【Basic Knowledge of Glossary Definitions for “Polymers and Materials”-011】Glossary definitions related to polymers

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What is the relationship between dynamic viscosity and intrinsic viscosity?

Dynamic viscosity Definition: The internal friction force generated when two layers of fluid, each with an area of 1 m2 and separated by a distance of 1 m, move relative to each other at a speed of 1 m/s. Unit: N•s/m² (newtons-seconds per square meter), which is also Pa•S (pascals-seconds). The physical quantity that measures the viscosity of a fluid is denoted as μ. The viscosity is numerically equal to the shear stress experienced by a fluid under a unit velocity gradient. The velocity gradient also represents the rate of angular deformation in fluid motion; therefore, viscosity represents the ratio between shear stress and the rate of angular deformation. In the International System of Units, the unit of viscosity is pascal-second. Sometimes poise or centipoise are also used (1 poise = 10-1 Pa·s, 1 centipoise = 10-2 poise). Viscosity is a property of fluids, and the viscosity values vary for different fluids. The viscosity of the same fluid is significantly dependent on temperature, while it is almost independent of pressure. The viscosity of gases increases as temperature rises, while that of liquids decreases. Viscosity can be determined experimentally or measured using a viscometer. In many formulas of fluid mechanics, viscosity often appears in the form of μ/ρ together with density ρ; hence, v = μ/ρ is defined. Since the unit of v, namely meters squared per second, consists only of kinematic units, it is called dynamic viscosity. For Newtonian fluids, the ratio of shear stress to shear rate is constant and is known as Newtonian viscosity. For non-Newtonian fluids, this ratio changes with shear stress, and the resulting viscosity is referred to as the \"apparent viscosity\" at that specific shear stress; plastics fall into the latter category. Instrumentation for measurement: Rotational rheometer, capillary rheometer. Specific viscosity Definition: When the concentration of a polymer solution is low, the logarithm of its relative viscosity divided by the mass concentration of the polymer solution gives the specific viscosity of that polymer. The intrinsic viscosity is defined as the \"specific viscosity\" (ηsp/c) or specific logarithmic relative viscosity (lnηr/c) when the concentration of the polymer solution approaches zero; that is, limc→0 ηsp/c=lnηr/c=. The value of the intrinsic viscosity depends on the relative molecular mass and structure of the polymer, as well as the temperature of the solution and the properties of the solvent. When the temperature and solvent remain constant, for a given polymer, its intrinsic viscosity is determined solely by its relative molecular mass. Therefore, if a quantitative relationship between the relative molecular mass and the intrinsic viscosity can be established, the relative molecular mass of the polymer can be determined by measuring the intrinsic viscosity. When the solvent and temperature are constant, for polymers with the same molecular structure, the relationship between their relative molecular mass and intrinsic viscosity can be determined using the Mark-Houwink equation, namely: =kMa. Testing instruments: Ubbelohde viscometer, capillary viscometer

Specific viscosity is the specific concentration viscosity of a solution at infinite dilution； Absolute viscosity is the usual viscosity; it is rather difficult to determine the absolute viscosity of a liquid directly through experiments. It is common to determine the relative viscosity of a liquid compared to a standard liquid such as water; by knowing the viscosity of the standard liquid, the absolute viscosity of the liquid in question can be determined. Absolute viscosity property: In the past, the viscosity of fluids, expressed in the dynamic viscosity unit of poise in the centimeter-gram-second system or its fractional unit of centipoise, was mistakenly called absolute viscosity. Actually, it is dynamic viscosity. Its definition is independent of the unit used (whether it is pascals or the SI unit pascal·second). See dynamic viscosity. A fluid whose viscosity does not change with shear force and shear rate is called a Newtonian fluid. Solutions of low-molecular-weight compounds and dilute solutions of polymers are Newtonian fluids. Its viscosity is called absolute viscosity.

There is a certain relationship between the intrinsic viscosity of polymers and their molecular weight; this relationship can be expressed using the Mark-Houwink-Sakurada equation: η∞ = KMα. Oh, it’s not displayed properly here – the exponent is indicated later. η∞ represents the extrapolated value of the specific viscosity as the concentration approaches zero, and it is known as the intrinsic viscosity. The value of α varies for different systems; it can be found in reference manuals

Shear viscosity is equal to the ratio of shear stress to the shear strain coefficient. Zero shear viscosity: In polymer solutions, or in the molten state, polymers are like clusters of soft, entangled threads; although each polymer chain tries to move, the points of entanglement between the chains help maintain the stability of their structure. This is why the very small shear forces at the initial stage are not sufficient to overcome the structural strength, allowing the structure to remain intact. The reason for this is the high viscosity, similar to that of a Newtonian fluid (where viscosity remains constant regardless of the shear rate); hence it is referred to as “zero-shear viscosity”. In simple terms, zero-shear viscosity is the viscosity when the shear rate is zero, and it is usually denoted by η0. It cannot be measured directly through experiments, so estimation methods or values obtained at very low shear rates are used as approximations. Apparent viscosity is the shear stress at any point on the shear stress–shear rate curve of a non-Newtonian fluid, divided by the shear rate. Intrinsic viscosity is a type of viscosity for polymer solutions, typically expressed as the value of the specific viscosity per concentration of the solution when the concentration approaches 0/c. In practice, it is common to calculate the viscosity-average molecular weight of polymers (using the Mark-Houwink equation); its unit is the reciprocal of concentration, such as dL/g or mL/g. Shear viscosity is a measure of the frictional resistance encountered by polymer melts during processing; the higher the shear viscosity, the worse the fluidity of the melt under shear forces. Zero shear viscosity characterizes the resistance encountered by polymer melts as they flow at low shear rates; generally, the flow of such melts follows the characteristics of Newtonian fluids.