Comparison of Nucleation of Different Colored Parts Made from Polypropylene Using a Single Point, Dynamic Avrami Analysis James A Browne

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1 Comparison of Nucleation of Different Colored Parts Made from Polypropylene Using a Single Point, Dynamic Avrami Analysis James A Browne ABSTRACT Polypropylene is a very common polymer used for a variety of applications due to its versatility and cost. Nucleation agents are often added to polypropylene to improve cycle time, properties, and in the case of clarifiers, optical properties. Besides nucleation agents, other compounds will also affect the nucleation of polypropylene including fillers and some colorants. In addition, some compounds will adversely affect the performance of nucleators, and some colorants will nucleate β spherulites in polypropylene. This paper utilizes a single point dynamic Avrami analysis to obtain a cursory, but useful analysis of nucleation characteristics of different colored polypropylene marker caps purchased from an office supply store. INTRODUCTION DSC is a powerful tool for obtaining useful information from materials based on their response to change in temperature including phase changes and various kinetic events. The extent to which polymers have been characterized by DSC also allows one to sometimes obtain compositional information normally utilized in conjunction with other analytical techniques for identifying polymers. DSC is often used to characterize and compare polymers both as a means of determining initial processing parameters and as a diagnostics tool for investigating processing problems. One common problem in polymer processing is variations in cycle time between plastics that are known to be the same. Often the addition of color concentrates, fillers, additives and other plastics can affect cycle times and other processing parameters in plastic materials. The manner in which materials crystallize will have a profound effect on processing as well as mechanical properties. When variations in processing behavior are observed, often an initial response is to initiate a thorough compositional analysis which may or may not yield an explanation. In contrast, a simple DSC experiment can often demonstrate whether real processing differences exist between similar materials which may vary in subtle ways. One way to obtain more information from a simple DSC experiment is to integrate the crystallization curve and fit the resulting function using the Avrami equation. This type of experiment is done at a constant cooling rate so it is non isothermal, but the generated data can be converted to a time scale easily. This will result in a useful comparison of a crystallization half time, rate constant, and geometric exponent in addition to T C. This is an excellent way to compare two or more samples quickly to determine if there is a need for more extensive kinetic study. From a practical standpoint, it is an effective means to determine if two supposedly identical or similar materials potentially have different processing characteristics, or to confirm observation of differences between good and bad samples. Essentially, this is a single point dynamic or non isothermal crystallization experiment and some basic definitions must be made. TA381 1

2 The Non Isothermal Single Point Avrami Experiment Isothermal crystallization studies of plastics and other materials have been extensively documented in the literature and many use the famous Avrami equation to fit conversional data as a function of time. The Avrami Equation In the isothermal crystallization DSC experiment, the fraction crystallized as a function of time can be expressed by Equation 1. Equation 1 X ( t) = t t t t dh dt dh dt C C dt ΔH t = ΔH C dt where: X(t) is fraction crystallized at time (t). ΔH C = Overall heat of crystallization area under the crystallization curve of the DSC experiment. ΔH t = enthalpy of crystallization released during infinitesimal time range (dt). t = defined as the time at initial crystallization. t = times during crystallization process t = time when crystallization process is complete Equation 2 na X ( t) = 1 exp( k a t ) where X(t) = relative crystallinity as a function of time k a = Avrami Rate Constant (function of nucleation and crystal growth rate) n a = Avrami Exponent (function of growth geometry) t = time (seconds or minutes) The linear form of the Avrami equation is: Equation 3 log( ln(1 X ( t)) = log k + n a a logt A plot of the log ( ln(1 X(t)) versus log t is linear and yields the Avrami parameters k a (antilog of intercept) and n a (slope). The Avrami exponent correlates with the nucleation growth geometry and is summarized in Table 1. TA381 2

