecimens. For example, it can increase the thermal stability and shelf life of model proteins such as Cytochrome c, lysozyme and interleukin-2. In the current study we determined the glass transition temperature (Tg) of mixtures of CDHP and trehalose using a Q-100 differential scanning calorimeter (TA Instruments). The calorimetric results show that the relationship between Tg and composition exhibited a pronounced deviation from the conventional Gordon-Taylor prediction. Specifically, there is a “fall-and-rise” trend within the range of 70 ∼ 90 wt% of trehalose. A general and accurate model for predicting the Tg can conserve experimental effort and lead to better insights about the interactions between sugars and salts. In this study we applied the Fox, Gordon-Taylor and Kwei equations to both literature data and new data acquired on trehalose/CDHP mixtures that are of interest in formulation science. The Kwei equation was found to have more generality and accuracy than the Fox and Gordon-Taylor equations. From a mathematical point of view, the curves of the Tg as a function of weight percentage modeled with the Kwei equation can be further grouped into three types (i.e., U, inverted U, and inverted S shapes) based on the values of its two parameters, k and q. It is believed that the deviations from the Gordon-Taylor prediction can be attributed to the strong interactions between the two components in a mixture as well as their structural and volumetric differences. Source of funding: This work was funded by grant #5RO1GM101796 from the National Institutes of Health. Conflict of interest: None declared. gdelliot@uncc.edu

Development of PVP/PEG mixtures as appropriate carriers for the preparation of drug solid dispersions by melt mixing technique and optimization of dissolution using artificial neural networks

The effect of plasticizer’s (PEG) molecular weight (MW) on PVP based solid dispersions (SDs), prepared by melt mixing, was evaluated in the present study using Tibolone as a poorly water soluble model drug. PEGs with MW of 400, 600, and 2000g/mol were tested, and the effect of drug content, time and temperature of melt mixing on the physical state of Tibolone, and the dissolution characteristics from SDs was investigated. PVP blends with PEG400 and PEG600 were completely miscible, while blends were heterogeneous. Furthermore, a single Tg recorded in all samples, indicating that Tibolone was dispersed in a molecular lever (or in the form of nanodispersions), varied with varying PEG’s molecular weight, melt mixing temperature, and drug content, while FTIR analysis indicated significant interactions between Tibolone and PVP/PEG matrices. All prepared solid dispersion showed long-term physical stability (18months in room temperature). The extent of interaction between mixture components was verified using Fox and Gordon–Taylor equations. Artificial neural networks, used to correlate the studied factors with selected dissolution characteristics, showed good prediction ability.

Miscibility studies of some semi-interpenetrating polymer networks based on an aromatic polyurethane and epoxy resin

Glass transition temperatures of some semi-interpenetrating polymer networks based on aromatic polyurethane and cross-linked epoxy resin were determined by differential scanning calorimetry. The influence of increasing epoxy network content on the glass transition temperatures was studied. Absolute heat capacities and cross-linking densities were determined. It was observed that the glass transition temperatures increased with increasing epoxy resin content until phase separation. Miscibility studies were conducted by applying Fox and Gordon–Taylor equations. Morphological studies were conducted by optical microscopy and scanning electron microscopy.

The Effect of Water Plasticization on the Molecular Mobility and Crystallization Tendency of Amorphous Disaccharides

To study how water plasticization affects the molecular mobility and crystallization tendency of freeze-dried trehalose, sucrose, melibiose and cellobiose. Freeze-dried disaccharides were subjected to different relative humidity atmospheres and their physical stabilities were evaluated. Lyophilizate water sorption tendencies and glass transition temperatures were modeled using Brunauer-Emmett-Teller (BET) and Gordon-Taylor (GT) equations, respectively. Sucrose and cellobiose crystallization tendencies were compared by using the concept of reduced crystallization temperature (RCT), and the molecular mobilities of trehalose and melibiose were compared by measuring their T(1)H relaxation time constants. Based on the BET and GT models, water sorption tendency and the resulting plasticizing effect were different in sucrose when compared to the other disaccharides. Trehalose and melibiose exhibited generally slower crystallization rates when compared to sucrose and cellobiose. Amorphous melibiose was shown to be particularly stable within the studied water content range, which may have partly been caused by its relatively slow molecular mobility. Slow amorphous-to-crystalline transition rate is known to be important for lyoprotecting excipients when formulating a robust drug product. The physical stabilities of amorphous trehalose and melibiose even with relatively high water contents might make their use advantageous in this respect compared to sucrose and cellobiose.

