ES2575653T3 - System and methods to determine a virtual density of a polymer - Google Patents

Description

System and methods to determine a virtual density of a polymer

Field of the invention

The present invention relates in general to the characterization of polymers as applied to the development of resins, and more particularly to the prediction of the virtual density of a polymer or various virtual polymer properties related to density as a means to design resins. for particular end-use applications that require various mechanical and physical properties.

Background

This section is intended to provide background information to facilitate a better understanding of the various aspects of the present invention. Consequently, these statements must be read in this context and not as admissions of the previous technique.

The development of polimerization techniques has resulted in the annual production of more than 280,000 million pounds, worldwide, of numerous polymers that are incorporated into various end-use products. Polyolefins, nylon, poly (styrene), poly (ester), poly (vinyl alcohol) (PVC) and polyurethanes are some of the polymers that are incorporated into products that can be used for retail and pharmaceutical packaging, food packaging and beverages, domestic and industrial containers, household appliances, furniture, carpets, automobile components, pipes, drums, fuel tanks, geomembranes, conduits, and various other industrial and consumer products.

the polymers are formed by linking small molecules (monomers) in chains during polymerization when the monomers are chemically bound to other monomers to form poly mer chains. If a single type of monomer is polymerized, the polymer is called a homopolymer. the polymerization of a mixture of two or more different monomers leads to the formation of a copolymer, wherein the two monomers have entered the chain. the polymerization may occur in any suitable polymerization reactor including, but not limited to, a liquid phase reactor, a loop reactor for suspensions, or a gas phase reactor.

The polymers are chemically described by the degree of polymerization, molecular weight (MW), molecular weight distribution (MWO), polydispersity index (POI), short chain branching (SGB) due to the distribution of copolymers, the degree of branch and distribution of SGB (SeBO), crystallinity and thermal properties.

During polymerization the molecules of a polymer can grow to different sizes, which results in a polymeric MW that is actually an average of the variation of the weights of the chain molecules. For example, the MW of the poly (ethylene) is usually expressed as the weight-average molecular weight (Mw) or as the number-average molecular weight (Mn). You can define Mn as the total weight of all molecules divided by the number of molecules. Mathematically, Mn is defined as indicated below, where Mi is the molecular weight in a particular mole fraction (xi) or weight (wi).

IV

If the weight of each MW species is taken into account instead of the number of molecules of a particular weight as with Mn, the weight average molecular weight Mw is used to describe the MWD of the polymer. The Mw is the sum of the total weights multiplied by their respective weights divided by the total weight of all the molecules. Mathematically, Mw is expressed as indicated below, where M; is the molecular weight in a particular molar fraction (xi) or weight (wi).

L, x¡M; L, II'¡M¡

Mw = Lx, .M, L II'¡

The MW significantly affects the behavior properties of a polymer. For example in polyolefins, as the Mw increases the viscosity of the melt, tensile strength, impact resistance and resistance to cracking due to environmental stresses increases, while the flow rate decreases. The Mw can be measured by various methods, including the dispersion of light by solutions and gel permeation chromatography (GPC).

The MWO in a polymer describes the relationship between the number of molecules of each polymer and the MW. A polymer normally consists of a molecular size distribution because the growth of the chain varies in the polymerization time interval and the way in which the monomers join the chain. Different types of polymerization processes and the use of different catalysts will lead to different types of MWD. the way

The MWO curve can be wide or narrow and can have one or more peaks. The MWO can be determined by GPe and by various fractionation techniques including selective dissolution.

The ratio of Mw to Mn is called the polydispersity index (POI) and can be used to express the width or amplitude of the MWO. The amplitude of the curve increases as the POI number increases. The POI has a value always greater than 1, but as the polymeric chains approach a uniform chain length the POI approaches unity.

As the polymer chains develop, they may be arranged in an orderly manner in which the polymer is crystalline, or they may form an interlaced structure that results in an amorphous polymer. Most polymers are semi-crystalline, which means they contain both crystalline and amorphous regions. Virtually amorphous polymers will be less dense than practically crystalline polymers. The density of the polymer will increase with the increase in crystallinity and decrease as the crystallinity decreases.

the polymeric architecture refers to the physical arrangement of the monomers along the main chain. The simplest architecture is a linear chain, a single main chain with no branches. Branches may be long chain branches or short chain branches. The size and length of the branches affect the physical properties of the polymer. For example, polymers with the same Mw will have different properties. depending on the type and number of branches. The copolymers have SGB that can be arranged along the main chain in a variety of forms of SeBO. SeB makes crystalline development difficult and lower crystallinity manifests itself in lower density. As the density changes with the number and type of branching, the physical properties are affected. For example, as density increases, tensile strength, stiffness and hardness increase, while elongation, resistance to cracking due to environmental stresses and permeability decrease. Therefore, density is an important property of polymers.

Manufacturers try to design resins to meet the specifications for various physical and mechanical properties by adjusting the conditions within the polymerization reactor, selecting the type of catalyst or cocatalyst used for the polymerization reaction, or making or mixing resins with additives or other resins. Traditionally, in order to determine a value of a desired physical or chemical property, a certain amount of the particular polymer resin was needed to make an article or a test sample, and then the resulting article or test sample was subsequently tested by means of the prescribed test analytical procedure to determine the value of the property. This procedure is cumbersome not only due to the time required for manufacturing, but also to the time required to perform the respective test analytical procedure. In addition, the traditional method, depending on the particular test, could require large amounts of polymer, often more than could be produced in the small-scale research laboratory or pilot plant apparatus.

Therefore, there is a need for methods to virtually determine a value of a desired polymer property without making samples or performing the analytical test for physical or chemical property.

US 2007/298508 discloses various methods for determining values of physical or chemical properties of polymers. In these methods, at least two polymeric training samples are provided. The characteristics of the polymeric microstructures of the test samples are correlated with values of physical or chemical properties of the training samples. These correlations are subsequently applied to the respective characteristics of the test polymer samples in order to determine the physical or chemical properties of the test samples.

US 6632680 relates to a method for determining the short chain branching ratio in a current olefin copolymer process. The short chain branching can also be determined as a function of the molecular weight in a sample having a range of molecular weights. In the method, at least two samples of olefinic training copolymer are provided. The respective samples have different known ratios of short chain branching. The infrared absorption spectra (for example FT-IR) of the training samples are obtained in a range of wave numbers. The calibration information is determined from the training samples by chemometrically correlating the differences in the infrared absorption spectra of the training samples with the differences in the short chain branching in the training samples. This step generates calibration information that allows the degree of short chain branching in a sample to be determined once its infrared absorption spectrum is obtained.

J. C. Majesle al. , Rheol Acta, vol. 37, December 31, 1998, pages 486-499, describes the viscoelalicity of non-interlaced low molecular weight polymers in poly (styrene) melts and the transition to the interlacing regime.

Brief summary of the invention

The present invention describes methods for determining a virtual property of a polymer wherein the property of the polymer is related to the microstructure of the polymer. Oiverse aspects of the invention

they include the determination of virtual density values using algorithms or equations that relate to the MW, MWD, and SGS of the polymer. In some aspects, software applications perform the analysis and in other aspects the software is included in systems that analyze the data and indicate the results.

According to the invention, a method as defined in appended claim 1 is provided.

Also described herein is a method in which a virtual density of a polymer is determined by relating the density of a polymer to the MW and profile of the MWD of the polymer. This method for determining a virtual density of a polymer comprises:

a) determining a plurality of density values as a function of a molecular weight (MW) and a molecular weight distribution profile (MWD) of the polymer wherein each value of the plurality of density values is determined at a different location of MW through the profile of the MWD; Y

b) add the plurality of density values to obtain the virtual density; wherein MW and MWD comprise data obtained as measured properties, data provided as a digitally determined value, data obtained by fitting to a curve the data obtained as measured properties, data provided as an arbitrarily assigned value or a combination thereof.

In another method described in this specification MW, MWD and SGB are used to determine a virtual density and are applicable to copolymers. This method for determining a virtual density of a polymer having short chain branches (SGS) comprises:

a) determining a plurality of density values as a function of a molecular weight (MW) and a molecular weight distribution profile (MWD) of the polymer wherein each value of the plurality of density values is determined at a different location of MW through the profile of the MWD; Y

b) adjusting the plurality of density values for a contribution of the SGB to the density suppression to obtain an adjusted density value; Y

c) add the adjusted density values to obtain a virtual density; wherein the SGS, MW and MWD comprise data obtained as measured properties, data provided as a digitally determined value, data obtained by fitting to a curve the data obtained as measured properties, data provided as an arbitrarily assigned value or a combination thereof .

A further method uses algorithms or equations of the invention to determine a virtual density of a polymer using ratios of MW and MWD with density. In this aspect, a method for determining a virtual density of a polymer comprises:

a) determine a calculated value of the density for each molecular weight (MW) through a molecular weight distribution profile of the polymer using an equation:

p = [a-bLogM]

to obtain a plurality of calculated density values;

where the coefficients a and b are determined by a least-squares adjustment to a data series of 109M and measured density values; and b) adding the plurality of density values calculated from step a) using an equation:

1 / p = ¿(lI ', IP.) = F'¡'C' ~~ 'A /) d log M

where: p = [a -bLogM]

to obtain the virtual density;

wherein the MW and the MWD comprise data obtained as measured properties, data provided as a digitally determined value, data obtained by fitting to a curve the data obtained as measured properties, data provided as an arbitrarily assigned value or a combination thereof.