3 Table 1 Simplified Avrami Exponent Interpretation Avrami Exponent Growth Geometry 1 < n < 2 1 dimensional, rod like 2 < n < 3 2 dimensional, disc like 3 < n < 4 3 dimensional, spherulitic The Non Isothermal Crystallization Experiment The Avrami equation is used extensively in isothermal crystallization studies but is also used in non isothermal or dynamic crystallization studies. Contrasted with the isothermal method, non isothermal kinetic data is obtained by heating or cooling the sample at different rates. In this experiment, we compare Avrami parameters k A and n A which are the Avrami rate constant and nucleation exponent respectively. In the isothermal experiment, the polymer is held above its melt temperature and rapidly cooled to a temperature of interest (T C ) below its melting temperature. The time at which the sample reaches T C is t. As the sample cools, the resulting exotherm is plotted as a function of time, and the time at some point of conversion (crystallization) is recorded. Typically this is the peak of the exotherm, and the time difference between t and this time is usually referred to at the crystallization half time or t 1/2 assuming the exotherm is reasonably symmetric. Determining T C and t The non isothermal experiment does not choose T C or t in the same manner as the isothermal experiment. The crystallization temperature is a function of the cooling rate instead of being chosen by the user. One approach is to choose the peak temperature of the crystallization curve. However, the crystallization temperature may not be the value corresponding to X(t) =.5 or t 1/2 or some other fractional conversion it may be incorrect to assume symmetry in the curve. The value for t 1/2 normally can be calculated from the crystallization data using Equation 6 below or determined from Equation 1 (X(t) =.5). From this time, the corresponding temperature can be determined from the DSC instrument data. For this experiment t is obtained by defining it at some point of constant conversion arbitrarily 1%. Simply stated, t is the time at which X(t) =.1 (Equation 1). Once t is established, the linear form of the Avrami equation (Equation 3) is utilized to plot log( ln(1 X(t)) versus log t between the limits of X(t) =.2 and X(t) =.8. This will yield a straight line of slope n and intercept log k. From these Avrami parameters, calculate t 1/2 using Equation 6. The suggested limits of X(t) =.2 to.8 are not absolute rules. If the material crystallizes too quickly, these limits may not be linear. One alternative that appears to work well is to obtain the derivative of the heat flow curve with respect to time and choose the inflection points on either side of T C as the limits for X(t). Crystallization Fraction as a Function of Temperature X(T) An analogous expression for Equation 1 is shown in Equation 4 for fraction converted as a function of temperature. TA381 3

4 Equation 4 X ( T ) = T T dh dt C ΔH C dt where: X(T) is fraction crystallized at temperature T. ΔH C = Overall heat of crystallization area under the crystallization curve of the DSC experiment. dh C /dt = enthalpy of crystallization released during infinitesimal temperature range dt. This is obtained from a table of integral values generated by the DSC instrument software from the data obtained during the DSC experiment. This can also be generated manually from heat flow rate information from the DSC experiment. T = defined as the temperature at initial crystallization. T = temperatures during crystallization process T = Temperature when crystallization process is complete Equation 4 can be related to Equation 1 by using Equation 5 to convert the temperature dependent data to time dependent data and fit using the Avrami equation. Equation 5 T T t = φ where t = time in minutes or seconds T = temperature at crystallization onset T = Temperature(s) during crystallization process φ= cooling rate ( C / min) The linear form of the Avrami equation (Equation 3) is convenient to use in a spreadsheet program and typically gives a straight line in the limits of X(t) =.2 to.8. Non Isothermal Crystallization Half Time Because the cooling curve may not be symmetric, the peak crystallization temperature and the time at which half of the sample crystallizes may not occur simultaneously e.g. T C does not occur at X t =.5. The non isothermal half time can be calculated from derived Avrami parameters using Equation 6. Equation 6 t 1/ 2 ln 2 = k 1/ n TA381 4

5 Avrami Analysis of Polypropylene y = x R 2 = log(-ln(1-x(t)) log (t) -.7 Figure 1 Example of Avrami Analysis Using Linear Form from X(t) =.2 to X(t) =.8 The Effect of Color Concentrates on Polypropylene Nucleation A common problem that plastics suppliers face is that their products sometimes appear to process inconsistently. This experiment illustrates that potential differences in processing behavior can be detected using a simple DSC cooling experiment typically part of a routine heat cool re heat experiment. Resin suppliers often are not involved with compounding color concentrates or pigments into the final products this is typically done by the customer or other compounding service. Pigments, dyes, and fillers are known to affect the crystallization properties of polypropylene, and many additives used in the dispersal of pigments can affect the performance of processing aids added to polypropylene. One example is the effect of metal salts of fatty acids on nucleators like sodium benzoate. EXPERIMENTAL Samples Samples used were marker pen caps in various colors purchased from a local office supplier. They are most likely polypropylene and may or may not contain a chemical nucleator to decrease cycle time we do not have access to the formulation. Sample colors include black, red, yellow, brown, orange, green, blue, and purple. We also include a cap made from polypropylene containing no pigments as a reference. Instrument and Experimental Parameters 1) Instrument: TA Instruments Q2 DSC 2) Sample Mass: 5 mg nominal 3) Purge Gas: N 2 at 5 ml / minute TA381 5

6 4) Temperature and Heat Flow Calibration: Indium and sapphire standards 5) Method Samples were heated to 235 C to remove all thermal history and subsequently cooled at 1 C / minute to C. RESULTS & DISCUSSION Figure 2 shows an overlay of non isothermal crystallization exotherms. It is obvious that the different colored caps yield a substantially different array of exotherms of differing shapes, symmetries, and crystallization temperatures. Figure 3 shows the fraction crystallized as a function of temperature generated from Equation 4. Figure 4 shows the fraction crystallized after converting to time domain (Equation 6) and applying Equation 1. One obvious observation is that the sample with the highest crystallization temperature is not necessarily the fastest to crystallize. 4 3 Yellow Cap Black Cap Blue Cap Brown Cap Green Cap Orange Cap Purple Cap Red Cap Clear Cap Heat Flow (W/g) 2 1 Exo Up Temperature ( C) Universal V4.7A TA Instruments Figure 2 Non Isothermal Crystallization Exotherms for Cap Samples TA381 6