State diagrams of freeze dried colostral whey powders: Effects of additives on the stability of colostral whey powders

The state diagrams of colostral whey (CW) powders with different additives were determined using freezing curve, glass transition line and maximal-freeze-concentration conditions and effects of different additives on the stability of CW powders were also investigated based on water activity and glass transition concepts. The Brunauer–Emmett–Teller (BET) and Gordon–Taylor equations were used to model water activity/moisture content and glass transition temperatures ( T g)/solids content relationships. The parameters of two models were applied for estimating water activity and T g at given moisture content. Results showed that addition with maltodextrin into CW powders increased T g of dry solids ( T gs) from 103.5 to 126.8 °C and end point of freezing ( T m ′ ) from −35.20 to −31.79 °C, whereas addition with sucrose decreased T gs to 80.1 °C and T m ′ to −36.18 °C, indicating maltodextrin was an excellent drying aid and cryoprotectant. The greater efforts were needed to make to combine the water activity and glass transition concepts for predicting the stability of food materials.

Miscible blends of poly(vinyl phenyl ketone) and poly(4‐vinyl phenol)

AbstractAn analysis by differential scanning calorimetry, modulated differential scanning calorimetry, and Fourier transform infrared spectroscopy (FTIR) indicates that blends of poly(vinyl phenyl ketone) (PVPhK) and poly(4‐vinyl phenol) (P4VPh) are miscible at ambient temperature. Miscibility, ascertained, is supported by the existence of a single glass transition for each composition of the PVPhK/P4VPh blends. The FTIR spectroscopy analysis demonstrates the formation of hydrogen bonds between carbonyl groups of PVPhK and hydroxyl groups of P4VPh. This specific interaction has a crucial role on the miscibility behavior of PVPhK/P4VPh blends. The evolution of the glass transition of the PVPhK, P4VPh, and its blends as a function of mixture composition shows negative deviations with to respect to the ideal mixing rule, and both Fox and Gordon–Taylor equations predict this behavior successfully. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2404–2411, 2006

Synthesis of hydroxyl‐terminated poly(ether ether ketone) with pendenttert‐butyl groups and its use as a toughener for epoxy resins

AbstractHydroxyl‐terminated poly(ether ether ketone) with pendenttert‐butyl groups (PEEKTOH) was synthesized by the nucleophilic substitution reaction of 4,4′‐difluorobenzophenone withtert‐butyl hydroquinone with potassium carbonate as a catalyst andN‐methyl‐2‐pyrrolidone as a solvent. Diglycidyl ether of bisphenol A epoxy resin was toughened with PEEKTOHs having different molecular weights. The melt‐mixed binary blends were homogeneous and showed a single composition‐dependent glass‐transition temperature (Tg). Kelley–Bueche and Gordon–Taylor equations gave good correlation with the experimentalTg. Scanning electron microscopy studies of the cured blends revealed a two‐phase morphology. A sea‐island morphology in which the thermoplastic was dispersed in a continuous matrix of epoxy resin was observed. Phase separation occurred by a nucleation and growth mechanism. The dynamic mechanical spectrum of the blends gave two peaks corresponding to epoxy‐rich and thermoplastic‐rich phases. TheTgof the epoxy‐rich phase was lower than that of the unmodified epoxy resin, indicating the presence of dissolved PEEKTOH in the epoxy matrix. There was an increase in the tensile strength with the addition of PEEKTOH. The fracture toughness increased by 135% with the addition of high‐molecular‐weight PEEKTOH. The improvement in the fracture toughness was dependent on the molecular weight and concentration of the oligomers present in the blend. Fracture mechanisms such as crack path deflection, ductile tearing of the thermoplastic, and local plastic deformation of the matrix occurred in the blends. The thermal stability of the blends was not affected by blending with PEEKTOH. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 541–556, 2006

Evaluating water activity and glass transition concepts for food stability

Water activity and glass transition temperature concepts were used to investigate the connection between the two distinct criteria of food stability. The data on sorption isotherms and glass transition temperatures were obtained from the literature. Two most commonly used models i.e. GAB and Gordon–Taylor equations were used to model water activity/moisture content and glass transition temperatures/solids content relationships. The models’ (GAB and Gordon–Taylor) parameters were used to estimate water activity and glass transition temperature at given moisture/solids content. Results indicate that there is a considerable discrepancy in the temperature-related stability criteria predicted by the concepts of water activity ( a w) and the glass phenomenon ( T g). A greater understanding of water sorption properties and T g is required to establish a sound processing and storage stability criteria.