A further method using equations of the invention also includes SGS and PDI of the polymer so that the density suppression due to SGB in copolymers is taken into account. A method for determining a virtual density of a polymer having short chain branching (SGS) comprises:

a) determine a calculated value of the density for each molecular weight (MW) through a molecular weight distribution profile of the polymer using an equation:

p ~ [a-bLogM]

to obtain a plurality of calculated density values;

where the coefficients a and b are determined by a least-squares adjustment to a data series of 109M and measured density values; Y

b) correlating a deletion of the plurality of calculated density values with an incorporation of SGB in relation to a POI of the polymer using an equation:

to obtain a change in density; wherein the coefficients n and G, -4 are determined from the fit data to a curve as measured properties; Y

c) calculate the virtual density using an equation:

where p = [the results in stage a) minus [the results in stage b); Y

where the MW, MWO, SGB, and POI comprise data obtained as measured properties, data provided as a digitally determined value, data obtained by fitting to a curve the data obtained as measured properties, data provided as an arbitrarily assigned value or a combination of the same.

Virtual polymer properties can be determined for the properties that are related to the density and microstructure of the polymer. Such a method can be used to design resins that impart specific properties to end-use products. A method for determining a value of a virtual property of a polymer comprises: selecting a property related to a polymer density and constructing a calibration curve based on measured density data and measured data of polymer property; and using the calibration curve to calculate the property value at each molecular weight point through a molecular weight distribution profile of the polymer to obtain a plurality of calculated values of the property; and add the calculated values of the property to obtain the value of the virtual property of the number; wherein the MW and the MWO comprise data obtained by fitting to a curve data obtained as measured properties, data provided as an arbitrarily assigned value or a combination thereof. Property values related to density may include, but are not limited to, the crystallinity, melting point, natural stretch ratio, Young's modulus, yield point or a combination thereof.

The polymer architecture data for the MW, MWO, and SGB can be obtained from SEC, GPG, SEG / FTIR, NMR or any other analysis method or system capable of providing the data. In one aspect, MWO distribution profiles from Schultz-Flory are used to provide MWO data.

The various aspects of the present invention are suitable for semicrystalline polymers and especially olefinic polymers. Poly (ethylene) is an olefinic polymer that was used as an example to demonstrate the present invention and provided consistent results for polymers having a density in the range of about 0.906 g / cm3 to about 1.01 g / cm3. The polymer can be a homopolymer or copolymer with mono-modal or bimodal architecture or a mixture of homopolymers, copolymers or a combination thereof. The poly (ethylene) serves as an example for purposes of describing the invention. Monomers that can be copolymerized with ethylene can typically have from three to about 20 carbon atoms in their molecular chain. Non-limiting examples of these monomers include 1-butene, 1-pentane, 1-hexene, 1-octene, 1-decene, O-styrene.

In another aspect of the invention, any of the method steps may be performed by a software application. In addition, the software application can be associated with a system capable of accepting data and calculating a result. Such a system may be contained in a unit, may comprise several modules linked together, or the methods may be carried out in separate modules and then combined for a result. For example, the method can be performed in association with a real-time or step polymerization reactor. Or the various methods can be performed on separate instrumentation devices and then the results for a final analysis combined. In another aspect, the methods can be performed in a system designed to measure or accept data and perform analyzes, then calculate the results.

Description of the drawings

Figure 1 represents a plot of density versus Log Mw.

Figure 2 illustrates a calibration curve used to estimate equilibrium densities.

Figure 3 represents the MWD for physical mixtures of two narrow MWD metallocene samples. (DMTE B).

Figure 4 represents the homopolymer density calculated as a function of the molecular weight distribution compared to the measured density.

Figure 5 represents comparisons of MWo for normal logarithmic synthetic distributions (Mw = 150 kg / mol).

Figure 6 shows examples of narrow molecular weight distributions.

Figure 7 shows examples of average molecular weight distributions.

Figure 8 shows examples of broad molecular weight distributions.

Figure 9 represents the fitting to a quadratic polynomial of the homopolymer density as a function of linear and quadratic terms in both Mw and POI.

Figure 10 shows the goodness of the fit calculated for quadratic and ANOVA polynomial data.

Figure 11 shows the inverted profile of SoB for sample MTE-16.

Figure 12 represents inverted profiles of SCB for bimodal samples of BM ZN-1 (data in blue) and oMTE-2 (data in red). The data circles are levels of SCB through the MWOs. The sample oMTE-1 is not represented, but it has a SCBO similar to oMTE-2. However, the OMTE-1 sample has less separation between SCB levels at low MW and high MW compared to OMTE-2.

Figure 13 shows the change in density (homopolymer versus copolymer) by SCB as the level of SCB increases in samples catalyzed by metallocenes.

Figure 14 demonstrates the influence of SCB and MWO on the density change observed for samples of Table 5A catalyzed by metallocenes of POI 2.3 (filled circles in black) and samples of Table 5B catalyzed by Ziegler Natta of POI 4 , 9 at comparable levels of SCB.

Figure 15 demonstrates the influence of SCB and MWO on the density change observed for samples catalyzed by metallocenes (filled circles in black), Ziegler Natta (open circles), and chromium (triangles).

Figure 16 shows the goodness of the adjustment graph for the density values indicated in Table 7. It represents the SCB / POIIl graphs versus the density changes calculated for the samples given in Tables 5A to 50, where the points Data were shifted to the left using a value of 0.32 for the POI exponent.

Figure 17 represents the density differences calculated from Eq. 4 as indicated in Table 6A through 60. The data points are given as symbols and the adjusted data using Eq. 4 are given as a solid line. The value for the exponent n of the POI was equal to 0.318975556. The goodness of the fit graph for the measured density change and that calculated using this algorithm shows a value of R2 of 0.9918 and demonstrates that the algorithm can be used to reasonably estimate this value.

Figure 18 shows the goodness of the adjustment graph for the density values indicated in Table 7.

Figure 19 shows a wide Gaussian MWO (POI = 14) where the slope is systematically changed to give an inverted SeBO,

Figure 20 a MWo adjusted from SEC-FTIR data for a bimodal polymer ZN. Seven SFos were used to adjust the experimental data.

Figure 21 shows SEC-FTIR data adjusted for a bimodal polymer ZN. The density measured for this sample is 0.948 g / cm3 and the density calculated is 0.950 g / cm3. Quantities of weight fractions of SCB (4.2 SCB / 1000 CT maximum) were added to the peak of homopolymer SFOs in order to match the experimental SCBo.

Figure 22 demonstrates the fit of predicted and experimental points in equation 5.

Figure 23 demonstrates the empirical calibration curve (solid line) that relates the density values to the melting points compared to the respective values indicated in the references cited. Assigned values of 20 ° C and 142.5 ° C were given for density values of 0.852 g / cm3 and 1.01 g / cm3, respectively (see detailed description).

Figure 24 demonstrates that the crystallinity values obtained from both WAX (black open circles) and density measurements (blue open circles) for poly (ethylene) samples as described by Stadler (epolymers 2009, not 040) are compared to the values calculated as described in the text. Also shown are data of crystallinity described by Mirabella (Joumal of Polymer $ cience, Part B: PoIymer Physics 2002, 40, 1637) obtained both from DSC (open triangles) and from XRO measurements (solid triangles) and compared with the calculated values. Finally, the data described by Bartczak (Polymer 2005, 46, 8210) obtained from ose (solid diamonds) and density measurements (open squares) are also shown and compared with the values calculated within ± 0.05. The dotted lines in this graph denote the deviation of ± 0.05 away from the ideal 1 to 1 correlation indicated as the solid line (in red).

Figure 25 demonstrates the direct relationship between density and crystallinity in weight fraction.

Figure 26 demonstrates the procedure for the PSP2 calculations and the typical data obtained.

Figure 27 demonstrates the calculated values of PSP2 to estimate a natural stretch ratio (NOR) of the sample using PSP values and the correlation graph.

Figure 28 illustrates the 5 equations.

Definitions

The following definitions are provided to help understand the detailed description of the present invention.

rNV / d Log M means the fraction of the Weight.

FTIR means infrared spectrophotometry of Fourier transform.

GPC means gel permeation chromatography.

MW means molecular weight.

MWO means molecular weight distribution. Mn is the average numerical MW. Mw is the weighted average MW. TREF means fractionation by elution with increasing temperature. SEC means size exclusion chromatography. NMR is nuclear magnetic resonance. The calculated density is used interchangeably with the virtual density, predicted density, or density

Dear. The calculated density is determined by calculation or methods other than the actual measurement of the property. The calculated density is a virtual density that is predicted from the ratio of the density to the micro-structure of a polymer.

Algorithms are used interchangeably with the term "equations" to refer to the developed equations

for various aspects of the invention. Experimental means the actual measurement of a property of a polymer; Expressions can also be used "experimental measure" or "measured property".

Digital or synthetic data - SECIFTIR, GPC, NMR data or a combination. seB-branching or short chain branching. seBO -distribution of short chain branches or the number of SeB per 1000 carbon atoms in each

MWa through the profile of the MWD of a polymer. Polymer and resin can be used interchangeably. Micro-polymer architecture, microstructures, or polymer architecture mean the quantity and distribution of

main structures of a polymer such as MW, MWO, SeB and SeBO. The global polymer refers to the composite material through sludges the MW and SCB levels of a polymer.

55 E1 0742966

Detailed description

The methods of the present invention are applicable to all classes of semicrystalline polymers that demonstrate correlation between the MW and any structural entity in the polymer that is to interrupt crystallization. For ease of understanding, polyolefin polymers are used as a non-limiting example to describe the various aspects of the invention, in particular homopolymers and copolymers of poly (ethylene). Although the inventions are described in terms of "comprising" various steps or elements, the inventions may also consist essentially of "or" consisting of "various stages or elements. It is understood that the present invention is not limited to the aspects and examples described herein, and that the present invention includes all alternatives, modifications, and equivalents that may be included within the spirit and scope of the specification and claims that follow .

