Rheological Properties of Topical Formulations

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1 Rheological Properties of Topical Formulations Hemi Nae, PhD Hydan Technologies, Inc. Key Words Complex Modulus, Creep/Recovery, Dilatant Flow, Dynamic Viscosity, Flow, Flow Curve, Flow Models, Frequency Sweep, Kinematic Viscosity, Loss Modulus (G ), Newtonian Flow, Non-Newtonian Fluid, Oscillatory Mode, Pseudoplastic Flow, Plastic Flow, Rheological Additive (Thickener), Rheology, Rheometer, Rotational Mode, Shear Rate, Shear Stress, Shear Thickening, Shear Thinning, Storage Modulus (G ), Strain Sweep, Thickening Mechanism, Thixotropy, Viscoelasticity, Viscometer, Viscosity, Yield Value Introduction This chapter reviews the principles of rheology and the rheological properties of topical formulations such as shear stress, shear rate, viscosity, yield value, viscoelasticity, storage and loss moduli. It discusses the measurement of these properties and the instruments typically used in measuring the rheological properties of topical formulations. It also describes various rheological additives, including natural gums, cellulose-based alkali-swellable polymers, associative thickeners, clay and organoclay rheological additives, and synthetic thickeners, their thickening mechanisms and the properties that they impart to topical formulations. The discussion and the sample of rheological measurements described in this chapter may serve as a general basic guide to the design and development of target rheological profiles for topical formulations. The scope and goal of the formulation chemist is to compose the optimal formulation that would exhibit the best possible application properties. The formulation chemist has to balance the ingredients used so that the product is stable, easy to apply and functions as designed during manufacturing, on the shelf, during application, and after application. Therefore, characterization of the properties of the product throughout these phases is important and may eventually save time and resources in the search for the optimal formulation that would be appealing to the consumer. Whether it is a pharmaceutical formulation, paint, ink, food, or a cosmetic 287

2 Rheological Properties of Topical Formulations formulation, the desired combination of ingredients should provide the user with the most efficient way to use the product. This means the creation of a complex three-dimensional network structure that would retain the structure before the product is used, exhibit the proper flow when utilized, and recover the structure after the application. Rheology is the science that studies how materials deform and flow under the influence of external forces. The word, which derives from the Greek Rheo (= flow), was suggested by Markus Reiner and Eugene C. Bingham. 1 They formed a new scientific discipline and founded the Society of Rheology in Reiner and Bingham were inspired by a quotation attributed to the Greek philosopher Heraclitus: Everything Flows (in Greek: - Panta Rei; some sources attribute the quotation to Simplicius). Plato paraphrased this observation as Everything Changes and Nothing Stands Still. Actually, the study of flowing systems has been progressing long before the formal inception of the field of rheology in 1929: Archimedes (~250 BC) studied the behavior of rigid bodies; Hooke (1678) studied the behavior of elastic solids; Newton (1687) studied rigid bodies and Newtonian liquids; Stokes (1845) studied the motion of fluids and the movement of rigid bodies in viscous fluids; Maxwell (1867) and Boltzmann (1878) studied linear viscoelasticity; Einstein (1906) studied the behavior of suspensions; and Trouton (1906) studied Newtonian liquids and extensional viscosity. Many other scientists contributed over the years to the evolution of the field of rheology. Details of these and other contributions to the development of the scientific field of rheology may be found in several reviews. 2,3 Characterization of the rheological properties of the system is important not only in the design of the product and its application, but during its processing and to ensure long shelf-life. Consider the application of a skin care product: we use a product in a container where it is already under an external force, the gravitational force. We pick a portion to apply on the skin; this is another external force. We then rub it onto the skin, forcing it to flow so that it forms a thin layer. Then, we remove the external force, leaving the thin layer to regain its original structure under gravity. These requirements seem to be contradictory: we force the product to exhibit homogenous flow to cover the application area but then require that it stops flowing and remain in place. To demonstrate the flow patterns of different systems, think about the difference between spreading honey on a slice of bread and spreading mayonnaise on that same slice. Honey is thick and seems to resists the application, while mayonnaise becomes thin and spreads easily. However, if we apply honey and mayonnaise on pieces of wood and turn them vertically, allowing the samples to flow under gravity, honey starts flowing immediately, while mayonnaise does not flow. In this chapter, we explore the rheological changes that our formulations experience when subjected to external forces, how the deformation and flow of systems used are measured, how we can modify the flow of systems we use, and how the formulation chemist may improve the application properties of the product by characterizing the rheological properties of the system. This chapter will also discuss various instruments that are available to the formulation chemist to measure the 288