Epoxy resin/poly(ϵ‐caprolactone) blends cured with 2,2‐bis[4‐(4‐aminophenoxy)phenyl]propane. I. Miscibility and crystallization kinetics

AbstractCrystalline thermosetting blends composed of 2,2′‐bis[4‐(4‐aminophenoxy)phenyl]propane (BAPP)‐cured epoxy resin (ER) and poly(ϵ‐caprolactone) (PCL) were prepared via the in situ curing reaction of epoxy monomers in the presence of PCL, which started from initially homogeneous mixtures of diglycidyl ether of bisphenol A (DGEBA), BAPP, and PCL. The miscibility of the blends after and before the curing reaction was established with differential scanning calorimetry and dynamic mechanical analysis. Single and composition‐dependent glass‐transition temperatures (Tg's) were observed in the entire blend composition after and before the crosslinking reaction. The experimental Tg's were in good agreement with the prediction by the Fox and Gordon–Taylor equations. The curing reaction caused a considerable increase in the overall crystallization rate and dramatically influenced the mechanism of nucleation and the growth of the PCL crystals. The equilibrium melting point depression was observed for the blends. An analysis of the kinetic data according to the Hoffman–Lauritzen crystallization kinetic theory showed that with an increasing amorphous content, the surface energy of the extremity surfaces increased dramatically for DGEBA/PCL blends but decreased for ER/PCL blends. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1085–1098, 2003

POLYURETHANE-EPOXY MALEATE OF BISPHENOL A BLENDS

Blends of polyurethane with epoxy maleate of Bisphenol A were synthesized and their miscibility, the physico-mechanical properties, as well as the thermal behavior were studied. Differential scanning calorimetry (DSC) measurements showed a single composition-dependent glass transition temperature (Tg), and is evidence for a good miscibility of the studied systems. The variation of Tg's of the blends versus composition (Fox, Gordon-Taylor, and Schneider equations) showed the presence of some physical interactions between polyurethane and epoxy maleate polymers. Generally, the physico-mechanical properties of the blends are lower as than those of polyurethane. This suggests that epoxy maleate of Bisphenol A operates in a mixture with polyurethane only as a plasticizer. The thermal behavior of the studied blends showed no large differences to that of polyurethane.

Water effect on the morphology of EVOH copolymers

The effect of water on the morphology of four ethylene vinyl alcohol copolymers (EVOH) with different ethylene contents was studied by differential scanning calorimetry (DSC). EVOH film samples equilibrated in controlled atmospheres at different relative humidities (RH) and 23°C were analyzed. Under dry conditions, the glass transition temperature (Tg) was unaffected by copolymer ethylene content. As RH increases, Tg decreases. It seems that the presence of water within the polymer matrix results in plasticization of the polymer. Tg varies from around 50°C (dry) to below room temperature. EVOH copolymers are glassy polymers when dry and rubbery polymers at high RHs. Fox and Gordon–Taylor's equations well describe Tg depletion at low water uptake, although severe water gain results in a considerable Tg decrease, which is not predicted by these theories. Melting temperature, Tm, and enthalpy, ΔHm, were also analyzed. When dry, Tm decreases as ethylene content increases. No significant water effect was found on either Tm or ΔHm. Hence, crystallinity seems to be unaffected by water presence. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 1201–1206, 1999

Glass transition behaviour of poly(ether ether ketone)/poly(ether imide) blends

Differential scanning calorimetry (d.s.c.), dynamic mechanical thermal analysis (d.m.t.a.) and dielectric relaxation spectroscopy (DRS) have been used to study the α-relaxation in amorphous blends of poly(ether ether ketone) (PEEK) and poly(ether imide) (PEI). The composition dependence of the d.s.c. T g is well described by the Couchman and Gordon-Taylor equations while the isothermal dielectric loss curves can be fitted by the empirical Havriliak-Negami (HN) function. The HN parameters can be represented in the form of cooperativity plots which show that they do not follow a weighted average with changing composition. The time scale for dipolar relaxation in the blends is dominated by PEI, which relaxes at a relatively slower rate compared with PEEK, while the composition dependence of the apparent activation energy shows a negative deviation from additive behaviour. It is likely that these observations are related to the interactions between the blend components which result in changes in the local molecular environment on blending.

Blends of Nitrile Polymers and Polar Moieties Containing Polyolefins

The phase behaviour of blends of poly(acrylonitrile:methyl acrylate: butadiene) (B210) and polyolefins modified with polar groups, either by copolymerization or grafting reactions, was examined using differential scanning calorimetry (DSC). Enhanced or complete miscibility was attained by synthetically incorporating molecular features which promote intermolecular attraction. Miscibility over the entire range of compositions was found for binary blends of B210 and poly(ethylene-co-maleic anhydride) (PEMA). For other blends such as B210 and poly(propylene-g-acrylic acid) (PP-g-AcA) or poly(ethylene-g-maleic anhydride) (PE-g-MA), miscibility was limited to the amorphous phase. Several equations commonly used in the literature to express the glass transition temperature-composition relationship have been applied to describe the miscible blend systems. Gordon-Taylor and Kwei equations best represent the Tg data of these polymer mixtures. The deviation from linearity of both experimental and predicted values was attributed to the existence of specific intermolecular interactions between the constituents of the individual polymer chains. This work has shown that it is possible to combine the desirable features of polyolefins (low permeability to moisture) and acrylonitrile-based polymers (good gas barrier properties) by creating a miscible blend through molecular modification.