Differences in the polymer microstructure, such as the MW, MWO profile, SCB, and the SCBO of a given polymer, can influence the resulting properties of that polymer and are useful in determining the properties of the polymer. For the purposes of the invention, data for these microstructural components can be provided as data obtained from the experimental measurement in real samples. You can also provide data as digitally assigned values that are selected arbitrarily. In addition, the adjustment of data curves of real measurements, or any combination of the above, can be used. For example, the experimental measurement data may comprise data obtained from measuring the microstructures of the polymers with any suitable technology including, but not limited to, nuclear magnetic resonance (NMR), gel penetration chromatography (GPC). ), size exclusion chromatography (SEC), elution fractionation with temperature increase (TREF), FTIR or any combination thereof. In addition, digitally assigned values can be provided that comprise an arbitrary value based on certain assumptions. For example, a certain MWD value can be provided to estimate other properties needed in a resin having the same properties as those known to come from resins with that MWO profile.

The MWO profile of a polymer can be provided by any suitable method and instrumentation. A non-limiting example of an analytical technique for determining the MWO profile of a polymer is the SEC or GPC. By nature, as used in this description, the MWO profile of a polymer can provide, among other data, the MWO and weight fraction data associated with each MW, including common terms useful in the art such as Mw and Mn. .

Similarly, the SCB and SCBO of a polymer can be provided by any suitable method and instrumentation. The techniques could include, but are not limited to, TREF, NMR, SEC-IR and SEC-FTIR. By nature, as used in this disclosure, the SCBO of a polymer can provide the number of SCBs per 1000 carbon atoms in each MW through the MWD profile.

One method to provide both the MWD profile and the SCBO of a polymer is SEC-FTIR using analysis

or experimental measurement, for example as described in U.S. Pat. No. 6,632,680 and U.S. Pat. No. 7,056,744 whose descriptions are incorporated by reference in their entirety herein. An advantage of the SEC-FTIR when referring to the methods of the present invention is the small amount of the polymeric training samples that are required for the analysis to determine the profile of the MWD and the SCBO.

The composite density of a polymer can be determined by any suitable method and instrumentation. Analytical techniques include, but are not limited to, refractive index, pycnometer for density column by ASTM test methods and any other ASTM test methods for density. The composite density of the resin is the density of the polymer as a whole, across all molecular weights and SCB levels.

The density of a polymer is important because many desirable physical and mechanical properties of a polymer end-use product are related to the density of the polymer. In addition, the density of a polymer is related to the microstructure of the polymer, such as MW, MWO, SGB, and BD. If the polymer density is controlled during the polymerization, various desirable properties can be obtained in the end-use product manufactured from the polymer.

For example, the density of a poly (ethylene) polymer can typically be controlled by varying the amount of short chain branching (SCB) in the polymer by copolymerizing ethylene with an alpha-olefin such as 1-butene, 1-hexene, or 1-octene. . The resulting copolymers have bulky side chains or short chain branching (SGB) that do not easily fit into the crystal structure of the polymer and form an amorphous region around and between crystallites. Branching controls crystallization because the size (thickness) of a crystalline layer is greatly influenced by the distance between these short chain branches. As the branching grows the crystallinity decreases and influences the density because the less crystalline the polymer, the less dense it is.

Because poly (ethylene) has both crystalline and amorphous regions, it is semi-crystalline and is often modeled as a two-phase material that is characterized by some weight fraction of crystalline material that

55 E1 0742966

it has a density of about 1.01 g / cm ~ and the remaining weight fraction of amorphous material having a density of about 0.852 g / cm3 at room temperature.

the average density of poly (ethylene) polymers is affected by the MW in addition to the amount of short chain branching (SCB) and to a lesser extent (ie, changes in successive significant figures) by the distribution of the SCB in the polymer. However, although homopolymers do not have SGB formed by the introduction of a co-monomer during polymerization, they are also semicrystalline because they have both crystalline and amorphous regions. One reason for this is that the chains of polymeric molecules intertwine with each other and at the "crossing" points of the chains the interlaced molecules do not fit into the crystal structure, thus contributing to the amorphous content of the polymer. the long chains of homopolymers have many such interlacing, and one would expect morfa material contributed by long chains.

In addition to the MVV, the density of a homopolymer is also a function of the shape of the MVVD of the polymer, and to estimate these effects the global profile of the MVVD is needed on a base of MW segments. Simply taking MW averages or their ratios (such as PDI values) will explain at best only approximately the effects of MWD on the homopolymer density. In addition to the effect of MW and MWD seen in a homopolymer, the density of a copolymer is affected by the presence of SCB.

Various aspects of the invention comprise methods, algorithms or equations, instrumentation, systems and software that estimate or calculate the effects of MVV, MWO, SBC and SCBO on the average density of poly (ethylene) resins. The quantities and distributions of these primary polymeric structures can be acquired experimentally from size exclusion chromatography (SEC) together with infrared Fourier Transfrontier (FTIR) spectroscopy (FTIR) online. Using SEC-FTIR data and developed algorithms, mean polymer density values for a variety of poly (ethylene) resins with different micropolymer architectures were calculated and compared to the measured density obtained using ASTM methods.

In one aspect of the invention, an equation was developed to quantify the effect of MVV on density. Using a group of homopolymers with known crystallinity and crystallization behavior, the density was determined as a function of the molecular weight log (lag M). density was plotted against log M Y showed a linear relationship up to lag M = 2,856 which represents a molecular weight of about 720 g / mol. All MW less than about 720 g / mol were assigned a density equal to 1.01 g / cm3. The density dependence of poly (ethylene) (slowly cooled) of the molecular weight effects was demonstrated and adequately captured using the developed equation. Using a number of homopolymer resins with various architectures we discovered that we could determine the density within ± 0.002 g / cm3 for the entire polymer using the weight fraction (dW / dlog M) versus log M values obtained from profiles of Dry

In another aspect of the invention, the effect of the MWD was determined and an equation was developed. In addition to the molecular weight, the density of a homopolymer is also a function of the shape of the MWD of the polymer, and the entire profile of the MWD on a segment-by-segment basis of MW is necessary to estimate these effects. Simply taking the molecular weight means or their ratios (such as PDI values) will explain at best only approximately the effects of the MWD on the homopolymer density. We compare the density change with the MW using a GPC curve in bell form. For each area under the curve that is equal to 1, all pieces added together must be equal to 1. Therefore, if the MW is determined for each segment that is measured, then the MW determines the density for each segment. When all the fractions are added, density is calculated for the entire polymer. An equation was developed to provide this function.

In another aspect, a calibration curve was invented to give the best fit of the coefficients a and b of the equation a + b (LogM) over the entire MWO for a set of calibration samples using the Solver function in Excel®. For example, SEC MWD data, from a particular sample, were placed in two columns, one containing all Log M values and the other the respective dw / dlog m values associated with a particular log M value. In a third column the values were placed for the product of (a + b (LogM »times the values of dw / log m for each value of lag M. the sum of the values of this last column gives the specific volume calculated for the polymer (ie, 1 / p), whose inverse is the predicted density of the polymer.A single set of values of a and b were determined and used in this third column so that the squared difference between the predicted or calculated density and the The known density of this particular sample was minimized using the Excel® Solver program.If more than one sample is being considered, this process can be performed simultaneously.For example, if two samples are used, a single set of values a and b would be determined by minimizing the unlike

square between the predicted densities and the known densities of both samples using the Excel® Solver program. In addition, if 10 or more samples are used, a single set of values of a and b would be determined by minimizing the squared difference between the predicted densities and the known densities of the 10 or more samples using the Excel® Solver program. As described herein, the values for a and b were varied until the squared density residues for the 10 or more samples are collectively minimized.

In another aspect, methods and equations were invented to determine the effect of the SCB on the suppression of density above that produced with the MW. If the density of a copolymer is calculated using the inventive techniques of the present invention, the structure of the copolymer must be considered because the copolymers have SCB and the polymers with more SCB have more disruption of crystallinity and lower density. Therefore, a second equation was invented to allow the suppression of homopolymer density with the incorporation of SCB. The data used comprised data mostly of SCB (both of NMR and FTIR) and polydispersity values of SEC (MwlMn) for a variety of 1-hexene copolymer samples with various architectures. It follows that the difference between copolymer density and homopolymer density is due to branching and this can be used to calculate the density of the copolymer. This change in density with the level of SCB was quantified by running tests on all types of poly (ethylene) resins because the amount of difference induced at a particular SCB level varies with the MWD of the polymer. You can test resins produced with metallocene catalysts, Ziegler Natta and chromium bimodal resins. The relationship between the term SCB normalized with respect to the MWO (ie, SCBIPOln) and the suppression of density above that which occurs with the MW, was quantified by fitting the data to a curve with an equation so that a universal curve for different MWO resins. The predicted results correlate well with the measured results (R2 = 0.9918) up to a SCB level of 0.1 SCBff1000 CT. The densities for a variety of poly (ethylene) copolymers with densities ranging from 0.880 to 0.967 g / cm3 were calculated within an average value of ± 0.002 g / cm3. The slopes of SCBO in the tested resins did not seem to influence the change in density, as calculated in three significant figures.

In another aspect, the accuracy of the algorithms used for the methods of the invention was tested. To demonstrate the accuracy of calculated or virtual density, the ASTM measured density values of the resins were compared to the calculated values and goodness of fit graph was used. However, any method can be used to show statistical discrepancy, such as standard deviation, fit, or R-square determination.

In another aspect, MWO and SCBO data acquired from SEC-FTIR were also used to estimate the overall polymer density by using peak adjustment techniques and the equations of the invention. Virtual density results can be obtained using this approach even for complex MWO and SCBO profiles such as bimodal and multimodal systems.

In additional aspects, arbitrary values were assigned for the MW, MWO and SCB to calculate the virtual density needed to produce resins with selected or desired properties that are density dependent. Given the ability to predict the density of any combination of MWO and SeBO, various structures can now be digitally evaluated for their potential application in a particular line of products. In addition, by selecting peaks with POls similar to those found in a particular type of resin, for example metallocene-catalyzed resins, there is the possibility of producing real resins through physical mixture that correspond to digitally constructed resins that comprise particular MW and SeBo distributions. These aspects may include the use of data that is digitally adjusted using the measured data, or that is digitally generated by assigning arbitrary values.