3 rheological properties of the system and the variety of rheological additives that are available to tailor its rheological properties. It will address typical questions that are frequently asked by formulation chemists, such as: We have several products that were formulated to have the same viscosity, so why do they behave so differently when we apply them? Our product settles/separates over time. How can we prevent it? We have two similar formulations. One regains its viscosity after application while the second formulation does not and continues to flow. Why does it happen and how can we fix it? To demonstrate the characterization of the rheological properties of skin care formulations, this chapter includes a discussion of a study in which a series of tests were performed on commercial products in order to differentiate their rheological attributes, aid in understanding their behavior, and assist in the redesign of their formulation. Rheological Measurements Flow Curves When we apply a topical formulation, the external force F deforms the product or causes the system to flow. Let us assume that the force F is applied to an area A as shown in Figure 1. Figure 1. Applying force to an area We define the shear stress (or pressure) σ as the force F over the area A: The units of the shear stress are Newtons per square meter (N/m 2 ) or Pascal (Pa). If the application of an external force results in the elongation of the system, such as stretching a rubber band, the material experiences shear strain. We define the shear strain as the change in length L= (L L 0 ) relative to the initial, un-deformed length L 0 of the material: The strain is dimensionless. The resistance of the material to the deformation, sometimes described as its stiffness, may be defined by the ratio between the shear stress and the shear strain, usually referred to as Young s modulus G: 289

4 Rheological Properties of Topical Formulations The units of the modulus are Newtons per square meter (N/m 2 ) or Pascal (Pa). If we plot the shear stress as a function of shear strain, the modulus G is represented by the tangent of the angle ( ) as shown in Figure 2. Figure 2. Shear stress as a function of shear strain We may visualize our product as a three-dimensional system that is made of many layers, occupying the space between two plates where the external force is forcing the plates to move in a certain direction (Figure 3). At rest, the material has a thickness X 0, length L 0 and width W 0. Assuming that the bottom plate is stationary, and the flow is laminar (i.e. the plates are sliding on top of each other, as opposed to a turbulent flow), the upper plate would be displaced by dl and the thickness by dx. Figure 3. Basic model for flow under an external force As a result, the system is moving in a speed (velocity) V. The shear rate is defined as the ratio between the change in velocity dv and the change in thickness dx: The units of the shear rate are (meter/second)/meter = 1/second or reciprocal second (s -1 ). If we mix a formulation with a laboratory mixer, for example, at a speed of 23 m/sec and the distance between the blade and the bottom of the beaker is 33 cm, the shear rate is 23/0.33 = /s. If we apply a cream on the skin at a speed of 25 cm/sec, forming a layer that is 75 microns thick, the shear rate is 3,333 1/s. Isaac Newton discovered that in certain fluids, the ratio between the shear stress and the shear rate is a constant

5 Fluids that exhibit a constant ratio of the shear stress to the shear rate are called ideal fluids or Newtonian fluids. Typical Newtonian fluids are water, various oils (such as olive oil and mineral oil) and most organic solvents. Newton defined the constant as the resistance which arises from the lack of slipperiness of the parts of the liquid, other things being equal, is proportional to the velocity with which the parts of the liquid are separated from one another. We refer to this resistance as the viscosity. The absolute viscosity is therefore defined as the ratio between the shear stress and the shear rate at any given experimental conditions (e.g., shear rate, temperature and pressure): = The units of viscosity are Pascal/1/sec or Pascal*sec (Pa.s). Sometimes, the viscosity is quoted in units of Poise. 1 Pascal*sec equals 10 Poise and correspondingly, 1 millipascal*sec equals 1 centipoise (cp). For ideal Newtonian fluids, the viscosity is constant at a given temperature and a given pressure and is independent of the change in shear rate. The viscosity of water at 20 o C and atmospheric pressure is 1 cp or 1 mpa.s. Table 1 summarizes the units of the rheological properties discussed thus far. Table 1. Units of rheological properties Property Units Conversion Stress Pascal (Pa), Newton/meter 2 (N/m 2 ) 1 Pa = 10 dyne/cm 2 Strain Dimensionless Shear Rate 1/second (1/s) Viscosity Pa.s, Poise 1000 millipa.s = 1 Pa.s 1 m Pa.s = 1 Centipoise (cp) 1 Pa.s = 10 Poise 1 Poise = 100 cp Modulus Pascal (Pa), Newton/meter 2 (N/m 2 ) 1 Pa = 10 dyne/cm 2 If we plot the shear stress as a function of shear rate for Newtonian fluids, the tangent represents the viscosity (Figure 4). If we plot the viscosity, instead of shear stress, as a function of shear rate for Newtonian fluids, it would show a straight line across the shear rate range (Figure 5). However, the viscosity of most fluid systems we use, including semi solid topical formulations, is not constant but changes with increasing shear rate. These fluids are called non-newtonian fluids. If the viscosity of the system decreases with increasing shear rate, we define the system as shear thinning. Figure 6 shows a flow profile of a non-newtonian fluid, in which the viscosity is plotted as a function of shear rate. If the viscosity of the system increases with increasing shear rate, we define the 291

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