7 Non-Isothermal Conversion as Function of Temperature φ = 1 o C / minute Fraction Crystallized X(t) Blue Cap Brown Cap Orange Ca Black Cap Green Cap Red Cap Yellow Cap Purple Cap Clear Cap Temperature ( o C) Figure 3 Non Isothermal Crystallized Fraction as a Function of Temperature TA381 7

8 Non-Isothermal Conversion as Function of Time φ = 1 o C / minute 1.9 t = X(t) =.1.8 Fraction Crystallized X(t) Blue Cap Brown Cap Orange Cap Black Cap Green Cap Red Cap Yellow Cap Purple Cap Clear Cap Time (min) Results and Discussion Figure 4 Fraction Crystallized as Function of Time The single point Avrami analysis is summarized in Table 2 and Figure 5. It is obvious that each color part has very different crystallization characteristics compared with each other and the reference (no colorant) polypropylene sample. We have no way of confirming the formulations used in the polypropylene resin or any changes made by compounders, but presumably the base resin is made from the same formulation. The Avrami exponent n is related to the nucleation geometry. It does not hold exactly the same meaning as in the isothermal experiment, but can be used to compare similar samples. The different values for n observed in the samples indicate that the materials crystallize differently and would likely have different physical properties. Typically commercial nucleators tend to yield values close to 2 in polypropylene while values close to 3 are observed in samples that do not contain a chemical nucleator. Each of the samples has a rate constant k that is substantially higher than the sample with no colorant. One interesting observation is that the yellow sample crystallizes fastest, but has a significantly lower value of T C than the purple sample which has the highest T C. The black and brown samples have the most similar value of n to the sample with no colorant, although both crystallize significantly faster. The brown sample also has a similar T C to the non colorant sample. TA381 8

9 Table 2 Summary of Single Point Avrami Analysis Sample T C C n k t 1/2 (min) τ (Reciprocal half timemin 1 ) Red Brown Black Purple Blue Orange Green Yellow No Colorant Avrami Fit (X(t).2 to.8).1 log(-ln(1-x(t)) Black Cap -.1 Blue Cap Yellow Cap -.2 Red Cap Purple Cap -.3 Brown Cap Green Cap -.4 Orange Cap Clear Cap log (t) -.8 Figure 5 Avrami Comparison of Colored Pen Caps TA381 9

10 CONCLUSIONS 1) A simple heat / cool experiment can yield significant information when comparing similar polymers by applying a simple, well established mathematical treatment to the crystallization data. The quality of the data is dependent upon the quality of the baseline. The Q2 DSC offers superior performance in this area. 2) The samples analyzed in the experiment above yield varying Avrami parameters and will likely process differently. It is likely that adjustments to the processing equipment have to be made based on the results assuming the resin formulations are the same and the differences observed are caused by the colorants or the additives in the color concentrates. 3) For polypropylene parts the effect of additives, pigments, fillers, etc. on the crystallization performance can be compared with a single point Avrami analysis as well as useful diagnostics of processing problems and predicting optimal process conditions. 4) The single point non isothermal experiment offers a convenient way of comparing materials that may exhibit different processing characteristics using a common heating rate. The data will not have the same meaning as an isothermal crystallization experiment, but is useful in comparing different samples of the same resin that exhibit different processing traits. REFERENCES 1) Razavi Nouri, Mohammad, Iranian Polymer Journal, 18 (2), 29, ) Maria Laura Di Lorenzo, Sossio Cimmino, and Clara Silvestre, Macromolecules 2, 33, ) Minqiao Ren,1 Jianbin Song,1 Qingxiang Zhao,2 Yuesheng Li,1 Qingyong Chen,1; Polym Int 53: (24) 1) Hongfang Zhang1 and Zhishen Mo1Pakin Thanomkiata, Duangdao Aht ongb, Pitt Supaphol, Polymer Testing 24 (25) ) P. Supaphol, J. Appl. Polym. Sci. 78 (2) 338 3) Q.X. Zhang, Z.H. Zhang, H.F. Zhang, Z.S. Mo, J. Polym. Sci. Polym. Phys. 4 (22) ) P. Supaphol, P. Thanomkiat, R.A. Phillips, Polym. Test 23 (24) ) Oct. 1, 23 Vol.5 No.1 P.81 Gao Jungang, Li Shurun, Li Zhiting Jiann Wen Huang, Ching Chih Chang, Chiun Chia Kang, Mou Yung Yeh; Thermochimica Acta 468 (28) TA381 1

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