The aspects of this invention also comprise the developed algorithms or equations, the software containing these algorithms, and the instruments that contain such software or configured to perform the calculations contained in the algorithms. The equations are illustrated in Figure 28.

Examples

In the following examples, density measurements were made using ASTM 01505. All density plates were made according to ASTM 04703 (Annex A1, Procedure C) and allowed to stand at room temperature for 40 hours before testing.

Molecular weights and weight distributions were obtained using high temperature SEC chromatography equipment Pl220 (Polymer Laboratories) with trichlorobenzene (TCB) as solvent, with a flow rate of 1 mUminute at a temperature of 145 ° C. BHT (2,6-di-tert-butyl-4-methylphenol) was used at a concentration of 0.5

gil as a stabilizer in the TeB. An injection volume of 200 III with a nominal polymer concentration of 1.5 mglmL was used. the solution of the sample in stabilized TCB was carried out by heating at 150 ° C for 4 hours with occasional, gentle agitation. The columns used were three Styragel® HMW 6E (Waters) columns and were calibrated with a broad pattern of linear polyethylene (Chevron Phillips Marlex® BHB 5003 poly (ethylene) resin) for which the molecular weight had been determined using a gas detector. Oawn multi-angle light scattering EOS (Wyatt).

The SCB data were obtained using a high temperature heated flow cell from SECIFTIR (Polymer Laboratories) as described in OesLauriers et al. in Polymer 43 (2002), 159.

Example 1 - Contributions of molecular weight to density

the microstructural architecture that affects the density of the poly (ethylene) polymers include the MW as well as both the amount and distribution of short chain branches (SeB) in the polymer. These

Primary microstructures influence the level of crystallinity of the polymer. To better quantify the effect of MW on density, the MWo profiles (determined by SEC) for a set of relatively narrow MWO metallocene homopolymers that have a POI of about 3.0, whose crystallinity and crystallization behavior were described by Jordens. et al. in Polymer, 41 (2000) 7175, they were reevaluated and used as a calibration set. These results are shown in Table 1.

the densities of these polymers were plotted as a function of the weighted average molecular weight as illustrated in Figure 1. The y-axis represents the density in g / cm3 and the x-axis is the lag M where M is equal to Mw value obtained for the homopolymer samples of the cal ibration set given in Table 1. These data demonstrated a linear relationship between the homopolymer density and Lag Mw. However, to better evaluate this correlation between the MW and the density taking into account the fact that each calibration sample has a POI> 1, the volume fractions (1 /, 0) weighted by the fractions by weight (w¡ ) were determined in each MW component through the MWo as shown in equation 1.

l / p = ¿(1V; l p ') (Eq. 1)

In addition, using the appropriate calibration curve, the homopolymer density for the global polymer was calculated by adding (segment by segment) the specific volume fractions weighted by the weight fractions of the various MW components that make up the MWo profile as is indicated in Equation 2.

where: p = [a -bLogM]

The coefficients a and b of this equation were determined by a least-squares adjustment to the SEC data for each of the samples indicated in Table 1. This procedure consisted of finding a single set of a and b values determined by collectively minimizing the difference to square between the predicted densities and the known densities of the 11 samples given in Table 1, using the program

Excel® Solver. Also shown in this Table are the final values for the absolute rest of density where the absolute rest of density is the square root of the difference between the calculated density and the measured density.

In this work, the following equation was used to estimate homopolymer density from molecular weight:

p = 1.0748 - (0.0241) LogM. (which was obtained using Eq. 3)

p = la-b logM] (Eq. 3)

However, considering only the linear relationship between molecular weight and density will overestimate the density at very low molecular weights and the selection of what density represents the maximum density (ie, the density of poly (ethylene) 100% crystalline) will dictate how much of the MWo should be used in the calculation. For example, densities greater than 1.01 g / cm 3, a value that is frequently cited as the density of 100% crystalline poly (ethylene), are predicted for molecular weight values less than 300 g / mol. If the density of 100% crystalline poly (ethylene) is considered to be 1.00 g / cm3, a commonly cited value as well, then all molecular weight values less than 800 g / mol should either be excluded from the cella or assigned to them. the maximum density value. For the calculations used in this specification, all molecular weights below 715 g / mol were assigned density values of 1.006 g / cm3.

It is also possible that linear correlation may result in the underestimation of true density at very high molecular weights. However, a simulation of a MWO was performed for a homopolymer sample of UHMW-PE (ie Gaussian MWo, 2,000 kg / mol of Mw and a POI of 4) and produced a calculated density of 0.932 g / cm3, which was in agreement with the expected values (that is, between 0.93 and 0.94 g / cm3). Therefore we expect the linear range of the calibration curve (Eq. 3) to range from 0.7 to 1x104 kg / mol. This range corresponds to density values of 1.01 to 0.906 g / cm3, respectively.

Table 1. Properties selected for the calibration set

Sample

Momominal (kg / mol) Nominal POI Density measured (g / cm3) Calculated density (g / cm3) Absolute rest of density (ABS)

MTE H1

750 3.5 0.938 0, 940 0.002

MTEH2

368 2.6 0.944 0, 945 0.001

MTEH3 MTEH4 MTEH5 MTEH6 MTE H7 MTEH8 MTEH9 MTE H10 MTE H11

283 201 193 13, 70 51 35 25 20

Figure 2 illustrates the calibration curve used to estimate the equilibrium densities of poly (ethylene) samples from the calibration set (solid line). After demonstrating the applicability of the invention to polymers of high molecular weight and low molecular weight, we conclude that in the majority of the samples of homopolymeric poly (ethylene) the majority of the sample falls within the linear range of our correlation. Using Equation 2 we calculate the virtual densities of poly (ethylene) homopolymers within an average of ± 0.002 g / cm3.

Example 2. Validation of the equations for homopolymers

To further demonstrate the applicability of the equations of the invention, the virtual densities for a number

Samples of poly (ethylene) homopolymers (validation resins) (both development and commercial) with various widths of MWD and microstructures were calculated and compared with their measured density values. These included resins polymerized by Ziegler Nalta and chromium catalysts, since each type of catalyzed resin will have different MWD and microstructure than those of the calibration set in Table 1 that were polymerized using metallocene catalysts. In addition, dual mixtures of metallocene resins were evaluated to determine the effect of the bimodal distribution, as well as a bimodal sample catalyzed by metallocenes. The results are shown in Tables 2A to 2e where the absolute remainder is the square root of the squared differential between the calculated or virtual density and the measured density. It should be noted that none of these subsequent samples were used in the construction of the calibration curve. Table 2A contains data for catalyzed resins of Ziegler Nalla; Table 28 contains chromium-catalyzed resins; Table 2e is for mixtures of resins produced with metallocene catalysts.

Table 2A. Validation resins for homopolymers (catalyzed samples from Ziegler Nalla)

Density Density Mwnominal absolute rest

Sample PDI nominal calculated density measure

(kg / mol)

(g / cm3) (g / cm3) (ABS) ZN-H1 44 5.7 0.970 0.971 0.001

ZN-H2 147 6.4 0.964 0.959 0.005 ZN-H3 132 5.9 0.954 0.959 0.005 ZN-H4 81 3.8 0.962 0.962 0.000 ZN-H5 72 4.3 0.962 0.964 0.002 ZN-H6 144 6.3 0.961 0.959 0.002 ZN-H7 136 5.1 0.961 0.959 0.002 AB $ average 0.002

3.4 2.5 3.5 3.1 2.8 2.3 3.6 2.5 3.2

0,947 0,951 0,950 0,955

0.954

0.969 0.973 0.975 0.976 0.950 0.952 0.954 0.957

0, 963

0.966 0.972 0.974 0.977 AB $ average

0.003 0.001 0.004 0.002 0.001 0.003 0.001 0.001 0.001

0.002

Table 2B Validation resins for homopolymers (samples catalyzed by chromium) Density Density Absolute rest

Mwnominal

Sample POI nominal calculated density measure

(kg / mol)

(g / cm3) (g / cm3) (ABS) Cr-H1 125 6.1 0.964 0.961 0.003 Cr-H2 145 8.7 0.962 0.962 0.000 Cr-H3 174 6.5 0.961 0.959 0.002 AB $ average 0.002

Table 2C. Resin validation of homopolymers (dual mixtures of metallocene resins) Comp. of the mixture Density Density Absolute rest

Mwnominal

Sample PDI nominal calculated density measure

(kg / mol)

% weight MIN (g / cm3) (g / cm3) (ABS) DMTE-H1 60 26K & 103 7.1 0.965 0.963 0.002 40 220K DMTE-H2 60 26K & 107 7.2 0.965 0.963 0.003 40 250K DMTE-H3 60 20K & 116 9.7 0.967 0.964 0.003 40300K DMTE-H4 60 26K & 119 8.0 0.966 0.963 0.003 40300K DMTE-H5 50 20K & 125 10.4 0.965 0.962 0.003 50 250K DMTE-H6 40 26K & 132 6.8 0.962 0,959 0,003 60 220K DMTE-H7 50 20K & 141 9,8 0,964 0,961 0,003 50300K DMTE-H8 30 20K & 143 7,1 0,961 0,958 0,003 70300K DMTE-H9 40 20K & 147 8,4 0,961 0,959 0,002 60 250K OMTE-H10 40 26K & 148 7.5 0.960 0.958 0.002 60 250K ABSMember 0.003

The mean absolute rest between the calculated and measured values for the validation sample sets as a whole was consistent with that found for the calibration set (ie, 0.002 g / cm3). This set of validation samples demonstrated the applicability of the invention for polymers that have many types of diverse architecture. For example, not only had the width of the MWD increased in this set of validation samples compared to the narrowest MINO of the metallocene samples (MET) of the

10 calibration set. but that the polymer architecture in the mixed metallocene dual samples of the

Validation samples varied considerably as shown in Figure 3. These results together suggest that the algorithm as proposed in Equations 2 and 3 can adequately calculate the virtual density for any homopolymer structure. Figure 4 demonstrates the goodness of fit for the samples in Tables 1 and 2.

