Coefficient of Expansion-Contraction

Linear coefficient of expansion-contraction (k) can be determined by the following formula  

AL is the expansion or contraction (in inches, centimeters, or other appropriate units) of the given material over the temperature range of AT, and L is the initiaf length (width, depth) of the material in the beginning of the temperature range, the upper or the lower end. 

The above formula shows that the dimension of the coefficient of expansion-contraction is 1°F or °C, whichever was used for temperature measurements. 

The above formula can be used for calculations of expansion-contraction of, say, composite deck boards on a deck, however, with many reservations. Let us consider these reservations in some detail. This would represent one more examples of how carefully laboratory data should be applied to the real world. 

As a rule, coefficients of linear expansion-contraction are calculated based on measurements of length of samples/ree/y placed, that is, in completely unrestrained conditions, under carefully controlled temperature. Freely placed here means that they are under unrestricted temperature-driven movement. For example, for GeoDeck boards the temperature coefficient is equal to 3.58X10 1/°F. This followed from an experimental fact that a 2-in. long GeoDeck sample initially placed at 30°F became 12.17 mil (0.01217 in.) longer at 140°F. 

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As previously discussed, the coefficient of expansion/contraction for petroleum products is dependent upon specific gravity. As fuels cool, their volume will be reduced. 

For neat plastics, the CTE is about twice as much compared with WPC boards, which are about 50% filled with nonplastic materials, which is wood liber and sometimes minerals. As the coefficients of expansion-contraction of both wood fiber and minerals are about ten times lower than those for WPC materials, hence, the reduction in the coefficient s value for filled WPC. In reality, the picture is somewhat more complicated because it is the expansion-contraction of wood along the grain that is 10 times lower compared to common WPC. Expansion-contraction of wood across the grain is close to that of WPC. That is, an orientation of wood fiber in a WPC material can increase or decrease the coefficient of expansion-contraction. 

According to some other data the coefficient of expansion-contraction for HDPE is 8-11 X 10 1/°F, for LDPE 13.1 X lO 1/°F, and for homopolymer PP 3.8 5.8 X 10 1/°F. That is, PP-based profiles can thermally move more compared with PE-based ones. 

Thermal expansion-contraction of inorganic fillers is much lower compared with that of plastics. Therefore, the higher the filler content, the lower the coefficient of expansion-contraction of the composite material (see Chapter 10). Many inorganic nonmetallic fillers decrease thermal conductivity of the composite material. For example, compared with thermal conductivity of aluminum (204 W/deg Km) to that of talc is of 0.02, titanium dioxide of 0.065, glass fiber of 1, and calcium carbonate of 2-3. Therefore, nonmetallic mineral fillers are rather thermal insulators than thermal conductors. This property of the fillers effects flowability of filled plastics and plastic-based composite materials in the extruder. 

Wollastonite is not yet used in commercial WPC materials, but it is currently under investigation to further enhance the properties of WPCs. The mineral is used worldwide in many plastic applications providing improvement in stiffness, impact, scratch resistance, lower thermal coefficient of expansion-contraction, and flame retardancy. The unique morphology of wollastonite and the variety size grades available can provide benefits that are not obtained by other minerals. In a number of cases, wollastonite has successfully replaced talc in plastic applications where further improvements in properties such as greater strength and improved scratch resistance were required. 

Physical objects can be isotropic or anisotropic by their nature. Isotropic objects expand and contract equally in all directions. Anisotropic objects expand and contract differently in length, width, and/or depth. A piece of wood is anisotropic in terms of expansion-contraction as a result of orientation of cellulose fiber. That is why wood is characterized by three linear coefficients of expansion-contraction, of... 

SOME RESERVATIONS IN APPLICABILITY OF COEFFICIENTS OF EXPANSION-CONTRACTION... 

TABLE 10.3 Effect of short and long fiber (wheat straw) on the coefficient of expansion-contraction of a polypropylene-based composite in the —40 to +25°C temperature range [3]... 

Table 10.5 shows a collection of data on coefficients of expansion-contraction for WPCs, including commercially available ones, and for some neat plastic lumber boards, as references. 

Introducing zinc borate (in amounts up to 3% w/w) to a WPC formulation does not effect the flexural strength and slightly increases flexural modulus (stiffness) of the materials (Table 13.4), which is understandable, as ZnB is an inorganic material. Besides, zinc borate in this amount does not effect the water absorption, as well as the postmanufactured shrinkage and the coefficient of expansion-contraction (Table 13.5). 

