Glass Transition Temperature (Fox)
Calculate the glass transition temperature (Tg) of a blend or copolymer by the Fox equation, 1 ÷ Tg = w₁/Tg₁ + w₂/Tg₂, from the mass fraction w₁ of component 1 (with w₂ = 1 − w₁) and the Tg of each pure component (in kelvin). The result, in K, is the temperature at which the mixture goes from the glassy (rigid) to the rubbery (flexible) state. The Fox equation predicts the Tg of miscible blends, random copolymers and plasticized systems, the basis for tuning a polymer's flexibility by adding plasticizers or comonomers. Enter the mass fraction of component 1 and the two Tg values.
Resultado
—
Temperatura de transição vítrea (equação de Fox)
A temperatura de transição vítrea (Tg) é uma das mais importantes de um polímero amorfo: abaixo dela, o material está no estado vítreo (duro, rígido e frágil, como o acrílico ou o poliestireno à temperatura ambiente); acima dela, passa ao estado borrachoso (mole e flexível). Quando se mistura dois polímeros miscíveis, se faz um copolímero aleatório de dois monômeros, ou se adiciona um plastificante a um polímero, a Tg resultante fica entre as dos componentes — e a equação de Fox prevê esse valor: 1 ÷ Tg = w₁/Tg₁ + w₂/Tg₂, onde w₁ e w₂ são as frações mássicas (w₂ = 1 − w₁) e Tg₁, Tg₂ são as transições vítreas dos componentes puros, em kelvin (a equação só funciona em escala absoluta). Note que é uma média harmônica ponderada (soma dos inversos), não aritmética — então a Tg da mistura é puxada para baixo de forma não linear. A aplicação prática mais importante é a plastificação: para tornar um plástico rígido (como o PVC, com Tg ~80 °C) flexível à temperatura ambiente (mangueiras, filmes, couro sintético), adiciona-se um plastificante de Tg muito baixa (ftalatos, com Tg muito negativa); a equação de Fox prevê quanto plastificante é preciso para baixar a Tg da mistura ao valor desejado. O mesmo raciocínio vale para projetar copolímeros com a flexibilidade-alvo (ex.: borrachas, adesivos) e para entender blendas poliméricas. (A equação de Fox assume miscibilidade completa; sistemas imiscíveis mostram duas Tg separadas.) Informe a fração mássica do componente 1 e as Tg dos dois componentes.
Related Tools
Intrinsic Viscosity (Mark-Houwink)
Calculate a polymer's intrinsic viscosity by the Mark-Houwink-Sakurada equation, [η] = K·Mᵃ, from the constants K and a (specific to the polymer-solvent-temperature system) and the viscosity-average molar mass M. The result, in dL/g, relates the viscosity of a dilute polymer solution to its molar mass — the basis of molar mass determination by viscometry, a simple and cheap technique. The exponent a (between 0.5 and 0.8) reflects the chain conformation in the solvent: 0.5 for a theta solvent (coiled chain) and up to 1.0 for an extended chain in good solvent. Enter the constants K, a and the molar mass.
Cutting Force by the Kienzle Equation
Computes the main cutting force with the Kienzle equation, F_c = k_c1.1 · b · h^(1 − m_c), where k_c1.1 is the tabulated specific cutting force of the workpiece material for a reference chip section of 1 mm × 1 mm, b is the chip width and h the chip thickness, and m_c is the exponent describing the size effect. That is exactly where it differs from the direct calculation F_c = k_s·b·h: the latter treats specific pressure as a material constant, while Kienzle embeds the experimental fact that thin chips cost far more force per unit area, because the cutting edge radius stops being negligible next to the chip thickness. With k_c1.1 = 1500 N/mm² and m_c = 0.26, a 0.2 mm thick chip works at 2279 N/mm², 52 % above the tabulated value — which is why very low feeds raise the power spent per cubic millimetre removed, and the tool wear with it, instead of saving them — even though the absolute force falls. Since k_c1.1 carries a hidden millimetre raised to m_c, the equation is not dimensionally pure: thickness and width have to be entered in millimetres, and switching units is off by orders of magnitude. Enter the specific force k_c1.1, the exponent m_c, the chip width and the chip thickness.
Cubic Equation Solver
Solve cubic ax³+bx²+cx+d=0 by Cardano formula. Shows real and complex roots.
Growing Degree Days (GDD)
Compute the growing degree days (GDD), GDD = (Tmax + Tmin)/2 − Tbase, the daily thermal accumulation above the base temperature below which the plant does not grow. Since crop development is driven by temperature, summing degree days predicts phenological stages — flowering, maturity, harvest — more accurately than the calendar. Also used for pests and insects. Enter the day's maximum and minimum temperatures and the crop base temperature.
Junction Temperature
Calculate the junction temperature of a power semiconductor, T_j = T_a + P × R_th, from the ambient temperature T_a, the dissipated power P and the total junction-to-ambient thermal resistance R_th (°C/W). The result, in °C, is the device's internal temperature (silicon junction), which must not exceed the manufacturer's limit (typically 150 °C) on pain of failure. The thermal resistance adds the junction-to-case, case-to-heatsink and heatsink-to-ambient stages. Lowering R_th (larger heatsink, ventilation, thermal paste) lowers the junction temperature. It is the central calculation of power electronics thermal design. Enter the ambient temperature, the dissipated power and the thermal resistance.
Larson-Miller Parameter (Creep)
Calculate the Larson-Miller parameter, LMP = T × (C + log₁₀ t), from the absolute temperature T (K), the material constant C (typically ~20) and the time to rupture t (hours). The parameter combines temperature and time into a single number that correlates creep behaviour: short high-temperature tests predict service life at lower temperatures over long periods. It is widely used to estimate the life of components operating hot under constant load — turbine blades, boiler tubing, pressure vessels. Enter the temperature, the constant C and the rupture time.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.