5 Example 3. Application of the equations

The equations were used to predict how the width of the molecular weight distribution affects the homopolymer density of a polymer. As shown in Figure 5, several normal logarithmic distributions of molecular weights generated synthetically or digitally were plotted, selecting the same weighted mean molecular weights but different widths or POls (Mv / M ,,). There are several things to highlight about these distributions in addition to their obvious differences in width. First, the peak of the distributions shifted to lower molecular weights as the widths increased. Second, and somewhat related to the first comment, the amount of low molecular weight material that was added greatly exceeded the amount of high molecular weight material that was added as the distributions widened. This was necessary to maintain the constant weighted mean molecular weights during

15 the widening of the distributions. The virtual homopolymer densities calculated in this Example are summarized in Table 3.

Table 3. Homopolymeric density calculated as a function of the POI for Mw = 150,000 g / mol

Nominal POI

Homopolymeric density calculated (g / cm3) Molecular weight of the peak (kg / mol) Onsity at the peak of the MWD (g / cm3)

two

0.9508 106.07 0.9512

3

0.9526 86.60 0.9532

5

0.9550 67.08 0.9558

8

0.9571 53,03 0.9951

12

0.9590 43.30 0.9602

16

0.9603 37.50 0.9616

twenty

0.9614 33.54 0.9627

Figures 6-8 show sets of synthetic distributions of molecular weights obtained from SEC

for a series of molecular weights of polydisperse resins. They appear as narrow (POI = 2.0) in Figure 6, 20 means (POI = 5) in Figure 7, and wide (POI = 20) in Figure 8. Density differences between the weights

higher and lower molecular weights with the same PDls were the same for narrow POI polymers,

medium, and wide, 0.0299 g / cm3 as shown in Table 4. Table 4 shows the expected changes in the

density as a result of a systematic change in the Mw and POI. It was also observed that for a molecular weight

Given, the difference in homopolymer density calculated between the narrowest (POI = 2) and wider (POI = 25 20) is 0.0106 g / cm3. Both are due to the fact that these synthetic distributions are distributions

normal logarithms and it is assumed that the density is linear in log M.

Table 4. Expected homopolymericities for various values of Mw

Mw

POI

Onsity (g / cml)

(kg / mol)

500

two 0.9388

500

5 0.9429

500

twenty 0.9494

25 E1 0742966

350 350 350

2 5 20 0.9423 0.9465 0.9529

150 150 150

2 5 20 0.9508 0.9550 0.9614

50 50 50

2 5 20 0.9617 0.9659 0.9723

25 25 25

2 5 20 0.9686 0.9728 0.9793

The data in Table 4 were further analyzed using statistical software to "model the model" and to project the data in three dimensions to illustrate how the expected homopolymer density is a nonlinear function of both variables. To obtain the graphical representation of Figure 9, the values were fitted with a quadratic polynomial with the density as a function of linear and quadratic terms in Mw and POI Y, a nominal density error of 0.0016 g / cm 3 was assigned. In addition, an additional statistical analysis of the density data generated by this invention from digital MWO curves allows to evaluate separately the influential effects that the individual structural variable such as MW and MWO have on the expected density values. For example, in Figure 10, the statistical values of F and P are given in the ANQVA table. These terms are statistical indicators of how much a variable affects a particular response. That is, the higher the values of F, the greater the influence of the variable on the response variable selected, in this case the density. On the other hand, the lower the value of p generated, the more influential is the variable. The data given in Figure 10 suggest that although both MW and MWO variables have important effects to change the density, the MW can be more effective in changing the density of the sample than the MWD of the sample, in addition the quadratic term of the MW has almost the same effect as the MWO. These data demonstrate other possible uses for the analysis of digital forms by this invention in conjunction with the use of statistical software.

Example 4 - Contributions of the SCB to density

After explaining the effects of MW, we explain the additional reduction in density due to the presence of SCB. A series of 1-hexene copolymers produced from different catalyst systems (and thus various architectures) were characterized using SEC and the structural data obtained are given in Tables 5A to 50 below. Table 5A comprises metallocene resins. Table 5B includes Zeigler Nalla resins, Table 5C reports on chromium resins and Table 50 lists resins that are structurally different from those of Tables 5A to 5C. The samples listed in 50 included both mono-modal and bimodal samples. The first of these samples (MTE-16) is a single resin catalyzed by metallocenes with a slightly wider MWO (POI = 3.1) and an inverted SCBO. That is, the level of SGB in this sample increases with the molecular weight as shown in Figure 11. In the same way, the inverted SCBOs are obtained from the bimodal samples BM ZN-1, DMTE-1 & 2 where Low molecular weight homopolymers are combined with higher molecular weight copolymers (Figure 12).

Table 5A. Density values calculated for samples of copolymers catalyzed by metallocenes

Mw p of the homopolymer p of the copolymer

Sample PDI SCB / 1000 CT .p óp / SCB

(kg / mol) calculated (g / cm3) measured (g / cm3)

MTE-1 162 2.42 0.1 0.951 0.957 0.005 0.049 MTE-2 139 2.5 1.2 0.956 0.942 0.014 0.012 MTE-3 159 2.34 2.3 0.953 0.937 0.016 0.007 MTE-4 142 3.13 3 , 5 0,955 0,933 0,022 0,006 MTE-5 129 2,3 3,7 0,956 0,933 0,023 0,006 MTE-6 134 2,72 3,7 0,955 0,936 0,019 0,005 MTE-7 111 2,75 6,8 0,957 0,931 0,027 0,004 MTE- 8 204 2.25 9.3 0.950 0.917 0.033 0.004 MTE-9 167 2.11 10.7 0.951 0.916 0.035 0.003 MT E-10 120 2.2 12.4 0.956 0.916 0.040 0.003 MT E-11 160 2.33 12 , 9 0,951 0,913 0,038 0,003 MT E-12 117 2,5 13,6 0,956 0,918 0,038 0,003 MT E-13 95 3,5 32 0,960 0,902 0,058 0,002 MTE-14 102 3,52 36,3 0,959 0,897 0,062 0,002 MTE- 15 147 2.63 49, 5 0.954 0.880 0.074 0.001

Mw p of the homopolymer p of the copolymer

Sample PDI SCB / 1000 CT .p óp / SCB

(kg / mol) caculate (g / cm 3) measured (g / cm3)

Table 58. Density values calculated for samples of Zeigler Natta catalyzed copolymers

ZN 1

133 5.02 1,5 0.958 0.947 0.012 0.008

ZN-2

123 4.2 2.0 0.959 0.944 0.015 0.007

ZN-3

120 3.9 2.0 0.959 0.944 0.015 0.007

ZN-4

120 4.8 3.0 0.960 0.944 0.016 0.005

ZN-5

112 5.3 3.3 0.961 0.944 0.017 0.005

ZN-6

439 4.4 3.6 0.946 0.929 0.017 0.005

ZN-7

91 4.3 6.5 0.962 0.937 0.025 0.004

ZN-B

138 4.7 7.1 0.958 0.936 0.022 0.003

ZN-9

144 4.9 7.3 0.957 0.935 0.023 0.003

ZN-10

130 4.7 12.6 0.958 0.926 0.032 0.003

ZN-11

135 4.6 12.6 0.958 0.927 0.031 0.002

ZN-12

131 4.9 13.9 0.958 0.924 0.035 0.002

ZN-13

115 4.8 22.4 0.959 0.915 0.045 0.002

Table 5C. Density values calculated for samples of chromium-catalyzed copolymers

Mw p of the homopolymer p of the copolymer

Sample PDI SCB / 1000 CT 6p 6p1SCB

(kg / mol) calculated (g / cm3) measured (glcm3)

Cr-1

140 10.4 14.0 0.961 0.925 0.036 0.003

Cr-2

216 16.6 5.59 0.960 0.937 0.023 0.004

Cr-3

228 19.0 3,4 0.959 0.944 0.015 0.004

Cr-4

328 36, 5 2.6 0.960 0.950 0.010 0.004

Cr-5

341 53, 7 2,1 0.961 0.950 0.010 0.005

Cr-6

483 66.1 1.6 0.958 0.950 0.008 0.005

Cr-7

500 73, 1 0.9 0.958 0.951 0.007 0.008

Cr-8

353 79.1 2.0 0.962 0.952 0.010 0.005

Table 50. Calculated density values for copolymer samples with inverted SCBO

Mw P of the homopolymer p of the copolymer

Sample PDI SCB / 1000 CT 6p I1pJSCB

(kg / mol) calculated (g / cm3) measured (glcm3)

MET-16 135 3.1 19.5 0.956 0.912 0.044 0.002

BM ZN-1 210 14,0 1.6 0.958 0.948 0.010 0.006

OMTE-1 231 14.5 1.5 0.959 0.950 0.009 0.006

OMTE-2 248 25.3 1.7 0.960 0.951 0.008 0.005

The SCBOs of these samples were also characterized by SEC-FTIR. For the first three samples of Table SA, a slope of zero (ie, flat SCB profile) was measured for the SCBO. The Zeigler Natta samples given in Table 5B showed all the common SCBO (plus SCB at the lower end of MW of the MWO). The slopes for these samples ranged from -0.5 to -6.5. The SCBO slopes for the chromium-catalyzed samples of Table 5C ranged from 0 to -9 and presented SeBOs similar to those in Table 5B. Finally, the mono-modal and bimodal samples of Table 50 have all so-called inverted SCBOs (plus SCB at the high MW end of the MWO).