Polyvinyl chloride (PVC) is the most widely used thermoplastic piping system. PVC is stronger and more rigid than the other thermoplastic materials. When specifying PVC thermoplastic piping systems particular attention must be paid to the high coefficient of expansion-contraction for these materials in addition to effects of temperature extremes on pressure rating, viscoelasticity, tensile creep, ductility, and brittleness. 

With the application of plastics in combination with other materials, the coefficient of expansion plays an important role in making design allowances for expansions (also contractions) of various materials at different temperatures so that satisfactory functions of products are ensured. 

Equations have been developed to estimate the total solids content of milk based on % fat and specific gravity (usually estimated using a lactometer). Such equations are empirical and suffer from a number of drawbacks for further discussion see Jenness and Patton (1959). The principal problem is the fact that the coefficient of expansion of milk fat is high and it contracts slowly on cooling and therefore the density of milk fat (Chapter 3) is not constant. Variations in the composition of milk fat and in the proportions of other milk constitiuents have less influence on these equations than the physical state of the fat. 

Empirical equations of the form T = aF + bD + c, expressing the relation between total solids (T), fat (F), and density (D), have been used for years. Such derivations assume constant values for the density of the fat and of the mixture of solids-not-fat which enter into the calculation of the coefficients (a, b, and c). Since milk fat has a high coefficient of expansion and contracts as it solidifies (note that the solid-liquid equilibrium is established slowly), the temperature of measurement and the previous history of the product must be controlled carefully (see Sharp and Hart 1936). Variations in the composition of... 

A third technique to produce tempered ware uses two glasses (or ceramics) formed together (laminated), each with different thermal coefficient of expansion. This is used to make Correll dishes by Coming. For this tableware, a pyrocer-amic material with one type of thermal coefficient of expansion is covered with another pyroceramic with a greater thermal coefficient of expansion and is then baked until the outer layer melts uniformly. Materials with greater thermal coefficients of expansion will expand more when heated and will contract more when cooled. The greater contraction (once cooled) of the outside material causes compression. 

Several determinations have been made of the expansion and contraction of ice with rise and fall of temperature, and the more important results for the coefficient of expansion are given in the accompanying table 3... 

Plastics can also be combined with other materials such as aluminum, steel, and wood to provide specific properties. Examples include extruded PVC/wood window frames and extruded plastic film/ aluminum-foil packaging material. All combinations may require that certain aspects of compatibility such as processing temperature, bondability, and coefficient of expansion or contraction exist. 

The various terms may now be interpreted as follows T(3Ss/3T)P r CP r is simply the heat capacity of the adsorbate at constant pressure and surface occupancy V - ns/As. The second term is the mechanical work involved in the expansion of Vs on heating here one may introduce a coefficient of expansion ap rVs (3V/3T)pr. For the third term we avail ourselves of the Maxwell relation in the series (5.2.VIII) of Table 5.2.1 T(3Ss/3P)t r — — T(3Vs/3T)p r — — TVsaP r once more this relates to mechanical work associated with an alteration of volume directly caused by pressure changes. The fourth term is related to the contraction of the adsorbate resulting from an increase in pressure this involves the compressibility / T rVs - — (3Vs/3P)t r. For a reformulation of the sixth term we introduce the Maxwell relation from Table 5.2.1, Section VIII T(dSs/dAs)T P>ris - T(d /3T)P r, relating to the temperature... 

Temperature gradients. These gradients produce cracks in rocks as a result of expansion-contraction cycles. The degree of expansion-contraction is dependent on the individual thermal expansion coefficients. Interestingly, it is believed that ancient civilizations took advantage of the expansion-contraction cycle of water/ice to split rocks apart for decorative and construction purposes. 

The various terms are interpreted as follows T(dSg/dT)p r represents the heat capacity, Cp r, of the adsorbate at constant pressure and surface occupancy r. The second term represents the mechanical work involved in the expansion of Vg on heating here the coefficient of expansion is relevant ap,r = V (dVg/dT)p r- In the third term we invoke the Maxwell relation that is specified in Eq. (5.2.8) of Table 5.2.1 T(dSg/dP)T,r = -T(dVg/dT)p r = —TVgap p, which again relates to mechanical work associated with the alteration of surface phase volume induced by pressure changes. The fourth term describes the contraction in volume of the surface phase due to the application of pressure. This effect is described by the isothermal compressibility fip.r = — V dVg/dP)T,r- The product —(pdAg obviously deals with the work of expanding the surface area. The sixth term is dealt with by use of the Maxwell relation from (5.2.8) from Table 5.2.1 T(dSg/dAg)T,p,ns = T d

temperature coefficient of the surface tension. We may therefore recast the above equation in the form... 

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