As shown in Figure 13, the density change by SCB was graphically plotted against the SCB for 1000 total carbons (Gl) for the resins given in Table 5A. The results shown in Figure 11 showed a non-linear relationship of how the density difference calculated between a copolymer and its homopolymer analog for samples catalyzed by metallocenes (global polymers) varied when expressed in terms of density change by SCB. That is, when the mean content of SCB increased above about 10 SCB / tOOO CT, the resulting decrease in density change by SCB appeared to be less than that produced at lower SGB levels. These values were calculated by dividing the density difference by the total SGB content of the polymer. Since we stipulate that the measured density was in equilibrium conditions, it was assumed that any variation away from the homopolymer density (due to the effect of the MW) was only attributed to the presence of SCB. The non-linear relationship shown met the expectations that the influence of SCB on density when it increased from 40 to 41 SCB / t OOO CT (total carbon) is lower than that observed when it increased from 1 to 2 SGB / 1,000 GT.

Another way to graphically represent these data was shown in Figure 14, where the observed global density change was graphically plotted against the average SCB content. This figure showed that the change in global density observed with the SGB content for samples with POI of approximately 2.3 can be described using a power law relationship. The generated algorithm given in Figure 14, together with the homopolymer algorithm (i.e., Eq. 3) as described above can be used to predict the density of narrow MW copolymers (ie, POI of about 2.3 ). A similar ratio over the same level of SCB was found for the slightly wider POI resins (POI of about 4.9) produced from Zeigler Natta catalysts (ZN) which are represented as open circles in Figure 14. However , for these ZN resins, a clear displacement was observed in the graphically represented data in comparison with the data of the metallocene resins (represented graphically as solid circles).

The displacement observed between the ZN and melalocenic resin conjuncts was probably associated with the POI of the samples. Normally at similar molecular weights, the broader POI samples have higher homopolymer densities, as demonstrated previously (see Table 4) from modeling studies using normal Gaussian molecular weight distribution profiles. As such, for a wide POI sample more SCB is needed to achieve a density equivalent to the samples with narrower POls. In contrast, at the same SCB level, the resulting density change for the wide POI sample will be smaller than that of the narrow POI sample. This was shown in figure 14.

Without being bound by any theory, it seems reasonable that resins with POI values other than 2.3 and 4.9 also have separate power law ratios for how SCB changes density in global polymer systems. It was difficult to systematically explore the effects of SCB levels on the density change at a constant POI> 5 due to the nature of the chromium catalysts and the reactor conditions normally used to produce these structures of broad molecular weights. Therefore, there is a lot of variation in both the SCB level and the POls of samples of commercial resins and pilot plants. However, these wide POI structures were examined.

For example, examination of the density changes for the chromium-catalyzed resins indicated in Table 5C suggested that if there are individual power laws for resins with different POls, then the relationship between each POI set is probably complex and non-linear. This last statement was demonstrated in Figure 13 indicating the relationship between the data generated for resins with the widest POls (samples of type Cr-5,6,7, & 8, POI> 54), those of POI of approximately 4, 7 and those of POI of approximately 2.3. Although there was a limited series of samples in the data set for resins with very wide and similar POls, it was obvious from these data sets as a whole that a complex expression was needed to adequately capture the influence of both the SGB and the MWO about the density change observed in these samples.

To normalize the SCB data for the polydispersity that is demonstrated by the data of the resins polymerized by different catalysts, we recognized that there was a non-linear relationship between the three datasets represented graphically in Figure 15. That is, the change between the adjusted data for the sets of resins of POI 2,3 and POI 4,9 shown in this figure was much higher than that observed between sets of resins of POI 4.0 and POI> 54. This point was expressed mathematically pointing out the differences between the pre-exponential factors in the respective equations (ie, 0.0115, 0.0095, and 0.0072 for the POI data sets 2.3, 4.7, and> 54, respectively.

To explain the non-linear nature of the data, the observed SGB values were divided by an exponential value of the POI of the samples (ie, PO ln). The value for the exponent n was determined by first dividing the SGB levels in each sample by the resin POln (where n is initially set equal to 1), plotting these values against the predicted density change, and then empirically reducing the value of the exponent for the POI until a value was determined that minimized the differences between the samples (through visual evaluation).

With these data we discovered that by assigning the exponent n equal to 0.32, various types of resins with different polymer architectures as detailed in Tables 5A through 50 can effectively be displaced in a single curve as shown in Figure 16. It is also evident from Figure 16 that the relationship between the density difference and the normalized SCB values (SCBIPOln) could be described using a double exponential equation. This particular exercise showed that with the proper selection of the n exponent, the influence of POI on the correlation of the density change (l! .P) with the levels of SCB in polydispersed samples was significantly minimized if it was not eliminated.

Using this approach, the sample data as indicated in Tables 5A to 50 were adjusted using the following equation:

(Eq. 4)

A subsequent adjustment of the data (including the exponent n) using the solver function in Excel® where the sum of the squares for the differences between the calculated l! .P and the observed l! .P were minimized, gave the following values for the coefficients of Equation 4 and the exponent n:

Cl = 0.01239302 (g / cm3) / (SCB per 1000 CT) c2

G2 = 0.49586823

C3 = 0.000345888 (g / cm3) / (SCB per 1000 CT) C3

C4 = -0.78067392

n = 0.318975556

E1 0742966

This equation does not explain the distribution of the short chain branching on the molecular weight distribution in the global polymer samples (ie, the slope of the SCBO) nor the type of SG8. The structures with long chain branching were also not considered.

The resulting predicted values for the resins of Tables 5A to 50 are given in Tables 6A to 60 and

5 are shown graphically in Figure 17. The copolymer density values calculated using Equations 3 and 4 are given in Table 7 while the goodness of the graphical representation of the fit is given in Figure 18. These results show that the methods and equations of the invention can suitably determine the virtual density for this set of samples with the mean absolute remainder of 0.0016 g / cm3. Interestingly, this error value is equal to that found for the estimates of homoporous densities using the Equation

10 3.

Table 6A. Values of o.p calculated for the resins of Table 5A using Eq. 4

measured p.p.p calculated

Sample PDI SCBI1000 CT SCBIPDln Absolute rest

(g / cm :) (g / cm3)

MTE-1

2.42 0.1 0.1 0.005 0.006 0.001

MTE-2

2, 5 1,2 0.9 0.014 0.012 0.002

MTE-3

2. 3. 4 2,3 1,8 0.016 0.017 0.001

MTE-4

3, 13 3.5 2,4 0.022 0.019 0.003

MTE-5

2. 3 3.7 2.8 0.023 0.021 0.002

MTE-6

2, 72 3.7 2.7 0.019 0.020 0.001

MTE-7

2, 75 6.8 4.9 0.027 0.027 0.001

MTE-8

2, 25 9.3 7.2 0.033 0.033 0,000

MTE-9

2, 11 10.7 8.4 0.035 0.036 0.001

MTE-l0

2, 2 12.4 9.6 0.040 0.038 0.002

MTE-l1

2, 33 12.9 9.8 0.038 0.039 0.001

MTE-12

2, 5 13.6 10.2 0.038 0.039 0.001

MTE-13

3, 5 32 21, 5 0.058 0.057 0.001

MTE-14

3, 52 36, 3 24, 3 0.062 0.060 0.001

MTE-15

2, 63 49, 5 36, 4 0.074 0.074 0,000

Table 68. IIp values calculated for the resins in Table 58 using Eq. 4

IIp measured IIp calculated Rest

Sample PDI SCB / l000 CT SCBIPDln

(g / cm3) (g / cm 3) absolute

ZN 1 ZN-2 ZN-3 ZN-4 ZN-5 ZN-6 ZN-7 ZN-8

5.02

4, 2

3.9

4, 8

5.3

4, 4 4, 3 4.69

fifteen

two 3 3, 3 3, 6

6.5

7, 1

0.9 1.3 1.3

1,8

1.9

2.2 4, 1 4, 3

0.012 0.015 0.015 0.016 0.017 0.017 0.025 0.022 0.012 0.014 0.014 0.017 0.017 0.019 0.025 0.026

0.000 0.001 0.000 0.001 0.001 0.001 0.000 0.003

ZN-9

4.89 7.3 4, 4 0.023 0.026 0.003

ZN-1 0

4.74 12.6 7.7 0, 032 0.034 0.002

ZN-1 1

4,575 12.6 7.8 0, 031 0.034 0.004

ZN-12

4.92 13.9 8.4 0, 035 0.036 0.001

ZN-13

4,765 22.4 13.6 0, 045 0.045 0,000

Table 6C. P0 values calculated for the resins of Table 5C using Eq. 4

Sample

POI SCB / 1000 CT SCB / POln measured opm (g / cm3) calculated p (g / cm3) Absolute rest

Cr-1

10.4 14.0 6.6 0.036 0.032 0.004

Cr-2

16.6 5.59 2,3 0.023 0.019 0.004

Cr-3

19.0 3,4 1,3 0.015 0.014 0,000

Cr-4

36, 5 2.6 0.8 0.010 0.012 0.001

Cr-5

53,7 2,1 0.6 0.010 0.010 0,000

Cr-6

66, 1 1.6 0.4 0.008 0.009 0.001

Cr-7

73.1 0.9 0.2 0.007 0.007 0,000

Cr-8

79.1 2.0 0.5 0.010 0.009 0.001

Table 60. EPO values calculated for the resins of Table 50 using Eq. 4

Sample

POI SCB / 1000 CT SCB / POln measured opm (g / cm3) calculated p (g / cm3) Absolute rest

MET-16

3.1 19.5 13.6 0, 044 0.045 0.001

BM ZN-1

14.0 1.6 0.7 0.010 0.011 0.001

DMTE-1

14.5 1,5 0.6 0.009 0.010 0.002

DMTE-2

25.3 1.7 0.6 0.008 0.010 0.002

Table 7. Copolymer densities calculated for the samples of Tables 5A to 50.

p of copolymer measured p of copolymer calculated

Sample Absolute Rest

(g / cm3) (g / cm3) E1 0742966

MTE-1

0.947 0.945 0.001

MTE-2

0.942 0.944 0.002

MTE-3

0.937 0.936 0.001

MTE-4

0.933 0.935 0.003

MTE-5

0.933 0.935 0.002

MTE-6

0.936 0.935 0.001

MTE-7

0.931 0.930 0.001

MTE-8 MTE-9 MTE-10 MTE-11 MTE-12 MTE-13 MTE-14 MTE-15 ZN-1 ZN-2 ZN-3 ZN-4 ZN-5 ZN <; ZN-7 ZN-8 ZN-9 ZN-10 ZN-1 1 ZN-12 ZN-13 Cr-1 Cr-2 Cr-3 Cr-4 Cr-5 Cr-6 Cr-7 Cr-8 MET-16 BM ZN-l OMTE-1 OMTE-2

0.917 0.916 0.916 0.913 0.918 0.902 0.897 0.880 0.947 0.944 0.944 0.944 0.944 0.929 0.937 0.936 0.935 0.926 0.927 0.930 0.915 0.925 0.937 0.944 0.950 0.950 0.950 0.951 0.952 0.912 0.948 0.950 0.951

0,917 0,915 0,918 0,945 0,944 0,943 0,943 0,928 0,937 0,932 0,918 0,923 0,923 0,914 0,929 0,993 0,993 0,944 0,949 0,980 0,946 0,945 0,944 0,943 0,943 0,943 0,928 0,937 0,932 0,931 0,924 0,923 0,923 0,914 0,929 0,993 0,993 0,944 0,949 0,950 0,949 0,949 0,945 0,923 0,944 0,943 0,943 0,946 0,949 0,950 0,000 0,001 0,002 0,001 0,001 0,001 0,001 0,000 0,000 0.001 0,000 0.001 0.001 0.001 0.000 0.003 0.003 0.002 0.004 0.001 0.000 0.004 0.004 0.000 0.001 0.000 0.001 0.000 0.001 0.001 0.001 0.002 0.002

As mentioned above, the profile of the SCBO was not taken into account in Equation 4. However, the results shown in Table 7 suggested that the slope of the SCBO had negligible contributions to the density change calculated for the samples tested. (at least within the calculation error). This was evident from the narrower POI metallocene-catalyzed samples, where the SCBO slopes for

the resins of Table 5A were equal to O as compared to 6.5 for sample MTE-16 of Table 50. The density difference observed for sample MTE-16 (0.044 gcm3) was comparable to the other MET samples with similar SCB / (POln) values (ie, between 10 and 14). A similar argument can be made for the samples listed in Table 5B and 5C where the slopes varied considerably, however the density change in all these samples was captured using the term SCBI) POW and Equation 4.

Finally, the insignificant contributions of the SCBO slope to the density change were also shown for the three tested bimodal resins, BM ZN-1, OMTE-1 & 2 shown in Table 50. These three samples are comparable to the mono- manners that have slopes sufficiently steep to analyze the resin meticulously. This was illustrated by considering what happens in a Gaussian wide MWO (POI = 14) when the slope was systematically changed as shown in Figure 19. In this graph the slope was increased from 0 to 3 so that the sample had an SCBO inverted As a result, the steeper slope produced a sample where half of the polymer was essentially homopolymer and the other half was copolymer, as in the bimodal samples. The fact that the three bimodal resins have values of SCBI) POI) n and lI.p similar to samples Cr-6, 7 & 8, which have flat SCBOs, confirms once again the use of Equations 3 and 4 to calculate the virtual density of limblet for specimens with complex MWO and SCBO profiles.

Example 5. Calculation of density change for digital MWO and SCB data

Example 5 demonstrates the use of this invention to calculate the density of a poly (ethylene) copolymer using described structural values such as MW, POI and SCB content, together with the use of digitally generated MW and SCB distributions. The structural data described by Mirabella al. , Joumal of Polymer SCience, Part B, 40 (2002) 1637, for a set of poly (ethylene) copolymers catalyzed by metallocenes and their calculated homopolymer densities are shown in Table 8. Without the benefit of having the samples in hand to physically measure the MWO and SGB, digitally generated MWO curves were used assuming a normal Guassiana for the molecular weight distribution for each sample described in Table 8. Furthermore, since these samples are catalyzed by metallocenes, a SCBD can be assigned flat through the MWO that has the value of the SCB level indicated. As you can see in this example, using this digital focus and the data described can easily calculate the densities of such samples. The densities virtually calculated as described are quite comparable with the measured values described by Mirabella. It should also be noted that these samples contained ethylic branches derived from the incorporation of 1-butene comonomers, which further illustrates that the applicability of the method for SCBs is not limited by the type of comonomer.

Table 8. Calculated density of copolymers using digital data from MWO and SCB

pde p de p

Rest

Mw indicated SCB / 1000 CT homopolymer copolymer copolymer

Shows absolute indicated POI of

(kg / mol) indicated calculated calculated indicated

density

(g / cm3) (g / cm3) (g / cm3)

M-6

108 2.2 18.5 0.958 0.910 0.911 0, 001

M-5

75 2.5 25.3 0.962 0.905 0.909 0, 004

M-.

81 2.2 30,7 0.961 0.900 0.901 0, 001

M-3

98 2,1 43.9 0.958 0.888 0.886 0, 002

M-2

137 two,' 51.4 0.956 0.880 0.879 0, 001

M-1

63 2,3 84.6 0.963 0.865 0.865 0, 000

Example 6. Calculation of the density change through the MWO

The contribution of the SCB to the density change calculated by Equation 4 used data acquired for most or all of the polymer using SCB values from NMR or SEC-FTIR and MW and MWO data obtained from SECo Sin However, this equation could also be used to calculate the global polymer density as segments using SEC-FTIR data. As in the case of the calculated homopolymer density, the density of a copolymer sample was assumed to be the sum of the densities across the molecular weight distribution. Consequently, the measured copolymer density was obtained by first calculating the homopolymer value for each segment using Equation 3, subtracting the calculated density change due to the presence of SCB (using Equation 4) and then adding the density values resulting on the MWO as previously described in Equation 2 and reiterated below;

IIp ~ (w, / p,) ~ JtCd l d '") d log M

og m Ec.2

where: p = Ec.3 -Ec.4

This approach was tested using SEG-FTIR data for selected resins previously described in Table 5A to 50. In order to calculate the respective densities for each MW segment in the structural profiles acquired by SEC-FTIR, the experimental data were reproduced first in a continuous way. This was done because the level of SCB described is a result of accumulated spectra, and therefore not every segment of MW has a corresponding value of SGB. In addition, experimental data from SeB are often absent at the end of the MWO due to signal noise problems. The missing part of the SeB data from the MWO can be up to about 20% of the total profile of the MWO. These points were illustrated in the SEC-FTIR data presented in Figures 17 and 18.

In the first step, a set of narrow MW profiles, MWO profiles with Schulz-Flory distribution (SFO) (POI of about 2) was used to adjust the MWO profile. For the MWO given in Figure 20, seven SFO peaks were used as shown in Figure 21. It was possible to use other peak shapes and use more than seven peaks. However, the various aspects of this invention comprise reproducing the MWO as accurately as possible with a minimum number of peaks. Therefore, seven peaks with Schulz-Flory distribution (SFO) appeared to be adequate. In the next step, the SeB experimental profile was reproduced using an additional set of SFOs. This second set of SFOs had the same MWO profiles (including the peak MW of each peak), however, an arbitrary amount of SCB (but constant) with a flat SCSO was assigned to each peak. The experimental SCBO was combined by digitally adding weight fractions of peaks from each set through the MWO.

For example, in one aspect a metallocene-catalyzed resin with a MWO that could be represented by a single SFO product and had a SCB level with a flat distribution of 6 SCB / 1000 CT, both the MWO data and the experimental SCBO data. digitally reproduced by adding 0.5 times the data segment of the SFO peak of "homopolymer" to 0.5 times the data of the SFO peak segment of "copolymer", where the latter had a SCB level with a flat distribution of 12 SCB / 1000 CT. Of course, if the copolymer peak is assigned a level of 24 SCB / 1000 CT, only a "weight fraction" of 0.25 will be needed. Both the experimental and the adjusted data are given in Figure 21. Although an exact fit for the SeBO in the MWO queues was not achieved (undoubtedly, the SeBO could be combined exactly if more SchulzFlory distributions were used), the data described in Figure 21 demonstrated that good agreement is obtained between the measured density and calculated density data using this approach even for complex MWO and SCBO profiles. Normally, the MWD derived from the SEC-FTIR has a slightly wider POI due to the large injection volume used. This last observation can add approximately 0.001 g / cm3 to the calculated final density.

It is also possible to predict SCB from known densities and then assign SCB levels in order to achieve a specific density objective. This is particularly useful in catalyst and resin design where it is known how a particular system incorporates comonomer and is also useful when dealing with "what if" scenarios, using digital data. For example, the SCB needed to achieve a particular density in a particular MW and MWD was calculated using equation 5. This equation was reached by re-plotting and adjusting the density change and the SCB data as SCBIPOln versus the change in density:

11 ({, c.

SeS / PDI = CI1 :::. P + CJ (6p) (Eq. 5)

where:

1780.355946

e2 137.0649808

e3 7196,543644

e4 2.026750223

n 0.318975556

The adjusted (model) and experimental values using this approach are shown in Figure 22 and illustrate the goodness of fit of this approach. In particular, this approach is very useful when dealing with scenarios of "what if" in the design of resins. Using the density value obtained from the MWO (ie the homopolymer density) and Equation 5, the density of any combination of MW, MWO or SGB and SeBO can be calculated from digital data. This approach should also find use when addressing comonomer additions at catalytic sites.

Example 7. Estimation of melting points of poly (ethylene)

Many properties of poly (ethylene) homopolymers and copolymers were calculated from the density. For example, the melting point (Tm) of a poly (ethylene) sample was calculated from a calibration curve based on the Tm and density data described in the literature (studies by Patel and Mi rabella, RM Patel , K. Sehanobish, P. Jain, SP Chum, GW Knight, J. Appl. Po / y. Se ;. 1996, 60, 749; FM Mirabella, A. Bafna, Joumal al Po / ymer Scienee, Parl B: Po / ymer Physics 2002, 40, 1637.), as well as assigned values for 100%: amorphous and crystalline poly (ethylene) samples. Several values for the density of both phases have been described in the literature. In this regard, a density of 0.852 g / cm 3 was assigned to the amorphous phase of poly (ethylene) (Jordens, G. L Wilkes, J. Janzen, OC Rohlfing, MB Welch, Polymer 2000, 41.7175.) To 20 "C and crystalline poly (ethylene) have a density value of 1.01 g / cm3 at its equilibrium melting temperature (Tm ')." Figure 23 shows the empirical calibration curve (solid line) that relates the values of density with those of melting points compared to the respective values described in the cited references Assigned values of 2 () <'C and 142.5 ° C were given for density values of 0.852 g / cm3 and 1.01 g / cm3, respectively.

The graphical representation of Figure 23 showed a reasonable relationship between the density values and the average melting points (Tm, oC) described by the fitted line. The melting point adjusted from the calibration curve for the density of 1.01 g / cm3 was found to be equal to 142.3 "C and was well within the uncertainty described (L, Mandelkern, GM Stack, Macromoleeules 1984,17, 871) of the mentioned Tmo (1 41.5 ± 1 ° C) The calibration curve provided estimates of Tm for the respective density in each MW segment, as in the density calculations, a sum of the data, segment by segment, weighted by the fractions by weight (w,) of the various components that make up the profile of the MWO, produced the respective value of Tm for all the polymer.

Example 8. Calculation of the crystallinity of the polymers

In another aspect, the crystallinity of the polymers was calculated using known ratios between polymer crystallinity and density. For example, the weight fraction and volume of crystallinity was calculated from the density of the polymers using the following equations:

Where Wc = fraction by weight of the crystallinity

p = calculated density of the global polymer from the sum on a segment basis by segment

Pe = 100% crystalline sample density (1.01 g / cm3 assigned)

po = density of the amorphous phase (0.852 g / cm3)

(le = fraction by volume of the crystallinity

In addition, since the density values were calculated directly from any level of MWO and SCB, digital data was used to estimate what could be expected from a proposed MWO and SCBD. For example, simply by using a Gaussian curve for the MWO of the polymer and a flat SeBO, the crystallinity for poly (ethylene) polymers catalyzed by metalicenes was calculated using described values of Mw, Mn and SCB found in the literature. In Figure 24, the data described for the weight fraction of crystallinity (Stadler el al: e-polymers 2009, no 040) are compared with the calculated values obtained as described above. As shown in Figure 24, there is a good correlation between the measured and calculated values.

In Figure 24 the crystallinity values obtained from both WAX (open black circles) and density measurements (open blue circles) for poly (ethylene) samples described by Stadler (e-polymers 2009, no 040) they are compared with the calculated values. Also shown are data of crystallinity described by Mirabella (Joumal of Polymer Scienee, Part B: Polymer Physies 2002, 40, 1637) obtained from both OSC (open triangles) and XRO measurements (solid triangles) and compared with the values calculated. Finally, the data described by Bartczak (Polymers 2005, 46,8210) obtained from DSC (solid diamonds) and density measurements (open squares) are also shown and compared with the values calculated within ± 0,05. The dotted lines of this graphical representation indicate the deviations of ± 0.05 with respect to the ideal correlation of 1 to 1 given as solid line (in red)

Figure 25 illustrates a direct relationship between density and weight fraction of crystallinity. Figure 25 shows the direct non-linear relationship between density and weight fraction of C-level and is compared with the values described directly from the works cited in the literature.

Example 9. Calculation of PSP2 values

In the U.S. patent application publication 2007298508 A1 primary structures such as molecular weight and short chain branching, as well as their respective distributions, were used to formulate a single parameter (PSP2) capable of rapidly estimating the potential resistance to slow growth of poly (ethylene) resin cracks. as determined by short-term test methods. This method was based on experimental data obtained directly from SEC-FTIR, bulk density values, and statistical calculations for the binding molecule probabilities as described by Huang & Brown. The value of the probability acquired statistically was treated essentially as a weighting factor (P,) for each segment of the MWD. Pi arbitrarily multiplied x100 and later it was defined as PSP2i. The sum of (w, pSP2,) through the MWD profile defined PSP2 for a particular resin. However, knowledge of both the SGB level of the samples and the density of the samples was necessary in order to estimate the effects of the SGB on the density of the samples. With this present invention, the effects of the SCB on the The density of the samples and subsequently the PSP2 values can be calculated directly from either experimental or digital data of the MWD and SCB without prior knowledge of the density of the samples.

The Pi lCs are mainly based on density estimates on a segment-by-segment basis, from which subsequent melting point and laminar thickness estimates were made in order to obtain the critical end-to-end distance of the chain required to form a link chain (ie, 21.:; + la) as described by Huang & Brown. We discovered that the effects of the primary structure on the density and corresponding values of Tm can be calculated empirically through the distribution of molecular weights within mean values of ± 0.002 g / cm3 and ± 2OC, respectively. From these values and relationships known as the Gibbs-Thompson and percentage crystallinity equations, the values for 21.:; + they were approximate. The thicknesses calculated both for him and the appear to be consistent with those described in

the bibliography when evaluated using comparable values p,; p .. and Tmo. Figure 26 illustrates the process for and typical data obtained from PSP2 calculations.

Example 10. Calculation of natural stretch ratios

Finally, the calculated values of PSP2 were used to estimate a natural stretch ratio of the samples (NRD) using PSP values and the correlation graph shown in Figure 27 as previously shown in the US patent application publication. .US. 2007298508 A1. Figure 27 illustrates values of

PSP2 calculated to estimate a natural stretch ratio (NRD) using PSP values and the corresponding correlation graph.

Having the ability to predict density gives an access to predict the tensile properties of polymers such as NDR, as mentioned above, or other tensile properties such as Young's modulus, yield strength and elasticity limit using corrections known (for example, J. Janzen & D. Register; Annual Technical Conference - Society of Plastics Engineers (1996), 54th (vol.2), 2190-2194) of the literature as shown below, or any combination thereof .

3.0

o Observed

2.5

--- Adjustment of ses 2.0

Module of / Young

E, GPa 1.5 1.0 0.5

0.0 '---'_-'-_ -, -_ -, -_, ---, _--, -_... l

0.900 0.910 0.920 0.930 0.940 0.950 0.960 0.970 0.980 pg / cm3

35 30 25 20

Ulimite, MPa

15 10 5

or averages of base products

~~ -

of dalos

!

-

Adjustment of Ec 5

Yield point

~ -? -.

--- ~

OL- ~ __- L__L- ~ __ ~ __ ~~ __ ~ 0,900 0,910 0,920 0,930 0,940 0,950 0,960 0,970 0,980

p, g / cm3

Limit of deformation

,

..

! ;; Iimite,% 10

,

"

~

'~

<J Metallocene

• e,

-

_..- Setting Eq. 4

OL- ~ __ ~ __ ~ __ ~ __ ~ __ ~ __ ~~

0.900 0.910 0.920 0.930 0.940 0.950 0.960 0.970 0.980

p, g / cm3

A particular application of this method is the visualization of structures and their expected mechanical properties. Others have shown dependence on the crislainity (density) of the modulus and tensile properties of poly (ethylene). In addition, we have shown that many tests related to stress cracking (such as the Pennsylvania Notch Test (PENT), constant traction load in a single-point specimen (SP-NCTL), and the natural stretch ratio (NDR)), can be directly related to structural parameters derived from the MWD, SCB levels and density data (Des Lauriers PJ, PoJyolefins 2006 Conference Proceeding). Given the ability to now predict the density of any combination of MWD and SCBD, several structures can now be evaluated digitally for their potential application in a line of

20 particular product. In addition, by selecting peaks with PDls similar to those found in resins catalyzed by metallocenes, there is the possibility of producing real resins through physical mixtures that correspond to digitally constructed resins with particular MW and SCB distributions.

Claims (9)

1. A method for determining a virtual density of a polymer having short chain branches (SCB), comprising: a) determining a plurality of density values as a function of a molecular weight (MW) and a molecular weight distribution (MWD) profile of the polymer wherein each value of the plurality of density values is determined in a different location of MW through the profile of the MWD; Y b) adjusting the plurality of density values for a contribution of the SCBs to the density suppression to obtain an adjusted density value; c) add the adjusted density values to obtain a virtual density; where SCB, MW and the MWD 10 comprise data obtained as measured properties, data provided as a digitally determined value, data obtained by fitting to a curve the data obtained as measured properties, data provided as an arbitrarily assigned value or a combination thereof, characterized by the method by which step b) the plurality of density values is adjusted using data from most of the SCB and polydispersity values of size exclusion chromatography for a variety of samples 15 of copolymers of 1-hexene with various architectures.

two.

The method of claim 1, wherein the MW, the MWD, or a combination thereof comprises SEC, GPC, NMR or SECIFTIR data.

3.

The method of claim 1, wherein the virtual density of the polymer is in a range of about 0.906 g / cm3 to about 1.01 g / cm3.

4. The method of claim 1, wherein the polymer is a homopolymer or copolymer with monomodal or bimodal architecture or a mixture of homopolymers, copolymers or a combination thereof.

5.

The method of claim 1, wherein the polymer is an olefin.

6

The method of claim 1, wherein the polymer comprises a comonomer.

The method of claim 6, wherein the comonomer is 1-hexene, 1-octene, 1-bulene, 1-pentene, 1-decene, styrene, or a combination thereof.

8

The method of claim 1, wherein the polymer is semi-crystalline.

9

The method of claim 1, wherein the MWD comprises MWD profiles of Schultz-Flory distribution.

10

The method of any of claims 1 to 9 made in association with a polymerization reactor.